Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(147\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69176 | −1.90336 | −0.951679 | − | 0.307093i | \(-0.900644\pi\) | ||||
−0.951679 | + | 0.307093i | \(0.900644\pi\) | |||||||
\(3\) | −2.97285 | −1.71638 | −0.858188 | − | 0.513335i | \(-0.828410\pi\) | ||||
−0.858188 | + | 0.513335i | \(0.828410\pi\) | |||||||
\(4\) | 5.24555 | 2.62277 | ||||||||
\(5\) | 2.64194 | 1.18151 | 0.590755 | − | 0.806851i | \(-0.298830\pi\) | ||||
0.590755 | + | 0.806851i | \(0.298830\pi\) | |||||||
\(6\) | 8.00219 | 3.26688 | ||||||||
\(7\) | −3.02993 | −1.14521 | −0.572603 | − | 0.819833i | \(-0.694066\pi\) | ||||
−0.572603 | + | 0.819833i | \(0.694066\pi\) | |||||||
\(8\) | −8.73623 | −3.08872 | ||||||||
\(9\) | 5.83784 | 1.94595 | ||||||||
\(10\) | −7.11145 | −2.24884 | ||||||||
\(11\) | 2.61803 | 0.789367 | 0.394683 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394683 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(12\) | −15.5942 | −4.50167 | ||||||||
\(13\) | −2.42112 | −0.671499 | −0.335750 | − | 0.941951i | \(-0.608990\pi\) | ||||
−0.335750 | + | 0.941951i | \(0.608990\pi\) | |||||||
\(14\) | 8.15583 | 2.17974 | ||||||||
\(15\) | −7.85409 | −2.02792 | ||||||||
\(16\) | 13.0247 | 3.25617 | ||||||||
\(17\) | 1.72491 | 0.418352 | 0.209176 | − | 0.977878i | \(-0.432922\pi\) | ||||
0.209176 | + | 0.977878i | \(0.432922\pi\) | |||||||
\(18\) | −15.7140 | −3.70384 | ||||||||
\(19\) | 4.82635 | 1.10724 | 0.553621 | − | 0.832769i | \(-0.313246\pi\) | ||||
0.553621 | + | 0.832769i | \(0.313246\pi\) | |||||||
\(20\) | 13.8584 | 3.09884 | ||||||||
\(21\) | 9.00753 | 1.96560 | ||||||||
\(22\) | −7.04710 | −1.50245 | ||||||||
\(23\) | 1.24633 | 0.259878 | 0.129939 | − | 0.991522i | \(-0.458522\pi\) | ||||
0.129939 | + | 0.991522i | \(0.458522\pi\) | |||||||
\(24\) | 25.9715 | 5.30141 | ||||||||
\(25\) | 1.97984 | 0.395967 | ||||||||
\(26\) | 6.51708 | 1.27810 | ||||||||
\(27\) | −8.43648 | −1.62360 | ||||||||
\(28\) | −15.8937 | −3.00362 | ||||||||
\(29\) | −2.50530 | −0.465223 | −0.232611 | − | 0.972570i | \(-0.574727\pi\) | ||||
−0.232611 | + | 0.972570i | \(0.574727\pi\) | |||||||
\(30\) | 21.1413 | 3.85985 | ||||||||
\(31\) | −1.61887 | −0.290758 | −0.145379 | − | 0.989376i | \(-0.546440\pi\) | ||||
−0.145379 | + | 0.989376i | \(0.546440\pi\) | |||||||
\(32\) | −17.5868 | −3.10894 | ||||||||
\(33\) | −7.78302 | −1.35485 | ||||||||
\(34\) | −4.64304 | −0.796275 | ||||||||
\(35\) | −8.00489 | −1.35307 | ||||||||
\(36\) | 30.6227 | 5.10378 | ||||||||
\(37\) | −2.98440 | −0.490632 | −0.245316 | − | 0.969443i | \(-0.578892\pi\) | ||||
−0.245316 | + | 0.969443i | \(0.578892\pi\) | |||||||
\(38\) | −12.9914 | −2.10748 | ||||||||
\(39\) | 7.19764 | 1.15255 | ||||||||
\(40\) | −23.0806 | −3.64936 | ||||||||
\(41\) | −11.3971 | −1.77994 | −0.889968 | − | 0.456024i | \(-0.849273\pi\) | ||||
−0.889968 | + | 0.456024i | \(0.849273\pi\) | |||||||
\(42\) | −24.2461 | −3.74125 | ||||||||
\(43\) | 6.95620 | 1.06081 | 0.530405 | − | 0.847744i | \(-0.322040\pi\) | ||||
0.530405 | + | 0.847744i | \(0.322040\pi\) | |||||||
\(44\) | 13.7330 | 2.07033 | ||||||||
\(45\) | 15.4232 | 2.29916 | ||||||||
\(46\) | −3.35482 | −0.494642 | ||||||||
\(47\) | 0.438274 | 0.0639288 | 0.0319644 | − | 0.999489i | \(-0.489824\pi\) | ||||
0.0319644 | + | 0.999489i | \(0.489824\pi\) | |||||||
\(48\) | −38.7205 | −5.58882 | ||||||||
\(49\) | 2.18048 | 0.311497 | ||||||||
\(50\) | −5.32924 | −0.753668 | ||||||||
\(51\) | −5.12790 | −0.718050 | ||||||||
\(52\) | −12.7001 | −1.76119 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 22.7089 | 3.09029 | ||||||||
\(55\) | 6.91668 | 0.932645 | ||||||||
\(56\) | 26.4702 | 3.53722 | ||||||||
\(57\) | −14.3480 | −1.90044 | ||||||||
\(58\) | 6.74366 | 0.885486 | ||||||||
\(59\) | 9.55262 | 1.24364 | 0.621822 | − | 0.783158i | \(-0.286393\pi\) | ||||
0.621822 | + | 0.783158i | \(0.286393\pi\) | |||||||
\(60\) | −41.1990 | −5.31877 | ||||||||
\(61\) | 11.1952 | 1.43340 | 0.716698 | − | 0.697384i | \(-0.245653\pi\) | ||||
0.716698 | + | 0.697384i | \(0.245653\pi\) | |||||||
\(62\) | 4.35761 | 0.553417 | ||||||||
\(63\) | −17.6883 | −2.22851 | ||||||||
\(64\) | 21.2901 | 2.66126 | ||||||||
\(65\) | −6.39646 | −0.793383 | ||||||||
\(66\) | 20.9500 | 2.57877 | ||||||||
\(67\) | 3.56140 | 0.435095 | 0.217547 | − | 0.976050i | \(-0.430194\pi\) | ||||
0.217547 | + | 0.976050i | \(0.430194\pi\) | |||||||
\(68\) | 9.04811 | 1.09724 | ||||||||
\(69\) | −3.70516 | −0.446049 | ||||||||
\(70\) | 21.5472 | 2.57538 | ||||||||
\(71\) | −6.18168 | −0.733630 | −0.366815 | − | 0.930294i | \(-0.619552\pi\) | ||||
−0.366815 | + | 0.930294i | \(0.619552\pi\) | |||||||
\(72\) | −51.0007 | −6.01049 | ||||||||
\(73\) | 8.98494 | 1.05161 | 0.525804 | − | 0.850606i | \(-0.323765\pi\) | ||||
0.525804 | + | 0.850606i | \(0.323765\pi\) | |||||||
\(74\) | 8.03327 | 0.933849 | ||||||||
\(75\) | −5.88576 | −0.679629 | ||||||||
\(76\) | 25.3169 | 2.90404 | ||||||||
\(77\) | −7.93246 | −0.903987 | ||||||||
\(78\) | −19.3743 | −2.19371 | ||||||||
\(79\) | 4.34119 | 0.488422 | 0.244211 | − | 0.969722i | \(-0.421471\pi\) | ||||
0.244211 | + | 0.969722i | \(0.421471\pi\) | |||||||
\(80\) | 34.4104 | 3.84720 | ||||||||
\(81\) | 7.56686 | 0.840763 | ||||||||
\(82\) | 30.6783 | 3.38786 | ||||||||
\(83\) | 0.593632 | 0.0651596 | 0.0325798 | − | 0.999469i | \(-0.489628\pi\) | ||||
0.0325798 | + | 0.999469i | \(0.489628\pi\) | |||||||
\(84\) | 47.2495 | 5.15534 | ||||||||
\(85\) | 4.55711 | 0.494288 | ||||||||
\(86\) | −18.7244 | −2.01910 | ||||||||
\(87\) | 7.44789 | 0.798497 | ||||||||
\(88\) | −22.8717 | −2.43813 | ||||||||
\(89\) | −11.4237 | −1.21091 | −0.605454 | − | 0.795881i | \(-0.707008\pi\) | ||||
−0.605454 | + | 0.795881i | \(0.707008\pi\) | |||||||
\(90\) | −41.5155 | −4.37612 | ||||||||
\(91\) | 7.33584 | 0.769005 | ||||||||
\(92\) | 6.53770 | 0.681602 | ||||||||
\(93\) | 4.81267 | 0.499050 | ||||||||
\(94\) | −1.17973 | −0.121679 | ||||||||
\(95\) | 12.7509 | 1.30822 | ||||||||
\(96\) | 52.2831 | 5.33612 | ||||||||
\(97\) | −13.0544 | −1.32547 | −0.662735 | − | 0.748854i | \(-0.730604\pi\) | ||||
−0.662735 | + | 0.748854i | \(0.730604\pi\) | |||||||
\(98\) | −5.86932 | −0.592891 | ||||||||
\(99\) | 15.2837 | 1.53607 | ||||||||
\(100\) | 10.3853 | 1.03853 | ||||||||
\(101\) | −10.0747 | −1.00247 | −0.501235 | − | 0.865311i | \(-0.667121\pi\) | ||||
−0.501235 | + | 0.865311i | \(0.667121\pi\) | |||||||
\(102\) | 13.8031 | 1.36671 | ||||||||
\(103\) | −15.1778 | −1.49551 | −0.747757 | − | 0.663973i | \(-0.768869\pi\) | ||||
−0.747757 | + | 0.663973i | \(0.768869\pi\) | |||||||
\(104\) | 21.1515 | 2.07407 | ||||||||
\(105\) | 23.7973 | 2.32238 | ||||||||
\(106\) | −2.69176 | −0.261446 | ||||||||
\(107\) | −3.44767 | −0.333298 | −0.166649 | − | 0.986016i | \(-0.553295\pi\) | ||||
−0.166649 | + | 0.986016i | \(0.553295\pi\) | |||||||
\(108\) | −44.2540 | −4.25834 | ||||||||
\(109\) | 3.68422 | 0.352884 | 0.176442 | − | 0.984311i | \(-0.443541\pi\) | ||||
0.176442 | + | 0.984311i | \(0.443541\pi\) | |||||||
\(110\) | −18.6180 | −1.77516 | ||||||||
\(111\) | 8.87217 | 0.842109 | ||||||||
\(112\) | −39.4639 | −3.72899 | ||||||||
\(113\) | −10.6508 | −1.00195 | −0.500973 | − | 0.865463i | \(-0.667024\pi\) | ||||
−0.500973 | + | 0.865463i | \(0.667024\pi\) | |||||||
\(114\) | 38.6214 | 3.61722 | ||||||||
\(115\) | 3.29273 | 0.307049 | ||||||||
\(116\) | −13.1417 | −1.22017 | ||||||||
\(117\) | −14.1341 | −1.30670 | ||||||||
\(118\) | −25.7133 | −2.36710 | ||||||||
\(119\) | −5.22636 | −0.479100 | ||||||||
\(120\) | 68.6151 | 6.26367 | ||||||||
\(121\) | −4.14591 | −0.376900 | ||||||||
\(122\) | −30.1347 | −2.72827 | ||||||||
\(123\) | 33.8820 | 3.05504 | ||||||||
\(124\) | −8.49188 | −0.762593 | ||||||||
\(125\) | −7.97908 | −0.713671 | ||||||||
\(126\) | 47.6125 | 4.24165 | ||||||||
\(127\) | −6.13403 | −0.544307 | −0.272153 | − | 0.962254i | \(-0.587736\pi\) | ||||
−0.272153 | + | 0.962254i | \(0.587736\pi\) | |||||||
\(128\) | −22.1341 | −1.95639 | ||||||||
\(129\) | −20.6797 | −1.82075 | ||||||||
\(130\) | 17.2177 | 1.51009 | ||||||||
\(131\) | 1.18583 | 0.103606 | 0.0518032 | − | 0.998657i | \(-0.483503\pi\) | ||||
0.0518032 | + | 0.998657i | \(0.483503\pi\) | |||||||
\(132\) | −40.8262 | −3.55347 | ||||||||
\(133\) | −14.6235 | −1.26802 | ||||||||
\(134\) | −9.58643 | −0.828141 | ||||||||
\(135\) | −22.2887 | −1.91830 | ||||||||
\(136\) | −15.0692 | −1.29217 | ||||||||
\(137\) | 18.9855 | 1.62204 | 0.811022 | − | 0.585016i | \(-0.198912\pi\) | ||||
0.811022 | + | 0.585016i | \(0.198912\pi\) | |||||||
\(138\) | 9.97339 | 0.848991 | ||||||||
\(139\) | −3.15838 | −0.267891 | −0.133945 | − | 0.990989i | \(-0.542765\pi\) | ||||
−0.133945 | + | 0.990989i | \(0.542765\pi\) | |||||||
\(140\) | −41.9900 | −3.54881 | ||||||||
\(141\) | −1.30292 | −0.109726 | ||||||||
\(142\) | 16.6396 | 1.39636 | ||||||||
\(143\) | −6.33858 | −0.530059 | ||||||||
\(144\) | 76.0361 | 6.33634 | ||||||||
\(145\) | −6.61885 | −0.549666 | ||||||||
\(146\) | −24.1853 | −2.00159 | ||||||||
\(147\) | −6.48224 | −0.534646 | ||||||||
\(148\) | −15.6548 | −1.28682 | ||||||||
\(149\) | 4.75810 | 0.389799 | 0.194899 | − | 0.980823i | \(-0.437562\pi\) | ||||
0.194899 | + | 0.980823i | \(0.437562\pi\) | |||||||
\(150\) | 15.8430 | 1.29358 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | −42.1641 | −3.41996 | ||||||||
\(153\) | 10.0698 | 0.814091 | ||||||||
\(154\) | 21.3522 | 1.72061 | ||||||||
\(155\) | −4.27696 | −0.343534 | ||||||||
\(156\) | 37.7556 | 3.02287 | ||||||||
\(157\) | −22.3291 | −1.78205 | −0.891026 | − | 0.453951i | \(-0.850014\pi\) | ||||
−0.891026 | + | 0.453951i | \(0.850014\pi\) | |||||||
\(158\) | −11.6854 | −0.929643 | ||||||||
\(159\) | −2.97285 | −0.235762 | ||||||||
\(160\) | −46.4633 | −3.67325 | ||||||||
\(161\) | −3.77630 | −0.297614 | ||||||||
\(162\) | −20.3682 | −1.60027 | ||||||||
\(163\) | −4.54889 | −0.356296 | −0.178148 | − | 0.984004i | \(-0.557011\pi\) | ||||
−0.178148 | + | 0.984004i | \(0.557011\pi\) | |||||||
\(164\) | −59.7843 | −4.66837 | ||||||||
\(165\) | −20.5623 | −1.60077 | ||||||||
\(166\) | −1.59791 | −0.124022 | ||||||||
\(167\) | 23.4645 | 1.81574 | 0.907869 | − | 0.419253i | \(-0.137708\pi\) | ||||
0.907869 | + | 0.419253i | \(0.137708\pi\) | |||||||
\(168\) | −78.6918 | −6.07121 | ||||||||
\(169\) | −7.13816 | −0.549089 | ||||||||
\(170\) | −12.2666 | −0.940807 | ||||||||
\(171\) | 28.1755 | 2.15463 | ||||||||
\(172\) | 36.4891 | 2.78227 | ||||||||
\(173\) | 20.9127 | 1.58996 | 0.794980 | − | 0.606636i | \(-0.207481\pi\) | ||||
0.794980 | + | 0.606636i | \(0.207481\pi\) | |||||||
\(174\) | −20.0479 | −1.51983 | ||||||||
\(175\) | −5.99877 | −0.453464 | ||||||||
\(176\) | 34.0991 | 2.57031 | ||||||||
\(177\) | −28.3985 | −2.13456 | ||||||||
\(178\) | 30.7497 | 2.30479 | ||||||||
\(179\) | 16.5057 | 1.23369 | 0.616846 | − | 0.787084i | \(-0.288410\pi\) | ||||
0.616846 | + | 0.787084i | \(0.288410\pi\) | |||||||
\(180\) | 80.9032 | 6.03017 | ||||||||
\(181\) | −10.3592 | −0.769995 | −0.384997 | − | 0.922918i | \(-0.625798\pi\) | ||||
−0.384997 | + | 0.922918i | \(0.625798\pi\) | |||||||
\(182\) | −19.7463 | −1.46369 | ||||||||
\(183\) | −33.2816 | −2.46025 | ||||||||
\(184\) | −10.8882 | −0.802692 | ||||||||
\(185\) | −7.88459 | −0.579687 | ||||||||
\(186\) | −12.9545 | −0.949872 | ||||||||
\(187\) | 4.51587 | 0.330233 | ||||||||
\(188\) | 2.29899 | 0.167671 | ||||||||
\(189\) | 25.5619 | 1.85936 | ||||||||
\(190\) | −34.3224 | −2.49001 | ||||||||
\(191\) | −18.2427 | −1.31999 | −0.659996 | − | 0.751269i | \(-0.729442\pi\) | ||||
−0.659996 | + | 0.751269i | \(0.729442\pi\) | |||||||
\(192\) | −63.2923 | −4.56773 | ||||||||
\(193\) | −9.91795 | −0.713909 | −0.356955 | − | 0.934122i | \(-0.616185\pi\) | ||||
−0.356955 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(194\) | 35.1392 | 2.52284 | ||||||||
\(195\) | 19.0157 | 1.36174 | ||||||||
\(196\) | 11.4378 | 0.816987 | ||||||||
\(197\) | −14.2158 | −1.01283 | −0.506417 | − | 0.862289i | \(-0.669030\pi\) | ||||
−0.506417 | + | 0.862289i | \(0.669030\pi\) | |||||||
\(198\) | −41.1399 | −2.92368 | ||||||||
\(199\) | 2.31605 | 0.164180 | 0.0820901 | − | 0.996625i | \(-0.473840\pi\) | ||||
0.0820901 | + | 0.996625i | \(0.473840\pi\) | |||||||
\(200\) | −17.2963 | −1.22303 | ||||||||
\(201\) | −10.5875 | −0.746786 | ||||||||
\(202\) | 27.1186 | 1.90806 | ||||||||
\(203\) | 7.59089 | 0.532776 | ||||||||
\(204\) | −26.8987 | −1.88328 | ||||||||
\(205\) | −30.1106 | −2.10301 | ||||||||
\(206\) | 40.8549 | 2.84650 | ||||||||
\(207\) | 7.27589 | 0.505709 | ||||||||
\(208\) | −31.5344 | −2.18652 | ||||||||
\(209\) | 12.6355 | 0.874019 | ||||||||
\(210\) | −64.0566 | −4.42033 | ||||||||
\(211\) | −4.69874 | −0.323475 | −0.161737 | − | 0.986834i | \(-0.551710\pi\) | ||||
−0.161737 | + | 0.986834i | \(0.551710\pi\) | |||||||
\(212\) | 5.24555 | 0.360266 | ||||||||
\(213\) | 18.3772 | 1.25918 | ||||||||
\(214\) | 9.28028 | 0.634387 | ||||||||
\(215\) | 18.3778 | 1.25336 | ||||||||
\(216\) | 73.7030 | 5.01485 | ||||||||
\(217\) | 4.90507 | 0.332978 | ||||||||
\(218\) | −9.91701 | −0.671665 | ||||||||
\(219\) | −26.7109 | −1.80495 | ||||||||
\(220\) | 36.2818 | 2.44612 | ||||||||
\(221\) | −4.17622 | −0.280923 | ||||||||
\(222\) | −23.8817 | −1.60284 | ||||||||
\(223\) | −2.58590 | −0.173165 | −0.0865825 | − | 0.996245i | \(-0.527595\pi\) | ||||
−0.0865825 | + | 0.996245i | \(0.527595\pi\) | |||||||
\(224\) | 53.2869 | 3.56038 | ||||||||
\(225\) | 11.5580 | 0.770532 | ||||||||
\(226\) | 28.6694 | 1.90706 | ||||||||
\(227\) | −11.1406 | −0.739426 | −0.369713 | − | 0.929146i | \(-0.620544\pi\) | ||||
−0.369713 | + | 0.929146i | \(0.620544\pi\) | |||||||
\(228\) | −75.2633 | −4.98443 | ||||||||
\(229\) | 16.6802 | 1.10226 | 0.551129 | − | 0.834420i | \(-0.314197\pi\) | ||||
0.551129 | + | 0.834420i | \(0.314197\pi\) | |||||||
\(230\) | −8.86323 | −0.584424 | ||||||||
\(231\) | 23.5820 | 1.55158 | ||||||||
\(232\) | 21.8869 | 1.43694 | ||||||||
\(233\) | −10.6844 | −0.699958 | −0.349979 | − | 0.936757i | \(-0.613811\pi\) | ||||
−0.349979 | + | 0.936757i | \(0.613811\pi\) | |||||||
\(234\) | 38.0457 | 2.48712 | ||||||||
\(235\) | 1.15789 | 0.0755326 | ||||||||
\(236\) | 50.1087 | 3.26180 | ||||||||
\(237\) | −12.9057 | −0.838317 | ||||||||
\(238\) | 14.0681 | 0.911899 | ||||||||
\(239\) | 0.889072 | 0.0575093 | 0.0287546 | − | 0.999586i | \(-0.490846\pi\) | ||||
0.0287546 | + | 0.999586i | \(0.490846\pi\) | |||||||
\(240\) | −102.297 | −6.60325 | ||||||||
\(241\) | 7.96341 | 0.512968 | 0.256484 | − | 0.966548i | \(-0.417436\pi\) | ||||
0.256484 | + | 0.966548i | \(0.417436\pi\) | |||||||
\(242\) | 11.1598 | 0.717377 | ||||||||
\(243\) | 2.81428 | 0.180536 | ||||||||
\(244\) | 58.7249 | 3.75948 | ||||||||
\(245\) | 5.76069 | 0.368037 | ||||||||
\(246\) | −91.2021 | −5.81483 | ||||||||
\(247\) | −11.6852 | −0.743511 | ||||||||
\(248\) | 14.1428 | 0.898071 | ||||||||
\(249\) | −1.76478 | −0.111838 | ||||||||
\(250\) | 21.4777 | 1.35837 | ||||||||
\(251\) | 15.4113 | 0.972753 | 0.486377 | − | 0.873749i | \(-0.338318\pi\) | ||||
0.486377 | + | 0.873749i | \(0.338318\pi\) | |||||||
\(252\) | −92.7846 | −5.84488 | ||||||||
\(253\) | 3.26294 | 0.205139 | ||||||||
\(254\) | 16.5113 | 1.03601 | ||||||||
\(255\) | −13.5476 | −0.848384 | ||||||||
\(256\) | 16.9993 | 1.06246 | ||||||||
\(257\) | −7.51205 | −0.468589 | −0.234294 | − | 0.972166i | \(-0.575278\pi\) | ||||
−0.234294 | + | 0.972166i | \(0.575278\pi\) | |||||||
\(258\) | 55.6648 | 3.46554 | ||||||||
\(259\) | 9.04252 | 0.561875 | ||||||||
\(260\) | −33.5530 | −2.08087 | ||||||||
\(261\) | −14.6256 | −0.905299 | ||||||||
\(262\) | −3.19196 | −0.197200 | ||||||||
\(263\) | −12.0556 | −0.743382 | −0.371691 | − | 0.928357i | \(-0.621222\pi\) | ||||
−0.371691 | + | 0.928357i | \(0.621222\pi\) | |||||||
\(264\) | 67.9942 | 4.18476 | ||||||||
\(265\) | 2.64194 | 0.162293 | ||||||||
\(266\) | 39.3629 | 2.41350 | ||||||||
\(267\) | 33.9609 | 2.07837 | ||||||||
\(268\) | 18.6815 | 1.14116 | ||||||||
\(269\) | 16.7234 | 1.01964 | 0.509822 | − | 0.860280i | \(-0.329711\pi\) | ||||
0.509822 | + | 0.860280i | \(0.329711\pi\) | |||||||
\(270\) | 59.9956 | 3.65122 | ||||||||
\(271\) | −8.03520 | −0.488103 | −0.244052 | − | 0.969762i | \(-0.578477\pi\) | ||||
−0.244052 | + | 0.969762i | \(0.578477\pi\) | |||||||
\(272\) | 22.4664 | 1.36223 | ||||||||
\(273\) | −21.8084 | −1.31990 | ||||||||
\(274\) | −51.1044 | −3.08733 | ||||||||
\(275\) | 5.18328 | 0.312563 | ||||||||
\(276\) | −19.4356 | −1.16989 | ||||||||
\(277\) | 23.2451 | 1.39666 | 0.698330 | − | 0.715776i | \(-0.253927\pi\) | ||||
0.698330 | + | 0.715776i | \(0.253927\pi\) | |||||||
\(278\) | 8.50160 | 0.509892 | ||||||||
\(279\) | −9.45072 | −0.565800 | ||||||||
\(280\) | 69.9325 | 4.17927 | ||||||||
\(281\) | −16.8127 | −1.00296 | −0.501480 | − | 0.865169i | \(-0.667211\pi\) | ||||
−0.501480 | + | 0.865169i | \(0.667211\pi\) | |||||||
\(282\) | 3.50715 | 0.208848 | ||||||||
\(283\) | 6.77640 | 0.402815 | 0.201408 | − | 0.979508i | \(-0.435448\pi\) | ||||
0.201408 | + | 0.979508i | \(0.435448\pi\) | |||||||
\(284\) | −32.4263 | −1.92415 | ||||||||
\(285\) | −37.9066 | −2.24539 | ||||||||
\(286\) | 17.0619 | 1.00889 | ||||||||
\(287\) | 34.5326 | 2.03839 | ||||||||
\(288\) | −102.669 | −6.04984 | ||||||||
\(289\) | −14.0247 | −0.824981 | ||||||||
\(290\) | 17.8163 | 1.04621 | ||||||||
\(291\) | 38.8087 | 2.27500 | ||||||||
\(292\) | 47.1310 | 2.75813 | ||||||||
\(293\) | 1.55060 | 0.0905869 | 0.0452935 | − | 0.998974i | \(-0.485578\pi\) | ||||
0.0452935 | + | 0.998974i | \(0.485578\pi\) | |||||||
\(294\) | 17.4486 | 1.01762 | ||||||||
\(295\) | 25.2374 | 1.46938 | ||||||||
\(296\) | 26.0724 | 1.51543 | ||||||||
\(297\) | −22.0870 | −1.28162 | ||||||||
\(298\) | −12.8076 | −0.741927 | ||||||||
\(299\) | −3.01753 | −0.174508 | ||||||||
\(300\) | −30.8740 | −1.78251 | ||||||||
\(301\) | −21.0768 | −1.21485 | ||||||||
\(302\) | −2.69176 | −0.154893 | ||||||||
\(303\) | 29.9506 | 1.72062 | ||||||||
\(304\) | 62.8618 | 3.60537 | ||||||||
\(305\) | 29.5770 | 1.69357 | ||||||||
\(306\) | −27.1053 | −1.54951 | ||||||||
\(307\) | 3.98608 | 0.227498 | 0.113749 | − | 0.993510i | \(-0.463714\pi\) | ||||
0.113749 | + | 0.993510i | \(0.463714\pi\) | |||||||
\(308\) | −41.6101 | −2.37096 | ||||||||
\(309\) | 45.1214 | 2.56686 | ||||||||
\(310\) | 11.5125 | 0.653868 | ||||||||
\(311\) | 10.9908 | 0.623229 | 0.311614 | − | 0.950209i | \(-0.399130\pi\) | ||||
0.311614 | + | 0.950209i | \(0.399130\pi\) | |||||||
\(312\) | −62.8802 | −3.55989 | ||||||||
\(313\) | −14.4532 | −0.816941 | −0.408470 | − | 0.912772i | \(-0.633938\pi\) | ||||
−0.408470 | + | 0.912772i | \(0.633938\pi\) | |||||||
\(314\) | 60.1044 | 3.39189 | ||||||||
\(315\) | −46.7313 | −2.63301 | ||||||||
\(316\) | 22.7719 | 1.28102 | ||||||||
\(317\) | 19.1325 | 1.07459 | 0.537294 | − | 0.843395i | \(-0.319446\pi\) | ||||
0.537294 | + | 0.843395i | \(0.319446\pi\) | |||||||
\(318\) | 8.00219 | 0.448740 | ||||||||
\(319\) | −6.55896 | −0.367231 | ||||||||
\(320\) | 56.2471 | 3.14431 | ||||||||
\(321\) | 10.2494 | 0.572066 | ||||||||
\(322\) | 10.1649 | 0.566466 | ||||||||
\(323\) | 8.32503 | 0.463217 | ||||||||
\(324\) | 39.6924 | 2.20513 | ||||||||
\(325\) | −4.79343 | −0.265892 | ||||||||
\(326\) | 12.2445 | 0.678160 | ||||||||
\(327\) | −10.9526 | −0.605682 | ||||||||
\(328\) | 99.5681 | 5.49773 | ||||||||
\(329\) | −1.32794 | −0.0732117 | ||||||||
\(330\) | 55.3486 | 3.04684 | ||||||||
\(331\) | 32.6928 | 1.79696 | 0.898479 | − | 0.439017i | \(-0.144673\pi\) | ||||
0.898479 | + | 0.439017i | \(0.144673\pi\) | |||||||
\(332\) | 3.11393 | 0.170899 | ||||||||
\(333\) | −17.4224 | −0.954744 | ||||||||
\(334\) | −63.1608 | −3.45600 | ||||||||
\(335\) | 9.40901 | 0.514069 | ||||||||
\(336\) | 117.320 | 6.40035 | ||||||||
\(337\) | −1.54569 | −0.0841989 | −0.0420994 | − | 0.999113i | \(-0.513405\pi\) | ||||
−0.0420994 | + | 0.999113i | \(0.513405\pi\) | |||||||
\(338\) | 19.2142 | 1.04511 | ||||||||
\(339\) | 31.6633 | 1.71972 | ||||||||
\(340\) | 23.9045 | 1.29641 | ||||||||
\(341\) | −4.23826 | −0.229515 | ||||||||
\(342\) | −75.8415 | −4.10104 | ||||||||
\(343\) | 14.6028 | 0.788478 | ||||||||
\(344\) | −60.7709 | −3.27655 | ||||||||
\(345\) | −9.78880 | −0.527011 | ||||||||
\(346\) | −56.2918 | −3.02626 | ||||||||
\(347\) | 10.3814 | 0.557300 | 0.278650 | − | 0.960393i | \(-0.410113\pi\) | ||||
0.278650 | + | 0.960393i | \(0.410113\pi\) | |||||||
\(348\) | 39.0683 | 2.09428 | ||||||||
\(349\) | 2.33316 | 0.124891 | 0.0624456 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624456 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(350\) | 16.1472 | 0.863105 | ||||||||
\(351\) | 20.4258 | 1.09025 | ||||||||
\(352\) | −46.0429 | −2.45410 | ||||||||
\(353\) | 20.8199 | 1.10813 | 0.554066 | − | 0.832473i | \(-0.313076\pi\) | ||||
0.554066 | + | 0.832473i | \(0.313076\pi\) | |||||||
\(354\) | 76.4418 | 4.06284 | ||||||||
\(355\) | −16.3316 | −0.866792 | ||||||||
\(356\) | −59.9235 | −3.17594 | ||||||||
\(357\) | 15.5372 | 0.822315 | ||||||||
\(358\) | −44.4292 | −2.34816 | ||||||||
\(359\) | 25.1936 | 1.32967 | 0.664834 | − | 0.746991i | \(-0.268502\pi\) | ||||
0.664834 | + | 0.746991i | \(0.268502\pi\) | |||||||
\(360\) | −134.741 | −7.10146 | ||||||||
\(361\) | 4.29368 | 0.225983 | ||||||||
\(362\) | 27.8845 | 1.46558 | ||||||||
\(363\) | 12.3252 | 0.646903 | ||||||||
\(364\) | 38.4805 | 2.01693 | ||||||||
\(365\) | 23.7377 | 1.24249 | ||||||||
\(366\) | 89.5860 | 4.68273 | ||||||||
\(367\) | −32.4969 | −1.69632 | −0.848162 | − | 0.529738i | \(-0.822290\pi\) | ||||
−0.848162 | + | 0.529738i | \(0.822290\pi\) | |||||||
\(368\) | 16.2331 | 0.846209 | ||||||||
\(369\) | −66.5347 | −3.46366 | ||||||||
\(370\) | 21.2234 | 1.10335 | ||||||||
\(371\) | −3.02993 | −0.157306 | ||||||||
\(372\) | 25.2451 | 1.30890 | ||||||||
\(373\) | −23.9888 | −1.24210 | −0.621048 | − | 0.783773i | \(-0.713293\pi\) | ||||
−0.621048 | + | 0.783773i | \(0.713293\pi\) | |||||||
\(374\) | −12.1556 | −0.628553 | ||||||||
\(375\) | 23.7206 | 1.22493 | ||||||||
\(376\) | −3.82886 | −0.197458 | ||||||||
\(377\) | 6.06565 | 0.312397 | ||||||||
\(378\) | −68.8065 | −3.53902 | ||||||||
\(379\) | −8.35439 | −0.429136 | −0.214568 | − | 0.976709i | \(-0.568834\pi\) | ||||
−0.214568 | + | 0.976709i | \(0.568834\pi\) | |||||||
\(380\) | 66.8856 | 3.43116 | ||||||||
\(381\) | 18.2355 | 0.934235 | ||||||||
\(382\) | 49.1048 | 2.51242 | ||||||||
\(383\) | −16.6276 | −0.849632 | −0.424816 | − | 0.905280i | \(-0.639661\pi\) | ||||
−0.424816 | + | 0.905280i | \(0.639661\pi\) | |||||||
\(384\) | 65.8012 | 3.35791 | ||||||||
\(385\) | −20.9571 | −1.06807 | ||||||||
\(386\) | 26.6967 | 1.35883 | ||||||||
\(387\) | 40.6092 | 2.06428 | ||||||||
\(388\) | −68.4773 | −3.47641 | ||||||||
\(389\) | 10.1342 | 0.513822 | 0.256911 | − | 0.966435i | \(-0.417295\pi\) | ||||
0.256911 | + | 0.966435i | \(0.417295\pi\) | |||||||
\(390\) | −51.1857 | −2.59189 | ||||||||
\(391\) | 2.14981 | 0.108721 | ||||||||
\(392\) | −19.0492 | −0.962128 | ||||||||
\(393\) | −3.52529 | −0.177828 | ||||||||
\(394\) | 38.2655 | 1.92779 | ||||||||
\(395\) | 11.4692 | 0.577076 | ||||||||
\(396\) | 80.1712 | 4.02875 | ||||||||
\(397\) | −4.78968 | −0.240387 | −0.120194 | − | 0.992750i | \(-0.538352\pi\) | ||||
−0.120194 | + | 0.992750i | \(0.538352\pi\) | |||||||
\(398\) | −6.23424 | −0.312494 | ||||||||
\(399\) | 43.4735 | 2.17640 | ||||||||
\(400\) | 25.7868 | 1.28934 | ||||||||
\(401\) | 17.1178 | 0.854823 | 0.427411 | − | 0.904057i | \(-0.359426\pi\) | ||||
0.427411 | + | 0.904057i | \(0.359426\pi\) | |||||||
\(402\) | 28.4990 | 1.42140 | ||||||||
\(403\) | 3.91949 | 0.195244 | ||||||||
\(404\) | −52.8474 | −2.62925 | ||||||||
\(405\) | 19.9912 | 0.993370 | ||||||||
\(406\) | −20.4328 | −1.01406 | ||||||||
\(407\) | −7.81325 | −0.387288 | ||||||||
\(408\) | 44.7985 | 2.21786 | ||||||||
\(409\) | 2.15727 | 0.106670 | 0.0533350 | − | 0.998577i | \(-0.483015\pi\) | ||||
0.0533350 | + | 0.998577i | \(0.483015\pi\) | |||||||
\(410\) | 81.0503 | 4.00279 | ||||||||
\(411\) | −56.4412 | −2.78404 | ||||||||
\(412\) | −79.6159 | −3.92240 | ||||||||
\(413\) | −28.9438 | −1.42423 | ||||||||
\(414\) | −19.5849 | −0.962546 | ||||||||
\(415\) | 1.56834 | 0.0769868 | ||||||||
\(416\) | 42.5799 | 2.08765 | ||||||||
\(417\) | 9.38940 | 0.459801 | ||||||||
\(418\) | −34.0118 | −1.66357 | ||||||||
\(419\) | 27.2992 | 1.33365 | 0.666827 | − | 0.745212i | \(-0.267652\pi\) | ||||
0.666827 | + | 0.745212i | \(0.267652\pi\) | |||||||
\(420\) | 124.830 | 6.09109 | ||||||||
\(421\) | −6.95347 | −0.338892 | −0.169446 | − | 0.985540i | \(-0.554198\pi\) | ||||
−0.169446 | + | 0.985540i | \(0.554198\pi\) | |||||||
\(422\) | 12.6479 | 0.615688 | ||||||||
\(423\) | 2.55857 | 0.124402 | ||||||||
\(424\) | −8.73623 | −0.424269 | ||||||||
\(425\) | 3.41504 | 0.165654 | ||||||||
\(426\) | −49.4669 | −2.39668 | ||||||||
\(427\) | −33.9206 | −1.64153 | ||||||||
\(428\) | −18.0849 | −0.874167 | ||||||||
\(429\) | 18.8437 | 0.909780 | ||||||||
\(430\) | −49.4687 | −2.38559 | ||||||||
\(431\) | −21.9338 | −1.05651 | −0.528257 | − | 0.849084i | \(-0.677154\pi\) | ||||
−0.528257 | + | 0.849084i | \(0.677154\pi\) | |||||||
\(432\) | −109.883 | −5.28673 | ||||||||
\(433\) | 2.44060 | 0.117288 | 0.0586438 | − | 0.998279i | \(-0.481322\pi\) | ||||
0.0586438 | + | 0.998279i | \(0.481322\pi\) | |||||||
\(434\) | −13.2033 | −0.633777 | ||||||||
\(435\) | 19.6769 | 0.943433 | ||||||||
\(436\) | 19.3257 | 0.925535 | ||||||||
\(437\) | 6.01524 | 0.287748 | ||||||||
\(438\) | 71.8992 | 3.43548 | ||||||||
\(439\) | −36.4387 | −1.73913 | −0.869563 | − | 0.493822i | \(-0.835599\pi\) | ||||
−0.869563 | + | 0.493822i | \(0.835599\pi\) | |||||||
\(440\) | −60.4257 | −2.88068 | ||||||||
\(441\) | 12.7293 | 0.606157 | ||||||||
\(442\) | 11.2414 | 0.534698 | ||||||||
\(443\) | 18.4596 | 0.877044 | 0.438522 | − | 0.898721i | \(-0.355502\pi\) | ||||
0.438522 | + | 0.898721i | \(0.355502\pi\) | |||||||
\(444\) | 46.5394 | 2.20866 | ||||||||
\(445\) | −30.1806 | −1.43070 | ||||||||
\(446\) | 6.96062 | 0.329595 | ||||||||
\(447\) | −14.1451 | −0.669041 | ||||||||
\(448\) | −64.5075 | −3.04769 | ||||||||
\(449\) | −2.50709 | −0.118317 | −0.0591586 | − | 0.998249i | \(-0.518842\pi\) | ||||
−0.0591586 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(450\) | −31.1112 | −1.46660 | ||||||||
\(451\) | −29.8381 | −1.40502 | ||||||||
\(452\) | −55.8694 | −2.62788 | ||||||||
\(453\) | −2.97285 | −0.139677 | ||||||||
\(454\) | 29.9877 | 1.40739 | ||||||||
\(455\) | 19.3808 | 0.908587 | ||||||||
\(456\) | 125.348 | 5.86994 | ||||||||
\(457\) | −16.6574 | −0.779203 | −0.389601 | − | 0.920984i | \(-0.627387\pi\) | ||||
−0.389601 | + | 0.920984i | \(0.627387\pi\) | |||||||
\(458\) | −44.8990 | −2.09799 | ||||||||
\(459\) | −14.5522 | −0.679237 | ||||||||
\(460\) | 17.2722 | 0.805320 | ||||||||
\(461\) | −17.2981 | −0.805652 | −0.402826 | − | 0.915277i | \(-0.631972\pi\) | ||||
−0.402826 | + | 0.915277i | \(0.631972\pi\) | |||||||
\(462\) | −63.4770 | −2.95322 | ||||||||
\(463\) | 16.9080 | 0.785783 | 0.392891 | − | 0.919585i | \(-0.371475\pi\) | ||||
0.392891 | + | 0.919585i | \(0.371475\pi\) | |||||||
\(464\) | −32.6308 | −1.51485 | ||||||||
\(465\) | 12.7148 | 0.589633 | ||||||||
\(466\) | 28.7598 | 1.33227 | ||||||||
\(467\) | −19.1393 | −0.885662 | −0.442831 | − | 0.896605i | \(-0.646026\pi\) | ||||
−0.442831 | + | 0.896605i | \(0.646026\pi\) | |||||||
\(468\) | −74.1413 | −3.42718 | ||||||||
\(469\) | −10.7908 | −0.498273 | ||||||||
\(470\) | −3.11676 | −0.143766 | ||||||||
\(471\) | 66.3810 | 3.05867 | ||||||||
\(472\) | −83.4538 | −3.84127 | ||||||||
\(473\) | 18.2115 | 0.837368 | ||||||||
\(474\) | 34.7390 | 1.59562 | ||||||||
\(475\) | 9.55539 | 0.438431 | ||||||||
\(476\) | −27.4151 | −1.25657 | ||||||||
\(477\) | 5.83784 | 0.267296 | ||||||||
\(478\) | −2.39316 | −0.109461 | ||||||||
\(479\) | −11.6466 | −0.532147 | −0.266074 | − | 0.963953i | \(-0.585726\pi\) | ||||
−0.266074 | + | 0.963953i | \(0.585726\pi\) | |||||||
\(480\) | 138.129 | 6.30468 | ||||||||
\(481\) | 7.22560 | 0.329459 | ||||||||
\(482\) | −21.4356 | −0.976363 | ||||||||
\(483\) | 11.2264 | 0.510818 | ||||||||
\(484\) | −21.7476 | −0.988525 | ||||||||
\(485\) | −34.4888 | −1.56606 | ||||||||
\(486\) | −7.57534 | −0.343625 | ||||||||
\(487\) | 27.9471 | 1.26640 | 0.633201 | − | 0.773987i | \(-0.281740\pi\) | ||||
0.633201 | + | 0.773987i | \(0.281740\pi\) | |||||||
\(488\) | −97.8037 | −4.42736 | ||||||||
\(489\) | 13.5232 | 0.611538 | ||||||||
\(490\) | −15.5064 | −0.700507 | ||||||||
\(491\) | −4.45926 | −0.201244 | −0.100622 | − | 0.994925i | \(-0.532083\pi\) | ||||
−0.100622 | + | 0.994925i | \(0.532083\pi\) | |||||||
\(492\) | 177.730 | 8.01268 | ||||||||
\(493\) | −4.32142 | −0.194627 | ||||||||
\(494\) | 31.4537 | 1.41517 | ||||||||
\(495\) | 40.3785 | 1.81488 | ||||||||
\(496\) | −21.0853 | −0.946759 | ||||||||
\(497\) | 18.7300 | 0.840158 | ||||||||
\(498\) | 4.75036 | 0.212869 | ||||||||
\(499\) | 8.77067 | 0.392629 | 0.196315 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196315 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(500\) | −41.8547 | −1.87180 | ||||||||
\(501\) | −69.7565 | −3.11649 | ||||||||
\(502\) | −41.4835 | −1.85150 | ||||||||
\(503\) | 23.8303 | 1.06254 | 0.531271 | − | 0.847202i | \(-0.321715\pi\) | ||||
0.531271 | + | 0.847202i | \(0.321715\pi\) | |||||||
\(504\) | 154.529 | 6.88325 | ||||||||
\(505\) | −26.6167 | −1.18443 | ||||||||
\(506\) | −8.78303 | −0.390453 | ||||||||
\(507\) | 21.2207 | 0.942443 | ||||||||
\(508\) | −32.1763 | −1.42759 | ||||||||
\(509\) | 2.76276 | 0.122457 | 0.0612286 | − | 0.998124i | \(-0.480498\pi\) | ||||
0.0612286 | + | 0.998124i | \(0.480498\pi\) | |||||||
\(510\) | 36.4668 | 1.61478 | ||||||||
\(511\) | −27.2238 | −1.20431 | ||||||||
\(512\) | −1.48982 | −0.0658414 | ||||||||
\(513\) | −40.7174 | −1.79772 | ||||||||
\(514\) | 20.2206 | 0.891892 | ||||||||
\(515\) | −40.0988 | −1.76697 | ||||||||
\(516\) | −108.477 | −4.77541 | ||||||||
\(517\) | 1.14742 | 0.0504633 | ||||||||
\(518\) | −24.3403 | −1.06945 | ||||||||
\(519\) | −62.1702 | −2.72897 | ||||||||
\(520\) | 55.8809 | 2.45054 | ||||||||
\(521\) | 27.7695 | 1.21661 | 0.608303 | − | 0.793705i | \(-0.291851\pi\) | ||||
0.608303 | + | 0.793705i | \(0.291851\pi\) | |||||||
\(522\) | 39.3684 | 1.72311 | ||||||||
\(523\) | 8.27930 | 0.362028 | 0.181014 | − | 0.983480i | \(-0.442062\pi\) | ||||
0.181014 | + | 0.983480i | \(0.442062\pi\) | |||||||
\(524\) | 6.22033 | 0.271736 | ||||||||
\(525\) | 17.8334 | 0.778315 | ||||||||
\(526\) | 32.4508 | 1.41492 | ||||||||
\(527\) | −2.79241 | −0.121639 | ||||||||
\(528\) | −101.371 | −4.41163 | ||||||||
\(529\) | −21.4467 | −0.932463 | ||||||||
\(530\) | −7.11145 | −0.308902 | ||||||||
\(531\) | 55.7667 | 2.42007 | ||||||||
\(532\) | −76.7084 | −3.32573 | ||||||||
\(533\) | 27.5939 | 1.19523 | ||||||||
\(534\) | −91.4144 | −3.95589 | ||||||||
\(535\) | −9.10852 | −0.393796 | ||||||||
\(536\) | −31.1132 | −1.34389 | ||||||||
\(537\) | −49.0689 | −2.11748 | ||||||||
\(538\) | −45.0153 | −1.94075 | ||||||||
\(539\) | 5.70856 | 0.245885 | ||||||||
\(540\) | −116.916 | −5.03127 | ||||||||
\(541\) | −13.1169 | −0.563938 | −0.281969 | − | 0.959424i | \(-0.590987\pi\) | ||||
−0.281969 | + | 0.959424i | \(0.590987\pi\) | |||||||
\(542\) | 21.6288 | 0.929036 | ||||||||
\(543\) | 30.7964 | 1.32160 | ||||||||
\(544\) | −30.3357 | −1.30063 | ||||||||
\(545\) | 9.73347 | 0.416936 | ||||||||
\(546\) | 58.7028 | 2.51225 | ||||||||
\(547\) | −18.4250 | −0.787796 | −0.393898 | − | 0.919154i | \(-0.628874\pi\) | ||||
−0.393898 | + | 0.919154i | \(0.628874\pi\) | |||||||
\(548\) | 99.5896 | 4.25426 | ||||||||
\(549\) | 65.3557 | 2.78931 | ||||||||
\(550\) | −13.9521 | −0.594920 | ||||||||
\(551\) | −12.0915 | −0.515114 | ||||||||
\(552\) | 32.3691 | 1.37772 | ||||||||
\(553\) | −13.1535 | −0.559344 | ||||||||
\(554\) | −62.5700 | −2.65835 | ||||||||
\(555\) | 23.4397 | 0.994961 | ||||||||
\(556\) | −16.5675 | −0.702617 | ||||||||
\(557\) | 30.0796 | 1.27451 | 0.637257 | − | 0.770652i | \(-0.280069\pi\) | ||||
0.637257 | + | 0.770652i | \(0.280069\pi\) | |||||||
\(558\) | 25.4390 | 1.07692 | ||||||||
\(559\) | −16.8418 | −0.712333 | ||||||||
\(560\) | −104.261 | −4.40584 | ||||||||
\(561\) | −13.4250 | −0.566805 | ||||||||
\(562\) | 45.2556 | 1.90899 | ||||||||
\(563\) | 17.0639 | 0.719157 | 0.359578 | − | 0.933115i | \(-0.382921\pi\) | ||||
0.359578 | + | 0.933115i | \(0.382921\pi\) | |||||||
\(564\) | −6.83455 | −0.287786 | ||||||||
\(565\) | −28.1388 | −1.18381 | ||||||||
\(566\) | −18.2404 | −0.766702 | ||||||||
\(567\) | −22.9271 | −0.962847 | ||||||||
\(568\) | 54.0045 | 2.26598 | ||||||||
\(569\) | −25.7629 | −1.08004 | −0.540018 | − | 0.841654i | \(-0.681582\pi\) | ||||
−0.540018 | + | 0.841654i | \(0.681582\pi\) | |||||||
\(570\) | 102.035 | 4.27379 | ||||||||
\(571\) | 18.8520 | 0.788931 | 0.394466 | − | 0.918911i | \(-0.370930\pi\) | ||||
0.394466 | + | 0.918911i | \(0.370930\pi\) | |||||||
\(572\) | −33.2494 | −1.39023 | ||||||||
\(573\) | 54.2327 | 2.26560 | ||||||||
\(574\) | −92.9532 | −3.87979 | ||||||||
\(575\) | 2.46753 | 0.102903 | ||||||||
\(576\) | 124.288 | 5.17867 | ||||||||
\(577\) | −3.45021 | −0.143634 | −0.0718170 | − | 0.997418i | \(-0.522880\pi\) | ||||
−0.0718170 | + | 0.997418i | \(0.522880\pi\) | |||||||
\(578\) | 37.7510 | 1.57024 | ||||||||
\(579\) | 29.4846 | 1.22534 | ||||||||
\(580\) | −34.7195 | −1.44165 | ||||||||
\(581\) | −1.79866 | −0.0746212 | ||||||||
\(582\) | −104.463 | −4.33015 | ||||||||
\(583\) | 2.61803 | 0.108428 | ||||||||
\(584\) | −78.4945 | −3.24813 | ||||||||
\(585\) | −37.3415 | −1.54388 | ||||||||
\(586\) | −4.17383 | −0.172419 | ||||||||
\(587\) | −46.2270 | −1.90799 | −0.953996 | − | 0.299820i | \(-0.903073\pi\) | ||||
−0.953996 | + | 0.299820i | \(0.903073\pi\) | |||||||
\(588\) | −34.0029 | −1.40226 | ||||||||
\(589\) | −7.81325 | −0.321939 | ||||||||
\(590\) | −67.9330 | −2.79676 | ||||||||
\(591\) | 42.2615 | 1.73840 | ||||||||
\(592\) | −38.8709 | −1.59758 | ||||||||
\(593\) | 35.0539 | 1.43949 | 0.719745 | − | 0.694239i | \(-0.244259\pi\) | ||||
0.719745 | + | 0.694239i | \(0.244259\pi\) | |||||||
\(594\) | 59.4527 | 2.43938 | ||||||||
\(595\) | −13.8077 | −0.566061 | ||||||||
\(596\) | 24.9588 | 1.02235 | ||||||||
\(597\) | −6.88526 | −0.281795 | ||||||||
\(598\) | 8.12244 | 0.332151 | ||||||||
\(599\) | 43.1300 | 1.76224 | 0.881122 | − | 0.472889i | \(-0.156789\pi\) | ||||
0.881122 | + | 0.472889i | \(0.156789\pi\) | |||||||
\(600\) | 51.4193 | 2.09919 | ||||||||
\(601\) | 1.49611 | 0.0610276 | 0.0305138 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305138 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(602\) | 56.7336 | 2.31229 | ||||||||
\(603\) | 20.7909 | 0.846671 | ||||||||
\(604\) | 5.24555 | 0.213438 | ||||||||
\(605\) | −10.9532 | −0.445312 | ||||||||
\(606\) | −80.6197 | −3.27495 | ||||||||
\(607\) | 37.5771 | 1.52521 | 0.762604 | − | 0.646866i | \(-0.223921\pi\) | ||||
0.762604 | + | 0.646866i | \(0.223921\pi\) | |||||||
\(608\) | −84.8803 | −3.44235 | ||||||||
\(609\) | −22.5666 | −0.914444 | ||||||||
\(610\) | −79.6140 | −3.22348 | ||||||||
\(611\) | −1.06112 | −0.0429281 | ||||||||
\(612\) | 52.8214 | 2.13518 | ||||||||
\(613\) | 6.77752 | 0.273742 | 0.136871 | − | 0.990589i | \(-0.456295\pi\) | ||||
0.136871 | + | 0.990589i | \(0.456295\pi\) | |||||||
\(614\) | −10.7296 | −0.433010 | ||||||||
\(615\) | 89.5142 | 3.60956 | ||||||||
\(616\) | 69.2998 | 2.79217 | ||||||||
\(617\) | −13.4229 | −0.540385 | −0.270192 | − | 0.962806i | \(-0.587087\pi\) | ||||
−0.270192 | + | 0.962806i | \(0.587087\pi\) | |||||||
\(618\) | −121.456 | −4.88566 | ||||||||
\(619\) | −31.4297 | −1.26327 | −0.631634 | − | 0.775267i | \(-0.717615\pi\) | ||||
−0.631634 | + | 0.775267i | \(0.717615\pi\) | |||||||
\(620\) | −22.4350 | −0.901012 | ||||||||
\(621\) | −10.5147 | −0.421939 | ||||||||
\(622\) | −29.5845 | −1.18623 | ||||||||
\(623\) | 34.6129 | 1.38674 | ||||||||
\(624\) | 93.7471 | 3.75289 | ||||||||
\(625\) | −30.9794 | −1.23918 | ||||||||
\(626\) | 38.9044 | 1.55493 | ||||||||
\(627\) | −37.5636 | −1.50015 | ||||||||
\(628\) | −117.128 | −4.67392 | ||||||||
\(629\) | −5.14782 | −0.205257 | ||||||||
\(630\) | 125.789 | 5.01156 | ||||||||
\(631\) | −21.8255 | −0.868858 | −0.434429 | − | 0.900706i | \(-0.643050\pi\) | ||||
−0.434429 | + | 0.900706i | \(0.643050\pi\) | |||||||
\(632\) | −37.9257 | −1.50860 | ||||||||
\(633\) | 13.9687 | 0.555204 | ||||||||
\(634\) | −51.5000 | −2.04533 | ||||||||
\(635\) | −16.2057 | −0.643104 | ||||||||
\(636\) | −15.5942 | −0.618352 | ||||||||
\(637\) | −5.27921 | −0.209170 | ||||||||
\(638\) | 17.6551 | 0.698973 | ||||||||
\(639\) | −36.0876 | −1.42761 | ||||||||
\(640\) | −58.4768 | −2.31150 | ||||||||
\(641\) | 22.8259 | 0.901570 | 0.450785 | − | 0.892633i | \(-0.351144\pi\) | ||||
0.450785 | + | 0.892633i | \(0.351144\pi\) | |||||||
\(642\) | −27.5889 | −1.08885 | ||||||||
\(643\) | −36.2852 | −1.43095 | −0.715474 | − | 0.698640i | \(-0.753789\pi\) | ||||
−0.715474 | + | 0.698640i | \(0.753789\pi\) | |||||||
\(644\) | −19.8088 | −0.780575 | ||||||||
\(645\) | −54.6346 | −2.15123 | ||||||||
\(646\) | −22.4089 | −0.881668 | ||||||||
\(647\) | −46.2899 | −1.81984 | −0.909922 | − | 0.414780i | \(-0.863858\pi\) | ||||
−0.909922 | + | 0.414780i | \(0.863858\pi\) | |||||||
\(648\) | −66.1058 | −2.59688 | ||||||||
\(649\) | 25.0091 | 0.981692 | ||||||||
\(650\) | 12.9028 | 0.506088 | ||||||||
\(651\) | −14.5820 | −0.571516 | ||||||||
\(652\) | −23.8614 | −0.934485 | ||||||||
\(653\) | −5.97064 | −0.233649 | −0.116825 | − | 0.993153i | \(-0.537272\pi\) | ||||
−0.116825 | + | 0.993153i | \(0.537272\pi\) | |||||||
\(654\) | 29.4818 | 1.15283 | ||||||||
\(655\) | 3.13289 | 0.122412 | ||||||||
\(656\) | −148.444 | −5.79578 | ||||||||
\(657\) | 52.4527 | 2.04637 | ||||||||
\(658\) | 3.57449 | 0.139348 | ||||||||
\(659\) | 39.3638 | 1.53340 | 0.766699 | − | 0.642007i | \(-0.221898\pi\) | ||||
0.766699 | + | 0.642007i | \(0.221898\pi\) | |||||||
\(660\) | −107.860 | −4.19846 | ||||||||
\(661\) | −0.773148 | −0.0300720 | −0.0150360 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150360 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(662\) | −88.0010 | −3.42026 | ||||||||
\(663\) | 12.4153 | 0.482170 | ||||||||
\(664\) | −5.18611 | −0.201260 | ||||||||
\(665\) | −38.6344 | −1.49818 | ||||||||
\(666\) | 46.8970 | 1.81722 | ||||||||
\(667\) | −3.12244 | −0.120901 | ||||||||
\(668\) | 123.084 | 4.76227 | ||||||||
\(669\) | 7.68751 | 0.297216 | ||||||||
\(670\) | −25.3267 | −0.978458 | ||||||||
\(671\) | 29.3094 | 1.13147 | ||||||||
\(672\) | −158.414 | −6.11095 | ||||||||
\(673\) | 16.0619 | 0.619139 | 0.309570 | − | 0.950877i | \(-0.399815\pi\) | ||||
0.309570 | + | 0.950877i | \(0.399815\pi\) | |||||||
\(674\) | 4.16061 | 0.160261 | ||||||||
\(675\) | −16.7029 | −0.642893 | ||||||||
\(676\) | −37.4436 | −1.44014 | ||||||||
\(677\) | 28.6621 | 1.10157 | 0.550786 | − | 0.834646i | \(-0.314328\pi\) | ||||
0.550786 | + | 0.834646i | \(0.314328\pi\) | |||||||
\(678\) | −85.2299 | −3.27324 | ||||||||
\(679\) | 39.5538 | 1.51794 | ||||||||
\(680\) | −39.8119 | −1.52672 | ||||||||
\(681\) | 33.1193 | 1.26913 | ||||||||
\(682\) | 11.4084 | 0.436849 | ||||||||
\(683\) | 21.4561 | 0.820995 | 0.410498 | − | 0.911862i | \(-0.365355\pi\) | ||||
0.410498 | + | 0.911862i | \(0.365355\pi\) | |||||||
\(684\) | 147.796 | 5.65112 | ||||||||
\(685\) | 50.1586 | 1.91646 | ||||||||
\(686\) | −39.3072 | −1.50076 | ||||||||
\(687\) | −49.5877 | −1.89189 | ||||||||
\(688\) | 90.6023 | 3.45418 | ||||||||
\(689\) | −2.42112 | −0.0922375 | ||||||||
\(690\) | 26.3491 | 1.00309 | ||||||||
\(691\) | −47.6507 | −1.81272 | −0.906359 | − | 0.422508i | \(-0.861150\pi\) | ||||
−0.906359 | + | 0.422508i | \(0.861150\pi\) | |||||||
\(692\) | 109.698 | 4.17011 | ||||||||
\(693\) | −46.3084 | −1.75911 | ||||||||
\(694\) | −27.9441 | −1.06074 | ||||||||
\(695\) | −8.34425 | −0.316516 | ||||||||
\(696\) | −65.0664 | −2.46634 | ||||||||
\(697\) | −19.6591 | −0.744640 | ||||||||
\(698\) | −6.28029 | −0.237713 | ||||||||
\(699\) | 31.7631 | 1.20139 | ||||||||
\(700\) | −31.4668 | −1.18933 | ||||||||
\(701\) | 24.4697 | 0.924208 | 0.462104 | − | 0.886826i | \(-0.347095\pi\) | ||||
0.462104 | + | 0.886826i | \(0.347095\pi\) | |||||||
\(702\) | −54.9812 | −2.07513 | ||||||||
\(703\) | −14.4038 | −0.543248 | ||||||||
\(704\) | 55.7382 | 2.10071 | ||||||||
\(705\) | −3.44224 | −0.129642 | ||||||||
\(706\) | −56.0421 | −2.10917 | ||||||||
\(707\) | 30.5257 | 1.14804 | ||||||||
\(708\) | −148.966 | −5.59848 | ||||||||
\(709\) | −8.28446 | −0.311130 | −0.155565 | − | 0.987826i | \(-0.549720\pi\) | ||||
−0.155565 | + | 0.987826i | \(0.549720\pi\) | |||||||
\(710\) | 43.9607 | 1.64982 | ||||||||
\(711\) | 25.3432 | 0.950444 | ||||||||
\(712\) | 99.7998 | 3.74016 | ||||||||
\(713\) | −2.01765 | −0.0755617 | ||||||||
\(714\) | −41.8223 | −1.56516 | ||||||||
\(715\) | −16.7461 | −0.626270 | ||||||||
\(716\) | 86.5813 | 3.23570 | ||||||||
\(717\) | −2.64308 | −0.0987075 | ||||||||
\(718\) | −67.8151 | −2.53084 | ||||||||
\(719\) | −12.4288 | −0.463515 | −0.231758 | − | 0.972774i | \(-0.574448\pi\) | ||||
−0.231758 | + | 0.972774i | \(0.574448\pi\) | |||||||
\(720\) | 200.883 | 7.48645 | ||||||||
\(721\) | 45.9877 | 1.71267 | ||||||||
\(722\) | −11.5575 | −0.430127 | ||||||||
\(723\) | −23.6740 | −0.880447 | ||||||||
\(724\) | −54.3398 | −2.01952 | ||||||||
\(725\) | −4.96009 | −0.184213 | ||||||||
\(726\) | −33.1763 | −1.23129 | ||||||||
\(727\) | 41.9968 | 1.55758 | 0.778788 | − | 0.627287i | \(-0.215835\pi\) | ||||
0.778788 | + | 0.627287i | \(0.215835\pi\) | |||||||
\(728\) | −64.0876 | −2.37524 | ||||||||
\(729\) | −31.0670 | −1.15063 | ||||||||
\(730\) | −63.8960 | −2.36490 | ||||||||
\(731\) | 11.9988 | 0.443792 | ||||||||
\(732\) | −174.580 | −6.45267 | ||||||||
\(733\) | −33.7036 | −1.24487 | −0.622436 | − | 0.782671i | \(-0.713857\pi\) | ||||
−0.622436 | + | 0.782671i | \(0.713857\pi\) | |||||||
\(734\) | 87.4737 | 3.22871 | ||||||||
\(735\) | −17.1257 | −0.631690 | ||||||||
\(736\) | −21.9190 | −0.807947 | ||||||||
\(737\) | 9.32387 | 0.343449 | ||||||||
\(738\) | 179.095 | 6.59259 | ||||||||
\(739\) | 27.4557 | 1.00998 | 0.504988 | − | 0.863127i | \(-0.331497\pi\) | ||||
0.504988 | + | 0.863127i | \(0.331497\pi\) | |||||||
\(740\) | −41.3590 | −1.52039 | ||||||||
\(741\) | 34.7384 | 1.27615 | ||||||||
\(742\) | 8.15583 | 0.299410 | ||||||||
\(743\) | −4.71004 | −0.172795 | −0.0863973 | − | 0.996261i | \(-0.527535\pi\) | ||||
−0.0863973 | + | 0.996261i | \(0.527535\pi\) | |||||||
\(744\) | −42.0446 | −1.54143 | ||||||||
\(745\) | 12.5706 | 0.460551 | ||||||||
\(746\) | 64.5721 | 2.36415 | ||||||||
\(747\) | 3.46553 | 0.126797 | ||||||||
\(748\) | 23.6882 | 0.866128 | ||||||||
\(749\) | 10.4462 | 0.381695 | ||||||||
\(750\) | −63.8501 | −2.33148 | ||||||||
\(751\) | 42.8360 | 1.56311 | 0.781554 | − | 0.623838i | \(-0.214428\pi\) | ||||
0.781554 | + | 0.623838i | \(0.214428\pi\) | |||||||
\(752\) | 5.70838 | 0.208163 | ||||||||
\(753\) | −45.8155 | −1.66961 | ||||||||
\(754\) | −16.3272 | −0.594603 | ||||||||
\(755\) | 2.64194 | 0.0961500 | ||||||||
\(756\) | 134.086 | 4.87668 | ||||||||
\(757\) | −20.9901 | −0.762897 | −0.381449 | − | 0.924390i | \(-0.624575\pi\) | ||||
−0.381449 | + | 0.924390i | \(0.624575\pi\) | |||||||
\(758\) | 22.4880 | 0.816800 | ||||||||
\(759\) | −9.70023 | −0.352096 | ||||||||
\(760\) | −111.395 | −4.04072 | ||||||||
\(761\) | −10.0006 | −0.362521 | −0.181261 | − | 0.983435i | \(-0.558018\pi\) | ||||
−0.181261 | + | 0.983435i | \(0.558018\pi\) | |||||||
\(762\) | −49.0856 | −1.77818 | ||||||||
\(763\) | −11.1629 | −0.404125 | ||||||||
\(764\) | −95.6927 | −3.46204 | ||||||||
\(765\) | 26.6037 | 0.961858 | ||||||||
\(766\) | 44.7575 | 1.61715 | ||||||||
\(767\) | −23.1281 | −0.835106 | ||||||||
\(768\) | −50.5363 | −1.82357 | ||||||||
\(769\) | −27.1420 | −0.978765 | −0.489382 | − | 0.872069i | \(-0.662778\pi\) | ||||
−0.489382 | + | 0.872069i | \(0.662778\pi\) | |||||||
\(770\) | 56.4113 | 2.03292 | ||||||||
\(771\) | 22.3322 | 0.804274 | ||||||||
\(772\) | −52.0251 | −1.87242 | ||||||||
\(773\) | −8.70667 | −0.313157 | −0.156579 | − | 0.987665i | \(-0.550046\pi\) | ||||
−0.156579 | + | 0.987665i | \(0.550046\pi\) | |||||||
\(774\) | −109.310 | −3.92907 | ||||||||
\(775\) | −3.20511 | −0.115131 | ||||||||
\(776\) | 114.046 | 4.09401 | ||||||||
\(777\) | −26.8821 | −0.964388 | ||||||||
\(778\) | −27.2787 | −0.977988 | ||||||||
\(779\) | −55.0066 | −1.97082 | ||||||||
\(780\) | 99.7479 | 3.57155 | ||||||||
\(781\) | −16.1838 | −0.579103 | ||||||||
\(782\) | −5.78677 | −0.206934 | ||||||||
\(783\) | 21.1359 | 0.755336 | ||||||||
\(784\) | 28.4001 | 1.01429 | ||||||||
\(785\) | −58.9920 | −2.10551 | ||||||||
\(786\) | 9.48923 | 0.338470 | ||||||||
\(787\) | 16.7454 | 0.596910 | 0.298455 | − | 0.954424i | \(-0.403529\pi\) | ||||
0.298455 | + | 0.954424i | \(0.403529\pi\) | |||||||
\(788\) | −74.5697 | −2.65644 | ||||||||
\(789\) | 35.8396 | 1.27592 | ||||||||
\(790\) | −30.8722 | −1.09838 | ||||||||
\(791\) | 32.2713 | 1.14743 | ||||||||
\(792\) | −133.522 | −4.74448 | ||||||||
\(793\) | −27.1049 | −0.962524 | ||||||||
\(794\) | 12.8926 | 0.457543 | ||||||||
\(795\) | −7.85409 | −0.278556 | ||||||||
\(796\) | 12.1489 | 0.430608 | ||||||||
\(797\) | 29.5969 | 1.04838 | 0.524188 | − | 0.851603i | \(-0.324369\pi\) | ||||
0.524188 | + | 0.851603i | \(0.324369\pi\) | |||||||
\(798\) | −117.020 | −4.14247 | ||||||||
\(799\) | 0.755983 | 0.0267448 | ||||||||
\(800\) | −34.8191 | −1.23104 | ||||||||
\(801\) | −66.6896 | −2.35636 | ||||||||
\(802\) | −46.0770 | −1.62703 | ||||||||
\(803\) | 23.5229 | 0.830104 | ||||||||
\(804\) | −55.5374 | −1.95865 | ||||||||
\(805\) | −9.97675 | −0.351634 | ||||||||
\(806\) | −10.5503 | −0.371619 | ||||||||
\(807\) | −49.7162 | −1.75009 | ||||||||
\(808\) | 88.0149 | 3.09635 | ||||||||
\(809\) | −7.92377 | −0.278585 | −0.139292 | − | 0.990251i | \(-0.544483\pi\) | ||||
−0.139292 | + | 0.990251i | \(0.544483\pi\) | |||||||
\(810\) | −53.8114 | −1.89074 | ||||||||
\(811\) | −54.0967 | −1.89959 | −0.949796 | − | 0.312869i | \(-0.898710\pi\) | ||||
−0.949796 | + | 0.312869i | \(0.898710\pi\) | |||||||
\(812\) | 39.8184 | 1.39735 | ||||||||
\(813\) | 23.8874 | 0.837769 | ||||||||
\(814\) | 21.0314 | 0.737149 | ||||||||
\(815\) | −12.0179 | −0.420968 | ||||||||
\(816\) | −66.7894 | −2.33810 | ||||||||
\(817\) | 33.5731 | 1.17457 | ||||||||
\(818\) | −5.80684 | −0.203031 | ||||||||
\(819\) | 42.8255 | 1.49644 | ||||||||
\(820\) | −157.946 | −5.51573 | ||||||||
\(821\) | −10.9468 | −0.382047 | −0.191024 | − | 0.981585i | \(-0.561181\pi\) | ||||
−0.191024 | + | 0.981585i | \(0.561181\pi\) | |||||||
\(822\) | 151.926 | 5.29902 | ||||||||
\(823\) | 31.7095 | 1.10532 | 0.552662 | − | 0.833405i | \(-0.313612\pi\) | ||||
0.552662 | + | 0.833405i | \(0.313612\pi\) | |||||||
\(824\) | 132.597 | 4.61923 | ||||||||
\(825\) | −15.4091 | −0.536476 | ||||||||
\(826\) | 77.9095 | 2.71082 | ||||||||
\(827\) | −32.1987 | −1.11966 | −0.559829 | − | 0.828608i | \(-0.689133\pi\) | ||||
−0.559829 | + | 0.828608i | \(0.689133\pi\) | |||||||
\(828\) | 38.1660 | 1.32636 | ||||||||
\(829\) | −11.0284 | −0.383031 | −0.191515 | − | 0.981490i | \(-0.561340\pi\) | ||||
−0.191515 | + | 0.981490i | \(0.561340\pi\) | |||||||
\(830\) | −4.22159 | −0.146533 | ||||||||
\(831\) | −69.1041 | −2.39719 | ||||||||
\(832\) | −51.5460 | −1.78703 | ||||||||
\(833\) | 3.76113 | 0.130315 | ||||||||
\(834\) | −25.2740 | −0.875166 | ||||||||
\(835\) | 61.9918 | 2.14531 | ||||||||
\(836\) | 66.2804 | 2.29236 | ||||||||
\(837\) | 13.6576 | 0.472075 | ||||||||
\(838\) | −73.4828 | −2.53842 | ||||||||
\(839\) | −47.2253 | −1.63040 | −0.815200 | − | 0.579180i | \(-0.803373\pi\) | ||||
−0.815200 | + | 0.579180i | \(0.803373\pi\) | |||||||
\(840\) | −207.899 | −7.17320 | ||||||||
\(841\) | −22.7235 | −0.783568 | ||||||||
\(842\) | 18.7171 | 0.645032 | ||||||||
\(843\) | 49.9816 | 1.72146 | ||||||||
\(844\) | −24.6475 | −0.848401 | ||||||||
\(845\) | −18.8586 | −0.648754 | ||||||||
\(846\) | −6.88705 | −0.236782 | ||||||||
\(847\) | 12.5618 | 0.431629 | ||||||||
\(848\) | 13.0247 | 0.447270 | ||||||||
\(849\) | −20.1452 | −0.691382 | ||||||||
\(850\) | −9.19246 | −0.315299 | ||||||||
\(851\) | −3.71955 | −0.127505 | ||||||||
\(852\) | 96.3985 | 3.30256 | ||||||||
\(853\) | 16.4614 | 0.563627 | 0.281813 | − | 0.959469i | \(-0.409064\pi\) | ||||
0.281813 | + | 0.959469i | \(0.409064\pi\) | |||||||
\(854\) | 91.3060 | 3.12443 | ||||||||
\(855\) | 74.4379 | 2.54572 | ||||||||
\(856\) | 30.1196 | 1.02947 | ||||||||
\(857\) | −4.59033 | −0.156803 | −0.0784014 | − | 0.996922i | \(-0.524982\pi\) | ||||
−0.0784014 | + | 0.996922i | \(0.524982\pi\) | |||||||
\(858\) | −50.7225 | −1.73164 | ||||||||
\(859\) | −19.6684 | −0.671077 | −0.335538 | − | 0.942027i | \(-0.608918\pi\) | ||||
−0.335538 | + | 0.942027i | \(0.608918\pi\) | |||||||
\(860\) | 96.4019 | 3.28728 | ||||||||
\(861\) | −102.660 | −3.49865 | ||||||||
\(862\) | 59.0405 | 2.01093 | ||||||||
\(863\) | 1.50286 | 0.0511580 | 0.0255790 | − | 0.999673i | \(-0.491857\pi\) | ||||
0.0255790 | + | 0.999673i | \(0.491857\pi\) | |||||||
\(864\) | 148.371 | 5.04768 | ||||||||
\(865\) | 55.2499 | 1.87855 | ||||||||
\(866\) | −6.56950 | −0.223241 | ||||||||
\(867\) | 41.6933 | 1.41598 | ||||||||
\(868\) | 25.7298 | 0.873326 | ||||||||
\(869\) | 11.3654 | 0.385544 | ||||||||
\(870\) | −52.9653 | −1.79569 | ||||||||
\(871\) | −8.62260 | −0.292166 | ||||||||
\(872\) | −32.1862 | −1.08996 | ||||||||
\(873\) | −76.2093 | −2.57929 | ||||||||
\(874\) | −16.1916 | −0.547687 | ||||||||
\(875\) | 24.1761 | 0.817300 | ||||||||
\(876\) | −140.113 | −4.73399 | ||||||||
\(877\) | 14.4133 | 0.486703 | 0.243351 | − | 0.969938i | \(-0.421753\pi\) | ||||
0.243351 | + | 0.969938i | \(0.421753\pi\) | |||||||
\(878\) | 98.0842 | 3.31018 | ||||||||
\(879\) | −4.60970 | −0.155481 | ||||||||
\(880\) | 90.0876 | 3.03685 | ||||||||
\(881\) | −18.0613 | −0.608501 | −0.304251 | − | 0.952592i | \(-0.598406\pi\) | ||||
−0.304251 | + | 0.952592i | \(0.598406\pi\) | |||||||
\(882\) | −34.2641 | −1.15373 | ||||||||
\(883\) | 16.8264 | 0.566253 | 0.283127 | − | 0.959083i | \(-0.408628\pi\) | ||||
0.283127 | + | 0.959083i | \(0.408628\pi\) | |||||||
\(884\) | −21.9066 | −0.736798 | ||||||||
\(885\) | −75.0271 | −2.52201 | ||||||||
\(886\) | −49.6888 | −1.66933 | ||||||||
\(887\) | 15.5878 | 0.523386 | 0.261693 | − | 0.965151i | \(-0.415719\pi\) | ||||
0.261693 | + | 0.965151i | \(0.415719\pi\) | |||||||
\(888\) | −77.5093 | −2.60104 | ||||||||
\(889\) | 18.5857 | 0.623343 | ||||||||
\(890\) | 81.2389 | 2.72313 | ||||||||
\(891\) | 19.8103 | 0.663670 | ||||||||
\(892\) | −13.5645 | −0.454173 | ||||||||
\(893\) | 2.11526 | 0.0707846 | ||||||||
\(894\) | 38.0752 | 1.27342 | ||||||||
\(895\) | 43.6070 | 1.45762 | ||||||||
\(896\) | 67.0647 | 2.24047 | ||||||||
\(897\) | 8.97065 | 0.299521 | ||||||||
\(898\) | 6.74849 | 0.225200 | ||||||||
\(899\) | 4.05577 | 0.135267 | ||||||||
\(900\) | 60.6279 | 2.02093 | ||||||||
\(901\) | 1.72491 | 0.0574651 | ||||||||
\(902\) | 80.3169 | 2.67426 | ||||||||
\(903\) | 62.6581 | 2.08513 | ||||||||
\(904\) | 93.0481 | 3.09473 | ||||||||
\(905\) | −27.3684 | −0.909757 | ||||||||
\(906\) | 8.00219 | 0.265855 | ||||||||
\(907\) | 49.1215 | 1.63105 | 0.815527 | − | 0.578719i | \(-0.196447\pi\) | ||||
0.815527 | + | 0.578719i | \(0.196447\pi\) | |||||||
\(908\) | −58.4384 | −1.93935 | ||||||||
\(909\) | −58.8145 | −1.95075 | ||||||||
\(910\) | −52.1685 | −1.72937 | ||||||||
\(911\) | −1.94257 | −0.0643601 | −0.0321800 | − | 0.999482i | \(-0.510245\pi\) | ||||
−0.0321800 | + | 0.999482i | \(0.510245\pi\) | |||||||
\(912\) | −186.879 | −6.18817 | ||||||||
\(913\) | 1.55415 | 0.0514348 | ||||||||
\(914\) | 44.8378 | 1.48310 | ||||||||
\(915\) | −87.9279 | −2.90681 | ||||||||
\(916\) | 87.4968 | 2.89097 | ||||||||
\(917\) | −3.59298 | −0.118651 | ||||||||
\(918\) | 39.1709 | 1.29283 | ||||||||
\(919\) | −43.6065 | −1.43844 | −0.719222 | − | 0.694780i | \(-0.755502\pi\) | ||||
−0.719222 | + | 0.694780i | \(0.755502\pi\) | |||||||
\(920\) | −28.7661 | −0.948389 | ||||||||
\(921\) | −11.8500 | −0.390472 | ||||||||
\(922\) | 46.5622 | 1.53344 | ||||||||
\(923\) | 14.9666 | 0.492632 | ||||||||
\(924\) | 123.701 | 4.06945 | ||||||||
\(925\) | −5.90862 | −0.194274 | ||||||||
\(926\) | −45.5123 | −1.49563 | ||||||||
\(927\) | −88.6056 | −2.91019 | ||||||||
\(928\) | 44.0603 | 1.44635 | ||||||||
\(929\) | −56.3550 | −1.84895 | −0.924474 | − | 0.381246i | \(-0.875495\pi\) | ||||
−0.924474 | + | 0.381246i | \(0.875495\pi\) | |||||||
\(930\) | −34.2251 | −1.12228 | ||||||||
\(931\) | 10.5238 | 0.344902 | ||||||||
\(932\) | −56.0456 | −1.83583 | ||||||||
\(933\) | −32.6739 | −1.06970 | ||||||||
\(934\) | 51.5184 | 1.68573 | ||||||||
\(935\) | 11.9307 | 0.390174 | ||||||||
\(936\) | 123.479 | 4.03604 | ||||||||
\(937\) | 10.7476 | 0.351108 | 0.175554 | − | 0.984470i | \(-0.443828\pi\) | ||||
0.175554 | + | 0.984470i | \(0.443828\pi\) | |||||||
\(938\) | 29.0462 | 0.948392 | ||||||||
\(939\) | 42.9671 | 1.40218 | ||||||||
\(940\) | 6.07378 | 0.198105 | ||||||||
\(941\) | −45.6863 | −1.48933 | −0.744665 | − | 0.667438i | \(-0.767391\pi\) | ||||
−0.744665 | + | 0.667438i | \(0.767391\pi\) | |||||||
\(942\) | −178.681 | −5.82175 | ||||||||
\(943\) | −14.2046 | −0.462566 | ||||||||
\(944\) | 124.420 | 4.04952 | ||||||||
\(945\) | 67.5331 | 2.19685 | ||||||||
\(946\) | −49.0210 | −1.59381 | ||||||||
\(947\) | −60.7725 | −1.97484 | −0.987420 | − | 0.158117i | \(-0.949458\pi\) | ||||
−0.987420 | + | 0.158117i | \(0.949458\pi\) | |||||||
\(948\) | −67.6976 | −2.19872 | ||||||||
\(949\) | −21.7537 | −0.706154 | ||||||||
\(950\) | −25.7208 | −0.834492 | ||||||||
\(951\) | −56.8781 | −1.84440 | ||||||||
\(952\) | 45.6587 | 1.47981 | ||||||||
\(953\) | −33.9325 | −1.09918 | −0.549590 | − | 0.835435i | \(-0.685216\pi\) | ||||
−0.549590 | + | 0.835435i | \(0.685216\pi\) | |||||||
\(954\) | −15.7140 | −0.508761 | ||||||||
\(955\) | −48.1960 | −1.55958 | ||||||||
\(956\) | 4.66367 | 0.150834 | ||||||||
\(957\) | 19.4988 | 0.630307 | ||||||||
\(958\) | 31.3498 | 1.01287 | ||||||||
\(959\) | −57.5249 | −1.85757 | ||||||||
\(960\) | −167.214 | −5.39682 | ||||||||
\(961\) | −28.3793 | −0.915460 | ||||||||
\(962\) | −19.4495 | −0.627079 | ||||||||
\(963\) | −20.1269 | −0.648581 | ||||||||
\(964\) | 41.7725 | 1.34540 | ||||||||
\(965\) | −26.2026 | −0.843492 | ||||||||
\(966\) | −30.2187 | −0.972270 | ||||||||
\(967\) | 24.4574 | 0.786498 | 0.393249 | − | 0.919432i | \(-0.371351\pi\) | ||||
0.393249 | + | 0.919432i | \(0.371351\pi\) | |||||||
\(968\) | 36.2196 | 1.16414 | ||||||||
\(969\) | −24.7491 | −0.795055 | ||||||||
\(970\) | 92.8355 | 2.98077 | ||||||||
\(971\) | −52.9047 | −1.69779 | −0.848896 | − | 0.528560i | \(-0.822732\pi\) | ||||
−0.848896 | + | 0.528560i | \(0.822732\pi\) | |||||||
\(972\) | 14.7624 | 0.473505 | ||||||||
\(973\) | 9.56968 | 0.306790 | ||||||||
\(974\) | −75.2267 | −2.41042 | ||||||||
\(975\) | 14.2502 | 0.456370 | ||||||||
\(976\) | 145.814 | 4.66739 | ||||||||
\(977\) | −44.9071 | −1.43671 | −0.718353 | − | 0.695679i | \(-0.755104\pi\) | ||||
−0.718353 | + | 0.695679i | \(0.755104\pi\) | |||||||
\(978\) | −36.4010 | −1.16398 | ||||||||
\(979\) | −29.9076 | −0.955849 | ||||||||
\(980\) | 30.2180 | 0.965278 | ||||||||
\(981\) | 21.5079 | 0.686694 | ||||||||
\(982\) | 12.0033 | 0.383039 | ||||||||
\(983\) | −21.1991 | −0.676147 | −0.338074 | − | 0.941120i | \(-0.609775\pi\) | ||||
−0.338074 | + | 0.941120i | \(0.609775\pi\) | |||||||
\(984\) | −296.001 | −9.43617 | ||||||||
\(985\) | −37.5573 | −1.19667 | ||||||||
\(986\) | 11.6322 | 0.370445 | ||||||||
\(987\) | 3.94777 | 0.125659 | ||||||||
\(988\) | −61.2953 | −1.95006 | ||||||||
\(989\) | 8.66973 | 0.275681 | ||||||||
\(990\) | −108.689 | −3.45436 | ||||||||
\(991\) | −32.2621 | −1.02484 | −0.512419 | − | 0.858735i | \(-0.671251\pi\) | ||||
−0.512419 | + | 0.858735i | \(0.671251\pi\) | |||||||
\(992\) | 28.4709 | 0.903951 | ||||||||
\(993\) | −97.1908 | −3.08426 | ||||||||
\(994\) | −50.4167 | −1.59912 | ||||||||
\(995\) | 6.11885 | 0.193981 | ||||||||
\(996\) | −9.25724 | −0.293327 | ||||||||
\(997\) | −30.5309 | −0.966922 | −0.483461 | − | 0.875366i | \(-0.660620\pi\) | ||||
−0.483461 | + | 0.875366i | \(0.660620\pi\) | |||||||
\(998\) | −23.6085 | −0.747314 | ||||||||
\(999\) | 25.1778 | 0.796591 |
(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 | 8003.2.a.a.1.5 | ✓ | 147 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.a.1.5 | ✓ | 147 | 1.1 | even | 1 | trivial |