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 | 1.1 | ||
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 | \(-0.727058\pi\) | ||||
−0.654350 | + | 0.756192i | \(0.727058\pi\) | |||||||
\(3\) | 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 | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(8\) | 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 | \(-0.569474\pi\) | ||||
−0.216530 | + | 0.976276i | \(0.569474\pi\) | |||||||
\(14\) | −33.7016 | −0.643366 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −77.1047 | −1.20476 | ||||||||
\(17\) | 61.8062 | 0.881777 | 0.440889 | − | 0.897562i | \(-0.354663\pi\) | ||||
0.440889 | + | 0.897562i | \(0.354663\pi\) | |||||||
\(18\) | −33.3141 | −0.436233 | ||||||||
\(19\) | 8.68594 | 0.104879 | 0.0524393 | − | 0.998624i | \(-0.483300\pi\) | ||||
0.0524393 | + | 0.998624i | \(0.483300\pi\) | |||||||
\(20\) | 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 | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(30\) | −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 | \(-0.517110\pi\) | ||||
−0.0537264 | + | 0.998556i | \(0.517110\pi\) | |||||||
\(42\) | −101.105 | −0.371447 | ||||||||
\(43\) | −265.884 | −0.942953 | −0.471477 | − | 0.881879i | \(-0.656279\pi\) | ||||
−0.471477 | + | 0.881879i | \(0.656279\pi\) | |||||||
\(44\) | 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 | \(-0.528372\pi\) | ||||
−0.0890142 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(62\) | 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 | \(-0.583226\pi\) | ||||
−0.258493 | + | 0.966013i | \(0.583226\pi\) | |||||||
\(74\) | −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 | \(-0.560565\pi\) | ||||
−0.189123 | + | 0.981953i | \(0.560565\pi\) | |||||||
\(80\) | −385.523 | −0.538785 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 104.419 | 0.140623 | ||||||||
\(83\) | 520.758 | 0.688682 | 0.344341 | − | 0.938845i | \(-0.388102\pi\) | ||||
0.344341 | + | 0.938845i | \(0.388102\pi\) | |||||||
\(84\) | 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 | \(-0.504273\pi\) | ||||
−0.0134239 | + | 0.999910i | \(0.504273\pi\) | |||||||
\(102\) | −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 | \(-0.779398\pi\) | ||||
−0.769306 | + | 0.638881i | \(0.779398\pi\) | |||||||
\(108\) | 153.942 | 0.137158 | ||||||||
\(109\) | −556.334 | −0.488873 | −0.244437 | − | 0.969665i | \(-0.578603\pi\) | ||||
−0.244437 | + | 0.969665i | \(0.578603\pi\) | |||||||
\(110\) | 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 | \(-0.224564\pi\) | ||||
0.761296 | + | 0.648405i | \(0.224564\pi\) | |||||||
\(128\) | −1044.05 | −0.720955 | ||||||||
\(129\) | −797.653 | −0.544414 | ||||||||
\(130\) | 375.680 | 0.253456 | ||||||||
\(131\) | 1951.11 | 1.30129 | 0.650645 | − | 0.759382i | \(-0.274499\pi\) | ||||
0.650645 | + | 0.759382i | \(0.274499\pi\) | |||||||
\(132\) | 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 | \(-0.274742\pi\) | ||||
0.650064 | + | 0.759880i | \(0.274742\pi\) | |||||||
\(140\) | 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 | \(-0.449835\pi\) | ||||
0.156946 | + | 0.987607i | \(0.449835\pi\) | |||||||
\(150\) | −277.617 | −0.151116 | ||||||||
\(151\) | −2154.78 | −1.16128 | −0.580641 | − | 0.814159i | \(-0.697198\pi\) | ||||
−0.580641 | + | 0.814159i | \(0.697198\pi\) | |||||||
\(152\) | 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 | \(-0.389649\pi\) | ||||
0.339775 | + | 0.940507i | \(0.389649\pi\) | |||||||
\(168\) | 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 | \(-0.489942\pi\) | ||||
0.0315939 | + | 0.999501i | \(0.489942\pi\) | |||||||
\(174\) | −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 | \(-0.233338\pi\) | ||||
0.743134 | + | 0.669143i | \(0.233338\pi\) | |||||||
\(194\) | 756.900 | 0.280115 | ||||||||
\(195\) | −304.477 | −0.111815 | ||||||||
\(196\) | −1483.00 | −0.540453 | ||||||||
\(197\) | −2262.00 | −0.818076 | −0.409038 | − | 0.912517i | \(-0.634136\pi\) | ||||
−0.409038 | + | 0.912517i | \(0.634136\pi\) | |||||||
\(198\) | 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 | \(-0.580000\pi\) | ||||
−0.248689 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(212\) | −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 | \(-0.693723\pi\) | ||||
−0.571717 | + | 0.820451i | \(0.693723\pi\) | |||||||
\(228\) | 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 | \(-0.709759\pi\) | ||||
−0.612308 | + | 0.790619i | \(0.709759\pi\) | |||||||
\(234\) | 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 | \(-0.721182\pi\) | ||||
−0.640281 | + | 0.768141i | \(0.721182\pi\) | |||||||
\(240\) | −1156.57 | −0.311068 | ||||||||
\(241\) | 1833.12 | 0.489966 | 0.244983 | − | 0.969527i | \(-0.421218\pi\) | ||||
0.244983 | + | 0.969527i | \(0.421218\pi\) | |||||||
\(242\) | 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 | \(-0.319413\pi\) | ||||
0.537383 | + | 0.843338i | \(0.319413\pi\) | |||||||
\(264\) | 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 | \(-0.451993\pi\) | ||||
0.150248 | + | 0.988648i | \(0.451993\pi\) | |||||||
\(272\) | −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 | \(-0.691595\pi\) | ||||
−0.566220 | + | 0.824254i | \(0.691595\pi\) | |||||||
\(278\) | −7886.66 | −1.70148 | ||||||||
\(279\) | −1428.60 | −0.306551 | ||||||||
\(280\) | 387.305 | 0.0826639 | ||||||||
\(281\) | 2494.68 | 0.529609 | 0.264804 | − | 0.964302i | \(-0.414693\pi\) | ||||
0.264804 | + | 0.964302i | \(0.414693\pi\) | |||||||
\(282\) | 5725.59 | 1.20906 | ||||||||
\(283\) | 4329.43 | 0.909391 | 0.454696 | − | 0.890647i | \(-0.349748\pi\) | ||||
0.454696 | + | 0.890647i | \(0.349748\pi\) | |||||||
\(284\) | −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 | \(-0.642110\pi\) | ||||
−0.431767 | + | 0.901985i | \(0.642110\pi\) | |||||||
\(294\) | 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 | \(-0.561105\pi\) | ||||
−0.190791 | + | 0.981631i | \(0.561105\pi\) | |||||||
\(308\) | 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 | \(-0.545416\pi\) | ||||
−0.142194 | + | 0.989839i | \(0.545416\pi\) | |||||||
\(338\) | 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 | \(-0.861939\pi\) | ||||
−0.907404 | + | 0.420260i | \(0.861939\pi\) | |||||||
\(348\) | 1469.48 | 0.226357 | ||||||||
\(349\) | −3152.38 | −0.483504 | −0.241752 | − | 0.970338i | \(-0.577722\pi\) | ||||
−0.241752 | + | 0.970338i | \(0.577722\pi\) | |||||||
\(350\) | −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 | \(-0.567396\pi\) | ||||
−0.210154 | + | 0.977668i | \(0.567396\pi\) | |||||||
\(360\) | 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 | \(-0.241908\pi\) | ||||
0.724852 | + | 0.688905i | \(0.241908\pi\) | |||||||
\(374\) | 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 | \(-0.568812\pi\) | ||||
−0.214499 | + | 0.976724i | \(0.568812\pi\) | |||||||
\(410\) | 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 | \(-0.751476\pi\) | ||||
−0.710378 | + | 0.703820i | \(0.751476\pi\) | |||||||
\(432\) | −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 | \(-0.616871\pi\) | ||||
−0.358968 | + | 0.933350i | \(0.616871\pi\) | |||||||
\(440\) | 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 | \(-0.559413\pi\) | ||||
−0.185569 | + | 0.982631i | \(0.559413\pi\) | |||||||
\(458\) | −10117.5 | −1.03223 | ||||||||
\(459\) | 1668.77 | 0.169698 | ||||||||
\(460\) | −3641.83 | −0.369133 | ||||||||
\(461\) | −18329.1 | −1.85178 | −0.925890 | − | 0.377794i | \(-0.876683\pi\) | ||||
−0.925890 | + | 0.377794i | \(0.876683\pi\) | |||||||
\(462\) | 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 | \(-0.512489\pi\) | ||||
−0.0392268 | + | 0.999230i | \(0.512489\pi\) | |||||||
\(480\) | 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 | \(-0.698182\pi\) | ||||
−0.583156 | + | 0.812360i | \(0.698182\pi\) | |||||||
\(492\) | −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 | \(-0.306853\pi\) | ||||
0.570233 | + | 0.821483i | \(0.306853\pi\) | |||||||
\(504\) | 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 | \(-0.560900\pi\) | ||||
−0.190157 | + | 0.981754i | \(0.560900\pi\) | |||||||
\(524\) | 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 | \(-0.381083\pi\) | ||||
0.364958 | + | 0.931024i | \(0.381083\pi\) | |||||||
\(542\) | −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 | \(-0.805715\pi\) | ||||
−0.819439 | + | 0.573167i | \(0.805715\pi\) | |||||||
\(548\) | −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 | \(-0.446201\pi\) | ||||
0.168211 | + | 0.985751i | \(0.446201\pi\) | |||||||
\(558\) | 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 | \(-0.427088\pi\) | ||||
0.227061 | + | 0.973881i | \(0.427088\pi\) | |||||||
\(564\) | −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 | \(-0.720590\pi\) | ||||
−0.638850 | + | 0.769331i | \(0.720590\pi\) | |||||||
\(570\) | −482.273 | −0.0354390 | ||||||||
\(571\) | −621.014 | −0.0455142 | −0.0227571 | − | 0.999741i | \(-0.507244\pi\) | ||||
−0.0227571 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(572\) | 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 | \(-0.347714\pi\) | ||||
0.460378 | + | 0.887723i | \(0.347714\pi\) | |||||||
\(594\) | 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 | \(-0.556349\pi\) | ||||
−0.176104 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(602\) | 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 | \(-0.152424\pi\) | ||||
0.887523 | + | 0.460763i | \(0.152424\pi\) | |||||||
\(608\) | 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 | \(-0.170603\pi\) | ||||
0.859776 | + | 0.510671i | \(0.170603\pi\) | |||||||
\(614\) | 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 | \(-0.374310\pi\) | ||||
0.384685 | + | 0.923048i | \(0.374310\pi\) | |||||||
\(660\) | 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 | \(-0.141617\pi\) | ||||
0.902653 | + | 0.430370i | \(0.141617\pi\) | |||||||
\(674\) | 6512.38 | 0.372177 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −10177.1 | −0.579036 | ||||||||
\(677\) | −12418.6 | −0.705000 | −0.352500 | − | 0.935812i | \(-0.614668\pi\) | ||||
−0.352500 | + | 0.935812i | \(0.614668\pi\) | |||||||
\(678\) | 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 | \(-0.808361\pi\) | ||||
−0.824176 | + | 0.566334i | \(0.808361\pi\) | |||||||
\(702\) | 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 | \(-0.419138\pi\) | ||||
0.251313 | + | 0.967906i | \(0.419138\pi\) | |||||||
\(734\) | 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 | \(-0.406940\pi\) | ||||
0.288209 | + | 0.957568i | \(0.406940\pi\) | |||||||
\(740\) | 3946.15 | 0.196031 | ||||||||
\(741\) | −528.933 | −0.0262225 | ||||||||
\(742\) | 15728.6 | 0.778186 | ||||||||
\(743\) | 20323.7 | 1.00351 | 0.501753 | − | 0.865011i | \(-0.332689\pi\) | ||||
0.501753 | + | 0.865011i | \(0.332689\pi\) | |||||||
\(744\) | −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 | \(-0.626847\pi\) | ||||
−0.388037 | + | 0.921644i | \(0.626847\pi\) | |||||||
\(762\) | −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 | \(-0.446710\pi\) | ||||
0.166636 | + | 0.986019i | \(0.446710\pi\) | |||||||
\(770\) | 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 | \(-0.649169\pi\) | ||||
−0.451664 | + | 0.892188i | \(0.649169\pi\) | |||||||
\(788\) | −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 | \(-0.392058\pi\) | ||||
0.332649 | + | 0.943051i | \(0.392058\pi\) | |||||||
\(810\) | −1499.13 | −0.0650298 | ||||||||
\(811\) | −22639.1 | −0.980229 | −0.490115 | − | 0.871658i | \(-0.663045\pi\) | ||||
−0.490115 | + | 0.871658i | \(0.663045\pi\) | |||||||
\(812\) | 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 | \(-0.229494\pi\) | ||||
0.751162 | + | 0.660118i | \(0.229494\pi\) | |||||||
\(822\) | 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 | \(-0.460058\pi\) | ||||
0.125153 | + | 0.992137i | \(0.460058\pi\) | |||||||
\(828\) | −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 | \(-0.377785\pi\) | ||||
0.374587 | + | 0.927192i | \(0.377785\pi\) | |||||||
\(854\) | 2858.47 | 0.114537 | ||||||||
\(855\) | 390.867 | 0.0156344 | ||||||||
\(856\) | −14488.5 | −0.578511 | ||||||||
\(857\) | −37192.5 | −1.48246 | −0.741232 | − | 0.671249i | \(-0.765758\pi\) | ||||
−0.741232 | + | 0.671249i | \(0.765758\pi\) | |||||||
\(858\) | 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 | \(-0.670994\pi\) | ||||
−0.511727 | + | 0.859148i | \(0.670994\pi\) | |||||||
\(878\) | 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 | \(-0.246821\pi\) | ||||
0.714134 | + | 0.700009i | \(0.246821\pi\) | |||||||
\(888\) | 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 | \(-0.763474\pi\) | ||||
−0.736397 | + | 0.676550i | \(0.763474\pi\) | |||||||
\(920\) | −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 | \(-0.625446\pi\) | ||||
−0.383977 | + | 0.923343i | \(0.625446\pi\) | |||||||
\(938\) | 2991.54 | 0.104134 | ||||||||
\(939\) | 20635.2 | 0.717150 | ||||||||
\(940\) | −14698.7 | −0.510019 | ||||||||
\(941\) | 24778.0 | 0.858386 | 0.429193 | − | 0.903213i | \(-0.358798\pi\) | ||||
0.429193 | + | 0.903213i | \(0.358798\pi\) | |||||||
\(942\) | 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 | \(-0.328363\pi\) | ||||
0.513463 | + | 0.858112i | \(0.328363\pi\) | |||||||
\(954\) | 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 | \(-0.696957\pi\) | ||||
−0.580024 | + | 0.814599i | \(0.696957\pi\) | |||||||
\(968\) | 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 | \(-0.223458\pi\) | ||||
0.763543 | + | 0.645757i | \(0.223458\pi\) | |||||||
\(998\) | 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.i.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 1815.4.a.o.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.i.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1815.4.a.o.1.2 | yes | 2 | 11.10 | odd | 2 |