Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,6,Mod(1,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, 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("560.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.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: | \(89.8149390953\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 560.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.0641500 | −0.0320750 | − | 0.999485i | \(-0.510212\pi\) | ||||
−0.0320750 | + | 0.999485i | \(0.510212\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −242.000 | −0.995885 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 453.000 | 1.12880 | 0.564399 | − | 0.825502i | \(-0.309108\pi\) | ||||
0.564399 | + | 0.825502i | \(0.309108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −969.000 | −1.59025 | −0.795125 | − | 0.606446i | \(-0.792595\pi\) | ||||
−0.795125 | + | 0.606446i | \(0.792595\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −25.0000 | −0.0286888 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1637.00 | 1.37381 | 0.686905 | − | 0.726748i | \(-0.258969\pi\) | ||||
0.686905 | + | 0.726748i | \(0.258969\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1550.00 | 0.985026 | 0.492513 | − | 0.870305i | \(-0.336078\pi\) | ||||
0.492513 | + | 0.870305i | \(0.336078\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 49.0000 | 0.0242464 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1654.00 | 0.651952 | 0.325976 | − | 0.945378i | \(-0.394307\pi\) | ||||
0.325976 | + | 0.945378i | \(0.394307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 485.000 | 0.128036 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4985.00 | −1.10070 | −0.550352 | − | 0.834933i | \(-0.685506\pi\) | ||||
−0.550352 | + | 0.834933i | \(0.685506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1192.00 | −0.222778 | −0.111389 | − | 0.993777i | \(-0.535530\pi\) | ||||
−0.111389 | + | 0.993777i | \(0.535530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −453.000 | −0.0724125 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1225.00 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11018.0 | −1.32312 | −0.661559 | − | 0.749893i | \(-0.730105\pi\) | ||||
−0.661559 | + | 0.749893i | \(0.730105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 969.000 | 0.102015 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1728.00 | −0.160540 | −0.0802702 | − | 0.996773i | \(-0.525578\pi\) | ||||
−0.0802702 | + | 0.996773i | \(0.525578\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10814.0 | 0.891898 | 0.445949 | − | 0.895058i | \(-0.352866\pi\) | ||||
0.445949 | + | 0.895058i | \(0.352866\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6050.00 | −0.445373 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −26237.0 | −1.73249 | −0.866243 | − | 0.499624i | \(-0.833472\pi\) | ||||
−0.866243 | + | 0.499624i | \(0.833472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1637.00 | −0.0881299 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25936.0 | 1.26827 | 0.634137 | − | 0.773220i | \(-0.281355\pi\) | ||||
0.634137 | + | 0.773220i | \(0.281355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11325.0 | 0.504814 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1550.00 | −0.0631894 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4580.00 | 0.171291 | 0.0856457 | − | 0.996326i | \(-0.472705\pi\) | ||||
0.0856457 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12488.0 | −0.429703 | −0.214851 | − | 0.976647i | \(-0.568927\pi\) | ||||
−0.214851 | + | 0.976647i | \(0.568927\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11858.0 | 0.376409 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −24225.0 | −0.711181 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15848.0 | 0.431308 | 0.215654 | − | 0.976470i | \(-0.430812\pi\) | ||||
0.215654 | + | 0.976470i | \(0.430812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1654.00 | −0.0418228 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51792.0 | −1.21932 | −0.609659 | − | 0.792664i | \(-0.708694\pi\) | ||||
−0.609659 | + | 0.792664i | \(0.708694\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4846.00 | 0.106433 | 0.0532165 | − | 0.998583i | \(-0.483053\pi\) | ||||
0.0532165 | + | 0.998583i | \(0.483053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −625.000 | −0.0128300 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22197.0 | −0.426646 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −62765.0 | −1.13149 | −0.565744 | − | 0.824581i | \(-0.691411\pi\) | ||||
−0.565744 | + | 0.824581i | \(0.691411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 58321.0 | 0.987671 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23644.0 | 0.376726 | 0.188363 | − | 0.982099i | \(-0.439682\pi\) | ||||
0.188363 | + | 0.982099i | \(0.439682\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40925.0 | 0.614386 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4985.00 | 0.0706101 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −147300. | −1.97119 | −0.985593 | − | 0.169133i | \(-0.945903\pi\) | ||||
−0.985593 | + | 0.169133i | \(0.945903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 47481.0 | 0.601058 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1192.00 | 0.0142912 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 38750.0 | 0.440517 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8343.00 | −0.0900312 | −0.0450156 | − | 0.998986i | \(-0.514334\pi\) | ||||
−0.0450156 | + | 0.998986i | \(0.514334\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −109626. | −1.12415 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11878.0 | −0.115862 | −0.0579308 | − | 0.998321i | \(-0.518450\pi\) | ||||
−0.0579308 | + | 0.998321i | \(0.518450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 132439. | 1.23005 | 0.615025 | − | 0.788508i | \(-0.289146\pi\) | ||||
0.615025 | + | 0.788508i | \(0.289146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1225.00 | 0.0108433 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −136842. | −1.15547 | −0.577737 | − | 0.816223i | \(-0.696064\pi\) | ||||
−0.577737 | + | 0.816223i | \(0.696064\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 109485. | 0.882650 | 0.441325 | − | 0.897347i | \(-0.354509\pi\) | ||||
0.441325 | + | 0.897347i | \(0.354509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11018.0 | 0.0848780 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −200934. | −1.48033 | −0.740163 | − | 0.672428i | \(-0.765252\pi\) | ||||
−0.740163 | + | 0.672428i | \(0.765252\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41350.0 | 0.291562 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 234498. | 1.58371 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −80213.0 | −0.519251 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 44158.0 | 0.274186 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1728.00 | 0.0102987 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −330692. | −1.81934 | −0.909671 | − | 0.415329i | \(-0.863666\pi\) | ||||
−0.909671 | + | 0.415329i | \(0.863666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10814.0 | −0.0572153 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −43982.0 | −0.223922 | −0.111961 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111961 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −75950.0 | −0.372305 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12125.0 | 0.0572595 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −99748.0 | −0.454049 | −0.227025 | − | 0.973889i | \(-0.572900\pi\) | ||||
−0.227025 | + | 0.973889i | \(0.572900\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −258930. | −1.13670 | −0.568349 | − | 0.822787i | \(-0.692418\pi\) | ||||
−0.568349 | + | 0.822787i | \(0.692418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26237.0 | 0.111139 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −438957. | −1.79507 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −124625. | −0.492249 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2401.00 | −0.00916429 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −498430. | −1.83924 | −0.919620 | − | 0.392809i | \(-0.871503\pi\) | ||||
−0.919620 | + | 0.392809i | \(0.871503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 245803. | 0.877293 | 0.438647 | − | 0.898660i | \(-0.355458\pi\) | ||||
0.438647 | + | 0.898660i | \(0.355458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −396154. | −1.36816 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29800.0 | −0.0996293 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −85478.0 | −0.276761 | −0.138381 | − | 0.990379i | \(-0.544190\pi\) | ||||
−0.138381 | + | 0.990379i | \(0.544190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25936.0 | −0.0813599 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −81046.0 | −0.246415 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −193026. | −0.569045 | −0.284523 | − | 0.958669i | \(-0.591835\pi\) | ||||
−0.284523 | + | 0.958669i | \(0.591835\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11325.0 | −0.0323838 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 157783. | 0.437793 | 0.218897 | − | 0.975748i | \(-0.429754\pi\) | ||||
0.218897 | + | 0.975748i | \(0.429754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 567668. | 1.52889 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −375100. | −0.980972 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −265659. | −0.674853 | −0.337427 | − | 0.941352i | \(-0.609556\pi\) | ||||
−0.337427 | + | 0.941352i | \(0.609556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4580.00 | −0.0109883 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −183660. | −0.428432 | −0.214216 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214216 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −635048. | −1.44082 | −0.720411 | − | 0.693548i | \(-0.756047\pi\) | ||||
−0.720411 | + | 0.693548i | \(0.756047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12488.0 | 0.0275655 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −275450. | −0.591716 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 741561. | 1.55075 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23765.0 | −0.0483931 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 226613. | 0.449471 | 0.224735 | − | 0.974420i | \(-0.427848\pi\) | ||||
0.224735 | + | 0.974420i | \(0.427848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 46476.0 | 0.0898122 | 0.0449061 | − | 0.998991i | \(-0.485701\pi\) | ||||
0.0449061 | + | 0.998991i | \(0.485701\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24225.0 | 0.0456223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 204972. | 0.376295 | 0.188148 | − | 0.982141i | \(-0.439752\pi\) | ||||
0.188148 | + | 0.982141i | \(0.439752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 953020. | 1.70596 | 0.852981 | − | 0.521942i | \(-0.174792\pi\) | ||||
0.852981 | + | 0.521942i | \(0.174792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15848.0 | −0.0276684 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 244265. | 0.416027 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −43200.0 | −0.0717958 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −400268. | −0.649270 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 702150. | 1.11190 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 223523. | 0.345634 | 0.172817 | − | 0.984954i | \(-0.444713\pi\) | ||||
0.172817 | + | 0.984954i | \(0.444713\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 51792.0 | 0.0782193 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 270350. | 0.398869 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 58408.0 | 0.0842021 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4846.00 | −0.00682768 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.58625e6 | −2.18470 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.01480e6 | −1.36653 | −0.683264 | − | 0.730171i | \(-0.739440\pi\) | ||||
−0.683264 | + | 0.730171i | \(0.739440\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −151250. | −0.199177 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −999797. | −1.28780 | −0.643898 | − | 0.765111i | \(-0.722684\pi\) | ||||
−0.643898 | + | 0.765111i | \(0.722684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −851120. | −1.07251 | −0.536256 | − | 0.844055i | \(-0.680162\pi\) | ||||
−0.536256 | + | 0.844055i | \(0.680162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22197.0 | 0.0273693 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.09270e6 | 1.31859 | 0.659295 | − | 0.751885i | \(-0.270855\pi\) | ||||
0.659295 | + | 0.751885i | \(0.270855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −655925. | −0.774791 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 62765.0 | 0.0725850 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −765905. | −0.867322 | −0.433661 | − | 0.901076i | \(-0.642778\pi\) | ||||
−0.433661 | + | 0.901076i | \(0.642778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.21094e6 | −1.34301 | −0.671505 | − | 0.741000i | \(-0.734352\pi\) | ||||
−0.671505 | + | 0.741000i | \(0.734352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −176176. | −0.191395 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.50195e6 | −1.56644 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23644.0 | −0.0241670 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −278262. | −0.278785 | −0.139393 | − | 0.990237i | \(-0.544515\pi\) | ||||
−0.139393 | + | 0.990237i | \(0.544515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 749262. | 0.735923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −40925.0 | −0.0394129 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −352998. | −0.333380 | −0.166690 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166690 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 539882. | 0.500091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20637e6 | 1.09617 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.55809e6 | 1.38901 | 0.694503 | − | 0.719490i | \(-0.255624\pi\) | ||||
0.694503 | + | 0.719490i | \(0.255624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 648400. | 0.567190 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 147300. | 0.126452 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.21963e6 | −1.02766 | −0.513828 | − | 0.857893i | \(-0.671773\pi\) | ||||
−0.513828 | + | 0.857893i | \(0.671773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −405792. | −0.335645 | −0.167823 | − | 0.985817i | \(-0.553674\pi\) | ||||
−0.167823 | + | 0.985817i | \(0.553674\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −47481.0 | −0.0385579 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 283125. | 0.225760 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 652442. | 0.510908 | 0.255454 | − | 0.966821i | \(-0.417775\pi\) | ||||
0.255454 | + | 0.966821i | \(0.417775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 288464. | 0.221861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 118827. | 0.0897737 | 0.0448869 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448869 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.48801e6 | −1.10443 | −0.552217 | − | 0.833700i | \(-0.686218\pi\) | ||||
−0.552217 | + | 0.833700i | \(0.686218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −38750.0 | −0.0282592 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 84672.0 | 0.0606785 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.25991e6 | 0.887351 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8343.00 | 0.00577550 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.89580e6 | 1.29010 | 0.645050 | − | 0.764140i | \(-0.276836\pi\) | ||||
0.645050 | + | 0.764140i | \(0.276836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 114500. | 0.0766038 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 219705. | 0.144527 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.60273e6 | −1.03677 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −529886. | −0.337106 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11878.0 | 0.00743253 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −312200. | −0.192169 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 821853. | 0.497678 | 0.248839 | − | 0.968545i | \(-0.419951\pi\) | ||||
0.248839 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −132439. | −0.0789078 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.09600e6 | 1.22882 | 0.614412 | − | 0.788985i | \(-0.289393\pi\) | ||||
0.614412 | + | 0.788985i | \(0.289393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 394571. | 0.227648 | 0.113824 | − | 0.993501i | \(-0.463690\pi\) | ||||
0.113824 | + | 0.993501i | \(0.463690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 296450. | 0.168335 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 321422. | 0.179650 | 0.0898250 | − | 0.995958i | \(-0.471369\pi\) | ||||
0.0898250 | + | 0.995958i | \(0.471369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.25820e6 | −1.24247 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 136842. | 0.0741237 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.53735e6 | 1.35324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −605625. | −0.318050 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −109485. | −0.0566220 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.28561e6 | 0.654818 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.23259e6 | 1.12005 | 0.560027 | − | 0.828475i | \(-0.310791\pi\) | ||||
0.560027 | + | 0.828475i | \(0.310791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.66636e6 | 1.31767 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 396200. | 0.192887 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.65656e6 | −1.75387 | −0.876936 | − | 0.480608i | \(-0.840416\pi\) | ||||
−0.876936 | + | 0.480608i | \(0.840416\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 200934. | 0.0949629 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −539976. | −0.251471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −41350.0 | −0.0187037 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.88962e6 | 0.842462 | 0.421231 | − | 0.906953i | \(-0.361598\pi\) | ||||
0.421231 | + | 0.906953i | \(0.361598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.69329e6 | −1.18364 | −0.591820 | − | 0.806070i | \(-0.701590\pi\) | ||||
−0.591820 | + | 0.806070i | \(0.701590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −469965. | −0.203609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.57468e6 | −0.672598 | −0.336299 | − | 0.941755i | \(-0.609175\pi\) | ||||
−0.336299 | + | 0.941755i | \(0.609175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.29480e6 | −0.545295 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 80213.0 | 0.0333100 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.05576e6 | −1.66087 | −0.830436 | − | 0.557114i | \(-0.811909\pi\) | ||||
−0.830436 | + | 0.557114i | \(0.811909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −73599.0 | −0.0297238 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −44158.0 | −0.0175891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 121150. | 0.0475983 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.90628e6 | 1.90146 | 0.950731 | − | 0.310018i | \(-0.100335\pi\) | ||||
0.950731 | + | 0.310018i | \(0.100335\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 418176. | 0.159880 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.27086e6 | −0.479363 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.45336e6 | −1.28520 | −0.642599 | − | 0.766202i | \(-0.722144\pi\) | ||||
−0.642599 | + | 0.766202i | \(0.722144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15625.0 | −0.00573775 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.83046e6 | 1.75039 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.23466e6 | 1.51433 | 0.757165 | − | 0.653224i | \(-0.226584\pi\) | ||||
0.757165 | + | 0.653224i | \(0.226584\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 330692. | 0.116711 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.86460e6 | 0.649516 | 0.324758 | − | 0.945797i | \(-0.394717\pi\) | ||||
0.324758 | + | 0.945797i | \(0.394717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −554925. | −0.190802 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.61699e6 | −0.888228 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.81502e6 | −1.61333 | −0.806666 | − | 0.591008i | \(-0.798730\pi\) | ||||
−0.806666 | + | 0.591008i | \(0.798730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.70760e6 | 0.895658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 43982.0 | 0.0143646 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.56912e6 | −0.506017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.21376e6 | 0.386505 | 0.193253 | − | 0.981149i | \(-0.438096\pi\) | ||||
0.193253 | + | 0.981149i | \(0.438096\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 75950.0 | 0.0238834 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.90442e6 | 1.83365 | 0.916824 | − | 0.399291i | \(-0.130744\pi\) | ||||
0.916824 | + | 0.399291i | \(0.130744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.15505e6 | 0.354272 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.45802e6 | 0.441700 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.99115e6 | −1.49353 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.84289e6 | 1.43152 | 0.715758 | − | 0.698348i | \(-0.246081\pi\) | ||||
0.715758 | + | 0.698348i | \(0.246081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 99748.0 | 0.0291273 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −224420. | −0.0647420 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 591100. | 0.168477 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 258930. | 0.0729193 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −270360. | −0.0752328 | −0.0376164 | − | 0.999292i | \(-0.511977\pi\) | ||||
−0.0376164 | + | 0.999292i | \(0.511977\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.13648e6 | 0.862456 | 0.431228 | − | 0.902243i | \(-0.358080\pi\) | ||||
0.431228 | + | 0.902243i | \(0.358080\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.34935e6 | 1.72536 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.02312e6 | 0.274762 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 611912. | 0.162412 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 438957. | 0.115154 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.87703e6 | 0.486719 | 0.243360 | − | 0.969936i | \(-0.421750\pi\) | ||||
0.243360 | + | 0.969936i | \(0.421750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.20357e6 | 0.821134 | 0.410567 | − | 0.911830i | \(-0.365331\pi\) | ||||
0.410567 | + | 0.911830i | \(0.365331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 124625. | 0.0315778 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.56370e6 | 0.642190 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.27209e6 | 1.55328 | 0.776642 | − | 0.629942i | \(-0.216921\pi\) | ||||
0.776642 | + | 0.629942i | \(0.216921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −581042. | −0.142269 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −724986. | −0.175517 | −0.0877587 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877587 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.68250e6 | −0.881541 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 498430. | 0.117987 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −875985. | −0.205060 | −0.102530 | − | 0.994730i | \(-0.532694\pi\) | ||||
−0.102530 | + | 0.994730i | \(0.532694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −782784. | −0.181218 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −245803. | −0.0562784 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.18702e6 | 0.268801 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −832668. | −0.186501 | −0.0932505 | − | 0.995643i | \(-0.529726\pi\) | ||||
−0.0932505 | + | 0.995643i | \(0.529726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 793945. | 0.175897 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.92115e6 | 1.29764 | 0.648820 | − | 0.760942i | \(-0.275263\pi\) | ||||
0.648820 | + | 0.760942i | \(0.275263\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −682776. | −0.148022 | −0.0740109 | − | 0.997257i | \(-0.523580\pi\) | ||||
−0.0740109 | + | 0.997257i | \(0.523580\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29800.0 | 0.00639122 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.41667e6 | 1.14932 | 0.574659 | − | 0.818393i | \(-0.305135\pi\) | ||||
0.574659 | + | 0.818393i | \(0.305135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −776552. | −0.163019 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 85478.0 | 0.0177542 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.89874e6 | 1.00677 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 968750. | 0.197005 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.27651e6 | −1.26306 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.98599e6 | −0.395493 | −0.197746 | − | 0.980253i | \(-0.563362\pi\) | ||||
−0.197746 | + | 0.980253i | \(0.563362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06764e7 | 2.10409 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 81046.0 | 0.0158075 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −208575. | −0.0402632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.06974e6 | 0.204388 | 0.102194 | − | 0.994764i | \(-0.467414\pi\) | ||||
0.102194 | + | 0.994764i | \(0.467414\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 193026. | 0.0365043 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.59246e6 | −0.859689 | −0.429844 | − | 0.902903i | \(-0.641432\pi\) | ||||
−0.429844 | + | 0.902903i | \(0.641432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.16045e6 | −1.51216 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.74065e6 | −0.502737 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.53781e6 | 0.460859 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.96066e6 | −0.352492 | −0.176246 | − | 0.984346i | \(-0.556395\pi\) | ||||
−0.176246 | + | 0.984346i | \(0.556395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −157783. | −0.0280844 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.51483e6 | −0.619419 | −0.309709 | − | 0.950831i | \(-0.600232\pi\) | ||||
−0.309709 | + | 0.950831i | \(0.600232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −296950. | −0.0518149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −567668. | −0.0980787 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.45211e6 | −0.248431 | −0.124215 | − | 0.992255i | \(-0.539641\pi\) | ||||
−0.124215 | + | 0.992255i | \(0.539641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −237454. | −0.0402279 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 751750. | 0.126119 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.31098e6 | 0.550095 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.18854e7 | −1.95563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 265659. | 0.0432918 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.24240e6 | −0.684726 | −0.342363 | − | 0.939568i | \(-0.611227\pi\) | ||||
−0.342363 | + | 0.939568i | \(0.611227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.56012e6 | 1.20858 | 0.604289 | − | 0.796765i | \(-0.293457\pi\) | ||||
0.604289 | + | 0.796765i | \(0.293457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30625.0 | 0.00484929 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.95130e6 | −0.306054 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.70063e6 | −0.574958 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.10836e6 | −0.170586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.67443e6 | 0.255299 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.42105e6 | −0.516743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 183660. | 0.0274839 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.08765e6 | 0.161257 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.24065e6 | 0.182245 | 0.0911224 | − | 0.995840i | \(-0.470955\pi\) | ||||
0.0911224 | + | 0.995840i | \(0.470955\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 635048. | 0.0924287 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.73712e6 | 0.394733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.85057e6 | 0.264446 | 0.132223 | − | 0.991220i | \(-0.457789\pi\) | ||||
0.132223 | + | 0.991220i | \(0.457789\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.02210e6 | 0.427935 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.72675e6 | −1.08422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.07548e6 | 0.427662 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 275450. | 0.0379586 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.77555e6 | 1.06192 | 0.530962 | − | 0.847396i | \(-0.321831\pi\) | ||||
0.530962 | + | 0.847396i | \(0.321831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.04788e7 | −1.41834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −741561. | −0.0994809 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.37716e6 | −1.11385 | −0.556924 | − | 0.830564i | \(-0.688018\pi\) | ||||
−0.556924 | + | 0.830564i | \(0.688018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.02335e6 | −0.662022 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.85773e6 | −0.373305 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.15591e6 | −0.797098 | −0.398549 | − | 0.917147i | \(-0.630486\pi\) | ||||
−0.398549 | + | 0.917147i | \(0.630486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.21513e6 | −0.926092 | −0.463046 | − | 0.886334i | \(-0.653243\pi\) | ||||
−0.463046 | + | 0.886334i | \(0.653243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −226613. | −0.0288336 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.03375e6 | 0.130390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.36699e7 | 1.70933 | 0.854666 | − | 0.519177i | \(-0.173762\pi\) | ||||
0.854666 | + | 0.519177i | \(0.173762\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −46476.0 | −0.00576146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.15856e6 | −0.142389 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17490e7 | 1.43163 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.86245e6 | 0.708255 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.00686e7 | 1.20608 | 0.603040 | − | 0.797711i | \(-0.293956\pi\) | ||||
0.603040 | + | 0.797711i | \(0.293956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.84760e6 | −0.219442 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −204972. | −0.0241394 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.80615e6 | 1.14515 | 0.572574 | − | 0.819853i | \(-0.305945\pi\) | ||||
0.572574 | + | 0.819853i | \(0.305945\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00532e6 | −0.232216 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −953020. | −0.109438 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.26257e6 | −0.940911 | −0.470455 | − | 0.882424i | \(-0.655910\pi\) | ||||
−0.470455 | + | 0.882424i | \(0.655910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.59492e6 | −0.405978 | −0.202989 | − | 0.979181i | \(-0.565066\pi\) | ||||
−0.202989 | + | 0.979181i | \(0.565066\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.83522e6 | −0.429533 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.10395e6 | 0.122620 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.32969e7 | 1.46480 | 0.732401 | − | 0.680873i | \(-0.238400\pi\) | ||||
0.732401 | + | 0.680873i | \(0.238400\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −244265. | −0.0266881 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.54237e7 | 2.75508 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.50327e6 | 0.269064 | 0.134532 | − | 0.990909i | \(-0.457047\pi\) | ||||
0.134532 | + | 0.990909i | \(0.457047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 43200.0 | 0.00460570 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.88254e6 | 0.199082 | 0.0995409 | − | 0.995033i | \(-0.468263\pi\) | ||||
0.0995409 | + | 0.995033i | \(0.468263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.21487e6 | −0.861736 | −0.430868 | − | 0.902415i | \(-0.641792\pi\) | ||||
−0.430868 | + | 0.902415i | \(0.641792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 802190. | 0.0834734 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.21770e6 | 0.745038 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −702150. | −0.0713282 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.80365e7 | −1.81771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.61155e7 | −1.61128 | −0.805638 | − | 0.592408i | \(-0.798177\pi\) | ||||
−0.805638 | + | 0.592408i | \(0.798177\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −223523. | −0.0221724 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.26730e6 | −0.813635 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.32657e6 | −0.227179 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.25337e7 | 1.21430 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.50544e6 | −0.817620 | −0.408810 | − | 0.912619i | \(-0.634056\pi\) | ||||
−0.408810 | + | 0.912619i | \(0.634056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.32191e7 | 1.26088 | 0.630440 | − | 0.776238i | \(-0.282874\pi\) | ||||
0.630440 | + | 0.776238i | \(0.282874\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −270350. | −0.0255875 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.89115e6 | −0.177609 | −0.0888047 | − | 0.996049i | \(-0.528305\pi\) | ||||
−0.0888047 | + | 0.996049i | \(0.528305\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.07474e6 | 0.193353 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −58408.0 | −0.00540157 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.90587e6 | 0.450228 | 0.225114 | − | 0.974332i | \(-0.427725\pi\) | ||||
0.225114 | + | 0.974332i | \(0.427725\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.09955e6 | −0.100141 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.17273e6 | −0.105995 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.36367e7 | −1.22319 | −0.611597 | − | 0.791169i | \(-0.709473\pi\) | ||||
−0.611597 | + | 0.791169i | \(0.709473\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.22345e6 | −0.197935 | −0.0989677 | − | 0.995091i | \(-0.531554\pi\) | ||||
−0.0989677 | + | 0.995091i | \(0.531554\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.58625e6 | 0.140149 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.89875e6 | −0.166500 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.24519e6 | −0.717606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.01480e6 | 0.0876629 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.65706e6 | −0.485048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.88484e6 | 0.415731 | 0.207865 | − | 0.978157i | \(-0.433348\pi\) | ||||
0.207865 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 303125. | 0.0256072 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.98785e7 | −1.66691 | −0.833453 | − | 0.552590i | \(-0.813640\pi\) | ||||
−0.833453 | + | 0.552590i | \(0.813640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 408807. | 0.0340286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 999797. | 0.0826122 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.27870e6 | −0.350962 | −0.175481 | − | 0.984483i | \(-0.556148\pi\) | ||||
−0.175481 | + | 0.984483i | \(0.556148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.49370e6 | −0.203057 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 851120. | 0.0688017 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.51320e7 | −2.01687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.48925e6 | −0.756026 | −0.378013 | − | 0.925800i | \(-0.623393\pi\) | ||||
−0.378013 | + | 0.925800i | \(0.623393\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.37167e6 | 0.424890 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.47325e6 | −0.508347 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.82874e6 | −0.220552 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.09270e6 | −0.0845875 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.86385e6 | −0.450700 | −0.225350 | − | 0.974278i | \(-0.572353\pi\) | ||||
−0.225350 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.70779e7 | −1.30331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 655925. | 0.0497029 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 582022. | 0.0437916 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.66670e6 | −0.199232 | −0.0996161 | − | 0.995026i | \(-0.531761\pi\) | ||||
−0.0996161 | + | 0.995026i | \(0.531761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.51891e7 | 1.12683 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.97157e6 | −0.145241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.09739e7 | −0.802781 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 765905. | 0.0556387 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.46629e6 | 0.322199 | 0.161100 | − | 0.986938i | \(-0.448496\pi\) | ||||
0.161100 | + | 0.986938i | \(0.448496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.48951e6 | −0.464915 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.21094e6 | 0.0861541 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.11562e6 | −0.220141 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.47757e6 | 0.524716 | 0.262358 | − | 0.964971i | \(-0.415500\pi\) | ||||
0.262358 | + | 0.964971i | \(0.415500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.39958e7 | −0.975393 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.77025e7 | 1.22530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.39751e6 | −0.302306 | −0.151153 | − | 0.988510i | \(-0.548299\pi\) | ||||
−0.151153 | + | 0.988510i | \(0.548299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −60025.0 | −0.00409840 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.17914e6 | 0.486860 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.84036e7 | −1.91321 | −0.956603 | − | 0.291395i | \(-0.905880\pi\) | ||||
−0.956603 | + | 0.291395i | \(0.905880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.50195e6 | 0.100487 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.96012e7 | 1.30260 | 0.651299 | − | 0.758821i | \(-0.274224\pi\) | ||||
0.651299 | + | 0.758821i | \(0.274224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.24608e7 | −0.822533 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.72185e6 | −0.375176 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.70526e6 | 0.436728 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.60344e6 | 0.168441 | 0.0842206 | − | 0.996447i | \(-0.473160\pi\) | ||||
0.0842206 | + | 0.996447i | \(0.473160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 278262. | 0.0178841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.14508e6 | 0.392337 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.98869e7 | −1.89558 | −0.947789 | − | 0.318899i | \(-0.896687\pi\) | ||||
−0.947789 | + | 0.318899i | \(0.896687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −749262. | −0.0472095 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.21470e7 | 0.760338 | 0.380169 | − | 0.924917i | \(-0.375866\pi\) | ||||
0.380169 | + | 0.924917i | \(0.375866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.36476e6 | −0.333610 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.90385e6 | −0.611858 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.43802e6 | −0.272396 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.53845e6 | 0.276753 | 0.138376 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138376 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 352998. | 0.0213863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.93330e7 | 1.16372 | 0.581861 | − | 0.813288i | \(-0.302325\pi\) | ||||
0.581861 | + | 0.813288i | \(0.302325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −745000. | −0.0445556 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −539882. | −0.0320809 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.67840e6 | −0.158136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.34618e7 | −1.37636 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.41772e6 | −0.140930 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.13695e6 | −0.123771 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.66392e7 | −0.957627 | −0.478814 | − | 0.877917i | \(-0.658933\pi\) | ||||
−0.478814 | + | 0.877917i | \(0.658933\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.55809e6 | −0.0891048 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.84577e6 | 0.559511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.21009e7 | 0.683335 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −648400. | −0.0363852 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.80409e7 | 1.00603 | 0.503017 | − | 0.864276i | \(-0.332223\pi\) | ||||
0.503017 | + | 0.864276i | \(0.332223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.29500e7 | −2.38010 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.56466e7 | 1.96307 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.19524e6 | 0.120141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.02615e6 | −0.110200 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.21963e6 | 0.0659241 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.33891e7 | 1.25644 | 0.628220 | − | 0.778036i | \(-0.283784\pi\) | ||||
0.628220 | + | 0.778036i | \(0.283784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.29037e7 | 1.22279 | 0.611397 | − | 0.791324i | \(-0.290608\pi\) | ||||
0.611397 | + | 0.791324i | \(0.290608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 405792. | 0.0215316 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.82565e6 | −0.254485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.67617e7 | 0.878543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.14904e7 | −0.598585 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.80745e7 | −0.935853 | −0.467926 | − | 0.883767i | \(-0.654999\pi\) | ||||
−0.467926 | + | 0.883767i | \(0.654999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.17989e7 | −0.607216 | −0.303608 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303608 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −283125. | −0.0144825 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.57650e6 | −0.130999 | −0.0654993 | − | 0.997853i | \(-0.520864\pi\) | ||||
−0.0654993 | + | 0.997853i | \(0.520864\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.84340e7 | −1.94236 | −0.971178 | − | 0.238356i | \(-0.923392\pi\) | ||||
−0.971178 | + | 0.238356i | \(0.923392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −652442. | −0.0327747 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.93044e6 | 0.196258 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.94458e6 | 0.195787 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −578120. | −0.0285236 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.24222e7 | 0.609247 | 0.304623 | − | 0.952473i | \(-0.401469\pi\) | ||||
0.304623 | + | 0.952473i | \(0.401469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.33908e6 | 0.211547 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −118827. | −0.00575899 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.41917e7 | 0.683743 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.16374e6 | −0.103633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.48801e6 | 0.0708495 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.82238e7 | −0.862610 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.92067e6 | 0.372726 | 0.186363 | − | 0.982481i | \(-0.440330\pi\) | ||||
0.186363 | + | 0.982481i | \(0.440330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.37750e6 | −0.438704 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.48983e7 | 0.692924 | 0.346462 | − | 0.938064i | \(-0.387383\pi\) | ||||
0.346462 | + | 0.938064i | \(0.387383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.38740e7 | 0.641534 | 0.320767 | − | 0.947158i | \(-0.396059\pi\) | ||||
0.320767 | + | 0.947158i | \(0.396059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −84672.0 | −0.00389253 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.25500e7 | −0.573610 | −0.286805 | − | 0.957989i | \(-0.592593\pi\) | ||||
−0.286805 | + | 0.957989i | \(0.592593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.64147e6 | −0.301804 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.25991e6 | −0.0569236 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.84325e7 | −1.27722 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.53567e7 | −0.685887 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.01901e6 | 0.0896607 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −765625. | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.86002e7 | −1.25565 | −0.627827 | − | 0.778353i | \(-0.716056\pi\) | ||||
−0.627827 | + | 0.778353i | \(0.716056\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.89580e6 | −0.0827600 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.09608e7 | 1.77799 | 0.888993 | − | 0.457922i | \(-0.151406\pi\) | ||||
0.888993 | + | 0.457922i | \(0.151406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.30504e7 | −0.563279 | −0.281639 | − | 0.959520i | \(-0.590878\pi\) | ||||
−0.281639 | + | 0.959520i | \(0.590878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −114500. | −0.00491414 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.53595e7 | −1.08226 | −0.541129 | − | 0.840939i | \(-0.682003\pi\) | ||||
−0.541129 | + | 0.840939i | \(0.682003\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.62039e7 | 0.687647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.64194e7 | 1.11488 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.06674e7 | −1.70654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.59150e6 | −0.191601 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.60273e6 | 0.0665087 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.94212e6 | 0.245212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.24572e7 | 1.74237 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 529886. | 0.0216253 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.58762e7 | −0.644355 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.98595e7 | −0.801585 | −0.400793 | − | 0.916169i | \(-0.631265\pi\) | ||||
−0.400793 | + | 0.916169i | \(0.631265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.87448e6 | 0.115385 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.99344e7 | 0.795808 | 0.397904 | − | 0.917427i | \(-0.369738\pi\) | ||||
0.397904 | + | 0.917427i | \(0.369738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.07107e7 | 0.425248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 312200. | 0.0123276 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.15512e6 | 0.0846346 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.10695e7 | 0.432355 | 0.216178 | − | 0.976354i | \(-0.430641\pi\) | ||||
0.216178 | + | 0.976354i | \(0.430641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −821853. | −0.0319260 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.01864e7 | 1.93902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.88625e6 | −0.264624 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.20502e7 | −1.22499 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.25682e7 | −1.23810 | −0.619048 | − | 0.785353i | \(-0.712481\pi\) | ||||
−0.619048 | + | 0.785353i | \(0.712481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.72155e6 | 0.140718 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.09600e6 | −0.0788291 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.85390e7 | 0.693518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.15690e7 | 1.17466 | 0.587329 | − | 0.809348i | \(-0.300179\pi\) | ||||
0.587329 | + | 0.809348i | \(0.300179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −394571. | −0.0146036 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.67997e7 | −1.35479 | −0.677393 | − | 0.735622i | \(-0.736890\pi\) | ||||
−0.677393 | + | 0.735622i | \(0.736890\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.85811e6 | −0.104665 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −594125. | −0.0216420 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.88453e7 | −0.682853 | −0.341426 | − | 0.939909i | \(-0.610910\pi\) | ||||
−0.341426 | + | 0.939909i | \(0.610910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.69577e6 | −0.169255 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −321422. | −0.0115246 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.25120e7 | −0.446265 | −0.223133 | − | 0.974788i | \(-0.571628\pi\) | ||||
−0.223133 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.66532e6 | 0.201009 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.25820e6 | 0.0797046 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.88765e6 | 0.171614 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72083e7 | −0.950370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.31158e7 | 1.15072 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.16190e6 | 0.0401652 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.42344e7 | 1.17733 | 0.588663 | − | 0.808379i | \(-0.299654\pi\) | ||||
0.588663 | + | 0.808379i | \(0.299654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.53735e6 | −0.0868102 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.62027e7 | 0.891864 | 0.445932 | − | 0.895067i | \(-0.352872\pi\) | ||||
0.445932 | + | 0.895067i | \(0.352872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.26876e7 | 0.429632 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 605625. | 0.0204029 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.01114e6 | −0.268508 | −0.134254 | − | 0.990947i | \(-0.542864\pi\) | ||||
−0.134254 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.67269e7 | −2.22507 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.64954e7 | −0.879017 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.60126e7 | 1.51877 | 0.759387 | − | 0.650639i | \(-0.225499\pi\) | ||||
0.759387 | + | 0.650639i | \(0.225499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.12430e6 | 0.168284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.28561e6 | −0.0420066 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.78864e7 | 0.581475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.75828e7 | 1.21564 | 0.607821 | − | 0.794074i | \(-0.292044\pi\) | ||||
0.607821 | + | 0.794074i | \(0.292044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.23259e6 | −0.0718514 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.38255e7 | 0.762929 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.22066e7 | 0.707529 | 0.353765 | − | 0.935334i | \(-0.384901\pi\) | ||||
0.353765 | + | 0.935334i | \(0.384901\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.34373e6 | −0.169407 |
(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 | 560.6.a.c.1.1 | 1 | ||
4.3 | odd | 2 | 35.6.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 315.6.a.a.1.1 | 1 | |||
20.3 | even | 4 | 175.6.b.b.99.2 | 2 | |||
20.7 | even | 4 | 175.6.b.b.99.1 | 2 | |||
20.19 | odd | 2 | 175.6.a.a.1.1 | 1 | |||
28.27 | even | 2 | 245.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
175.6.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
175.6.b.b.99.1 | 2 | 20.7 | even | 4 | |||
175.6.b.b.99.2 | 2 | 20.3 | even | 4 | |||
245.6.a.a.1.1 | 1 | 28.27 | even | 2 | |||
315.6.a.a.1.1 | 1 | 12.11 | even | 2 | |||
560.6.a.c.1.1 | 1 | 1.1 | even | 1 | trivial |