Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1340,3,Mod(669,1340)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1340, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1340.669");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1340 = 2^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1340.g (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: | \(36.5123554243\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 669.54 | ||
Character | \(\chi\) | \(=\) | 1340.669 |
Dual form | 1340.3.g.a.669.53 |
$q$-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 \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).
\(n\) | \(537\) | \(671\) | \(1141\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.94848 | 1.31616 | 0.658080 | − | 0.752948i | \(-0.271369\pi\) | ||||
0.658080 | + | 0.752948i | \(0.271369\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.78326 | − | 1.45617i | −0.956652 | − | 0.291235i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.855885 | −0.122269 | −0.0611346 | − | 0.998130i | \(-0.519472\pi\) | ||||
−0.0611346 | + | 0.998130i | \(0.519472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.59049 | 0.732276 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.32833i | − | 0.393485i | −0.980455 | − | 0.196742i | \(-0.936964\pi\) | ||
0.980455 | − | 0.196742i | \(-0.0630362\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.61600 | 0.355077 | 0.177538 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177538 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.8866 | − | 5.74968i | −1.25911 | − | 0.383312i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 10.0593i | − | 0.591723i | −0.955231 | − | 0.295862i | \(-0.904393\pi\) | ||
0.955231 | − | 0.295862i | \(-0.0956067\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.3780 | 1.28305 | 0.641527 | − | 0.767100i | \(-0.278301\pi\) | ||||
0.641527 | + | 0.767100i | \(0.278301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.37944 | −0.160926 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.78769i | 0.425552i | 0.977101 | + | 0.212776i | \(0.0682504\pi\) | ||||
−0.977101 | + | 0.212776i | \(0.931750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.7591 | + | 13.9305i | 0.830364 | + | 0.557221i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.51391 | −0.352367 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22.5771 | −0.778519 | −0.389260 | − | 0.921128i | \(-0.627269\pi\) | ||||
−0.389260 | + | 0.921128i | \(0.627269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 47.6840i | − | 1.53819i | −0.639132 | − | 0.769097i | \(-0.720706\pi\) | ||
0.639132 | − | 0.769097i | \(-0.279294\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 17.0903i | − | 0.517889i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.09392 | + | 1.24632i | 0.116969 | + | 0.0356091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 62.4066i | − | 1.68666i | −0.537392 | − | 0.843332i | \(-0.680590\pi\) | ||
0.537392 | − | 0.843332i | \(-0.319410\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.2262 | 0.467337 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.4289i | 0.522656i | 0.965250 | + | 0.261328i | \(0.0841604\pi\) | ||||
−0.965250 | + | 0.261328i | \(0.915840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.3265 | −0.705268 | −0.352634 | − | 0.935761i | \(-0.614714\pi\) | ||||
−0.352634 | + | 0.935761i | \(0.614714\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −31.5240 | − | 9.59690i | −0.700533 | − | 0.213265i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 25.3886i | − | 0.540184i | −0.962835 | − | 0.270092i | \(-0.912946\pi\) | ||
0.962835 | − | 0.270092i | \(-0.0870541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.2675 | −0.985050 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 39.7189i | − | 0.778802i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 41.4423 | 0.781930 | 0.390965 | − | 0.920406i | \(-0.372141\pi\) | ||||
0.390965 | + | 0.920406i | \(0.372141\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.30281 | + | 20.7035i | −0.114596 | + | 0.376428i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 96.2562 | 1.68870 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −28.8520 | −0.489018 | −0.244509 | − | 0.969647i | \(-0.578627\pi\) | ||||
−0.244509 | + | 0.969647i | \(0.578627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 98.4653i | − | 1.61418i | −0.590425 | − | 0.807092i | \(-0.701040\pi\) | ||
0.590425 | − | 0.807092i | \(-0.298960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.64070 | −0.0895349 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.0795 | − | 6.72170i | −0.339685 | − | 0.103411i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18.9961 | − | 64.2507i | −0.283524 | − | 0.958965i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 38.6465i | 0.560094i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 118.560 | 1.66986 | 0.834928 | − | 0.550359i | \(-0.185509\pi\) | ||||
0.834928 | + | 0.550359i | \(0.185509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 90.6692i | − | 1.24204i | −0.783793 | − | 0.621022i | \(-0.786718\pi\) | ||
0.783793 | − | 0.621022i | \(-0.213282\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 81.9669 | + | 55.0044i | 1.09289 | + | 0.733392i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.70455i | 0.0481111i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 137.981i | − | 1.74659i | −0.487191 | − | 0.873295i | \(-0.661979\pi\) | ||
0.487191 | − | 0.873295i | \(-0.338021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −96.8799 | −1.19605 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.9932i | 0.216785i | 0.994108 | + | 0.108393i | \(0.0345704\pi\) | ||||
−0.994108 | + | 0.108393i | \(0.965430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.6481 | + | 48.1162i | −0.172330 | + | 0.566073i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −89.1451 | −1.02466 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 107.490 | 1.20775 | 0.603876 | − | 0.797079i | \(-0.293622\pi\) | ||||
0.603876 | + | 0.797079i | \(0.293622\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.95076 | −0.0434150 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 188.279i | − | 2.02451i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −116.606 | − | 35.4987i | −1.22744 | − | 0.373670i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −121.609 | −1.25370 | −0.626852 | − | 0.779139i | \(-0.715657\pi\) | ||||
−0.626852 | + | 0.779139i | \(0.715657\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 28.5258i | − | 0.288140i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 133.352i | − | 1.32032i | −0.751125 | − | 0.660161i | \(-0.770488\pi\) | ||
0.751125 | − | 0.660161i | \(-0.229512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 145.855i | 1.41607i | 0.706177 | + | 0.708035i | \(0.250418\pi\) | ||||
−0.706177 | + | 0.708035i | \(0.749582\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.1648 | + | 4.92106i | 0.153950 | + | 0.0468673i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 179.341i | 1.67608i | 0.545609 | + | 0.838040i | \(0.316299\pi\) | ||||
−0.545609 | + | 0.838040i | \(0.683701\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 117.813i | − | 1.08085i | −0.841391 | − | 0.540427i | \(-0.818263\pi\) | ||
0.841391 | − | 0.540427i | \(-0.181737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 246.411i | − | 2.21992i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −81.1018 | −0.717715 | −0.358858 | − | 0.933392i | \(-0.616834\pi\) | ||||
−0.358858 | + | 0.933392i | \(0.616834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.2526 | − | 46.8171i | 0.123936 | − | 0.407105i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.4217 | 0.260014 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.60960i | 0.0723496i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 102.266 | 0.845170 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 84.6116i | 0.687899i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −79.0109 | − | 96.8622i | −0.632087 | − | 0.774897i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 31.2818i | − | 0.246314i | −0.992387 | − | 0.123157i | \(-0.960698\pi\) | ||
0.992387 | − | 0.123157i | \(-0.0393018\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −119.744 | −0.928245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 181.724 | 1.38721 | 0.693603 | − | 0.720358i | \(-0.256022\pi\) | ||||
0.693603 | + | 0.720358i | \(0.256022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.8648 | −0.156878 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 45.5075 | + | 13.8539i | 0.337092 | + | 0.102622i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 194.446 | 1.41931 | 0.709657 | − | 0.704547i | \(-0.248850\pi\) | ||||
0.709657 | + | 0.704547i | \(0.248850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 194.020i | 1.39583i | 0.716180 | + | 0.697915i | \(0.245889\pi\) | ||||
−0.716180 | + | 0.697915i | \(0.754111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 100.247i | − | 0.710968i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 19.9796i | − | 0.139717i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 107.992 | + | 32.8761i | 0.744772 | + | 0.226732i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −190.583 | −1.29648 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 100.073 | 0.671634 | 0.335817 | − | 0.941927i | \(-0.390988\pi\) | ||||
0.335817 | + | 0.941927i | \(0.390988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −32.3260 | −0.214080 | −0.107040 | − | 0.994255i | \(-0.534137\pi\) | ||||
−0.107040 | + | 0.994255i | \(0.534137\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 66.2956i | − | 0.433305i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −69.4363 | + | 228.085i | −0.447976 | + | 1.47152i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 251.363i | 1.60104i | 0.599309 | + | 0.800518i | \(0.295442\pi\) | ||||
−0.599309 | + | 0.800518i | \(0.704558\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 163.634 | 1.02914 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8.37714i | − | 0.0520319i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 232.856i | 1.42856i | 0.699858 | + | 0.714282i | \(0.253247\pi\) | ||||
−0.699858 | + | 0.714282i | \(0.746753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −24.8865 | + | 81.7474i | −0.150827 | + | 0.495439i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 230.268i | 1.37885i | 0.724358 | + | 0.689424i | \(0.242136\pi\) | ||||
−0.724358 | + | 0.689424i | \(0.757864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −147.693 | −0.873921 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 160.663 | 0.939551 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0120i | 0.0636532i | 0.999493 | + | 0.0318266i | \(0.0101324\pi\) | ||||
−0.999493 | + | 0.0318266i | \(0.989868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.7674 | − | 11.9229i | −0.101528 | − | 0.0681310i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −113.922 | −0.643625 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 43.1431i | 0.241023i | 0.992712 | + | 0.120511i | \(0.0384534\pi\) | ||||
−0.992712 | + | 0.120511i | \(0.961547\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −29.5436 | −0.163225 | −0.0816123 | − | 0.996664i | \(-0.526007\pi\) | ||||
−0.0816123 | + | 0.996664i | \(0.526007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 388.788i | − | 2.12452i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −90.8749 | + | 298.507i | −0.491216 | + | 1.61355i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −43.5399 | −0.232834 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.14281 | 0.0430837 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 148.942i | − | 0.779803i | −0.920857 | − | 0.389902i | \(-0.872509\pi\) | ||
0.920857 | − | 0.389902i | \(-0.127491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 48.6412i | 0.252027i | 0.992029 | + | 0.126013i | \(0.0402183\pi\) | ||||
−0.992029 | + | 0.126013i | \(0.959782\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −87.1804 | − | 26.5405i | −0.447079 | − | 0.136105i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −143.069 | −0.726237 | −0.363119 | − | 0.931743i | \(-0.618288\pi\) | ||||
−0.363119 | + | 0.931743i | \(0.618288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8535 | 0.0696156 | 0.0348078 | − | 0.999394i | \(-0.488918\pi\) | ||||
0.0348078 | + | 0.999394i | \(0.488918\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −75.0057 | − | 253.692i | −0.373163 | − | 1.26215i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.3234 | 0.0951890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.2042 | − | 102.500i | 0.152216 | − | 0.500000i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64.5057i | 0.311622i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 105.516i | − | 0.504862i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.59113 | 0.0264983 | 0.0132491 | − | 0.999912i | \(-0.495783\pi\) | ||||
0.0132491 | + | 0.999912i | \(0.495783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 468.131 | 2.19780 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 145.060 | + | 44.1607i | 0.674695 | + | 0.205399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40.8120i | 0.188074i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 358.005i | − | 1.63473i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 46.4336i | − | 0.210107i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 101.379i | − | 0.454613i | −0.973823 | − | 0.227306i | \(-0.927008\pi\) | ||
0.973823 | − | 0.227306i | \(-0.0729919\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 136.813 | + | 91.8089i | 0.608056 | + | 0.408040i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 255.116i | 1.12386i | 0.827184 | + | 0.561930i | \(0.189941\pi\) | ||||
−0.827184 | + | 0.561930i | \(0.810059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.7615i | 0.116862i | 0.998291 | + | 0.0584311i | \(0.0186098\pi\) | ||||
−0.998291 | + | 0.0584311i | \(0.981390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.6274i | 0.0633219i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −413.650 | −1.77532 | −0.887662 | − | 0.460496i | \(-0.847672\pi\) | ||||
−0.887662 | + | 0.460496i | \(0.847672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.9703 | + | 121.440i | −0.157320 | + | 0.516768i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 544.814i | − | 2.29879i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 422.347i | 1.76714i | 0.468297 | + | 0.883571i | \(0.344868\pi\) | ||||
−0.468297 | + | 0.883571i | \(0.655132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 317.835 | 1.31882 | 0.659409 | − | 0.751785i | \(-0.270807\pi\) | ||||
0.659409 | + | 0.751785i | \(0.270807\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −296.903 | −1.22182 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 230.876 | + | 70.2859i | 0.942350 | + | 0.286881i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 112.529 | 0.455583 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 71.0457i | 0.285324i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 371.440i | − | 1.47984i | −0.672695 | − | 0.739920i | \(-0.734864\pi\) | ||
0.672695 | − | 0.739920i | \(-0.265136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.3644 | 0.167448 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −57.8377 | + | 189.986i | −0.226814 | + | 0.745042i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 188.712i | − | 0.734290i | −0.930164 | − | 0.367145i | \(-0.880335\pi\) | ||
0.930164 | − | 0.367145i | \(-0.119665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 53.4129i | 0.206227i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −148.794 | −0.570091 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 246.987i | − | 0.939113i | −0.882902 | − | 0.469557i | \(-0.844414\pi\) | ||
0.882902 | − | 0.469557i | \(-0.155586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −198.229 | − | 60.3472i | −0.748034 | − | 0.227725i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 424.421 | 1.58959 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −141.598 | −0.526386 | −0.263193 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263193 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 414.334i | − | 1.52891i | −0.644679 | − | 0.764453i | \(-0.723009\pi\) | ||
0.644679 | − | 0.764453i | \(-0.276991\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.5995 | −0.0571410 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60.2959 | − | 89.8523i | 0.219258 | − | 0.326736i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 53.9517i | 0.194771i | 0.995247 | + | 0.0973857i | \(0.0310480\pi\) | ||||
−0.995247 | + | 0.0973857i | \(0.968952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 314.261i | − | 1.12638i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 326.327i | 1.16130i | 0.814152 | + | 0.580652i | \(0.197202\pi\) | ||||
−0.814152 | + | 0.580652i | \(0.802798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 287.048i | − | 1.01430i | −0.861857 | − | 0.507151i | \(-0.830698\pi\) | ||
0.861857 | − | 0.507151i | \(-0.169302\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −460.418 | − | 140.166i | −1.61550 | − | 0.491810i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 18.3407i | − | 0.0639048i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 187.811 | 0.649864 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −480.172 | −1.65007 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 144.806i | − | 0.494220i | −0.968987 | − | 0.247110i | \(-0.920519\pi\) | ||
0.968987 | − | 0.247110i | \(-0.0794808\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 138.007 | + | 42.0136i | 0.467820 | + | 0.142419i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 41.1793i | 0.138651i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 45.1799i | 0.151103i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.9560 | 0.0862326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 526.539i | − | 1.73775i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −143.383 | + | 470.985i | −0.470107 | + | 1.54421i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 119.545i | − | 0.389399i | −0.980863 | − | 0.194699i | \(-0.937627\pi\) | ||
0.980863 | − | 0.194699i | \(-0.0623731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 575.907i | 1.86378i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 192.248i | 0.618160i | 0.951036 | + | 0.309080i | \(0.100021\pi\) | ||||
−0.951036 | + | 0.309080i | \(0.899979\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 358.885 | 1.14660 | 0.573299 | − | 0.819346i | \(-0.305663\pi\) | ||||
0.573299 | + | 0.819346i | \(0.305663\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.9809 | + | 8.21385i | 0.0856537 | + | 0.0260757i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 297.142i | 0.937356i | 0.883369 | + | 0.468678i | \(0.155270\pi\) | ||||
−0.883369 | + | 0.468678i | \(0.844730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 97.7210i | 0.306335i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 708.123i | 2.20599i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 245.226i | − | 0.759213i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 95.8240 | + | 64.3032i | 0.294843 | + | 0.197856i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 465.183i | − | 1.42258i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.7298i | 0.0660479i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 488.872i | − | 1.47696i | −0.674278 | − | 0.738478i | \(-0.735545\pi\) | ||
0.674278 | − | 0.738478i | \(-0.264455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 411.290i | − | 1.23511i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.69693 | + | 334.989i | −0.00805055 | + | 0.999968i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 265.223 | 0.787012 | 0.393506 | − | 0.919322i | \(-0.371262\pi\) | ||||
0.393506 | + | 0.919322i | \(0.371262\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −320.229 | −0.944628 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −206.392 | −0.605256 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 83.2498 | 0.242711 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 56.2761 | − | 184.856i | 0.163119 | − | 0.535815i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.22662 | −0.0121805 | −0.00609023 | − | 0.999981i | \(-0.501939\pi\) | ||||
−0.00609023 | + | 0.999981i | \(0.501939\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 86.7812 | 0.248657 | 0.124328 | − | 0.992241i | \(-0.460322\pi\) | ||||
0.124328 | + | 0.992241i | \(0.460322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −43.9162 | −0.125117 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 476.102 | 1.34873 | 0.674365 | − | 0.738398i | \(-0.264417\pi\) | ||||
0.674365 | + | 0.738398i | \(0.264417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −567.102 | − | 172.644i | −1.59747 | − | 0.486320i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.9948i | 0.0952236i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −392.646 | −1.09372 | −0.546860 | − | 0.837224i | \(-0.684177\pi\) | ||||
−0.546860 | + | 0.837224i | \(0.684177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 233.289 | 0.646229 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 403.793 | 1.11238 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −132.030 | + | 433.694i | −0.361726 | + | 1.18820i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −454.204 | −1.23761 | −0.618806 | − | 0.785544i | \(-0.712383\pi\) | ||||
−0.618806 | + | 0.785544i | \(0.712383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 141.227i | 0.382729i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.4698 | −0.0956060 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −596.464 | −1.59910 | −0.799549 | − | 0.600600i | \(-0.794928\pi\) | ||||
−0.799549 | + | 0.600600i | \(0.794928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −311.973 | − | 382.458i | −0.831928 | − | 1.01989i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −104.216 | −0.276434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 232.359i | 0.613085i | 0.951857 | + | 0.306542i | \(0.0991721\pi\) | ||||
−0.951857 | + | 0.306542i | \(0.900828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 123.516i | − | 0.324188i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 669.728 | 1.74864 | 0.874318 | − | 0.485354i | \(-0.161309\pi\) | ||||
0.874318 | + | 0.485354i | \(0.161309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.39448 | − | 17.7198i | 0.0140116 | − | 0.0460256i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −199.867 | −0.516451 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 192.318 | 0.494391 | 0.247195 | − | 0.968966i | \(-0.420491\pi\) | ||||
0.247195 | + | 0.968966i | \(0.420491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 98.4573 | 0.251809 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 717.533 | 1.82578 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −200.924 | + | 659.997i | −0.508668 | + | 1.67088i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 198.527i | 0.500067i | 0.968237 | + | 0.250034i | \(0.0804417\pi\) | ||||
−0.968237 | + | 0.250034i | \(0.919558\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −82.3842 | −0.206477 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 484.388i | 1.20795i | 0.797004 | + | 0.603975i | \(0.206417\pi\) | ||||
−0.797004 | + | 0.603975i | \(0.793583\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 220.109i | − | 0.546177i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 463.401 | + | 141.074i | 1.14420 | + | 0.348331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −270.116 | −0.663677 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 37.3002i | − | 0.0911984i | −0.998960 | − | 0.0455992i | \(-0.985480\pi\) | ||
0.998960 | − | 0.0455992i | \(-0.0145197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 767.766 | 1.86804 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.6940 | 0.0597919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.2012 | − | 86.0661i | 0.0631355 | − | 0.207388i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 766.086i | 1.83714i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 572.901 | 1.36730 | 0.683652 | − | 0.729808i | \(-0.260390\pi\) | ||||
0.683652 | + | 0.729808i | \(0.260390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −308.037 | −0.731679 | −0.365839 | − | 0.930678i | \(-0.619218\pi\) | ||||
−0.365839 | + | 0.930678i | \(0.619218\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 167.324i | − | 0.395564i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 140.131 | − | 208.822i | 0.329720 | − | 0.491346i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 84.2749i | 0.197365i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 78.8889i | − | 0.183890i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −127.773 | −0.296458 | −0.148229 | − | 0.988953i | \(-0.547357\pi\) | ||||
−0.148229 | + | 0.988953i | \(0.547357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −305.662 | −0.705918 | −0.352959 | − | 0.935639i | \(-0.614824\pi\) | ||||
−0.352959 | + | 0.935639i | \(0.614824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 426.404 | + | 129.811i | 0.980239 | + | 0.298416i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 238.605i | 0.546006i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −823.344 | −1.87550 | −0.937750 | − | 0.347311i | \(-0.887095\pi\) | ||||
−0.937750 | + | 0.347311i | \(0.887095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −318.106 | −0.721329 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −49.6007 | −0.111966 | −0.0559828 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559828 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −514.152 | − | 156.524i | −1.15540 | − | 0.351739i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 395.138 | 0.883978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −411.512 | −0.916507 | −0.458253 | − | 0.888822i | \(-0.651525\pi\) | ||||
−0.458253 | + | 0.888822i | \(0.651525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 92.7514 | 0.205657 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −127.639 | −0.281763 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.8975 | + | 5.75300i | 0.0415330 | + | 0.0126440i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 874.960i | 1.91457i | 0.289141 | + | 0.957287i | \(0.406630\pi\) | ||||
−0.289141 | + | 0.957287i | \(0.593370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 95.7032i | 0.208504i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 254.000 | 0.550976 | 0.275488 | − | 0.961305i | \(-0.411161\pi\) | ||||
0.275488 | + | 0.961305i | \(0.411161\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −286.494 | −0.618778 | −0.309389 | − | 0.950935i | \(-0.600125\pi\) | ||||
−0.309389 | + | 0.950935i | \(0.600125\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −274.168 | + | 900.589i | −0.589608 | + | 1.93675i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 50.3602i | 0.107838i | 0.998545 | + | 0.0539188i | \(0.0171712\pi\) | ||||
−0.998545 | + | 0.0539188i | \(0.982829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2585 | + | 54.9912i | 0.0346663 | + | 0.117252i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 992.500i | 2.10722i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 131.263i | 0.277512i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 506.066 | + | 339.599i | 1.06540 | + | 0.714945i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 273.125 | 0.572589 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 425.646 | 0.888614 | 0.444307 | − | 0.895875i | \(-0.353450\pi\) | ||||
0.444307 | + | 0.895875i | \(0.353450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 288.069i | − | 0.598895i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 33.0770i | − | 0.0684823i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 581.688 | + | 177.084i | 1.19936 | + | 0.365122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 538.993 | 1.10676 | 0.553381 | − | 0.832928i | \(-0.313337\pi\) | ||||
0.553381 | + | 0.832928i | \(0.313337\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 919.427i | 1.88022i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −245.190 | −0.499369 | −0.249684 | − | 0.968327i | \(-0.580327\pi\) | ||||
−0.249684 | + | 0.968327i | \(0.580327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 227.109i | 0.460668i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −41.5386 | + | 136.446i | −0.0839163 | + | 0.275649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −101.474 | −0.204172 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 75.1075i | 0.150516i | 0.997164 | + | 0.0752580i | \(0.0239780\pi\) | ||||
−0.997164 | + | 0.0752580i | \(0.976022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 909.207i | 1.81478i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 792.671 | 1.57589 | 0.787943 | − | 0.615748i | \(-0.211146\pi\) | ||||
0.787943 | + | 0.615748i | \(0.211146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −194.184 | + | 637.859i | −0.384524 | + | 1.26309i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −583.161 | −1.15022 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −340.537 | −0.669031 | −0.334516 | − | 0.942390i | \(-0.608573\pi\) | ||||
−0.334516 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 77.6024i | 0.151864i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −231.930 | −0.452106 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 212.391 | − | 697.663i | 0.412409 | − | 1.35469i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −109.890 | −0.212554 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.4807i | 0.0837778i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 286.334i | 0.549585i | 0.961503 | + | 0.274793i | \(0.0886092\pi\) | ||||
−0.961503 | + | 0.274793i | \(0.911391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 433.254i | − | 0.828402i | −0.910185 | − | 0.414201i | \(-0.864061\pi\) | ||
0.910185 | − | 0.414201i | \(-0.135939\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −70.1543 | − | 47.0774i | −0.133627 | − | 0.0896713i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −479.667 | −0.910185 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 433.201 | 0.818906 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −190.149 | −0.358096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 98.9157i | 0.185583i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 261.151 | − | 857.832i | 0.488133 | − | 1.60342i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 170.349i | 0.317224i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 208.918i | 0.387602i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 444.429i | 0.821495i | 0.911749 | + | 0.410747i | \(0.134732\pi\) | ||||
−0.911749 | + | 0.410747i | \(0.865268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −116.652 | −0.214830 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −171.557 | + | 563.531i | −0.314783 | + | 1.03400i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 597.311 | 1.09198 | 0.545988 | − | 0.837793i | \(-0.316154\pi\) | ||||
0.545988 | + | 0.837793i | \(0.316154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 648.934i | − | 1.18203i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −550.384 | −0.998883 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 118.096i | 0.213554i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −358.818 | + | 1178.65i | −0.646518 | + | 2.12369i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 70.7209i | 0.126968i | 0.997983 | + | 0.0634838i | \(0.0202211\pi\) | ||||
−0.997983 | + | 0.0634838i | \(0.979779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −139.987 | −0.250424 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −171.917 | −0.306447 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −587.393 | −1.04333 | −0.521663 | − | 0.853152i | \(-0.674688\pi\) | ||||
−0.521663 | + | 0.853152i | \(0.674688\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 387.931 | + | 118.098i | 0.686603 | + | 0.209024i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 82.9180 | 0.146240 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 676.561 | 1.18903 | 0.594517 | − | 0.804083i | \(-0.297343\pi\) | ||||
0.594517 | + | 0.804083i | \(0.297343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 954.240 | 1.67117 | 0.835587 | − | 0.549359i | \(-0.185128\pi\) | ||||
0.835587 | + | 0.549359i | \(0.185128\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 588.096i | − | 1.02635i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −136.348 | + | 203.184i | −0.237126 | + | 0.353363i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 74.9435 | 0.129885 | 0.0649423 | − | 0.997889i | \(-0.479314\pi\) | ||||
0.0649423 | + | 0.997889i | \(0.479314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 192.059i | 0.331708i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 15.4001i | − | 0.0265062i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 179.376i | − | 0.307677i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −145.515 | − | 44.2993i | −0.248743 | − | 0.0757252i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −477.974 | −0.814266 | −0.407133 | − | 0.913369i | \(-0.633472\pi\) | ||||
−0.407133 | + | 0.913369i | \(0.633472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1162.44i | − | 1.97359i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −564.904 | −0.955844 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −526.649 | −0.888109 | −0.444055 | − | 0.896000i | \(-0.646460\pi\) | ||||
−0.444055 | + | 0.896000i | \(0.646460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.5371 | − | 41.1819i | 0.0210707 | − | 0.0692133i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 54.7003 | 0.0916252 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 279.733i | 0.467000i | 0.972357 | + | 0.233500i | \(0.0750178\pi\) | ||||
−0.972357 | + | 0.233500i | \(0.924982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −417.113 | −0.694032 | −0.347016 | − | 0.937859i | \(-0.612805\pi\) | ||||
−0.347016 | + | 0.937859i | \(0.612805\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −125.194 | − | 423.443i | −0.207618 | − | 0.702228i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −489.162 | − | 148.917i | −0.808533 | − | 0.246143i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 481.778i | − | 0.793703i | −0.917883 | − | 0.396852i | \(-0.870103\pi\) | ||
0.917883 | − | 0.396852i | \(-0.129897\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 76.2979 | 0.125284 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 117.194i | − | 0.191807i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 120.957i | 0.197320i | 0.995121 | + | 0.0986600i | \(0.0314556\pi\) | ||||
−0.995121 | + | 0.0986600i | \(0.968544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 123.209 | − | 404.719i | 0.200340 | − | 0.658080i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 665.767i | − | 1.07904i | −0.841973 | − | 0.539520i | \(-0.818606\pi\) | ||
0.841973 | − | 0.539520i | \(-0.181394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 659.991 | 1.06622 | 0.533110 | − | 0.846046i | \(-0.321023\pi\) | ||||
0.533110 | + | 0.846046i | \(0.321023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 93.1192i | − | 0.149950i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −91.9990 | −0.147671 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 236.881 | + | 578.370i | 0.379010 | + | 0.925393i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 416.629i | − | 0.664479i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −627.766 | −0.998039 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 343.720i | − | 0.544723i | −0.962195 | − | 0.272361i | \(-0.912195\pi\) | ||
0.962195 | − | 0.272361i | \(-0.0878046\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.0765 | 0.0348759 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −45.5518 | + | 149.629i | −0.0717351 | + | 0.235636i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −222.802 | −0.349768 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 781.367 | 1.22280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1020.34i | 1.59179i | 0.605432 | + | 0.795897i | \(0.293001\pi\) | ||||
−0.605432 | + | 0.795897i | \(0.706999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 450.851i | 0.701168i | 0.936531 | + | 0.350584i | \(0.114017\pi\) | ||||
−0.936531 | + | 0.350584i | \(0.885983\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 572.765 | + | 174.368i | 0.888007 | + | 0.270337i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 782.802 | 1.20989 | 0.604947 | − | 0.796265i | \(-0.293194\pi\) | ||||
0.604947 | + | 0.796265i | \(0.293194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 124.881i | 0.192421i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 161.145i | 0.247535i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1083.86 | 1.65981 | 0.829906 | − | 0.557904i | \(-0.188394\pi\) | ||||
0.829906 | + | 0.557904i | \(0.188394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −869.232 | − | 264.622i | −1.32707 | − | 0.404003i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 597.554i | − | 0.909519i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −153.081 | −0.232293 | −0.116147 | − | 0.993232i | \(-0.537054\pi\) | ||||
−0.116147 | + | 0.993232i | \(0.537054\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1000.18i | 1.51313i | 0.653917 | + | 0.756566i | \(0.273125\pi\) | ||||
−0.653917 | + | 0.756566i | \(0.726875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 183.342i | − | 0.276534i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 99.8017 | + | 30.3828i | 0.150078 | + | 0.0456884i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 220.977i | − | 0.331300i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 400.291i | − | 0.598343i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −426.190 | −0.635157 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1121.64 | 1.66662 | 0.833310 | − | 0.552806i | \(-0.186443\pi\) | ||||
0.833310 | + | 0.552806i | \(0.186443\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −197.500 | − | 132.534i | −0.292593 | − | 0.196346i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 892.185 | 1.31785 | 0.658925 | − | 0.752209i | \(-0.271011\pi\) | ||||
0.658925 | + | 0.752209i | \(0.271011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 104.084 | 0.153289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1007.32i | 1.47918i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −843.556 | −1.23507 | −0.617537 | − | 0.786542i | \(-0.711870\pi\) | ||||
−0.617537 | + | 0.786542i | \(0.711870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −930.086 | − | 283.148i | −1.35779 | − | 0.413354i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 105.667i | 0.153809i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 191.297 | 0.277645 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −76.3031 | −0.110424 | −0.0552121 | − | 0.998475i | \(-0.517584\pi\) | ||||
−0.0552121 | + | 0.998475i | \(0.517584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.4148i | 0.0352306i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 282.528 | − | 928.050i | 0.406515 | − | 1.33532i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 215.560 | 0.309268 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1633.29 | −2.33661 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 124.798i | 0.178028i | 0.996030 | + | 0.0890142i | \(0.0283717\pi\) | ||||
−0.996030 | + | 0.0890142i | \(0.971628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1521.35i | − | 2.16408i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −145.976 | + | 479.505i | −0.207059 | + | 0.680149i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 114.134i | 0.161435i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0337 | −0.0169728 | −0.00848639 | − | 0.999964i | \(-0.502701\pi\) | ||||
−0.00848639 | + | 0.999964i | \(0.502701\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 909.360i | − | 1.27899i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 466.716 | 0.654581 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.0937 | + | 95.5674i | −0.0406905 | + | 0.133661i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1667.63i | 2.32584i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 494.946 | 0.688381 | 0.344191 | − | 0.938900i | \(-0.388153\pi\) | ||||
0.344191 | + | 0.938900i | \(0.388153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 124.835i | − | 0.173142i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1254.97 | 1.73577 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −468.680 | − | 314.510i | −0.646455 | − | 0.433807i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −543.442 | −0.747514 | −0.373757 | − | 0.927527i | \(-0.621931\pi\) | ||||
−0.373757 | + | 0.927527i | \(0.621931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −300.396 | −0.412066 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 305.063i | 0.417323i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −588.900 | −0.803411 | −0.401706 | − | 0.915769i | \(-0.631582\pi\) | ||||
−0.401706 | + | 0.915769i | \(0.631582\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 911.608 | + | 277.522i | 1.24028 | + | 0.377581i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −278.098 | + | 82.2214i | −0.377338 | + | 0.111562i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 799.430i | − | 1.08177i | −0.841096 | − | 0.540886i | \(-0.818089\pi\) | ||
0.841096 | − | 0.540886i | \(-0.181911\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 444.318 | 0.599619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 726.353i | − | 0.977595i | −0.872397 | − | 0.488797i | \(-0.837436\pi\) | ||
0.872397 | − | 0.488797i | \(-0.162564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −478.677 | − | 145.724i | −0.642520 | − | 0.195603i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 118.584i | 0.158747i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 153.495i | − | 0.204933i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 596.715 | 0.794561 | 0.397280 | − | 0.917697i | \(-0.369954\pi\) | ||||
0.397280 | + | 0.917697i | \(0.369954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1466.62i | − | 1.94770i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 154.624 | + | 47.0724i | 0.204800 | + | 0.0623475i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1419.77 | −1.87553 | −0.937763 | − | 0.347275i | \(-0.887107\pi\) | ||||
−0.937763 | + | 0.347275i | \(0.887107\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 167.275 | 0.220388 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1309.80 | −1.72116 | −0.860578 | − | 0.509319i | \(-0.829897\pi\) | ||||
−0.860578 | + | 0.509319i | \(0.829897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 100.835i | 0.132155i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −96.5380 | + | 317.109i | −0.126194 | + | 0.414522i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −133.181 | −0.173639 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 64.2236i | − | 0.0835157i | −0.999128 | − | 0.0417578i | \(-0.986704\pi\) | ||
0.999128 | − | 0.0417578i | \(-0.0132958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 745.127i | − | 0.966443i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1244.26i | − | 1.60965i | −0.593510 | − | 0.804826i | \(-0.702258\pi\) | ||
0.593510 | − | 0.804826i | \(-0.297742\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 664.263 | − | 989.878i | 0.857114 | − | 1.27726i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 210.900i | 0.271428i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 522.394i | 0.670596i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 513.166i | − | 0.657063i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 214.796 | 0.274324 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 366.028 | − | 1202.33i | 0.466278 | − | 1.53163i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 502.425 | 0.638405 | 0.319203 | − | 0.947686i | \(-0.396585\pi\) | ||||
0.319203 | + | 0.947686i | \(0.396585\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 975.222i | − | 1.23602i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 69.4138 | 0.0877545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 454.515i | − | 0.573159i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −782.703 | − | 238.280i | −0.984533 | − | 0.299723i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 161.557i | − | 0.202707i | −0.994850 | − | 0.101353i | \(-0.967683\pi\) | ||
0.994850 | − | 0.101353i | \(-0.0323173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −255.392 | −0.319639 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 708.411 | 0.884408 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −392.446 | −0.488725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.1986 | + | 40.0700i | −0.0151535 | + | 0.0497764i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −559.096 | −0.692808 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 415.623i | − | 0.513749i | −0.966445 | − | 0.256875i | \(-0.917307\pi\) | ||
0.966445 | − | 0.256875i | \(-0.0826927\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.3139i | 0.0460098i | 0.999735 | + | 0.0230049i | \(0.00732333\pi\) | ||||
−0.999735 | + | 0.0230049i | \(0.992677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1635.99i | − | 2.01228i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 339.079 | − | 1113.81i | 0.416048 | − | 1.36664i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −739.301 | −0.904897 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.0374 | −0.0317918 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −113.419 | −0.138147 | −0.0690736 | − | 0.997612i | \(-0.522004\pi\) | ||||
−0.0690736 | + | 0.997612i | \(0.522004\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 927.557i | − | 1.12704i | −0.826101 | − | 0.563522i | \(-0.809446\pi\) | ||
0.826101 | − | 0.563522i | \(-0.190554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 238.077 | − | 354.780i | 0.288578 | − | 0.430036i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 555.504i | − | 0.671709i | −0.941914 | − | 0.335855i | \(-0.890975\pi\) | ||
0.941914 | − | 0.335855i | \(-0.109025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1271.89 | 1.53425 | 0.767125 | − | 0.641498i | \(-0.221687\pi\) | ||||
0.767125 | + | 0.641498i | \(0.221687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 213.027i | 0.256350i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 485.536i | 0.582877i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 335.310 | − | 1101.43i | 0.401569 | − | 1.31908i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 453.661i | 0.542009i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −296.616 | −0.353536 | −0.176768 | − | 0.984253i | \(-0.556564\pi\) | ||||
−0.176768 | + | 0.984253i | \(0.556564\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −331.276 | −0.393908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1288.49i | 1.52846i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 706.452 | + | 215.066i | 0.836038 | + | 0.254516i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −87.5276 | −0.103338 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1133.40i | − | 1.33498i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 610.817 | 0.717763 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 522.324i | − | 0.612337i | −0.951977 | − | 0.306169i | \(-0.900953\pi\) | ||
0.951977 | − | 0.306169i | \(-0.0990471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −768.493 | − | 233.954i | −0.898822 | − | 0.273630i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.49590 | −0.00174550 | −0.000872752 | − | 1.00000i | \(-0.500278\pi\) | ||||
−0.000872752 | 1.00000i | \(0.500278\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 99.3975 | 0.115713 | 0.0578565 | − | 0.998325i | \(-0.481573\pi\) | ||||
0.0578565 | + | 0.998325i | \(0.481573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 72.4178i | − | 0.0841089i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 745.165i | 0.863458i | 0.902003 | + | 0.431729i | \(0.142096\pi\) | ||||
−0.902003 | + | 0.431729i | \(0.857904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0354 | − | 52.6733i | 0.0185380 | − | 0.0608940i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 741.566 | 0.855325 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −597.226 | −0.687257 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −87.6859 | − | 296.581i | −0.100673 | − | 0.340506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −801.464 | −0.918058 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 67.6243 | + | 82.9029i | 0.0772849 | + | 0.0947461i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 711.369i | 0.811139i | 0.914064 | + | 0.405569i | \(0.132927\pi\) | ||||
−0.914064 | + | 0.405569i | \(0.867073\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 571.765i | − | 0.650472i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 846.618 | 0.960974 | 0.480487 | − | 0.877002i | \(-0.340460\pi\) | ||||
0.480487 | + | 0.877002i | \(0.340460\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −175.673 | −0.198950 | −0.0994751 | − | 0.995040i | \(-0.531716\pi\) | ||||
−0.0994751 | + | 0.995040i | \(0.531716\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 544.917 | + | 165.890i | 0.615725 | + | 0.187446i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 947.905i | − | 1.06866i | −0.845275 | − | 0.534332i | \(-0.820563\pi\) | ||
0.845275 | − | 0.534332i | \(-0.179437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.7736i | 0.0301166i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 419.328i | 0.470626i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 618.925i | − | 0.693085i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.8238 | − | 206.364i | 0.0701942 | − | 0.230575i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 178.392i | 0.198876i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1076.56i | 1.19751i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 416.880i | − | 0.462686i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 102.487 | 0.113496 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 141.315 | + | 43.0207i | 0.156149 | + | 0.0475367i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1490.99i | 1.64387i | 0.569584 | + | 0.821933i | \(0.307105\pi\) | ||||
−0.569584 | + | 0.821933i | \(0.692895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 878.858i | − | 0.966840i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −944.741 | −1.03704 | −0.518519 | − | 0.855066i | \(-0.673516\pi\) | ||||
−0.518519 | + | 0.855066i | \(0.673516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77.8805 | 0.0853017 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −566.143 | + | 1859.67i | −0.618736 | + | 2.03243i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −155.535 | −0.169613 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 635.953i | − | 0.692006i | −0.938233 | − | 0.346003i | \(-0.887539\pi\) | ||
0.938233 | − | 0.346003i | \(-0.112461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 472.022i | − | 0.512511i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 547.271 | 0.592927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 869.356 | − | 1295.51i | 0.939845 | − | 1.40055i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 961.258i | 1.03696i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 197.204i | 0.212276i | 0.994351 | + | 0.106138i | \(0.0338485\pi\) | ||||
−0.994351 | + | 0.106138i | \(0.966152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1176.67 | −1.26387 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 759.087i | 0.813598i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 208.263 | + | 63.4018i | 0.222741 | + | 0.0678094i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 135.186 | 0.144275 | 0.0721376 | − | 0.997395i | \(-0.477018\pi\) | ||||
0.0721376 | + | 0.997395i | \(0.477018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1417.05 | 1.50911 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 682.975i | 0.725796i | 0.931829 | + | 0.362898i | \(0.118213\pi\) | ||||
−0.931829 | + | 0.362898i | \(0.881787\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −209.739 | −0.222417 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38.9492 | − | 11.8574i | −0.0412160 | − | 0.0125475i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 852.671i | − | 0.900392i | −0.892930 | − | 0.450196i | \(-0.851354\pi\) | ||
0.892930 | − | 0.450196i | \(-0.148646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 418.528i | − | 0.441020i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1173.26i | 1.23371i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 613.623i | − | 0.643885i | −0.946759 | − | 0.321943i | \(-0.895664\pi\) | ||
0.946759 | − | 0.321943i | \(-0.104336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −216.886 | + | 712.430i | −0.227106 | + | 0.746000i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 385.849i | 0.403186i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −166.424 | −0.173539 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1312.77 | −1.36604 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1181.94i | 1.22735i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70.8301 | − | 232.663i | 0.0733991 | − | 0.241102i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 381.193i | 0.394201i | 0.980383 | + | 0.197101i | \(0.0631526\pi\) | ||||
−0.980383 | + | 0.197101i | \(0.936847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 968.269i | − | 0.999245i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.35190 | −0.00757147 | −0.00378574 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378574 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 166.059i | − | 0.170667i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 378.359 | + | 253.900i | 0.388060 | + | 0.260410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 216.621i | 0.221721i | 0.993836 | + | 0.110861i | \(0.0353607\pi\) | ||||
−0.993836 | + | 0.110861i | \(0.964639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 465.252i | − | 0.475232i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 776.446i | − | 0.791484i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1734.51 | −1.76451 | −0.882256 | − | 0.470770i | \(-0.843976\pi\) | ||||
−0.882256 | + | 0.470770i | \(0.843976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 684.335 | + | 208.333i | 0.694756 | + | 0.211506i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 85.7995i | 0.0869296i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 296.827i | − | 0.300128i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1044.62i | − | 1.05411i | −0.849831 | − | 0.527055i | \(-0.823296\pi\) | ||
0.849831 | − | 0.527055i | \(-0.176704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1930.30i | − | 1.94391i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −66.2649 | − | 20.1731i | −0.0665979 | − | 0.0202745i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1105.59i | 1.10892i | 0.832211 | + | 0.554460i | \(0.187075\pi\) | ||||
−0.832211 | + | 0.554460i | \(0.812925\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 593.731i | 0.594325i |
(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 | 1340.3.g.a.669.54 | yes | 68 | |
5.4 | even | 2 | inner | 1340.3.g.a.669.16 | yes | 68 | |
67.66 | odd | 2 | inner | 1340.3.g.a.669.15 | ✓ | 68 | |
335.334 | odd | 2 | inner | 1340.3.g.a.669.53 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1340.3.g.a.669.15 | ✓ | 68 | 67.66 | odd | 2 | inner | |
1340.3.g.a.669.16 | yes | 68 | 5.4 | even | 2 | inner | |
1340.3.g.a.669.53 | yes | 68 | 335.334 | odd | 2 | inner | |
1340.3.g.a.669.54 | yes | 68 | 1.1 | even | 1 | trivial |