Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, 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("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.72607 | −1.92762 | −0.963812 | − | 0.266583i | \(-0.914105\pi\) | ||||
−0.963812 | + | 0.266583i | \(0.914105\pi\) | |||||||
\(3\) | −2.28516 | −1.31934 | −0.659670 | − | 0.751555i | \(-0.729304\pi\) | ||||
−0.659670 | + | 0.751555i | \(0.729304\pi\) | |||||||
\(4\) | 5.43147 | 2.71573 | ||||||||
\(5\) | 2.07141 | 0.926361 | 0.463180 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463180 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(6\) | 6.22952 | 2.54319 | ||||||||
\(7\) | −3.86589 | −1.46117 | −0.730584 | − | 0.682823i | \(-0.760752\pi\) | ||||
−0.730584 | + | 0.682823i | \(0.760752\pi\) | |||||||
\(8\) | −9.35442 | −3.30729 | ||||||||
\(9\) | 2.22198 | 0.740659 | ||||||||
\(10\) | −5.64680 | −1.78567 | ||||||||
\(11\) | −6.14227 | −1.85196 | −0.925982 | − | 0.377567i | \(-0.876761\pi\) | ||||
−0.925982 | + | 0.377567i | \(0.876761\pi\) | |||||||
\(12\) | −12.4118 | −3.58298 | ||||||||
\(13\) | 3.18989 | 0.884717 | 0.442358 | − | 0.896838i | \(-0.354142\pi\) | ||||
0.442358 | + | 0.896838i | \(0.354142\pi\) | |||||||
\(14\) | 10.5387 | 2.81658 | ||||||||
\(15\) | −4.73350 | −1.22219 | ||||||||
\(16\) | 14.6379 | 3.65947 | ||||||||
\(17\) | 6.05605 | 1.46881 | 0.734404 | − | 0.678712i | \(-0.237462\pi\) | ||||
0.734404 | + | 0.678712i | \(0.237462\pi\) | |||||||
\(18\) | −6.05727 | −1.42771 | ||||||||
\(19\) | 0.757799 | 0.173851 | 0.0869255 | − | 0.996215i | \(-0.472296\pi\) | ||||
0.0869255 | + | 0.996215i | \(0.472296\pi\) | |||||||
\(20\) | 11.2508 | 2.51575 | ||||||||
\(21\) | 8.83419 | 1.92778 | ||||||||
\(22\) | 16.7443 | 3.56989 | ||||||||
\(23\) | 7.32285 | 1.52692 | 0.763460 | − | 0.645855i | \(-0.223499\pi\) | ||||
0.763460 | + | 0.645855i | \(0.223499\pi\) | |||||||
\(24\) | 21.3764 | 4.36344 | ||||||||
\(25\) | −0.709281 | −0.141856 | ||||||||
\(26\) | −8.69587 | −1.70540 | ||||||||
\(27\) | 1.77791 | 0.342158 | ||||||||
\(28\) | −20.9974 | −3.96814 | ||||||||
\(29\) | −9.79643 | −1.81915 | −0.909576 | − | 0.415538i | \(-0.863593\pi\) | ||||
−0.909576 | + | 0.415538i | \(0.863593\pi\) | |||||||
\(30\) | 12.9039 | 2.35591 | ||||||||
\(31\) | −5.39248 | −0.968517 | −0.484259 | − | 0.874925i | \(-0.660911\pi\) | ||||
−0.484259 | + | 0.874925i | \(0.660911\pi\) | |||||||
\(32\) | −21.1951 | −3.74680 | ||||||||
\(33\) | 14.0361 | 2.44337 | ||||||||
\(34\) | −16.5092 | −2.83131 | ||||||||
\(35\) | −8.00782 | −1.35357 | ||||||||
\(36\) | 12.0686 | 2.01143 | ||||||||
\(37\) | 3.62339 | 0.595682 | 0.297841 | − | 0.954616i | \(-0.403734\pi\) | ||||
0.297841 | + | 0.954616i | \(0.403734\pi\) | |||||||
\(38\) | −2.06581 | −0.335119 | ||||||||
\(39\) | −7.28943 | −1.16724 | ||||||||
\(40\) | −19.3768 | −3.06374 | ||||||||
\(41\) | 9.52390 | 1.48738 | 0.743691 | − | 0.668523i | \(-0.233073\pi\) | ||||
0.743691 | + | 0.668523i | \(0.233073\pi\) | |||||||
\(42\) | −24.0826 | −3.71603 | ||||||||
\(43\) | −12.9396 | −1.97327 | −0.986634 | − | 0.162954i | \(-0.947898\pi\) | ||||
−0.986634 | + | 0.162954i | \(0.947898\pi\) | |||||||
\(44\) | −33.3615 | −5.02944 | ||||||||
\(45\) | 4.60262 | 0.686118 | ||||||||
\(46\) | −19.9626 | −2.94333 | ||||||||
\(47\) | 4.38641 | 0.639823 | 0.319912 | − | 0.947447i | \(-0.396347\pi\) | ||||
0.319912 | + | 0.947447i | \(0.396347\pi\) | |||||||
\(48\) | −33.4500 | −4.82809 | ||||||||
\(49\) | 7.94507 | 1.13501 | ||||||||
\(50\) | 1.93355 | 0.273445 | ||||||||
\(51\) | −13.8391 | −1.93786 | ||||||||
\(52\) | 17.3258 | 2.40265 | ||||||||
\(53\) | 4.51083 | 0.619611 | 0.309805 | − | 0.950800i | \(-0.399736\pi\) | ||||
0.309805 | + | 0.950800i | \(0.399736\pi\) | |||||||
\(54\) | −4.84670 | −0.659553 | ||||||||
\(55\) | −12.7231 | −1.71559 | ||||||||
\(56\) | 36.1631 | 4.83250 | ||||||||
\(57\) | −1.73169 | −0.229369 | ||||||||
\(58\) | 26.7058 | 3.50664 | ||||||||
\(59\) | −3.57226 | −0.465069 | −0.232535 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232535 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(60\) | −25.7099 | −3.31913 | ||||||||
\(61\) | 6.45296 | 0.826217 | 0.413109 | − | 0.910682i | \(-0.364443\pi\) | ||||
0.413109 | + | 0.910682i | \(0.364443\pi\) | |||||||
\(62\) | 14.7003 | 1.86694 | ||||||||
\(63\) | −8.58991 | −1.08223 | ||||||||
\(64\) | 28.5036 | 3.56295 | ||||||||
\(65\) | 6.60756 | 0.819567 | ||||||||
\(66\) | −38.2634 | −4.70990 | ||||||||
\(67\) | −11.1385 | −1.36079 | −0.680395 | − | 0.732846i | \(-0.738192\pi\) | ||||
−0.680395 | + | 0.732846i | \(0.738192\pi\) | |||||||
\(68\) | 32.8933 | 3.98889 | ||||||||
\(69\) | −16.7339 | −2.01453 | ||||||||
\(70\) | 21.8299 | 2.60917 | ||||||||
\(71\) | −11.9182 | −1.41443 | −0.707217 | − | 0.706996i | \(-0.750050\pi\) | ||||
−0.707217 | + | 0.706996i | \(0.750050\pi\) | |||||||
\(72\) | −20.7853 | −2.44957 | ||||||||
\(73\) | −1.29003 | −0.150986 | −0.0754931 | − | 0.997146i | \(-0.524053\pi\) | ||||
−0.0754931 | + | 0.997146i | \(0.524053\pi\) | |||||||
\(74\) | −9.87762 | −1.14825 | ||||||||
\(75\) | 1.62082 | 0.187157 | ||||||||
\(76\) | 4.11596 | 0.472133 | ||||||||
\(77\) | 23.7453 | 2.70603 | ||||||||
\(78\) | 19.8715 | 2.25000 | ||||||||
\(79\) | 0.820910 | 0.0923596 | 0.0461798 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461798 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(80\) | 30.3210 | 3.38999 | ||||||||
\(81\) | −10.7287 | −1.19208 | ||||||||
\(82\) | −25.9628 | −2.86711 | ||||||||
\(83\) | 2.94992 | 0.323796 | 0.161898 | − | 0.986807i | \(-0.448238\pi\) | ||||
0.161898 | + | 0.986807i | \(0.448238\pi\) | |||||||
\(84\) | 47.9826 | 5.23533 | ||||||||
\(85\) | 12.5445 | 1.36065 | ||||||||
\(86\) | 35.2742 | 3.80372 | ||||||||
\(87\) | 22.3865 | 2.40008 | ||||||||
\(88\) | 57.4574 | 6.12498 | ||||||||
\(89\) | −17.1833 | −1.82142 | −0.910712 | − | 0.413041i | \(-0.864467\pi\) | ||||
−0.910712 | + | 0.413041i | \(0.864467\pi\) | |||||||
\(90\) | −12.5471 | −1.32258 | ||||||||
\(91\) | −12.3318 | −1.29272 | ||||||||
\(92\) | 39.7738 | 4.14671 | ||||||||
\(93\) | 12.3227 | 1.27780 | ||||||||
\(94\) | −11.9577 | −1.23334 | ||||||||
\(95\) | 1.56971 | 0.161049 | ||||||||
\(96\) | 48.4343 | 4.94330 | ||||||||
\(97\) | −17.2215 | −1.74857 | −0.874287 | − | 0.485409i | \(-0.838671\pi\) | ||||
−0.874287 | + | 0.485409i | \(0.838671\pi\) | |||||||
\(98\) | −21.6588 | −2.18787 | ||||||||
\(99\) | −13.6480 | −1.37167 | ||||||||
\(100\) | −3.85243 | −0.385243 | ||||||||
\(101\) | 10.5025 | 1.04504 | 0.522520 | − | 0.852627i | \(-0.324992\pi\) | ||||
0.522520 | + | 0.852627i | \(0.324992\pi\) | |||||||
\(102\) | 37.7263 | 3.73546 | ||||||||
\(103\) | 3.98854 | 0.393002 | 0.196501 | − | 0.980504i | \(-0.437042\pi\) | ||||
0.196501 | + | 0.980504i | \(0.437042\pi\) | |||||||
\(104\) | −29.8396 | −2.92601 | ||||||||
\(105\) | 18.2992 | 1.78582 | ||||||||
\(106\) | −12.2969 | −1.19438 | ||||||||
\(107\) | 17.1240 | 1.65544 | 0.827719 | − | 0.561143i | \(-0.189638\pi\) | ||||
0.827719 | + | 0.561143i | \(0.189638\pi\) | |||||||
\(108\) | 9.65665 | 0.929211 | ||||||||
\(109\) | −8.22514 | −0.787826 | −0.393913 | − | 0.919148i | \(-0.628879\pi\) | ||||
−0.393913 | + | 0.919148i | \(0.628879\pi\) | |||||||
\(110\) | 34.6842 | 3.30701 | ||||||||
\(111\) | −8.28004 | −0.785907 | ||||||||
\(112\) | −56.5884 | −5.34710 | ||||||||
\(113\) | −2.46347 | −0.231744 | −0.115872 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115872 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(114\) | 4.72072 | 0.442136 | ||||||||
\(115\) | 15.1686 | 1.41448 | ||||||||
\(116\) | −53.2090 | −4.94033 | ||||||||
\(117\) | 7.08787 | 0.655274 | ||||||||
\(118\) | 9.73825 | 0.896478 | ||||||||
\(119\) | −23.4120 | −2.14618 | ||||||||
\(120\) | 44.2792 | 4.04212 | ||||||||
\(121\) | 26.7275 | 2.42977 | ||||||||
\(122\) | −17.5912 | −1.59264 | ||||||||
\(123\) | −21.7637 | −1.96236 | ||||||||
\(124\) | −29.2891 | −2.63023 | ||||||||
\(125\) | −11.8262 | −1.05777 | ||||||||
\(126\) | 23.4167 | 2.08613 | ||||||||
\(127\) | 6.82351 | 0.605489 | 0.302744 | − | 0.953072i | \(-0.402097\pi\) | ||||
0.302744 | + | 0.953072i | \(0.402097\pi\) | |||||||
\(128\) | −35.3126 | −3.12122 | ||||||||
\(129\) | 29.5691 | 2.60341 | ||||||||
\(130\) | −18.0127 | −1.57982 | ||||||||
\(131\) | 1.49699 | 0.130792 | 0.0653961 | − | 0.997859i | \(-0.479169\pi\) | ||||
0.0653961 | + | 0.997859i | \(0.479169\pi\) | |||||||
\(132\) | 76.2366 | 6.63555 | ||||||||
\(133\) | −2.92956 | −0.254025 | ||||||||
\(134\) | 30.3645 | 2.62309 | ||||||||
\(135\) | 3.68277 | 0.316962 | ||||||||
\(136\) | −56.6509 | −4.85777 | ||||||||
\(137\) | 4.34202 | 0.370964 | 0.185482 | − | 0.982648i | \(-0.440615\pi\) | ||||
0.185482 | + | 0.982648i | \(0.440615\pi\) | |||||||
\(138\) | 45.6179 | 3.88325 | ||||||||
\(139\) | −1.39765 | −0.118547 | −0.0592735 | − | 0.998242i | \(-0.518878\pi\) | ||||
−0.0592735 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(140\) | −43.4942 | −3.67593 | ||||||||
\(141\) | −10.0237 | −0.844145 | ||||||||
\(142\) | 32.4900 | 2.72650 | ||||||||
\(143\) | −19.5932 | −1.63846 | ||||||||
\(144\) | 32.5251 | 2.71042 | ||||||||
\(145\) | −20.2924 | −1.68519 | ||||||||
\(146\) | 3.51670 | 0.291045 | ||||||||
\(147\) | −18.1558 | −1.49746 | ||||||||
\(148\) | 19.6803 | 1.61771 | ||||||||
\(149\) | −1.19151 | −0.0976121 | −0.0488060 | − | 0.998808i | \(-0.515542\pi\) | ||||
−0.0488060 | + | 0.998808i | \(0.515542\pi\) | |||||||
\(150\) | −4.41848 | −0.360767 | ||||||||
\(151\) | −0.814696 | −0.0662990 | −0.0331495 | − | 0.999450i | \(-0.510554\pi\) | ||||
−0.0331495 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(152\) | −7.08877 | −0.574975 | ||||||||
\(153\) | 13.4564 | 1.08789 | ||||||||
\(154\) | −64.7314 | −5.21621 | ||||||||
\(155\) | −11.1700 | −0.897196 | ||||||||
\(156\) | −39.5923 | −3.16992 | ||||||||
\(157\) | −13.8336 | −1.10404 | −0.552020 | − | 0.833831i | \(-0.686143\pi\) | ||||
−0.552020 | + | 0.833831i | \(0.686143\pi\) | |||||||
\(158\) | −2.23786 | −0.178035 | ||||||||
\(159\) | −10.3080 | −0.817477 | ||||||||
\(160\) | −43.9036 | −3.47089 | ||||||||
\(161\) | −28.3093 | −2.23109 | ||||||||
\(162\) | 29.2473 | 2.29789 | ||||||||
\(163\) | 0.666862 | 0.0522327 | 0.0261163 | − | 0.999659i | \(-0.491686\pi\) | ||||
0.0261163 | + | 0.999659i | \(0.491686\pi\) | |||||||
\(164\) | 51.7287 | 4.03933 | ||||||||
\(165\) | 29.0745 | 2.26344 | ||||||||
\(166\) | −8.04170 | −0.624157 | ||||||||
\(167\) | −8.40688 | −0.650544 | −0.325272 | − | 0.945620i | \(-0.605456\pi\) | ||||
−0.325272 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(168\) | −82.6387 | −6.37571 | ||||||||
\(169\) | −2.82459 | −0.217276 | ||||||||
\(170\) | −34.1973 | −2.62281 | ||||||||
\(171\) | 1.68381 | 0.128764 | ||||||||
\(172\) | −70.2809 | −5.35887 | ||||||||
\(173\) | 7.04223 | 0.535411 | 0.267705 | − | 0.963501i | \(-0.413735\pi\) | ||||
0.267705 | + | 0.963501i | \(0.413735\pi\) | |||||||
\(174\) | −61.0271 | −4.62645 | ||||||||
\(175\) | 2.74200 | 0.207276 | ||||||||
\(176\) | −89.9099 | −6.77721 | ||||||||
\(177\) | 8.16321 | 0.613585 | ||||||||
\(178\) | 46.8429 | 3.51102 | ||||||||
\(179\) | 17.2678 | 1.29065 | 0.645327 | − | 0.763907i | \(-0.276721\pi\) | ||||
0.645327 | + | 0.763907i | \(0.276721\pi\) | |||||||
\(180\) | 24.9990 | 1.86331 | ||||||||
\(181\) | −14.2990 | −1.06284 | −0.531419 | − | 0.847109i | \(-0.678341\pi\) | ||||
−0.531419 | + | 0.847109i | \(0.678341\pi\) | |||||||
\(182\) | 33.6172 | 2.49188 | ||||||||
\(183\) | −14.7461 | −1.09006 | ||||||||
\(184\) | −68.5010 | −5.04996 | ||||||||
\(185\) | 7.50551 | 0.551816 | ||||||||
\(186\) | −33.5926 | −2.46313 | ||||||||
\(187\) | −37.1979 | −2.72018 | ||||||||
\(188\) | 23.8246 | 1.73759 | ||||||||
\(189\) | −6.87319 | −0.499951 | ||||||||
\(190\) | −4.27914 | −0.310441 | ||||||||
\(191\) | −10.1148 | −0.731881 | −0.365941 | − | 0.930638i | \(-0.619253\pi\) | ||||
−0.365941 | + | 0.930638i | \(0.619253\pi\) | |||||||
\(192\) | −65.1354 | −4.70074 | ||||||||
\(193\) | −0.585380 | −0.0421366 | −0.0210683 | − | 0.999778i | \(-0.506707\pi\) | ||||
−0.0210683 | + | 0.999778i | \(0.506707\pi\) | |||||||
\(194\) | 46.9469 | 3.37059 | ||||||||
\(195\) | −15.0994 | −1.08129 | ||||||||
\(196\) | 43.1534 | 3.08238 | ||||||||
\(197\) | 7.04891 | 0.502214 | 0.251107 | − | 0.967959i | \(-0.419205\pi\) | ||||
0.251107 | + | 0.967959i | \(0.419205\pi\) | |||||||
\(198\) | 37.2054 | 2.64407 | ||||||||
\(199\) | 1.25169 | 0.0887299 | 0.0443649 | − | 0.999015i | \(-0.485874\pi\) | ||||
0.0443649 | + | 0.999015i | \(0.485874\pi\) | |||||||
\(200\) | 6.63491 | 0.469159 | ||||||||
\(201\) | 25.4534 | 1.79535 | ||||||||
\(202\) | −28.6306 | −2.01444 | ||||||||
\(203\) | 37.8719 | 2.65808 | ||||||||
\(204\) | −75.1665 | −5.26271 | ||||||||
\(205\) | 19.7278 | 1.37785 | ||||||||
\(206\) | −10.8730 | −0.757560 | ||||||||
\(207\) | 16.2712 | 1.13093 | ||||||||
\(208\) | 46.6933 | 3.23760 | ||||||||
\(209\) | −4.65460 | −0.321966 | ||||||||
\(210\) | −49.8849 | −3.44238 | ||||||||
\(211\) | 21.8109 | 1.50153 | 0.750763 | − | 0.660572i | \(-0.229686\pi\) | ||||
0.750763 | + | 0.660572i | \(0.229686\pi\) | |||||||
\(212\) | 24.5004 | 1.68270 | ||||||||
\(213\) | 27.2351 | 1.86612 | ||||||||
\(214\) | −46.6812 | −3.19106 | ||||||||
\(215\) | −26.8031 | −1.82796 | ||||||||
\(216\) | −16.6313 | −1.13162 | ||||||||
\(217\) | 20.8467 | 1.41517 | ||||||||
\(218\) | 22.4223 | 1.51863 | ||||||||
\(219\) | 2.94792 | 0.199202 | ||||||||
\(220\) | −69.1053 | −4.65908 | ||||||||
\(221\) | 19.3182 | 1.29948 | ||||||||
\(222\) | 22.5720 | 1.51493 | ||||||||
\(223\) | 2.05986 | 0.137938 | 0.0689691 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689691 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(224\) | 81.9378 | 5.47470 | ||||||||
\(225\) | −1.57601 | −0.105067 | ||||||||
\(226\) | 6.71560 | 0.446715 | ||||||||
\(227\) | 18.5597 | 1.23185 | 0.615925 | − | 0.787805i | \(-0.288783\pi\) | ||||
0.615925 | + | 0.787805i | \(0.288783\pi\) | |||||||
\(228\) | −9.40564 | −0.622904 | ||||||||
\(229\) | −9.21881 | −0.609196 | −0.304598 | − | 0.952481i | \(-0.598522\pi\) | ||||
−0.304598 | + | 0.952481i | \(0.598522\pi\) | |||||||
\(230\) | −41.3507 | −2.72658 | ||||||||
\(231\) | −54.2620 | −3.57017 | ||||||||
\(232\) | 91.6399 | 6.01646 | ||||||||
\(233\) | −10.1405 | −0.664326 | −0.332163 | − | 0.943222i | \(-0.607778\pi\) | ||||
−0.332163 | + | 0.943222i | \(0.607778\pi\) | |||||||
\(234\) | −19.3220 | −1.26312 | ||||||||
\(235\) | 9.08602 | 0.592707 | ||||||||
\(236\) | −19.4026 | −1.26300 | ||||||||
\(237\) | −1.87592 | −0.121854 | ||||||||
\(238\) | 63.8228 | 4.13702 | ||||||||
\(239\) | 9.08903 | 0.587920 | 0.293960 | − | 0.955818i | \(-0.405027\pi\) | ||||
0.293960 | + | 0.955818i | \(0.405027\pi\) | |||||||
\(240\) | −69.2885 | −4.47255 | ||||||||
\(241\) | −3.46533 | −0.223222 | −0.111611 | − | 0.993752i | \(-0.535601\pi\) | ||||
−0.111611 | + | 0.993752i | \(0.535601\pi\) | |||||||
\(242\) | −72.8610 | −4.68369 | ||||||||
\(243\) | 19.1832 | 1.23060 | ||||||||
\(244\) | 35.0490 | 2.24379 | ||||||||
\(245\) | 16.4575 | 1.05143 | ||||||||
\(246\) | 59.3293 | 3.78270 | ||||||||
\(247\) | 2.41730 | 0.153809 | ||||||||
\(248\) | 50.4435 | 3.20317 | ||||||||
\(249\) | −6.74106 | −0.427197 | ||||||||
\(250\) | 32.2392 | 2.03898 | ||||||||
\(251\) | 16.6526 | 1.05110 | 0.525552 | − | 0.850761i | \(-0.323859\pi\) | ||||
0.525552 | + | 0.850761i | \(0.323859\pi\) | |||||||
\(252\) | −46.6558 | −2.93904 | ||||||||
\(253\) | −44.9789 | −2.82780 | ||||||||
\(254\) | −18.6014 | −1.16715 | ||||||||
\(255\) | −28.6663 | −1.79516 | ||||||||
\(256\) | 39.2575 | 2.45359 | ||||||||
\(257\) | −3.01780 | −0.188245 | −0.0941226 | − | 0.995561i | \(-0.530005\pi\) | ||||
−0.0941226 | + | 0.995561i | \(0.530005\pi\) | |||||||
\(258\) | −80.6074 | −5.01840 | ||||||||
\(259\) | −14.0076 | −0.870391 | ||||||||
\(260\) | 35.8887 | 2.22572 | ||||||||
\(261\) | −21.7675 | −1.34737 | ||||||||
\(262\) | −4.08089 | −0.252118 | ||||||||
\(263\) | −2.67198 | −0.164762 | −0.0823808 | − | 0.996601i | \(-0.526252\pi\) | ||||
−0.0823808 | + | 0.996601i | \(0.526252\pi\) | |||||||
\(264\) | −131.300 | −8.08093 | ||||||||
\(265\) | 9.34376 | 0.573983 | ||||||||
\(266\) | 7.98620 | 0.489665 | ||||||||
\(267\) | 39.2666 | 2.40308 | ||||||||
\(268\) | −60.4986 | −3.69554 | ||||||||
\(269\) | 24.2020 | 1.47562 | 0.737811 | − | 0.675008i | \(-0.235860\pi\) | ||||
0.737811 | + | 0.675008i | \(0.235860\pi\) | |||||||
\(270\) | −10.0395 | −0.610984 | ||||||||
\(271\) | −22.2819 | −1.35353 | −0.676764 | − | 0.736200i | \(-0.736618\pi\) | ||||
−0.676764 | + | 0.736200i | \(0.736618\pi\) | |||||||
\(272\) | 88.6479 | 5.37507 | ||||||||
\(273\) | 28.1801 | 1.70554 | ||||||||
\(274\) | −11.8367 | −0.715079 | ||||||||
\(275\) | 4.35659 | 0.262712 | ||||||||
\(276\) | −90.8897 | −5.47092 | ||||||||
\(277\) | 6.64264 | 0.399118 | 0.199559 | − | 0.979886i | \(-0.436049\pi\) | ||||
0.199559 | + | 0.979886i | \(0.436049\pi\) | |||||||
\(278\) | 3.81009 | 0.228514 | ||||||||
\(279\) | −11.9820 | −0.717341 | ||||||||
\(280\) | 74.9085 | 4.47664 | ||||||||
\(281\) | −22.5868 | −1.34742 | −0.673709 | − | 0.738997i | \(-0.735300\pi\) | ||||
−0.673709 | + | 0.738997i | \(0.735300\pi\) | |||||||
\(282\) | 27.3252 | 1.62719 | ||||||||
\(283\) | 28.3625 | 1.68598 | 0.842988 | − | 0.537932i | \(-0.180794\pi\) | ||||
0.842988 | + | 0.537932i | \(0.180794\pi\) | |||||||
\(284\) | −64.7335 | −3.84123 | ||||||||
\(285\) | −3.58704 | −0.212478 | ||||||||
\(286\) | 53.4124 | 3.15834 | ||||||||
\(287\) | −36.8183 | −2.17331 | ||||||||
\(288\) | −47.0951 | −2.77510 | ||||||||
\(289\) | 19.6758 | 1.15740 | ||||||||
\(290\) | 55.3185 | 3.24841 | ||||||||
\(291\) | 39.3539 | 2.30697 | ||||||||
\(292\) | −7.00673 | −0.410038 | ||||||||
\(293\) | −9.03494 | −0.527827 | −0.263913 | − | 0.964546i | \(-0.585013\pi\) | ||||
−0.263913 | + | 0.964546i | \(0.585013\pi\) | |||||||
\(294\) | 49.4940 | 2.88655 | ||||||||
\(295\) | −7.39961 | −0.430822 | ||||||||
\(296\) | −33.8947 | −1.97009 | ||||||||
\(297\) | −10.9204 | −0.633665 | ||||||||
\(298\) | 3.24813 | 0.188159 | ||||||||
\(299\) | 23.3591 | 1.35089 | ||||||||
\(300\) | 8.80344 | 0.508267 | ||||||||
\(301\) | 50.0229 | 2.88327 | ||||||||
\(302\) | 2.22092 | 0.127800 | ||||||||
\(303\) | −24.0000 | −1.37876 | ||||||||
\(304\) | 11.0926 | 0.636203 | ||||||||
\(305\) | 13.3667 | 0.765375 | ||||||||
\(306\) | −36.6832 | −2.09704 | ||||||||
\(307\) | 15.2929 | 0.872809 | 0.436405 | − | 0.899750i | \(-0.356252\pi\) | ||||
0.436405 | + | 0.899750i | \(0.356252\pi\) | |||||||
\(308\) | 128.972 | 7.34885 | ||||||||
\(309\) | −9.11446 | −0.518504 | ||||||||
\(310\) | 30.4502 | 1.72946 | ||||||||
\(311\) | −24.7082 | −1.40108 | −0.700538 | − | 0.713615i | \(-0.747057\pi\) | ||||
−0.700538 | + | 0.713615i | \(0.747057\pi\) | |||||||
\(312\) | 68.1884 | 3.86041 | ||||||||
\(313\) | −19.5869 | −1.10712 | −0.553558 | − | 0.832811i | \(-0.686730\pi\) | ||||
−0.553558 | + | 0.832811i | \(0.686730\pi\) | |||||||
\(314\) | 37.7113 | 2.12817 | ||||||||
\(315\) | −17.7932 | −1.00253 | ||||||||
\(316\) | 4.45875 | 0.250824 | ||||||||
\(317\) | −9.19818 | −0.516621 | −0.258311 | − | 0.966062i | \(-0.583166\pi\) | ||||
−0.258311 | + | 0.966062i | \(0.583166\pi\) | |||||||
\(318\) | 28.1003 | 1.57579 | ||||||||
\(319\) | 60.1723 | 3.36900 | ||||||||
\(320\) | 59.0424 | 3.30057 | ||||||||
\(321\) | −39.1311 | −2.18409 | ||||||||
\(322\) | 77.1732 | 4.30069 | ||||||||
\(323\) | 4.58927 | 0.255354 | ||||||||
\(324\) | −58.2728 | −3.23738 | ||||||||
\(325\) | −2.26253 | −0.125502 | ||||||||
\(326\) | −1.81791 | −0.100685 | ||||||||
\(327\) | 18.7958 | 1.03941 | ||||||||
\(328\) | −89.0905 | −4.91920 | ||||||||
\(329\) | −16.9573 | −0.934889 | ||||||||
\(330\) | −79.2590 | −4.36307 | ||||||||
\(331\) | 1.61729 | 0.0888941 | 0.0444471 | − | 0.999012i | \(-0.485847\pi\) | ||||
0.0444471 | + | 0.999012i | \(0.485847\pi\) | |||||||
\(332\) | 16.0224 | 0.879344 | ||||||||
\(333\) | 8.05109 | 0.441197 | ||||||||
\(334\) | 22.9178 | 1.25400 | ||||||||
\(335\) | −23.0724 | −1.26058 | ||||||||
\(336\) | 129.314 | 7.05465 | ||||||||
\(337\) | −1.76799 | −0.0963084 | −0.0481542 | − | 0.998840i | \(-0.515334\pi\) | ||||
−0.0481542 | + | 0.998840i | \(0.515334\pi\) | |||||||
\(338\) | 7.70004 | 0.418827 | ||||||||
\(339\) | 5.62944 | 0.305749 | ||||||||
\(340\) | 68.1353 | 3.69515 | ||||||||
\(341\) | 33.1220 | 1.79366 | ||||||||
\(342\) | −4.59019 | −0.248209 | ||||||||
\(343\) | −3.65354 | −0.197272 | ||||||||
\(344\) | 121.042 | 6.52616 | ||||||||
\(345\) | −34.6627 | −1.86618 | ||||||||
\(346\) | −19.1976 | −1.03207 | ||||||||
\(347\) | −2.65348 | −0.142446 | −0.0712231 | − | 0.997460i | \(-0.522690\pi\) | ||||
−0.0712231 | + | 0.997460i | \(0.522690\pi\) | |||||||
\(348\) | 121.591 | 6.51798 | ||||||||
\(349\) | 18.2086 | 0.974682 | 0.487341 | − | 0.873212i | \(-0.337967\pi\) | ||||
0.487341 | + | 0.873212i | \(0.337967\pi\) | |||||||
\(350\) | −7.47488 | −0.399549 | ||||||||
\(351\) | 5.67133 | 0.302713 | ||||||||
\(352\) | 130.186 | 6.93894 | ||||||||
\(353\) | 16.7903 | 0.893658 | 0.446829 | − | 0.894619i | \(-0.352553\pi\) | ||||
0.446829 | + | 0.894619i | \(0.352553\pi\) | |||||||
\(354\) | −22.2535 | −1.18276 | ||||||||
\(355\) | −24.6875 | −1.31028 | ||||||||
\(356\) | −93.3304 | −4.94650 | ||||||||
\(357\) | 53.5003 | 2.83154 | ||||||||
\(358\) | −47.0732 | −2.48789 | ||||||||
\(359\) | 24.5247 | 1.29437 | 0.647183 | − | 0.762335i | \(-0.275947\pi\) | ||||
0.647183 | + | 0.762335i | \(0.275947\pi\) | |||||||
\(360\) | −43.0548 | −2.26919 | ||||||||
\(361\) | −18.4257 | −0.969776 | ||||||||
\(362\) | 38.9802 | 2.04875 | ||||||||
\(363\) | −61.0767 | −3.20570 | ||||||||
\(364\) | −66.9795 | −3.51068 | ||||||||
\(365\) | −2.67217 | −0.139868 | ||||||||
\(366\) | 40.1989 | 2.10123 | ||||||||
\(367\) | −2.94049 | −0.153493 | −0.0767463 | − | 0.997051i | \(-0.524453\pi\) | ||||
−0.0767463 | + | 0.997051i | \(0.524453\pi\) | |||||||
\(368\) | 107.191 | 5.58772 | ||||||||
\(369\) | 21.1619 | 1.10164 | ||||||||
\(370\) | −20.4606 | −1.06369 | ||||||||
\(371\) | −17.4384 | −0.905355 | ||||||||
\(372\) | 66.9303 | 3.47017 | ||||||||
\(373\) | 5.86834 | 0.303851 | 0.151926 | − | 0.988392i | \(-0.451453\pi\) | ||||
0.151926 | + | 0.988392i | \(0.451453\pi\) | |||||||
\(374\) | 101.404 | 5.24349 | ||||||||
\(375\) | 27.0249 | 1.39556 | ||||||||
\(376\) | −41.0323 | −2.11608 | ||||||||
\(377\) | −31.2495 | −1.60943 | ||||||||
\(378\) | 18.7368 | 0.963717 | ||||||||
\(379\) | 8.04106 | 0.413042 | 0.206521 | − | 0.978442i | \(-0.433786\pi\) | ||||
0.206521 | + | 0.978442i | \(0.433786\pi\) | |||||||
\(380\) | 8.52582 | 0.437365 | ||||||||
\(381\) | −15.5929 | −0.798846 | ||||||||
\(382\) | 27.5737 | 1.41079 | ||||||||
\(383\) | 17.8121 | 0.910158 | 0.455079 | − | 0.890451i | \(-0.349611\pi\) | ||||
0.455079 | + | 0.890451i | \(0.349611\pi\) | |||||||
\(384\) | 80.6951 | 4.11795 | ||||||||
\(385\) | 49.1862 | 2.50676 | ||||||||
\(386\) | 1.59579 | 0.0812235 | ||||||||
\(387\) | −28.7515 | −1.46152 | ||||||||
\(388\) | −93.5378 | −4.74866 | ||||||||
\(389\) | −9.02834 | −0.457755 | −0.228878 | − | 0.973455i | \(-0.573506\pi\) | ||||
−0.228878 | + | 0.973455i | \(0.573506\pi\) | |||||||
\(390\) | 41.1619 | 2.08432 | ||||||||
\(391\) | 44.3476 | 2.24275 | ||||||||
\(392\) | −74.3215 | −3.75381 | ||||||||
\(393\) | −3.42086 | −0.172559 | ||||||||
\(394\) | −19.2158 | −0.968079 | ||||||||
\(395\) | 1.70044 | 0.0855583 | ||||||||
\(396\) | −74.1286 | −3.72510 | ||||||||
\(397\) | 10.4179 | 0.522860 | 0.261430 | − | 0.965222i | \(-0.415806\pi\) | ||||
0.261430 | + | 0.965222i | \(0.415806\pi\) | |||||||
\(398\) | −3.41219 | −0.171038 | ||||||||
\(399\) | 6.69453 | 0.335146 | ||||||||
\(400\) | −10.3824 | −0.519119 | ||||||||
\(401\) | 26.2170 | 1.30921 | 0.654607 | − | 0.755969i | \(-0.272834\pi\) | ||||
0.654607 | + | 0.755969i | \(0.272834\pi\) | |||||||
\(402\) | −69.3878 | −3.46075 | ||||||||
\(403\) | −17.2014 | −0.856863 | ||||||||
\(404\) | 57.0441 | 2.83805 | ||||||||
\(405\) | −22.2236 | −1.10430 | ||||||||
\(406\) | −103.241 | −5.12379 | ||||||||
\(407\) | −22.2558 | −1.10318 | ||||||||
\(408\) | 129.457 | 6.40906 | ||||||||
\(409\) | −30.6635 | −1.51621 | −0.758106 | − | 0.652131i | \(-0.773875\pi\) | ||||
−0.758106 | + | 0.652131i | \(0.773875\pi\) | |||||||
\(410\) | −53.7795 | −2.65598 | ||||||||
\(411\) | −9.92224 | −0.489428 | ||||||||
\(412\) | 21.6636 | 1.06729 | ||||||||
\(413\) | 13.8100 | 0.679544 | ||||||||
\(414\) | −44.3565 | −2.18000 | ||||||||
\(415\) | 6.11049 | 0.299952 | ||||||||
\(416\) | −67.6101 | −3.31486 | ||||||||
\(417\) | 3.19386 | 0.156404 | ||||||||
\(418\) | 12.6888 | 0.620629 | ||||||||
\(419\) | 20.2022 | 0.986943 | 0.493472 | − | 0.869762i | \(-0.335728\pi\) | ||||
0.493472 | + | 0.869762i | \(0.335728\pi\) | |||||||
\(420\) | 99.3914 | 4.84980 | ||||||||
\(421\) | −40.9927 | −1.99786 | −0.998931 | − | 0.0462359i | \(-0.985277\pi\) | ||||
−0.998931 | + | 0.0462359i | \(0.985277\pi\) | |||||||
\(422\) | −59.4581 | −2.89438 | ||||||||
\(423\) | 9.74650 | 0.473891 | ||||||||
\(424\) | −42.1962 | −2.04923 | ||||||||
\(425\) | −4.29544 | −0.208359 | ||||||||
\(426\) | −74.2449 | −3.59718 | ||||||||
\(427\) | −24.9464 | −1.20724 | ||||||||
\(428\) | 93.0083 | 4.49573 | ||||||||
\(429\) | 44.7736 | 2.16169 | ||||||||
\(430\) | 73.0672 | 3.52361 | ||||||||
\(431\) | 24.3088 | 1.17091 | 0.585457 | − | 0.810704i | \(-0.300915\pi\) | ||||
0.585457 | + | 0.810704i | \(0.300915\pi\) | |||||||
\(432\) | 26.0248 | 1.25212 | ||||||||
\(433\) | −12.3844 | −0.595158 | −0.297579 | − | 0.954697i | \(-0.596179\pi\) | ||||
−0.297579 | + | 0.954697i | \(0.596179\pi\) | |||||||
\(434\) | −56.8296 | −2.72791 | ||||||||
\(435\) | 46.3714 | 2.22334 | ||||||||
\(436\) | −44.6746 | −2.13952 | ||||||||
\(437\) | 5.54925 | 0.265457 | ||||||||
\(438\) | −8.03625 | −0.383987 | ||||||||
\(439\) | −24.4620 | −1.16751 | −0.583754 | − | 0.811930i | \(-0.698417\pi\) | ||||
−0.583754 | + | 0.811930i | \(0.698417\pi\) | |||||||
\(440\) | 119.018 | 5.67394 | ||||||||
\(441\) | 17.6538 | 0.840656 | ||||||||
\(442\) | −52.6627 | −2.50491 | ||||||||
\(443\) | −23.6989 | −1.12597 | −0.562984 | − | 0.826468i | \(-0.690347\pi\) | ||||
−0.562984 | + | 0.826468i | \(0.690347\pi\) | |||||||
\(444\) | −44.9728 | −2.13431 | ||||||||
\(445\) | −35.5935 | −1.68730 | ||||||||
\(446\) | −5.61532 | −0.265893 | ||||||||
\(447\) | 2.72279 | 0.128784 | ||||||||
\(448\) | −110.192 | −5.20606 | ||||||||
\(449\) | 2.04498 | 0.0965085 | 0.0482543 | − | 0.998835i | \(-0.484634\pi\) | ||||
0.0482543 | + | 0.998835i | \(0.484634\pi\) | |||||||
\(450\) | 4.29631 | 0.202530 | ||||||||
\(451\) | −58.4983 | −2.75458 | ||||||||
\(452\) | −13.3803 | −0.629355 | ||||||||
\(453\) | 1.86172 | 0.0874710 | ||||||||
\(454\) | −50.5950 | −2.37454 | ||||||||
\(455\) | −25.5441 | −1.19752 | ||||||||
\(456\) | 16.1990 | 0.758588 | ||||||||
\(457\) | 30.4406 | 1.42395 | 0.711975 | − | 0.702205i | \(-0.247801\pi\) | ||||
0.711975 | + | 0.702205i | \(0.247801\pi\) | |||||||
\(458\) | 25.1311 | 1.17430 | ||||||||
\(459\) | 10.7671 | 0.502565 | ||||||||
\(460\) | 82.3877 | 3.84135 | ||||||||
\(461\) | −9.32831 | −0.434463 | −0.217231 | − | 0.976120i | \(-0.569703\pi\) | ||||
−0.217231 | + | 0.976120i | \(0.569703\pi\) | |||||||
\(462\) | 147.922 | 6.88195 | ||||||||
\(463\) | 30.4538 | 1.41531 | 0.707653 | − | 0.706560i | \(-0.249754\pi\) | ||||
0.707653 | + | 0.706560i | \(0.249754\pi\) | |||||||
\(464\) | −143.399 | −6.65714 | ||||||||
\(465\) | 25.5253 | 1.18371 | ||||||||
\(466\) | 27.6437 | 1.28057 | ||||||||
\(467\) | 1.33346 | 0.0617054 | 0.0308527 | − | 0.999524i | \(-0.490178\pi\) | ||||
0.0308527 | + | 0.999524i | \(0.490178\pi\) | |||||||
\(468\) | 38.4975 | 1.77955 | ||||||||
\(469\) | 43.0603 | 1.98834 | ||||||||
\(470\) | −24.7692 | −1.14252 | ||||||||
\(471\) | 31.6120 | 1.45660 | ||||||||
\(472\) | 33.4165 | 1.53812 | ||||||||
\(473\) | 79.4784 | 3.65442 | ||||||||
\(474\) | 5.11388 | 0.234888 | ||||||||
\(475\) | −0.537492 | −0.0246618 | ||||||||
\(476\) | −127.162 | −5.82844 | ||||||||
\(477\) | 10.0230 | 0.458920 | ||||||||
\(478\) | −24.7773 | −1.13329 | ||||||||
\(479\) | 6.55120 | 0.299332 | 0.149666 | − | 0.988737i | \(-0.452180\pi\) | ||||
0.149666 | + | 0.988737i | \(0.452180\pi\) | |||||||
\(480\) | 100.327 | 4.57928 | ||||||||
\(481\) | 11.5582 | 0.527010 | ||||||||
\(482\) | 9.44675 | 0.430288 | ||||||||
\(483\) | 64.6914 | 2.94356 | ||||||||
\(484\) | 145.169 | 6.59861 | ||||||||
\(485\) | −35.6726 | −1.61981 | ||||||||
\(486\) | −52.2949 | −2.37214 | ||||||||
\(487\) | 6.62625 | 0.300264 | 0.150132 | − | 0.988666i | \(-0.452030\pi\) | ||||
0.150132 | + | 0.988666i | \(0.452030\pi\) | |||||||
\(488\) | −60.3637 | −2.73254 | ||||||||
\(489\) | −1.52389 | −0.0689127 | ||||||||
\(490\) | −44.8642 | −2.02676 | ||||||||
\(491\) | −12.1796 | −0.549656 | −0.274828 | − | 0.961493i | \(-0.588621\pi\) | ||||
−0.274828 | + | 0.961493i | \(0.588621\pi\) | |||||||
\(492\) | −118.209 | −5.32926 | ||||||||
\(493\) | −59.3277 | −2.67199 | ||||||||
\(494\) | −6.58972 | −0.296486 | ||||||||
\(495\) | −28.2705 | −1.27067 | ||||||||
\(496\) | −78.9345 | −3.54426 | ||||||||
\(497\) | 46.0745 | 2.06673 | ||||||||
\(498\) | 18.3766 | 0.823476 | ||||||||
\(499\) | −17.1691 | −0.768595 | −0.384297 | − | 0.923209i | \(-0.625556\pi\) | ||||
−0.384297 | + | 0.923209i | \(0.625556\pi\) | |||||||
\(500\) | −64.2338 | −2.87262 | ||||||||
\(501\) | 19.2111 | 0.858289 | ||||||||
\(502\) | −45.3963 | −2.02613 | ||||||||
\(503\) | 29.3780 | 1.30990 | 0.654950 | − | 0.755672i | \(-0.272690\pi\) | ||||
0.654950 | + | 0.755672i | \(0.272690\pi\) | |||||||
\(504\) | 80.3537 | 3.57924 | ||||||||
\(505\) | 21.7550 | 0.968084 | ||||||||
\(506\) | 122.616 | 5.45094 | ||||||||
\(507\) | 6.45466 | 0.286661 | ||||||||
\(508\) | 37.0617 | 1.64435 | ||||||||
\(509\) | 40.9727 | 1.81608 | 0.908041 | − | 0.418881i | \(-0.137578\pi\) | ||||
0.908041 | + | 0.418881i | \(0.137578\pi\) | |||||||
\(510\) | 78.1465 | 3.46039 | ||||||||
\(511\) | 4.98709 | 0.220616 | ||||||||
\(512\) | −36.3935 | −1.60838 | ||||||||
\(513\) | 1.34730 | 0.0594846 | ||||||||
\(514\) | 8.22674 | 0.362866 | ||||||||
\(515\) | 8.26187 | 0.364062 | ||||||||
\(516\) | 160.603 | 7.07017 | ||||||||
\(517\) | −26.9425 | −1.18493 | ||||||||
\(518\) | 38.1858 | 1.67779 | ||||||||
\(519\) | −16.0926 | −0.706389 | ||||||||
\(520\) | −61.8099 | −2.71054 | ||||||||
\(521\) | 24.0855 | 1.05520 | 0.527602 | − | 0.849491i | \(-0.323091\pi\) | ||||
0.527602 | + | 0.849491i | \(0.323091\pi\) | |||||||
\(522\) | 59.3396 | 2.59723 | ||||||||
\(523\) | 1.72203 | 0.0752990 | 0.0376495 | − | 0.999291i | \(-0.488013\pi\) | ||||
0.0376495 | + | 0.999291i | \(0.488013\pi\) | |||||||
\(524\) | 8.13083 | 0.355197 | ||||||||
\(525\) | −6.26592 | −0.273467 | ||||||||
\(526\) | 7.28402 | 0.317598 | ||||||||
\(527\) | −32.6571 | −1.42257 | ||||||||
\(528\) | 205.459 | 8.94145 | ||||||||
\(529\) | 30.6242 | 1.33149 | ||||||||
\(530\) | −25.4718 | −1.10642 | ||||||||
\(531\) | −7.93749 | −0.344458 | ||||||||
\(532\) | −15.9118 | −0.689865 | ||||||||
\(533\) | 30.3802 | 1.31591 | ||||||||
\(534\) | −107.044 | −4.63223 | ||||||||
\(535\) | 35.4707 | 1.53353 | ||||||||
\(536\) | 104.195 | 4.50052 | ||||||||
\(537\) | −39.4597 | −1.70281 | ||||||||
\(538\) | −65.9764 | −2.84444 | ||||||||
\(539\) | −48.8008 | −2.10200 | ||||||||
\(540\) | 20.0028 | 0.860785 | ||||||||
\(541\) | 21.5318 | 0.925723 | 0.462862 | − | 0.886431i | \(-0.346823\pi\) | ||||
0.462862 | + | 0.886431i | \(0.346823\pi\) | |||||||
\(542\) | 60.7420 | 2.60909 | ||||||||
\(543\) | 32.6756 | 1.40225 | ||||||||
\(544\) | −128.359 | −5.50333 | ||||||||
\(545\) | −17.0376 | −0.729811 | ||||||||
\(546\) | −76.8210 | −3.28763 | ||||||||
\(547\) | 33.6962 | 1.44075 | 0.720374 | − | 0.693586i | \(-0.243970\pi\) | ||||
0.720374 | + | 0.693586i | \(0.243970\pi\) | |||||||
\(548\) | 23.5836 | 1.00744 | ||||||||
\(549\) | 14.3383 | 0.611945 | ||||||||
\(550\) | −11.8764 | −0.506411 | ||||||||
\(551\) | −7.42372 | −0.316261 | ||||||||
\(552\) | 156.536 | 6.66262 | ||||||||
\(553\) | −3.17354 | −0.134953 | ||||||||
\(554\) | −18.1083 | −0.769349 | ||||||||
\(555\) | −17.1513 | −0.728033 | ||||||||
\(556\) | −7.59129 | −0.321942 | ||||||||
\(557\) | 43.7948 | 1.85565 | 0.927823 | − | 0.373020i | \(-0.121678\pi\) | ||||
0.927823 | + | 0.373020i | \(0.121678\pi\) | |||||||
\(558\) | 32.6637 | 1.38276 | ||||||||
\(559\) | −41.2759 | −1.74578 | ||||||||
\(560\) | −117.218 | −4.95335 | ||||||||
\(561\) | 85.0034 | 3.58885 | ||||||||
\(562\) | 61.5734 | 2.59732 | ||||||||
\(563\) | −34.3526 | −1.44779 | −0.723894 | − | 0.689911i | \(-0.757650\pi\) | ||||
−0.723894 | + | 0.689911i | \(0.757650\pi\) | |||||||
\(564\) | −54.4432 | −2.29247 | ||||||||
\(565\) | −5.10285 | −0.214679 | ||||||||
\(566\) | −77.3182 | −3.24993 | ||||||||
\(567\) | 41.4761 | 1.74183 | ||||||||
\(568\) | 111.488 | 4.67794 | ||||||||
\(569\) | 37.5780 | 1.57535 | 0.787677 | − | 0.616089i | \(-0.211284\pi\) | ||||
0.787677 | + | 0.616089i | \(0.211284\pi\) | |||||||
\(570\) | 9.77853 | 0.409578 | ||||||||
\(571\) | 8.45535 | 0.353845 | 0.176923 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176923 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(572\) | −106.420 | −4.44963 | ||||||||
\(573\) | 23.1140 | 0.965601 | ||||||||
\(574\) | 100.369 | 4.18933 | ||||||||
\(575\) | −5.19396 | −0.216603 | ||||||||
\(576\) | 63.3343 | 2.63893 | ||||||||
\(577\) | 4.84244 | 0.201593 | 0.100797 | − | 0.994907i | \(-0.467861\pi\) | ||||
0.100797 | + | 0.994907i | \(0.467861\pi\) | |||||||
\(578\) | −53.6376 | −2.23103 | ||||||||
\(579\) | 1.33769 | 0.0555925 | ||||||||
\(580\) | −110.217 | −4.57653 | ||||||||
\(581\) | −11.4041 | −0.473120 | ||||||||
\(582\) | −107.282 | −4.44696 | ||||||||
\(583\) | −27.7068 | −1.14750 | ||||||||
\(584\) | 12.0675 | 0.499355 | ||||||||
\(585\) | 14.6819 | 0.607020 | ||||||||
\(586\) | 24.6299 | 1.01745 | ||||||||
\(587\) | 24.0691 | 0.993438 | 0.496719 | − | 0.867911i | \(-0.334538\pi\) | ||||
0.496719 | + | 0.867911i | \(0.334538\pi\) | |||||||
\(588\) | −98.6126 | −4.06671 | ||||||||
\(589\) | −4.08641 | −0.168378 | ||||||||
\(590\) | 20.1719 | 0.830462 | ||||||||
\(591\) | −16.1079 | −0.662591 | ||||||||
\(592\) | 53.0388 | 2.17988 | ||||||||
\(593\) | −19.1666 | −0.787078 | −0.393539 | − | 0.919308i | \(-0.628749\pi\) | ||||
−0.393539 | + | 0.919308i | \(0.628749\pi\) | |||||||
\(594\) | 29.7698 | 1.22147 | ||||||||
\(595\) | −48.4958 | −1.98813 | ||||||||
\(596\) | −6.47163 | −0.265088 | ||||||||
\(597\) | −2.86031 | −0.117065 | ||||||||
\(598\) | −63.6786 | −2.60401 | ||||||||
\(599\) | 28.2490 | 1.15422 | 0.577112 | − | 0.816665i | \(-0.304180\pi\) | ||||
0.577112 | + | 0.816665i | \(0.304180\pi\) | |||||||
\(600\) | −15.1619 | −0.618980 | ||||||||
\(601\) | 25.5535 | 1.04235 | 0.521174 | − | 0.853450i | \(-0.325494\pi\) | ||||
0.521174 | + | 0.853450i | \(0.325494\pi\) | |||||||
\(602\) | −136.366 | −5.55787 | ||||||||
\(603\) | −24.7496 | −1.00788 | ||||||||
\(604\) | −4.42499 | −0.180050 | ||||||||
\(605\) | 55.3635 | 2.25084 | ||||||||
\(606\) | 65.4257 | 2.65774 | ||||||||
\(607\) | 8.41061 | 0.341376 | 0.170688 | − | 0.985325i | \(-0.445401\pi\) | ||||
0.170688 | + | 0.985325i | \(0.445401\pi\) | |||||||
\(608\) | −16.0616 | −0.651385 | ||||||||
\(609\) | −86.5435 | −3.50692 | ||||||||
\(610\) | −36.4386 | −1.47535 | ||||||||
\(611\) | 13.9922 | 0.566062 | ||||||||
\(612\) | 73.0881 | 2.95441 | ||||||||
\(613\) | 25.7072 | 1.03831 | 0.519153 | − | 0.854681i | \(-0.326248\pi\) | ||||
0.519153 | + | 0.854681i | \(0.326248\pi\) | |||||||
\(614\) | −41.6894 | −1.68245 | ||||||||
\(615\) | −45.0814 | −1.81786 | ||||||||
\(616\) | −222.124 | −8.94962 | ||||||||
\(617\) | 2.90387 | 0.116905 | 0.0584526 | − | 0.998290i | \(-0.481383\pi\) | ||||
0.0584526 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(618\) | 24.8467 | 0.999480 | ||||||||
\(619\) | −2.49905 | −0.100445 | −0.0502226 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502226 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(620\) | −60.6695 | −2.43655 | ||||||||
\(621\) | 13.0194 | 0.522449 | ||||||||
\(622\) | 67.3564 | 2.70075 | ||||||||
\(623\) | 66.4286 | 2.66141 | ||||||||
\(624\) | −106.702 | −4.27149 | ||||||||
\(625\) | −20.9505 | −0.838021 | ||||||||
\(626\) | 53.3952 | 2.13410 | ||||||||
\(627\) | 10.6365 | 0.424782 | ||||||||
\(628\) | −75.1366 | −2.99828 | ||||||||
\(629\) | 21.9434 | 0.874942 | ||||||||
\(630\) | 48.5055 | 1.93251 | ||||||||
\(631\) | −3.67302 | −0.146221 | −0.0731103 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731103 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(632\) | −7.67914 | −0.305460 | ||||||||
\(633\) | −49.8416 | −1.98102 | ||||||||
\(634\) | 25.0749 | 0.995851 | ||||||||
\(635\) | 14.1343 | 0.560901 | ||||||||
\(636\) | −55.9875 | −2.22005 | ||||||||
\(637\) | 25.3439 | 1.00416 | ||||||||
\(638\) | −164.034 | −6.49417 | ||||||||
\(639\) | −26.4821 | −1.04761 | ||||||||
\(640\) | −73.1467 | −2.89138 | ||||||||
\(641\) | −13.8263 | −0.546105 | −0.273053 | − | 0.961999i | \(-0.588033\pi\) | ||||
−0.273053 | + | 0.961999i | \(0.588033\pi\) | |||||||
\(642\) | 106.674 | 4.21010 | ||||||||
\(643\) | −25.4295 | −1.00284 | −0.501421 | − | 0.865203i | \(-0.667189\pi\) | ||||
−0.501421 | + | 0.865203i | \(0.667189\pi\) | |||||||
\(644\) | −153.761 | −6.05903 | ||||||||
\(645\) | 61.2495 | 2.41170 | ||||||||
\(646\) | −12.5107 | −0.492226 | ||||||||
\(647\) | 16.0789 | 0.632128 | 0.316064 | − | 0.948738i | \(-0.397639\pi\) | ||||
0.316064 | + | 0.948738i | \(0.397639\pi\) | |||||||
\(648\) | 100.361 | 3.94256 | ||||||||
\(649\) | 21.9418 | 0.861291 | ||||||||
\(650\) | 6.16781 | 0.241922 | ||||||||
\(651\) | −47.6381 | −1.86709 | ||||||||
\(652\) | 3.62204 | 0.141850 | ||||||||
\(653\) | 24.9361 | 0.975824 | 0.487912 | − | 0.872893i | \(-0.337759\pi\) | ||||
0.487912 | + | 0.872893i | \(0.337759\pi\) | |||||||
\(654\) | −51.2387 | −2.00359 | ||||||||
\(655\) | 3.10086 | 0.121161 | ||||||||
\(656\) | 139.410 | 5.44304 | ||||||||
\(657\) | −2.86641 | −0.111829 | ||||||||
\(658\) | 46.2269 | 1.80211 | ||||||||
\(659\) | 43.7648 | 1.70483 | 0.852417 | − | 0.522862i | \(-0.175136\pi\) | ||||
0.852417 | + | 0.522862i | \(0.175136\pi\) | |||||||
\(660\) | 157.917 | 6.14691 | ||||||||
\(661\) | −6.71325 | −0.261115 | −0.130558 | − | 0.991441i | \(-0.541677\pi\) | ||||
−0.130558 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(662\) | −4.40884 | −0.171354 | ||||||||
\(663\) | −44.1452 | −1.71446 | ||||||||
\(664\) | −27.5948 | −1.07089 | ||||||||
\(665\) | −6.06831 | −0.235319 | ||||||||
\(666\) | −21.9479 | −0.850462 | ||||||||
\(667\) | −71.7378 | −2.77770 | ||||||||
\(668\) | −45.6617 | −1.76670 | ||||||||
\(669\) | −4.70711 | −0.181988 | ||||||||
\(670\) | 62.8971 | 2.42993 | ||||||||
\(671\) | −39.6358 | −1.53012 | ||||||||
\(672\) | −187.241 | −7.22300 | ||||||||
\(673\) | −18.6325 | −0.718232 | −0.359116 | − | 0.933293i | \(-0.616922\pi\) | ||||
−0.359116 | + | 0.933293i | \(0.616922\pi\) | |||||||
\(674\) | 4.81966 | 0.185646 | ||||||||
\(675\) | −1.26104 | −0.0485373 | ||||||||
\(676\) | −15.3417 | −0.590064 | ||||||||
\(677\) | 2.65791 | 0.102152 | 0.0510760 | − | 0.998695i | \(-0.483735\pi\) | ||||
0.0510760 | + | 0.998695i | \(0.483735\pi\) | |||||||
\(678\) | −15.3463 | −0.589370 | ||||||||
\(679\) | 66.5762 | 2.55496 | ||||||||
\(680\) | −117.347 | −4.50005 | ||||||||
\(681\) | −42.4119 | −1.62523 | ||||||||
\(682\) | −90.2931 | −3.45750 | ||||||||
\(683\) | −13.4241 | −0.513660 | −0.256830 | − | 0.966457i | \(-0.582678\pi\) | ||||
−0.256830 | + | 0.966457i | \(0.582678\pi\) | |||||||
\(684\) | 9.14557 | 0.349690 | ||||||||
\(685\) | 8.99409 | 0.343647 | ||||||||
\(686\) | 9.95980 | 0.380267 | ||||||||
\(687\) | 21.0665 | 0.803737 | ||||||||
\(688\) | −189.408 | −7.22112 | ||||||||
\(689\) | 14.3891 | 0.548180 | ||||||||
\(690\) | 94.4931 | 3.59729 | ||||||||
\(691\) | 47.1512 | 1.79371 | 0.896857 | − | 0.442320i | \(-0.145844\pi\) | ||||
0.896857 | + | 0.442320i | \(0.145844\pi\) | |||||||
\(692\) | 38.2496 | 1.45403 | ||||||||
\(693\) | 52.7616 | 2.00425 | ||||||||
\(694\) | 7.23358 | 0.274583 | ||||||||
\(695\) | −2.89510 | −0.109817 | ||||||||
\(696\) | −209.412 | −7.93776 | ||||||||
\(697\) | 57.6772 | 2.18468 | ||||||||
\(698\) | −49.6378 | −1.87882 | ||||||||
\(699\) | 23.1727 | 0.876472 | ||||||||
\(700\) | 14.8931 | 0.562905 | ||||||||
\(701\) | −2.30639 | −0.0871113 | −0.0435556 | − | 0.999051i | \(-0.513869\pi\) | ||||
−0.0435556 | + | 0.999051i | \(0.513869\pi\) | |||||||
\(702\) | −15.4605 | −0.583517 | ||||||||
\(703\) | 2.74580 | 0.103560 | ||||||||
\(704\) | −175.077 | −6.59845 | ||||||||
\(705\) | −20.7631 | −0.781982 | ||||||||
\(706\) | −45.7716 | −1.72264 | ||||||||
\(707\) | −40.6015 | −1.52698 | ||||||||
\(708\) | 44.3382 | 1.66633 | ||||||||
\(709\) | 13.5611 | 0.509297 | 0.254648 | − | 0.967034i | \(-0.418040\pi\) | ||||
0.254648 | + | 0.967034i | \(0.418040\pi\) | |||||||
\(710\) | 67.2999 | 2.52572 | ||||||||
\(711\) | 1.82404 | 0.0684070 | ||||||||
\(712\) | 160.740 | 6.02398 | ||||||||
\(713\) | −39.4883 | −1.47885 | ||||||||
\(714\) | −145.846 | −5.45814 | ||||||||
\(715\) | −40.5854 | −1.51781 | ||||||||
\(716\) | 93.7893 | 3.50507 | ||||||||
\(717\) | −20.7699 | −0.775667 | ||||||||
\(718\) | −66.8562 | −2.49505 | ||||||||
\(719\) | 10.6361 | 0.396658 | 0.198329 | − | 0.980136i | \(-0.436449\pi\) | ||||
0.198329 | + | 0.980136i | \(0.436449\pi\) | |||||||
\(720\) | 67.3726 | 2.51083 | ||||||||
\(721\) | −15.4192 | −0.574242 | ||||||||
\(722\) | 50.2299 | 1.86936 | ||||||||
\(723\) | 7.91886 | 0.294506 | ||||||||
\(724\) | −77.6647 | −2.88639 | ||||||||
\(725\) | 6.94842 | 0.258058 | ||||||||
\(726\) | 166.500 | 6.17938 | ||||||||
\(727\) | 0.990585 | 0.0367388 | 0.0183694 | − | 0.999831i | \(-0.494153\pi\) | ||||
0.0183694 | + | 0.999831i | \(0.494153\pi\) | |||||||
\(728\) | 115.356 | 4.27539 | ||||||||
\(729\) | −11.6506 | −0.431504 | ||||||||
\(730\) | 7.28452 | 0.269612 | ||||||||
\(731\) | −78.3628 | −2.89835 | ||||||||
\(732\) | −80.0928 | −2.96032 | ||||||||
\(733\) | −12.8622 | −0.475078 | −0.237539 | − | 0.971378i | \(-0.576341\pi\) | ||||
−0.237539 | + | 0.971378i | \(0.576341\pi\) | |||||||
\(734\) | 8.01600 | 0.295876 | ||||||||
\(735\) | −37.6080 | −1.38719 | ||||||||
\(736\) | −155.209 | −5.72106 | ||||||||
\(737\) | 68.4160 | 2.52013 | ||||||||
\(738\) | −57.6888 | −2.12356 | ||||||||
\(739\) | 26.4736 | 0.973847 | 0.486924 | − | 0.873445i | \(-0.338119\pi\) | ||||
0.486924 | + | 0.873445i | \(0.338119\pi\) | |||||||
\(740\) | 40.7659 | 1.49858 | ||||||||
\(741\) | −5.52392 | −0.202926 | ||||||||
\(742\) | 47.5382 | 1.74518 | ||||||||
\(743\) | 2.41005 | 0.0884160 | 0.0442080 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442080 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(744\) | −115.272 | −4.22607 | ||||||||
\(745\) | −2.46809 | −0.0904240 | ||||||||
\(746\) | −15.9975 | −0.585711 | ||||||||
\(747\) | 6.55466 | 0.239823 | ||||||||
\(748\) | −202.039 | −7.38729 | ||||||||
\(749\) | −66.1993 | −2.41887 | ||||||||
\(750\) | −73.6718 | −2.69011 | ||||||||
\(751\) | −15.0691 | −0.549878 | −0.274939 | − | 0.961462i | \(-0.588658\pi\) | ||||
−0.274939 | + | 0.961462i | \(0.588658\pi\) | |||||||
\(752\) | 64.2077 | 2.34142 | ||||||||
\(753\) | −38.0540 | −1.38677 | ||||||||
\(754\) | 85.1885 | 3.10238 | ||||||||
\(755\) | −1.68757 | −0.0614168 | ||||||||
\(756\) | −37.3315 | −1.35773 | ||||||||
\(757\) | 16.8635 | 0.612913 | 0.306457 | − | 0.951885i | \(-0.400857\pi\) | ||||
0.306457 | + | 0.951885i | \(0.400857\pi\) | |||||||
\(758\) | −21.9205 | −0.796189 | ||||||||
\(759\) | 102.784 | 3.73083 | ||||||||
\(760\) | −14.6837 | −0.532634 | ||||||||
\(761\) | 33.1020 | 1.19995 | 0.599973 | − | 0.800020i | \(-0.295178\pi\) | ||||
0.599973 | + | 0.800020i | \(0.295178\pi\) | |||||||
\(762\) | 42.5072 | 1.53987 | ||||||||
\(763\) | 31.7975 | 1.15115 | ||||||||
\(764\) | −54.9382 | −1.98759 | ||||||||
\(765\) | 27.8737 | 1.00778 | ||||||||
\(766\) | −48.5572 | −1.75444 | ||||||||
\(767\) | −11.3951 | −0.411454 | ||||||||
\(768\) | −89.7098 | −3.23712 | ||||||||
\(769\) | 21.4190 | 0.772388 | 0.386194 | − | 0.922418i | \(-0.373789\pi\) | ||||
0.386194 | + | 0.922418i | \(0.373789\pi\) | |||||||
\(770\) | −134.085 | −4.83209 | ||||||||
\(771\) | 6.89617 | 0.248360 | ||||||||
\(772\) | −3.17947 | −0.114432 | ||||||||
\(773\) | −23.6280 | −0.849839 | −0.424919 | − | 0.905231i | \(-0.639698\pi\) | ||||
−0.424919 | + | 0.905231i | \(0.639698\pi\) | |||||||
\(774\) | 78.3786 | 2.81726 | ||||||||
\(775\) | 3.82478 | 0.137390 | ||||||||
\(776\) | 161.097 | 5.78304 | ||||||||
\(777\) | 32.0097 | 1.14834 | ||||||||
\(778\) | 24.6119 | 0.882379 | ||||||||
\(779\) | 7.21720 | 0.258583 | ||||||||
\(780\) | −82.0117 | −2.93649 | ||||||||
\(781\) | 73.2050 | 2.61948 | ||||||||
\(782\) | −120.895 | −4.32319 | ||||||||
\(783\) | −17.4171 | −0.622438 | ||||||||
\(784\) | 116.299 | 4.15354 | ||||||||
\(785\) | −28.6550 | −1.02274 | ||||||||
\(786\) | 9.32550 | 0.332630 | ||||||||
\(787\) | −16.5227 | −0.588971 | −0.294485 | − | 0.955656i | \(-0.595148\pi\) | ||||
−0.294485 | + | 0.955656i | \(0.595148\pi\) | |||||||
\(788\) | 38.2859 | 1.36388 | ||||||||
\(789\) | 6.10593 | 0.217377 | ||||||||
\(790\) | −4.63551 | −0.164924 | ||||||||
\(791\) | 9.52351 | 0.338617 | ||||||||
\(792\) | 127.669 | 4.53652 | ||||||||
\(793\) | 20.5842 | 0.730968 | ||||||||
\(794\) | −28.4000 | −1.00788 | ||||||||
\(795\) | −21.3520 | −0.757279 | ||||||||
\(796\) | 6.79850 | 0.240967 | ||||||||
\(797\) | 24.8378 | 0.879801 | 0.439901 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439901 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(798\) | −18.2498 | −0.646035 | ||||||||
\(799\) | 26.5643 | 0.939778 | ||||||||
\(800\) | 15.0333 | 0.531506 | ||||||||
\(801\) | −38.1809 | −1.34906 | ||||||||
\(802\) | −71.4694 | −2.52367 | ||||||||
\(803\) | 7.92369 | 0.279621 | ||||||||
\(804\) | 138.249 | 4.87568 | ||||||||
\(805\) | −58.6400 | −2.06679 | ||||||||
\(806\) | 46.8923 | 1.65171 | ||||||||
\(807\) | −55.3055 | −1.94685 | ||||||||
\(808\) | −98.2450 | −3.45625 | ||||||||
\(809\) | 0.279752 | 0.00983556 | 0.00491778 | − | 0.999988i | \(-0.498435\pi\) | ||||
0.00491778 | + | 0.999988i | \(0.498435\pi\) | |||||||
\(810\) | 60.5831 | 2.12867 | ||||||||
\(811\) | 15.9210 | 0.559062 | 0.279531 | − | 0.960137i | \(-0.409821\pi\) | ||||
0.279531 | + | 0.960137i | \(0.409821\pi\) | |||||||
\(812\) | 205.700 | 7.21865 | ||||||||
\(813\) | 50.9178 | 1.78576 | ||||||||
\(814\) | 60.6710 | 2.12652 | ||||||||
\(815\) | 1.38134 | 0.0483863 | ||||||||
\(816\) | −202.575 | −7.09154 | ||||||||
\(817\) | −9.80560 | −0.343054 | ||||||||
\(818\) | 83.5909 | 2.92269 | ||||||||
\(819\) | −27.4009 | −0.957465 | ||||||||
\(820\) | 107.151 | 3.74188 | ||||||||
\(821\) | 40.4564 | 1.41194 | 0.705969 | − | 0.708242i | \(-0.250512\pi\) | ||||
0.705969 | + | 0.708242i | \(0.250512\pi\) | |||||||
\(822\) | 27.0487 | 0.943433 | ||||||||
\(823\) | −24.7327 | −0.862129 | −0.431065 | − | 0.902321i | \(-0.641862\pi\) | ||||
−0.431065 | + | 0.902321i | \(0.641862\pi\) | |||||||
\(824\) | −37.3105 | −1.29977 | ||||||||
\(825\) | −9.95553 | −0.346607 | ||||||||
\(826\) | −37.6469 | −1.30990 | ||||||||
\(827\) | −44.1088 | −1.53381 | −0.766907 | − | 0.641758i | \(-0.778205\pi\) | ||||
−0.766907 | + | 0.641758i | \(0.778205\pi\) | |||||||
\(828\) | 88.3766 | 3.07130 | ||||||||
\(829\) | −22.0942 | −0.767363 | −0.383681 | − | 0.923465i | \(-0.625344\pi\) | ||||
−0.383681 | + | 0.923465i | \(0.625344\pi\) | |||||||
\(830\) | −16.6576 | −0.578194 | ||||||||
\(831\) | −15.1795 | −0.526572 | ||||||||
\(832\) | 90.9233 | 3.15220 | ||||||||
\(833\) | 48.1158 | 1.66711 | ||||||||
\(834\) | −8.70669 | −0.301488 | ||||||||
\(835\) | −17.4141 | −0.602638 | ||||||||
\(836\) | −25.2813 | −0.874373 | ||||||||
\(837\) | −9.58732 | −0.331386 | ||||||||
\(838\) | −55.0727 | −1.90245 | ||||||||
\(839\) | −1.24134 | −0.0428559 | −0.0214280 | − | 0.999770i | \(-0.506821\pi\) | ||||
−0.0214280 | + | 0.999770i | \(0.506821\pi\) | |||||||
\(840\) | −171.178 | −5.90621 | ||||||||
\(841\) | 66.9700 | 2.30931 | ||||||||
\(842\) | 111.749 | 3.85112 | ||||||||
\(843\) | 51.6147 | 1.77770 | ||||||||
\(844\) | 118.465 | 4.07774 | ||||||||
\(845\) | −5.85087 | −0.201276 | ||||||||
\(846\) | −26.5697 | −0.913484 | ||||||||
\(847\) | −103.325 | −3.55030 | ||||||||
\(848\) | 66.0291 | 2.26745 | ||||||||
\(849\) | −64.8130 | −2.22438 | ||||||||
\(850\) | 11.7097 | 0.401639 | ||||||||
\(851\) | 26.5335 | 0.909558 | ||||||||
\(852\) | 147.927 | 5.06788 | ||||||||
\(853\) | 32.5193 | 1.11344 | 0.556719 | − | 0.830701i | \(-0.312060\pi\) | ||||
0.556719 | + | 0.830701i | \(0.312060\pi\) | |||||||
\(854\) | 68.0057 | 2.32711 | ||||||||
\(855\) | 3.48786 | 0.119282 | ||||||||
\(856\) | −160.185 | −5.47501 | ||||||||
\(857\) | −0.592345 | −0.0202341 | −0.0101171 | − | 0.999949i | \(-0.503220\pi\) | ||||
−0.0101171 | + | 0.999949i | \(0.503220\pi\) | |||||||
\(858\) | −122.056 | −4.16693 | ||||||||
\(859\) | −57.4210 | −1.95918 | −0.979589 | − | 0.201012i | \(-0.935577\pi\) | ||||
−0.979589 | + | 0.201012i | \(0.935577\pi\) | |||||||
\(860\) | −145.580 | −4.96424 | ||||||||
\(861\) | 84.1359 | 2.86734 | ||||||||
\(862\) | −66.2675 | −2.25708 | ||||||||
\(863\) | −0.0219008 | −0.000745512 0 | −0.000372756 | − | 1.00000i | \(-0.500119\pi\) | ||||
−0.000372756 | 1.00000i | \(0.500119\pi\) | ||||||||
\(864\) | −37.6829 | −1.28200 | ||||||||
\(865\) | 14.5873 | 0.495983 | ||||||||
\(866\) | 33.7608 | 1.14724 | ||||||||
\(867\) | −44.9624 | −1.52700 | ||||||||
\(868\) | 113.228 | 3.84321 | ||||||||
\(869\) | −5.04225 | −0.171047 | ||||||||
\(870\) | −126.412 | −4.28576 | ||||||||
\(871\) | −35.5307 | −1.20391 | ||||||||
\(872\) | 76.9415 | 2.60557 | ||||||||
\(873\) | −38.2657 | −1.29510 | ||||||||
\(874\) | −15.1276 | −0.511700 | ||||||||
\(875\) | 45.7189 | 1.54558 | ||||||||
\(876\) | 16.0115 | 0.540980 | ||||||||
\(877\) | −14.0224 | −0.473504 | −0.236752 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236752 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(878\) | 66.6852 | 2.25052 | ||||||||
\(879\) | 20.6463 | 0.696383 | ||||||||
\(880\) | −186.240 | −6.27814 | ||||||||
\(881\) | −17.6017 | −0.593016 | −0.296508 | − | 0.955030i | \(-0.595822\pi\) | ||||
−0.296508 | + | 0.955030i | \(0.595822\pi\) | |||||||
\(882\) | −48.1255 | −1.62047 | ||||||||
\(883\) | 1.39119 | 0.0468174 | 0.0234087 | − | 0.999726i | \(-0.492548\pi\) | ||||
0.0234087 | + | 0.999726i | \(0.492548\pi\) | |||||||
\(884\) | 104.926 | 3.52904 | ||||||||
\(885\) | 16.9093 | 0.568401 | ||||||||
\(886\) | 64.6048 | 2.17044 | ||||||||
\(887\) | −29.5738 | −0.992991 | −0.496495 | − | 0.868039i | \(-0.665380\pi\) | ||||
−0.496495 | + | 0.868039i | \(0.665380\pi\) | |||||||
\(888\) | 77.4550 | 2.59922 | ||||||||
\(889\) | −26.3789 | −0.884721 | ||||||||
\(890\) | 97.0306 | 3.25247 | ||||||||
\(891\) | 65.8989 | 2.20770 | ||||||||
\(892\) | 11.1880 | 0.374604 | ||||||||
\(893\) | 3.32401 | 0.111234 | ||||||||
\(894\) | −7.42252 | −0.248246 | ||||||||
\(895\) | 35.7685 | 1.19561 | ||||||||
\(896\) | 136.514 | 4.56063 | ||||||||
\(897\) | −53.3794 | −1.78229 | ||||||||
\(898\) | −5.57476 | −0.186032 | ||||||||
\(899\) | 52.8270 | 1.76188 | ||||||||
\(900\) | −8.56002 | −0.285334 | ||||||||
\(901\) | 27.3178 | 0.910089 | ||||||||
\(902\) | 159.471 | 5.30979 | ||||||||
\(903\) | −114.311 | −3.80402 | ||||||||
\(904\) | 23.0444 | 0.766444 | ||||||||
\(905\) | −29.6191 | −0.984572 | ||||||||
\(906\) | −5.07517 | −0.168611 | ||||||||
\(907\) | 51.3212 | 1.70409 | 0.852046 | − | 0.523467i | \(-0.175362\pi\) | ||||
0.852046 | + | 0.523467i | \(0.175362\pi\) | |||||||
\(908\) | 100.806 | 3.34537 | ||||||||
\(909\) | 23.3364 | 0.774019 | ||||||||
\(910\) | 69.6349 | 2.30838 | ||||||||
\(911\) | −2.21296 | −0.0733188 | −0.0366594 | − | 0.999328i | \(-0.511672\pi\) | ||||
−0.0366594 | + | 0.999328i | \(0.511672\pi\) | |||||||
\(912\) | −25.3484 | −0.839368 | ||||||||
\(913\) | −18.1192 | −0.599659 | ||||||||
\(914\) | −82.9831 | −2.74484 | ||||||||
\(915\) | −30.5451 | −1.00979 | ||||||||
\(916\) | −50.0716 | −1.65441 | ||||||||
\(917\) | −5.78717 | −0.191109 | ||||||||
\(918\) | −29.3519 | −0.968757 | ||||||||
\(919\) | −17.0559 | −0.562622 | −0.281311 | − | 0.959617i | \(-0.590769\pi\) | ||||
−0.281311 | + | 0.959617i | \(0.590769\pi\) | |||||||
\(920\) | −141.893 | −4.67809 | ||||||||
\(921\) | −34.9467 | −1.15153 | ||||||||
\(922\) | 25.4296 | 0.837481 | ||||||||
\(923\) | −38.0179 | −1.25137 | ||||||||
\(924\) | −294.722 | −9.69564 | ||||||||
\(925\) | −2.57000 | −0.0845011 | ||||||||
\(926\) | −83.0192 | −2.72818 | ||||||||
\(927\) | 8.86244 | 0.291081 | ||||||||
\(928\) | 207.636 | 6.81600 | ||||||||
\(929\) | −26.6813 | −0.875384 | −0.437692 | − | 0.899125i | \(-0.644204\pi\) | ||||
−0.437692 | + | 0.899125i | \(0.644204\pi\) | |||||||
\(930\) | −69.5838 | −2.28174 | ||||||||
\(931\) | 6.02076 | 0.197323 | ||||||||
\(932\) | −55.0778 | −1.80413 | ||||||||
\(933\) | 56.4624 | 1.84850 | ||||||||
\(934\) | −3.63512 | −0.118945 | ||||||||
\(935\) | −77.0520 | −2.51987 | ||||||||
\(936\) | −66.3029 | −2.16718 | ||||||||
\(937\) | −9.89749 | −0.323337 | −0.161668 | − | 0.986845i | \(-0.551688\pi\) | ||||
−0.161668 | + | 0.986845i | \(0.551688\pi\) | |||||||
\(938\) | −117.386 | −3.83277 | ||||||||
\(939\) | 44.7592 | 1.46066 | ||||||||
\(940\) | 49.3504 | 1.60963 | ||||||||
\(941\) | −24.7747 | −0.807633 | −0.403817 | − | 0.914840i | \(-0.632317\pi\) | ||||
−0.403817 | + | 0.914840i | \(0.632317\pi\) | |||||||
\(942\) | −86.1766 | −2.80779 | ||||||||
\(943\) | 69.7421 | 2.27111 | ||||||||
\(944\) | −52.2904 | −1.70191 | ||||||||
\(945\) | −14.2372 | −0.463135 | ||||||||
\(946\) | −216.664 | −7.04435 | ||||||||
\(947\) | −35.2983 | −1.14704 | −0.573521 | − | 0.819191i | \(-0.694423\pi\) | ||||
−0.573521 | + | 0.819191i | \(0.694423\pi\) | |||||||
\(948\) | −10.1890 | −0.330922 | ||||||||
\(949\) | −4.11504 | −0.133580 | ||||||||
\(950\) | 1.46524 | 0.0475387 | ||||||||
\(951\) | 21.0194 | 0.681599 | ||||||||
\(952\) | 219.006 | 7.09802 | ||||||||
\(953\) | 56.5330 | 1.83128 | 0.915642 | − | 0.401995i | \(-0.131683\pi\) | ||||
0.915642 | + | 0.401995i | \(0.131683\pi\) | |||||||
\(954\) | −27.3233 | −0.884626 | ||||||||
\(955\) | −20.9519 | −0.677986 | ||||||||
\(956\) | 49.3667 | 1.59663 | ||||||||
\(957\) | −137.504 | −4.44486 | ||||||||
\(958\) | −17.8590 | −0.577000 | ||||||||
\(959\) | −16.7858 | −0.542041 | ||||||||
\(960\) | −134.922 | −4.35458 | ||||||||
\(961\) | −1.92120 | −0.0619743 | ||||||||
\(962\) | −31.5085 | −1.01588 | ||||||||
\(963\) | 38.0491 | 1.22612 | ||||||||
\(964\) | −18.8218 | −0.606211 | ||||||||
\(965\) | −1.21256 | −0.0390337 | ||||||||
\(966\) | −176.353 | −5.67408 | ||||||||
\(967\) | 20.8090 | 0.669173 | 0.334586 | − | 0.942365i | \(-0.391403\pi\) | ||||
0.334586 | + | 0.942365i | \(0.391403\pi\) | |||||||
\(968\) | −250.020 | −8.03595 | ||||||||
\(969\) | −10.4872 | −0.336899 | ||||||||
\(970\) | 97.2461 | 3.12239 | ||||||||
\(971\) | −4.13974 | −0.132851 | −0.0664253 | − | 0.997791i | \(-0.521159\pi\) | ||||
−0.0664253 | + | 0.997791i | \(0.521159\pi\) | |||||||
\(972\) | 104.193 | 3.34199 | ||||||||
\(973\) | 5.40315 | 0.173217 | ||||||||
\(974\) | −18.0636 | −0.578796 | ||||||||
\(975\) | 5.17025 | 0.165581 | ||||||||
\(976\) | 94.4578 | 3.02352 | ||||||||
\(977\) | 20.3941 | 0.652466 | 0.326233 | − | 0.945289i | \(-0.394221\pi\) | ||||
0.326233 | + | 0.945289i | \(0.394221\pi\) | |||||||
\(978\) | 4.15423 | 0.132838 | ||||||||
\(979\) | 105.544 | 3.37321 | ||||||||
\(980\) | 89.3881 | 2.85540 | ||||||||
\(981\) | −18.2761 | −0.583511 | ||||||||
\(982\) | 33.2024 | 1.05953 | ||||||||
\(983\) | −15.5371 | −0.495558 | −0.247779 | − | 0.968817i | \(-0.579701\pi\) | ||||
−0.247779 | + | 0.968817i | \(0.579701\pi\) | |||||||
\(984\) | 203.587 | 6.49010 | ||||||||
\(985\) | 14.6011 | 0.465231 | ||||||||
\(986\) | 161.732 | 5.15058 | ||||||||
\(987\) | 38.7503 | 1.23344 | ||||||||
\(988\) | 13.1295 | 0.417704 | ||||||||
\(989\) | −94.7546 | −3.01302 | ||||||||
\(990\) | 77.0675 | 2.44936 | ||||||||
\(991\) | 4.87743 | 0.154937 | 0.0774683 | − | 0.996995i | \(-0.475316\pi\) | ||||
0.0774683 | + | 0.996995i | \(0.475316\pi\) | |||||||
\(992\) | 114.294 | 3.62884 | ||||||||
\(993\) | −3.69577 | −0.117282 | ||||||||
\(994\) | −125.602 | −3.98387 | ||||||||
\(995\) | 2.59275 | 0.0821958 | ||||||||
\(996\) | −36.6138 | −1.16015 | ||||||||
\(997\) | −29.0403 | −0.919715 | −0.459858 | − | 0.887993i | \(-0.652100\pi\) | ||||
−0.459858 | + | 0.887993i | \(0.652100\pi\) | |||||||
\(998\) | 46.8042 | 1.48156 | ||||||||
\(999\) | 6.44205 | 0.203818 |
(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 | 4027.2.a.c.1.2 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.c.1.2 | ✓ | 174 | 1.1 | even | 1 | trivial |