Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64748 | −1.87205 | −0.936026 | − | 0.351932i | \(-0.885525\pi\) | ||||
−0.936026 | + | 0.351932i | \(0.885525\pi\) | |||||||
\(3\) | 2.89261 | 1.67005 | 0.835026 | − | 0.550211i | \(-0.185453\pi\) | ||||
0.835026 | + | 0.550211i | \(0.185453\pi\) | |||||||
\(4\) | 5.00915 | 2.50458 | ||||||||
\(5\) | 3.62616 | 1.62167 | 0.810833 | − | 0.585277i | \(-0.199014\pi\) | ||||
0.810833 | + | 0.585277i | \(0.199014\pi\) | |||||||
\(6\) | −7.65814 | −3.12642 | ||||||||
\(7\) | 1.08314 | 0.409388 | 0.204694 | − | 0.978826i | \(-0.434380\pi\) | ||||
0.204694 | + | 0.978826i | \(0.434380\pi\) | |||||||
\(8\) | −7.96667 | −2.81664 | ||||||||
\(9\) | 5.36721 | 1.78907 | ||||||||
\(10\) | −9.60018 | −3.03584 | ||||||||
\(11\) | −4.28161 | −1.29095 | −0.645476 | − | 0.763780i | \(-0.723341\pi\) | ||||
−0.645476 | + | 0.763780i | \(0.723341\pi\) | |||||||
\(12\) | 14.4895 | 4.18277 | ||||||||
\(13\) | 5.59638 | 1.55216 | 0.776078 | − | 0.630637i | \(-0.217206\pi\) | ||||
0.776078 | + | 0.630637i | \(0.217206\pi\) | |||||||
\(14\) | −2.86759 | −0.766396 | ||||||||
\(15\) | 10.4891 | 2.70827 | ||||||||
\(16\) | 11.0733 | 2.76833 | ||||||||
\(17\) | 1.81985 | 0.441378 | 0.220689 | − | 0.975344i | \(-0.429169\pi\) | ||||
0.220689 | + | 0.975344i | \(0.429169\pi\) | |||||||
\(18\) | −14.2096 | −3.34923 | ||||||||
\(19\) | −7.75770 | −1.77974 | −0.889869 | − | 0.456217i | \(-0.849204\pi\) | ||||
−0.889869 | + | 0.456217i | \(0.849204\pi\) | |||||||
\(20\) | 18.1640 | 4.06159 | ||||||||
\(21\) | 3.13311 | 0.683700 | ||||||||
\(22\) | 11.3355 | 2.41673 | ||||||||
\(23\) | 4.67094 | 0.973959 | 0.486979 | − | 0.873413i | \(-0.338099\pi\) | ||||
0.486979 | + | 0.873413i | \(0.338099\pi\) | |||||||
\(24\) | −23.0445 | −4.70394 | ||||||||
\(25\) | 8.14901 | 1.62980 | ||||||||
\(26\) | −14.8163 | −2.90571 | ||||||||
\(27\) | 6.84743 | 1.31779 | ||||||||
\(28\) | 5.42561 | 1.02534 | ||||||||
\(29\) | 9.07311 | 1.68483 | 0.842417 | − | 0.538826i | \(-0.181132\pi\) | ||||
0.842417 | + | 0.538826i | \(0.181132\pi\) | |||||||
\(30\) | −27.7696 | −5.07001 | ||||||||
\(31\) | 5.85538 | 1.05166 | 0.525829 | − | 0.850590i | \(-0.323755\pi\) | ||||
0.525829 | + | 0.850590i | \(0.323755\pi\) | |||||||
\(32\) | −13.3830 | −2.36580 | ||||||||
\(33\) | −12.3850 | −2.15596 | ||||||||
\(34\) | −4.81801 | −0.826282 | ||||||||
\(35\) | 3.92764 | 0.663892 | ||||||||
\(36\) | 26.8852 | 4.48087 | ||||||||
\(37\) | −0.0758430 | −0.0124685 | −0.00623425 | − | 0.999981i | \(-0.501984\pi\) | ||||
−0.00623425 | + | 0.999981i | \(0.501984\pi\) | |||||||
\(38\) | 20.5383 | 3.33176 | ||||||||
\(39\) | 16.1882 | 2.59218 | ||||||||
\(40\) | −28.8884 | −4.56766 | ||||||||
\(41\) | 8.62838 | 1.34753 | 0.673764 | − | 0.738947i | \(-0.264677\pi\) | ||||
0.673764 | + | 0.738947i | \(0.264677\pi\) | |||||||
\(42\) | −8.29483 | −1.27992 | ||||||||
\(43\) | −5.57989 | −0.850925 | −0.425463 | − | 0.904976i | \(-0.639889\pi\) | ||||
−0.425463 | + | 0.904976i | \(0.639889\pi\) | |||||||
\(44\) | −21.4472 | −3.23329 | ||||||||
\(45\) | 19.4624 | 2.90128 | ||||||||
\(46\) | −12.3662 | −1.82330 | ||||||||
\(47\) | −10.9631 | −1.59914 | −0.799569 | − | 0.600574i | \(-0.794939\pi\) | ||||
−0.799569 | + | 0.600574i | \(0.794939\pi\) | |||||||
\(48\) | 32.0308 | 4.62325 | ||||||||
\(49\) | −5.82681 | −0.832401 | ||||||||
\(50\) | −21.5744 | −3.05107 | ||||||||
\(51\) | 5.26412 | 0.737124 | ||||||||
\(52\) | 28.0331 | 3.88749 | ||||||||
\(53\) | 4.13375 | 0.567814 | 0.283907 | − | 0.958852i | \(-0.408369\pi\) | ||||
0.283907 | + | 0.958852i | \(0.408369\pi\) | |||||||
\(54\) | −18.1284 | −2.46697 | ||||||||
\(55\) | −15.5258 | −2.09349 | ||||||||
\(56\) | −8.62902 | −1.15310 | ||||||||
\(57\) | −22.4400 | −2.97225 | ||||||||
\(58\) | −24.0209 | −3.15410 | ||||||||
\(59\) | 14.6491 | 1.90716 | 0.953578 | − | 0.301147i | \(-0.0973694\pi\) | ||||
0.953578 | + | 0.301147i | \(0.0973694\pi\) | |||||||
\(60\) | 52.5414 | 6.78306 | ||||||||
\(61\) | −11.0384 | −1.41332 | −0.706658 | − | 0.707555i | \(-0.749798\pi\) | ||||
−0.706658 | + | 0.707555i | \(0.749798\pi\) | |||||||
\(62\) | −15.5020 | −1.96876 | ||||||||
\(63\) | 5.81344 | 0.732425 | ||||||||
\(64\) | 13.2846 | 1.66058 | ||||||||
\(65\) | 20.2933 | 2.51708 | ||||||||
\(66\) | 32.7891 | 4.03606 | ||||||||
\(67\) | −6.78760 | −0.829237 | −0.414618 | − | 0.909995i | \(-0.636085\pi\) | ||||
−0.414618 | + | 0.909995i | \(0.636085\pi\) | |||||||
\(68\) | 9.11589 | 1.10546 | ||||||||
\(69\) | 13.5112 | 1.62656 | ||||||||
\(70\) | −10.3983 | −1.24284 | ||||||||
\(71\) | −5.11064 | −0.606521 | −0.303261 | − | 0.952908i | \(-0.598075\pi\) | ||||
−0.303261 | + | 0.952908i | \(0.598075\pi\) | |||||||
\(72\) | −42.7588 | −5.03918 | ||||||||
\(73\) | −13.7830 | −1.61317 | −0.806587 | − | 0.591116i | \(-0.798688\pi\) | ||||
−0.806587 | + | 0.591116i | \(0.798688\pi\) | |||||||
\(74\) | 0.200793 | 0.0233417 | ||||||||
\(75\) | 23.5719 | 2.72185 | ||||||||
\(76\) | −38.8595 | −4.45749 | ||||||||
\(77\) | −4.63758 | −0.528501 | ||||||||
\(78\) | −42.8578 | −4.85269 | ||||||||
\(79\) | −5.34405 | −0.601252 | −0.300626 | − | 0.953742i | \(-0.597196\pi\) | ||||
−0.300626 | + | 0.953742i | \(0.597196\pi\) | |||||||
\(80\) | 40.1535 | 4.48930 | ||||||||
\(81\) | 3.70534 | 0.411704 | ||||||||
\(82\) | −22.8435 | −2.52264 | ||||||||
\(83\) | −10.2636 | −1.12658 | −0.563288 | − | 0.826261i | \(-0.690464\pi\) | ||||
−0.563288 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(84\) | 15.6942 | 1.71238 | ||||||||
\(85\) | 6.59905 | 0.715768 | ||||||||
\(86\) | 14.7727 | 1.59298 | ||||||||
\(87\) | 26.2450 | 2.81376 | ||||||||
\(88\) | 34.1101 | 3.63615 | ||||||||
\(89\) | 0.730464 | 0.0774290 | 0.0387145 | − | 0.999250i | \(-0.487674\pi\) | ||||
0.0387145 | + | 0.999250i | \(0.487674\pi\) | |||||||
\(90\) | −51.5262 | −5.43134 | ||||||||
\(91\) | 6.06166 | 0.635434 | ||||||||
\(92\) | 23.3975 | 2.43935 | ||||||||
\(93\) | 16.9374 | 1.75632 | ||||||||
\(94\) | 29.0247 | 2.99367 | ||||||||
\(95\) | −28.1306 | −2.88614 | ||||||||
\(96\) | −38.7119 | −3.95101 | ||||||||
\(97\) | 9.43142 | 0.957616 | 0.478808 | − | 0.877920i | \(-0.341069\pi\) | ||||
0.478808 | + | 0.877920i | \(0.341069\pi\) | |||||||
\(98\) | 15.4264 | 1.55830 | ||||||||
\(99\) | −22.9803 | −2.30961 | ||||||||
\(100\) | 40.8196 | 4.08196 | ||||||||
\(101\) | −6.89393 | −0.685972 | −0.342986 | − | 0.939341i | \(-0.611438\pi\) | ||||
−0.342986 | + | 0.939341i | \(0.611438\pi\) | |||||||
\(102\) | −13.9366 | −1.37993 | ||||||||
\(103\) | 12.3202 | 1.21395 | 0.606974 | − | 0.794722i | \(-0.292383\pi\) | ||||
0.606974 | + | 0.794722i | \(0.292383\pi\) | |||||||
\(104\) | −44.5845 | −4.37187 | ||||||||
\(105\) | 11.3611 | 1.10873 | ||||||||
\(106\) | −10.9440 | −1.06298 | ||||||||
\(107\) | 10.0047 | 0.967190 | 0.483595 | − | 0.875292i | \(-0.339331\pi\) | ||||
0.483595 | + | 0.875292i | \(0.339331\pi\) | |||||||
\(108\) | 34.2998 | 3.30050 | ||||||||
\(109\) | −1.52346 | −0.145921 | −0.0729603 | − | 0.997335i | \(-0.523245\pi\) | ||||
−0.0729603 | + | 0.997335i | \(0.523245\pi\) | |||||||
\(110\) | 41.1042 | 3.91913 | ||||||||
\(111\) | −0.219384 | −0.0208230 | ||||||||
\(112\) | 11.9939 | 1.13332 | ||||||||
\(113\) | 3.01613 | 0.283734 | 0.141867 | − | 0.989886i | \(-0.454690\pi\) | ||||
0.141867 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(114\) | 59.4095 | 5.56421 | ||||||||
\(115\) | 16.9376 | 1.57944 | ||||||||
\(116\) | 45.4486 | 4.21980 | ||||||||
\(117\) | 30.0369 | 2.77692 | ||||||||
\(118\) | −38.7833 | −3.57029 | ||||||||
\(119\) | 1.97115 | 0.180695 | ||||||||
\(120\) | −83.5630 | −7.62822 | ||||||||
\(121\) | 7.33214 | 0.666559 | ||||||||
\(122\) | 29.2238 | 2.64580 | ||||||||
\(123\) | 24.9586 | 2.25044 | ||||||||
\(124\) | 29.3305 | 2.63396 | ||||||||
\(125\) | 11.4188 | 1.02133 | ||||||||
\(126\) | −15.3910 | −1.37114 | ||||||||
\(127\) | −0.197600 | −0.0175341 | −0.00876707 | − | 0.999962i | \(-0.502791\pi\) | ||||
−0.00876707 | + | 0.999962i | \(0.502791\pi\) | |||||||
\(128\) | −8.40482 | −0.742889 | ||||||||
\(129\) | −16.1405 | −1.42109 | ||||||||
\(130\) | −53.7262 | −4.71210 | ||||||||
\(131\) | 6.83446 | 0.597130 | 0.298565 | − | 0.954389i | \(-0.403492\pi\) | ||||
0.298565 | + | 0.954389i | \(0.403492\pi\) | |||||||
\(132\) | −62.0385 | −5.39976 | ||||||||
\(133\) | −8.40267 | −0.728604 | ||||||||
\(134\) | 17.9700 | 1.55237 | ||||||||
\(135\) | 24.8299 | 2.13701 | ||||||||
\(136\) | −14.4981 | −1.24320 | ||||||||
\(137\) | 16.3806 | 1.39949 | 0.699744 | − | 0.714393i | \(-0.253297\pi\) | ||||
0.699744 | + | 0.714393i | \(0.253297\pi\) | |||||||
\(138\) | −35.7707 | −3.04501 | ||||||||
\(139\) | −0.374348 | −0.0317517 | −0.0158759 | − | 0.999874i | \(-0.505054\pi\) | ||||
−0.0158759 | + | 0.999874i | \(0.505054\pi\) | |||||||
\(140\) | 19.6741 | 1.66277 | ||||||||
\(141\) | −31.7121 | −2.67064 | ||||||||
\(142\) | 13.5303 | 1.13544 | ||||||||
\(143\) | −23.9615 | −2.00376 | ||||||||
\(144\) | 59.4328 | 4.95273 | ||||||||
\(145\) | 32.9005 | 2.73224 | ||||||||
\(146\) | 36.4901 | 3.01994 | ||||||||
\(147\) | −16.8547 | −1.39015 | ||||||||
\(148\) | −0.379909 | −0.0312283 | ||||||||
\(149\) | 3.75611 | 0.307712 | 0.153856 | − | 0.988093i | \(-0.450831\pi\) | ||||
0.153856 | + | 0.988093i | \(0.450831\pi\) | |||||||
\(150\) | −62.4063 | −5.09545 | ||||||||
\(151\) | −5.76659 | −0.469278 | −0.234639 | − | 0.972083i | \(-0.575391\pi\) | ||||
−0.234639 | + | 0.972083i | \(0.575391\pi\) | |||||||
\(152\) | 61.8030 | 5.01289 | ||||||||
\(153\) | 9.76751 | 0.789656 | ||||||||
\(154\) | 12.2779 | 0.989381 | ||||||||
\(155\) | 21.2325 | 1.70544 | ||||||||
\(156\) | 81.0889 | 6.49231 | ||||||||
\(157\) | −14.9576 | −1.19375 | −0.596873 | − | 0.802336i | \(-0.703590\pi\) | ||||
−0.596873 | + | 0.802336i | \(0.703590\pi\) | |||||||
\(158\) | 14.1483 | 1.12557 | ||||||||
\(159\) | 11.9573 | 0.948279 | ||||||||
\(160\) | −48.5289 | −3.83655 | ||||||||
\(161\) | 5.05928 | 0.398727 | ||||||||
\(162\) | −9.80982 | −0.770732 | ||||||||
\(163\) | −19.7624 | −1.54791 | −0.773957 | − | 0.633238i | \(-0.781725\pi\) | ||||
−0.773957 | + | 0.633238i | \(0.781725\pi\) | |||||||
\(164\) | 43.2209 | 3.37498 | ||||||||
\(165\) | −44.9101 | −3.49624 | ||||||||
\(166\) | 27.1727 | 2.10901 | ||||||||
\(167\) | −13.0546 | −1.01020 | −0.505099 | − | 0.863061i | \(-0.668544\pi\) | ||||
−0.505099 | + | 0.863061i | \(0.668544\pi\) | |||||||
\(168\) | −24.9604 | −1.92574 | ||||||||
\(169\) | 18.3194 | 1.40919 | ||||||||
\(170\) | −17.4709 | −1.33995 | ||||||||
\(171\) | −41.6372 | −3.18408 | ||||||||
\(172\) | −27.9505 | −2.13121 | ||||||||
\(173\) | −22.4559 | −1.70729 | −0.853646 | − | 0.520854i | \(-0.825614\pi\) | ||||
−0.853646 | + | 0.520854i | \(0.825614\pi\) | |||||||
\(174\) | −69.4831 | −5.26750 | ||||||||
\(175\) | 8.82652 | 0.667222 | ||||||||
\(176\) | −47.4115 | −3.57378 | ||||||||
\(177\) | 42.3743 | 3.18505 | ||||||||
\(178\) | −1.93389 | −0.144951 | ||||||||
\(179\) | 13.2450 | 0.989977 | 0.494988 | − | 0.868900i | \(-0.335172\pi\) | ||||
0.494988 | + | 0.868900i | \(0.335172\pi\) | |||||||
\(180\) | 97.4899 | 7.26647 | ||||||||
\(181\) | 14.1328 | 1.05048 | 0.525242 | − | 0.850953i | \(-0.323975\pi\) | ||||
0.525242 | + | 0.850953i | \(0.323975\pi\) | |||||||
\(182\) | −16.0481 | −1.18957 | ||||||||
\(183\) | −31.9297 | −2.36031 | ||||||||
\(184\) | −37.2119 | −2.74330 | ||||||||
\(185\) | −0.275019 | −0.0202198 | ||||||||
\(186\) | −44.8413 | −3.28793 | ||||||||
\(187\) | −7.79187 | −0.569798 | ||||||||
\(188\) | −54.9160 | −4.00516 | ||||||||
\(189\) | 7.41673 | 0.539488 | ||||||||
\(190\) | 74.4753 | 5.40300 | ||||||||
\(191\) | −5.81177 | −0.420525 | −0.210263 | − | 0.977645i | \(-0.567432\pi\) | ||||
−0.210263 | + | 0.977645i | \(0.567432\pi\) | |||||||
\(192\) | 38.4273 | 2.77326 | ||||||||
\(193\) | 7.21340 | 0.519232 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(194\) | −24.9695 | −1.79271 | ||||||||
\(195\) | 58.7008 | 4.20365 | ||||||||
\(196\) | −29.1874 | −2.08481 | ||||||||
\(197\) | −6.42877 | −0.458031 | −0.229015 | − | 0.973423i | \(-0.573551\pi\) | ||||
−0.229015 | + | 0.973423i | \(0.573551\pi\) | |||||||
\(198\) | 60.8399 | 4.32370 | ||||||||
\(199\) | 26.7237 | 1.89439 | 0.947197 | − | 0.320651i | \(-0.103902\pi\) | ||||
0.947197 | + | 0.320651i | \(0.103902\pi\) | |||||||
\(200\) | −64.9205 | −4.59057 | ||||||||
\(201\) | −19.6339 | −1.38487 | ||||||||
\(202\) | 18.2515 | 1.28417 | ||||||||
\(203\) | 9.82745 | 0.689752 | ||||||||
\(204\) | 26.3688 | 1.84618 | ||||||||
\(205\) | 31.2879 | 2.18524 | ||||||||
\(206\) | −32.6176 | −2.27257 | ||||||||
\(207\) | 25.0699 | 1.74248 | ||||||||
\(208\) | 61.9704 | 4.29687 | ||||||||
\(209\) | 33.2154 | 2.29756 | ||||||||
\(210\) | −30.0784 | −2.07560 | ||||||||
\(211\) | −8.88244 | −0.611493 | −0.305746 | − | 0.952113i | \(-0.598906\pi\) | ||||
−0.305746 | + | 0.952113i | \(0.598906\pi\) | |||||||
\(212\) | 20.7066 | 1.42213 | ||||||||
\(213\) | −14.7831 | −1.01292 | ||||||||
\(214\) | −26.4872 | −1.81063 | ||||||||
\(215\) | −20.2336 | −1.37992 | ||||||||
\(216\) | −54.5513 | −3.71174 | ||||||||
\(217\) | 6.34220 | 0.430537 | ||||||||
\(218\) | 4.03332 | 0.273171 | ||||||||
\(219\) | −39.8688 | −2.69408 | ||||||||
\(220\) | −77.7710 | −5.24332 | ||||||||
\(221\) | 10.1846 | 0.685087 | ||||||||
\(222\) | 0.580816 | 0.0389818 | ||||||||
\(223\) | −3.25366 | −0.217881 | −0.108941 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108941 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(224\) | −14.4957 | −0.968533 | ||||||||
\(225\) | 43.7375 | 2.91583 | ||||||||
\(226\) | −7.98515 | −0.531164 | ||||||||
\(227\) | 15.1823 | 1.00768 | 0.503842 | − | 0.863796i | \(-0.331919\pi\) | ||||
0.503842 | + | 0.863796i | \(0.331919\pi\) | |||||||
\(228\) | −112.405 | −7.44423 | ||||||||
\(229\) | −2.33262 | −0.154144 | −0.0770719 | − | 0.997026i | \(-0.524557\pi\) | ||||
−0.0770719 | + | 0.997026i | \(0.524557\pi\) | |||||||
\(230\) | −44.8419 | −2.95679 | ||||||||
\(231\) | −13.4147 | −0.882624 | ||||||||
\(232\) | −72.2825 | −4.74558 | ||||||||
\(233\) | −9.45867 | −0.619658 | −0.309829 | − | 0.950792i | \(-0.600272\pi\) | ||||
−0.309829 | + | 0.950792i | \(0.600272\pi\) | |||||||
\(234\) | −79.5222 | −5.19853 | ||||||||
\(235\) | −39.7541 | −2.59327 | ||||||||
\(236\) | 73.3798 | 4.77662 | ||||||||
\(237\) | −15.4583 | −1.00412 | ||||||||
\(238\) | −5.21858 | −0.338270 | ||||||||
\(239\) | −26.7926 | −1.73307 | −0.866533 | − | 0.499119i | \(-0.833657\pi\) | ||||
−0.866533 | + | 0.499119i | \(0.833657\pi\) | |||||||
\(240\) | 116.149 | 7.49736 | ||||||||
\(241\) | −13.6719 | −0.880686 | −0.440343 | − | 0.897830i | \(-0.645143\pi\) | ||||
−0.440343 | + | 0.897830i | \(0.645143\pi\) | |||||||
\(242\) | −19.4117 | −1.24783 | ||||||||
\(243\) | −9.82418 | −0.630222 | ||||||||
\(244\) | −55.2928 | −3.53976 | ||||||||
\(245\) | −21.1289 | −1.34988 | ||||||||
\(246\) | −66.0774 | −4.21294 | ||||||||
\(247\) | −43.4150 | −2.76243 | ||||||||
\(248\) | −46.6479 | −2.96215 | ||||||||
\(249\) | −29.6886 | −1.88144 | ||||||||
\(250\) | −30.2311 | −1.91198 | ||||||||
\(251\) | −5.25740 | −0.331844 | −0.165922 | − | 0.986139i | \(-0.553060\pi\) | ||||
−0.165922 | + | 0.986139i | \(0.553060\pi\) | |||||||
\(252\) | 29.1204 | 1.83441 | ||||||||
\(253\) | −19.9991 | −1.25733 | ||||||||
\(254\) | 0.523141 | 0.0328248 | ||||||||
\(255\) | 19.0885 | 1.19537 | ||||||||
\(256\) | −4.31769 | −0.269855 | ||||||||
\(257\) | 2.72408 | 0.169923 | 0.0849616 | − | 0.996384i | \(-0.472923\pi\) | ||||
0.0849616 | + | 0.996384i | \(0.472923\pi\) | |||||||
\(258\) | 42.7316 | 2.66035 | ||||||||
\(259\) | −0.0821486 | −0.00510446 | ||||||||
\(260\) | 101.652 | 6.30422 | ||||||||
\(261\) | 48.6973 | 3.01429 | ||||||||
\(262\) | −18.0941 | −1.11786 | ||||||||
\(263\) | 9.87419 | 0.608869 | 0.304434 | − | 0.952533i | \(-0.401533\pi\) | ||||
0.304434 | + | 0.952533i | \(0.401533\pi\) | |||||||
\(264\) | 98.6675 | 6.07256 | ||||||||
\(265\) | 14.9896 | 0.920805 | ||||||||
\(266\) | 22.2459 | 1.36398 | ||||||||
\(267\) | 2.11295 | 0.129310 | ||||||||
\(268\) | −34.0001 | −2.07689 | ||||||||
\(269\) | −1.39306 | −0.0849364 | −0.0424682 | − | 0.999098i | \(-0.513522\pi\) | ||||
−0.0424682 | + | 0.999098i | \(0.513522\pi\) | |||||||
\(270\) | −65.7366 | −4.00060 | ||||||||
\(271\) | 22.6658 | 1.37685 | 0.688425 | − | 0.725307i | \(-0.258302\pi\) | ||||
0.688425 | + | 0.725307i | \(0.258302\pi\) | |||||||
\(272\) | 20.1517 | 1.22188 | ||||||||
\(273\) | 17.5340 | 1.06121 | ||||||||
\(274\) | −43.3673 | −2.61991 | ||||||||
\(275\) | −34.8909 | −2.10400 | ||||||||
\(276\) | 67.6798 | 4.07385 | ||||||||
\(277\) | 21.4396 | 1.28818 | 0.644090 | − | 0.764949i | \(-0.277236\pi\) | ||||
0.644090 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(278\) | 0.991078 | 0.0594409 | ||||||||
\(279\) | 31.4271 | 1.88149 | ||||||||
\(280\) | −31.2902 | −1.86995 | ||||||||
\(281\) | 24.5703 | 1.46574 | 0.732870 | − | 0.680368i | \(-0.238180\pi\) | ||||
0.732870 | + | 0.680368i | \(0.238180\pi\) | |||||||
\(282\) | 83.9572 | 4.99958 | ||||||||
\(283\) | 9.30052 | 0.552859 | 0.276429 | − | 0.961034i | \(-0.410849\pi\) | ||||
0.276429 | + | 0.961034i | \(0.410849\pi\) | |||||||
\(284\) | −25.6000 | −1.51908 | ||||||||
\(285\) | −81.3710 | −4.82000 | ||||||||
\(286\) | 63.4375 | 3.75114 | ||||||||
\(287\) | 9.34575 | 0.551662 | ||||||||
\(288\) | −71.8295 | −4.23259 | ||||||||
\(289\) | −13.6882 | −0.805186 | ||||||||
\(290\) | −87.1035 | −5.11489 | ||||||||
\(291\) | 27.2815 | 1.59927 | ||||||||
\(292\) | −69.0410 | −4.04032 | ||||||||
\(293\) | 15.8700 | 0.927137 | 0.463569 | − | 0.886061i | \(-0.346569\pi\) | ||||
0.463569 | + | 0.886061i | \(0.346569\pi\) | |||||||
\(294\) | 44.6225 | 2.60244 | ||||||||
\(295\) | 53.1201 | 3.09277 | ||||||||
\(296\) | 0.604216 | 0.0351193 | ||||||||
\(297\) | −29.3180 | −1.70120 | ||||||||
\(298\) | −9.94421 | −0.576053 | ||||||||
\(299\) | 26.1404 | 1.51174 | ||||||||
\(300\) | 118.075 | 6.81709 | ||||||||
\(301\) | −6.04380 | −0.348359 | ||||||||
\(302\) | 15.2669 | 0.878513 | ||||||||
\(303\) | −19.9415 | −1.14561 | ||||||||
\(304\) | −85.9033 | −4.92689 | ||||||||
\(305\) | −40.0268 | −2.29193 | ||||||||
\(306\) | −25.8593 | −1.47828 | ||||||||
\(307\) | −8.17943 | −0.466825 | −0.233412 | − | 0.972378i | \(-0.574989\pi\) | ||||
−0.233412 | + | 0.972378i | \(0.574989\pi\) | |||||||
\(308\) | −23.2303 | −1.32367 | ||||||||
\(309\) | 35.6377 | 2.02736 | ||||||||
\(310\) | −56.2127 | −3.19267 | ||||||||
\(311\) | 9.29348 | 0.526985 | 0.263492 | − | 0.964661i | \(-0.415126\pi\) | ||||
0.263492 | + | 0.964661i | \(0.415126\pi\) | |||||||
\(312\) | −128.966 | −7.30125 | ||||||||
\(313\) | 25.2307 | 1.42612 | 0.713062 | − | 0.701101i | \(-0.247308\pi\) | ||||
0.713062 | + | 0.701101i | \(0.247308\pi\) | |||||||
\(314\) | 39.5999 | 2.23475 | ||||||||
\(315\) | 21.0805 | 1.18775 | ||||||||
\(316\) | −26.7691 | −1.50588 | ||||||||
\(317\) | −12.3336 | −0.692726 | −0.346363 | − | 0.938101i | \(-0.612583\pi\) | ||||
−0.346363 | + | 0.938101i | \(0.612583\pi\) | |||||||
\(318\) | −31.6568 | −1.77523 | ||||||||
\(319\) | −38.8475 | −2.17504 | ||||||||
\(320\) | 48.1722 | 2.69291 | ||||||||
\(321\) | 28.9397 | 1.61526 | ||||||||
\(322\) | −13.3944 | −0.746438 | ||||||||
\(323\) | −14.1178 | −0.785537 | ||||||||
\(324\) | 18.5606 | 1.03115 | ||||||||
\(325\) | 45.6049 | 2.52971 | ||||||||
\(326\) | 52.3207 | 2.89777 | ||||||||
\(327\) | −4.40677 | −0.243695 | ||||||||
\(328\) | −68.7395 | −3.79550 | ||||||||
\(329\) | −11.8746 | −0.654669 | ||||||||
\(330\) | 118.899 | 6.54515 | ||||||||
\(331\) | −9.53761 | −0.524234 | −0.262117 | − | 0.965036i | \(-0.584421\pi\) | ||||
−0.262117 | + | 0.965036i | \(0.584421\pi\) | |||||||
\(332\) | −51.4119 | −2.82159 | ||||||||
\(333\) | −0.407065 | −0.0223070 | ||||||||
\(334\) | 34.5619 | 1.89114 | ||||||||
\(335\) | −24.6129 | −1.34475 | ||||||||
\(336\) | 34.6938 | 1.89270 | ||||||||
\(337\) | 15.3667 | 0.837076 | 0.418538 | − | 0.908199i | \(-0.362543\pi\) | ||||
0.418538 | + | 0.908199i | \(0.362543\pi\) | |||||||
\(338\) | −48.5003 | −2.63807 | ||||||||
\(339\) | 8.72450 | 0.473850 | ||||||||
\(340\) | 33.0557 | 1.79269 | ||||||||
\(341\) | −25.0704 | −1.35764 | ||||||||
\(342\) | 110.234 | 5.96076 | ||||||||
\(343\) | −13.8932 | −0.750164 | ||||||||
\(344\) | 44.4532 | 2.39675 | ||||||||
\(345\) | 48.9938 | 2.63774 | ||||||||
\(346\) | 59.4516 | 3.19614 | ||||||||
\(347\) | −7.15827 | −0.384276 | −0.192138 | − | 0.981368i | \(-0.561542\pi\) | ||||
−0.192138 | + | 0.981368i | \(0.561542\pi\) | |||||||
\(348\) | 131.465 | 7.04728 | ||||||||
\(349\) | −15.6055 | −0.835343 | −0.417671 | − | 0.908598i | \(-0.637154\pi\) | ||||
−0.417671 | + | 0.908598i | \(0.637154\pi\) | |||||||
\(350\) | −23.3680 | −1.24907 | ||||||||
\(351\) | 38.3208 | 2.04541 | ||||||||
\(352\) | 57.3008 | 3.05414 | ||||||||
\(353\) | −35.1808 | −1.87248 | −0.936242 | − | 0.351356i | \(-0.885721\pi\) | ||||
−0.936242 | + | 0.351356i | \(0.885721\pi\) | |||||||
\(354\) | −112.185 | −5.96257 | ||||||||
\(355\) | −18.5320 | −0.983576 | ||||||||
\(356\) | 3.65900 | 0.193927 | ||||||||
\(357\) | 5.70177 | 0.301770 | ||||||||
\(358\) | −35.0658 | −1.85329 | ||||||||
\(359\) | 12.9142 | 0.681583 | 0.340792 | − | 0.940139i | \(-0.389305\pi\) | ||||
0.340792 | + | 0.940139i | \(0.389305\pi\) | |||||||
\(360\) | −155.050 | −8.17186 | ||||||||
\(361\) | 41.1818 | 2.16747 | ||||||||
\(362\) | −37.4163 | −1.96656 | ||||||||
\(363\) | 21.2091 | 1.11319 | ||||||||
\(364\) | 30.3638 | 1.59149 | ||||||||
\(365\) | −49.9792 | −2.61603 | ||||||||
\(366\) | 84.5332 | 4.41862 | ||||||||
\(367\) | −22.6161 | −1.18055 | −0.590275 | − | 0.807202i | \(-0.700981\pi\) | ||||
−0.590275 | + | 0.807202i | \(0.700981\pi\) | |||||||
\(368\) | 51.7228 | 2.69624 | ||||||||
\(369\) | 46.3104 | 2.41082 | ||||||||
\(370\) | 0.728106 | 0.0378524 | ||||||||
\(371\) | 4.47743 | 0.232457 | ||||||||
\(372\) | 84.8418 | 4.39884 | ||||||||
\(373\) | −17.6455 | −0.913650 | −0.456825 | − | 0.889557i | \(-0.651013\pi\) | ||||
−0.456825 | + | 0.889557i | \(0.651013\pi\) | |||||||
\(374\) | 20.6288 | 1.06669 | ||||||||
\(375\) | 33.0302 | 1.70567 | ||||||||
\(376\) | 87.3397 | 4.50420 | ||||||||
\(377\) | 50.7765 | 2.61513 | ||||||||
\(378\) | −19.6356 | −1.00995 | ||||||||
\(379\) | −19.0429 | −0.978167 | −0.489083 | − | 0.872237i | \(-0.662669\pi\) | ||||
−0.489083 | + | 0.872237i | \(0.662669\pi\) | |||||||
\(380\) | −140.911 | −7.22856 | ||||||||
\(381\) | −0.571580 | −0.0292829 | ||||||||
\(382\) | 15.3866 | 0.787245 | ||||||||
\(383\) | −12.9167 | −0.660010 | −0.330005 | − | 0.943979i | \(-0.607051\pi\) | ||||
−0.330005 | + | 0.943979i | \(0.607051\pi\) | |||||||
\(384\) | −24.3119 | −1.24066 | ||||||||
\(385\) | −16.8166 | −0.857052 | ||||||||
\(386\) | −19.0973 | −0.972028 | ||||||||
\(387\) | −29.9485 | −1.52237 | ||||||||
\(388\) | 47.2434 | 2.39842 | ||||||||
\(389\) | 29.7573 | 1.50875 | 0.754376 | − | 0.656442i | \(-0.227939\pi\) | ||||
0.754376 | + | 0.656442i | \(0.227939\pi\) | |||||||
\(390\) | −155.409 | −7.86945 | ||||||||
\(391\) | 8.50040 | 0.429884 | ||||||||
\(392\) | 46.4203 | 2.34458 | ||||||||
\(393\) | 19.7695 | 0.997237 | ||||||||
\(394\) | 17.0200 | 0.857458 | ||||||||
\(395\) | −19.3783 | −0.975030 | ||||||||
\(396\) | −115.112 | −5.78458 | ||||||||
\(397\) | 22.3698 | 1.12271 | 0.561355 | − | 0.827575i | \(-0.310280\pi\) | ||||
0.561355 | + | 0.827575i | \(0.310280\pi\) | |||||||
\(398\) | −70.7505 | −3.54640 | ||||||||
\(399\) | −24.3057 | −1.21681 | ||||||||
\(400\) | 90.2365 | 4.51182 | ||||||||
\(401\) | −11.6158 | −0.580066 | −0.290033 | − | 0.957017i | \(-0.593666\pi\) | ||||
−0.290033 | + | 0.957017i | \(0.593666\pi\) | |||||||
\(402\) | 51.9803 | 2.59254 | ||||||||
\(403\) | 32.7689 | 1.63234 | ||||||||
\(404\) | −34.5328 | −1.71807 | ||||||||
\(405\) | 13.4361 | 0.667647 | ||||||||
\(406\) | −26.0180 | −1.29125 | ||||||||
\(407\) | 0.324730 | 0.0160963 | ||||||||
\(408\) | −41.9375 | −2.07621 | ||||||||
\(409\) | 12.9847 | 0.642051 | 0.321025 | − | 0.947071i | \(-0.395973\pi\) | ||||
0.321025 | + | 0.947071i | \(0.395973\pi\) | |||||||
\(410\) | −82.8340 | −4.09088 | ||||||||
\(411\) | 47.3827 | 2.33722 | ||||||||
\(412\) | 61.7139 | 3.04042 | ||||||||
\(413\) | 15.8671 | 0.780767 | ||||||||
\(414\) | −66.3722 | −3.26202 | ||||||||
\(415\) | −37.2174 | −1.82693 | ||||||||
\(416\) | −74.8964 | −3.67210 | ||||||||
\(417\) | −1.08284 | −0.0530270 | ||||||||
\(418\) | −87.9371 | −4.30114 | ||||||||
\(419\) | −3.17947 | −0.155327 | −0.0776635 | − | 0.996980i | \(-0.524746\pi\) | ||||
−0.0776635 | + | 0.996980i | \(0.524746\pi\) | |||||||
\(420\) | 56.9096 | 2.77691 | ||||||||
\(421\) | 6.80322 | 0.331569 | 0.165784 | − | 0.986162i | \(-0.446984\pi\) | ||||
0.165784 | + | 0.986162i | \(0.446984\pi\) | |||||||
\(422\) | 23.5161 | 1.14475 | ||||||||
\(423\) | −58.8415 | −2.86097 | ||||||||
\(424\) | −32.9322 | −1.59933 | ||||||||
\(425\) | 14.8300 | 0.719359 | ||||||||
\(426\) | 39.1380 | 1.89624 | ||||||||
\(427\) | −11.9561 | −0.578595 | ||||||||
\(428\) | 50.1150 | 2.42240 | ||||||||
\(429\) | −69.3113 | −3.34638 | ||||||||
\(430\) | 53.5679 | 2.58328 | ||||||||
\(431\) | −3.44615 | −0.165995 | −0.0829975 | − | 0.996550i | \(-0.526449\pi\) | ||||
−0.0829975 | + | 0.996550i | \(0.526449\pi\) | |||||||
\(432\) | 75.8237 | 3.64807 | ||||||||
\(433\) | −8.31846 | −0.399760 | −0.199880 | − | 0.979820i | \(-0.564055\pi\) | ||||
−0.199880 | + | 0.979820i | \(0.564055\pi\) | |||||||
\(434\) | −16.7908 | −0.805987 | ||||||||
\(435\) | 95.1685 | 4.56298 | ||||||||
\(436\) | −7.63122 | −0.365469 | ||||||||
\(437\) | −36.2358 | −1.73339 | ||||||||
\(438\) | 105.552 | 5.04346 | ||||||||
\(439\) | −12.8921 | −0.615306 | −0.307653 | − | 0.951499i | \(-0.599544\pi\) | ||||
−0.307653 | + | 0.951499i | \(0.599544\pi\) | |||||||
\(440\) | 123.689 | 5.89663 | ||||||||
\(441\) | −31.2737 | −1.48922 | ||||||||
\(442\) | −26.9634 | −1.28252 | ||||||||
\(443\) | 7.60334 | 0.361245 | 0.180623 | − | 0.983552i | \(-0.442189\pi\) | ||||
0.180623 | + | 0.983552i | \(0.442189\pi\) | |||||||
\(444\) | −1.09893 | −0.0521529 | ||||||||
\(445\) | 2.64878 | 0.125564 | ||||||||
\(446\) | 8.61400 | 0.407885 | ||||||||
\(447\) | 10.8650 | 0.513895 | ||||||||
\(448\) | 14.3891 | 0.679823 | ||||||||
\(449\) | −33.5784 | −1.58466 | −0.792331 | − | 0.610091i | \(-0.791133\pi\) | ||||
−0.792331 | + | 0.610091i | \(0.791133\pi\) | |||||||
\(450\) | −115.794 | −5.45859 | ||||||||
\(451\) | −36.9433 | −1.73959 | ||||||||
\(452\) | 15.1083 | 0.710633 | ||||||||
\(453\) | −16.6805 | −0.783719 | ||||||||
\(454\) | −40.1948 | −1.88644 | ||||||||
\(455\) | 21.9805 | 1.03046 | ||||||||
\(456\) | 178.772 | 8.37178 | ||||||||
\(457\) | 21.3349 | 0.998004 | 0.499002 | − | 0.866601i | \(-0.333700\pi\) | ||||
0.499002 | + | 0.866601i | \(0.333700\pi\) | |||||||
\(458\) | 6.17557 | 0.288565 | ||||||||
\(459\) | 12.4613 | 0.581643 | ||||||||
\(460\) | 84.8429 | 3.95582 | ||||||||
\(461\) | 14.1583 | 0.659419 | 0.329709 | − | 0.944082i | \(-0.393049\pi\) | ||||
0.329709 | + | 0.944082i | \(0.393049\pi\) | |||||||
\(462\) | 35.5152 | 1.65232 | ||||||||
\(463\) | −36.8277 | −1.71153 | −0.855764 | − | 0.517367i | \(-0.826912\pi\) | ||||
−0.855764 | + | 0.517367i | \(0.826912\pi\) | |||||||
\(464\) | 100.469 | 4.66417 | ||||||||
\(465\) | 61.4175 | 2.84817 | ||||||||
\(466\) | 25.0416 | 1.16003 | ||||||||
\(467\) | 24.9682 | 1.15539 | 0.577696 | − | 0.816252i | \(-0.303952\pi\) | ||||
0.577696 | + | 0.816252i | \(0.303952\pi\) | |||||||
\(468\) | 150.460 | 6.95500 | ||||||||
\(469\) | −7.35192 | −0.339480 | ||||||||
\(470\) | 105.248 | 4.85473 | ||||||||
\(471\) | −43.2665 | −1.99362 | ||||||||
\(472\) | −116.705 | −5.37178 | ||||||||
\(473\) | 23.8909 | 1.09850 | ||||||||
\(474\) | 40.9254 | 1.87977 | ||||||||
\(475\) | −63.2176 | −2.90062 | ||||||||
\(476\) | 9.87379 | 0.452564 | ||||||||
\(477\) | 22.1867 | 1.01586 | ||||||||
\(478\) | 70.9328 | 3.24439 | ||||||||
\(479\) | −18.6823 | −0.853618 | −0.426809 | − | 0.904342i | \(-0.640362\pi\) | ||||
−0.426809 | + | 0.904342i | \(0.640362\pi\) | |||||||
\(480\) | −140.375 | −6.40723 | ||||||||
\(481\) | −0.424446 | −0.0193531 | ||||||||
\(482\) | 36.1962 | 1.64869 | ||||||||
\(483\) | 14.6346 | 0.665895 | ||||||||
\(484\) | 36.7278 | 1.66945 | ||||||||
\(485\) | 34.1998 | 1.55293 | ||||||||
\(486\) | 26.0093 | 1.17981 | ||||||||
\(487\) | 12.4357 | 0.563515 | 0.281757 | − | 0.959486i | \(-0.409083\pi\) | ||||
0.281757 | + | 0.959486i | \(0.409083\pi\) | |||||||
\(488\) | 87.9389 | 3.98081 | ||||||||
\(489\) | −57.1651 | −2.58510 | ||||||||
\(490\) | 55.9384 | 2.52704 | ||||||||
\(491\) | 4.15707 | 0.187606 | 0.0938031 | − | 0.995591i | \(-0.470098\pi\) | ||||
0.0938031 | + | 0.995591i | \(0.470098\pi\) | |||||||
\(492\) | 125.021 | 5.63640 | ||||||||
\(493\) | 16.5117 | 0.743649 | ||||||||
\(494\) | 114.940 | 5.17141 | ||||||||
\(495\) | −83.3301 | −3.74541 | ||||||||
\(496\) | 64.8384 | 2.91133 | ||||||||
\(497\) | −5.53554 | −0.248303 | ||||||||
\(498\) | 78.6000 | 3.52215 | ||||||||
\(499\) | −6.33437 | −0.283566 | −0.141783 | − | 0.989898i | \(-0.545283\pi\) | ||||
−0.141783 | + | 0.989898i | \(0.545283\pi\) | |||||||
\(500\) | 57.1986 | 2.55800 | ||||||||
\(501\) | −37.7620 | −1.68708 | ||||||||
\(502\) | 13.9189 | 0.621230 | ||||||||
\(503\) | −10.4867 | −0.467579 | −0.233789 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233789 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(504\) | −46.3138 | −2.06298 | ||||||||
\(505\) | −24.9985 | −1.11242 | ||||||||
\(506\) | 52.9473 | 2.35380 | ||||||||
\(507\) | 52.9910 | 2.35341 | ||||||||
\(508\) | −0.989807 | −0.0439156 | ||||||||
\(509\) | −33.5799 | −1.48840 | −0.744202 | − | 0.667954i | \(-0.767170\pi\) | ||||
−0.744202 | + | 0.667954i | \(0.767170\pi\) | |||||||
\(510\) | −50.5365 | −2.23779 | ||||||||
\(511\) | −14.9289 | −0.660415 | ||||||||
\(512\) | 28.2406 | 1.24807 | ||||||||
\(513\) | −53.1203 | −2.34532 | ||||||||
\(514\) | −7.21194 | −0.318105 | ||||||||
\(515\) | 44.6751 | 1.96862 | ||||||||
\(516\) | −80.8501 | −3.55923 | ||||||||
\(517\) | 46.9398 | 2.06441 | ||||||||
\(518\) | 0.217487 | 0.00955582 | ||||||||
\(519\) | −64.9563 | −2.85127 | ||||||||
\(520\) | −161.670 | −7.08971 | ||||||||
\(521\) | 39.4913 | 1.73014 | 0.865072 | − | 0.501649i | \(-0.167273\pi\) | ||||
0.865072 | + | 0.501649i | \(0.167273\pi\) | |||||||
\(522\) | −128.925 | −5.64290 | ||||||||
\(523\) | 40.4774 | 1.76995 | 0.884976 | − | 0.465636i | \(-0.154174\pi\) | ||||
0.884976 | + | 0.465636i | \(0.154174\pi\) | |||||||
\(524\) | 34.2349 | 1.49556 | ||||||||
\(525\) | 25.5317 | 1.11430 | ||||||||
\(526\) | −26.1417 | −1.13983 | ||||||||
\(527\) | 10.6559 | 0.464178 | ||||||||
\(528\) | −137.143 | −5.96839 | ||||||||
\(529\) | −1.18229 | −0.0514041 | ||||||||
\(530\) | −39.6847 | −1.72379 | ||||||||
\(531\) | 78.6251 | 3.41204 | ||||||||
\(532\) | −42.0903 | −1.82484 | ||||||||
\(533\) | 48.2877 | 2.09157 | ||||||||
\(534\) | −5.59399 | −0.242076 | ||||||||
\(535\) | 36.2786 | 1.56846 | ||||||||
\(536\) | 54.0745 | 2.33566 | ||||||||
\(537\) | 38.3126 | 1.65331 | ||||||||
\(538\) | 3.68810 | 0.159005 | ||||||||
\(539\) | 24.9481 | 1.07459 | ||||||||
\(540\) | 124.377 | 5.35232 | ||||||||
\(541\) | 37.5916 | 1.61619 | 0.808094 | − | 0.589054i | \(-0.200499\pi\) | ||||
0.808094 | + | 0.589054i | \(0.200499\pi\) | |||||||
\(542\) | −60.0073 | −2.57753 | ||||||||
\(543\) | 40.8808 | 1.75436 | ||||||||
\(544\) | −24.3550 | −1.04421 | ||||||||
\(545\) | −5.52429 | −0.236635 | ||||||||
\(546\) | −46.4210 | −1.98664 | ||||||||
\(547\) | −16.7892 | −0.717855 | −0.358927 | − | 0.933366i | \(-0.616857\pi\) | ||||
−0.358927 | + | 0.933366i | \(0.616857\pi\) | |||||||
\(548\) | 82.0529 | 3.50513 | ||||||||
\(549\) | −59.2452 | −2.52852 | ||||||||
\(550\) | 92.3729 | 3.93879 | ||||||||
\(551\) | −70.3864 | −2.99856 | ||||||||
\(552\) | −107.640 | −4.58144 | ||||||||
\(553\) | −5.78835 | −0.246146 | ||||||||
\(554\) | −56.7609 | −2.41154 | ||||||||
\(555\) | −0.795522 | −0.0337680 | ||||||||
\(556\) | −1.87516 | −0.0795247 | ||||||||
\(557\) | 5.76993 | 0.244480 | 0.122240 | − | 0.992501i | \(-0.460992\pi\) | ||||
0.122240 | + | 0.992501i | \(0.460992\pi\) | |||||||
\(558\) | −83.2026 | −3.52225 | ||||||||
\(559\) | −31.2272 | −1.32077 | ||||||||
\(560\) | 43.4919 | 1.83787 | ||||||||
\(561\) | −22.5389 | −0.951592 | ||||||||
\(562\) | −65.0494 | −2.74394 | ||||||||
\(563\) | −12.1989 | −0.514124 | −0.257062 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257062 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(564\) | −158.851 | −6.68883 | ||||||||
\(565\) | 10.9370 | 0.460121 | ||||||||
\(566\) | −24.6230 | −1.03498 | ||||||||
\(567\) | 4.01340 | 0.168547 | ||||||||
\(568\) | 40.7148 | 1.70836 | ||||||||
\(569\) | 31.9559 | 1.33966 | 0.669830 | − | 0.742515i | \(-0.266367\pi\) | ||||
0.669830 | + | 0.742515i | \(0.266367\pi\) | |||||||
\(570\) | 215.428 | 9.02329 | ||||||||
\(571\) | −35.2509 | −1.47521 | −0.737603 | − | 0.675234i | \(-0.764042\pi\) | ||||
−0.737603 | + | 0.675234i | \(0.764042\pi\) | |||||||
\(572\) | −120.027 | −5.01857 | ||||||||
\(573\) | −16.8112 | −0.702298 | ||||||||
\(574\) | −24.7427 | −1.03274 | ||||||||
\(575\) | 38.0636 | 1.58736 | ||||||||
\(576\) | 71.3015 | 2.97090 | ||||||||
\(577\) | −17.7779 | −0.740103 | −0.370051 | − | 0.929011i | \(-0.620660\pi\) | ||||
−0.370051 | + | 0.929011i | \(0.620660\pi\) | |||||||
\(578\) | 36.2391 | 1.50735 | ||||||||
\(579\) | 20.8656 | 0.867144 | ||||||||
\(580\) | 164.804 | 6.84310 | ||||||||
\(581\) | −11.1169 | −0.461207 | ||||||||
\(582\) | −72.2271 | −2.99391 | ||||||||
\(583\) | −17.6991 | −0.733021 | ||||||||
\(584\) | 109.804 | 4.54374 | ||||||||
\(585\) | 108.919 | 4.50323 | ||||||||
\(586\) | −42.0156 | −1.73565 | ||||||||
\(587\) | 40.2878 | 1.66285 | 0.831427 | − | 0.555634i | \(-0.187524\pi\) | ||||
0.831427 | + | 0.555634i | \(0.187524\pi\) | |||||||
\(588\) | −84.4278 | −3.48174 | ||||||||
\(589\) | −45.4243 | −1.87167 | ||||||||
\(590\) | −140.634 | −5.78983 | ||||||||
\(591\) | −18.5960 | −0.764935 | ||||||||
\(592\) | −0.839832 | −0.0345169 | ||||||||
\(593\) | 15.8728 | 0.651817 | 0.325908 | − | 0.945401i | \(-0.394330\pi\) | ||||
0.325908 | + | 0.945401i | \(0.394330\pi\) | |||||||
\(594\) | 77.6189 | 3.18474 | ||||||||
\(595\) | 7.14770 | 0.293027 | ||||||||
\(596\) | 18.8149 | 0.770688 | ||||||||
\(597\) | 77.3014 | 3.16374 | ||||||||
\(598\) | −69.2061 | −2.83005 | ||||||||
\(599\) | −8.67101 | −0.354288 | −0.177144 | − | 0.984185i | \(-0.556686\pi\) | ||||
−0.177144 | + | 0.984185i | \(0.556686\pi\) | |||||||
\(600\) | −187.790 | −7.66649 | ||||||||
\(601\) | −26.3945 | −1.07665 | −0.538327 | − | 0.842736i | \(-0.680943\pi\) | ||||
−0.538327 | + | 0.842736i | \(0.680943\pi\) | |||||||
\(602\) | 16.0008 | 0.652146 | ||||||||
\(603\) | −36.4305 | −1.48356 | ||||||||
\(604\) | −28.8857 | −1.17534 | ||||||||
\(605\) | 26.5875 | 1.08094 | ||||||||
\(606\) | 52.7947 | 2.14464 | ||||||||
\(607\) | −4.02326 | −0.163299 | −0.0816496 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816496 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(608\) | 103.821 | 4.21051 | ||||||||
\(609\) | 28.4270 | 1.15192 | ||||||||
\(610\) | 105.970 | 4.29061 | ||||||||
\(611\) | −61.3539 | −2.48211 | ||||||||
\(612\) | 48.9269 | 1.97775 | ||||||||
\(613\) | 5.25999 | 0.212449 | 0.106224 | − | 0.994342i | \(-0.466124\pi\) | ||||
0.106224 | + | 0.994342i | \(0.466124\pi\) | |||||||
\(614\) | 21.6549 | 0.873920 | ||||||||
\(615\) | 90.5037 | 3.64946 | ||||||||
\(616\) | 36.9461 | 1.48860 | ||||||||
\(617\) | −11.6549 | −0.469209 | −0.234604 | − | 0.972091i | \(-0.575379\pi\) | ||||
−0.234604 | + | 0.972091i | \(0.575379\pi\) | |||||||
\(618\) | −94.3500 | −3.79531 | ||||||||
\(619\) | −9.86867 | −0.396656 | −0.198328 | − | 0.980136i | \(-0.563551\pi\) | ||||
−0.198328 | + | 0.980136i | \(0.563551\pi\) | |||||||
\(620\) | 106.357 | 4.27140 | ||||||||
\(621\) | 31.9840 | 1.28347 | ||||||||
\(622\) | −24.6043 | −0.986542 | ||||||||
\(623\) | 0.791194 | 0.0316985 | ||||||||
\(624\) | 179.256 | 7.17600 | ||||||||
\(625\) | 0.661348 | 0.0264539 | ||||||||
\(626\) | −66.7978 | −2.66978 | ||||||||
\(627\) | 96.0793 | 3.83704 | ||||||||
\(628\) | −74.9249 | −2.98983 | ||||||||
\(629\) | −0.138023 | −0.00550332 | ||||||||
\(630\) | −55.8101 | −2.22353 | ||||||||
\(631\) | 4.02347 | 0.160172 | 0.0800859 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800859 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(632\) | 42.5743 | 1.69351 | ||||||||
\(633\) | −25.6935 | −1.02122 | ||||||||
\(634\) | 32.6530 | 1.29682 | ||||||||
\(635\) | −0.716528 | −0.0284345 | ||||||||
\(636\) | 59.8961 | 2.37504 | ||||||||
\(637\) | −32.6090 | −1.29202 | ||||||||
\(638\) | 102.848 | 4.07179 | ||||||||
\(639\) | −27.4299 | −1.08511 | ||||||||
\(640\) | −30.4772 | −1.20472 | ||||||||
\(641\) | 17.7703 | 0.701885 | 0.350942 | − | 0.936397i | \(-0.385861\pi\) | ||||
0.350942 | + | 0.936397i | \(0.385861\pi\) | |||||||
\(642\) | −76.6173 | −3.02384 | ||||||||
\(643\) | 14.3452 | 0.565719 | 0.282860 | − | 0.959161i | \(-0.408717\pi\) | ||||
0.282860 | + | 0.959161i | \(0.408717\pi\) | |||||||
\(644\) | 25.3427 | 0.998643 | ||||||||
\(645\) | −58.5279 | −2.30453 | ||||||||
\(646\) | 37.3767 | 1.47056 | ||||||||
\(647\) | −25.3910 | −0.998224 | −0.499112 | − | 0.866537i | \(-0.666340\pi\) | ||||
−0.499112 | + | 0.866537i | \(0.666340\pi\) | |||||||
\(648\) | −29.5192 | −1.15962 | ||||||||
\(649\) | −62.7218 | −2.46205 | ||||||||
\(650\) | −120.738 | −4.73574 | ||||||||
\(651\) | 18.3455 | 0.719018 | ||||||||
\(652\) | −98.9931 | −3.87687 | ||||||||
\(653\) | 15.8088 | 0.618646 | 0.309323 | − | 0.950957i | \(-0.399898\pi\) | ||||
0.309323 | + | 0.950957i | \(0.399898\pi\) | |||||||
\(654\) | 11.6668 | 0.456209 | ||||||||
\(655\) | 24.7828 | 0.968345 | ||||||||
\(656\) | 95.5447 | 3.73039 | ||||||||
\(657\) | −73.9761 | −2.88608 | ||||||||
\(658\) | 31.4378 | 1.22557 | ||||||||
\(659\) | 3.07014 | 0.119596 | 0.0597979 | − | 0.998211i | \(-0.480954\pi\) | ||||
0.0597979 | + | 0.998211i | \(0.480954\pi\) | |||||||
\(660\) | −224.961 | −8.75661 | ||||||||
\(661\) | −19.9291 | −0.775151 | −0.387575 | − | 0.921838i | \(-0.626687\pi\) | ||||
−0.387575 | + | 0.921838i | \(0.626687\pi\) | |||||||
\(662\) | 25.2506 | 0.981394 | ||||||||
\(663\) | 29.4600 | 1.14413 | ||||||||
\(664\) | 81.7667 | 3.17316 | ||||||||
\(665\) | −30.4694 | −1.18155 | ||||||||
\(666\) | 1.07770 | 0.0417599 | ||||||||
\(667\) | 42.3800 | 1.64096 | ||||||||
\(668\) | −65.3927 | −2.53012 | ||||||||
\(669\) | −9.41158 | −0.363873 | ||||||||
\(670\) | 65.1621 | 2.51743 | ||||||||
\(671\) | 47.2619 | 1.82452 | ||||||||
\(672\) | −41.9304 | −1.61750 | ||||||||
\(673\) | −28.4756 | −1.09765 | −0.548826 | − | 0.835937i | \(-0.684925\pi\) | ||||
−0.548826 | + | 0.835937i | \(0.684925\pi\) | |||||||
\(674\) | −40.6830 | −1.56705 | ||||||||
\(675\) | 55.7998 | 2.14774 | ||||||||
\(676\) | 91.7648 | 3.52942 | ||||||||
\(677\) | −14.6200 | −0.561893 | −0.280946 | − | 0.959723i | \(-0.590648\pi\) | ||||
−0.280946 | + | 0.959723i | \(0.590648\pi\) | |||||||
\(678\) | −23.0979 | −0.887071 | ||||||||
\(679\) | 10.2156 | 0.392037 | ||||||||
\(680\) | −52.5725 | −2.01606 | ||||||||
\(681\) | 43.9165 | 1.68288 | ||||||||
\(682\) | 66.3735 | 2.54157 | ||||||||
\(683\) | 30.3090 | 1.15974 | 0.579870 | − | 0.814709i | \(-0.303103\pi\) | ||||
0.579870 | + | 0.814709i | \(0.303103\pi\) | |||||||
\(684\) | −208.567 | −7.97476 | ||||||||
\(685\) | 59.3986 | 2.26950 | ||||||||
\(686\) | 36.7820 | 1.40435 | ||||||||
\(687\) | −6.74737 | −0.257428 | ||||||||
\(688\) | −61.7878 | −2.35564 | ||||||||
\(689\) | 23.1340 | 0.881336 | ||||||||
\(690\) | −129.710 | −4.93798 | ||||||||
\(691\) | −20.4529 | −0.778064 | −0.389032 | − | 0.921224i | \(-0.627190\pi\) | ||||
−0.389032 | + | 0.921224i | \(0.627190\pi\) | |||||||
\(692\) | −112.485 | −4.27604 | ||||||||
\(693\) | −24.8909 | −0.945526 | ||||||||
\(694\) | 18.9514 | 0.719385 | ||||||||
\(695\) | −1.35744 | −0.0514907 | ||||||||
\(696\) | −209.085 | −7.92536 | ||||||||
\(697\) | 15.7023 | 0.594769 | ||||||||
\(698\) | 41.3152 | 1.56380 | ||||||||
\(699\) | −27.3603 | −1.03486 | ||||||||
\(700\) | 44.2134 | 1.67111 | ||||||||
\(701\) | 7.05619 | 0.266509 | 0.133254 | − | 0.991082i | \(-0.457457\pi\) | ||||
0.133254 | + | 0.991082i | \(0.457457\pi\) | |||||||
\(702\) | −101.454 | −3.82912 | ||||||||
\(703\) | 0.588367 | 0.0221907 | ||||||||
\(704\) | −56.8796 | −2.14373 | ||||||||
\(705\) | −114.993 | −4.33089 | ||||||||
\(706\) | 93.1404 | 3.50539 | ||||||||
\(707\) | −7.46709 | −0.280829 | ||||||||
\(708\) | 212.259 | 7.97719 | ||||||||
\(709\) | −45.7817 | −1.71937 | −0.859683 | − | 0.510827i | \(-0.829339\pi\) | ||||
−0.859683 | + | 0.510827i | \(0.829339\pi\) | |||||||
\(710\) | 49.0631 | 1.84130 | ||||||||
\(711\) | −28.6826 | −1.07568 | ||||||||
\(712\) | −5.81936 | −0.218090 | ||||||||
\(713\) | 27.3502 | 1.02427 | ||||||||
\(714\) | −15.0953 | −0.564929 | ||||||||
\(715\) | −86.8881 | −3.24943 | ||||||||
\(716\) | 66.3462 | 2.47947 | ||||||||
\(717\) | −77.5005 | −2.89431 | ||||||||
\(718\) | −34.1900 | −1.27596 | ||||||||
\(719\) | −10.4873 | −0.391110 | −0.195555 | − | 0.980693i | \(-0.562651\pi\) | ||||
−0.195555 | + | 0.980693i | \(0.562651\pi\) | |||||||
\(720\) | 215.513 | 8.03168 | ||||||||
\(721\) | 13.3445 | 0.496976 | ||||||||
\(722\) | −109.028 | −4.05761 | ||||||||
\(723\) | −39.5476 | −1.47079 | ||||||||
\(724\) | 70.7934 | 2.63102 | ||||||||
\(725\) | 73.9369 | 2.74595 | ||||||||
\(726\) | −56.1506 | −2.08394 | ||||||||
\(727\) | 15.8430 | 0.587585 | 0.293792 | − | 0.955869i | \(-0.405083\pi\) | ||||
0.293792 | + | 0.955869i | \(0.405083\pi\) | |||||||
\(728\) | −48.2912 | −1.78979 | ||||||||
\(729\) | −39.5336 | −1.46421 | ||||||||
\(730\) | 132.319 | 4.89734 | ||||||||
\(731\) | −10.1545 | −0.375580 | ||||||||
\(732\) | −159.941 | −5.91158 | ||||||||
\(733\) | −5.74382 | −0.212153 | −0.106076 | − | 0.994358i | \(-0.533829\pi\) | ||||
−0.106076 | + | 0.994358i | \(0.533829\pi\) | |||||||
\(734\) | 59.8757 | 2.21005 | ||||||||
\(735\) | −61.1178 | −2.25436 | ||||||||
\(736\) | −62.5113 | −2.30420 | ||||||||
\(737\) | 29.0618 | 1.07051 | ||||||||
\(738\) | −122.606 | −4.51318 | ||||||||
\(739\) | 14.4032 | 0.529830 | 0.264915 | − | 0.964272i | \(-0.414656\pi\) | ||||
0.264915 | + | 0.964272i | \(0.414656\pi\) | |||||||
\(740\) | −1.37761 | −0.0506419 | ||||||||
\(741\) | −125.583 | −4.61340 | ||||||||
\(742\) | −11.8539 | −0.435171 | ||||||||
\(743\) | −37.1271 | −1.36206 | −0.681031 | − | 0.732255i | \(-0.738468\pi\) | ||||
−0.681031 | + | 0.732255i | \(0.738468\pi\) | |||||||
\(744\) | −134.934 | −4.94694 | ||||||||
\(745\) | 13.6202 | 0.499006 | ||||||||
\(746\) | 46.7161 | 1.71040 | ||||||||
\(747\) | −55.0869 | −2.01552 | ||||||||
\(748\) | −39.0307 | −1.42710 | ||||||||
\(749\) | 10.8365 | 0.395956 | ||||||||
\(750\) | −87.4469 | −3.19311 | ||||||||
\(751\) | 15.6616 | 0.571501 | 0.285751 | − | 0.958304i | \(-0.407757\pi\) | ||||
0.285751 | + | 0.958304i | \(0.407757\pi\) | |||||||
\(752\) | −121.398 | −4.42694 | ||||||||
\(753\) | −15.2076 | −0.554197 | ||||||||
\(754\) | −134.430 | −4.89565 | ||||||||
\(755\) | −20.9106 | −0.761013 | ||||||||
\(756\) | 37.1515 | 1.35119 | ||||||||
\(757\) | 44.9984 | 1.63549 | 0.817747 | − | 0.575578i | \(-0.195223\pi\) | ||||
0.817747 | + | 0.575578i | \(0.195223\pi\) | |||||||
\(758\) | 50.4156 | 1.83118 | ||||||||
\(759\) | −57.8498 | −2.09981 | ||||||||
\(760\) | 224.107 | 8.12923 | ||||||||
\(761\) | −18.7194 | −0.678579 | −0.339290 | − | 0.940682i | \(-0.610187\pi\) | ||||
−0.339290 | + | 0.940682i | \(0.610187\pi\) | |||||||
\(762\) | 1.51325 | 0.0548191 | ||||||||
\(763\) | −1.65012 | −0.0597382 | ||||||||
\(764\) | −29.1121 | −1.05324 | ||||||||
\(765\) | 35.4185 | 1.28056 | ||||||||
\(766\) | 34.1966 | 1.23557 | ||||||||
\(767\) | 81.9821 | 2.96020 | ||||||||
\(768\) | −12.4894 | −0.450672 | ||||||||
\(769\) | −11.2397 | −0.405314 | −0.202657 | − | 0.979250i | \(-0.564958\pi\) | ||||
−0.202657 | + | 0.979250i | \(0.564958\pi\) | |||||||
\(770\) | 44.5216 | 1.60445 | ||||||||
\(771\) | 7.87970 | 0.283780 | ||||||||
\(772\) | 36.1330 | 1.30046 | ||||||||
\(773\) | 16.3028 | 0.586371 | 0.293185 | − | 0.956056i | \(-0.405285\pi\) | ||||
0.293185 | + | 0.956056i | \(0.405285\pi\) | |||||||
\(774\) | 79.2880 | 2.84995 | ||||||||
\(775\) | 47.7156 | 1.71399 | ||||||||
\(776\) | −75.1371 | −2.69726 | ||||||||
\(777\) | −0.237624 | −0.00852471 | ||||||||
\(778\) | −78.7817 | −2.82446 | ||||||||
\(779\) | −66.9364 | −2.39824 | ||||||||
\(780\) | 294.041 | 10.5284 | ||||||||
\(781\) | 21.8817 | 0.782991 | ||||||||
\(782\) | −22.5047 | −0.804765 | ||||||||
\(783\) | 62.1275 | 2.22026 | ||||||||
\(784\) | −64.5220 | −2.30436 | ||||||||
\(785\) | −54.2386 | −1.93586 | ||||||||
\(786\) | −52.3392 | −1.86688 | ||||||||
\(787\) | 22.1732 | 0.790389 | 0.395194 | − | 0.918598i | \(-0.370677\pi\) | ||||
0.395194 | + | 0.918598i | \(0.370677\pi\) | |||||||
\(788\) | −32.2027 | −1.14717 | ||||||||
\(789\) | 28.5622 | 1.01684 | ||||||||
\(790\) | 51.3038 | 1.82531 | ||||||||
\(791\) | 3.26689 | 0.116157 | ||||||||
\(792\) | 183.076 | 6.50534 | ||||||||
\(793\) | −61.7748 | −2.19369 | ||||||||
\(794\) | −59.2237 | −2.10177 | ||||||||
\(795\) | 43.3592 | 1.53779 | ||||||||
\(796\) | 133.863 | 4.74466 | ||||||||
\(797\) | −19.8872 | −0.704442 | −0.352221 | − | 0.935917i | \(-0.614573\pi\) | ||||
−0.352221 | + | 0.935917i | \(0.614573\pi\) | |||||||
\(798\) | 64.3488 | 2.27792 | ||||||||
\(799\) | −19.9512 | −0.705824 | ||||||||
\(800\) | −109.058 | −3.85579 | ||||||||
\(801\) | 3.92055 | 0.138526 | ||||||||
\(802\) | 30.7526 | 1.08591 | ||||||||
\(803\) | 59.0132 | 2.08253 | ||||||||
\(804\) | −98.3492 | −3.46851 | ||||||||
\(805\) | 18.3458 | 0.646603 | ||||||||
\(806\) | −86.7551 | −3.05582 | ||||||||
\(807\) | −4.02959 | −0.141848 | ||||||||
\(808\) | 54.9217 | 1.93214 | ||||||||
\(809\) | −15.0672 | −0.529733 | −0.264867 | − | 0.964285i | \(-0.585328\pi\) | ||||
−0.264867 | + | 0.964285i | \(0.585328\pi\) | |||||||
\(810\) | −35.5719 | −1.24987 | ||||||||
\(811\) | −36.2069 | −1.27139 | −0.635697 | − | 0.771938i | \(-0.719287\pi\) | ||||
−0.635697 | + | 0.771938i | \(0.719287\pi\) | |||||||
\(812\) | 49.2272 | 1.72754 | ||||||||
\(813\) | 65.5634 | 2.29941 | ||||||||
\(814\) | −0.859715 | −0.0301330 | ||||||||
\(815\) | −71.6617 | −2.51020 | ||||||||
\(816\) | 58.2911 | 2.04060 | ||||||||
\(817\) | 43.2871 | 1.51442 | ||||||||
\(818\) | −34.3767 | −1.20195 | ||||||||
\(819\) | 32.5342 | 1.13684 | ||||||||
\(820\) | 156.726 | 5.47310 | ||||||||
\(821\) | 33.9167 | 1.18370 | 0.591851 | − | 0.806047i | \(-0.298397\pi\) | ||||
0.591851 | + | 0.806047i | \(0.298397\pi\) | |||||||
\(822\) | −125.445 | −4.37539 | ||||||||
\(823\) | −26.3234 | −0.917575 | −0.458788 | − | 0.888546i | \(-0.651716\pi\) | ||||
−0.458788 | + | 0.888546i | \(0.651716\pi\) | |||||||
\(824\) | −98.1512 | −3.41926 | ||||||||
\(825\) | −100.926 | −3.51378 | ||||||||
\(826\) | −42.0078 | −1.46164 | ||||||||
\(827\) | 15.3608 | 0.534149 | 0.267074 | − | 0.963676i | \(-0.413943\pi\) | ||||
0.267074 | + | 0.963676i | \(0.413943\pi\) | |||||||
\(828\) | 125.579 | 4.36418 | ||||||||
\(829\) | −23.3827 | −0.812115 | −0.406057 | − | 0.913848i | \(-0.633097\pi\) | ||||
−0.406057 | + | 0.913848i | \(0.633097\pi\) | |||||||
\(830\) | 98.5323 | 3.42011 | ||||||||
\(831\) | 62.0165 | 2.15133 | ||||||||
\(832\) | 74.3459 | 2.57748 | ||||||||
\(833\) | −10.6039 | −0.367403 | ||||||||
\(834\) | 2.86681 | 0.0992693 | ||||||||
\(835\) | −47.3382 | −1.63820 | ||||||||
\(836\) | 166.381 | 5.75441 | ||||||||
\(837\) | 40.0944 | 1.38586 | ||||||||
\(838\) | 8.41757 | 0.290780 | ||||||||
\(839\) | 44.4168 | 1.53344 | 0.766719 | − | 0.641982i | \(-0.221888\pi\) | ||||
0.766719 | + | 0.641982i | \(0.221888\pi\) | |||||||
\(840\) | −90.5104 | −3.12291 | ||||||||
\(841\) | 53.3213 | 1.83867 | ||||||||
\(842\) | −18.0114 | −0.620713 | ||||||||
\(843\) | 71.0724 | 2.44786 | ||||||||
\(844\) | −44.4935 | −1.53153 | ||||||||
\(845\) | 66.4291 | 2.28523 | ||||||||
\(846\) | 155.782 | 5.35589 | ||||||||
\(847\) | 7.94174 | 0.272881 | ||||||||
\(848\) | 45.7743 | 1.57189 | ||||||||
\(849\) | 26.9028 | 0.923303 | ||||||||
\(850\) | −39.2620 | −1.34668 | ||||||||
\(851\) | −0.354258 | −0.0121438 | ||||||||
\(852\) | −74.0508 | −2.53694 | ||||||||
\(853\) | −41.4600 | −1.41956 | −0.709782 | − | 0.704421i | \(-0.751207\pi\) | ||||
−0.709782 | + | 0.704421i | \(0.751207\pi\) | |||||||
\(854\) | 31.6535 | 1.08316 | ||||||||
\(855\) | −150.983 | −5.16351 | ||||||||
\(856\) | −79.7041 | −2.72423 | ||||||||
\(857\) | −9.23705 | −0.315531 | −0.157766 | − | 0.987477i | \(-0.550429\pi\) | ||||
−0.157766 | + | 0.987477i | \(0.550429\pi\) | |||||||
\(858\) | 183.500 | 6.26460 | ||||||||
\(859\) | −28.2804 | −0.964915 | −0.482458 | − | 0.875919i | \(-0.660256\pi\) | ||||
−0.482458 | + | 0.875919i | \(0.660256\pi\) | |||||||
\(860\) | −101.353 | −3.45611 | ||||||||
\(861\) | 27.0336 | 0.921304 | ||||||||
\(862\) | 9.12360 | 0.310751 | ||||||||
\(863\) | −3.49136 | −0.118847 | −0.0594237 | − | 0.998233i | \(-0.518926\pi\) | ||||
−0.0594237 | + | 0.998233i | \(0.518926\pi\) | |||||||
\(864\) | −91.6393 | −3.11763 | ||||||||
\(865\) | −81.4287 | −2.76866 | ||||||||
\(866\) | 22.0230 | 0.748370 | ||||||||
\(867\) | −39.5945 | −1.34470 | ||||||||
\(868\) | 31.7690 | 1.07831 | ||||||||
\(869\) | 22.8811 | 0.776188 | ||||||||
\(870\) | −251.957 | −8.54213 | ||||||||
\(871\) | −37.9859 | −1.28710 | ||||||||
\(872\) | 12.1369 | 0.411006 | ||||||||
\(873\) | 50.6205 | 1.71324 | ||||||||
\(874\) | 95.9334 | 3.24500 | ||||||||
\(875\) | 12.3682 | 0.418121 | ||||||||
\(876\) | −199.709 | −6.74754 | ||||||||
\(877\) | −18.9583 | −0.640175 | −0.320088 | − | 0.947388i | \(-0.603712\pi\) | ||||
−0.320088 | + | 0.947388i | \(0.603712\pi\) | |||||||
\(878\) | 34.1316 | 1.15188 | ||||||||
\(879\) | 45.9059 | 1.54837 | ||||||||
\(880\) | −171.922 | −5.79548 | ||||||||
\(881\) | −40.7163 | −1.37177 | −0.685883 | − | 0.727712i | \(-0.740584\pi\) | ||||
−0.685883 | + | 0.727712i | \(0.740584\pi\) | |||||||
\(882\) | 82.7966 | 2.78791 | ||||||||
\(883\) | −8.94377 | −0.300982 | −0.150491 | − | 0.988611i | \(-0.548085\pi\) | ||||
−0.150491 | + | 0.988611i | \(0.548085\pi\) | |||||||
\(884\) | 51.0160 | 1.71585 | ||||||||
\(885\) | 153.656 | 5.16509 | ||||||||
\(886\) | −20.1297 | −0.676270 | ||||||||
\(887\) | −15.5298 | −0.521439 | −0.260719 | − | 0.965415i | \(-0.583960\pi\) | ||||
−0.260719 | + | 0.965415i | \(0.583960\pi\) | |||||||
\(888\) | 1.74776 | 0.0586511 | ||||||||
\(889\) | −0.214028 | −0.00717828 | ||||||||
\(890\) | −7.01258 | −0.235062 | ||||||||
\(891\) | −15.8648 | −0.531491 | ||||||||
\(892\) | −16.2981 | −0.545700 | ||||||||
\(893\) | 85.0487 | 2.84605 | ||||||||
\(894\) | −28.7648 | −0.962038 | ||||||||
\(895\) | 48.0284 | 1.60541 | ||||||||
\(896\) | −9.10360 | −0.304130 | ||||||||
\(897\) | 75.6139 | 2.52468 | ||||||||
\(898\) | 88.8981 | 2.96657 | ||||||||
\(899\) | 53.1265 | 1.77187 | ||||||||
\(900\) | 219.088 | 7.30293 | ||||||||
\(901\) | 7.52279 | 0.250621 | ||||||||
\(902\) | 97.8068 | 3.25661 | ||||||||
\(903\) | −17.4824 | −0.581777 | ||||||||
\(904\) | −24.0285 | −0.799177 | ||||||||
\(905\) | 51.2478 | 1.70353 | ||||||||
\(906\) | 44.1613 | 1.46716 | ||||||||
\(907\) | 22.0161 | 0.731031 | 0.365516 | − | 0.930805i | \(-0.380893\pi\) | ||||
0.365516 | + | 0.930805i | \(0.380893\pi\) | |||||||
\(908\) | 76.0504 | 2.52382 | ||||||||
\(909\) | −37.0012 | −1.22725 | ||||||||
\(910\) | −58.1930 | −1.92908 | ||||||||
\(911\) | 0.623853 | 0.0206692 | 0.0103346 | − | 0.999947i | \(-0.496710\pi\) | ||||
0.0103346 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(912\) | −248.485 | −8.22816 | ||||||||
\(913\) | 43.9447 | 1.45436 | ||||||||
\(914\) | −56.4837 | −1.86831 | ||||||||
\(915\) | −115.782 | −3.82764 | ||||||||
\(916\) | −11.6845 | −0.386065 | ||||||||
\(917\) | 7.40268 | 0.244458 | ||||||||
\(918\) | −32.9910 | −1.08887 | ||||||||
\(919\) | −14.9507 | −0.493179 | −0.246589 | − | 0.969120i | \(-0.579310\pi\) | ||||
−0.246589 | + | 0.969120i | \(0.579310\pi\) | |||||||
\(920\) | −134.936 | −4.44871 | ||||||||
\(921\) | −23.6599 | −0.779622 | ||||||||
\(922\) | −37.4839 | −1.23447 | ||||||||
\(923\) | −28.6011 | −0.941416 | ||||||||
\(924\) | −67.1964 | −2.21060 | ||||||||
\(925\) | −0.618045 | −0.0203212 | ||||||||
\(926\) | 97.5006 | 3.20407 | ||||||||
\(927\) | 66.1253 | 2.17184 | ||||||||
\(928\) | −121.426 | −3.98599 | ||||||||
\(929\) | −48.5592 | −1.59318 | −0.796588 | − | 0.604523i | \(-0.793364\pi\) | ||||
−0.796588 | + | 0.604523i | \(0.793364\pi\) | |||||||
\(930\) | −162.602 | −5.33192 | ||||||||
\(931\) | 45.2026 | 1.48146 | ||||||||
\(932\) | −47.3799 | −1.55198 | ||||||||
\(933\) | 26.8824 | 0.880091 | ||||||||
\(934\) | −66.1029 | −2.16295 | ||||||||
\(935\) | −28.2545 | −0.924022 | ||||||||
\(936\) | −239.294 | −7.82159 | ||||||||
\(937\) | −44.0875 | −1.44028 | −0.720138 | − | 0.693831i | \(-0.755922\pi\) | ||||
−0.720138 | + | 0.693831i | \(0.755922\pi\) | |||||||
\(938\) | 19.4641 | 0.635524 | ||||||||
\(939\) | 72.9827 | 2.38170 | ||||||||
\(940\) | −199.134 | −6.49504 | ||||||||
\(941\) | −20.5729 | −0.670657 | −0.335328 | − | 0.942101i | \(-0.608847\pi\) | ||||
−0.335328 | + | 0.942101i | \(0.608847\pi\) | |||||||
\(942\) | 114.547 | 3.73215 | ||||||||
\(943\) | 40.3027 | 1.31244 | ||||||||
\(944\) | 162.214 | 5.27963 | ||||||||
\(945\) | 26.8942 | 0.874869 | ||||||||
\(946\) | −63.2507 | −2.05646 | ||||||||
\(947\) | −2.11136 | −0.0686101 | −0.0343050 | − | 0.999411i | \(-0.510922\pi\) | ||||
−0.0343050 | + | 0.999411i | \(0.510922\pi\) | |||||||
\(948\) | −77.4328 | −2.51490 | ||||||||
\(949\) | −77.1346 | −2.50390 | ||||||||
\(950\) | 167.367 | 5.43011 | ||||||||
\(951\) | −35.6764 | −1.15689 | ||||||||
\(952\) | −15.7035 | −0.508953 | ||||||||
\(953\) | 9.19987 | 0.298013 | 0.149007 | − | 0.988836i | \(-0.452392\pi\) | ||||
0.149007 | + | 0.988836i | \(0.452392\pi\) | |||||||
\(954\) | −58.7389 | −1.90174 | ||||||||
\(955\) | −21.0744 | −0.681952 | ||||||||
\(956\) | −134.208 | −4.34060 | ||||||||
\(957\) | −112.371 | −3.63243 | ||||||||
\(958\) | 49.4611 | 1.59802 | ||||||||
\(959\) | 17.7425 | 0.572934 | ||||||||
\(960\) | 139.344 | 4.49730 | ||||||||
\(961\) | 3.28551 | 0.105984 | ||||||||
\(962\) | 1.12371 | 0.0362299 | ||||||||
\(963\) | 53.6973 | 1.73037 | ||||||||
\(964\) | −68.4848 | −2.20575 | ||||||||
\(965\) | 26.1569 | 0.842021 | ||||||||
\(966\) | −38.7447 | −1.24659 | ||||||||
\(967\) | 41.8641 | 1.34626 | 0.673129 | − | 0.739525i | \(-0.264950\pi\) | ||||
0.673129 | + | 0.739525i | \(0.264950\pi\) | |||||||
\(968\) | −58.4128 | −1.87746 | ||||||||
\(969\) | −40.8374 | −1.31189 | ||||||||
\(970\) | −90.5433 | −2.90717 | ||||||||
\(971\) | −39.8545 | −1.27899 | −0.639495 | − | 0.768795i | \(-0.720857\pi\) | ||||
−0.639495 | + | 0.768795i | \(0.720857\pi\) | |||||||
\(972\) | −49.2108 | −1.57844 | ||||||||
\(973\) | −0.405471 | −0.0129988 | ||||||||
\(974\) | −32.9232 | −1.05493 | ||||||||
\(975\) | 131.917 | 4.22474 | ||||||||
\(976\) | −122.231 | −3.91252 | ||||||||
\(977\) | 56.8097 | 1.81750 | 0.908752 | − | 0.417337i | \(-0.137036\pi\) | ||||
0.908752 | + | 0.417337i | \(0.137036\pi\) | |||||||
\(978\) | 151.344 | 4.83943 | ||||||||
\(979\) | −3.12756 | −0.0999572 | ||||||||
\(980\) | −105.838 | −3.38087 | ||||||||
\(981\) | −8.17671 | −0.261062 | ||||||||
\(982\) | −11.0058 | −0.351208 | ||||||||
\(983\) | −13.8591 | −0.442036 | −0.221018 | − | 0.975270i | \(-0.570938\pi\) | ||||
−0.221018 | + | 0.975270i | \(0.570938\pi\) | |||||||
\(984\) | −198.837 | −6.33869 | ||||||||
\(985\) | −23.3117 | −0.742774 | ||||||||
\(986\) | −43.7143 | −1.39215 | ||||||||
\(987\) | −34.3487 | −1.09333 | ||||||||
\(988\) | −217.472 | −6.91871 | ||||||||
\(989\) | −26.0633 | −0.828766 | ||||||||
\(990\) | 220.615 | 7.01160 | ||||||||
\(991\) | −13.7035 | −0.435305 | −0.217653 | − | 0.976026i | \(-0.569840\pi\) | ||||
−0.217653 | + | 0.976026i | \(0.569840\pi\) | |||||||
\(992\) | −78.3626 | −2.48802 | ||||||||
\(993\) | −27.5886 | −0.875498 | ||||||||
\(994\) | 14.6552 | 0.464836 | ||||||||
\(995\) | 96.9044 | 3.07208 | ||||||||
\(996\) | −148.715 | −4.71221 | ||||||||
\(997\) | 23.8106 | 0.754088 | 0.377044 | − | 0.926195i | \(-0.376940\pi\) | ||||
0.377044 | + | 0.926195i | \(0.376940\pi\) | |||||||
\(998\) | 16.7701 | 0.530849 | ||||||||
\(999\) | −0.519330 | −0.0164309 |
(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 | 4003.2.a.c.1.4 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.c.1.4 | ✓ | 179 | 1.1 | even | 1 | trivial |