Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | −1.00000 | −0.0641500 | −0.0320750 | − | 0.999485i | \(-0.510212\pi\) | ||||
−0.0320750 | + | 0.999485i | \(0.510212\pi\) | |||||||
\(4\) | 32.0000 | 1.00000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 8.00000 | 0.0907218 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −242.000 | −0.995885 | ||||||||
\(10\) | 200.000 | 0.632456 | ||||||||
\(11\) | −453.000 | −1.12880 | −0.564399 | − | 0.825502i | \(-0.690892\pi\) | ||||
−0.564399 | + | 0.825502i | \(0.690892\pi\) | |||||||
\(12\) | −32.0000 | −0.0641500 | ||||||||
\(13\) | 969.000 | 1.59025 | 0.795125 | − | 0.606446i | \(-0.207405\pi\) | ||||
0.795125 | + | 0.606446i | \(0.207405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0000 | 0.0286888 | ||||||||
\(16\) | −1024.00 | −1.00000 | ||||||||
\(17\) | −1637.00 | −1.37381 | −0.686905 | − | 0.726748i | \(-0.741031\pi\) | ||||
−0.686905 | + | 0.726748i | \(0.741031\pi\) | |||||||
\(18\) | 1936.00 | 1.40839 | ||||||||
\(19\) | 1550.00 | 0.985026 | 0.492513 | − | 0.870305i | \(-0.336078\pi\) | ||||
0.492513 | + | 0.870305i | \(0.336078\pi\) | |||||||
\(20\) | −800.000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3624.00 | 1.59636 | ||||||||
\(23\) | −1654.00 | −0.651952 | −0.325976 | − | 0.945378i | \(-0.605693\pi\) | ||||
−0.325976 | + | 0.945378i | \(0.605693\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −7752.00 | −2.24895 | ||||||||
\(27\) | 485.000 | 0.128036 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4985.00 | −1.10070 | −0.550352 | − | 0.834933i | \(-0.685506\pi\) | ||||
−0.550352 | + | 0.834933i | \(0.685506\pi\) | |||||||
\(30\) | −200.000 | −0.0405720 | ||||||||
\(31\) | −1192.00 | −0.222778 | −0.111389 | − | 0.993777i | \(-0.535530\pi\) | ||||
−0.111389 | + | 0.993777i | \(0.535530\pi\) | |||||||
\(32\) | 8192.00 | 1.41421 | ||||||||
\(33\) | 453.000 | 0.0724125 | ||||||||
\(34\) | 13096.0 | 1.94286 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7744.00 | −0.995885 | ||||||||
\(37\) | −11018.0 | −1.32312 | −0.661559 | − | 0.749893i | \(-0.730105\pi\) | ||||
−0.661559 | + | 0.749893i | \(0.730105\pi\) | |||||||
\(38\) | −12400.0 | −1.39304 | ||||||||
\(39\) | −969.000 | −0.102015 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1728.00 | 0.160540 | 0.0802702 | − | 0.996773i | \(-0.474422\pi\) | ||||
0.0802702 | + | 0.996773i | \(0.474422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10814.0 | −0.891898 | −0.445949 | − | 0.895058i | \(-0.647134\pi\) | ||||
−0.445949 | + | 0.895058i | \(0.647134\pi\) | |||||||
\(44\) | −14496.0 | −1.12880 | ||||||||
\(45\) | 6050.00 | 0.445373 | ||||||||
\(46\) | 13232.0 | 0.922000 | ||||||||
\(47\) | −26237.0 | −1.73249 | −0.866243 | − | 0.499624i | \(-0.833472\pi\) | ||||
−0.866243 | + | 0.499624i | \(0.833472\pi\) | |||||||
\(48\) | 1024.00 | 0.0641500 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5000.00 | −0.282843 | ||||||||
\(51\) | 1637.00 | 0.0881299 | ||||||||
\(52\) | 31008.0 | 1.59025 | ||||||||
\(53\) | 25936.0 | 1.26827 | 0.634137 | − | 0.773220i | \(-0.281355\pi\) | ||||
0.634137 | + | 0.773220i | \(0.281355\pi\) | |||||||
\(54\) | −3880.00 | −0.181070 | ||||||||
\(55\) | 11325.0 | 0.504814 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1550.00 | −0.0631894 | ||||||||
\(58\) | 39880.0 | 1.55663 | ||||||||
\(59\) | 4580.00 | 0.171291 | 0.0856457 | − | 0.996326i | \(-0.472705\pi\) | ||||
0.0856457 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(60\) | 800.000 | 0.0286888 | ||||||||
\(61\) | 12488.0 | 0.429703 | 0.214851 | − | 0.976647i | \(-0.431073\pi\) | ||||
0.214851 | + | 0.976647i | \(0.431073\pi\) | |||||||
\(62\) | 9536.00 | 0.315055 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −1.00000 | ||||||||
\(65\) | −24225.0 | −0.711181 | ||||||||
\(66\) | −3624.00 | −0.102407 | ||||||||
\(67\) | −15848.0 | −0.431308 | −0.215654 | − | 0.976470i | \(-0.569188\pi\) | ||||
−0.215654 | + | 0.976470i | \(0.569188\pi\) | |||||||
\(68\) | −52384.0 | −1.37381 | ||||||||
\(69\) | 1654.00 | 0.0418228 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 51792.0 | 1.21932 | 0.609659 | − | 0.792664i | \(-0.291306\pi\) | ||||
0.609659 | + | 0.792664i | \(0.291306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4846.00 | −0.106433 | −0.0532165 | − | 0.998583i | \(-0.516947\pi\) | ||||
−0.0532165 | + | 0.998583i | \(0.516947\pi\) | |||||||
\(74\) | 88144.0 | 1.87117 | ||||||||
\(75\) | −625.000 | −0.0128300 | ||||||||
\(76\) | 49600.0 | 0.985026 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7752.00 | 0.144270 | ||||||||
\(79\) | 62765.0 | 1.13149 | 0.565744 | − | 0.824581i | \(-0.308589\pi\) | ||||
0.565744 | + | 0.824581i | \(0.308589\pi\) | |||||||
\(80\) | 25600.0 | 0.447214 | ||||||||
\(81\) | 58321.0 | 0.987671 | ||||||||
\(82\) | −13824.0 | −0.227038 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 86512.0 | 1.26133 | ||||||||
\(87\) | 4985.00 | 0.0706101 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 147300. | 1.97119 | 0.985593 | − | 0.169133i | \(-0.0540967\pi\) | ||||
0.985593 | + | 0.169133i | \(0.0540967\pi\) | |||||||
\(90\) | −48400.0 | −0.629853 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −52928.0 | −0.651952 | ||||||||
\(93\) | 1192.00 | 0.0142912 | ||||||||
\(94\) | 209896. | 2.45010 | ||||||||
\(95\) | −38750.0 | −0.440517 | ||||||||
\(96\) | −8192.00 | −0.0907218 | ||||||||
\(97\) | 8343.00 | 0.0900312 | 0.0450156 | − | 0.998986i | \(-0.485666\pi\) | ||||
0.0450156 | + | 0.998986i | \(0.485666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 109626. | 1.12415 | ||||||||
\(100\) | 20000.0 | 0.200000 | ||||||||
\(101\) | 11878.0 | 0.115862 | 0.0579308 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579308 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(102\) | −13096.0 | −0.124634 | ||||||||
\(103\) | 132439. | 1.23005 | 0.615025 | − | 0.788508i | \(-0.289146\pi\) | ||||
0.615025 | + | 0.788508i | \(0.289146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −207488. | −1.79361 | ||||||||
\(107\) | 136842. | 1.15547 | 0.577737 | − | 0.816223i | \(-0.303936\pi\) | ||||
0.577737 | + | 0.816223i | \(0.303936\pi\) | |||||||
\(108\) | 15520.0 | 0.128036 | ||||||||
\(109\) | 109485. | 0.882650 | 0.441325 | − | 0.897347i | \(-0.354509\pi\) | ||||
0.441325 | + | 0.897347i | \(0.354509\pi\) | |||||||
\(110\) | −90600.0 | −0.713915 | ||||||||
\(111\) | 11018.0 | 0.0848780 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −200934. | −1.48033 | −0.740163 | − | 0.672428i | \(-0.765252\pi\) | ||||
−0.740163 | + | 0.672428i | \(0.765252\pi\) | |||||||
\(114\) | 12400.0 | 0.0893634 | ||||||||
\(115\) | 41350.0 | 0.291562 | ||||||||
\(116\) | −159520. | −1.10070 | ||||||||
\(117\) | −234498. | −1.58371 | ||||||||
\(118\) | −36640.0 | −0.242243 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 44158.0 | 0.274186 | ||||||||
\(122\) | −99904.0 | −0.607692 | ||||||||
\(123\) | −1728.00 | −0.0102987 | ||||||||
\(124\) | −38144.0 | −0.222778 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 330692. | 1.81934 | 0.909671 | − | 0.415329i | \(-0.136334\pi\) | ||||
0.909671 | + | 0.415329i | \(0.136334\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10814.0 | 0.0572153 | ||||||||
\(130\) | 193800. | 1.00576 | ||||||||
\(131\) | −43982.0 | −0.223922 | −0.111961 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111961 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(132\) | 14496.0 | 0.0724125 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 126784. | 0.609962 | ||||||||
\(135\) | −12125.0 | −0.0572595 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −99748.0 | −0.454049 | −0.227025 | − | 0.973889i | \(-0.572900\pi\) | ||||
−0.227025 | + | 0.973889i | \(0.572900\pi\) | |||||||
\(138\) | −13232.0 | −0.0591463 | ||||||||
\(139\) | −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 | ||||||||
\(142\) | −414336. | −1.72438 | ||||||||
\(143\) | −438957. | −1.79507 | ||||||||
\(144\) | 247808. | 0.995885 | ||||||||
\(145\) | 124625. | 0.492249 | ||||||||
\(146\) | 38768.0 | 0.150519 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −352576. | −1.32312 | ||||||||
\(149\) | −498430. | −1.83924 | −0.919620 | − | 0.392809i | \(-0.871503\pi\) | ||||
−0.919620 | + | 0.392809i | \(0.871503\pi\) | |||||||
\(150\) | 5000.00 | 0.0181444 | ||||||||
\(151\) | −245803. | −0.877293 | −0.438647 | − | 0.898660i | \(-0.644542\pi\) | ||||
−0.438647 | + | 0.898660i | \(0.644542\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 396154. | 1.36816 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29800.0 | 0.0996293 | ||||||||
\(156\) | −31008.0 | −0.102015 | ||||||||
\(157\) | 85478.0 | 0.276761 | 0.138381 | − | 0.990379i | \(-0.455810\pi\) | ||||
0.138381 | + | 0.990379i | \(0.455810\pi\) | |||||||
\(158\) | −502120. | −1.60017 | ||||||||
\(159\) | −25936.0 | −0.0813599 | ||||||||
\(160\) | −204800. | −0.632456 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −466568. | −1.39678 | ||||||||
\(163\) | 193026. | 0.569045 | 0.284523 | − | 0.958669i | \(-0.408165\pi\) | ||||
0.284523 | + | 0.958669i | \(0.408165\pi\) | |||||||
\(164\) | 55296.0 | 0.160540 | ||||||||
\(165\) | −11325.0 | −0.0323838 | ||||||||
\(166\) | −189152. | −0.532771 | ||||||||
\(167\) | 157783. | 0.437793 | 0.218897 | − | 0.975748i | \(-0.429754\pi\) | ||||
0.218897 | + | 0.975748i | \(0.429754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 567668. | 1.52889 | ||||||||
\(170\) | −327400. | −0.868873 | ||||||||
\(171\) | −375100. | −0.980972 | ||||||||
\(172\) | −346048. | −0.891898 | ||||||||
\(173\) | 265659. | 0.674853 | 0.337427 | − | 0.941352i | \(-0.390444\pi\) | ||||
0.337427 | + | 0.941352i | \(0.390444\pi\) | |||||||
\(174\) | −39880.0 | −0.0998578 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 463872. | 1.12880 | ||||||||
\(177\) | −4580.00 | −0.0109883 | ||||||||
\(178\) | −1.17840e6 | −2.78768 | ||||||||
\(179\) | 183660. | 0.428432 | 0.214216 | − | 0.976786i | \(-0.431280\pi\) | ||||
0.214216 | + | 0.976786i | \(0.431280\pi\) | |||||||
\(180\) | 193600. | 0.445373 | ||||||||
\(181\) | 635048. | 1.44082 | 0.720411 | − | 0.693548i | \(-0.243953\pi\) | ||||
0.720411 | + | 0.693548i | \(0.243953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12488.0 | −0.0275655 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 275450. | 0.591716 | ||||||||
\(186\) | −9536.00 | −0.0202108 | ||||||||
\(187\) | 741561. | 1.55075 | ||||||||
\(188\) | −839584. | −1.73249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 310000. | 0.622985 | ||||||||
\(191\) | −226613. | −0.449471 | −0.224735 | − | 0.974420i | \(-0.572152\pi\) | ||||
−0.224735 | + | 0.974420i | \(0.572152\pi\) | |||||||
\(192\) | 32768.0 | 0.0641500 | ||||||||
\(193\) | 46476.0 | 0.0898122 | 0.0449061 | − | 0.998991i | \(-0.485701\pi\) | ||||
0.0449061 | + | 0.998991i | \(0.485701\pi\) | |||||||
\(194\) | −66744.0 | −0.127323 | ||||||||
\(195\) | 24225.0 | 0.0456223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 204972. | 0.376295 | 0.188148 | − | 0.982141i | \(-0.439752\pi\) | ||||
0.188148 | + | 0.982141i | \(0.439752\pi\) | |||||||
\(198\) | −877008. | −1.58979 | ||||||||
\(199\) | 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 | ||||||||
\(202\) | −95024.0 | −0.163853 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 52384.0 | 0.0881299 | ||||||||
\(205\) | −43200.0 | −0.0717958 | ||||||||
\(206\) | −1.05951e6 | −1.73955 | ||||||||
\(207\) | 400268. | 0.649270 | ||||||||
\(208\) | −992256. | −1.59025 | ||||||||
\(209\) | −702150. | −1.11190 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −223523. | −0.345634 | −0.172817 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172817 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(212\) | 829952. | 1.26827 | ||||||||
\(213\) | −51792.0 | −0.0782193 | ||||||||
\(214\) | −1.09474e6 | −1.63409 | ||||||||
\(215\) | 270350. | 0.398869 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −875880. | −1.24826 | ||||||||
\(219\) | 4846.00 | 0.00682768 | ||||||||
\(220\) | 362400. | 0.504814 | ||||||||
\(221\) | −1.58625e6 | −2.18470 | ||||||||
\(222\) | −88144.0 | −0.120036 | ||||||||
\(223\) | −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 | ||||||||
\(226\) | 1.60747e6 | 2.09350 | ||||||||
\(227\) | −999797. | −1.28780 | −0.643898 | − | 0.765111i | \(-0.722684\pi\) | ||||
−0.643898 | + | 0.765111i | \(0.722684\pi\) | |||||||
\(228\) | −49600.0 | −0.0631894 | ||||||||
\(229\) | 851120. | 1.07251 | 0.536256 | − | 0.844055i | \(-0.319838\pi\) | ||||
0.536256 | + | 0.844055i | \(0.319838\pi\) | |||||||
\(230\) | −330800. | −0.412331 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.09270e6 | 1.31859 | 0.659295 | − | 0.751885i | \(-0.270855\pi\) | ||||
0.659295 | + | 0.751885i | \(0.270855\pi\) | |||||||
\(234\) | 1.87598e6 | 2.23970 | ||||||||
\(235\) | 655925. | 0.774791 | ||||||||
\(236\) | 146560. | 0.171291 | ||||||||
\(237\) | −62765.0 | −0.0725850 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 765905. | 0.867322 | 0.433661 | − | 0.901076i | \(-0.357222\pi\) | ||||
0.433661 | + | 0.901076i | \(0.357222\pi\) | |||||||
\(240\) | −25600.0 | −0.0286888 | ||||||||
\(241\) | 1.21094e6 | 1.34301 | 0.671505 | − | 0.741000i | \(-0.265648\pi\) | ||||
0.671505 | + | 0.741000i | \(0.265648\pi\) | |||||||
\(242\) | −353264. | −0.387758 | ||||||||
\(243\) | −176176. | −0.191395 | ||||||||
\(244\) | 399616. | 0.429703 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13824.0 | 0.0145645 | ||||||||
\(247\) | 1.50195e6 | 1.56644 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23644.0 | −0.0241670 | ||||||||
\(250\) | 125000. | 0.126491 | ||||||||
\(251\) | −278262. | −0.278785 | −0.139393 | − | 0.990237i | \(-0.544515\pi\) | ||||
−0.139393 | + | 0.990237i | \(0.544515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 749262. | 0.735923 | ||||||||
\(254\) | −2.64554e6 | −2.57294 | ||||||||
\(255\) | −40925.0 | −0.0394129 | ||||||||
\(256\) | 1.04858e6 | 1.00000 | ||||||||
\(257\) | 352998. | 0.333380 | 0.166690 | − | 0.986009i | \(-0.446692\pi\) | ||||
0.166690 | + | 0.986009i | \(0.446692\pi\) | |||||||
\(258\) | −86512.0 | −0.0809146 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −775200. | −0.711181 | ||||||||
\(261\) | 1.20637e6 | 1.09617 | ||||||||
\(262\) | 351856. | 0.316674 | ||||||||
\(263\) | −1.55809e6 | −1.38901 | −0.694503 | − | 0.719490i | \(-0.744376\pi\) | ||||
−0.694503 | + | 0.719490i | \(0.744376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −648400. | −0.567190 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −147300. | −0.126452 | ||||||||
\(268\) | −507136. | −0.431308 | ||||||||
\(269\) | 1.21963e6 | 1.02766 | 0.513828 | − | 0.857893i | \(-0.328227\pi\) | ||||
0.513828 | + | 0.857893i | \(0.328227\pi\) | |||||||
\(270\) | 97000.0 | 0.0809771 | ||||||||
\(271\) | −405792. | −0.335645 | −0.167823 | − | 0.985817i | \(-0.553674\pi\) | ||||
−0.167823 | + | 0.985817i | \(0.553674\pi\) | |||||||
\(272\) | 1.67629e6 | 1.37381 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 797984. | 0.642122 | ||||||||
\(275\) | −283125. | −0.225760 | ||||||||
\(276\) | 52928.0 | 0.0418228 | ||||||||
\(277\) | 652442. | 0.510908 | 0.255454 | − | 0.966821i | \(-0.417775\pi\) | ||||
0.255454 | + | 0.966821i | \(0.417775\pi\) | |||||||
\(278\) | 2.07144e6 | 1.60753 | ||||||||
\(279\) | 288464. | 0.221861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 118827. | 0.0897737 | 0.0448869 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448869 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(282\) | −209896. | −0.157174 | ||||||||
\(283\) | −1.48801e6 | −1.10443 | −0.552217 | − | 0.833700i | \(-0.686218\pi\) | ||||
−0.552217 | + | 0.833700i | \(0.686218\pi\) | |||||||
\(284\) | 1.65734e6 | 1.21932 | ||||||||
\(285\) | 38750.0 | 0.0282592 | ||||||||
\(286\) | 3.51166e6 | 2.53862 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.98246e6 | −1.40839 | ||||||||
\(289\) | 1.25991e6 | 0.887351 | ||||||||
\(290\) | −997000. | −0.696146 | ||||||||
\(291\) | −8343.00 | −0.00577550 | ||||||||
\(292\) | −155072. | −0.106433 | ||||||||
\(293\) | −1.89580e6 | −1.29010 | −0.645050 | − | 0.764140i | \(-0.723164\pi\) | ||||
−0.645050 | + | 0.764140i | \(0.723164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −114500. | −0.0766038 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −219705. | −0.144527 | ||||||||
\(298\) | 3.98744e6 | 2.60108 | ||||||||
\(299\) | −1.60273e6 | −1.03677 | ||||||||
\(300\) | −20000.0 | −0.0128300 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.96642e6 | 1.24068 | ||||||||
\(303\) | −11878.0 | −0.00743253 | ||||||||
\(304\) | −1.58720e6 | −0.985026 | ||||||||
\(305\) | −312200. | −0.192169 | ||||||||
\(306\) | −3.16923e6 | −1.93486 | ||||||||
\(307\) | 821853. | 0.497678 | 0.248839 | − | 0.968545i | \(-0.419951\pi\) | ||||
0.248839 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −132439. | −0.0789078 | ||||||||
\(310\) | −238400. | −0.140897 | ||||||||
\(311\) | 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 | \(-0.536310\pi\) | ||||
−0.113824 | + | 0.993501i | \(0.536310\pi\) | |||||||
\(314\) | −683824. | −0.391399 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00848e6 | 1.13149 | ||||||||
\(317\) | 321422. | 0.179650 | 0.0898250 | − | 0.995958i | \(-0.471369\pi\) | ||||
0.0898250 | + | 0.995958i | \(0.471369\pi\) | |||||||
\(318\) | 207488. | 0.115060 | ||||||||
\(319\) | 2.25820e6 | 1.24247 | ||||||||
\(320\) | 819200. | 0.447214 | ||||||||
\(321\) | −136842. | −0.0741237 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.53735e6 | −1.35324 | ||||||||
\(324\) | 1.86627e6 | 0.987671 | ||||||||
\(325\) | 605625. | 0.318050 | ||||||||
\(326\) | −1.54421e6 | −0.804752 | ||||||||
\(327\) | −109485. | −0.0566220 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 90600.0 | 0.0457977 | ||||||||
\(331\) | −2.23259e6 | −1.12005 | −0.560027 | − | 0.828475i | \(-0.689209\pi\) | ||||
−0.560027 | + | 0.828475i | \(0.689209\pi\) | |||||||
\(332\) | 756608. | 0.376726 | ||||||||
\(333\) | 2.66636e6 | 1.31767 | ||||||||
\(334\) | −1.26226e6 | −0.619133 | ||||||||
\(335\) | 396200. | 0.192887 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.65656e6 | −1.75387 | −0.876936 | − | 0.480608i | \(-0.840416\pi\) | ||||
−0.876936 | + | 0.480608i | \(0.840416\pi\) | |||||||
\(338\) | −4.54134e6 | −2.16218 | ||||||||
\(339\) | 200934. | 0.0949629 | ||||||||
\(340\) | 1.30960e6 | 0.614386 | ||||||||
\(341\) | 539976. | 0.251471 | ||||||||
\(342\) | 3.00080e6 | 1.38730 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −41350.0 | −0.0187037 | ||||||||
\(346\) | −2.12527e6 | −0.954386 | ||||||||
\(347\) | −1.88962e6 | −0.842462 | −0.421231 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421231 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(348\) | 159520. | 0.0706101 | ||||||||
\(349\) | 2.69329e6 | 1.18364 | 0.591820 | − | 0.806070i | \(-0.298410\pi\) | ||||
0.591820 | + | 0.806070i | \(0.298410\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 469965. | 0.203609 | ||||||||
\(352\) | −3.71098e6 | −1.59636 | ||||||||
\(353\) | 1.57468e6 | 0.672598 | 0.336299 | − | 0.941755i | \(-0.390825\pi\) | ||||
0.336299 | + | 0.941755i | \(0.390825\pi\) | |||||||
\(354\) | 36640.0 | 0.0155399 | ||||||||
\(355\) | −1.29480e6 | −0.545295 | ||||||||
\(356\) | 4.71360e6 | 1.97119 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.46928e6 | −0.605894 | ||||||||
\(359\) | 4.05576e6 | 1.66087 | 0.830436 | − | 0.557114i | \(-0.188091\pi\) | ||||
0.830436 | + | 0.557114i | \(0.188091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −73599.0 | −0.0297238 | ||||||||
\(362\) | −5.08038e6 | −2.03763 | ||||||||
\(363\) | −44158.0 | −0.0175891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 121150. | 0.0475983 | ||||||||
\(366\) | 99904.0 | 0.0389834 | ||||||||
\(367\) | 4.90628e6 | 1.90146 | 0.950731 | − | 0.310018i | \(-0.100335\pi\) | ||||
0.950731 | + | 0.310018i | \(0.100335\pi\) | |||||||
\(368\) | 1.69370e6 | 0.651952 | ||||||||
\(369\) | −418176. | −0.159880 | ||||||||
\(370\) | −2.20360e6 | −0.836813 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 38144.0 | 0.0142912 | ||||||||
\(373\) | −3.45336e6 | −1.28520 | −0.642599 | − | 0.766202i | \(-0.722144\pi\) | ||||
−0.642599 | + | 0.766202i | \(0.722144\pi\) | |||||||
\(374\) | −5.93249e6 | −2.19310 | ||||||||
\(375\) | 15625.0 | 0.00573775 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.83046e6 | −1.75039 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.23466e6 | −1.51433 | −0.757165 | − | 0.653224i | \(-0.773416\pi\) | ||||
−0.757165 | + | 0.653224i | \(0.773416\pi\) | |||||||
\(380\) | −1.24000e6 | −0.440517 | ||||||||
\(381\) | −330692. | −0.116711 | ||||||||
\(382\) | 1.81290e6 | 0.635648 | ||||||||
\(383\) | 1.86460e6 | 0.649516 | 0.324758 | − | 0.945797i | \(-0.394717\pi\) | ||||
0.324758 | + | 0.945797i | \(0.394717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −371808. | −0.127014 | ||||||||
\(387\) | 2.61699e6 | 0.888228 | ||||||||
\(388\) | 266976. | 0.0900312 | ||||||||
\(389\) | −4.81502e6 | −1.61333 | −0.806666 | − | 0.591008i | \(-0.798730\pi\) | ||||
−0.806666 | + | 0.591008i | \(0.798730\pi\) | |||||||
\(390\) | −193800. | −0.0645197 | ||||||||
\(391\) | 2.70760e6 | 0.895658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 43982.0 | 0.0143646 | ||||||||
\(394\) | −1.63978e6 | −0.532162 | ||||||||
\(395\) | −1.56912e6 | −0.506017 | ||||||||
\(396\) | 3.50803e6 | 1.12415 | ||||||||
\(397\) | −1.21376e6 | −0.386505 | −0.193253 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193253 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(398\) | −7.62416e6 | −2.41259 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −640000. | −0.200000 | ||||||||
\(401\) | 5.90442e6 | 1.83365 | 0.916824 | − | 0.399291i | \(-0.130744\pi\) | ||||
0.916824 | + | 0.399291i | \(0.130744\pi\) | |||||||
\(402\) | −126784. | −0.0391291 | ||||||||
\(403\) | −1.15505e6 | −0.354272 | ||||||||
\(404\) | 380096. | 0.115862 | ||||||||
\(405\) | −1.45802e6 | −0.441700 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.99115e6 | 1.49353 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.84289e6 | −1.43152 | −0.715758 | − | 0.698348i | \(-0.753919\pi\) | ||||
−0.715758 | + | 0.698348i | \(0.753919\pi\) | |||||||
\(410\) | 345600. | 0.101535 | ||||||||
\(411\) | 99748.0 | 0.0291273 | ||||||||
\(412\) | 4.23805e6 | 1.23005 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.20214e6 | −0.918206 | ||||||||
\(415\) | −591100. | −0.168477 | ||||||||
\(416\) | 7.93805e6 | 2.24895 | ||||||||
\(417\) | 258930. | 0.0729193 | ||||||||
\(418\) | 5.61720e6 | 1.57246 | ||||||||
\(419\) | −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 | \(0.358080\pi\) | |||||||
\(422\) | 1.78818e6 | 0.488800 | ||||||||
\(423\) | 6.34935e6 | 1.72536 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.02312e6 | −0.274762 | ||||||||
\(426\) | 414336. | 0.110619 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.37894e6 | 1.15547 | ||||||||
\(429\) | 438957. | 0.115154 | ||||||||
\(430\) | −2.16280e6 | −0.564086 | ||||||||
\(431\) | −1.87703e6 | −0.486719 | −0.243360 | − | 0.969936i | \(-0.578250\pi\) | ||||
−0.243360 | + | 0.969936i | \(0.578250\pi\) | |||||||
\(432\) | −496640. | −0.128036 | ||||||||
\(433\) | −3.20357e6 | −0.821134 | −0.410567 | − | 0.911830i | \(-0.634669\pi\) | ||||
−0.410567 | + | 0.911830i | \(0.634669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −124625. | −0.0315778 | ||||||||
\(436\) | 3.50352e6 | 0.882650 | ||||||||
\(437\) | −2.56370e6 | −0.642190 | ||||||||
\(438\) | −38768.0 | −0.00965580 | ||||||||
\(439\) | 6.27209e6 | 1.55328 | 0.776642 | − | 0.629942i | \(-0.216921\pi\) | ||||
0.776642 | + | 0.629942i | \(0.216921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.26900e7 | 3.08963 | ||||||||
\(443\) | 724986. | 0.175517 | 0.0877587 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877587 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(444\) | 352576. | 0.0848780 | ||||||||
\(445\) | −3.68250e6 | −0.881541 | ||||||||
\(446\) | 8.11841e6 | 1.93256 | ||||||||
\(447\) | 498430. | 0.117987 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −875985. | −0.205060 | −0.102530 | − | 0.994730i | \(-0.532694\pi\) | ||||
−0.102530 | + | 0.994730i | \(0.532694\pi\) | |||||||
\(450\) | 1.21000e6 | 0.281679 | ||||||||
\(451\) | −782784. | −0.181218 | ||||||||
\(452\) | −6.42989e6 | −1.48033 | ||||||||
\(453\) | 245803. | 0.0562784 | ||||||||
\(454\) | 7.99838e6 | 1.82122 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −832668. | −0.186501 | −0.0932505 | − | 0.995643i | \(-0.529726\pi\) | ||||
−0.0932505 | + | 0.995643i | \(0.529726\pi\) | |||||||
\(458\) | −6.80896e6 | −1.51676 | ||||||||
\(459\) | −793945. | −0.175897 | ||||||||
\(460\) | 1.32320e6 | 0.291562 | ||||||||
\(461\) | −5.92115e6 | −1.29764 | −0.648820 | − | 0.760942i | \(-0.724737\pi\) | ||||
−0.648820 | + | 0.760942i | \(0.724737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 682776. | 0.148022 | 0.0740109 | − | 0.997257i | \(-0.476420\pi\) | ||||
0.0740109 | + | 0.997257i | \(0.476420\pi\) | |||||||
\(464\) | 5.10464e6 | 1.10070 | ||||||||
\(465\) | −29800.0 | −0.00639122 | ||||||||
\(466\) | −8.74157e6 | −1.86477 | ||||||||
\(467\) | 5.41667e6 | 1.14932 | 0.574659 | − | 0.818393i | \(-0.305135\pi\) | ||||
0.574659 | + | 0.818393i | \(0.305135\pi\) | |||||||
\(468\) | −7.50394e6 | −1.58371 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.24740e6 | −1.09572 | ||||||||
\(471\) | −85478.0 | −0.0177542 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.89874e6 | 1.00677 | ||||||||
\(474\) | 502120. | 0.102651 | ||||||||
\(475\) | 968750. | 0.197005 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.27651e6 | −1.26306 | ||||||||
\(478\) | −6.12724e6 | −1.22658 | ||||||||
\(479\) | −1.98599e6 | −0.395493 | −0.197746 | − | 0.980253i | \(-0.563362\pi\) | ||||
−0.197746 | + | 0.980253i | \(0.563362\pi\) | |||||||
\(480\) | 204800. | 0.0405720 | ||||||||
\(481\) | −1.06764e7 | −2.10409 | ||||||||
\(482\) | −9.68750e6 | −1.89930 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.41306e6 | 0.274186 | ||||||||
\(485\) | −208575. | −0.0402632 | ||||||||
\(486\) | 1.40941e6 | 0.270674 | ||||||||
\(487\) | −1.06974e6 | −0.204388 | −0.102194 | − | 0.994764i | \(-0.532586\pi\) | ||||
−0.102194 | + | 0.994764i | \(0.532586\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −193026. | −0.0365043 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.59246e6 | 0.859689 | 0.429844 | − | 0.902903i | \(-0.358568\pi\) | ||||
0.429844 | + | 0.902903i | \(0.358568\pi\) | |||||||
\(492\) | −55296.0 | −0.0102987 | ||||||||
\(493\) | 8.16045e6 | 1.51216 | ||||||||
\(494\) | −1.20156e7 | −2.21528 | ||||||||
\(495\) | −2.74065e6 | −0.502737 | ||||||||
\(496\) | 1.22061e6 | 0.222778 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 189152. | 0.0341773 | ||||||||
\(499\) | 1.96066e6 | 0.352492 | 0.176246 | − | 0.984346i | \(-0.443605\pi\) | ||||
0.176246 | + | 0.984346i | \(0.443605\pi\) | |||||||
\(500\) | −500000. | −0.0894427 | ||||||||
\(501\) | −157783. | −0.0280844 | ||||||||
\(502\) | 2.22610e6 | 0.394262 | ||||||||
\(503\) | −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 | ||||||||
\(506\) | −5.99410e6 | −1.04075 | ||||||||
\(507\) | −567668. | −0.0980787 | ||||||||
\(508\) | 1.05821e7 | 1.81934 | ||||||||
\(509\) | 1.45211e6 | 0.248431 | 0.124215 | − | 0.992255i | \(-0.460359\pi\) | ||||
0.124215 | + | 0.992255i | \(0.460359\pi\) | |||||||
\(510\) | 327400. | 0.0557382 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.38861e6 | −1.41421 | ||||||||
\(513\) | 751750. | 0.126119 | ||||||||
\(514\) | −2.82398e6 | −0.471470 | ||||||||
\(515\) | −3.31098e6 | −0.550095 | ||||||||
\(516\) | 346048. | 0.0572153 | ||||||||
\(517\) | 1.18854e7 | 1.95563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −265659. | −0.0432918 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.24240e6 | 0.684726 | 0.342363 | − | 0.939568i | \(-0.388773\pi\) | ||||
0.342363 | + | 0.939568i | \(0.388773\pi\) | |||||||
\(522\) | −9.65096e6 | −1.55022 | ||||||||
\(523\) | 7.56012e6 | 1.20858 | 0.604289 | − | 0.796765i | \(-0.293457\pi\) | ||||
0.604289 | + | 0.796765i | \(0.293457\pi\) | |||||||
\(524\) | −1.40742e6 | −0.223922 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.24648e7 | 1.96435 | ||||||||
\(527\) | 1.95130e6 | 0.306054 | ||||||||
\(528\) | −463872. | −0.0724125 | ||||||||
\(529\) | −3.70063e6 | −0.574958 | ||||||||
\(530\) | 5.18720e6 | 0.802127 | ||||||||
\(531\) | −1.10836e6 | −0.170586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.67443e6 | 0.255299 | ||||||||
\(534\) | 1.17840e6 | 0.178830 | ||||||||
\(535\) | −3.42105e6 | −0.516743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −183660. | −0.0274839 | ||||||||
\(538\) | −9.75704e6 | −1.45332 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −388000. | −0.0572595 | ||||||||
\(541\) | 1.24065e6 | 0.182245 | 0.0911224 | − | 0.995840i | \(-0.470955\pi\) | ||||
0.0911224 | + | 0.995840i | \(0.470955\pi\) | |||||||
\(542\) | 3.24634e6 | 0.474674 | ||||||||
\(543\) | −635048. | −0.0924287 | ||||||||
\(544\) | −1.34103e7 | −1.94286 | ||||||||
\(545\) | −2.73712e6 | −0.394733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.85057e6 | −0.264446 | −0.132223 | − | 0.991220i | \(-0.542211\pi\) | ||||
−0.132223 | + | 0.991220i | \(0.542211\pi\) | |||||||
\(548\) | −3.19194e6 | −0.454049 | ||||||||
\(549\) | −3.02210e6 | −0.427935 | ||||||||
\(550\) | 2.26500e6 | 0.319272 | ||||||||
\(551\) | −7.72675e6 | −1.08422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.21954e6 | −0.722533 | ||||||||
\(555\) | −275450. | −0.0379586 | ||||||||
\(556\) | −8.28576e6 | −1.13670 | ||||||||
\(557\) | 7.77555e6 | 1.06192 | 0.530962 | − | 0.847396i | \(-0.321831\pi\) | ||||
0.530962 | + | 0.847396i | \(0.321831\pi\) | |||||||
\(558\) | −2.30771e6 | −0.313759 | ||||||||
\(559\) | −1.04788e7 | −1.41834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −741561. | −0.0994809 | ||||||||
\(562\) | −950616. | −0.126959 | ||||||||
\(563\) | −8.37716e6 | −1.11385 | −0.556924 | − | 0.830564i | \(-0.688018\pi\) | ||||
−0.556924 | + | 0.830564i | \(0.688018\pi\) | |||||||
\(564\) | 839584. | 0.111139 | ||||||||
\(565\) | 5.02335e6 | 0.662022 | ||||||||
\(566\) | 1.19041e7 | 1.56191 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.15591e6 | −0.797098 | −0.398549 | − | 0.917147i | \(-0.630486\pi\) | ||||
−0.398549 | + | 0.917147i | \(0.630486\pi\) | |||||||
\(570\) | −310000. | −0.0399645 | ||||||||
\(571\) | 7.21513e6 | 0.926092 | 0.463046 | − | 0.886334i | \(-0.346757\pi\) | ||||
0.463046 | + | 0.886334i | \(0.346757\pi\) | |||||||
\(572\) | −1.40466e7 | −1.79507 | ||||||||
\(573\) | 226613. | 0.0288336 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.03375e6 | −0.130390 | ||||||||
\(576\) | 7.92986e6 | 0.995885 | ||||||||
\(577\) | −1.36699e7 | −1.70933 | −0.854666 | − | 0.519177i | \(-0.826238\pi\) | ||||
−0.854666 | + | 0.519177i | \(0.826238\pi\) | |||||||
\(578\) | −1.00793e7 | −1.25490 | ||||||||
\(579\) | −46476.0 | −0.00576146 | ||||||||
\(580\) | 3.98800e6 | 0.492249 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 66744.0 | 0.00816779 | ||||||||
\(583\) | −1.17490e7 | −1.43163 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.86245e6 | 0.708255 | ||||||||
\(586\) | 1.51664e7 | 1.82448 | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 916000. | 0.108334 | ||||||||
\(591\) | −204972. | −0.0241394 | ||||||||
\(592\) | 1.12824e7 | 1.32312 | ||||||||
\(593\) | −9.80615e6 | −1.14515 | −0.572574 | − | 0.819853i | \(-0.694055\pi\) | ||||
−0.572574 | + | 0.819853i | \(0.694055\pi\) | |||||||
\(594\) | 1.75764e6 | 0.204392 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.59498e7 | −1.83924 | ||||||||
\(597\) | −953020. | −0.109438 | ||||||||
\(598\) | 1.28218e7 | 1.46621 | ||||||||
\(599\) | 8.26257e6 | 0.940911 | 0.470455 | − | 0.882424i | \(-0.344090\pi\) | ||||
0.470455 | + | 0.882424i | \(0.344090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.59492e6 | 0.405978 | 0.202989 | − | 0.979181i | \(-0.434934\pi\) | ||||
0.202989 | + | 0.979181i | \(0.434934\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.83522e6 | 0.429533 | ||||||||
\(604\) | −7.86570e6 | −0.877293 | ||||||||
\(605\) | −1.10395e6 | −0.122620 | ||||||||
\(606\) | 95024.0 | 0.0105112 | ||||||||
\(607\) | 1.32969e7 | 1.46480 | 0.732401 | − | 0.680873i | \(-0.238400\pi\) | ||||
0.732401 | + | 0.680873i | \(0.238400\pi\) | |||||||
\(608\) | 1.26976e7 | 1.39304 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.49760e6 | 0.271768 | ||||||||
\(611\) | −2.54237e7 | −2.75508 | ||||||||
\(612\) | 1.26769e7 | 1.36816 | ||||||||
\(613\) | 2.50327e6 | 0.269064 | 0.134532 | − | 0.990909i | \(-0.457047\pi\) | ||||
0.134532 | + | 0.990909i | \(0.457047\pi\) | |||||||
\(614\) | −6.57482e6 | −0.703823 | ||||||||
\(615\) | 43200.0 | 0.00460570 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.88254e6 | 0.199082 | 0.0995409 | − | 0.995033i | \(-0.468263\pi\) | ||||
0.0995409 | + | 0.995033i | \(0.468263\pi\) | |||||||
\(618\) | 1.05951e6 | 0.111592 | ||||||||
\(619\) | −8.21487e6 | −0.861736 | −0.430868 | − | 0.902415i | \(-0.641792\pi\) | ||||
−0.430868 | + | 0.902415i | \(0.641792\pi\) | |||||||
\(620\) | 953600. | 0.0996293 | ||||||||
\(621\) | −802190. | −0.0834734 | ||||||||
\(622\) | −1.67680e7 | −1.73782 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 992256. | 0.102015 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 3.15657e6 | 0.321943 | ||||||||
\(627\) | 702150. | 0.0713282 | ||||||||
\(628\) | 2.73530e6 | 0.276761 | ||||||||
\(629\) | 1.80365e7 | 1.81771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.61155e7 | 1.61128 | 0.805638 | − | 0.592408i | \(-0.201823\pi\) | ||||
0.805638 | + | 0.592408i | \(0.201823\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 223523. | 0.0221724 | ||||||||
\(634\) | −2.57138e6 | −0.254064 | ||||||||
\(635\) | −8.26730e6 | −0.813635 | ||||||||
\(636\) | −829952. | −0.0813599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.80656e7 | −1.75712 | ||||||||
\(639\) | −1.25337e7 | −1.21430 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.50544e6 | −0.817620 | −0.408810 | − | 0.912619i | \(-0.634056\pi\) | ||||
−0.408810 | + | 0.912619i | \(0.634056\pi\) | |||||||
\(642\) | 1.09474e6 | 0.104827 | ||||||||
\(643\) | 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 | ||||||||
\(646\) | 2.02988e7 | 1.91377 | ||||||||
\(647\) | −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 | ||||||||
\(650\) | −4.84500e6 | −0.449791 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.17683e6 | 0.569045 | ||||||||
\(653\) | 4.90587e6 | 0.450228 | 0.225114 | − | 0.974332i | \(-0.427725\pi\) | ||||
0.225114 | + | 0.974332i | \(0.427725\pi\) | |||||||
\(654\) | 875880. | 0.0800756 | ||||||||
\(655\) | 1.09955e6 | 0.100141 | ||||||||
\(656\) | −1.76947e6 | −0.160540 | ||||||||
\(657\) | 1.17273e6 | 0.105995 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.36367e7 | 1.22319 | 0.611597 | − | 0.791169i | \(-0.290527\pi\) | ||||
0.611597 | + | 0.791169i | \(0.290527\pi\) | |||||||
\(660\) | −362400. | −0.0323838 | ||||||||
\(661\) | 2.22345e6 | 0.197935 | 0.0989677 | − | 0.995091i | \(-0.468446\pi\) | ||||
0.0989677 | + | 0.995091i | \(0.468446\pi\) | |||||||
\(662\) | 1.78607e7 | 1.58399 | ||||||||
\(663\) | 1.58625e6 | 0.140149 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.13308e7 | −1.86347 | ||||||||
\(667\) | 8.24519e6 | 0.717606 | ||||||||
\(668\) | 5.04906e6 | 0.437793 | ||||||||
\(669\) | 1.01480e6 | 0.0876629 | ||||||||
\(670\) | −3.16960e6 | −0.272783 | ||||||||
\(671\) | −5.65706e6 | −0.485048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.88484e6 | 0.415731 | 0.207865 | − | 0.978157i | \(-0.433348\pi\) | ||||
0.207865 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(674\) | 2.92525e7 | 2.48035 | ||||||||
\(675\) | 303125. | 0.0256072 | ||||||||
\(676\) | 1.81654e7 | 1.52889 | ||||||||
\(677\) | 1.98785e7 | 1.66691 | 0.833453 | − | 0.552590i | \(-0.186360\pi\) | ||||
0.833453 | + | 0.552590i | \(0.186360\pi\) | |||||||
\(678\) | −1.60747e6 | −0.134298 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 999797. | 0.0826122 | ||||||||
\(682\) | −4.31981e6 | −0.355634 | ||||||||
\(683\) | 4.27870e6 | 0.350962 | 0.175481 | − | 0.984483i | \(-0.443852\pi\) | ||||
0.175481 | + | 0.984483i | \(0.443852\pi\) | |||||||
\(684\) | −1.20032e7 | −0.980972 | ||||||||
\(685\) | 2.49370e6 | 0.203057 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −851120. | −0.0688017 | ||||||||
\(688\) | 1.10735e7 | 0.891898 | ||||||||
\(689\) | 2.51320e7 | 2.01687 | ||||||||
\(690\) | 330800. | 0.0264510 | ||||||||
\(691\) | −9.48925e6 | −0.756026 | −0.378013 | − | 0.925800i | \(-0.623393\pi\) | ||||
−0.378013 | + | 0.925800i | \(0.623393\pi\) | |||||||
\(692\) | 8.50109e6 | 0.674853 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.51169e7 | 1.19142 | ||||||||
\(695\) | 6.47325e6 | 0.508347 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.82874e6 | −0.220552 | ||||||||
\(698\) | −2.15463e7 | −1.67392 | ||||||||
\(699\) | −1.09270e6 | −0.0845875 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.86385e6 | −0.450700 | −0.225350 | − | 0.974278i | \(-0.572353\pi\) | ||||
−0.225350 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(702\) | −3.75972e6 | −0.287947 | ||||||||
\(703\) | −1.70779e7 | −1.30331 | ||||||||
\(704\) | 1.48439e7 | 1.12880 | ||||||||
\(705\) | −655925. | −0.0497029 | ||||||||
\(706\) | −1.25974e7 | −0.951197 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −146560. | −0.0109883 | ||||||||
\(709\) | −2.66670e6 | −0.199232 | −0.0996161 | − | 0.995026i | \(-0.531761\pi\) | ||||
−0.0996161 | + | 0.995026i | \(0.531761\pi\) | |||||||
\(710\) | 1.03584e7 | 0.771164 | ||||||||
\(711\) | −1.51891e7 | −1.12683 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.97157e6 | 0.145241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.09739e7 | 0.802781 | ||||||||
\(716\) | 5.87712e6 | 0.428432 | ||||||||
\(717\) | −765905. | −0.0556387 | ||||||||
\(718\) | −3.24461e7 | −2.34883 | ||||||||
\(719\) | 4.46629e6 | 0.322199 | 0.161100 | − | 0.986938i | \(-0.448496\pi\) | ||||
0.161100 | + | 0.986938i | \(0.448496\pi\) | |||||||
\(720\) | −6.19520e6 | −0.445373 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 588792. | 0.0420358 | ||||||||
\(723\) | −1.21094e6 | −0.0861541 | ||||||||
\(724\) | 2.03215e7 | 1.44082 | ||||||||
\(725\) | −3.11562e6 | −0.220141 | ||||||||
\(726\) | 353264. | 0.0248747 | ||||||||
\(727\) | 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 | ||||||||
\(730\) | −969200. | −0.0673141 | ||||||||
\(731\) | 1.77025e7 | 1.22530 | ||||||||
\(732\) | −399616. | −0.0275655 | ||||||||
\(733\) | 4.39751e6 | 0.302306 | 0.151153 | − | 0.988510i | \(-0.451701\pi\) | ||||
0.151153 | + | 0.988510i | \(0.451701\pi\) | |||||||
\(734\) | −3.92503e7 | −2.68907 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.35496e7 | −0.922000 | ||||||||
\(737\) | 7.17914e6 | 0.486860 | ||||||||
\(738\) | 3.34541e6 | 0.226104 | ||||||||
\(739\) | 2.84036e7 | 1.91321 | 0.956603 | − | 0.291395i | \(-0.0941195\pi\) | ||||
0.956603 | + | 0.291395i | \(0.0941195\pi\) | |||||||
\(740\) | 8.81440e6 | 0.591716 | ||||||||
\(741\) | −1.50195e6 | −0.100487 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.96012e7 | −1.30260 | −0.651299 | − | 0.758821i | \(-0.725776\pi\) | ||||
−0.651299 | + | 0.758821i | \(0.725776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.24608e7 | 0.822533 | ||||||||
\(746\) | 2.76269e7 | 1.81755 | ||||||||
\(747\) | −5.72185e6 | −0.375176 | ||||||||
\(748\) | 2.37300e7 | 1.55075 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −125000. | −0.00811441 | ||||||||
\(751\) | −2.60344e6 | −0.168441 | −0.0842206 | − | 0.996447i | \(-0.526840\pi\) | ||||
−0.0842206 | + | 0.996447i | \(0.526840\pi\) | |||||||
\(752\) | 2.68667e7 | 1.73249 | ||||||||
\(753\) | 278262. | 0.0178841 | ||||||||
\(754\) | 3.86437e7 | 2.47543 | ||||||||
\(755\) | 6.14508e6 | 0.392337 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.98869e7 | −1.89558 | −0.947789 | − | 0.318899i | \(-0.896687\pi\) | ||||
−0.947789 | + | 0.318899i | \(0.896687\pi\) | |||||||
\(758\) | 3.38773e7 | 2.14159 | ||||||||
\(759\) | −749262. | −0.0472095 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.21470e7 | −0.760338 | −0.380169 | − | 0.924917i | \(-0.624134\pi\) | ||||
−0.380169 | + | 0.924917i | \(0.624134\pi\) | |||||||
\(762\) | 2.64554e6 | 0.165054 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.25162e6 | −0.449471 | ||||||||
\(765\) | −9.90385e6 | −0.611858 | ||||||||
\(766\) | −1.49168e7 | −0.918554 | ||||||||
\(767\) | 4.43802e6 | 0.272396 | ||||||||
\(768\) | −1.04858e6 | −0.0641500 | ||||||||
\(769\) | −4.53845e6 | −0.276753 | −0.138376 | − | 0.990380i | \(-0.544188\pi\) | ||||
−0.138376 | + | 0.990380i | \(0.544188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −352998. | −0.0213863 | ||||||||
\(772\) | 1.48723e6 | 0.0898122 | ||||||||
\(773\) | −1.93330e7 | −1.16372 | −0.581861 | − | 0.813288i | \(-0.697675\pi\) | ||||
−0.581861 | + | 0.813288i | \(0.697675\pi\) | |||||||
\(774\) | −2.09359e7 | −1.25614 | ||||||||
\(775\) | −745000. | −0.0445556 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.85201e7 | 2.28160 | ||||||||
\(779\) | 2.67840e6 | 0.158136 | ||||||||
\(780\) | 775200. | 0.0456223 | ||||||||
\(781\) | −2.34618e7 | −1.37636 | ||||||||
\(782\) | −2.16608e7 | −1.26665 | ||||||||
\(783\) | −2.41772e6 | −0.140930 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.13695e6 | −0.123771 | ||||||||
\(786\) | −351856. | −0.0203146 | ||||||||
\(787\) | −1.66392e7 | −0.957627 | −0.478814 | − | 0.877917i | \(-0.658933\pi\) | ||||
−0.478814 | + | 0.877917i | \(0.658933\pi\) | |||||||
\(788\) | 6.55910e6 | 0.376295 | ||||||||
\(789\) | 1.55809e6 | 0.0891048 | ||||||||
\(790\) | 1.25530e7 | 0.715616 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.21009e7 | 0.683335 | ||||||||
\(794\) | 9.71006e6 | 0.546601 | ||||||||
\(795\) | 648400. | 0.0363852 | ||||||||
\(796\) | 3.04966e7 | 1.70596 | ||||||||
\(797\) | −1.80409e7 | −1.00603 | −0.503017 | − | 0.864276i | \(-0.667777\pi\) | ||||
−0.503017 | + | 0.864276i | \(0.667777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.29500e7 | 2.38010 | ||||||||
\(800\) | 5.12000e6 | 0.282843 | ||||||||
\(801\) | −3.56466e7 | −1.96307 | ||||||||
\(802\) | −4.72353e7 | −2.59317 | ||||||||
\(803\) | 2.19524e6 | 0.120141 | ||||||||
\(804\) | 507136. | 0.0276684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.24038e6 | 0.501017 | ||||||||
\(807\) | −1.21963e6 | −0.0659241 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.33891e7 | 1.25644 | 0.628220 | − | 0.778036i | \(-0.283784\pi\) | ||||
0.628220 | + | 0.778036i | \(0.283784\pi\) | |||||||
\(810\) | 1.16642e7 | 0.624658 | ||||||||
\(811\) | 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 | ||||||||
\(814\) | −3.99292e7 | −2.11218 | ||||||||
\(815\) | −4.82565e6 | −0.254485 | ||||||||
\(816\) | −1.67629e6 | −0.0881299 | ||||||||
\(817\) | −1.67617e7 | −0.878543 | ||||||||
\(818\) | 3.87431e7 | 2.02447 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.38240e6 | −0.0717958 | ||||||||
\(821\) | −1.80745e7 | −0.935853 | −0.467926 | − | 0.883767i | \(-0.654999\pi\) | ||||
−0.467926 | + | 0.883767i | \(0.654999\pi\) | |||||||
\(822\) | −797984. | −0.0411922 | ||||||||
\(823\) | 1.17989e7 | 0.607216 | 0.303608 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303608 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 283125. | 0.0144825 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.57650e6 | 0.130999 | 0.0654993 | − | 0.997853i | \(-0.479136\pi\) | ||||
0.0654993 | + | 0.997853i | \(0.479136\pi\) | |||||||
\(828\) | 1.28086e7 | 0.649270 | ||||||||
\(829\) | 3.84340e7 | 1.94236 | 0.971178 | − | 0.238356i | \(-0.0766084\pi\) | ||||
0.971178 | + | 0.238356i | \(0.0766084\pi\) | |||||||
\(830\) | 4.72880e6 | 0.238263 | ||||||||
\(831\) | −652442. | −0.0327747 | ||||||||
\(832\) | −3.17522e7 | −1.59025 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.07144e6 | −0.103123 | ||||||||
\(835\) | −3.94458e6 | −0.195787 | ||||||||
\(836\) | −2.24688e7 | −1.11190 | ||||||||
\(837\) | −578120. | −0.0285236 | ||||||||
\(838\) | 2.16288e6 | 0.106395 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | −2.50918e7 | −1.21970 | ||||||||
\(843\) | −118827. | −0.00575899 | ||||||||
\(844\) | −7.15274e6 | −0.345634 | ||||||||
\(845\) | −1.41917e7 | −0.683743 | ||||||||
\(846\) | −5.07948e7 | −2.44002 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.65585e7 | −1.26827 | ||||||||
\(849\) | 1.48801e6 | 0.0708495 | ||||||||
\(850\) | 8.18500e6 | 0.388572 | ||||||||
\(851\) | 1.82238e7 | 0.862610 | ||||||||
\(852\) | −1.65734e6 | −0.0782193 | ||||||||
\(853\) | −7.92067e6 | −0.372726 | −0.186363 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186363 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.37750e6 | 0.438704 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.48983e7 | −0.692924 | −0.346462 | − | 0.938064i | \(-0.612617\pi\) | ||||
−0.346462 | + | 0.938064i | \(0.612617\pi\) | |||||||
\(858\) | −3.51166e6 | −0.162852 | ||||||||
\(859\) | 1.38740e7 | 0.641534 | 0.320767 | − | 0.947158i | \(-0.396059\pi\) | ||||
0.320767 | + | 0.947158i | \(0.396059\pi\) | |||||||
\(860\) | 8.65120e6 | 0.398869 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.50163e7 | 0.688325 | ||||||||
\(863\) | 1.25500e7 | 0.573610 | 0.286805 | − | 0.957989i | \(-0.407407\pi\) | ||||
0.286805 | + | 0.957989i | \(0.407407\pi\) | |||||||
\(864\) | 3.97312e6 | 0.181070 | ||||||||
\(865\) | −6.64147e6 | −0.301804 | ||||||||
\(866\) | 2.56285e7 | 1.16126 | ||||||||
\(867\) | −1.25991e6 | −0.0569236 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.84325e7 | −1.27722 | ||||||||
\(870\) | 997000. | 0.0446578 | ||||||||
\(871\) | −1.53567e7 | −0.685887 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.01901e6 | −0.0896607 | ||||||||
\(874\) | 2.05096e7 | 0.908194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 155072. | 0.00682768 | ||||||||
\(877\) | −2.86002e7 | −1.25565 | −0.627827 | − | 0.778353i | \(-0.716056\pi\) | ||||
−0.627827 | + | 0.778353i | \(0.716056\pi\) | |||||||
\(878\) | −5.01767e7 | −2.19668 | ||||||||
\(879\) | 1.89580e6 | 0.0827600 | ||||||||
\(880\) | −1.15968e7 | −0.504814 | ||||||||
\(881\) | −4.09608e7 | −1.77799 | −0.888993 | − | 0.457922i | \(-0.848594\pi\) | ||||
−0.888993 | + | 0.457922i | \(0.848594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.30504e7 | 0.563279 | 0.281639 | − | 0.959520i | \(-0.409122\pi\) | ||||
0.281639 | + | 0.959520i | \(0.409122\pi\) | |||||||
\(884\) | −5.07601e7 | −2.18470 | ||||||||
\(885\) | 114500. | 0.00491414 | ||||||||
\(886\) | −5.79989e6 | −0.248219 | ||||||||
\(887\) | −2.53595e7 | −1.08226 | −0.541129 | − | 0.840939i | \(-0.682003\pi\) | ||||
−0.541129 | + | 0.840939i | \(0.682003\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.94600e7 | 1.24669 | ||||||||
\(891\) | −2.64194e7 | −1.11488 | ||||||||
\(892\) | −3.24736e7 | −1.36653 | ||||||||
\(893\) | −4.06674e7 | −1.70654 | ||||||||
\(894\) | −3.98744e6 | −0.166859 | ||||||||
\(895\) | −4.59150e6 | −0.191601 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.60273e6 | 0.0665087 | ||||||||
\(898\) | 7.00788e6 | 0.289999 | ||||||||
\(899\) | 5.94212e6 | 0.245212 | ||||||||
\(900\) | −4.84000e6 | −0.199177 | ||||||||
\(901\) | −4.24572e7 | −1.74237 | ||||||||
\(902\) | 6.26227e6 | 0.256281 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.58762e7 | −0.644355 | ||||||||
\(906\) | −1.96642e6 | −0.0795897 | ||||||||
\(907\) | 1.98595e7 | 0.801585 | 0.400793 | − | 0.916169i | \(-0.368735\pi\) | ||||
0.400793 | + | 0.916169i | \(0.368735\pi\) | |||||||
\(908\) | −3.19935e7 | −1.28780 | ||||||||
\(909\) | −2.87448e6 | −0.115385 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.99344e7 | −0.795808 | −0.397904 | − | 0.917427i | \(-0.630262\pi\) | ||||
−0.397904 | + | 0.917427i | \(0.630262\pi\) | |||||||
\(912\) | 1.58720e6 | 0.0631894 | ||||||||
\(913\) | −1.07107e7 | −0.425248 | ||||||||
\(914\) | 6.66134e6 | 0.263752 | ||||||||
\(915\) | 312200. | 0.0123276 | ||||||||
\(916\) | 2.72358e7 | 1.07251 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.35156e6 | 0.248756 | ||||||||
\(919\) | −1.10695e7 | −0.432355 | −0.216178 | − | 0.976354i | \(-0.569359\pi\) | ||||
−0.216178 | + | 0.976354i | \(0.569359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −821853. | −0.0319260 | ||||||||
\(922\) | 4.73692e7 | 1.83514 | ||||||||
\(923\) | 5.01864e7 | 1.93902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.88625e6 | −0.264624 | ||||||||
\(926\) | −5.46221e6 | −0.209334 | ||||||||
\(927\) | −3.20502e7 | −1.22499 | ||||||||
\(928\) | −4.08371e7 | −1.55663 | ||||||||
\(929\) | 3.25682e7 | 1.23810 | 0.619048 | − | 0.785353i | \(-0.287519\pi\) | ||||
0.619048 | + | 0.785353i | \(0.287519\pi\) | |||||||
\(930\) | 238400. | 0.00903855 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.49663e7 | 1.31859 | ||||||||
\(933\) | −2.09600e6 | −0.0788291 | ||||||||
\(934\) | −4.33334e7 | −1.62538 | ||||||||
\(935\) | −1.85390e7 | −0.693518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.15690e7 | −1.17466 | −0.587329 | − | 0.809348i | \(-0.699821\pi\) | ||||
−0.587329 | + | 0.809348i | \(0.699821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 394571. | 0.0146036 | ||||||||
\(940\) | 2.09896e7 | 0.774791 | ||||||||
\(941\) | 3.67997e7 | 1.35479 | 0.677393 | − | 0.735622i | \(-0.263110\pi\) | ||||
0.677393 | + | 0.735622i | \(0.263110\pi\) | |||||||
\(942\) | 683824. | 0.0251083 | ||||||||
\(943\) | −2.85811e6 | −0.104665 | ||||||||
\(944\) | −4.68992e6 | −0.171291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.91899e7 | −1.42379 | ||||||||
\(947\) | 1.88453e7 | 0.682853 | 0.341426 | − | 0.939909i | \(-0.389090\pi\) | ||||
0.341426 | + | 0.939909i | \(0.389090\pi\) | |||||||
\(948\) | −2.00848e6 | −0.0725850 | ||||||||
\(949\) | −4.69577e6 | −0.169255 | ||||||||
\(950\) | −7.75000e6 | −0.278607 | ||||||||
\(951\) | −321422. | −0.0115246 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.25120e7 | −0.446265 | −0.223133 | − | 0.974788i | \(-0.571628\pi\) | ||||
−0.223133 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(954\) | 5.02121e7 | 1.78623 | ||||||||
\(955\) | 5.66532e6 | 0.201009 | ||||||||
\(956\) | 2.45090e7 | 0.867322 | ||||||||
\(957\) | −2.25820e6 | −0.0797046 | ||||||||
\(958\) | 1.58879e7 | 0.559311 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −819200. | −0.0286888 | ||||||||
\(961\) | −2.72083e7 | −0.950370 | ||||||||
\(962\) | 8.54115e7 | 2.97563 | ||||||||
\(963\) | −3.31158e7 | −1.15072 | ||||||||
\(964\) | 3.87500e7 | 1.34301 | ||||||||
\(965\) | −1.16190e6 | −0.0401652 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.42344e7 | −1.17733 | −0.588663 | − | 0.808379i | \(-0.700346\pi\) | ||||
−0.588663 | + | 0.808379i | \(0.700346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.53735e6 | 0.0868102 | ||||||||
\(970\) | 1.66860e6 | 0.0569407 | ||||||||
\(971\) | 2.62027e7 | 0.891864 | 0.445932 | − | 0.895067i | \(-0.352872\pi\) | ||||
0.445932 | + | 0.895067i | \(0.352872\pi\) | |||||||
\(972\) | −5.63763e6 | −0.191395 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.55790e6 | 0.289048 | ||||||||
\(975\) | −605625. | −0.0204029 | ||||||||
\(976\) | −1.27877e7 | −0.429703 | ||||||||
\(977\) | −8.01114e6 | −0.268508 | −0.134254 | − | 0.990947i | \(-0.542864\pi\) | ||||
−0.134254 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(978\) | 1.54421e6 | 0.0516248 | ||||||||
\(979\) | −6.67269e7 | −2.22507 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.64954e7 | −0.879017 | ||||||||
\(982\) | −3.67397e7 | −1.21578 | ||||||||
\(983\) | 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 | ||||||||
\(986\) | −6.52836e7 | −2.13851 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.80624e7 | 1.56644 | ||||||||
\(989\) | 1.78864e7 | 0.581475 | ||||||||
\(990\) | 2.19252e7 | 0.710977 | ||||||||
\(991\) | −3.75828e7 | −1.21564 | −0.607821 | − | 0.794074i | \(-0.707956\pi\) | ||||
−0.607821 | + | 0.794074i | \(0.707956\pi\) | |||||||
\(992\) | −9.76486e6 | −0.315055 | ||||||||
\(993\) | 2.23259e6 | 0.0718514 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.38255e7 | −0.762929 | ||||||||
\(996\) | −756608. | −0.0241670 | ||||||||
\(997\) | −2.22066e7 | −0.707529 | −0.353765 | − | 0.935334i | \(-0.615099\pi\) | ||||
−0.353765 | + | 0.935334i | \(0.615099\pi\) | |||||||
\(998\) | −1.56852e7 | −0.498500 | ||||||||
\(999\) | −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 | 245.6.a.a.1.1 | 1 | ||
7.6 | odd | 2 | 35.6.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 315.6.a.a.1.1 | 1 | |||
28.27 | even | 2 | 560.6.a.c.1.1 | 1 | |||
35.13 | even | 4 | 175.6.b.b.99.2 | 2 | |||
35.27 | even | 4 | 175.6.b.b.99.1 | 2 | |||
35.34 | odd | 2 | 175.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
175.6.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
175.6.b.b.99.1 | 2 | 35.27 | even | 4 | |||
175.6.b.b.99.2 | 2 | 35.13 | even | 4 | |||
245.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
315.6.a.a.1.1 | 1 | 21.20 | even | 2 | |||
560.6.a.c.1.1 | 1 | 28.27 | even | 2 |