Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, 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("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29392 | 0.914937 | 0.457469 | − | 0.889226i | \(-0.348756\pi\) | ||||
0.457469 | + | 0.889226i | \(0.348756\pi\) | |||||||
\(3\) | 2.84985 | 1.64536 | 0.822680 | − | 0.568505i | \(-0.192478\pi\) | ||||
0.822680 | + | 0.568505i | \(0.192478\pi\) | |||||||
\(4\) | −0.325780 | −0.162890 | ||||||||
\(5\) | −3.15298 | −1.41006 | −0.705028 | − | 0.709180i | \(-0.749065\pi\) | ||||
−0.705028 | + | 0.709180i | \(0.749065\pi\) | |||||||
\(6\) | 3.68746 | 1.50540 | ||||||||
\(7\) | 5.03078 | 1.90145 | 0.950727 | − | 0.310028i | \(-0.100339\pi\) | ||||
0.950727 | + | 0.310028i | \(0.100339\pi\) | |||||||
\(8\) | −3.00937 | −1.06397 | ||||||||
\(9\) | 5.12162 | 1.70721 | ||||||||
\(10\) | −4.07969 | −1.29011 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.928422 | −0.268012 | ||||||||
\(13\) | 5.37940 | 1.49198 | 0.745989 | − | 0.665958i | \(-0.231977\pi\) | ||||
0.745989 | + | 0.665958i | \(0.231977\pi\) | |||||||
\(14\) | 6.50941 | 1.73971 | ||||||||
\(15\) | −8.98551 | −2.32005 | ||||||||
\(16\) | −3.24231 | −0.810577 | ||||||||
\(17\) | 3.74023 | 0.907139 | 0.453570 | − | 0.891221i | \(-0.350150\pi\) | ||||
0.453570 | + | 0.891221i | \(0.350150\pi\) | |||||||
\(18\) | 6.62696 | 1.56199 | ||||||||
\(19\) | 4.04082 | 0.927028 | 0.463514 | − | 0.886090i | \(-0.346588\pi\) | ||||
0.463514 | + | 0.886090i | \(0.346588\pi\) | |||||||
\(20\) | 1.02718 | 0.229684 | ||||||||
\(21\) | 14.3369 | 3.12858 | ||||||||
\(22\) | −1.29392 | −0.275864 | ||||||||
\(23\) | −8.31179 | −1.73313 | −0.866564 | − | 0.499065i | \(-0.833677\pi\) | ||||
−0.866564 | + | 0.499065i | \(0.833677\pi\) | |||||||
\(24\) | −8.57623 | −1.75062 | ||||||||
\(25\) | 4.94128 | 0.988256 | ||||||||
\(26\) | 6.96050 | 1.36507 | ||||||||
\(27\) | 6.04630 | 1.16361 | ||||||||
\(28\) | −1.63892 | −0.309728 | ||||||||
\(29\) | −2.39261 | −0.444296 | −0.222148 | − | 0.975013i | \(-0.571307\pi\) | ||||
−0.222148 | + | 0.975013i | \(0.571307\pi\) | |||||||
\(30\) | −11.6265 | −2.12270 | ||||||||
\(31\) | −7.43729 | −1.33578 | −0.667889 | − | 0.744261i | \(-0.732802\pi\) | ||||
−0.667889 | + | 0.744261i | \(0.732802\pi\) | |||||||
\(32\) | 1.82345 | 0.322344 | ||||||||
\(33\) | −2.84985 | −0.496095 | ||||||||
\(34\) | 4.83955 | 0.829976 | ||||||||
\(35\) | −15.8619 | −2.68116 | ||||||||
\(36\) | −1.66852 | −0.278087 | ||||||||
\(37\) | −1.77422 | −0.291679 | −0.145840 | − | 0.989308i | \(-0.546588\pi\) | ||||
−0.145840 | + | 0.989308i | \(0.546588\pi\) | |||||||
\(38\) | 5.22848 | 0.848172 | ||||||||
\(39\) | 15.3305 | 2.45484 | ||||||||
\(40\) | 9.48847 | 1.50026 | ||||||||
\(41\) | 0.711385 | 0.111100 | 0.0555498 | − | 0.998456i | \(-0.482309\pi\) | ||||
0.0555498 | + | 0.998456i | \(0.482309\pi\) | |||||||
\(42\) | 18.5508 | 2.86245 | ||||||||
\(43\) | −5.80652 | −0.885486 | −0.442743 | − | 0.896648i | \(-0.645995\pi\) | ||||
−0.442743 | + | 0.896648i | \(0.645995\pi\) | |||||||
\(44\) | 0.325780 | 0.0491131 | ||||||||
\(45\) | −16.1484 | −2.40726 | ||||||||
\(46\) | −10.7548 | −1.58570 | ||||||||
\(47\) | −1.38780 | −0.202432 | −0.101216 | − | 0.994864i | \(-0.532273\pi\) | ||||
−0.101216 | + | 0.994864i | \(0.532273\pi\) | |||||||
\(48\) | −9.24008 | −1.33369 | ||||||||
\(49\) | 18.3087 | 2.61553 | ||||||||
\(50\) | 6.39360 | 0.904192 | ||||||||
\(51\) | 10.6591 | 1.49257 | ||||||||
\(52\) | −1.75250 | −0.243028 | ||||||||
\(53\) | −5.60689 | −0.770166 | −0.385083 | − | 0.922882i | \(-0.625827\pi\) | ||||
−0.385083 | + | 0.922882i | \(0.625827\pi\) | |||||||
\(54\) | 7.82341 | 1.06463 | ||||||||
\(55\) | 3.15298 | 0.425148 | ||||||||
\(56\) | −15.1394 | −2.02309 | ||||||||
\(57\) | 11.5157 | 1.52529 | ||||||||
\(58\) | −3.09583 | −0.406503 | ||||||||
\(59\) | −7.84688 | −1.02158 | −0.510788 | − | 0.859707i | \(-0.670646\pi\) | ||||
−0.510788 | + | 0.859707i | \(0.670646\pi\) | |||||||
\(60\) | 2.92729 | 0.377912 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −9.62324 | −1.22215 | ||||||||
\(63\) | 25.7657 | 3.24618 | ||||||||
\(64\) | 8.84401 | 1.10550 | ||||||||
\(65\) | −16.9611 | −2.10377 | ||||||||
\(66\) | −3.68746 | −0.453895 | ||||||||
\(67\) | −13.8486 | −1.69188 | −0.845940 | − | 0.533279i | \(-0.820960\pi\) | ||||
−0.845940 | + | 0.533279i | \(0.820960\pi\) | |||||||
\(68\) | −1.21849 | −0.147764 | ||||||||
\(69\) | −23.6873 | −2.85162 | ||||||||
\(70\) | −20.5240 | −2.45309 | ||||||||
\(71\) | −5.49805 | −0.652498 | −0.326249 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326249 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(72\) | −15.4128 | −1.81642 | ||||||||
\(73\) | 2.39993 | 0.280891 | 0.140446 | − | 0.990088i | \(-0.455147\pi\) | ||||
0.140446 | + | 0.990088i | \(0.455147\pi\) | |||||||
\(74\) | −2.29569 | −0.266868 | ||||||||
\(75\) | 14.0819 | 1.62604 | ||||||||
\(76\) | −1.31642 | −0.151003 | ||||||||
\(77\) | −5.03078 | −0.573310 | ||||||||
\(78\) | 19.8364 | 2.24603 | ||||||||
\(79\) | 0.369632 | 0.0415869 | 0.0207934 | − | 0.999784i | \(-0.493381\pi\) | ||||
0.0207934 | + | 0.999784i | \(0.493381\pi\) | |||||||
\(80\) | 10.2229 | 1.14296 | ||||||||
\(81\) | 1.86616 | 0.207352 | ||||||||
\(82\) | 0.920473 | 0.101649 | ||||||||
\(83\) | 9.97158 | 1.09452 | 0.547261 | − | 0.836962i | \(-0.315670\pi\) | ||||
0.547261 | + | 0.836962i | \(0.315670\pi\) | |||||||
\(84\) | −4.67068 | −0.509613 | ||||||||
\(85\) | −11.7929 | −1.27912 | ||||||||
\(86\) | −7.51316 | −0.810164 | ||||||||
\(87\) | −6.81856 | −0.731026 | ||||||||
\(88\) | 3.00937 | 0.320799 | ||||||||
\(89\) | 7.27038 | 0.770658 | 0.385329 | − | 0.922779i | \(-0.374088\pi\) | ||||
0.385329 | + | 0.922779i | \(0.374088\pi\) | |||||||
\(90\) | −20.8947 | −2.20249 | ||||||||
\(91\) | 27.0626 | 2.83693 | ||||||||
\(92\) | 2.70781 | 0.282309 | ||||||||
\(93\) | −21.1951 | −2.19783 | ||||||||
\(94\) | −1.79570 | −0.185212 | ||||||||
\(95\) | −12.7406 | −1.30716 | ||||||||
\(96\) | 5.19656 | 0.530372 | ||||||||
\(97\) | −2.78798 | −0.283076 | −0.141538 | − | 0.989933i | \(-0.545205\pi\) | ||||
−0.141538 | + | 0.989933i | \(0.545205\pi\) | |||||||
\(98\) | 23.6899 | 2.39305 | ||||||||
\(99\) | −5.12162 | −0.514743 | ||||||||
\(100\) | −1.60977 | −0.160977 | ||||||||
\(101\) | 7.38635 | 0.734970 | 0.367485 | − | 0.930030i | \(-0.380219\pi\) | ||||
0.367485 | + | 0.930030i | \(0.380219\pi\) | |||||||
\(102\) | 13.7920 | 1.36561 | ||||||||
\(103\) | 13.7508 | 1.35491 | 0.677453 | − | 0.735566i | \(-0.263084\pi\) | ||||
0.677453 | + | 0.735566i | \(0.263084\pi\) | |||||||
\(104\) | −16.1886 | −1.58742 | ||||||||
\(105\) | −45.2041 | −4.41147 | ||||||||
\(106\) | −7.25485 | −0.704653 | ||||||||
\(107\) | −17.2838 | −1.67089 | −0.835443 | − | 0.549578i | \(-0.814789\pi\) | ||||
−0.835443 | + | 0.549578i | \(0.814789\pi\) | |||||||
\(108\) | −1.96976 | −0.189540 | ||||||||
\(109\) | −6.93762 | −0.664503 | −0.332252 | − | 0.943191i | \(-0.607808\pi\) | ||||
−0.332252 | + | 0.943191i | \(0.607808\pi\) | |||||||
\(110\) | 4.07969 | 0.388983 | ||||||||
\(111\) | −5.05624 | −0.479917 | ||||||||
\(112\) | −16.3113 | −1.54128 | ||||||||
\(113\) | −7.67083 | −0.721611 | −0.360806 | − | 0.932641i | \(-0.617498\pi\) | ||||
−0.360806 | + | 0.932641i | \(0.617498\pi\) | |||||||
\(114\) | 14.9004 | 1.39555 | ||||||||
\(115\) | 26.2069 | 2.44381 | ||||||||
\(116\) | 0.779462 | 0.0723712 | ||||||||
\(117\) | 27.5513 | 2.54712 | ||||||||
\(118\) | −10.1532 | −0.934678 | ||||||||
\(119\) | 18.8163 | 1.72488 | ||||||||
\(120\) | 27.0407 | 2.46846 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.29392 | 0.117146 | ||||||||
\(123\) | 2.02734 | 0.182799 | ||||||||
\(124\) | 2.42292 | 0.217584 | ||||||||
\(125\) | 0.185143 | 0.0165597 | ||||||||
\(126\) | 33.3387 | 2.97005 | ||||||||
\(127\) | 3.54653 | 0.314704 | 0.157352 | − | 0.987543i | \(-0.449704\pi\) | ||||
0.157352 | + | 0.987543i | \(0.449704\pi\) | |||||||
\(128\) | 7.79651 | 0.689121 | ||||||||
\(129\) | −16.5477 | −1.45694 | ||||||||
\(130\) | −21.9463 | −1.92482 | ||||||||
\(131\) | 14.8844 | 1.30046 | 0.650230 | − | 0.759738i | \(-0.274673\pi\) | ||||
0.650230 | + | 0.759738i | \(0.274673\pi\) | |||||||
\(132\) | 0.928422 | 0.0808087 | ||||||||
\(133\) | 20.3285 | 1.76270 | ||||||||
\(134\) | −17.9190 | −1.54796 | ||||||||
\(135\) | −19.0639 | −1.64076 | ||||||||
\(136\) | −11.2557 | −0.965170 | ||||||||
\(137\) | 6.65631 | 0.568687 | 0.284343 | − | 0.958722i | \(-0.408224\pi\) | ||||
0.284343 | + | 0.958722i | \(0.408224\pi\) | |||||||
\(138\) | −30.6494 | −2.60905 | ||||||||
\(139\) | −3.67190 | −0.311446 | −0.155723 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155723 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(140\) | 5.16749 | 0.436733 | ||||||||
\(141\) | −3.95502 | −0.333073 | ||||||||
\(142\) | −7.11401 | −0.596995 | ||||||||
\(143\) | −5.37940 | −0.449848 | ||||||||
\(144\) | −16.6059 | −1.38382 | ||||||||
\(145\) | 7.54384 | 0.626482 | ||||||||
\(146\) | 3.10532 | 0.256998 | ||||||||
\(147\) | 52.1770 | 4.30349 | ||||||||
\(148\) | 0.578003 | 0.0475116 | ||||||||
\(149\) | 18.1524 | 1.48710 | 0.743552 | − | 0.668678i | \(-0.233139\pi\) | ||||
0.743552 | + | 0.668678i | \(0.233139\pi\) | |||||||
\(150\) | 18.2208 | 1.48772 | ||||||||
\(151\) | −1.81849 | −0.147987 | −0.0739934 | − | 0.997259i | \(-0.523574\pi\) | ||||
−0.0739934 | + | 0.997259i | \(0.523574\pi\) | |||||||
\(152\) | −12.1603 | −0.986331 | ||||||||
\(153\) | 19.1561 | 1.54868 | ||||||||
\(154\) | −6.50941 | −0.524543 | ||||||||
\(155\) | 23.4496 | 1.88352 | ||||||||
\(156\) | −4.99436 | −0.399868 | ||||||||
\(157\) | −5.49676 | −0.438689 | −0.219344 | − | 0.975647i | \(-0.570392\pi\) | ||||
−0.219344 | + | 0.975647i | \(0.570392\pi\) | |||||||
\(158\) | 0.478274 | 0.0380494 | ||||||||
\(159\) | −15.9788 | −1.26720 | ||||||||
\(160\) | −5.74931 | −0.454523 | ||||||||
\(161\) | −41.8148 | −3.29547 | ||||||||
\(162\) | 2.41466 | 0.189714 | ||||||||
\(163\) | 8.57144 | 0.671367 | 0.335683 | − | 0.941975i | \(-0.391033\pi\) | ||||
0.335683 | + | 0.941975i | \(0.391033\pi\) | |||||||
\(164\) | −0.231755 | −0.0180970 | ||||||||
\(165\) | 8.98551 | 0.699521 | ||||||||
\(166\) | 12.9024 | 1.00142 | ||||||||
\(167\) | 15.2797 | 1.18238 | 0.591188 | − | 0.806534i | \(-0.298659\pi\) | ||||
0.591188 | + | 0.806534i | \(0.298659\pi\) | |||||||
\(168\) | −43.1451 | −3.32872 | ||||||||
\(169\) | 15.9380 | 1.22600 | ||||||||
\(170\) | −15.2590 | −1.17031 | ||||||||
\(171\) | 20.6956 | 1.58263 | ||||||||
\(172\) | 1.89165 | 0.144237 | ||||||||
\(173\) | 6.95831 | 0.529031 | 0.264515 | − | 0.964381i | \(-0.414788\pi\) | ||||
0.264515 | + | 0.964381i | \(0.414788\pi\) | |||||||
\(174\) | −8.82265 | −0.668843 | ||||||||
\(175\) | 24.8585 | 1.87912 | ||||||||
\(176\) | 3.24231 | 0.244398 | ||||||||
\(177\) | −22.3624 | −1.68086 | ||||||||
\(178\) | 9.40726 | 0.705104 | ||||||||
\(179\) | 17.9416 | 1.34102 | 0.670509 | − | 0.741902i | \(-0.266076\pi\) | ||||
0.670509 | + | 0.741902i | \(0.266076\pi\) | |||||||
\(180\) | 5.26081 | 0.392118 | ||||||||
\(181\) | −21.9095 | −1.62852 | −0.814259 | − | 0.580502i | \(-0.802856\pi\) | ||||
−0.814259 | + | 0.580502i | \(0.802856\pi\) | |||||||
\(182\) | 35.0167 | 2.59561 | ||||||||
\(183\) | 2.84985 | 0.210667 | ||||||||
\(184\) | 25.0132 | 1.84400 | ||||||||
\(185\) | 5.59407 | 0.411284 | ||||||||
\(186\) | −27.4248 | −2.01088 | ||||||||
\(187\) | −3.74023 | −0.273513 | ||||||||
\(188\) | 0.452118 | 0.0329741 | ||||||||
\(189\) | 30.4176 | 2.21255 | ||||||||
\(190\) | −16.4853 | −1.19597 | ||||||||
\(191\) | 4.31134 | 0.311958 | 0.155979 | − | 0.987760i | \(-0.450147\pi\) | ||||
0.155979 | + | 0.987760i | \(0.450147\pi\) | |||||||
\(192\) | 25.2041 | 1.81895 | ||||||||
\(193\) | −1.70398 | −0.122655 | −0.0613276 | − | 0.998118i | \(-0.519533\pi\) | ||||
−0.0613276 | + | 0.998118i | \(0.519533\pi\) | |||||||
\(194\) | −3.60741 | −0.258997 | ||||||||
\(195\) | −48.3367 | −3.46146 | ||||||||
\(196\) | −5.96460 | −0.426043 | ||||||||
\(197\) | −16.9503 | −1.20766 | −0.603830 | − | 0.797113i | \(-0.706359\pi\) | ||||
−0.603830 | + | 0.797113i | \(0.706359\pi\) | |||||||
\(198\) | −6.62696 | −0.470957 | ||||||||
\(199\) | −19.5638 | −1.38684 | −0.693421 | − | 0.720533i | \(-0.743897\pi\) | ||||
−0.693421 | + | 0.720533i | \(0.743897\pi\) | |||||||
\(200\) | −14.8701 | −1.05148 | ||||||||
\(201\) | −39.4665 | −2.78375 | ||||||||
\(202\) | 9.55733 | 0.672451 | ||||||||
\(203\) | −12.0367 | −0.844808 | ||||||||
\(204\) | −3.47251 | −0.243124 | ||||||||
\(205\) | −2.24298 | −0.156657 | ||||||||
\(206\) | 17.7924 | 1.23965 | ||||||||
\(207\) | −42.5699 | −2.95881 | ||||||||
\(208\) | −17.4417 | −1.20936 | ||||||||
\(209\) | −4.04082 | −0.279509 | ||||||||
\(210\) | −58.4903 | −4.03621 | ||||||||
\(211\) | −18.5985 | −1.28037 | −0.640186 | − | 0.768220i | \(-0.721143\pi\) | ||||
−0.640186 | + | 0.768220i | \(0.721143\pi\) | |||||||
\(212\) | 1.82661 | 0.125452 | ||||||||
\(213\) | −15.6686 | −1.07359 | ||||||||
\(214\) | −22.3638 | −1.52876 | ||||||||
\(215\) | 18.3078 | 1.24858 | ||||||||
\(216\) | −18.1955 | −1.23805 | ||||||||
\(217\) | −37.4154 | −2.53992 | ||||||||
\(218\) | −8.97670 | −0.607979 | ||||||||
\(219\) | 6.83944 | 0.462167 | ||||||||
\(220\) | −1.02718 | −0.0692522 | ||||||||
\(221\) | 20.1202 | 1.35343 | ||||||||
\(222\) | −6.54236 | −0.439094 | ||||||||
\(223\) | −11.6508 | −0.780196 | −0.390098 | − | 0.920773i | \(-0.627559\pi\) | ||||
−0.390098 | + | 0.920773i | \(0.627559\pi\) | |||||||
\(224\) | 9.17338 | 0.612922 | ||||||||
\(225\) | 25.3074 | 1.68716 | ||||||||
\(226\) | −9.92542 | −0.660229 | ||||||||
\(227\) | 4.05285 | 0.268997 | 0.134499 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134499 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(228\) | −3.75158 | −0.248455 | ||||||||
\(229\) | 4.67351 | 0.308834 | 0.154417 | − | 0.988006i | \(-0.450650\pi\) | ||||
0.154417 | + | 0.988006i | \(0.450650\pi\) | |||||||
\(230\) | 33.9096 | 2.23593 | ||||||||
\(231\) | −14.3369 | −0.943301 | ||||||||
\(232\) | 7.20022 | 0.472718 | ||||||||
\(233\) | 14.7430 | 0.965847 | 0.482923 | − | 0.875663i | \(-0.339575\pi\) | ||||
0.482923 | + | 0.875663i | \(0.339575\pi\) | |||||||
\(234\) | 35.6491 | 2.33045 | ||||||||
\(235\) | 4.37571 | 0.285440 | ||||||||
\(236\) | 2.55635 | 0.166404 | ||||||||
\(237\) | 1.05340 | 0.0684254 | ||||||||
\(238\) | 24.3467 | 1.57816 | ||||||||
\(239\) | 0.0283176 | 0.00183171 | 0.000915856 | − | 1.00000i | \(-0.499708\pi\) | ||||
0.000915856 | 1.00000i | \(0.499708\pi\) | ||||||||
\(240\) | 29.1338 | 1.88058 | ||||||||
\(241\) | 13.0050 | 0.837723 | 0.418861 | − | 0.908050i | \(-0.362429\pi\) | ||||
0.418861 | + | 0.908050i | \(0.362429\pi\) | |||||||
\(242\) | 1.29392 | 0.0831761 | ||||||||
\(243\) | −12.8206 | −0.822444 | ||||||||
\(244\) | −0.325780 | −0.0208559 | ||||||||
\(245\) | −57.7270 | −3.68804 | ||||||||
\(246\) | 2.62321 | 0.167249 | ||||||||
\(247\) | 21.7372 | 1.38310 | ||||||||
\(248\) | 22.3815 | 1.42123 | ||||||||
\(249\) | 28.4175 | 1.80088 | ||||||||
\(250\) | 0.239560 | 0.0151511 | ||||||||
\(251\) | 9.82317 | 0.620033 | 0.310016 | − | 0.950731i | \(-0.399665\pi\) | ||||
0.310016 | + | 0.950731i | \(0.399665\pi\) | |||||||
\(252\) | −8.39395 | −0.528769 | ||||||||
\(253\) | 8.31179 | 0.522558 | ||||||||
\(254\) | 4.58892 | 0.287934 | ||||||||
\(255\) | −33.6079 | −2.10461 | ||||||||
\(256\) | −7.59999 | −0.474999 | ||||||||
\(257\) | 14.2555 | 0.889234 | 0.444617 | − | 0.895721i | \(-0.353340\pi\) | ||||
0.444617 | + | 0.895721i | \(0.353340\pi\) | |||||||
\(258\) | −21.4113 | −1.33301 | ||||||||
\(259\) | −8.92568 | −0.554615 | ||||||||
\(260\) | 5.52560 | 0.342683 | ||||||||
\(261\) | −12.2540 | −0.758505 | ||||||||
\(262\) | 19.2592 | 1.18984 | ||||||||
\(263\) | −15.4903 | −0.955176 | −0.477588 | − | 0.878584i | \(-0.658489\pi\) | ||||
−0.477588 | + | 0.878584i | \(0.658489\pi\) | |||||||
\(264\) | 8.57623 | 0.527830 | ||||||||
\(265\) | 17.6784 | 1.08598 | ||||||||
\(266\) | 26.3033 | 1.61276 | ||||||||
\(267\) | 20.7195 | 1.26801 | ||||||||
\(268\) | 4.51160 | 0.275590 | ||||||||
\(269\) | −13.4623 | −0.820810 | −0.410405 | − | 0.911903i | \(-0.634613\pi\) | ||||
−0.410405 | + | 0.911903i | \(0.634613\pi\) | |||||||
\(270\) | −24.6671 | −1.50119 | ||||||||
\(271\) | −24.3809 | −1.48103 | −0.740517 | − | 0.672037i | \(-0.765419\pi\) | ||||
−0.740517 | + | 0.672037i | \(0.765419\pi\) | |||||||
\(272\) | −12.1270 | −0.735306 | ||||||||
\(273\) | 77.1242 | 4.66777 | ||||||||
\(274\) | 8.61271 | 0.520313 | ||||||||
\(275\) | −4.94128 | −0.297970 | ||||||||
\(276\) | 7.71685 | 0.464500 | ||||||||
\(277\) | −26.4547 | −1.58951 | −0.794756 | − | 0.606929i | \(-0.792401\pi\) | ||||
−0.794756 | + | 0.606929i | \(0.792401\pi\) | |||||||
\(278\) | −4.75113 | −0.284954 | ||||||||
\(279\) | −38.0910 | −2.28045 | ||||||||
\(280\) | 47.7343 | 2.85267 | ||||||||
\(281\) | 29.5269 | 1.76143 | 0.880714 | − | 0.473648i | \(-0.157063\pi\) | ||||
0.880714 | + | 0.473648i | \(0.157063\pi\) | |||||||
\(282\) | −5.11747 | −0.304741 | ||||||||
\(283\) | 14.6613 | 0.871524 | 0.435762 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435762 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(284\) | 1.79115 | 0.106285 | ||||||||
\(285\) | −36.3088 | −2.15075 | ||||||||
\(286\) | −6.96050 | −0.411583 | ||||||||
\(287\) | 3.57882 | 0.211251 | ||||||||
\(288\) | 9.33904 | 0.550308 | ||||||||
\(289\) | −3.01067 | −0.177098 | ||||||||
\(290\) | 9.76110 | 0.573191 | ||||||||
\(291\) | −7.94531 | −0.465762 | ||||||||
\(292\) | −0.781850 | −0.0457543 | ||||||||
\(293\) | 16.1198 | 0.941727 | 0.470863 | − | 0.882206i | \(-0.343942\pi\) | ||||
0.470863 | + | 0.882206i | \(0.343942\pi\) | |||||||
\(294\) | 67.5127 | 3.93742 | ||||||||
\(295\) | 24.7410 | 1.44048 | ||||||||
\(296\) | 5.33926 | 0.310338 | ||||||||
\(297\) | −6.04630 | −0.350842 | ||||||||
\(298\) | 23.4877 | 1.36061 | ||||||||
\(299\) | −44.7125 | −2.58579 | ||||||||
\(300\) | −4.58759 | −0.264865 | ||||||||
\(301\) | −29.2113 | −1.68371 | ||||||||
\(302\) | −2.35298 | −0.135399 | ||||||||
\(303\) | 21.0500 | 1.20929 | ||||||||
\(304\) | −13.1016 | −0.751427 | ||||||||
\(305\) | −3.15298 | −0.180539 | ||||||||
\(306\) | 24.7863 | 1.41694 | ||||||||
\(307\) | 15.7370 | 0.898160 | 0.449080 | − | 0.893492i | \(-0.351752\pi\) | ||||
0.449080 | + | 0.893492i | \(0.351752\pi\) | |||||||
\(308\) | 1.63892 | 0.0933864 | ||||||||
\(309\) | 39.1876 | 2.22931 | ||||||||
\(310\) | 30.3419 | 1.72330 | ||||||||
\(311\) | −3.98071 | −0.225725 | −0.112863 | − | 0.993611i | \(-0.536002\pi\) | ||||
−0.112863 | + | 0.993611i | \(0.536002\pi\) | |||||||
\(312\) | −46.1350 | −2.61188 | ||||||||
\(313\) | 28.0839 | 1.58740 | 0.793699 | − | 0.608311i | \(-0.208153\pi\) | ||||
0.793699 | + | 0.608311i | \(0.208153\pi\) | |||||||
\(314\) | −7.11234 | −0.401373 | ||||||||
\(315\) | −81.2389 | −4.57729 | ||||||||
\(316\) | −0.120419 | −0.00677408 | ||||||||
\(317\) | −13.7782 | −0.773858 | −0.386929 | − | 0.922109i | \(-0.626464\pi\) | ||||
−0.386929 | + | 0.922109i | \(0.626464\pi\) | |||||||
\(318\) | −20.6752 | −1.15941 | ||||||||
\(319\) | 2.39261 | 0.133960 | ||||||||
\(320\) | −27.8850 | −1.55882 | ||||||||
\(321\) | −49.2561 | −2.74921 | ||||||||
\(322\) | −54.1048 | −3.01514 | ||||||||
\(323\) | 15.1136 | 0.840943 | ||||||||
\(324\) | −0.607958 | −0.0337754 | ||||||||
\(325\) | 26.5811 | 1.47446 | ||||||||
\(326\) | 11.0907 | 0.614258 | ||||||||
\(327\) | −19.7711 | −1.09335 | ||||||||
\(328\) | −2.14082 | −0.118207 | ||||||||
\(329\) | −6.98172 | −0.384915 | ||||||||
\(330\) | 11.6265 | 0.640018 | ||||||||
\(331\) | 2.44629 | 0.134460 | 0.0672301 | − | 0.997737i | \(-0.478584\pi\) | ||||
0.0672301 | + | 0.997737i | \(0.478584\pi\) | |||||||
\(332\) | −3.24854 | −0.178287 | ||||||||
\(333\) | −9.08687 | −0.497957 | ||||||||
\(334\) | 19.7706 | 1.08180 | ||||||||
\(335\) | 43.6644 | 2.38564 | ||||||||
\(336\) | −46.4848 | −2.53595 | ||||||||
\(337\) | 10.9925 | 0.598798 | 0.299399 | − | 0.954128i | \(-0.403214\pi\) | ||||
0.299399 | + | 0.954128i | \(0.403214\pi\) | |||||||
\(338\) | 20.6224 | 1.12171 | ||||||||
\(339\) | −21.8607 | −1.18731 | ||||||||
\(340\) | 3.84188 | 0.208355 | ||||||||
\(341\) | 7.43729 | 0.402752 | ||||||||
\(342\) | 26.7783 | 1.44801 | ||||||||
\(343\) | 56.8916 | 3.07186 | ||||||||
\(344\) | 17.4739 | 0.942132 | ||||||||
\(345\) | 74.6857 | 4.02094 | ||||||||
\(346\) | 9.00348 | 0.484030 | ||||||||
\(347\) | −8.68794 | −0.466393 | −0.233196 | − | 0.972430i | \(-0.574919\pi\) | ||||
−0.233196 | + | 0.972430i | \(0.574919\pi\) | |||||||
\(348\) | 2.22135 | 0.119077 | ||||||||
\(349\) | −7.57440 | −0.405448 | −0.202724 | − | 0.979236i | \(-0.564979\pi\) | ||||
−0.202724 | + | 0.979236i | \(0.564979\pi\) | |||||||
\(350\) | 32.1648 | 1.71928 | ||||||||
\(351\) | 32.5255 | 1.73608 | ||||||||
\(352\) | −1.82345 | −0.0971904 | ||||||||
\(353\) | −0.0404881 | −0.00215496 | −0.00107748 | − | 0.999999i | \(-0.500343\pi\) | ||||
−0.00107748 | + | 0.999999i | \(0.500343\pi\) | |||||||
\(354\) | −28.9351 | −1.53788 | ||||||||
\(355\) | 17.3352 | 0.920058 | ||||||||
\(356\) | −2.36854 | −0.125532 | ||||||||
\(357\) | 53.6235 | 2.83805 | ||||||||
\(358\) | 23.2149 | 1.22695 | ||||||||
\(359\) | −25.6439 | −1.35343 | −0.676716 | − | 0.736244i | \(-0.736598\pi\) | ||||
−0.676716 | + | 0.736244i | \(0.736598\pi\) | |||||||
\(360\) | 48.5964 | 2.56125 | ||||||||
\(361\) | −2.67178 | −0.140620 | ||||||||
\(362\) | −28.3490 | −1.48999 | ||||||||
\(363\) | 2.84985 | 0.149578 | ||||||||
\(364\) | −8.81643 | −0.462107 | ||||||||
\(365\) | −7.56694 | −0.396072 | ||||||||
\(366\) | 3.68746 | 0.192747 | ||||||||
\(367\) | −16.9367 | −0.884088 | −0.442044 | − | 0.896993i | \(-0.645747\pi\) | ||||
−0.442044 | + | 0.896993i | \(0.645747\pi\) | |||||||
\(368\) | 26.9494 | 1.40483 | ||||||||
\(369\) | 3.64345 | 0.189670 | ||||||||
\(370\) | 7.23826 | 0.376299 | ||||||||
\(371\) | −28.2070 | −1.46444 | ||||||||
\(372\) | 6.90495 | 0.358005 | ||||||||
\(373\) | 25.4130 | 1.31583 | 0.657917 | − | 0.753091i | \(-0.271438\pi\) | ||||
0.657917 | + | 0.753091i | \(0.271438\pi\) | |||||||
\(374\) | −4.83955 | −0.250247 | ||||||||
\(375\) | 0.527629 | 0.0272466 | ||||||||
\(376\) | 4.17640 | 0.215382 | ||||||||
\(377\) | −12.8708 | −0.662880 | ||||||||
\(378\) | 39.3578 | 2.02435 | ||||||||
\(379\) | −23.6354 | −1.21407 | −0.607035 | − | 0.794675i | \(-0.707641\pi\) | ||||
−0.607035 | + | 0.794675i | \(0.707641\pi\) | |||||||
\(380\) | 4.15063 | 0.212923 | ||||||||
\(381\) | 10.1071 | 0.517801 | ||||||||
\(382\) | 5.57852 | 0.285422 | ||||||||
\(383\) | 8.02500 | 0.410058 | 0.205029 | − | 0.978756i | \(-0.434271\pi\) | ||||
0.205029 | + | 0.978756i | \(0.434271\pi\) | |||||||
\(384\) | 22.2189 | 1.13385 | ||||||||
\(385\) | 15.8619 | 0.808399 | ||||||||
\(386\) | −2.20481 | −0.112222 | ||||||||
\(387\) | −29.7388 | −1.51171 | ||||||||
\(388\) | 0.908267 | 0.0461102 | ||||||||
\(389\) | 26.0896 | 1.32279 | 0.661397 | − | 0.750036i | \(-0.269964\pi\) | ||||
0.661397 | + | 0.750036i | \(0.269964\pi\) | |||||||
\(390\) | −62.5436 | −3.16702 | ||||||||
\(391\) | −31.0880 | −1.57219 | ||||||||
\(392\) | −55.0976 | −2.78285 | ||||||||
\(393\) | 42.4184 | 2.13972 | ||||||||
\(394\) | −21.9323 | −1.10493 | ||||||||
\(395\) | −1.16544 | −0.0586398 | ||||||||
\(396\) | 1.66852 | 0.0838463 | ||||||||
\(397\) | 9.00408 | 0.451902 | 0.225951 | − | 0.974139i | \(-0.427451\pi\) | ||||
0.225951 | + | 0.974139i | \(0.427451\pi\) | |||||||
\(398\) | −25.3139 | −1.26887 | ||||||||
\(399\) | 57.9330 | 2.90028 | ||||||||
\(400\) | −16.0212 | −0.801058 | ||||||||
\(401\) | 28.5072 | 1.42358 | 0.711792 | − | 0.702391i | \(-0.247884\pi\) | ||||
0.711792 | + | 0.702391i | \(0.247884\pi\) | |||||||
\(402\) | −51.0663 | −2.54696 | ||||||||
\(403\) | −40.0082 | −1.99295 | ||||||||
\(404\) | −2.40632 | −0.119719 | ||||||||
\(405\) | −5.88398 | −0.292377 | ||||||||
\(406\) | −15.5744 | −0.772947 | ||||||||
\(407\) | 1.77422 | 0.0879446 | ||||||||
\(408\) | −32.0771 | −1.58805 | ||||||||
\(409\) | 22.9317 | 1.13390 | 0.566949 | − | 0.823753i | \(-0.308124\pi\) | ||||
0.566949 | + | 0.823753i | \(0.308124\pi\) | |||||||
\(410\) | −2.90223 | −0.143331 | ||||||||
\(411\) | 18.9695 | 0.935695 | ||||||||
\(412\) | −4.47973 | −0.220700 | ||||||||
\(413\) | −39.4759 | −1.94248 | ||||||||
\(414\) | −55.0819 | −2.70713 | ||||||||
\(415\) | −31.4402 | −1.54334 | ||||||||
\(416\) | 9.80909 | 0.480930 | ||||||||
\(417\) | −10.4643 | −0.512441 | ||||||||
\(418\) | −5.22848 | −0.255733 | ||||||||
\(419\) | −6.83008 | −0.333671 | −0.166836 | − | 0.985985i | \(-0.553355\pi\) | ||||
−0.166836 | + | 0.985985i | \(0.553355\pi\) | |||||||
\(420\) | 14.7266 | 0.718583 | ||||||||
\(421\) | 2.09584 | 0.102145 | 0.0510724 | − | 0.998695i | \(-0.483736\pi\) | ||||
0.0510724 | + | 0.998695i | \(0.483736\pi\) | |||||||
\(422\) | −24.0649 | −1.17146 | ||||||||
\(423\) | −7.10780 | −0.345593 | ||||||||
\(424\) | 16.8732 | 0.819434 | ||||||||
\(425\) | 18.4815 | 0.896486 | ||||||||
\(426\) | −20.2738 | −0.982271 | ||||||||
\(427\) | 5.03078 | 0.243456 | ||||||||
\(428\) | 5.63070 | 0.272170 | ||||||||
\(429\) | −15.3305 | −0.740162 | ||||||||
\(430\) | 23.6888 | 1.14238 | ||||||||
\(431\) | −19.5477 | −0.941580 | −0.470790 | − | 0.882245i | \(-0.656031\pi\) | ||||
−0.470790 | + | 0.882245i | \(0.656031\pi\) | |||||||
\(432\) | −19.6040 | −0.943197 | ||||||||
\(433\) | −22.9539 | −1.10310 | −0.551548 | − | 0.834143i | \(-0.685963\pi\) | ||||
−0.551548 | + | 0.834143i | \(0.685963\pi\) | |||||||
\(434\) | −48.4124 | −2.32387 | ||||||||
\(435\) | 21.4988 | 1.03079 | ||||||||
\(436\) | 2.26013 | 0.108241 | ||||||||
\(437\) | −33.5865 | −1.60666 | ||||||||
\(438\) | 8.84967 | 0.422854 | ||||||||
\(439\) | 7.32646 | 0.349673 | 0.174836 | − | 0.984597i | \(-0.444060\pi\) | ||||
0.174836 | + | 0.984597i | \(0.444060\pi\) | |||||||
\(440\) | −9.48847 | −0.452345 | ||||||||
\(441\) | 93.7703 | 4.46525 | ||||||||
\(442\) | 26.0339 | 1.23831 | ||||||||
\(443\) | 4.91021 | 0.233291 | 0.116645 | − | 0.993174i | \(-0.462786\pi\) | ||||
0.116645 | + | 0.993174i | \(0.462786\pi\) | |||||||
\(444\) | 1.64722 | 0.0781736 | ||||||||
\(445\) | −22.9233 | −1.08667 | ||||||||
\(446\) | −15.0752 | −0.713830 | ||||||||
\(447\) | 51.7316 | 2.44682 | ||||||||
\(448\) | 44.4922 | 2.10206 | ||||||||
\(449\) | −4.43139 | −0.209130 | −0.104565 | − | 0.994518i | \(-0.533345\pi\) | ||||
−0.104565 | + | 0.994518i | \(0.533345\pi\) | |||||||
\(450\) | 32.7456 | 1.54364 | ||||||||
\(451\) | −0.711385 | −0.0334978 | ||||||||
\(452\) | 2.49900 | 0.117543 | ||||||||
\(453\) | −5.18242 | −0.243492 | ||||||||
\(454\) | 5.24406 | 0.246116 | ||||||||
\(455\) | −85.3277 | −4.00023 | ||||||||
\(456\) | −34.6550 | −1.62287 | ||||||||
\(457\) | 17.1757 | 0.803445 | 0.401722 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401722 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(458\) | 6.04713 | 0.282564 | ||||||||
\(459\) | 22.6146 | 1.05556 | ||||||||
\(460\) | −8.53768 | −0.398071 | ||||||||
\(461\) | −16.3294 | −0.760536 | −0.380268 | − | 0.924876i | \(-0.624168\pi\) | ||||
−0.380268 | + | 0.924876i | \(0.624168\pi\) | |||||||
\(462\) | −18.5508 | −0.863062 | ||||||||
\(463\) | 34.7208 | 1.61361 | 0.806806 | − | 0.590816i | \(-0.201194\pi\) | ||||
0.806806 | + | 0.590816i | \(0.201194\pi\) | |||||||
\(464\) | 7.75757 | 0.360136 | ||||||||
\(465\) | 66.8279 | 3.09907 | ||||||||
\(466\) | 19.0762 | 0.883689 | ||||||||
\(467\) | 20.4386 | 0.945786 | 0.472893 | − | 0.881120i | \(-0.343210\pi\) | ||||
0.472893 | + | 0.881120i | \(0.343210\pi\) | |||||||
\(468\) | −8.97565 | −0.414899 | ||||||||
\(469\) | −69.6693 | −3.21703 | ||||||||
\(470\) | 5.66181 | 0.261160 | ||||||||
\(471\) | −15.6649 | −0.721801 | ||||||||
\(472\) | 23.6141 | 1.08693 | ||||||||
\(473\) | 5.80652 | 0.266984 | ||||||||
\(474\) | 1.36301 | 0.0626049 | ||||||||
\(475\) | 19.9668 | 0.916141 | ||||||||
\(476\) | −6.12996 | −0.280966 | ||||||||
\(477\) | −28.7164 | −1.31483 | ||||||||
\(478\) | 0.0366406 | 0.00167590 | ||||||||
\(479\) | 12.8281 | 0.586132 | 0.293066 | − | 0.956092i | \(-0.405324\pi\) | ||||
0.293066 | + | 0.956092i | \(0.405324\pi\) | |||||||
\(480\) | −16.3846 | −0.747854 | ||||||||
\(481\) | −9.54423 | −0.435179 | ||||||||
\(482\) | 16.8273 | 0.766464 | ||||||||
\(483\) | −119.166 | −5.42223 | ||||||||
\(484\) | −0.325780 | −0.0148082 | ||||||||
\(485\) | 8.79044 | 0.399153 | ||||||||
\(486\) | −16.5888 | −0.752485 | ||||||||
\(487\) | 16.3096 | 0.739058 | 0.369529 | − | 0.929219i | \(-0.379519\pi\) | ||||
0.369529 | + | 0.929219i | \(0.379519\pi\) | |||||||
\(488\) | −3.00937 | −0.136228 | ||||||||
\(489\) | 24.4273 | 1.10464 | ||||||||
\(490\) | −74.6939 | −3.37433 | ||||||||
\(491\) | −24.6215 | −1.11115 | −0.555576 | − | 0.831466i | \(-0.687502\pi\) | ||||
−0.555576 | + | 0.831466i | \(0.687502\pi\) | |||||||
\(492\) | −0.660465 | −0.0297761 | ||||||||
\(493\) | −8.94890 | −0.403038 | ||||||||
\(494\) | 28.1261 | 1.26545 | ||||||||
\(495\) | 16.1484 | 0.725816 | ||||||||
\(496\) | 24.1140 | 1.08275 | ||||||||
\(497\) | −27.6594 | −1.24070 | ||||||||
\(498\) | 36.7698 | 1.64770 | ||||||||
\(499\) | 27.1576 | 1.21574 | 0.607871 | − | 0.794036i | \(-0.292024\pi\) | ||||
0.607871 | + | 0.794036i | \(0.292024\pi\) | |||||||
\(500\) | −0.0603158 | −0.00269740 | ||||||||
\(501\) | 43.5447 | 1.94543 | ||||||||
\(502\) | 12.7104 | 0.567291 | ||||||||
\(503\) | 14.1547 | 0.631125 | 0.315563 | − | 0.948905i | \(-0.397807\pi\) | ||||
0.315563 | + | 0.948905i | \(0.397807\pi\) | |||||||
\(504\) | −77.5385 | −3.45384 | ||||||||
\(505\) | −23.2890 | −1.03635 | ||||||||
\(506\) | 10.7548 | 0.478108 | ||||||||
\(507\) | 45.4208 | 2.01721 | ||||||||
\(508\) | −1.15539 | −0.0512621 | ||||||||
\(509\) | −8.64166 | −0.383035 | −0.191517 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191517 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(510\) | −43.4858 | −1.92558 | ||||||||
\(511\) | 12.0735 | 0.534102 | ||||||||
\(512\) | −25.4268 | −1.12372 | ||||||||
\(513\) | 24.4320 | 1.07870 | ||||||||
\(514\) | 18.4454 | 0.813593 | ||||||||
\(515\) | −43.3560 | −1.91049 | ||||||||
\(516\) | 5.39090 | 0.237321 | ||||||||
\(517\) | 1.38780 | 0.0610355 | ||||||||
\(518\) | −11.5491 | −0.507438 | ||||||||
\(519\) | 19.8301 | 0.870446 | ||||||||
\(520\) | 51.0423 | 2.23835 | ||||||||
\(521\) | −28.1013 | −1.23114 | −0.615571 | − | 0.788082i | \(-0.711075\pi\) | ||||
−0.615571 | + | 0.788082i | \(0.711075\pi\) | |||||||
\(522\) | −15.8557 | −0.693985 | ||||||||
\(523\) | 25.0944 | 1.09730 | 0.548651 | − | 0.836051i | \(-0.315141\pi\) | ||||
0.548651 | + | 0.836051i | \(0.315141\pi\) | |||||||
\(524\) | −4.84905 | −0.211832 | ||||||||
\(525\) | 70.8428 | 3.09183 | ||||||||
\(526\) | −20.0432 | −0.873926 | ||||||||
\(527\) | −27.8172 | −1.21174 | ||||||||
\(528\) | 9.24008 | 0.402123 | ||||||||
\(529\) | 46.0859 | 2.00374 | ||||||||
\(530\) | 22.8744 | 0.993600 | ||||||||
\(531\) | −40.1888 | −1.74404 | ||||||||
\(532\) | −6.62260 | −0.287126 | ||||||||
\(533\) | 3.82683 | 0.165758 | ||||||||
\(534\) | 26.8092 | 1.16015 | ||||||||
\(535\) | 54.4954 | 2.35604 | ||||||||
\(536\) | 41.6756 | 1.80011 | ||||||||
\(537\) | 51.1308 | 2.20646 | ||||||||
\(538\) | −17.4191 | −0.750990 | ||||||||
\(539\) | −18.3087 | −0.788612 | ||||||||
\(540\) | 6.21062 | 0.267263 | ||||||||
\(541\) | −21.2427 | −0.913294 | −0.456647 | − | 0.889648i | \(-0.650950\pi\) | ||||
−0.456647 | + | 0.889648i | \(0.650950\pi\) | |||||||
\(542\) | −31.5469 | −1.35505 | ||||||||
\(543\) | −62.4386 | −2.67950 | ||||||||
\(544\) | 6.82014 | 0.292411 | ||||||||
\(545\) | 21.8742 | 0.936986 | ||||||||
\(546\) | 99.7923 | 4.27071 | ||||||||
\(547\) | 20.8371 | 0.890929 | 0.445464 | − | 0.895300i | \(-0.353039\pi\) | ||||
0.445464 | + | 0.895300i | \(0.353039\pi\) | |||||||
\(548\) | −2.16849 | −0.0926333 | ||||||||
\(549\) | 5.12162 | 0.218586 | ||||||||
\(550\) | −6.39360 | −0.272624 | ||||||||
\(551\) | −9.66809 | −0.411874 | ||||||||
\(552\) | 71.2838 | 3.03404 | ||||||||
\(553\) | 1.85954 | 0.0790756 | ||||||||
\(554\) | −34.2302 | −1.45430 | ||||||||
\(555\) | 15.9422 | 0.676710 | ||||||||
\(556\) | 1.19623 | 0.0507314 | ||||||||
\(557\) | 17.8131 | 0.754766 | 0.377383 | − | 0.926057i | \(-0.376824\pi\) | ||||
0.377383 | + | 0.926057i | \(0.376824\pi\) | |||||||
\(558\) | −49.2866 | −2.08647 | ||||||||
\(559\) | −31.2356 | −1.32113 | ||||||||
\(560\) | 51.4293 | 2.17328 | ||||||||
\(561\) | −10.6591 | −0.450027 | ||||||||
\(562\) | 38.2054 | 1.61160 | ||||||||
\(563\) | 26.1629 | 1.10263 | 0.551317 | − | 0.834296i | \(-0.314126\pi\) | ||||
0.551317 | + | 0.834296i | \(0.314126\pi\) | |||||||
\(564\) | 1.28847 | 0.0542542 | ||||||||
\(565\) | 24.1860 | 1.01751 | ||||||||
\(566\) | 18.9705 | 0.797389 | ||||||||
\(567\) | 9.38825 | 0.394270 | ||||||||
\(568\) | 16.5456 | 0.694239 | ||||||||
\(569\) | 37.5330 | 1.57347 | 0.786733 | − | 0.617293i | \(-0.211771\pi\) | ||||
0.786733 | + | 0.617293i | \(0.211771\pi\) | |||||||
\(570\) | −46.9806 | −1.96780 | ||||||||
\(571\) | −16.3419 | −0.683887 | −0.341944 | − | 0.939720i | \(-0.611085\pi\) | ||||
−0.341944 | + | 0.939720i | \(0.611085\pi\) | |||||||
\(572\) | 1.75250 | 0.0732757 | ||||||||
\(573\) | 12.2867 | 0.513283 | ||||||||
\(574\) | 4.63069 | 0.193281 | ||||||||
\(575\) | −41.0709 | −1.71278 | ||||||||
\(576\) | 45.2957 | 1.88732 | ||||||||
\(577\) | −39.5536 | −1.64664 | −0.823320 | − | 0.567578i | \(-0.807881\pi\) | ||||
−0.823320 | + | 0.567578i | \(0.807881\pi\) | |||||||
\(578\) | −3.89556 | −0.162034 | ||||||||
\(579\) | −4.85608 | −0.201812 | ||||||||
\(580\) | −2.45763 | −0.102047 | ||||||||
\(581\) | 50.1648 | 2.08119 | ||||||||
\(582\) | −10.2806 | −0.426143 | ||||||||
\(583\) | 5.60689 | 0.232214 | ||||||||
\(584\) | −7.22228 | −0.298860 | ||||||||
\(585\) | −86.8686 | −3.59158 | ||||||||
\(586\) | 20.8576 | 0.861621 | ||||||||
\(587\) | −11.4662 | −0.473263 | −0.236631 | − | 0.971600i | \(-0.576043\pi\) | ||||
−0.236631 | + | 0.971600i | \(0.576043\pi\) | |||||||
\(588\) | −16.9982 | −0.700994 | ||||||||
\(589\) | −30.0528 | −1.23830 | ||||||||
\(590\) | 32.0129 | 1.31795 | ||||||||
\(591\) | −48.3058 | −1.98703 | ||||||||
\(592\) | 5.75256 | 0.236429 | ||||||||
\(593\) | 32.0395 | 1.31571 | 0.657853 | − | 0.753147i | \(-0.271465\pi\) | ||||
0.657853 | + | 0.753147i | \(0.271465\pi\) | |||||||
\(594\) | −7.82341 | −0.320999 | ||||||||
\(595\) | −59.3273 | −2.43218 | ||||||||
\(596\) | −5.91369 | −0.242234 | ||||||||
\(597\) | −55.7538 | −2.28185 | ||||||||
\(598\) | −57.8542 | −2.36584 | ||||||||
\(599\) | 2.76637 | 0.113031 | 0.0565153 | − | 0.998402i | \(-0.482001\pi\) | ||||
0.0565153 | + | 0.998402i | \(0.482001\pi\) | |||||||
\(600\) | −42.3775 | −1.73006 | ||||||||
\(601\) | 12.5085 | 0.510230 | 0.255115 | − | 0.966911i | \(-0.417887\pi\) | ||||
0.255115 | + | 0.966911i | \(0.417887\pi\) | |||||||
\(602\) | −37.7970 | −1.54049 | ||||||||
\(603\) | −70.9275 | −2.88839 | ||||||||
\(604\) | 0.592428 | 0.0241055 | ||||||||
\(605\) | −3.15298 | −0.128187 | ||||||||
\(606\) | 27.2369 | 1.10642 | ||||||||
\(607\) | 37.2492 | 1.51190 | 0.755950 | − | 0.654630i | \(-0.227176\pi\) | ||||
0.755950 | + | 0.654630i | \(0.227176\pi\) | |||||||
\(608\) | 7.36824 | 0.298822 | ||||||||
\(609\) | −34.3026 | −1.39001 | ||||||||
\(610\) | −4.07969 | −0.165182 | ||||||||
\(611\) | −7.46555 | −0.302024 | ||||||||
\(612\) | −6.24065 | −0.252263 | ||||||||
\(613\) | 31.6955 | 1.28017 | 0.640084 | − | 0.768305i | \(-0.278900\pi\) | ||||
0.640084 | + | 0.768305i | \(0.278900\pi\) | |||||||
\(614\) | 20.3624 | 0.821760 | ||||||||
\(615\) | −6.39215 | −0.257756 | ||||||||
\(616\) | 15.1394 | 0.609985 | ||||||||
\(617\) | −9.04103 | −0.363978 | −0.181989 | − | 0.983301i | \(-0.558254\pi\) | ||||
−0.181989 | + | 0.983301i | \(0.558254\pi\) | |||||||
\(618\) | 50.7055 | 2.03968 | ||||||||
\(619\) | −11.5307 | −0.463459 | −0.231730 | − | 0.972780i | \(-0.574438\pi\) | ||||
−0.231730 | + | 0.972780i | \(0.574438\pi\) | |||||||
\(620\) | −7.63941 | −0.306806 | ||||||||
\(621\) | −50.2556 | −2.01669 | ||||||||
\(622\) | −5.15071 | −0.206525 | ||||||||
\(623\) | 36.5756 | 1.46537 | ||||||||
\(624\) | −49.7061 | −1.98984 | ||||||||
\(625\) | −25.2902 | −1.01161 | ||||||||
\(626\) | 36.3383 | 1.45237 | ||||||||
\(627\) | −11.5157 | −0.459893 | ||||||||
\(628\) | 1.79073 | 0.0714579 | ||||||||
\(629\) | −6.63598 | −0.264594 | ||||||||
\(630\) | −105.116 | −4.18793 | ||||||||
\(631\) | −19.6315 | −0.781519 | −0.390760 | − | 0.920493i | \(-0.627788\pi\) | ||||
−0.390760 | + | 0.920493i | \(0.627788\pi\) | |||||||
\(632\) | −1.11236 | −0.0442473 | ||||||||
\(633\) | −53.0028 | −2.10667 | ||||||||
\(634\) | −17.8278 | −0.708032 | ||||||||
\(635\) | −11.1821 | −0.443750 | ||||||||
\(636\) | 5.20556 | 0.206414 | ||||||||
\(637\) | 98.4899 | 3.90231 | ||||||||
\(638\) | 3.09583 | 0.122565 | ||||||||
\(639\) | −28.1589 | −1.11395 | ||||||||
\(640\) | −24.5822 | −0.971698 | ||||||||
\(641\) | 3.04359 | 0.120215 | 0.0601073 | − | 0.998192i | \(-0.480856\pi\) | ||||
0.0601073 | + | 0.998192i | \(0.480856\pi\) | |||||||
\(642\) | −63.7333 | −2.51535 | ||||||||
\(643\) | −13.3214 | −0.525345 | −0.262672 | − | 0.964885i | \(-0.584604\pi\) | ||||
−0.262672 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(644\) | 13.6224 | 0.536798 | ||||||||
\(645\) | 52.1746 | 2.05437 | ||||||||
\(646\) | 19.5557 | 0.769410 | ||||||||
\(647\) | 49.2657 | 1.93683 | 0.968417 | − | 0.249335i | \(-0.0802120\pi\) | ||||
0.968417 | + | 0.249335i | \(0.0802120\pi\) | |||||||
\(648\) | −5.61597 | −0.220616 | ||||||||
\(649\) | 7.84688 | 0.308017 | ||||||||
\(650\) | 34.3938 | 1.34904 | ||||||||
\(651\) | −106.628 | −4.17908 | ||||||||
\(652\) | −2.79240 | −0.109359 | ||||||||
\(653\) | −31.5895 | −1.23619 | −0.618096 | − | 0.786103i | \(-0.712096\pi\) | ||||
−0.618096 | + | 0.786103i | \(0.712096\pi\) | |||||||
\(654\) | −25.5822 | −1.00034 | ||||||||
\(655\) | −46.9303 | −1.83372 | ||||||||
\(656\) | −2.30653 | −0.0900548 | ||||||||
\(657\) | 12.2916 | 0.479540 | ||||||||
\(658\) | −9.03377 | −0.352173 | ||||||||
\(659\) | −4.83782 | −0.188455 | −0.0942274 | − | 0.995551i | \(-0.530038\pi\) | ||||
−0.0942274 | + | 0.995551i | \(0.530038\pi\) | |||||||
\(660\) | −2.92729 | −0.113945 | ||||||||
\(661\) | 8.00928 | 0.311525 | 0.155762 | − | 0.987795i | \(-0.450217\pi\) | ||||
0.155762 | + | 0.987795i | \(0.450217\pi\) | |||||||
\(662\) | 3.16530 | 0.123023 | ||||||||
\(663\) | 57.3395 | 2.22688 | ||||||||
\(664\) | −30.0081 | −1.16454 | ||||||||
\(665\) | −64.0952 | −2.48551 | ||||||||
\(666\) | −11.7577 | −0.455600 | ||||||||
\(667\) | 19.8868 | 0.770022 | ||||||||
\(668\) | −4.97781 | −0.192597 | ||||||||
\(669\) | −33.2030 | −1.28370 | ||||||||
\(670\) | 56.4981 | 2.18271 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 26.1427 | 1.00848 | ||||||||
\(673\) | 7.62088 | 0.293763 | 0.146882 | − | 0.989154i | \(-0.453076\pi\) | ||||
0.146882 | + | 0.989154i | \(0.453076\pi\) | |||||||
\(674\) | 14.2233 | 0.547862 | ||||||||
\(675\) | 29.8765 | 1.14995 | ||||||||
\(676\) | −5.19227 | −0.199703 | ||||||||
\(677\) | −29.8047 | −1.14549 | −0.572745 | − | 0.819734i | \(-0.694121\pi\) | ||||
−0.572745 | + | 0.819734i | \(0.694121\pi\) | |||||||
\(678\) | −28.2859 | −1.08631 | ||||||||
\(679\) | −14.0257 | −0.538257 | ||||||||
\(680\) | 35.4891 | 1.36094 | ||||||||
\(681\) | 11.5500 | 0.442597 | ||||||||
\(682\) | 9.62324 | 0.368493 | ||||||||
\(683\) | −28.0157 | −1.07199 | −0.535995 | − | 0.844221i | \(-0.680063\pi\) | ||||
−0.535995 | + | 0.844221i | \(0.680063\pi\) | |||||||
\(684\) | −6.74219 | −0.257794 | ||||||||
\(685\) | −20.9872 | −0.801880 | ||||||||
\(686\) | 73.6130 | 2.81056 | ||||||||
\(687\) | 13.3188 | 0.508143 | ||||||||
\(688\) | 18.8265 | 0.717755 | ||||||||
\(689\) | −30.1617 | −1.14907 | ||||||||
\(690\) | 96.6371 | 3.67891 | ||||||||
\(691\) | 27.5320 | 1.04737 | 0.523684 | − | 0.851913i | \(-0.324557\pi\) | ||||
0.523684 | + | 0.851913i | \(0.324557\pi\) | |||||||
\(692\) | −2.26688 | −0.0861737 | ||||||||
\(693\) | −25.7657 | −0.978760 | ||||||||
\(694\) | −11.2415 | −0.426720 | ||||||||
\(695\) | 11.5774 | 0.439157 | ||||||||
\(696\) | 20.5195 | 0.777791 | ||||||||
\(697\) | 2.66074 | 0.100783 | ||||||||
\(698\) | −9.80065 | −0.370960 | ||||||||
\(699\) | 42.0153 | 1.58917 | ||||||||
\(700\) | −8.09838 | −0.306090 | ||||||||
\(701\) | −23.7575 | −0.897307 | −0.448654 | − | 0.893706i | \(-0.648096\pi\) | ||||
−0.448654 | + | 0.893706i | \(0.648096\pi\) | |||||||
\(702\) | 42.0853 | 1.58841 | ||||||||
\(703\) | −7.16929 | −0.270395 | ||||||||
\(704\) | −8.84401 | −0.333321 | ||||||||
\(705\) | 12.4701 | 0.469651 | ||||||||
\(706\) | −0.0523882 | −0.00197165 | ||||||||
\(707\) | 37.1591 | 1.39751 | ||||||||
\(708\) | 7.28521 | 0.273795 | ||||||||
\(709\) | 17.2900 | 0.649340 | 0.324670 | − | 0.945827i | \(-0.394747\pi\) | ||||
0.324670 | + | 0.945827i | \(0.394747\pi\) | |||||||
\(710\) | 22.4303 | 0.841796 | ||||||||
\(711\) | 1.89312 | 0.0709975 | ||||||||
\(712\) | −21.8792 | −0.819958 | ||||||||
\(713\) | 61.8173 | 2.31507 | ||||||||
\(714\) | 69.3843 | 2.59664 | ||||||||
\(715\) | 16.9611 | 0.634311 | ||||||||
\(716\) | −5.84501 | −0.218438 | ||||||||
\(717\) | 0.0807007 | 0.00301382 | ||||||||
\(718\) | −33.1811 | −1.23831 | ||||||||
\(719\) | 21.2476 | 0.792400 | 0.396200 | − | 0.918164i | \(-0.370329\pi\) | ||||
0.396200 | + | 0.918164i | \(0.370329\pi\) | |||||||
\(720\) | 52.3580 | 1.95127 | ||||||||
\(721\) | 69.1772 | 2.57629 | ||||||||
\(722\) | −3.45706 | −0.128658 | ||||||||
\(723\) | 37.0621 | 1.37836 | ||||||||
\(724\) | 7.13765 | 0.265269 | ||||||||
\(725\) | −11.8225 | −0.439078 | ||||||||
\(726\) | 3.68746 | 0.136855 | ||||||||
\(727\) | −32.5988 | −1.20902 | −0.604510 | − | 0.796597i | \(-0.706631\pi\) | ||||
−0.604510 | + | 0.796597i | \(0.706631\pi\) | |||||||
\(728\) | −81.4412 | −3.01841 | ||||||||
\(729\) | −42.1353 | −1.56057 | ||||||||
\(730\) | −9.79100 | −0.362381 | ||||||||
\(731\) | −21.7177 | −0.803260 | ||||||||
\(732\) | −0.928422 | −0.0343155 | ||||||||
\(733\) | −25.1980 | −0.930709 | −0.465355 | − | 0.885124i | \(-0.654073\pi\) | ||||
−0.465355 | + | 0.885124i | \(0.654073\pi\) | |||||||
\(734\) | −21.9147 | −0.808885 | ||||||||
\(735\) | −164.513 | −6.06815 | ||||||||
\(736\) | −15.1562 | −0.558664 | ||||||||
\(737\) | 13.8486 | 0.510121 | ||||||||
\(738\) | 4.71431 | 0.173536 | ||||||||
\(739\) | −43.7239 | −1.60841 | −0.804204 | − | 0.594353i | \(-0.797408\pi\) | ||||
−0.804204 | + | 0.594353i | \(0.797408\pi\) | |||||||
\(740\) | −1.82243 | −0.0669940 | ||||||||
\(741\) | 61.9477 | 2.27570 | ||||||||
\(742\) | −36.4975 | −1.33987 | ||||||||
\(743\) | −6.25851 | −0.229603 | −0.114801 | − | 0.993388i | \(-0.536623\pi\) | ||||
−0.114801 | + | 0.993388i | \(0.536623\pi\) | |||||||
\(744\) | 63.7839 | 2.33843 | ||||||||
\(745\) | −57.2342 | −2.09690 | ||||||||
\(746\) | 32.8823 | 1.20391 | ||||||||
\(747\) | 51.0707 | 1.86858 | ||||||||
\(748\) | 1.21849 | 0.0445524 | ||||||||
\(749\) | −86.9508 | −3.17711 | ||||||||
\(750\) | 0.682708 | 0.0249290 | ||||||||
\(751\) | −7.65511 | −0.279339 | −0.139670 | − | 0.990198i | \(-0.544604\pi\) | ||||
−0.139670 | + | 0.990198i | \(0.544604\pi\) | |||||||
\(752\) | 4.49968 | 0.164087 | ||||||||
\(753\) | 27.9945 | 1.02018 | ||||||||
\(754\) | −16.6537 | −0.606493 | ||||||||
\(755\) | 5.73367 | 0.208670 | ||||||||
\(756\) | −9.90943 | −0.360403 | ||||||||
\(757\) | 33.6873 | 1.22439 | 0.612193 | − | 0.790708i | \(-0.290288\pi\) | ||||
0.612193 | + | 0.790708i | \(0.290288\pi\) | |||||||
\(758\) | −30.5823 | −1.11080 | ||||||||
\(759\) | 23.6873 | 0.859796 | ||||||||
\(760\) | 38.3412 | 1.39078 | ||||||||
\(761\) | 28.3400 | 1.02733 | 0.513663 | − | 0.857992i | \(-0.328288\pi\) | ||||
0.513663 | + | 0.857992i | \(0.328288\pi\) | |||||||
\(762\) | 13.0777 | 0.473756 | ||||||||
\(763\) | −34.9016 | −1.26352 | ||||||||
\(764\) | −1.40455 | −0.0508148 | ||||||||
\(765\) | −60.3987 | −2.18372 | ||||||||
\(766\) | 10.3837 | 0.375178 | ||||||||
\(767\) | −42.2115 | −1.52417 | ||||||||
\(768\) | −21.6588 | −0.781545 | ||||||||
\(769\) | 2.44448 | 0.0881501 | 0.0440751 | − | 0.999028i | \(-0.485966\pi\) | ||||
0.0440751 | + | 0.999028i | \(0.485966\pi\) | |||||||
\(770\) | 20.5240 | 0.739634 | ||||||||
\(771\) | 40.6260 | 1.46311 | ||||||||
\(772\) | 0.555122 | 0.0199793 | ||||||||
\(773\) | −30.7973 | −1.10770 | −0.553851 | − | 0.832616i | \(-0.686842\pi\) | ||||
−0.553851 | + | 0.832616i | \(0.686842\pi\) | |||||||
\(774\) | −38.4796 | −1.38312 | ||||||||
\(775\) | −36.7498 | −1.32009 | ||||||||
\(776\) | 8.39005 | 0.301185 | ||||||||
\(777\) | −25.4368 | −0.912541 | ||||||||
\(778\) | 33.7577 | 1.21027 | ||||||||
\(779\) | 2.87458 | 0.102992 | ||||||||
\(780\) | 15.7471 | 0.563837 | ||||||||
\(781\) | 5.49805 | 0.196736 | ||||||||
\(782\) | −40.2253 | −1.43845 | ||||||||
\(783\) | −14.4664 | −0.516988 | ||||||||
\(784\) | −59.3625 | −2.12009 | ||||||||
\(785\) | 17.3312 | 0.618576 | ||||||||
\(786\) | 54.8858 | 1.95771 | ||||||||
\(787\) | 24.7391 | 0.881853 | 0.440926 | − | 0.897543i | \(-0.354650\pi\) | ||||
0.440926 | + | 0.897543i | \(0.354650\pi\) | |||||||
\(788\) | 5.52206 | 0.196715 | ||||||||
\(789\) | −44.1451 | −1.57161 | ||||||||
\(790\) | −1.50799 | −0.0536518 | ||||||||
\(791\) | −38.5902 | −1.37211 | ||||||||
\(792\) | 15.4128 | 0.547671 | ||||||||
\(793\) | 5.37940 | 0.191028 | ||||||||
\(794\) | 11.6505 | 0.413462 | ||||||||
\(795\) | 50.3808 | 1.78682 | ||||||||
\(796\) | 6.37349 | 0.225902 | ||||||||
\(797\) | −31.1840 | −1.10459 | −0.552296 | − | 0.833648i | \(-0.686248\pi\) | ||||
−0.552296 | + | 0.833648i | \(0.686248\pi\) | |||||||
\(798\) | 74.9605 | 2.65357 | ||||||||
\(799\) | −5.19070 | −0.183634 | ||||||||
\(800\) | 9.01019 | 0.318558 | ||||||||
\(801\) | 37.2361 | 1.31567 | ||||||||
\(802\) | 36.8860 | 1.30249 | ||||||||
\(803\) | −2.39993 | −0.0846918 | ||||||||
\(804\) | 12.8574 | 0.453444 | ||||||||
\(805\) | 131.841 | 4.64679 | ||||||||
\(806\) | −51.7673 | −1.82342 | ||||||||
\(807\) | −38.3655 | −1.35053 | ||||||||
\(808\) | −22.2282 | −0.781986 | ||||||||
\(809\) | −22.6010 | −0.794610 | −0.397305 | − | 0.917687i | \(-0.630054\pi\) | ||||
−0.397305 | + | 0.917687i | \(0.630054\pi\) | |||||||
\(810\) | −7.61338 | −0.267507 | ||||||||
\(811\) | −31.9391 | −1.12153 | −0.560767 | − | 0.827974i | \(-0.689494\pi\) | ||||
−0.560767 | + | 0.827974i | \(0.689494\pi\) | |||||||
\(812\) | 3.92130 | 0.137611 | ||||||||
\(813\) | −69.4818 | −2.43683 | ||||||||
\(814\) | 2.29569 | 0.0804638 | ||||||||
\(815\) | −27.0256 | −0.946664 | ||||||||
\(816\) | −34.5600 | −1.20984 | ||||||||
\(817\) | −23.4631 | −0.820870 | ||||||||
\(818\) | 29.6717 | 1.03745 | ||||||||
\(819\) | 138.604 | 4.84323 | ||||||||
\(820\) | 0.730718 | 0.0255178 | ||||||||
\(821\) | −32.6809 | −1.14057 | −0.570285 | − | 0.821447i | \(-0.693167\pi\) | ||||
−0.570285 | + | 0.821447i | \(0.693167\pi\) | |||||||
\(822\) | 24.5449 | 0.856102 | ||||||||
\(823\) | 21.3237 | 0.743297 | 0.371649 | − | 0.928373i | \(-0.378793\pi\) | ||||
0.371649 | + | 0.928373i | \(0.378793\pi\) | |||||||
\(824\) | −41.3812 | −1.44158 | ||||||||
\(825\) | −14.0819 | −0.490268 | ||||||||
\(826\) | −51.0785 | −1.77725 | ||||||||
\(827\) | 20.8252 | 0.724163 | 0.362081 | − | 0.932146i | \(-0.382066\pi\) | ||||
0.362081 | + | 0.932146i | \(0.382066\pi\) | |||||||
\(828\) | 13.8684 | 0.481960 | ||||||||
\(829\) | −21.2732 | −0.738849 | −0.369424 | − | 0.929261i | \(-0.620445\pi\) | ||||
−0.369424 | + | 0.929261i | \(0.620445\pi\) | |||||||
\(830\) | −40.6810 | −1.41206 | ||||||||
\(831\) | −75.3920 | −2.61532 | ||||||||
\(832\) | 47.5755 | 1.64938 | ||||||||
\(833\) | 68.4788 | 2.37265 | ||||||||
\(834\) | −13.5400 | −0.468852 | ||||||||
\(835\) | −48.1765 | −1.66722 | ||||||||
\(836\) | 1.31642 | 0.0455292 | ||||||||
\(837\) | −44.9681 | −1.55433 | ||||||||
\(838\) | −8.83756 | −0.305288 | ||||||||
\(839\) | 57.8074 | 1.99573 | 0.997866 | − | 0.0652934i | \(-0.0207983\pi\) | ||||
0.997866 | + | 0.0652934i | \(0.0207983\pi\) | |||||||
\(840\) | 136.036 | 4.69367 | ||||||||
\(841\) | −23.2754 | −0.802601 | ||||||||
\(842\) | 2.71184 | 0.0934561 | ||||||||
\(843\) | 84.1472 | 2.89818 | ||||||||
\(844\) | 6.05901 | 0.208560 | ||||||||
\(845\) | −50.2521 | −1.72873 | ||||||||
\(846\) | −9.19690 | −0.316196 | ||||||||
\(847\) | 5.03078 | 0.172860 | ||||||||
\(848\) | 18.1793 | 0.624279 | ||||||||
\(849\) | 41.7824 | 1.43397 | ||||||||
\(850\) | 23.9136 | 0.820228 | ||||||||
\(851\) | 14.7469 | 0.505518 | ||||||||
\(852\) | 5.10451 | 0.174878 | ||||||||
\(853\) | 5.94693 | 0.203619 | 0.101809 | − | 0.994804i | \(-0.467537\pi\) | ||||
0.101809 | + | 0.994804i | \(0.467537\pi\) | |||||||
\(854\) | 6.50941 | 0.222747 | ||||||||
\(855\) | −65.2527 | −2.23159 | ||||||||
\(856\) | 52.0132 | 1.77777 | ||||||||
\(857\) | −55.1181 | −1.88280 | −0.941400 | − | 0.337293i | \(-0.890489\pi\) | ||||
−0.941400 | + | 0.337293i | \(0.890489\pi\) | |||||||
\(858\) | −19.8364 | −0.677202 | ||||||||
\(859\) | 3.34358 | 0.114082 | 0.0570408 | − | 0.998372i | \(-0.481833\pi\) | ||||
0.0570408 | + | 0.998372i | \(0.481833\pi\) | |||||||
\(860\) | −5.96432 | −0.203382 | ||||||||
\(861\) | 10.1991 | 0.347584 | ||||||||
\(862\) | −25.2931 | −0.861487 | ||||||||
\(863\) | 18.3209 | 0.623651 | 0.311825 | − | 0.950139i | \(-0.399060\pi\) | ||||
0.311825 | + | 0.950139i | \(0.399060\pi\) | |||||||
\(864\) | 11.0252 | 0.375083 | ||||||||
\(865\) | −21.9394 | −0.745963 | ||||||||
\(866\) | −29.7005 | −1.00926 | ||||||||
\(867\) | −8.57995 | −0.291390 | ||||||||
\(868\) | 12.1892 | 0.413727 | ||||||||
\(869\) | −0.369632 | −0.0125389 | ||||||||
\(870\) | 27.8176 | 0.943106 | ||||||||
\(871\) | −74.4974 | −2.52425 | ||||||||
\(872\) | 20.8778 | 0.707012 | ||||||||
\(873\) | −14.2790 | −0.483270 | ||||||||
\(874\) | −43.4581 | −1.46999 | ||||||||
\(875\) | 0.931413 | 0.0314875 | ||||||||
\(876\) | −2.22815 | −0.0752823 | ||||||||
\(877\) | 11.0283 | 0.372401 | 0.186200 | − | 0.982512i | \(-0.440383\pi\) | ||||
0.186200 | + | 0.982512i | \(0.440383\pi\) | |||||||
\(878\) | 9.47983 | 0.319929 | ||||||||
\(879\) | 45.9389 | 1.54948 | ||||||||
\(880\) | −10.2229 | −0.344615 | ||||||||
\(881\) | −42.1619 | −1.42047 | −0.710235 | − | 0.703964i | \(-0.751411\pi\) | ||||
−0.710235 | + | 0.703964i | \(0.751411\pi\) | |||||||
\(882\) | 121.331 | 4.08543 | ||||||||
\(883\) | −50.5867 | −1.70238 | −0.851189 | − | 0.524859i | \(-0.824118\pi\) | ||||
−0.851189 | + | 0.524859i | \(0.824118\pi\) | |||||||
\(884\) | −6.55475 | −0.220460 | ||||||||
\(885\) | 70.5082 | 2.37011 | ||||||||
\(886\) | 6.35340 | 0.213447 | ||||||||
\(887\) | −20.5497 | −0.689993 | −0.344996 | − | 0.938604i | \(-0.612120\pi\) | ||||
−0.344996 | + | 0.938604i | \(0.612120\pi\) | |||||||
\(888\) | 15.2161 | 0.510618 | ||||||||
\(889\) | 17.8418 | 0.598395 | ||||||||
\(890\) | −29.6609 | −0.994236 | ||||||||
\(891\) | −1.86616 | −0.0625188 | ||||||||
\(892\) | 3.79559 | 0.127086 | ||||||||
\(893\) | −5.60786 | −0.187660 | ||||||||
\(894\) | 66.9364 | 2.23869 | ||||||||
\(895\) | −56.5695 | −1.89091 | ||||||||
\(896\) | 39.2225 | 1.31033 | ||||||||
\(897\) | −127.424 | −4.25455 | ||||||||
\(898\) | −5.73385 | −0.191341 | ||||||||
\(899\) | 17.7945 | 0.593480 | ||||||||
\(900\) | −8.24463 | −0.274821 | ||||||||
\(901\) | −20.9711 | −0.698648 | ||||||||
\(902\) | −0.920473 | −0.0306484 | ||||||||
\(903\) | −83.2478 | −2.77031 | ||||||||
\(904\) | 23.0843 | 0.767773 | ||||||||
\(905\) | 69.0801 | 2.29630 | ||||||||
\(906\) | −6.70562 | −0.222779 | ||||||||
\(907\) | 8.06583 | 0.267821 | 0.133911 | − | 0.990993i | \(-0.457246\pi\) | ||||
0.133911 | + | 0.990993i | \(0.457246\pi\) | |||||||
\(908\) | −1.32034 | −0.0438169 | ||||||||
\(909\) | 37.8301 | 1.25475 | ||||||||
\(910\) | −110.407 | −3.65996 | ||||||||
\(911\) | 24.4560 | 0.810264 | 0.405132 | − | 0.914258i | \(-0.367226\pi\) | ||||
0.405132 | + | 0.914258i | \(0.367226\pi\) | |||||||
\(912\) | −37.3375 | −1.23637 | ||||||||
\(913\) | −9.97158 | −0.330011 | ||||||||
\(914\) | 22.2239 | 0.735102 | ||||||||
\(915\) | −8.98551 | −0.297052 | ||||||||
\(916\) | −1.52253 | −0.0503060 | ||||||||
\(917\) | 74.8803 | 2.47276 | ||||||||
\(918\) | 29.2614 | 0.965769 | ||||||||
\(919\) | 6.99410 | 0.230714 | 0.115357 | − | 0.993324i | \(-0.463199\pi\) | ||||
0.115357 | + | 0.993324i | \(0.463199\pi\) | |||||||
\(920\) | −78.8662 | −2.60014 | ||||||||
\(921\) | 44.8481 | 1.47780 | ||||||||
\(922\) | −21.1289 | −0.695842 | ||||||||
\(923\) | −29.5762 | −0.973513 | ||||||||
\(924\) | 4.67068 | 0.153654 | ||||||||
\(925\) | −8.76690 | −0.288254 | ||||||||
\(926\) | 44.9258 | 1.47635 | ||||||||
\(927\) | 70.4264 | 2.31311 | ||||||||
\(928\) | −4.36280 | −0.143216 | ||||||||
\(929\) | 41.4648 | 1.36042 | 0.680209 | − | 0.733019i | \(-0.261889\pi\) | ||||
0.680209 | + | 0.733019i | \(0.261889\pi\) | |||||||
\(930\) | 86.4697 | 2.83545 | ||||||||
\(931\) | 73.9822 | 2.42467 | ||||||||
\(932\) | −4.80297 | −0.157327 | ||||||||
\(933\) | −11.3444 | −0.371399 | ||||||||
\(934\) | 26.4458 | 0.865334 | ||||||||
\(935\) | 11.7929 | 0.385668 | ||||||||
\(936\) | −82.9119 | −2.71006 | ||||||||
\(937\) | −42.3323 | −1.38293 | −0.691467 | − | 0.722408i | \(-0.743035\pi\) | ||||
−0.691467 | + | 0.722408i | \(0.743035\pi\) | |||||||
\(938\) | −90.1463 | −2.94338 | ||||||||
\(939\) | 80.0349 | 2.61184 | ||||||||
\(940\) | −1.42552 | −0.0464953 | ||||||||
\(941\) | 11.6346 | 0.379278 | 0.189639 | − | 0.981854i | \(-0.439268\pi\) | ||||
0.189639 | + | 0.981854i | \(0.439268\pi\) | |||||||
\(942\) | −20.2691 | −0.660403 | ||||||||
\(943\) | −5.91288 | −0.192550 | ||||||||
\(944\) | 25.4420 | 0.828067 | ||||||||
\(945\) | −95.9061 | −3.11982 | ||||||||
\(946\) | 7.51316 | 0.244274 | ||||||||
\(947\) | −29.1141 | −0.946081 | −0.473040 | − | 0.881041i | \(-0.656844\pi\) | ||||
−0.473040 | + | 0.881041i | \(0.656844\pi\) | |||||||
\(948\) | −0.343175 | −0.0111458 | ||||||||
\(949\) | 12.9102 | 0.419083 | ||||||||
\(950\) | 25.8354 | 0.838211 | ||||||||
\(951\) | −39.2656 | −1.27328 | ||||||||
\(952\) | −56.6250 | −1.83523 | ||||||||
\(953\) | 5.14787 | 0.166756 | 0.0833779 | − | 0.996518i | \(-0.473429\pi\) | ||||
0.0833779 | + | 0.996518i | \(0.473429\pi\) | |||||||
\(954\) | −37.1566 | −1.20299 | ||||||||
\(955\) | −13.5936 | −0.439878 | ||||||||
\(956\) | −0.00922528 | −0.000298367 0 | ||||||||
\(957\) | 6.81856 | 0.220413 | ||||||||
\(958\) | 16.5985 | 0.536274 | ||||||||
\(959\) | 33.4864 | 1.08133 | ||||||||
\(960\) | −79.4679 | −2.56482 | ||||||||
\(961\) | 24.3133 | 0.784301 | ||||||||
\(962\) | −12.3494 | −0.398162 | ||||||||
\(963\) | −88.5210 | −2.85255 | ||||||||
\(964\) | −4.23675 | −0.136456 | ||||||||
\(965\) | 5.37261 | 0.172951 | ||||||||
\(966\) | −154.190 | −4.96100 | ||||||||
\(967\) | 25.7412 | 0.827783 | 0.413891 | − | 0.910326i | \(-0.364169\pi\) | ||||
0.413891 | + | 0.910326i | \(0.364169\pi\) | |||||||
\(968\) | −3.00937 | −0.0967247 | ||||||||
\(969\) | 43.0714 | 1.38365 | ||||||||
\(970\) | 11.3741 | 0.365200 | ||||||||
\(971\) | 11.3852 | 0.365369 | 0.182685 | − | 0.983172i | \(-0.441521\pi\) | ||||
0.182685 | + | 0.983172i | \(0.441521\pi\) | |||||||
\(972\) | 4.17670 | 0.133968 | ||||||||
\(973\) | −18.4725 | −0.592201 | ||||||||
\(974\) | 21.1032 | 0.676191 | ||||||||
\(975\) | 75.7522 | 2.42601 | ||||||||
\(976\) | −3.24231 | −0.103784 | ||||||||
\(977\) | −32.2201 | −1.03081 | −0.515407 | − | 0.856946i | \(-0.672359\pi\) | ||||
−0.515407 | + | 0.856946i | \(0.672359\pi\) | |||||||
\(978\) | 31.6069 | 1.01068 | ||||||||
\(979\) | −7.27038 | −0.232362 | ||||||||
\(980\) | 18.8063 | 0.600744 | ||||||||
\(981\) | −35.5319 | −1.13445 | ||||||||
\(982\) | −31.8581 | −1.01663 | ||||||||
\(983\) | −27.9462 | −0.891344 | −0.445672 | − | 0.895196i | \(-0.647035\pi\) | ||||
−0.445672 | + | 0.895196i | \(0.647035\pi\) | |||||||
\(984\) | −6.10100 | −0.194493 | ||||||||
\(985\) | 53.4440 | 1.70287 | ||||||||
\(986\) | −11.5791 | −0.368755 | ||||||||
\(987\) | −19.8968 | −0.633323 | ||||||||
\(988\) | −7.08154 | −0.225294 | ||||||||
\(989\) | 48.2626 | 1.53466 | ||||||||
\(990\) | 20.8947 | 0.664076 | ||||||||
\(991\) | 35.9854 | 1.14311 | 0.571556 | − | 0.820563i | \(-0.306340\pi\) | ||||
0.571556 | + | 0.820563i | \(0.306340\pi\) | |||||||
\(992\) | −13.5616 | −0.430580 | ||||||||
\(993\) | 6.97155 | 0.221235 | ||||||||
\(994\) | −35.7890 | −1.13516 | ||||||||
\(995\) | 61.6843 | 1.95552 | ||||||||
\(996\) | −9.25783 | −0.293346 | ||||||||
\(997\) | −1.62823 | −0.0515667 | −0.0257834 | − | 0.999668i | \(-0.508208\pi\) | ||||
−0.0257834 | + | 0.999668i | \(0.508208\pi\) | |||||||
\(998\) | 35.1397 | 1.11233 | ||||||||
\(999\) | −10.7275 | −0.339402 |
(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 | 671.2.a.d.1.15 | ✓ | 21 | |
3.2 | odd | 2 | 6039.2.a.l.1.7 | 21 | |||
11.10 | odd | 2 | 7381.2.a.j.1.7 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.d.1.15 | ✓ | 21 | 1.1 | even | 1 | trivial | |
6039.2.a.l.1.7 | 21 | 3.2 | odd | 2 | |||
7381.2.a.j.1.7 | 21 | 11.10 | odd | 2 |