Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(7.84929451869\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42129 | −1.71211 | −0.856056 | − | 0.516883i | \(-0.827092\pi\) | ||||
−0.856056 | + | 0.516883i | \(0.827092\pi\) | |||||||
\(3\) | 0.803744 | 0.464042 | 0.232021 | − | 0.972711i | \(-0.425466\pi\) | ||||
0.232021 | + | 0.972711i | \(0.425466\pi\) | |||||||
\(4\) | 3.86265 | 1.93133 | ||||||||
\(5\) | 3.28925 | 1.47100 | 0.735499 | − | 0.677526i | \(-0.236948\pi\) | ||||
0.735499 | + | 0.677526i | \(0.236948\pi\) | |||||||
\(6\) | −1.94610 | −0.794492 | ||||||||
\(7\) | 3.29937 | 1.24704 | 0.623522 | − | 0.781806i | \(-0.285701\pi\) | ||||
0.623522 | + | 0.781806i | \(0.285701\pi\) | |||||||
\(8\) | −4.51003 | −1.59454 | ||||||||
\(9\) | −2.35400 | −0.784665 | ||||||||
\(10\) | −7.96423 | −2.51851 | ||||||||
\(11\) | 6.14409 | 1.85251 | 0.926256 | − | 0.376894i | \(-0.123008\pi\) | ||||
0.926256 | + | 0.376894i | \(0.123008\pi\) | |||||||
\(12\) | 3.10459 | 0.896217 | ||||||||
\(13\) | 1.33980 | 0.371593 | 0.185796 | − | 0.982588i | \(-0.440513\pi\) | ||||
0.185796 | + | 0.982588i | \(0.440513\pi\) | |||||||
\(14\) | −7.98873 | −2.13508 | ||||||||
\(15\) | 2.64372 | 0.682604 | ||||||||
\(16\) | 3.19479 | 0.798697 | ||||||||
\(17\) | −1.21072 | −0.293643 | −0.146822 | − | 0.989163i | \(-0.546904\pi\) | ||||
−0.146822 | + | 0.989163i | \(0.546904\pi\) | |||||||
\(18\) | 5.69971 | 1.34343 | ||||||||
\(19\) | 2.94674 | 0.676028 | 0.338014 | − | 0.941141i | \(-0.390245\pi\) | ||||
0.338014 | + | 0.941141i | \(0.390245\pi\) | |||||||
\(20\) | 12.7052 | 2.84098 | ||||||||
\(21\) | 2.65185 | 0.578680 | ||||||||
\(22\) | −14.8766 | −3.17171 | ||||||||
\(23\) | 6.73380 | 1.40409 | 0.702047 | − | 0.712131i | \(-0.252270\pi\) | ||||
0.702047 | + | 0.712131i | \(0.252270\pi\) | |||||||
\(24\) | −3.62491 | −0.739931 | ||||||||
\(25\) | 5.81917 | 1.16383 | ||||||||
\(26\) | −3.24404 | −0.636209 | ||||||||
\(27\) | −4.30324 | −0.828159 | ||||||||
\(28\) | 12.7443 | 2.40845 | ||||||||
\(29\) | −9.21882 | −1.71189 | −0.855946 | − | 0.517066i | \(-0.827024\pi\) | ||||
−0.855946 | + | 0.517066i | \(0.827024\pi\) | |||||||
\(30\) | −6.40121 | −1.16870 | ||||||||
\(31\) | 8.05855 | 1.44736 | 0.723679 | − | 0.690136i | \(-0.242450\pi\) | ||||
0.723679 | + | 0.690136i | \(0.242450\pi\) | |||||||
\(32\) | 1.28454 | 0.227078 | ||||||||
\(33\) | 4.93828 | 0.859644 | ||||||||
\(34\) | 2.93151 | 0.502750 | ||||||||
\(35\) | 10.8524 | 1.83440 | ||||||||
\(36\) | −9.09267 | −1.51544 | ||||||||
\(37\) | −7.06873 | −1.16209 | −0.581046 | − | 0.813870i | \(-0.697356\pi\) | ||||
−0.581046 | + | 0.813870i | \(0.697356\pi\) | |||||||
\(38\) | −7.13492 | −1.15744 | ||||||||
\(39\) | 1.07685 | 0.172435 | ||||||||
\(40\) | −14.8346 | −2.34556 | ||||||||
\(41\) | −11.2443 | −1.75606 | −0.878029 | − | 0.478607i | \(-0.841142\pi\) | ||||
−0.878029 | + | 0.478607i | \(0.841142\pi\) | |||||||
\(42\) | −6.42089 | −0.990765 | ||||||||
\(43\) | 3.36362 | 0.512947 | 0.256474 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256474 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(44\) | 23.7325 | 3.57781 | ||||||||
\(45\) | −7.74288 | −1.15424 | ||||||||
\(46\) | −16.3045 | −2.40397 | ||||||||
\(47\) | −9.40914 | −1.37246 | −0.686232 | − | 0.727382i | \(-0.740737\pi\) | ||||
−0.686232 | + | 0.727382i | \(0.740737\pi\) | |||||||
\(48\) | 2.56779 | 0.370629 | ||||||||
\(49\) | 3.88582 | 0.555117 | ||||||||
\(50\) | −14.0899 | −1.99261 | ||||||||
\(51\) | −0.973110 | −0.136263 | ||||||||
\(52\) | 5.17517 | 0.717668 | ||||||||
\(53\) | −9.27055 | −1.27341 | −0.636704 | − | 0.771109i | \(-0.719703\pi\) | ||||
−0.636704 | + | 0.771109i | \(0.719703\pi\) | |||||||
\(54\) | 10.4194 | 1.41790 | ||||||||
\(55\) | 20.2094 | 2.72504 | ||||||||
\(56\) | −14.8802 | −1.98846 | ||||||||
\(57\) | 2.36842 | 0.313706 | ||||||||
\(58\) | 22.3214 | 2.93095 | ||||||||
\(59\) | −1.86338 | −0.242592 | −0.121296 | − | 0.992616i | \(-0.538705\pi\) | ||||
−0.121296 | + | 0.992616i | \(0.538705\pi\) | |||||||
\(60\) | 10.2118 | 1.31833 | ||||||||
\(61\) | 3.12115 | 0.399623 | 0.199811 | − | 0.979834i | \(-0.435967\pi\) | ||||
0.199811 | + | 0.979834i | \(0.435967\pi\) | |||||||
\(62\) | −19.5121 | −2.47804 | ||||||||
\(63\) | −7.76669 | −0.978511 | ||||||||
\(64\) | −9.49983 | −1.18748 | ||||||||
\(65\) | 4.40693 | 0.546612 | ||||||||
\(66\) | −11.9570 | −1.47181 | ||||||||
\(67\) | −14.6369 | −1.78818 | −0.894091 | − | 0.447885i | \(-0.852177\pi\) | ||||
−0.894091 | + | 0.447885i | \(0.852177\pi\) | |||||||
\(68\) | −4.67660 | −0.567121 | ||||||||
\(69\) | 5.41225 | 0.651558 | ||||||||
\(70\) | −26.2769 | −3.14069 | ||||||||
\(71\) | −16.2584 | −1.92951 | −0.964757 | − | 0.263142i | \(-0.915241\pi\) | ||||
−0.964757 | + | 0.263142i | \(0.915241\pi\) | |||||||
\(72\) | 10.6166 | 1.25118 | ||||||||
\(73\) | 0.808970 | 0.0946828 | 0.0473414 | − | 0.998879i | \(-0.484925\pi\) | ||||
0.0473414 | + | 0.998879i | \(0.484925\pi\) | |||||||
\(74\) | 17.1155 | 1.98963 | ||||||||
\(75\) | 4.67712 | 0.540067 | ||||||||
\(76\) | 11.3822 | 1.30563 | ||||||||
\(77\) | 20.2716 | 2.31016 | ||||||||
\(78\) | −2.60738 | −0.295227 | ||||||||
\(79\) | 0.804882 | 0.0905563 | 0.0452781 | − | 0.998974i | \(-0.485583\pi\) | ||||
0.0452781 | + | 0.998974i | \(0.485583\pi\) | |||||||
\(80\) | 10.5085 | 1.17488 | ||||||||
\(81\) | 3.60328 | 0.400364 | ||||||||
\(82\) | 27.2256 | 3.00657 | ||||||||
\(83\) | 11.0360 | 1.21136 | 0.605680 | − | 0.795709i | \(-0.292901\pi\) | ||||
0.605680 | + | 0.795709i | \(0.292901\pi\) | |||||||
\(84\) | 10.2432 | 1.11762 | ||||||||
\(85\) | −3.98237 | −0.431948 | ||||||||
\(86\) | −8.14431 | −0.878223 | ||||||||
\(87\) | −7.40957 | −0.794389 | ||||||||
\(88\) | −27.7100 | −2.95390 | ||||||||
\(89\) | −2.88249 | −0.305544 | −0.152772 | − | 0.988261i | \(-0.548820\pi\) | ||||
−0.152772 | + | 0.988261i | \(0.548820\pi\) | |||||||
\(90\) | 18.7478 | 1.97619 | ||||||||
\(91\) | 4.42048 | 0.463392 | ||||||||
\(92\) | 26.0103 | 2.71176 | ||||||||
\(93\) | 6.47701 | 0.671635 | ||||||||
\(94\) | 22.7823 | 2.34981 | ||||||||
\(95\) | 9.69256 | 0.994436 | ||||||||
\(96\) | 1.03245 | 0.105373 | ||||||||
\(97\) | 8.89616 | 0.903268 | 0.451634 | − | 0.892203i | \(-0.350841\pi\) | ||||
0.451634 | + | 0.892203i | \(0.350841\pi\) | |||||||
\(98\) | −9.40870 | −0.950422 | ||||||||
\(99\) | −14.4632 | −1.45360 | ||||||||
\(100\) | 22.4774 | 2.24774 | ||||||||
\(101\) | 5.30180 | 0.527549 | 0.263775 | − | 0.964584i | \(-0.415032\pi\) | ||||
0.263775 | + | 0.964584i | \(0.415032\pi\) | |||||||
\(102\) | 2.35618 | 0.233297 | ||||||||
\(103\) | 7.45869 | 0.734927 | 0.367463 | − | 0.930038i | \(-0.380226\pi\) | ||||
0.367463 | + | 0.930038i | \(0.380226\pi\) | |||||||
\(104\) | −6.04253 | −0.592518 | ||||||||
\(105\) | 8.72259 | 0.851237 | ||||||||
\(106\) | 22.4467 | 2.18022 | ||||||||
\(107\) | 6.18674 | 0.598094 | 0.299047 | − | 0.954238i | \(-0.403331\pi\) | ||||
0.299047 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(108\) | −16.6219 | −1.59945 | ||||||||
\(109\) | 6.29568 | 0.603017 | 0.301508 | − | 0.953464i | \(-0.402510\pi\) | ||||
0.301508 | + | 0.953464i | \(0.402510\pi\) | |||||||
\(110\) | −48.9330 | −4.66558 | ||||||||
\(111\) | −5.68145 | −0.539260 | ||||||||
\(112\) | 10.5408 | 0.996009 | ||||||||
\(113\) | −15.0787 | −1.41849 | −0.709244 | − | 0.704963i | \(-0.750963\pi\) | ||||
−0.709244 | + | 0.704963i | \(0.750963\pi\) | |||||||
\(114\) | −5.73465 | −0.537099 | ||||||||
\(115\) | 22.1491 | 2.06542 | ||||||||
\(116\) | −35.6091 | −3.30622 | ||||||||
\(117\) | −3.15388 | −0.291576 | ||||||||
\(118\) | 4.51179 | 0.415344 | ||||||||
\(119\) | −3.99461 | −0.366186 | ||||||||
\(120\) | −11.9232 | −1.08844 | ||||||||
\(121\) | 26.7498 | 2.43180 | ||||||||
\(122\) | −7.55722 | −0.684199 | ||||||||
\(123\) | −9.03751 | −0.814885 | ||||||||
\(124\) | 31.1274 | 2.79532 | ||||||||
\(125\) | 2.69444 | 0.240998 | ||||||||
\(126\) | 18.8054 | 1.67532 | ||||||||
\(127\) | 8.43191 | 0.748211 | 0.374105 | − | 0.927386i | \(-0.377950\pi\) | ||||
0.374105 | + | 0.927386i | \(0.377950\pi\) | |||||||
\(128\) | 20.4328 | 1.80602 | ||||||||
\(129\) | 2.70349 | 0.238029 | ||||||||
\(130\) | −10.6705 | −0.935861 | ||||||||
\(131\) | −20.3969 | −1.78208 | −0.891041 | − | 0.453923i | \(-0.850024\pi\) | ||||
−0.891041 | + | 0.453923i | \(0.850024\pi\) | |||||||
\(132\) | 19.0749 | 1.66025 | ||||||||
\(133\) | 9.72237 | 0.843037 | ||||||||
\(134\) | 35.4402 | 3.06157 | ||||||||
\(135\) | −14.1544 | −1.21822 | ||||||||
\(136\) | 5.46039 | 0.468224 | ||||||||
\(137\) | 5.36786 | 0.458607 | 0.229304 | − | 0.973355i | \(-0.426355\pi\) | ||||
0.229304 | + | 0.973355i | \(0.426355\pi\) | |||||||
\(138\) | −13.1046 | −1.11554 | ||||||||
\(139\) | −12.7662 | −1.08282 | −0.541409 | − | 0.840759i | \(-0.682109\pi\) | ||||
−0.541409 | + | 0.840759i | \(0.682109\pi\) | |||||||
\(140\) | 41.9192 | 3.54282 | ||||||||
\(141\) | −7.56254 | −0.636881 | ||||||||
\(142\) | 39.3663 | 3.30354 | ||||||||
\(143\) | 8.23184 | 0.688381 | ||||||||
\(144\) | −7.52052 | −0.626710 | ||||||||
\(145\) | −30.3230 | −2.51819 | ||||||||
\(146\) | −1.95875 | −0.162107 | ||||||||
\(147\) | 3.12320 | 0.257597 | ||||||||
\(148\) | −27.3041 | −2.24438 | ||||||||
\(149\) | −9.43354 | −0.772826 | −0.386413 | − | 0.922326i | \(-0.626286\pi\) | ||||
−0.386413 | + | 0.922326i | \(0.626286\pi\) | |||||||
\(150\) | −11.3247 | −0.924656 | ||||||||
\(151\) | −1.65838 | −0.134957 | −0.0674785 | − | 0.997721i | \(-0.521495\pi\) | ||||
−0.0674785 | + | 0.997721i | \(0.521495\pi\) | |||||||
\(152\) | −13.2899 | −1.07795 | ||||||||
\(153\) | 2.85003 | 0.230412 | ||||||||
\(154\) | −49.0835 | −3.95526 | ||||||||
\(155\) | 26.5066 | 2.12906 | ||||||||
\(156\) | 4.15952 | 0.333028 | ||||||||
\(157\) | 10.3429 | 0.825451 | 0.412726 | − | 0.910855i | \(-0.364577\pi\) | ||||
0.412726 | + | 0.910855i | \(0.364577\pi\) | |||||||
\(158\) | −1.94885 | −0.155042 | ||||||||
\(159\) | −7.45115 | −0.590914 | ||||||||
\(160\) | 4.22519 | 0.334030 | ||||||||
\(161\) | 22.2173 | 1.75097 | ||||||||
\(162\) | −8.72459 | −0.685469 | ||||||||
\(163\) | −2.74614 | −0.215095 | −0.107547 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107547 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(164\) | −43.4327 | −3.39152 | ||||||||
\(165\) | 16.2432 | 1.26453 | ||||||||
\(166\) | −26.7214 | −2.07398 | ||||||||
\(167\) | 16.9268 | 1.30983 | 0.654916 | − | 0.755702i | \(-0.272704\pi\) | ||||
0.654916 | + | 0.755702i | \(0.272704\pi\) | |||||||
\(168\) | −11.9599 | −0.922726 | ||||||||
\(169\) | −11.2049 | −0.861919 | ||||||||
\(170\) | 9.64247 | 0.739544 | ||||||||
\(171\) | −6.93661 | −0.530456 | ||||||||
\(172\) | 12.9925 | 0.990669 | ||||||||
\(173\) | 17.3079 | 1.31590 | 0.657950 | − | 0.753062i | \(-0.271424\pi\) | ||||
0.657950 | + | 0.753062i | \(0.271424\pi\) | |||||||
\(174\) | 17.9407 | 1.36008 | ||||||||
\(175\) | 19.1996 | 1.45135 | ||||||||
\(176\) | 19.6291 | 1.47960 | ||||||||
\(177\) | −1.49768 | −0.112573 | ||||||||
\(178\) | 6.97936 | 0.523125 | ||||||||
\(179\) | 6.41225 | 0.479274 | 0.239637 | − | 0.970863i | \(-0.422972\pi\) | ||||
0.239637 | + | 0.970863i | \(0.422972\pi\) | |||||||
\(180\) | −29.9081 | −2.22922 | ||||||||
\(181\) | 5.30566 | 0.394366 | 0.197183 | − | 0.980367i | \(-0.436821\pi\) | ||||
0.197183 | + | 0.980367i | \(0.436821\pi\) | |||||||
\(182\) | −10.7033 | −0.793380 | ||||||||
\(183\) | 2.50861 | 0.185442 | ||||||||
\(184\) | −30.3696 | −2.23888 | ||||||||
\(185\) | −23.2508 | −1.70944 | ||||||||
\(186\) | −15.6827 | −1.14991 | ||||||||
\(187\) | −7.43878 | −0.543978 | ||||||||
\(188\) | −36.3443 | −2.65068 | ||||||||
\(189\) | −14.1980 | −1.03275 | ||||||||
\(190\) | −23.4685 | −1.70259 | ||||||||
\(191\) | 6.66755 | 0.482447 | 0.241223 | − | 0.970470i | \(-0.422451\pi\) | ||||
0.241223 | + | 0.970470i | \(0.422451\pi\) | |||||||
\(192\) | −7.63543 | −0.551040 | ||||||||
\(193\) | 17.2573 | 1.24221 | 0.621104 | − | 0.783728i | \(-0.286684\pi\) | ||||
0.621104 | + | 0.783728i | \(0.286684\pi\) | |||||||
\(194\) | −21.5402 | −1.54650 | ||||||||
\(195\) | 3.54204 | 0.253651 | ||||||||
\(196\) | 15.0096 | 1.07211 | ||||||||
\(197\) | −21.1512 | −1.50696 | −0.753481 | − | 0.657470i | \(-0.771627\pi\) | ||||
−0.753481 | + | 0.657470i | \(0.771627\pi\) | |||||||
\(198\) | 35.0195 | 2.48873 | ||||||||
\(199\) | −5.65771 | −0.401065 | −0.200532 | − | 0.979687i | \(-0.564267\pi\) | ||||
−0.200532 | + | 0.979687i | \(0.564267\pi\) | |||||||
\(200\) | −26.2446 | −1.85577 | ||||||||
\(201\) | −11.7643 | −0.829791 | ||||||||
\(202\) | −12.8372 | −0.903223 | ||||||||
\(203\) | −30.4163 | −2.13480 | ||||||||
\(204\) | −3.75879 | −0.263168 | ||||||||
\(205\) | −36.9852 | −2.58316 | ||||||||
\(206\) | −18.0597 | −1.25828 | ||||||||
\(207\) | −15.8513 | −1.10174 | ||||||||
\(208\) | 4.28037 | 0.296790 | ||||||||
\(209\) | 18.1050 | 1.25235 | ||||||||
\(210\) | −21.1199 | −1.45741 | ||||||||
\(211\) | −15.9055 | −1.09498 | −0.547488 | − | 0.836813i | \(-0.684416\pi\) | ||||
−0.547488 | + | 0.836813i | \(0.684416\pi\) | |||||||
\(212\) | −35.8089 | −2.45937 | ||||||||
\(213\) | −13.0676 | −0.895375 | ||||||||
\(214\) | −14.9799 | −1.02400 | ||||||||
\(215\) | 11.0638 | 0.754544 | ||||||||
\(216\) | 19.4077 | 1.32053 | ||||||||
\(217\) | 26.5881 | 1.80492 | ||||||||
\(218\) | −15.2437 | −1.03243 | ||||||||
\(219\) | 0.650205 | 0.0439368 | ||||||||
\(220\) | 78.0621 | 5.26295 | ||||||||
\(221\) | −1.62212 | −0.109116 | ||||||||
\(222\) | 13.7565 | 0.923273 | ||||||||
\(223\) | 12.1633 | 0.814513 | 0.407256 | − | 0.913314i | \(-0.366486\pi\) | ||||
0.407256 | + | 0.913314i | \(0.366486\pi\) | |||||||
\(224\) | 4.23818 | 0.283176 | ||||||||
\(225\) | −13.6983 | −0.913219 | ||||||||
\(226\) | 36.5100 | 2.42861 | ||||||||
\(227\) | 2.24524 | 0.149022 | 0.0745110 | − | 0.997220i | \(-0.476260\pi\) | ||||
0.0745110 | + | 0.997220i | \(0.476260\pi\) | |||||||
\(228\) | 9.14841 | 0.605868 | ||||||||
\(229\) | 2.30927 | 0.152601 | 0.0763005 | − | 0.997085i | \(-0.475689\pi\) | ||||
0.0763005 | + | 0.997085i | \(0.475689\pi\) | |||||||
\(230\) | −53.6295 | −3.53623 | ||||||||
\(231\) | 16.2932 | 1.07201 | ||||||||
\(232\) | 41.5771 | 2.72967 | ||||||||
\(233\) | 16.5492 | 1.08417 | 0.542086 | − | 0.840323i | \(-0.317635\pi\) | ||||
0.542086 | + | 0.840323i | \(0.317635\pi\) | |||||||
\(234\) | 7.63646 | 0.499211 | ||||||||
\(235\) | −30.9490 | −2.01889 | ||||||||
\(236\) | −7.19760 | −0.468524 | ||||||||
\(237\) | 0.646919 | 0.0420219 | ||||||||
\(238\) | 9.67213 | 0.626951 | ||||||||
\(239\) | −1.64872 | −0.106647 | −0.0533234 | − | 0.998577i | \(-0.516981\pi\) | ||||
−0.0533234 | + | 0.998577i | \(0.516981\pi\) | |||||||
\(240\) | 8.44611 | 0.545194 | ||||||||
\(241\) | −23.7503 | −1.52989 | −0.764945 | − | 0.644096i | \(-0.777234\pi\) | ||||
−0.764945 | + | 0.644096i | \(0.777234\pi\) | |||||||
\(242\) | −64.7692 | −4.16352 | ||||||||
\(243\) | 15.8058 | 1.01395 | ||||||||
\(244\) | 12.0559 | 0.771802 | ||||||||
\(245\) | 12.7814 | 0.816575 | ||||||||
\(246\) | 21.8824 | 1.39517 | ||||||||
\(247\) | 3.94803 | 0.251207 | ||||||||
\(248\) | −36.3443 | −2.30787 | ||||||||
\(249\) | 8.87013 | 0.562121 | ||||||||
\(250\) | −6.52404 | −0.412616 | ||||||||
\(251\) | 26.1399 | 1.64993 | 0.824967 | − | 0.565181i | \(-0.191194\pi\) | ||||
0.824967 | + | 0.565181i | \(0.191194\pi\) | |||||||
\(252\) | −30.0000 | −1.88983 | ||||||||
\(253\) | 41.3730 | 2.60110 | ||||||||
\(254\) | −20.4161 | −1.28102 | ||||||||
\(255\) | −3.20080 | −0.200442 | ||||||||
\(256\) | −30.4740 | −1.90463 | ||||||||
\(257\) | −12.3353 | −0.769456 | −0.384728 | − | 0.923030i | \(-0.625705\pi\) | ||||
−0.384728 | + | 0.923030i | \(0.625705\pi\) | |||||||
\(258\) | −6.54594 | −0.407532 | ||||||||
\(259\) | −23.3223 | −1.44918 | ||||||||
\(260\) | 17.0224 | 1.05569 | ||||||||
\(261\) | 21.7011 | 1.34326 | ||||||||
\(262\) | 49.3868 | 3.05112 | ||||||||
\(263\) | −9.11640 | −0.562141 | −0.281071 | − | 0.959687i | \(-0.590690\pi\) | ||||
−0.281071 | + | 0.959687i | \(0.590690\pi\) | |||||||
\(264\) | −22.2718 | −1.37073 | ||||||||
\(265\) | −30.4931 | −1.87318 | ||||||||
\(266\) | −23.5407 | −1.44337 | ||||||||
\(267\) | −2.31679 | −0.141785 | ||||||||
\(268\) | −56.5373 | −3.45356 | ||||||||
\(269\) | 9.01140 | 0.549434 | 0.274717 | − | 0.961525i | \(-0.411416\pi\) | ||||
0.274717 | + | 0.961525i | \(0.411416\pi\) | |||||||
\(270\) | 34.2720 | 2.08573 | ||||||||
\(271\) | −3.07864 | −0.187014 | −0.0935070 | − | 0.995619i | \(-0.529808\pi\) | ||||
−0.0935070 | + | 0.995619i | \(0.529808\pi\) | |||||||
\(272\) | −3.86800 | −0.234532 | ||||||||
\(273\) | 3.55294 | 0.215034 | ||||||||
\(274\) | −12.9972 | −0.785187 | ||||||||
\(275\) | 35.7535 | 2.15602 | ||||||||
\(276\) | 20.9056 | 1.25837 | ||||||||
\(277\) | 17.9366 | 1.07771 | 0.538853 | − | 0.842400i | \(-0.318858\pi\) | ||||
0.538853 | + | 0.842400i | \(0.318858\pi\) | |||||||
\(278\) | 30.9108 | 1.85391 | ||||||||
\(279\) | −18.9698 | −1.13569 | ||||||||
\(280\) | −48.9448 | −2.92501 | ||||||||
\(281\) | −12.1412 | −0.724281 | −0.362141 | − | 0.932123i | \(-0.617954\pi\) | ||||
−0.362141 | + | 0.932123i | \(0.617954\pi\) | |||||||
\(282\) | 18.3111 | 1.09041 | ||||||||
\(283\) | 22.6686 | 1.34751 | 0.673755 | − | 0.738954i | \(-0.264680\pi\) | ||||
0.673755 | + | 0.738954i | \(0.264680\pi\) | |||||||
\(284\) | −62.8005 | −3.72652 | ||||||||
\(285\) | 7.79034 | 0.461460 | ||||||||
\(286\) | −19.9317 | −1.17858 | ||||||||
\(287\) | −37.0989 | −2.18988 | ||||||||
\(288\) | −3.02381 | −0.178180 | ||||||||
\(289\) | −15.5342 | −0.913774 | ||||||||
\(290\) | 73.4208 | 4.31142 | ||||||||
\(291\) | 7.15023 | 0.419154 | ||||||||
\(292\) | 3.12477 | 0.182863 | ||||||||
\(293\) | −5.07419 | −0.296438 | −0.148219 | − | 0.988955i | \(-0.547354\pi\) | ||||
−0.148219 | + | 0.988955i | \(0.547354\pi\) | |||||||
\(294\) | −7.56218 | −0.441036 | ||||||||
\(295\) | −6.12913 | −0.356852 | ||||||||
\(296\) | 31.8802 | 1.85300 | ||||||||
\(297\) | −26.4395 | −1.53418 | ||||||||
\(298\) | 22.8414 | 1.32316 | ||||||||
\(299\) | 9.02192 | 0.521751 | ||||||||
\(300\) | 18.0661 | 1.04305 | ||||||||
\(301\) | 11.0978 | 0.639668 | ||||||||
\(302\) | 4.01542 | 0.231061 | ||||||||
\(303\) | 4.26129 | 0.244805 | ||||||||
\(304\) | 9.41421 | 0.539942 | ||||||||
\(305\) | 10.2663 | 0.587844 | ||||||||
\(306\) | −6.90076 | −0.394490 | ||||||||
\(307\) | −19.3639 | −1.10515 | −0.552577 | − | 0.833462i | \(-0.686356\pi\) | ||||
−0.552577 | + | 0.833462i | \(0.686356\pi\) | |||||||
\(308\) | 78.3022 | 4.46168 | ||||||||
\(309\) | 5.99488 | 0.341037 | ||||||||
\(310\) | −64.1802 | −3.64519 | ||||||||
\(311\) | −13.2713 | −0.752546 | −0.376273 | − | 0.926509i | \(-0.622795\pi\) | ||||
−0.376273 | + | 0.926509i | \(0.622795\pi\) | |||||||
\(312\) | −4.85664 | −0.274953 | ||||||||
\(313\) | −19.1230 | −1.08089 | −0.540447 | − | 0.841378i | \(-0.681745\pi\) | ||||
−0.540447 | + | 0.841378i | \(0.681745\pi\) | |||||||
\(314\) | −25.0431 | −1.41326 | ||||||||
\(315\) | −25.5466 | −1.43939 | ||||||||
\(316\) | 3.10898 | 0.174894 | ||||||||
\(317\) | 13.6712 | 0.767849 | 0.383924 | − | 0.923365i | \(-0.374572\pi\) | ||||
0.383924 | + | 0.923365i | \(0.374572\pi\) | |||||||
\(318\) | 18.0414 | 1.01171 | ||||||||
\(319\) | −56.6412 | −3.17130 | ||||||||
\(320\) | −31.2473 | −1.74678 | ||||||||
\(321\) | 4.97255 | 0.277541 | ||||||||
\(322\) | −53.7945 | −2.99785 | ||||||||
\(323\) | −3.56768 | −0.198511 | ||||||||
\(324\) | 13.9182 | 0.773235 | ||||||||
\(325\) | 7.79650 | 0.432472 | ||||||||
\(326\) | 6.64922 | 0.368266 | ||||||||
\(327\) | 5.06011 | 0.279825 | ||||||||
\(328\) | 50.7119 | 2.80010 | ||||||||
\(329\) | −31.0442 | −1.71152 | ||||||||
\(330\) | −39.3296 | −2.16502 | ||||||||
\(331\) | 18.5842 | 1.02148 | 0.510741 | − | 0.859734i | \(-0.329371\pi\) | ||||
0.510741 | + | 0.859734i | \(0.329371\pi\) | |||||||
\(332\) | 42.6283 | 2.33953 | ||||||||
\(333\) | 16.6398 | 0.911854 | ||||||||
\(334\) | −40.9846 | −2.24258 | ||||||||
\(335\) | −48.1444 | −2.63041 | ||||||||
\(336\) | 8.47209 | 0.462190 | ||||||||
\(337\) | 31.1121 | 1.69479 | 0.847393 | − | 0.530966i | \(-0.178171\pi\) | ||||
0.847393 | + | 0.530966i | \(0.178171\pi\) | |||||||
\(338\) | 27.1304 | 1.47570 | ||||||||
\(339\) | −12.1194 | −0.658238 | ||||||||
\(340\) | −15.3825 | −0.834233 | ||||||||
\(341\) | 49.5125 | 2.68125 | ||||||||
\(342\) | 16.7956 | 0.908200 | ||||||||
\(343\) | −10.2748 | −0.554789 | ||||||||
\(344\) | −15.1700 | −0.817913 | ||||||||
\(345\) | 17.8022 | 0.958440 | ||||||||
\(346\) | −41.9076 | −2.25297 | ||||||||
\(347\) | 6.38552 | 0.342793 | 0.171396 | − | 0.985202i | \(-0.445172\pi\) | ||||
0.171396 | + | 0.985202i | \(0.445172\pi\) | |||||||
\(348\) | −28.6206 | −1.53423 | ||||||||
\(349\) | 28.4885 | 1.52495 | 0.762477 | − | 0.647015i | \(-0.223983\pi\) | ||||
0.762477 | + | 0.647015i | \(0.223983\pi\) | |||||||
\(350\) | −46.4877 | −2.48487 | ||||||||
\(351\) | −5.76547 | −0.307738 | ||||||||
\(352\) | 7.89236 | 0.420664 | ||||||||
\(353\) | −7.94868 | −0.423065 | −0.211533 | − | 0.977371i | \(-0.567845\pi\) | ||||
−0.211533 | + | 0.977371i | \(0.567845\pi\) | |||||||
\(354\) | 3.62633 | 0.192737 | ||||||||
\(355\) | −53.4779 | −2.83831 | ||||||||
\(356\) | −11.1341 | −0.590105 | ||||||||
\(357\) | −3.21065 | −0.169925 | ||||||||
\(358\) | −15.5259 | −0.820570 | ||||||||
\(359\) | 5.61107 | 0.296141 | 0.148071 | − | 0.988977i | \(-0.452694\pi\) | ||||
0.148071 | + | 0.988977i | \(0.452694\pi\) | |||||||
\(360\) | 34.9206 | 1.84048 | ||||||||
\(361\) | −10.3167 | −0.542986 | ||||||||
\(362\) | −12.8465 | −0.675199 | ||||||||
\(363\) | 21.5000 | 1.12846 | ||||||||
\(364\) | 17.0748 | 0.894962 | ||||||||
\(365\) | 2.66090 | 0.139278 | ||||||||
\(366\) | −6.07407 | −0.317497 | ||||||||
\(367\) | −13.6352 | −0.711751 | −0.355875 | − | 0.934533i | \(-0.615817\pi\) | ||||
−0.355875 | + | 0.934533i | \(0.615817\pi\) | |||||||
\(368\) | 21.5130 | 1.12145 | ||||||||
\(369\) | 26.4689 | 1.37792 | ||||||||
\(370\) | 56.2971 | 2.92674 | ||||||||
\(371\) | −30.5869 | −1.58799 | ||||||||
\(372\) | 25.0185 | 1.29715 | ||||||||
\(373\) | −18.3438 | −0.949804 | −0.474902 | − | 0.880039i | \(-0.657516\pi\) | ||||
−0.474902 | + | 0.880039i | \(0.657516\pi\) | |||||||
\(374\) | 18.0115 | 0.931351 | ||||||||
\(375\) | 2.16564 | 0.111833 | ||||||||
\(376\) | 42.4355 | 2.18844 | ||||||||
\(377\) | −12.3513 | −0.636127 | ||||||||
\(378\) | 34.3774 | 1.76818 | ||||||||
\(379\) | 24.4662 | 1.25674 | 0.628371 | − | 0.777914i | \(-0.283722\pi\) | ||||
0.628371 | + | 0.777914i | \(0.283722\pi\) | |||||||
\(380\) | 37.4390 | 1.92058 | ||||||||
\(381\) | 6.77710 | 0.347201 | ||||||||
\(382\) | −16.1441 | −0.826003 | ||||||||
\(383\) | 27.6006 | 1.41033 | 0.705163 | − | 0.709045i | \(-0.250874\pi\) | ||||
0.705163 | + | 0.709045i | \(0.250874\pi\) | |||||||
\(384\) | 16.4227 | 0.838069 | ||||||||
\(385\) | 66.6784 | 3.39824 | ||||||||
\(386\) | −41.7850 | −2.12680 | ||||||||
\(387\) | −7.91795 | −0.402492 | ||||||||
\(388\) | 34.3628 | 1.74451 | ||||||||
\(389\) | −15.7915 | −0.800659 | −0.400329 | − | 0.916371i | \(-0.631104\pi\) | ||||
−0.400329 | + | 0.916371i | \(0.631104\pi\) | |||||||
\(390\) | −8.57632 | −0.434279 | ||||||||
\(391\) | −8.15275 | −0.412302 | ||||||||
\(392\) | −17.5251 | −0.885154 | ||||||||
\(393\) | −16.3939 | −0.826961 | ||||||||
\(394\) | 51.2133 | 2.58009 | ||||||||
\(395\) | 2.64746 | 0.133208 | ||||||||
\(396\) | −55.8662 | −2.80738 | ||||||||
\(397\) | 8.54584 | 0.428903 | 0.214452 | − | 0.976735i | \(-0.431204\pi\) | ||||
0.214452 | + | 0.976735i | \(0.431204\pi\) | |||||||
\(398\) | 13.6990 | 0.686668 | ||||||||
\(399\) | 7.81430 | 0.391204 | ||||||||
\(400\) | 18.5910 | 0.929550 | ||||||||
\(401\) | −22.1699 | −1.10711 | −0.553555 | − | 0.832813i | \(-0.686729\pi\) | ||||
−0.553555 | + | 0.832813i | \(0.686729\pi\) | |||||||
\(402\) | 28.4849 | 1.42070 | ||||||||
\(403\) | 10.7968 | 0.537828 | ||||||||
\(404\) | 20.4790 | 1.01887 | ||||||||
\(405\) | 11.8521 | 0.588935 | ||||||||
\(406\) | 73.6466 | 3.65502 | ||||||||
\(407\) | −43.4309 | −2.15279 | ||||||||
\(408\) | 4.38876 | 0.217276 | ||||||||
\(409\) | 4.50609 | 0.222812 | 0.111406 | − | 0.993775i | \(-0.464465\pi\) | ||||
0.111406 | + | 0.993775i | \(0.464465\pi\) | |||||||
\(410\) | 89.5519 | 4.42265 | ||||||||
\(411\) | 4.31438 | 0.212813 | ||||||||
\(412\) | 28.8103 | 1.41938 | ||||||||
\(413\) | −6.14798 | −0.302522 | ||||||||
\(414\) | 38.3807 | 1.88631 | ||||||||
\(415\) | 36.3002 | 1.78191 | ||||||||
\(416\) | 1.72103 | 0.0843804 | ||||||||
\(417\) | −10.2608 | −0.502473 | ||||||||
\(418\) | −43.8376 | −2.14417 | ||||||||
\(419\) | −7.62431 | −0.372472 | −0.186236 | − | 0.982505i | \(-0.559629\pi\) | ||||
−0.186236 | + | 0.982505i | \(0.559629\pi\) | |||||||
\(420\) | 33.6923 | 1.64402 | ||||||||
\(421\) | 1.89700 | 0.0924543 | 0.0462271 | − | 0.998931i | \(-0.485280\pi\) | ||||
0.0462271 | + | 0.998931i | \(0.485280\pi\) | |||||||
\(422\) | 38.5117 | 1.87472 | ||||||||
\(423\) | 22.1491 | 1.07693 | ||||||||
\(424\) | 41.8104 | 2.03049 | ||||||||
\(425\) | −7.04539 | −0.341752 | ||||||||
\(426\) | 31.6404 | 1.53298 | ||||||||
\(427\) | 10.2978 | 0.498347 | ||||||||
\(428\) | 23.8972 | 1.15512 | ||||||||
\(429\) | 6.61629 | 0.319438 | ||||||||
\(430\) | −26.7887 | −1.29186 | ||||||||
\(431\) | 25.4036 | 1.22365 | 0.611824 | − | 0.790994i | \(-0.290436\pi\) | ||||
0.611824 | + | 0.790994i | \(0.290436\pi\) | |||||||
\(432\) | −13.7479 | −0.661448 | ||||||||
\(433\) | −24.9618 | −1.19959 | −0.599793 | − | 0.800155i | \(-0.704750\pi\) | ||||
−0.599793 | + | 0.800155i | \(0.704750\pi\) | |||||||
\(434\) | −64.3776 | −3.09022 | ||||||||
\(435\) | −24.3719 | −1.16854 | ||||||||
\(436\) | 24.3180 | 1.16462 | ||||||||
\(437\) | 19.8427 | 0.949207 | ||||||||
\(438\) | −1.57434 | −0.0752247 | ||||||||
\(439\) | 7.59473 | 0.362476 | 0.181238 | − | 0.983439i | \(-0.441989\pi\) | ||||
0.181238 | + | 0.983439i | \(0.441989\pi\) | |||||||
\(440\) | −91.1452 | −4.34518 | ||||||||
\(441\) | −9.14720 | −0.435581 | ||||||||
\(442\) | 3.92763 | 0.186818 | ||||||||
\(443\) | −2.20249 | −0.104644 | −0.0523218 | − | 0.998630i | \(-0.516662\pi\) | ||||
−0.0523218 | + | 0.998630i | \(0.516662\pi\) | |||||||
\(444\) | −21.9455 | −1.04149 | ||||||||
\(445\) | −9.48124 | −0.449454 | ||||||||
\(446\) | −29.4508 | −1.39454 | ||||||||
\(447\) | −7.58215 | −0.358624 | ||||||||
\(448\) | −31.3434 | −1.48084 | ||||||||
\(449\) | 14.5271 | 0.685575 | 0.342788 | − | 0.939413i | \(-0.388629\pi\) | ||||
0.342788 | + | 0.939413i | \(0.388629\pi\) | |||||||
\(450\) | 33.1676 | 1.56353 | ||||||||
\(451\) | −69.0858 | −3.25312 | ||||||||
\(452\) | −58.2439 | −2.73956 | ||||||||
\(453\) | −1.33291 | −0.0626257 | ||||||||
\(454\) | −5.43639 | −0.255142 | ||||||||
\(455\) | 14.5401 | 0.681649 | ||||||||
\(456\) | −10.6817 | −0.500215 | ||||||||
\(457\) | 16.7787 | 0.784874 | 0.392437 | − | 0.919779i | \(-0.371632\pi\) | ||||
0.392437 | + | 0.919779i | \(0.371632\pi\) | |||||||
\(458\) | −5.59142 | −0.261270 | ||||||||
\(459\) | 5.21003 | 0.243183 | ||||||||
\(460\) | 85.5545 | 3.98900 | ||||||||
\(461\) | 10.9469 | 0.509849 | 0.254925 | − | 0.966961i | \(-0.417949\pi\) | ||||
0.254925 | + | 0.966961i | \(0.417949\pi\) | |||||||
\(462\) | −39.4505 | −1.83541 | ||||||||
\(463\) | 13.0103 | 0.604642 | 0.302321 | − | 0.953206i | \(-0.402239\pi\) | ||||
0.302321 | + | 0.953206i | \(0.402239\pi\) | |||||||
\(464\) | −29.4522 | −1.36728 | ||||||||
\(465\) | 21.3045 | 0.987973 | ||||||||
\(466\) | −40.0703 | −1.85622 | ||||||||
\(467\) | 6.05147 | 0.280028 | 0.140014 | − | 0.990149i | \(-0.455285\pi\) | ||||
0.140014 | + | 0.990149i | \(0.455285\pi\) | |||||||
\(468\) | −12.1823 | −0.563129 | ||||||||
\(469\) | −48.2925 | −2.22994 | ||||||||
\(470\) | 74.9366 | 3.45657 | ||||||||
\(471\) | 8.31302 | 0.383044 | ||||||||
\(472\) | 8.40391 | 0.386821 | ||||||||
\(473\) | 20.6664 | 0.950242 | ||||||||
\(474\) | −1.56638 | −0.0719462 | ||||||||
\(475\) | 17.1476 | 0.786784 | ||||||||
\(476\) | −15.4298 | −0.707224 | ||||||||
\(477\) | 21.8228 | 0.999198 | ||||||||
\(478\) | 3.99203 | 0.182591 | ||||||||
\(479\) | −1.27446 | −0.0582317 | −0.0291159 | − | 0.999576i | \(-0.509269\pi\) | ||||
−0.0291159 | + | 0.999576i | \(0.509269\pi\) | |||||||
\(480\) | 3.39597 | 0.155004 | ||||||||
\(481\) | −9.47067 | −0.431825 | ||||||||
\(482\) | 57.5063 | 2.61934 | ||||||||
\(483\) | 17.8570 | 0.812521 | ||||||||
\(484\) | 103.325 | 4.69661 | ||||||||
\(485\) | 29.2617 | 1.32870 | ||||||||
\(486\) | −38.2706 | −1.73599 | ||||||||
\(487\) | 1.09275 | 0.0495174 | 0.0247587 | − | 0.999693i | \(-0.492118\pi\) | ||||
0.0247587 | + | 0.999693i | \(0.492118\pi\) | |||||||
\(488\) | −14.0765 | −0.637213 | ||||||||
\(489\) | −2.20720 | −0.0998129 | ||||||||
\(490\) | −30.9476 | −1.39807 | ||||||||
\(491\) | 7.14892 | 0.322626 | 0.161313 | − | 0.986903i | \(-0.448427\pi\) | ||||
0.161313 | + | 0.986903i | \(0.448427\pi\) | |||||||
\(492\) | −34.9088 | −1.57381 | ||||||||
\(493\) | 11.1614 | 0.502685 | ||||||||
\(494\) | −9.55934 | −0.430095 | ||||||||
\(495\) | −47.5730 | −2.13825 | ||||||||
\(496\) | 25.7454 | 1.15600 | ||||||||
\(497\) | −53.6423 | −2.40619 | ||||||||
\(498\) | −21.4772 | −0.962415 | ||||||||
\(499\) | −9.58772 | −0.429205 | −0.214603 | − | 0.976701i | \(-0.568846\pi\) | ||||
−0.214603 | + | 0.976701i | \(0.568846\pi\) | |||||||
\(500\) | 10.4077 | 0.465447 | ||||||||
\(501\) | 13.6048 | 0.607817 | ||||||||
\(502\) | −63.2923 | −2.82487 | ||||||||
\(503\) | 1.43629 | 0.0640409 | 0.0320205 | − | 0.999487i | \(-0.489806\pi\) | ||||
0.0320205 | + | 0.999487i | \(0.489806\pi\) | |||||||
\(504\) | 35.0280 | 1.56027 | ||||||||
\(505\) | 17.4390 | 0.776023 | ||||||||
\(506\) | −100.176 | −4.45338 | ||||||||
\(507\) | −9.00591 | −0.399966 | ||||||||
\(508\) | 32.5695 | 1.44504 | ||||||||
\(509\) | −12.9579 | −0.574350 | −0.287175 | − | 0.957878i | \(-0.592716\pi\) | ||||
−0.287175 | + | 0.957878i | \(0.592716\pi\) | |||||||
\(510\) | 7.75008 | 0.343179 | ||||||||
\(511\) | 2.66909 | 0.118073 | ||||||||
\(512\) | 32.9210 | 1.45492 | ||||||||
\(513\) | −12.6805 | −0.559859 | ||||||||
\(514\) | 29.8674 | 1.31739 | ||||||||
\(515\) | 24.5335 | 1.08108 | ||||||||
\(516\) | 10.4427 | 0.459712 | ||||||||
\(517\) | −57.8106 | −2.54251 | ||||||||
\(518\) | 56.4702 | 2.48116 | ||||||||
\(519\) | 13.9112 | 0.610632 | ||||||||
\(520\) | −19.8754 | −0.871593 | ||||||||
\(521\) | −6.60279 | −0.289274 | −0.144637 | − | 0.989485i | \(-0.546201\pi\) | ||||
−0.144637 | + | 0.989485i | \(0.546201\pi\) | |||||||
\(522\) | −52.5446 | −2.29981 | ||||||||
\(523\) | 23.2758 | 1.01778 | 0.508890 | − | 0.860832i | \(-0.330056\pi\) | ||||
0.508890 | + | 0.860832i | \(0.330056\pi\) | |||||||
\(524\) | −78.7860 | −3.44178 | ||||||||
\(525\) | 15.4315 | 0.673487 | ||||||||
\(526\) | 22.0735 | 0.962449 | ||||||||
\(527\) | −9.75666 | −0.425007 | ||||||||
\(528\) | 15.7767 | 0.686595 | ||||||||
\(529\) | 22.3440 | 0.971478 | ||||||||
\(530\) | 73.8328 | 3.20709 | ||||||||
\(531\) | 4.38639 | 0.190353 | ||||||||
\(532\) | 37.5542 | 1.62818 | ||||||||
\(533\) | −15.0650 | −0.652539 | ||||||||
\(534\) | 5.60962 | 0.242752 | ||||||||
\(535\) | 20.3497 | 0.879795 | ||||||||
\(536\) | 66.0128 | 2.85132 | ||||||||
\(537\) | 5.15381 | 0.222403 | ||||||||
\(538\) | −21.8192 | −0.940693 | ||||||||
\(539\) | 23.8748 | 1.02836 | ||||||||
\(540\) | −54.6737 | −2.35278 | ||||||||
\(541\) | −0.834327 | −0.0358705 | −0.0179353 | − | 0.999839i | \(-0.505709\pi\) | ||||
−0.0179353 | + | 0.999839i | \(0.505709\pi\) | |||||||
\(542\) | 7.45428 | 0.320189 | ||||||||
\(543\) | 4.26439 | 0.183003 | ||||||||
\(544\) | −1.55523 | −0.0666798 | ||||||||
\(545\) | 20.7081 | 0.887036 | ||||||||
\(546\) | −8.60270 | −0.368161 | ||||||||
\(547\) | −0.150874 | −0.00645091 | −0.00322545 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322545 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(548\) | 20.7342 | 0.885720 | ||||||||
\(549\) | −7.34718 | −0.313570 | ||||||||
\(550\) | −86.5696 | −3.69134 | ||||||||
\(551\) | −27.1655 | −1.15729 | ||||||||
\(552\) | −24.4094 | −1.03893 | ||||||||
\(553\) | 2.65560 | 0.112928 | ||||||||
\(554\) | −43.4297 | −1.84515 | ||||||||
\(555\) | −18.6877 | −0.793250 | ||||||||
\(556\) | −49.3116 | −2.09128 | ||||||||
\(557\) | −24.3484 | −1.03168 | −0.515838 | − | 0.856686i | \(-0.672519\pi\) | ||||
−0.515838 | + | 0.856686i | \(0.672519\pi\) | |||||||
\(558\) | 45.9314 | 1.94443 | ||||||||
\(559\) | 4.50657 | 0.190608 | ||||||||
\(560\) | 34.6712 | 1.46513 | ||||||||
\(561\) | −5.97888 | −0.252428 | ||||||||
\(562\) | 29.3973 | 1.24005 | ||||||||
\(563\) | 23.9303 | 1.00854 | 0.504271 | − | 0.863545i | \(-0.331761\pi\) | ||||
0.504271 | + | 0.863545i | \(0.331761\pi\) | |||||||
\(564\) | −29.2115 | −1.23003 | ||||||||
\(565\) | −49.5977 | −2.08659 | ||||||||
\(566\) | −54.8874 | −2.30709 | ||||||||
\(567\) | 11.8885 | 0.499272 | ||||||||
\(568\) | 73.3257 | 3.07668 | ||||||||
\(569\) | −31.7158 | −1.32959 | −0.664797 | − | 0.747024i | \(-0.731482\pi\) | ||||
−0.664797 | + | 0.747024i | \(0.731482\pi\) | |||||||
\(570\) | −18.8627 | −0.790071 | ||||||||
\(571\) | −12.8077 | −0.535983 | −0.267992 | − | 0.963421i | \(-0.586360\pi\) | ||||
−0.267992 | + | 0.963421i | \(0.586360\pi\) | |||||||
\(572\) | 31.7967 | 1.32949 | ||||||||
\(573\) | 5.35900 | 0.223876 | ||||||||
\(574\) | 89.8273 | 3.74932 | ||||||||
\(575\) | 39.1851 | 1.63413 | ||||||||
\(576\) | 22.3626 | 0.931773 | ||||||||
\(577\) | −38.4001 | −1.59862 | −0.799309 | − | 0.600921i | \(-0.794801\pi\) | ||||
−0.799309 | + | 0.600921i | \(0.794801\pi\) | |||||||
\(578\) | 37.6127 | 1.56448 | ||||||||
\(579\) | 13.8705 | 0.576437 | ||||||||
\(580\) | −117.127 | −4.86344 | ||||||||
\(581\) | 36.4118 | 1.51062 | ||||||||
\(582\) | −17.3128 | −0.717639 | ||||||||
\(583\) | −56.9591 | −2.35900 | ||||||||
\(584\) | −3.64848 | −0.150975 | ||||||||
\(585\) | −10.3739 | −0.428908 | ||||||||
\(586\) | 12.2861 | 0.507534 | ||||||||
\(587\) | −32.6561 | −1.34786 | −0.673932 | − | 0.738794i | \(-0.735396\pi\) | ||||
−0.673932 | + | 0.738794i | \(0.735396\pi\) | |||||||
\(588\) | 12.0639 | 0.497505 | ||||||||
\(589\) | 23.7465 | 0.978456 | ||||||||
\(590\) | 14.8404 | 0.610970 | ||||||||
\(591\) | −17.0002 | −0.699293 | ||||||||
\(592\) | −22.5831 | −0.928160 | ||||||||
\(593\) | 14.3464 | 0.589137 | 0.294569 | − | 0.955630i | \(-0.404824\pi\) | ||||
0.294569 | + | 0.955630i | \(0.404824\pi\) | |||||||
\(594\) | 64.0178 | 2.62668 | ||||||||
\(595\) | −13.1393 | −0.538658 | ||||||||
\(596\) | −36.4385 | −1.49258 | ||||||||
\(597\) | −4.54735 | −0.186111 | ||||||||
\(598\) | −21.8447 | −0.893296 | ||||||||
\(599\) | −3.28237 | −0.134114 | −0.0670570 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670570 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(600\) | −21.0940 | −0.861157 | ||||||||
\(601\) | 15.8292 | 0.645686 | 0.322843 | − | 0.946453i | \(-0.395361\pi\) | ||||
0.322843 | + | 0.946453i | \(0.395361\pi\) | |||||||
\(602\) | −26.8711 | −1.09518 | ||||||||
\(603\) | 34.4552 | 1.40312 | ||||||||
\(604\) | −6.40574 | −0.260646 | ||||||||
\(605\) | 87.9869 | 3.57718 | ||||||||
\(606\) | −10.3178 | −0.419133 | ||||||||
\(607\) | 33.3281 | 1.35275 | 0.676373 | − | 0.736559i | \(-0.263551\pi\) | ||||
0.676373 | + | 0.736559i | \(0.263551\pi\) | |||||||
\(608\) | 3.78522 | 0.153511 | ||||||||
\(609\) | −24.4469 | −0.990638 | ||||||||
\(610\) | −24.8576 | −1.00645 | ||||||||
\(611\) | −12.6063 | −0.509998 | ||||||||
\(612\) | 11.0087 | 0.445000 | ||||||||
\(613\) | 25.1970 | 1.01770 | 0.508848 | − | 0.860857i | \(-0.330072\pi\) | ||||
0.508848 | + | 0.860857i | \(0.330072\pi\) | |||||||
\(614\) | 46.8856 | 1.89215 | ||||||||
\(615\) | −29.7266 | −1.19869 | ||||||||
\(616\) | −91.4255 | −3.68364 | ||||||||
\(617\) | −23.1096 | −0.930356 | −0.465178 | − | 0.885217i | \(-0.654010\pi\) | ||||
−0.465178 | + | 0.885217i | \(0.654010\pi\) | |||||||
\(618\) | −14.5154 | −0.583893 | ||||||||
\(619\) | −27.8661 | −1.12003 | −0.560017 | − | 0.828481i | \(-0.689206\pi\) | ||||
−0.560017 | + | 0.828481i | \(0.689206\pi\) | |||||||
\(620\) | 102.386 | 4.11191 | ||||||||
\(621\) | −28.9772 | −1.16281 | ||||||||
\(622\) | 32.1337 | 1.28844 | ||||||||
\(623\) | −9.51040 | −0.381026 | ||||||||
\(624\) | 3.44032 | 0.137723 | ||||||||
\(625\) | −20.2331 | −0.809325 | ||||||||
\(626\) | 46.3023 | 1.85061 | ||||||||
\(627\) | 14.5518 | 0.581144 | ||||||||
\(628\) | 39.9509 | 1.59422 | ||||||||
\(629\) | 8.55827 | 0.341240 | ||||||||
\(630\) | 61.8558 | 2.46439 | ||||||||
\(631\) | −41.4360 | −1.64954 | −0.824770 | − | 0.565469i | \(-0.808695\pi\) | ||||
−0.824770 | + | 0.565469i | \(0.808695\pi\) | |||||||
\(632\) | −3.63004 | −0.144395 | ||||||||
\(633\) | −12.7839 | −0.508115 | ||||||||
\(634\) | −33.1019 | −1.31464 | ||||||||
\(635\) | 27.7347 | 1.10062 | ||||||||
\(636\) | −28.7812 | −1.14125 | ||||||||
\(637\) | 5.20621 | 0.206277 | ||||||||
\(638\) | 137.145 | 5.42962 | ||||||||
\(639\) | 38.2721 | 1.51402 | ||||||||
\(640\) | 67.2085 | 2.65665 | ||||||||
\(641\) | −16.1050 | −0.636107 | −0.318054 | − | 0.948073i | \(-0.603029\pi\) | ||||
−0.318054 | + | 0.948073i | \(0.603029\pi\) | |||||||
\(642\) | −12.0400 | −0.475181 | ||||||||
\(643\) | −0.458480 | −0.0180807 | −0.00904034 | − | 0.999959i | \(-0.502878\pi\) | ||||
−0.00904034 | + | 0.999959i | \(0.502878\pi\) | |||||||
\(644\) | 85.8176 | 3.38169 | ||||||||
\(645\) | 8.89246 | 0.350140 | ||||||||
\(646\) | 8.63840 | 0.339873 | ||||||||
\(647\) | −36.3681 | −1.42978 | −0.714890 | − | 0.699237i | \(-0.753523\pi\) | ||||
−0.714890 | + | 0.699237i | \(0.753523\pi\) | |||||||
\(648\) | −16.2509 | −0.638396 | ||||||||
\(649\) | −11.4488 | −0.449404 | ||||||||
\(650\) | −18.8776 | −0.740441 | ||||||||
\(651\) | 21.3700 | 0.837558 | ||||||||
\(652\) | −10.6074 | −0.415418 | ||||||||
\(653\) | −32.2652 | −1.26263 | −0.631317 | − | 0.775525i | \(-0.717485\pi\) | ||||
−0.631317 | + | 0.775525i | \(0.717485\pi\) | |||||||
\(654\) | −12.2520 | −0.479092 | ||||||||
\(655\) | −67.0904 | −2.62144 | ||||||||
\(656\) | −35.9230 | −1.40256 | ||||||||
\(657\) | −1.90431 | −0.0742943 | ||||||||
\(658\) | 75.1671 | 2.93032 | ||||||||
\(659\) | 32.6197 | 1.27068 | 0.635341 | − | 0.772232i | \(-0.280859\pi\) | ||||
0.635341 | + | 0.772232i | \(0.280859\pi\) | |||||||
\(660\) | 62.7420 | 2.44223 | ||||||||
\(661\) | −37.7214 | −1.46719 | −0.733596 | − | 0.679586i | \(-0.762159\pi\) | ||||
−0.733596 | + | 0.679586i | \(0.762159\pi\) | |||||||
\(662\) | −44.9979 | −1.74889 | ||||||||
\(663\) | −1.30377 | −0.0506343 | ||||||||
\(664\) | −49.7727 | −1.93156 | ||||||||
\(665\) | 31.9793 | 1.24010 | ||||||||
\(666\) | −40.2897 | −1.56120 | ||||||||
\(667\) | −62.0776 | −2.40366 | ||||||||
\(668\) | 65.3822 | 2.52971 | ||||||||
\(669\) | 9.77616 | 0.377968 | ||||||||
\(670\) | 116.572 | 4.50356 | ||||||||
\(671\) | 19.1766 | 0.740306 | ||||||||
\(672\) | 3.40641 | 0.131405 | ||||||||
\(673\) | −7.79588 | −0.300509 | −0.150255 | − | 0.988647i | \(-0.548009\pi\) | ||||
−0.150255 | + | 0.988647i | \(0.548009\pi\) | |||||||
\(674\) | −75.3315 | −2.90166 | ||||||||
\(675\) | −25.0413 | −0.963839 | ||||||||
\(676\) | −43.2808 | −1.66465 | ||||||||
\(677\) | 14.2574 | 0.547955 | 0.273977 | − | 0.961736i | \(-0.411661\pi\) | ||||
0.273977 | + | 0.961736i | \(0.411661\pi\) | |||||||
\(678\) | 29.3447 | 1.12698 | ||||||||
\(679\) | 29.3517 | 1.12641 | ||||||||
\(680\) | 17.9606 | 0.688757 | ||||||||
\(681\) | 1.80460 | 0.0691525 | ||||||||
\(682\) | −119.884 | −4.59060 | ||||||||
\(683\) | 21.4229 | 0.819725 | 0.409863 | − | 0.912147i | \(-0.365577\pi\) | ||||
0.409863 | + | 0.912147i | \(0.365577\pi\) | |||||||
\(684\) | −26.7937 | −1.02448 | ||||||||
\(685\) | 17.6562 | 0.674610 | ||||||||
\(686\) | 24.8784 | 0.949860 | ||||||||
\(687\) | 1.85606 | 0.0708132 | ||||||||
\(688\) | 10.7461 | 0.409690 | ||||||||
\(689\) | −12.4207 | −0.473189 | ||||||||
\(690\) | −43.1044 | −1.64096 | ||||||||
\(691\) | −30.9626 | −1.17787 | −0.588936 | − | 0.808180i | \(-0.700453\pi\) | ||||
−0.588936 | + | 0.808180i | \(0.700453\pi\) | |||||||
\(692\) | 66.8546 | 2.54143 | ||||||||
\(693\) | −47.7193 | −1.81270 | ||||||||
\(694\) | −15.4612 | −0.586899 | ||||||||
\(695\) | −41.9913 | −1.59282 | ||||||||
\(696\) | 33.4174 | 1.26668 | ||||||||
\(697\) | 13.6137 | 0.515655 | ||||||||
\(698\) | −68.9790 | −2.61089 | ||||||||
\(699\) | 13.3013 | 0.503101 | ||||||||
\(700\) | 74.1613 | 2.80303 | ||||||||
\(701\) | −16.0964 | −0.607951 | −0.303976 | − | 0.952680i | \(-0.598314\pi\) | ||||
−0.303976 | + | 0.952680i | \(0.598314\pi\) | |||||||
\(702\) | 13.9599 | 0.526882 | ||||||||
\(703\) | −20.8297 | −0.785608 | ||||||||
\(704\) | −58.3678 | −2.19982 | ||||||||
\(705\) | −24.8751 | −0.936850 | ||||||||
\(706\) | 19.2461 | 0.724335 | ||||||||
\(707\) | 17.4926 | 0.657877 | ||||||||
\(708\) | −5.78503 | −0.217415 | ||||||||
\(709\) | −19.3427 | −0.726432 | −0.363216 | − | 0.931705i | \(-0.618321\pi\) | ||||
−0.363216 | + | 0.931705i | \(0.618321\pi\) | |||||||
\(710\) | 129.486 | 4.85950 | ||||||||
\(711\) | −1.89469 | −0.0710563 | ||||||||
\(712\) | 13.0001 | 0.487200 | ||||||||
\(713\) | 54.2646 | 2.03223 | ||||||||
\(714\) | 7.77391 | 0.290931 | ||||||||
\(715\) | 27.0766 | 1.01261 | ||||||||
\(716\) | 24.7683 | 0.925635 | ||||||||
\(717\) | −1.32515 | −0.0494886 | ||||||||
\(718\) | −13.5860 | −0.507027 | ||||||||
\(719\) | −3.42701 | −0.127806 | −0.0639030 | − | 0.997956i | \(-0.520355\pi\) | ||||
−0.0639030 | + | 0.997956i | \(0.520355\pi\) | |||||||
\(720\) | −24.7369 | −0.921888 | ||||||||
\(721\) | 24.6090 | 0.916485 | ||||||||
\(722\) | 24.9798 | 0.929652 | ||||||||
\(723\) | −19.0891 | −0.709933 | ||||||||
\(724\) | 20.4939 | 0.761650 | ||||||||
\(725\) | −53.6458 | −1.99236 | ||||||||
\(726\) | −52.0578 | −1.93205 | ||||||||
\(727\) | 30.6237 | 1.13577 | 0.567886 | − | 0.823108i | \(-0.307762\pi\) | ||||
0.567886 | + | 0.823108i | \(0.307762\pi\) | |||||||
\(728\) | −19.9365 | −0.738896 | ||||||||
\(729\) | 1.89401 | 0.0701486 | ||||||||
\(730\) | −6.44283 | −0.238460 | ||||||||
\(731\) | −4.07241 | −0.150623 | ||||||||
\(732\) | 9.68989 | 0.358149 | ||||||||
\(733\) | 3.39721 | 0.125479 | 0.0627394 | − | 0.998030i | \(-0.480016\pi\) | ||||
0.0627394 | + | 0.998030i | \(0.480016\pi\) | |||||||
\(734\) | 33.0147 | 1.21860 | ||||||||
\(735\) | 10.2730 | 0.378925 | ||||||||
\(736\) | 8.64986 | 0.318838 | ||||||||
\(737\) | −89.9304 | −3.31263 | ||||||||
\(738\) | −64.0890 | −2.35915 | ||||||||
\(739\) | −35.9271 | −1.32160 | −0.660800 | − | 0.750562i | \(-0.729783\pi\) | ||||
−0.660800 | + | 0.750562i | \(0.729783\pi\) | |||||||
\(740\) | −89.8099 | −3.30148 | ||||||||
\(741\) | 3.17321 | 0.116571 | ||||||||
\(742\) | 74.0599 | 2.71882 | ||||||||
\(743\) | −32.3705 | −1.18756 | −0.593780 | − | 0.804627i | \(-0.702365\pi\) | ||||
−0.593780 | + | 0.804627i | \(0.702365\pi\) | |||||||
\(744\) | −29.2115 | −1.07095 | ||||||||
\(745\) | −31.0293 | −1.13682 | ||||||||
\(746\) | 44.4156 | 1.62617 | ||||||||
\(747\) | −25.9787 | −0.950511 | ||||||||
\(748\) | −28.7334 | −1.05060 | ||||||||
\(749\) | 20.4123 | 0.745850 | ||||||||
\(750\) | −5.24366 | −0.191471 | ||||||||
\(751\) | −6.53721 | −0.238546 | −0.119273 | − | 0.992861i | \(-0.538056\pi\) | ||||
−0.119273 | + | 0.992861i | \(0.538056\pi\) | |||||||
\(752\) | −30.0602 | −1.09618 | ||||||||
\(753\) | 21.0098 | 0.765639 | ||||||||
\(754\) | 29.9062 | 1.08912 | ||||||||
\(755\) | −5.45482 | −0.198521 | ||||||||
\(756\) | −54.8419 | −1.99458 | ||||||||
\(757\) | −20.6167 | −0.749326 | −0.374663 | − | 0.927161i | \(-0.622242\pi\) | ||||
−0.374663 | + | 0.927161i | \(0.622242\pi\) | |||||||
\(758\) | −59.2397 | −2.15168 | ||||||||
\(759\) | 33.2533 | 1.20702 | ||||||||
\(760\) | −43.7137 | −1.58566 | ||||||||
\(761\) | 10.8207 | 0.392249 | 0.196124 | − | 0.980579i | \(-0.437164\pi\) | ||||
0.196124 | + | 0.980579i | \(0.437164\pi\) | |||||||
\(762\) | −16.4093 | −0.594447 | ||||||||
\(763\) | 20.7717 | 0.751988 | ||||||||
\(764\) | 25.7544 | 0.931763 | ||||||||
\(765\) | 9.37447 | 0.338935 | ||||||||
\(766\) | −66.8292 | −2.41464 | ||||||||
\(767\) | −2.49656 | −0.0901454 | ||||||||
\(768\) | −24.4933 | −0.883827 | ||||||||
\(769\) | −9.55581 | −0.344591 | −0.172296 | − | 0.985045i | \(-0.555118\pi\) | ||||
−0.172296 | + | 0.985045i | \(0.555118\pi\) | |||||||
\(770\) | −161.448 | −5.81817 | ||||||||
\(771\) | −9.91444 | −0.357060 | ||||||||
\(772\) | 66.6590 | 2.39911 | ||||||||
\(773\) | 4.47482 | 0.160948 | 0.0804741 | − | 0.996757i | \(-0.474357\pi\) | ||||
0.0804741 | + | 0.996757i | \(0.474357\pi\) | |||||||
\(774\) | 19.1717 | 0.689111 | ||||||||
\(775\) | 46.8941 | 1.68448 | ||||||||
\(776\) | −40.1219 | −1.44029 | ||||||||
\(777\) | −18.7452 | −0.672480 | ||||||||
\(778\) | 38.2357 | 1.37082 | ||||||||
\(779\) | −33.1339 | −1.18715 | ||||||||
\(780\) | 13.6817 | 0.489883 | ||||||||
\(781\) | −99.8929 | −3.57445 | ||||||||
\(782\) | 19.7402 | 0.705908 | ||||||||
\(783\) | 39.6708 | 1.41772 | ||||||||
\(784\) | 12.4144 | 0.443370 | ||||||||
\(785\) | 34.0203 | 1.21424 | ||||||||
\(786\) | 39.6943 | 1.41585 | ||||||||
\(787\) | 14.3480 | 0.511452 | 0.255726 | − | 0.966749i | \(-0.417686\pi\) | ||||
0.255726 | + | 0.966749i | \(0.417686\pi\) | |||||||
\(788\) | −81.6998 | −2.91044 | ||||||||
\(789\) | −7.32726 | −0.260857 | ||||||||
\(790\) | −6.41027 | −0.228067 | ||||||||
\(791\) | −49.7503 | −1.76892 | ||||||||
\(792\) | 65.2293 | 2.31782 | ||||||||
\(793\) | 4.18171 | 0.148497 | ||||||||
\(794\) | −20.6920 | −0.734331 | ||||||||
\(795\) | −24.5087 | −0.869233 | ||||||||
\(796\) | −21.8538 | −0.774587 | ||||||||
\(797\) | 20.0333 | 0.709617 | 0.354809 | − | 0.934939i | \(-0.384546\pi\) | ||||
0.354809 | + | 0.934939i | \(0.384546\pi\) | |||||||
\(798\) | −18.9207 | −0.669786 | ||||||||
\(799\) | 11.3919 | 0.403015 | ||||||||
\(800\) | 7.47498 | 0.264280 | ||||||||
\(801\) | 6.78538 | 0.239749 | ||||||||
\(802\) | 53.6797 | 1.89550 | ||||||||
\(803\) | 4.97038 | 0.175401 | ||||||||
\(804\) | −45.4415 | −1.60260 | ||||||||
\(805\) | 73.0781 | 2.57567 | ||||||||
\(806\) | −26.1423 | −0.920822 | ||||||||
\(807\) | 7.24286 | 0.254961 | ||||||||
\(808\) | −23.9113 | −0.841196 | ||||||||
\(809\) | 14.3152 | 0.503295 | 0.251647 | − | 0.967819i | \(-0.419028\pi\) | ||||
0.251647 | + | 0.967819i | \(0.419028\pi\) | |||||||
\(810\) | −28.6974 | −1.00832 | ||||||||
\(811\) | 24.0754 | 0.845402 | 0.422701 | − | 0.906269i | \(-0.361082\pi\) | ||||
0.422701 | + | 0.906269i | \(0.361082\pi\) | |||||||
\(812\) | −117.487 | −4.12300 | ||||||||
\(813\) | −2.47444 | −0.0867823 | ||||||||
\(814\) | 105.159 | 3.68582 | ||||||||
\(815\) | −9.03276 | −0.316404 | ||||||||
\(816\) | −3.10888 | −0.108833 | ||||||||
\(817\) | 9.91172 | 0.346767 | ||||||||
\(818\) | −10.9106 | −0.381479 | ||||||||
\(819\) | −10.4058 | −0.363608 | ||||||||
\(820\) | −142.861 | −4.98892 | ||||||||
\(821\) | 6.50109 | 0.226889 | 0.113445 | − | 0.993544i | \(-0.463812\pi\) | ||||
0.113445 | + | 0.993544i | \(0.463812\pi\) | |||||||
\(822\) | −10.4464 | −0.364359 | ||||||||
\(823\) | 44.6737 | 1.55723 | 0.778614 | − | 0.627503i | \(-0.215923\pi\) | ||||
0.778614 | + | 0.627503i | \(0.215923\pi\) | |||||||
\(824\) | −33.6389 | −1.17187 | ||||||||
\(825\) | 28.7367 | 1.00048 | ||||||||
\(826\) | 14.8861 | 0.517952 | ||||||||
\(827\) | 51.2060 | 1.78061 | 0.890303 | − | 0.455369i | \(-0.150493\pi\) | ||||
0.890303 | + | 0.455369i | \(0.150493\pi\) | |||||||
\(828\) | −61.2282 | −2.12783 | ||||||||
\(829\) | −15.0751 | −0.523581 | −0.261790 | − | 0.965125i | \(-0.584313\pi\) | ||||
−0.261790 | + | 0.965125i | \(0.584313\pi\) | |||||||
\(830\) | −87.8934 | −3.05082 | ||||||||
\(831\) | 14.4164 | 0.500101 | ||||||||
\(832\) | −12.7279 | −0.441259 | ||||||||
\(833\) | −4.70464 | −0.163006 | ||||||||
\(834\) | 24.8444 | 0.860290 | ||||||||
\(835\) | 55.6763 | 1.92676 | ||||||||
\(836\) | 69.9335 | 2.41870 | ||||||||
\(837\) | −34.6779 | −1.19864 | ||||||||
\(838\) | 18.4607 | 0.637713 | ||||||||
\(839\) | −31.1054 | −1.07388 | −0.536939 | − | 0.843621i | \(-0.680419\pi\) | ||||
−0.536939 | + | 0.843621i | \(0.680419\pi\) | |||||||
\(840\) | −39.3391 | −1.35733 | ||||||||
\(841\) | 55.9866 | 1.93057 | ||||||||
\(842\) | −4.59320 | −0.158292 | ||||||||
\(843\) | −9.75839 | −0.336097 | ||||||||
\(844\) | −61.4373 | −2.11476 | ||||||||
\(845\) | −36.8559 | −1.26788 | ||||||||
\(846\) | −53.6294 | −1.84382 | ||||||||
\(847\) | 88.2575 | 3.03256 | ||||||||
\(848\) | −29.6174 | −1.01707 | ||||||||
\(849\) | 18.2198 | 0.625301 | ||||||||
\(850\) | 17.0589 | 0.585117 | ||||||||
\(851\) | −47.5994 | −1.63169 | ||||||||
\(852\) | −50.4755 | −1.72926 | ||||||||
\(853\) | 47.7800 | 1.63596 | 0.817978 | − | 0.575250i | \(-0.195095\pi\) | ||||
0.817978 | + | 0.575250i | \(0.195095\pi\) | |||||||
\(854\) | −24.9340 | −0.853225 | ||||||||
\(855\) | −22.8163 | −0.780299 | ||||||||
\(856\) | −27.9024 | −0.953683 | ||||||||
\(857\) | −8.56877 | −0.292704 | −0.146352 | − | 0.989233i | \(-0.546753\pi\) | ||||
−0.146352 | + | 0.989233i | \(0.546753\pi\) | |||||||
\(858\) | −16.0200 | −0.546913 | ||||||||
\(859\) | −2.51035 | −0.0856520 | −0.0428260 | − | 0.999083i | \(-0.513636\pi\) | ||||
−0.0428260 | + | 0.999083i | \(0.513636\pi\) | |||||||
\(860\) | 42.7356 | 1.45727 | ||||||||
\(861\) | −29.8181 | −1.01620 | ||||||||
\(862\) | −61.5095 | −2.09502 | ||||||||
\(863\) | 48.3935 | 1.64733 | 0.823666 | − | 0.567075i | \(-0.191925\pi\) | ||||
0.823666 | + | 0.567075i | \(0.191925\pi\) | |||||||
\(864\) | −5.52771 | −0.188056 | ||||||||
\(865\) | 56.9302 | 1.93568 | ||||||||
\(866\) | 60.4397 | 2.05383 | ||||||||
\(867\) | −12.4855 | −0.424029 | ||||||||
\(868\) | 102.701 | 3.48589 | ||||||||
\(869\) | 4.94527 | 0.167757 | ||||||||
\(870\) | 59.0116 | 2.00068 | ||||||||
\(871\) | −19.6105 | −0.664476 | ||||||||
\(872\) | −28.3937 | −0.961532 | ||||||||
\(873\) | −20.9415 | −0.708763 | ||||||||
\(874\) | −48.0451 | −1.62515 | ||||||||
\(875\) | 8.88996 | 0.300535 | ||||||||
\(876\) | 2.51152 | 0.0848563 | ||||||||
\(877\) | −19.4485 | −0.656731 | −0.328365 | − | 0.944551i | \(-0.606498\pi\) | ||||
−0.328365 | + | 0.944551i | \(0.606498\pi\) | |||||||
\(878\) | −18.3890 | −0.620600 | ||||||||
\(879\) | −4.07835 | −0.137559 | ||||||||
\(880\) | 64.5649 | 2.17648 | ||||||||
\(881\) | 52.0215 | 1.75265 | 0.876325 | − | 0.481721i | \(-0.159988\pi\) | ||||
0.876325 | + | 0.481721i | \(0.159988\pi\) | |||||||
\(882\) | 22.1480 | 0.745763 | ||||||||
\(883\) | 22.6883 | 0.763522 | 0.381761 | − | 0.924261i | \(-0.375318\pi\) | ||||
0.381761 | + | 0.924261i | \(0.375318\pi\) | |||||||
\(884\) | −6.26569 | −0.210738 | ||||||||
\(885\) | −4.92625 | −0.165594 | ||||||||
\(886\) | 5.33288 | 0.179162 | ||||||||
\(887\) | −7.55308 | −0.253608 | −0.126804 | − | 0.991928i | \(-0.540472\pi\) | ||||
−0.126804 | + | 0.991928i | \(0.540472\pi\) | |||||||
\(888\) | 25.6235 | 0.859869 | ||||||||
\(889\) | 27.8200 | 0.933051 | ||||||||
\(890\) | 22.9569 | 0.769515 | ||||||||
\(891\) | 22.1389 | 0.741680 | ||||||||
\(892\) | 46.9825 | 1.57309 | ||||||||
\(893\) | −27.7263 | −0.927825 | ||||||||
\(894\) | 18.3586 | 0.614004 | ||||||||
\(895\) | 21.0915 | 0.705011 | ||||||||
\(896\) | 67.4152 | 2.25218 | ||||||||
\(897\) | 7.25132 | 0.242114 | ||||||||
\(898\) | −35.1743 | −1.17378 | ||||||||
\(899\) | −74.2903 | −2.47772 | ||||||||
\(900\) | −52.9118 | −1.76373 | ||||||||
\(901\) | 11.2240 | 0.373927 | ||||||||
\(902\) | 167.277 | 5.56971 | ||||||||
\(903\) | 8.91981 | 0.296833 | ||||||||
\(904\) | 68.0055 | 2.26183 | ||||||||
\(905\) | 17.4516 | 0.580112 | ||||||||
\(906\) | 3.22737 | 0.107222 | ||||||||
\(907\) | 41.6658 | 1.38349 | 0.691746 | − | 0.722141i | \(-0.256842\pi\) | ||||
0.691746 | + | 0.722141i | \(0.256842\pi\) | |||||||
\(908\) | 8.67260 | 0.287810 | ||||||||
\(909\) | −12.4804 | −0.413949 | ||||||||
\(910\) | −35.2058 | −1.16706 | ||||||||
\(911\) | 19.7433 | 0.654126 | 0.327063 | − | 0.945003i | \(-0.393941\pi\) | ||||
0.327063 | + | 0.945003i | \(0.393941\pi\) | |||||||
\(912\) | 7.56661 | 0.250556 | ||||||||
\(913\) | 67.8062 | 2.24406 | ||||||||
\(914\) | −40.6261 | −1.34379 | ||||||||
\(915\) | 8.25144 | 0.272784 | ||||||||
\(916\) | 8.91992 | 0.294722 | ||||||||
\(917\) | −67.2967 | −2.22233 | ||||||||
\(918\) | −12.6150 | −0.416357 | ||||||||
\(919\) | −20.2294 | −0.667307 | −0.333653 | − | 0.942696i | \(-0.608282\pi\) | ||||
−0.333653 | + | 0.942696i | \(0.608282\pi\) | |||||||
\(920\) | −99.8933 | −3.29338 | ||||||||
\(921\) | −15.5636 | −0.512838 | ||||||||
\(922\) | −26.5057 | −0.872919 | ||||||||
\(923\) | −21.7829 | −0.716994 | ||||||||
\(924\) | 62.9349 | 2.07041 | ||||||||
\(925\) | −41.1341 | −1.35248 | ||||||||
\(926\) | −31.5019 | −1.03522 | ||||||||
\(927\) | −17.5577 | −0.576671 | ||||||||
\(928\) | −11.8420 | −0.388732 | ||||||||
\(929\) | 36.8216 | 1.20808 | 0.604038 | − | 0.796955i | \(-0.293557\pi\) | ||||
0.604038 | + | 0.796955i | \(0.293557\pi\) | |||||||
\(930\) | −51.5845 | −1.69152 | ||||||||
\(931\) | 11.4505 | 0.375275 | ||||||||
\(932\) | 63.9237 | 2.09389 | ||||||||
\(933\) | −10.6667 | −0.349213 | ||||||||
\(934\) | −14.6524 | −0.479440 | ||||||||
\(935\) | −24.4680 | −0.800190 | ||||||||
\(936\) | 14.2241 | 0.464928 | ||||||||
\(937\) | −5.09128 | −0.166325 | −0.0831624 | − | 0.996536i | \(-0.526502\pi\) | ||||
−0.0831624 | + | 0.996536i | \(0.526502\pi\) | |||||||
\(938\) | 116.930 | 3.81791 | ||||||||
\(939\) | −15.3700 | −0.501580 | ||||||||
\(940\) | −119.545 | −3.89914 | ||||||||
\(941\) | 16.2549 | 0.529895 | 0.264948 | − | 0.964263i | \(-0.414645\pi\) | ||||
0.264948 | + | 0.964263i | \(0.414645\pi\) | |||||||
\(942\) | −20.1283 | −0.655814 | ||||||||
\(943\) | −75.7166 | −2.46567 | ||||||||
\(944\) | −5.95311 | −0.193757 | ||||||||
\(945\) | −46.7007 | −1.51917 | ||||||||
\(946\) | −50.0394 | −1.62692 | ||||||||
\(947\) | 40.0445 | 1.30127 | 0.650635 | − | 0.759391i | \(-0.274503\pi\) | ||||
0.650635 | + | 0.759391i | \(0.274503\pi\) | |||||||
\(948\) | 2.49882 | 0.0811580 | ||||||||
\(949\) | 1.08386 | 0.0351834 | ||||||||
\(950\) | −41.5193 | −1.34706 | ||||||||
\(951\) | 10.9881 | 0.356314 | ||||||||
\(952\) | 18.0158 | 0.583896 | ||||||||
\(953\) | 21.4494 | 0.694813 | 0.347407 | − | 0.937715i | \(-0.387062\pi\) | ||||
0.347407 | + | 0.937715i | \(0.387062\pi\) | |||||||
\(954\) | −52.8394 | −1.71074 | ||||||||
\(955\) | 21.9312 | 0.709678 | ||||||||
\(956\) | −6.36844 | −0.205970 | ||||||||
\(957\) | −45.5251 | −1.47162 | ||||||||
\(958\) | 3.08585 | 0.0996992 | ||||||||
\(959\) | 17.7105 | 0.571903 | ||||||||
\(960\) | −25.1149 | −0.810578 | ||||||||
\(961\) | 33.9402 | 1.09485 | ||||||||
\(962\) | 22.9313 | 0.739333 | ||||||||
\(963\) | −14.5636 | −0.469304 | ||||||||
\(964\) | −91.7391 | −2.95472 | ||||||||
\(965\) | 56.7636 | 1.82729 | ||||||||
\(966\) | −43.2370 | −1.39113 | ||||||||
\(967\) | 53.0430 | 1.70575 | 0.852874 | − | 0.522116i | \(-0.174857\pi\) | ||||
0.852874 | + | 0.522116i | \(0.174857\pi\) | |||||||
\(968\) | −120.643 | −3.87760 | ||||||||
\(969\) | −2.86750 | −0.0921175 | ||||||||
\(970\) | −70.8511 | −2.27489 | ||||||||
\(971\) | 30.5076 | 0.979035 | 0.489518 | − | 0.871993i | \(-0.337173\pi\) | ||||
0.489518 | + | 0.871993i | \(0.337173\pi\) | |||||||
\(972\) | 61.0525 | 1.95826 | ||||||||
\(973\) | −42.1205 | −1.35032 | ||||||||
\(974\) | −2.64588 | −0.0847794 | ||||||||
\(975\) | 6.26640 | 0.200685 | ||||||||
\(976\) | 9.97142 | 0.319177 | ||||||||
\(977\) | 14.8942 | 0.476506 | 0.238253 | − | 0.971203i | \(-0.423425\pi\) | ||||
0.238253 | + | 0.971203i | \(0.423425\pi\) | |||||||
\(978\) | 5.34427 | 0.170891 | ||||||||
\(979\) | −17.7103 | −0.566024 | ||||||||
\(980\) | 49.3702 | 1.57707 | ||||||||
\(981\) | −14.8200 | −0.473166 | ||||||||
\(982\) | −17.3096 | −0.552372 | ||||||||
\(983\) | 1.00000 | 0.0318950 | ||||||||
\(984\) | 40.7594 | 1.29936 | ||||||||
\(985\) | −69.5716 | −2.21674 | ||||||||
\(986\) | −27.0251 | −0.860653 | ||||||||
\(987\) | −24.9516 | −0.794218 | ||||||||
\(988\) | 15.2499 | 0.485164 | ||||||||
\(989\) | 22.6499 | 0.720226 | ||||||||
\(990\) | 115.188 | 3.66091 | ||||||||
\(991\) | −22.8058 | −0.724450 | −0.362225 | − | 0.932091i | \(-0.617983\pi\) | ||||
−0.362225 | + | 0.932091i | \(0.617983\pi\) | |||||||
\(992\) | 10.3516 | 0.328663 | ||||||||
\(993\) | 14.9370 | 0.474011 | ||||||||
\(994\) | 129.884 | 4.11966 | ||||||||
\(995\) | −18.6096 | −0.589965 | ||||||||
\(996\) | 34.2622 | 1.08564 | ||||||||
\(997\) | 22.6404 | 0.717029 | 0.358514 | − | 0.933524i | \(-0.383283\pi\) | ||||
0.358514 | + | 0.933524i | \(0.383283\pi\) | |||||||
\(998\) | 23.2147 | 0.734847 | ||||||||
\(999\) | 30.4185 | 0.962398 |
(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 | 983.2.a.b.1.5 | ✓ | 54 | |
3.2 | odd | 2 | 8847.2.a.g.1.50 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.2.a.b.1.5 | ✓ | 54 | 1.1 | even | 1 | trivial | |
8847.2.a.g.1.50 | 54 | 3.2 | odd | 2 |