Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.0820624 | −0.0473788 | −0.0236894 | − | 0.999719i | \(-0.507541\pi\) | ||||
−0.0236894 | + | 0.999719i | \(0.507541\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.26458 | −1.45996 | −0.729982 | − | 0.683467i | \(-0.760471\pi\) | ||||
−0.729982 | + | 0.683467i | \(0.760471\pi\) | |||||||
\(6\) | 0.0820624 | 0.0335018 | ||||||||
\(7\) | −0.430136 | −0.162576 | −0.0812880 | − | 0.996691i | \(-0.525903\pi\) | ||||
−0.0812880 | + | 0.996691i | \(0.525903\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.99327 | −0.997755 | ||||||||
\(10\) | 3.26458 | 1.03235 | ||||||||
\(11\) | 4.69415 | 1.41534 | 0.707669 | − | 0.706544i | \(-0.249747\pi\) | ||||
0.707669 | + | 0.706544i | \(0.249747\pi\) | |||||||
\(12\) | −0.0820624 | −0.0236894 | ||||||||
\(13\) | 7.01292 | 1.94503 | 0.972517 | − | 0.232830i | \(-0.0747987\pi\) | ||||
0.972517 | + | 0.232830i | \(0.0747987\pi\) | |||||||
\(14\) | 0.430136 | 0.114959 | ||||||||
\(15\) | 0.267899 | 0.0691713 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.392111 | 0.0951009 | 0.0475504 | − | 0.998869i | \(-0.484859\pi\) | ||||
0.0475504 | + | 0.998869i | \(0.484859\pi\) | |||||||
\(18\) | 2.99327 | 0.705520 | ||||||||
\(19\) | 8.43997 | 1.93626 | 0.968131 | − | 0.250446i | \(-0.0805772\pi\) | ||||
0.968131 | + | 0.250446i | \(0.0805772\pi\) | |||||||
\(20\) | −3.26458 | −0.729982 | ||||||||
\(21\) | 0.0352980 | 0.00770265 | ||||||||
\(22\) | −4.69415 | −1.00080 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.0820624 | 0.0167509 | ||||||||
\(25\) | 5.65746 | 1.13149 | ||||||||
\(26\) | −7.01292 | −1.37535 | ||||||||
\(27\) | 0.491822 | 0.0946512 | ||||||||
\(28\) | −0.430136 | −0.0812880 | ||||||||
\(29\) | 0.423629 | 0.0786659 | 0.0393330 | − | 0.999226i | \(-0.487477\pi\) | ||||
0.0393330 | + | 0.999226i | \(0.487477\pi\) | |||||||
\(30\) | −0.267899 | −0.0489115 | ||||||||
\(31\) | 8.04433 | 1.44480 | 0.722402 | − | 0.691473i | \(-0.243038\pi\) | ||||
0.722402 | + | 0.691473i | \(0.243038\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.385213 | −0.0670570 | ||||||||
\(34\) | −0.392111 | −0.0672465 | ||||||||
\(35\) | 1.40421 | 0.237355 | ||||||||
\(36\) | −2.99327 | −0.498878 | ||||||||
\(37\) | −3.06092 | −0.503212 | −0.251606 | − | 0.967830i | \(-0.580959\pi\) | ||||
−0.251606 | + | 0.967830i | \(0.580959\pi\) | |||||||
\(38\) | −8.43997 | −1.36914 | ||||||||
\(39\) | −0.575497 | −0.0921533 | ||||||||
\(40\) | 3.26458 | 0.516175 | ||||||||
\(41\) | 6.59524 | 1.03000 | 0.515002 | − | 0.857189i | \(-0.327791\pi\) | ||||
0.515002 | + | 0.857189i | \(0.327791\pi\) | |||||||
\(42\) | −0.0352980 | −0.00544660 | ||||||||
\(43\) | −2.90818 | −0.443494 | −0.221747 | − | 0.975104i | \(-0.571176\pi\) | ||||
−0.221747 | + | 0.975104i | \(0.571176\pi\) | |||||||
\(44\) | 4.69415 | 0.707669 | ||||||||
\(45\) | 9.77175 | 1.45669 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.57331 | −1.25055 | −0.625273 | − | 0.780406i | \(-0.715012\pi\) | ||||
−0.625273 | + | 0.780406i | \(0.715012\pi\) | |||||||
\(48\) | −0.0820624 | −0.0118447 | ||||||||
\(49\) | −6.81498 | −0.973569 | ||||||||
\(50\) | −5.65746 | −0.800086 | ||||||||
\(51\) | −0.0321776 | −0.00450576 | ||||||||
\(52\) | 7.01292 | 0.972517 | ||||||||
\(53\) | −10.7899 | −1.48211 | −0.741055 | − | 0.671444i | \(-0.765674\pi\) | ||||
−0.741055 | + | 0.671444i | \(0.765674\pi\) | |||||||
\(54\) | −0.491822 | −0.0669285 | ||||||||
\(55\) | −15.3244 | −2.06634 | ||||||||
\(56\) | 0.430136 | 0.0574793 | ||||||||
\(57\) | −0.692604 | −0.0917377 | ||||||||
\(58\) | −0.423629 | −0.0556252 | ||||||||
\(59\) | −1.19489 | −0.155561 | −0.0777806 | − | 0.996971i | \(-0.524783\pi\) | ||||
−0.0777806 | + | 0.996971i | \(0.524783\pi\) | |||||||
\(60\) | 0.267899 | 0.0345856 | ||||||||
\(61\) | 7.80797 | 0.999709 | 0.499854 | − | 0.866110i | \(-0.333387\pi\) | ||||
0.499854 | + | 0.866110i | \(0.333387\pi\) | |||||||
\(62\) | −8.04433 | −1.02163 | ||||||||
\(63\) | 1.28751 | 0.162211 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −22.8942 | −2.83968 | ||||||||
\(66\) | 0.385213 | 0.0474165 | ||||||||
\(67\) | −4.56048 | −0.557152 | −0.278576 | − | 0.960414i | \(-0.589862\pi\) | ||||
−0.278576 | + | 0.960414i | \(0.589862\pi\) | |||||||
\(68\) | 0.392111 | 0.0475504 | ||||||||
\(69\) | −0.0820624 | −0.00987916 | ||||||||
\(70\) | −1.40421 | −0.167835 | ||||||||
\(71\) | −2.37416 | −0.281761 | −0.140880 | − | 0.990027i | \(-0.544993\pi\) | ||||
−0.140880 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(72\) | 2.99327 | 0.352760 | ||||||||
\(73\) | 10.1037 | 1.18255 | 0.591273 | − | 0.806472i | \(-0.298626\pi\) | ||||
0.591273 | + | 0.806472i | \(0.298626\pi\) | |||||||
\(74\) | 3.06092 | 0.355824 | ||||||||
\(75\) | −0.464265 | −0.0536087 | ||||||||
\(76\) | 8.43997 | 0.968131 | ||||||||
\(77\) | −2.01912 | −0.230100 | ||||||||
\(78\) | 0.575497 | 0.0651623 | ||||||||
\(79\) | 2.93297 | 0.329985 | 0.164993 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164993 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(80\) | −3.26458 | −0.364991 | ||||||||
\(81\) | 8.93944 | 0.993271 | ||||||||
\(82\) | −6.59524 | −0.728323 | ||||||||
\(83\) | −5.21951 | −0.572916 | −0.286458 | − | 0.958093i | \(-0.592478\pi\) | ||||
−0.286458 | + | 0.958093i | \(0.592478\pi\) | |||||||
\(84\) | 0.0352980 | 0.00385133 | ||||||||
\(85\) | −1.28008 | −0.138844 | ||||||||
\(86\) | 2.90818 | 0.313597 | ||||||||
\(87\) | −0.0347640 | −0.00372709 | ||||||||
\(88\) | −4.69415 | −0.500398 | ||||||||
\(89\) | 1.31862 | 0.139774 | 0.0698869 | − | 0.997555i | \(-0.477736\pi\) | ||||
0.0698869 | + | 0.997555i | \(0.477736\pi\) | |||||||
\(90\) | −9.77175 | −1.03003 | ||||||||
\(91\) | −3.01651 | −0.316216 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −0.660137 | −0.0684530 | ||||||||
\(94\) | 8.57331 | 0.884269 | ||||||||
\(95\) | −27.5529 | −2.82687 | ||||||||
\(96\) | 0.0820624 | 0.00837546 | ||||||||
\(97\) | −8.70998 | −0.884365 | −0.442182 | − | 0.896925i | \(-0.645796\pi\) | ||||
−0.442182 | + | 0.896925i | \(0.645796\pi\) | |||||||
\(98\) | 6.81498 | 0.688417 | ||||||||
\(99\) | −14.0508 | −1.41216 | ||||||||
\(100\) | 5.65746 | 0.565746 | ||||||||
\(101\) | 14.4610 | 1.43892 | 0.719460 | − | 0.694534i | \(-0.244389\pi\) | ||||
0.719460 | + | 0.694534i | \(0.244389\pi\) | |||||||
\(102\) | 0.0321776 | 0.00318605 | ||||||||
\(103\) | 5.41642 | 0.533696 | 0.266848 | − | 0.963739i | \(-0.414018\pi\) | ||||
0.266848 | + | 0.963739i | \(0.414018\pi\) | |||||||
\(104\) | −7.01292 | −0.687674 | ||||||||
\(105\) | −0.115233 | −0.0112456 | ||||||||
\(106\) | 10.7899 | 1.04801 | ||||||||
\(107\) | 7.98644 | 0.772079 | 0.386039 | − | 0.922482i | \(-0.373843\pi\) | ||||
0.386039 | + | 0.922482i | \(0.373843\pi\) | |||||||
\(108\) | 0.491822 | 0.0473256 | ||||||||
\(109\) | −4.86800 | −0.466269 | −0.233135 | − | 0.972444i | \(-0.574898\pi\) | ||||
−0.233135 | + | 0.972444i | \(0.574898\pi\) | |||||||
\(110\) | 15.3244 | 1.46112 | ||||||||
\(111\) | 0.251186 | 0.0238416 | ||||||||
\(112\) | −0.430136 | −0.0406440 | ||||||||
\(113\) | −10.6438 | −1.00128 | −0.500640 | − | 0.865656i | \(-0.666902\pi\) | ||||
−0.500640 | + | 0.865656i | \(0.666902\pi\) | |||||||
\(114\) | 0.692604 | 0.0648683 | ||||||||
\(115\) | −3.26458 | −0.304423 | ||||||||
\(116\) | 0.423629 | 0.0393330 | ||||||||
\(117\) | −20.9915 | −1.94067 | ||||||||
\(118\) | 1.19489 | 0.109998 | ||||||||
\(119\) | −0.168661 | −0.0154611 | ||||||||
\(120\) | −0.267899 | −0.0244557 | ||||||||
\(121\) | 11.0350 | 1.00318 | ||||||||
\(122\) | −7.80797 | −0.706901 | ||||||||
\(123\) | −0.541222 | −0.0488003 | ||||||||
\(124\) | 8.04433 | 0.722402 | ||||||||
\(125\) | −2.14634 | −0.191975 | ||||||||
\(126\) | −1.28751 | −0.114701 | ||||||||
\(127\) | −9.85596 | −0.874575 | −0.437287 | − | 0.899322i | \(-0.644061\pi\) | ||||
−0.437287 | + | 0.899322i | \(0.644061\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.238653 | 0.0210122 | ||||||||
\(130\) | 22.8942 | 2.00796 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −0.385213 | −0.0335285 | ||||||||
\(133\) | −3.63033 | −0.314790 | ||||||||
\(134\) | 4.56048 | 0.393966 | ||||||||
\(135\) | −1.60559 | −0.138187 | ||||||||
\(136\) | −0.392111 | −0.0336232 | ||||||||
\(137\) | 9.24072 | 0.789488 | 0.394744 | − | 0.918791i | \(-0.370833\pi\) | ||||
0.394744 | + | 0.918791i | \(0.370833\pi\) | |||||||
\(138\) | 0.0820624 | 0.00698562 | ||||||||
\(139\) | 8.94770 | 0.758934 | 0.379467 | − | 0.925205i | \(-0.376107\pi\) | ||||
0.379467 | + | 0.925205i | \(0.376107\pi\) | |||||||
\(140\) | 1.40421 | 0.118678 | ||||||||
\(141\) | 0.703546 | 0.0592493 | ||||||||
\(142\) | 2.37416 | 0.199235 | ||||||||
\(143\) | 32.9197 | 2.75288 | ||||||||
\(144\) | −2.99327 | −0.249439 | ||||||||
\(145\) | −1.38297 | −0.114849 | ||||||||
\(146\) | −10.1037 | −0.836186 | ||||||||
\(147\) | 0.559254 | 0.0461265 | ||||||||
\(148\) | −3.06092 | −0.251606 | ||||||||
\(149\) | −15.0343 | −1.23166 | −0.615830 | − | 0.787879i | \(-0.711179\pi\) | ||||
−0.615830 | + | 0.787879i | \(0.711179\pi\) | |||||||
\(150\) | 0.464265 | 0.0379071 | ||||||||
\(151\) | −6.88891 | −0.560612 | −0.280306 | − | 0.959911i | \(-0.590436\pi\) | ||||
−0.280306 | + | 0.959911i | \(0.590436\pi\) | |||||||
\(152\) | −8.43997 | −0.684572 | ||||||||
\(153\) | −1.17369 | −0.0948874 | ||||||||
\(154\) | 2.01912 | 0.162705 | ||||||||
\(155\) | −26.2613 | −2.10936 | ||||||||
\(156\) | −0.575497 | −0.0460767 | ||||||||
\(157\) | 1.52244 | 0.121504 | 0.0607519 | − | 0.998153i | \(-0.480650\pi\) | ||||
0.0607519 | + | 0.998153i | \(0.480650\pi\) | |||||||
\(158\) | −2.93297 | −0.233335 | ||||||||
\(159\) | 0.885448 | 0.0702206 | ||||||||
\(160\) | 3.26458 | 0.258087 | ||||||||
\(161\) | −0.430136 | −0.0338995 | ||||||||
\(162\) | −8.93944 | −0.702349 | ||||||||
\(163\) | −9.15878 | −0.717371 | −0.358685 | − | 0.933459i | \(-0.616775\pi\) | ||||
−0.358685 | + | 0.933459i | \(0.616775\pi\) | |||||||
\(164\) | 6.59524 | 0.515002 | ||||||||
\(165\) | 1.25756 | 0.0979007 | ||||||||
\(166\) | 5.21951 | 0.405113 | ||||||||
\(167\) | 17.4206 | 1.34805 | 0.674023 | − | 0.738711i | \(-0.264565\pi\) | ||||
0.674023 | + | 0.738711i | \(0.264565\pi\) | |||||||
\(168\) | −0.0352980 | −0.00272330 | ||||||||
\(169\) | 36.1811 | 2.78316 | ||||||||
\(170\) | 1.28008 | 0.0981774 | ||||||||
\(171\) | −25.2631 | −1.93191 | ||||||||
\(172\) | −2.90818 | −0.221747 | ||||||||
\(173\) | 20.3398 | 1.54641 | 0.773203 | − | 0.634159i | \(-0.218654\pi\) | ||||
0.773203 | + | 0.634159i | \(0.218654\pi\) | |||||||
\(174\) | 0.0347640 | 0.00263545 | ||||||||
\(175\) | −2.43348 | −0.183954 | ||||||||
\(176\) | 4.69415 | 0.353835 | ||||||||
\(177\) | 0.0980554 | 0.00737030 | ||||||||
\(178\) | −1.31862 | −0.0988349 | ||||||||
\(179\) | −16.5115 | −1.23412 | −0.617062 | − | 0.786914i | \(-0.711677\pi\) | ||||
−0.617062 | + | 0.786914i | \(0.711677\pi\) | |||||||
\(180\) | 9.77175 | 0.728343 | ||||||||
\(181\) | 16.1923 | 1.20357 | 0.601784 | − | 0.798659i | \(-0.294457\pi\) | ||||
0.601784 | + | 0.798659i | \(0.294457\pi\) | |||||||
\(182\) | 3.01651 | 0.223599 | ||||||||
\(183\) | −0.640741 | −0.0473650 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 9.99260 | 0.734671 | ||||||||
\(186\) | 0.660137 | 0.0484036 | ||||||||
\(187\) | 1.84063 | 0.134600 | ||||||||
\(188\) | −8.57331 | −0.625273 | ||||||||
\(189\) | −0.211550 | −0.0153880 | ||||||||
\(190\) | 27.5529 | 1.99890 | ||||||||
\(191\) | 3.52330 | 0.254937 | 0.127469 | − | 0.991843i | \(-0.459315\pi\) | ||||
0.127469 | + | 0.991843i | \(0.459315\pi\) | |||||||
\(192\) | −0.0820624 | −0.00592235 | ||||||||
\(193\) | 11.1232 | 0.800666 | 0.400333 | − | 0.916370i | \(-0.368895\pi\) | ||||
0.400333 | + | 0.916370i | \(0.368895\pi\) | |||||||
\(194\) | 8.70998 | 0.625340 | ||||||||
\(195\) | 1.87876 | 0.134541 | ||||||||
\(196\) | −6.81498 | −0.486785 | ||||||||
\(197\) | −12.4197 | −0.884869 | −0.442435 | − | 0.896801i | \(-0.645885\pi\) | ||||
−0.442435 | + | 0.896801i | \(0.645885\pi\) | |||||||
\(198\) | 14.0508 | 0.998549 | ||||||||
\(199\) | 18.0071 | 1.27649 | 0.638244 | − | 0.769834i | \(-0.279661\pi\) | ||||
0.638244 | + | 0.769834i | \(0.279661\pi\) | |||||||
\(200\) | −5.65746 | −0.400043 | ||||||||
\(201\) | 0.374244 | 0.0263972 | ||||||||
\(202\) | −14.4610 | −1.01747 | ||||||||
\(203\) | −0.182218 | −0.0127892 | ||||||||
\(204\) | −0.0321776 | −0.00225288 | ||||||||
\(205\) | −21.5307 | −1.50377 | ||||||||
\(206\) | −5.41642 | −0.377380 | ||||||||
\(207\) | −2.99327 | −0.208046 | ||||||||
\(208\) | 7.01292 | 0.486259 | ||||||||
\(209\) | 39.6184 | 2.74046 | ||||||||
\(210\) | 0.115233 | 0.00795184 | ||||||||
\(211\) | 11.1671 | 0.768774 | 0.384387 | − | 0.923172i | \(-0.374413\pi\) | ||||
0.384387 | + | 0.923172i | \(0.374413\pi\) | |||||||
\(212\) | −10.7899 | −0.741055 | ||||||||
\(213\) | 0.194829 | 0.0133495 | ||||||||
\(214\) | −7.98644 | −0.545942 | ||||||||
\(215\) | 9.49399 | 0.647484 | ||||||||
\(216\) | −0.491822 | −0.0334642 | ||||||||
\(217\) | −3.46015 | −0.234891 | ||||||||
\(218\) | 4.86800 | 0.329702 | ||||||||
\(219\) | −0.829132 | −0.0560276 | ||||||||
\(220\) | −15.3244 | −1.03317 | ||||||||
\(221\) | 2.74984 | 0.184974 | ||||||||
\(222\) | −0.251186 | −0.0168585 | ||||||||
\(223\) | 3.20050 | 0.214322 | 0.107161 | − | 0.994242i | \(-0.465824\pi\) | ||||
0.107161 | + | 0.994242i | \(0.465824\pi\) | |||||||
\(224\) | 0.430136 | 0.0287397 | ||||||||
\(225\) | −16.9343 | −1.12895 | ||||||||
\(226\) | 10.6438 | 0.708012 | ||||||||
\(227\) | 23.5821 | 1.56520 | 0.782598 | − | 0.622527i | \(-0.213894\pi\) | ||||
0.782598 | + | 0.622527i | \(0.213894\pi\) | |||||||
\(228\) | −0.692604 | −0.0458688 | ||||||||
\(229\) | 12.0256 | 0.794673 | 0.397336 | − | 0.917673i | \(-0.369935\pi\) | ||||
0.397336 | + | 0.917673i | \(0.369935\pi\) | |||||||
\(230\) | 3.26458 | 0.215260 | ||||||||
\(231\) | 0.165694 | 0.0109019 | ||||||||
\(232\) | −0.423629 | −0.0278126 | ||||||||
\(233\) | 23.4503 | 1.53628 | 0.768140 | − | 0.640282i | \(-0.221183\pi\) | ||||
0.768140 | + | 0.640282i | \(0.221183\pi\) | |||||||
\(234\) | 20.9915 | 1.37226 | ||||||||
\(235\) | 27.9882 | 1.82575 | ||||||||
\(236\) | −1.19489 | −0.0777806 | ||||||||
\(237\) | −0.240687 | −0.0156343 | ||||||||
\(238\) | 0.168661 | 0.0109327 | ||||||||
\(239\) | −26.3555 | −1.70480 | −0.852398 | − | 0.522894i | \(-0.824852\pi\) | ||||
−0.852398 | + | 0.522894i | \(0.824852\pi\) | |||||||
\(240\) | 0.267899 | 0.0172928 | ||||||||
\(241\) | 20.2788 | 1.30627 | 0.653135 | − | 0.757241i | \(-0.273453\pi\) | ||||
0.653135 | + | 0.757241i | \(0.273453\pi\) | |||||||
\(242\) | −11.0350 | −0.709357 | ||||||||
\(243\) | −2.20906 | −0.141711 | ||||||||
\(244\) | 7.80797 | 0.499854 | ||||||||
\(245\) | 22.2480 | 1.42138 | ||||||||
\(246\) | 0.541222 | 0.0345070 | ||||||||
\(247\) | 59.1888 | 3.76610 | ||||||||
\(248\) | −8.04433 | −0.510815 | ||||||||
\(249\) | 0.428326 | 0.0271440 | ||||||||
\(250\) | 2.14634 | 0.135747 | ||||||||
\(251\) | 9.30325 | 0.587216 | 0.293608 | − | 0.955926i | \(-0.405144\pi\) | ||||
0.293608 | + | 0.955926i | \(0.405144\pi\) | |||||||
\(252\) | 1.28751 | 0.0811056 | ||||||||
\(253\) | 4.69415 | 0.295118 | ||||||||
\(254\) | 9.85596 | 0.618418 | ||||||||
\(255\) | 0.105046 | 0.00657825 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0778 | 0.691016 | 0.345508 | − | 0.938416i | \(-0.387707\pi\) | ||||
0.345508 | + | 0.938416i | \(0.387707\pi\) | |||||||
\(258\) | −0.238653 | −0.0148579 | ||||||||
\(259\) | 1.31661 | 0.0818102 | ||||||||
\(260\) | −22.8942 | −1.41984 | ||||||||
\(261\) | −1.26803 | −0.0784893 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 6.39419 | 0.394282 | 0.197141 | − | 0.980375i | \(-0.436834\pi\) | ||||
0.197141 | + | 0.980375i | \(0.436834\pi\) | |||||||
\(264\) | 0.385213 | 0.0237082 | ||||||||
\(265\) | 35.2245 | 2.16383 | ||||||||
\(266\) | 3.63033 | 0.222590 | ||||||||
\(267\) | −0.108209 | −0.00662231 | ||||||||
\(268\) | −4.56048 | −0.278576 | ||||||||
\(269\) | −3.13554 | −0.191177 | −0.0955885 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955885 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(270\) | 1.60559 | 0.0977131 | ||||||||
\(271\) | −4.59049 | −0.278852 | −0.139426 | − | 0.990232i | \(-0.544526\pi\) | ||||
−0.139426 | + | 0.990232i | \(0.544526\pi\) | |||||||
\(272\) | 0.392111 | 0.0237752 | ||||||||
\(273\) | 0.247542 | 0.0149819 | ||||||||
\(274\) | −9.24072 | −0.558252 | ||||||||
\(275\) | 26.5570 | 1.60145 | ||||||||
\(276\) | −0.0820624 | −0.00493958 | ||||||||
\(277\) | 10.2904 | 0.618291 | 0.309146 | − | 0.951015i | \(-0.399957\pi\) | ||||
0.309146 | + | 0.951015i | \(0.399957\pi\) | |||||||
\(278\) | −8.94770 | −0.536648 | ||||||||
\(279\) | −24.0788 | −1.44156 | ||||||||
\(280\) | −1.40421 | −0.0839177 | ||||||||
\(281\) | −3.94747 | −0.235487 | −0.117743 | − | 0.993044i | \(-0.537566\pi\) | ||||
−0.117743 | + | 0.993044i | \(0.537566\pi\) | |||||||
\(282\) | −0.703546 | −0.0418956 | ||||||||
\(283\) | −32.5566 | −1.93529 | −0.967643 | − | 0.252322i | \(-0.918806\pi\) | ||||
−0.967643 | + | 0.252322i | \(0.918806\pi\) | |||||||
\(284\) | −2.37416 | −0.140880 | ||||||||
\(285\) | 2.26106 | 0.133934 | ||||||||
\(286\) | −32.9197 | −1.94658 | ||||||||
\(287\) | −2.83685 | −0.167454 | ||||||||
\(288\) | 2.99327 | 0.176380 | ||||||||
\(289\) | −16.8462 | −0.990956 | ||||||||
\(290\) | 1.38297 | 0.0812107 | ||||||||
\(291\) | 0.714763 | 0.0419001 | ||||||||
\(292\) | 10.1037 | 0.591273 | ||||||||
\(293\) | −32.9645 | −1.92580 | −0.962902 | − | 0.269851i | \(-0.913025\pi\) | ||||
−0.962902 | + | 0.269851i | \(0.913025\pi\) | |||||||
\(294\) | −0.559254 | −0.0326164 | ||||||||
\(295\) | 3.90080 | 0.227114 | ||||||||
\(296\) | 3.06092 | 0.177912 | ||||||||
\(297\) | 2.30868 | 0.133963 | ||||||||
\(298\) | 15.0343 | 0.870915 | ||||||||
\(299\) | 7.01292 | 0.405568 | ||||||||
\(300\) | −0.464265 | −0.0268044 | ||||||||
\(301\) | 1.25091 | 0.0721015 | ||||||||
\(302\) | 6.88891 | 0.396412 | ||||||||
\(303\) | −1.18670 | −0.0681742 | ||||||||
\(304\) | 8.43997 | 0.484065 | ||||||||
\(305\) | −25.4897 | −1.45954 | ||||||||
\(306\) | 1.17369 | 0.0670955 | ||||||||
\(307\) | −25.9169 | −1.47916 | −0.739578 | − | 0.673070i | \(-0.764975\pi\) | ||||
−0.739578 | + | 0.673070i | \(0.764975\pi\) | |||||||
\(308\) | −2.01912 | −0.115050 | ||||||||
\(309\) | −0.444485 | −0.0252859 | ||||||||
\(310\) | 26.2613 | 1.49154 | ||||||||
\(311\) | −3.83774 | −0.217618 | −0.108809 | − | 0.994063i | \(-0.534704\pi\) | ||||
−0.108809 | + | 0.994063i | \(0.534704\pi\) | |||||||
\(312\) | 0.575497 | 0.0325811 | ||||||||
\(313\) | −6.24693 | −0.353097 | −0.176549 | − | 0.984292i | \(-0.556493\pi\) | ||||
−0.176549 | + | 0.984292i | \(0.556493\pi\) | |||||||
\(314\) | −1.52244 | −0.0859162 | ||||||||
\(315\) | −4.20318 | −0.236822 | ||||||||
\(316\) | 2.93297 | 0.164993 | ||||||||
\(317\) | −25.3907 | −1.42609 | −0.713043 | − | 0.701120i | \(-0.752684\pi\) | ||||
−0.713043 | + | 0.701120i | \(0.752684\pi\) | |||||||
\(318\) | −0.885448 | −0.0496534 | ||||||||
\(319\) | 1.98858 | 0.111339 | ||||||||
\(320\) | −3.26458 | −0.182495 | ||||||||
\(321\) | −0.655387 | −0.0365801 | ||||||||
\(322\) | 0.430136 | 0.0239705 | ||||||||
\(323\) | 3.30940 | 0.184140 | ||||||||
\(324\) | 8.93944 | 0.496635 | ||||||||
\(325\) | 39.6754 | 2.20079 | ||||||||
\(326\) | 9.15878 | 0.507258 | ||||||||
\(327\) | 0.399480 | 0.0220913 | ||||||||
\(328\) | −6.59524 | −0.364161 | ||||||||
\(329\) | 3.68769 | 0.203309 | ||||||||
\(330\) | −1.25756 | −0.0692263 | ||||||||
\(331\) | −7.53905 | −0.414384 | −0.207192 | − | 0.978300i | \(-0.566432\pi\) | ||||
−0.207192 | + | 0.978300i | \(0.566432\pi\) | |||||||
\(332\) | −5.21951 | −0.286458 | ||||||||
\(333\) | 9.16214 | 0.502082 | ||||||||
\(334\) | −17.4206 | −0.953212 | ||||||||
\(335\) | 14.8880 | 0.813421 | ||||||||
\(336\) | 0.0352980 | 0.00192566 | ||||||||
\(337\) | 11.9190 | 0.649271 | 0.324636 | − | 0.945839i | \(-0.394758\pi\) | ||||
0.324636 | + | 0.945839i | \(0.394758\pi\) | |||||||
\(338\) | −36.1811 | −1.96799 | ||||||||
\(339\) | 0.873452 | 0.0474394 | ||||||||
\(340\) | −1.28008 | −0.0694219 | ||||||||
\(341\) | 37.7613 | 2.04489 | ||||||||
\(342\) | 25.2631 | 1.36607 | ||||||||
\(343\) | 5.94232 | 0.320855 | ||||||||
\(344\) | 2.90818 | 0.156799 | ||||||||
\(345\) | 0.267899 | 0.0144232 | ||||||||
\(346\) | −20.3398 | −1.09347 | ||||||||
\(347\) | 7.36904 | 0.395591 | 0.197795 | − | 0.980243i | \(-0.436622\pi\) | ||||
0.197795 | + | 0.980243i | \(0.436622\pi\) | |||||||
\(348\) | −0.0347640 | −0.00186355 | ||||||||
\(349\) | −21.0168 | −1.12501 | −0.562503 | − | 0.826796i | \(-0.690161\pi\) | ||||
−0.562503 | + | 0.826796i | \(0.690161\pi\) | |||||||
\(350\) | 2.43348 | 0.130075 | ||||||||
\(351\) | 3.44911 | 0.184100 | ||||||||
\(352\) | −4.69415 | −0.250199 | ||||||||
\(353\) | 15.1586 | 0.806812 | 0.403406 | − | 0.915021i | \(-0.367826\pi\) | ||||
0.403406 | + | 0.915021i | \(0.367826\pi\) | |||||||
\(354\) | −0.0980554 | −0.00521159 | ||||||||
\(355\) | 7.75062 | 0.411360 | ||||||||
\(356\) | 1.31862 | 0.0698869 | ||||||||
\(357\) | 0.0138407 | 0.000732529 0 | ||||||||
\(358\) | 16.5115 | 0.872658 | ||||||||
\(359\) | −2.44671 | −0.129132 | −0.0645662 | − | 0.997913i | \(-0.520566\pi\) | ||||
−0.0645662 | + | 0.997913i | \(0.520566\pi\) | |||||||
\(360\) | −9.77175 | −0.515016 | ||||||||
\(361\) | 52.2330 | 2.74911 | ||||||||
\(362\) | −16.1923 | −0.851051 | ||||||||
\(363\) | −0.905560 | −0.0475296 | ||||||||
\(364\) | −3.01651 | −0.158108 | ||||||||
\(365\) | −32.9842 | −1.72647 | ||||||||
\(366\) | 0.640741 | 0.0334921 | ||||||||
\(367\) | −24.1705 | −1.26169 | −0.630844 | − | 0.775910i | \(-0.717291\pi\) | ||||
−0.630844 | + | 0.775910i | \(0.717291\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −19.7413 | −1.02769 | ||||||||
\(370\) | −9.99260 | −0.519491 | ||||||||
\(371\) | 4.64113 | 0.240956 | ||||||||
\(372\) | −0.660137 | −0.0342265 | ||||||||
\(373\) | −26.0960 | −1.35120 | −0.675599 | − | 0.737269i | \(-0.736115\pi\) | ||||
−0.675599 | + | 0.737269i | \(0.736115\pi\) | |||||||
\(374\) | −1.84063 | −0.0951765 | ||||||||
\(375\) | 0.176134 | 0.00909553 | ||||||||
\(376\) | 8.57331 | 0.442135 | ||||||||
\(377\) | 2.97088 | 0.153008 | ||||||||
\(378\) | 0.211550 | 0.0108810 | ||||||||
\(379\) | −14.3027 | −0.734682 | −0.367341 | − | 0.930086i | \(-0.619732\pi\) | ||||
−0.367341 | + | 0.930086i | \(0.619732\pi\) | |||||||
\(380\) | −27.5529 | −1.41344 | ||||||||
\(381\) | 0.808804 | 0.0414363 | ||||||||
\(382\) | −3.52330 | −0.180268 | ||||||||
\(383\) | 24.4379 | 1.24872 | 0.624360 | − | 0.781136i | \(-0.285360\pi\) | ||||
0.624360 | + | 0.781136i | \(0.285360\pi\) | |||||||
\(384\) | 0.0820624 | 0.00418773 | ||||||||
\(385\) | 6.59158 | 0.335938 | ||||||||
\(386\) | −11.1232 | −0.566156 | ||||||||
\(387\) | 8.70496 | 0.442498 | ||||||||
\(388\) | −8.70998 | −0.442182 | ||||||||
\(389\) | −27.4047 | −1.38947 | −0.694736 | − | 0.719265i | \(-0.744479\pi\) | ||||
−0.694736 | + | 0.719265i | \(0.744479\pi\) | |||||||
\(390\) | −1.87876 | −0.0951345 | ||||||||
\(391\) | 0.392111 | 0.0198299 | ||||||||
\(392\) | 6.81498 | 0.344209 | ||||||||
\(393\) | 0.0820624 | 0.00413950 | ||||||||
\(394\) | 12.4197 | 0.625697 | ||||||||
\(395\) | −9.57491 | −0.481766 | ||||||||
\(396\) | −14.0508 | −0.706081 | ||||||||
\(397\) | 31.6805 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(398\) | −18.0071 | −0.902614 | ||||||||
\(399\) | 0.297914 | 0.0149144 | ||||||||
\(400\) | 5.65746 | 0.282873 | ||||||||
\(401\) | 7.56755 | 0.377905 | 0.188953 | − | 0.981986i | \(-0.439491\pi\) | ||||
0.188953 | + | 0.981986i | \(0.439491\pi\) | |||||||
\(402\) | −0.374244 | −0.0186656 | ||||||||
\(403\) | 56.4143 | 2.81019 | ||||||||
\(404\) | 14.4610 | 0.719460 | ||||||||
\(405\) | −29.1835 | −1.45014 | ||||||||
\(406\) | 0.182218 | 0.00904333 | ||||||||
\(407\) | −14.3684 | −0.712215 | ||||||||
\(408\) | 0.0321776 | 0.00159303 | ||||||||
\(409\) | 5.13400 | 0.253860 | 0.126930 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126930 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(410\) | 21.5307 | 1.06332 | ||||||||
\(411\) | −0.758316 | −0.0374050 | ||||||||
\(412\) | 5.41642 | 0.266848 | ||||||||
\(413\) | 0.513964 | 0.0252905 | ||||||||
\(414\) | 2.99327 | 0.147111 | ||||||||
\(415\) | 17.0395 | 0.836436 | ||||||||
\(416\) | −7.01292 | −0.343837 | ||||||||
\(417\) | −0.734270 | −0.0359574 | ||||||||
\(418\) | −39.6184 | −1.93780 | ||||||||
\(419\) | 8.27791 | 0.404402 | 0.202201 | − | 0.979344i | \(-0.435191\pi\) | ||||
0.202201 | + | 0.979344i | \(0.435191\pi\) | |||||||
\(420\) | −0.115233 | −0.00562280 | ||||||||
\(421\) | −5.80953 | −0.283139 | −0.141570 | − | 0.989928i | \(-0.545215\pi\) | ||||
−0.141570 | + | 0.989928i | \(0.545215\pi\) | |||||||
\(422\) | −11.1671 | −0.543605 | ||||||||
\(423\) | 25.6622 | 1.24774 | ||||||||
\(424\) | 10.7899 | 0.524005 | ||||||||
\(425\) | 2.21835 | 0.107606 | ||||||||
\(426\) | −0.194829 | −0.00943950 | ||||||||
\(427\) | −3.35849 | −0.162529 | ||||||||
\(428\) | 7.98644 | 0.386039 | ||||||||
\(429\) | −2.70147 | −0.130428 | ||||||||
\(430\) | −9.49399 | −0.457841 | ||||||||
\(431\) | −5.55309 | −0.267483 | −0.133741 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133741 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(432\) | 0.491822 | 0.0236628 | ||||||||
\(433\) | −33.3320 | −1.60183 | −0.800916 | − | 0.598776i | \(-0.795654\pi\) | ||||
−0.800916 | + | 0.598776i | \(0.795654\pi\) | |||||||
\(434\) | 3.46015 | 0.166093 | ||||||||
\(435\) | 0.113490 | 0.00544142 | ||||||||
\(436\) | −4.86800 | −0.233135 | ||||||||
\(437\) | 8.43997 | 0.403738 | ||||||||
\(438\) | 0.829132 | 0.0396175 | ||||||||
\(439\) | −19.1564 | −0.914287 | −0.457144 | − | 0.889393i | \(-0.651127\pi\) | ||||
−0.457144 | + | 0.889393i | \(0.651127\pi\) | |||||||
\(440\) | 15.3244 | 0.730562 | ||||||||
\(441\) | 20.3991 | 0.971384 | ||||||||
\(442\) | −2.74984 | −0.130797 | ||||||||
\(443\) | 16.5825 | 0.787856 | 0.393928 | − | 0.919141i | \(-0.371116\pi\) | ||||
0.393928 | + | 0.919141i | \(0.371116\pi\) | |||||||
\(444\) | 0.251186 | 0.0119208 | ||||||||
\(445\) | −4.30475 | −0.204064 | ||||||||
\(446\) | −3.20050 | −0.151548 | ||||||||
\(447\) | 1.23375 | 0.0583545 | ||||||||
\(448\) | −0.430136 | −0.0203220 | ||||||||
\(449\) | −25.5612 | −1.20631 | −0.603153 | − | 0.797626i | \(-0.706089\pi\) | ||||
−0.603153 | + | 0.797626i | \(0.706089\pi\) | |||||||
\(450\) | 16.9343 | 0.798290 | ||||||||
\(451\) | 30.9590 | 1.45780 | ||||||||
\(452\) | −10.6438 | −0.500640 | ||||||||
\(453\) | 0.565321 | 0.0265611 | ||||||||
\(454\) | −23.5821 | −1.10676 | ||||||||
\(455\) | 9.84763 | 0.461664 | ||||||||
\(456\) | 0.692604 | 0.0324342 | ||||||||
\(457\) | 37.4064 | 1.74980 | 0.874898 | − | 0.484307i | \(-0.160928\pi\) | ||||
0.874898 | + | 0.484307i | \(0.160928\pi\) | |||||||
\(458\) | −12.0256 | −0.561918 | ||||||||
\(459\) | 0.192849 | 0.00900141 | ||||||||
\(460\) | −3.26458 | −0.152212 | ||||||||
\(461\) | −14.4246 | −0.671823 | −0.335911 | − | 0.941894i | \(-0.609044\pi\) | ||||
−0.335911 | + | 0.941894i | \(0.609044\pi\) | |||||||
\(462\) | −0.165694 | −0.00770878 | ||||||||
\(463\) | 2.35074 | 0.109248 | 0.0546241 | − | 0.998507i | \(-0.482604\pi\) | ||||
0.0546241 | + | 0.998507i | \(0.482604\pi\) | |||||||
\(464\) | 0.423629 | 0.0196665 | ||||||||
\(465\) | 2.15507 | 0.0999389 | ||||||||
\(466\) | −23.4503 | −1.08631 | ||||||||
\(467\) | −18.1238 | −0.838671 | −0.419335 | − | 0.907831i | \(-0.637737\pi\) | ||||
−0.419335 | + | 0.907831i | \(0.637737\pi\) | |||||||
\(468\) | −20.9915 | −0.970334 | ||||||||
\(469\) | 1.96163 | 0.0905795 | ||||||||
\(470\) | −27.9882 | −1.29100 | ||||||||
\(471\) | −0.124935 | −0.00575670 | ||||||||
\(472\) | 1.19489 | 0.0549992 | ||||||||
\(473\) | −13.6514 | −0.627694 | ||||||||
\(474\) | 0.240687 | 0.0110551 | ||||||||
\(475\) | 47.7488 | 2.19087 | ||||||||
\(476\) | −0.168661 | −0.00773056 | ||||||||
\(477\) | 32.2971 | 1.47878 | ||||||||
\(478\) | 26.3555 | 1.20547 | ||||||||
\(479\) | 12.6937 | 0.579988 | 0.289994 | − | 0.957028i | \(-0.406347\pi\) | ||||
0.289994 | + | 0.957028i | \(0.406347\pi\) | |||||||
\(480\) | −0.267899 | −0.0122279 | ||||||||
\(481\) | −21.4660 | −0.978764 | ||||||||
\(482\) | −20.2788 | −0.923672 | ||||||||
\(483\) | 0.0352980 | 0.00160611 | ||||||||
\(484\) | 11.0350 | 0.501591 | ||||||||
\(485\) | 28.4344 | 1.29114 | ||||||||
\(486\) | 2.20906 | 0.100205 | ||||||||
\(487\) | −10.0632 | −0.456008 | −0.228004 | − | 0.973660i | \(-0.573220\pi\) | ||||
−0.228004 | + | 0.973660i | \(0.573220\pi\) | |||||||
\(488\) | −7.80797 | −0.353450 | ||||||||
\(489\) | 0.751591 | 0.0339881 | ||||||||
\(490\) | −22.2480 | −1.00506 | ||||||||
\(491\) | −1.30028 | −0.0586808 | −0.0293404 | − | 0.999569i | \(-0.509341\pi\) | ||||
−0.0293404 | + | 0.999569i | \(0.509341\pi\) | |||||||
\(492\) | −0.541222 | −0.0244002 | ||||||||
\(493\) | 0.166109 | 0.00748120 | ||||||||
\(494\) | −59.1888 | −2.66303 | ||||||||
\(495\) | 45.8700 | 2.06170 | ||||||||
\(496\) | 8.04433 | 0.361201 | ||||||||
\(497\) | 1.02121 | 0.0458075 | ||||||||
\(498\) | −0.428326 | −0.0191937 | ||||||||
\(499\) | −27.0515 | −1.21099 | −0.605496 | − | 0.795848i | \(-0.707025\pi\) | ||||
−0.605496 | + | 0.795848i | \(0.707025\pi\) | |||||||
\(500\) | −2.14634 | −0.0959874 | ||||||||
\(501\) | −1.42958 | −0.0638687 | ||||||||
\(502\) | −9.30325 | −0.415224 | ||||||||
\(503\) | −27.1135 | −1.20893 | −0.604465 | − | 0.796632i | \(-0.706613\pi\) | ||||
−0.604465 | + | 0.796632i | \(0.706613\pi\) | |||||||
\(504\) | −1.28751 | −0.0573503 | ||||||||
\(505\) | −47.2089 | −2.10077 | ||||||||
\(506\) | −4.69415 | −0.208680 | ||||||||
\(507\) | −2.96911 | −0.131863 | ||||||||
\(508\) | −9.85596 | −0.437287 | ||||||||
\(509\) | 9.56850 | 0.424116 | 0.212058 | − | 0.977257i | \(-0.431983\pi\) | ||||
0.212058 | + | 0.977257i | \(0.431983\pi\) | |||||||
\(510\) | −0.105046 | −0.00465152 | ||||||||
\(511\) | −4.34595 | −0.192254 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.15096 | 0.183269 | ||||||||
\(514\) | −11.0778 | −0.488622 | ||||||||
\(515\) | −17.6823 | −0.779176 | ||||||||
\(516\) | 0.238653 | 0.0105061 | ||||||||
\(517\) | −40.2444 | −1.76994 | ||||||||
\(518\) | −1.31661 | −0.0578486 | ||||||||
\(519\) | −1.66913 | −0.0732668 | ||||||||
\(520\) | 22.8942 | 1.00398 | ||||||||
\(521\) | 20.1657 | 0.883476 | 0.441738 | − | 0.897144i | \(-0.354362\pi\) | ||||
0.441738 | + | 0.897144i | \(0.354362\pi\) | |||||||
\(522\) | 1.26803 | 0.0555003 | ||||||||
\(523\) | 28.4827 | 1.24546 | 0.622730 | − | 0.782437i | \(-0.286023\pi\) | ||||
0.622730 | + | 0.782437i | \(0.286023\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 0.199697 | 0.00871550 | ||||||||
\(526\) | −6.39419 | −0.278800 | ||||||||
\(527\) | 3.15427 | 0.137402 | ||||||||
\(528\) | −0.385213 | −0.0167642 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −35.2245 | −1.53006 | ||||||||
\(531\) | 3.57662 | 0.155212 | ||||||||
\(532\) | −3.63033 | −0.157395 | ||||||||
\(533\) | 46.2519 | 2.00339 | ||||||||
\(534\) | 0.108209 | 0.00468268 | ||||||||
\(535\) | −26.0724 | −1.12721 | ||||||||
\(536\) | 4.56048 | 0.196983 | ||||||||
\(537\) | 1.35497 | 0.0584713 | ||||||||
\(538\) | 3.13554 | 0.135183 | ||||||||
\(539\) | −31.9905 | −1.37793 | ||||||||
\(540\) | −1.60559 | −0.0690936 | ||||||||
\(541\) | 28.2408 | 1.21417 | 0.607084 | − | 0.794638i | \(-0.292339\pi\) | ||||
0.607084 | + | 0.794638i | \(0.292339\pi\) | |||||||
\(542\) | 4.59049 | 0.197178 | ||||||||
\(543\) | −1.32878 | −0.0570235 | ||||||||
\(544\) | −0.392111 | −0.0168116 | ||||||||
\(545\) | 15.8919 | 0.680736 | ||||||||
\(546\) | −0.247542 | −0.0105938 | ||||||||
\(547\) | −37.5444 | −1.60528 | −0.802642 | − | 0.596461i | \(-0.796573\pi\) | ||||
−0.802642 | + | 0.596461i | \(0.796573\pi\) | |||||||
\(548\) | 9.24072 | 0.394744 | ||||||||
\(549\) | −23.3713 | −0.997464 | ||||||||
\(550\) | −26.5570 | −1.13239 | ||||||||
\(551\) | 3.57541 | 0.152318 | ||||||||
\(552\) | 0.0820624 | 0.00349281 | ||||||||
\(553\) | −1.26158 | −0.0536477 | ||||||||
\(554\) | −10.2904 | −0.437198 | ||||||||
\(555\) | −0.820017 | −0.0348078 | ||||||||
\(556\) | 8.94770 | 0.379467 | ||||||||
\(557\) | 10.6696 | 0.452085 | 0.226042 | − | 0.974117i | \(-0.427421\pi\) | ||||
0.226042 | + | 0.974117i | \(0.427421\pi\) | |||||||
\(558\) | 24.0788 | 1.01934 | ||||||||
\(559\) | −20.3949 | −0.862611 | ||||||||
\(560\) | 1.40421 | 0.0593388 | ||||||||
\(561\) | −0.151046 | −0.00637718 | ||||||||
\(562\) | 3.94747 | 0.166514 | ||||||||
\(563\) | −16.5551 | −0.697713 | −0.348857 | − | 0.937176i | \(-0.613430\pi\) | ||||
−0.348857 | + | 0.937176i | \(0.613430\pi\) | |||||||
\(564\) | 0.703546 | 0.0296246 | ||||||||
\(565\) | 34.7474 | 1.46183 | ||||||||
\(566\) | 32.5566 | 1.36845 | ||||||||
\(567\) | −3.84517 | −0.161482 | ||||||||
\(568\) | 2.37416 | 0.0996174 | ||||||||
\(569\) | −21.4970 | −0.901199 | −0.450600 | − | 0.892726i | \(-0.648790\pi\) | ||||
−0.450600 | + | 0.892726i | \(0.648790\pi\) | |||||||
\(570\) | −2.26106 | −0.0947054 | ||||||||
\(571\) | 14.8688 | 0.622241 | 0.311120 | − | 0.950371i | \(-0.399296\pi\) | ||||
0.311120 | + | 0.950371i | \(0.399296\pi\) | |||||||
\(572\) | 32.9197 | 1.37644 | ||||||||
\(573\) | −0.289131 | −0.0120786 | ||||||||
\(574\) | 2.83685 | 0.118408 | ||||||||
\(575\) | 5.65746 | 0.235933 | ||||||||
\(576\) | −2.99327 | −0.124719 | ||||||||
\(577\) | −9.89497 | −0.411933 | −0.205966 | − | 0.978559i | \(-0.566034\pi\) | ||||
−0.205966 | + | 0.978559i | \(0.566034\pi\) | |||||||
\(578\) | 16.8462 | 0.700712 | ||||||||
\(579\) | −0.912797 | −0.0379346 | ||||||||
\(580\) | −1.38297 | −0.0574247 | ||||||||
\(581\) | 2.24510 | 0.0931424 | ||||||||
\(582\) | −0.714763 | −0.0296279 | ||||||||
\(583\) | −50.6495 | −2.09769 | ||||||||
\(584\) | −10.1037 | −0.418093 | ||||||||
\(585\) | 68.5285 | 2.83331 | ||||||||
\(586\) | 32.9645 | 1.36175 | ||||||||
\(587\) | 20.1117 | 0.830099 | 0.415049 | − | 0.909799i | \(-0.363764\pi\) | ||||
0.415049 | + | 0.909799i | \(0.363764\pi\) | |||||||
\(588\) | 0.559254 | 0.0230632 | ||||||||
\(589\) | 67.8939 | 2.79752 | ||||||||
\(590\) | −3.90080 | −0.160594 | ||||||||
\(591\) | 1.01919 | 0.0419240 | ||||||||
\(592\) | −3.06092 | −0.125803 | ||||||||
\(593\) | −5.05075 | −0.207409 | −0.103705 | − | 0.994608i | \(-0.533070\pi\) | ||||
−0.103705 | + | 0.994608i | \(0.533070\pi\) | |||||||
\(594\) | −2.30868 | −0.0947265 | ||||||||
\(595\) | 0.550607 | 0.0225727 | ||||||||
\(596\) | −15.0343 | −0.615830 | ||||||||
\(597\) | −1.47770 | −0.0604784 | ||||||||
\(598\) | −7.01292 | −0.286780 | ||||||||
\(599\) | 15.7237 | 0.642453 | 0.321227 | − | 0.947002i | \(-0.395905\pi\) | ||||
0.321227 | + | 0.947002i | \(0.395905\pi\) | |||||||
\(600\) | 0.464265 | 0.0189536 | ||||||||
\(601\) | 25.1582 | 1.02622 | 0.513112 | − | 0.858321i | \(-0.328492\pi\) | ||||
0.513112 | + | 0.858321i | \(0.328492\pi\) | |||||||
\(602\) | −1.25091 | −0.0509834 | ||||||||
\(603\) | 13.6507 | 0.555901 | ||||||||
\(604\) | −6.88891 | −0.280306 | ||||||||
\(605\) | −36.0246 | −1.46461 | ||||||||
\(606\) | 1.18670 | 0.0482065 | ||||||||
\(607\) | 49.1008 | 1.99294 | 0.996470 | − | 0.0839514i | \(-0.0267541\pi\) | ||||
0.996470 | + | 0.0839514i | \(0.0267541\pi\) | |||||||
\(608\) | −8.43997 | −0.342286 | ||||||||
\(609\) | 0.0149533 | 0.000605936 0 | ||||||||
\(610\) | 25.4897 | 1.03205 | ||||||||
\(611\) | −60.1239 | −2.43235 | ||||||||
\(612\) | −1.17369 | −0.0474437 | ||||||||
\(613\) | 27.2840 | 1.10199 | 0.550996 | − | 0.834508i | \(-0.314248\pi\) | ||||
0.550996 | + | 0.834508i | \(0.314248\pi\) | |||||||
\(614\) | 25.9169 | 1.04592 | ||||||||
\(615\) | 1.76686 | 0.0712467 | ||||||||
\(616\) | 2.01912 | 0.0813527 | ||||||||
\(617\) | 20.0601 | 0.807589 | 0.403794 | − | 0.914850i | \(-0.367691\pi\) | ||||
0.403794 | + | 0.914850i | \(0.367691\pi\) | |||||||
\(618\) | 0.444485 | 0.0178798 | ||||||||
\(619\) | 27.2731 | 1.09620 | 0.548099 | − | 0.836414i | \(-0.315352\pi\) | ||||
0.548099 | + | 0.836414i | \(0.315352\pi\) | |||||||
\(620\) | −26.2613 | −1.05468 | ||||||||
\(621\) | 0.491822 | 0.0197361 | ||||||||
\(622\) | 3.83774 | 0.153879 | ||||||||
\(623\) | −0.567187 | −0.0227239 | ||||||||
\(624\) | −0.575497 | −0.0230383 | ||||||||
\(625\) | −21.2804 | −0.851217 | ||||||||
\(626\) | 6.24693 | 0.249677 | ||||||||
\(627\) | −3.25119 | −0.129840 | ||||||||
\(628\) | 1.52244 | 0.0607519 | ||||||||
\(629\) | −1.20022 | −0.0478559 | ||||||||
\(630\) | 4.20318 | 0.167459 | ||||||||
\(631\) | −12.0792 | −0.480867 | −0.240434 | − | 0.970666i | \(-0.577290\pi\) | ||||
−0.240434 | + | 0.970666i | \(0.577290\pi\) | |||||||
\(632\) | −2.93297 | −0.116667 | ||||||||
\(633\) | −0.916398 | −0.0364236 | ||||||||
\(634\) | 25.3907 | 1.00840 | ||||||||
\(635\) | 32.1755 | 1.27685 | ||||||||
\(636\) | 0.885448 | 0.0351103 | ||||||||
\(637\) | −47.7929 | −1.89363 | ||||||||
\(638\) | −1.98858 | −0.0787285 | ||||||||
\(639\) | 7.10648 | 0.281128 | ||||||||
\(640\) | 3.26458 | 0.129044 | ||||||||
\(641\) | 9.73303 | 0.384432 | 0.192216 | − | 0.981353i | \(-0.438433\pi\) | ||||
0.192216 | + | 0.981353i | \(0.438433\pi\) | |||||||
\(642\) | 0.655387 | 0.0258661 | ||||||||
\(643\) | 42.3437 | 1.66987 | 0.834935 | − | 0.550348i | \(-0.185505\pi\) | ||||
0.834935 | + | 0.550348i | \(0.185505\pi\) | |||||||
\(644\) | −0.430136 | −0.0169497 | ||||||||
\(645\) | −0.779100 | −0.0306770 | ||||||||
\(646\) | −3.30940 | −0.130207 | ||||||||
\(647\) | −9.99405 | −0.392907 | −0.196453 | − | 0.980513i | \(-0.562942\pi\) | ||||
−0.196453 | + | 0.980513i | \(0.562942\pi\) | |||||||
\(648\) | −8.93944 | −0.351174 | ||||||||
\(649\) | −5.60898 | −0.220172 | ||||||||
\(650\) | −39.6754 | −1.55620 | ||||||||
\(651\) | 0.283949 | 0.0111288 | ||||||||
\(652\) | −9.15878 | −0.358685 | ||||||||
\(653\) | −2.21195 | −0.0865604 | −0.0432802 | − | 0.999063i | \(-0.513781\pi\) | ||||
−0.0432802 | + | 0.999063i | \(0.513781\pi\) | |||||||
\(654\) | −0.399480 | −0.0156209 | ||||||||
\(655\) | 3.26458 | 0.127558 | ||||||||
\(656\) | 6.59524 | 0.257501 | ||||||||
\(657\) | −30.2430 | −1.17989 | ||||||||
\(658\) | −3.68769 | −0.143761 | ||||||||
\(659\) | 47.8327 | 1.86330 | 0.931648 | − | 0.363362i | \(-0.118371\pi\) | ||||
0.931648 | + | 0.363362i | \(0.118371\pi\) | |||||||
\(660\) | 1.25756 | 0.0489504 | ||||||||
\(661\) | −33.3845 | −1.29851 | −0.649254 | − | 0.760572i | \(-0.724919\pi\) | ||||
−0.649254 | + | 0.760572i | \(0.724919\pi\) | |||||||
\(662\) | 7.53905 | 0.293014 | ||||||||
\(663\) | −0.225659 | −0.00876386 | ||||||||
\(664\) | 5.21951 | 0.202556 | ||||||||
\(665\) | 11.8515 | 0.459582 | ||||||||
\(666\) | −9.16214 | −0.355026 | ||||||||
\(667\) | 0.423629 | 0.0164030 | ||||||||
\(668\) | 17.4206 | 0.674023 | ||||||||
\(669\) | −0.262641 | −0.0101543 | ||||||||
\(670\) | −14.8880 | −0.575175 | ||||||||
\(671\) | 36.6518 | 1.41493 | ||||||||
\(672\) | −0.0352980 | −0.00136165 | ||||||||
\(673\) | 26.7251 | 1.03018 | 0.515088 | − | 0.857137i | \(-0.327759\pi\) | ||||
0.515088 | + | 0.857137i | \(0.327759\pi\) | |||||||
\(674\) | −11.9190 | −0.459104 | ||||||||
\(675\) | 2.78247 | 0.107097 | ||||||||
\(676\) | 36.1811 | 1.39158 | ||||||||
\(677\) | −7.53143 | −0.289457 | −0.144728 | − | 0.989471i | \(-0.546231\pi\) | ||||
−0.144728 | + | 0.989471i | \(0.546231\pi\) | |||||||
\(678\) | −0.873452 | −0.0335447 | ||||||||
\(679\) | 3.74648 | 0.143777 | ||||||||
\(680\) | 1.28008 | 0.0490887 | ||||||||
\(681\) | −1.93520 | −0.0741571 | ||||||||
\(682\) | −37.7613 | −1.44595 | ||||||||
\(683\) | 49.0461 | 1.87670 | 0.938348 | − | 0.345693i | \(-0.112356\pi\) | ||||
0.938348 | + | 0.345693i | \(0.112356\pi\) | |||||||
\(684\) | −25.2631 | −0.965957 | ||||||||
\(685\) | −30.1670 | −1.15262 | ||||||||
\(686\) | −5.94232 | −0.226879 | ||||||||
\(687\) | −0.986848 | −0.0376506 | ||||||||
\(688\) | −2.90818 | −0.110873 | ||||||||
\(689\) | −75.6689 | −2.88276 | ||||||||
\(690\) | −0.267899 | −0.0101987 | ||||||||
\(691\) | 44.6339 | 1.69795 | 0.848977 | − | 0.528430i | \(-0.177219\pi\) | ||||
0.848977 | + | 0.528430i | \(0.177219\pi\) | |||||||
\(692\) | 20.3398 | 0.773203 | ||||||||
\(693\) | 6.04377 | 0.229584 | ||||||||
\(694\) | −7.36904 | −0.279725 | ||||||||
\(695\) | −29.2105 | −1.10802 | ||||||||
\(696\) | 0.0347640 | 0.00131773 | ||||||||
\(697\) | 2.58607 | 0.0979543 | ||||||||
\(698\) | 21.0168 | 0.795499 | ||||||||
\(699\) | −1.92439 | −0.0727870 | ||||||||
\(700\) | −2.43348 | −0.0919768 | ||||||||
\(701\) | 24.2366 | 0.915404 | 0.457702 | − | 0.889106i | \(-0.348673\pi\) | ||||
0.457702 | + | 0.889106i | \(0.348673\pi\) | |||||||
\(702\) | −3.44911 | −0.130178 | ||||||||
\(703\) | −25.8340 | −0.974349 | ||||||||
\(704\) | 4.69415 | 0.176917 | ||||||||
\(705\) | −2.29678 | −0.0865018 | ||||||||
\(706\) | −15.1586 | −0.570502 | ||||||||
\(707\) | −6.22018 | −0.233934 | ||||||||
\(708\) | 0.0980554 | 0.00368515 | ||||||||
\(709\) | −5.50590 | −0.206778 | −0.103389 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103389 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(710\) | −7.75062 | −0.290876 | ||||||||
\(711\) | −8.77916 | −0.329244 | ||||||||
\(712\) | −1.31862 | −0.0494175 | ||||||||
\(713\) | 8.04433 | 0.301262 | ||||||||
\(714\) | −0.0138407 | −0.000517976 0 | ||||||||
\(715\) | −107.469 | −4.01911 | ||||||||
\(716\) | −16.5115 | −0.617062 | ||||||||
\(717\) | 2.16280 | 0.0807711 | ||||||||
\(718\) | 2.44671 | 0.0913104 | ||||||||
\(719\) | 45.7831 | 1.70742 | 0.853711 | − | 0.520747i | \(-0.174347\pi\) | ||||
0.853711 | + | 0.520747i | \(0.174347\pi\) | |||||||
\(720\) | 9.77175 | 0.364172 | ||||||||
\(721\) | −2.32980 | −0.0867662 | ||||||||
\(722\) | −52.2330 | −1.94391 | ||||||||
\(723\) | −1.66412 | −0.0618895 | ||||||||
\(724\) | 16.1923 | 0.601784 | ||||||||
\(725\) | 2.39667 | 0.0890099 | ||||||||
\(726\) | 0.905560 | 0.0336085 | ||||||||
\(727\) | 0.748945 | 0.0277768 | 0.0138884 | − | 0.999904i | \(-0.495579\pi\) | ||||
0.0138884 | + | 0.999904i | \(0.495579\pi\) | |||||||
\(728\) | 3.01651 | 0.111799 | ||||||||
\(729\) | −26.6370 | −0.986557 | ||||||||
\(730\) | 32.9842 | 1.22080 | ||||||||
\(731\) | −1.14033 | −0.0421766 | ||||||||
\(732\) | −0.640741 | −0.0236825 | ||||||||
\(733\) | −3.00665 | −0.111053 | −0.0555266 | − | 0.998457i | \(-0.517684\pi\) | ||||
−0.0555266 | + | 0.998457i | \(0.517684\pi\) | |||||||
\(734\) | 24.1705 | 0.892148 | ||||||||
\(735\) | −1.82573 | −0.0673430 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −21.4076 | −0.788558 | ||||||||
\(738\) | 19.7413 | 0.726688 | ||||||||
\(739\) | −6.88295 | −0.253193 | −0.126597 | − | 0.991954i | \(-0.540405\pi\) | ||||
−0.126597 | + | 0.991954i | \(0.540405\pi\) | |||||||
\(740\) | 9.99260 | 0.367335 | ||||||||
\(741\) | −4.85718 | −0.178433 | ||||||||
\(742\) | −4.64113 | −0.170381 | ||||||||
\(743\) | −37.5100 | −1.37611 | −0.688054 | − | 0.725660i | \(-0.741535\pi\) | ||||
−0.688054 | + | 0.725660i | \(0.741535\pi\) | |||||||
\(744\) | 0.660137 | 0.0242018 | ||||||||
\(745\) | 49.0807 | 1.79818 | ||||||||
\(746\) | 26.0960 | 0.955441 | ||||||||
\(747\) | 15.6234 | 0.571630 | ||||||||
\(748\) | 1.84063 | 0.0673000 | ||||||||
\(749\) | −3.43526 | −0.125522 | ||||||||
\(750\) | −0.176134 | −0.00643151 | ||||||||
\(751\) | −19.5694 | −0.714096 | −0.357048 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357048 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(752\) | −8.57331 | −0.312636 | ||||||||
\(753\) | −0.763447 | −0.0278216 | ||||||||
\(754\) | −2.97088 | −0.108193 | ||||||||
\(755\) | 22.4894 | 0.818473 | ||||||||
\(756\) | −0.211550 | −0.00769401 | ||||||||
\(757\) | 44.6420 | 1.62254 | 0.811271 | − | 0.584670i | \(-0.198776\pi\) | ||||
0.811271 | + | 0.584670i | \(0.198776\pi\) | |||||||
\(758\) | 14.3027 | 0.519499 | ||||||||
\(759\) | −0.385213 | −0.0139823 | ||||||||
\(760\) | 27.5529 | 0.999450 | ||||||||
\(761\) | −13.3607 | −0.484327 | −0.242163 | − | 0.970236i | \(-0.577857\pi\) | ||||
−0.242163 | + | 0.970236i | \(0.577857\pi\) | |||||||
\(762\) | −0.808804 | −0.0292999 | ||||||||
\(763\) | 2.09390 | 0.0758043 | ||||||||
\(764\) | 3.52330 | 0.127469 | ||||||||
\(765\) | 3.83161 | 0.138532 | ||||||||
\(766\) | −24.4379 | −0.882979 | ||||||||
\(767\) | −8.37966 | −0.302572 | ||||||||
\(768\) | −0.0820624 | −0.00296117 | ||||||||
\(769\) | 19.8318 | 0.715152 | 0.357576 | − | 0.933884i | \(-0.383603\pi\) | ||||
0.357576 | + | 0.933884i | \(0.383603\pi\) | |||||||
\(770\) | −6.59158 | −0.237544 | ||||||||
\(771\) | −0.909074 | −0.0327395 | ||||||||
\(772\) | 11.1232 | 0.400333 | ||||||||
\(773\) | 13.0489 | 0.469338 | 0.234669 | − | 0.972075i | \(-0.424599\pi\) | ||||
0.234669 | + | 0.972075i | \(0.424599\pi\) | |||||||
\(774\) | −8.70496 | −0.312893 | ||||||||
\(775\) | 45.5105 | 1.63479 | ||||||||
\(776\) | 8.70998 | 0.312670 | ||||||||
\(777\) | −0.108044 | −0.00387607 | ||||||||
\(778\) | 27.4047 | 0.982505 | ||||||||
\(779\) | 55.6636 | 1.99436 | ||||||||
\(780\) | 1.87876 | 0.0672703 | ||||||||
\(781\) | −11.1446 | −0.398787 | ||||||||
\(782\) | −0.392111 | −0.0140219 | ||||||||
\(783\) | 0.208350 | 0.00744582 | ||||||||
\(784\) | −6.81498 | −0.243392 | ||||||||
\(785\) | −4.97012 | −0.177391 | ||||||||
\(786\) | −0.0820624 | −0.00292707 | ||||||||
\(787\) | −42.2986 | −1.50778 | −0.753892 | − | 0.656999i | \(-0.771826\pi\) | ||||
−0.753892 | + | 0.656999i | \(0.771826\pi\) | |||||||
\(788\) | −12.4197 | −0.442435 | ||||||||
\(789\) | −0.524722 | −0.0186806 | ||||||||
\(790\) | 9.57491 | 0.340660 | ||||||||
\(791\) | 4.57826 | 0.162784 | ||||||||
\(792\) | 14.0508 | 0.499274 | ||||||||
\(793\) | 54.7567 | 1.94447 | ||||||||
\(794\) | −31.6805 | −1.12430 | ||||||||
\(795\) | −2.89061 | −0.102519 | ||||||||
\(796\) | 18.0071 | 0.638244 | ||||||||
\(797\) | 21.2221 | 0.751725 | 0.375862 | − | 0.926676i | \(-0.377347\pi\) | ||||
0.375862 | + | 0.926676i | \(0.377347\pi\) | |||||||
\(798\) | −0.297914 | −0.0105460 | ||||||||
\(799\) | −3.36169 | −0.118928 | ||||||||
\(800\) | −5.65746 | −0.200022 | ||||||||
\(801\) | −3.94699 | −0.139460 | ||||||||
\(802\) | −7.56755 | −0.267219 | ||||||||
\(803\) | 47.4281 | 1.67370 | ||||||||
\(804\) | 0.374244 | 0.0131986 | ||||||||
\(805\) | 1.40421 | 0.0494920 | ||||||||
\(806\) | −56.4143 | −1.98711 | ||||||||
\(807\) | 0.257310 | 0.00905773 | ||||||||
\(808\) | −14.4610 | −0.508735 | ||||||||
\(809\) | 25.8723 | 0.909620 | 0.454810 | − | 0.890588i | \(-0.349707\pi\) | ||||
0.454810 | + | 0.890588i | \(0.349707\pi\) | |||||||
\(810\) | 29.1835 | 1.02540 | ||||||||
\(811\) | 15.1785 | 0.532989 | 0.266494 | − | 0.963836i | \(-0.414135\pi\) | ||||
0.266494 | + | 0.963836i | \(0.414135\pi\) | |||||||
\(812\) | −0.182218 | −0.00639460 | ||||||||
\(813\) | 0.376706 | 0.0132117 | ||||||||
\(814\) | 14.3684 | 0.503612 | ||||||||
\(815\) | 29.8995 | 1.04734 | ||||||||
\(816\) | −0.0321776 | −0.00112644 | ||||||||
\(817\) | −24.5450 | −0.858720 | ||||||||
\(818\) | −5.13400 | −0.179506 | ||||||||
\(819\) | 9.02922 | 0.315506 | ||||||||
\(820\) | −21.5307 | −0.751884 | ||||||||
\(821\) | 11.3213 | 0.395115 | 0.197557 | − | 0.980291i | \(-0.436699\pi\) | ||||
0.197557 | + | 0.980291i | \(0.436699\pi\) | |||||||
\(822\) | 0.758316 | 0.0264493 | ||||||||
\(823\) | −26.6435 | −0.928736 | −0.464368 | − | 0.885642i | \(-0.653718\pi\) | ||||
−0.464368 | + | 0.885642i | \(0.653718\pi\) | |||||||
\(824\) | −5.41642 | −0.188690 | ||||||||
\(825\) | −2.17933 | −0.0758745 | ||||||||
\(826\) | −0.513964 | −0.0178831 | ||||||||
\(827\) | 21.0126 | 0.730681 | 0.365341 | − | 0.930874i | \(-0.380953\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380953\pi\) | |||||||
\(828\) | −2.99327 | −0.104023 | ||||||||
\(829\) | 22.5989 | 0.784891 | 0.392446 | − | 0.919775i | \(-0.371629\pi\) | ||||
0.392446 | + | 0.919775i | \(0.371629\pi\) | |||||||
\(830\) | −17.0395 | −0.591450 | ||||||||
\(831\) | −0.844457 | −0.0292939 | ||||||||
\(832\) | 7.01292 | 0.243129 | ||||||||
\(833\) | −2.67223 | −0.0925873 | ||||||||
\(834\) | 0.734270 | 0.0254257 | ||||||||
\(835\) | −56.8709 | −1.96810 | ||||||||
\(836\) | 39.6184 | 1.37023 | ||||||||
\(837\) | 3.95638 | 0.136752 | ||||||||
\(838\) | −8.27791 | −0.285956 | ||||||||
\(839\) | −19.1141 | −0.659892 | −0.329946 | − | 0.944000i | \(-0.607030\pi\) | ||||
−0.329946 | + | 0.944000i | \(0.607030\pi\) | |||||||
\(840\) | 0.115233 | 0.00397592 | ||||||||
\(841\) | −28.8205 | −0.993812 | ||||||||
\(842\) | 5.80953 | 0.200210 | ||||||||
\(843\) | 0.323939 | 0.0111571 | ||||||||
\(844\) | 11.1671 | 0.384387 | ||||||||
\(845\) | −118.116 | −4.06331 | ||||||||
\(846\) | −25.6622 | −0.882284 | ||||||||
\(847\) | −4.74655 | −0.163094 | ||||||||
\(848\) | −10.7899 | −0.370528 | ||||||||
\(849\) | 2.67167 | 0.0916915 | ||||||||
\(850\) | −2.21835 | −0.0760889 | ||||||||
\(851\) | −3.06092 | −0.104927 | ||||||||
\(852\) | 0.194829 | 0.00667474 | ||||||||
\(853\) | −7.28828 | −0.249546 | −0.124773 | − | 0.992185i | \(-0.539820\pi\) | ||||
−0.124773 | + | 0.992185i | \(0.539820\pi\) | |||||||
\(854\) | 3.35849 | 0.114925 | ||||||||
\(855\) | 82.4732 | 2.82052 | ||||||||
\(856\) | −7.98644 | −0.272971 | ||||||||
\(857\) | −21.7676 | −0.743568 | −0.371784 | − | 0.928319i | \(-0.621254\pi\) | ||||
−0.371784 | + | 0.928319i | \(0.621254\pi\) | |||||||
\(858\) | 2.70147 | 0.0922266 | ||||||||
\(859\) | 39.7270 | 1.35547 | 0.677734 | − | 0.735307i | \(-0.262962\pi\) | ||||
0.677734 | + | 0.735307i | \(0.262962\pi\) | |||||||
\(860\) | 9.49399 | 0.323742 | ||||||||
\(861\) | 0.232799 | 0.00793376 | ||||||||
\(862\) | 5.55309 | 0.189139 | ||||||||
\(863\) | 23.1937 | 0.789522 | 0.394761 | − | 0.918784i | \(-0.370827\pi\) | ||||
0.394761 | + | 0.918784i | \(0.370827\pi\) | |||||||
\(864\) | −0.491822 | −0.0167321 | ||||||||
\(865\) | −66.4008 | −2.25769 | ||||||||
\(866\) | 33.3320 | 1.13267 | ||||||||
\(867\) | 1.38244 | 0.0469503 | ||||||||
\(868\) | −3.46015 | −0.117445 | ||||||||
\(869\) | 13.7678 | 0.467041 | ||||||||
\(870\) | −0.113490 | −0.00384766 | ||||||||
\(871\) | −31.9823 | −1.08368 | ||||||||
\(872\) | 4.86800 | 0.164851 | ||||||||
\(873\) | 26.0713 | 0.882380 | ||||||||
\(874\) | −8.43997 | −0.285486 | ||||||||
\(875\) | 0.923219 | 0.0312105 | ||||||||
\(876\) | −0.829132 | −0.0280138 | ||||||||
\(877\) | −35.2424 | −1.19005 | −0.595025 | − | 0.803707i | \(-0.702858\pi\) | ||||
−0.595025 | + | 0.803707i | \(0.702858\pi\) | |||||||
\(878\) | 19.1564 | 0.646499 | ||||||||
\(879\) | 2.70514 | 0.0912422 | ||||||||
\(880\) | −15.3244 | −0.516586 | ||||||||
\(881\) | −0.0754909 | −0.00254335 | −0.00127168 | − | 0.999999i | \(-0.500405\pi\) | ||||
−0.00127168 | + | 0.999999i | \(0.500405\pi\) | |||||||
\(882\) | −20.3991 | −0.686872 | ||||||||
\(883\) | 14.1303 | 0.475523 | 0.237762 | − | 0.971324i | \(-0.423586\pi\) | ||||
0.237762 | + | 0.971324i | \(0.423586\pi\) | |||||||
\(884\) | 2.74984 | 0.0924872 | ||||||||
\(885\) | −0.320109 | −0.0107604 | ||||||||
\(886\) | −16.5825 | −0.557099 | ||||||||
\(887\) | −24.3394 | −0.817238 | −0.408619 | − | 0.912705i | \(-0.633990\pi\) | ||||
−0.408619 | + | 0.912705i | \(0.633990\pi\) | |||||||
\(888\) | −0.251186 | −0.00842926 | ||||||||
\(889\) | 4.23940 | 0.142185 | ||||||||
\(890\) | 4.30475 | 0.144295 | ||||||||
\(891\) | 41.9630 | 1.40581 | ||||||||
\(892\) | 3.20050 | 0.107161 | ||||||||
\(893\) | −72.3584 | −2.42138 | ||||||||
\(894\) | −1.23375 | −0.0412629 | ||||||||
\(895\) | 53.9029 | 1.80178 | ||||||||
\(896\) | 0.430136 | 0.0143698 | ||||||||
\(897\) | −0.575497 | −0.0192153 | ||||||||
\(898\) | 25.5612 | 0.852987 | ||||||||
\(899\) | 3.40781 | 0.113657 | ||||||||
\(900\) | −16.9343 | −0.564476 | ||||||||
\(901\) | −4.23085 | −0.140950 | ||||||||
\(902\) | −30.9590 | −1.03082 | ||||||||
\(903\) | −0.102653 | −0.00341608 | ||||||||
\(904\) | 10.6438 | 0.354006 | ||||||||
\(905\) | −52.8611 | −1.75716 | ||||||||
\(906\) | −0.565321 | −0.0187815 | ||||||||
\(907\) | −19.1072 | −0.634445 | −0.317223 | − | 0.948351i | \(-0.602750\pi\) | ||||
−0.317223 | + | 0.948351i | \(0.602750\pi\) | |||||||
\(908\) | 23.5821 | 0.782598 | ||||||||
\(909\) | −43.2855 | −1.43569 | ||||||||
\(910\) | −9.84763 | −0.326446 | ||||||||
\(911\) | 5.66835 | 0.187801 | 0.0939004 | − | 0.995582i | \(-0.470066\pi\) | ||||
0.0939004 | + | 0.995582i | \(0.470066\pi\) | |||||||
\(912\) | −0.692604 | −0.0229344 | ||||||||
\(913\) | −24.5012 | −0.810870 | ||||||||
\(914\) | −37.4064 | −1.23729 | ||||||||
\(915\) | 2.09175 | 0.0691511 | ||||||||
\(916\) | 12.0256 | 0.397336 | ||||||||
\(917\) | 0.430136 | 0.0142043 | ||||||||
\(918\) | −0.192849 | −0.00636496 | ||||||||
\(919\) | −16.5208 | −0.544971 | −0.272486 | − | 0.962160i | \(-0.587846\pi\) | ||||
−0.272486 | + | 0.962160i | \(0.587846\pi\) | |||||||
\(920\) | 3.26458 | 0.107630 | ||||||||
\(921\) | 2.12681 | 0.0700806 | ||||||||
\(922\) | 14.4246 | 0.475050 | ||||||||
\(923\) | −16.6498 | −0.548034 | ||||||||
\(924\) | 0.165694 | 0.00545093 | ||||||||
\(925\) | −17.3170 | −0.569381 | ||||||||
\(926\) | −2.35074 | −0.0772501 | ||||||||
\(927\) | −16.2128 | −0.532498 | ||||||||
\(928\) | −0.423629 | −0.0139063 | ||||||||
\(929\) | −8.32030 | −0.272980 | −0.136490 | − | 0.990641i | \(-0.543582\pi\) | ||||
−0.136490 | + | 0.990641i | \(0.543582\pi\) | |||||||
\(930\) | −2.15507 | −0.0706675 | ||||||||
\(931\) | −57.5182 | −1.88508 | ||||||||
\(932\) | 23.4503 | 0.768140 | ||||||||
\(933\) | 0.314934 | 0.0103105 | ||||||||
\(934\) | 18.1238 | 0.593030 | ||||||||
\(935\) | −6.00887 | −0.196511 | ||||||||
\(936\) | 20.9915 | 0.686130 | ||||||||
\(937\) | 17.6298 | 0.575941 | 0.287970 | − | 0.957639i | \(-0.407020\pi\) | ||||
0.287970 | + | 0.957639i | \(0.407020\pi\) | |||||||
\(938\) | −1.96163 | −0.0640494 | ||||||||
\(939\) | 0.512638 | 0.0167293 | ||||||||
\(940\) | 27.9882 | 0.912875 | ||||||||
\(941\) | 20.4441 | 0.666459 | 0.333229 | − | 0.942846i | \(-0.391862\pi\) | ||||
0.333229 | + | 0.942846i | \(0.391862\pi\) | |||||||
\(942\) | 0.124935 | 0.00407060 | ||||||||
\(943\) | 6.59524 | 0.214771 | ||||||||
\(944\) | −1.19489 | −0.0388903 | ||||||||
\(945\) | 0.690622 | 0.0224659 | ||||||||
\(946\) | 13.6514 | 0.443846 | ||||||||
\(947\) | 40.4257 | 1.31366 | 0.656830 | − | 0.754039i | \(-0.271897\pi\) | ||||
0.656830 | + | 0.754039i | \(0.271897\pi\) | |||||||
\(948\) | −0.240687 | −0.00781714 | ||||||||
\(949\) | 70.8563 | 2.30009 | ||||||||
\(950\) | −47.7488 | −1.54918 | ||||||||
\(951\) | 2.08363 | 0.0675662 | ||||||||
\(952\) | 0.168661 | 0.00546633 | ||||||||
\(953\) | 61.6500 | 1.99704 | 0.998520 | − | 0.0543781i | \(-0.0173176\pi\) | ||||
0.998520 | + | 0.0543781i | \(0.0173176\pi\) | |||||||
\(954\) | −32.2971 | −1.04566 | ||||||||
\(955\) | −11.5021 | −0.372199 | ||||||||
\(956\) | −26.3555 | −0.852398 | ||||||||
\(957\) | −0.163187 | −0.00527510 | ||||||||
\(958\) | −12.6937 | −0.410113 | ||||||||
\(959\) | −3.97477 | −0.128352 | ||||||||
\(960\) | 0.267899 | 0.00864641 | ||||||||
\(961\) | 33.7112 | 1.08746 | ||||||||
\(962\) | 21.4660 | 0.692091 | ||||||||
\(963\) | −23.9055 | −0.770345 | ||||||||
\(964\) | 20.2788 | 0.653135 | ||||||||
\(965\) | −36.3126 | −1.16894 | ||||||||
\(966\) | −0.0352980 | −0.00113569 | ||||||||
\(967\) | 24.1797 | 0.777565 | 0.388783 | − | 0.921330i | \(-0.372896\pi\) | ||||
0.388783 | + | 0.921330i | \(0.372896\pi\) | |||||||
\(968\) | −11.0350 | −0.354679 | ||||||||
\(969\) | −0.271578 | −0.00872433 | ||||||||
\(970\) | −28.4344 | −0.912974 | ||||||||
\(971\) | −21.4891 | −0.689617 | −0.344808 | − | 0.938673i | \(-0.612056\pi\) | ||||
−0.344808 | + | 0.938673i | \(0.612056\pi\) | |||||||
\(972\) | −2.20906 | −0.0708556 | ||||||||
\(973\) | −3.84873 | −0.123385 | ||||||||
\(974\) | 10.0632 | 0.322447 | ||||||||
\(975\) | −3.25586 | −0.104271 | ||||||||
\(976\) | 7.80797 | 0.249927 | ||||||||
\(977\) | −6.93961 | −0.222018 | −0.111009 | − | 0.993819i | \(-0.535408\pi\) | ||||
−0.111009 | + | 0.993819i | \(0.535408\pi\) | |||||||
\(978\) | −0.751591 | −0.0240332 | ||||||||
\(979\) | 6.18981 | 0.197827 | ||||||||
\(980\) | 22.2480 | 0.710688 | ||||||||
\(981\) | 14.5712 | 0.465223 | ||||||||
\(982\) | 1.30028 | 0.0414936 | ||||||||
\(983\) | −16.7848 | −0.535352 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(984\) | 0.541222 | 0.0172535 | ||||||||
\(985\) | 40.5452 | 1.29188 | ||||||||
\(986\) | −0.166109 | −0.00529000 | ||||||||
\(987\) | −0.302621 | −0.00963252 | ||||||||
\(988\) | 59.1888 | 1.88305 | ||||||||
\(989\) | −2.90818 | −0.0924748 | ||||||||
\(990\) | −45.8700 | −1.45784 | ||||||||
\(991\) | 19.0338 | 0.604629 | 0.302314 | − | 0.953208i | \(-0.402241\pi\) | ||||
0.302314 | + | 0.953208i | \(0.402241\pi\) | |||||||
\(992\) | −8.04433 | −0.255408 | ||||||||
\(993\) | 0.618673 | 0.0196330 | ||||||||
\(994\) | −1.02121 | −0.0323908 | ||||||||
\(995\) | −58.7855 | −1.86363 | ||||||||
\(996\) | 0.428326 | 0.0135720 | ||||||||
\(997\) | 38.5516 | 1.22094 | 0.610471 | − | 0.792038i | \(-0.290980\pi\) | ||||
0.610471 | + | 0.792038i | \(0.290980\pi\) | |||||||
\(998\) | 27.0515 | 0.856300 | ||||||||
\(999\) | −1.50543 | −0.0476296 |
(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 | 6026.2.a.j.1.16 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.j.1.16 | ✓ | 33 | 1.1 | even | 1 | trivial |