Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-2.67178\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67178 | 1.88923 | 0.944617 | − | 0.328174i | \(-0.106433\pi\) | ||||
0.944617 | + | 0.328174i | \(0.106433\pi\) | |||||||
\(3\) | −2.26915 | −1.31009 | −0.655047 | − | 0.755588i | \(-0.727351\pi\) | ||||
−0.655047 | + | 0.755588i | \(0.727351\pi\) | |||||||
\(4\) | 5.13841 | 2.56921 | ||||||||
\(5\) | −3.81472 | −1.70599 | −0.852997 | − | 0.521917i | \(-0.825217\pi\) | ||||
−0.852997 | + | 0.521917i | \(0.825217\pi\) | |||||||
\(6\) | −6.06267 | −2.47507 | ||||||||
\(7\) | 0.767070 | 0.289925 | 0.144963 | − | 0.989437i | \(-0.453694\pi\) | ||||
0.144963 | + | 0.989437i | \(0.453694\pi\) | |||||||
\(8\) | 8.38515 | 2.96460 | ||||||||
\(9\) | 2.14904 | 0.716347 | ||||||||
\(10\) | −10.1921 | −3.22302 | ||||||||
\(11\) | −3.50387 | −1.05646 | −0.528228 | − | 0.849102i | \(-0.677143\pi\) | ||||
−0.528228 | + | 0.849102i | \(0.677143\pi\) | |||||||
\(12\) | −11.6598 | −3.36590 | ||||||||
\(13\) | −3.99988 | −1.10937 | −0.554683 | − | 0.832062i | \(-0.687160\pi\) | ||||
−0.554683 | + | 0.832062i | \(0.687160\pi\) | |||||||
\(14\) | 2.04944 | 0.547737 | ||||||||
\(15\) | 8.65616 | 2.23501 | ||||||||
\(16\) | 12.1265 | 3.03161 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.74176 | 1.35335 | ||||||||
\(19\) | −7.48497 | −1.71717 | −0.858585 | − | 0.512672i | \(-0.828656\pi\) | ||||
−0.858585 | + | 0.512672i | \(0.828656\pi\) | |||||||
\(20\) | −19.6016 | −4.38305 | ||||||||
\(21\) | −1.74060 | −0.379829 | ||||||||
\(22\) | −9.36157 | −1.99589 | ||||||||
\(23\) | −3.35147 | −0.698829 | −0.349415 | − | 0.936968i | \(-0.613620\pi\) | ||||
−0.349415 | + | 0.936968i | \(0.613620\pi\) | |||||||
\(24\) | −19.0272 | −3.88390 | ||||||||
\(25\) | 9.55206 | 1.91041 | ||||||||
\(26\) | −10.6868 | −2.09585 | ||||||||
\(27\) | 1.93096 | 0.371613 | ||||||||
\(28\) | 3.94152 | 0.744878 | ||||||||
\(29\) | −7.76321 | −1.44159 | −0.720796 | − | 0.693147i | \(-0.756224\pi\) | ||||
−0.720796 | + | 0.693147i | \(0.756224\pi\) | |||||||
\(30\) | 23.1274 | 4.22246 | ||||||||
\(31\) | 3.78202 | 0.679270 | 0.339635 | − | 0.940557i | \(-0.389696\pi\) | ||||
0.339635 | + | 0.940557i | \(0.389696\pi\) | |||||||
\(32\) | 15.6289 | 2.76283 | ||||||||
\(33\) | 7.95080 | 1.38406 | ||||||||
\(34\) | 2.67178 | 0.458207 | ||||||||
\(35\) | −2.92616 | −0.494611 | ||||||||
\(36\) | 11.0427 | 1.84044 | ||||||||
\(37\) | −0.775849 | −0.127549 | −0.0637744 | − | 0.997964i | \(-0.520314\pi\) | ||||
−0.0637744 | + | 0.997964i | \(0.520314\pi\) | |||||||
\(38\) | −19.9982 | −3.24414 | ||||||||
\(39\) | 9.07632 | 1.45337 | ||||||||
\(40\) | −31.9870 | −5.05758 | ||||||||
\(41\) | −0.124996 | −0.0195211 | −0.00976056 | − | 0.999952i | \(-0.503107\pi\) | ||||
−0.00976056 | + | 0.999952i | \(0.503107\pi\) | |||||||
\(42\) | −4.65049 | −0.717587 | ||||||||
\(43\) | 9.78511 | 1.49222 | 0.746108 | − | 0.665825i | \(-0.231920\pi\) | ||||
0.746108 | + | 0.665825i | \(0.231920\pi\) | |||||||
\(44\) | −18.0043 | −2.71425 | ||||||||
\(45\) | −8.19798 | −1.22208 | ||||||||
\(46\) | −8.95439 | −1.32025 | ||||||||
\(47\) | −10.9899 | −1.60304 | −0.801519 | − | 0.597969i | \(-0.795975\pi\) | ||||
−0.801519 | + | 0.597969i | \(0.795975\pi\) | |||||||
\(48\) | −27.5167 | −3.97170 | ||||||||
\(49\) | −6.41160 | −0.915943 | ||||||||
\(50\) | 25.5210 | 3.60922 | ||||||||
\(51\) | −2.26915 | −0.317744 | ||||||||
\(52\) | −20.5530 | −2.85019 | ||||||||
\(53\) | −1.16150 | −0.159544 | −0.0797721 | − | 0.996813i | \(-0.525419\pi\) | ||||
−0.0797721 | + | 0.996813i | \(0.525419\pi\) | |||||||
\(54\) | 5.15909 | 0.702064 | ||||||||
\(55\) | 13.3663 | 1.80231 | ||||||||
\(56\) | 6.43200 | 0.859512 | ||||||||
\(57\) | 16.9845 | 2.24965 | ||||||||
\(58\) | −20.7416 | −2.72350 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 44.4789 | 5.74221 | ||||||||
\(61\) | 3.16854 | 0.405690 | 0.202845 | − | 0.979211i | \(-0.434981\pi\) | ||||
0.202845 | + | 0.979211i | \(0.434981\pi\) | |||||||
\(62\) | 10.1047 | 1.28330 | ||||||||
\(63\) | 1.64846 | 0.207687 | ||||||||
\(64\) | 17.5042 | 2.18802 | ||||||||
\(65\) | 15.2584 | 1.89257 | ||||||||
\(66\) | 21.2428 | 2.61481 | ||||||||
\(67\) | 5.57191 | 0.680717 | 0.340359 | − | 0.940296i | \(-0.389452\pi\) | ||||
0.340359 | + | 0.940296i | \(0.389452\pi\) | |||||||
\(68\) | 5.13841 | 0.623124 | ||||||||
\(69\) | 7.60498 | 0.915532 | ||||||||
\(70\) | −7.81805 | −0.934435 | ||||||||
\(71\) | 3.02937 | 0.359520 | 0.179760 | − | 0.983710i | \(-0.442468\pi\) | ||||
0.179760 | + | 0.983710i | \(0.442468\pi\) | |||||||
\(72\) | 18.0200 | 2.12368 | ||||||||
\(73\) | 3.42854 | 0.401280 | 0.200640 | − | 0.979665i | \(-0.435698\pi\) | ||||
0.200640 | + | 0.979665i | \(0.435698\pi\) | |||||||
\(74\) | −2.07290 | −0.240969 | ||||||||
\(75\) | −21.6751 | −2.50282 | ||||||||
\(76\) | −38.4609 | −4.41176 | ||||||||
\(77\) | −2.68771 | −0.306293 | ||||||||
\(78\) | 24.2499 | 2.74576 | ||||||||
\(79\) | 3.29209 | 0.370389 | 0.185195 | − | 0.982702i | \(-0.440708\pi\) | ||||
0.185195 | + | 0.982702i | \(0.440708\pi\) | |||||||
\(80\) | −46.2590 | −5.17191 | ||||||||
\(81\) | −10.8287 | −1.20319 | ||||||||
\(82\) | −0.333962 | −0.0368800 | ||||||||
\(83\) | −16.2473 | −1.78337 | −0.891684 | − | 0.452658i | \(-0.850476\pi\) | ||||
−0.891684 | + | 0.452658i | \(0.850476\pi\) | |||||||
\(84\) | −8.94391 | −0.975860 | ||||||||
\(85\) | −3.81472 | −0.413764 | ||||||||
\(86\) | 26.1437 | 2.81914 | ||||||||
\(87\) | 17.6159 | 1.88862 | ||||||||
\(88\) | −29.3805 | −3.13197 | ||||||||
\(89\) | 12.4772 | 1.32258 | 0.661289 | − | 0.750132i | \(-0.270010\pi\) | ||||
0.661289 | + | 0.750132i | \(0.270010\pi\) | |||||||
\(90\) | −21.9032 | −2.30880 | ||||||||
\(91\) | −3.06819 | −0.321633 | ||||||||
\(92\) | −17.2212 | −1.79544 | ||||||||
\(93\) | −8.58196 | −0.889908 | ||||||||
\(94\) | −29.3626 | −3.02852 | ||||||||
\(95\) | 28.5530 | 2.92948 | ||||||||
\(96\) | −35.4644 | −3.61957 | ||||||||
\(97\) | 11.3482 | 1.15223 | 0.576117 | − | 0.817367i | \(-0.304567\pi\) | ||||
0.576117 | + | 0.817367i | \(0.304567\pi\) | |||||||
\(98\) | −17.1304 | −1.73043 | ||||||||
\(99\) | −7.52995 | −0.756789 | ||||||||
\(100\) | 49.0824 | 4.90824 | ||||||||
\(101\) | 10.2160 | 1.01653 | 0.508264 | − | 0.861201i | \(-0.330287\pi\) | ||||
0.508264 | + | 0.861201i | \(0.330287\pi\) | |||||||
\(102\) | −6.06267 | −0.600294 | ||||||||
\(103\) | −4.33526 | −0.427166 | −0.213583 | − | 0.976925i | \(-0.568513\pi\) | ||||
−0.213583 | + | 0.976925i | \(0.568513\pi\) | |||||||
\(104\) | −33.5396 | −3.28882 | ||||||||
\(105\) | 6.63988 | 0.647986 | ||||||||
\(106\) | −3.10327 | −0.301416 | ||||||||
\(107\) | 15.7399 | 1.52163 | 0.760815 | − | 0.648969i | \(-0.224799\pi\) | ||||
0.760815 | + | 0.648969i | \(0.224799\pi\) | |||||||
\(108\) | 9.92205 | 0.954750 | ||||||||
\(109\) | −18.8167 | −1.80231 | −0.901157 | − | 0.433492i | \(-0.857281\pi\) | ||||
−0.901157 | + | 0.433492i | \(0.857281\pi\) | |||||||
\(110\) | 35.7117 | 3.40498 | ||||||||
\(111\) | 1.76052 | 0.167101 | ||||||||
\(112\) | 9.30184 | 0.878942 | ||||||||
\(113\) | 3.80652 | 0.358088 | 0.179044 | − | 0.983841i | \(-0.442700\pi\) | ||||
0.179044 | + | 0.983841i | \(0.442700\pi\) | |||||||
\(114\) | 45.3789 | 4.25012 | ||||||||
\(115\) | 12.7849 | 1.19220 | ||||||||
\(116\) | −39.8906 | −3.70375 | ||||||||
\(117\) | −8.59589 | −0.794691 | ||||||||
\(118\) | 2.67178 | 0.245957 | ||||||||
\(119\) | 0.767070 | 0.0703172 | ||||||||
\(120\) | 72.5832 | 6.62591 | ||||||||
\(121\) | 1.27710 | 0.116100 | ||||||||
\(122\) | 8.46564 | 0.766443 | ||||||||
\(123\) | 0.283635 | 0.0255745 | ||||||||
\(124\) | 19.4336 | 1.74519 | ||||||||
\(125\) | −17.3648 | −1.55316 | ||||||||
\(126\) | 4.40434 | 0.392369 | ||||||||
\(127\) | 1.05083 | 0.0932461 | 0.0466231 | − | 0.998913i | \(-0.485154\pi\) | ||||
0.0466231 | + | 0.998913i | \(0.485154\pi\) | |||||||
\(128\) | 15.5094 | 1.37085 | ||||||||
\(129\) | −22.2039 | −1.95494 | ||||||||
\(130\) | 40.7671 | 3.57551 | ||||||||
\(131\) | 1.64347 | 0.143590 | 0.0717951 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717951 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(132\) | 40.8545 | 3.55593 | ||||||||
\(133\) | −5.74150 | −0.497851 | ||||||||
\(134\) | 14.8869 | 1.28603 | ||||||||
\(135\) | −7.36605 | −0.633969 | ||||||||
\(136\) | 8.38515 | 0.719021 | ||||||||
\(137\) | −6.24128 | −0.533228 | −0.266614 | − | 0.963803i | \(-0.585905\pi\) | ||||
−0.266614 | + | 0.963803i | \(0.585905\pi\) | |||||||
\(138\) | 20.3188 | 1.72966 | ||||||||
\(139\) | 16.1620 | 1.37084 | 0.685420 | − | 0.728148i | \(-0.259619\pi\) | ||||
0.685420 | + | 0.728148i | \(0.259619\pi\) | |||||||
\(140\) | −15.0358 | −1.27076 | ||||||||
\(141\) | 24.9377 | 2.10013 | ||||||||
\(142\) | 8.09382 | 0.679218 | ||||||||
\(143\) | 14.0150 | 1.17200 | ||||||||
\(144\) | 26.0602 | 2.17169 | ||||||||
\(145\) | 29.6144 | 2.45935 | ||||||||
\(146\) | 9.16031 | 0.758113 | ||||||||
\(147\) | 14.5489 | 1.19997 | ||||||||
\(148\) | −3.98663 | −0.327699 | ||||||||
\(149\) | −2.77682 | −0.227486 | −0.113743 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113743 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(150\) | −57.9110 | −4.72841 | ||||||||
\(151\) | −19.1274 | −1.55656 | −0.778281 | − | 0.627916i | \(-0.783908\pi\) | ||||
−0.778281 | + | 0.627916i | \(0.783908\pi\) | |||||||
\(152\) | −62.7626 | −5.09072 | ||||||||
\(153\) | 2.14904 | 0.173740 | ||||||||
\(154\) | −7.18098 | −0.578660 | ||||||||
\(155\) | −14.4273 | −1.15883 | ||||||||
\(156\) | 46.6379 | 3.73402 | ||||||||
\(157\) | 15.5064 | 1.23755 | 0.618773 | − | 0.785570i | \(-0.287630\pi\) | ||||
0.618773 | + | 0.785570i | \(0.287630\pi\) | |||||||
\(158\) | 8.79574 | 0.699752 | ||||||||
\(159\) | 2.63562 | 0.209018 | ||||||||
\(160\) | −59.6200 | −4.71337 | ||||||||
\(161\) | −2.57081 | −0.202608 | ||||||||
\(162\) | −28.9320 | −2.27312 | ||||||||
\(163\) | −18.6605 | −1.46160 | −0.730802 | − | 0.682589i | \(-0.760854\pi\) | ||||
−0.730802 | + | 0.682589i | \(0.760854\pi\) | |||||||
\(164\) | −0.642282 | −0.0501538 | ||||||||
\(165\) | −30.3301 | −2.36119 | ||||||||
\(166\) | −43.4091 | −3.36920 | ||||||||
\(167\) | −4.43275 | −0.343016 | −0.171508 | − | 0.985183i | \(-0.554864\pi\) | ||||
−0.171508 | + | 0.985183i | \(0.554864\pi\) | |||||||
\(168\) | −14.5952 | −1.12604 | ||||||||
\(169\) | 2.99901 | 0.230693 | ||||||||
\(170\) | −10.1921 | −0.781697 | ||||||||
\(171\) | −16.0855 | −1.23009 | ||||||||
\(172\) | 50.2799 | 3.83381 | ||||||||
\(173\) | −12.3574 | −0.939516 | −0.469758 | − | 0.882795i | \(-0.655659\pi\) | ||||
−0.469758 | + | 0.882795i | \(0.655659\pi\) | |||||||
\(174\) | 47.0658 | 3.56805 | ||||||||
\(175\) | 7.32710 | 0.553877 | ||||||||
\(176\) | −42.4895 | −3.20277 | ||||||||
\(177\) | −2.26915 | −0.170560 | ||||||||
\(178\) | 33.3363 | 2.49866 | ||||||||
\(179\) | 13.8715 | 1.03681 | 0.518403 | − | 0.855136i | \(-0.326527\pi\) | ||||
0.518403 | + | 0.855136i | \(0.326527\pi\) | |||||||
\(180\) | −42.1246 | −3.13978 | ||||||||
\(181\) | −4.42893 | −0.329200 | −0.164600 | − | 0.986360i | \(-0.552633\pi\) | ||||
−0.164600 | + | 0.986360i | \(0.552633\pi\) | |||||||
\(182\) | −8.19752 | −0.607641 | ||||||||
\(183\) | −7.18989 | −0.531492 | ||||||||
\(184\) | −28.1026 | −2.07175 | ||||||||
\(185\) | 2.95964 | 0.217597 | ||||||||
\(186\) | −22.9291 | −1.68124 | ||||||||
\(187\) | −3.50387 | −0.256228 | ||||||||
\(188\) | −56.4705 | −4.11854 | ||||||||
\(189\) | 1.48118 | 0.107740 | ||||||||
\(190\) | 76.2874 | 5.53447 | ||||||||
\(191\) | −21.0811 | −1.52537 | −0.762687 | − | 0.646767i | \(-0.776121\pi\) | ||||
−0.762687 | + | 0.646767i | \(0.776121\pi\) | |||||||
\(192\) | −39.7196 | −2.86651 | ||||||||
\(193\) | −13.7189 | −0.987509 | −0.493755 | − | 0.869601i | \(-0.664376\pi\) | ||||
−0.493755 | + | 0.869601i | \(0.664376\pi\) | |||||||
\(194\) | 30.3199 | 2.17684 | ||||||||
\(195\) | −34.6236 | −2.47945 | ||||||||
\(196\) | −32.9455 | −2.35325 | ||||||||
\(197\) | −13.5079 | −0.962400 | −0.481200 | − | 0.876611i | \(-0.659799\pi\) | ||||
−0.481200 | + | 0.876611i | \(0.659799\pi\) | |||||||
\(198\) | −20.1184 | −1.42975 | ||||||||
\(199\) | 24.5871 | 1.74293 | 0.871465 | − | 0.490457i | \(-0.163170\pi\) | ||||
0.871465 | + | 0.490457i | \(0.163170\pi\) | |||||||
\(200\) | 80.0955 | 5.66360 | ||||||||
\(201\) | −12.6435 | −0.891803 | ||||||||
\(202\) | 27.2949 | 1.92046 | ||||||||
\(203\) | −5.95493 | −0.417954 | ||||||||
\(204\) | −11.6598 | −0.816351 | ||||||||
\(205\) | 0.476825 | 0.0333029 | ||||||||
\(206\) | −11.5829 | −0.807016 | ||||||||
\(207\) | −7.20244 | −0.500604 | ||||||||
\(208\) | −48.5043 | −3.36317 | ||||||||
\(209\) | 26.2263 | 1.81411 | ||||||||
\(210\) | 17.7403 | 1.22420 | ||||||||
\(211\) | −10.7605 | −0.740782 | −0.370391 | − | 0.928876i | \(-0.620776\pi\) | ||||
−0.370391 | + | 0.928876i | \(0.620776\pi\) | |||||||
\(212\) | −5.96826 | −0.409902 | ||||||||
\(213\) | −6.87410 | −0.471005 | ||||||||
\(214\) | 42.0535 | 2.87472 | ||||||||
\(215\) | −37.3274 | −2.54571 | ||||||||
\(216\) | 16.1914 | 1.10168 | ||||||||
\(217\) | 2.90107 | 0.196938 | ||||||||
\(218\) | −50.2741 | −3.40499 | ||||||||
\(219\) | −7.77987 | −0.525715 | ||||||||
\(220\) | 68.6814 | 4.63050 | ||||||||
\(221\) | −3.99988 | −0.269061 | ||||||||
\(222\) | 4.70371 | 0.315693 | ||||||||
\(223\) | 0.960530 | 0.0643219 | 0.0321609 | − | 0.999483i | \(-0.489761\pi\) | ||||
0.0321609 | + | 0.999483i | \(0.489761\pi\) | |||||||
\(224\) | 11.9885 | 0.801015 | ||||||||
\(225\) | 20.5278 | 1.36852 | ||||||||
\(226\) | 10.1702 | 0.676511 | ||||||||
\(227\) | −24.1708 | −1.60428 | −0.802138 | − | 0.597139i | \(-0.796304\pi\) | ||||
−0.802138 | + | 0.597139i | \(0.796304\pi\) | |||||||
\(228\) | 87.2734 | 5.77982 | ||||||||
\(229\) | −2.64948 | −0.175082 | −0.0875412 | − | 0.996161i | \(-0.527901\pi\) | ||||
−0.0875412 | + | 0.996161i | \(0.527901\pi\) | |||||||
\(230\) | 34.1585 | 2.25234 | ||||||||
\(231\) | 6.09882 | 0.401273 | ||||||||
\(232\) | −65.0957 | −4.27374 | ||||||||
\(233\) | −19.1172 | −1.25241 | −0.626206 | − | 0.779658i | \(-0.715393\pi\) | ||||
−0.626206 | + | 0.779658i | \(0.715393\pi\) | |||||||
\(234\) | −22.9663 | −1.50136 | ||||||||
\(235\) | 41.9233 | 2.73477 | ||||||||
\(236\) | 5.13841 | 0.334482 | ||||||||
\(237\) | −7.47025 | −0.485245 | ||||||||
\(238\) | 2.04944 | 0.132846 | ||||||||
\(239\) | −12.0938 | −0.782282 | −0.391141 | − | 0.920331i | \(-0.627920\pi\) | ||||
−0.391141 | + | 0.920331i | \(0.627920\pi\) | |||||||
\(240\) | 104.969 | 6.77569 | ||||||||
\(241\) | −18.5384 | −1.19416 | −0.597081 | − | 0.802181i | \(-0.703673\pi\) | ||||
−0.597081 | + | 0.802181i | \(0.703673\pi\) | |||||||
\(242\) | 3.41213 | 0.219340 | ||||||||
\(243\) | 18.7792 | 1.20468 | ||||||||
\(244\) | 16.2813 | 1.04230 | ||||||||
\(245\) | 24.4584 | 1.56259 | ||||||||
\(246\) | 0.757811 | 0.0483163 | ||||||||
\(247\) | 29.9389 | 1.90497 | ||||||||
\(248\) | 31.7128 | 2.01376 | ||||||||
\(249\) | 36.8675 | 2.33638 | ||||||||
\(250\) | −46.3950 | −2.93428 | ||||||||
\(251\) | 23.6940 | 1.49555 | 0.747776 | − | 0.663951i | \(-0.231122\pi\) | ||||
0.747776 | + | 0.663951i | \(0.231122\pi\) | |||||||
\(252\) | 8.47049 | 0.533591 | ||||||||
\(253\) | 11.7431 | 0.738283 | ||||||||
\(254\) | 2.80759 | 0.176164 | ||||||||
\(255\) | 8.65616 | 0.542070 | ||||||||
\(256\) | 6.42948 | 0.401843 | ||||||||
\(257\) | −30.2718 | −1.88830 | −0.944151 | − | 0.329514i | \(-0.893115\pi\) | ||||
−0.944151 | + | 0.329514i | \(0.893115\pi\) | |||||||
\(258\) | −59.3239 | −3.69334 | ||||||||
\(259\) | −0.595130 | −0.0369796 | ||||||||
\(260\) | 78.4039 | 4.86240 | ||||||||
\(261\) | −16.6834 | −1.03268 | ||||||||
\(262\) | 4.39098 | 0.271276 | ||||||||
\(263\) | 17.9576 | 1.10731 | 0.553655 | − | 0.832746i | \(-0.313233\pi\) | ||||
0.553655 | + | 0.832746i | \(0.313233\pi\) | |||||||
\(264\) | 66.6687 | 4.10317 | ||||||||
\(265\) | 4.43079 | 0.272181 | ||||||||
\(266\) | −15.3400 | −0.940557 | ||||||||
\(267\) | −28.3126 | −1.73270 | ||||||||
\(268\) | 28.6308 | 1.74890 | ||||||||
\(269\) | −16.7717 | −1.02259 | −0.511294 | − | 0.859406i | \(-0.670834\pi\) | ||||
−0.511294 | + | 0.859406i | \(0.670834\pi\) | |||||||
\(270\) | −19.6805 | −1.19772 | ||||||||
\(271\) | 4.86900 | 0.295771 | 0.147885 | − | 0.989005i | \(-0.452753\pi\) | ||||
0.147885 | + | 0.989005i | \(0.452753\pi\) | |||||||
\(272\) | 12.1265 | 0.735274 | ||||||||
\(273\) | 6.96217 | 0.421370 | ||||||||
\(274\) | −16.6753 | −1.00739 | ||||||||
\(275\) | −33.4692 | −2.01827 | ||||||||
\(276\) | 39.0775 | 2.35219 | ||||||||
\(277\) | −6.76053 | −0.406201 | −0.203100 | − | 0.979158i | \(-0.565102\pi\) | ||||
−0.203100 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(278\) | 43.1812 | 2.58984 | ||||||||
\(279\) | 8.12770 | 0.486593 | ||||||||
\(280\) | −24.5363 | −1.46632 | ||||||||
\(281\) | −15.6033 | −0.930814 | −0.465407 | − | 0.885097i | \(-0.654092\pi\) | ||||
−0.465407 | + | 0.885097i | \(0.654092\pi\) | |||||||
\(282\) | 66.6280 | 3.96764 | ||||||||
\(283\) | −12.2312 | −0.727070 | −0.363535 | − | 0.931581i | \(-0.618430\pi\) | ||||
−0.363535 | + | 0.931581i | \(0.618430\pi\) | |||||||
\(284\) | 15.5662 | 0.923682 | ||||||||
\(285\) | −64.7911 | −3.83789 | ||||||||
\(286\) | 37.4451 | 2.21418 | ||||||||
\(287\) | −0.0958809 | −0.00565967 | ||||||||
\(288\) | 33.5872 | 1.97914 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 79.1233 | 4.64628 | ||||||||
\(291\) | −25.7507 | −1.50953 | ||||||||
\(292\) | 17.6173 | 1.03097 | ||||||||
\(293\) | −15.8721 | −0.927257 | −0.463629 | − | 0.886030i | \(-0.653453\pi\) | ||||
−0.463629 | + | 0.886030i | \(0.653453\pi\) | |||||||
\(294\) | 38.8714 | 2.26703 | ||||||||
\(295\) | −3.81472 | −0.222101 | ||||||||
\(296\) | −6.50561 | −0.378131 | ||||||||
\(297\) | −6.76582 | −0.392593 | ||||||||
\(298\) | −7.41905 | −0.429774 | ||||||||
\(299\) | 13.4055 | 0.775258 | ||||||||
\(300\) | −111.375 | −6.43026 | ||||||||
\(301\) | 7.50587 | 0.432631 | ||||||||
\(302\) | −51.1041 | −2.94071 | ||||||||
\(303\) | −23.1816 | −1.33175 | ||||||||
\(304\) | −90.7661 | −5.20580 | ||||||||
\(305\) | −12.0871 | −0.692104 | ||||||||
\(306\) | 5.74176 | 0.328235 | ||||||||
\(307\) | −1.90522 | −0.108737 | −0.0543683 | − | 0.998521i | \(-0.517314\pi\) | ||||
−0.0543683 | + | 0.998521i | \(0.517314\pi\) | |||||||
\(308\) | −13.8106 | −0.786931 | ||||||||
\(309\) | 9.83735 | 0.559627 | ||||||||
\(310\) | −38.5466 | −2.18930 | ||||||||
\(311\) | 9.99366 | 0.566689 | 0.283344 | − | 0.959018i | \(-0.408556\pi\) | ||||
0.283344 | + | 0.959018i | \(0.408556\pi\) | |||||||
\(312\) | 76.1063 | 4.30867 | ||||||||
\(313\) | −25.7403 | −1.45493 | −0.727464 | − | 0.686145i | \(-0.759301\pi\) | ||||
−0.727464 | + | 0.686145i | \(0.759301\pi\) | |||||||
\(314\) | 41.4297 | 2.33801 | ||||||||
\(315\) | −6.28842 | −0.354313 | ||||||||
\(316\) | 16.9161 | 0.951606 | ||||||||
\(317\) | −0.205570 | −0.0115459 | −0.00577297 | − | 0.999983i | \(-0.501838\pi\) | ||||
−0.00577297 | + | 0.999983i | \(0.501838\pi\) | |||||||
\(318\) | 7.04179 | 0.394884 | ||||||||
\(319\) | 27.2013 | 1.52298 | ||||||||
\(320\) | −66.7735 | −3.73275 | ||||||||
\(321\) | −35.7161 | −1.99348 | ||||||||
\(322\) | −6.86865 | −0.382775 | ||||||||
\(323\) | −7.48497 | −0.416475 | ||||||||
\(324\) | −55.6426 | −3.09125 | ||||||||
\(325\) | −38.2071 | −2.11935 | ||||||||
\(326\) | −49.8568 | −2.76131 | ||||||||
\(327\) | 42.6979 | 2.36120 | ||||||||
\(328\) | −1.04811 | −0.0578723 | ||||||||
\(329\) | −8.43001 | −0.464762 | ||||||||
\(330\) | −81.0353 | −4.46084 | ||||||||
\(331\) | 15.8494 | 0.871160 | 0.435580 | − | 0.900150i | \(-0.356543\pi\) | ||||
0.435580 | + | 0.900150i | \(0.356543\pi\) | |||||||
\(332\) | −83.4851 | −4.58184 | ||||||||
\(333\) | −1.66733 | −0.0913691 | ||||||||
\(334\) | −11.8433 | −0.648038 | ||||||||
\(335\) | −21.2553 | −1.16130 | ||||||||
\(336\) | −21.1073 | −1.15150 | ||||||||
\(337\) | 28.8732 | 1.57282 | 0.786412 | − | 0.617703i | \(-0.211937\pi\) | ||||
0.786412 | + | 0.617703i | \(0.211937\pi\) | |||||||
\(338\) | 8.01270 | 0.435833 | ||||||||
\(339\) | −8.63757 | −0.469128 | ||||||||
\(340\) | −19.6016 | −1.06305 | ||||||||
\(341\) | −13.2517 | −0.717619 | ||||||||
\(342\) | −42.9769 | −2.32393 | ||||||||
\(343\) | −10.2876 | −0.555480 | ||||||||
\(344\) | 82.0496 | 4.42382 | ||||||||
\(345\) | −29.0109 | −1.56189 | ||||||||
\(346\) | −33.0163 | −1.77497 | ||||||||
\(347\) | 8.01828 | 0.430444 | 0.215222 | − | 0.976565i | \(-0.430953\pi\) | ||||
0.215222 | + | 0.976565i | \(0.430953\pi\) | |||||||
\(348\) | 90.5177 | 4.85226 | ||||||||
\(349\) | −27.8072 | −1.48848 | −0.744242 | − | 0.667910i | \(-0.767189\pi\) | ||||
−0.744242 | + | 0.667910i | \(0.767189\pi\) | |||||||
\(350\) | 19.5764 | 1.04640 | ||||||||
\(351\) | −7.72359 | −0.412255 | ||||||||
\(352\) | −54.7617 | −2.91881 | ||||||||
\(353\) | −12.4845 | −0.664480 | −0.332240 | − | 0.943195i | \(-0.607804\pi\) | ||||
−0.332240 | + | 0.943195i | \(0.607804\pi\) | |||||||
\(354\) | −6.06267 | −0.322227 | ||||||||
\(355\) | −11.5562 | −0.613339 | ||||||||
\(356\) | 64.1128 | 3.39797 | ||||||||
\(357\) | −1.74060 | −0.0921222 | ||||||||
\(358\) | 37.0617 | 1.95877 | ||||||||
\(359\) | 37.2241 | 1.96461 | 0.982307 | − | 0.187276i | \(-0.0599657\pi\) | ||||
0.982307 | + | 0.187276i | \(0.0599657\pi\) | |||||||
\(360\) | −68.7413 | −3.62298 | ||||||||
\(361\) | 37.0248 | 1.94867 | ||||||||
\(362\) | −11.8331 | −0.621935 | ||||||||
\(363\) | −2.89793 | −0.152102 | ||||||||
\(364\) | −15.7656 | −0.826342 | ||||||||
\(365\) | −13.0789 | −0.684581 | ||||||||
\(366\) | −19.2098 | −1.00411 | ||||||||
\(367\) | 21.1015 | 1.10149 | 0.550745 | − | 0.834674i | \(-0.314344\pi\) | ||||
0.550745 | + | 0.834674i | \(0.314344\pi\) | |||||||
\(368\) | −40.6414 | −2.11858 | ||||||||
\(369\) | −0.268622 | −0.0139839 | ||||||||
\(370\) | 7.90752 | 0.411092 | ||||||||
\(371\) | −0.890951 | −0.0462559 | ||||||||
\(372\) | −44.0977 | −2.28636 | ||||||||
\(373\) | 26.1408 | 1.35352 | 0.676758 | − | 0.736205i | \(-0.263384\pi\) | ||||
0.676758 | + | 0.736205i | \(0.263384\pi\) | |||||||
\(374\) | −9.36157 | −0.484075 | ||||||||
\(375\) | 39.4034 | 2.03478 | ||||||||
\(376\) | −92.1518 | −4.75237 | ||||||||
\(377\) | 31.0519 | 1.59925 | ||||||||
\(378\) | 3.95739 | 0.203546 | ||||||||
\(379\) | 18.2354 | 0.936687 | 0.468344 | − | 0.883546i | \(-0.344851\pi\) | ||||
0.468344 | + | 0.883546i | \(0.344851\pi\) | |||||||
\(380\) | 146.717 | 7.52644 | ||||||||
\(381\) | −2.38449 | −0.122161 | ||||||||
\(382\) | −56.3241 | −2.88179 | ||||||||
\(383\) | −8.90122 | −0.454831 | −0.227416 | − | 0.973798i | \(-0.573028\pi\) | ||||
−0.227416 | + | 0.973798i | \(0.573028\pi\) | |||||||
\(384\) | −35.1932 | −1.79595 | ||||||||
\(385\) | 10.2529 | 0.522534 | ||||||||
\(386\) | −36.6539 | −1.86564 | ||||||||
\(387\) | 21.0286 | 1.06894 | ||||||||
\(388\) | 58.3116 | 2.96033 | ||||||||
\(389\) | −16.7355 | −0.848524 | −0.424262 | − | 0.905539i | \(-0.639467\pi\) | ||||
−0.424262 | + | 0.905539i | \(0.639467\pi\) | |||||||
\(390\) | −92.5066 | −4.68425 | ||||||||
\(391\) | −3.35147 | −0.169491 | ||||||||
\(392\) | −53.7623 | −2.71540 | ||||||||
\(393\) | −3.72927 | −0.188117 | ||||||||
\(394\) | −36.0902 | −1.81820 | ||||||||
\(395\) | −12.5584 | −0.631881 | ||||||||
\(396\) | −38.6920 | −1.94435 | ||||||||
\(397\) | −0.222447 | −0.0111643 | −0.00558215 | − | 0.999984i | \(-0.501777\pi\) | ||||
−0.00558215 | + | 0.999984i | \(0.501777\pi\) | |||||||
\(398\) | 65.6912 | 3.29280 | ||||||||
\(399\) | 13.0283 | 0.652232 | ||||||||
\(400\) | 115.833 | 5.79163 | ||||||||
\(401\) | −31.4214 | −1.56911 | −0.784554 | − | 0.620060i | \(-0.787108\pi\) | ||||
−0.784554 | + | 0.620060i | \(0.787108\pi\) | |||||||
\(402\) | −33.7806 | −1.68483 | ||||||||
\(403\) | −15.1276 | −0.753559 | ||||||||
\(404\) | 52.4939 | 2.61167 | ||||||||
\(405\) | 41.3086 | 2.05264 | ||||||||
\(406\) | −15.9103 | −0.789613 | ||||||||
\(407\) | 2.71847 | 0.134750 | ||||||||
\(408\) | −19.0272 | −0.941985 | ||||||||
\(409\) | 34.2231 | 1.69222 | 0.846112 | − | 0.533005i | \(-0.178937\pi\) | ||||
0.846112 | + | 0.533005i | \(0.178937\pi\) | |||||||
\(410\) | 1.27397 | 0.0629170 | ||||||||
\(411\) | 14.1624 | 0.698579 | ||||||||
\(412\) | −22.2763 | −1.09748 | ||||||||
\(413\) | 0.767070 | 0.0377451 | ||||||||
\(414\) | −19.2433 | −0.945758 | ||||||||
\(415\) | 61.9787 | 3.04241 | ||||||||
\(416\) | −62.5138 | −3.06499 | ||||||||
\(417\) | −36.6739 | −1.79593 | ||||||||
\(418\) | 70.0711 | 3.42729 | ||||||||
\(419\) | 2.04697 | 0.100001 | 0.0500005 | − | 0.998749i | \(-0.484078\pi\) | ||||
0.0500005 | + | 0.998749i | \(0.484078\pi\) | |||||||
\(420\) | 34.1185 | 1.66481 | ||||||||
\(421\) | 6.70804 | 0.326930 | 0.163465 | − | 0.986549i | \(-0.447733\pi\) | ||||
0.163465 | + | 0.986549i | \(0.447733\pi\) | |||||||
\(422\) | −28.7496 | −1.39951 | ||||||||
\(423\) | −23.6177 | −1.14833 | ||||||||
\(424\) | −9.73934 | −0.472984 | ||||||||
\(425\) | 9.55206 | 0.463343 | ||||||||
\(426\) | −18.3661 | −0.889839 | ||||||||
\(427\) | 2.43049 | 0.117620 | ||||||||
\(428\) | 80.8779 | 3.90938 | ||||||||
\(429\) | −31.8022 | −1.53543 | ||||||||
\(430\) | −99.7307 | −4.80944 | ||||||||
\(431\) | 39.0860 | 1.88271 | 0.941354 | − | 0.337421i | \(-0.109554\pi\) | ||||
0.941354 | + | 0.337421i | \(0.109554\pi\) | |||||||
\(432\) | 23.4157 | 1.12659 | ||||||||
\(433\) | −24.8823 | −1.19577 | −0.597883 | − | 0.801583i | \(-0.703991\pi\) | ||||
−0.597883 | + | 0.801583i | \(0.703991\pi\) | |||||||
\(434\) | 7.75103 | 0.372061 | ||||||||
\(435\) | −67.1996 | −3.22197 | ||||||||
\(436\) | −96.6881 | −4.63052 | ||||||||
\(437\) | 25.0856 | 1.20001 | ||||||||
\(438\) | −20.7861 | −0.993199 | ||||||||
\(439\) | −25.1140 | −1.19863 | −0.599313 | − | 0.800515i | \(-0.704560\pi\) | ||||
−0.599313 | + | 0.800515i | \(0.704560\pi\) | |||||||
\(440\) | 112.078 | 5.34312 | ||||||||
\(441\) | −13.7788 | −0.656133 | ||||||||
\(442\) | −10.6868 | −0.508319 | ||||||||
\(443\) | 5.96511 | 0.283411 | 0.141706 | − | 0.989909i | \(-0.454741\pi\) | ||||
0.141706 | + | 0.989909i | \(0.454741\pi\) | |||||||
\(444\) | 9.04626 | 0.429317 | ||||||||
\(445\) | −47.5969 | −2.25631 | ||||||||
\(446\) | 2.56633 | 0.121519 | ||||||||
\(447\) | 6.30101 | 0.298028 | ||||||||
\(448\) | 13.4269 | 0.634363 | ||||||||
\(449\) | 3.99223 | 0.188405 | 0.0942026 | − | 0.995553i | \(-0.469970\pi\) | ||||
0.0942026 | + | 0.995553i | \(0.469970\pi\) | |||||||
\(450\) | 54.8457 | 2.58545 | ||||||||
\(451\) | 0.437970 | 0.0206232 | ||||||||
\(452\) | 19.5595 | 0.920001 | ||||||||
\(453\) | 43.4028 | 2.03924 | ||||||||
\(454\) | −64.5792 | −3.03085 | ||||||||
\(455\) | 11.7043 | 0.548704 | ||||||||
\(456\) | 142.418 | 6.66932 | ||||||||
\(457\) | 32.2678 | 1.50943 | 0.754713 | − | 0.656055i | \(-0.227776\pi\) | ||||
0.754713 | + | 0.656055i | \(0.227776\pi\) | |||||||
\(458\) | −7.07882 | −0.330772 | ||||||||
\(459\) | 1.93096 | 0.0901293 | ||||||||
\(460\) | 65.6941 | 3.06300 | ||||||||
\(461\) | −11.2929 | −0.525963 | −0.262982 | − | 0.964801i | \(-0.584706\pi\) | ||||
−0.262982 | + | 0.964801i | \(0.584706\pi\) | |||||||
\(462\) | 16.2947 | 0.758099 | ||||||||
\(463\) | 4.17184 | 0.193882 | 0.0969410 | − | 0.995290i | \(-0.469094\pi\) | ||||
0.0969410 | + | 0.995290i | \(0.469094\pi\) | |||||||
\(464\) | −94.1402 | −4.37035 | ||||||||
\(465\) | 32.7378 | 1.51818 | ||||||||
\(466\) | −51.0771 | −2.36610 | ||||||||
\(467\) | 8.77446 | 0.406034 | 0.203017 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203017 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(468\) | −44.1692 | −2.04172 | ||||||||
\(469\) | 4.27405 | 0.197357 | ||||||||
\(470\) | 112.010 | 5.16663 | ||||||||
\(471\) | −35.1863 | −1.62130 | ||||||||
\(472\) | 8.38515 | 0.385958 | ||||||||
\(473\) | −34.2857 | −1.57646 | ||||||||
\(474\) | −19.9589 | −0.916741 | ||||||||
\(475\) | −71.4969 | −3.28050 | ||||||||
\(476\) | 3.94152 | 0.180659 | ||||||||
\(477\) | −2.49611 | −0.114289 | ||||||||
\(478\) | −32.3120 | −1.47791 | ||||||||
\(479\) | 5.74847 | 0.262655 | 0.131327 | − | 0.991339i | \(-0.458076\pi\) | ||||
0.131327 | + | 0.991339i | \(0.458076\pi\) | |||||||
\(480\) | 135.287 | 6.17496 | ||||||||
\(481\) | 3.10330 | 0.141498 | ||||||||
\(482\) | −49.5305 | −2.25605 | ||||||||
\(483\) | 5.83356 | 0.265436 | ||||||||
\(484\) | 6.56226 | 0.298284 | ||||||||
\(485\) | −43.2901 | −1.96570 | ||||||||
\(486\) | 50.1738 | 2.27593 | ||||||||
\(487\) | −15.1688 | −0.687365 | −0.343682 | − | 0.939086i | \(-0.611674\pi\) | ||||
−0.343682 | + | 0.939086i | \(0.611674\pi\) | |||||||
\(488\) | 26.5687 | 1.20271 | ||||||||
\(489\) | 42.3435 | 1.91484 | ||||||||
\(490\) | 65.3476 | 2.95210 | ||||||||
\(491\) | 20.4825 | 0.924361 | 0.462180 | − | 0.886786i | \(-0.347067\pi\) | ||||
0.462180 | + | 0.886786i | \(0.347067\pi\) | |||||||
\(492\) | 1.45743 | 0.0657062 | ||||||||
\(493\) | −7.76321 | −0.349637 | ||||||||
\(494\) | 79.9903 | 3.59893 | ||||||||
\(495\) | 28.7246 | 1.29108 | ||||||||
\(496\) | 45.8625 | 2.05929 | ||||||||
\(497\) | 2.32374 | 0.104234 | ||||||||
\(498\) | 98.5018 | 4.41397 | ||||||||
\(499\) | −5.96562 | −0.267058 | −0.133529 | − | 0.991045i | \(-0.542631\pi\) | ||||
−0.133529 | + | 0.991045i | \(0.542631\pi\) | |||||||
\(500\) | −89.2276 | −3.99038 | ||||||||
\(501\) | 10.0586 | 0.449384 | ||||||||
\(502\) | 63.3052 | 2.82545 | ||||||||
\(503\) | 17.2200 | 0.767800 | 0.383900 | − | 0.923375i | \(-0.374581\pi\) | ||||
0.383900 | + | 0.923375i | \(0.374581\pi\) | |||||||
\(504\) | 13.8226 | 0.615708 | ||||||||
\(505\) | −38.9711 | −1.73419 | ||||||||
\(506\) | 31.3750 | 1.39479 | ||||||||
\(507\) | −6.80520 | −0.302230 | ||||||||
\(508\) | 5.39960 | 0.239569 | ||||||||
\(509\) | −2.35476 | −0.104373 | −0.0521864 | − | 0.998637i | \(-0.516619\pi\) | ||||
−0.0521864 | + | 0.998637i | \(0.516619\pi\) | |||||||
\(510\) | 23.1274 | 1.02410 | ||||||||
\(511\) | 2.62993 | 0.116341 | ||||||||
\(512\) | −13.8407 | −0.611679 | ||||||||
\(513\) | −14.4531 | −0.638122 | ||||||||
\(514\) | −80.8796 | −3.56744 | ||||||||
\(515\) | 16.5378 | 0.728741 | ||||||||
\(516\) | −114.093 | −5.02265 | ||||||||
\(517\) | 38.5071 | 1.69354 | ||||||||
\(518\) | −1.59006 | −0.0698631 | ||||||||
\(519\) | 28.0408 | 1.23085 | ||||||||
\(520\) | 127.944 | 5.61071 | ||||||||
\(521\) | −23.5218 | −1.03051 | −0.515255 | − | 0.857037i | \(-0.672303\pi\) | ||||
−0.515255 | + | 0.857037i | \(0.672303\pi\) | |||||||
\(522\) | −44.5745 | −1.95097 | ||||||||
\(523\) | −23.0810 | −1.00926 | −0.504630 | − | 0.863336i | \(-0.668371\pi\) | ||||
−0.504630 | + | 0.863336i | \(0.668371\pi\) | |||||||
\(524\) | 8.44480 | 0.368913 | ||||||||
\(525\) | −16.6263 | −0.725631 | ||||||||
\(526\) | 47.9786 | 2.09197 | ||||||||
\(527\) | 3.78202 | 0.164747 | ||||||||
\(528\) | 96.4151 | 4.19593 | ||||||||
\(529\) | −11.7677 | −0.511637 | ||||||||
\(530\) | 11.8381 | 0.514214 | ||||||||
\(531\) | 2.14904 | 0.0932604 | ||||||||
\(532\) | −29.5022 | −1.27908 | ||||||||
\(533\) | 0.499969 | 0.0216561 | ||||||||
\(534\) | −75.6449 | −3.27348 | ||||||||
\(535\) | −60.0431 | −2.59589 | ||||||||
\(536\) | 46.7213 | 2.01805 | ||||||||
\(537\) | −31.4766 | −1.35831 | ||||||||
\(538\) | −44.8103 | −1.93191 | ||||||||
\(539\) | 22.4654 | 0.967654 | ||||||||
\(540\) | −37.8498 | −1.62880 | ||||||||
\(541\) | 22.8307 | 0.981566 | 0.490783 | − | 0.871282i | \(-0.336711\pi\) | ||||
0.490783 | + | 0.871282i | \(0.336711\pi\) | |||||||
\(542\) | 13.0089 | 0.558780 | ||||||||
\(543\) | 10.0499 | 0.431283 | ||||||||
\(544\) | 15.6289 | 0.670085 | ||||||||
\(545\) | 71.7804 | 3.07474 | ||||||||
\(546\) | 18.6014 | 0.796066 | ||||||||
\(547\) | 22.2941 | 0.953229 | 0.476614 | − | 0.879112i | \(-0.341864\pi\) | ||||
0.476614 | + | 0.879112i | \(0.341864\pi\) | |||||||
\(548\) | −32.0703 | −1.36997 | ||||||||
\(549\) | 6.80931 | 0.290614 | ||||||||
\(550\) | −89.4223 | −3.81298 | ||||||||
\(551\) | 58.1074 | 2.47546 | ||||||||
\(552\) | 63.7689 | 2.71419 | ||||||||
\(553\) | 2.52526 | 0.107385 | ||||||||
\(554\) | −18.0627 | −0.767409 | ||||||||
\(555\) | −6.71587 | −0.285073 | ||||||||
\(556\) | 83.0468 | 3.52197 | ||||||||
\(557\) | 4.54047 | 0.192386 | 0.0961930 | − | 0.995363i | \(-0.469333\pi\) | ||||
0.0961930 | + | 0.995363i | \(0.469333\pi\) | |||||||
\(558\) | 21.7154 | 0.919288 | ||||||||
\(559\) | −39.1392 | −1.65541 | ||||||||
\(560\) | −35.4839 | −1.49947 | ||||||||
\(561\) | 7.95080 | 0.335683 | ||||||||
\(562\) | −41.6886 | −1.75853 | ||||||||
\(563\) | 46.8592 | 1.97488 | 0.987440 | − | 0.157995i | \(-0.0505031\pi\) | ||||
0.987440 | + | 0.157995i | \(0.0505031\pi\) | |||||||
\(564\) | 128.140 | 5.39567 | ||||||||
\(565\) | −14.5208 | −0.610895 | ||||||||
\(566\) | −32.6791 | −1.37360 | ||||||||
\(567\) | −8.30641 | −0.348836 | ||||||||
\(568\) | 25.4017 | 1.06583 | ||||||||
\(569\) | −1.78407 | −0.0747919 | −0.0373960 | − | 0.999301i | \(-0.511906\pi\) | ||||
−0.0373960 | + | 0.999301i | \(0.511906\pi\) | |||||||
\(570\) | −173.108 | −7.25068 | ||||||||
\(571\) | 10.6689 | 0.446481 | 0.223241 | − | 0.974763i | \(-0.428336\pi\) | ||||
0.223241 | + | 0.974763i | \(0.428336\pi\) | |||||||
\(572\) | 72.0151 | 3.01110 | ||||||||
\(573\) | 47.8362 | 1.99838 | ||||||||
\(574\) | −0.256173 | −0.0106924 | ||||||||
\(575\) | −32.0134 | −1.33505 | ||||||||
\(576\) | 37.6172 | 1.56738 | ||||||||
\(577\) | 16.0025 | 0.666192 | 0.333096 | − | 0.942893i | \(-0.391907\pi\) | ||||
0.333096 | + | 0.942893i | \(0.391907\pi\) | |||||||
\(578\) | 2.67178 | 0.111131 | ||||||||
\(579\) | 31.1303 | 1.29373 | ||||||||
\(580\) | 152.171 | 6.31857 | ||||||||
\(581\) | −12.4628 | −0.517044 | ||||||||
\(582\) | −68.8003 | −2.85186 | ||||||||
\(583\) | 4.06974 | 0.168551 | ||||||||
\(584\) | 28.7488 | 1.18963 | ||||||||
\(585\) | 32.7909 | 1.35574 | ||||||||
\(586\) | −42.4067 | −1.75181 | ||||||||
\(587\) | −42.0016 | −1.73359 | −0.866796 | − | 0.498662i | \(-0.833825\pi\) | ||||
−0.866796 | + | 0.498662i | \(0.833825\pi\) | |||||||
\(588\) | 74.7582 | 3.08298 | ||||||||
\(589\) | −28.3083 | −1.16642 | ||||||||
\(590\) | −10.1921 | −0.419602 | ||||||||
\(591\) | 30.6515 | 1.26083 | ||||||||
\(592\) | −9.40830 | −0.386679 | ||||||||
\(593\) | −16.9108 | −0.694443 | −0.347221 | − | 0.937783i | \(-0.612875\pi\) | ||||
−0.347221 | + | 0.937783i | \(0.612875\pi\) | |||||||
\(594\) | −18.0768 | −0.741699 | ||||||||
\(595\) | −2.92616 | −0.119961 | ||||||||
\(596\) | −14.2684 | −0.584458 | ||||||||
\(597\) | −55.7917 | −2.28340 | ||||||||
\(598\) | 35.8164 | 1.46464 | ||||||||
\(599\) | −6.45589 | −0.263780 | −0.131890 | − | 0.991264i | \(-0.542105\pi\) | ||||
−0.131890 | + | 0.991264i | \(0.542105\pi\) | |||||||
\(600\) | −181.749 | −7.41985 | ||||||||
\(601\) | 22.1832 | 0.904872 | 0.452436 | − | 0.891797i | \(-0.350555\pi\) | ||||
0.452436 | + | 0.891797i | \(0.350555\pi\) | |||||||
\(602\) | 20.0540 | 0.817341 | ||||||||
\(603\) | 11.9743 | 0.487629 | ||||||||
\(604\) | −98.2842 | −3.99913 | ||||||||
\(605\) | −4.87177 | −0.198066 | ||||||||
\(606\) | −61.9361 | −2.51598 | ||||||||
\(607\) | −22.8614 | −0.927916 | −0.463958 | − | 0.885857i | \(-0.653571\pi\) | ||||
−0.463958 | + | 0.885857i | \(0.653571\pi\) | |||||||
\(608\) | −116.982 | −4.74425 | ||||||||
\(609\) | 13.5126 | 0.547559 | ||||||||
\(610\) | −32.2940 | −1.30755 | ||||||||
\(611\) | 43.9582 | 1.77836 | ||||||||
\(612\) | 11.0427 | 0.446373 | ||||||||
\(613\) | −15.9785 | −0.645367 | −0.322684 | − | 0.946507i | \(-0.604585\pi\) | ||||
−0.322684 | + | 0.946507i | \(0.604585\pi\) | |||||||
\(614\) | −5.09032 | −0.205429 | ||||||||
\(615\) | −1.08199 | −0.0436299 | ||||||||
\(616\) | −22.5369 | −0.908037 | ||||||||
\(617\) | −47.0320 | −1.89344 | −0.946719 | − | 0.322062i | \(-0.895624\pi\) | ||||
−0.946719 | + | 0.322062i | \(0.895624\pi\) | |||||||
\(618\) | 26.2832 | 1.05727 | ||||||||
\(619\) | 21.0374 | 0.845564 | 0.422782 | − | 0.906231i | \(-0.361054\pi\) | ||||
0.422782 | + | 0.906231i | \(0.361054\pi\) | |||||||
\(620\) | −74.1335 | −2.97727 | ||||||||
\(621\) | −6.47154 | −0.259694 | ||||||||
\(622\) | 26.7009 | 1.07061 | ||||||||
\(623\) | 9.57086 | 0.383449 | ||||||||
\(624\) | 110.064 | 4.40607 | ||||||||
\(625\) | 18.4816 | 0.739263 | ||||||||
\(626\) | −68.7725 | −2.74870 | ||||||||
\(627\) | −59.5115 | −2.37666 | ||||||||
\(628\) | 79.6783 | 3.17951 | ||||||||
\(629\) | −0.775849 | −0.0309351 | ||||||||
\(630\) | −16.8013 | −0.669379 | ||||||||
\(631\) | −2.63139 | −0.104754 | −0.0523771 | − | 0.998627i | \(-0.516680\pi\) | ||||
−0.0523771 | + | 0.998627i | \(0.516680\pi\) | |||||||
\(632\) | 27.6047 | 1.09805 | ||||||||
\(633\) | 24.4171 | 0.970494 | ||||||||
\(634\) | −0.549237 | −0.0218130 | ||||||||
\(635\) | −4.00862 | −0.159077 | ||||||||
\(636\) | 13.5429 | 0.537010 | ||||||||
\(637\) | 25.6456 | 1.01612 | ||||||||
\(638\) | 72.6758 | 2.87726 | ||||||||
\(639\) | 6.51024 | 0.257541 | ||||||||
\(640\) | −59.1641 | −2.33867 | ||||||||
\(641\) | −4.04389 | −0.159724 | −0.0798620 | − | 0.996806i | \(-0.525448\pi\) | ||||
−0.0798620 | + | 0.996806i | \(0.525448\pi\) | |||||||
\(642\) | −95.4256 | −3.76615 | ||||||||
\(643\) | 22.9665 | 0.905710 | 0.452855 | − | 0.891584i | \(-0.350406\pi\) | ||||
0.452855 | + | 0.891584i | \(0.350406\pi\) | |||||||
\(644\) | −13.2099 | −0.520543 | ||||||||
\(645\) | 84.7015 | 3.33512 | ||||||||
\(646\) | −19.9982 | −0.786818 | ||||||||
\(647\) | 28.8990 | 1.13614 | 0.568068 | − | 0.822982i | \(-0.307691\pi\) | ||||
0.568068 | + | 0.822982i | \(0.307691\pi\) | |||||||
\(648\) | −90.8007 | −3.56699 | ||||||||
\(649\) | −3.50387 | −0.137539 | ||||||||
\(650\) | −102.081 | −4.00394 | ||||||||
\(651\) | −6.58297 | −0.258007 | ||||||||
\(652\) | −95.8854 | −3.75516 | ||||||||
\(653\) | 2.23346 | 0.0874021 | 0.0437010 | − | 0.999045i | \(-0.486085\pi\) | ||||
0.0437010 | + | 0.999045i | \(0.486085\pi\) | |||||||
\(654\) | 114.080 | 4.46086 | ||||||||
\(655\) | −6.26936 | −0.244964 | ||||||||
\(656\) | −1.51576 | −0.0591805 | ||||||||
\(657\) | 7.36807 | 0.287456 | ||||||||
\(658\) | −22.5231 | −0.878043 | ||||||||
\(659\) | −23.6620 | −0.921739 | −0.460869 | − | 0.887468i | \(-0.652462\pi\) | ||||
−0.460869 | + | 0.887468i | \(0.652462\pi\) | |||||||
\(660\) | −155.848 | −6.06639 | ||||||||
\(661\) | 11.3385 | 0.441017 | 0.220509 | − | 0.975385i | \(-0.429228\pi\) | ||||
0.220509 | + | 0.975385i | \(0.429228\pi\) | |||||||
\(662\) | 42.3461 | 1.64583 | ||||||||
\(663\) | 9.07632 | 0.352495 | ||||||||
\(664\) | −136.236 | −5.28697 | ||||||||
\(665\) | 21.9022 | 0.849330 | ||||||||
\(666\) | −4.45474 | −0.172618 | ||||||||
\(667\) | 26.0182 | 1.00743 | ||||||||
\(668\) | −22.7773 | −0.881280 | ||||||||
\(669\) | −2.17959 | −0.0842677 | ||||||||
\(670\) | −56.7894 | −2.19397 | ||||||||
\(671\) | −11.1021 | −0.428593 | ||||||||
\(672\) | −27.2037 | −1.04940 | ||||||||
\(673\) | −2.33543 | −0.0900243 | −0.0450121 | − | 0.998986i | \(-0.514333\pi\) | ||||
−0.0450121 | + | 0.998986i | \(0.514333\pi\) | |||||||
\(674\) | 77.1428 | 2.97143 | ||||||||
\(675\) | 18.4446 | 0.709934 | ||||||||
\(676\) | 15.4101 | 0.592698 | ||||||||
\(677\) | 20.2424 | 0.777978 | 0.388989 | − | 0.921242i | \(-0.372824\pi\) | ||||
0.388989 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(678\) | −23.0777 | −0.886293 | ||||||||
\(679\) | 8.70485 | 0.334062 | ||||||||
\(680\) | −31.9870 | −1.22664 | ||||||||
\(681\) | 54.8473 | 2.10175 | ||||||||
\(682\) | −35.4056 | −1.35575 | ||||||||
\(683\) | −20.0654 | −0.767780 | −0.383890 | − | 0.923379i | \(-0.625416\pi\) | ||||
−0.383890 | + | 0.923379i | \(0.625416\pi\) | |||||||
\(684\) | −82.6539 | −3.16035 | ||||||||
\(685\) | 23.8087 | 0.909684 | ||||||||
\(686\) | −27.4863 | −1.04943 | ||||||||
\(687\) | 6.01206 | 0.229374 | ||||||||
\(688\) | 118.659 | 4.52382 | ||||||||
\(689\) | 4.64585 | 0.176993 | ||||||||
\(690\) | −77.5106 | −2.95078 | ||||||||
\(691\) | 37.7139 | 1.43470 | 0.717352 | − | 0.696711i | \(-0.245354\pi\) | ||||
0.717352 | + | 0.696711i | \(0.245354\pi\) | |||||||
\(692\) | −63.4974 | −2.41381 | ||||||||
\(693\) | −5.77600 | −0.219412 | ||||||||
\(694\) | 21.4231 | 0.813209 | ||||||||
\(695\) | −61.6533 | −2.33864 | ||||||||
\(696\) | 147.712 | 5.59900 | ||||||||
\(697\) | −0.124996 | −0.00473457 | ||||||||
\(698\) | −74.2947 | −2.81209 | ||||||||
\(699\) | 43.3799 | 1.64078 | ||||||||
\(700\) | 37.6497 | 1.42302 | ||||||||
\(701\) | 6.86230 | 0.259186 | 0.129593 | − | 0.991567i | \(-0.458633\pi\) | ||||
0.129593 | + | 0.991567i | \(0.458633\pi\) | |||||||
\(702\) | −20.6357 | −0.778845 | ||||||||
\(703\) | 5.80720 | 0.219023 | ||||||||
\(704\) | −61.3323 | −2.31155 | ||||||||
\(705\) | −95.1302 | −3.58281 | ||||||||
\(706\) | −33.3557 | −1.25536 | ||||||||
\(707\) | 7.83638 | 0.294717 | ||||||||
\(708\) | −11.6598 | −0.438203 | ||||||||
\(709\) | 31.9055 | 1.19824 | 0.599118 | − | 0.800661i | \(-0.295518\pi\) | ||||
0.599118 | + | 0.800661i | \(0.295518\pi\) | |||||||
\(710\) | −30.8756 | −1.15874 | ||||||||
\(711\) | 7.07483 | 0.265327 | ||||||||
\(712\) | 104.623 | 3.92091 | ||||||||
\(713\) | −12.6753 | −0.474694 | ||||||||
\(714\) | −4.65049 | −0.174040 | ||||||||
\(715\) | −53.4634 | −1.99942 | ||||||||
\(716\) | 71.2776 | 2.66377 | ||||||||
\(717\) | 27.4426 | 1.02486 | ||||||||
\(718\) | 99.4547 | 3.71162 | ||||||||
\(719\) | −12.1883 | −0.454546 | −0.227273 | − | 0.973831i | \(-0.572981\pi\) | ||||
−0.227273 | + | 0.973831i | \(0.572981\pi\) | |||||||
\(720\) | −99.4124 | −3.70488 | ||||||||
\(721\) | −3.32545 | −0.123846 | ||||||||
\(722\) | 98.9220 | 3.68150 | ||||||||
\(723\) | 42.0663 | 1.56446 | ||||||||
\(724\) | −22.7577 | −0.845782 | ||||||||
\(725\) | −74.1547 | −2.75403 | ||||||||
\(726\) | −7.74262 | −0.287356 | ||||||||
\(727\) | −35.3177 | −1.30986 | −0.654930 | − | 0.755690i | \(-0.727302\pi\) | ||||
−0.654930 | + | 0.755690i | \(0.727302\pi\) | |||||||
\(728\) | −25.7272 | −0.953513 | ||||||||
\(729\) | −10.1265 | −0.375056 | ||||||||
\(730\) | −34.9440 | −1.29333 | ||||||||
\(731\) | 9.78511 | 0.361915 | ||||||||
\(732\) | −36.9446 | −1.36551 | ||||||||
\(733\) | −8.41218 | −0.310711 | −0.155355 | − | 0.987859i | \(-0.549652\pi\) | ||||
−0.155355 | + | 0.987859i | \(0.549652\pi\) | |||||||
\(734\) | 56.3786 | 2.08097 | ||||||||
\(735\) | −55.4999 | −2.04714 | ||||||||
\(736\) | −52.3799 | −1.93075 | ||||||||
\(737\) | −19.5232 | −0.719148 | ||||||||
\(738\) | −0.717699 | −0.0264188 | ||||||||
\(739\) | 22.5183 | 0.828348 | 0.414174 | − | 0.910198i | \(-0.364071\pi\) | ||||
0.414174 | + | 0.910198i | \(0.364071\pi\) | |||||||
\(740\) | 15.2079 | 0.559052 | ||||||||
\(741\) | −67.9359 | −2.49569 | ||||||||
\(742\) | −2.38043 | −0.0873882 | ||||||||
\(743\) | −14.1883 | −0.520520 | −0.260260 | − | 0.965539i | \(-0.583808\pi\) | ||||
−0.260260 | + | 0.965539i | \(0.583808\pi\) | |||||||
\(744\) | −71.9610 | −2.63822 | ||||||||
\(745\) | 10.5928 | 0.388089 | ||||||||
\(746\) | 69.8424 | 2.55711 | ||||||||
\(747\) | −34.9160 | −1.27751 | ||||||||
\(748\) | −18.0043 | −0.658303 | ||||||||
\(749\) | 12.0736 | 0.441159 | ||||||||
\(750\) | 105.277 | 3.84418 | ||||||||
\(751\) | 15.7702 | 0.575464 | 0.287732 | − | 0.957711i | \(-0.407099\pi\) | ||||
0.287732 | + | 0.957711i | \(0.407099\pi\) | |||||||
\(752\) | −133.268 | −4.85980 | ||||||||
\(753\) | −53.7653 | −1.95931 | ||||||||
\(754\) | 82.9638 | 3.02136 | ||||||||
\(755\) | 72.9654 | 2.65548 | ||||||||
\(756\) | 7.61091 | 0.276806 | ||||||||
\(757\) | −41.1460 | −1.49548 | −0.747739 | − | 0.663993i | \(-0.768861\pi\) | ||||
−0.747739 | + | 0.663993i | \(0.768861\pi\) | |||||||
\(758\) | 48.7209 | 1.76962 | ||||||||
\(759\) | −26.6469 | −0.967220 | ||||||||
\(760\) | 239.421 | 8.68473 | ||||||||
\(761\) | 44.3560 | 1.60790 | 0.803952 | − | 0.594694i | \(-0.202727\pi\) | ||||
0.803952 | + | 0.594694i | \(0.202727\pi\) | |||||||
\(762\) | −6.37084 | −0.230791 | ||||||||
\(763\) | −14.4337 | −0.522537 | ||||||||
\(764\) | −108.323 | −3.91900 | ||||||||
\(765\) | −8.19798 | −0.296398 | ||||||||
\(766\) | −23.7821 | −0.859283 | ||||||||
\(767\) | −3.99988 | −0.144427 | ||||||||
\(768\) | −14.5895 | −0.526452 | ||||||||
\(769\) | −4.23858 | −0.152847 | −0.0764235 | − | 0.997075i | \(-0.524350\pi\) | ||||
−0.0764235 | + | 0.997075i | \(0.524350\pi\) | |||||||
\(770\) | 27.3934 | 0.987190 | ||||||||
\(771\) | 68.6912 | 2.47385 | ||||||||
\(772\) | −70.4935 | −2.53712 | ||||||||
\(773\) | −51.2288 | −1.84257 | −0.921287 | − | 0.388884i | \(-0.872861\pi\) | ||||
−0.921287 | + | 0.388884i | \(0.872861\pi\) | |||||||
\(774\) | 56.1838 | 2.01948 | ||||||||
\(775\) | 36.1261 | 1.29769 | ||||||||
\(776\) | 95.1562 | 3.41591 | ||||||||
\(777\) | 1.35044 | 0.0484468 | ||||||||
\(778\) | −44.7136 | −1.60306 | ||||||||
\(779\) | 0.935593 | 0.0335211 | ||||||||
\(780\) | −177.910 | −6.37021 | ||||||||
\(781\) | −10.6145 | −0.379817 | ||||||||
\(782\) | −8.95439 | −0.320208 | ||||||||
\(783\) | −14.9904 | −0.535714 | ||||||||
\(784\) | −77.7500 | −2.77679 | ||||||||
\(785\) | −59.1525 | −2.11124 | ||||||||
\(786\) | −9.96379 | −0.355397 | ||||||||
\(787\) | 22.8310 | 0.813836 | 0.406918 | − | 0.913465i | \(-0.366603\pi\) | ||||
0.406918 | + | 0.913465i | \(0.366603\pi\) | |||||||
\(788\) | −69.4093 | −2.47260 | ||||||||
\(789\) | −40.7484 | −1.45068 | ||||||||
\(790\) | −33.5533 | −1.19377 | ||||||||
\(791\) | 2.91987 | 0.103819 | ||||||||
\(792\) | −63.1398 | −2.24357 | ||||||||
\(793\) | −12.6738 | −0.450058 | ||||||||
\(794\) | −0.594330 | −0.0210920 | ||||||||
\(795\) | −10.0541 | −0.356583 | ||||||||
\(796\) | 126.338 | 4.47795 | ||||||||
\(797\) | −19.6521 | −0.696112 | −0.348056 | − | 0.937474i | \(-0.613158\pi\) | ||||
−0.348056 | + | 0.937474i | \(0.613158\pi\) | |||||||
\(798\) | 34.8088 | 1.23222 | ||||||||
\(799\) | −10.9899 | −0.388794 | ||||||||
\(800\) | 149.289 | 5.27815 | ||||||||
\(801\) | 26.8139 | 0.947423 | ||||||||
\(802\) | −83.9510 | −2.96441 | ||||||||
\(803\) | −12.0132 | −0.423935 | ||||||||
\(804\) | −64.9675 | −2.29123 | ||||||||
\(805\) | 9.80692 | 0.345648 | ||||||||
\(806\) | −40.4176 | −1.42365 | ||||||||
\(807\) | 38.0575 | 1.33969 | ||||||||
\(808\) | 85.6625 | 3.01360 | ||||||||
\(809\) | 11.6148 | 0.408355 | 0.204177 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204177 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(810\) | 110.368 | 3.87792 | ||||||||
\(811\) | −4.00231 | −0.140540 | −0.0702701 | − | 0.997528i | \(-0.522386\pi\) | ||||
−0.0702701 | + | 0.997528i | \(0.522386\pi\) | |||||||
\(812\) | −30.5989 | −1.07381 | ||||||||
\(813\) | −11.0485 | −0.387487 | ||||||||
\(814\) | 7.26316 | 0.254574 | ||||||||
\(815\) | 71.1846 | 2.49349 | ||||||||
\(816\) | −27.5167 | −0.963279 | ||||||||
\(817\) | −73.2412 | −2.56239 | ||||||||
\(818\) | 91.4366 | 3.19701 | ||||||||
\(819\) | −6.59365 | −0.230401 | ||||||||
\(820\) | 2.45012 | 0.0855620 | ||||||||
\(821\) | −20.2533 | −0.706845 | −0.353423 | − | 0.935464i | \(-0.614982\pi\) | ||||
−0.353423 | + | 0.935464i | \(0.614982\pi\) | |||||||
\(822\) | 37.8388 | 1.31978 | ||||||||
\(823\) | −11.4210 | −0.398111 | −0.199055 | − | 0.979988i | \(-0.563787\pi\) | ||||
−0.199055 | + | 0.979988i | \(0.563787\pi\) | |||||||
\(824\) | −36.3518 | −1.26637 | ||||||||
\(825\) | 75.9466 | 2.64412 | ||||||||
\(826\) | 2.04944 | 0.0713093 | ||||||||
\(827\) | 27.5765 | 0.958928 | 0.479464 | − | 0.877561i | \(-0.340831\pi\) | ||||
0.479464 | + | 0.877561i | \(0.340831\pi\) | |||||||
\(828\) | −37.0091 | −1.28616 | ||||||||
\(829\) | 46.8822 | 1.62829 | 0.814143 | − | 0.580665i | \(-0.197207\pi\) | ||||
0.814143 | + | 0.580665i | \(0.197207\pi\) | |||||||
\(830\) | 165.593 | 5.74783 | ||||||||
\(831\) | 15.3407 | 0.532161 | ||||||||
\(832\) | −70.0145 | −2.42732 | ||||||||
\(833\) | −6.41160 | −0.222149 | ||||||||
\(834\) | −97.9846 | −3.39293 | ||||||||
\(835\) | 16.9097 | 0.585183 | ||||||||
\(836\) | 134.762 | 4.66083 | ||||||||
\(837\) | 7.30291 | 0.252426 | ||||||||
\(838\) | 5.46906 | 0.188925 | ||||||||
\(839\) | −40.0729 | −1.38347 | −0.691735 | − | 0.722151i | \(-0.743153\pi\) | ||||
−0.691735 | + | 0.722151i | \(0.743153\pi\) | |||||||
\(840\) | 55.6764 | 1.92102 | ||||||||
\(841\) | 31.2674 | 1.07819 | ||||||||
\(842\) | 17.9224 | 0.617647 | ||||||||
\(843\) | 35.4062 | 1.21945 | ||||||||
\(844\) | −55.2918 | −1.90322 | ||||||||
\(845\) | −11.4404 | −0.393561 | ||||||||
\(846\) | −63.1013 | −2.16947 | ||||||||
\(847\) | 0.979624 | 0.0336603 | ||||||||
\(848\) | −14.0849 | −0.483676 | ||||||||
\(849\) | 27.7544 | 0.952529 | ||||||||
\(850\) | 25.5210 | 0.875364 | ||||||||
\(851\) | 2.60023 | 0.0891348 | ||||||||
\(852\) | −35.3219 | −1.21011 | ||||||||
\(853\) | −18.5871 | −0.636410 | −0.318205 | − | 0.948022i | \(-0.603080\pi\) | ||||
−0.318205 | + | 0.948022i | \(0.603080\pi\) | |||||||
\(854\) | 6.49374 | 0.222211 | ||||||||
\(855\) | 61.3616 | 2.09852 | ||||||||
\(856\) | 131.981 | 4.51102 | ||||||||
\(857\) | 5.34419 | 0.182554 | 0.0912770 | − | 0.995826i | \(-0.470905\pi\) | ||||
0.0912770 | + | 0.995826i | \(0.470905\pi\) | |||||||
\(858\) | −84.9686 | −2.90078 | ||||||||
\(859\) | 24.3690 | 0.831461 | 0.415730 | − | 0.909488i | \(-0.363526\pi\) | ||||
0.415730 | + | 0.909488i | \(0.363526\pi\) | |||||||
\(860\) | −191.804 | −6.54045 | ||||||||
\(861\) | 0.217568 | 0.00741470 | ||||||||
\(862\) | 104.429 | 3.55688 | ||||||||
\(863\) | −42.4753 | −1.44588 | −0.722938 | − | 0.690913i | \(-0.757209\pi\) | ||||
−0.722938 | + | 0.690913i | \(0.757209\pi\) | |||||||
\(864\) | 30.1788 | 1.02670 | ||||||||
\(865\) | 47.1400 | 1.60281 | ||||||||
\(866\) | −66.4800 | −2.25908 | ||||||||
\(867\) | −2.26915 | −0.0770644 | ||||||||
\(868\) | 14.9069 | 0.505973 | ||||||||
\(869\) | −11.5351 | −0.391300 | ||||||||
\(870\) | −179.543 | −6.08706 | ||||||||
\(871\) | −22.2869 | −0.755164 | ||||||||
\(872\) | −157.781 | −5.34314 | ||||||||
\(873\) | 24.3877 | 0.825398 | ||||||||
\(874\) | 67.0233 | 2.26710 | ||||||||
\(875\) | −13.3200 | −0.450300 | ||||||||
\(876\) | −39.9762 | −1.35067 | ||||||||
\(877\) | −22.1463 | −0.747828 | −0.373914 | − | 0.927463i | \(-0.621985\pi\) | ||||
−0.373914 | + | 0.927463i | \(0.621985\pi\) | |||||||
\(878\) | −67.0991 | −2.26449 | ||||||||
\(879\) | 36.0161 | 1.21479 | ||||||||
\(880\) | 162.085 | 5.46390 | ||||||||
\(881\) | 6.67204 | 0.224787 | 0.112393 | − | 0.993664i | \(-0.464148\pi\) | ||||
0.112393 | + | 0.993664i | \(0.464148\pi\) | |||||||
\(882\) | −36.8139 | −1.23959 | ||||||||
\(883\) | −22.8348 | −0.768451 | −0.384226 | − | 0.923239i | \(-0.625532\pi\) | ||||
−0.384226 | + | 0.923239i | \(0.625532\pi\) | |||||||
\(884\) | −20.5530 | −0.691273 | ||||||||
\(885\) | 8.65616 | 0.290974 | ||||||||
\(886\) | 15.9375 | 0.535430 | ||||||||
\(887\) | −42.9163 | −1.44099 | −0.720494 | − | 0.693461i | \(-0.756085\pi\) | ||||
−0.720494 | + | 0.693461i | \(0.756085\pi\) | |||||||
\(888\) | 14.7622 | 0.495387 | ||||||||
\(889\) | 0.806061 | 0.0270344 | ||||||||
\(890\) | −127.168 | −4.26269 | ||||||||
\(891\) | 37.9425 | 1.27112 | ||||||||
\(892\) | 4.93560 | 0.165256 | ||||||||
\(893\) | 82.2589 | 2.75269 | ||||||||
\(894\) | 16.8349 | 0.563044 | ||||||||
\(895\) | −52.9159 | −1.76878 | ||||||||
\(896\) | 11.8968 | 0.397445 | ||||||||
\(897\) | −30.4190 | −1.01566 | ||||||||
\(898\) | 10.6664 | 0.355942 | ||||||||
\(899\) | −29.3606 | −0.979231 | ||||||||
\(900\) | 105.480 | 3.51600 | ||||||||
\(901\) | −1.16150 | −0.0386951 | ||||||||
\(902\) | 1.17016 | 0.0389621 | ||||||||
\(903\) | −17.0319 | −0.566787 | ||||||||
\(904\) | 31.9183 | 1.06159 | ||||||||
\(905\) | 16.8951 | 0.561612 | ||||||||
\(906\) | 115.963 | 3.85261 | ||||||||
\(907\) | −9.84282 | −0.326825 | −0.163413 | − | 0.986558i | \(-0.552250\pi\) | ||||
−0.163413 | + | 0.986558i | \(0.552250\pi\) | |||||||
\(908\) | −124.200 | −4.12171 | ||||||||
\(909\) | 21.9545 | 0.728186 | ||||||||
\(910\) | 31.2712 | 1.03663 | ||||||||
\(911\) | −11.8399 | −0.392274 | −0.196137 | − | 0.980577i | \(-0.562840\pi\) | ||||
−0.196137 | + | 0.980577i | \(0.562840\pi\) | |||||||
\(912\) | 205.962 | 6.82008 | ||||||||
\(913\) | 56.9283 | 1.88405 | ||||||||
\(914\) | 86.2126 | 2.85166 | ||||||||
\(915\) | 27.4274 | 0.906721 | ||||||||
\(916\) | −13.6141 | −0.449823 | ||||||||
\(917\) | 1.26065 | 0.0416304 | ||||||||
\(918\) | 5.15909 | 0.170275 | ||||||||
\(919\) | −5.14193 | −0.169617 | −0.0848083 | − | 0.996397i | \(-0.527028\pi\) | ||||
−0.0848083 | + | 0.996397i | \(0.527028\pi\) | |||||||
\(920\) | 107.203 | 3.53439 | ||||||||
\(921\) | 4.32322 | 0.142455 | ||||||||
\(922\) | −30.1722 | −0.993668 | ||||||||
\(923\) | −12.1171 | −0.398840 | ||||||||
\(924\) | 31.3383 | 1.03095 | ||||||||
\(925\) | −7.41095 | −0.243671 | ||||||||
\(926\) | 11.1462 | 0.366288 | ||||||||
\(927\) | −9.31664 | −0.305999 | ||||||||
\(928\) | −121.331 | −3.98288 | ||||||||
\(929\) | −13.5741 | −0.445351 | −0.222675 | − | 0.974893i | \(-0.571479\pi\) | ||||
−0.222675 | + | 0.974893i | \(0.571479\pi\) | |||||||
\(930\) | 87.4681 | 2.86819 | ||||||||
\(931\) | 47.9906 | 1.57283 | ||||||||
\(932\) | −98.2323 | −3.21770 | ||||||||
\(933\) | −22.6771 | −0.742415 | ||||||||
\(934\) | 23.4434 | 0.767093 | ||||||||
\(935\) | 13.3663 | 0.437124 | ||||||||
\(936\) | −72.0778 | −2.35594 | ||||||||
\(937\) | −46.4188 | −1.51644 | −0.758219 | − | 0.652000i | \(-0.773930\pi\) | ||||
−0.758219 | + | 0.652000i | \(0.773930\pi\) | |||||||
\(938\) | 11.4193 | 0.372854 | ||||||||
\(939\) | 58.4086 | 1.90609 | ||||||||
\(940\) | 215.419 | 7.02620 | ||||||||
\(941\) | 13.7666 | 0.448777 | 0.224388 | − | 0.974500i | \(-0.427962\pi\) | ||||
0.224388 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(942\) | −94.0102 | −3.06302 | ||||||||
\(943\) | 0.418921 | 0.0136419 | ||||||||
\(944\) | 12.1265 | 0.394683 | ||||||||
\(945\) | −5.65028 | −0.183804 | ||||||||
\(946\) | −91.6040 | −2.97830 | ||||||||
\(947\) | −24.3920 | −0.792635 | −0.396317 | − | 0.918114i | \(-0.629712\pi\) | ||||
−0.396317 | + | 0.918114i | \(0.629712\pi\) | |||||||
\(948\) | −38.3852 | −1.24669 | ||||||||
\(949\) | −13.7137 | −0.445167 | ||||||||
\(950\) | −191.024 | −6.19764 | ||||||||
\(951\) | 0.466468 | 0.0151263 | ||||||||
\(952\) | 6.43200 | 0.208462 | ||||||||
\(953\) | −1.48563 | −0.0481242 | −0.0240621 | − | 0.999710i | \(-0.507660\pi\) | ||||
−0.0240621 | + | 0.999710i | \(0.507660\pi\) | |||||||
\(954\) | −6.66905 | −0.215919 | ||||||||
\(955\) | 80.4184 | 2.60228 | ||||||||
\(956\) | −62.1429 | −2.00984 | ||||||||
\(957\) | −61.7237 | −1.99525 | ||||||||
\(958\) | 15.3587 | 0.496216 | ||||||||
\(959\) | −4.78750 | −0.154596 | ||||||||
\(960\) | 151.519 | 4.89025 | ||||||||
\(961\) | −16.6963 | −0.538592 | ||||||||
\(962\) | 8.29133 | 0.267323 | ||||||||
\(963\) | 33.8256 | 1.09001 | ||||||||
\(964\) | −95.2578 | −3.06805 | ||||||||
\(965\) | 52.3338 | 1.68468 | ||||||||
\(966\) | 15.5860 | 0.501471 | ||||||||
\(967\) | −10.9743 | −0.352910 | −0.176455 | − | 0.984309i | \(-0.556463\pi\) | ||||
−0.176455 | + | 0.984309i | \(0.556463\pi\) | |||||||
\(968\) | 10.7087 | 0.344189 | ||||||||
\(969\) | 16.9845 | 0.545621 | ||||||||
\(970\) | −115.662 | −3.71367 | ||||||||
\(971\) | −17.0103 | −0.545887 | −0.272943 | − | 0.962030i | \(-0.587997\pi\) | ||||
−0.272943 | + | 0.962030i | \(0.587997\pi\) | |||||||
\(972\) | 96.4952 | 3.09508 | ||||||||
\(973\) | 12.3974 | 0.397441 | ||||||||
\(974\) | −40.5277 | −1.29859 | ||||||||
\(975\) | 86.6975 | 2.77654 | ||||||||
\(976\) | 38.4231 | 1.22989 | ||||||||
\(977\) | 39.2934 | 1.25711 | 0.628553 | − | 0.777767i | \(-0.283648\pi\) | ||||
0.628553 | + | 0.777767i | \(0.283648\pi\) | |||||||
\(978\) | 113.133 | 3.61758 | ||||||||
\(979\) | −43.7184 | −1.39724 | ||||||||
\(980\) | 125.678 | 4.01462 | ||||||||
\(981\) | −40.4379 | −1.29108 | ||||||||
\(982\) | 54.7247 | 1.74633 | ||||||||
\(983\) | 16.4962 | 0.526148 | 0.263074 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263074 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(984\) | 2.37832 | 0.0758182 | ||||||||
\(985\) | 51.5289 | 1.64185 | ||||||||
\(986\) | −20.7416 | −0.660547 | ||||||||
\(987\) | 19.1290 | 0.608881 | ||||||||
\(988\) | 153.839 | 4.89426 | ||||||||
\(989\) | −32.7945 | −1.04280 | ||||||||
\(990\) | 76.7459 | 2.43915 | ||||||||
\(991\) | 26.7174 | 0.848706 | 0.424353 | − | 0.905497i | \(-0.360502\pi\) | ||||
0.424353 | + | 0.905497i | \(0.360502\pi\) | |||||||
\(992\) | 59.1089 | 1.87671 | ||||||||
\(993\) | −35.9646 | −1.14130 | ||||||||
\(994\) | 6.20853 | 0.196922 | ||||||||
\(995\) | −93.7927 | −2.97343 | ||||||||
\(996\) | 189.440 | 6.00264 | ||||||||
\(997\) | 39.8210 | 1.26114 | 0.630572 | − | 0.776131i | \(-0.282820\pi\) | ||||
0.630572 | + | 0.776131i | \(0.282820\pi\) | |||||||
\(998\) | −15.9388 | −0.504534 | ||||||||
\(999\) | −1.49813 | −0.0473987 |
(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 | 1003.2.a.h.1.16 | ✓ | 16 | |
3.2 | odd | 2 | 9027.2.a.n.1.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.h.1.16 | ✓ | 16 | 1.1 | even | 1 | trivial | |
9027.2.a.n.1.1 | 16 | 3.2 | odd | 2 |