Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, 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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.275495\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.275495 | 0.159057 | 0.0795285 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795285 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.829257 | −0.370855 | −0.185428 | − | 0.982658i | \(-0.559367\pi\) | ||||
−0.185428 | + | 0.982658i | \(0.559367\pi\) | |||||||
\(6\) | −0.275495 | −0.112470 | ||||||||
\(7\) | 4.83738 | 1.82836 | 0.914178 | − | 0.405313i | \(-0.132837\pi\) | ||||
0.914178 | + | 0.405313i | \(0.132837\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.92410 | −0.974701 | ||||||||
\(10\) | 0.829257 | 0.262234 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.275495 | 0.0795285 | ||||||||
\(13\) | −4.69193 | −1.30131 | −0.650654 | − | 0.759374i | \(-0.725505\pi\) | ||||
−0.650654 | + | 0.759374i | \(0.725505\pi\) | |||||||
\(14\) | −4.83738 | −1.29284 | ||||||||
\(15\) | −0.228456 | −0.0589871 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.61821 | −0.877546 | −0.438773 | − | 0.898598i | \(-0.644587\pi\) | ||||
−0.438773 | + | 0.898598i | \(0.644587\pi\) | |||||||
\(18\) | 2.92410 | 0.689218 | ||||||||
\(19\) | 3.96753 | 0.910213 | 0.455107 | − | 0.890437i | \(-0.349601\pi\) | ||||
0.455107 | + | 0.890437i | \(0.349601\pi\) | |||||||
\(20\) | −0.829257 | −0.185428 | ||||||||
\(21\) | 1.33267 | 0.290813 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.89394 | 0.811942 | 0.405971 | − | 0.913886i | \(-0.366933\pi\) | ||||
0.405971 | + | 0.913886i | \(0.366933\pi\) | |||||||
\(24\) | −0.275495 | −0.0562352 | ||||||||
\(25\) | −4.31233 | −0.862466 | ||||||||
\(26\) | 4.69193 | 0.920163 | ||||||||
\(27\) | −1.63206 | −0.314090 | ||||||||
\(28\) | 4.83738 | 0.914178 | ||||||||
\(29\) | 7.12691 | 1.32343 | 0.661717 | − | 0.749754i | \(-0.269828\pi\) | ||||
0.661717 | + | 0.749754i | \(0.269828\pi\) | |||||||
\(30\) | 0.228456 | 0.0417102 | ||||||||
\(31\) | −5.82010 | −1.04532 | −0.522661 | − | 0.852541i | \(-0.675060\pi\) | ||||
−0.522661 | + | 0.852541i | \(0.675060\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.275495 | 0.0479575 | ||||||||
\(34\) | 3.61821 | 0.620519 | ||||||||
\(35\) | −4.01143 | −0.678055 | ||||||||
\(36\) | −2.92410 | −0.487350 | ||||||||
\(37\) | −7.26441 | −1.19426 | −0.597131 | − | 0.802144i | \(-0.703693\pi\) | ||||
−0.597131 | + | 0.802144i | \(0.703693\pi\) | |||||||
\(38\) | −3.96753 | −0.643618 | ||||||||
\(39\) | −1.29260 | −0.206982 | ||||||||
\(40\) | 0.829257 | 0.131117 | ||||||||
\(41\) | −2.08579 | −0.325746 | −0.162873 | − | 0.986647i | \(-0.552076\pi\) | ||||
−0.162873 | + | 0.986647i | \(0.552076\pi\) | |||||||
\(42\) | −1.33267 | −0.205636 | ||||||||
\(43\) | −10.3214 | −1.57399 | −0.786996 | − | 0.616958i | \(-0.788365\pi\) | ||||
−0.786996 | + | 0.616958i | \(0.788365\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 2.42483 | 0.361473 | ||||||||
\(46\) | −3.89394 | −0.574130 | ||||||||
\(47\) | 5.67256 | 0.827428 | 0.413714 | − | 0.910407i | \(-0.364231\pi\) | ||||
0.413714 | + | 0.910407i | \(0.364231\pi\) | |||||||
\(48\) | 0.275495 | 0.0397643 | ||||||||
\(49\) | 16.4002 | 2.34289 | ||||||||
\(50\) | 4.31233 | 0.609856 | ||||||||
\(51\) | −0.996800 | −0.139580 | ||||||||
\(52\) | −4.69193 | −0.650654 | ||||||||
\(53\) | 8.95166 | 1.22961 | 0.614803 | − | 0.788681i | \(-0.289236\pi\) | ||||
0.614803 | + | 0.788681i | \(0.289236\pi\) | |||||||
\(54\) | 1.63206 | 0.222095 | ||||||||
\(55\) | −0.829257 | −0.111817 | ||||||||
\(56\) | −4.83738 | −0.646422 | ||||||||
\(57\) | 1.09303 | 0.144776 | ||||||||
\(58\) | −7.12691 | −0.935809 | ||||||||
\(59\) | −9.73543 | −1.26744 | −0.633722 | − | 0.773560i | \(-0.718474\pi\) | ||||
−0.633722 | + | 0.773560i | \(0.718474\pi\) | |||||||
\(60\) | −0.228456 | −0.0294936 | ||||||||
\(61\) | −12.1961 | −1.56155 | −0.780775 | − | 0.624812i | \(-0.785176\pi\) | ||||
−0.780775 | + | 0.624812i | \(0.785176\pi\) | |||||||
\(62\) | 5.82010 | 0.739154 | ||||||||
\(63\) | −14.1450 | −1.78210 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.89082 | 0.482597 | ||||||||
\(66\) | −0.275495 | −0.0339111 | ||||||||
\(67\) | 12.1658 | 1.48628 | 0.743142 | − | 0.669134i | \(-0.233335\pi\) | ||||
0.743142 | + | 0.669134i | \(0.233335\pi\) | |||||||
\(68\) | −3.61821 | −0.438773 | ||||||||
\(69\) | 1.07276 | 0.129145 | ||||||||
\(70\) | 4.01143 | 0.479458 | ||||||||
\(71\) | −7.84656 | −0.931216 | −0.465608 | − | 0.884991i | \(-0.654164\pi\) | ||||
−0.465608 | + | 0.884991i | \(0.654164\pi\) | |||||||
\(72\) | 2.92410 | 0.344609 | ||||||||
\(73\) | −0.146186 | −0.0171098 | −0.00855491 | − | 0.999963i | \(-0.502723\pi\) | ||||
−0.00855491 | + | 0.999963i | \(0.502723\pi\) | |||||||
\(74\) | 7.26441 | 0.844470 | ||||||||
\(75\) | −1.18803 | −0.137181 | ||||||||
\(76\) | 3.96753 | 0.455107 | ||||||||
\(77\) | 4.83738 | 0.551270 | ||||||||
\(78\) | 1.29260 | 0.146358 | ||||||||
\(79\) | −6.17885 | −0.695174 | −0.347587 | − | 0.937648i | \(-0.612999\pi\) | ||||
−0.347587 | + | 0.937648i | \(0.612999\pi\) | |||||||
\(80\) | −0.829257 | −0.0927138 | ||||||||
\(81\) | 8.32268 | 0.924743 | ||||||||
\(82\) | 2.08579 | 0.230337 | ||||||||
\(83\) | −13.7221 | −1.50620 | −0.753100 | − | 0.657906i | \(-0.771443\pi\) | ||||
−0.753100 | + | 0.657906i | \(0.771443\pi\) | |||||||
\(84\) | 1.33267 | 0.145406 | ||||||||
\(85\) | 3.00043 | 0.325442 | ||||||||
\(86\) | 10.3214 | 1.11298 | ||||||||
\(87\) | 1.96343 | 0.210502 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −5.85899 | −0.621052 | −0.310526 | − | 0.950565i | \(-0.600505\pi\) | ||||
−0.310526 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(90\) | −2.42483 | −0.255600 | ||||||||
\(91\) | −22.6966 | −2.37925 | ||||||||
\(92\) | 3.89394 | 0.405971 | ||||||||
\(93\) | −1.60341 | −0.166266 | ||||||||
\(94\) | −5.67256 | −0.585080 | ||||||||
\(95\) | −3.29010 | −0.337557 | ||||||||
\(96\) | −0.275495 | −0.0281176 | ||||||||
\(97\) | −12.1296 | −1.23157 | −0.615786 | − | 0.787913i | \(-0.711161\pi\) | ||||
−0.615786 | + | 0.787913i | \(0.711161\pi\) | |||||||
\(98\) | −16.4002 | −1.65667 | ||||||||
\(99\) | −2.92410 | −0.293883 | ||||||||
\(100\) | −4.31233 | −0.431233 | ||||||||
\(101\) | −10.1809 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(102\) | 0.996800 | 0.0986979 | ||||||||
\(103\) | −9.12868 | −0.899475 | −0.449738 | − | 0.893161i | \(-0.648483\pi\) | ||||
−0.449738 | + | 0.893161i | \(0.648483\pi\) | |||||||
\(104\) | 4.69193 | 0.460082 | ||||||||
\(105\) | −1.10513 | −0.107849 | ||||||||
\(106\) | −8.95166 | −0.869462 | ||||||||
\(107\) | 3.59450 | 0.347494 | 0.173747 | − | 0.984790i | \(-0.444413\pi\) | ||||
0.173747 | + | 0.984790i | \(0.444413\pi\) | |||||||
\(108\) | −1.63206 | −0.157045 | ||||||||
\(109\) | 2.25058 | 0.215567 | 0.107783 | − | 0.994174i | \(-0.465625\pi\) | ||||
0.107783 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(110\) | 0.829257 | 0.0790666 | ||||||||
\(111\) | −2.00131 | −0.189956 | ||||||||
\(112\) | 4.83738 | 0.457089 | ||||||||
\(113\) | 0.169648 | 0.0159591 | 0.00797955 | − | 0.999968i | \(-0.497460\pi\) | ||||
0.00797955 | + | 0.999968i | \(0.497460\pi\) | |||||||
\(114\) | −1.09303 | −0.102372 | ||||||||
\(115\) | −3.22908 | −0.301113 | ||||||||
\(116\) | 7.12691 | 0.661717 | ||||||||
\(117\) | 13.7197 | 1.26839 | ||||||||
\(118\) | 9.73543 | 0.896219 | ||||||||
\(119\) | −17.5027 | −1.60447 | ||||||||
\(120\) | 0.228456 | 0.0208551 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 12.1961 | 1.10418 | ||||||||
\(123\) | −0.574625 | −0.0518121 | ||||||||
\(124\) | −5.82010 | −0.522661 | ||||||||
\(125\) | 7.72232 | 0.690705 | ||||||||
\(126\) | 14.1450 | 1.26014 | ||||||||
\(127\) | 9.99362 | 0.886790 | 0.443395 | − | 0.896326i | \(-0.353774\pi\) | ||||
0.443395 | + | 0.896326i | \(0.353774\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.84348 | −0.250354 | ||||||||
\(130\) | −3.89082 | −0.341247 | ||||||||
\(131\) | 12.0832 | 1.05572 | 0.527858 | − | 0.849333i | \(-0.322995\pi\) | ||||
0.527858 | + | 0.849333i | \(0.322995\pi\) | |||||||
\(132\) | 0.275495 | 0.0239788 | ||||||||
\(133\) | 19.1924 | 1.66419 | ||||||||
\(134\) | −12.1658 | −1.05096 | ||||||||
\(135\) | 1.35340 | 0.116482 | ||||||||
\(136\) | 3.61821 | 0.310259 | ||||||||
\(137\) | 18.5604 | 1.58572 | 0.792860 | − | 0.609404i | \(-0.208591\pi\) | ||||
0.792860 | + | 0.609404i | \(0.208591\pi\) | |||||||
\(138\) | −1.07276 | −0.0913193 | ||||||||
\(139\) | 7.49907 | 0.636063 | 0.318032 | − | 0.948080i | \(-0.396978\pi\) | ||||
0.318032 | + | 0.948080i | \(0.396978\pi\) | |||||||
\(140\) | −4.01143 | −0.339028 | ||||||||
\(141\) | 1.56276 | 0.131608 | ||||||||
\(142\) | 7.84656 | 0.658469 | ||||||||
\(143\) | −4.69193 | −0.392359 | ||||||||
\(144\) | −2.92410 | −0.243675 | ||||||||
\(145\) | −5.91004 | −0.490802 | ||||||||
\(146\) | 0.146186 | 0.0120985 | ||||||||
\(147\) | 4.51817 | 0.372653 | ||||||||
\(148\) | −7.26441 | −0.597131 | ||||||||
\(149\) | 5.94309 | 0.486877 | 0.243438 | − | 0.969916i | \(-0.421725\pi\) | ||||
0.243438 | + | 0.969916i | \(0.421725\pi\) | |||||||
\(150\) | 1.18803 | 0.0970019 | ||||||||
\(151\) | −23.7015 | −1.92880 | −0.964400 | − | 0.264448i | \(-0.914810\pi\) | ||||
−0.964400 | + | 0.264448i | \(0.914810\pi\) | |||||||
\(152\) | −3.96753 | −0.321809 | ||||||||
\(153\) | 10.5800 | 0.855345 | ||||||||
\(154\) | −4.83738 | −0.389807 | ||||||||
\(155\) | 4.82636 | 0.387663 | ||||||||
\(156\) | −1.29260 | −0.103491 | ||||||||
\(157\) | −9.43485 | −0.752983 | −0.376491 | − | 0.926420i | \(-0.622870\pi\) | ||||
−0.376491 | + | 0.926420i | \(0.622870\pi\) | |||||||
\(158\) | 6.17885 | 0.491563 | ||||||||
\(159\) | 2.46614 | 0.195577 | ||||||||
\(160\) | 0.829257 | 0.0655586 | ||||||||
\(161\) | 18.8364 | 1.48452 | ||||||||
\(162\) | −8.32268 | −0.653892 | ||||||||
\(163\) | −9.82480 | −0.769537 | −0.384769 | − | 0.923013i | \(-0.625719\pi\) | ||||
−0.384769 | + | 0.923013i | \(0.625719\pi\) | |||||||
\(164\) | −2.08579 | −0.162873 | ||||||||
\(165\) | −0.228456 | −0.0177853 | ||||||||
\(166\) | 13.7221 | 1.06504 | ||||||||
\(167\) | −10.1212 | −0.783206 | −0.391603 | − | 0.920134i | \(-0.628079\pi\) | ||||
−0.391603 | + | 0.920134i | \(0.628079\pi\) | |||||||
\(168\) | −1.33267 | −0.102818 | ||||||||
\(169\) | 9.01422 | 0.693402 | ||||||||
\(170\) | −3.00043 | −0.230123 | ||||||||
\(171\) | −11.6015 | −0.887185 | ||||||||
\(172\) | −10.3214 | −0.786996 | ||||||||
\(173\) | 8.49931 | 0.646191 | 0.323095 | − | 0.946366i | \(-0.395277\pi\) | ||||
0.323095 | + | 0.946366i | \(0.395277\pi\) | |||||||
\(174\) | −1.96343 | −0.148847 | ||||||||
\(175\) | −20.8604 | −1.57690 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −2.68206 | −0.201596 | ||||||||
\(178\) | 5.85899 | 0.439150 | ||||||||
\(179\) | 9.56658 | 0.715040 | 0.357520 | − | 0.933906i | \(-0.383622\pi\) | ||||
0.357520 | + | 0.933906i | \(0.383622\pi\) | |||||||
\(180\) | 2.42483 | 0.180736 | ||||||||
\(181\) | −3.88330 | −0.288644 | −0.144322 | − | 0.989531i | \(-0.546100\pi\) | ||||
−0.144322 | + | 0.989531i | \(0.546100\pi\) | |||||||
\(182\) | 22.6966 | 1.68239 | ||||||||
\(183\) | −3.35996 | −0.248376 | ||||||||
\(184\) | −3.89394 | −0.287065 | ||||||||
\(185\) | 6.02406 | 0.442898 | ||||||||
\(186\) | 1.60341 | 0.117568 | ||||||||
\(187\) | −3.61821 | −0.264590 | ||||||||
\(188\) | 5.67256 | 0.413714 | ||||||||
\(189\) | −7.89489 | −0.574269 | ||||||||
\(190\) | 3.29010 | 0.238689 | ||||||||
\(191\) | 7.50821 | 0.543275 | 0.271637 | − | 0.962400i | \(-0.412435\pi\) | ||||
0.271637 | + | 0.962400i | \(0.412435\pi\) | |||||||
\(192\) | 0.275495 | 0.0198821 | ||||||||
\(193\) | −3.61012 | −0.259862 | −0.129931 | − | 0.991523i | \(-0.541476\pi\) | ||||
−0.129931 | + | 0.991523i | \(0.541476\pi\) | |||||||
\(194\) | 12.1296 | 0.870853 | ||||||||
\(195\) | 1.07190 | 0.0767604 | ||||||||
\(196\) | 16.4002 | 1.17144 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 2.92410 | 0.207807 | ||||||||
\(199\) | −3.39694 | −0.240803 | −0.120401 | − | 0.992725i | \(-0.538418\pi\) | ||||
−0.120401 | + | 0.992725i | \(0.538418\pi\) | |||||||
\(200\) | 4.31233 | 0.304928 | ||||||||
\(201\) | 3.35160 | 0.236404 | ||||||||
\(202\) | 10.1809 | 0.716329 | ||||||||
\(203\) | 34.4755 | 2.41971 | ||||||||
\(204\) | −0.996800 | −0.0697899 | ||||||||
\(205\) | 1.72966 | 0.120804 | ||||||||
\(206\) | 9.12868 | 0.636025 | ||||||||
\(207\) | −11.3863 | −0.791400 | ||||||||
\(208\) | −4.69193 | −0.325327 | ||||||||
\(209\) | 3.96753 | 0.274440 | ||||||||
\(210\) | 1.10513 | 0.0762611 | ||||||||
\(211\) | −6.08249 | −0.418736 | −0.209368 | − | 0.977837i | \(-0.567141\pi\) | ||||
−0.209368 | + | 0.977837i | \(0.567141\pi\) | |||||||
\(212\) | 8.95166 | 0.614803 | ||||||||
\(213\) | −2.16169 | −0.148116 | ||||||||
\(214\) | −3.59450 | −0.245715 | ||||||||
\(215\) | 8.55906 | 0.583723 | ||||||||
\(216\) | 1.63206 | 0.111048 | ||||||||
\(217\) | −28.1540 | −1.91122 | ||||||||
\(218\) | −2.25058 | −0.152429 | ||||||||
\(219\) | −0.0402736 | −0.00272144 | ||||||||
\(220\) | −0.829257 | −0.0559085 | ||||||||
\(221\) | 16.9764 | 1.14196 | ||||||||
\(222\) | 2.00131 | 0.134319 | ||||||||
\(223\) | −6.28035 | −0.420563 | −0.210282 | − | 0.977641i | \(-0.567438\pi\) | ||||
−0.210282 | + | 0.977641i | \(0.567438\pi\) | |||||||
\(224\) | −4.83738 | −0.323211 | ||||||||
\(225\) | 12.6097 | 0.840647 | ||||||||
\(226\) | −0.169648 | −0.0112848 | ||||||||
\(227\) | −20.0570 | −1.33123 | −0.665615 | − | 0.746295i | \(-0.731831\pi\) | ||||
−0.665615 | + | 0.746295i | \(0.731831\pi\) | |||||||
\(228\) | 1.09303 | 0.0723879 | ||||||||
\(229\) | −5.47928 | −0.362081 | −0.181040 | − | 0.983476i | \(-0.557946\pi\) | ||||
−0.181040 | + | 0.983476i | \(0.557946\pi\) | |||||||
\(230\) | 3.22908 | 0.212919 | ||||||||
\(231\) | 1.33267 | 0.0876834 | ||||||||
\(232\) | −7.12691 | −0.467905 | ||||||||
\(233\) | 6.96448 | 0.456258 | 0.228129 | − | 0.973631i | \(-0.426739\pi\) | ||||
0.228129 | + | 0.973631i | \(0.426739\pi\) | |||||||
\(234\) | −13.7197 | −0.896884 | ||||||||
\(235\) | −4.70401 | −0.306856 | ||||||||
\(236\) | −9.73543 | −0.633722 | ||||||||
\(237\) | −1.70224 | −0.110572 | ||||||||
\(238\) | 17.5027 | 1.13453 | ||||||||
\(239\) | −4.60506 | −0.297876 | −0.148938 | − | 0.988847i | \(-0.547586\pi\) | ||||
−0.148938 | + | 0.988847i | \(0.547586\pi\) | |||||||
\(240\) | −0.228456 | −0.0147468 | ||||||||
\(241\) | 7.16729 | 0.461686 | 0.230843 | − | 0.972991i | \(-0.425852\pi\) | ||||
0.230843 | + | 0.972991i | \(0.425852\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 7.18904 | 0.461177 | ||||||||
\(244\) | −12.1961 | −0.780775 | ||||||||
\(245\) | −13.6000 | −0.868872 | ||||||||
\(246\) | 0.574625 | 0.0366367 | ||||||||
\(247\) | −18.6154 | −1.18447 | ||||||||
\(248\) | 5.82010 | 0.369577 | ||||||||
\(249\) | −3.78038 | −0.239572 | ||||||||
\(250\) | −7.72232 | −0.488402 | ||||||||
\(251\) | 0.901357 | 0.0568931 | 0.0284466 | − | 0.999595i | \(-0.490944\pi\) | ||||
0.0284466 | + | 0.999595i | \(0.490944\pi\) | |||||||
\(252\) | −14.1450 | −0.891050 | ||||||||
\(253\) | 3.89394 | 0.244810 | ||||||||
\(254\) | −9.99362 | −0.627055 | ||||||||
\(255\) | 0.826604 | 0.0517639 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.9133 | −1.67881 | −0.839403 | − | 0.543509i | \(-0.817095\pi\) | ||||
−0.839403 | + | 0.543509i | \(0.817095\pi\) | |||||||
\(258\) | 2.84348 | 0.177027 | ||||||||
\(259\) | −35.1407 | −2.18353 | ||||||||
\(260\) | 3.89082 | 0.241298 | ||||||||
\(261\) | −20.8398 | −1.28995 | ||||||||
\(262\) | −12.0832 | −0.746504 | ||||||||
\(263\) | −7.91989 | −0.488361 | −0.244181 | − | 0.969730i | \(-0.578519\pi\) | ||||
−0.244181 | + | 0.969730i | \(0.578519\pi\) | |||||||
\(264\) | −0.275495 | −0.0169555 | ||||||||
\(265\) | −7.42323 | −0.456006 | ||||||||
\(266\) | −19.1924 | −1.17676 | ||||||||
\(267\) | −1.61412 | −0.0987826 | ||||||||
\(268\) | 12.1658 | 0.743142 | ||||||||
\(269\) | −13.3200 | −0.812137 | −0.406069 | − | 0.913843i | \(-0.633101\pi\) | ||||
−0.406069 | + | 0.913843i | \(0.633101\pi\) | |||||||
\(270\) | −1.35340 | −0.0823652 | ||||||||
\(271\) | 2.17709 | 0.132249 | 0.0661243 | − | 0.997811i | \(-0.478937\pi\) | ||||
0.0661243 | + | 0.997811i | \(0.478937\pi\) | |||||||
\(272\) | −3.61821 | −0.219386 | ||||||||
\(273\) | −6.25281 | −0.378437 | ||||||||
\(274\) | −18.5604 | −1.12127 | ||||||||
\(275\) | −4.31233 | −0.260043 | ||||||||
\(276\) | 1.07276 | 0.0645725 | ||||||||
\(277\) | 0.716770 | 0.0430666 | 0.0215333 | − | 0.999768i | \(-0.493145\pi\) | ||||
0.0215333 | + | 0.999768i | \(0.493145\pi\) | |||||||
\(278\) | −7.49907 | −0.449765 | ||||||||
\(279\) | 17.0186 | 1.01888 | ||||||||
\(280\) | 4.01143 | 0.239729 | ||||||||
\(281\) | 4.61908 | 0.275551 | 0.137776 | − | 0.990463i | \(-0.456005\pi\) | ||||
0.137776 | + | 0.990463i | \(0.456005\pi\) | |||||||
\(282\) | −1.56276 | −0.0930611 | ||||||||
\(283\) | −17.5616 | −1.04393 | −0.521965 | − | 0.852967i | \(-0.674801\pi\) | ||||
−0.521965 | + | 0.852967i | \(0.674801\pi\) | |||||||
\(284\) | −7.84656 | −0.465608 | ||||||||
\(285\) | −0.906406 | −0.0536909 | ||||||||
\(286\) | 4.69193 | 0.277440 | ||||||||
\(287\) | −10.0898 | −0.595579 | ||||||||
\(288\) | 2.92410 | 0.172304 | ||||||||
\(289\) | −3.90852 | −0.229913 | ||||||||
\(290\) | 5.91004 | 0.347050 | ||||||||
\(291\) | −3.34164 | −0.195890 | ||||||||
\(292\) | −0.146186 | −0.00855491 | ||||||||
\(293\) | 14.6631 | 0.856629 | 0.428314 | − | 0.903630i | \(-0.359108\pi\) | ||||
0.428314 | + | 0.903630i | \(0.359108\pi\) | |||||||
\(294\) | −4.51817 | −0.263505 | ||||||||
\(295\) | 8.07318 | 0.470039 | ||||||||
\(296\) | 7.26441 | 0.422235 | ||||||||
\(297\) | −1.63206 | −0.0947017 | ||||||||
\(298\) | −5.94309 | −0.344274 | ||||||||
\(299\) | −18.2701 | −1.05659 | ||||||||
\(300\) | −1.18803 | −0.0685907 | ||||||||
\(301\) | −49.9283 | −2.87782 | ||||||||
\(302\) | 23.7015 | 1.36387 | ||||||||
\(303\) | −2.80480 | −0.161131 | ||||||||
\(304\) | 3.96753 | 0.227553 | ||||||||
\(305\) | 10.1137 | 0.579109 | ||||||||
\(306\) | −10.5800 | −0.604820 | ||||||||
\(307\) | 13.5913 | 0.775695 | 0.387847 | − | 0.921724i | \(-0.373219\pi\) | ||||
0.387847 | + | 0.921724i | \(0.373219\pi\) | |||||||
\(308\) | 4.83738 | 0.275635 | ||||||||
\(309\) | −2.51490 | −0.143068 | ||||||||
\(310\) | −4.82636 | −0.274119 | ||||||||
\(311\) | −23.4225 | −1.32817 | −0.664084 | − | 0.747658i | \(-0.731178\pi\) | ||||
−0.664084 | + | 0.747658i | \(0.731178\pi\) | |||||||
\(312\) | 1.29260 | 0.0731792 | ||||||||
\(313\) | −16.2882 | −0.920664 | −0.460332 | − | 0.887747i | \(-0.652270\pi\) | ||||
−0.460332 | + | 0.887747i | \(0.652270\pi\) | |||||||
\(314\) | 9.43485 | 0.532439 | ||||||||
\(315\) | 11.7298 | 0.660901 | ||||||||
\(316\) | −6.17885 | −0.347587 | ||||||||
\(317\) | 23.3554 | 1.31177 | 0.655884 | − | 0.754862i | \(-0.272296\pi\) | ||||
0.655884 | + | 0.754862i | \(0.272296\pi\) | |||||||
\(318\) | −2.46614 | −0.138294 | ||||||||
\(319\) | 7.12691 | 0.399030 | ||||||||
\(320\) | −0.829257 | −0.0463569 | ||||||||
\(321\) | 0.990267 | 0.0552713 | ||||||||
\(322\) | −18.8364 | −1.04971 | ||||||||
\(323\) | −14.3554 | −0.798754 | ||||||||
\(324\) | 8.32268 | 0.462371 | ||||||||
\(325\) | 20.2332 | 1.12233 | ||||||||
\(326\) | 9.82480 | 0.544145 | ||||||||
\(327\) | 0.620024 | 0.0342874 | ||||||||
\(328\) | 2.08579 | 0.115168 | ||||||||
\(329\) | 27.4403 | 1.51283 | ||||||||
\(330\) | 0.228456 | 0.0125761 | ||||||||
\(331\) | 34.2480 | 1.88244 | 0.941220 | − | 0.337793i | \(-0.109680\pi\) | ||||
0.941220 | + | 0.337793i | \(0.109680\pi\) | |||||||
\(332\) | −13.7221 | −0.753100 | ||||||||
\(333\) | 21.2419 | 1.16405 | ||||||||
\(334\) | 10.1212 | 0.553810 | ||||||||
\(335\) | −10.0885 | −0.551196 | ||||||||
\(336\) | 1.33267 | 0.0727032 | ||||||||
\(337\) | −25.7171 | −1.40090 | −0.700450 | − | 0.713701i | \(-0.747017\pi\) | ||||
−0.700450 | + | 0.713701i | \(0.747017\pi\) | |||||||
\(338\) | −9.01422 | −0.490309 | ||||||||
\(339\) | 0.0467370 | 0.00253841 | ||||||||
\(340\) | 3.00043 | 0.162721 | ||||||||
\(341\) | −5.82010 | −0.315176 | ||||||||
\(342\) | 11.6015 | 0.627335 | ||||||||
\(343\) | 45.4723 | 2.45527 | ||||||||
\(344\) | 10.3214 | 0.556490 | ||||||||
\(345\) | −0.889594 | −0.0478941 | ||||||||
\(346\) | −8.49931 | −0.456926 | ||||||||
\(347\) | 26.8693 | 1.44242 | 0.721210 | − | 0.692717i | \(-0.243586\pi\) | ||||
0.721210 | + | 0.692717i | \(0.243586\pi\) | |||||||
\(348\) | 1.96343 | 0.105251 | ||||||||
\(349\) | −19.8151 | −1.06068 | −0.530339 | − | 0.847786i | \(-0.677935\pi\) | ||||
−0.530339 | + | 0.847786i | \(0.677935\pi\) | |||||||
\(350\) | 20.8604 | 1.11503 | ||||||||
\(351\) | 7.65751 | 0.408728 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −23.1388 | −1.23156 | −0.615778 | − | 0.787920i | \(-0.711158\pi\) | ||||
−0.615778 | + | 0.787920i | \(0.711158\pi\) | |||||||
\(354\) | 2.68206 | 0.142550 | ||||||||
\(355\) | 6.50682 | 0.345346 | ||||||||
\(356\) | −5.85899 | −0.310526 | ||||||||
\(357\) | −4.82189 | −0.255202 | ||||||||
\(358\) | −9.56658 | −0.505609 | ||||||||
\(359\) | −35.3470 | −1.86554 | −0.932771 | − | 0.360468i | \(-0.882617\pi\) | ||||
−0.932771 | + | 0.360468i | \(0.882617\pi\) | |||||||
\(360\) | −2.42483 | −0.127800 | ||||||||
\(361\) | −3.25873 | −0.171512 | ||||||||
\(362\) | 3.88330 | 0.204102 | ||||||||
\(363\) | 0.275495 | 0.0144597 | ||||||||
\(364\) | −22.6966 | −1.18963 | ||||||||
\(365\) | 0.121226 | 0.00634526 | ||||||||
\(366\) | 3.35996 | 0.175628 | ||||||||
\(367\) | −1.43254 | −0.0747779 | −0.0373890 | − | 0.999301i | \(-0.511904\pi\) | ||||
−0.0373890 | + | 0.999301i | \(0.511904\pi\) | |||||||
\(368\) | 3.89394 | 0.202985 | ||||||||
\(369\) | 6.09906 | 0.317505 | ||||||||
\(370\) | −6.02406 | −0.313176 | ||||||||
\(371\) | 43.3026 | 2.24816 | ||||||||
\(372\) | −1.60341 | −0.0831328 | ||||||||
\(373\) | 21.8486 | 1.13128 | 0.565639 | − | 0.824653i | \(-0.308630\pi\) | ||||
0.565639 | + | 0.824653i | \(0.308630\pi\) | |||||||
\(374\) | 3.61821 | 0.187093 | ||||||||
\(375\) | 2.12746 | 0.109862 | ||||||||
\(376\) | −5.67256 | −0.292540 | ||||||||
\(377\) | −33.4390 | −1.72219 | ||||||||
\(378\) | 7.89489 | 0.406069 | ||||||||
\(379\) | −17.0176 | −0.874135 | −0.437067 | − | 0.899429i | \(-0.643983\pi\) | ||||
−0.437067 | + | 0.899429i | \(0.643983\pi\) | |||||||
\(380\) | −3.29010 | −0.168779 | ||||||||
\(381\) | 2.75319 | 0.141050 | ||||||||
\(382\) | −7.50821 | −0.384153 | ||||||||
\(383\) | 22.3816 | 1.14365 | 0.571823 | − | 0.820377i | \(-0.306236\pi\) | ||||
0.571823 | + | 0.820377i | \(0.306236\pi\) | |||||||
\(384\) | −0.275495 | −0.0140588 | ||||||||
\(385\) | −4.01143 | −0.204441 | ||||||||
\(386\) | 3.61012 | 0.183750 | ||||||||
\(387\) | 30.1807 | 1.53417 | ||||||||
\(388\) | −12.1296 | −0.615786 | ||||||||
\(389\) | −17.5665 | −0.890655 | −0.445328 | − | 0.895368i | \(-0.646913\pi\) | ||||
−0.445328 | + | 0.895368i | \(0.646913\pi\) | |||||||
\(390\) | −1.07190 | −0.0542778 | ||||||||
\(391\) | −14.0891 | −0.712516 | ||||||||
\(392\) | −16.4002 | −0.828335 | ||||||||
\(393\) | 3.32887 | 0.167919 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 5.12385 | 0.257809 | ||||||||
\(396\) | −2.92410 | −0.146942 | ||||||||
\(397\) | −17.3428 | −0.870411 | −0.435205 | − | 0.900331i | \(-0.643324\pi\) | ||||
−0.435205 | + | 0.900331i | \(0.643324\pi\) | |||||||
\(398\) | 3.39694 | 0.170273 | ||||||||
\(399\) | 5.28741 | 0.264702 | ||||||||
\(400\) | −4.31233 | −0.215617 | ||||||||
\(401\) | 9.02318 | 0.450596 | 0.225298 | − | 0.974290i | \(-0.427664\pi\) | ||||
0.225298 | + | 0.974290i | \(0.427664\pi\) | |||||||
\(402\) | −3.35160 | −0.167163 | ||||||||
\(403\) | 27.3075 | 1.36028 | ||||||||
\(404\) | −10.1809 | −0.506521 | ||||||||
\(405\) | −6.90165 | −0.342946 | ||||||||
\(406\) | −34.4755 | −1.71099 | ||||||||
\(407\) | −7.26441 | −0.360083 | ||||||||
\(408\) | 0.996800 | 0.0493489 | ||||||||
\(409\) | 4.77298 | 0.236008 | 0.118004 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118004 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(410\) | −1.72966 | −0.0854217 | ||||||||
\(411\) | 5.11329 | 0.252220 | ||||||||
\(412\) | −9.12868 | −0.449738 | ||||||||
\(413\) | −47.0939 | −2.31734 | ||||||||
\(414\) | 11.3863 | 0.559605 | ||||||||
\(415\) | 11.3792 | 0.558582 | ||||||||
\(416\) | 4.69193 | 0.230041 | ||||||||
\(417\) | 2.06596 | 0.101170 | ||||||||
\(418\) | −3.96753 | −0.194058 | ||||||||
\(419\) | −25.3146 | −1.23670 | −0.618350 | − | 0.785903i | \(-0.712199\pi\) | ||||
−0.618350 | + | 0.785903i | \(0.712199\pi\) | |||||||
\(420\) | −1.10513 | −0.0539247 | ||||||||
\(421\) | −29.7629 | −1.45056 | −0.725279 | − | 0.688455i | \(-0.758289\pi\) | ||||
−0.725279 | + | 0.688455i | \(0.758289\pi\) | |||||||
\(422\) | 6.08249 | 0.296091 | ||||||||
\(423\) | −16.5871 | −0.806495 | ||||||||
\(424\) | −8.95166 | −0.434731 | ||||||||
\(425\) | 15.6029 | 0.756854 | ||||||||
\(426\) | 2.16169 | 0.104734 | ||||||||
\(427\) | −58.9971 | −2.85507 | ||||||||
\(428\) | 3.59450 | 0.173747 | ||||||||
\(429\) | −1.29260 | −0.0624075 | ||||||||
\(430\) | −8.55906 | −0.412755 | ||||||||
\(431\) | −6.96059 | −0.335280 | −0.167640 | − | 0.985848i | \(-0.553615\pi\) | ||||
−0.167640 | + | 0.985848i | \(0.553615\pi\) | |||||||
\(432\) | −1.63206 | −0.0785225 | ||||||||
\(433\) | 30.8500 | 1.48256 | 0.741278 | − | 0.671198i | \(-0.234220\pi\) | ||||
0.741278 | + | 0.671198i | \(0.234220\pi\) | |||||||
\(434\) | 28.1540 | 1.35144 | ||||||||
\(435\) | −1.62819 | −0.0780656 | ||||||||
\(436\) | 2.25058 | 0.107783 | ||||||||
\(437\) | 15.4493 | 0.739040 | ||||||||
\(438\) | 0.0402736 | 0.00192435 | ||||||||
\(439\) | 22.4922 | 1.07349 | 0.536747 | − | 0.843743i | \(-0.319653\pi\) | ||||
0.536747 | + | 0.843743i | \(0.319653\pi\) | |||||||
\(440\) | 0.829257 | 0.0395333 | ||||||||
\(441\) | −47.9559 | −2.28361 | ||||||||
\(442\) | −16.9764 | −0.807486 | ||||||||
\(443\) | −4.94585 | −0.234984 | −0.117492 | − | 0.993074i | \(-0.537486\pi\) | ||||
−0.117492 | + | 0.993074i | \(0.537486\pi\) | |||||||
\(444\) | −2.00131 | −0.0949778 | ||||||||
\(445\) | 4.85861 | 0.230320 | ||||||||
\(446\) | 6.28035 | 0.297383 | ||||||||
\(447\) | 1.63729 | 0.0774412 | ||||||||
\(448\) | 4.83738 | 0.228545 | ||||||||
\(449\) | 29.3948 | 1.38723 | 0.693614 | − | 0.720347i | \(-0.256017\pi\) | ||||
0.693614 | + | 0.720347i | \(0.256017\pi\) | |||||||
\(450\) | −12.6097 | −0.594427 | ||||||||
\(451\) | −2.08579 | −0.0982160 | ||||||||
\(452\) | 0.169648 | 0.00797955 | ||||||||
\(453\) | −6.52964 | −0.306789 | ||||||||
\(454\) | 20.0570 | 0.941322 | ||||||||
\(455\) | 18.8214 | 0.882359 | ||||||||
\(456\) | −1.09303 | −0.0511860 | ||||||||
\(457\) | −31.6624 | −1.48110 | −0.740552 | − | 0.671999i | \(-0.765436\pi\) | ||||
−0.740552 | + | 0.671999i | \(0.765436\pi\) | |||||||
\(458\) | 5.47928 | 0.256030 | ||||||||
\(459\) | 5.90514 | 0.275628 | ||||||||
\(460\) | −3.22908 | −0.150556 | ||||||||
\(461\) | 16.7107 | 0.778296 | 0.389148 | − | 0.921175i | \(-0.372769\pi\) | ||||
0.389148 | + | 0.921175i | \(0.372769\pi\) | |||||||
\(462\) | −1.33267 | −0.0620015 | ||||||||
\(463\) | −26.5138 | −1.23220 | −0.616100 | − | 0.787668i | \(-0.711288\pi\) | ||||
−0.616100 | + | 0.787668i | \(0.711288\pi\) | |||||||
\(464\) | 7.12691 | 0.330859 | ||||||||
\(465\) | 1.32964 | 0.0616605 | ||||||||
\(466\) | −6.96448 | −0.322623 | ||||||||
\(467\) | −15.2806 | −0.707104 | −0.353552 | − | 0.935415i | \(-0.615026\pi\) | ||||
−0.353552 | + | 0.935415i | \(0.615026\pi\) | |||||||
\(468\) | 13.7197 | 0.634193 | ||||||||
\(469\) | 58.8503 | 2.71746 | ||||||||
\(470\) | 4.70401 | 0.216980 | ||||||||
\(471\) | −2.59925 | −0.119767 | ||||||||
\(472\) | 9.73543 | 0.448109 | ||||||||
\(473\) | −10.3214 | −0.474576 | ||||||||
\(474\) | 1.70224 | 0.0781865 | ||||||||
\(475\) | −17.1093 | −0.785028 | ||||||||
\(476\) | −17.5027 | −0.802233 | ||||||||
\(477\) | −26.1756 | −1.19850 | ||||||||
\(478\) | 4.60506 | 0.210630 | ||||||||
\(479\) | 37.3582 | 1.70694 | 0.853469 | − | 0.521143i | \(-0.174494\pi\) | ||||
0.853469 | + | 0.521143i | \(0.174494\pi\) | |||||||
\(480\) | 0.228456 | 0.0104276 | ||||||||
\(481\) | 34.0841 | 1.55410 | ||||||||
\(482\) | −7.16729 | −0.326461 | ||||||||
\(483\) | 5.18934 | 0.236123 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.0585 | 0.456735 | ||||||||
\(486\) | −7.18904 | −0.326101 | ||||||||
\(487\) | −18.2127 | −0.825296 | −0.412648 | − | 0.910891i | \(-0.635396\pi\) | ||||
−0.412648 | + | 0.910891i | \(0.635396\pi\) | |||||||
\(488\) | 12.1961 | 0.552091 | ||||||||
\(489\) | −2.70668 | −0.122400 | ||||||||
\(490\) | 13.6000 | 0.614385 | ||||||||
\(491\) | −40.6739 | −1.83559 | −0.917795 | − | 0.397055i | \(-0.870032\pi\) | ||||
−0.917795 | + | 0.397055i | \(0.870032\pi\) | |||||||
\(492\) | −0.574625 | −0.0259061 | ||||||||
\(493\) | −25.7867 | −1.16137 | ||||||||
\(494\) | 18.6154 | 0.837545 | ||||||||
\(495\) | 2.42483 | 0.108988 | ||||||||
\(496\) | −5.82010 | −0.261330 | ||||||||
\(497\) | −37.9568 | −1.70259 | ||||||||
\(498\) | 3.78038 | 0.169403 | ||||||||
\(499\) | 11.0473 | 0.494544 | 0.247272 | − | 0.968946i | \(-0.420466\pi\) | ||||
0.247272 | + | 0.968946i | \(0.420466\pi\) | |||||||
\(500\) | 7.72232 | 0.345353 | ||||||||
\(501\) | −2.78835 | −0.124574 | ||||||||
\(502\) | −0.901357 | −0.0402295 | ||||||||
\(503\) | −16.2803 | −0.725904 | −0.362952 | − | 0.931808i | \(-0.618231\pi\) | ||||
−0.362952 | + | 0.931808i | \(0.618231\pi\) | |||||||
\(504\) | 14.1450 | 0.630068 | ||||||||
\(505\) | 8.44262 | 0.375692 | ||||||||
\(506\) | −3.89394 | −0.173107 | ||||||||
\(507\) | 2.48337 | 0.110290 | ||||||||
\(508\) | 9.99362 | 0.443395 | ||||||||
\(509\) | −4.58003 | −0.203006 | −0.101503 | − | 0.994835i | \(-0.532365\pi\) | ||||
−0.101503 | + | 0.994835i | \(0.532365\pi\) | |||||||
\(510\) | −0.826604 | −0.0366026 | ||||||||
\(511\) | −0.707158 | −0.0312828 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.47524 | −0.285889 | ||||||||
\(514\) | 26.9133 | 1.18710 | ||||||||
\(515\) | 7.57002 | 0.333575 | ||||||||
\(516\) | −2.84348 | −0.125177 | ||||||||
\(517\) | 5.67256 | 0.249479 | ||||||||
\(518\) | 35.1407 | 1.54399 | ||||||||
\(519\) | 2.34152 | 0.102781 | ||||||||
\(520\) | −3.89082 | −0.170624 | ||||||||
\(521\) | 21.0983 | 0.924334 | 0.462167 | − | 0.886793i | \(-0.347072\pi\) | ||||
0.462167 | + | 0.886793i | \(0.347072\pi\) | |||||||
\(522\) | 20.8398 | 0.912134 | ||||||||
\(523\) | −26.1173 | −1.14203 | −0.571015 | − | 0.820939i | \(-0.693450\pi\) | ||||
−0.571015 | + | 0.820939i | \(0.693450\pi\) | |||||||
\(524\) | 12.0832 | 0.527858 | ||||||||
\(525\) | −5.74693 | −0.250816 | ||||||||
\(526\) | 7.91989 | 0.345324 | ||||||||
\(527\) | 21.0584 | 0.917317 | ||||||||
\(528\) | 0.275495 | 0.0119894 | ||||||||
\(529\) | −7.83726 | −0.340751 | ||||||||
\(530\) | 7.42323 | 0.322445 | ||||||||
\(531\) | 28.4674 | 1.23538 | ||||||||
\(532\) | 19.1924 | 0.832097 | ||||||||
\(533\) | 9.78638 | 0.423895 | ||||||||
\(534\) | 1.61412 | 0.0698499 | ||||||||
\(535\) | −2.98077 | −0.128870 | ||||||||
\(536\) | −12.1658 | −0.525481 | ||||||||
\(537\) | 2.63554 | 0.113732 | ||||||||
\(538\) | 13.3200 | 0.574268 | ||||||||
\(539\) | 16.4002 | 0.706407 | ||||||||
\(540\) | 1.35340 | 0.0582410 | ||||||||
\(541\) | −46.2299 | −1.98758 | −0.993788 | − | 0.111287i | \(-0.964503\pi\) | ||||
−0.993788 | + | 0.111287i | \(0.964503\pi\) | |||||||
\(542\) | −2.17709 | −0.0935139 | ||||||||
\(543\) | −1.06983 | −0.0459108 | ||||||||
\(544\) | 3.61821 | 0.155130 | ||||||||
\(545\) | −1.86631 | −0.0799441 | ||||||||
\(546\) | 6.25281 | 0.267595 | ||||||||
\(547\) | 41.5825 | 1.77794 | 0.888969 | − | 0.457967i | \(-0.151422\pi\) | ||||
0.888969 | + | 0.457967i | \(0.151422\pi\) | |||||||
\(548\) | 18.5604 | 0.792860 | ||||||||
\(549\) | 35.6626 | 1.52204 | ||||||||
\(550\) | 4.31233 | 0.183878 | ||||||||
\(551\) | 28.2762 | 1.20461 | ||||||||
\(552\) | −1.07276 | −0.0456597 | ||||||||
\(553\) | −29.8894 | −1.27103 | ||||||||
\(554\) | −0.716770 | −0.0304527 | ||||||||
\(555\) | 1.65960 | 0.0704460 | ||||||||
\(556\) | 7.49907 | 0.318032 | ||||||||
\(557\) | −40.7343 | −1.72597 | −0.862984 | − | 0.505232i | \(-0.831407\pi\) | ||||
−0.862984 | + | 0.505232i | \(0.831407\pi\) | |||||||
\(558\) | −17.0186 | −0.720454 | ||||||||
\(559\) | 48.4271 | 2.04825 | ||||||||
\(560\) | −4.01143 | −0.169514 | ||||||||
\(561\) | −0.996800 | −0.0420849 | ||||||||
\(562\) | −4.61908 | −0.194844 | ||||||||
\(563\) | 11.4817 | 0.483895 | 0.241947 | − | 0.970289i | \(-0.422214\pi\) | ||||
0.241947 | + | 0.970289i | \(0.422214\pi\) | |||||||
\(564\) | 1.56276 | 0.0658041 | ||||||||
\(565\) | −0.140681 | −0.00591851 | ||||||||
\(566\) | 17.5616 | 0.738169 | ||||||||
\(567\) | 40.2599 | 1.69076 | ||||||||
\(568\) | 7.84656 | 0.329235 | ||||||||
\(569\) | 27.8058 | 1.16568 | 0.582841 | − | 0.812586i | \(-0.301941\pi\) | ||||
0.582841 | + | 0.812586i | \(0.301941\pi\) | |||||||
\(570\) | 0.906406 | 0.0379652 | ||||||||
\(571\) | −12.9931 | −0.543746 | −0.271873 | − | 0.962333i | \(-0.587643\pi\) | ||||
−0.271873 | + | 0.962333i | \(0.587643\pi\) | |||||||
\(572\) | −4.69193 | −0.196180 | ||||||||
\(573\) | 2.06847 | 0.0864117 | ||||||||
\(574\) | 10.0898 | 0.421138 | ||||||||
\(575\) | −16.7919 | −0.700272 | ||||||||
\(576\) | −2.92410 | −0.121838 | ||||||||
\(577\) | −7.55341 | −0.314453 | −0.157226 | − | 0.987563i | \(-0.550255\pi\) | ||||
−0.157226 | + | 0.987563i | \(0.550255\pi\) | |||||||
\(578\) | 3.90852 | 0.162573 | ||||||||
\(579\) | −0.994569 | −0.0413329 | ||||||||
\(580\) | −5.91004 | −0.245401 | ||||||||
\(581\) | −66.3792 | −2.75387 | ||||||||
\(582\) | 3.34164 | 0.138515 | ||||||||
\(583\) | 8.95166 | 0.370740 | ||||||||
\(584\) | 0.146186 | 0.00604923 | ||||||||
\(585\) | −11.3772 | −0.470387 | ||||||||
\(586\) | −14.6631 | −0.605728 | ||||||||
\(587\) | −27.0191 | −1.11520 | −0.557600 | − | 0.830110i | \(-0.688278\pi\) | ||||
−0.557600 | + | 0.830110i | \(0.688278\pi\) | |||||||
\(588\) | 4.51817 | 0.186326 | ||||||||
\(589\) | −23.0914 | −0.951465 | ||||||||
\(590\) | −8.07318 | −0.332367 | ||||||||
\(591\) | 0.275495 | 0.0113323 | ||||||||
\(592\) | −7.26441 | −0.298565 | ||||||||
\(593\) | −38.9055 | −1.59766 | −0.798829 | − | 0.601559i | \(-0.794547\pi\) | ||||
−0.798829 | + | 0.601559i | \(0.794547\pi\) | |||||||
\(594\) | 1.63206 | 0.0669642 | ||||||||
\(595\) | 14.5142 | 0.595025 | ||||||||
\(596\) | 5.94309 | 0.243438 | ||||||||
\(597\) | −0.935839 | −0.0383013 | ||||||||
\(598\) | 18.2701 | 0.747119 | ||||||||
\(599\) | −32.3648 | −1.32239 | −0.661195 | − | 0.750214i | \(-0.729950\pi\) | ||||
−0.661195 | + | 0.750214i | \(0.729950\pi\) | |||||||
\(600\) | 1.18803 | 0.0485009 | ||||||||
\(601\) | 13.9539 | 0.569189 | 0.284595 | − | 0.958648i | \(-0.408141\pi\) | ||||
0.284595 | + | 0.958648i | \(0.408141\pi\) | |||||||
\(602\) | 49.9283 | 2.03492 | ||||||||
\(603\) | −35.5739 | −1.44868 | ||||||||
\(604\) | −23.7015 | −0.964400 | ||||||||
\(605\) | −0.829257 | −0.0337141 | ||||||||
\(606\) | 2.80480 | 0.113937 | ||||||||
\(607\) | 25.2293 | 1.02403 | 0.512013 | − | 0.858978i | \(-0.328900\pi\) | ||||
0.512013 | + | 0.858978i | \(0.328900\pi\) | |||||||
\(608\) | −3.96753 | −0.160904 | ||||||||
\(609\) | 9.49784 | 0.384872 | ||||||||
\(610\) | −10.1137 | −0.409492 | ||||||||
\(611\) | −26.6153 | −1.07674 | ||||||||
\(612\) | 10.5800 | 0.427672 | ||||||||
\(613\) | 42.7405 | 1.72627 | 0.863135 | − | 0.504973i | \(-0.168497\pi\) | ||||
0.863135 | + | 0.504973i | \(0.168497\pi\) | |||||||
\(614\) | −13.5913 | −0.548499 | ||||||||
\(615\) | 0.476512 | 0.0192148 | ||||||||
\(616\) | −4.83738 | −0.194903 | ||||||||
\(617\) | −16.1662 | −0.650828 | −0.325414 | − | 0.945572i | \(-0.605504\pi\) | ||||
−0.325414 | + | 0.945572i | \(0.605504\pi\) | |||||||
\(618\) | 2.51490 | 0.101164 | ||||||||
\(619\) | 23.6337 | 0.949917 | 0.474958 | − | 0.880008i | \(-0.342463\pi\) | ||||
0.474958 | + | 0.880008i | \(0.342463\pi\) | |||||||
\(620\) | 4.82636 | 0.193831 | ||||||||
\(621\) | −6.35514 | −0.255023 | ||||||||
\(622\) | 23.4225 | 0.939156 | ||||||||
\(623\) | −28.3421 | −1.13550 | ||||||||
\(624\) | −1.29260 | −0.0517455 | ||||||||
\(625\) | 15.1579 | 0.606315 | ||||||||
\(626\) | 16.2882 | 0.651008 | ||||||||
\(627\) | 1.09303 | 0.0436515 | ||||||||
\(628\) | −9.43485 | −0.376491 | ||||||||
\(629\) | 26.2842 | 1.04802 | ||||||||
\(630\) | −11.7298 | −0.467328 | ||||||||
\(631\) | −15.9302 | −0.634171 | −0.317085 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317085 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(632\) | 6.17885 | 0.245781 | ||||||||
\(633\) | −1.67569 | −0.0666029 | ||||||||
\(634\) | −23.3554 | −0.927560 | ||||||||
\(635\) | −8.28728 | −0.328871 | ||||||||
\(636\) | 2.46614 | 0.0977887 | ||||||||
\(637\) | −76.9486 | −3.04882 | ||||||||
\(638\) | −7.12691 | −0.282157 | ||||||||
\(639\) | 22.9442 | 0.907657 | ||||||||
\(640\) | 0.829257 | 0.0327793 | ||||||||
\(641\) | 44.2360 | 1.74722 | 0.873608 | − | 0.486630i | \(-0.161774\pi\) | ||||
0.873608 | + | 0.486630i | \(0.161774\pi\) | |||||||
\(642\) | −0.990267 | −0.0390827 | ||||||||
\(643\) | 40.0020 | 1.57752 | 0.788762 | − | 0.614698i | \(-0.210722\pi\) | ||||
0.788762 | + | 0.614698i | \(0.210722\pi\) | |||||||
\(644\) | 18.8364 | 0.742259 | ||||||||
\(645\) | 2.35798 | 0.0928453 | ||||||||
\(646\) | 14.3554 | 0.564804 | ||||||||
\(647\) | 11.3381 | 0.445748 | 0.222874 | − | 0.974847i | \(-0.428456\pi\) | ||||
0.222874 | + | 0.974847i | \(0.428456\pi\) | |||||||
\(648\) | −8.32268 | −0.326946 | ||||||||
\(649\) | −9.73543 | −0.382149 | ||||||||
\(650\) | −20.2332 | −0.793610 | ||||||||
\(651\) | −7.75629 | −0.303993 | ||||||||
\(652\) | −9.82480 | −0.384769 | ||||||||
\(653\) | 6.92242 | 0.270895 | 0.135448 | − | 0.990785i | \(-0.456753\pi\) | ||||
0.135448 | + | 0.990785i | \(0.456753\pi\) | |||||||
\(654\) | −0.620024 | −0.0242449 | ||||||||
\(655\) | −10.0201 | −0.391518 | ||||||||
\(656\) | −2.08579 | −0.0814364 | ||||||||
\(657\) | 0.427464 | 0.0166769 | ||||||||
\(658\) | −27.4403 | −1.06973 | ||||||||
\(659\) | 15.1395 | 0.589750 | 0.294875 | − | 0.955536i | \(-0.404722\pi\) | ||||
0.294875 | + | 0.955536i | \(0.404722\pi\) | |||||||
\(660\) | −0.228456 | −0.00889265 | ||||||||
\(661\) | −34.8415 | −1.35518 | −0.677588 | − | 0.735442i | \(-0.736975\pi\) | ||||
−0.677588 | + | 0.735442i | \(0.736975\pi\) | |||||||
\(662\) | −34.2480 | −1.33109 | ||||||||
\(663\) | 4.67692 | 0.181636 | ||||||||
\(664\) | 13.7221 | 0.532522 | ||||||||
\(665\) | −15.9155 | −0.617175 | ||||||||
\(666\) | −21.2419 | −0.823106 | ||||||||
\(667\) | 27.7517 | 1.07455 | ||||||||
\(668\) | −10.1212 | −0.391603 | ||||||||
\(669\) | −1.73020 | −0.0668936 | ||||||||
\(670\) | 10.0885 | 0.389754 | ||||||||
\(671\) | −12.1961 | −0.470825 | ||||||||
\(672\) | −1.33267 | −0.0514090 | ||||||||
\(673\) | 42.6829 | 1.64531 | 0.822653 | − | 0.568544i | \(-0.192493\pi\) | ||||
0.822653 | + | 0.568544i | \(0.192493\pi\) | |||||||
\(674\) | 25.7171 | 0.990586 | ||||||||
\(675\) | 7.03798 | 0.270892 | ||||||||
\(676\) | 9.01422 | 0.346701 | ||||||||
\(677\) | 23.8986 | 0.918500 | 0.459250 | − | 0.888307i | \(-0.348118\pi\) | ||||
0.459250 | + | 0.888307i | \(0.348118\pi\) | |||||||
\(678\) | −0.0467370 | −0.00179492 | ||||||||
\(679\) | −58.6753 | −2.25175 | ||||||||
\(680\) | −3.00043 | −0.115061 | ||||||||
\(681\) | −5.52560 | −0.211741 | ||||||||
\(682\) | 5.82010 | 0.222863 | ||||||||
\(683\) | −14.9459 | −0.571887 | −0.285944 | − | 0.958246i | \(-0.592307\pi\) | ||||
−0.285944 | + | 0.958246i | \(0.592307\pi\) | |||||||
\(684\) | −11.6015 | −0.443593 | ||||||||
\(685\) | −15.3913 | −0.588072 | ||||||||
\(686\) | −45.4723 | −1.73614 | ||||||||
\(687\) | −1.50951 | −0.0575915 | ||||||||
\(688\) | −10.3214 | −0.393498 | ||||||||
\(689\) | −42.0006 | −1.60009 | ||||||||
\(690\) | 0.889594 | 0.0338663 | ||||||||
\(691\) | 21.4833 | 0.817263 | 0.408632 | − | 0.912699i | \(-0.366006\pi\) | ||||
0.408632 | + | 0.912699i | \(0.366006\pi\) | |||||||
\(692\) | 8.49931 | 0.323095 | ||||||||
\(693\) | −14.1450 | −0.537323 | ||||||||
\(694\) | −26.8693 | −1.01994 | ||||||||
\(695\) | −6.21866 | −0.235887 | ||||||||
\(696\) | −1.96343 | −0.0744235 | ||||||||
\(697\) | 7.54684 | 0.285857 | ||||||||
\(698\) | 19.8151 | 0.750012 | ||||||||
\(699\) | 1.91868 | 0.0725711 | ||||||||
\(700\) | −20.8604 | −0.788448 | ||||||||
\(701\) | 35.2764 | 1.33237 | 0.666186 | − | 0.745785i | \(-0.267926\pi\) | ||||
0.666186 | + | 0.745785i | \(0.267926\pi\) | |||||||
\(702\) | −7.65751 | −0.289014 | ||||||||
\(703\) | −28.8217 | −1.08703 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −1.29593 | −0.0488076 | ||||||||
\(706\) | 23.1388 | 0.870842 | ||||||||
\(707\) | −49.2491 | −1.85220 | ||||||||
\(708\) | −2.68206 | −0.100798 | ||||||||
\(709\) | 24.3875 | 0.915893 | 0.457947 | − | 0.888980i | \(-0.348585\pi\) | ||||
0.457947 | + | 0.888980i | \(0.348585\pi\) | |||||||
\(710\) | −6.50682 | −0.244197 | ||||||||
\(711\) | 18.0676 | 0.677587 | ||||||||
\(712\) | 5.85899 | 0.219575 | ||||||||
\(713\) | −22.6631 | −0.848740 | ||||||||
\(714\) | 4.82189 | 0.180455 | ||||||||
\(715\) | 3.89082 | 0.145508 | ||||||||
\(716\) | 9.56658 | 0.357520 | ||||||||
\(717\) | −1.26867 | −0.0473793 | ||||||||
\(718\) | 35.3470 | 1.31914 | ||||||||
\(719\) | 6.56128 | 0.244695 | 0.122347 | − | 0.992487i | \(-0.460958\pi\) | ||||
0.122347 | + | 0.992487i | \(0.460958\pi\) | |||||||
\(720\) | 2.42483 | 0.0903682 | ||||||||
\(721\) | −44.1588 | −1.64456 | ||||||||
\(722\) | 3.25873 | 0.121277 | ||||||||
\(723\) | 1.97455 | 0.0734344 | ||||||||
\(724\) | −3.88330 | −0.144322 | ||||||||
\(725\) | −30.7336 | −1.14142 | ||||||||
\(726\) | −0.275495 | −0.0102246 | ||||||||
\(727\) | 24.5434 | 0.910264 | 0.455132 | − | 0.890424i | \(-0.349592\pi\) | ||||
0.455132 | + | 0.890424i | \(0.349592\pi\) | |||||||
\(728\) | 22.6966 | 0.841193 | ||||||||
\(729\) | −22.9875 | −0.851389 | ||||||||
\(730\) | −0.121226 | −0.00448678 | ||||||||
\(731\) | 37.3449 | 1.38125 | ||||||||
\(732\) | −3.35996 | −0.124188 | ||||||||
\(733\) | −3.91980 | −0.144781 | −0.0723906 | − | 0.997376i | \(-0.523063\pi\) | ||||
−0.0723906 | + | 0.997376i | \(0.523063\pi\) | |||||||
\(734\) | 1.43254 | 0.0528760 | ||||||||
\(735\) | −3.74673 | −0.138200 | ||||||||
\(736\) | −3.89394 | −0.143532 | ||||||||
\(737\) | 12.1658 | 0.448131 | ||||||||
\(738\) | −6.09906 | −0.224510 | ||||||||
\(739\) | 25.0985 | 0.923263 | 0.461632 | − | 0.887072i | \(-0.347264\pi\) | ||||
0.461632 | + | 0.887072i | \(0.347264\pi\) | |||||||
\(740\) | 6.02406 | 0.221449 | ||||||||
\(741\) | −5.12844 | −0.188398 | ||||||||
\(742\) | −43.3026 | −1.58969 | ||||||||
\(743\) | 23.4706 | 0.861051 | 0.430526 | − | 0.902578i | \(-0.358328\pi\) | ||||
0.430526 | + | 0.902578i | \(0.358328\pi\) | |||||||
\(744\) | 1.60341 | 0.0587838 | ||||||||
\(745\) | −4.92835 | −0.180561 | ||||||||
\(746\) | −21.8486 | −0.799934 | ||||||||
\(747\) | 40.1250 | 1.46810 | ||||||||
\(748\) | −3.61821 | −0.132295 | ||||||||
\(749\) | 17.3880 | 0.635342 | ||||||||
\(750\) | −2.12746 | −0.0776839 | ||||||||
\(751\) | 10.1705 | 0.371127 | 0.185564 | − | 0.982632i | \(-0.440589\pi\) | ||||
0.185564 | + | 0.982632i | \(0.440589\pi\) | |||||||
\(752\) | 5.67256 | 0.206857 | ||||||||
\(753\) | 0.248319 | 0.00904925 | ||||||||
\(754\) | 33.4390 | 1.21778 | ||||||||
\(755\) | 19.6546 | 0.715305 | ||||||||
\(756\) | −7.89489 | −0.287134 | ||||||||
\(757\) | −37.6292 | −1.36766 | −0.683828 | − | 0.729643i | \(-0.739686\pi\) | ||||
−0.683828 | + | 0.729643i | \(0.739686\pi\) | |||||||
\(758\) | 17.0176 | 0.618106 | ||||||||
\(759\) | 1.07276 | 0.0389387 | ||||||||
\(760\) | 3.29010 | 0.119345 | ||||||||
\(761\) | 0.0484792 | 0.00175737 | 0.000878684 | − | 1.00000i | \(-0.499720\pi\) | ||||
0.000878684 | 1.00000i | \(0.499720\pi\) | ||||||||
\(762\) | −2.75319 | −0.0997376 | ||||||||
\(763\) | 10.8869 | 0.394133 | ||||||||
\(764\) | 7.50821 | 0.271637 | ||||||||
\(765\) | −8.77357 | −0.317209 | ||||||||
\(766\) | −22.3816 | −0.808680 | ||||||||
\(767\) | 45.6780 | 1.64934 | ||||||||
\(768\) | 0.275495 | 0.00994107 | ||||||||
\(769\) | 38.9130 | 1.40324 | 0.701620 | − | 0.712551i | \(-0.252460\pi\) | ||||
0.701620 | + | 0.712551i | \(0.252460\pi\) | |||||||
\(770\) | 4.01143 | 0.144562 | ||||||||
\(771\) | −7.41448 | −0.267026 | ||||||||
\(772\) | −3.61012 | −0.129931 | ||||||||
\(773\) | 50.5900 | 1.81960 | 0.909798 | − | 0.415051i | \(-0.136236\pi\) | ||||
0.909798 | + | 0.415051i | \(0.136236\pi\) | |||||||
\(774\) | −30.1807 | −1.08482 | ||||||||
\(775\) | 25.0982 | 0.901554 | ||||||||
\(776\) | 12.1296 | 0.435426 | ||||||||
\(777\) | −9.68107 | −0.347307 | ||||||||
\(778\) | 17.5665 | 0.629788 | ||||||||
\(779\) | −8.27543 | −0.296498 | ||||||||
\(780\) | 1.07190 | 0.0383802 | ||||||||
\(781\) | −7.84656 | −0.280772 | ||||||||
\(782\) | 14.0891 | 0.503825 | ||||||||
\(783\) | −11.6315 | −0.415678 | ||||||||
\(784\) | 16.4002 | 0.585722 | ||||||||
\(785\) | 7.82392 | 0.279248 | ||||||||
\(786\) | −3.32887 | −0.118737 | ||||||||
\(787\) | −14.1567 | −0.504632 | −0.252316 | − | 0.967645i | \(-0.581192\pi\) | ||||
−0.252316 | + | 0.967645i | \(0.581192\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | −2.18189 | −0.0776773 | ||||||||
\(790\) | −5.12385 | −0.182299 | ||||||||
\(791\) | 0.820649 | 0.0291789 | ||||||||
\(792\) | 2.92410 | 0.103903 | ||||||||
\(793\) | 57.2233 | 2.03206 | ||||||||
\(794\) | 17.3428 | 0.615473 | ||||||||
\(795\) | −2.04506 | −0.0725309 | ||||||||
\(796\) | −3.39694 | −0.120401 | ||||||||
\(797\) | 14.8443 | 0.525811 | 0.262905 | − | 0.964822i | \(-0.415319\pi\) | ||||
0.262905 | + | 0.964822i | \(0.415319\pi\) | |||||||
\(798\) | −5.28741 | −0.187172 | ||||||||
\(799\) | −20.5245 | −0.726106 | ||||||||
\(800\) | 4.31233 | 0.152464 | ||||||||
\(801\) | 17.1323 | 0.605340 | ||||||||
\(802\) | −9.02318 | −0.318620 | ||||||||
\(803\) | −0.146186 | −0.00515880 | ||||||||
\(804\) | 3.35160 | 0.118202 | ||||||||
\(805\) | −15.6203 | −0.550542 | ||||||||
\(806\) | −27.3075 | −0.961866 | ||||||||
\(807\) | −3.66960 | −0.129176 | ||||||||
\(808\) | 10.1809 | 0.358164 | ||||||||
\(809\) | −2.79386 | −0.0982271 | −0.0491135 | − | 0.998793i | \(-0.515640\pi\) | ||||
−0.0491135 | + | 0.998793i | \(0.515640\pi\) | |||||||
\(810\) | 6.90165 | 0.242499 | ||||||||
\(811\) | −8.96871 | −0.314934 | −0.157467 | − | 0.987524i | \(-0.550333\pi\) | ||||
−0.157467 | + | 0.987524i | \(0.550333\pi\) | |||||||
\(812\) | 34.4755 | 1.20985 | ||||||||
\(813\) | 0.599777 | 0.0210351 | ||||||||
\(814\) | 7.26441 | 0.254617 | ||||||||
\(815\) | 8.14729 | 0.285387 | ||||||||
\(816\) | −0.996800 | −0.0348950 | ||||||||
\(817\) | −40.9503 | −1.43267 | ||||||||
\(818\) | −4.77298 | −0.166883 | ||||||||
\(819\) | 66.3673 | 2.31906 | ||||||||
\(820\) | 1.72966 | 0.0604022 | ||||||||
\(821\) | 28.1486 | 0.982392 | 0.491196 | − | 0.871049i | \(-0.336560\pi\) | ||||
0.491196 | + | 0.871049i | \(0.336560\pi\) | |||||||
\(822\) | −5.11329 | −0.178346 | ||||||||
\(823\) | −24.6879 | −0.860566 | −0.430283 | − | 0.902694i | \(-0.641586\pi\) | ||||
−0.430283 | + | 0.902694i | \(0.641586\pi\) | |||||||
\(824\) | 9.12868 | 0.318013 | ||||||||
\(825\) | −1.18803 | −0.0413617 | ||||||||
\(826\) | 47.0939 | 1.63861 | ||||||||
\(827\) | 44.8396 | 1.55923 | 0.779613 | − | 0.626261i | \(-0.215416\pi\) | ||||
0.779613 | + | 0.626261i | \(0.215416\pi\) | |||||||
\(828\) | −11.3863 | −0.395700 | ||||||||
\(829\) | −12.0773 | −0.419463 | −0.209732 | − | 0.977759i | \(-0.567259\pi\) | ||||
−0.209732 | + | 0.977759i | \(0.567259\pi\) | |||||||
\(830\) | −11.3792 | −0.394977 | ||||||||
\(831\) | 0.197467 | 0.00685004 | ||||||||
\(832\) | −4.69193 | −0.162663 | ||||||||
\(833\) | −59.3395 | −2.05599 | ||||||||
\(834\) | −2.06596 | −0.0715382 | ||||||||
\(835\) | 8.39312 | 0.290456 | ||||||||
\(836\) | 3.96753 | 0.137220 | ||||||||
\(837\) | 9.49875 | 0.328325 | ||||||||
\(838\) | 25.3146 | 0.874479 | ||||||||
\(839\) | −53.8304 | −1.85843 | −0.929216 | − | 0.369537i | \(-0.879516\pi\) | ||||
−0.929216 | + | 0.369537i | \(0.879516\pi\) | |||||||
\(840\) | 1.10513 | 0.0381306 | ||||||||
\(841\) | 21.7929 | 0.751478 | ||||||||
\(842\) | 29.7629 | 1.02570 | ||||||||
\(843\) | 1.27253 | 0.0438283 | ||||||||
\(844\) | −6.08249 | −0.209368 | ||||||||
\(845\) | −7.47511 | −0.257152 | ||||||||
\(846\) | 16.5871 | 0.570278 | ||||||||
\(847\) | 4.83738 | 0.166214 | ||||||||
\(848\) | 8.95166 | 0.307401 | ||||||||
\(849\) | −4.83813 | −0.166044 | ||||||||
\(850\) | −15.6029 | −0.535177 | ||||||||
\(851\) | −28.2871 | −0.969670 | ||||||||
\(852\) | −2.16169 | −0.0740582 | ||||||||
\(853\) | 23.6977 | 0.811393 | 0.405697 | − | 0.914008i | \(-0.367029\pi\) | ||||
0.405697 | + | 0.914008i | \(0.367029\pi\) | |||||||
\(854\) | 58.9971 | 2.01884 | ||||||||
\(855\) | 9.62059 | 0.329017 | ||||||||
\(856\) | −3.59450 | −0.122858 | ||||||||
\(857\) | −34.2047 | −1.16841 | −0.584204 | − | 0.811607i | \(-0.698593\pi\) | ||||
−0.584204 | + | 0.811607i | \(0.698593\pi\) | |||||||
\(858\) | 1.29260 | 0.0441287 | ||||||||
\(859\) | −10.7322 | −0.366180 | −0.183090 | − | 0.983096i | \(-0.558610\pi\) | ||||
−0.183090 | + | 0.983096i | \(0.558610\pi\) | |||||||
\(860\) | 8.55906 | 0.291862 | ||||||||
\(861\) | −2.77967 | −0.0947311 | ||||||||
\(862\) | 6.96059 | 0.237079 | ||||||||
\(863\) | 12.8060 | 0.435922 | 0.217961 | − | 0.975957i | \(-0.430059\pi\) | ||||
0.217961 | + | 0.975957i | \(0.430059\pi\) | |||||||
\(864\) | 1.63206 | 0.0555238 | ||||||||
\(865\) | −7.04812 | −0.239643 | ||||||||
\(866\) | −30.8500 | −1.04833 | ||||||||
\(867\) | −1.07678 | −0.0365693 | ||||||||
\(868\) | −28.1540 | −0.955610 | ||||||||
\(869\) | −6.17885 | −0.209603 | ||||||||
\(870\) | 1.62819 | 0.0552007 | ||||||||
\(871\) | −57.0809 | −1.93411 | ||||||||
\(872\) | −2.25058 | −0.0762144 | ||||||||
\(873\) | 35.4681 | 1.20041 | ||||||||
\(874\) | −15.4493 | −0.522580 | ||||||||
\(875\) | 37.3558 | 1.26286 | ||||||||
\(876\) | −0.0402736 | −0.00136072 | ||||||||
\(877\) | −40.5951 | −1.37080 | −0.685399 | − | 0.728168i | \(-0.740372\pi\) | ||||
−0.685399 | + | 0.728168i | \(0.740372\pi\) | |||||||
\(878\) | −22.4922 | −0.759075 | ||||||||
\(879\) | 4.03962 | 0.136253 | ||||||||
\(880\) | −0.829257 | −0.0279543 | ||||||||
\(881\) | −26.1642 | −0.881496 | −0.440748 | − | 0.897631i | \(-0.645287\pi\) | ||||
−0.440748 | + | 0.897631i | \(0.645287\pi\) | |||||||
\(882\) | 47.9559 | 1.61476 | ||||||||
\(883\) | 2.99051 | 0.100639 | 0.0503194 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503194 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(884\) | 16.9764 | 0.570979 | ||||||||
\(885\) | 2.22412 | 0.0747629 | ||||||||
\(886\) | 4.94585 | 0.166159 | ||||||||
\(887\) | −24.8922 | −0.835797 | −0.417899 | − | 0.908494i | \(-0.637233\pi\) | ||||
−0.417899 | + | 0.908494i | \(0.637233\pi\) | |||||||
\(888\) | 2.00131 | 0.0671595 | ||||||||
\(889\) | 48.3429 | 1.62137 | ||||||||
\(890\) | −4.85861 | −0.162861 | ||||||||
\(891\) | 8.32268 | 0.278820 | ||||||||
\(892\) | −6.28035 | −0.210282 | ||||||||
\(893\) | 22.5060 | 0.753136 | ||||||||
\(894\) | −1.63729 | −0.0547592 | ||||||||
\(895\) | −7.93316 | −0.265176 | ||||||||
\(896\) | −4.83738 | −0.161605 | ||||||||
\(897\) | −5.03331 | −0.168057 | ||||||||
\(898\) | −29.3948 | −0.980918 | ||||||||
\(899\) | −41.4793 | −1.38341 | ||||||||
\(900\) | 12.6097 | 0.420323 | ||||||||
\(901\) | −32.3890 | −1.07904 | ||||||||
\(902\) | 2.08579 | 0.0694492 | ||||||||
\(903\) | −13.7550 | −0.457737 | ||||||||
\(904\) | −0.169648 | −0.00564239 | ||||||||
\(905\) | 3.22026 | 0.107045 | ||||||||
\(906\) | 6.52964 | 0.216933 | ||||||||
\(907\) | −1.84829 | −0.0613714 | −0.0306857 | − | 0.999529i | \(-0.509769\pi\) | ||||
−0.0306857 | + | 0.999529i | \(0.509769\pi\) | |||||||
\(908\) | −20.0570 | −0.665615 | ||||||||
\(909\) | 29.7701 | 0.987413 | ||||||||
\(910\) | −18.8214 | −0.623922 | ||||||||
\(911\) | −2.63136 | −0.0871808 | −0.0435904 | − | 0.999049i | \(-0.513880\pi\) | ||||
−0.0435904 | + | 0.999049i | \(0.513880\pi\) | |||||||
\(912\) | 1.09303 | 0.0361940 | ||||||||
\(913\) | −13.7221 | −0.454137 | ||||||||
\(914\) | 31.6624 | 1.04730 | ||||||||
\(915\) | 2.78627 | 0.0921114 | ||||||||
\(916\) | −5.47928 | −0.181040 | ||||||||
\(917\) | 58.4511 | 1.93023 | ||||||||
\(918\) | −5.90514 | −0.194899 | ||||||||
\(919\) | −42.5543 | −1.40374 | −0.701868 | − | 0.712307i | \(-0.747650\pi\) | ||||
−0.701868 | + | 0.712307i | \(0.747650\pi\) | |||||||
\(920\) | 3.22908 | 0.106459 | ||||||||
\(921\) | 3.74432 | 0.123380 | ||||||||
\(922\) | −16.7107 | −0.550339 | ||||||||
\(923\) | 36.8155 | 1.21180 | ||||||||
\(924\) | 1.33267 | 0.0438417 | ||||||||
\(925\) | 31.3265 | 1.03001 | ||||||||
\(926\) | 26.5138 | 0.871298 | ||||||||
\(927\) | 26.6932 | 0.876719 | ||||||||
\(928\) | −7.12691 | −0.233952 | ||||||||
\(929\) | −19.6061 | −0.643255 | −0.321628 | − | 0.946866i | \(-0.604230\pi\) | ||||
−0.321628 | + | 0.946866i | \(0.604230\pi\) | |||||||
\(930\) | −1.32964 | −0.0436006 | ||||||||
\(931\) | 65.0682 | 2.13253 | ||||||||
\(932\) | 6.96448 | 0.228129 | ||||||||
\(933\) | −6.45277 | −0.211254 | ||||||||
\(934\) | 15.2806 | 0.499998 | ||||||||
\(935\) | 3.00043 | 0.0981246 | ||||||||
\(936\) | −13.7197 | −0.448442 | ||||||||
\(937\) | 27.8111 | 0.908550 | 0.454275 | − | 0.890861i | \(-0.349898\pi\) | ||||
0.454275 | + | 0.890861i | \(0.349898\pi\) | |||||||
\(938\) | −58.8503 | −1.92153 | ||||||||
\(939\) | −4.48732 | −0.146438 | ||||||||
\(940\) | −4.70401 | −0.153428 | ||||||||
\(941\) | −22.8584 | −0.745161 | −0.372581 | − | 0.928000i | \(-0.621527\pi\) | ||||
−0.372581 | + | 0.928000i | \(0.621527\pi\) | |||||||
\(942\) | 2.59925 | 0.0846882 | ||||||||
\(943\) | −8.12193 | −0.264487 | ||||||||
\(944\) | −9.73543 | −0.316861 | ||||||||
\(945\) | 6.54689 | 0.212970 | ||||||||
\(946\) | 10.3214 | 0.335576 | ||||||||
\(947\) | −5.64337 | −0.183385 | −0.0916925 | − | 0.995787i | \(-0.529228\pi\) | ||||
−0.0916925 | + | 0.995787i | \(0.529228\pi\) | |||||||
\(948\) | −1.70224 | −0.0552862 | ||||||||
\(949\) | 0.685896 | 0.0222651 | ||||||||
\(950\) | 17.1093 | 0.555099 | ||||||||
\(951\) | 6.43428 | 0.208646 | ||||||||
\(952\) | 17.5027 | 0.567265 | ||||||||
\(953\) | −3.87642 | −0.125570 | −0.0627848 | − | 0.998027i | \(-0.519998\pi\) | ||||
−0.0627848 | + | 0.998027i | \(0.519998\pi\) | |||||||
\(954\) | 26.1756 | 0.847466 | ||||||||
\(955\) | −6.22624 | −0.201476 | ||||||||
\(956\) | −4.60506 | −0.148938 | ||||||||
\(957\) | 1.96343 | 0.0634686 | ||||||||
\(958\) | −37.3582 | −1.20699 | ||||||||
\(959\) | 89.7835 | 2.89926 | ||||||||
\(960\) | −0.228456 | −0.00737339 | ||||||||
\(961\) | 2.87358 | 0.0926961 | ||||||||
\(962\) | −34.0841 | −1.09892 | ||||||||
\(963\) | −10.5107 | −0.338702 | ||||||||
\(964\) | 7.16729 | 0.230843 | ||||||||
\(965\) | 2.99372 | 0.0963711 | ||||||||
\(966\) | −5.18934 | −0.166964 | ||||||||
\(967\) | 42.7324 | 1.37418 | 0.687091 | − | 0.726572i | \(-0.258888\pi\) | ||||
0.687091 | + | 0.726572i | \(0.258888\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −3.95483 | −0.127047 | ||||||||
\(970\) | −10.0585 | −0.322960 | ||||||||
\(971\) | −23.2887 | −0.747371 | −0.373685 | − | 0.927556i | \(-0.621906\pi\) | ||||
−0.373685 | + | 0.927556i | \(0.621906\pi\) | |||||||
\(972\) | 7.18904 | 0.230588 | ||||||||
\(973\) | 36.2758 | 1.16295 | ||||||||
\(974\) | 18.2127 | 0.583572 | ||||||||
\(975\) | 5.57413 | 0.178515 | ||||||||
\(976\) | −12.1961 | −0.390388 | ||||||||
\(977\) | −22.7720 | −0.728541 | −0.364270 | − | 0.931293i | \(-0.618682\pi\) | ||||
−0.364270 | + | 0.931293i | \(0.618682\pi\) | |||||||
\(978\) | 2.70668 | 0.0865501 | ||||||||
\(979\) | −5.85899 | −0.187254 | ||||||||
\(980\) | −13.6000 | −0.434436 | ||||||||
\(981\) | −6.58094 | −0.210113 | ||||||||
\(982\) | 40.6739 | 1.29796 | ||||||||
\(983\) | 51.6985 | 1.64892 | 0.824462 | − | 0.565917i | \(-0.191478\pi\) | ||||
0.824462 | + | 0.565917i | \(0.191478\pi\) | |||||||
\(984\) | 0.574625 | 0.0183184 | ||||||||
\(985\) | −0.829257 | −0.0264223 | ||||||||
\(986\) | 25.7867 | 0.821216 | ||||||||
\(987\) | 7.55966 | 0.240627 | ||||||||
\(988\) | −18.6154 | −0.592234 | ||||||||
\(989\) | −40.1907 | −1.27799 | ||||||||
\(990\) | −2.42483 | −0.0770663 | ||||||||
\(991\) | −28.4828 | −0.904787 | −0.452393 | − | 0.891819i | \(-0.649430\pi\) | ||||
−0.452393 | + | 0.891819i | \(0.649430\pi\) | |||||||
\(992\) | 5.82010 | 0.184788 | ||||||||
\(993\) | 9.43515 | 0.299415 | ||||||||
\(994\) | 37.9568 | 1.20392 | ||||||||
\(995\) | 2.81694 | 0.0893029 | ||||||||
\(996\) | −3.78038 | −0.119786 | ||||||||
\(997\) | 48.3041 | 1.52980 | 0.764902 | − | 0.644146i | \(-0.222787\pi\) | ||||
0.764902 | + | 0.644146i | \(0.222787\pi\) | |||||||
\(998\) | −11.0473 | −0.349696 | ||||||||
\(999\) | 11.8559 | 0.375106 |
(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 | 4334.2.a.a.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial |