Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\Q(\zeta_{44})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.563465\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.563465 | 0.398430 | 0.199215 | − | 0.979956i | \(-0.436161\pi\) | ||||
0.199215 | + | 0.979956i | \(0.436161\pi\) | |||||||
\(3\) | 2.07496 | 1.19798 | 0.598991 | − | 0.800756i | \(-0.295569\pi\) | ||||
0.598991 | + | 0.800756i | \(0.295569\pi\) | |||||||
\(4\) | −1.68251 | −0.841254 | ||||||||
\(5\) | 1.25580 | 0.561610 | 0.280805 | − | 0.959765i | \(-0.409399\pi\) | ||||
0.280805 | + | 0.959765i | \(0.409399\pi\) | |||||||
\(6\) | 1.16917 | 0.477312 | ||||||||
\(7\) | −1.91459 | −0.723645 | −0.361823 | − | 0.932247i | \(-0.617845\pi\) | ||||
−0.361823 | + | 0.932247i | \(0.617845\pi\) | |||||||
\(8\) | −2.07496 | −0.733611 | ||||||||
\(9\) | 1.30548 | 0.435159 | ||||||||
\(10\) | 0.707599 | 0.223762 | ||||||||
\(11\) | 0.634356 | 0.191266 | 0.0956328 | − | 0.995417i | \(-0.469513\pi\) | ||||
0.0956328 | + | 0.995417i | \(0.469513\pi\) | |||||||
\(12\) | −3.49114 | −1.00781 | ||||||||
\(13\) | −5.68965 | −1.57802 | −0.789012 | − | 0.614377i | \(-0.789407\pi\) | ||||
−0.789012 | + | 0.614377i | \(0.789407\pi\) | |||||||
\(14\) | −1.07880 | −0.288322 | ||||||||
\(15\) | 2.60574 | 0.672799 | ||||||||
\(16\) | 2.19584 | 0.548961 | ||||||||
\(17\) | −5.78084 | −1.40206 | −0.701030 | − | 0.713132i | \(-0.747276\pi\) | ||||
−0.701030 | + | 0.713132i | \(0.747276\pi\) | |||||||
\(18\) | 0.735591 | 0.173380 | ||||||||
\(19\) | −3.28109 | −0.752734 | −0.376367 | − | 0.926471i | \(-0.622827\pi\) | ||||
−0.376367 | + | 0.926471i | \(0.622827\pi\) | |||||||
\(20\) | −2.11289 | −0.472457 | ||||||||
\(21\) | −3.97270 | −0.866913 | ||||||||
\(22\) | 0.357438 | 0.0762060 | ||||||||
\(23\) | 9.50494 | 1.98192 | 0.990958 | − | 0.134172i | \(-0.0428374\pi\) | ||||
0.990958 | + | 0.134172i | \(0.0428374\pi\) | |||||||
\(24\) | −4.30548 | −0.878852 | ||||||||
\(25\) | −3.42297 | −0.684594 | ||||||||
\(26\) | −3.20592 | −0.628732 | ||||||||
\(27\) | −3.51608 | −0.676669 | ||||||||
\(28\) | 3.22130 | 0.608769 | ||||||||
\(29\) | −4.12807 | −0.766563 | −0.383281 | − | 0.923632i | \(-0.625206\pi\) | ||||
−0.383281 | + | 0.923632i | \(0.625206\pi\) | |||||||
\(30\) | 1.46824 | 0.268063 | ||||||||
\(31\) | 3.12343 | 0.560984 | 0.280492 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280492 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(32\) | 5.38721 | 0.952333 | ||||||||
\(33\) | 1.31627 | 0.229133 | ||||||||
\(34\) | −3.25730 | −0.558623 | ||||||||
\(35\) | −2.40433 | −0.406407 | ||||||||
\(36\) | −2.19647 | −0.366079 | ||||||||
\(37\) | −10.6751 | −1.75497 | −0.877486 | − | 0.479603i | \(-0.840781\pi\) | ||||
−0.877486 | + | 0.479603i | \(0.840781\pi\) | |||||||
\(38\) | −1.84878 | −0.299912 | ||||||||
\(39\) | −11.8058 | −1.89044 | ||||||||
\(40\) | −2.60574 | −0.412003 | ||||||||
\(41\) | −2.15325 | −0.336282 | −0.168141 | − | 0.985763i | \(-0.553776\pi\) | ||||
−0.168141 | + | 0.985763i | \(0.553776\pi\) | |||||||
\(42\) | −2.23848 | −0.345404 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −1.06731 | −0.160903 | ||||||||
\(45\) | 1.63942 | 0.244390 | ||||||||
\(46\) | 5.35570 | 0.789655 | ||||||||
\(47\) | 1.01308 | 0.147772 | 0.0738861 | − | 0.997267i | \(-0.476460\pi\) | ||||
0.0738861 | + | 0.997267i | \(0.476460\pi\) | |||||||
\(48\) | 4.55630 | 0.657645 | ||||||||
\(49\) | −3.33436 | −0.476338 | ||||||||
\(50\) | −1.92872 | −0.272763 | ||||||||
\(51\) | −11.9950 | −1.67964 | ||||||||
\(52\) | 9.57287 | 1.32752 | ||||||||
\(53\) | 2.43788 | 0.334869 | 0.167434 | − | 0.985883i | \(-0.446452\pi\) | ||||
0.167434 | + | 0.985883i | \(0.446452\pi\) | |||||||
\(54\) | −1.98119 | −0.269605 | ||||||||
\(55\) | 0.796624 | 0.107417 | ||||||||
\(56\) | 3.97270 | 0.530874 | ||||||||
\(57\) | −6.80815 | −0.901761 | ||||||||
\(58\) | −2.32602 | −0.305422 | ||||||||
\(59\) | 1.54924 | 0.201693 | 0.100847 | − | 0.994902i | \(-0.467845\pi\) | ||||
0.100847 | + | 0.994902i | \(0.467845\pi\) | |||||||
\(60\) | −4.38417 | −0.565994 | ||||||||
\(61\) | 3.56631 | 0.456620 | 0.228310 | − | 0.973589i | \(-0.426680\pi\) | ||||
0.228310 | + | 0.973589i | \(0.426680\pi\) | |||||||
\(62\) | 1.75994 | 0.223513 | ||||||||
\(63\) | −2.49945 | −0.314901 | ||||||||
\(64\) | −1.35618 | −0.169523 | ||||||||
\(65\) | −7.14505 | −0.886235 | ||||||||
\(66\) | 0.741670 | 0.0912933 | ||||||||
\(67\) | −5.63797 | −0.688788 | −0.344394 | − | 0.938825i | \(-0.611916\pi\) | ||||
−0.344394 | + | 0.938825i | \(0.611916\pi\) | |||||||
\(68\) | 9.72631 | 1.17949 | ||||||||
\(69\) | 19.7224 | 2.37430 | ||||||||
\(70\) | −1.35476 | −0.161925 | ||||||||
\(71\) | 12.9142 | 1.53264 | 0.766319 | − | 0.642461i | \(-0.222086\pi\) | ||||
0.766319 | + | 0.642461i | \(0.222086\pi\) | |||||||
\(72\) | −2.70882 | −0.319237 | ||||||||
\(73\) | −5.02757 | −0.588433 | −0.294217 | − | 0.955739i | \(-0.595059\pi\) | ||||
−0.294217 | + | 0.955739i | \(0.595059\pi\) | |||||||
\(74\) | −6.01503 | −0.699233 | ||||||||
\(75\) | −7.10254 | −0.820131 | ||||||||
\(76\) | 5.52046 | 0.633240 | ||||||||
\(77\) | −1.21453 | −0.138408 | ||||||||
\(78\) | −6.65217 | −0.753210 | ||||||||
\(79\) | 8.13626 | 0.915400 | 0.457700 | − | 0.889107i | \(-0.348673\pi\) | ||||
0.457700 | + | 0.889107i | \(0.348673\pi\) | |||||||
\(80\) | 2.75754 | 0.308302 | ||||||||
\(81\) | −11.2122 | −1.24580 | ||||||||
\(82\) | −1.21328 | −0.133985 | ||||||||
\(83\) | 3.15484 | 0.346288 | 0.173144 | − | 0.984897i | \(-0.444607\pi\) | ||||
0.173144 | + | 0.984897i | \(0.444607\pi\) | |||||||
\(84\) | 6.68409 | 0.729294 | ||||||||
\(85\) | −7.25957 | −0.787411 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.56559 | −0.918328 | ||||||||
\(88\) | −1.31627 | −0.140314 | ||||||||
\(89\) | 0.861116 | 0.0912781 | 0.0456390 | − | 0.998958i | \(-0.485468\pi\) | ||||
0.0456390 | + | 0.998958i | \(0.485468\pi\) | |||||||
\(90\) | 0.923754 | 0.0973722 | ||||||||
\(91\) | 10.8933 | 1.14193 | ||||||||
\(92\) | −15.9921 | −1.66729 | ||||||||
\(93\) | 6.48100 | 0.672048 | ||||||||
\(94\) | 0.570833 | 0.0588769 | ||||||||
\(95\) | −4.12039 | −0.422743 | ||||||||
\(96\) | 11.1783 | 1.14088 | ||||||||
\(97\) | −15.6367 | −1.58767 | −0.793834 | − | 0.608135i | \(-0.791918\pi\) | ||||
−0.793834 | + | 0.608135i | \(0.791918\pi\) | |||||||
\(98\) | −1.87880 | −0.189787 | ||||||||
\(99\) | 0.828137 | 0.0832309 | ||||||||
\(100\) | 5.75917 | 0.575917 | ||||||||
\(101\) | −11.4425 | −1.13857 | −0.569286 | − | 0.822140i | \(-0.692780\pi\) | ||||
−0.569286 | + | 0.822140i | \(0.692780\pi\) | |||||||
\(102\) | −6.75879 | −0.669220 | ||||||||
\(103\) | −0.697420 | −0.0687189 | −0.0343594 | − | 0.999410i | \(-0.510939\pi\) | ||||
−0.0343594 | + | 0.999410i | \(0.510939\pi\) | |||||||
\(104\) | 11.8058 | 1.15766 | ||||||||
\(105\) | −4.98891 | −0.486868 | ||||||||
\(106\) | 1.37366 | 0.133422 | ||||||||
\(107\) | 7.07010 | 0.683492 | 0.341746 | − | 0.939792i | \(-0.388982\pi\) | ||||
0.341746 | + | 0.939792i | \(0.388982\pi\) | |||||||
\(108\) | 5.91582 | 0.569250 | ||||||||
\(109\) | −1.79842 | −0.172257 | −0.0861286 | − | 0.996284i | \(-0.527450\pi\) | ||||
−0.0861286 | + | 0.996284i | \(0.527450\pi\) | |||||||
\(110\) | 0.448870 | 0.0427981 | ||||||||
\(111\) | −22.1504 | −2.10242 | ||||||||
\(112\) | −4.20413 | −0.397253 | ||||||||
\(113\) | 11.9556 | 1.12469 | 0.562344 | − | 0.826903i | \(-0.309900\pi\) | ||||
0.562344 | + | 0.826903i | \(0.309900\pi\) | |||||||
\(114\) | −3.83615 | −0.359289 | ||||||||
\(115\) | 11.9363 | 1.11306 | ||||||||
\(116\) | 6.94550 | 0.644874 | ||||||||
\(117\) | −7.42770 | −0.686691 | ||||||||
\(118\) | 0.872941 | 0.0803607 | ||||||||
\(119\) | 11.0679 | 1.01459 | ||||||||
\(120\) | −5.40681 | −0.493572 | ||||||||
\(121\) | −10.5976 | −0.963417 | ||||||||
\(122\) | 2.00949 | 0.181931 | ||||||||
\(123\) | −4.46792 | −0.402859 | ||||||||
\(124\) | −5.25519 | −0.471930 | ||||||||
\(125\) | −10.5776 | −0.946085 | ||||||||
\(126\) | −1.40835 | −0.125466 | ||||||||
\(127\) | 9.81007 | 0.870503 | 0.435252 | − | 0.900309i | \(-0.356659\pi\) | ||||
0.435252 | + | 0.900309i | \(0.356659\pi\) | |||||||
\(128\) | −11.5386 | −1.01988 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.02599 | −0.353103 | ||||||||
\(131\) | 16.3144 | 1.42540 | 0.712699 | − | 0.701470i | \(-0.247472\pi\) | ||||
0.712699 | + | 0.701470i | \(0.247472\pi\) | |||||||
\(132\) | −2.21463 | −0.192759 | ||||||||
\(133\) | 6.28193 | 0.544712 | ||||||||
\(134\) | −3.17680 | −0.274434 | ||||||||
\(135\) | −4.41548 | −0.380024 | ||||||||
\(136\) | 11.9950 | 1.02857 | ||||||||
\(137\) | 15.3101 | 1.30803 | 0.654017 | − | 0.756480i | \(-0.273082\pi\) | ||||
0.654017 | + | 0.756480i | \(0.273082\pi\) | |||||||
\(138\) | 11.1129 | 0.945992 | ||||||||
\(139\) | −13.0189 | −1.10425 | −0.552124 | − | 0.833762i | \(-0.686183\pi\) | ||||
−0.552124 | + | 0.833762i | \(0.686183\pi\) | |||||||
\(140\) | 4.04531 | 0.341891 | ||||||||
\(141\) | 2.10210 | 0.177028 | ||||||||
\(142\) | 7.27672 | 0.610649 | ||||||||
\(143\) | −3.60926 | −0.301822 | ||||||||
\(144\) | 2.86662 | 0.238885 | ||||||||
\(145\) | −5.18402 | −0.430510 | ||||||||
\(146\) | −2.83286 | −0.234449 | ||||||||
\(147\) | −6.91868 | −0.570643 | ||||||||
\(148\) | 17.9609 | 1.47638 | ||||||||
\(149\) | 6.87119 | 0.562910 | 0.281455 | − | 0.959574i | \(-0.409183\pi\) | ||||
0.281455 | + | 0.959574i | \(0.409183\pi\) | |||||||
\(150\) | −4.00203 | −0.326765 | ||||||||
\(151\) | −12.5372 | −1.02026 | −0.510132 | − | 0.860096i | \(-0.670404\pi\) | ||||
−0.510132 | + | 0.860096i | \(0.670404\pi\) | |||||||
\(152\) | 6.80815 | 0.552213 | ||||||||
\(153\) | −7.54675 | −0.610119 | ||||||||
\(154\) | −0.684345 | −0.0551461 | ||||||||
\(155\) | 3.92240 | 0.315054 | ||||||||
\(156\) | 19.8634 | 1.59034 | ||||||||
\(157\) | −4.64464 | −0.370682 | −0.185341 | − | 0.982674i | \(-0.559339\pi\) | ||||
−0.185341 | + | 0.982674i | \(0.559339\pi\) | |||||||
\(158\) | 4.58450 | 0.364723 | ||||||||
\(159\) | 5.05852 | 0.401167 | ||||||||
\(160\) | 6.76525 | 0.534840 | ||||||||
\(161\) | −18.1980 | −1.43420 | ||||||||
\(162\) | −6.31766 | −0.496362 | ||||||||
\(163\) | 5.69669 | 0.446199 | 0.223099 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223099 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(164\) | 3.62286 | 0.282898 | ||||||||
\(165\) | 1.65297 | 0.128683 | ||||||||
\(166\) | 1.77764 | 0.137972 | ||||||||
\(167\) | −5.50814 | −0.426233 | −0.213116 | − | 0.977027i | \(-0.568361\pi\) | ||||
−0.213116 | + | 0.977027i | \(0.568361\pi\) | |||||||
\(168\) | 8.24320 | 0.635977 | ||||||||
\(169\) | 19.3721 | 1.49016 | ||||||||
\(170\) | −4.09052 | −0.313728 | ||||||||
\(171\) | −4.28339 | −0.327559 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0002 | −0.912355 | −0.456178 | − | 0.889889i | \(-0.650782\pi\) | ||||
−0.456178 | + | 0.889889i | \(0.650782\pi\) | |||||||
\(174\) | −4.82641 | −0.365889 | ||||||||
\(175\) | 6.55357 | 0.495403 | ||||||||
\(176\) | 1.39295 | 0.104997 | ||||||||
\(177\) | 3.21461 | 0.241625 | ||||||||
\(178\) | 0.485209 | 0.0363679 | ||||||||
\(179\) | −14.1631 | −1.05860 | −0.529299 | − | 0.848436i | \(-0.677545\pi\) | ||||
−0.529299 | + | 0.848436i | \(0.677545\pi\) | |||||||
\(180\) | −2.75833 | −0.205594 | ||||||||
\(181\) | −8.35239 | −0.620828 | −0.310414 | − | 0.950601i | \(-0.600468\pi\) | ||||
−0.310414 | + | 0.950601i | \(0.600468\pi\) | |||||||
\(182\) | 6.13801 | 0.454979 | ||||||||
\(183\) | 7.39997 | 0.547022 | ||||||||
\(184\) | −19.7224 | −1.45395 | ||||||||
\(185\) | −13.4057 | −0.985610 | ||||||||
\(186\) | 3.65182 | 0.267764 | ||||||||
\(187\) | −3.66711 | −0.268166 | ||||||||
\(188\) | −1.70451 | −0.124314 | ||||||||
\(189\) | 6.73183 | 0.489668 | ||||||||
\(190\) | −2.32170 | −0.168434 | ||||||||
\(191\) | 4.69247 | 0.339535 | 0.169768 | − | 0.985484i | \(-0.445698\pi\) | ||||
0.169768 | + | 0.985484i | \(0.445698\pi\) | |||||||
\(192\) | −2.81403 | −0.203085 | ||||||||
\(193\) | 5.59833 | 0.402976 | 0.201488 | − | 0.979491i | \(-0.435422\pi\) | ||||
0.201488 | + | 0.979491i | \(0.435422\pi\) | |||||||
\(194\) | −8.81074 | −0.632574 | ||||||||
\(195\) | −14.8257 | −1.06169 | ||||||||
\(196\) | 5.61009 | 0.400721 | ||||||||
\(197\) | 13.3380 | 0.950296 | 0.475148 | − | 0.879906i | \(-0.342395\pi\) | ||||
0.475148 | + | 0.879906i | \(0.342395\pi\) | |||||||
\(198\) | 0.466626 | 0.0331617 | ||||||||
\(199\) | −21.6651 | −1.53580 | −0.767898 | − | 0.640572i | \(-0.778697\pi\) | ||||
−0.767898 | + | 0.640572i | \(0.778697\pi\) | |||||||
\(200\) | 7.10254 | 0.502225 | ||||||||
\(201\) | −11.6986 | −0.825155 | ||||||||
\(202\) | −6.44745 | −0.453641 | ||||||||
\(203\) | 7.90354 | 0.554720 | ||||||||
\(204\) | 20.1817 | 1.41300 | ||||||||
\(205\) | −2.70405 | −0.188859 | ||||||||
\(206\) | −0.392972 | −0.0273797 | ||||||||
\(207\) | 12.4085 | 0.862448 | ||||||||
\(208\) | −12.4936 | −0.866274 | ||||||||
\(209\) | −2.08138 | −0.143972 | ||||||||
\(210\) | −2.81108 | −0.193983 | ||||||||
\(211\) | 10.1882 | 0.701385 | 0.350692 | − | 0.936491i | \(-0.385946\pi\) | ||||
0.350692 | + | 0.936491i | \(0.385946\pi\) | |||||||
\(212\) | −4.10175 | −0.281710 | ||||||||
\(213\) | 26.7966 | 1.83607 | ||||||||
\(214\) | 3.98375 | 0.272324 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.29573 | 0.496412 | ||||||||
\(217\) | −5.98007 | −0.405953 | ||||||||
\(218\) | −1.01335 | −0.0686324 | ||||||||
\(219\) | −10.4320 | −0.704932 | ||||||||
\(220\) | −1.34033 | −0.0903647 | ||||||||
\(221\) | 32.8910 | 2.21249 | ||||||||
\(222\) | −12.4810 | −0.837668 | ||||||||
\(223\) | −9.65168 | −0.646324 | −0.323162 | − | 0.946344i | \(-0.604746\pi\) | ||||
−0.323162 | + | 0.946344i | \(0.604746\pi\) | |||||||
\(224\) | −10.3143 | −0.689151 | ||||||||
\(225\) | −4.46861 | −0.297907 | ||||||||
\(226\) | 6.73656 | 0.448109 | ||||||||
\(227\) | 28.1295 | 1.86702 | 0.933510 | − | 0.358553i | \(-0.116730\pi\) | ||||
0.933510 | + | 0.358553i | \(0.116730\pi\) | |||||||
\(228\) | 11.4548 | 0.758610 | ||||||||
\(229\) | 6.24141 | 0.412444 | 0.206222 | − | 0.978505i | \(-0.433883\pi\) | ||||
0.206222 | + | 0.978505i | \(0.433883\pi\) | |||||||
\(230\) | 6.72568 | 0.443478 | ||||||||
\(231\) | −2.52010 | −0.165811 | ||||||||
\(232\) | 8.56559 | 0.562359 | ||||||||
\(233\) | 17.5410 | 1.14915 | 0.574574 | − | 0.818452i | \(-0.305168\pi\) | ||||
0.574574 | + | 0.818452i | \(0.305168\pi\) | |||||||
\(234\) | −4.18525 | −0.273598 | ||||||||
\(235\) | 1.27222 | 0.0829904 | ||||||||
\(236\) | −2.60660 | −0.169675 | ||||||||
\(237\) | 16.8824 | 1.09663 | ||||||||
\(238\) | 6.23638 | 0.404245 | ||||||||
\(239\) | −12.5969 | −0.814826 | −0.407413 | − | 0.913244i | \(-0.633569\pi\) | ||||
−0.407413 | + | 0.913244i | \(0.633569\pi\) | |||||||
\(240\) | 5.72179 | 0.369340 | ||||||||
\(241\) | −13.0691 | −0.841853 | −0.420926 | − | 0.907095i | \(-0.638295\pi\) | ||||
−0.420926 | + | 0.907095i | \(0.638295\pi\) | |||||||
\(242\) | −5.97137 | −0.383854 | ||||||||
\(243\) | −12.7166 | −0.815771 | ||||||||
\(244\) | −6.00035 | −0.384133 | ||||||||
\(245\) | −4.18729 | −0.267516 | ||||||||
\(246\) | −2.51752 | −0.160511 | ||||||||
\(247\) | 18.6683 | 1.18783 | ||||||||
\(248\) | −6.48100 | −0.411544 | ||||||||
\(249\) | 6.54617 | 0.414847 | ||||||||
\(250\) | −5.96008 | −0.376949 | ||||||||
\(251\) | 11.1178 | 0.701747 | 0.350873 | − | 0.936423i | \(-0.385885\pi\) | ||||
0.350873 | + | 0.936423i | \(0.385885\pi\) | |||||||
\(252\) | 4.20534 | 0.264911 | ||||||||
\(253\) | 6.02952 | 0.379072 | ||||||||
\(254\) | 5.52763 | 0.346835 | ||||||||
\(255\) | −15.0634 | −0.943304 | ||||||||
\(256\) | −3.78922 | −0.236826 | ||||||||
\(257\) | 19.6332 | 1.22469 | 0.612344 | − | 0.790592i | \(-0.290227\pi\) | ||||
0.612344 | + | 0.790592i | \(0.290227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.4383 | 1.26998 | ||||||||
\(260\) | 12.0216 | 0.745548 | ||||||||
\(261\) | −5.38910 | −0.333577 | ||||||||
\(262\) | 9.19261 | 0.567922 | ||||||||
\(263\) | −20.0090 | −1.23381 | −0.616905 | − | 0.787037i | \(-0.711614\pi\) | ||||
−0.616905 | + | 0.787037i | \(0.711614\pi\) | |||||||
\(264\) | −2.73121 | −0.168094 | ||||||||
\(265\) | 3.06149 | 0.188066 | ||||||||
\(266\) | 3.53965 | 0.217030 | ||||||||
\(267\) | 1.78678 | 0.109349 | ||||||||
\(268\) | 9.48593 | 0.579445 | ||||||||
\(269\) | −12.7559 | −0.777743 | −0.388871 | − | 0.921292i | \(-0.627135\pi\) | ||||
−0.388871 | + | 0.921292i | \(0.627135\pi\) | |||||||
\(270\) | −2.48797 | −0.151413 | ||||||||
\(271\) | −23.2586 | −1.41286 | −0.706430 | − | 0.707783i | \(-0.749696\pi\) | ||||
−0.706430 | + | 0.707783i | \(0.749696\pi\) | |||||||
\(272\) | −12.6938 | −0.769676 | ||||||||
\(273\) | 22.6032 | 1.36801 | ||||||||
\(274\) | 8.62673 | 0.521160 | ||||||||
\(275\) | −2.17138 | −0.130939 | ||||||||
\(276\) | −33.1831 | −1.99739 | ||||||||
\(277\) | −13.8873 | −0.834404 | −0.417202 | − | 0.908814i | \(-0.636989\pi\) | ||||
−0.417202 | + | 0.908814i | \(0.636989\pi\) | |||||||
\(278\) | −7.33570 | −0.439966 | ||||||||
\(279\) | 4.07756 | 0.244117 | ||||||||
\(280\) | 4.98891 | 0.298144 | ||||||||
\(281\) | −11.6035 | −0.692208 | −0.346104 | − | 0.938196i | \(-0.612496\pi\) | ||||
−0.346104 | + | 0.938196i | \(0.612496\pi\) | |||||||
\(282\) | 1.18446 | 0.0705334 | ||||||||
\(283\) | 2.67279 | 0.158881 | 0.0794403 | − | 0.996840i | \(-0.474687\pi\) | ||||
0.0794403 | + | 0.996840i | \(0.474687\pi\) | |||||||
\(284\) | −21.7283 | −1.28934 | ||||||||
\(285\) | −8.54966 | −0.506438 | ||||||||
\(286\) | −2.03369 | −0.120255 | ||||||||
\(287\) | 4.12259 | 0.243349 | ||||||||
\(288\) | 7.03288 | 0.414416 | ||||||||
\(289\) | 16.4181 | 0.965772 | ||||||||
\(290\) | −2.92102 | −0.171528 | ||||||||
\(291\) | −32.4456 | −1.90200 | ||||||||
\(292\) | 8.45893 | 0.495021 | ||||||||
\(293\) | 23.8266 | 1.39196 | 0.695982 | − | 0.718059i | \(-0.254969\pi\) | ||||
0.695982 | + | 0.718059i | \(0.254969\pi\) | |||||||
\(294\) | −3.89844 | −0.227361 | ||||||||
\(295\) | 1.94553 | 0.113273 | ||||||||
\(296\) | 22.1504 | 1.28747 | ||||||||
\(297\) | −2.23044 | −0.129424 | ||||||||
\(298\) | 3.87168 | 0.224280 | ||||||||
\(299\) | −54.0797 | −3.12751 | ||||||||
\(300\) | 11.9501 | 0.689938 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.06429 | −0.406504 | ||||||||
\(303\) | −23.7428 | −1.36399 | ||||||||
\(304\) | −7.20476 | −0.413222 | ||||||||
\(305\) | 4.47857 | 0.256442 | ||||||||
\(306\) | −4.25233 | −0.243090 | ||||||||
\(307\) | −5.33565 | −0.304521 | −0.152261 | − | 0.988340i | \(-0.548655\pi\) | ||||
−0.152261 | + | 0.988340i | \(0.548655\pi\) | |||||||
\(308\) | 2.04345 | 0.116437 | ||||||||
\(309\) | −1.44712 | −0.0823239 | ||||||||
\(310\) | 2.21013 | 0.125527 | ||||||||
\(311\) | −23.0284 | −1.30582 | −0.652911 | − | 0.757435i | \(-0.726452\pi\) | ||||
−0.652911 | + | 0.757435i | \(0.726452\pi\) | |||||||
\(312\) | 24.4967 | 1.38685 | ||||||||
\(313\) | 1.74238 | 0.0984852 | 0.0492426 | − | 0.998787i | \(-0.484319\pi\) | ||||
0.0492426 | + | 0.998787i | \(0.484319\pi\) | |||||||
\(314\) | −2.61709 | −0.147691 | ||||||||
\(315\) | −3.13880 | −0.176851 | ||||||||
\(316\) | −13.6893 | −0.770084 | ||||||||
\(317\) | 32.5720 | 1.82942 | 0.914712 | − | 0.404106i | \(-0.132417\pi\) | ||||
0.914712 | + | 0.404106i | \(0.132417\pi\) | |||||||
\(318\) | 2.85030 | 0.159837 | ||||||||
\(319\) | −2.61867 | −0.146617 | ||||||||
\(320\) | −1.70309 | −0.0952058 | ||||||||
\(321\) | 14.6702 | 0.818811 | ||||||||
\(322\) | −10.2539 | −0.571430 | ||||||||
\(323\) | 18.9675 | 1.05538 | ||||||||
\(324\) | 18.8645 | 1.04803 | ||||||||
\(325\) | 19.4755 | 1.08031 | ||||||||
\(326\) | 3.20988 | 0.177779 | ||||||||
\(327\) | −3.73165 | −0.206361 | ||||||||
\(328\) | 4.46792 | 0.246700 | ||||||||
\(329\) | −1.93962 | −0.106935 | ||||||||
\(330\) | 0.931389 | 0.0512713 | ||||||||
\(331\) | 14.0839 | 0.774120 | 0.387060 | − | 0.922055i | \(-0.373491\pi\) | ||||
0.387060 | + | 0.922055i | \(0.373491\pi\) | |||||||
\(332\) | −5.30803 | −0.291316 | ||||||||
\(333\) | −13.9361 | −0.763691 | ||||||||
\(334\) | −3.10364 | −0.169824 | ||||||||
\(335\) | −7.08016 | −0.386830 | ||||||||
\(336\) | −8.72342 | −0.475902 | ||||||||
\(337\) | −20.3596 | −1.10906 | −0.554530 | − | 0.832163i | \(-0.687102\pi\) | ||||
−0.554530 | + | 0.832163i | \(0.687102\pi\) | |||||||
\(338\) | 10.9155 | 0.593725 | ||||||||
\(339\) | 24.8074 | 1.34735 | ||||||||
\(340\) | 12.2143 | 0.662413 | ||||||||
\(341\) | 1.98136 | 0.107297 | ||||||||
\(342\) | −2.41354 | −0.130509 | ||||||||
\(343\) | 19.7860 | 1.06834 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.7674 | 1.33343 | ||||||||
\(346\) | −6.76167 | −0.363510 | ||||||||
\(347\) | 13.6840 | 0.734597 | 0.367299 | − | 0.930103i | \(-0.380283\pi\) | ||||
0.367299 | + | 0.930103i | \(0.380283\pi\) | |||||||
\(348\) | 14.4117 | 0.772547 | ||||||||
\(349\) | −14.7755 | −0.790917 | −0.395458 | − | 0.918484i | \(-0.629414\pi\) | ||||
−0.395458 | + | 0.918484i | \(0.629414\pi\) | |||||||
\(350\) | 3.69271 | 0.197383 | ||||||||
\(351\) | 20.0052 | 1.06780 | ||||||||
\(352\) | 3.41741 | 0.182149 | ||||||||
\(353\) | −26.9956 | −1.43683 | −0.718414 | − | 0.695616i | \(-0.755132\pi\) | ||||
−0.718414 | + | 0.695616i | \(0.755132\pi\) | |||||||
\(354\) | 1.81132 | 0.0962706 | ||||||||
\(355\) | 16.2177 | 0.860745 | ||||||||
\(356\) | −1.44883 | −0.0767880 | ||||||||
\(357\) | 22.9655 | 1.21546 | ||||||||
\(358\) | −7.98039 | −0.421777 | ||||||||
\(359\) | 11.7883 | 0.622165 | 0.311082 | − | 0.950383i | \(-0.399308\pi\) | ||||
0.311082 | + | 0.950383i | \(0.399308\pi\) | |||||||
\(360\) | −3.40173 | −0.179287 | ||||||||
\(361\) | −8.23445 | −0.433392 | ||||||||
\(362\) | −4.70628 | −0.247357 | ||||||||
\(363\) | −21.9896 | −1.15416 | ||||||||
\(364\) | −18.3281 | −0.960653 | ||||||||
\(365\) | −6.31362 | −0.330470 | ||||||||
\(366\) | 4.16963 | 0.217950 | ||||||||
\(367\) | −25.1670 | −1.31371 | −0.656853 | − | 0.754019i | \(-0.728113\pi\) | ||||
−0.656853 | + | 0.754019i | \(0.728113\pi\) | |||||||
\(368\) | 20.8714 | 1.08799 | ||||||||
\(369\) | −2.81102 | −0.146336 | ||||||||
\(370\) | −7.55367 | −0.392697 | ||||||||
\(371\) | −4.66753 | −0.242326 | ||||||||
\(372\) | −10.9043 | −0.565363 | ||||||||
\(373\) | 14.2790 | 0.739337 | 0.369668 | − | 0.929164i | \(-0.379471\pi\) | ||||
0.369668 | + | 0.929164i | \(0.379471\pi\) | |||||||
\(374\) | −2.06629 | −0.106845 | ||||||||
\(375\) | −21.9480 | −1.13339 | ||||||||
\(376\) | −2.10210 | −0.108407 | ||||||||
\(377\) | 23.4873 | 1.20966 | ||||||||
\(378\) | 3.79315 | 0.195099 | ||||||||
\(379\) | 9.38475 | 0.482062 | 0.241031 | − | 0.970517i | \(-0.422514\pi\) | ||||
0.241031 | + | 0.970517i | \(0.422514\pi\) | |||||||
\(380\) | 6.93258 | 0.355634 | ||||||||
\(381\) | 20.3555 | 1.04285 | ||||||||
\(382\) | 2.64404 | 0.135281 | ||||||||
\(383\) | 7.68512 | 0.392691 | 0.196346 | − | 0.980535i | \(-0.437093\pi\) | ||||
0.196346 | + | 0.980535i | \(0.437093\pi\) | |||||||
\(384\) | −23.9421 | −1.22179 | ||||||||
\(385\) | −1.52520 | −0.0777316 | ||||||||
\(386\) | 3.15446 | 0.160558 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 26.3089 | 1.33563 | ||||||||
\(389\) | −21.1580 | −1.07275 | −0.536376 | − | 0.843979i | \(-0.680207\pi\) | ||||
−0.536376 | + | 0.843979i | \(0.680207\pi\) | |||||||
\(390\) | −8.35378 | −0.423010 | ||||||||
\(391\) | −54.9465 | −2.77877 | ||||||||
\(392\) | 6.91868 | 0.349446 | ||||||||
\(393\) | 33.8519 | 1.70760 | ||||||||
\(394\) | 7.51552 | 0.378626 | ||||||||
\(395\) | 10.2175 | 0.514098 | ||||||||
\(396\) | −1.39335 | −0.0700183 | ||||||||
\(397\) | 15.0722 | 0.756454 | 0.378227 | − | 0.925713i | \(-0.376534\pi\) | ||||
0.378227 | + | 0.925713i | \(0.376534\pi\) | |||||||
\(398\) | −12.2075 | −0.611907 | ||||||||
\(399\) | 13.0348 | 0.652555 | ||||||||
\(400\) | −7.51631 | −0.375815 | ||||||||
\(401\) | 2.77241 | 0.138447 | 0.0692237 | − | 0.997601i | \(-0.477948\pi\) | ||||
0.0692237 | + | 0.997601i | \(0.477948\pi\) | |||||||
\(402\) | −6.59175 | −0.328766 | ||||||||
\(403\) | −17.7712 | −0.885246 | ||||||||
\(404\) | 19.2521 | 0.957827 | ||||||||
\(405\) | −14.0802 | −0.699652 | ||||||||
\(406\) | 4.45337 | 0.221017 | ||||||||
\(407\) | −6.77180 | −0.335666 | ||||||||
\(408\) | 24.8893 | 1.23220 | ||||||||
\(409\) | 19.1827 | 0.948523 | 0.474261 | − | 0.880384i | \(-0.342715\pi\) | ||||
0.474261 | + | 0.880384i | \(0.342715\pi\) | |||||||
\(410\) | −1.52364 | −0.0752472 | ||||||||
\(411\) | 31.7680 | 1.56700 | ||||||||
\(412\) | 1.17341 | 0.0578100 | ||||||||
\(413\) | −2.96615 | −0.145955 | ||||||||
\(414\) | 6.99174 | 0.343625 | ||||||||
\(415\) | 3.96184 | 0.194479 | ||||||||
\(416\) | −30.6513 | −1.50281 | ||||||||
\(417\) | −27.0138 | −1.32287 | ||||||||
\(418\) | −1.17279 | −0.0573628 | ||||||||
\(419\) | −0.575111 | −0.0280960 | −0.0140480 | − | 0.999901i | \(-0.504472\pi\) | ||||
−0.0140480 | + | 0.999901i | \(0.504472\pi\) | |||||||
\(420\) | 8.39387 | 0.409579 | ||||||||
\(421\) | −7.75469 | −0.377940 | −0.188970 | − | 0.981983i | \(-0.560515\pi\) | ||||
−0.188970 | + | 0.981983i | \(0.560515\pi\) | |||||||
\(422\) | 5.74070 | 0.279453 | ||||||||
\(423\) | 1.32255 | 0.0643044 | ||||||||
\(424\) | −5.05852 | −0.245663 | ||||||||
\(425\) | 19.7876 | 0.959842 | ||||||||
\(426\) | 15.0989 | 0.731546 | ||||||||
\(427\) | −6.82801 | −0.330431 | ||||||||
\(428\) | −11.8955 | −0.574990 | ||||||||
\(429\) | −7.48909 | −0.361577 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.8493 | −1.48596 | −0.742980 | − | 0.669314i | \(-0.766588\pi\) | ||||
−0.742980 | + | 0.669314i | \(0.766588\pi\) | |||||||
\(432\) | −7.72075 | −0.371465 | ||||||||
\(433\) | −19.4062 | −0.932602 | −0.466301 | − | 0.884626i | \(-0.654414\pi\) | ||||
−0.466301 | + | 0.884626i | \(0.654414\pi\) | |||||||
\(434\) | −3.36956 | −0.161744 | ||||||||
\(435\) | −10.7567 | −0.515742 | ||||||||
\(436\) | 3.02585 | 0.144912 | ||||||||
\(437\) | −31.1866 | −1.49186 | ||||||||
\(438\) | −5.87809 | −0.280866 | ||||||||
\(439\) | 12.8683 | 0.614170 | 0.307085 | − | 0.951682i | \(-0.400646\pi\) | ||||
0.307085 | + | 0.951682i | \(0.400646\pi\) | |||||||
\(440\) | −1.65297 | −0.0788021 | ||||||||
\(441\) | −4.35293 | −0.207283 | ||||||||
\(442\) | 18.5329 | 0.881521 | ||||||||
\(443\) | 2.87049 | 0.136381 | 0.0681906 | − | 0.997672i | \(-0.478277\pi\) | ||||
0.0681906 | + | 0.997672i | \(0.478277\pi\) | |||||||
\(444\) | 37.2682 | 1.76867 | ||||||||
\(445\) | 1.08139 | 0.0512627 | ||||||||
\(446\) | −5.43838 | −0.257515 | ||||||||
\(447\) | 14.2575 | 0.674356 | ||||||||
\(448\) | 2.59653 | 0.122674 | ||||||||
\(449\) | 18.3534 | 0.866150 | 0.433075 | − | 0.901358i | \(-0.357428\pi\) | ||||
0.433075 | + | 0.901358i | \(0.357428\pi\) | |||||||
\(450\) | −2.51790 | −0.118695 | ||||||||
\(451\) | −1.36593 | −0.0643191 | ||||||||
\(452\) | −20.1154 | −0.946148 | ||||||||
\(453\) | −26.0143 | −1.22226 | ||||||||
\(454\) | 15.8500 | 0.743876 | ||||||||
\(455\) | 13.6798 | 0.641320 | ||||||||
\(456\) | 14.1267 | 0.661541 | ||||||||
\(457\) | −30.4630 | −1.42500 | −0.712500 | − | 0.701672i | \(-0.752437\pi\) | ||||
−0.712500 | + | 0.701672i | \(0.752437\pi\) | |||||||
\(458\) | 3.51682 | 0.164330 | ||||||||
\(459\) | 20.3259 | 0.948731 | ||||||||
\(460\) | −20.0829 | −0.936370 | ||||||||
\(461\) | −13.6332 | −0.634961 | −0.317480 | − | 0.948265i | \(-0.602837\pi\) | ||||
−0.317480 | + | 0.948265i | \(0.602837\pi\) | |||||||
\(462\) | −1.41999 | −0.0660640 | ||||||||
\(463\) | −4.57394 | −0.212569 | −0.106285 | − | 0.994336i | \(-0.533895\pi\) | ||||
−0.106285 | + | 0.994336i | \(0.533895\pi\) | |||||||
\(464\) | −9.06459 | −0.420813 | ||||||||
\(465\) | 8.13883 | 0.377429 | ||||||||
\(466\) | 9.88374 | 0.457855 | ||||||||
\(467\) | 32.0492 | 1.48306 | 0.741530 | − | 0.670920i | \(-0.234100\pi\) | ||||
0.741530 | + | 0.670920i | \(0.234100\pi\) | |||||||
\(468\) | 12.4972 | 0.577682 | ||||||||
\(469\) | 10.7944 | 0.498438 | ||||||||
\(470\) | 0.716851 | 0.0330659 | ||||||||
\(471\) | −9.63746 | −0.444071 | ||||||||
\(472\) | −3.21461 | −0.147964 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.51267 | 0.436931 | ||||||||
\(475\) | 11.2311 | 0.515317 | ||||||||
\(476\) | −18.6218 | −0.853531 | ||||||||
\(477\) | 3.18260 | 0.145721 | ||||||||
\(478\) | −7.09792 | −0.324651 | ||||||||
\(479\) | −30.6305 | −1.39954 | −0.699771 | − | 0.714367i | \(-0.746715\pi\) | ||||
−0.699771 | + | 0.714367i | \(0.746715\pi\) | |||||||
\(480\) | 14.0377 | 0.640728 | ||||||||
\(481\) | 60.7374 | 2.76939 | ||||||||
\(482\) | −7.36396 | −0.335419 | ||||||||
\(483\) | −37.7602 | −1.71815 | ||||||||
\(484\) | 17.8305 | 0.810478 | ||||||||
\(485\) | −19.6366 | −0.891651 | ||||||||
\(486\) | −7.16536 | −0.325028 | ||||||||
\(487\) | 13.6789 | 0.619852 | 0.309926 | − | 0.950761i | \(-0.399696\pi\) | ||||
0.309926 | + | 0.950761i | \(0.399696\pi\) | |||||||
\(488\) | −7.39997 | −0.334981 | ||||||||
\(489\) | 11.8204 | 0.534538 | ||||||||
\(490\) | −2.35939 | −0.106586 | ||||||||
\(491\) | 4.72280 | 0.213137 | 0.106569 | − | 0.994305i | \(-0.466014\pi\) | ||||
0.106569 | + | 0.994305i | \(0.466014\pi\) | |||||||
\(492\) | 7.51731 | 0.338907 | ||||||||
\(493\) | 23.8637 | 1.07477 | ||||||||
\(494\) | 10.5189 | 0.473268 | ||||||||
\(495\) | 1.03997 | 0.0467434 | ||||||||
\(496\) | 6.85856 | 0.307958 | ||||||||
\(497\) | −24.7254 | −1.10909 | ||||||||
\(498\) | 3.68854 | 0.165287 | ||||||||
\(499\) | 22.2197 | 0.994691 | 0.497345 | − | 0.867553i | \(-0.334308\pi\) | ||||
0.497345 | + | 0.867553i | \(0.334308\pi\) | |||||||
\(500\) | 17.7968 | 0.795898 | ||||||||
\(501\) | −11.4292 | −0.510619 | ||||||||
\(502\) | 6.26447 | 0.279597 | ||||||||
\(503\) | 5.99796 | 0.267436 | 0.133718 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133718 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(504\) | 5.18626 | 0.231014 | ||||||||
\(505\) | −14.3695 | −0.639433 | ||||||||
\(506\) | 3.39742 | 0.151034 | ||||||||
\(507\) | 40.1964 | 1.78519 | ||||||||
\(508\) | −16.5055 | −0.732314 | ||||||||
\(509\) | −7.51237 | −0.332980 | −0.166490 | − | 0.986043i | \(-0.553243\pi\) | ||||
−0.166490 | + | 0.986043i | \(0.553243\pi\) | |||||||
\(510\) | −8.48768 | −0.375841 | ||||||||
\(511\) | 9.62572 | 0.425817 | ||||||||
\(512\) | 20.9421 | 0.925517 | ||||||||
\(513\) | 11.5366 | 0.509352 | ||||||||
\(514\) | 11.0626 | 0.487952 | ||||||||
\(515\) | −0.875820 | −0.0385932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.642651 | 0.0282638 | ||||||||
\(518\) | 11.5163 | 0.505997 | ||||||||
\(519\) | −24.8999 | −1.09298 | ||||||||
\(520\) | 14.8257 | 0.650151 | ||||||||
\(521\) | 10.2926 | 0.450925 | 0.225462 | − | 0.974252i | \(-0.427611\pi\) | ||||
0.225462 | + | 0.974252i | \(0.427611\pi\) | |||||||
\(522\) | −3.03657 | −0.132907 | ||||||||
\(523\) | −11.3478 | −0.496206 | −0.248103 | − | 0.968734i | \(-0.579807\pi\) | ||||
−0.248103 | + | 0.968734i | \(0.579807\pi\) | |||||||
\(524\) | −27.4491 | −1.19912 | ||||||||
\(525\) | 13.5984 | 0.593484 | ||||||||
\(526\) | −11.2744 | −0.491587 | ||||||||
\(527\) | −18.0560 | −0.786533 | ||||||||
\(528\) | 2.89032 | 0.125785 | ||||||||
\(529\) | 67.3438 | 2.92799 | ||||||||
\(530\) | 1.72504 | 0.0749311 | ||||||||
\(531\) | 2.02249 | 0.0877687 | ||||||||
\(532\) | −10.5694 | −0.458241 | ||||||||
\(533\) | 12.2513 | 0.530661 | ||||||||
\(534\) | 1.00679 | 0.0435681 | ||||||||
\(535\) | 8.87862 | 0.383856 | ||||||||
\(536\) | 11.6986 | 0.505302 | ||||||||
\(537\) | −29.3879 | −1.26818 | ||||||||
\(538\) | −7.18752 | −0.309876 | ||||||||
\(539\) | −2.11517 | −0.0911070 | ||||||||
\(540\) | 7.42908 | 0.319697 | ||||||||
\(541\) | −26.7275 | −1.14911 | −0.574553 | − | 0.818467i | \(-0.694824\pi\) | ||||
−0.574553 | + | 0.818467i | \(0.694824\pi\) | |||||||
\(542\) | −13.1054 | −0.562926 | ||||||||
\(543\) | −17.3309 | −0.743740 | ||||||||
\(544\) | −31.1426 | −1.33523 | ||||||||
\(545\) | −2.25845 | −0.0967414 | ||||||||
\(546\) | 12.7361 | 0.545057 | ||||||||
\(547\) | 30.6376 | 1.30997 | 0.654984 | − | 0.755643i | \(-0.272676\pi\) | ||||
0.654984 | + | 0.755643i | \(0.272676\pi\) | |||||||
\(548\) | −25.7594 | −1.10039 | ||||||||
\(549\) | 4.65574 | 0.198702 | ||||||||
\(550\) | −1.22350 | −0.0521701 | ||||||||
\(551\) | 13.5446 | 0.577018 | ||||||||
\(552\) | −40.9233 | −1.74181 | ||||||||
\(553\) | −15.5776 | −0.662425 | ||||||||
\(554\) | −7.82499 | −0.332452 | ||||||||
\(555\) | −27.8164 | −1.18074 | ||||||||
\(556\) | 21.9044 | 0.928953 | ||||||||
\(557\) | −14.3011 | −0.605955 | −0.302978 | − | 0.952998i | \(-0.597981\pi\) | ||||
−0.302978 | + | 0.952998i | \(0.597981\pi\) | |||||||
\(558\) | 2.29756 | 0.0972636 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5.27954 | −0.223101 | ||||||||
\(561\) | −7.60913 | −0.321258 | ||||||||
\(562\) | −6.53818 | −0.275797 | ||||||||
\(563\) | 24.6057 | 1.03701 | 0.518503 | − | 0.855076i | \(-0.326490\pi\) | ||||
0.518503 | + | 0.855076i | \(0.326490\pi\) | |||||||
\(564\) | −3.53679 | −0.148926 | ||||||||
\(565\) | 15.0138 | 0.631636 | ||||||||
\(566\) | 1.50602 | 0.0633028 | ||||||||
\(567\) | 21.4666 | 0.901514 | ||||||||
\(568\) | −26.7966 | −1.12436 | ||||||||
\(569\) | 0.00221871 | 9.30130e−5 0 | 4.65065e−5 | − | 1.00000i | \(-0.499985\pi\) | ||||
4.65065e−5 | 1.00000i | \(0.499985\pi\) | ||||||||
\(570\) | −4.81744 | −0.201780 | ||||||||
\(571\) | −17.1054 | −0.715837 | −0.357919 | − | 0.933753i | \(-0.616513\pi\) | ||||
−0.357919 | + | 0.933753i | \(0.616513\pi\) | |||||||
\(572\) | 6.07261 | 0.253909 | ||||||||
\(573\) | 9.73670 | 0.406757 | ||||||||
\(574\) | 2.32293 | 0.0969574 | ||||||||
\(575\) | −32.5351 | −1.35681 | ||||||||
\(576\) | −1.77047 | −0.0737694 | ||||||||
\(577\) | −7.99163 | −0.332696 | −0.166348 | − | 0.986067i | \(-0.553197\pi\) | ||||
−0.166348 | + | 0.986067i | \(0.553197\pi\) | |||||||
\(578\) | 9.25104 | 0.384793 | ||||||||
\(579\) | 11.6163 | 0.482758 | ||||||||
\(580\) | 8.72216 | 0.362168 | ||||||||
\(581\) | −6.04020 | −0.250590 | ||||||||
\(582\) | −18.2820 | −0.757812 | ||||||||
\(583\) | 1.54649 | 0.0640489 | ||||||||
\(584\) | 10.4320 | 0.431681 | ||||||||
\(585\) | −9.32770 | −0.385653 | ||||||||
\(586\) | 13.4254 | 0.554600 | ||||||||
\(587\) | −39.0328 | −1.61106 | −0.805529 | − | 0.592557i | \(-0.798119\pi\) | ||||
−0.805529 | + | 0.592557i | \(0.798119\pi\) | |||||||
\(588\) | 11.6407 | 0.480056 | ||||||||
\(589\) | −10.2482 | −0.422272 | ||||||||
\(590\) | 1.09624 | 0.0451314 | ||||||||
\(591\) | 27.6759 | 1.13844 | ||||||||
\(592\) | −23.4408 | −0.963411 | ||||||||
\(593\) | −22.5910 | −0.927700 | −0.463850 | − | 0.885914i | \(-0.653532\pi\) | ||||
−0.463850 | + | 0.885914i | \(0.653532\pi\) | |||||||
\(594\) | −1.25678 | −0.0515662 | ||||||||
\(595\) | 13.8991 | 0.569807 | ||||||||
\(596\) | −11.5608 | −0.473550 | ||||||||
\(597\) | −44.9542 | −1.83985 | ||||||||
\(598\) | −30.4721 | −1.24609 | ||||||||
\(599\) | −28.3674 | −1.15906 | −0.579529 | − | 0.814951i | \(-0.696764\pi\) | ||||
−0.579529 | + | 0.814951i | \(0.696764\pi\) | |||||||
\(600\) | 14.7375 | 0.601656 | ||||||||
\(601\) | −12.7606 | −0.520517 | −0.260259 | − | 0.965539i | \(-0.583808\pi\) | ||||
−0.260259 | + | 0.965539i | \(0.583808\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.36024 | −0.299732 | ||||||||
\(604\) | 21.0940 | 0.858301 | ||||||||
\(605\) | −13.3084 | −0.541065 | ||||||||
\(606\) | −13.3782 | −0.543453 | ||||||||
\(607\) | −20.7954 | −0.844058 | −0.422029 | − | 0.906582i | \(-0.638682\pi\) | ||||
−0.422029 | + | 0.906582i | \(0.638682\pi\) | |||||||
\(608\) | −17.6759 | −0.716853 | ||||||||
\(609\) | 16.3996 | 0.664544 | ||||||||
\(610\) | 2.52352 | 0.102174 | ||||||||
\(611\) | −5.76404 | −0.233188 | ||||||||
\(612\) | 12.6975 | 0.513265 | ||||||||
\(613\) | −22.2261 | −0.897704 | −0.448852 | − | 0.893606i | \(-0.648167\pi\) | ||||
−0.448852 | + | 0.893606i | \(0.648167\pi\) | |||||||
\(614\) | −3.00645 | −0.121330 | ||||||||
\(615\) | −5.61081 | −0.226250 | ||||||||
\(616\) | 2.52010 | 0.101538 | ||||||||
\(617\) | −18.1174 | −0.729379 | −0.364689 | − | 0.931129i | \(-0.618825\pi\) | ||||
−0.364689 | + | 0.931129i | \(0.618825\pi\) | |||||||
\(618\) | −0.815403 | −0.0328003 | ||||||||
\(619\) | 1.85051 | 0.0743785 | 0.0371892 | − | 0.999308i | \(-0.488160\pi\) | ||||
0.0371892 | + | 0.999308i | \(0.488160\pi\) | |||||||
\(620\) | −6.59946 | −0.265041 | ||||||||
\(621\) | −33.4201 | −1.34110 | ||||||||
\(622\) | −12.9757 | −0.520279 | ||||||||
\(623\) | −1.64868 | −0.0660530 | ||||||||
\(624\) | −25.9237 | −1.03778 | ||||||||
\(625\) | 3.83156 | 0.153263 | ||||||||
\(626\) | 0.981771 | 0.0392395 | ||||||||
\(627\) | −4.31879 | −0.172476 | ||||||||
\(628\) | 7.81464 | 0.311838 | ||||||||
\(629\) | 61.7109 | 2.46058 | ||||||||
\(630\) | −1.76861 | −0.0704629 | ||||||||
\(631\) | 19.4877 | 0.775793 | 0.387896 | − | 0.921703i | \(-0.373202\pi\) | ||||
0.387896 | + | 0.921703i | \(0.373202\pi\) | |||||||
\(632\) | −16.8824 | −0.671547 | ||||||||
\(633\) | 21.1402 | 0.840246 | ||||||||
\(634\) | 18.3532 | 0.728897 | ||||||||
\(635\) | 12.3195 | 0.488884 | ||||||||
\(636\) | −8.51099 | −0.337483 | ||||||||
\(637\) | 18.9714 | 0.751672 | ||||||||
\(638\) | −1.47553 | −0.0584167 | ||||||||
\(639\) | 16.8592 | 0.666941 | ||||||||
\(640\) | −14.4901 | −0.572773 | ||||||||
\(641\) | 41.1921 | 1.62699 | 0.813496 | − | 0.581571i | \(-0.197562\pi\) | ||||
0.813496 | + | 0.581571i | \(0.197562\pi\) | |||||||
\(642\) | 8.26615 | 0.326239 | ||||||||
\(643\) | 39.7276 | 1.56670 | 0.783352 | − | 0.621578i | \(-0.213508\pi\) | ||||
0.783352 | + | 0.621578i | \(0.213508\pi\) | |||||||
\(644\) | 30.6183 | 1.20653 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.6875 | 0.420494 | ||||||||
\(647\) | 15.7885 | 0.620711 | 0.310356 | − | 0.950621i | \(-0.399552\pi\) | ||||
0.310356 | + | 0.950621i | \(0.399552\pi\) | |||||||
\(648\) | 23.2648 | 0.913929 | ||||||||
\(649\) | 0.982768 | 0.0385770 | ||||||||
\(650\) | 10.9738 | 0.430426 | ||||||||
\(651\) | −12.4084 | −0.486324 | ||||||||
\(652\) | −9.58471 | −0.375366 | ||||||||
\(653\) | −4.71375 | −0.184463 | −0.0922316 | − | 0.995738i | \(-0.529400\pi\) | ||||
−0.0922316 | + | 0.995738i | \(0.529400\pi\) | |||||||
\(654\) | −2.10266 | −0.0822203 | ||||||||
\(655\) | 20.4876 | 0.800518 | ||||||||
\(656\) | −4.72821 | −0.184605 | ||||||||
\(657\) | −6.56338 | −0.256062 | ||||||||
\(658\) | −1.09291 | −0.0426060 | ||||||||
\(659\) | −21.6336 | −0.842724 | −0.421362 | − | 0.906893i | \(-0.638448\pi\) | ||||
−0.421362 | + | 0.906893i | \(0.638448\pi\) | |||||||
\(660\) | −2.78113 | −0.108255 | ||||||||
\(661\) | 12.2966 | 0.478283 | 0.239142 | − | 0.970985i | \(-0.423134\pi\) | ||||
0.239142 | + | 0.970985i | \(0.423134\pi\) | |||||||
\(662\) | 7.93577 | 0.308432 | ||||||||
\(663\) | 68.2476 | 2.65052 | ||||||||
\(664\) | −6.54617 | −0.254041 | ||||||||
\(665\) | 7.88884 | 0.305916 | ||||||||
\(666\) | −7.85248 | −0.304278 | ||||||||
\(667\) | −39.2370 | −1.51926 | ||||||||
\(668\) | 9.26748 | 0.358570 | ||||||||
\(669\) | −20.0269 | −0.774284 | ||||||||
\(670\) | −3.98942 | −0.154125 | ||||||||
\(671\) | 2.26231 | 0.0873356 | ||||||||
\(672\) | −21.4017 | −0.825590 | ||||||||
\(673\) | 36.4097 | 1.40349 | 0.701745 | − | 0.712428i | \(-0.252404\pi\) | ||||
0.701745 | + | 0.712428i | \(0.252404\pi\) | |||||||
\(674\) | −11.4720 | −0.441883 | ||||||||
\(675\) | 12.0354 | 0.463243 | ||||||||
\(676\) | −32.5937 | −1.25360 | ||||||||
\(677\) | −8.71539 | −0.334960 | −0.167480 | − | 0.985876i | \(-0.553563\pi\) | ||||
−0.167480 | + | 0.985876i | \(0.553563\pi\) | |||||||
\(678\) | 13.9781 | 0.536827 | ||||||||
\(679\) | 29.9378 | 1.14891 | ||||||||
\(680\) | 15.0634 | 0.577653 | ||||||||
\(681\) | 58.3677 | 2.23665 | ||||||||
\(682\) | 1.11643 | 0.0427503 | ||||||||
\(683\) | 17.6293 | 0.674565 | 0.337282 | − | 0.941403i | \(-0.390492\pi\) | ||||
0.337282 | + | 0.941403i | \(0.390492\pi\) | |||||||
\(684\) | 7.20683 | 0.275560 | ||||||||
\(685\) | 19.2265 | 0.734605 | ||||||||
\(686\) | 11.1487 | 0.425661 | ||||||||
\(687\) | 12.9507 | 0.494100 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.8707 | −0.528431 | ||||||||
\(690\) | 13.9555 | 0.531279 | ||||||||
\(691\) | 31.9988 | 1.21729 | 0.608645 | − | 0.793443i | \(-0.291713\pi\) | ||||
0.608645 | + | 0.793443i | \(0.291713\pi\) | |||||||
\(692\) | 20.1904 | 0.767522 | ||||||||
\(693\) | −1.58554 | −0.0602297 | ||||||||
\(694\) | 7.71047 | 0.292686 | ||||||||
\(695\) | −16.3491 | −0.620158 | ||||||||
\(696\) | 17.7733 | 0.673695 | ||||||||
\(697\) | 12.4476 | 0.471487 | ||||||||
\(698\) | −8.32550 | −0.315125 | ||||||||
\(699\) | 36.3969 | 1.37666 | ||||||||
\(700\) | −11.0264 | −0.416760 | ||||||||
\(701\) | −38.1378 | −1.44045 | −0.720223 | − | 0.693743i | \(-0.755961\pi\) | ||||
−0.720223 | + | 0.693743i | \(0.755961\pi\) | |||||||
\(702\) | 11.2723 | 0.425444 | ||||||||
\(703\) | 35.0259 | 1.32103 | ||||||||
\(704\) | −0.860303 | −0.0324239 | ||||||||
\(705\) | 2.63981 | 0.0994210 | ||||||||
\(706\) | −15.2111 | −0.572476 | ||||||||
\(707\) | 21.9076 | 0.823922 | ||||||||
\(708\) | −5.40861 | −0.203268 | ||||||||
\(709\) | 15.0765 | 0.566212 | 0.283106 | − | 0.959089i | \(-0.408635\pi\) | ||||
0.283106 | + | 0.959089i | \(0.408635\pi\) | |||||||
\(710\) | 9.13810 | 0.342947 | ||||||||
\(711\) | 10.6217 | 0.398345 | ||||||||
\(712\) | −1.78678 | −0.0669626 | ||||||||
\(713\) | 29.6880 | 1.11182 | ||||||||
\(714\) | 12.9403 | 0.484278 | ||||||||
\(715\) | −4.53251 | −0.169506 | ||||||||
\(716\) | 23.8295 | 0.890549 | ||||||||
\(717\) | −26.1381 | −0.976146 | ||||||||
\(718\) | 6.64232 | 0.247889 | ||||||||
\(719\) | 6.43610 | 0.240026 | 0.120013 | − | 0.992772i | \(-0.461706\pi\) | ||||
0.120013 | + | 0.992772i | \(0.461706\pi\) | |||||||
\(720\) | 3.59990 | 0.134160 | ||||||||
\(721\) | 1.33527 | 0.0497281 | ||||||||
\(722\) | −4.63982 | −0.172676 | ||||||||
\(723\) | −27.1179 | −1.00852 | ||||||||
\(724\) | 14.0530 | 0.522274 | ||||||||
\(725\) | 14.1302 | 0.524784 | ||||||||
\(726\) | −12.3904 | −0.459850 | ||||||||
\(727\) | −23.3433 | −0.865754 | −0.432877 | − | 0.901453i | \(-0.642502\pi\) | ||||
−0.432877 | + | 0.901453i | \(0.642502\pi\) | |||||||
\(728\) | −22.6032 | −0.837732 | ||||||||
\(729\) | 7.24998 | 0.268518 | ||||||||
\(730\) | −3.55751 | −0.131669 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −12.4505 | −0.460184 | ||||||||
\(733\) | −34.2172 | −1.26384 | −0.631921 | − | 0.775033i | \(-0.717733\pi\) | ||||
−0.631921 | + | 0.775033i | \(0.717733\pi\) | |||||||
\(734\) | −14.1807 | −0.523420 | ||||||||
\(735\) | −8.68848 | −0.320479 | ||||||||
\(736\) | 51.2051 | 1.88744 | ||||||||
\(737\) | −3.57648 | −0.131741 | ||||||||
\(738\) | −1.58391 | −0.0583046 | ||||||||
\(739\) | −47.8055 | −1.75855 | −0.879277 | − | 0.476310i | \(-0.841974\pi\) | ||||
−0.879277 | + | 0.476310i | \(0.841974\pi\) | |||||||
\(740\) | 22.5553 | 0.829148 | ||||||||
\(741\) | 38.7360 | 1.42300 | ||||||||
\(742\) | −2.62999 | −0.0965501 | ||||||||
\(743\) | −11.1786 | −0.410102 | −0.205051 | − | 0.978751i | \(-0.565736\pi\) | ||||
−0.205051 | + | 0.978751i | \(0.565736\pi\) | |||||||
\(744\) | −13.4478 | −0.493022 | ||||||||
\(745\) | 8.62884 | 0.316136 | ||||||||
\(746\) | 8.04570 | 0.294574 | ||||||||
\(747\) | 4.11856 | 0.150690 | ||||||||
\(748\) | 6.16994 | 0.225595 | ||||||||
\(749\) | −13.5363 | −0.494606 | ||||||||
\(750\) | −12.3670 | −0.451578 | ||||||||
\(751\) | 18.6023 | 0.678808 | 0.339404 | − | 0.940641i | \(-0.389775\pi\) | ||||
0.339404 | + | 0.940641i | \(0.389775\pi\) | |||||||
\(752\) | 2.22456 | 0.0811212 | ||||||||
\(753\) | 23.0690 | 0.840679 | ||||||||
\(754\) | 13.2342 | 0.481963 | ||||||||
\(755\) | −15.7442 | −0.572991 | ||||||||
\(756\) | −11.3263 | −0.411935 | ||||||||
\(757\) | 12.9317 | 0.470011 | 0.235006 | − | 0.971994i | \(-0.424489\pi\) | ||||
0.235006 | + | 0.971994i | \(0.424489\pi\) | |||||||
\(758\) | 5.28798 | 0.192068 | ||||||||
\(759\) | 12.5110 | 0.454122 | ||||||||
\(760\) | 8.54966 | 0.310129 | ||||||||
\(761\) | 31.3101 | 1.13499 | 0.567495 | − | 0.823377i | \(-0.307913\pi\) | ||||
0.567495 | + | 0.823377i | \(0.307913\pi\) | |||||||
\(762\) | 11.4696 | 0.415501 | ||||||||
\(763\) | 3.44322 | 0.124653 | ||||||||
\(764\) | −7.89511 | −0.285635 | ||||||||
\(765\) | −9.47720 | −0.342649 | ||||||||
\(766\) | 4.33030 | 0.156460 | ||||||||
\(767\) | −8.81461 | −0.318277 | ||||||||
\(768\) | −7.86250 | −0.283714 | ||||||||
\(769\) | −33.2208 | −1.19797 | −0.598987 | − | 0.800759i | \(-0.704430\pi\) | ||||
−0.598987 | + | 0.800759i | \(0.704430\pi\) | |||||||
\(770\) | −0.859399 | −0.0309706 | ||||||||
\(771\) | 40.7383 | 1.46715 | ||||||||
\(772\) | −9.41923 | −0.339005 | ||||||||
\(773\) | −15.9707 | −0.574425 | −0.287212 | − | 0.957867i | \(-0.592729\pi\) | ||||
−0.287212 | + | 0.957867i | \(0.592729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.6914 | −0.384046 | ||||||||
\(776\) | 32.4456 | 1.16473 | ||||||||
\(777\) | 42.4088 | 1.52141 | ||||||||
\(778\) | −11.9218 | −0.427416 | ||||||||
\(779\) | 7.06502 | 0.253131 | ||||||||
\(780\) | 24.9444 | 0.893153 | ||||||||
\(781\) | 8.19222 | 0.293141 | ||||||||
\(782\) | −30.9605 | −1.10714 | ||||||||
\(783\) | 14.5146 | 0.518709 | ||||||||
\(784\) | −7.32174 | −0.261491 | ||||||||
\(785\) | −5.83273 | −0.208179 | ||||||||
\(786\) | 19.0743 | 0.680359 | ||||||||
\(787\) | −10.8741 | −0.387620 | −0.193810 | − | 0.981039i | \(-0.562084\pi\) | ||||
−0.193810 | + | 0.981039i | \(0.562084\pi\) | |||||||
\(788\) | −22.4413 | −0.799439 | ||||||||
\(789\) | −41.5181 | −1.47808 | ||||||||
\(790\) | 5.75721 | 0.204832 | ||||||||
\(791\) | −22.8900 | −0.813875 | ||||||||
\(792\) | −1.71836 | −0.0610591 | ||||||||
\(793\) | −20.2911 | −0.720557 | ||||||||
\(794\) | 8.49269 | 0.301394 | ||||||||
\(795\) | 6.35248 | 0.225299 | ||||||||
\(796\) | 36.4516 | 1.29199 | ||||||||
\(797\) | 16.2345 | 0.575056 | 0.287528 | − | 0.957772i | \(-0.407167\pi\) | ||||
0.287528 | + | 0.957772i | \(0.407167\pi\) | |||||||
\(798\) | 7.34464 | 0.259997 | ||||||||
\(799\) | −5.85643 | −0.207186 | ||||||||
\(800\) | −18.4403 | −0.651961 | ||||||||
\(801\) | 1.12417 | 0.0397205 | ||||||||
\(802\) | 1.56215 | 0.0551616 | ||||||||
\(803\) | −3.18927 | −0.112547 | ||||||||
\(804\) | 19.6830 | 0.694164 | ||||||||
\(805\) | −22.8530 | −0.805464 | ||||||||
\(806\) | −10.0135 | −0.352709 | ||||||||
\(807\) | −26.4681 | −0.931721 | ||||||||
\(808\) | 23.7428 | 0.835268 | ||||||||
\(809\) | −28.3771 | −0.997687 | −0.498843 | − | 0.866692i | \(-0.666242\pi\) | ||||
−0.498843 | + | 0.866692i | \(0.666242\pi\) | |||||||
\(810\) | −7.93371 | −0.278762 | ||||||||
\(811\) | −10.5723 | −0.371242 | −0.185621 | − | 0.982621i | \(-0.559430\pi\) | ||||
−0.185621 | + | 0.982621i | \(0.559430\pi\) | |||||||
\(812\) | −13.2978 | −0.466660 | ||||||||
\(813\) | −48.2608 | −1.69258 | ||||||||
\(814\) | −3.81567 | −0.133739 | ||||||||
\(815\) | 7.15389 | 0.250590 | ||||||||
\(816\) | −26.3392 | −0.922058 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 10.8088 | 0.377920 | ||||||||
\(819\) | 14.2210 | 0.496921 | ||||||||
\(820\) | 4.54959 | 0.158878 | ||||||||
\(821\) | −0.785288 | −0.0274067 | −0.0137034 | − | 0.999906i | \(-0.504362\pi\) | ||||
−0.0137034 | + | 0.999906i | \(0.504362\pi\) | |||||||
\(822\) | 17.9002 | 0.624340 | ||||||||
\(823\) | 11.3968 | 0.397267 | 0.198634 | − | 0.980074i | \(-0.436350\pi\) | ||||
0.198634 | + | 0.980074i | \(0.436350\pi\) | |||||||
\(824\) | 1.44712 | 0.0504129 | ||||||||
\(825\) | −4.50554 | −0.156863 | ||||||||
\(826\) | −1.67132 | −0.0581527 | ||||||||
\(827\) | −17.9989 | −0.625885 | −0.312942 | − | 0.949772i | \(-0.601315\pi\) | ||||
−0.312942 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(828\) | −20.8773 | −0.725538 | ||||||||
\(829\) | 17.4920 | 0.607523 | 0.303762 | − | 0.952748i | \(-0.401757\pi\) | ||||
0.303762 | + | 0.952748i | \(0.401757\pi\) | |||||||
\(830\) | 2.23236 | 0.0774863 | ||||||||
\(831\) | −28.8156 | −0.999601 | ||||||||
\(832\) | 7.71621 | 0.267511 | ||||||||
\(833\) | 19.2754 | 0.667854 | ||||||||
\(834\) | −15.2213 | −0.527071 | ||||||||
\(835\) | −6.91712 | −0.239377 | ||||||||
\(836\) | 3.50194 | 0.121117 | ||||||||
\(837\) | −10.9822 | −0.379600 | ||||||||
\(838\) | −0.324055 | −0.0111943 | ||||||||
\(839\) | −5.28064 | −0.182308 | −0.0911539 | − | 0.995837i | \(-0.529056\pi\) | ||||
−0.0911539 | + | 0.995837i | \(0.529056\pi\) | |||||||
\(840\) | 10.3518 | 0.357171 | ||||||||
\(841\) | −11.9591 | −0.412381 | ||||||||
\(842\) | −4.36950 | −0.150583 | ||||||||
\(843\) | −24.0769 | −0.829253 | ||||||||
\(844\) | −17.1417 | −0.590042 | ||||||||
\(845\) | 24.3275 | 0.836890 | ||||||||
\(846\) | 0.745209 | 0.0256208 | ||||||||
\(847\) | 20.2900 | 0.697172 | ||||||||
\(848\) | 5.35321 | 0.183830 | ||||||||
\(849\) | 5.54594 | 0.190336 | ||||||||
\(850\) | 11.1496 | 0.382430 | ||||||||
\(851\) | −101.466 | −3.47821 | ||||||||
\(852\) | −45.0854 | −1.54460 | ||||||||
\(853\) | −44.8997 | −1.53734 | −0.768668 | − | 0.639648i | \(-0.779080\pi\) | ||||
−0.768668 | + | 0.639648i | \(0.779080\pi\) | |||||||
\(854\) | −3.84735 | −0.131653 | ||||||||
\(855\) | −5.37907 | −0.183960 | ||||||||
\(856\) | −14.6702 | −0.501417 | ||||||||
\(857\) | −27.8117 | −0.950028 | −0.475014 | − | 0.879978i | \(-0.657557\pi\) | ||||
−0.475014 | + | 0.879978i | \(0.657557\pi\) | |||||||
\(858\) | −4.21984 | −0.144063 | ||||||||
\(859\) | −30.8667 | −1.05316 | −0.526579 | − | 0.850126i | \(-0.676526\pi\) | ||||
−0.526579 | + | 0.850126i | \(0.676526\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.55422 | 0.291527 | ||||||||
\(862\) | −17.3825 | −0.592051 | ||||||||
\(863\) | 31.3545 | 1.06732 | 0.533661 | − | 0.845699i | \(-0.320816\pi\) | ||||
0.533661 | + | 0.845699i | \(0.320816\pi\) | |||||||
\(864\) | −18.9418 | −0.644414 | ||||||||
\(865\) | −15.0698 | −0.512388 | ||||||||
\(866\) | −10.9347 | −0.371577 | ||||||||
\(867\) | 34.0670 | 1.15698 | ||||||||
\(868\) | 10.0615 | 0.341510 | ||||||||
\(869\) | 5.16128 | 0.175085 | ||||||||
\(870\) | −6.06100 | −0.205487 | ||||||||
\(871\) | 32.0781 | 1.08692 | ||||||||
\(872\) | 3.73165 | 0.126370 | ||||||||
\(873\) | −20.4134 | −0.690888 | ||||||||
\(874\) | −17.5725 | −0.594400 | ||||||||
\(875\) | 20.2516 | 0.684630 | ||||||||
\(876\) | 17.5520 | 0.593026 | ||||||||
\(877\) | −54.2804 | −1.83292 | −0.916460 | − | 0.400127i | \(-0.868966\pi\) | ||||
−0.916460 | + | 0.400127i | \(0.868966\pi\) | |||||||
\(878\) | 7.25083 | 0.244704 | ||||||||
\(879\) | 49.4393 | 1.66755 | ||||||||
\(880\) | 1.74926 | 0.0589676 | ||||||||
\(881\) | −38.8494 | −1.30887 | −0.654435 | − | 0.756118i | \(-0.727093\pi\) | ||||
−0.654435 | + | 0.756118i | \(0.727093\pi\) | |||||||
\(882\) | −2.45273 | −0.0825876 | ||||||||
\(883\) | 18.1383 | 0.610402 | 0.305201 | − | 0.952288i | \(-0.401276\pi\) | ||||
0.305201 | + | 0.952288i | \(0.401276\pi\) | |||||||
\(884\) | −55.3393 | −1.86126 | ||||||||
\(885\) | 4.03691 | 0.135699 | ||||||||
\(886\) | 1.61742 | 0.0543383 | ||||||||
\(887\) | −15.1762 | −0.509567 | −0.254783 | − | 0.966998i | \(-0.582004\pi\) | ||||
−0.254783 | + | 0.966998i | \(0.582004\pi\) | |||||||
\(888\) | 45.9613 | 1.54236 | ||||||||
\(889\) | −18.7822 | −0.629935 | ||||||||
\(890\) | 0.609325 | 0.0204246 | ||||||||
\(891\) | −7.11250 | −0.238278 | ||||||||
\(892\) | 16.2390 | 0.543722 | ||||||||
\(893\) | −3.32399 | −0.111233 | ||||||||
\(894\) | 8.03359 | 0.268683 | ||||||||
\(895\) | −17.7860 | −0.594519 | ||||||||
\(896\) | 22.0916 | 0.738029 | ||||||||
\(897\) | −112.214 | −3.74670 | ||||||||
\(898\) | 10.3415 | 0.345100 | ||||||||
\(899\) | −12.8937 | −0.430029 | ||||||||
\(900\) | 7.51846 | 0.250615 | ||||||||
\(901\) | −14.0930 | −0.469506 | ||||||||
\(902\) | −0.769654 | −0.0256267 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8074 | −0.825083 | ||||||||
\(905\) | −10.4889 | −0.348664 | ||||||||
\(906\) | −14.6581 | −0.486984 | ||||||||
\(907\) | 30.5772 | 1.01530 | 0.507650 | − | 0.861563i | \(-0.330514\pi\) | ||||
0.507650 | + | 0.861563i | \(0.330514\pi\) | |||||||
\(908\) | −47.3280 | −1.57064 | ||||||||
\(909\) | −14.9379 | −0.495459 | ||||||||
\(910\) | 7.70810 | 0.255521 | ||||||||
\(911\) | −28.9994 | −0.960792 | −0.480396 | − | 0.877052i | \(-0.659507\pi\) | ||||
−0.480396 | + | 0.877052i | \(0.659507\pi\) | |||||||
\(912\) | −14.9496 | −0.495032 | ||||||||
\(913\) | 2.00129 | 0.0662330 | ||||||||
\(914\) | −17.1648 | −0.567762 | ||||||||
\(915\) | 9.29288 | 0.307213 | ||||||||
\(916\) | −10.5012 | −0.346970 | ||||||||
\(917\) | −31.2354 | −1.03148 | ||||||||
\(918\) | 11.4529 | 0.378003 | ||||||||
\(919\) | −19.1384 | −0.631317 | −0.315658 | − | 0.948873i | \(-0.602225\pi\) | ||||
−0.315658 | + | 0.948873i | \(0.602225\pi\) | |||||||
\(920\) | −24.7674 | −0.816556 | ||||||||
\(921\) | −11.0713 | −0.364811 | ||||||||
\(922\) | −7.68183 | −0.252987 | ||||||||
\(923\) | −73.4774 | −2.41854 | ||||||||
\(924\) | 4.24009 | 0.139489 | ||||||||
\(925\) | 36.5405 | 1.20144 | ||||||||
\(926\) | −2.57726 | −0.0846939 | ||||||||
\(927\) | −0.910466 | −0.0299036 | ||||||||
\(928\) | −22.2388 | −0.730023 | ||||||||
\(929\) | 13.2547 | 0.434873 | 0.217437 | − | 0.976074i | \(-0.430230\pi\) | ||||
0.217437 | + | 0.976074i | \(0.430230\pi\) | |||||||
\(930\) | 4.58595 | 0.150379 | ||||||||
\(931\) | 10.9403 | 0.358555 | ||||||||
\(932\) | −29.5128 | −0.966726 | ||||||||
\(933\) | −47.7831 | −1.56435 | ||||||||
\(934\) | 18.0586 | 0.590896 | ||||||||
\(935\) | −4.60516 | −0.150605 | ||||||||
\(936\) | 15.4122 | 0.503764 | ||||||||
\(937\) | 34.7757 | 1.13607 | 0.568037 | − | 0.823003i | \(-0.307703\pi\) | ||||
0.568037 | + | 0.823003i | \(0.307703\pi\) | |||||||
\(938\) | 6.08226 | 0.198593 | ||||||||
\(939\) | 3.61538 | 0.117983 | ||||||||
\(940\) | −2.14052 | −0.0698160 | ||||||||
\(941\) | 35.2449 | 1.14895 | 0.574475 | − | 0.818522i | \(-0.305206\pi\) | ||||
0.574475 | + | 0.818522i | \(0.305206\pi\) | |||||||
\(942\) | −5.43037 | −0.176931 | ||||||||
\(943\) | −20.4665 | −0.666482 | ||||||||
\(944\) | 3.40188 | 0.110722 | ||||||||
\(945\) | 8.45382 | 0.275003 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.1252 | −1.59635 | −0.798177 | − | 0.602424i | \(-0.794202\pi\) | ||||
−0.798177 | + | 0.602424i | \(0.794202\pi\) | |||||||
\(948\) | −28.4048 | −0.922546 | ||||||||
\(949\) | 28.6051 | 0.928562 | ||||||||
\(950\) | 6.32832 | 0.205318 | ||||||||
\(951\) | 67.5857 | 2.19162 | ||||||||
\(952\) | −22.9655 | −0.744317 | ||||||||
\(953\) | −34.1506 | −1.10625 | −0.553123 | − | 0.833099i | \(-0.686564\pi\) | ||||
−0.553123 | + | 0.833099i | \(0.686564\pi\) | |||||||
\(954\) | 1.79328 | 0.0580597 | ||||||||
\(955\) | 5.89280 | 0.190686 | ||||||||
\(956\) | 21.1944 | 0.685475 | ||||||||
\(957\) | −5.43364 | −0.175645 | ||||||||
\(958\) | −17.2592 | −0.557620 | ||||||||
\(959\) | −29.3126 | −0.946553 | ||||||||
\(960\) | −3.53386 | −0.114055 | ||||||||
\(961\) | −21.2442 | −0.685297 | ||||||||
\(962\) | 34.2234 | 1.10341 | ||||||||
\(963\) | 9.22985 | 0.297428 | ||||||||
\(964\) | 21.9888 | 0.708212 | ||||||||
\(965\) | 7.03037 | 0.226316 | ||||||||
\(966\) | −21.2766 | −0.684562 | ||||||||
\(967\) | −8.62632 | −0.277404 | −0.138702 | − | 0.990334i | \(-0.544293\pi\) | ||||
−0.138702 | + | 0.990334i | \(0.544293\pi\) | |||||||
\(968\) | 21.9896 | 0.706773 | ||||||||
\(969\) | 39.3568 | 1.26432 | ||||||||
\(970\) | −11.0645 | −0.355260 | ||||||||
\(971\) | −49.0762 | −1.57493 | −0.787465 | − | 0.616359i | \(-0.788607\pi\) | ||||
−0.787465 | + | 0.616359i | \(0.788607\pi\) | |||||||
\(972\) | 21.3958 | 0.686270 | ||||||||
\(973\) | 24.9258 | 0.799084 | ||||||||
\(974\) | 7.70761 | 0.246968 | ||||||||
\(975\) | 40.4110 | 1.29419 | ||||||||
\(976\) | 7.83107 | 0.250666 | ||||||||
\(977\) | −46.6369 | −1.49205 | −0.746023 | − | 0.665921i | \(-0.768039\pi\) | ||||
−0.746023 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(978\) | 6.66039 | 0.212976 | ||||||||
\(979\) | 0.546254 | 0.0174584 | ||||||||
\(980\) | 7.04514 | 0.225049 | ||||||||
\(981\) | −2.34779 | −0.0749592 | ||||||||
\(982\) | 2.66114 | 0.0849202 | ||||||||
\(983\) | 30.4945 | 0.972624 | 0.486312 | − | 0.873785i | \(-0.338342\pi\) | ||||
0.486312 | + | 0.873785i | \(0.338342\pi\) | |||||||
\(984\) | 9.27078 | 0.295542 | ||||||||
\(985\) | 16.7499 | 0.533696 | ||||||||
\(986\) | 13.4464 | 0.428220 | ||||||||
\(987\) | −4.02464 | −0.128106 | ||||||||
\(988\) | −31.4095 | −0.999268 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.585989 | 0.0186240 | ||||||||
\(991\) | −19.3735 | −0.615420 | −0.307710 | − | 0.951480i | \(-0.599563\pi\) | ||||
−0.307710 | + | 0.951480i | \(0.599563\pi\) | |||||||
\(992\) | 16.8266 | 0.534244 | ||||||||
\(993\) | 29.2235 | 0.927381 | ||||||||
\(994\) | −13.9319 | −0.441893 | ||||||||
\(995\) | −27.2070 | −0.862519 | ||||||||
\(996\) | −11.0140 | −0.348991 | ||||||||
\(997\) | −53.7576 | −1.70252 | −0.851261 | − | 0.524743i | \(-0.824161\pi\) | ||||
−0.851261 | + | 0.524743i | \(0.824161\pi\) | |||||||
\(998\) | 12.5200 | 0.396315 | ||||||||
\(999\) | 37.5344 | 1.18753 |
(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 | 1849.2.a.m.1.6 | yes | 10 | |
43.42 | odd | 2 | inner | 1849.2.a.m.1.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.m.1.5 | ✓ | 10 | 43.42 | odd | 2 | inner | |
1849.2.a.m.1.6 | yes | 10 | 1.1 | even | 1 | trivial |