Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, 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("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.52131\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.52131 | 1.24497 | 0.622486 | − | 0.782631i | \(-0.286123\pi\) | ||||
0.622486 | + | 0.782631i | \(0.286123\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.39964 | 0.549955 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 10.5639 | 0.718785 | ||||||||
\(7\) | −8.86571 | −0.478703 | −0.239352 | − | 0.970933i | \(-0.576935\pi\) | ||||
−0.239352 | + | 0.970933i | \(0.576935\pi\) | |||||||
\(8\) | −12.6780 | −0.560293 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −17.6066 | −0.556768 | ||||||||
\(11\) | −61.9492 | −1.69804 | −0.849018 | − | 0.528364i | \(-0.822806\pi\) | ||||
−0.849018 | + | 0.528364i | \(0.822806\pi\) | |||||||
\(12\) | 13.1989 | 0.317517 | ||||||||
\(13\) | 31.6208 | 0.674618 | 0.337309 | − | 0.941394i | \(-0.390483\pi\) | ||||
0.337309 | + | 0.941394i | \(0.390483\pi\) | |||||||
\(14\) | −31.2189 | −0.595972 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −79.8403 | −1.24750 | ||||||||
\(17\) | −48.6694 | −0.694357 | −0.347178 | − | 0.937799i | \(-0.612860\pi\) | ||||
−0.347178 | + | 0.937799i | \(0.612860\pi\) | |||||||
\(18\) | 31.6918 | 0.414991 | ||||||||
\(19\) | −127.727 | −1.54224 | −0.771118 | − | 0.636692i | \(-0.780302\pi\) | ||||
−0.771118 | + | 0.636692i | \(0.780302\pi\) | |||||||
\(20\) | −21.9982 | −0.245948 | ||||||||
\(21\) | −26.5971 | −0.276379 | ||||||||
\(22\) | −218.143 | −2.11401 | ||||||||
\(23\) | 184.026 | 1.66835 | 0.834175 | − | 0.551501i | \(-0.185945\pi\) | ||||
0.834175 | + | 0.551501i | \(0.185945\pi\) | |||||||
\(24\) | −38.0339 | −0.323485 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 111.347 | 0.839881 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −39.0059 | −0.263265 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | −52.8197 | −0.321450 | ||||||||
\(31\) | −251.985 | −1.45993 | −0.729965 | − | 0.683484i | \(-0.760464\pi\) | ||||
−0.729965 | + | 0.683484i | \(0.760464\pi\) | |||||||
\(32\) | −179.719 | −0.992815 | ||||||||
\(33\) | −185.848 | −0.980361 | ||||||||
\(34\) | −171.380 | −0.864455 | ||||||||
\(35\) | 44.3285 | 0.214083 | ||||||||
\(36\) | 39.5968 | 0.183318 | ||||||||
\(37\) | 197.740 | 0.878600 | 0.439300 | − | 0.898340i | \(-0.355226\pi\) | ||||
0.439300 | + | 0.898340i | \(0.355226\pi\) | |||||||
\(38\) | −449.765 | −1.92004 | ||||||||
\(39\) | 94.8624 | 0.389491 | ||||||||
\(40\) | 63.3899 | 0.250571 | ||||||||
\(41\) | −163.446 | −0.622585 | −0.311293 | − | 0.950314i | \(-0.600762\pi\) | ||||
−0.311293 | + | 0.950314i | \(0.600762\pi\) | |||||||
\(42\) | −93.6568 | −0.344085 | ||||||||
\(43\) | −33.2231 | −0.117825 | −0.0589124 | − | 0.998263i | \(-0.518763\pi\) | ||||
−0.0589124 | + | 0.998263i | \(0.518763\pi\) | |||||||
\(44\) | −272.555 | −0.933844 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 648.012 | 2.07705 | ||||||||
\(47\) | 528.945 | 1.64159 | 0.820793 | − | 0.571226i | \(-0.193532\pi\) | ||||
0.820793 | + | 0.571226i | \(0.193532\pi\) | |||||||
\(48\) | −239.521 | −0.720247 | ||||||||
\(49\) | −264.399 | −0.770843 | ||||||||
\(50\) | 88.0328 | 0.248994 | ||||||||
\(51\) | −146.008 | −0.400887 | ||||||||
\(52\) | 139.120 | 0.371010 | ||||||||
\(53\) | −240.256 | −0.622673 | −0.311336 | − | 0.950300i | \(-0.600777\pi\) | ||||
−0.311336 | + | 0.950300i | \(0.600777\pi\) | |||||||
\(54\) | 95.0754 | 0.239595 | ||||||||
\(55\) | 309.746 | 0.759385 | ||||||||
\(56\) | 112.399 | 0.268214 | ||||||||
\(57\) | −383.180 | −0.890411 | ||||||||
\(58\) | −102.118 | −0.231186 | ||||||||
\(59\) | −202.976 | −0.447885 | −0.223942 | − | 0.974602i | \(-0.571893\pi\) | ||||
−0.223942 | + | 0.974602i | \(0.571893\pi\) | |||||||
\(60\) | −65.9947 | −0.141998 | ||||||||
\(61\) | 492.192 | 1.03309 | 0.516547 | − | 0.856259i | \(-0.327217\pi\) | ||||
0.516547 | + | 0.856259i | \(0.327217\pi\) | |||||||
\(62\) | −887.318 | −1.81757 | ||||||||
\(63\) | −79.7914 | −0.159568 | ||||||||
\(64\) | 5.87624 | 0.0114770 | ||||||||
\(65\) | −158.104 | −0.301698 | ||||||||
\(66\) | −654.428 | −1.22052 | ||||||||
\(67\) | −229.556 | −0.418577 | −0.209289 | − | 0.977854i | \(-0.567115\pi\) | ||||
−0.209289 | + | 0.977854i | \(0.567115\pi\) | |||||||
\(68\) | −214.128 | −0.381865 | ||||||||
\(69\) | 552.077 | 0.963222 | ||||||||
\(70\) | 156.095 | 0.266527 | ||||||||
\(71\) | 21.2064 | 0.0354471 | 0.0177235 | − | 0.999843i | \(-0.494358\pi\) | ||||
0.0177235 | + | 0.999843i | \(0.494358\pi\) | |||||||
\(72\) | −114.102 | −0.186764 | ||||||||
\(73\) | −1145.48 | −1.83656 | −0.918279 | − | 0.395934i | \(-0.870421\pi\) | ||||
−0.918279 | + | 0.395934i | \(0.870421\pi\) | |||||||
\(74\) | 696.303 | 1.09383 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | −561.952 | −0.848161 | ||||||||
\(77\) | 549.224 | 0.812855 | ||||||||
\(78\) | 334.040 | 0.484905 | ||||||||
\(79\) | 95.6307 | 0.136194 | 0.0680968 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680968 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(80\) | 399.201 | 0.557901 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −575.545 | −0.775101 | ||||||||
\(83\) | 1239.97 | 1.63982 | 0.819908 | − | 0.572496i | \(-0.194025\pi\) | ||||
0.819908 | + | 0.572496i | \(0.194025\pi\) | |||||||
\(84\) | −117.018 | −0.151996 | ||||||||
\(85\) | 243.347 | 0.310526 | ||||||||
\(86\) | −116.989 | −0.146689 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | 785.391 | 0.951397 | ||||||||
\(89\) | 116.863 | 0.139185 | 0.0695927 | − | 0.997575i | \(-0.477830\pi\) | ||||
0.0695927 | + | 0.997575i | \(0.477830\pi\) | |||||||
\(90\) | −158.459 | −0.185589 | ||||||||
\(91\) | −280.341 | −0.322942 | ||||||||
\(92\) | 809.648 | 0.917518 | ||||||||
\(93\) | −755.955 | −0.842891 | ||||||||
\(94\) | 1862.58 | 2.04373 | ||||||||
\(95\) | 638.633 | 0.689709 | ||||||||
\(96\) | −539.156 | −0.573202 | ||||||||
\(97\) | −275.722 | −0.288611 | −0.144306 | − | 0.989533i | \(-0.546095\pi\) | ||||
−0.144306 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(98\) | −931.032 | −0.959678 | ||||||||
\(99\) | −557.543 | −0.566012 | ||||||||
\(100\) | 109.991 | 0.109991 | ||||||||
\(101\) | −1909.39 | −1.88111 | −0.940553 | − | 0.339648i | \(-0.889692\pi\) | ||||
−0.940553 | + | 0.339648i | \(0.889692\pi\) | |||||||
\(102\) | −514.141 | −0.499093 | ||||||||
\(103\) | 1501.97 | 1.43683 | 0.718415 | − | 0.695614i | \(-0.244868\pi\) | ||||
0.718415 | + | 0.695614i | \(0.244868\pi\) | |||||||
\(104\) | −400.888 | −0.377984 | ||||||||
\(105\) | 132.986 | 0.123601 | ||||||||
\(106\) | −846.016 | −0.775210 | ||||||||
\(107\) | 1434.61 | 1.29616 | 0.648080 | − | 0.761572i | \(-0.275572\pi\) | ||||
0.648080 | + | 0.761572i | \(0.275572\pi\) | |||||||
\(108\) | 118.790 | 0.105839 | ||||||||
\(109\) | −347.951 | −0.305758 | −0.152879 | − | 0.988245i | \(-0.548855\pi\) | ||||
−0.152879 | + | 0.988245i | \(0.548855\pi\) | |||||||
\(110\) | 1090.71 | 0.945413 | ||||||||
\(111\) | 593.219 | 0.507260 | ||||||||
\(112\) | 707.840 | 0.597184 | ||||||||
\(113\) | −1812.68 | −1.50905 | −0.754524 | − | 0.656272i | \(-0.772132\pi\) | ||||
−0.754524 | + | 0.656272i | \(0.772132\pi\) | |||||||
\(114\) | −1349.30 | −1.10854 | ||||||||
\(115\) | −920.129 | −0.746108 | ||||||||
\(116\) | −127.590 | −0.102124 | ||||||||
\(117\) | 284.587 | 0.224873 | ||||||||
\(118\) | −714.742 | −0.557604 | ||||||||
\(119\) | 431.489 | 0.332391 | ||||||||
\(120\) | 190.170 | 0.144667 | ||||||||
\(121\) | 2506.71 | 1.88333 | ||||||||
\(122\) | 1733.16 | 1.28617 | ||||||||
\(123\) | −490.338 | −0.359450 | ||||||||
\(124\) | −1108.64 | −0.802897 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −280.970 | −0.198657 | ||||||||
\(127\) | 550.739 | 0.384804 | 0.192402 | − | 0.981316i | \(-0.438372\pi\) | ||||
0.192402 | + | 0.981316i | \(0.438372\pi\) | |||||||
\(128\) | 1458.44 | 1.00710 | ||||||||
\(129\) | −99.6692 | −0.0680262 | ||||||||
\(130\) | −556.734 | −0.375606 | ||||||||
\(131\) | −124.824 | −0.0832515 | −0.0416257 | − | 0.999133i | \(-0.513254\pi\) | ||||
−0.0416257 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(132\) | −817.664 | −0.539155 | ||||||||
\(133\) | 1132.39 | 0.738273 | ||||||||
\(134\) | −808.337 | −0.521117 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 617.030 | 0.389043 | ||||||||
\(137\) | −549.879 | −0.342915 | −0.171458 | − | 0.985192i | \(-0.554848\pi\) | ||||
−0.171458 | + | 0.985192i | \(0.554848\pi\) | |||||||
\(138\) | 1944.04 | 1.19918 | ||||||||
\(139\) | −2243.32 | −1.36889 | −0.684445 | − | 0.729065i | \(-0.739955\pi\) | ||||
−0.684445 | + | 0.729065i | \(0.739955\pi\) | |||||||
\(140\) | 195.030 | 0.117736 | ||||||||
\(141\) | 1586.83 | 0.947770 | ||||||||
\(142\) | 74.6745 | 0.0441306 | ||||||||
\(143\) | −1958.88 | −1.14553 | ||||||||
\(144\) | −718.563 | −0.415835 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | −4033.61 | −2.28646 | ||||||||
\(147\) | −793.198 | −0.445047 | ||||||||
\(148\) | 869.984 | 0.483191 | ||||||||
\(149\) | −614.305 | −0.337757 | −0.168879 | − | 0.985637i | \(-0.554015\pi\) | ||||
−0.168879 | + | 0.985637i | \(0.554015\pi\) | |||||||
\(150\) | 264.098 | 0.143757 | ||||||||
\(151\) | −1121.72 | −0.604531 | −0.302266 | − | 0.953224i | \(-0.597743\pi\) | ||||
−0.302266 | + | 0.953224i | \(0.597743\pi\) | |||||||
\(152\) | 1619.32 | 0.864104 | ||||||||
\(153\) | −438.025 | −0.231452 | ||||||||
\(154\) | 1933.99 | 1.01198 | ||||||||
\(155\) | 1259.92 | 0.652901 | ||||||||
\(156\) | 417.361 | 0.214203 | ||||||||
\(157\) | 3238.34 | 1.64616 | 0.823082 | − | 0.567923i | \(-0.192253\pi\) | ||||
0.823082 | + | 0.567923i | \(0.192253\pi\) | |||||||
\(158\) | 336.746 | 0.169557 | ||||||||
\(159\) | −720.767 | −0.359500 | ||||||||
\(160\) | 898.594 | 0.444001 | ||||||||
\(161\) | −1631.52 | −0.798644 | ||||||||
\(162\) | 285.226 | 0.138330 | ||||||||
\(163\) | −2973.43 | −1.42881 | −0.714407 | − | 0.699730i | \(-0.753303\pi\) | ||||
−0.714407 | + | 0.699730i | \(0.753303\pi\) | |||||||
\(164\) | −719.105 | −0.342394 | ||||||||
\(165\) | 929.238 | 0.438431 | ||||||||
\(166\) | 4366.33 | 2.04152 | ||||||||
\(167\) | 4133.13 | 1.91515 | 0.957577 | − | 0.288176i | \(-0.0930489\pi\) | ||||
0.957577 | + | 0.288176i | \(0.0930489\pi\) | |||||||
\(168\) | 337.198 | 0.154853 | ||||||||
\(169\) | −1197.12 | −0.544890 | ||||||||
\(170\) | 856.901 | 0.386596 | ||||||||
\(171\) | −1149.54 | −0.514079 | ||||||||
\(172\) | −146.170 | −0.0647984 | ||||||||
\(173\) | 347.755 | 0.152829 | 0.0764143 | − | 0.997076i | \(-0.475653\pi\) | ||||
0.0764143 | + | 0.997076i | \(0.475653\pi\) | |||||||
\(174\) | −306.354 | −0.133475 | ||||||||
\(175\) | −221.643 | −0.0957406 | ||||||||
\(176\) | 4946.04 | 2.11831 | ||||||||
\(177\) | −608.928 | −0.258587 | ||||||||
\(178\) | 411.513 | 0.173282 | ||||||||
\(179\) | 789.082 | 0.329490 | 0.164745 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164745 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(180\) | −197.984 | −0.0819825 | ||||||||
\(181\) | −4547.86 | −1.86762 | −0.933812 | − | 0.357763i | \(-0.883539\pi\) | ||||
−0.933812 | + | 0.357763i | \(0.883539\pi\) | |||||||
\(182\) | −987.168 | −0.402054 | ||||||||
\(183\) | 1476.58 | 0.596458 | ||||||||
\(184\) | −2333.08 | −0.934764 | ||||||||
\(185\) | −988.699 | −0.392922 | ||||||||
\(186\) | −2661.95 | −1.04938 | ||||||||
\(187\) | 3015.03 | 1.17904 | ||||||||
\(188\) | 2327.17 | 0.902799 | ||||||||
\(189\) | −239.374 | −0.0921265 | ||||||||
\(190\) | 2248.83 | 0.858669 | ||||||||
\(191\) | −1121.45 | −0.424843 | −0.212421 | − | 0.977178i | \(-0.568135\pi\) | ||||
−0.212421 | + | 0.977178i | \(0.568135\pi\) | |||||||
\(192\) | 17.6287 | 0.00662627 | ||||||||
\(193\) | −3950.05 | −1.47322 | −0.736608 | − | 0.676320i | \(-0.763574\pi\) | ||||
−0.736608 | + | 0.676320i | \(0.763574\pi\) | |||||||
\(194\) | −970.902 | −0.359313 | ||||||||
\(195\) | −474.312 | −0.174186 | ||||||||
\(196\) | −1163.26 | −0.423930 | ||||||||
\(197\) | −436.434 | −0.157841 | −0.0789205 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789205 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(198\) | −1963.28 | −0.704669 | ||||||||
\(199\) | 775.787 | 0.276352 | 0.138176 | − | 0.990408i | \(-0.455876\pi\) | ||||
0.138176 | + | 0.990408i | \(0.455876\pi\) | |||||||
\(200\) | −316.949 | −0.112059 | ||||||||
\(201\) | −688.667 | −0.241666 | ||||||||
\(202\) | −6723.57 | −2.34192 | ||||||||
\(203\) | 257.105 | 0.0888929 | ||||||||
\(204\) | −642.384 | −0.220470 | ||||||||
\(205\) | 817.231 | 0.278429 | ||||||||
\(206\) | 5288.91 | 1.78881 | ||||||||
\(207\) | 1656.23 | 0.556116 | ||||||||
\(208\) | −2524.61 | −0.841589 | ||||||||
\(209\) | 7912.57 | 2.61877 | ||||||||
\(210\) | 468.284 | 0.153879 | ||||||||
\(211\) | 2474.44 | 0.807335 | 0.403667 | − | 0.914906i | \(-0.367735\pi\) | ||||
0.403667 | + | 0.914906i | \(0.367735\pi\) | |||||||
\(212\) | −1057.04 | −0.342442 | ||||||||
\(213\) | 63.6193 | 0.0204654 | ||||||||
\(214\) | 5051.71 | 1.61368 | ||||||||
\(215\) | 166.115 | 0.0526929 | ||||||||
\(216\) | −342.305 | −0.107828 | ||||||||
\(217\) | 2234.02 | 0.698873 | ||||||||
\(218\) | −1225.24 | −0.380660 | ||||||||
\(219\) | −3436.45 | −1.06034 | ||||||||
\(220\) | 1362.77 | 0.417628 | ||||||||
\(221\) | −1538.97 | −0.468426 | ||||||||
\(222\) | 2088.91 | 0.631525 | ||||||||
\(223\) | −1035.62 | −0.310987 | −0.155494 | − | 0.987837i | \(-0.549697\pi\) | ||||
−0.155494 | + | 0.987837i | \(0.549697\pi\) | |||||||
\(224\) | 1593.33 | 0.475264 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −6383.01 | −1.87872 | ||||||||
\(227\) | −1068.43 | −0.312398 | −0.156199 | − | 0.987726i | \(-0.549924\pi\) | ||||
−0.156199 | + | 0.987726i | \(0.549924\pi\) | |||||||
\(228\) | −1685.85 | −0.489686 | ||||||||
\(229\) | −638.809 | −0.184339 | −0.0921696 | − | 0.995743i | \(-0.529380\pi\) | ||||
−0.0921696 | + | 0.995743i | \(0.529380\pi\) | |||||||
\(230\) | −3240.06 | −0.928884 | ||||||||
\(231\) | 1647.67 | 0.469302 | ||||||||
\(232\) | 367.661 | 0.104044 | ||||||||
\(233\) | 4199.81 | 1.18085 | 0.590427 | − | 0.807091i | \(-0.298959\pi\) | ||||
0.590427 | + | 0.807091i | \(0.298959\pi\) | |||||||
\(234\) | 1002.12 | 0.279960 | ||||||||
\(235\) | −2644.72 | −0.734139 | ||||||||
\(236\) | −893.022 | −0.246317 | ||||||||
\(237\) | 286.892 | 0.0786314 | ||||||||
\(238\) | 1519.41 | 0.413817 | ||||||||
\(239\) | 1481.20 | 0.400882 | 0.200441 | − | 0.979706i | \(-0.435763\pi\) | ||||
0.200441 | + | 0.979706i | \(0.435763\pi\) | |||||||
\(240\) | 1197.60 | 0.322104 | ||||||||
\(241\) | 7144.57 | 1.90964 | 0.954818 | − | 0.297191i | \(-0.0960498\pi\) | ||||
0.954818 | + | 0.297191i | \(0.0960498\pi\) | |||||||
\(242\) | 8826.90 | 2.34469 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2165.47 | 0.568156 | ||||||||
\(245\) | 1322.00 | 0.344732 | ||||||||
\(246\) | −1726.64 | −0.447505 | ||||||||
\(247\) | −4038.82 | −1.04042 | ||||||||
\(248\) | 3194.66 | 0.817988 | ||||||||
\(249\) | 3719.92 | 0.946748 | ||||||||
\(250\) | −440.164 | −0.111354 | ||||||||
\(251\) | −5209.72 | −1.31010 | −0.655049 | − | 0.755587i | \(-0.727352\pi\) | ||||
−0.655049 | + | 0.755587i | \(0.727352\pi\) | |||||||
\(252\) | −351.054 | −0.0877551 | ||||||||
\(253\) | −11400.3 | −2.83292 | ||||||||
\(254\) | 1939.32 | 0.479071 | ||||||||
\(255\) | 730.041 | 0.179282 | ||||||||
\(256\) | 5088.62 | 1.24234 | ||||||||
\(257\) | 3431.65 | 0.832919 | 0.416460 | − | 0.909154i | \(-0.363271\pi\) | ||||
0.416460 | + | 0.909154i | \(0.363271\pi\) | |||||||
\(258\) | −350.966 | −0.0846907 | ||||||||
\(259\) | −1753.10 | −0.420589 | ||||||||
\(260\) | −695.602 | −0.165921 | ||||||||
\(261\) | −261.000 | −0.0618984 | ||||||||
\(262\) | −439.545 | −0.103646 | ||||||||
\(263\) | −1738.29 | −0.407558 | −0.203779 | − | 0.979017i | \(-0.565322\pi\) | ||||
−0.203779 | + | 0.979017i | \(0.565322\pi\) | |||||||
\(264\) | 2356.17 | 0.549290 | ||||||||
\(265\) | 1201.28 | 0.278468 | ||||||||
\(266\) | 3987.49 | 0.919130 | ||||||||
\(267\) | 350.590 | 0.0803587 | ||||||||
\(268\) | −1009.96 | −0.230199 | ||||||||
\(269\) | 2829.31 | 0.641287 | 0.320643 | − | 0.947200i | \(-0.396101\pi\) | ||||
0.320643 | + | 0.947200i | \(0.396101\pi\) | |||||||
\(270\) | −475.377 | −0.107150 | ||||||||
\(271\) | −1399.29 | −0.313657 | −0.156828 | − | 0.987626i | \(-0.550127\pi\) | ||||
−0.156828 | + | 0.987626i | \(0.550127\pi\) | |||||||
\(272\) | 3885.78 | 0.866213 | ||||||||
\(273\) | −841.022 | −0.186451 | ||||||||
\(274\) | −1936.30 | −0.426920 | ||||||||
\(275\) | −1548.73 | −0.339607 | ||||||||
\(276\) | 2428.94 | 0.529729 | ||||||||
\(277\) | −3526.40 | −0.764912 | −0.382456 | − | 0.923974i | \(-0.624922\pi\) | ||||
−0.382456 | + | 0.923974i | \(0.624922\pi\) | |||||||
\(278\) | −7899.42 | −1.70423 | ||||||||
\(279\) | −2267.86 | −0.486643 | ||||||||
\(280\) | −561.996 | −0.119949 | ||||||||
\(281\) | −857.124 | −0.181963 | −0.0909817 | − | 0.995853i | \(-0.529000\pi\) | ||||
−0.0909817 | + | 0.995853i | \(0.529000\pi\) | |||||||
\(282\) | 5587.74 | 1.17995 | ||||||||
\(283\) | −7197.47 | −1.51182 | −0.755910 | − | 0.654676i | \(-0.772805\pi\) | ||||
−0.755910 | + | 0.654676i | \(0.772805\pi\) | |||||||
\(284\) | 93.3008 | 0.0194943 | ||||||||
\(285\) | 1915.90 | 0.398204 | ||||||||
\(286\) | −6897.85 | −1.42615 | ||||||||
\(287\) | 1449.07 | 0.298034 | ||||||||
\(288\) | −1617.47 | −0.330938 | ||||||||
\(289\) | −2544.29 | −0.517869 | ||||||||
\(290\) | 510.590 | 0.103389 | ||||||||
\(291\) | −827.165 | −0.166630 | ||||||||
\(292\) | −5039.72 | −1.01003 | ||||||||
\(293\) | 2936.05 | 0.585412 | 0.292706 | − | 0.956202i | \(-0.405444\pi\) | ||||
0.292706 | + | 0.956202i | \(0.405444\pi\) | |||||||
\(294\) | −2793.10 | −0.554071 | ||||||||
\(295\) | 1014.88 | 0.200300 | ||||||||
\(296\) | −2506.94 | −0.492274 | ||||||||
\(297\) | −1672.63 | −0.326787 | ||||||||
\(298\) | −2163.16 | −0.420498 | ||||||||
\(299\) | 5819.04 | 1.12550 | ||||||||
\(300\) | 329.973 | 0.0635034 | ||||||||
\(301\) | 294.546 | 0.0564031 | ||||||||
\(302\) | −3949.93 | −0.752625 | ||||||||
\(303\) | −5728.18 | −1.08606 | ||||||||
\(304\) | 10197.7 | 1.92395 | ||||||||
\(305\) | −2460.96 | −0.462014 | ||||||||
\(306\) | −1542.42 | −0.288152 | ||||||||
\(307\) | −3828.27 | −0.711698 | −0.355849 | − | 0.934544i | \(-0.615808\pi\) | ||||
−0.355849 | + | 0.934544i | \(0.615808\pi\) | |||||||
\(308\) | 2416.39 | 0.447034 | ||||||||
\(309\) | 4505.91 | 0.829555 | ||||||||
\(310\) | 4436.59 | 0.812843 | ||||||||
\(311\) | −8035.81 | −1.46517 | −0.732587 | − | 0.680673i | \(-0.761687\pi\) | ||||
−0.732587 | + | 0.680673i | \(0.761687\pi\) | |||||||
\(312\) | −1202.66 | −0.218229 | ||||||||
\(313\) | −1288.78 | −0.232736 | −0.116368 | − | 0.993206i | \(-0.537125\pi\) | ||||
−0.116368 | + | 0.993206i | \(0.537125\pi\) | |||||||
\(314\) | 11403.2 | 2.04943 | ||||||||
\(315\) | 398.957 | 0.0713608 | ||||||||
\(316\) | 420.741 | 0.0749004 | ||||||||
\(317\) | 8166.90 | 1.44700 | 0.723499 | − | 0.690325i | \(-0.242532\pi\) | ||||
0.723499 | + | 0.690325i | \(0.242532\pi\) | |||||||
\(318\) | −2538.05 | −0.447568 | ||||||||
\(319\) | 1796.53 | 0.315317 | ||||||||
\(320\) | −29.3812 | −0.00513269 | ||||||||
\(321\) | 4303.83 | 0.748338 | ||||||||
\(322\) | −5745.09 | −0.994289 | ||||||||
\(323\) | 6216.38 | 1.07086 | ||||||||
\(324\) | 356.371 | 0.0611062 | ||||||||
\(325\) | 790.520 | 0.134924 | ||||||||
\(326\) | −10470.4 | −1.77883 | ||||||||
\(327\) | −1043.85 | −0.176530 | ||||||||
\(328\) | 2072.17 | 0.348830 | ||||||||
\(329\) | −4689.47 | −0.785832 | ||||||||
\(330\) | 3272.14 | 0.545834 | ||||||||
\(331\) | −5018.85 | −0.833417 | −0.416708 | − | 0.909040i | \(-0.636816\pi\) | ||||
−0.416708 | + | 0.909040i | \(0.636816\pi\) | |||||||
\(332\) | 5455.44 | 0.901825 | ||||||||
\(333\) | 1779.66 | 0.292867 | ||||||||
\(334\) | 14554.0 | 2.38431 | ||||||||
\(335\) | 1147.78 | 0.187194 | ||||||||
\(336\) | 2123.52 | 0.344785 | ||||||||
\(337\) | −3702.30 | −0.598448 | −0.299224 | − | 0.954183i | \(-0.596728\pi\) | ||||
−0.299224 | + | 0.954183i | \(0.596728\pi\) | |||||||
\(338\) | −4215.45 | −0.678373 | ||||||||
\(339\) | −5438.03 | −0.871249 | ||||||||
\(340\) | 1070.64 | 0.170775 | ||||||||
\(341\) | 15610.3 | 2.47901 | ||||||||
\(342\) | −4047.89 | −0.640014 | ||||||||
\(343\) | 5385.02 | 0.847708 | ||||||||
\(344\) | 421.201 | 0.0660164 | ||||||||
\(345\) | −2760.39 | −0.430766 | ||||||||
\(346\) | 1224.56 | 0.190267 | ||||||||
\(347\) | 1084.12 | 0.167719 | 0.0838594 | − | 0.996478i | \(-0.473275\pi\) | ||||
0.0838594 | + | 0.996478i | \(0.473275\pi\) | |||||||
\(348\) | −382.769 | −0.0589614 | ||||||||
\(349\) | −3145.52 | −0.482453 | −0.241226 | − | 0.970469i | \(-0.577550\pi\) | ||||
−0.241226 | + | 0.970469i | \(0.577550\pi\) | |||||||
\(350\) | −780.473 | −0.119194 | ||||||||
\(351\) | 853.762 | 0.129830 | ||||||||
\(352\) | 11133.4 | 1.68584 | ||||||||
\(353\) | −7477.34 | −1.12742 | −0.563709 | − | 0.825974i | \(-0.690626\pi\) | ||||
−0.563709 | + | 0.825974i | \(0.690626\pi\) | |||||||
\(354\) | −2144.23 | −0.321933 | ||||||||
\(355\) | −106.032 | −0.0158524 | ||||||||
\(356\) | 514.157 | 0.0765458 | ||||||||
\(357\) | 1294.47 | 0.191906 | ||||||||
\(358\) | 2778.60 | 0.410206 | ||||||||
\(359\) | 3987.75 | 0.586255 | 0.293128 | − | 0.956073i | \(-0.405304\pi\) | ||||
0.293128 | + | 0.956073i | \(0.405304\pi\) | |||||||
\(360\) | 570.509 | 0.0835235 | ||||||||
\(361\) | 9455.09 | 1.37849 | ||||||||
\(362\) | −16014.5 | −2.32514 | ||||||||
\(363\) | 7520.12 | 1.08734 | ||||||||
\(364\) | −1233.40 | −0.177604 | ||||||||
\(365\) | 5727.42 | 0.821334 | ||||||||
\(366\) | 5199.49 | 0.742573 | ||||||||
\(367\) | 6261.36 | 0.890573 | 0.445286 | − | 0.895388i | \(-0.353102\pi\) | ||||
0.445286 | + | 0.895388i | \(0.353102\pi\) | |||||||
\(368\) | −14692.7 | −2.08127 | ||||||||
\(369\) | −1471.02 | −0.207528 | ||||||||
\(370\) | −3481.52 | −0.489177 | ||||||||
\(371\) | 2130.04 | 0.298075 | ||||||||
\(372\) | −3325.93 | −0.463553 | ||||||||
\(373\) | −9332.46 | −1.29549 | −0.647743 | − | 0.761859i | \(-0.724287\pi\) | ||||
−0.647743 | + | 0.761859i | \(0.724287\pi\) | |||||||
\(374\) | 10616.9 | 1.46788 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −6705.95 | −0.919769 | ||||||||
\(377\) | −917.004 | −0.125273 | ||||||||
\(378\) | −842.911 | −0.114695 | ||||||||
\(379\) | −4570.38 | −0.619432 | −0.309716 | − | 0.950829i | \(-0.600234\pi\) | ||||
−0.309716 | + | 0.950829i | \(0.600234\pi\) | |||||||
\(380\) | 2809.76 | 0.379309 | ||||||||
\(381\) | 1652.22 | 0.222167 | ||||||||
\(382\) | −3948.96 | −0.528918 | ||||||||
\(383\) | 2266.02 | 0.302320 | 0.151160 | − | 0.988509i | \(-0.451699\pi\) | ||||
0.151160 | + | 0.988509i | \(0.451699\pi\) | |||||||
\(384\) | 4375.33 | 0.581452 | ||||||||
\(385\) | −2746.12 | −0.363520 | ||||||||
\(386\) | −13909.4 | −1.83411 | ||||||||
\(387\) | −299.008 | −0.0392750 | ||||||||
\(388\) | −1213.08 | −0.158723 | ||||||||
\(389\) | 3874.40 | 0.504987 | 0.252494 | − | 0.967599i | \(-0.418749\pi\) | ||||
0.252494 | + | 0.967599i | \(0.418749\pi\) | |||||||
\(390\) | −1670.20 | −0.216856 | ||||||||
\(391\) | −8956.43 | −1.15843 | ||||||||
\(392\) | 3352.05 | 0.431898 | ||||||||
\(393\) | −374.473 | −0.0480653 | ||||||||
\(394\) | −1536.82 | −0.196508 | ||||||||
\(395\) | −478.154 | −0.0609076 | ||||||||
\(396\) | −2452.99 | −0.311281 | ||||||||
\(397\) | −10370.5 | −1.31104 | −0.655519 | − | 0.755179i | \(-0.727550\pi\) | ||||
−0.655519 | + | 0.755179i | \(0.727550\pi\) | |||||||
\(398\) | 2731.79 | 0.344051 | ||||||||
\(399\) | 3397.16 | 0.426242 | ||||||||
\(400\) | −1996.01 | −0.249501 | ||||||||
\(401\) | −10537.9 | −1.31231 | −0.656155 | − | 0.754626i | \(-0.727818\pi\) | ||||
−0.656155 | + | 0.754626i | \(0.727818\pi\) | |||||||
\(402\) | −2425.01 | −0.300867 | ||||||||
\(403\) | −7967.97 | −0.984895 | ||||||||
\(404\) | −8400.65 | −1.03452 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 905.349 | 0.110669 | ||||||||
\(407\) | −12249.8 | −1.49189 | ||||||||
\(408\) | 1851.09 | 0.224614 | ||||||||
\(409\) | −4052.17 | −0.489894 | −0.244947 | − | 0.969536i | \(-0.578771\pi\) | ||||
−0.244947 | + | 0.969536i | \(0.578771\pi\) | |||||||
\(410\) | 2877.73 | 0.346636 | ||||||||
\(411\) | −1649.64 | −0.197982 | ||||||||
\(412\) | 6608.14 | 0.790193 | ||||||||
\(413\) | 1799.52 | 0.214404 | ||||||||
\(414\) | 5832.11 | 0.692349 | ||||||||
\(415\) | −6199.86 | −0.733348 | ||||||||
\(416\) | −5682.85 | −0.669771 | ||||||||
\(417\) | −6729.95 | −0.790329 | ||||||||
\(418\) | 27862.6 | 3.26030 | ||||||||
\(419\) | −12386.0 | −1.44414 | −0.722071 | − | 0.691819i | \(-0.756810\pi\) | ||||
−0.722071 | + | 0.691819i | \(0.756810\pi\) | |||||||
\(420\) | 585.089 | 0.0679748 | ||||||||
\(421\) | −16516.0 | −1.91198 | −0.955989 | − | 0.293402i | \(-0.905213\pi\) | ||||
−0.955989 | + | 0.293402i | \(0.905213\pi\) | |||||||
\(422\) | 8713.29 | 1.00511 | ||||||||
\(423\) | 4760.50 | 0.547195 | ||||||||
\(424\) | 3045.96 | 0.348879 | ||||||||
\(425\) | −1216.74 | −0.138871 | ||||||||
\(426\) | 224.024 | 0.0254788 | ||||||||
\(427\) | −4363.63 | −0.494546 | ||||||||
\(428\) | 6311.78 | 0.712830 | ||||||||
\(429\) | −5876.65 | −0.661370 | ||||||||
\(430\) | 584.944 | 0.0656012 | ||||||||
\(431\) | 11987.2 | 1.33969 | 0.669843 | − | 0.742503i | \(-0.266361\pi\) | ||||
0.669843 | + | 0.742503i | \(0.266361\pi\) | |||||||
\(432\) | −2155.69 | −0.240082 | ||||||||
\(433\) | −14217.4 | −1.57793 | −0.788965 | − | 0.614439i | \(-0.789383\pi\) | ||||
−0.788965 | + | 0.614439i | \(0.789383\pi\) | |||||||
\(434\) | 7866.70 | 0.870078 | ||||||||
\(435\) | 435.000 | 0.0479463 | ||||||||
\(436\) | −1530.86 | −0.168153 | ||||||||
\(437\) | −23505.0 | −2.57299 | ||||||||
\(438\) | −12100.8 | −1.32009 | ||||||||
\(439\) | 685.738 | 0.0745524 | 0.0372762 | − | 0.999305i | \(-0.488132\pi\) | ||||
0.0372762 | + | 0.999305i | \(0.488132\pi\) | |||||||
\(440\) | −3926.96 | −0.425478 | ||||||||
\(441\) | −2379.59 | −0.256948 | ||||||||
\(442\) | −5419.18 | −0.583177 | ||||||||
\(443\) | −13828.1 | −1.48305 | −0.741527 | − | 0.670923i | \(-0.765898\pi\) | ||||
−0.741527 | + | 0.670923i | \(0.765898\pi\) | |||||||
\(444\) | 2609.95 | 0.278971 | ||||||||
\(445\) | −584.317 | −0.0622456 | ||||||||
\(446\) | −3646.74 | −0.387170 | ||||||||
\(447\) | −1842.92 | −0.195004 | ||||||||
\(448\) | −52.0970 | −0.00549409 | ||||||||
\(449\) | −4346.88 | −0.456887 | −0.228443 | − | 0.973557i | \(-0.573364\pi\) | ||||
−0.228443 | + | 0.973557i | \(0.573364\pi\) | |||||||
\(450\) | 792.295 | 0.0829981 | ||||||||
\(451\) | 10125.4 | 1.05717 | ||||||||
\(452\) | −7975.14 | −0.829909 | ||||||||
\(453\) | −3365.16 | −0.349026 | ||||||||
\(454\) | −3762.29 | −0.388927 | ||||||||
\(455\) | 1401.70 | 0.144424 | ||||||||
\(456\) | 4857.95 | 0.498891 | ||||||||
\(457\) | 2375.45 | 0.243149 | 0.121574 | − | 0.992582i | \(-0.461206\pi\) | ||||
0.121574 | + | 0.992582i | \(0.461206\pi\) | |||||||
\(458\) | −2249.45 | −0.229497 | ||||||||
\(459\) | −1314.07 | −0.133629 | ||||||||
\(460\) | −4048.24 | −0.410326 | ||||||||
\(461\) | −5656.94 | −0.571519 | −0.285759 | − | 0.958301i | \(-0.592246\pi\) | ||||
−0.285759 | + | 0.958301i | \(0.592246\pi\) | |||||||
\(462\) | 5801.96 | 0.584268 | ||||||||
\(463\) | −11017.3 | −1.10587 | −0.552935 | − | 0.833225i | \(-0.686492\pi\) | ||||
−0.552935 | + | 0.833225i | \(0.686492\pi\) | |||||||
\(464\) | 2315.37 | 0.231656 | ||||||||
\(465\) | 3779.77 | 0.376952 | ||||||||
\(466\) | 14788.9 | 1.47013 | ||||||||
\(467\) | −4441.89 | −0.440142 | −0.220071 | − | 0.975484i | \(-0.570629\pi\) | ||||
−0.220071 | + | 0.975484i | \(0.570629\pi\) | |||||||
\(468\) | 1252.08 | 0.123670 | ||||||||
\(469\) | 2035.17 | 0.200374 | ||||||||
\(470\) | −9312.90 | −0.913983 | ||||||||
\(471\) | 9715.02 | 0.950413 | ||||||||
\(472\) | 2573.32 | 0.250947 | ||||||||
\(473\) | 2058.14 | 0.200071 | ||||||||
\(474\) | 1010.24 | 0.0978939 | ||||||||
\(475\) | −3193.17 | −0.308447 | ||||||||
\(476\) | 1898.40 | 0.182800 | ||||||||
\(477\) | −2162.30 | −0.207558 | ||||||||
\(478\) | 5215.76 | 0.499087 | ||||||||
\(479\) | −6919.43 | −0.660035 | −0.330017 | − | 0.943975i | \(-0.607055\pi\) | ||||
−0.330017 | + | 0.943975i | \(0.607055\pi\) | |||||||
\(480\) | 2695.78 | 0.256344 | ||||||||
\(481\) | 6252.69 | 0.592720 | ||||||||
\(482\) | 25158.3 | 2.37744 | ||||||||
\(483\) | −4894.56 | −0.461097 | ||||||||
\(484\) | 11028.6 | 1.03575 | ||||||||
\(485\) | 1378.61 | 0.129071 | ||||||||
\(486\) | 855.679 | 0.0798650 | ||||||||
\(487\) | 4439.83 | 0.413116 | 0.206558 | − | 0.978434i | \(-0.433774\pi\) | ||||
0.206558 | + | 0.978434i | \(0.433774\pi\) | |||||||
\(488\) | −6240.01 | −0.578836 | ||||||||
\(489\) | −8920.28 | −0.824926 | ||||||||
\(490\) | 4655.16 | 0.429181 | ||||||||
\(491\) | 12089.1 | 1.11115 | 0.555575 | − | 0.831466i | \(-0.312498\pi\) | ||||
0.555575 | + | 0.831466i | \(0.312498\pi\) | |||||||
\(492\) | −2157.31 | −0.197681 | ||||||||
\(493\) | 1411.41 | 0.128939 | ||||||||
\(494\) | −14221.9 | −1.29529 | ||||||||
\(495\) | 2787.72 | 0.253128 | ||||||||
\(496\) | 20118.6 | 1.82127 | ||||||||
\(497\) | −188.010 | −0.0169686 | ||||||||
\(498\) | 13099.0 | 1.17867 | ||||||||
\(499\) | 7312.25 | 0.655994 | 0.327997 | − | 0.944679i | \(-0.393626\pi\) | ||||
0.327997 | + | 0.944679i | \(0.393626\pi\) | |||||||
\(500\) | −549.955 | −0.0491895 | ||||||||
\(501\) | 12399.4 | 1.10572 | ||||||||
\(502\) | −18345.0 | −1.63103 | ||||||||
\(503\) | 7487.34 | 0.663706 | 0.331853 | − | 0.943331i | \(-0.392326\pi\) | ||||
0.331853 | + | 0.943331i | \(0.392326\pi\) | |||||||
\(504\) | 1011.59 | 0.0894046 | ||||||||
\(505\) | 9546.96 | 0.841256 | ||||||||
\(506\) | −40143.9 | −3.52690 | ||||||||
\(507\) | −3591.37 | −0.314593 | ||||||||
\(508\) | 2423.05 | 0.211625 | ||||||||
\(509\) | −16901.9 | −1.47184 | −0.735919 | − | 0.677070i | \(-0.763250\pi\) | ||||
−0.735919 | + | 0.677070i | \(0.763250\pi\) | |||||||
\(510\) | 2570.70 | 0.223201 | ||||||||
\(511\) | 10155.5 | 0.879166 | ||||||||
\(512\) | 6251.09 | 0.539574 | ||||||||
\(513\) | −3448.62 | −0.296804 | ||||||||
\(514\) | 12083.9 | 1.03696 | ||||||||
\(515\) | −7509.85 | −0.642570 | ||||||||
\(516\) | −438.509 | −0.0374114 | ||||||||
\(517\) | −32767.7 | −2.78747 | ||||||||
\(518\) | −6173.22 | −0.523621 | ||||||||
\(519\) | 1043.27 | 0.0882356 | ||||||||
\(520\) | 2004.44 | 0.169039 | ||||||||
\(521\) | −8351.65 | −0.702289 | −0.351144 | − | 0.936321i | \(-0.614207\pi\) | ||||
−0.351144 | + | 0.936321i | \(0.614207\pi\) | |||||||
\(522\) | −919.063 | −0.0770618 | ||||||||
\(523\) | 5420.89 | 0.453230 | 0.226615 | − | 0.973984i | \(-0.427234\pi\) | ||||
0.226615 | + | 0.973984i | \(0.427234\pi\) | |||||||
\(524\) | −549.182 | −0.0457846 | ||||||||
\(525\) | −664.928 | −0.0552759 | ||||||||
\(526\) | −6121.07 | −0.507398 | ||||||||
\(527\) | 12264.0 | 1.01371 | ||||||||
\(528\) | 14838.1 | 1.22301 | ||||||||
\(529\) | 21698.5 | 1.78339 | ||||||||
\(530\) | 4230.08 | 0.346685 | ||||||||
\(531\) | −1826.78 | −0.149295 | ||||||||
\(532\) | 4982.10 | 0.406018 | ||||||||
\(533\) | −5168.30 | −0.420007 | ||||||||
\(534\) | 1234.54 | 0.100044 | ||||||||
\(535\) | −7173.05 | −0.579660 | ||||||||
\(536\) | 2910.30 | 0.234526 | ||||||||
\(537\) | 2367.25 | 0.190231 | ||||||||
\(538\) | 9962.89 | 0.798384 | ||||||||
\(539\) | 16379.3 | 1.30892 | ||||||||
\(540\) | −593.952 | −0.0473326 | ||||||||
\(541\) | 14428.9 | 1.14667 | 0.573333 | − | 0.819323i | \(-0.305650\pi\) | ||||
0.573333 | + | 0.819323i | \(0.305650\pi\) | |||||||
\(542\) | −4927.34 | −0.390494 | ||||||||
\(543\) | −13643.6 | −1.07827 | ||||||||
\(544\) | 8746.81 | 0.689368 | ||||||||
\(545\) | 1739.75 | 0.136739 | ||||||||
\(546\) | −2961.50 | −0.232126 | ||||||||
\(547\) | 4990.35 | 0.390077 | 0.195038 | − | 0.980796i | \(-0.437517\pi\) | ||||
0.195038 | + | 0.980796i | \(0.437517\pi\) | |||||||
\(548\) | −2419.27 | −0.188588 | ||||||||
\(549\) | 4429.73 | 0.344365 | ||||||||
\(550\) | −5453.57 | −0.422801 | ||||||||
\(551\) | 3704.07 | 0.286386 | ||||||||
\(552\) | −6999.23 | −0.539686 | ||||||||
\(553\) | −847.834 | −0.0651963 | ||||||||
\(554\) | −12417.5 | −0.952294 | ||||||||
\(555\) | −2966.10 | −0.226854 | ||||||||
\(556\) | −9869.80 | −0.752828 | ||||||||
\(557\) | 23481.4 | 1.78625 | 0.893123 | − | 0.449812i | \(-0.148509\pi\) | ||||
0.893123 | + | 0.449812i | \(0.148509\pi\) | |||||||
\(558\) | −7985.86 | −0.605857 | ||||||||
\(559\) | −1050.54 | −0.0794868 | ||||||||
\(560\) | −3539.20 | −0.267069 | ||||||||
\(561\) | 9045.10 | 0.680721 | ||||||||
\(562\) | −3018.20 | −0.226539 | ||||||||
\(563\) | 8869.38 | 0.663943 | 0.331972 | − | 0.943289i | \(-0.392286\pi\) | ||||
0.331972 | + | 0.943289i | \(0.392286\pi\) | |||||||
\(564\) | 6981.51 | 0.521231 | ||||||||
\(565\) | 9063.39 | 0.674867 | ||||||||
\(566\) | −25344.5 | −1.88217 | ||||||||
\(567\) | −718.122 | −0.0531892 | ||||||||
\(568\) | −268.855 | −0.0198607 | ||||||||
\(569\) | 25722.7 | 1.89517 | 0.947585 | − | 0.319503i | \(-0.103516\pi\) | ||||
0.947585 | + | 0.319503i | \(0.103516\pi\) | |||||||
\(570\) | 6746.48 | 0.495753 | ||||||||
\(571\) | 26056.8 | 1.90971 | 0.954853 | − | 0.297078i | \(-0.0960122\pi\) | ||||
0.954853 | + | 0.297078i | \(0.0960122\pi\) | |||||||
\(572\) | −8618.40 | −0.629988 | ||||||||
\(573\) | −3364.34 | −0.245283 | ||||||||
\(574\) | 5102.61 | 0.371043 | ||||||||
\(575\) | 4600.64 | 0.333670 | ||||||||
\(576\) | 52.8862 | 0.00382568 | ||||||||
\(577\) | −25737.2 | −1.85694 | −0.928471 | − | 0.371406i | \(-0.878876\pi\) | ||||
−0.928471 | + | 0.371406i | \(0.878876\pi\) | |||||||
\(578\) | −8959.23 | −0.644732 | ||||||||
\(579\) | −11850.1 | −0.850562 | ||||||||
\(580\) | 637.948 | 0.0456713 | ||||||||
\(581\) | −10993.2 | −0.784985 | ||||||||
\(582\) | −2912.71 | −0.207449 | ||||||||
\(583\) | 14883.7 | 1.05732 | ||||||||
\(584\) | 14522.4 | 1.02901 | ||||||||
\(585\) | −1422.94 | −0.100566 | ||||||||
\(586\) | 10338.7 | 0.728822 | ||||||||
\(587\) | −6862.44 | −0.482527 | −0.241263 | − | 0.970460i | \(-0.577562\pi\) | ||||
−0.241263 | + | 0.970460i | \(0.577562\pi\) | |||||||
\(588\) | −3489.79 | −0.244756 | ||||||||
\(589\) | 32185.2 | 2.25156 | ||||||||
\(590\) | 3573.71 | 0.249368 | ||||||||
\(591\) | −1309.30 | −0.0911295 | ||||||||
\(592\) | −15787.6 | −1.09606 | ||||||||
\(593\) | 4016.32 | 0.278129 | 0.139065 | − | 0.990283i | \(-0.455590\pi\) | ||||
0.139065 | + | 0.990283i | \(0.455590\pi\) | |||||||
\(594\) | −5889.85 | −0.406841 | ||||||||
\(595\) | −2157.44 | −0.148650 | ||||||||
\(596\) | −2702.72 | −0.185751 | ||||||||
\(597\) | 2327.36 | 0.159552 | ||||||||
\(598\) | 20490.7 | 1.40121 | ||||||||
\(599\) | −1729.64 | −0.117982 | −0.0589911 | − | 0.998259i | \(-0.518788\pi\) | ||||
−0.0589911 | + | 0.998259i | \(0.518788\pi\) | |||||||
\(600\) | −950.848 | −0.0646970 | ||||||||
\(601\) | 2597.41 | 0.176291 | 0.0881453 | − | 0.996108i | \(-0.471906\pi\) | ||||
0.0881453 | + | 0.996108i | \(0.471906\pi\) | |||||||
\(602\) | 1037.19 | 0.0702203 | ||||||||
\(603\) | −2066.00 | −0.139526 | ||||||||
\(604\) | −4935.17 | −0.332465 | ||||||||
\(605\) | −12533.5 | −0.842249 | ||||||||
\(606\) | −20170.7 | −1.35211 | ||||||||
\(607\) | −13844.6 | −0.925755 | −0.462877 | − | 0.886422i | \(-0.653183\pi\) | ||||
−0.462877 | + | 0.886422i | \(0.653183\pi\) | |||||||
\(608\) | 22954.9 | 1.53116 | ||||||||
\(609\) | 771.316 | 0.0513224 | ||||||||
\(610\) | −8665.82 | −0.575195 | ||||||||
\(611\) | 16725.7 | 1.10744 | ||||||||
\(612\) | −1927.15 | −0.127288 | ||||||||
\(613\) | 1127.16 | 0.0742667 | 0.0371334 | − | 0.999310i | \(-0.488177\pi\) | ||||
0.0371334 | + | 0.999310i | \(0.488177\pi\) | |||||||
\(614\) | −13480.6 | −0.886044 | ||||||||
\(615\) | 2451.69 | 0.160751 | ||||||||
\(616\) | −6963.05 | −0.455437 | ||||||||
\(617\) | 29575.8 | 1.92978 | 0.964892 | − | 0.262645i | \(-0.0845949\pi\) | ||||
0.964892 | + | 0.262645i | \(0.0845949\pi\) | |||||||
\(618\) | 15866.7 | 1.03277 | ||||||||
\(619\) | 12535.0 | 0.813935 | 0.406967 | − | 0.913443i | \(-0.366586\pi\) | ||||
0.406967 | + | 0.913443i | \(0.366586\pi\) | |||||||
\(620\) | 5543.22 | 0.359066 | ||||||||
\(621\) | 4968.70 | 0.321074 | ||||||||
\(622\) | −28296.6 | −1.82410 | ||||||||
\(623\) | −1036.08 | −0.0666285 | ||||||||
\(624\) | −7573.84 | −0.485892 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −4538.20 | −0.289749 | ||||||||
\(627\) | 23737.7 | 1.51195 | ||||||||
\(628\) | 14247.5 | 0.905316 | ||||||||
\(629\) | −9623.88 | −0.610062 | ||||||||
\(630\) | 1404.85 | 0.0888423 | ||||||||
\(631\) | 15162.1 | 0.956569 | 0.478284 | − | 0.878205i | \(-0.341259\pi\) | ||||
0.478284 | + | 0.878205i | \(0.341259\pi\) | |||||||
\(632\) | −1212.40 | −0.0763083 | ||||||||
\(633\) | 7423.33 | 0.466115 | ||||||||
\(634\) | 28758.2 | 1.80147 | ||||||||
\(635\) | −2753.69 | −0.172090 | ||||||||
\(636\) | −3171.12 | −0.197709 | ||||||||
\(637\) | −8360.52 | −0.520025 | ||||||||
\(638\) | 6326.14 | 0.392561 | ||||||||
\(639\) | 190.858 | 0.0118157 | ||||||||
\(640\) | −7292.21 | −0.450391 | ||||||||
\(641\) | −10138.5 | −0.624722 | −0.312361 | − | 0.949964i | \(-0.601120\pi\) | ||||
−0.312361 | + | 0.949964i | \(0.601120\pi\) | |||||||
\(642\) | 15155.1 | 0.931660 | ||||||||
\(643\) | 29580.6 | 1.81423 | 0.907113 | − | 0.420888i | \(-0.138282\pi\) | ||||
0.907113 | + | 0.420888i | \(0.138282\pi\) | |||||||
\(644\) | −7178.10 | −0.439219 | ||||||||
\(645\) | 498.346 | 0.0304223 | ||||||||
\(646\) | 21889.8 | 1.33319 | ||||||||
\(647\) | 30140.7 | 1.83146 | 0.915728 | − | 0.401798i | \(-0.131615\pi\) | ||||
0.915728 | + | 0.401798i | \(0.131615\pi\) | |||||||
\(648\) | −1026.92 | −0.0622548 | ||||||||
\(649\) | 12574.2 | 0.760525 | ||||||||
\(650\) | 2783.67 | 0.167976 | ||||||||
\(651\) | 6702.07 | 0.403495 | ||||||||
\(652\) | −13082.0 | −0.785784 | ||||||||
\(653\) | −10094.0 | −0.604911 | −0.302456 | − | 0.953163i | \(-0.597806\pi\) | ||||
−0.302456 | + | 0.953163i | \(0.597806\pi\) | |||||||
\(654\) | −3675.73 | −0.219774 | ||||||||
\(655\) | 624.121 | 0.0372312 | ||||||||
\(656\) | 13049.6 | 0.776678 | ||||||||
\(657\) | −10309.4 | −0.612186 | ||||||||
\(658\) | −16513.1 | −0.978339 | ||||||||
\(659\) | 16019.7 | 0.946947 | 0.473473 | − | 0.880808i | \(-0.343000\pi\) | ||||
0.473473 | + | 0.880808i | \(0.343000\pi\) | |||||||
\(660\) | 4088.32 | 0.241118 | ||||||||
\(661\) | −26006.5 | −1.53031 | −0.765157 | − | 0.643844i | \(-0.777338\pi\) | ||||
−0.765157 | + | 0.643844i | \(0.777338\pi\) | |||||||
\(662\) | −17672.9 | −1.03758 | ||||||||
\(663\) | −4616.90 | −0.270446 | ||||||||
\(664\) | −15720.3 | −0.918777 | ||||||||
\(665\) | −5661.93 | −0.330166 | ||||||||
\(666\) | 6266.73 | 0.364611 | ||||||||
\(667\) | −5336.75 | −0.309805 | ||||||||
\(668\) | 18184.3 | 1.05325 | ||||||||
\(669\) | −3106.85 | −0.179549 | ||||||||
\(670\) | 4041.69 | 0.233051 | ||||||||
\(671\) | −30490.9 | −1.75423 | ||||||||
\(672\) | 4780.00 | 0.274394 | ||||||||
\(673\) | 30662.4 | 1.75624 | 0.878119 | − | 0.478443i | \(-0.158799\pi\) | ||||
0.878119 | + | 0.478443i | \(0.158799\pi\) | |||||||
\(674\) | −13036.9 | −0.745051 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −5266.92 | −0.299665 | ||||||||
\(677\) | −4128.37 | −0.234366 | −0.117183 | − | 0.993110i | \(-0.537386\pi\) | ||||
−0.117183 | + | 0.993110i | \(0.537386\pi\) | |||||||
\(678\) | −19149.0 | −1.08468 | ||||||||
\(679\) | 2444.47 | 0.138159 | ||||||||
\(680\) | −3085.15 | −0.173985 | ||||||||
\(681\) | −3205.30 | −0.180363 | ||||||||
\(682\) | 54968.7 | 3.08630 | ||||||||
\(683\) | −19130.6 | −1.07176 | −0.535881 | − | 0.844294i | \(-0.680020\pi\) | ||||
−0.535881 | + | 0.844294i | \(0.680020\pi\) | |||||||
\(684\) | −5057.56 | −0.282720 | ||||||||
\(685\) | 2749.40 | 0.153356 | ||||||||
\(686\) | 18962.4 | 1.05537 | ||||||||
\(687\) | −1916.43 | −0.106428 | ||||||||
\(688\) | 2652.54 | 0.146987 | ||||||||
\(689\) | −7597.08 | −0.420066 | ||||||||
\(690\) | −9720.19 | −0.536292 | ||||||||
\(691\) | 27493.6 | 1.51361 | 0.756807 | − | 0.653638i | \(-0.226758\pi\) | ||||
0.756807 | + | 0.653638i | \(0.226758\pi\) | |||||||
\(692\) | 1530.00 | 0.0840489 | ||||||||
\(693\) | 4943.01 | 0.270952 | ||||||||
\(694\) | 3817.51 | 0.208805 | ||||||||
\(695\) | 11216.6 | 0.612186 | ||||||||
\(696\) | 1102.98 | 0.0600697 | ||||||||
\(697\) | 7954.83 | 0.432296 | ||||||||
\(698\) | −11076.4 | −0.600640 | ||||||||
\(699\) | 12599.4 | 0.681766 | ||||||||
\(700\) | −975.149 | −0.0526531 | ||||||||
\(701\) | 13029.3 | 0.702010 | 0.351005 | − | 0.936374i | \(-0.385840\pi\) | ||||
0.351005 | + | 0.936374i | \(0.385840\pi\) | |||||||
\(702\) | 3006.36 | 0.161635 | ||||||||
\(703\) | −25256.6 | −1.35501 | ||||||||
\(704\) | −364.029 | −0.0194884 | ||||||||
\(705\) | −7934.17 | −0.423856 | ||||||||
\(706\) | −26330.0 | −1.40360 | ||||||||
\(707\) | 16928.1 | 0.900491 | ||||||||
\(708\) | −2679.07 | −0.142211 | ||||||||
\(709\) | −33140.8 | −1.75547 | −0.877735 | − | 0.479146i | \(-0.840946\pi\) | ||||
−0.877735 | + | 0.479146i | \(0.840946\pi\) | |||||||
\(710\) | −373.373 | −0.0197358 | ||||||||
\(711\) | 860.676 | 0.0453979 | ||||||||
\(712\) | −1481.59 | −0.0779846 | ||||||||
\(713\) | −46371.7 | −2.43567 | ||||||||
\(714\) | 4558.22 | 0.238918 | ||||||||
\(715\) | 9794.42 | 0.512295 | ||||||||
\(716\) | 3471.68 | 0.181205 | ||||||||
\(717\) | 4443.59 | 0.231449 | ||||||||
\(718\) | 14042.1 | 0.729871 | ||||||||
\(719\) | 23672.8 | 1.22788 | 0.613940 | − | 0.789353i | \(-0.289584\pi\) | ||||
0.613940 | + | 0.789353i | \(0.289584\pi\) | |||||||
\(720\) | 3592.81 | 0.185967 | ||||||||
\(721\) | −13316.0 | −0.687815 | ||||||||
\(722\) | 33294.3 | 1.71619 | ||||||||
\(723\) | 21433.7 | 1.10253 | ||||||||
\(724\) | −20009.0 | −1.02711 | ||||||||
\(725\) | −725.000 | −0.0371391 | ||||||||
\(726\) | 26480.7 | 1.35371 | ||||||||
\(727\) | 16424.5 | 0.837895 | 0.418947 | − | 0.908010i | \(-0.362399\pi\) | ||||
0.418947 | + | 0.908010i | \(0.362399\pi\) | |||||||
\(728\) | 3554.16 | 0.180942 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 20168.0 | 1.02254 | ||||||||
\(731\) | 1616.95 | 0.0818125 | ||||||||
\(732\) | 6496.41 | 0.328025 | ||||||||
\(733\) | 19399.9 | 0.977559 | 0.488780 | − | 0.872407i | \(-0.337442\pi\) | ||||
0.488780 | + | 0.872407i | \(0.337442\pi\) | |||||||
\(734\) | 22048.2 | 1.10874 | ||||||||
\(735\) | 3965.99 | 0.199031 | ||||||||
\(736\) | −33072.9 | −1.65636 | ||||||||
\(737\) | 14220.8 | 0.710759 | ||||||||
\(738\) | −5179.91 | −0.258367 | ||||||||
\(739\) | −5065.65 | −0.252156 | −0.126078 | − | 0.992020i | \(-0.540239\pi\) | ||||
−0.126078 | + | 0.992020i | \(0.540239\pi\) | |||||||
\(740\) | −4349.92 | −0.216090 | ||||||||
\(741\) | −12116.5 | −0.600687 | ||||||||
\(742\) | 7500.53 | 0.371096 | ||||||||
\(743\) | −15186.2 | −0.749833 | −0.374917 | − | 0.927059i | \(-0.622329\pi\) | ||||
−0.374917 | + | 0.927059i | \(0.622329\pi\) | |||||||
\(744\) | 9583.98 | 0.472266 | ||||||||
\(745\) | 3071.53 | 0.151050 | ||||||||
\(746\) | −32862.5 | −1.61284 | ||||||||
\(747\) | 11159.8 | 0.546605 | ||||||||
\(748\) | 13265.1 | 0.648421 | ||||||||
\(749\) | −12718.8 | −0.620476 | ||||||||
\(750\) | −1320.49 | −0.0642901 | ||||||||
\(751\) | −25919.9 | −1.25943 | −0.629713 | − | 0.776828i | \(-0.716828\pi\) | ||||
−0.629713 | + | 0.776828i | \(0.716828\pi\) | |||||||
\(752\) | −42231.1 | −2.04789 | ||||||||
\(753\) | −15629.2 | −0.756385 | ||||||||
\(754\) | −3229.06 | −0.155962 | ||||||||
\(755\) | 5608.60 | 0.270355 | ||||||||
\(756\) | −1053.16 | −0.0506655 | ||||||||
\(757\) | 25691.7 | 1.23353 | 0.616765 | − | 0.787148i | \(-0.288443\pi\) | ||||
0.616765 | + | 0.787148i | \(0.288443\pi\) | |||||||
\(758\) | −16093.7 | −0.771175 | ||||||||
\(759\) | −34200.8 | −1.63559 | ||||||||
\(760\) | −8096.58 | −0.386439 | ||||||||
\(761\) | 3453.84 | 0.164523 | 0.0822613 | − | 0.996611i | \(-0.473786\pi\) | ||||
0.0822613 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(762\) | 5817.97 | 0.276592 | ||||||||
\(763\) | 3084.83 | 0.146367 | ||||||||
\(764\) | −4933.96 | −0.233645 | ||||||||
\(765\) | 2190.12 | 0.103509 | ||||||||
\(766\) | 7979.38 | 0.376379 | ||||||||
\(767\) | −6418.26 | −0.302151 | ||||||||
\(768\) | 15265.9 | 0.717265 | ||||||||
\(769\) | 24995.5 | 1.17212 | 0.586060 | − | 0.810268i | \(-0.300678\pi\) | ||||
0.586060 | + | 0.810268i | \(0.300678\pi\) | |||||||
\(770\) | −9669.94 | −0.452572 | ||||||||
\(771\) | 10294.9 | 0.480886 | ||||||||
\(772\) | −17378.8 | −0.810203 | ||||||||
\(773\) | 15444.9 | 0.718648 | 0.359324 | − | 0.933213i | \(-0.383007\pi\) | ||||
0.359324 | + | 0.933213i | \(0.383007\pi\) | |||||||
\(774\) | −1052.90 | −0.0488962 | ||||||||
\(775\) | −6299.62 | −0.291986 | ||||||||
\(776\) | 3495.59 | 0.161707 | ||||||||
\(777\) | −5259.31 | −0.242827 | ||||||||
\(778\) | 13643.0 | 0.628695 | ||||||||
\(779\) | 20876.4 | 0.960174 | ||||||||
\(780\) | −2086.80 | −0.0957943 | ||||||||
\(781\) | −1313.72 | −0.0601904 | ||||||||
\(782\) | −31538.4 | −1.44221 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | 21109.7 | 0.961630 | ||||||||
\(785\) | −16191.7 | −0.736187 | ||||||||
\(786\) | −1318.64 | −0.0598399 | ||||||||
\(787\) | −30204.3 | −1.36807 | −0.684033 | − | 0.729451i | \(-0.739776\pi\) | ||||
−0.684033 | + | 0.729451i | \(0.739776\pi\) | |||||||
\(788\) | −1920.16 | −0.0868055 | ||||||||
\(789\) | −5214.88 | −0.235304 | ||||||||
\(790\) | −1683.73 | −0.0758283 | ||||||||
\(791\) | 16070.7 | 0.722386 | ||||||||
\(792\) | 7068.52 | 0.317132 | ||||||||
\(793\) | 15563.5 | 0.696944 | ||||||||
\(794\) | −36517.9 | −1.63220 | ||||||||
\(795\) | 3603.84 | 0.160773 | ||||||||
\(796\) | 3413.19 | 0.151981 | ||||||||
\(797\) | 44520.9 | 1.97869 | 0.989343 | − | 0.145606i | \(-0.0465131\pi\) | ||||
0.989343 | + | 0.145606i | \(0.0465131\pi\) | |||||||
\(798\) | 11962.5 | 0.530660 | ||||||||
\(799\) | −25743.4 | −1.13985 | ||||||||
\(800\) | −4492.97 | −0.198563 | ||||||||
\(801\) | 1051.77 | 0.0463951 | ||||||||
\(802\) | −37107.1 | −1.63379 | ||||||||
\(803\) | 70961.8 | 3.11854 | ||||||||
\(804\) | −3029.89 | −0.132905 | ||||||||
\(805\) | 8157.59 | 0.357164 | ||||||||
\(806\) | −28057.7 | −1.22617 | ||||||||
\(807\) | 8487.93 | 0.370247 | ||||||||
\(808\) | 24207.2 | 1.05397 | ||||||||
\(809\) | −10369.6 | −0.450651 | −0.225326 | − | 0.974284i | \(-0.572345\pi\) | ||||
−0.225326 | + | 0.974284i | \(0.572345\pi\) | |||||||
\(810\) | −1426.13 | −0.0618632 | ||||||||
\(811\) | 24341.6 | 1.05394 | 0.526972 | − | 0.849883i | \(-0.323327\pi\) | ||||
0.526972 | + | 0.849883i | \(0.323327\pi\) | |||||||
\(812\) | 1131.17 | 0.0488872 | ||||||||
\(813\) | −4197.88 | −0.181090 | ||||||||
\(814\) | −43135.5 | −1.85737 | ||||||||
\(815\) | 14867.1 | 0.638985 | ||||||||
\(816\) | 11657.3 | 0.500108 | ||||||||
\(817\) | 4243.47 | 0.181714 | ||||||||
\(818\) | −14268.9 | −0.609905 | ||||||||
\(819\) | −2523.07 | −0.107647 | ||||||||
\(820\) | 3595.52 | 0.153123 | ||||||||
\(821\) | −17287.1 | −0.734864 | −0.367432 | − | 0.930050i | \(-0.619763\pi\) | ||||
−0.367432 | + | 0.930050i | \(0.619763\pi\) | |||||||
\(822\) | −5808.89 | −0.246482 | ||||||||
\(823\) | 5724.85 | 0.242474 | 0.121237 | − | 0.992624i | \(-0.461314\pi\) | ||||
0.121237 | + | 0.992624i | \(0.461314\pi\) | |||||||
\(824\) | −19042.0 | −0.805046 | ||||||||
\(825\) | −4646.19 | −0.196072 | ||||||||
\(826\) | 6336.69 | 0.266927 | ||||||||
\(827\) | 25964.5 | 1.09175 | 0.545874 | − | 0.837867i | \(-0.316198\pi\) | ||||
0.545874 | + | 0.837867i | \(0.316198\pi\) | |||||||
\(828\) | 7286.83 | 0.305839 | ||||||||
\(829\) | −13876.2 | −0.581349 | −0.290675 | − | 0.956822i | \(-0.593880\pi\) | ||||
−0.290675 | + | 0.956822i | \(0.593880\pi\) | |||||||
\(830\) | −21831.7 | −0.912997 | ||||||||
\(831\) | −10579.2 | −0.441622 | ||||||||
\(832\) | 185.812 | 0.00774262 | ||||||||
\(833\) | 12868.2 | 0.535240 | ||||||||
\(834\) | −23698.3 | −0.983937 | ||||||||
\(835\) | −20665.6 | −0.856483 | ||||||||
\(836\) | 34812.5 | 1.44021 | ||||||||
\(837\) | −6803.59 | −0.280964 | ||||||||
\(838\) | −43615.0 | −1.79792 | ||||||||
\(839\) | −20190.6 | −0.830818 | −0.415409 | − | 0.909635i | \(-0.636362\pi\) | ||||
−0.415409 | + | 0.909635i | \(0.636362\pi\) | |||||||
\(840\) | −1685.99 | −0.0692525 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −58158.2 | −2.38036 | ||||||||
\(843\) | −2571.37 | −0.105057 | ||||||||
\(844\) | 10886.7 | 0.443998 | ||||||||
\(845\) | 5985.62 | 0.243682 | ||||||||
\(846\) | 16763.2 | 0.681243 | ||||||||
\(847\) | −22223.7 | −0.901554 | ||||||||
\(848\) | 19182.1 | 0.776787 | ||||||||
\(849\) | −21592.4 | −0.872849 | ||||||||
\(850\) | −4284.51 | −0.172891 | ||||||||
\(851\) | 36389.2 | 1.46581 | ||||||||
\(852\) | 279.902 | 0.0112550 | ||||||||
\(853\) | −14388.2 | −0.577542 | −0.288771 | − | 0.957398i | \(-0.593247\pi\) | ||||
−0.288771 | + | 0.957398i | \(0.593247\pi\) | |||||||
\(854\) | −15365.7 | −0.615696 | ||||||||
\(855\) | 5747.70 | 0.229903 | ||||||||
\(856\) | −18188.0 | −0.726229 | ||||||||
\(857\) | −12095.7 | −0.482125 | −0.241063 | − | 0.970510i | \(-0.577496\pi\) | ||||
−0.241063 | + | 0.970510i | \(0.577496\pi\) | |||||||
\(858\) | −20693.5 | −0.823387 | ||||||||
\(859\) | −16863.4 | −0.669815 | −0.334907 | − | 0.942251i | \(-0.608705\pi\) | ||||
−0.334907 | + | 0.942251i | \(0.608705\pi\) | |||||||
\(860\) | 730.848 | 0.0289787 | ||||||||
\(861\) | 4347.20 | 0.172070 | ||||||||
\(862\) | 42210.8 | 1.66787 | ||||||||
\(863\) | 6575.91 | 0.259382 | 0.129691 | − | 0.991554i | \(-0.458601\pi\) | ||||
0.129691 | + | 0.991554i | \(0.458601\pi\) | |||||||
\(864\) | −4852.41 | −0.191067 | ||||||||
\(865\) | −1738.78 | −0.0683470 | ||||||||
\(866\) | −50063.8 | −1.96448 | ||||||||
\(867\) | −7632.86 | −0.298992 | ||||||||
\(868\) | 9828.91 | 0.384349 | ||||||||
\(869\) | −5924.25 | −0.231262 | ||||||||
\(870\) | 1531.77 | 0.0596918 | ||||||||
\(871\) | −7258.74 | −0.282380 | ||||||||
\(872\) | 4411.31 | 0.171314 | ||||||||
\(873\) | −2481.50 | −0.0962038 | ||||||||
\(874\) | −82768.4 | −3.20330 | ||||||||
\(875\) | 1108.21 | 0.0428165 | ||||||||
\(876\) | −15119.2 | −0.583138 | ||||||||
\(877\) | −2474.27 | −0.0952683 | −0.0476341 | − | 0.998865i | \(-0.515168\pi\) | ||||
−0.0476341 | + | 0.998865i | \(0.515168\pi\) | |||||||
\(878\) | 2414.70 | 0.0928157 | ||||||||
\(879\) | 8808.15 | 0.337988 | ||||||||
\(880\) | −24730.2 | −0.947336 | ||||||||
\(881\) | 39922.4 | 1.52670 | 0.763349 | − | 0.645987i | \(-0.223554\pi\) | ||||
0.763349 | + | 0.645987i | \(0.223554\pi\) | |||||||
\(882\) | −8379.29 | −0.319893 | ||||||||
\(883\) | 15872.9 | 0.604944 | 0.302472 | − | 0.953158i | \(-0.402188\pi\) | ||||
0.302472 | + | 0.953158i | \(0.402188\pi\) | |||||||
\(884\) | −6770.90 | −0.257613 | ||||||||
\(885\) | 3044.64 | 0.115643 | ||||||||
\(886\) | −48693.0 | −1.84636 | ||||||||
\(887\) | −48655.2 | −1.84181 | −0.920903 | − | 0.389792i | \(-0.872547\pi\) | ||||
−0.920903 | + | 0.389792i | \(0.872547\pi\) | |||||||
\(888\) | −7520.82 | −0.284214 | ||||||||
\(889\) | −4882.69 | −0.184207 | ||||||||
\(890\) | −2057.56 | −0.0774940 | ||||||||
\(891\) | −5017.89 | −0.188671 | ||||||||
\(892\) | −4556.35 | −0.171029 | ||||||||
\(893\) | −67560.3 | −2.53171 | ||||||||
\(894\) | −6489.48 | −0.242775 | ||||||||
\(895\) | −3945.41 | −0.147352 | ||||||||
\(896\) | −12930.1 | −0.482104 | ||||||||
\(897\) | 17457.1 | 0.649807 | ||||||||
\(898\) | −15306.7 | −0.568811 | ||||||||
\(899\) | 7307.56 | 0.271102 | ||||||||
\(900\) | 989.920 | 0.0366637 | ||||||||
\(901\) | 11693.1 | 0.432357 | ||||||||
\(902\) | 35654.6 | 1.31615 | ||||||||
\(903\) | 883.638 | 0.0325644 | ||||||||
\(904\) | 22981.1 | 0.845509 | ||||||||
\(905\) | 22739.3 | 0.835227 | ||||||||
\(906\) | −11849.8 | −0.434528 | ||||||||
\(907\) | −26851.3 | −0.983001 | −0.491501 | − | 0.870877i | \(-0.663551\pi\) | ||||
−0.491501 | + | 0.870877i | \(0.663551\pi\) | |||||||
\(908\) | −4700.73 | −0.171805 | ||||||||
\(909\) | −17184.5 | −0.627035 | ||||||||
\(910\) | 4935.84 | 0.179804 | ||||||||
\(911\) | 29057.6 | 1.05677 | 0.528387 | − | 0.849003i | \(-0.322797\pi\) | ||||
0.528387 | + | 0.849003i | \(0.322797\pi\) | |||||||
\(912\) | 30593.2 | 1.11079 | ||||||||
\(913\) | −76815.3 | −2.78447 | ||||||||
\(914\) | 8364.72 | 0.302714 | ||||||||
\(915\) | −7382.89 | −0.266744 | ||||||||
\(916\) | −2810.53 | −0.101378 | ||||||||
\(917\) | 1106.65 | 0.0398527 | ||||||||
\(918\) | −4627.27 | −0.166364 | ||||||||
\(919\) | 24093.6 | 0.864825 | 0.432413 | − | 0.901676i | \(-0.357662\pi\) | ||||
0.432413 | + | 0.901676i | \(0.357662\pi\) | |||||||
\(920\) | 11665.4 | 0.418039 | ||||||||
\(921\) | −11484.8 | −0.410899 | ||||||||
\(922\) | −19919.9 | −0.711525 | ||||||||
\(923\) | 670.565 | 0.0239132 | ||||||||
\(924\) | 7249.17 | 0.258095 | ||||||||
\(925\) | 4943.49 | 0.175720 | ||||||||
\(926\) | −38795.4 | −1.37678 | ||||||||
\(927\) | 13517.7 | 0.478944 | ||||||||
\(928\) | 5211.84 | 0.184361 | ||||||||
\(929\) | −53631.6 | −1.89408 | −0.947038 | − | 0.321123i | \(-0.895940\pi\) | ||||
−0.947038 | + | 0.321123i | \(0.895940\pi\) | |||||||
\(930\) | 13309.8 | 0.469295 | ||||||||
\(931\) | 33770.8 | 1.18882 | ||||||||
\(932\) | 18477.7 | 0.649417 | ||||||||
\(933\) | −24107.4 | −0.845919 | ||||||||
\(934\) | −15641.3 | −0.547964 | ||||||||
\(935\) | −15075.2 | −0.527284 | ||||||||
\(936\) | −3607.99 | −0.125995 | ||||||||
\(937\) | 26075.5 | 0.909125 | 0.454562 | − | 0.890715i | \(-0.349796\pi\) | ||||
0.454562 | + | 0.890715i | \(0.349796\pi\) | |||||||
\(938\) | 7166.48 | 0.249460 | ||||||||
\(939\) | −3866.34 | −0.134370 | ||||||||
\(940\) | −11635.8 | −0.403744 | ||||||||
\(941\) | −18872.4 | −0.653796 | −0.326898 | − | 0.945060i | \(-0.606003\pi\) | ||||
−0.326898 | + | 0.945060i | \(0.606003\pi\) | |||||||
\(942\) | 34209.6 | 1.18324 | ||||||||
\(943\) | −30078.3 | −1.03869 | ||||||||
\(944\) | 16205.7 | 0.558739 | ||||||||
\(945\) | 1196.87 | 0.0412002 | ||||||||
\(946\) | 7247.37 | 0.249083 | ||||||||
\(947\) | −9904.80 | −0.339876 | −0.169938 | − | 0.985455i | \(-0.554357\pi\) | ||||
−0.169938 | + | 0.985455i | \(0.554357\pi\) | |||||||
\(948\) | 1262.22 | 0.0432438 | ||||||||
\(949\) | −36221.1 | −1.23898 | ||||||||
\(950\) | −11244.1 | −0.384008 | ||||||||
\(951\) | 24500.7 | 0.835425 | ||||||||
\(952\) | −5470.41 | −0.186236 | ||||||||
\(953\) | 11915.9 | 0.405029 | 0.202514 | − | 0.979279i | \(-0.435089\pi\) | ||||
0.202514 | + | 0.979279i | \(0.435089\pi\) | |||||||
\(954\) | −7614.14 | −0.258403 | ||||||||
\(955\) | 5607.23 | 0.189996 | ||||||||
\(956\) | 6516.74 | 0.220467 | ||||||||
\(957\) | 5389.58 | 0.182049 | ||||||||
\(958\) | −24365.5 | −0.821725 | ||||||||
\(959\) | 4875.07 | 0.164155 | ||||||||
\(960\) | −88.1436 | −0.00296336 | ||||||||
\(961\) | 33705.4 | 1.13140 | ||||||||
\(962\) | 22017.7 | 0.737919 | ||||||||
\(963\) | 12911.5 | 0.432053 | ||||||||
\(964\) | 31433.6 | 1.05021 | ||||||||
\(965\) | 19750.2 | 0.658842 | ||||||||
\(966\) | −17235.3 | −0.574053 | ||||||||
\(967\) | 38119.9 | 1.26769 | 0.633843 | − | 0.773462i | \(-0.281477\pi\) | ||||
0.633843 | + | 0.773462i | \(0.281477\pi\) | |||||||
\(968\) | −31780.0 | −1.05521 | ||||||||
\(969\) | 18649.1 | 0.618263 | ||||||||
\(970\) | 4854.51 | 0.160690 | ||||||||
\(971\) | −12393.2 | −0.409593 | −0.204797 | − | 0.978805i | \(-0.565653\pi\) | ||||
−0.204797 | + | 0.978805i | \(0.565653\pi\) | |||||||
\(972\) | 1069.11 | 0.0352797 | ||||||||
\(973\) | 19888.6 | 0.655292 | ||||||||
\(974\) | 15634.0 | 0.514318 | ||||||||
\(975\) | 2371.56 | 0.0778982 | ||||||||
\(976\) | −39296.8 | −1.28879 | ||||||||
\(977\) | 36796.8 | 1.20495 | 0.602474 | − | 0.798138i | \(-0.294182\pi\) | ||||
0.602474 | + | 0.798138i | \(0.294182\pi\) | |||||||
\(978\) | −31411.1 | −1.02701 | ||||||||
\(979\) | −7239.60 | −0.236342 | ||||||||
\(980\) | 5816.31 | 0.189587 | ||||||||
\(981\) | −3131.56 | −0.101919 | ||||||||
\(982\) | 42569.6 | 1.38335 | ||||||||
\(983\) | 17819.2 | 0.578174 | 0.289087 | − | 0.957303i | \(-0.406648\pi\) | ||||
0.289087 | + | 0.957303i | \(0.406648\pi\) | |||||||
\(984\) | 6216.50 | 0.201397 | ||||||||
\(985\) | 2182.17 | 0.0705886 | ||||||||
\(986\) | 4970.03 | 0.160525 | ||||||||
\(987\) | −14068.4 | −0.453700 | ||||||||
\(988\) | −17769.4 | −0.572185 | ||||||||
\(989\) | −6113.90 | −0.196573 | ||||||||
\(990\) | 9816.42 | 0.315138 | ||||||||
\(991\) | −832.856 | −0.0266968 | −0.0133484 | − | 0.999911i | \(-0.504249\pi\) | ||||
−0.0133484 | + | 0.999911i | \(0.504249\pi\) | |||||||
\(992\) | 45286.4 | 1.44944 | ||||||||
\(993\) | −15056.5 | −0.481173 | ||||||||
\(994\) | −662.042 | −0.0211255 | ||||||||
\(995\) | −3878.94 | −0.123589 | ||||||||
\(996\) | 16366.3 | 0.520669 | ||||||||
\(997\) | −5156.04 | −0.163785 | −0.0818923 | − | 0.996641i | \(-0.526096\pi\) | ||||
−0.0818923 | + | 0.996641i | \(0.526096\pi\) | |||||||
\(998\) | 25748.7 | 0.816694 | ||||||||
\(999\) | 5338.97 | 0.169087 |
(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 | 435.4.a.j.1.6 | ✓ | 7 | |
3.2 | odd | 2 | 1305.4.a.m.1.2 | 7 | |||
5.4 | even | 2 | 2175.4.a.m.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.j.1.6 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.4.a.m.1.2 | 7 | 3.2 | odd | 2 | |||
2175.4.a.m.1.2 | 7 | 5.4 | even | 2 |