Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(1101,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.e (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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 89x^{12} + 3026x^{10} + 49092x^{8} + 390297x^{6} + 1440495x^{4} + 1994425x^{2} + 151875 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1101.12 | ||
Root | \(4.58743i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.g.1101.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 4.58743i | 1.52914i | 0.644539 | + | 0.764572i | \(0.277049\pi\) | ||||
−0.644539 | + | 0.764572i | \(0.722951\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52935 | −0.218478 | −0.109239 | − | 0.994016i | \(-0.534841\pi\) | ||||
−0.109239 | + | 0.994016i | \(0.534841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −12.0445 | −1.33828 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.7663 | 1.79693 | 0.898467 | − | 0.439042i | \(-0.144682\pi\) | ||||
0.898467 | + | 0.439042i | \(0.144682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 16.2291i | − | 1.24839i | −0.781267 | − | 0.624197i | \(-0.785426\pi\) | ||
0.781267 | − | 0.624197i | \(-0.214574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.9769 | 0.939819 | 0.469909 | − | 0.882715i | \(-0.344287\pi\) | ||||
0.469909 | + | 0.882715i | \(0.344287\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.9164 | − | 1.78065i | −0.995599 | − | 0.0937182i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.01577i | − | 0.334084i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −37.5766 | −1.63377 | −0.816883 | − | 0.576804i | \(-0.804300\pi\) | ||||
−0.816883 | + | 0.576804i | \(0.804300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 13.9665i | − | 0.517279i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 31.5765i | 1.08885i | 0.838811 | + | 0.544423i | \(0.183251\pi\) | ||||
−0.838811 | + | 0.544423i | \(0.816749\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.9409i | 1.25616i | 0.778149 | + | 0.628080i | \(0.216159\pi\) | ||||
−0.778149 | + | 0.628080i | \(0.783841\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 90.6764i | 2.74777i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 39.1052i | − | 1.05690i | −0.848965 | − | 0.528449i | \(-0.822774\pi\) | ||
0.848965 | − | 0.528449i | \(-0.177226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 74.4499 | 1.90897 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 69.4666i | 1.69431i | 0.531348 | + | 0.847154i | \(0.321686\pi\) | ||||
−0.531348 | + | 0.847154i | \(0.678314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.5777 | 0.385528 | 0.192764 | − | 0.981245i | \(-0.438255\pi\) | ||||
0.192764 | + | 0.981245i | \(0.438255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −52.0477 | −1.10740 | −0.553699 | − | 0.832717i | \(-0.686784\pi\) | ||||
−0.553699 | + | 0.832717i | \(0.686784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −46.6611 | −0.952267 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 73.2930i | 1.43712i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16.8503i | 0.317931i | 0.987284 | + | 0.158965i | \(0.0508158\pi\) | ||||
−0.987284 | + | 0.158965i | \(0.949184\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.16859 | − | 86.7776i | 0.143309 | − | 1.52241i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.5930i | 1.56937i | 0.619893 | + | 0.784686i | \(0.287176\pi\) | ||||
−0.619893 | + | 0.784686i | \(0.712824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.5327 | 0.844798 | 0.422399 | − | 0.906410i | \(-0.361188\pi\) | ||||
0.422399 | + | 0.906410i | \(0.361188\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18.4202 | 0.292385 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48.7310i | 0.727328i | 0.931530 | + | 0.363664i | \(0.118474\pi\) | ||||
−0.931530 | + | 0.363664i | \(0.881526\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 172.380i | − | 2.49826i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.51515i | − | 0.0776782i | −0.999245 | − | 0.0388391i | \(-0.987634\pi\) | ||
0.999245 | − | 0.0388391i | \(-0.0123660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 62.8328 | 0.860723 | 0.430362 | − | 0.902657i | \(-0.358386\pi\) | ||||
0.430362 | + | 0.902657i | \(0.358386\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −30.2295 | −0.392590 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 146.361i | 1.85268i | 0.376692 | + | 0.926338i | \(0.377061\pi\) | ||||
−0.376692 | + | 0.926338i | \(0.622939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −44.3302 | −0.547287 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −157.433 | −1.89678 | −0.948391 | − | 0.317103i | \(-0.897290\pi\) | ||||
−0.948391 | + | 0.317103i | \(0.897290\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −144.855 | −1.66500 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 87.6554i | 0.984893i | 0.870343 | + | 0.492446i | \(0.163897\pi\) | ||||
−0.870343 | + | 0.492446i | \(0.836103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.8199i | 0.272746i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −178.639 | −1.92085 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 115.339i | − | 1.18906i | −0.804073 | − | 0.594531i | \(-0.797338\pi\) | ||
0.804073 | − | 0.594531i | \(-0.202662\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −238.075 | −2.40480 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −105.886 | −1.04837 | −0.524186 | − | 0.851604i | \(-0.675631\pi\) | ||||
−0.524186 | + | 0.851604i | \(0.675631\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 72.5992i | 0.704847i | 0.935841 | + | 0.352423i | \(0.114642\pi\) | ||||
−0.935841 | + | 0.352423i | \(0.885358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.35545i | − | 0.0220135i | −0.999939 | − | 0.0110068i | \(-0.996496\pi\) | ||
0.999939 | − | 0.0110068i | \(-0.00350363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 182.099i | − | 1.67063i | −0.549772 | − | 0.835315i | \(-0.685285\pi\) | ||
0.549772 | − | 0.835315i | \(-0.314715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 179.393 | 1.61615 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 86.4522i | 0.765064i | 0.923942 | + | 0.382532i | \(0.124948\pi\) | ||||
−0.923942 | + | 0.382532i | \(0.875052\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 195.472i | 1.67070i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.4342 | −0.205330 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269.705 | 2.22897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −318.673 | −2.59084 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 119.187i | 0.938480i | 0.883071 | + | 0.469240i | \(0.155472\pi\) | ||||
−0.883071 | + | 0.469240i | \(0.844528\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 76.0491i | 0.589528i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 111.536 | 0.851423 | 0.425712 | − | 0.904859i | \(-0.360024\pi\) | ||||
0.425712 | + | 0.904859i | \(0.360024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.9297 | + | 2.72322i | 0.217516 | + | 0.0204754i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 82.0424 | 0.598849 | 0.299425 | − | 0.954120i | \(-0.403205\pi\) | ||||
0.299425 | + | 0.954120i | \(0.403205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −169.587 | −1.22005 | −0.610027 | − | 0.792381i | \(-0.708841\pi\) | ||||
−0.610027 | + | 0.792381i | \(0.708841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 238.765i | − | 1.69337i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 320.789i | − | 2.24328i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 214.055i | − | 1.45615i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 67.4940 | 0.452980 | 0.226490 | − | 0.974013i | \(-0.427275\pi\) | ||||
0.226490 | + | 0.974013i | \(0.427275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 152.293i | − | 1.00856i | −0.863540 | − | 0.504280i | \(-0.831758\pi\) | ||
0.863540 | − | 0.504280i | \(-0.168242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −192.434 | −1.25774 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 50.8926 | 0.324157 | 0.162078 | − | 0.986778i | \(-0.448180\pi\) | ||||
0.162078 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −77.2997 | −0.486162 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 57.4676 | 0.356942 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 56.1081 | 0.344222 | 0.172111 | − | 0.985078i | \(-0.444941\pi\) | ||||
0.172111 | + | 0.985078i | \(0.444941\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 172.992i | 1.03588i | 0.855418 | + | 0.517939i | \(0.173301\pi\) | ||||
−0.855418 | + | 0.517939i | \(0.826699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −94.3840 | −0.558485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 227.839 | + | 21.4470i | 1.33239 | + | 0.125421i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 85.4671i | − | 0.494030i | −0.969012 | − | 0.247015i | \(-0.920550\pi\) | ||
0.969012 | − | 0.247015i | \(-0.0794496\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −424.764 | −2.39980 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 181.685i | − | 1.01500i | −0.861652 | − | 0.507500i | \(-0.830570\pi\) | ||
0.861652 | − | 0.507500i | \(-0.169430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 98.1169i | 0.542083i | 0.962568 | + | 0.271041i | \(0.0873680\pi\) | ||||
−0.962568 | + | 0.271041i | \(0.912632\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 236.403i | 1.29182i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 315.804 | 1.68879 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.3596i | 0.113014i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −150.077 | −0.785741 | −0.392871 | − | 0.919594i | \(-0.628518\pi\) | ||||
−0.392871 | + | 0.919594i | \(0.628518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 20.0780i | − | 0.104031i | −0.998646 | − | 0.0520156i | \(-0.983435\pi\) | ||
0.998646 | − | 0.0520156i | \(-0.0165645\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −109.441 | −0.555536 | −0.277768 | − | 0.960648i | \(-0.589595\pi\) | ||||
−0.277768 | + | 0.960648i | \(0.589595\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 29.0917 | 0.146189 | 0.0730947 | − | 0.997325i | \(-0.476712\pi\) | ||||
0.0730947 | + | 0.997325i | \(0.476712\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −223.550 | −1.11219 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 48.2914i | − | 0.237889i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 452.592 | 2.18643 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −373.906 | − | 35.1967i | −1.78902 | − | 0.168405i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 134.671i | − | 0.638249i | −0.947713 | − | 0.319125i | \(-0.896611\pi\) | ||
0.947713 | − | 0.319125i | \(-0.103389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.3004 | 0.118781 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 59.5541i | − | 0.274443i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 288.241i | 1.31617i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 259.291i | − | 1.17326i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 201.645i | − | 0.904236i | −0.891958 | − | 0.452118i | \(-0.850669\pi\) | ||
0.891958 | − | 0.452118i | \(-0.149331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 435.566i | 1.91879i | 0.282064 | + | 0.959396i | \(0.408981\pi\) | ||||
−0.282064 | + | 0.959396i | \(0.591019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 336.632 | 1.47001 | 0.735003 | − | 0.678063i | \(-0.237181\pi\) | ||||
0.735003 | + | 0.678063i | \(0.237181\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 138.676i | − | 0.600327i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −270.736 | −1.16196 | −0.580979 | − | 0.813919i | \(-0.697330\pi\) | ||||
−0.580979 | + | 0.813919i | \(0.697330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −671.423 | −2.83301 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 111.441 | 0.466279 | 0.233139 | − | 0.972443i | \(-0.425100\pi\) | ||||
0.233139 | + | 0.972443i | \(0.425100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 269.049i | − | 1.11639i | −0.829711 | − | 0.558194i | \(-0.811495\pi\) | ||
0.829711 | − | 0.558194i | \(-0.188505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 329.061i | − | 1.35416i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.8983 | + | 306.996i | −0.116997 | + | 1.24290i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 722.213i | − | 2.90045i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −69.8084 | −0.278121 | −0.139061 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139061 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −742.749 | −2.93577 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 205.201i | 0.798448i | 0.916853 | + | 0.399224i | \(0.130720\pi\) | ||||
−0.916853 | + | 0.399224i | \(0.869280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 59.8054i | 0.230909i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 380.324i | − | 1.45718i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 369.721 | 1.40578 | 0.702892 | − | 0.711297i | \(-0.251892\pi\) | ||||
0.702892 | + | 0.711297i | \(0.251892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −402.113 | −1.50604 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 56.1803i | 0.208849i | 0.994533 | + | 0.104424i | \(0.0333000\pi\) | ||||
−0.994533 | + | 0.104424i | \(0.966700\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −108.318 | −0.399697 | −0.199849 | − | 0.979827i | \(-0.564045\pi\) | ||||
−0.199849 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −113.860 | −0.417068 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −186.564 | −0.673517 | −0.336758 | − | 0.941591i | \(-0.609331\pi\) | ||||
−0.336758 | + | 0.941591i | \(0.609331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 469.025i | − | 1.68109i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 136.711i | 0.486516i | 0.969962 | + | 0.243258i | \(0.0782161\pi\) | ||||
−0.969962 | + | 0.243258i | \(0.921784\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −100.842 | −0.356332 | −0.178166 | − | 0.984000i | \(-0.557016\pi\) | ||||
−0.178166 | + | 0.984000i | \(0.557016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 106.238i | − | 0.370169i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.7382 | −0.116741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 529.110 | 1.81825 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 345.837i | 1.18033i | 0.807283 | + | 0.590165i | \(0.200937\pi\) | ||||
−0.807283 | + | 0.590165i | \(0.799063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 276.066i | − | 0.929515i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 609.835i | 2.03958i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.3531 | −0.0842294 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 485.743i | − | 1.60311i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 212.148i | − | 0.691035i | −0.938412 | − | 0.345518i | \(-0.887703\pi\) | ||
0.938412 | − | 0.345518i | \(-0.112297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −333.044 | −1.07781 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 534.396 | 1.71832 | 0.859158 | − | 0.511711i | \(-0.170988\pi\) | ||||
0.859158 | + | 0.511711i | \(0.170988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −242.134 | −0.773590 | −0.386795 | − | 0.922166i | \(-0.626418\pi\) | ||||
−0.386795 | + | 0.922166i | \(0.626418\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 448.993i | − | 1.41638i | −0.706021 | − | 0.708191i | \(-0.749512\pi\) | ||
0.706021 | − | 0.708191i | \(-0.250488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 624.150i | 1.95658i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.8055 | 0.0336619 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −302.225 | − | 28.4492i | −0.935682 | − | 0.0880781i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 835.365 | 2.55463 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 79.5989 | 0.241942 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 444.084i | 1.34164i | 0.741618 | + | 0.670822i | \(0.234059\pi\) | ||||
−0.741618 | + | 0.670822i | \(0.765941\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 471.004i | 1.41443i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 517.271i | 1.53493i | 0.641092 | + | 0.767464i | \(0.278482\pi\) | ||||
−0.641092 | + | 0.767464i | \(0.721518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −396.593 | −1.16989 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 769.717i | 2.25723i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 146.299 | 0.426527 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.8683 | −0.0889576 | −0.0444788 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444788 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −156.386 | −0.448097 | −0.224049 | − | 0.974578i | \(-0.571927\pi\) | ||||
−0.224049 | + | 0.974578i | \(0.571927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −226.664 | −0.645767 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 569.039 | 1.61201 | 0.806005 | − | 0.591909i | \(-0.201626\pi\) | ||||
0.806005 | + | 0.591909i | \(0.201626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 112.090i | − | 0.313978i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −339.420 | −0.945459 | −0.472729 | − | 0.881208i | \(-0.656731\pi\) | ||||
−0.472729 | + | 0.881208i | \(0.656731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 354.659 | + | 67.3667i | 0.982434 | + | 0.186611i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1237.25i | 3.40841i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 72.4587 | 0.197435 | 0.0987176 | − | 0.995115i | \(-0.468526\pi\) | ||||
0.0987176 | + | 0.995115i | \(0.468526\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 836.692i | − | 2.26746i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 25.7700i | − | 0.0694608i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 480.589i | − | 1.28844i | −0.764840 | − | 0.644221i | \(-0.777182\pi\) | ||
0.764840 | − | 0.644221i | \(-0.222818\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 512.459 | 1.35931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 343.159i | 0.905433i | 0.891654 | + | 0.452717i | \(0.149545\pi\) | ||||
−0.891654 | + | 0.452717i | \(0.850455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −546.762 | −1.43507 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 380.989i | − | 0.994751i | −0.867536 | − | 0.497375i | \(-0.834297\pi\) | ||
0.867536 | − | 0.497375i | \(-0.165703\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −199.671 | −0.515945 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 153.297 | 0.394081 | 0.197040 | − | 0.980395i | \(-0.436867\pi\) | ||||
0.197040 | + | 0.980395i | \(0.436867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −600.358 | −1.53544 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 511.666i | 1.30195i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −410.383 | −1.03371 | −0.516855 | − | 0.856073i | \(-0.672897\pi\) | ||||
−0.516855 | + | 0.856073i | \(0.672897\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.4926 | + | 132.713i | −0.0313098 | + | 0.332614i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 96.2006i | − | 0.239902i | −0.992780 | − | 0.119951i | \(-0.961726\pi\) | ||
0.992780 | − | 0.119951i | \(-0.0382737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 631.977 | 1.56818 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 772.964i | − | 1.89918i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 804.488i | 1.96696i | 0.181008 | + | 0.983482i | \(0.442064\pi\) | ||||
−0.181008 | + | 0.983482i | \(0.557936\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 376.364i | 0.915727i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 141.607i | − | 0.342873i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 777.970i | − | 1.86564i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 105.005 | 0.250609 | 0.125304 | − | 0.992118i | \(-0.460009\pi\) | ||||
0.125304 | + | 0.992118i | \(0.460009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 228.201i | 0.542045i | 0.962573 | + | 0.271023i | \(0.0873618\pi\) | ||||
−0.962573 | + | 0.271023i | \(0.912638\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 626.890 | 1.48201 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −78.8113 | −0.184570 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1471.60 | 3.43030 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 182.455i | − | 0.423329i | −0.977342 | − | 0.211665i | \(-0.932112\pi\) | ||
0.977342 | − | 0.211665i | \(-0.0678884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.9156i | − | 0.0690890i | −0.999403 | − | 0.0345445i | \(-0.989002\pi\) | ||
0.999403 | − | 0.0345445i | \(-0.0109980\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 710.813 | + | 66.9106i | 1.62657 | + | 0.153113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 497.696i | − | 1.13370i | −0.823820 | − | 0.566852i | \(-0.808161\pi\) | ||
0.823820 | − | 0.566852i | \(-0.191839\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 562.011 | 1.27440 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 348.602 | 0.786912 | 0.393456 | − | 0.919343i | \(-0.371279\pi\) | ||||
0.393456 | + | 0.919343i | \(0.371279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 309.624i | 0.692672i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 285.726i | 0.636360i | 0.948030 | + | 0.318180i | \(0.103072\pi\) | ||||
−0.948030 | + | 0.318180i | \(0.896928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1373.10i | 3.04456i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 698.632 | 1.54223 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −394.636 | −0.863535 | −0.431768 | − | 0.901985i | \(-0.642110\pi\) | ||||
−0.431768 | + | 0.901985i | \(0.642110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 223.142i | − | 0.486148i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.9653 | −0.0346318 | −0.0173159 | − | 0.999850i | \(-0.505512\pi\) | ||||
−0.0173159 | + | 0.999850i | \(0.505512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −291.052 | −0.628623 | −0.314311 | − | 0.949320i | \(-0.601774\pi\) | ||||
−0.314311 | + | 0.949320i | \(0.601774\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 592.490 | 1.26871 | 0.634357 | − | 0.773040i | \(-0.281265\pi\) | ||||
0.634357 | + | 0.773040i | \(0.281265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 74.5265i | − | 0.158905i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 233.466i | 0.495682i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 327.679 | 0.692768 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 202.954i | − | 0.425480i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 198.971 | 0.415389 | 0.207695 | − | 0.978194i | \(-0.433404\pi\) | ||||
0.207695 | + | 0.978194i | \(0.433404\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −634.643 | −1.31942 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 263.629i | 0.545815i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 136.234i | 0.279741i | 0.990170 | + | 0.139871i | \(0.0446687\pi\) | ||||
−0.990170 | + | 0.139871i | \(0.955331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 257.392i | 0.526364i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 220.115 | 0.448299 | 0.224149 | − | 0.974555i | \(-0.428040\pi\) | ||||
0.224149 | + | 0.974555i | \(0.428040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 504.495i | 1.02332i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.43457i | 0.0169710i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 929.974 | 1.86367 | 0.931837 | − | 0.362877i | \(-0.118205\pi\) | ||||
0.931837 | + | 0.362877i | \(0.118205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −793.587 | −1.58401 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −606.816 | −1.20639 | −0.603196 | − | 0.797593i | \(-0.706107\pi\) | ||||
−0.603196 | + | 0.797593i | \(0.706107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 432.980i | − | 0.854004i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 342.999i | 0.673869i | 0.941528 | + | 0.336935i | \(0.109390\pi\) | ||||
−0.941528 | + | 0.336935i | \(0.890610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −96.0931 | −0.188049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.8694 | + | 264.196i | −0.0484784 | + | 0.515002i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1028.79 | −1.98992 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 392.074 | 0.755442 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 303.047i | − | 0.581664i | −0.956774 | − | 0.290832i | \(-0.906068\pi\) | ||
0.956774 | − | 0.290832i | \(-0.0939320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 839.474i | − | 1.60511i | −0.596576 | − | 0.802556i | \(-0.703473\pi\) | ||
0.596576 | − | 0.802556i | \(-0.296527\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 622.156i | 1.18056i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 883.001 | 1.66919 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1115.24i | − | 2.10026i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1127.38 | 2.11516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 833.468 | 1.55208 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −922.316 | −1.71116 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −673.205 | −1.24437 | −0.622186 | − | 0.782869i | \(-0.713755\pi\) | ||||
−0.622186 | + | 0.782869i | \(0.713755\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −450.105 | −0.828922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 393.199i | 0.718828i | 0.933178 | + | 0.359414i | \(0.117023\pi\) | ||||
−0.933178 | + | 0.359414i | \(0.882977\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −620.686 | −1.13058 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.2266 | − | 597.313i | 0.102045 | − | 1.08405i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 223.837i | − | 0.404769i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 62.2937 | 0.111838 | 0.0559189 | − | 0.998435i | \(-0.482191\pi\) | ||||
0.0559189 | + | 0.998435i | \(0.482191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 269.042i | − | 0.481291i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1448.73i | 2.58240i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 763.894i | 1.35683i | 0.734680 | + | 0.678414i | \(0.237332\pi\) | ||||
−0.734680 | + | 0.678414i | \(0.762668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 67.7962 | 0.119570 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 344.276i | − | 0.605055i | −0.953141 | − | 0.302527i | \(-0.902170\pi\) | ||
0.953141 | − | 0.302527i | \(-0.0978304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −394.946 | −0.691675 | −0.345837 | − | 0.938294i | \(-0.612405\pi\) | ||||
−0.345837 | + | 0.938294i | \(0.612405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 688.466i | − | 1.20151i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −491.043 | −0.851027 | −0.425514 | − | 0.904952i | \(-0.639907\pi\) | ||||
−0.425514 | + | 0.904952i | \(0.639907\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 92.1065 | 0.159079 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 240.769 | 0.414405 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 333.068i | 0.571300i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 99.3437 | 0.169240 | 0.0846198 | − | 0.996413i | \(-0.473032\pi\) | ||||
0.0846198 | + | 0.996413i | \(0.473032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 69.3400 | − | 736.621i | 0.117725 | − | 1.25063i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 502.052i | − | 0.849495i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −879.094 | −1.48245 | −0.741226 | − | 0.671256i | \(-0.765755\pi\) | ||||
−0.741226 | + | 0.671256i | \(0.765755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 133.456i | 0.223545i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.4131i | 0.0240620i | 0.999928 | + | 0.0120310i | \(0.00382967\pi\) | ||||
−0.999928 | + | 0.0120310i | \(0.996170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 485.996i | − | 0.808645i | −0.914617 | − | 0.404322i | \(-0.867507\pi\) | ||
0.914617 | − | 0.404322i | \(-0.132493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 586.941i | − | 0.973368i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 249.106i | − | 0.410389i | −0.978721 | − | 0.205195i | \(-0.934217\pi\) | ||
0.978721 | − | 0.205195i | \(-0.0657827\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 221.533 | 0.363766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 844.688i | 1.38247i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 439.644 | 0.717200 | 0.358600 | − | 0.933491i | \(-0.383254\pi\) | ||||
0.358600 | + | 0.933491i | \(0.383254\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.6889 | 0.0513597 | 0.0256798 | − | 0.999670i | \(-0.491825\pi\) | ||||
0.0256798 | + | 0.999670i | \(0.491825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −590.945 | −0.954677 | −0.477339 | − | 0.878719i | \(-0.658398\pi\) | ||||
−0.477339 | + | 0.878719i | \(0.658398\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 524.814i | 0.845112i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 134.055i | − | 0.215177i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 161.462 | − | 1715.27i | 0.257516 | − | 2.73568i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 624.781i | − | 0.993293i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −144.511 | −0.229019 | −0.114509 | − | 0.993422i | \(-0.536530\pi\) | ||||
−0.114509 | + | 0.993422i | \(0.536530\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 617.792 | 0.975975 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 757.268i | 1.18880i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 66.4273i | 0.103955i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 41.9005i | − | 0.0653674i | −0.999466 | − | 0.0326837i | \(-0.989595\pi\) | ||
0.999466 | − | 0.0326837i | \(-0.0104054\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 847.463 | 1.31798 | 0.658992 | − | 0.752150i | \(-0.270983\pi\) | ||||
0.658992 | + | 0.752150i | \(0.270983\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 828.509 | 1.28054 | 0.640269 | − | 0.768150i | \(-0.278823\pi\) | ||||
0.640269 | + | 0.768150i | \(0.278823\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1830.22i | 2.82006i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 273.200 | 0.419663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 376.647 | 0.576795 | 0.288397 | − | 0.957511i | \(-0.406878\pi\) | ||||
0.288397 | + | 0.957511i | \(0.406878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −756.791 | −1.15189 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 656.057i | 0.995534i | 0.867311 | + | 0.497767i | \(0.165846\pi\) | ||||
−0.867311 | + | 0.497767i | \(0.834154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 837.563i | − | 1.26712i | −0.773696 | − | 0.633558i | \(-0.781594\pi\) | ||
0.773696 | − | 0.633558i | \(-0.218406\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1189.48 | 1.79409 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1186.54i | − | 1.77892i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 925.030 | 1.38271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1018.61 | 1.51805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 383.937i | − | 0.570486i | −0.958455 | − | 0.285243i | \(-0.907926\pi\) | ||
0.958455 | − | 0.285243i | \(-0.0920743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 597.994i | 0.883300i | 0.897187 | + | 0.441650i | \(0.145607\pi\) | ||||
−0.897187 | + | 0.441650i | \(0.854393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 176.393i | 0.259784i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1998.13 | −2.93411 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 814.772i | 1.19293i | 0.802639 | + | 0.596466i | \(0.203429\pi\) | ||||
−0.802639 | + | 0.596466i | \(0.796571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1544.27i | 2.24785i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 273.466 | 0.396903 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 183.046 | 0.264900 | 0.132450 | − | 0.991190i | \(-0.457716\pi\) | ||||
0.132450 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 364.099 | 0.525396 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1109.86i | 1.59234i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1241.98i | − | 1.77680i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.2332 | 0.0288633 | 0.0144317 | − | 0.999896i | \(-0.495406\pi\) | ||||
0.0144317 | + | 0.999896i | \(0.495406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −69.6325 | + | 739.729i | −0.0990506 | + | 1.05225i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 161.936 | 0.229046 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 348.032 | 0.490877 | 0.245438 | − | 0.969412i | \(-0.421068\pi\) | ||||
0.245438 | + | 0.969412i | \(0.421068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1762.85i | − | 2.47940i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1463.27i | − | 2.05227i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 511.226i | 0.713007i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1282.72 | −1.78403 | −0.892014 | − | 0.452007i | \(-0.850708\pi\) | ||||
−0.892014 | + | 0.452007i | \(0.850708\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 111.029i | − | 0.153993i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1234.25 | 1.70712 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 203.759 | 0.280274 | 0.140137 | − | 0.990132i | \(-0.455246\pi\) | ||||
0.140137 | + | 0.990132i | \(0.455246\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1110.57 | 1.52342 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 264.861 | 0.362327 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −350.631 | −0.478350 | −0.239175 | − | 0.970976i | \(-0.576877\pi\) | ||||
−0.239175 | + | 0.970976i | \(0.576877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 963.229i | 1.30696i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1288.92 | 1.74415 | 0.872073 | − | 0.489375i | \(-0.162775\pi\) | ||||
0.872073 | + | 0.489375i | \(0.162775\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1408.32 | − | 132.569i | −1.90057 | − | 0.178905i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1222.62i | − | 1.64551i | −0.568393 | − | 0.822757i | \(-0.692435\pi\) | ||
0.568393 | − | 0.822757i | \(-0.307565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1896.20 | 2.53843 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.60229i | 0.00480947i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1256.47i | − | 1.67306i | −0.547919 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547919 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 320.241i | − | 0.425287i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 680.666 | 0.899162 | 0.449581 | − | 0.893240i | \(-0.351573\pi\) | ||||
0.449581 | + | 0.893240i | \(0.351573\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3407.31i | − | 4.48921i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 656.481 | 0.862656 | 0.431328 | − | 0.902195i | \(-0.358045\pi\) | ||||
0.431328 | + | 0.902195i | \(0.358045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 278.492i | 0.364996i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1502.70 | 1.95919 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −429.894 | −0.559030 | −0.279515 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279515 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −941.346 | −1.22094 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1410.12i | − | 1.82422i | −0.409943 | − | 0.912111i | \(-0.634451\pi\) | ||
0.409943 | − | 0.912111i | \(-0.365549\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −274.353 | −0.353093 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 123.695 | − | 1314.06i | 0.158787 | − | 1.68685i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 109.014i | − | 0.139582i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 441.014 | 0.563236 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 696.889i | − | 0.885501i | −0.896645 | − | 0.442750i | \(-0.854003\pi\) | ||
0.896645 | − | 0.442750i | \(-0.145997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1696.07i | 2.14964i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 132.215i | − | 0.167150i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 836.330i | − | 1.05464i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1145.32i | − | 1.43704i | −0.695506 | − | 0.718520i | \(-0.744820\pi\) | ||
0.695506 | − | 0.718520i | \(-0.255180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −831.562 | −1.04075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1055.77i | − | 1.31806i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1241.97 | 1.54666 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −257.723 | −0.319360 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 355.323 | 0.439212 | 0.219606 | − | 0.975589i | \(-0.429523\pi\) | ||||
0.219606 | + | 0.975589i | \(0.429523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 108.258i | 0.133487i | 0.997770 | + | 0.0667437i | \(0.0212610\pi\) | ||||
−0.997770 | + | 0.0667437i | \(0.978739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 496.901i | − | 0.611195i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −313.590 | − | 29.5190i | −0.383831 | − | 0.0361310i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 298.944i | − | 0.365011i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −470.491 | −0.573071 | −0.286535 | − | 0.958070i | \(-0.592504\pi\) | ||||
−0.286535 | + | 0.958070i | \(0.592504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 986.856 | 1.19910 | 0.599548 | − | 0.800339i | \(-0.295347\pi\) | ||||
0.599548 | + | 0.800339i | \(0.295347\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1180.91i | 1.42794i | 0.700174 | + | 0.713972i | \(0.253106\pi\) | ||||
−0.700174 | + | 0.713972i | \(0.746894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 357.631i | − | 0.431401i | −0.976460 | − | 0.215701i | \(-0.930797\pi\) | ||
0.976460 | − | 0.215701i | \(-0.0692035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 855.850i | − | 1.02990i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −745.500 | −0.894959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 543.869 | 0.649784 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1334.94i | 1.59111i | 0.605884 | + | 0.795553i | \(0.292819\pi\) | ||||
−0.605884 | + | 0.795553i | \(0.707181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −156.076 | −0.185584 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −627.152 | −0.743952 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −412.473 | −0.486981 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 462.605i | − | 0.544882i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1469.44i | 1.72672i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1346.94 | −1.57906 | −0.789529 | − | 0.613713i | \(-0.789675\pi\) | ||||
−0.789529 | + | 0.613713i | \(0.789675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.3502i | 0.0120773i | 0.999982 | + | 0.00603863i | \(0.00192217\pi\) | ||||
−0.999982 | + | 0.00603863i | \(0.998078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1026.42 | 1.19490 | 0.597449 | − | 0.801907i | \(-0.296181\pi\) | ||||
0.597449 | + | 0.801907i | \(0.296181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 487.362 | 0.566041 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1145.76i | 1.32764i | 0.747891 | + | 0.663822i | \(0.231067\pi\) | ||||
−0.747891 | + | 0.663822i | \(0.768933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 154.772i | − | 0.178514i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2893.02i | 3.32914i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 790.860 | 0.907991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1389.20i | 1.59130i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1242.23i | 1.41645i | 0.705987 | + | 0.708225i | \(0.250504\pi\) | ||||
−0.705987 | + | 0.708225i | \(0.749496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1586.50 | −1.80489 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1102.73 | −1.25168 | −0.625842 | − | 0.779950i | \(-0.715244\pi\) | ||||
−0.625842 | + | 0.779950i | \(0.715244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 597.580 | 0.676761 | 0.338381 | − | 0.941009i | \(-0.390121\pi\) | ||||
0.338381 | + | 0.941009i | \(0.390121\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 327.216i | 0.368902i | 0.982842 | + | 0.184451i | \(0.0590507\pi\) | ||||
−0.982842 | + | 0.184451i | \(0.940949\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 182.278i | − | 0.205037i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −876.243 | −0.983438 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 984.554 | + | 92.6785i | 1.10252 | + | 0.103783i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2797.57 | −3.11881 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1229.62 | −1.36776 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 269.216i | 0.298797i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 116.305i | − | 0.128799i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 253.226i | − | 0.279190i | −0.990209 | − | 0.139595i | \(-0.955420\pi\) | ||
0.990209 | − | 0.139595i | \(-0.0445801\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1275.34 | 1.40302 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1122.92i | − | 1.23263i | −0.787500 | − | 0.616314i | \(-0.788625\pi\) | ||
0.787500 | − | 0.616314i | \(-0.211375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3111.86 | −3.40839 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −170.578 | −0.186017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 967.325 | 1.05258 | 0.526292 | − | 0.850304i | \(-0.323582\pi\) | ||||
0.526292 | + | 0.850304i | \(0.323582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 973.213 | 1.05669 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −89.5060 | −0.0969729 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 874.423i | − | 0.943282i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 374.642 | 0.403275 | 0.201637 | − | 0.979460i | \(-0.435374\pi\) | ||||
0.201637 | + | 0.979460i | \(0.435374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 882.659 | + | 83.0869i | 0.948076 | + | 0.0892448i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2451.51i | 2.62755i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −310.678 | −0.331567 | −0.165783 | − | 0.986162i | \(-0.553015\pi\) | ||||
−0.165783 | + | 0.986162i | \(0.553015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1110.77i | − | 1.18293i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 118.112i | − | 0.125518i | −0.998029 | − | 0.0627589i | \(-0.980010\pi\) | ||
0.998029 | − | 0.0627589i | \(-0.0199899\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2610.32i | − | 2.76810i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −553.081 | −0.584034 | −0.292017 | − | 0.956413i | \(-0.594326\pi\) | ||||
−0.292017 | + | 0.956413i | \(0.594326\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1019.72i | − | 1.07452i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2059.72 | 2.16585 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 375.463i | − | 0.393980i | −0.980406 | − | 0.196990i | \(-0.936883\pi\) | ||
0.980406 | − | 0.196990i | \(-0.0631166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2863.24 | −2.99189 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −125.471 | −0.130835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −555.396 | −0.577936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.3702i | 0.0294603i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1280.32 | −1.32401 | −0.662004 | − | 0.749500i | \(-0.730294\pi\) | ||||
−0.662004 | + | 0.749500i | \(0.730294\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 130.509 | − | 1386.44i | 0.134684 | − | 1.43079i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 487.041i | − | 0.501587i | −0.968041 | − | 0.250793i | \(-0.919309\pi\) | ||
0.968041 | − | 0.250793i | \(-0.0806915\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 259.358 | 0.266555 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 85.6576i | − | 0.0876741i | −0.999039 | − | 0.0438371i | \(-0.986042\pi\) | ||
0.999039 | − | 0.0438371i | \(-0.0139582\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1732.62i | 1.76979i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2193.29i | 2.23577i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 220.950i | − | 0.224771i | −0.993665 | − | 0.112386i | \(-0.964151\pi\) | ||
0.993665 | − | 0.112386i | \(-0.0358492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 365.155i | 0.369964i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −622.934 | −0.629862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1569.41i | 1.58367i | 0.610737 | + | 0.791834i | \(0.290873\pi\) | ||||
−0.610737 | + | 0.791834i | \(0.709127\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2037.21 | −2.05157 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1821.95 | 1.82743 | 0.913715 | − | 0.406355i | \(-0.133200\pi\) | ||||
0.913715 | + | 0.406355i | \(0.133200\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −546.164 | −0.546711 |
(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 | 1900.3.e.g.1101.12 | yes | 14 | |
5.2 | odd | 4 | 1900.3.g.d.949.24 | 28 | |||
5.3 | odd | 4 | 1900.3.g.d.949.5 | 28 | |||
5.4 | even | 2 | 1900.3.e.h.1101.3 | yes | 14 | ||
19.18 | odd | 2 | inner | 1900.3.e.g.1101.3 | ✓ | 14 | |
95.18 | even | 4 | 1900.3.g.d.949.23 | 28 | |||
95.37 | even | 4 | 1900.3.g.d.949.6 | 28 | |||
95.94 | odd | 2 | 1900.3.e.h.1101.12 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.3.e.g.1101.3 | ✓ | 14 | 19.18 | odd | 2 | inner | |
1900.3.e.g.1101.12 | yes | 14 | 1.1 | even | 1 | trivial | |
1900.3.e.h.1101.3 | yes | 14 | 5.4 | even | 2 | ||
1900.3.e.h.1101.12 | yes | 14 | 95.94 | odd | 2 | ||
1900.3.g.d.949.5 | 28 | 5.3 | odd | 4 | |||
1900.3.g.d.949.6 | 28 | 95.37 | even | 4 | |||
1900.3.g.d.949.23 | 28 | 95.18 | even | 4 | |||
1900.3.g.d.949.24 | 28 | 5.2 | odd | 4 |