Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,6,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.a (trivial) |
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: | yes |
Analytic conductor: | \(173.214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.15881.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 29x - 55 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.33626\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 85.5605 | 0.659976 | 0.329988 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329988 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 99.8209 | 0.248737 | 0.124368 | − | 0.992236i | \(-0.460310\pi\) | ||||
0.124368 | + | 0.992236i | \(0.460310\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −546.179 | −0.896348 | −0.448174 | − | 0.893946i | \(-0.647926\pi\) | ||||
−0.448174 | + | 0.893946i | \(0.647926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 424.929 | 0.356610 | 0.178305 | − | 0.983975i | \(-0.442939\pi\) | ||||
0.178305 | + | 0.983975i | \(0.442939\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2122.20 | 1.34866 | 0.674331 | − | 0.738429i | \(-0.264432\pi\) | ||||
0.674331 | + | 0.738429i | \(0.264432\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3450.04 | 1.35989 | 0.679946 | − | 0.733262i | \(-0.262003\pi\) | ||||
0.679946 | + | 0.733262i | \(0.262003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6876.76 | −1.51841 | −0.759205 | − | 0.650852i | \(-0.774412\pi\) | ||||
−0.759205 | + | 0.650852i | \(0.774412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2989.87 | 0.558790 | 0.279395 | − | 0.960176i | \(-0.409866\pi\) | ||||
0.279395 | + | 0.960176i | \(0.409866\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2139.01 | −0.295150 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14200.2 | −1.70526 | −0.852629 | − | 0.522517i | \(-0.824993\pi\) | ||||
−0.852629 | + | 0.522517i | \(0.824993\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −423.869 | −0.0393797 | −0.0196898 | − | 0.999806i | \(-0.506268\pi\) | ||||
−0.0196898 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3569.67 | −0.294413 | −0.147207 | − | 0.989106i | \(-0.547028\pi\) | ||||
−0.147207 | + | 0.989106i | \(0.547028\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 928.769 | 0.0613286 | 0.0306643 | − | 0.999530i | \(-0.490238\pi\) | ||||
0.0306643 | + | 0.999530i | \(0.490238\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9486.39 | −0.564431 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33234.4 | 1.62517 | 0.812584 | − | 0.582844i | \(-0.198060\pi\) | ||||
0.812584 | + | 0.582844i | \(0.198060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2495.52 | −0.111238 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17830.1 | 0.666845 | 0.333423 | − | 0.942778i | \(-0.391796\pi\) | ||||
0.333423 | + | 0.942778i | \(0.391796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30245.0 | 1.04071 | 0.520354 | − | 0.853951i | \(-0.325800\pi\) | ||||
0.520354 | + | 0.853951i | \(0.325800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13654.5 | 0.400859 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20790.3 | 0.565815 | 0.282908 | − | 0.959147i | \(-0.408701\pi\) | ||||
0.282908 | + | 0.959147i | \(0.408701\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −19209.9 | −0.452250 | −0.226125 | − | 0.974098i | \(-0.572606\pi\) | ||||
−0.226125 | + | 0.974098i | \(0.572606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −83174.8 | −1.82677 | −0.913386 | − | 0.407094i | \(-0.866542\pi\) | ||||
−0.913386 | + | 0.407094i | \(0.866542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8540.73 | 0.164160 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42514.1 | 0.766418 | 0.383209 | − | 0.923662i | \(-0.374819\pi\) | ||||
0.383209 | + | 0.923662i | \(0.374819\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 93576.0 | 1.49097 | 0.745486 | − | 0.666522i | \(-0.232218\pi\) | ||||
0.745486 | + | 0.666522i | \(0.232218\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10623.2 | −0.159481 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −72645.6 | −0.972152 | −0.486076 | − | 0.873917i | \(-0.661572\pi\) | ||||
−0.486076 | + | 0.873917i | \(0.661572\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −46731.4 | −0.591569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −53055.1 | −0.603140 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16741.0 | 0.180655 | 0.0903277 | − | 0.995912i | \(-0.471209\pi\) | ||||
0.0903277 | + | 0.995912i | \(0.471209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5922.83 | 0.0577731 | 0.0288866 | − | 0.999583i | \(-0.490804\pi\) | ||||
0.0288866 | + | 0.999583i | \(0.490804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −142022. | −1.31906 | −0.659528 | − | 0.751680i | \(-0.729244\pi\) | ||||
−0.659528 | + | 0.751680i | \(0.729244\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3404.42 | 0.0287464 | 0.0143732 | − | 0.999897i | \(-0.495425\pi\) | ||||
0.0143732 | + | 0.999897i | \(0.495425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 132231. | 1.06602 | 0.533012 | − | 0.846107i | \(-0.321060\pi\) | ||||
0.533012 | + | 0.846107i | \(0.321060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −212816. | −1.56786 | −0.783932 | − | 0.620847i | \(-0.786789\pi\) | ||||
−0.783932 | + | 0.620847i | \(0.786789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −86250.9 | −0.608162 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 36357.1 | 0.235354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −151087. | −0.938130 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 304653. | 1.67608 | 0.838042 | − | 0.545606i | \(-0.183700\pi\) | ||||
0.838042 | + | 0.545606i | \(0.183700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 103961. | 0.529290 | 0.264645 | − | 0.964346i | \(-0.414745\pi\) | ||||
0.264645 | + | 0.964346i | \(0.414745\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 181577. | 0.890085 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4202.17 | −0.0191281 | −0.00956405 | − | 0.999954i | \(-0.503044\pi\) | ||||
−0.00956405 | + | 0.999954i | \(0.503044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 154249. | 0.677151 | 0.338575 | − | 0.940939i | \(-0.390055\pi\) | ||||
0.338575 | + | 0.940939i | \(0.390055\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −54520.1 | −0.222955 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 171919. | 0.679054 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 288038. | 1.06288 | 0.531439 | − | 0.847096i | \(-0.321651\pi\) | ||||
0.531439 | + | 0.847096i | \(0.321651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 51586.3 | 0.184116 | 0.0920581 | − | 0.995754i | \(-0.470655\pi\) | ||||
0.0920581 | + | 0.995754i | \(0.470655\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −74746.9 | −0.249899 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −247275. | −0.800627 | −0.400314 | − | 0.916378i | \(-0.631099\pi\) | ||||
−0.400314 | + | 0.916378i | \(0.631099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 295187. | 0.897496 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −278761. | −0.821794 | −0.410897 | − | 0.911682i | \(-0.634784\pi\) | ||||
−0.410897 | + | 0.911682i | \(0.634784\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 489181. | 1.35731 | 0.678654 | − | 0.734459i | \(-0.262564\pi\) | ||||
0.678654 | + | 0.734459i | \(0.262564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −72981.4 | −0.196560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 577120. | 1.46606 | 0.733029 | − | 0.680198i | \(-0.238106\pi\) | ||||
0.733029 | + | 0.680198i | \(0.238106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53475.3 | 0.131995 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 617817. | 1.44121 | 0.720605 | − | 0.693346i | \(-0.243864\pi\) | ||||
0.720605 | + | 0.693346i | \(0.243864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −265079. | −0.601421 | −0.300711 | − | 0.953715i | \(-0.597224\pi\) | ||||
−0.300711 | + | 0.953715i | \(0.597224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 355005. | 0.762615 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42416.8 | 0.0887021 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 30593.3 | 0.0606797 | 0.0303398 | − | 0.999540i | \(-0.490341\pi\) | ||||
0.0303398 | + | 0.999540i | \(0.490341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 463235. | 0.895176 | 0.447588 | − | 0.894240i | \(-0.352283\pi\) | ||||
0.447588 | + | 0.894240i | \(0.352283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −518076. | −0.951104 | −0.475552 | − | 0.879688i | \(-0.657752\pi\) | ||||
−0.475552 | + | 0.879688i | \(0.657752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −53461.6 | −0.0956993 | −0.0478497 | − | 0.998855i | \(-0.515237\pi\) | ||||
−0.0478497 | + | 0.998855i | \(0.515237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −588380. | −1.00211 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10596.7 | 0.0176111 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 211840. | 0.335462 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −318155. | −0.491963 | −0.245982 | − | 0.969275i | \(-0.579110\pi\) | ||||
−0.245982 | + | 0.969275i | \(0.579110\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 89241.8 | 0.131666 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 255815. | 0.368788 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −232087. | −0.319647 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 282126. | 0.379911 | 0.189955 | − | 0.981793i | \(-0.439166\pi\) | ||||
0.189955 | + | 0.981793i | \(0.439166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 599160. | 0.771753 | 0.385877 | − | 0.922550i | \(-0.373899\pi\) | ||||
0.385877 | + | 0.922550i | \(0.373899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.29257e6 | 1.62879 | 0.814394 | − | 0.580313i | \(-0.197070\pi\) | ||||
0.814394 | + | 0.580313i | \(0.197070\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 611411. | 0.737808 | 0.368904 | − | 0.929467i | \(-0.379733\pi\) | ||||
0.368904 | + | 0.929467i | \(0.379733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23219.2 | −0.0274270 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 960138. | 1.08727 | 0.543637 | − | 0.839320i | \(-0.317047\pi\) | ||||
0.543637 | + | 0.839320i | \(0.317047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −345926. | −0.383655 | −0.191828 | − | 0.981429i | \(-0.561441\pi\) | ||||
−0.191828 | + | 0.981429i | \(0.561441\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 237160. | 0.252421 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.15910e6 | −1.20887 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 711996. | 0.713335 | 0.356667 | − | 0.934231i | \(-0.383913\pi\) | ||||
0.356667 | + | 0.934231i | \(0.383913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 344386. | 0.338255 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 305560. | 0.288578 | 0.144289 | − | 0.989536i | \(-0.453910\pi\) | ||||
0.144289 | + | 0.989536i | \(0.453910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.21498e6 | −1.12543 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.69549e6 | 1.51149 | 0.755744 | − | 0.654867i | \(-0.227275\pi\) | ||||
0.755744 | + | 0.654867i | \(0.227275\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −830860. | −0.726797 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −577207. | −0.486352 | −0.243176 | − | 0.969982i | \(-0.578189\pi\) | ||||
−0.243176 | + | 0.969982i | \(0.578189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.65995e6 | −1.37300 | −0.686501 | − | 0.727129i | \(-0.740854\pi\) | ||||
−0.686501 | + | 0.727129i | \(0.740854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 62388.1 | 0.0497473 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.25880e6 | 0.985732 | 0.492866 | − | 0.870105i | \(-0.335949\pi\) | ||||
0.492866 | + | 0.870105i | \(0.335949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.69319e6 | 1.27921 | 0.639604 | − | 0.768705i | \(-0.279099\pi\) | ||||
0.639604 | + | 0.768705i | \(0.279099\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.97014e6 | 1.46228 | 0.731142 | − | 0.682225i | \(-0.238988\pi\) | ||||
0.731142 | + | 0.682225i | \(0.238988\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36266.5 | −0.0259897 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.23929e6 | −0.872829 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.69945e6 | 1.83699 | 0.918494 | − | 0.395435i | \(-0.129406\pi\) | ||||
0.918494 | + | 0.395435i | \(0.129406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −445754. | −0.298222 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.88434e6 | −1.21894 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −305423. | −0.194306 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −756125. | −0.465419 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.46875e6 | 0.889410 | 0.444705 | − | 0.895677i | \(-0.353308\pi\) | ||||
0.444705 | + | 0.895677i | \(0.353308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 681620. | 0.399614 | 0.199807 | − | 0.979835i | \(-0.435968\pi\) | ||||
0.199807 | + | 0.979835i | \(0.435968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −642495. | −0.370688 | −0.185344 | − | 0.982674i | \(-0.559340\pi\) | ||||
−0.185344 | + | 0.982674i | \(0.559340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.63094e6 | 1.47049 | 0.735245 | − | 0.677801i | \(-0.237067\pi\) | ||||
0.735245 | + | 0.677801i | \(0.237067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −686445. | −0.377684 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 901786. | 0.480947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −341362. | −0.179270 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 79465.9 | 0.0404754 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 739507. | 0.370999 | 0.185499 | − | 0.982644i | \(-0.440610\pi\) | ||||
0.185499 | + | 0.982644i | \(0.440610\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −519759. | −0.253040 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.86873e6 | 1.37599 | 0.687996 | − | 0.725715i | \(-0.258491\pi\) | ||||
0.687996 | + | 0.725715i | \(0.258491\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 298452. | 0.138992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.24968e6 | −1.03249 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 358901. | 0.160011 | 0.0800057 | − | 0.996794i | \(-0.474506\pi\) | ||||
0.0800057 | + | 0.996794i | \(0.474506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.96201e6 | 1.30174 | 0.650869 | − | 0.759190i | \(-0.274405\pi\) | ||||
0.650869 | + | 0.759190i | \(0.274405\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.02769e6 | −0.866095 | −0.433048 | − | 0.901371i | \(-0.642562\pi\) | ||||
−0.433048 | + | 0.901371i | \(0.642562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 480246. | 0.202252 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.52540e6 | 1.85319 | 0.926596 | − | 0.376058i | \(-0.122721\pi\) | ||||
0.926596 | + | 0.376058i | \(0.122721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.02765e6 | 0.818890 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.07937e6 | 0.816958 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58235e6 | −1.38836 | −0.694182 | − | 0.719800i | \(-0.744234\pi\) | ||||
−0.694182 | + | 0.719800i | \(0.744234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.84355e6 | 1.07257 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.87995e6 | −0.699638 | −0.349819 | − | 0.936817i | \(-0.613757\pi\) | ||||
−0.349819 | + | 0.936817i | \(0.613757\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.75594e6 | 1.36102 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.50759e6 | −0.539121 | −0.269560 | − | 0.962983i | \(-0.586878\pi\) | ||||
−0.269560 | + | 0.962983i | \(0.586878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.72039e6 | −1.29596 | −0.647980 | − | 0.761658i | \(-0.724386\pi\) | ||||
−0.647980 | + | 0.761658i | \(0.724386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −213518. | −0.0734148 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.42840e6 | 0.478603 | 0.239302 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239302 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.46602e6 | 0.484951 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.06285e6 | −0.342752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.52884e6 | −0.805276 | −0.402638 | − | 0.915359i | \(-0.631907\pi\) | ||||
−0.402638 | + | 0.915359i | \(0.631907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −730346. | −0.226813 | −0.113406 | − | 0.993549i | \(-0.536176\pi\) | ||||
−0.113406 | + | 0.993549i | \(0.536176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.63301e6 | −0.500871 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.41748e6 | −0.424160 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.51732e6 | −0.448506 | −0.224253 | − | 0.974531i | \(-0.571994\pi\) | ||||
−0.224253 | + | 0.974531i | \(0.571994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.52556e6 | 0.440102 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.33940e6 | −0.666783 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.36661e6 | 0.380286 | 0.190143 | − | 0.981756i | \(-0.439105\pi\) | ||||
0.190143 | + | 0.981756i | \(0.439105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.20736e6 | 0.881946 | 0.440973 | − | 0.897520i | \(-0.354633\pi\) | ||||
0.440973 | + | 0.897520i | \(0.354633\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 265581. | 0.0713221 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.58778e6 | 0.686843 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.51920e6 | 1.17184 | 0.585920 | − | 0.810369i | \(-0.300733\pi\) | ||||
0.585920 | + | 0.810369i | \(0.300733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.08506e6 | 1.30340 | 0.651698 | − | 0.758478i | \(-0.274057\pi\) | ||||
0.651698 | + | 0.758478i | \(0.274057\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.32169e6 | 1.83403 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.67597e6 | 0.415054 | 0.207527 | − | 0.978229i | \(-0.433459\pi\) | ||||
0.207527 | + | 0.978229i | \(0.433459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.33137e6 | 1.77491 | 0.887454 | − | 0.460897i | \(-0.152472\pi\) | ||||
0.887454 | + | 0.460897i | \(0.152472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.81614e6 | 0.434759 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.68385e6 | 0.862354 | 0.431177 | − | 0.902267i | \(-0.358098\pi\) | ||||
0.431177 | + | 0.902267i | \(0.358098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42311.0 | −0.00979518 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.16828e6 | 0.264557 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −810253. | −0.181480 | −0.0907402 | − | 0.995875i | \(-0.528923\pi\) | ||||
−0.0907402 | + | 0.995875i | \(0.528923\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.76965e6 | −1.04528 | −0.522642 | − | 0.852552i | \(-0.675053\pi\) | ||||
−0.522642 | + | 0.852552i | \(0.675053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.70653e6 | 0.803554 | 0.401777 | − | 0.915738i | \(-0.368393\pi\) | ||||
0.401777 | + | 0.915738i | \(0.368393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.33319e6 | −0.707241 | −0.353621 | − | 0.935389i | \(-0.615050\pi\) | ||||
−0.353621 | + | 0.935389i | \(0.615050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.77883e6 | 0.373425 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −356328. | −0.0732314 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.32638e6 | 0.269732 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.99488e6 | 0.596404 | 0.298202 | − | 0.954503i | \(-0.403613\pi\) | ||||
0.298202 | + | 0.954503i | \(0.403613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.75585e6 | 1.52850 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −418524. | −0.0807916 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.71593e6 | −1.47423 | −0.737116 | − | 0.675766i | \(-0.763813\pi\) | ||||
−0.737116 | + | 0.675766i | \(0.763813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.65091e6 | 0.496239 | 0.248120 | − | 0.968729i | \(-0.420187\pi\) | ||||
0.248120 | + | 0.968729i | \(0.420187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.92214e6 | −0.541481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.64361e6 | −0.298474 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.29296e6 | 0.592019 | 0.296010 | − | 0.955185i | \(-0.404344\pi\) | ||||
0.296010 | + | 0.955185i | \(0.404344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.22340e6 | −0.215600 | −0.107800 | − | 0.994173i | \(-0.534381\pi\) | ||||
−0.107800 | + | 0.994173i | \(0.534381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −148071. | −0.0258369 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.10782e6 | −0.873858 | −0.436929 | − | 0.899496i | \(-0.643934\pi\) | ||||
−0.436929 | + | 0.899496i | \(0.643934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.11648e6 | −1.20563 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.55055e6 | 0.589899 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 92710.6 | 0.0152547 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −115812. | −0.0186922 | −0.00934611 | − | 0.999956i | \(-0.502975\pi\) | ||||
−0.00934611 | + | 0.999956i | \(0.502975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.72323e6 | −1.07479 | −0.537395 | − | 0.843330i | \(-0.680592\pi\) | ||||
−0.537395 | + | 0.843330i | \(0.680592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.27048e6 | 0.199270 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.46642e6 | 0.849305 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 231509. | 0.0352979 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −85110.6 | −0.0128558 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −946941. | −0.140395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.33904e6 | −1.37186 | −0.685929 | − | 0.727669i | \(-0.740604\pi\) | ||||
−0.685929 | + | 0.727669i | \(0.740604\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.30578e6 | −0.476741 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.29689e6 | −0.185325 | −0.0926626 | − | 0.995698i | \(-0.529538\pi\) | ||||
−0.0926626 | + | 0.995698i | \(0.529538\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.45939e7 | −2.04782 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.63753e6 | 0.505818 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.88461e6 | −0.393958 | −0.196979 | − | 0.980408i | \(-0.563113\pi\) | ||||
−0.196979 | + | 0.980408i | \(0.563113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.94968e6 | 0.263897 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.96177e6 | 1.05862 | 0.529308 | − | 0.848430i | \(-0.322452\pi\) | ||||
0.529308 | + | 0.848430i | \(0.322452\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.32040e6 | 0.701170 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.36853e6 | 0.436174 | 0.218087 | − | 0.975929i | \(-0.430018\pi\) | ||||
0.218087 | + | 0.975929i | \(0.430018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.43608e7 | −1.84327 | −0.921633 | − | 0.388063i | \(-0.873144\pi\) | ||||
−0.921633 | + | 0.388063i | \(0.873144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.15627e6 | 0.271978 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.67748e6 | −0.709930 | −0.354965 | − | 0.934880i | \(-0.615507\pi\) | ||||
−0.354965 | + | 0.934880i | \(0.615507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00641e6 | 0.984006 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.31749e6 | 0.404239 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.30937e6 | −0.516201 | −0.258101 | − | 0.966118i | \(-0.583097\pi\) | ||||
−0.258101 | + | 0.966118i | \(0.583097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.34513e6 | 0.753619 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.30041e6 | −0.618975 | −0.309487 | − | 0.950904i | \(-0.600157\pi\) | ||||
−0.309487 | + | 0.950904i | \(0.600157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −908929. | −0.105254 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −479201. | −0.0545696 | −0.0272848 | − | 0.999628i | \(-0.508686\pi\) | ||||
−0.0272848 | + | 0.999628i | \(0.508686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.07294e6 | 0.685825 | 0.342912 | − | 0.939367i | \(-0.388587\pi\) | ||||
0.342912 | + | 0.939367i | \(0.388587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.77717e6 | 0.419545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.45020e6 | −0.820722 | −0.410361 | − | 0.911923i | \(-0.634597\pi\) | ||||
−0.410361 | + | 0.911923i | \(0.634597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −507274. | −0.0549718 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.15156e7 | 1.23776 | 0.618878 | − | 0.785487i | \(-0.287587\pi\) | ||||
0.618878 | + | 0.785487i | \(0.287587\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.00826e7 | −1.06625 | −0.533126 | − | 0.846036i | \(-0.678983\pi\) | ||||
−0.533126 | + | 0.846036i | \(0.678983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.39730e7 | −1.46576 | −0.732882 | − | 0.680355i | \(-0.761825\pi\) | ||||
−0.732882 | + | 0.680355i | \(0.761825\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.21559e6 | −0.641597 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.03407e6 | −0.608113 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.09736e6 | 0.609633 | 0.304817 | − | 0.952411i | \(-0.401405\pi\) | ||||
0.304817 | + | 0.952411i | \(0.401405\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.61632e6 | −0.749568 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.18127e6 | 0.505927 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −548849. | −0.0527604 | −0.0263802 | − | 0.999652i | \(-0.508398\pi\) | ||||
−0.0263802 | + | 0.999652i | \(0.508398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.29095e7 | −1.23135 | −0.615677 | − | 0.787999i | \(-0.711117\pi\) | ||||
−0.615677 | + | 0.787999i | \(0.711117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.71727e6 | 0.161279 | 0.0806397 | − | 0.996743i | \(-0.474304\pi\) | ||||
0.0806397 | + | 0.996743i | \(0.474304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.77982e6 | 0.165869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.15426e7 | −1.05931 | −0.529653 | − | 0.848214i | \(-0.677678\pi\) | ||||
−0.529653 | + | 0.848214i | \(0.677678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.59904e6 | −0.236706 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.09831e7 | −0.985169 | −0.492585 | − | 0.870265i | \(-0.663948\pi\) | ||||
−0.492585 | + | 0.870265i | \(0.663948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.79023e7 | 1.59370 | 0.796849 | − | 0.604178i | \(-0.206499\pi\) | ||||
0.796849 | + | 0.604178i | \(0.206499\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.53942e6 | −0.398058 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.37251e7 | −2.06487 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.01908e6 | 0.258862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.51352e7 | 1.28810 | 0.644050 | − | 0.764983i | \(-0.277253\pi\) | ||||
0.644050 | + | 0.764983i | \(0.277253\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.74374e6 | −0.146221 | −0.0731105 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731105 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.43237e6 | 0.119228 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.91354e6 | −0.321010 | −0.160505 | − | 0.987035i | \(-0.551312\pi\) | ||||
−0.160505 | + | 0.987035i | \(0.551312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 105054. | 0.00855434 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.81519e7 | −1.45672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.09646e7 | 1.67029 | 0.835143 | − | 0.550032i | \(-0.185385\pi\) | ||||
0.835143 | + | 0.550032i | \(0.185385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.85622e6 | −0.302831 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −180114. | −0.0140432 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.37397e7 | 1.05604 | 0.528022 | − | 0.849231i | \(-0.322934\pi\) | ||||
0.528022 | + | 0.849231i | \(0.322934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.01357e7 | −2.29982 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 506761. | 0.0381289 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.09118e6 | 0.604500 | 0.302250 | − | 0.953229i | \(-0.402262\pi\) | ||||
0.302250 | + | 0.953229i | \(0.402262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.03152e7 | 0.759894 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.36300e6 | 0.0997084 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.50696e6 | 0.613694 | 0.306847 | − | 0.951759i | \(-0.400726\pi\) | ||||
0.306847 | + | 0.951759i | \(0.400726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.21515e7 | −0.870545 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.29798e6 | −0.303682 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.35919e7 | −0.953771 | −0.476885 | − | 0.878966i | \(-0.658234\pi\) | ||||
−0.476885 | + | 0.878966i | \(0.658234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.51686e6 | −0.104991 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.21454e7 | 0.834932 | 0.417466 | − | 0.908692i | \(-0.362918\pi\) | ||||
0.417466 | + | 0.908692i | \(0.362918\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.07531e6 | 0.140739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.50729e6 | −0.303602 | −0.151801 | − | 0.988411i | \(-0.548507\pi\) | ||||
−0.151801 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.82273e6 | 0.519860 | 0.259930 | − | 0.965628i | \(-0.416301\pi\) | ||||
0.259930 | + | 0.965628i | \(0.416301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.20094e6 | −0.475334 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 291284. | 0.0189720 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.62764e7 | 1.05307 | 0.526537 | − | 0.850152i | \(-0.323490\pi\) | ||||
0.526537 | + | 0.850152i | \(0.323490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.28966e6 | −0.0823393 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.05461e6 | 0.320588 | 0.160294 | − | 0.987069i | \(-0.448756\pi\) | ||||
0.160294 | + | 0.987069i | \(0.448756\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −786485. | −0.0492299 | −0.0246149 | − | 0.999697i | \(-0.507836\pi\) | ||||
−0.0246149 | + | 0.999697i | \(0.507836\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.13138e7 | 0.703551 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.73845e6 | −0.597725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.44258e7 | 0.879679 | 0.439840 | − | 0.898076i | \(-0.355035\pi\) | ||||
0.439840 | + | 0.898076i | \(0.355035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.81060e7 | −1.08987 | −0.544935 | − | 0.838478i | \(-0.683446\pi\) | ||||
−0.544935 | + | 0.838478i | \(0.683446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.86867e6 | 0.111758 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −899537. | −0.0531099 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.91755e6 | −0.112491 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.18187e6 | 0.358051 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.86788e7 | 1.07501 | 0.537504 | − | 0.843261i | \(-0.319367\pi\) | ||||
0.537504 | + | 0.843261i | \(0.319367\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.82087e7 | −1.03475 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65192e7 | −0.932836 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.99446e6 | 0.334275 | 0.167138 | − | 0.985934i | \(-0.446548\pi\) | ||||
0.167138 | + | 0.985934i | \(0.446548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 394661. | 0.0218704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.30259e6 | −0.454386 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.37968e6 | −0.401373 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.85790e7 | −0.998047 | −0.499023 | − | 0.866589i | \(-0.666308\pi\) | ||||
−0.499023 | + | 0.866589i | \(0.666308\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.31663e7 | −1.23682 | −0.618408 | − | 0.785857i | \(-0.712222\pi\) | ||||
−0.618408 | + | 0.785857i | \(0.712222\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.96902e6 | 0.367517 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.57558e6 | −0.397064 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.02639e7 | −0.531440 | −0.265720 | − | 0.964050i | \(-0.585610\pi\) | ||||
−0.265720 | + | 0.964050i | \(0.585610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.46900e7 | 1.78527 | 0.892637 | − | 0.450776i | \(-0.148853\pi\) | ||||
0.892637 | + | 0.450776i | \(0.148853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.50380e7 | −0.764585 | −0.382293 | − | 0.924041i | \(-0.624865\pi\) | ||||
−0.382293 | + | 0.924041i | \(0.624865\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.38937e7 | −0.702155 | −0.351078 | − | 0.936346i | \(-0.614185\pi\) | ||||
−0.351078 | + | 0.936346i | \(0.614185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.03104e6 | −0.201282 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.22295e7 | −0.607006 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.79014e7 | 0.877973 | 0.438986 | − | 0.898494i | \(-0.355338\pi\) | ||||
0.438986 | + | 0.898494i | \(0.355338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.67787e7 | 1.30557 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.82454e6 | 0.0879044 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.29271e7 | −0.619144 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.89912e7 | −2.31897 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.07670e7 | 0.506664 | 0.253332 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253332 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.76117e7 | −0.819122 | −0.409561 | − | 0.912283i | \(-0.634318\pi\) | ||||
−0.409561 | + | 0.912283i | \(0.634318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.95268e7 | 0.902917 | 0.451458 | − | 0.892292i | \(-0.350904\pi\) | ||||
0.451458 | + | 0.892292i | \(0.350904\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.78308e7 | −1.72910 | −0.864548 | − | 0.502550i | \(-0.832395\pi\) | ||||
−0.864548 | + | 0.502550i | \(0.832395\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.44280e7 | −0.655641 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.24380e6 | 0.190636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.13553e7 | −0.507168 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.33688e6 | −0.0590301 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.51942e6 | 0.198419 | 0.0992096 | − | 0.995067i | \(-0.468369\pi\) | ||||
0.0992096 | + | 0.995067i | \(0.468369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.48399e7 | −1.07823 | −0.539114 | − | 0.842233i | \(-0.681241\pi\) | ||||
−0.539114 | + | 0.842233i | \(0.681241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.40390e6 | −0.190080 | −0.0950399 | − | 0.995473i | \(-0.530298\pi\) | ||||
−0.0950399 | + | 0.995473i | \(0.530298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.67390e7 | −1.56790 | −0.783951 | − | 0.620823i | \(-0.786799\pi\) | ||||
−0.783951 | + | 0.620823i | \(0.786799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.60663e7 | 1.10618 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.97104e6 | 0.0827116 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.54454e7 | −0.644528 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.05607e7 | −0.848473 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.41223e7 | 0.579552 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.62697e6 | 0.268964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.61944e6 | −0.146091 | −0.0730454 | − | 0.997329i | \(-0.523272\pi\) | ||||
−0.0730454 | + | 0.997329i | \(0.523272\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.06846e7 | −0.426543 | −0.213271 | − | 0.976993i | \(-0.568412\pi\) | ||||
−0.213271 | + | 0.976993i | \(0.568412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.34084e6 | 0.370859 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.89499e6 | 0.349319 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 423307. | 0.0165336 | 0.00826679 | − | 0.999966i | \(-0.497369\pi\) | ||||
0.00826679 | + | 0.999966i | \(0.497369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.04920e7 | 0.405373 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.87512e6 | −0.341052 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.51666e6 | 0.0956720 | 0.0478360 | − | 0.998855i | \(-0.484768\pi\) | ||||
0.0478360 | + | 0.998855i | \(0.484768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.01321e7 | −0.761227 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.06042e6 | −0.0396688 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.39054e7 | −0.517408 | −0.258704 | − | 0.965957i | \(-0.583295\pi\) | ||||
−0.258704 | + | 0.965957i | \(0.583295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.15658e7 | −0.425795 | −0.212897 | − | 0.977075i | \(-0.568290\pi\) | ||||
−0.212897 | + | 0.977075i | \(0.568290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.46237e6 | −0.0535521 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.37017e7 | 0.858826 | 0.429413 | − | 0.903108i | \(-0.358721\pi\) | ||||
0.429413 | + | 0.903108i | \(0.358721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.54283e7 | 1.63742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.67313e6 | −0.0596757 | −0.0298378 | − | 0.999555i | \(-0.509499\pi\) | ||||
−0.0298378 | + | 0.999555i | \(0.509499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −764833. | −0.0271368 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −359540. | −0.0126241 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96898e7 | −0.687753 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.15809e7 | −0.400335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.69820e7 | −0.927915 | −0.463957 | − | 0.885858i | \(-0.653571\pi\) | ||||
−0.463957 | + | 0.885858i | \(0.653571\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.59915e7 | 1.22504 | 0.612522 | − | 0.790454i | \(-0.290155\pi\) | ||||
0.612522 | + | 0.790454i | \(0.290155\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.31976e7 | 0.446903 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.65489e7 | −1.56017 | −0.780087 | − | 0.625671i | \(-0.784825\pi\) | ||||
−0.780087 | + | 0.625671i | \(0.784825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.25155e6 | −0.241810 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.41850e7 | −1.12837 | −0.564186 | − | 0.825648i | \(-0.690810\pi\) | ||||
−0.564186 | + | 0.825648i | \(0.690810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.29519e7 | 0.425346 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.23155e7 | −0.400370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.37070e7 | −1.41373 | −0.706866 | − | 0.707347i | \(-0.749892\pi\) | ||||
−0.706866 | + | 0.707347i | \(0.749892\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.33654e6 | 0.0427980 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.73468e7 | −0.552689 | −0.276344 | − | 0.961059i | \(-0.589123\pi\) | ||||
−0.276344 | + | 0.961059i | \(0.589123\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.6.a.e.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1080.6.a.g.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.6.a.e.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.6.a.g.1.3 | yes | 3 | 3.2 | odd | 2 |