Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [799,2,Mod(1,799)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(799, 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("799.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 799 = 17 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 799.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: | \(6.38004712150\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + 1280 x^{12} - 24559 x^{11} + 3411 x^{10} + 49829 x^{9} - 15132 x^{8} - 58070 x^{7} + \cdots + 63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.74861\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 799.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74861 | −1.94356 | −0.971779 | − | 0.235892i | \(-0.924199\pi\) | ||||
−0.971779 | + | 0.235892i | \(0.924199\pi\) | |||||||
\(3\) | 0.350871 | 0.202576 | 0.101288 | − | 0.994857i | \(-0.467704\pi\) | ||||
0.101288 | + | 0.994857i | \(0.467704\pi\) | |||||||
\(4\) | 5.55484 | 2.77742 | ||||||||
\(5\) | 4.31399 | 1.92927 | 0.964637 | − | 0.263582i | \(-0.0849039\pi\) | ||||
0.964637 | + | 0.263582i | \(0.0849039\pi\) | |||||||
\(6\) | −0.964407 | −0.393718 | ||||||||
\(7\) | −1.95626 | −0.739398 | −0.369699 | − | 0.929152i | \(-0.620539\pi\) | ||||
−0.369699 | + | 0.929152i | \(0.620539\pi\) | |||||||
\(8\) | −9.77085 | −3.45452 | ||||||||
\(9\) | −2.87689 | −0.958963 | ||||||||
\(10\) | −11.8575 | −3.74966 | ||||||||
\(11\) | 0.406909 | 0.122688 | 0.0613439 | − | 0.998117i | \(-0.480461\pi\) | ||||
0.0613439 | + | 0.998117i | \(0.480461\pi\) | |||||||
\(12\) | 1.94903 | 0.562637 | ||||||||
\(13\) | 1.40203 | 0.388853 | 0.194427 | − | 0.980917i | \(-0.437715\pi\) | ||||
0.194427 | + | 0.980917i | \(0.437715\pi\) | |||||||
\(14\) | 5.37700 | 1.43706 | ||||||||
\(15\) | 1.51365 | 0.390824 | ||||||||
\(16\) | 15.7465 | 3.93664 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 7.90744 | 1.86380 | ||||||||
\(19\) | −1.50045 | −0.344228 | −0.172114 | − | 0.985077i | \(-0.555060\pi\) | ||||
−0.172114 | + | 0.985077i | \(0.555060\pi\) | |||||||
\(20\) | 23.9635 | 5.35840 | ||||||||
\(21\) | −0.686397 | −0.149784 | ||||||||
\(22\) | −1.11843 | −0.238451 | ||||||||
\(23\) | 5.78890 | 1.20707 | 0.603534 | − | 0.797337i | \(-0.293759\pi\) | ||||
0.603534 | + | 0.797337i | \(0.293759\pi\) | |||||||
\(24\) | −3.42831 | −0.699801 | ||||||||
\(25\) | 13.6105 | 2.72210 | ||||||||
\(26\) | −3.85363 | −0.755759 | ||||||||
\(27\) | −2.06203 | −0.396838 | ||||||||
\(28\) | −10.8667 | −2.05362 | ||||||||
\(29\) | 6.87157 | 1.27602 | 0.638009 | − | 0.770029i | \(-0.279758\pi\) | ||||
0.638009 | + | 0.770029i | \(0.279758\pi\) | |||||||
\(30\) | −4.16044 | −0.759589 | ||||||||
\(31\) | −1.67590 | −0.301000 | −0.150500 | − | 0.988610i | \(-0.548088\pi\) | ||||
−0.150500 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(32\) | −23.7394 | −4.19657 | ||||||||
\(33\) | 0.142773 | 0.0248536 | ||||||||
\(34\) | 2.74861 | 0.471382 | ||||||||
\(35\) | −8.43930 | −1.42650 | ||||||||
\(36\) | −15.9807 | −2.66344 | ||||||||
\(37\) | 8.97370 | 1.47527 | 0.737634 | − | 0.675201i | \(-0.235943\pi\) | ||||
0.737634 | + | 0.675201i | \(0.235943\pi\) | |||||||
\(38\) | 4.12416 | 0.669027 | ||||||||
\(39\) | 0.491932 | 0.0787721 | ||||||||
\(40\) | −42.1513 | −6.66471 | ||||||||
\(41\) | 11.7431 | 1.83397 | 0.916985 | − | 0.398921i | \(-0.130615\pi\) | ||||
0.916985 | + | 0.398921i | \(0.130615\pi\) | |||||||
\(42\) | 1.88663 | 0.291114 | ||||||||
\(43\) | −6.25773 | −0.954295 | −0.477148 | − | 0.878823i | \(-0.658329\pi\) | ||||
−0.477148 | + | 0.878823i | \(0.658329\pi\) | |||||||
\(44\) | 2.26032 | 0.340755 | ||||||||
\(45\) | −12.4109 | −1.85010 | ||||||||
\(46\) | −15.9114 | −2.34601 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 5.52501 | 0.797467 | ||||||||
\(49\) | −3.17303 | −0.453291 | ||||||||
\(50\) | −37.4099 | −5.29056 | ||||||||
\(51\) | −0.350871 | −0.0491318 | ||||||||
\(52\) | 7.78805 | 1.08001 | ||||||||
\(53\) | −2.13587 | −0.293384 | −0.146692 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146692 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(54\) | 5.66771 | 0.771278 | ||||||||
\(55\) | 1.75540 | 0.236698 | ||||||||
\(56\) | 19.1144 | 2.55426 | ||||||||
\(57\) | −0.526467 | −0.0697322 | ||||||||
\(58\) | −18.8872 | −2.48002 | ||||||||
\(59\) | 13.8777 | 1.80673 | 0.903364 | − | 0.428875i | \(-0.141090\pi\) | ||||
0.903364 | + | 0.428875i | \(0.141090\pi\) | |||||||
\(60\) | 8.40811 | 1.08548 | ||||||||
\(61\) | 1.07857 | 0.138097 | 0.0690484 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690484 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(62\) | 4.60638 | 0.585011 | ||||||||
\(63\) | 5.62795 | 0.709055 | ||||||||
\(64\) | 33.7571 | 4.21964 | ||||||||
\(65\) | 6.04834 | 0.750204 | ||||||||
\(66\) | −0.392426 | −0.0483043 | ||||||||
\(67\) | −10.7462 | −1.31286 | −0.656430 | − | 0.754387i | \(-0.727934\pi\) | ||||
−0.656430 | + | 0.754387i | \(0.727934\pi\) | |||||||
\(68\) | −5.55484 | −0.673623 | ||||||||
\(69\) | 2.03116 | 0.244523 | ||||||||
\(70\) | 23.1963 | 2.77249 | ||||||||
\(71\) | 9.62778 | 1.14261 | 0.571304 | − | 0.820739i | \(-0.306438\pi\) | ||||
0.571304 | + | 0.820739i | \(0.306438\pi\) | |||||||
\(72\) | 28.1097 | 3.31275 | ||||||||
\(73\) | −2.68137 | −0.313831 | −0.156915 | − | 0.987612i | \(-0.550155\pi\) | ||||
−0.156915 | + | 0.987612i | \(0.550155\pi\) | |||||||
\(74\) | −24.6652 | −2.86727 | ||||||||
\(75\) | 4.77553 | 0.551431 | ||||||||
\(76\) | −8.33478 | −0.956065 | ||||||||
\(77\) | −0.796022 | −0.0907151 | ||||||||
\(78\) | −1.35213 | −0.153098 | ||||||||
\(79\) | 13.5667 | 1.52638 | 0.763188 | − | 0.646177i | \(-0.223633\pi\) | ||||
0.763188 | + | 0.646177i | \(0.223633\pi\) | |||||||
\(80\) | 67.9304 | 7.59485 | ||||||||
\(81\) | 7.90716 | 0.878573 | ||||||||
\(82\) | −32.2773 | −3.56443 | ||||||||
\(83\) | −0.391596 | −0.0429833 | −0.0214916 | − | 0.999769i | \(-0.506842\pi\) | ||||
−0.0214916 | + | 0.999769i | \(0.506842\pi\) | |||||||
\(84\) | −3.81282 | −0.416013 | ||||||||
\(85\) | −4.31399 | −0.467918 | ||||||||
\(86\) | 17.2000 | 1.85473 | ||||||||
\(87\) | 2.41104 | 0.258490 | ||||||||
\(88\) | −3.97585 | −0.423827 | ||||||||
\(89\) | −2.71107 | −0.287373 | −0.143687 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143687 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(90\) | 34.1126 | 3.59578 | ||||||||
\(91\) | −2.74274 | −0.287517 | ||||||||
\(92\) | 32.1564 | 3.35253 | ||||||||
\(93\) | −0.588024 | −0.0609753 | ||||||||
\(94\) | −2.74861 | −0.283497 | ||||||||
\(95\) | −6.47294 | −0.664110 | ||||||||
\(96\) | −8.32946 | −0.850122 | ||||||||
\(97\) | −12.3441 | −1.25335 | −0.626675 | − | 0.779281i | \(-0.715584\pi\) | ||||
−0.626675 | + | 0.779281i | \(0.715584\pi\) | |||||||
\(98\) | 8.72142 | 0.880997 | ||||||||
\(99\) | −1.17063 | −0.117653 | ||||||||
\(100\) | 75.6041 | 7.56041 | ||||||||
\(101\) | 7.41866 | 0.738184 | 0.369092 | − | 0.929393i | \(-0.379669\pi\) | ||||
0.369092 | + | 0.929393i | \(0.379669\pi\) | |||||||
\(102\) | 0.964407 | 0.0954905 | ||||||||
\(103\) | −3.56783 | −0.351549 | −0.175774 | − | 0.984431i | \(-0.556243\pi\) | ||||
−0.175774 | + | 0.984431i | \(0.556243\pi\) | |||||||
\(104\) | −13.6990 | −1.34330 | ||||||||
\(105\) | −2.96111 | −0.288974 | ||||||||
\(106\) | 5.87067 | 0.570210 | ||||||||
\(107\) | −11.4161 | −1.10363 | −0.551816 | − | 0.833966i | \(-0.686065\pi\) | ||||
−0.551816 | + | 0.833966i | \(0.686065\pi\) | |||||||
\(108\) | −11.4543 | −1.10219 | ||||||||
\(109\) | −1.04844 | −0.100422 | −0.0502112 | − | 0.998739i | \(-0.515989\pi\) | ||||
−0.0502112 | + | 0.998739i | \(0.515989\pi\) | |||||||
\(110\) | −4.82491 | −0.460037 | ||||||||
\(111\) | 3.14861 | 0.298853 | ||||||||
\(112\) | −30.8044 | −2.91074 | ||||||||
\(113\) | −2.05435 | −0.193257 | −0.0966283 | − | 0.995321i | \(-0.530806\pi\) | ||||
−0.0966283 | + | 0.995321i | \(0.530806\pi\) | |||||||
\(114\) | 1.44705 | 0.135529 | ||||||||
\(115\) | 24.9732 | 2.32877 | ||||||||
\(116\) | 38.1704 | 3.54404 | ||||||||
\(117\) | −4.03348 | −0.372896 | ||||||||
\(118\) | −38.1444 | −3.51148 | ||||||||
\(119\) | 1.95626 | 0.179330 | ||||||||
\(120\) | −14.7897 | −1.35011 | ||||||||
\(121\) | −10.8344 | −0.984948 | ||||||||
\(122\) | −2.96457 | −0.268399 | ||||||||
\(123\) | 4.12033 | 0.371518 | ||||||||
\(124\) | −9.30934 | −0.836003 | ||||||||
\(125\) | 37.1456 | 3.32240 | ||||||||
\(126\) | −15.4690 | −1.37809 | ||||||||
\(127\) | −12.6407 | −1.12168 | −0.560842 | − | 0.827923i | \(-0.689522\pi\) | ||||
−0.560842 | + | 0.827923i | \(0.689522\pi\) | |||||||
\(128\) | −45.3062 | −4.00454 | ||||||||
\(129\) | −2.19566 | −0.193317 | ||||||||
\(130\) | −16.6245 | −1.45807 | ||||||||
\(131\) | −16.9115 | −1.47757 | −0.738783 | − | 0.673943i | \(-0.764599\pi\) | ||||
−0.738783 | + | 0.673943i | \(0.764599\pi\) | |||||||
\(132\) | 0.793080 | 0.0690288 | ||||||||
\(133\) | 2.93528 | 0.254521 | ||||||||
\(134\) | 29.5372 | 2.55162 | ||||||||
\(135\) | −8.89558 | −0.765610 | ||||||||
\(136\) | 9.77085 | 0.837844 | ||||||||
\(137\) | 5.38302 | 0.459902 | 0.229951 | − | 0.973202i | \(-0.426143\pi\) | ||||
0.229951 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(138\) | −5.58285 | −0.475244 | ||||||||
\(139\) | 1.65232 | 0.140148 | 0.0700741 | − | 0.997542i | \(-0.477676\pi\) | ||||
0.0700741 | + | 0.997542i | \(0.477676\pi\) | |||||||
\(140\) | −46.8789 | −3.96199 | ||||||||
\(141\) | 0.350871 | 0.0295487 | ||||||||
\(142\) | −26.4630 | −2.22072 | ||||||||
\(143\) | 0.570499 | 0.0477075 | ||||||||
\(144\) | −45.3011 | −3.77509 | ||||||||
\(145\) | 29.6439 | 2.46179 | ||||||||
\(146\) | 7.37004 | 0.609949 | ||||||||
\(147\) | −1.11333 | −0.0918256 | ||||||||
\(148\) | 49.8475 | 4.09744 | ||||||||
\(149\) | −1.20271 | −0.0985296 | −0.0492648 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492648 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(150\) | −13.1261 | −1.07174 | ||||||||
\(151\) | −0.365814 | −0.0297696 | −0.0148848 | − | 0.999889i | \(-0.504738\pi\) | ||||
−0.0148848 | + | 0.999889i | \(0.504738\pi\) | |||||||
\(152\) | 14.6607 | 1.18914 | ||||||||
\(153\) | 2.87689 | 0.232583 | ||||||||
\(154\) | 2.18795 | 0.176310 | ||||||||
\(155\) | −7.22980 | −0.580712 | ||||||||
\(156\) | 2.73260 | 0.218783 | ||||||||
\(157\) | −13.4026 | −1.06965 | −0.534823 | − | 0.844964i | \(-0.679622\pi\) | ||||
−0.534823 | + | 0.844964i | \(0.679622\pi\) | |||||||
\(158\) | −37.2896 | −2.96660 | ||||||||
\(159\) | −0.749416 | −0.0594325 | ||||||||
\(160\) | −102.411 | −8.09633 | ||||||||
\(161\) | −11.3246 | −0.892504 | ||||||||
\(162\) | −21.7337 | −1.70756 | ||||||||
\(163\) | 8.48728 | 0.664775 | 0.332387 | − | 0.943143i | \(-0.392146\pi\) | ||||
0.332387 | + | 0.943143i | \(0.392146\pi\) | |||||||
\(164\) | 65.2312 | 5.09370 | ||||||||
\(165\) | 0.615920 | 0.0479493 | ||||||||
\(166\) | 1.07634 | 0.0835405 | ||||||||
\(167\) | 5.56470 | 0.430609 | 0.215305 | − | 0.976547i | \(-0.430926\pi\) | ||||
0.215305 | + | 0.976547i | \(0.430926\pi\) | |||||||
\(168\) | 6.70668 | 0.517432 | ||||||||
\(169\) | −11.0343 | −0.848793 | ||||||||
\(170\) | 11.8575 | 0.909425 | ||||||||
\(171\) | 4.31664 | 0.330102 | ||||||||
\(172\) | −34.7607 | −2.65048 | ||||||||
\(173\) | 18.9290 | 1.43914 | 0.719571 | − | 0.694419i | \(-0.244339\pi\) | ||||
0.719571 | + | 0.694419i | \(0.244339\pi\) | |||||||
\(174\) | −6.62699 | −0.502391 | ||||||||
\(175\) | −26.6257 | −2.01271 | ||||||||
\(176\) | 6.40742 | 0.482977 | ||||||||
\(177\) | 4.86930 | 0.365999 | ||||||||
\(178\) | 7.45167 | 0.558526 | ||||||||
\(179\) | 10.7361 | 0.802451 | 0.401226 | − | 0.915979i | \(-0.368584\pi\) | ||||
0.401226 | + | 0.915979i | \(0.368584\pi\) | |||||||
\(180\) | −68.9404 | −5.13851 | ||||||||
\(181\) | 17.1488 | 1.27466 | 0.637330 | − | 0.770591i | \(-0.280039\pi\) | ||||
0.637330 | + | 0.770591i | \(0.280039\pi\) | |||||||
\(182\) | 7.53871 | 0.558806 | ||||||||
\(183\) | 0.378440 | 0.0279751 | ||||||||
\(184\) | −56.5624 | −4.16984 | ||||||||
\(185\) | 38.7124 | 2.84620 | ||||||||
\(186\) | 1.61625 | 0.118509 | ||||||||
\(187\) | −0.406909 | −0.0297562 | ||||||||
\(188\) | 5.55484 | 0.405128 | ||||||||
\(189\) | 4.03388 | 0.293421 | ||||||||
\(190\) | 17.7916 | 1.29074 | ||||||||
\(191\) | −15.8722 | −1.14848 | −0.574238 | − | 0.818689i | \(-0.694702\pi\) | ||||
−0.574238 | + | 0.818689i | \(0.694702\pi\) | |||||||
\(192\) | 11.8444 | 0.854795 | ||||||||
\(193\) | 11.7532 | 0.846014 | 0.423007 | − | 0.906126i | \(-0.360975\pi\) | ||||
0.423007 | + | 0.906126i | \(0.360975\pi\) | |||||||
\(194\) | 33.9290 | 2.43596 | ||||||||
\(195\) | 2.12219 | 0.151973 | ||||||||
\(196\) | −17.6257 | −1.25898 | ||||||||
\(197\) | −0.777080 | −0.0553647 | −0.0276823 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276823 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(198\) | 3.21761 | 0.228666 | ||||||||
\(199\) | 11.8282 | 0.838478 | 0.419239 | − | 0.907876i | \(-0.362297\pi\) | ||||
0.419239 | + | 0.907876i | \(0.362297\pi\) | |||||||
\(200\) | −132.986 | −9.40354 | ||||||||
\(201\) | −3.77054 | −0.265954 | ||||||||
\(202\) | −20.3910 | −1.43470 | ||||||||
\(203\) | −13.4426 | −0.943485 | ||||||||
\(204\) | −1.94903 | −0.136460 | ||||||||
\(205\) | 50.6598 | 3.53823 | ||||||||
\(206\) | 9.80655 | 0.683255 | ||||||||
\(207\) | −16.6540 | −1.15753 | ||||||||
\(208\) | 22.0771 | 1.53077 | ||||||||
\(209\) | −0.610549 | −0.0422326 | ||||||||
\(210\) | 8.13892 | 0.561639 | ||||||||
\(211\) | 1.35124 | 0.0930229 | 0.0465115 | − | 0.998918i | \(-0.485190\pi\) | ||||
0.0465115 | + | 0.998918i | \(0.485190\pi\) | |||||||
\(212\) | −11.8644 | −0.814852 | ||||||||
\(213\) | 3.37811 | 0.231464 | ||||||||
\(214\) | 31.3782 | 2.14497 | ||||||||
\(215\) | −26.9958 | −1.84110 | ||||||||
\(216\) | 20.1478 | 1.37088 | ||||||||
\(217\) | 3.27850 | 0.222559 | ||||||||
\(218\) | 2.88175 | 0.195177 | ||||||||
\(219\) | −0.940817 | −0.0635745 | ||||||||
\(220\) | 9.75098 | 0.657411 | ||||||||
\(221\) | −1.40203 | −0.0943107 | ||||||||
\(222\) | −8.65430 | −0.580839 | ||||||||
\(223\) | 21.2996 | 1.42633 | 0.713164 | − | 0.700998i | \(-0.247262\pi\) | ||||
0.713164 | + | 0.700998i | \(0.247262\pi\) | |||||||
\(224\) | 46.4405 | 3.10293 | ||||||||
\(225\) | −39.1559 | −2.61039 | ||||||||
\(226\) | 5.64659 | 0.375605 | ||||||||
\(227\) | −9.21913 | −0.611895 | −0.305948 | − | 0.952048i | \(-0.598973\pi\) | ||||
−0.305948 | + | 0.952048i | \(0.598973\pi\) | |||||||
\(228\) | −2.92444 | −0.193676 | ||||||||
\(229\) | 0.0267800 | 0.00176967 | 0.000884835 | − | 1.00000i | \(-0.499718\pi\) | ||||
0.000884835 | 1.00000i | \(0.499718\pi\) | ||||||||
\(230\) | −68.6416 | −4.52609 | ||||||||
\(231\) | −0.279301 | −0.0183767 | ||||||||
\(232\) | −67.1411 | −4.40803 | ||||||||
\(233\) | −2.88690 | −0.189127 | −0.0945635 | − | 0.995519i | \(-0.530146\pi\) | ||||
−0.0945635 | + | 0.995519i | \(0.530146\pi\) | |||||||
\(234\) | 11.0865 | 0.724745 | ||||||||
\(235\) | 4.31399 | 0.281414 | ||||||||
\(236\) | 77.0886 | 5.01804 | ||||||||
\(237\) | 4.76017 | 0.309206 | ||||||||
\(238\) | −5.37700 | −0.348539 | ||||||||
\(239\) | −25.9997 | −1.68178 | −0.840891 | − | 0.541204i | \(-0.817969\pi\) | ||||
−0.840891 | + | 0.541204i | \(0.817969\pi\) | |||||||
\(240\) | 23.8348 | 1.53853 | ||||||||
\(241\) | −11.2112 | −0.722177 | −0.361088 | − | 0.932532i | \(-0.617595\pi\) | ||||
−0.361088 | + | 0.932532i | \(0.617595\pi\) | |||||||
\(242\) | 29.7796 | 1.91430 | ||||||||
\(243\) | 8.96049 | 0.574816 | ||||||||
\(244\) | 5.99129 | 0.383553 | ||||||||
\(245\) | −13.6884 | −0.874522 | ||||||||
\(246\) | −11.3252 | −0.722066 | ||||||||
\(247\) | −2.10368 | −0.133854 | ||||||||
\(248\) | 16.3749 | 1.03981 | ||||||||
\(249\) | −0.137400 | −0.00870737 | ||||||||
\(250\) | −102.099 | −6.45728 | ||||||||
\(251\) | −20.5618 | −1.29785 | −0.648925 | − | 0.760852i | \(-0.724781\pi\) | ||||
−0.648925 | + | 0.760852i | \(0.724781\pi\) | |||||||
\(252\) | 31.2624 | 1.96934 | ||||||||
\(253\) | 2.35556 | 0.148093 | ||||||||
\(254\) | 34.7444 | 2.18006 | ||||||||
\(255\) | −1.51365 | −0.0947887 | ||||||||
\(256\) | 57.0148 | 3.56342 | ||||||||
\(257\) | −15.8886 | −0.991102 | −0.495551 | − | 0.868579i | \(-0.665034\pi\) | ||||
−0.495551 | + | 0.868579i | \(0.665034\pi\) | |||||||
\(258\) | 6.03500 | 0.375723 | ||||||||
\(259\) | −17.5549 | −1.09081 | ||||||||
\(260\) | 33.5975 | 2.08363 | ||||||||
\(261\) | −19.7687 | −1.22365 | ||||||||
\(262\) | 46.4831 | 2.87174 | ||||||||
\(263\) | −8.75695 | −0.539977 | −0.269988 | − | 0.962864i | \(-0.587020\pi\) | ||||
−0.269988 | + | 0.962864i | \(0.587020\pi\) | |||||||
\(264\) | −1.39501 | −0.0858571 | ||||||||
\(265\) | −9.21412 | −0.566019 | ||||||||
\(266\) | −8.06794 | −0.494677 | ||||||||
\(267\) | −0.951237 | −0.0582148 | ||||||||
\(268\) | −59.6936 | −3.64636 | ||||||||
\(269\) | 17.2294 | 1.05050 | 0.525249 | − | 0.850949i | \(-0.323972\pi\) | ||||
0.525249 | + | 0.850949i | \(0.323972\pi\) | |||||||
\(270\) | 24.4504 | 1.48801 | ||||||||
\(271\) | −13.5236 | −0.821500 | −0.410750 | − | 0.911748i | \(-0.634733\pi\) | ||||
−0.410750 | + | 0.911748i | \(0.634733\pi\) | |||||||
\(272\) | −15.7465 | −0.954775 | ||||||||
\(273\) | −0.962348 | −0.0582440 | ||||||||
\(274\) | −14.7958 | −0.893847 | ||||||||
\(275\) | 5.53824 | 0.333968 | ||||||||
\(276\) | 11.2828 | 0.679142 | ||||||||
\(277\) | 22.7299 | 1.36571 | 0.682854 | − | 0.730555i | \(-0.260739\pi\) | ||||
0.682854 | + | 0.730555i | \(0.260739\pi\) | |||||||
\(278\) | −4.54159 | −0.272386 | ||||||||
\(279\) | 4.82137 | 0.288648 | ||||||||
\(280\) | 82.4591 | 4.92787 | ||||||||
\(281\) | −27.2854 | −1.62771 | −0.813854 | − | 0.581069i | \(-0.802634\pi\) | ||||
−0.813854 | + | 0.581069i | \(0.802634\pi\) | |||||||
\(282\) | −0.964407 | −0.0574296 | ||||||||
\(283\) | −8.24456 | −0.490088 | −0.245044 | − | 0.969512i | \(-0.578802\pi\) | ||||
−0.245044 | + | 0.969512i | \(0.578802\pi\) | |||||||
\(284\) | 53.4808 | 3.17350 | ||||||||
\(285\) | −2.27117 | −0.134533 | ||||||||
\(286\) | −1.56808 | −0.0927224 | ||||||||
\(287\) | −22.9727 | −1.35603 | ||||||||
\(288\) | 68.2955 | 4.02435 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −81.4793 | −4.78463 | ||||||||
\(291\) | −4.33118 | −0.253898 | ||||||||
\(292\) | −14.8946 | −0.871640 | ||||||||
\(293\) | 10.5197 | 0.614570 | 0.307285 | − | 0.951618i | \(-0.400579\pi\) | ||||
0.307285 | + | 0.951618i | \(0.400579\pi\) | |||||||
\(294\) | 3.06010 | 0.178468 | ||||||||
\(295\) | 59.8684 | 3.48567 | ||||||||
\(296\) | −87.6807 | −5.09634 | ||||||||
\(297\) | −0.839060 | −0.0486872 | ||||||||
\(298\) | 3.30577 | 0.191498 | ||||||||
\(299\) | 8.11620 | 0.469372 | ||||||||
\(300\) | 26.5273 | 1.53155 | ||||||||
\(301\) | 12.2418 | 0.705604 | ||||||||
\(302\) | 1.00548 | 0.0578589 | ||||||||
\(303\) | 2.60299 | 0.149538 | ||||||||
\(304\) | −23.6270 | −1.35510 | ||||||||
\(305\) | 4.65294 | 0.266427 | ||||||||
\(306\) | −7.90744 | −0.452038 | ||||||||
\(307\) | −22.7339 | −1.29749 | −0.648746 | − | 0.761005i | \(-0.724706\pi\) | ||||
−0.648746 | + | 0.761005i | \(0.724706\pi\) | |||||||
\(308\) | −4.42177 | −0.251954 | ||||||||
\(309\) | −1.25185 | −0.0712152 | ||||||||
\(310\) | 19.8719 | 1.12865 | ||||||||
\(311\) | −14.6846 | −0.832690 | −0.416345 | − | 0.909207i | \(-0.636689\pi\) | ||||
−0.416345 | + | 0.909207i | \(0.636689\pi\) | |||||||
\(312\) | −4.80659 | −0.272120 | ||||||||
\(313\) | −5.06283 | −0.286168 | −0.143084 | − | 0.989711i | \(-0.545702\pi\) | ||||
−0.143084 | + | 0.989711i | \(0.545702\pi\) | |||||||
\(314\) | 36.8385 | 2.07892 | ||||||||
\(315\) | 24.2789 | 1.36796 | ||||||||
\(316\) | 75.3609 | 4.23938 | ||||||||
\(317\) | 11.0611 | 0.621255 | 0.310627 | − | 0.950532i | \(-0.399461\pi\) | ||||
0.310627 | + | 0.950532i | \(0.399461\pi\) | |||||||
\(318\) | 2.05985 | 0.115511 | ||||||||
\(319\) | 2.79611 | 0.156552 | ||||||||
\(320\) | 145.628 | 8.14083 | ||||||||
\(321\) | −4.00557 | −0.223569 | ||||||||
\(322\) | 31.1269 | 1.73463 | ||||||||
\(323\) | 1.50045 | 0.0834875 | ||||||||
\(324\) | 43.9230 | 2.44017 | ||||||||
\(325\) | 19.0823 | 1.05850 | ||||||||
\(326\) | −23.3282 | −1.29203 | ||||||||
\(327\) | −0.367867 | −0.0203431 | ||||||||
\(328\) | −114.740 | −6.33548 | ||||||||
\(329\) | −1.95626 | −0.107852 | ||||||||
\(330\) | −1.69292 | −0.0931923 | ||||||||
\(331\) | −30.3272 | −1.66693 | −0.833466 | − | 0.552570i | \(-0.813647\pi\) | ||||
−0.833466 | + | 0.552570i | \(0.813647\pi\) | |||||||
\(332\) | −2.17526 | −0.119383 | ||||||||
\(333\) | −25.8163 | −1.41473 | ||||||||
\(334\) | −15.2952 | −0.836914 | ||||||||
\(335\) | −46.3591 | −2.53287 | ||||||||
\(336\) | −10.8084 | −0.589645 | ||||||||
\(337\) | −24.6850 | −1.34468 | −0.672338 | − | 0.740244i | \(-0.734710\pi\) | ||||
−0.672338 | + | 0.740244i | \(0.734710\pi\) | |||||||
\(338\) | 30.3290 | 1.64968 | ||||||||
\(339\) | −0.720811 | −0.0391491 | ||||||||
\(340\) | −23.9635 | −1.29960 | ||||||||
\(341\) | −0.681939 | −0.0369290 | ||||||||
\(342\) | −11.8648 | −0.641572 | ||||||||
\(343\) | 19.9011 | 1.07456 | ||||||||
\(344\) | 61.1434 | 3.29663 | ||||||||
\(345\) | 8.76239 | 0.471751 | ||||||||
\(346\) | −52.0282 | −2.79706 | ||||||||
\(347\) | 27.8592 | 1.49556 | 0.747779 | − | 0.663947i | \(-0.231120\pi\) | ||||
0.747779 | + | 0.663947i | \(0.231120\pi\) | |||||||
\(348\) | 13.3929 | 0.717936 | ||||||||
\(349\) | −5.95414 | −0.318718 | −0.159359 | − | 0.987221i | \(-0.550943\pi\) | ||||
−0.159359 | + | 0.987221i | \(0.550943\pi\) | |||||||
\(350\) | 73.1836 | 3.91183 | ||||||||
\(351\) | −2.89103 | −0.154312 | ||||||||
\(352\) | −9.65977 | −0.514868 | ||||||||
\(353\) | 6.23521 | 0.331867 | 0.165933 | − | 0.986137i | \(-0.446936\pi\) | ||||
0.165933 | + | 0.986137i | \(0.446936\pi\) | |||||||
\(354\) | −13.3838 | −0.711340 | ||||||||
\(355\) | 41.5341 | 2.20440 | ||||||||
\(356\) | −15.0596 | −0.798156 | ||||||||
\(357\) | 0.686397 | 0.0363280 | ||||||||
\(358\) | −29.5092 | −1.55961 | ||||||||
\(359\) | 1.35822 | 0.0716839 | 0.0358419 | − | 0.999357i | \(-0.488589\pi\) | ||||
0.0358419 | + | 0.999357i | \(0.488589\pi\) | |||||||
\(360\) | 121.265 | 6.39121 | ||||||||
\(361\) | −16.7486 | −0.881507 | ||||||||
\(362\) | −47.1353 | −2.47738 | ||||||||
\(363\) | −3.80149 | −0.199526 | ||||||||
\(364\) | −15.2355 | −0.798556 | ||||||||
\(365\) | −11.5674 | −0.605466 | ||||||||
\(366\) | −1.04018 | −0.0543712 | ||||||||
\(367\) | 4.33377 | 0.226221 | 0.113111 | − | 0.993582i | \(-0.463919\pi\) | ||||
0.113111 | + | 0.993582i | \(0.463919\pi\) | |||||||
\(368\) | 91.1551 | 4.75179 | ||||||||
\(369\) | −33.7837 | −1.75871 | ||||||||
\(370\) | −106.405 | −5.53175 | ||||||||
\(371\) | 4.17833 | 0.216928 | ||||||||
\(372\) | −3.26638 | −0.169354 | ||||||||
\(373\) | 7.10364 | 0.367812 | 0.183906 | − | 0.982944i | \(-0.441126\pi\) | ||||
0.183906 | + | 0.982944i | \(0.441126\pi\) | |||||||
\(374\) | 1.11843 | 0.0578328 | ||||||||
\(375\) | 13.0333 | 0.673037 | ||||||||
\(376\) | −9.77085 | −0.503893 | ||||||||
\(377\) | 9.63414 | 0.496183 | ||||||||
\(378\) | −11.0875 | −0.570282 | ||||||||
\(379\) | 3.14399 | 0.161496 | 0.0807479 | − | 0.996735i | \(-0.474269\pi\) | ||||
0.0807479 | + | 0.996735i | \(0.474269\pi\) | |||||||
\(380\) | −35.9562 | −1.84451 | ||||||||
\(381\) | −4.43527 | −0.227226 | ||||||||
\(382\) | 43.6266 | 2.23213 | ||||||||
\(383\) | 27.5124 | 1.40582 | 0.702909 | − | 0.711280i | \(-0.251884\pi\) | ||||
0.702909 | + | 0.711280i | \(0.251884\pi\) | |||||||
\(384\) | −15.8966 | −0.811222 | ||||||||
\(385\) | −3.43403 | −0.175014 | ||||||||
\(386\) | −32.3049 | −1.64428 | ||||||||
\(387\) | 18.0028 | 0.915134 | ||||||||
\(388\) | −68.5692 | −3.48108 | ||||||||
\(389\) | −30.6229 | −1.55264 | −0.776321 | − | 0.630338i | \(-0.782916\pi\) | ||||
−0.776321 | + | 0.630338i | \(0.782916\pi\) | |||||||
\(390\) | −5.83306 | −0.295369 | ||||||||
\(391\) | −5.78890 | −0.292757 | ||||||||
\(392\) | 31.0032 | 1.56590 | ||||||||
\(393\) | −5.93377 | −0.299319 | ||||||||
\(394\) | 2.13589 | 0.107604 | ||||||||
\(395\) | 58.5267 | 2.94480 | ||||||||
\(396\) | −6.50268 | −0.326772 | ||||||||
\(397\) | −8.99118 | −0.451254 | −0.225627 | − | 0.974214i | \(-0.572443\pi\) | ||||
−0.225627 | + | 0.974214i | \(0.572443\pi\) | |||||||
\(398\) | −32.5110 | −1.62963 | ||||||||
\(399\) | 1.02991 | 0.0515598 | ||||||||
\(400\) | 214.318 | 10.7159 | ||||||||
\(401\) | 35.8105 | 1.78829 | 0.894145 | − | 0.447778i | \(-0.147784\pi\) | ||||
0.894145 | + | 0.447778i | \(0.147784\pi\) | |||||||
\(402\) | 10.3637 | 0.516896 | ||||||||
\(403\) | −2.34966 | −0.117045 | ||||||||
\(404\) | 41.2094 | 2.05025 | ||||||||
\(405\) | 34.1114 | 1.69501 | ||||||||
\(406\) | 36.9484 | 1.83372 | ||||||||
\(407\) | 3.65148 | 0.180997 | ||||||||
\(408\) | 3.42831 | 0.169727 | ||||||||
\(409\) | 27.8153 | 1.37538 | 0.687690 | − | 0.726004i | \(-0.258625\pi\) | ||||
0.687690 | + | 0.726004i | \(0.258625\pi\) | |||||||
\(410\) | −139.244 | −6.87676 | ||||||||
\(411\) | 1.88875 | 0.0931650 | ||||||||
\(412\) | −19.8187 | −0.976397 | ||||||||
\(413\) | −27.1485 | −1.33589 | ||||||||
\(414\) | 45.7753 | 2.24973 | ||||||||
\(415\) | −1.68934 | −0.0829266 | ||||||||
\(416\) | −33.2833 | −1.63185 | ||||||||
\(417\) | 0.579753 | 0.0283906 | ||||||||
\(418\) | 1.67816 | 0.0820815 | ||||||||
\(419\) | −23.4932 | −1.14772 | −0.573860 | − | 0.818953i | \(-0.694555\pi\) | ||||
−0.573860 | + | 0.818953i | \(0.694555\pi\) | |||||||
\(420\) | −16.4485 | −0.802603 | ||||||||
\(421\) | 3.66561 | 0.178651 | 0.0893254 | − | 0.996002i | \(-0.471529\pi\) | ||||
0.0893254 | + | 0.996002i | \(0.471529\pi\) | |||||||
\(422\) | −3.71402 | −0.180795 | ||||||||
\(423\) | −2.87689 | −0.139879 | ||||||||
\(424\) | 20.8693 | 1.01350 | ||||||||
\(425\) | −13.6105 | −0.660206 | ||||||||
\(426\) | −9.28510 | −0.449865 | ||||||||
\(427\) | −2.10997 | −0.102109 | ||||||||
\(428\) | −63.4143 | −3.06525 | ||||||||
\(429\) | 0.200172 | 0.00966438 | ||||||||
\(430\) | 74.2008 | 3.57828 | ||||||||
\(431\) | −23.0348 | −1.10955 | −0.554774 | − | 0.832001i | \(-0.687195\pi\) | ||||
−0.554774 | + | 0.832001i | \(0.687195\pi\) | |||||||
\(432\) | −32.4699 | −1.56221 | ||||||||
\(433\) | −3.61439 | −0.173696 | −0.0868482 | − | 0.996222i | \(-0.527680\pi\) | ||||
−0.0868482 | + | 0.996222i | \(0.527680\pi\) | |||||||
\(434\) | −9.01130 | −0.432556 | ||||||||
\(435\) | 10.4012 | 0.498698 | ||||||||
\(436\) | −5.82391 | −0.278915 | ||||||||
\(437\) | −8.68598 | −0.415507 | ||||||||
\(438\) | 2.58594 | 0.123561 | ||||||||
\(439\) | 2.78594 | 0.132966 | 0.0664828 | − | 0.997788i | \(-0.478822\pi\) | ||||
0.0664828 | + | 0.997788i | \(0.478822\pi\) | |||||||
\(440\) | −17.1518 | −0.817679 | ||||||||
\(441\) | 9.12847 | 0.434689 | ||||||||
\(442\) | 3.85363 | 0.183298 | ||||||||
\(443\) | −6.60108 | −0.313627 | −0.156813 | − | 0.987628i | \(-0.550122\pi\) | ||||
−0.156813 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(444\) | 17.4900 | 0.830041 | ||||||||
\(445\) | −11.6955 | −0.554421 | ||||||||
\(446\) | −58.5442 | −2.77215 | ||||||||
\(447\) | −0.421995 | −0.0199597 | ||||||||
\(448\) | −66.0377 | −3.11999 | ||||||||
\(449\) | −33.0598 | −1.56019 | −0.780094 | − | 0.625662i | \(-0.784829\pi\) | ||||
−0.780094 | + | 0.625662i | \(0.784829\pi\) | |||||||
\(450\) | 107.624 | 5.07345 | ||||||||
\(451\) | 4.77839 | 0.225006 | ||||||||
\(452\) | −11.4116 | −0.536754 | ||||||||
\(453\) | −0.128354 | −0.00603059 | ||||||||
\(454\) | 25.3398 | 1.18925 | ||||||||
\(455\) | −11.8321 | −0.554699 | ||||||||
\(456\) | 5.14403 | 0.240891 | ||||||||
\(457\) | −3.88614 | −0.181786 | −0.0908930 | − | 0.995861i | \(-0.528972\pi\) | ||||
−0.0908930 | + | 0.995861i | \(0.528972\pi\) | |||||||
\(458\) | −0.0736076 | −0.00343946 | ||||||||
\(459\) | 2.06203 | 0.0962474 | ||||||||
\(460\) | 138.722 | 6.46796 | ||||||||
\(461\) | 15.6610 | 0.729407 | 0.364703 | − | 0.931124i | \(-0.381170\pi\) | ||||
0.364703 | + | 0.931124i | \(0.381170\pi\) | |||||||
\(462\) | 0.767689 | 0.0357161 | ||||||||
\(463\) | −30.0299 | −1.39561 | −0.697804 | − | 0.716288i | \(-0.745840\pi\) | ||||
−0.697804 | + | 0.716288i | \(0.745840\pi\) | |||||||
\(464\) | 108.203 | 5.02322 | ||||||||
\(465\) | −2.53673 | −0.117638 | ||||||||
\(466\) | 7.93495 | 0.367579 | ||||||||
\(467\) | −37.6970 | −1.74441 | −0.872204 | − | 0.489142i | \(-0.837310\pi\) | ||||
−0.872204 | + | 0.489142i | \(0.837310\pi\) | |||||||
\(468\) | −22.4053 | −1.03569 | ||||||||
\(469\) | 21.0225 | 0.970727 | ||||||||
\(470\) | −11.8575 | −0.546944 | ||||||||
\(471\) | −4.70259 | −0.216684 | ||||||||
\(472\) | −135.597 | −6.24137 | ||||||||
\(473\) | −2.54633 | −0.117080 | ||||||||
\(474\) | −13.0838 | −0.600961 | ||||||||
\(475\) | −20.4219 | −0.937022 | ||||||||
\(476\) | 10.8667 | 0.498076 | ||||||||
\(477\) | 6.14466 | 0.281345 | ||||||||
\(478\) | 71.4630 | 3.26864 | ||||||||
\(479\) | 3.47398 | 0.158730 | 0.0793651 | − | 0.996846i | \(-0.474711\pi\) | ||||
0.0793651 | + | 0.996846i | \(0.474711\pi\) | |||||||
\(480\) | −35.9332 | −1.64012 | ||||||||
\(481\) | 12.5814 | 0.573662 | ||||||||
\(482\) | 30.8152 | 1.40359 | ||||||||
\(483\) | −3.97348 | −0.180800 | ||||||||
\(484\) | −60.1835 | −2.73561 | ||||||||
\(485\) | −53.2521 | −2.41805 | ||||||||
\(486\) | −24.6289 | −1.11719 | ||||||||
\(487\) | 7.00218 | 0.317299 | 0.158650 | − | 0.987335i | \(-0.449286\pi\) | ||||
0.158650 | + | 0.987335i | \(0.449286\pi\) | |||||||
\(488\) | −10.5386 | −0.477058 | ||||||||
\(489\) | 2.97794 | 0.134667 | ||||||||
\(490\) | 37.6241 | 1.69968 | ||||||||
\(491\) | 1.89534 | 0.0855356 | 0.0427678 | − | 0.999085i | \(-0.486382\pi\) | ||||
0.0427678 | + | 0.999085i | \(0.486382\pi\) | |||||||
\(492\) | 22.8878 | 1.03186 | ||||||||
\(493\) | −6.87157 | −0.309480 | ||||||||
\(494\) | 5.78219 | 0.260153 | ||||||||
\(495\) | −5.05010 | −0.226985 | ||||||||
\(496\) | −26.3896 | −1.18493 | ||||||||
\(497\) | −18.8345 | −0.844842 | ||||||||
\(498\) | 0.377658 | 0.0169233 | ||||||||
\(499\) | 35.0912 | 1.57090 | 0.785449 | − | 0.618926i | \(-0.212432\pi\) | ||||
0.785449 | + | 0.618926i | \(0.212432\pi\) | |||||||
\(500\) | 206.338 | 9.22770 | ||||||||
\(501\) | 1.95249 | 0.0872309 | ||||||||
\(502\) | 56.5164 | 2.52245 | ||||||||
\(503\) | −27.6667 | −1.23360 | −0.616799 | − | 0.787121i | \(-0.711571\pi\) | ||||
−0.616799 | + | 0.787121i | \(0.711571\pi\) | |||||||
\(504\) | −54.9899 | −2.44944 | ||||||||
\(505\) | 32.0040 | 1.42416 | ||||||||
\(506\) | −6.47450 | −0.287827 | ||||||||
\(507\) | −3.87162 | −0.171945 | ||||||||
\(508\) | −70.2172 | −3.11538 | ||||||||
\(509\) | −9.29983 | −0.412208 | −0.206104 | − | 0.978530i | \(-0.566078\pi\) | ||||
−0.206104 | + | 0.978530i | \(0.566078\pi\) | |||||||
\(510\) | 4.16044 | 0.184227 | ||||||||
\(511\) | 5.24547 | 0.232046 | ||||||||
\(512\) | −66.0987 | −2.92118 | ||||||||
\(513\) | 3.09399 | 0.136603 | ||||||||
\(514\) | 43.6714 | 1.92626 | ||||||||
\(515\) | −15.3916 | −0.678233 | ||||||||
\(516\) | −12.1965 | −0.536922 | ||||||||
\(517\) | 0.406909 | 0.0178959 | ||||||||
\(518\) | 48.2516 | 2.12005 | ||||||||
\(519\) | 6.64163 | 0.291535 | ||||||||
\(520\) | −59.0974 | −2.59159 | ||||||||
\(521\) | −14.5550 | −0.637665 | −0.318832 | − | 0.947811i | \(-0.603291\pi\) | ||||
−0.318832 | + | 0.947811i | \(0.603291\pi\) | |||||||
\(522\) | 54.3365 | 2.37824 | ||||||||
\(523\) | −12.3264 | −0.538994 | −0.269497 | − | 0.963001i | \(-0.586857\pi\) | ||||
−0.269497 | + | 0.963001i | \(0.586857\pi\) | |||||||
\(524\) | −93.9408 | −4.10382 | ||||||||
\(525\) | −9.34220 | −0.407727 | ||||||||
\(526\) | 24.0694 | 1.04948 | ||||||||
\(527\) | 1.67590 | 0.0730032 | ||||||||
\(528\) | 2.24818 | 0.0978395 | ||||||||
\(529\) | 10.5113 | 0.457014 | ||||||||
\(530\) | 25.3260 | 1.10009 | ||||||||
\(531\) | −39.9247 | −1.73259 | ||||||||
\(532\) | 16.3050 | 0.706913 | ||||||||
\(533\) | 16.4642 | 0.713145 | ||||||||
\(534\) | 2.61458 | 0.113144 | ||||||||
\(535\) | −49.2487 | −2.12921 | ||||||||
\(536\) | 105.000 | 4.53530 | ||||||||
\(537\) | 3.76698 | 0.162557 | ||||||||
\(538\) | −47.3570 | −2.04170 | ||||||||
\(539\) | −1.29114 | −0.0556132 | ||||||||
\(540\) | −49.4135 | −2.12642 | ||||||||
\(541\) | 31.7045 | 1.36308 | 0.681541 | − | 0.731780i | \(-0.261310\pi\) | ||||
0.681541 | + | 0.731780i | \(0.261310\pi\) | |||||||
\(542\) | 37.1710 | 1.59663 | ||||||||
\(543\) | 6.01702 | 0.258215 | ||||||||
\(544\) | 23.7394 | 1.01782 | ||||||||
\(545\) | −4.52296 | −0.193742 | ||||||||
\(546\) | 2.64512 | 0.113201 | ||||||||
\(547\) | 26.0380 | 1.11330 | 0.556652 | − | 0.830745i | \(-0.312086\pi\) | ||||
0.556652 | + | 0.830745i | \(0.312086\pi\) | |||||||
\(548\) | 29.9018 | 1.27734 | ||||||||
\(549\) | −3.10293 | −0.132430 | ||||||||
\(550\) | −15.2224 | −0.649087 | ||||||||
\(551\) | −10.3105 | −0.439241 | ||||||||
\(552\) | −19.8461 | −0.844708 | ||||||||
\(553\) | −26.5401 | −1.12860 | ||||||||
\(554\) | −62.4755 | −2.65433 | ||||||||
\(555\) | 13.5831 | 0.576570 | ||||||||
\(556\) | 9.17839 | 0.389251 | ||||||||
\(557\) | 24.3865 | 1.03329 | 0.516645 | − | 0.856200i | \(-0.327181\pi\) | ||||
0.516645 | + | 0.856200i | \(0.327181\pi\) | |||||||
\(558\) | −13.2521 | −0.561004 | ||||||||
\(559\) | −8.77353 | −0.371081 | ||||||||
\(560\) | −132.890 | −5.61562 | ||||||||
\(561\) | −0.142773 | −0.00602787 | ||||||||
\(562\) | 74.9967 | 3.16355 | ||||||||
\(563\) | −9.89978 | −0.417226 | −0.208613 | − | 0.977998i | \(-0.566895\pi\) | ||||
−0.208613 | + | 0.977998i | \(0.566895\pi\) | |||||||
\(564\) | 1.94903 | 0.0820691 | ||||||||
\(565\) | −8.86242 | −0.372845 | ||||||||
\(566\) | 22.6610 | 0.952515 | ||||||||
\(567\) | −15.4685 | −0.649615 | ||||||||
\(568\) | −94.0716 | −3.94716 | ||||||||
\(569\) | −0.423335 | −0.0177471 | −0.00887357 | − | 0.999961i | \(-0.502825\pi\) | ||||
−0.00887357 | + | 0.999961i | \(0.502825\pi\) | |||||||
\(570\) | 6.24255 | 0.261472 | ||||||||
\(571\) | 6.43127 | 0.269140 | 0.134570 | − | 0.990904i | \(-0.457035\pi\) | ||||
0.134570 | + | 0.990904i | \(0.457035\pi\) | |||||||
\(572\) | 3.16903 | 0.132504 | ||||||||
\(573\) | −5.56912 | −0.232653 | ||||||||
\(574\) | 63.1428 | 2.63553 | ||||||||
\(575\) | 78.7897 | 3.28576 | ||||||||
\(576\) | −97.1154 | −4.04647 | ||||||||
\(577\) | −24.7007 | −1.02830 | −0.514151 | − | 0.857700i | \(-0.671893\pi\) | ||||
−0.514151 | + | 0.857700i | \(0.671893\pi\) | |||||||
\(578\) | −2.74861 | −0.114327 | ||||||||
\(579\) | 4.12386 | 0.171382 | ||||||||
\(580\) | 164.667 | 6.83742 | ||||||||
\(581\) | 0.766066 | 0.0317818 | ||||||||
\(582\) | 11.9047 | 0.493466 | ||||||||
\(583\) | −0.869106 | −0.0359947 | ||||||||
\(584\) | 26.1993 | 1.08413 | ||||||||
\(585\) | −17.4004 | −0.719418 | ||||||||
\(586\) | −28.9146 | −1.19445 | ||||||||
\(587\) | 41.1627 | 1.69897 | 0.849483 | − | 0.527616i | \(-0.176914\pi\) | ||||
0.849483 | + | 0.527616i | \(0.176914\pi\) | |||||||
\(588\) | −6.18435 | −0.255038 | ||||||||
\(589\) | 2.51461 | 0.103613 | ||||||||
\(590\) | −164.555 | −6.77461 | ||||||||
\(591\) | −0.272655 | −0.0112155 | ||||||||
\(592\) | 141.305 | 5.80759 | ||||||||
\(593\) | 30.8520 | 1.26694 | 0.633470 | − | 0.773767i | \(-0.281630\pi\) | ||||
0.633470 | + | 0.773767i | \(0.281630\pi\) | |||||||
\(594\) | 2.30625 | 0.0946264 | ||||||||
\(595\) | 8.43930 | 0.345977 | ||||||||
\(596\) | −6.68084 | −0.273658 | ||||||||
\(597\) | 4.15017 | 0.169855 | ||||||||
\(598\) | −22.3083 | −0.912252 | ||||||||
\(599\) | 5.72917 | 0.234088 | 0.117044 | − | 0.993127i | \(-0.462658\pi\) | ||||
0.117044 | + | 0.993127i | \(0.462658\pi\) | |||||||
\(600\) | −46.6610 | −1.90493 | ||||||||
\(601\) | −41.5788 | −1.69603 | −0.848017 | − | 0.529968i | \(-0.822204\pi\) | ||||
−0.848017 | + | 0.529968i | \(0.822204\pi\) | |||||||
\(602\) | −33.6478 | −1.37138 | ||||||||
\(603\) | 30.9157 | 1.25899 | ||||||||
\(604\) | −2.03204 | −0.0826825 | ||||||||
\(605\) | −46.7396 | −1.90023 | ||||||||
\(606\) | −7.15461 | −0.290636 | ||||||||
\(607\) | −1.47724 | −0.0599592 | −0.0299796 | − | 0.999551i | \(-0.509544\pi\) | ||||
−0.0299796 | + | 0.999551i | \(0.509544\pi\) | |||||||
\(608\) | 35.6198 | 1.44458 | ||||||||
\(609\) | −4.71662 | −0.191127 | ||||||||
\(610\) | −12.7891 | −0.517816 | ||||||||
\(611\) | 1.40203 | 0.0567200 | ||||||||
\(612\) | 15.9807 | 0.645980 | ||||||||
\(613\) | 11.1506 | 0.450370 | 0.225185 | − | 0.974316i | \(-0.427701\pi\) | ||||
0.225185 | + | 0.974316i | \(0.427701\pi\) | |||||||
\(614\) | 62.4865 | 2.52175 | ||||||||
\(615\) | 17.7751 | 0.716759 | ||||||||
\(616\) | 7.77781 | 0.313377 | ||||||||
\(617\) | −26.8750 | −1.08195 | −0.540974 | − | 0.841039i | \(-0.681944\pi\) | ||||
−0.540974 | + | 0.841039i | \(0.681944\pi\) | |||||||
\(618\) | 3.44084 | 0.138411 | ||||||||
\(619\) | −34.5972 | −1.39058 | −0.695290 | − | 0.718729i | \(-0.744724\pi\) | ||||
−0.695290 | + | 0.718729i | \(0.744724\pi\) | |||||||
\(620\) | −40.1604 | −1.61288 | ||||||||
\(621\) | −11.9369 | −0.479011 | ||||||||
\(622\) | 40.3623 | 1.61838 | ||||||||
\(623\) | 5.30357 | 0.212483 | ||||||||
\(624\) | 7.74623 | 0.310097 | ||||||||
\(625\) | 92.1931 | 3.68772 | ||||||||
\(626\) | 13.9157 | 0.556185 | ||||||||
\(627\) | −0.214224 | −0.00855529 | ||||||||
\(628\) | −74.4494 | −2.97085 | ||||||||
\(629\) | −8.97370 | −0.357805 | ||||||||
\(630\) | −66.7332 | −2.65871 | ||||||||
\(631\) | −11.7872 | −0.469241 | −0.234621 | − | 0.972087i | \(-0.575385\pi\) | ||||
−0.234621 | + | 0.972087i | \(0.575385\pi\) | |||||||
\(632\) | −132.558 | −5.27289 | ||||||||
\(633\) | 0.474110 | 0.0188442 | ||||||||
\(634\) | −30.4027 | −1.20744 | ||||||||
\(635\) | −54.5319 | −2.16403 | ||||||||
\(636\) | −4.16288 | −0.165069 | ||||||||
\(637\) | −4.44869 | −0.176263 | ||||||||
\(638\) | −7.68539 | −0.304268 | ||||||||
\(639\) | −27.6981 | −1.09572 | ||||||||
\(640\) | −195.450 | −7.72586 | ||||||||
\(641\) | −18.2278 | −0.719955 | −0.359977 | − | 0.932961i | \(-0.617216\pi\) | ||||
−0.359977 | + | 0.932961i | \(0.617216\pi\) | |||||||
\(642\) | 11.0097 | 0.434519 | ||||||||
\(643\) | −20.4687 | −0.807207 | −0.403604 | − | 0.914934i | \(-0.632243\pi\) | ||||
−0.403604 | + | 0.914934i | \(0.632243\pi\) | |||||||
\(644\) | −62.9063 | −2.47886 | ||||||||
\(645\) | −9.47205 | −0.372961 | ||||||||
\(646\) | −4.12416 | −0.162263 | ||||||||
\(647\) | −14.3087 | −0.562533 | −0.281267 | − | 0.959630i | \(-0.590755\pi\) | ||||
−0.281267 | + | 0.959630i | \(0.590755\pi\) | |||||||
\(648\) | −77.2597 | −3.03505 | ||||||||
\(649\) | 5.64698 | 0.221664 | ||||||||
\(650\) | −52.4498 | −2.05725 | ||||||||
\(651\) | 1.15033 | 0.0450850 | ||||||||
\(652\) | 47.1454 | 1.84636 | ||||||||
\(653\) | 25.5265 | 0.998927 | 0.499464 | − | 0.866335i | \(-0.333530\pi\) | ||||
0.499464 | + | 0.866335i | \(0.333530\pi\) | |||||||
\(654\) | 1.01112 | 0.0395380 | ||||||||
\(655\) | −72.9561 | −2.85063 | ||||||||
\(656\) | 184.914 | 7.21968 | ||||||||
\(657\) | 7.71401 | 0.300952 | ||||||||
\(658\) | 5.37700 | 0.209617 | ||||||||
\(659\) | 13.0927 | 0.510018 | 0.255009 | − | 0.966939i | \(-0.417922\pi\) | ||||
0.255009 | + | 0.966939i | \(0.417922\pi\) | |||||||
\(660\) | 3.42134 | 0.133175 | ||||||||
\(661\) | −15.4120 | −0.599458 | −0.299729 | − | 0.954024i | \(-0.596896\pi\) | ||||
−0.299729 | + | 0.954024i | \(0.596896\pi\) | |||||||
\(662\) | 83.3575 | 3.23978 | ||||||||
\(663\) | −0.491932 | −0.0191051 | ||||||||
\(664\) | 3.82623 | 0.148487 | ||||||||
\(665\) | 12.6628 | 0.491042 | ||||||||
\(666\) | 70.9590 | 2.74960 | ||||||||
\(667\) | 39.7788 | 1.54024 | ||||||||
\(668\) | 30.9110 | 1.19598 | ||||||||
\(669\) | 7.47342 | 0.288939 | ||||||||
\(670\) | 127.423 | 4.92278 | ||||||||
\(671\) | 0.438881 | 0.0169428 | ||||||||
\(672\) | 16.2946 | 0.628579 | ||||||||
\(673\) | 14.9941 | 0.577980 | 0.288990 | − | 0.957332i | \(-0.406681\pi\) | ||||
0.288990 | + | 0.957332i | \(0.406681\pi\) | |||||||
\(674\) | 67.8493 | 2.61346 | ||||||||
\(675\) | −28.0653 | −1.08023 | ||||||||
\(676\) | −61.2938 | −2.35745 | ||||||||
\(677\) | 42.6395 | 1.63877 | 0.819384 | − | 0.573245i | \(-0.194316\pi\) | ||||
0.819384 | + | 0.573245i | \(0.194316\pi\) | |||||||
\(678\) | 1.98123 | 0.0760885 | ||||||||
\(679\) | 24.1482 | 0.926724 | ||||||||
\(680\) | 42.1513 | 1.61643 | ||||||||
\(681\) | −3.23473 | −0.123955 | ||||||||
\(682\) | 1.87438 | 0.0717737 | ||||||||
\(683\) | −9.51113 | −0.363933 | −0.181967 | − | 0.983305i | \(-0.558246\pi\) | ||||
−0.181967 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(684\) | 23.9783 | 0.916831 | ||||||||
\(685\) | 23.2223 | 0.887277 | ||||||||
\(686\) | −54.7004 | −2.08847 | ||||||||
\(687\) | 0.00939632 | 0.000358492 0 | ||||||||
\(688\) | −98.5377 | −3.75672 | ||||||||
\(689\) | −2.99455 | −0.114083 | ||||||||
\(690\) | −24.0844 | −0.916876 | ||||||||
\(691\) | 37.1334 | 1.41262 | 0.706311 | − | 0.707902i | \(-0.250358\pi\) | ||||
0.706311 | + | 0.707902i | \(0.250358\pi\) | |||||||
\(692\) | 105.147 | 3.99710 | ||||||||
\(693\) | 2.29007 | 0.0869925 | ||||||||
\(694\) | −76.5739 | −2.90671 | ||||||||
\(695\) | 7.12811 | 0.270384 | ||||||||
\(696\) | −23.5579 | −0.892959 | ||||||||
\(697\) | −11.7431 | −0.444803 | ||||||||
\(698\) | 16.3656 | 0.619446 | ||||||||
\(699\) | −1.01293 | −0.0383125 | ||||||||
\(700\) | −147.901 | −5.59015 | ||||||||
\(701\) | −34.1038 | −1.28808 | −0.644041 | − | 0.764991i | \(-0.722743\pi\) | ||||
−0.644041 | + | 0.764991i | \(0.722743\pi\) | |||||||
\(702\) | 7.94630 | 0.299914 | ||||||||
\(703\) | −13.4646 | −0.507828 | ||||||||
\(704\) | 13.7361 | 0.517698 | ||||||||
\(705\) | 1.51365 | 0.0570075 | ||||||||
\(706\) | −17.1381 | −0.645002 | ||||||||
\(707\) | −14.5128 | −0.545812 | ||||||||
\(708\) | 27.0482 | 1.01653 | ||||||||
\(709\) | 2.08603 | 0.0783426 | 0.0391713 | − | 0.999233i | \(-0.487528\pi\) | ||||
0.0391713 | + | 0.999233i | \(0.487528\pi\) | |||||||
\(710\) | −114.161 | −4.28439 | ||||||||
\(711\) | −39.0300 | −1.46374 | ||||||||
\(712\) | 26.4895 | 0.992735 | ||||||||
\(713\) | −9.70160 | −0.363328 | ||||||||
\(714\) | −1.88663 | −0.0706055 | ||||||||
\(715\) | 2.46113 | 0.0920409 | ||||||||
\(716\) | 59.6371 | 2.22874 | ||||||||
\(717\) | −9.12256 | −0.340688 | ||||||||
\(718\) | −3.73320 | −0.139322 | ||||||||
\(719\) | −25.0163 | −0.932949 | −0.466474 | − | 0.884535i | \(-0.654476\pi\) | ||||
−0.466474 | + | 0.884535i | \(0.654476\pi\) | |||||||
\(720\) | −195.428 | −7.28318 | ||||||||
\(721\) | 6.97961 | 0.259934 | ||||||||
\(722\) | 46.0354 | 1.71326 | ||||||||
\(723\) | −3.93369 | −0.146295 | ||||||||
\(724\) | 95.2588 | 3.54026 | ||||||||
\(725\) | 93.5254 | 3.47345 | ||||||||
\(726\) | 10.4488 | 0.387791 | ||||||||
\(727\) | 38.4223 | 1.42500 | 0.712502 | − | 0.701670i | \(-0.247562\pi\) | ||||
0.712502 | + | 0.701670i | \(0.247562\pi\) | |||||||
\(728\) | 26.7989 | 0.993233 | ||||||||
\(729\) | −20.5775 | −0.762130 | ||||||||
\(730\) | 31.7943 | 1.17676 | ||||||||
\(731\) | 6.25773 | 0.231451 | ||||||||
\(732\) | 2.10217 | 0.0776985 | ||||||||
\(733\) | 9.33100 | 0.344648 | 0.172324 | − | 0.985040i | \(-0.444872\pi\) | ||||
0.172324 | + | 0.985040i | \(0.444872\pi\) | |||||||
\(734\) | −11.9118 | −0.439674 | ||||||||
\(735\) | −4.80288 | −0.177157 | ||||||||
\(736\) | −137.425 | −5.06554 | ||||||||
\(737\) | −4.37274 | −0.161072 | ||||||||
\(738\) | 92.8581 | 3.41816 | ||||||||
\(739\) | 37.2271 | 1.36942 | 0.684710 | − | 0.728816i | \(-0.259929\pi\) | ||||
0.684710 | + | 0.728816i | \(0.259929\pi\) | |||||||
\(740\) | 215.041 | 7.90508 | ||||||||
\(741\) | −0.738122 | −0.0271156 | ||||||||
\(742\) | −11.4846 | −0.421612 | ||||||||
\(743\) | 25.6971 | 0.942734 | 0.471367 | − | 0.881937i | \(-0.343761\pi\) | ||||
0.471367 | + | 0.881937i | \(0.343761\pi\) | |||||||
\(744\) | 5.74550 | 0.210640 | ||||||||
\(745\) | −5.18846 | −0.190091 | ||||||||
\(746\) | −19.5251 | −0.714865 | ||||||||
\(747\) | 1.12658 | 0.0412194 | ||||||||
\(748\) | −2.26032 | −0.0826453 | ||||||||
\(749\) | 22.3328 | 0.816023 | ||||||||
\(750\) | −35.8234 | −1.30809 | ||||||||
\(751\) | 3.69461 | 0.134818 | 0.0674090 | − | 0.997725i | \(-0.478527\pi\) | ||||
0.0674090 | + | 0.997725i | \(0.478527\pi\) | |||||||
\(752\) | 15.7465 | 0.574218 | ||||||||
\(753\) | −7.21455 | −0.262913 | ||||||||
\(754\) | −26.4805 | −0.964362 | ||||||||
\(755\) | −1.57812 | −0.0574336 | ||||||||
\(756\) | 22.4075 | 0.814954 | ||||||||
\(757\) | −50.3992 | −1.83179 | −0.915895 | − | 0.401418i | \(-0.868518\pi\) | ||||
−0.915895 | + | 0.401418i | \(0.868518\pi\) | |||||||
\(758\) | −8.64159 | −0.313877 | ||||||||
\(759\) | 0.826497 | 0.0299999 | ||||||||
\(760\) | 63.2462 | 2.29418 | ||||||||
\(761\) | −33.3475 | −1.20884 | −0.604422 | − | 0.796664i | \(-0.706596\pi\) | ||||
−0.604422 | + | 0.796664i | \(0.706596\pi\) | |||||||
\(762\) | 12.1908 | 0.441626 | ||||||||
\(763\) | 2.05102 | 0.0742521 | ||||||||
\(764\) | −88.1678 | −3.18980 | ||||||||
\(765\) | 12.4109 | 0.448716 | ||||||||
\(766\) | −75.6207 | −2.73229 | ||||||||
\(767\) | 19.4570 | 0.702552 | ||||||||
\(768\) | 20.0048 | 0.721863 | ||||||||
\(769\) | −21.3320 | −0.769253 | −0.384626 | − | 0.923072i | \(-0.625670\pi\) | ||||
−0.384626 | + | 0.923072i | \(0.625670\pi\) | |||||||
\(770\) | 9.43880 | 0.340151 | ||||||||
\(771\) | −5.57484 | −0.200773 | ||||||||
\(772\) | 65.2872 | 2.34974 | ||||||||
\(773\) | −38.9994 | −1.40271 | −0.701355 | − | 0.712812i | \(-0.747421\pi\) | ||||
−0.701355 | + | 0.712812i | \(0.747421\pi\) | |||||||
\(774\) | −49.4826 | −1.77862 | ||||||||
\(775\) | −22.8098 | −0.819352 | ||||||||
\(776\) | 120.612 | 4.32972 | ||||||||
\(777\) | −6.15952 | −0.220971 | ||||||||
\(778\) | 84.1703 | 3.01765 | ||||||||
\(779\) | −17.6201 | −0.631304 | ||||||||
\(780\) | 11.7884 | 0.422093 | ||||||||
\(781\) | 3.91764 | 0.140184 | ||||||||
\(782\) | 15.9114 | 0.568990 | ||||||||
\(783\) | −14.1694 | −0.506373 | ||||||||
\(784\) | −49.9643 | −1.78444 | ||||||||
\(785\) | −57.8187 | −2.06364 | ||||||||
\(786\) | 16.3096 | 0.581744 | ||||||||
\(787\) | −26.0410 | −0.928260 | −0.464130 | − | 0.885767i | \(-0.653633\pi\) | ||||
−0.464130 | + | 0.885767i | \(0.653633\pi\) | |||||||
\(788\) | −4.31655 | −0.153771 | ||||||||
\(789\) | −3.07256 | −0.109386 | ||||||||
\(790\) | −160.867 | −5.72338 | ||||||||
\(791\) | 4.01884 | 0.142894 | ||||||||
\(792\) | 11.4381 | 0.406435 | ||||||||
\(793\) | 1.51219 | 0.0536994 | ||||||||
\(794\) | 24.7132 | 0.877039 | ||||||||
\(795\) | −3.23297 | −0.114662 | ||||||||
\(796\) | 65.7037 | 2.32881 | ||||||||
\(797\) | −39.3971 | −1.39552 | −0.697758 | − | 0.716334i | \(-0.745819\pi\) | ||||
−0.697758 | + | 0.716334i | \(0.745819\pi\) | |||||||
\(798\) | −2.83081 | −0.100210 | ||||||||
\(799\) | −1.00000 | −0.0353775 | ||||||||
\(800\) | −323.104 | −11.4235 | ||||||||
\(801\) | 7.79946 | 0.275580 | ||||||||
\(802\) | −98.4289 | −3.47565 | ||||||||
\(803\) | −1.09108 | −0.0385032 | ||||||||
\(804\) | −20.9448 | −0.738665 | ||||||||
\(805\) | −48.8542 | −1.72188 | ||||||||
\(806\) | 6.45828 | 0.227483 | ||||||||
\(807\) | 6.04532 | 0.212805 | ||||||||
\(808\) | −72.4866 | −2.55007 | ||||||||
\(809\) | 46.8692 | 1.64783 | 0.823917 | − | 0.566710i | \(-0.191784\pi\) | ||||
0.823917 | + | 0.566710i | \(0.191784\pi\) | |||||||
\(810\) | −93.7588 | −3.29435 | ||||||||
\(811\) | 10.8519 | 0.381062 | 0.190531 | − | 0.981681i | \(-0.438979\pi\) | ||||
0.190531 | + | 0.981681i | \(0.438979\pi\) | |||||||
\(812\) | −74.6714 | −2.62045 | ||||||||
\(813\) | −4.74504 | −0.166416 | ||||||||
\(814\) | −10.0365 | −0.351779 | ||||||||
\(815\) | 36.6140 | 1.28253 | ||||||||
\(816\) | −5.52501 | −0.193414 | ||||||||
\(817\) | 9.38945 | 0.328495 | ||||||||
\(818\) | −76.4534 | −2.67313 | ||||||||
\(819\) | 7.89056 | 0.275718 | ||||||||
\(820\) | 281.407 | 9.82715 | ||||||||
\(821\) | 20.3411 | 0.709910 | 0.354955 | − | 0.934883i | \(-0.384496\pi\) | ||||
0.354955 | + | 0.934883i | \(0.384496\pi\) | |||||||
\(822\) | −5.19142 | −0.181072 | ||||||||
\(823\) | −42.5915 | −1.48465 | −0.742324 | − | 0.670041i | \(-0.766276\pi\) | ||||
−0.742324 | + | 0.670041i | \(0.766276\pi\) | |||||||
\(824\) | 34.8607 | 1.21443 | ||||||||
\(825\) | 1.94321 | 0.0676538 | ||||||||
\(826\) | 74.6206 | 2.59638 | ||||||||
\(827\) | −18.0281 | −0.626898 | −0.313449 | − | 0.949605i | \(-0.601485\pi\) | ||||
−0.313449 | + | 0.949605i | \(0.601485\pi\) | |||||||
\(828\) | −92.5104 | −3.21496 | ||||||||
\(829\) | −20.3525 | −0.706870 | −0.353435 | − | 0.935459i | \(-0.614987\pi\) | ||||
−0.353435 | + | 0.935459i | \(0.614987\pi\) | |||||||
\(830\) | 4.64334 | 0.161173 | ||||||||
\(831\) | 7.97527 | 0.276659 | ||||||||
\(832\) | 47.3284 | 1.64082 | ||||||||
\(833\) | 3.17303 | 0.109939 | ||||||||
\(834\) | −1.59351 | −0.0551788 | ||||||||
\(835\) | 24.0060 | 0.830763 | ||||||||
\(836\) | −3.39150 | −0.117298 | ||||||||
\(837\) | 3.45575 | 0.119448 | ||||||||
\(838\) | 64.5737 | 2.23066 | ||||||||
\(839\) | 52.2392 | 1.80350 | 0.901749 | − | 0.432261i | \(-0.142284\pi\) | ||||
0.901749 | + | 0.432261i | \(0.142284\pi\) | |||||||
\(840\) | 28.9325 | 0.998267 | ||||||||
\(841\) | 18.2184 | 0.628222 | ||||||||
\(842\) | −10.0753 | −0.347218 | ||||||||
\(843\) | −9.57365 | −0.329734 | ||||||||
\(844\) | 7.50590 | 0.258364 | ||||||||
\(845\) | −47.6019 | −1.63755 | ||||||||
\(846\) | 7.90744 | 0.271863 | ||||||||
\(847\) | 21.1950 | 0.728268 | ||||||||
\(848\) | −33.6326 | −1.15495 | ||||||||
\(849\) | −2.89278 | −0.0992799 | ||||||||
\(850\) | 37.4099 | 1.28315 | ||||||||
\(851\) | 51.9478 | 1.78075 | ||||||||
\(852\) | 18.7649 | 0.642874 | ||||||||
\(853\) | 19.8078 | 0.678206 | 0.339103 | − | 0.940749i | \(-0.389876\pi\) | ||||
0.339103 | + | 0.940749i | \(0.389876\pi\) | |||||||
\(854\) | 5.79948 | 0.198454 | ||||||||
\(855\) | 18.6219 | 0.636857 | ||||||||
\(856\) | 111.545 | 3.81251 | ||||||||
\(857\) | 26.4493 | 0.903491 | 0.451745 | − | 0.892147i | \(-0.350802\pi\) | ||||
0.451745 | + | 0.892147i | \(0.350802\pi\) | |||||||
\(858\) | −0.550193 | −0.0187833 | ||||||||
\(859\) | 10.5925 | 0.361412 | 0.180706 | − | 0.983537i | \(-0.442162\pi\) | ||||
0.180706 | + | 0.983537i | \(0.442162\pi\) | |||||||
\(860\) | −149.957 | −5.11350 | ||||||||
\(861\) | −8.06045 | −0.274699 | ||||||||
\(862\) | 63.3137 | 2.15647 | ||||||||
\(863\) | 51.8825 | 1.76610 | 0.883051 | − | 0.469277i | \(-0.155486\pi\) | ||||
0.883051 | + | 0.469277i | \(0.155486\pi\) | |||||||
\(864\) | 48.9513 | 1.66536 | ||||||||
\(865\) | 81.6593 | 2.77650 | ||||||||
\(866\) | 9.93453 | 0.337589 | ||||||||
\(867\) | 0.350871 | 0.0119162 | ||||||||
\(868\) | 18.2115 | 0.618139 | ||||||||
\(869\) | 5.52043 | 0.187268 | ||||||||
\(870\) | −28.5888 | −0.969249 | ||||||||
\(871\) | −15.0665 | −0.510510 | ||||||||
\(872\) | 10.2442 | 0.346911 | ||||||||
\(873\) | 35.5125 | 1.20192 | ||||||||
\(874\) | 23.8743 | 0.807561 | ||||||||
\(875\) | −72.6665 | −2.45658 | ||||||||
\(876\) | −5.22609 | −0.176573 | ||||||||
\(877\) | 20.7211 | 0.699702 | 0.349851 | − | 0.936805i | \(-0.386232\pi\) | ||||
0.349851 | + | 0.936805i | \(0.386232\pi\) | |||||||
\(878\) | −7.65745 | −0.258426 | ||||||||
\(879\) | 3.69108 | 0.124497 | ||||||||
\(880\) | 27.6415 | 0.931796 | ||||||||
\(881\) | 4.66339 | 0.157114 | 0.0785568 | − | 0.996910i | \(-0.474969\pi\) | ||||
0.0785568 | + | 0.996910i | \(0.474969\pi\) | |||||||
\(882\) | −25.0906 | −0.844843 | ||||||||
\(883\) | 44.6349 | 1.50208 | 0.751042 | − | 0.660254i | \(-0.229551\pi\) | ||||
0.751042 | + | 0.660254i | \(0.229551\pi\) | |||||||
\(884\) | −7.78805 | −0.261940 | ||||||||
\(885\) | 21.0061 | 0.706112 | ||||||||
\(886\) | 18.1438 | 0.609552 | ||||||||
\(887\) | −28.9999 | −0.973722 | −0.486861 | − | 0.873479i | \(-0.661858\pi\) | ||||
−0.486861 | + | 0.873479i | \(0.661858\pi\) | |||||||
\(888\) | −30.7646 | −1.03239 | ||||||||
\(889\) | 24.7286 | 0.829370 | ||||||||
\(890\) | 32.1464 | 1.07755 | ||||||||
\(891\) | 3.21750 | 0.107790 | ||||||||
\(892\) | 118.316 | 3.96151 | ||||||||
\(893\) | −1.50045 | −0.0502108 | ||||||||
\(894\) | 1.15990 | 0.0387928 | ||||||||
\(895\) | 46.3153 | 1.54815 | ||||||||
\(896\) | 88.6309 | 2.96095 | ||||||||
\(897\) | 2.84774 | 0.0950834 | ||||||||
\(898\) | 90.8683 | 3.03232 | ||||||||
\(899\) | −11.5160 | −0.384082 | ||||||||
\(900\) | −217.505 | −7.25015 | ||||||||
\(901\) | 2.13587 | 0.0711562 | ||||||||
\(902\) | −13.1339 | −0.437312 | ||||||||
\(903\) | 4.29529 | 0.142938 | ||||||||
\(904\) | 20.0727 | 0.667608 | ||||||||
\(905\) | 73.9797 | 2.45917 | ||||||||
\(906\) | 0.352794 | 0.0117208 | ||||||||
\(907\) | −21.6716 | −0.719594 | −0.359797 | − | 0.933031i | \(-0.617154\pi\) | ||||
−0.359797 | + | 0.933031i | \(0.617154\pi\) | |||||||
\(908\) | −51.2108 | −1.69949 | ||||||||
\(909\) | −21.3427 | −0.707891 | ||||||||
\(910\) | 32.5219 | 1.07809 | ||||||||
\(911\) | −27.5487 | −0.912729 | −0.456364 | − | 0.889793i | \(-0.650849\pi\) | ||||
−0.456364 | + | 0.889793i | \(0.650849\pi\) | |||||||
\(912\) | −8.29003 | −0.274510 | ||||||||
\(913\) | −0.159344 | −0.00527353 | ||||||||
\(914\) | 10.6815 | 0.353312 | ||||||||
\(915\) | 1.63258 | 0.0539716 | ||||||||
\(916\) | 0.148758 | 0.00491511 | ||||||||
\(917\) | 33.0834 | 1.09251 | ||||||||
\(918\) | −5.66771 | −0.187062 | ||||||||
\(919\) | 6.98726 | 0.230488 | 0.115244 | − | 0.993337i | \(-0.463235\pi\) | ||||
0.115244 | + | 0.993337i | \(0.463235\pi\) | |||||||
\(920\) | −244.010 | −8.04476 | ||||||||
\(921\) | −7.97667 | −0.262840 | ||||||||
\(922\) | −43.0460 | −1.41764 | ||||||||
\(923\) | 13.4984 | 0.444306 | ||||||||
\(924\) | −1.55147 | −0.0510397 | ||||||||
\(925\) | 122.137 | 4.01582 | ||||||||
\(926\) | 82.5404 | 2.71245 | ||||||||
\(927\) | 10.2642 | 0.337122 | ||||||||
\(928\) | −163.127 | −5.35490 | ||||||||
\(929\) | 56.1725 | 1.84296 | 0.921479 | − | 0.388427i | \(-0.126981\pi\) | ||||
0.921479 | + | 0.388427i | \(0.126981\pi\) | |||||||
\(930\) | 6.97247 | 0.228636 | ||||||||
\(931\) | 4.76099 | 0.156035 | ||||||||
\(932\) | −16.0363 | −0.525285 | ||||||||
\(933\) | −5.15242 | −0.168683 | ||||||||
\(934\) | 103.614 | 3.39036 | ||||||||
\(935\) | −1.75540 | −0.0574078 | ||||||||
\(936\) | 39.4106 | 1.28817 | ||||||||
\(937\) | −31.7554 | −1.03740 | −0.518702 | − | 0.854955i | \(-0.673584\pi\) | ||||
−0.518702 | + | 0.854955i | \(0.673584\pi\) | |||||||
\(938\) | −57.7824 | −1.88666 | ||||||||
\(939\) | −1.77640 | −0.0579707 | ||||||||
\(940\) | 23.9635 | 0.781603 | ||||||||
\(941\) | −22.6325 | −0.737799 | −0.368900 | − | 0.929469i | \(-0.620265\pi\) | ||||
−0.368900 | + | 0.929469i | \(0.620265\pi\) | |||||||
\(942\) | 12.9256 | 0.421138 | ||||||||
\(943\) | 67.9798 | 2.21373 | ||||||||
\(944\) | 218.527 | 7.11243 | ||||||||
\(945\) | 17.4021 | 0.566090 | ||||||||
\(946\) | 6.99886 | 0.227553 | ||||||||
\(947\) | −11.7369 | −0.381397 | −0.190699 | − | 0.981649i | \(-0.561075\pi\) | ||||
−0.190699 | + | 0.981649i | \(0.561075\pi\) | |||||||
\(948\) | 26.4420 | 0.858796 | ||||||||
\(949\) | −3.75936 | −0.122034 | ||||||||
\(950\) | 56.1319 | 1.82116 | ||||||||
\(951\) | 3.88103 | 0.125851 | ||||||||
\(952\) | −19.1144 | −0.619500 | ||||||||
\(953\) | 46.4149 | 1.50353 | 0.751764 | − | 0.659433i | \(-0.229203\pi\) | ||||
0.751764 | + | 0.659433i | \(0.229203\pi\) | |||||||
\(954\) | −16.8893 | −0.546810 | ||||||||
\(955\) | −68.4727 | −2.21572 | ||||||||
\(956\) | −144.424 | −4.67102 | ||||||||
\(957\) | 0.981073 | 0.0317136 | ||||||||
\(958\) | −9.54860 | −0.308501 | ||||||||
\(959\) | −10.5306 | −0.340051 | ||||||||
\(960\) | 51.0966 | 1.64913 | ||||||||
\(961\) | −28.1914 | −0.909399 | ||||||||
\(962\) | −34.5813 | −1.11495 | ||||||||
\(963\) | 32.8427 | 1.05834 | ||||||||
\(964\) | −62.2764 | −2.00579 | ||||||||
\(965\) | 50.7032 | 1.63219 | ||||||||
\(966\) | 10.9215 | 0.351394 | ||||||||
\(967\) | −13.5855 | −0.436882 | −0.218441 | − | 0.975850i | \(-0.570097\pi\) | ||||
−0.218441 | + | 0.975850i | \(0.570097\pi\) | |||||||
\(968\) | 105.862 | 3.40252 | ||||||||
\(969\) | 0.526467 | 0.0169125 | ||||||||
\(970\) | 146.369 | 4.69963 | ||||||||
\(971\) | −33.3713 | −1.07094 | −0.535468 | − | 0.844555i | \(-0.679865\pi\) | ||||
−0.535468 | + | 0.844555i | \(0.679865\pi\) | |||||||
\(972\) | 49.7741 | 1.59650 | ||||||||
\(973\) | −3.23238 | −0.103625 | ||||||||
\(974\) | −19.2462 | −0.616690 | ||||||||
\(975\) | 6.69544 | 0.214426 | ||||||||
\(976\) | 16.9838 | 0.543637 | ||||||||
\(977\) | −20.4950 | −0.655692 | −0.327846 | − | 0.944731i | \(-0.606323\pi\) | ||||
−0.327846 | + | 0.944731i | \(0.606323\pi\) | |||||||
\(978\) | −8.18519 | −0.261733 | ||||||||
\(979\) | −1.10316 | −0.0352572 | ||||||||
\(980\) | −76.0370 | −2.42891 | ||||||||
\(981\) | 3.01625 | 0.0963013 | ||||||||
\(982\) | −5.20955 | −0.166243 | ||||||||
\(983\) | −26.9348 | −0.859088 | −0.429544 | − | 0.903046i | \(-0.641326\pi\) | ||||
−0.429544 | + | 0.903046i | \(0.641326\pi\) | |||||||
\(984\) | −40.2591 | −1.28341 | ||||||||
\(985\) | −3.35231 | −0.106814 | ||||||||
\(986\) | 18.8872 | 0.601492 | ||||||||
\(987\) | −0.686397 | −0.0218482 | ||||||||
\(988\) | −11.6856 | −0.371769 | ||||||||
\(989\) | −36.2254 | −1.15190 | ||||||||
\(990\) | 13.8807 | 0.441159 | ||||||||
\(991\) | 9.19984 | 0.292243 | 0.146121 | − | 0.989267i | \(-0.453321\pi\) | ||||
0.146121 | + | 0.989267i | \(0.453321\pi\) | |||||||
\(992\) | 39.7847 | 1.26317 | ||||||||
\(993\) | −10.6409 | −0.337680 | ||||||||
\(994\) | 51.7686 | 1.64200 | ||||||||
\(995\) | 51.0267 | 1.61765 | ||||||||
\(996\) | −0.763235 | −0.0241840 | ||||||||
\(997\) | −7.35984 | −0.233088 | −0.116544 | − | 0.993186i | \(-0.537182\pi\) | ||||
−0.116544 | + | 0.993186i | \(0.537182\pi\) | |||||||
\(998\) | −96.4520 | −3.05313 | ||||||||
\(999\) | −18.5041 | −0.585442 |
(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 | 799.2.a.g.1.1 | ✓ | 20 | |
3.2 | odd | 2 | 7191.2.a.bb.1.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
799.2.a.g.1.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
7191.2.a.bb.1.20 | 20 | 3.2 | odd | 2 |