Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,4,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1815.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(107.088466660\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.70156 | 1.30870 | 0.654350 | − | 0.756192i | \(-0.272942\pi\) | ||||
0.654350 | + | 0.756192i | \(0.272942\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 5.70156 | 0.712695 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 11.1047 | 0.755578 | ||||||||
\(7\) | −9.10469 | −0.491607 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(8\) | −8.50781 | −0.375996 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 18.5078 | 0.585268 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 17.1047 | 0.411475 | ||||||||
\(13\) | 20.2984 | 0.433060 | 0.216530 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216530 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(14\) | −33.7016 | −0.643366 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −77.1047 | −1.20476 | ||||||||
\(17\) | −61.8062 | −0.881777 | −0.440889 | − | 0.897562i | \(-0.645337\pi\) | ||||
−0.440889 | + | 0.897562i | \(0.645337\pi\) | |||||||
\(18\) | 33.3141 | 0.436233 | ||||||||
\(19\) | −8.68594 | −0.104879 | −0.0524393 | − | 0.998624i | \(-0.516700\pi\) | ||||
−0.0524393 | + | 0.998624i | \(0.516700\pi\) | |||||||
\(20\) | 28.5078 | 0.318727 | ||||||||
\(21\) | −27.3141 | −0.283829 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −127.748 | −1.15815 | −0.579074 | − | 0.815275i | \(-0.696586\pi\) | ||||
−0.579074 | + | 0.815275i | \(0.696586\pi\) | |||||||
\(24\) | −25.5234 | −0.217081 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 75.1359 | 0.566745 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −51.9109 | −0.350366 | ||||||||
\(29\) | −85.9109 | −0.550112 | −0.275056 | − | 0.961428i | \(-0.588696\pi\) | ||||
−0.275056 | + | 0.961428i | \(0.588696\pi\) | |||||||
\(30\) | 55.5234 | 0.337905 | ||||||||
\(31\) | −158.733 | −0.919653 | −0.459827 | − | 0.888009i | \(-0.652088\pi\) | ||||
−0.459827 | + | 0.888009i | \(0.652088\pi\) | |||||||
\(32\) | −217.345 | −1.20067 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −228.780 | −1.15398 | ||||||||
\(35\) | −45.5234 | −0.219853 | ||||||||
\(36\) | 51.3141 | 0.237565 | ||||||||
\(37\) | 138.423 | 0.615045 | 0.307523 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(38\) | −32.1515 | −0.137254 | ||||||||
\(39\) | 60.8953 | 0.250027 | ||||||||
\(40\) | −42.5391 | −0.168150 | ||||||||
\(41\) | 28.2094 | 0.107453 | 0.0537264 | − | 0.998556i | \(-0.482890\pi\) | ||||
0.0537264 | + | 0.998556i | \(0.482890\pi\) | |||||||
\(42\) | −101.105 | −0.371447 | ||||||||
\(43\) | 265.884 | 0.942953 | 0.471477 | − | 0.881879i | \(-0.343721\pi\) | ||||
0.471477 | + | 0.881879i | \(0.343721\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −472.869 | −1.51567 | ||||||||
\(47\) | −515.602 | −1.60017 | −0.800087 | − | 0.599883i | \(-0.795214\pi\) | ||||
−0.800087 | + | 0.599883i | \(0.795214\pi\) | |||||||
\(48\) | −231.314 | −0.695569 | ||||||||
\(49\) | −260.105 | −0.758323 | ||||||||
\(50\) | 92.5391 | 0.261740 | ||||||||
\(51\) | −185.419 | −0.509094 | ||||||||
\(52\) | 115.733 | 0.308639 | ||||||||
\(53\) | −466.702 | −1.20955 | −0.604777 | − | 0.796395i | \(-0.706738\pi\) | ||||
−0.604777 | + | 0.796395i | \(0.706738\pi\) | |||||||
\(54\) | 99.9422 | 0.251859 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 77.4609 | 0.184842 | ||||||||
\(57\) | −26.0578 | −0.0605516 | ||||||||
\(58\) | −318.005 | −0.719932 | ||||||||
\(59\) | 373.475 | 0.824107 | 0.412053 | − | 0.911160i | \(-0.364812\pi\) | ||||
0.412053 | + | 0.911160i | \(0.364812\pi\) | |||||||
\(60\) | 85.5234 | 0.184017 | ||||||||
\(61\) | 84.8172 | 0.178028 | 0.0890142 | − | 0.996030i | \(-0.471628\pi\) | ||||
0.0890142 | + | 0.996030i | \(0.471628\pi\) | |||||||
\(62\) | −587.559 | −1.20355 | ||||||||
\(63\) | −81.9422 | −0.163869 | ||||||||
\(64\) | −187.680 | −0.366562 | ||||||||
\(65\) | 101.492 | 0.193670 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.7657 | −0.161858 | −0.0809288 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809288 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(68\) | −352.392 | −0.628439 | ||||||||
\(69\) | −383.245 | −0.668657 | ||||||||
\(70\) | −168.508 | −0.287722 | ||||||||
\(71\) | −536.695 | −0.897099 | −0.448549 | − | 0.893758i | \(-0.648059\pi\) | ||||
−0.448549 | + | 0.893758i | \(0.648059\pi\) | |||||||
\(72\) | −76.5703 | −0.125332 | ||||||||
\(73\) | 322.450 | 0.516985 | 0.258493 | − | 0.966013i | \(-0.416774\pi\) | ||||
0.258493 | + | 0.966013i | \(0.416774\pi\) | |||||||
\(74\) | 512.383 | 0.804909 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | −49.5234 | −0.0747464 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 225.408 | 0.327210 | ||||||||
\(79\) | 265.592 | 0.378246 | 0.189123 | − | 0.981953i | \(-0.439435\pi\) | ||||
0.189123 | + | 0.981953i | \(0.439435\pi\) | |||||||
\(80\) | −385.523 | −0.538785 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 104.419 | 0.140623 | ||||||||
\(83\) | −520.758 | −0.688682 | −0.344341 | − | 0.938845i | \(-0.611898\pi\) | ||||
−0.344341 | + | 0.938845i | \(0.611898\pi\) | |||||||
\(84\) | −155.733 | −0.202284 | ||||||||
\(85\) | −309.031 | −0.394343 | ||||||||
\(86\) | 984.187 | 1.23404 | ||||||||
\(87\) | −257.733 | −0.317608 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −464.713 | −0.553477 | −0.276738 | − | 0.960945i | \(-0.589254\pi\) | ||||
−0.276738 | + | 0.960945i | \(0.589254\pi\) | |||||||
\(90\) | 166.570 | 0.195089 | ||||||||
\(91\) | −184.811 | −0.212895 | ||||||||
\(92\) | −728.366 | −0.825406 | ||||||||
\(93\) | −476.198 | −0.530962 | ||||||||
\(94\) | −1908.53 | −2.09415 | ||||||||
\(95\) | −43.4297 | −0.0469031 | ||||||||
\(96\) | −652.036 | −0.693210 | ||||||||
\(97\) | −204.481 | −0.214040 | −0.107020 | − | 0.994257i | \(-0.534131\pi\) | ||||
−0.107020 | + | 0.994257i | \(0.534131\pi\) | |||||||
\(98\) | −962.794 | −0.992417 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 142.539 | 0.142539 | ||||||||
\(101\) | 27.2516 | 0.0268479 | 0.0134239 | − | 0.999910i | \(-0.495727\pi\) | ||||
0.0134239 | + | 0.999910i | \(0.495727\pi\) | |||||||
\(102\) | −686.339 | −0.666252 | ||||||||
\(103\) | 1062.80 | 1.01671 | 0.508353 | − | 0.861149i | \(-0.330255\pi\) | ||||
0.508353 | + | 0.861149i | \(0.330255\pi\) | |||||||
\(104\) | −172.695 | −0.162828 | ||||||||
\(105\) | −136.570 | −0.126932 | ||||||||
\(106\) | −1727.52 | −1.58294 | ||||||||
\(107\) | 1702.96 | 1.53861 | 0.769306 | − | 0.638881i | \(-0.220602\pi\) | ||||
0.769306 | + | 0.638881i | \(0.220602\pi\) | |||||||
\(108\) | 153.942 | 0.137158 | ||||||||
\(109\) | 556.334 | 0.488873 | 0.244437 | − | 0.969665i | \(-0.421397\pi\) | ||||
0.244437 | + | 0.969665i | \(0.421397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 415.270 | 0.355096 | ||||||||
\(112\) | 702.014 | 0.592269 | ||||||||
\(113\) | −2088.31 | −1.73851 | −0.869256 | − | 0.494363i | \(-0.835401\pi\) | ||||
−0.869256 | + | 0.494363i | \(0.835401\pi\) | |||||||
\(114\) | −96.4546 | −0.0792439 | ||||||||
\(115\) | −638.742 | −0.517939 | ||||||||
\(116\) | −489.827 | −0.392063 | ||||||||
\(117\) | 182.686 | 0.144353 | ||||||||
\(118\) | 1382.44 | 1.07851 | ||||||||
\(119\) | 562.727 | 0.433488 | ||||||||
\(120\) | −127.617 | −0.0970817 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 313.956 | 0.232986 | ||||||||
\(123\) | 84.6281 | 0.0620379 | ||||||||
\(124\) | −905.025 | −0.655433 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −303.314 | −0.214455 | ||||||||
\(127\) | −2179.16 | −1.52259 | −0.761296 | − | 0.648405i | \(-0.775436\pi\) | ||||
−0.761296 | + | 0.648405i | \(0.775436\pi\) | |||||||
\(128\) | 1044.05 | 0.720955 | ||||||||
\(129\) | 797.653 | 0.544414 | ||||||||
\(130\) | 375.680 | 0.253456 | ||||||||
\(131\) | −1951.11 | −1.30129 | −0.650645 | − | 0.759382i | \(-0.725501\pi\) | ||||
−0.650645 | + | 0.759382i | \(0.725501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 79.0828 | 0.0515590 | ||||||||
\(134\) | −328.572 | −0.211823 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 525.836 | 0.331545 | ||||||||
\(137\) | −613.425 | −0.382543 | −0.191272 | − | 0.981537i | \(-0.561261\pi\) | ||||
−0.191272 | + | 0.981537i | \(0.561261\pi\) | |||||||
\(138\) | −1418.61 | −0.875071 | ||||||||
\(139\) | −2130.63 | −1.30013 | −0.650064 | − | 0.759880i | \(-0.725258\pi\) | ||||
−0.650064 | + | 0.759880i | \(0.725258\pi\) | |||||||
\(140\) | −259.555 | −0.156688 | ||||||||
\(141\) | −1546.80 | −0.923861 | ||||||||
\(142\) | −1986.61 | −1.17403 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −693.942 | −0.401587 | ||||||||
\(145\) | −429.555 | −0.246018 | ||||||||
\(146\) | 1193.57 | 0.676578 | ||||||||
\(147\) | −780.314 | −0.437818 | ||||||||
\(148\) | 789.230 | 0.438340 | ||||||||
\(149\) | −570.900 | −0.313892 | −0.156946 | − | 0.987607i | \(-0.550165\pi\) | ||||
−0.156946 | + | 0.987607i | \(0.550165\pi\) | |||||||
\(150\) | 277.617 | 0.151116 | ||||||||
\(151\) | 2154.78 | 1.16128 | 0.580641 | − | 0.814159i | \(-0.302802\pi\) | ||||
0.580641 | + | 0.814159i | \(0.302802\pi\) | |||||||
\(152\) | 73.8983 | 0.0394339 | ||||||||
\(153\) | −556.256 | −0.293926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −793.664 | −0.411281 | ||||||||
\(156\) | 347.198 | 0.178193 | ||||||||
\(157\) | −157.105 | −0.0798619 | −0.0399310 | − | 0.999202i | \(-0.512714\pi\) | ||||
−0.0399310 | + | 0.999202i | \(0.512714\pi\) | |||||||
\(158\) | 983.106 | 0.495011 | ||||||||
\(159\) | −1400.10 | −0.698337 | ||||||||
\(160\) | −1086.73 | −0.536958 | ||||||||
\(161\) | 1163.11 | 0.569353 | ||||||||
\(162\) | 299.827 | 0.145411 | ||||||||
\(163\) | 1736.66 | 0.834512 | 0.417256 | − | 0.908789i | \(-0.362992\pi\) | ||||
0.417256 | + | 0.908789i | \(0.362992\pi\) | |||||||
\(164\) | 160.837 | 0.0765811 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1927.62 | −0.901278 | ||||||||
\(167\) | −1466.55 | −0.679549 | −0.339775 | − | 0.940507i | \(-0.610351\pi\) | ||||
−0.339775 | + | 0.940507i | \(0.610351\pi\) | |||||||
\(168\) | 232.383 | 0.106719 | ||||||||
\(169\) | −1784.97 | −0.812459 | ||||||||
\(170\) | −1143.90 | −0.516076 | ||||||||
\(171\) | −78.1735 | −0.0349595 | ||||||||
\(172\) | 1515.96 | 0.672038 | ||||||||
\(173\) | −143.781 | −0.0631878 | −0.0315939 | − | 0.999501i | \(-0.510058\pi\) | ||||
−0.0315939 | + | 0.999501i | \(0.510058\pi\) | |||||||
\(174\) | −954.014 | −0.415653 | ||||||||
\(175\) | −227.617 | −0.0983214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1120.42 | 0.475798 | ||||||||
\(178\) | −1720.16 | −0.724335 | ||||||||
\(179\) | −1412.93 | −0.589984 | −0.294992 | − | 0.955500i | \(-0.595317\pi\) | ||||
−0.294992 | + | 0.955500i | \(0.595317\pi\) | |||||||
\(180\) | 256.570 | 0.106242 | ||||||||
\(181\) | −2239.25 | −0.919570 | −0.459785 | − | 0.888030i | \(-0.652073\pi\) | ||||
−0.459785 | + | 0.888030i | \(0.652073\pi\) | |||||||
\(182\) | −684.089 | −0.278616 | ||||||||
\(183\) | 254.452 | 0.102785 | ||||||||
\(184\) | 1086.86 | 0.435458 | ||||||||
\(185\) | 692.117 | 0.275057 | ||||||||
\(186\) | −1762.68 | −0.694870 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2939.73 | −1.14044 | ||||||||
\(189\) | −245.827 | −0.0946098 | ||||||||
\(190\) | −160.758 | −0.0613821 | ||||||||
\(191\) | 1745.94 | 0.661425 | 0.330712 | − | 0.943732i | \(-0.392711\pi\) | ||||
0.330712 | + | 0.943732i | \(0.392711\pi\) | |||||||
\(192\) | −563.039 | −0.211635 | ||||||||
\(193\) | −3985.04 | −1.48627 | −0.743134 | − | 0.669143i | \(-0.766662\pi\) | ||||
−0.743134 | + | 0.669143i | \(0.766662\pi\) | |||||||
\(194\) | −756.900 | −0.280115 | ||||||||
\(195\) | 304.477 | 0.111815 | ||||||||
\(196\) | −1483.00 | −0.540453 | ||||||||
\(197\) | 2262.00 | 0.818076 | 0.409038 | − | 0.912517i | \(-0.365864\pi\) | ||||
0.409038 | + | 0.912517i | \(0.365864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2340.15 | 0.833613 | 0.416806 | − | 0.908995i | \(-0.363149\pi\) | ||||
0.416806 | + | 0.908995i | \(0.363149\pi\) | |||||||
\(200\) | −212.695 | −0.0751991 | ||||||||
\(201\) | −266.297 | −0.0934485 | ||||||||
\(202\) | 100.873 | 0.0351358 | ||||||||
\(203\) | 782.192 | 0.270439 | ||||||||
\(204\) | −1057.18 | −0.362829 | ||||||||
\(205\) | 141.047 | 0.0480543 | ||||||||
\(206\) | 3934.01 | 1.33056 | ||||||||
\(207\) | −1149.74 | −0.386049 | ||||||||
\(208\) | −1565.10 | −0.521733 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −505.523 | −0.166116 | ||||||||
\(211\) | 1524.44 | 0.497377 | 0.248689 | − | 0.968583i | \(-0.420000\pi\) | ||||
0.248689 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(212\) | −2660.93 | −0.862044 | ||||||||
\(213\) | −1610.09 | −0.517940 | ||||||||
\(214\) | 6303.62 | 2.01358 | ||||||||
\(215\) | 1329.42 | 0.421701 | ||||||||
\(216\) | −229.711 | −0.0723604 | ||||||||
\(217\) | 1445.21 | 0.452108 | ||||||||
\(218\) | 2059.31 | 0.639788 | ||||||||
\(219\) | 967.350 | 0.298482 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1254.57 | −0.381862 | ||||||||
\(222\) | 1537.15 | 0.464715 | ||||||||
\(223\) | 5083.42 | 1.52651 | 0.763253 | − | 0.646100i | \(-0.223601\pi\) | ||||
0.763253 | + | 0.646100i | \(0.223601\pi\) | |||||||
\(224\) | 1978.86 | 0.590260 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −7730.01 | −2.27519 | ||||||||
\(227\) | 3910.66 | 1.14343 | 0.571717 | − | 0.820451i | \(-0.306277\pi\) | ||||
0.571717 | + | 0.820451i | \(0.306277\pi\) | |||||||
\(228\) | −148.570 | −0.0431549 | ||||||||
\(229\) | 2733.31 | 0.788743 | 0.394371 | − | 0.918951i | \(-0.370962\pi\) | ||||
0.394371 | + | 0.918951i | \(0.370962\pi\) | |||||||
\(230\) | −2364.34 | −0.677827 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 730.914 | 0.206840 | ||||||||
\(233\) | 4355.46 | 1.22462 | 0.612308 | − | 0.790619i | \(-0.290241\pi\) | ||||
0.612308 | + | 0.790619i | \(0.290241\pi\) | |||||||
\(234\) | 676.223 | 0.188915 | ||||||||
\(235\) | −2578.01 | −0.715620 | ||||||||
\(236\) | 2129.39 | 0.587337 | ||||||||
\(237\) | 796.777 | 0.218381 | ||||||||
\(238\) | 2082.97 | 0.567305 | ||||||||
\(239\) | 4731.48 | 1.28056 | 0.640281 | − | 0.768141i | \(-0.278818\pi\) | ||||
0.640281 | + | 0.768141i | \(0.278818\pi\) | |||||||
\(240\) | −1156.57 | −0.311068 | ||||||||
\(241\) | −1833.12 | −0.489966 | −0.244983 | − | 0.969527i | \(-0.578782\pi\) | ||||
−0.244983 | + | 0.969527i | \(0.578782\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 483.591 | 0.126880 | ||||||||
\(245\) | −1300.52 | −0.339132 | ||||||||
\(246\) | 313.256 | 0.0811890 | ||||||||
\(247\) | −176.311 | −0.0454186 | ||||||||
\(248\) | 1350.47 | 0.345786 | ||||||||
\(249\) | −1562.27 | −0.397611 | ||||||||
\(250\) | 462.695 | 0.117054 | ||||||||
\(251\) | −3168.31 | −0.796741 | −0.398370 | − | 0.917225i | \(-0.630424\pi\) | ||||
−0.398370 | + | 0.917225i | \(0.630424\pi\) | |||||||
\(252\) | −467.198 | −0.116789 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8066.29 | −1.99262 | ||||||||
\(255\) | −927.094 | −0.227674 | ||||||||
\(256\) | 5366.07 | 1.31008 | ||||||||
\(257\) | 5378.55 | 1.30547 | 0.652733 | − | 0.757588i | \(-0.273622\pi\) | ||||
0.652733 | + | 0.757588i | \(0.273622\pi\) | |||||||
\(258\) | 2952.56 | 0.712475 | ||||||||
\(259\) | −1260.30 | −0.302360 | ||||||||
\(260\) | 578.664 | 0.138028 | ||||||||
\(261\) | −773.198 | −0.183371 | ||||||||
\(262\) | −7222.14 | −1.70300 | ||||||||
\(263\) | −4584.03 | −1.07477 | −0.537383 | − | 0.843338i | \(-0.680587\pi\) | ||||
−0.537383 | + | 0.843338i | \(0.680587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2333.51 | −0.540929 | ||||||||
\(266\) | 292.730 | 0.0674752 | ||||||||
\(267\) | −1394.14 | −0.319550 | ||||||||
\(268\) | −506.103 | −0.115355 | ||||||||
\(269\) | −1741.03 | −0.394618 | −0.197309 | − | 0.980341i | \(-0.563220\pi\) | ||||
−0.197309 | + | 0.980341i | \(0.563220\pi\) | |||||||
\(270\) | 499.711 | 0.112635 | ||||||||
\(271\) | −1340.58 | −0.300495 | −0.150248 | − | 0.988648i | \(-0.548007\pi\) | ||||
−0.150248 | + | 0.988648i | \(0.548007\pi\) | |||||||
\(272\) | 4765.55 | 1.06233 | ||||||||
\(273\) | −554.433 | −0.122915 | ||||||||
\(274\) | −2270.63 | −0.500634 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2185.10 | −0.476548 | ||||||||
\(277\) | 5220.77 | 1.13244 | 0.566220 | − | 0.824254i | \(-0.308405\pi\) | ||||
0.566220 | + | 0.824254i | \(0.308405\pi\) | |||||||
\(278\) | −7886.66 | −1.70148 | ||||||||
\(279\) | −1428.60 | −0.306551 | ||||||||
\(280\) | 387.305 | 0.0826639 | ||||||||
\(281\) | −2494.68 | −0.529609 | −0.264804 | − | 0.964302i | \(-0.585307\pi\) | ||||
−0.264804 | + | 0.964302i | \(0.585307\pi\) | |||||||
\(282\) | −5725.59 | −1.20906 | ||||||||
\(283\) | −4329.43 | −0.909391 | −0.454696 | − | 0.890647i | \(-0.650252\pi\) | ||||
−0.454696 | + | 0.890647i | \(0.650252\pi\) | |||||||
\(284\) | −3060.00 | −0.639358 | ||||||||
\(285\) | −130.289 | −0.0270795 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −256.837 | −0.0528245 | ||||||||
\(288\) | −1956.11 | −0.400225 | ||||||||
\(289\) | −1092.99 | −0.222468 | ||||||||
\(290\) | −1590.02 | −0.321963 | ||||||||
\(291\) | −613.444 | −0.123576 | ||||||||
\(292\) | 1838.47 | 0.368453 | ||||||||
\(293\) | 4330.93 | 0.863534 | 0.431767 | − | 0.901985i | \(-0.357890\pi\) | ||||
0.431767 | + | 0.901985i | \(0.357890\pi\) | |||||||
\(294\) | −2888.38 | −0.572972 | ||||||||
\(295\) | 1867.37 | 0.368552 | ||||||||
\(296\) | −1177.68 | −0.231254 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2113.22 | −0.410791 | ||||||||
\(299\) | −2593.09 | −0.501547 | ||||||||
\(300\) | 427.617 | 0.0822950 | ||||||||
\(301\) | −2420.79 | −0.463562 | ||||||||
\(302\) | 7976.06 | 1.51977 | ||||||||
\(303\) | 81.7547 | 0.0155006 | ||||||||
\(304\) | 669.727 | 0.126353 | ||||||||
\(305\) | 424.086 | 0.0796167 | ||||||||
\(306\) | −2059.02 | −0.384661 | ||||||||
\(307\) | 2052.56 | 0.381582 | 0.190791 | − | 0.981631i | \(-0.438895\pi\) | ||||
0.190791 | + | 0.981631i | \(0.438895\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3188.39 | 0.586995 | ||||||||
\(310\) | −2937.80 | −0.538244 | ||||||||
\(311\) | 2627.76 | 0.479121 | 0.239561 | − | 0.970881i | \(-0.422997\pi\) | ||||
0.239561 | + | 0.970881i | \(0.422997\pi\) | |||||||
\(312\) | −518.086 | −0.0940091 | ||||||||
\(313\) | 6878.40 | 1.24214 | 0.621070 | − | 0.783755i | \(-0.286698\pi\) | ||||
0.621070 | + | 0.783755i | \(0.286698\pi\) | |||||||
\(314\) | −581.533 | −0.104515 | ||||||||
\(315\) | −409.711 | −0.0732844 | ||||||||
\(316\) | 1514.29 | 0.269574 | ||||||||
\(317\) | −3026.05 | −0.536151 | −0.268076 | − | 0.963398i | \(-0.586388\pi\) | ||||
−0.268076 | + | 0.963398i | \(0.586388\pi\) | |||||||
\(318\) | −5182.57 | −0.913913 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −938.398 | −0.163931 | ||||||||
\(321\) | 5108.88 | 0.888318 | ||||||||
\(322\) | 4305.32 | 0.745112 | ||||||||
\(323\) | 536.845 | 0.0924795 | ||||||||
\(324\) | 461.827 | 0.0791884 | ||||||||
\(325\) | 507.461 | 0.0866119 | ||||||||
\(326\) | 6428.34 | 1.09213 | ||||||||
\(327\) | 1669.00 | 0.282251 | ||||||||
\(328\) | −240.000 | −0.0404018 | ||||||||
\(329\) | 4694.39 | 0.786657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4326.50 | −0.718447 | −0.359223 | − | 0.933252i | \(-0.616958\pi\) | ||||
−0.359223 | + | 0.933252i | \(0.616958\pi\) | |||||||
\(332\) | −2969.13 | −0.490820 | ||||||||
\(333\) | 1245.81 | 0.205015 | ||||||||
\(334\) | −5428.51 | −0.889326 | ||||||||
\(335\) | −443.828 | −0.0723849 | ||||||||
\(336\) | 2106.04 | 0.341946 | ||||||||
\(337\) | 1759.36 | 0.284387 | 0.142194 | − | 0.989839i | \(-0.454584\pi\) | ||||
0.142194 | + | 0.989839i | \(0.454584\pi\) | |||||||
\(338\) | −6607.19 | −1.06327 | ||||||||
\(339\) | −6264.93 | −1.00373 | ||||||||
\(340\) | −1761.96 | −0.281046 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −289.364 | −0.0457515 | ||||||||
\(343\) | 5491.08 | 0.864403 | ||||||||
\(344\) | −2262.09 | −0.354546 | ||||||||
\(345\) | −1916.23 | −0.299032 | ||||||||
\(346\) | −532.215 | −0.0826939 | ||||||||
\(347\) | 11730.7 | 1.81481 | 0.907404 | − | 0.420260i | \(-0.138061\pi\) | ||||
0.907404 | + | 0.420260i | \(0.138061\pi\) | |||||||
\(348\) | −1469.48 | −0.226357 | ||||||||
\(349\) | 3152.38 | 0.483504 | 0.241752 | − | 0.970338i | \(-0.422278\pi\) | ||||
0.241752 | + | 0.970338i | \(0.422278\pi\) | |||||||
\(350\) | −842.539 | −0.128673 | ||||||||
\(351\) | 548.058 | 0.0833423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6881.03 | −1.03751 | −0.518754 | − | 0.854923i | \(-0.673604\pi\) | ||||
−0.518754 | + | 0.854923i | \(0.673604\pi\) | |||||||
\(354\) | 4147.32 | 0.622677 | ||||||||
\(355\) | −2683.48 | −0.401195 | ||||||||
\(356\) | −2649.59 | −0.394460 | ||||||||
\(357\) | 1688.18 | 0.250274 | ||||||||
\(358\) | −5230.04 | −0.772112 | ||||||||
\(359\) | 2858.96 | 0.420307 | 0.210154 | − | 0.977668i | \(-0.432604\pi\) | ||||
0.210154 | + | 0.977668i | \(0.432604\pi\) | |||||||
\(360\) | −382.851 | −0.0560501 | ||||||||
\(361\) | −6783.55 | −0.989001 | ||||||||
\(362\) | −8288.72 | −1.20344 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1053.71 | −0.151729 | ||||||||
\(365\) | 1612.25 | 0.231203 | ||||||||
\(366\) | 941.868 | 0.134514 | ||||||||
\(367\) | −10973.4 | −1.56079 | −0.780393 | − | 0.625289i | \(-0.784981\pi\) | ||||
−0.780393 | + | 0.625289i | \(0.784981\pi\) | |||||||
\(368\) | 9850.00 | 1.39529 | ||||||||
\(369\) | 253.884 | 0.0358176 | ||||||||
\(370\) | 2561.91 | 0.359966 | ||||||||
\(371\) | 4249.17 | 0.594625 | ||||||||
\(372\) | −2715.07 | −0.378414 | ||||||||
\(373\) | −10443.4 | −1.44970 | −0.724852 | − | 0.688905i | \(-0.758092\pi\) | ||||
−0.724852 | + | 0.688905i | \(0.758092\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 4386.64 | 0.601659 | ||||||||
\(377\) | −1743.86 | −0.238231 | ||||||||
\(378\) | −909.942 | −0.123816 | ||||||||
\(379\) | −7405.86 | −1.00373 | −0.501865 | − | 0.864946i | \(-0.667352\pi\) | ||||
−0.501865 | + | 0.864946i | \(0.667352\pi\) | |||||||
\(380\) | −247.617 | −0.0334276 | ||||||||
\(381\) | −6537.48 | −0.879069 | ||||||||
\(382\) | 6462.72 | 0.865607 | ||||||||
\(383\) | 14155.0 | 1.88848 | 0.944238 | − | 0.329264i | \(-0.106801\pi\) | ||||
0.944238 | + | 0.329264i | \(0.106801\pi\) | |||||||
\(384\) | 3132.16 | 0.416244 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14750.9 | −1.94508 | ||||||||
\(387\) | 2392.96 | 0.314318 | ||||||||
\(388\) | −1165.86 | −0.152546 | ||||||||
\(389\) | −13031.6 | −1.69853 | −0.849263 | − | 0.527970i | \(-0.822953\pi\) | ||||
−0.849263 | + | 0.527970i | \(0.822953\pi\) | |||||||
\(390\) | 1127.04 | 0.146333 | ||||||||
\(391\) | 7895.65 | 1.02123 | ||||||||
\(392\) | 2212.92 | 0.285126 | ||||||||
\(393\) | −5853.32 | −0.751300 | ||||||||
\(394\) | 8372.94 | 1.07062 | ||||||||
\(395\) | 1327.96 | 0.169157 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2281.02 | 0.288366 | 0.144183 | − | 0.989551i | \(-0.453945\pi\) | ||||
0.144183 | + | 0.989551i | \(0.453945\pi\) | |||||||
\(398\) | 8662.22 | 1.09095 | ||||||||
\(399\) | 237.248 | 0.0297676 | ||||||||
\(400\) | −1927.62 | −0.240952 | ||||||||
\(401\) | −13017.7 | −1.62114 | −0.810568 | − | 0.585645i | \(-0.800841\pi\) | ||||
−0.810568 | + | 0.585645i | \(0.800841\pi\) | |||||||
\(402\) | −985.715 | −0.122296 | ||||||||
\(403\) | −3222.03 | −0.398265 | ||||||||
\(404\) | 155.377 | 0.0191343 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 2895.33 | 0.353924 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1577.51 | 0.191417 | ||||||||
\(409\) | 3548.46 | 0.428998 | 0.214499 | − | 0.976724i | \(-0.431188\pi\) | ||||
0.214499 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(410\) | 522.094 | 0.0628887 | ||||||||
\(411\) | −1840.27 | −0.220861 | ||||||||
\(412\) | 6059.61 | 0.724601 | ||||||||
\(413\) | −3400.37 | −0.405136 | ||||||||
\(414\) | −4255.82 | −0.505222 | ||||||||
\(415\) | −2603.79 | −0.307988 | ||||||||
\(416\) | −4411.77 | −0.519964 | ||||||||
\(417\) | −6391.89 | −0.750629 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14801.3 | −1.72575 | −0.862876 | − | 0.505416i | \(-0.831339\pi\) | ||||
−0.862876 | + | 0.505416i | \(0.831339\pi\) | |||||||
\(420\) | −778.664 | −0.0904641 | ||||||||
\(421\) | 11542.8 | 1.33625 | 0.668123 | − | 0.744051i | \(-0.267098\pi\) | ||||
0.668123 | + | 0.744051i | \(0.267098\pi\) | |||||||
\(422\) | 5642.80 | 0.650918 | ||||||||
\(423\) | −4640.41 | −0.533392 | ||||||||
\(424\) | 3970.61 | 0.454787 | ||||||||
\(425\) | −1545.16 | −0.176355 | ||||||||
\(426\) | −5959.83 | −0.677828 | ||||||||
\(427\) | −772.234 | −0.0875200 | ||||||||
\(428\) | 9709.54 | 1.09656 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4920.94 | 0.551881 | ||||||||
\(431\) | 12712.6 | 1.42076 | 0.710378 | − | 0.703820i | \(-0.248524\pi\) | ||||
0.710378 | + | 0.703820i | \(0.248524\pi\) | |||||||
\(432\) | −2081.83 | −0.231856 | ||||||||
\(433\) | −16385.4 | −1.81855 | −0.909273 | − | 0.416200i | \(-0.863361\pi\) | ||||
−0.909273 | + | 0.416200i | \(0.863361\pi\) | |||||||
\(434\) | 5349.54 | 0.591674 | ||||||||
\(435\) | −1288.66 | −0.142038 | ||||||||
\(436\) | 3171.97 | 0.348418 | ||||||||
\(437\) | 1109.62 | 0.121465 | ||||||||
\(438\) | 3580.71 | 0.390623 | ||||||||
\(439\) | 6603.62 | 0.717935 | 0.358968 | − | 0.933350i | \(-0.383129\pi\) | ||||
0.358968 | + | 0.933350i | \(0.383129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2340.94 | −0.252774 | ||||||||
\(442\) | −4643.87 | −0.499743 | ||||||||
\(443\) | −11641.0 | −1.24849 | −0.624244 | − | 0.781230i | \(-0.714593\pi\) | ||||
−0.624244 | + | 0.781230i | \(0.714593\pi\) | |||||||
\(444\) | 2367.69 | 0.253076 | ||||||||
\(445\) | −2323.56 | −0.247522 | ||||||||
\(446\) | 18816.6 | 1.99774 | ||||||||
\(447\) | −1712.70 | −0.181226 | ||||||||
\(448\) | 1708.76 | 0.180204 | ||||||||
\(449\) | 13886.8 | 1.45960 | 0.729799 | − | 0.683662i | \(-0.239614\pi\) | ||||
0.729799 | + | 0.683662i | \(0.239614\pi\) | |||||||
\(450\) | 832.851 | 0.0872467 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11906.6 | −1.23903 | ||||||||
\(453\) | 6464.35 | 0.670467 | ||||||||
\(454\) | 14475.6 | 1.49641 | ||||||||
\(455\) | −924.055 | −0.0952096 | ||||||||
\(456\) | 221.695 | 0.0227672 | ||||||||
\(457\) | 3625.85 | 0.371138 | 0.185569 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185569 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(458\) | 10117.5 | 1.03223 | ||||||||
\(459\) | −1668.77 | −0.169698 | ||||||||
\(460\) | −3641.83 | −0.369133 | ||||||||
\(461\) | 18329.1 | 1.85178 | 0.925890 | − | 0.377794i | \(-0.123317\pi\) | ||||
0.925890 | + | 0.377794i | \(0.123317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10760.7 | 1.08011 | 0.540056 | − | 0.841629i | \(-0.318403\pi\) | ||||
0.540056 | + | 0.841629i | \(0.318403\pi\) | |||||||
\(464\) | 6624.14 | 0.662754 | ||||||||
\(465\) | −2380.99 | −0.237453 | ||||||||
\(466\) | 16122.0 | 1.60265 | ||||||||
\(467\) | −7964.29 | −0.789172 | −0.394586 | − | 0.918859i | \(-0.629112\pi\) | ||||
−0.394586 | + | 0.918859i | \(0.629112\pi\) | |||||||
\(468\) | 1041.60 | 0.102880 | ||||||||
\(469\) | 808.184 | 0.0795703 | ||||||||
\(470\) | −9542.66 | −0.936532 | ||||||||
\(471\) | −471.314 | −0.0461083 | ||||||||
\(472\) | −3177.45 | −0.309861 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2949.32 | 0.285795 | ||||||||
\(475\) | −217.149 | −0.0209757 | ||||||||
\(476\) | 3208.42 | 0.308945 | ||||||||
\(477\) | −4200.31 | −0.403185 | ||||||||
\(478\) | 17513.9 | 1.67587 | ||||||||
\(479\) | 822.463 | 0.0784536 | 0.0392268 | − | 0.999230i | \(-0.487511\pi\) | ||||
0.0392268 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(480\) | −3260.18 | −0.310013 | ||||||||
\(481\) | 2809.78 | 0.266351 | ||||||||
\(482\) | −6785.41 | −0.641218 | ||||||||
\(483\) | 3489.33 | 0.328716 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1022.41 | −0.0957218 | ||||||||
\(486\) | 899.480 | 0.0839531 | ||||||||
\(487\) | 6709.58 | 0.624312 | 0.312156 | − | 0.950031i | \(-0.398949\pi\) | ||||
0.312156 | + | 0.950031i | \(0.398949\pi\) | |||||||
\(488\) | −721.609 | −0.0669379 | ||||||||
\(489\) | 5209.97 | 0.481806 | ||||||||
\(490\) | −4813.97 | −0.443822 | ||||||||
\(491\) | 12689.3 | 1.16631 | 0.583156 | − | 0.812360i | \(-0.301818\pi\) | ||||
0.583156 | + | 0.812360i | \(0.301818\pi\) | |||||||
\(492\) | 482.512 | 0.0442141 | ||||||||
\(493\) | 5309.83 | 0.485077 | ||||||||
\(494\) | −652.626 | −0.0594394 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12239.0 | 1.10796 | ||||||||
\(497\) | 4886.44 | 0.441020 | ||||||||
\(498\) | −5782.85 | −0.520353 | ||||||||
\(499\) | −9810.79 | −0.880143 | −0.440072 | − | 0.897963i | \(-0.645047\pi\) | ||||
−0.440072 | + | 0.897963i | \(0.645047\pi\) | |||||||
\(500\) | 712.695 | 0.0637454 | ||||||||
\(501\) | −4399.64 | −0.392338 | ||||||||
\(502\) | −11727.7 | −1.04269 | ||||||||
\(503\) | −12865.7 | −1.14047 | −0.570233 | − | 0.821483i | \(-0.693147\pi\) | ||||
−0.570233 | + | 0.821483i | \(0.693147\pi\) | |||||||
\(504\) | 697.149 | 0.0616140 | ||||||||
\(505\) | 136.258 | 0.0120067 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5354.92 | −0.469074 | ||||||||
\(508\) | −12424.6 | −1.08514 | ||||||||
\(509\) | 2551.78 | 0.222211 | 0.111106 | − | 0.993809i | \(-0.464561\pi\) | ||||
0.111106 | + | 0.993809i | \(0.464561\pi\) | |||||||
\(510\) | −3431.70 | −0.297957 | ||||||||
\(511\) | −2935.81 | −0.254153 | ||||||||
\(512\) | 11510.4 | 0.993541 | ||||||||
\(513\) | −234.520 | −0.0201839 | ||||||||
\(514\) | 19909.0 | 1.70846 | ||||||||
\(515\) | 5313.99 | 0.454684 | ||||||||
\(516\) | 4547.87 | 0.388001 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4665.09 | −0.395699 | ||||||||
\(519\) | −431.344 | −0.0364815 | ||||||||
\(520\) | −863.476 | −0.0728191 | ||||||||
\(521\) | 9761.13 | 0.820812 | 0.410406 | − | 0.911903i | \(-0.365387\pi\) | ||||
0.410406 | + | 0.911903i | \(0.365387\pi\) | |||||||
\(522\) | −2862.04 | −0.239977 | ||||||||
\(523\) | 4548.79 | 0.380315 | 0.190157 | − | 0.981754i | \(-0.439100\pi\) | ||||
0.190157 | + | 0.981754i | \(0.439100\pi\) | |||||||
\(524\) | −11124.4 | −0.927423 | ||||||||
\(525\) | −682.851 | −0.0567659 | ||||||||
\(526\) | −16968.1 | −1.40655 | ||||||||
\(527\) | 9810.68 | 0.810930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4152.66 | 0.341305 | ||||||||
\(530\) | −8637.62 | −0.707914 | ||||||||
\(531\) | 3361.27 | 0.274702 | ||||||||
\(532\) | 450.895 | 0.0367458 | ||||||||
\(533\) | 572.606 | 0.0465334 | ||||||||
\(534\) | −5160.49 | −0.418195 | ||||||||
\(535\) | 8514.80 | 0.688088 | ||||||||
\(536\) | 755.202 | 0.0608577 | ||||||||
\(537\) | −4238.78 | −0.340628 | ||||||||
\(538\) | −6444.52 | −0.516437 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 769.711 | 0.0613390 | ||||||||
\(541\) | −9184.79 | −0.729917 | −0.364958 | − | 0.931024i | \(-0.618917\pi\) | ||||
−0.364958 | + | 0.931024i | \(0.618917\pi\) | |||||||
\(542\) | −4962.23 | −0.393258 | ||||||||
\(543\) | −6717.75 | −0.530914 | ||||||||
\(544\) | 13433.3 | 1.05873 | ||||||||
\(545\) | 2781.67 | 0.218631 | ||||||||
\(546\) | −2052.27 | −0.160859 | ||||||||
\(547\) | 20966.6 | 1.63888 | 0.819439 | − | 0.573167i | \(-0.194285\pi\) | ||||
0.819439 | + | 0.573167i | \(0.194285\pi\) | |||||||
\(548\) | −3497.48 | −0.272637 | ||||||||
\(549\) | 763.355 | 0.0593428 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 746.217 | 0.0576950 | ||||||||
\(552\) | 3260.58 | 0.251412 | ||||||||
\(553\) | −2418.13 | −0.185948 | ||||||||
\(554\) | 19325.0 | 1.48202 | ||||||||
\(555\) | 2076.35 | 0.158804 | ||||||||
\(556\) | −12147.9 | −0.926595 | ||||||||
\(557\) | −4422.49 | −0.336422 | −0.168211 | − | 0.985751i | \(-0.553799\pi\) | ||||
−0.168211 | + | 0.985751i | \(0.553799\pi\) | |||||||
\(558\) | −5288.03 | −0.401183 | ||||||||
\(559\) | 5397.04 | 0.408355 | ||||||||
\(560\) | 3510.07 | 0.264871 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9234.21 | −0.693099 | ||||||||
\(563\) | −6066.46 | −0.454122 | −0.227061 | − | 0.973881i | \(-0.572912\pi\) | ||||
−0.227061 | + | 0.973881i | \(0.572912\pi\) | |||||||
\(564\) | −8819.20 | −0.658432 | ||||||||
\(565\) | −10441.6 | −0.777486 | ||||||||
\(566\) | −16025.6 | −1.19012 | ||||||||
\(567\) | −737.480 | −0.0546230 | ||||||||
\(568\) | 4566.10 | 0.337305 | ||||||||
\(569\) | 17341.9 | 1.27770 | 0.638850 | − | 0.769331i | \(-0.279410\pi\) | ||||
0.638850 | + | 0.769331i | \(0.279410\pi\) | |||||||
\(570\) | −482.273 | −0.0354390 | ||||||||
\(571\) | 621.014 | 0.0455142 | 0.0227571 | − | 0.999741i | \(-0.492756\pi\) | ||||
0.0227571 | + | 0.999741i | \(0.492756\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5237.83 | 0.381874 | ||||||||
\(574\) | −950.700 | −0.0691314 | ||||||||
\(575\) | −3193.71 | −0.231629 | ||||||||
\(576\) | −1689.12 | −0.122187 | ||||||||
\(577\) | 4458.77 | 0.321700 | 0.160850 | − | 0.986979i | \(-0.448576\pi\) | ||||
0.160850 | + | 0.986979i | \(0.448576\pi\) | |||||||
\(578\) | −4045.76 | −0.291144 | ||||||||
\(579\) | −11955.1 | −0.858097 | ||||||||
\(580\) | −2449.13 | −0.175336 | ||||||||
\(581\) | 4741.34 | 0.338561 | ||||||||
\(582\) | −2270.70 | −0.161724 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2743.34 | −0.194384 | ||||||||
\(585\) | 913.430 | 0.0645567 | ||||||||
\(586\) | 16031.2 | 1.13011 | ||||||||
\(587\) | 1326.96 | 0.0933038 | 0.0466519 | − | 0.998911i | \(-0.485145\pi\) | ||||
0.0466519 | + | 0.998911i | \(0.485145\pi\) | |||||||
\(588\) | −4449.01 | −0.312031 | ||||||||
\(589\) | 1378.74 | 0.0964519 | ||||||||
\(590\) | 6912.20 | 0.482324 | ||||||||
\(591\) | 6786.01 | 0.472317 | ||||||||
\(592\) | −10673.1 | −0.740982 | ||||||||
\(593\) | −13296.2 | −0.920756 | −0.460378 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460378 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2813.63 | 0.193862 | ||||||||
\(596\) | −3255.02 | −0.223710 | ||||||||
\(597\) | 7020.45 | 0.481287 | ||||||||
\(598\) | −9598.50 | −0.656374 | ||||||||
\(599\) | −7420.72 | −0.506181 | −0.253091 | − | 0.967443i | \(-0.581447\pi\) | ||||
−0.253091 | + | 0.967443i | \(0.581447\pi\) | |||||||
\(600\) | −638.086 | −0.0434162 | ||||||||
\(601\) | 5189.31 | 0.352207 | 0.176104 | − | 0.984372i | \(-0.443651\pi\) | ||||
0.176104 | + | 0.984372i | \(0.443651\pi\) | |||||||
\(602\) | −8960.72 | −0.606664 | ||||||||
\(603\) | −798.891 | −0.0539525 | ||||||||
\(604\) | 12285.6 | 0.827641 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 302.620 | 0.0202857 | ||||||||
\(607\) | −26545.6 | −1.77505 | −0.887523 | − | 0.460763i | \(-0.847576\pi\) | ||||
−0.887523 | + | 0.460763i | \(0.847576\pi\) | |||||||
\(608\) | 1887.85 | 0.125925 | ||||||||
\(609\) | 2346.58 | 0.156138 | ||||||||
\(610\) | 1569.78 | 0.104194 | ||||||||
\(611\) | −10465.9 | −0.692971 | ||||||||
\(612\) | −3171.53 | −0.209480 | ||||||||
\(613\) | −26097.9 | −1.71955 | −0.859776 | − | 0.510671i | \(-0.829397\pi\) | ||||
−0.859776 | + | 0.510671i | \(0.829397\pi\) | |||||||
\(614\) | 7597.67 | 0.499377 | ||||||||
\(615\) | 423.141 | 0.0277442 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12275.1 | 0.800933 | 0.400466 | − | 0.916311i | \(-0.368848\pi\) | ||||
0.400466 | + | 0.916311i | \(0.368848\pi\) | |||||||
\(618\) | 11802.0 | 0.768200 | ||||||||
\(619\) | 6067.21 | 0.393961 | 0.196980 | − | 0.980407i | \(-0.436886\pi\) | ||||
0.196980 | + | 0.980407i | \(0.436886\pi\) | |||||||
\(620\) | −4525.12 | −0.293118 | ||||||||
\(621\) | −3449.21 | −0.222886 | ||||||||
\(622\) | 9726.82 | 0.627026 | ||||||||
\(623\) | 4231.06 | 0.272093 | ||||||||
\(624\) | −4695.31 | −0.301223 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 25460.8 | 1.62559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −895.742 | −0.0569172 | ||||||||
\(629\) | −8555.43 | −0.542333 | ||||||||
\(630\) | −1516.57 | −0.0959073 | ||||||||
\(631\) | 3074.16 | 0.193947 | 0.0969733 | − | 0.995287i | \(-0.469084\pi\) | ||||
0.0969733 | + | 0.995287i | \(0.469084\pi\) | |||||||
\(632\) | −2259.61 | −0.142219 | ||||||||
\(633\) | 4573.31 | 0.287161 | ||||||||
\(634\) | −11201.1 | −0.701661 | ||||||||
\(635\) | −10895.8 | −0.680924 | ||||||||
\(636\) | −7982.78 | −0.497701 | ||||||||
\(637\) | −5279.72 | −0.328399 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4830.26 | −0.299033 | ||||||||
\(640\) | 5220.27 | 0.322421 | ||||||||
\(641\) | −10825.9 | −0.667080 | −0.333540 | − | 0.942736i | \(-0.608243\pi\) | ||||
−0.333540 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(642\) | 18910.8 | 1.16254 | ||||||||
\(643\) | −117.142 | −0.00718450 | −0.00359225 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359225 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(644\) | 6631.54 | 0.405775 | ||||||||
\(645\) | 3988.27 | 0.243469 | ||||||||
\(646\) | 1987.17 | 0.121028 | ||||||||
\(647\) | 23811.6 | 1.44688 | 0.723439 | − | 0.690388i | \(-0.242560\pi\) | ||||
0.723439 | + | 0.690388i | \(0.242560\pi\) | |||||||
\(648\) | −689.133 | −0.0417773 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1878.40 | 0.113349 | ||||||||
\(651\) | 4335.64 | 0.261025 | ||||||||
\(652\) | 9901.65 | 0.594753 | ||||||||
\(653\) | −17773.3 | −1.06512 | −0.532560 | − | 0.846392i | \(-0.678770\pi\) | ||||
−0.532560 | + | 0.846392i | \(0.678770\pi\) | |||||||
\(654\) | 6177.92 | 0.369382 | ||||||||
\(655\) | −9755.53 | −0.581954 | ||||||||
\(656\) | −2175.07 | −0.129455 | ||||||||
\(657\) | 2902.05 | 0.172328 | ||||||||
\(658\) | 17376.6 | 1.02950 | ||||||||
\(659\) | −13015.6 | −0.769370 | −0.384685 | − | 0.923048i | \(-0.625690\pi\) | ||||
−0.384685 | + | 0.923048i | \(0.625690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15769.6 | 0.927935 | 0.463968 | − | 0.885852i | \(-0.346425\pi\) | ||||
0.463968 | + | 0.885852i | \(0.346425\pi\) | |||||||
\(662\) | −16014.8 | −0.940231 | ||||||||
\(663\) | −3763.71 | −0.220468 | ||||||||
\(664\) | 4430.51 | 0.258941 | ||||||||
\(665\) | 395.414 | 0.0230579 | ||||||||
\(666\) | 4611.45 | 0.268303 | ||||||||
\(667\) | 10975.0 | 0.637111 | ||||||||
\(668\) | −8361.60 | −0.484311 | ||||||||
\(669\) | 15250.3 | 0.881329 | ||||||||
\(670\) | −1642.86 | −0.0947301 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5936.58 | 0.340787 | ||||||||
\(673\) | −31519.1 | −1.80531 | −0.902653 | − | 0.430370i | \(-0.858383\pi\) | ||||
−0.902653 | + | 0.430370i | \(0.858383\pi\) | |||||||
\(674\) | 6512.38 | 0.372177 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −10177.1 | −0.579036 | ||||||||
\(677\) | 12418.6 | 0.705000 | 0.352500 | − | 0.935812i | \(-0.385332\pi\) | ||||
0.352500 | + | 0.935812i | \(0.385332\pi\) | |||||||
\(678\) | −23190.0 | −1.31358 | ||||||||
\(679\) | 1861.74 | 0.105224 | ||||||||
\(680\) | 2629.18 | 0.148271 | ||||||||
\(681\) | 11732.0 | 0.660162 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23543.0 | 1.31896 | 0.659478 | − | 0.751724i | \(-0.270777\pi\) | ||||
0.659478 | + | 0.751724i | \(0.270777\pi\) | |||||||
\(684\) | −445.711 | −0.0249155 | ||||||||
\(685\) | −3067.12 | −0.171079 | ||||||||
\(686\) | 20325.6 | 1.13124 | ||||||||
\(687\) | 8199.92 | 0.455381 | ||||||||
\(688\) | −20500.9 | −1.13603 | ||||||||
\(689\) | −9473.31 | −0.523809 | ||||||||
\(690\) | −7093.03 | −0.391344 | ||||||||
\(691\) | −9642.84 | −0.530870 | −0.265435 | − | 0.964129i | \(-0.585516\pi\) | ||||
−0.265435 | + | 0.964129i | \(0.585516\pi\) | |||||||
\(692\) | −819.778 | −0.0450336 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43422.0 | 2.37504 | ||||||||
\(695\) | −10653.2 | −0.581435 | ||||||||
\(696\) | 2192.74 | 0.119419 | ||||||||
\(697\) | −1743.52 | −0.0947494 | ||||||||
\(698\) | 11668.7 | 0.632762 | ||||||||
\(699\) | 13066.4 | 0.707032 | ||||||||
\(700\) | −1297.77 | −0.0700732 | ||||||||
\(701\) | 30593.3 | 1.64835 | 0.824176 | − | 0.566334i | \(-0.191639\pi\) | ||||
0.824176 | + | 0.566334i | \(0.191639\pi\) | |||||||
\(702\) | 2028.67 | 0.109070 | ||||||||
\(703\) | −1202.34 | −0.0645050 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7734.02 | −0.413163 | ||||||||
\(706\) | −25470.6 | −1.35779 | ||||||||
\(707\) | −248.117 | −0.0131986 | ||||||||
\(708\) | 6388.17 | 0.339099 | ||||||||
\(709\) | −30248.4 | −1.60226 | −0.801130 | − | 0.598491i | \(-0.795767\pi\) | ||||
−0.801130 | + | 0.598491i | \(0.795767\pi\) | |||||||
\(710\) | −9933.05 | −0.525044 | ||||||||
\(711\) | 2390.33 | 0.126082 | ||||||||
\(712\) | 3953.69 | 0.208105 | ||||||||
\(713\) | 20277.9 | 1.06509 | ||||||||
\(714\) | 6248.90 | 0.327534 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8055.90 | −0.420479 | ||||||||
\(717\) | 14194.4 | 0.739332 | ||||||||
\(718\) | 10582.6 | 0.550056 | ||||||||
\(719\) | 30471.8 | 1.58054 | 0.790269 | − | 0.612761i | \(-0.209941\pi\) | ||||
0.790269 | + | 0.612761i | \(0.209941\pi\) | |||||||
\(720\) | −3469.71 | −0.179595 | ||||||||
\(721\) | −9676.45 | −0.499819 | ||||||||
\(722\) | −25109.7 | −1.29430 | ||||||||
\(723\) | −5499.37 | −0.282882 | ||||||||
\(724\) | −12767.2 | −0.655373 | ||||||||
\(725\) | −2147.77 | −0.110022 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25149.9 | 1.28302 | 0.641511 | − | 0.767114i | \(-0.278308\pi\) | ||||
0.641511 | + | 0.767114i | \(0.278308\pi\) | |||||||
\(728\) | 1572.34 | 0.0800476 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5967.84 | 0.302575 | ||||||||
\(731\) | −16433.3 | −0.831475 | ||||||||
\(732\) | 1450.77 | 0.0732542 | ||||||||
\(733\) | −9974.73 | −0.502626 | −0.251313 | − | 0.967906i | \(-0.580862\pi\) | ||||
−0.251313 | + | 0.967906i | \(0.580862\pi\) | |||||||
\(734\) | −40618.8 | −2.04260 | ||||||||
\(735\) | −3901.57 | −0.195798 | ||||||||
\(736\) | 27765.5 | 1.39056 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 939.769 | 0.0468745 | ||||||||
\(739\) | −11579.9 | −0.576418 | −0.288209 | − | 0.957568i | \(-0.593060\pi\) | ||||
−0.288209 | + | 0.957568i | \(0.593060\pi\) | |||||||
\(740\) | 3946.15 | 0.196031 | ||||||||
\(741\) | −528.933 | −0.0262225 | ||||||||
\(742\) | 15728.6 | 0.778186 | ||||||||
\(743\) | −20323.7 | −1.00351 | −0.501753 | − | 0.865011i | \(-0.667311\pi\) | ||||
−0.501753 | + | 0.865011i | \(0.667311\pi\) | |||||||
\(744\) | 4051.41 | 0.199639 | ||||||||
\(745\) | −2854.50 | −0.140377 | ||||||||
\(746\) | −38656.9 | −1.89723 | ||||||||
\(747\) | −4686.82 | −0.229561 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15504.9 | −0.756392 | ||||||||
\(750\) | 1388.09 | 0.0675810 | ||||||||
\(751\) | 8023.94 | 0.389877 | 0.194939 | − | 0.980815i | \(-0.437549\pi\) | ||||
0.194939 | + | 0.980815i | \(0.437549\pi\) | |||||||
\(752\) | 39755.3 | 1.92783 | ||||||||
\(753\) | −9504.93 | −0.459998 | ||||||||
\(754\) | −6455.00 | −0.311773 | ||||||||
\(755\) | 10773.9 | 0.519342 | ||||||||
\(756\) | −1401.60 | −0.0674279 | ||||||||
\(757\) | 542.713 | 0.0260571 | 0.0130285 | − | 0.999915i | \(-0.495853\pi\) | ||||
0.0130285 | + | 0.999915i | \(0.495853\pi\) | |||||||
\(758\) | −27413.2 | −1.31358 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 369.492 | 0.0176354 | ||||||||
\(761\) | 16292.2 | 0.776073 | 0.388037 | − | 0.921644i | \(-0.373153\pi\) | ||||
0.388037 | + | 0.921644i | \(0.373153\pi\) | |||||||
\(762\) | −24198.9 | −1.15044 | ||||||||
\(763\) | −5065.25 | −0.240333 | ||||||||
\(764\) | 9954.61 | 0.471394 | ||||||||
\(765\) | −2781.28 | −0.131448 | ||||||||
\(766\) | 52395.6 | 2.47145 | ||||||||
\(767\) | 7580.96 | 0.356887 | ||||||||
\(768\) | 16098.2 | 0.756373 | ||||||||
\(769\) | −7107.01 | −0.333271 | −0.166636 | − | 0.986019i | \(-0.553290\pi\) | ||||
−0.166636 | + | 0.986019i | \(0.553290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16135.7 | 0.753711 | ||||||||
\(772\) | −22721.0 | −1.05926 | ||||||||
\(773\) | −19776.7 | −0.920204 | −0.460102 | − | 0.887866i | \(-0.652187\pi\) | ||||
−0.460102 | + | 0.887866i | \(0.652187\pi\) | |||||||
\(774\) | 8857.69 | 0.411348 | ||||||||
\(775\) | −3968.32 | −0.183931 | ||||||||
\(776\) | 1739.69 | 0.0804783 | ||||||||
\(777\) | −3780.91 | −0.174568 | ||||||||
\(778\) | −48237.1 | −2.22286 | ||||||||
\(779\) | −245.025 | −0.0112695 | ||||||||
\(780\) | 1735.99 | 0.0796904 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 29226.2 | 1.33648 | ||||||||
\(783\) | −2319.60 | −0.105869 | ||||||||
\(784\) | 20055.3 | 0.913597 | ||||||||
\(785\) | −785.523 | −0.0357153 | ||||||||
\(786\) | −21666.4 | −0.983226 | ||||||||
\(787\) | 19943.8 | 0.903327 | 0.451664 | − | 0.892188i | \(-0.350831\pi\) | ||||
0.451664 | + | 0.892188i | \(0.350831\pi\) | |||||||
\(788\) | 12896.9 | 0.583039 | ||||||||
\(789\) | −13752.1 | −0.620517 | ||||||||
\(790\) | 4915.53 | 0.221376 | ||||||||
\(791\) | 19013.4 | 0.854664 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1721.66 | 0.0770969 | ||||||||
\(794\) | 8443.34 | 0.377384 | ||||||||
\(795\) | −7000.52 | −0.312306 | ||||||||
\(796\) | 13342.5 | 0.594112 | ||||||||
\(797\) | −24333.8 | −1.08149 | −0.540744 | − | 0.841187i | \(-0.681857\pi\) | ||||
−0.540744 | + | 0.841187i | \(0.681857\pi\) | |||||||
\(798\) | 878.189 | 0.0389568 | ||||||||
\(799\) | 31867.4 | 1.41100 | ||||||||
\(800\) | −5433.63 | −0.240135 | ||||||||
\(801\) | −4182.41 | −0.184492 | ||||||||
\(802\) | −48186.0 | −2.12158 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1518.31 | −0.0666003 | ||||||||
\(805\) | 5815.55 | 0.254622 | ||||||||
\(806\) | −11926.5 | −0.521209 | ||||||||
\(807\) | −5223.08 | −0.227833 | ||||||||
\(808\) | −231.851 | −0.0100947 | ||||||||
\(809\) | −15308.7 | −0.665298 | −0.332649 | − | 0.943051i | \(-0.607942\pi\) | ||||
−0.332649 | + | 0.943051i | \(0.607942\pi\) | |||||||
\(810\) | 1499.13 | 0.0650298 | ||||||||
\(811\) | 22639.1 | 0.980229 | 0.490115 | − | 0.871658i | \(-0.336955\pi\) | ||||
0.490115 | + | 0.871658i | \(0.336955\pi\) | |||||||
\(812\) | 4459.72 | 0.192741 | ||||||||
\(813\) | −4021.73 | −0.173491 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8683.28 | 0.373205 | ||||||||
\(816\) | 14296.7 | 0.613337 | ||||||||
\(817\) | −2309.46 | −0.0988955 | ||||||||
\(818\) | 13134.8 | 0.561429 | ||||||||
\(819\) | −1663.30 | −0.0709650 | ||||||||
\(820\) | 804.187 | 0.0342481 | ||||||||
\(821\) | −35341.0 | −1.50232 | −0.751162 | − | 0.660118i | \(-0.770506\pi\) | ||||
−0.751162 | + | 0.660118i | \(0.770506\pi\) | |||||||
\(822\) | −6811.89 | −0.289041 | ||||||||
\(823\) | 28121.5 | 1.19107 | 0.595536 | − | 0.803329i | \(-0.296940\pi\) | ||||
0.595536 | + | 0.803329i | \(0.296940\pi\) | |||||||
\(824\) | −9042.09 | −0.382277 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12586.7 | −0.530202 | ||||||||
\(827\) | −5952.92 | −0.250306 | −0.125153 | − | 0.992137i | \(-0.539942\pi\) | ||||
−0.125153 | + | 0.992137i | \(0.539942\pi\) | |||||||
\(828\) | −6555.29 | −0.275135 | ||||||||
\(829\) | 18696.9 | 0.783316 | 0.391658 | − | 0.920111i | \(-0.371902\pi\) | ||||
0.391658 | + | 0.920111i | \(0.371902\pi\) | |||||||
\(830\) | −9638.09 | −0.403064 | ||||||||
\(831\) | 15662.3 | 0.653814 | ||||||||
\(832\) | −3809.60 | −0.158743 | ||||||||
\(833\) | 16076.1 | 0.668672 | ||||||||
\(834\) | −23660.0 | −0.982348 | ||||||||
\(835\) | −7332.73 | −0.303904 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4285.79 | −0.176987 | ||||||||
\(838\) | −54787.9 | −2.25849 | ||||||||
\(839\) | −25774.1 | −1.06057 | −0.530287 | − | 0.847818i | \(-0.677916\pi\) | ||||
−0.530287 | + | 0.847818i | \(0.677916\pi\) | |||||||
\(840\) | 1161.91 | 0.0477260 | ||||||||
\(841\) | −17008.3 | −0.697376 | ||||||||
\(842\) | 42726.2 | 1.74874 | ||||||||
\(843\) | −7484.04 | −0.305770 | ||||||||
\(844\) | 8691.68 | 0.354478 | ||||||||
\(845\) | −8924.87 | −0.363343 | ||||||||
\(846\) | −17176.8 | −0.698049 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 35984.9 | 1.45722 | ||||||||
\(849\) | −12988.3 | −0.525037 | ||||||||
\(850\) | −5719.49 | −0.230796 | ||||||||
\(851\) | −17683.4 | −0.712313 | ||||||||
\(852\) | −9180.00 | −0.369134 | ||||||||
\(853\) | −18664.1 | −0.749174 | −0.374587 | − | 0.927192i | \(-0.622215\pi\) | ||||
−0.374587 | + | 0.927192i | \(0.622215\pi\) | |||||||
\(854\) | −2858.47 | −0.114537 | ||||||||
\(855\) | −390.867 | −0.0156344 | ||||||||
\(856\) | −14488.5 | −0.578511 | ||||||||
\(857\) | 37192.5 | 1.48246 | 0.741232 | − | 0.671249i | \(-0.234242\pi\) | ||||
0.741232 | + | 0.671249i | \(0.234242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46306.0 | 1.83928 | 0.919640 | − | 0.392763i | \(-0.128481\pi\) | ||||
0.919640 | + | 0.392763i | \(0.128481\pi\) | |||||||
\(860\) | 7579.78 | 0.300545 | ||||||||
\(861\) | −770.512 | −0.0304983 | ||||||||
\(862\) | 47056.6 | 1.85934 | ||||||||
\(863\) | −19587.1 | −0.772599 | −0.386299 | − | 0.922373i | \(-0.626247\pi\) | ||||
−0.386299 | + | 0.922373i | \(0.626247\pi\) | |||||||
\(864\) | −5868.32 | −0.231070 | ||||||||
\(865\) | −718.907 | −0.0282584 | ||||||||
\(866\) | −60651.4 | −2.37993 | ||||||||
\(867\) | −3278.96 | −0.128442 | ||||||||
\(868\) | 8239.97 | 0.322215 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4770.07 | −0.185886 | ||||||||
\(871\) | −1801.80 | −0.0700939 | ||||||||
\(872\) | −4733.19 | −0.183814 | ||||||||
\(873\) | −1840.33 | −0.0713468 | ||||||||
\(874\) | 4107.31 | 0.158961 | ||||||||
\(875\) | −1138.09 | −0.0439707 | ||||||||
\(876\) | 5515.41 | 0.212726 | ||||||||
\(877\) | 26580.8 | 1.02345 | 0.511727 | − | 0.859148i | \(-0.329006\pi\) | ||||
0.511727 | + | 0.859148i | \(0.329006\pi\) | |||||||
\(878\) | 24443.7 | 0.939562 | ||||||||
\(879\) | 12992.8 | 0.498561 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −731.459 | −0.0279722 | −0.0139861 | − | 0.999902i | \(-0.504452\pi\) | ||||
−0.0139861 | + | 0.999902i | \(0.504452\pi\) | |||||||
\(882\) | −8665.14 | −0.330806 | ||||||||
\(883\) | −45291.1 | −1.72612 | −0.863062 | − | 0.505099i | \(-0.831456\pi\) | ||||
−0.863062 | + | 0.505099i | \(0.831456\pi\) | |||||||
\(884\) | −7153.01 | −0.272151 | ||||||||
\(885\) | 5602.12 | 0.212783 | ||||||||
\(886\) | −43089.8 | −1.63390 | ||||||||
\(887\) | −37730.7 | −1.42827 | −0.714134 | − | 0.700009i | \(-0.753179\pi\) | ||||
−0.714134 | + | 0.700009i | \(0.753179\pi\) | |||||||
\(888\) | −3533.04 | −0.133515 | ||||||||
\(889\) | 19840.6 | 0.748516 | ||||||||
\(890\) | −8600.81 | −0.323932 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28983.4 | 1.08793 | ||||||||
\(893\) | 4478.48 | 0.167824 | ||||||||
\(894\) | −6339.67 | −0.237170 | ||||||||
\(895\) | −7064.64 | −0.263849 | ||||||||
\(896\) | −9505.79 | −0.354426 | ||||||||
\(897\) | −7779.28 | −0.289568 | ||||||||
\(898\) | 51402.9 | 1.91017 | ||||||||
\(899\) | 13636.9 | 0.505913 | ||||||||
\(900\) | 1282.85 | 0.0475130 | ||||||||
\(901\) | 28845.1 | 1.06656 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7262.38 | −0.267638 | ||||||||
\(904\) | 17767.0 | 0.653673 | ||||||||
\(905\) | −11196.2 | −0.411244 | ||||||||
\(906\) | 23928.2 | 0.877440 | ||||||||
\(907\) | 25846.2 | 0.946208 | 0.473104 | − | 0.881007i | \(-0.343134\pi\) | ||||
0.473104 | + | 0.881007i | \(0.343134\pi\) | |||||||
\(908\) | 22296.9 | 0.814920 | ||||||||
\(909\) | 245.264 | 0.00894928 | ||||||||
\(910\) | −3420.45 | −0.124601 | ||||||||
\(911\) | −30349.8 | −1.10377 | −0.551885 | − | 0.833920i | \(-0.686091\pi\) | ||||
−0.551885 | + | 0.833920i | \(0.686091\pi\) | |||||||
\(912\) | 2009.18 | 0.0729502 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13421.3 | 0.485708 | ||||||||
\(915\) | 1272.26 | 0.0459667 | ||||||||
\(916\) | 15584.1 | 0.562133 | ||||||||
\(917\) | 17764.2 | 0.639723 | ||||||||
\(918\) | −6177.05 | −0.222084 | ||||||||
\(919\) | 41031.3 | 1.47279 | 0.736397 | − | 0.676550i | \(-0.236526\pi\) | ||||
0.736397 | + | 0.676550i | \(0.236526\pi\) | |||||||
\(920\) | 5434.30 | 0.194743 | ||||||||
\(921\) | 6157.68 | 0.220307 | ||||||||
\(922\) | 67846.2 | 2.42342 | ||||||||
\(923\) | −10894.1 | −0.388497 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3460.59 | 0.123009 | ||||||||
\(926\) | 39831.4 | 1.41354 | ||||||||
\(927\) | 9565.18 | 0.338902 | ||||||||
\(928\) | 18672.3 | 0.660506 | ||||||||
\(929\) | −3859.82 | −0.136315 | −0.0681575 | − | 0.997675i | \(-0.521712\pi\) | ||||
−0.0681575 | + | 0.997675i | \(0.521712\pi\) | |||||||
\(930\) | −8813.39 | −0.310755 | ||||||||
\(931\) | 2259.25 | 0.0795317 | ||||||||
\(932\) | 24832.9 | 0.872778 | ||||||||
\(933\) | 7883.29 | 0.276621 | ||||||||
\(934\) | −29480.3 | −1.03279 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1554.26 | −0.0542762 | ||||||||
\(937\) | 22026.5 | 0.767955 | 0.383977 | − | 0.923343i | \(-0.374554\pi\) | ||||
0.383977 | + | 0.923343i | \(0.374554\pi\) | |||||||
\(938\) | 2991.54 | 0.104134 | ||||||||
\(939\) | 20635.2 | 0.717150 | ||||||||
\(940\) | −14698.7 | −0.510019 | ||||||||
\(941\) | −24778.0 | −0.858386 | −0.429193 | − | 0.903213i | \(-0.641202\pi\) | ||||
−0.429193 | + | 0.903213i | \(0.641202\pi\) | |||||||
\(942\) | −1744.60 | −0.0603419 | ||||||||
\(943\) | −3603.70 | −0.124446 | ||||||||
\(944\) | −28796.7 | −0.992851 | ||||||||
\(945\) | −1229.13 | −0.0423108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34055.7 | 1.16860 | 0.584299 | − | 0.811539i | \(-0.301370\pi\) | ||||
0.584299 | + | 0.811539i | \(0.301370\pi\) | |||||||
\(948\) | 4542.87 | 0.155639 | ||||||||
\(949\) | 6545.23 | 0.223885 | ||||||||
\(950\) | −803.789 | −0.0274509 | ||||||||
\(951\) | −9078.15 | −0.309547 | ||||||||
\(952\) | −4787.57 | −0.162990 | ||||||||
\(953\) | −30211.9 | −1.02693 | −0.513463 | − | 0.858112i | \(-0.671637\pi\) | ||||
−0.513463 | + | 0.858112i | \(0.671637\pi\) | |||||||
\(954\) | −15547.7 | −0.527648 | ||||||||
\(955\) | 8729.72 | 0.295798 | ||||||||
\(956\) | 26976.8 | 0.912650 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3044.40 | 0.102672 | ||||||||
\(959\) | 5585.04 | 0.188061 | ||||||||
\(960\) | −2815.19 | −0.0946459 | ||||||||
\(961\) | −4594.90 | −0.154238 | ||||||||
\(962\) | 10400.6 | 0.348574 | ||||||||
\(963\) | 15326.6 | 0.512871 | ||||||||
\(964\) | −10451.7 | −0.349196 | ||||||||
\(965\) | −19925.2 | −0.664679 | ||||||||
\(966\) | 12916.0 | 0.430191 | ||||||||
\(967\) | 34883.2 | 1.16005 | 0.580024 | − | 0.814599i | \(-0.303043\pi\) | ||||
0.580024 | + | 0.814599i | \(0.303043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1610.54 | 0.0533931 | ||||||||
\(970\) | −3784.50 | −0.125271 | ||||||||
\(971\) | 19753.0 | 0.652835 | 0.326418 | − | 0.945226i | \(-0.394158\pi\) | ||||
0.326418 | + | 0.945226i | \(0.394158\pi\) | |||||||
\(972\) | 1385.48 | 0.0457194 | ||||||||
\(973\) | 19398.7 | 0.639152 | ||||||||
\(974\) | 24835.9 | 0.817038 | ||||||||
\(975\) | 1522.38 | 0.0500054 | ||||||||
\(976\) | −6539.80 | −0.214482 | ||||||||
\(977\) | −2208.90 | −0.0723326 | −0.0361663 | − | 0.999346i | \(-0.511515\pi\) | ||||
−0.0361663 | + | 0.999346i | \(0.511515\pi\) | |||||||
\(978\) | 19285.0 | 0.630539 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −7415.02 | −0.241698 | ||||||||
\(981\) | 5007.01 | 0.162958 | ||||||||
\(982\) | 46970.2 | 1.52635 | ||||||||
\(983\) | −40306.0 | −1.30779 | −0.653897 | − | 0.756583i | \(-0.726867\pi\) | ||||
−0.653897 | + | 0.756583i | \(0.726867\pi\) | |||||||
\(984\) | −720.000 | −0.0233260 | ||||||||
\(985\) | 11310.0 | 0.365855 | ||||||||
\(986\) | 19654.7 | 0.634820 | ||||||||
\(987\) | 14083.2 | 0.454177 | ||||||||
\(988\) | −1005.25 | −0.0323696 | ||||||||
\(989\) | −33966.3 | −1.09208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15199.4 | −0.487211 | −0.243605 | − | 0.969874i | \(-0.578330\pi\) | ||||
−0.243605 | + | 0.969874i | \(0.578330\pi\) | |||||||
\(992\) | 34499.8 | 1.10420 | ||||||||
\(993\) | −12979.5 | −0.414796 | ||||||||
\(994\) | 18087.5 | 0.577163 | ||||||||
\(995\) | 11700.8 | 0.372803 | ||||||||
\(996\) | −8907.40 | −0.283375 | ||||||||
\(997\) | −48073.6 | −1.52709 | −0.763543 | − | 0.645757i | \(-0.776542\pi\) | ||||
−0.763543 | + | 0.645757i | \(0.776542\pi\) | |||||||
\(998\) | −36315.3 | −1.15184 | ||||||||
\(999\) | 3737.43 | 0.118365 |
(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 | 1815.4.a.o.1.2 | yes | 2 | |
11.10 | odd | 2 | 1815.4.a.i.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.i.1.1 | ✓ | 2 | 11.10 | odd | 2 | ||
1815.4.a.o.1.2 | yes | 2 | 1.1 | even | 1 | trivial |