Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.66164 | 0.959346 | 0.479673 | − | 0.877447i | \(-0.340755\pi\) | ||||
0.479673 | + | 0.877447i | \(0.340755\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0681057 | 0.0304578 | 0.0152289 | − | 0.999884i | \(-0.495152\pi\) | ||||
0.0152289 | + | 0.999884i | \(0.495152\pi\) | |||||||
\(6\) | −1.66164 | −0.678360 | ||||||||
\(7\) | 0.103168 | 0.0389939 | 0.0194970 | − | 0.999810i | \(-0.493794\pi\) | ||||
0.0194970 | + | 0.999810i | \(0.493794\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.238964 | −0.0796546 | ||||||||
\(10\) | −0.0681057 | −0.0215369 | ||||||||
\(11\) | −0.129315 | −0.0389898 | −0.0194949 | − | 0.999810i | \(-0.506206\pi\) | ||||
−0.0194949 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(12\) | 1.66164 | 0.479673 | ||||||||
\(13\) | −1.57480 | −0.436772 | −0.218386 | − | 0.975863i | \(-0.570079\pi\) | ||||
−0.218386 | + | 0.975863i | \(0.570079\pi\) | |||||||
\(14\) | −0.103168 | −0.0275729 | ||||||||
\(15\) | 0.113167 | 0.0292196 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.28009 | 1.03807 | 0.519037 | − | 0.854752i | \(-0.326291\pi\) | ||||
0.519037 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(18\) | 0.238964 | 0.0563243 | ||||||||
\(19\) | 4.77084 | 1.09451 | 0.547253 | − | 0.836967i | \(-0.315674\pi\) | ||||
0.547253 | + | 0.836967i | \(0.315674\pi\) | |||||||
\(20\) | 0.0681057 | 0.0152289 | ||||||||
\(21\) | 0.171428 | 0.0374087 | ||||||||
\(22\) | 0.129315 | 0.0275700 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.66164 | −0.339180 | ||||||||
\(25\) | −4.99536 | −0.999072 | ||||||||
\(26\) | 1.57480 | 0.308844 | ||||||||
\(27\) | −5.38198 | −1.03576 | ||||||||
\(28\) | 0.103168 | 0.0194970 | ||||||||
\(29\) | −5.98015 | −1.11049 | −0.555243 | − | 0.831688i | \(-0.687375\pi\) | ||||
−0.555243 | + | 0.831688i | \(0.687375\pi\) | |||||||
\(30\) | −0.113167 | −0.0206614 | ||||||||
\(31\) | 3.37662 | 0.606459 | 0.303230 | − | 0.952917i | \(-0.401935\pi\) | ||||
0.303230 | + | 0.952917i | \(0.401935\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.214874 | −0.0374048 | ||||||||
\(34\) | −4.28009 | −0.734029 | ||||||||
\(35\) | 0.00702635 | 0.00118767 | ||||||||
\(36\) | −0.238964 | −0.0398273 | ||||||||
\(37\) | −6.98679 | −1.14862 | −0.574311 | − | 0.818637i | \(-0.694730\pi\) | ||||
−0.574311 | + | 0.818637i | \(0.694730\pi\) | |||||||
\(38\) | −4.77084 | −0.773933 | ||||||||
\(39\) | −2.61675 | −0.419015 | ||||||||
\(40\) | −0.0681057 | −0.0107685 | ||||||||
\(41\) | −0.948349 | −0.148107 | −0.0740536 | − | 0.997254i | \(-0.523594\pi\) | ||||
−0.0740536 | + | 0.997254i | \(0.523594\pi\) | |||||||
\(42\) | −0.171428 | −0.0264519 | ||||||||
\(43\) | −13.0487 | −1.98991 | −0.994956 | − | 0.100315i | \(-0.968015\pi\) | ||||
−0.994956 | + | 0.100315i | \(0.968015\pi\) | |||||||
\(44\) | −0.129315 | −0.0194949 | ||||||||
\(45\) | −0.0162748 | −0.00242611 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.273217 | −0.0398528 | −0.0199264 | − | 0.999801i | \(-0.506343\pi\) | ||||
−0.0199264 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(48\) | 1.66164 | 0.239837 | ||||||||
\(49\) | −6.98936 | −0.998479 | ||||||||
\(50\) | 4.99536 | 0.706451 | ||||||||
\(51\) | 7.11195 | 0.995873 | ||||||||
\(52\) | −1.57480 | −0.218386 | ||||||||
\(53\) | −3.18399 | −0.437354 | −0.218677 | − | 0.975797i | \(-0.570174\pi\) | ||||
−0.218677 | + | 0.975797i | \(0.570174\pi\) | |||||||
\(54\) | 5.38198 | 0.732395 | ||||||||
\(55\) | −0.00880707 | −0.00118755 | ||||||||
\(56\) | −0.103168 | −0.0137864 | ||||||||
\(57\) | 7.92741 | 1.05001 | ||||||||
\(58\) | 5.98015 | 0.785232 | ||||||||
\(59\) | −9.41679 | −1.22596 | −0.612981 | − | 0.790098i | \(-0.710030\pi\) | ||||
−0.612981 | + | 0.790098i | \(0.710030\pi\) | |||||||
\(60\) | 0.113167 | 0.0146098 | ||||||||
\(61\) | −4.95302 | −0.634169 | −0.317084 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317084 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(62\) | −3.37662 | −0.428832 | ||||||||
\(63\) | −0.0246535 | −0.00310605 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.107253 | −0.0133031 | ||||||||
\(66\) | 0.214874 | 0.0264492 | ||||||||
\(67\) | 13.4210 | 1.63963 | 0.819816 | − | 0.572626i | \(-0.194075\pi\) | ||||
0.819816 | + | 0.572626i | \(0.194075\pi\) | |||||||
\(68\) | 4.28009 | 0.519037 | ||||||||
\(69\) | −1.66164 | −0.200038 | ||||||||
\(70\) | −0.00702635 | −0.000839809 0 | ||||||||
\(71\) | 3.25184 | 0.385922 | 0.192961 | − | 0.981206i | \(-0.438191\pi\) | ||||
0.192961 | + | 0.981206i | \(0.438191\pi\) | |||||||
\(72\) | 0.238964 | 0.0281622 | ||||||||
\(73\) | 2.62561 | 0.307304 | 0.153652 | − | 0.988125i | \(-0.450896\pi\) | ||||
0.153652 | + | 0.988125i | \(0.450896\pi\) | |||||||
\(74\) | 6.98679 | 0.812198 | ||||||||
\(75\) | −8.30048 | −0.958456 | ||||||||
\(76\) | 4.77084 | 0.547253 | ||||||||
\(77\) | −0.0133412 | −0.00152037 | ||||||||
\(78\) | 2.61675 | 0.296289 | ||||||||
\(79\) | 2.17954 | 0.245218 | 0.122609 | − | 0.992455i | \(-0.460874\pi\) | ||||
0.122609 | + | 0.992455i | \(0.460874\pi\) | |||||||
\(80\) | 0.0681057 | 0.00761445 | ||||||||
\(81\) | −8.22600 | −0.914001 | ||||||||
\(82\) | 0.948349 | 0.104728 | ||||||||
\(83\) | −2.80733 | −0.308144 | −0.154072 | − | 0.988060i | \(-0.549239\pi\) | ||||
−0.154072 | + | 0.988060i | \(0.549239\pi\) | |||||||
\(84\) | 0.171428 | 0.0187043 | ||||||||
\(85\) | 0.291499 | 0.0316175 | ||||||||
\(86\) | 13.0487 | 1.40708 | ||||||||
\(87\) | −9.93683 | −1.06534 | ||||||||
\(88\) | 0.129315 | 0.0137850 | ||||||||
\(89\) | 8.53563 | 0.904775 | 0.452388 | − | 0.891821i | \(-0.350572\pi\) | ||||
0.452388 | + | 0.891821i | \(0.350572\pi\) | |||||||
\(90\) | 0.0162748 | 0.00171552 | ||||||||
\(91\) | −0.162470 | −0.0170314 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 5.61072 | 0.581805 | ||||||||
\(94\) | 0.273217 | 0.0281802 | ||||||||
\(95\) | 0.324922 | 0.0333363 | ||||||||
\(96\) | −1.66164 | −0.169590 | ||||||||
\(97\) | 10.8859 | 1.10529 | 0.552646 | − | 0.833416i | \(-0.313618\pi\) | ||||
0.552646 | + | 0.833416i | \(0.313618\pi\) | |||||||
\(98\) | 6.98936 | 0.706032 | ||||||||
\(99\) | 0.0309015 | 0.00310572 | ||||||||
\(100\) | −4.99536 | −0.499536 | ||||||||
\(101\) | 1.91639 | 0.190688 | 0.0953442 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953442 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(102\) | −7.11195 | −0.704188 | ||||||||
\(103\) | 6.22040 | 0.612915 | 0.306457 | − | 0.951884i | \(-0.400856\pi\) | ||||
0.306457 | + | 0.951884i | \(0.400856\pi\) | |||||||
\(104\) | 1.57480 | 0.154422 | ||||||||
\(105\) | 0.0116752 | 0.00113939 | ||||||||
\(106\) | 3.18399 | 0.309256 | ||||||||
\(107\) | 6.76105 | 0.653616 | 0.326808 | − | 0.945091i | \(-0.394027\pi\) | ||||
0.326808 | + | 0.945091i | \(0.394027\pi\) | |||||||
\(108\) | −5.38198 | −0.517881 | ||||||||
\(109\) | −5.02739 | −0.481537 | −0.240768 | − | 0.970583i | \(-0.577399\pi\) | ||||
−0.240768 | + | 0.970583i | \(0.577399\pi\) | |||||||
\(110\) | 0.00880707 | 0.000839721 0 | ||||||||
\(111\) | −11.6095 | −1.10193 | ||||||||
\(112\) | 0.103168 | 0.00974848 | ||||||||
\(113\) | −19.2653 | −1.81233 | −0.906164 | − | 0.422926i | \(-0.861003\pi\) | ||||
−0.906164 | + | 0.422926i | \(0.861003\pi\) | |||||||
\(114\) | −7.92741 | −0.742470 | ||||||||
\(115\) | −0.0681057 | −0.00635089 | ||||||||
\(116\) | −5.98015 | −0.555243 | ||||||||
\(117\) | 0.376321 | 0.0347909 | ||||||||
\(118\) | 9.41679 | 0.866886 | ||||||||
\(119\) | 0.441569 | 0.0404786 | ||||||||
\(120\) | −0.113167 | −0.0103307 | ||||||||
\(121\) | −10.9833 | −0.998480 | ||||||||
\(122\) | 4.95302 | 0.448425 | ||||||||
\(123\) | −1.57581 | −0.142086 | ||||||||
\(124\) | 3.37662 | 0.303230 | ||||||||
\(125\) | −0.680742 | −0.0608874 | ||||||||
\(126\) | 0.0246535 | 0.00219631 | ||||||||
\(127\) | 3.87668 | 0.344000 | 0.172000 | − | 0.985097i | \(-0.444977\pi\) | ||||
0.172000 | + | 0.985097i | \(0.444977\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −21.6822 | −1.90901 | ||||||||
\(130\) | 0.107253 | 0.00940672 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −0.214874 | −0.0187024 | ||||||||
\(133\) | 0.492199 | 0.0426791 | ||||||||
\(134\) | −13.4210 | −1.15940 | ||||||||
\(135\) | −0.366544 | −0.0315471 | ||||||||
\(136\) | −4.28009 | −0.367015 | ||||||||
\(137\) | −6.06546 | −0.518207 | −0.259104 | − | 0.965850i | \(-0.583427\pi\) | ||||
−0.259104 | + | 0.965850i | \(0.583427\pi\) | |||||||
\(138\) | 1.66164 | 0.141448 | ||||||||
\(139\) | 3.01603 | 0.255817 | 0.127908 | − | 0.991786i | \(-0.459174\pi\) | ||||
0.127908 | + | 0.991786i | \(0.459174\pi\) | |||||||
\(140\) | 0.00702635 | 0.000593835 0 | ||||||||
\(141\) | −0.453988 | −0.0382327 | ||||||||
\(142\) | −3.25184 | −0.272888 | ||||||||
\(143\) | 0.203645 | 0.0170297 | ||||||||
\(144\) | −0.238964 | −0.0199137 | ||||||||
\(145\) | −0.407282 | −0.0338230 | ||||||||
\(146\) | −2.62561 | −0.217297 | ||||||||
\(147\) | −11.6138 | −0.957888 | ||||||||
\(148\) | −6.98679 | −0.574311 | ||||||||
\(149\) | 22.4253 | 1.83715 | 0.918576 | − | 0.395245i | \(-0.129340\pi\) | ||||
0.918576 | + | 0.395245i | \(0.129340\pi\) | |||||||
\(150\) | 8.30048 | 0.677731 | ||||||||
\(151\) | −0.552905 | −0.0449948 | −0.0224974 | − | 0.999747i | \(-0.507162\pi\) | ||||
−0.0224974 | + | 0.999747i | \(0.507162\pi\) | |||||||
\(152\) | −4.77084 | −0.386966 | ||||||||
\(153\) | −1.02279 | −0.0826874 | ||||||||
\(154\) | 0.0133412 | 0.00107506 | ||||||||
\(155\) | 0.229967 | 0.0184714 | ||||||||
\(156\) | −2.61675 | −0.209508 | ||||||||
\(157\) | −1.07714 | −0.0859655 | −0.0429828 | − | 0.999076i | \(-0.513686\pi\) | ||||
−0.0429828 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(158\) | −2.17954 | −0.173395 | ||||||||
\(159\) | −5.29063 | −0.419574 | ||||||||
\(160\) | −0.0681057 | −0.00538423 | ||||||||
\(161\) | −0.103168 | −0.00813079 | ||||||||
\(162\) | 8.22600 | 0.646296 | ||||||||
\(163\) | 1.63737 | 0.128249 | 0.0641245 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641245 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(164\) | −0.948349 | −0.0740536 | ||||||||
\(165\) | −0.0146342 | −0.00113927 | ||||||||
\(166\) | 2.80733 | 0.217891 | ||||||||
\(167\) | 8.65968 | 0.670106 | 0.335053 | − | 0.942199i | \(-0.391246\pi\) | ||||
0.335053 | + | 0.942199i | \(0.391246\pi\) | |||||||
\(168\) | −0.171428 | −0.0132260 | ||||||||
\(169\) | −10.5200 | −0.809230 | ||||||||
\(170\) | −0.291499 | −0.0223569 | ||||||||
\(171\) | −1.14006 | −0.0871825 | ||||||||
\(172\) | −13.0487 | −0.994956 | ||||||||
\(173\) | −19.0933 | −1.45163 | −0.725817 | − | 0.687888i | \(-0.758538\pi\) | ||||
−0.725817 | + | 0.687888i | \(0.758538\pi\) | |||||||
\(174\) | 9.93683 | 0.753309 | ||||||||
\(175\) | −0.515363 | −0.0389577 | ||||||||
\(176\) | −0.129315 | −0.00974746 | ||||||||
\(177\) | −15.6473 | −1.17612 | ||||||||
\(178\) | −8.53563 | −0.639773 | ||||||||
\(179\) | −19.5982 | −1.46484 | −0.732419 | − | 0.680854i | \(-0.761609\pi\) | ||||
−0.732419 | + | 0.680854i | \(0.761609\pi\) | |||||||
\(180\) | −0.0162748 | −0.00121305 | ||||||||
\(181\) | −16.7947 | −1.24834 | −0.624172 | − | 0.781287i | \(-0.714563\pi\) | ||||
−0.624172 | + | 0.781287i | \(0.714563\pi\) | |||||||
\(182\) | 0.162470 | 0.0120430 | ||||||||
\(183\) | −8.23011 | −0.608387 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −0.475841 | −0.0349845 | ||||||||
\(186\) | −5.61072 | −0.411398 | ||||||||
\(187\) | −0.553478 | −0.0404743 | ||||||||
\(188\) | −0.273217 | −0.0199264 | ||||||||
\(189\) | −0.555249 | −0.0403884 | ||||||||
\(190\) | −0.324922 | −0.0235723 | ||||||||
\(191\) | 22.5027 | 1.62824 | 0.814118 | − | 0.580700i | \(-0.197221\pi\) | ||||
0.814118 | + | 0.580700i | \(0.197221\pi\) | |||||||
\(192\) | 1.66164 | 0.119918 | ||||||||
\(193\) | 1.78146 | 0.128232 | 0.0641161 | − | 0.997942i | \(-0.479577\pi\) | ||||
0.0641161 | + | 0.997942i | \(0.479577\pi\) | |||||||
\(194\) | −10.8859 | −0.781560 | ||||||||
\(195\) | −0.178216 | −0.0127623 | ||||||||
\(196\) | −6.98936 | −0.499240 | ||||||||
\(197\) | −6.52172 | −0.464653 | −0.232327 | − | 0.972638i | \(-0.574634\pi\) | ||||
−0.232327 | + | 0.972638i | \(0.574634\pi\) | |||||||
\(198\) | −0.0309015 | −0.00219608 | ||||||||
\(199\) | −15.2926 | −1.08406 | −0.542031 | − | 0.840358i | \(-0.682345\pi\) | ||||
−0.542031 | + | 0.840358i | \(0.682345\pi\) | |||||||
\(200\) | 4.99536 | 0.353225 | ||||||||
\(201\) | 22.3008 | 1.57298 | ||||||||
\(202\) | −1.91639 | −0.134837 | ||||||||
\(203\) | −0.616961 | −0.0433022 | ||||||||
\(204\) | 7.11195 | 0.497936 | ||||||||
\(205\) | −0.0645880 | −0.00451102 | ||||||||
\(206\) | −6.22040 | −0.433396 | ||||||||
\(207\) | 0.238964 | 0.0166091 | ||||||||
\(208\) | −1.57480 | −0.109193 | ||||||||
\(209\) | −0.616940 | −0.0426746 | ||||||||
\(210\) | −0.0116752 | −0.000805668 0 | ||||||||
\(211\) | −22.3879 | −1.54124 | −0.770622 | − | 0.637292i | \(-0.780054\pi\) | ||||
−0.770622 | + | 0.637292i | \(0.780054\pi\) | |||||||
\(212\) | −3.18399 | −0.218677 | ||||||||
\(213\) | 5.40337 | 0.370233 | ||||||||
\(214\) | −6.76105 | −0.462176 | ||||||||
\(215\) | −0.888693 | −0.0606084 | ||||||||
\(216\) | 5.38198 | 0.366197 | ||||||||
\(217\) | 0.348360 | 0.0236482 | ||||||||
\(218\) | 5.02739 | 0.340498 | ||||||||
\(219\) | 4.36281 | 0.294811 | ||||||||
\(220\) | −0.00880707 | −0.000593773 0 | ||||||||
\(221\) | −6.74030 | −0.453401 | ||||||||
\(222\) | 11.6095 | 0.779179 | ||||||||
\(223\) | −24.0032 | −1.60737 | −0.803687 | − | 0.595052i | \(-0.797131\pi\) | ||||
−0.803687 | + | 0.595052i | \(0.797131\pi\) | |||||||
\(224\) | −0.103168 | −0.00689322 | ||||||||
\(225\) | 1.19371 | 0.0795807 | ||||||||
\(226\) | 19.2653 | 1.28151 | ||||||||
\(227\) | 15.5676 | 1.03326 | 0.516629 | − | 0.856209i | \(-0.327186\pi\) | ||||
0.516629 | + | 0.856209i | \(0.327186\pi\) | |||||||
\(228\) | 7.92741 | 0.525005 | ||||||||
\(229\) | −11.0634 | −0.731088 | −0.365544 | − | 0.930794i | \(-0.619117\pi\) | ||||
−0.365544 | + | 0.930794i | \(0.619117\pi\) | |||||||
\(230\) | 0.0681057 | 0.00449076 | ||||||||
\(231\) | −0.0221682 | −0.00145856 | ||||||||
\(232\) | 5.98015 | 0.392616 | ||||||||
\(233\) | −15.7481 | −1.03169 | −0.515846 | − | 0.856681i | \(-0.672522\pi\) | ||||
−0.515846 | + | 0.856681i | \(0.672522\pi\) | |||||||
\(234\) | −0.376321 | −0.0246009 | ||||||||
\(235\) | −0.0186077 | −0.00121383 | ||||||||
\(236\) | −9.41679 | −0.612981 | ||||||||
\(237\) | 3.62161 | 0.235249 | ||||||||
\(238\) | −0.441569 | −0.0286227 | ||||||||
\(239\) | 19.4788 | 1.25998 | 0.629989 | − | 0.776604i | \(-0.283059\pi\) | ||||
0.629989 | + | 0.776604i | \(0.283059\pi\) | |||||||
\(240\) | 0.113167 | 0.00730490 | ||||||||
\(241\) | 25.5974 | 1.64887 | 0.824435 | − | 0.565956i | \(-0.191493\pi\) | ||||
0.824435 | + | 0.565956i | \(0.191493\pi\) | |||||||
\(242\) | 10.9833 | 0.706032 | ||||||||
\(243\) | 2.47731 | 0.158920 | ||||||||
\(244\) | −4.95302 | −0.317084 | ||||||||
\(245\) | −0.476015 | −0.0304115 | ||||||||
\(246\) | 1.57581 | 0.100470 | ||||||||
\(247\) | −7.51313 | −0.478049 | ||||||||
\(248\) | −3.37662 | −0.214416 | ||||||||
\(249\) | −4.66476 | −0.295617 | ||||||||
\(250\) | 0.680742 | 0.0430539 | ||||||||
\(251\) | −27.2530 | −1.72020 | −0.860098 | − | 0.510129i | \(-0.829598\pi\) | ||||
−0.860098 | + | 0.510129i | \(0.829598\pi\) | |||||||
\(252\) | −0.0246535 | −0.00155302 | ||||||||
\(253\) | 0.129315 | 0.00812994 | ||||||||
\(254\) | −3.87668 | −0.243245 | ||||||||
\(255\) | 0.484365 | 0.0303321 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.7783 | 1.67038 | 0.835192 | − | 0.549958i | \(-0.185356\pi\) | ||||
0.835192 | + | 0.549958i | \(0.185356\pi\) | |||||||
\(258\) | 21.6822 | 1.34988 | ||||||||
\(259\) | −0.720815 | −0.0447893 | ||||||||
\(260\) | −0.107253 | −0.00665156 | ||||||||
\(261\) | 1.42904 | 0.0884553 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 19.4072 | 1.19670 | 0.598350 | − | 0.801235i | \(-0.295823\pi\) | ||||
0.598350 | + | 0.801235i | \(0.295823\pi\) | |||||||
\(264\) | 0.214874 | 0.0132246 | ||||||||
\(265\) | −0.216848 | −0.0133209 | ||||||||
\(266\) | −0.492199 | −0.0301787 | ||||||||
\(267\) | 14.1831 | 0.867993 | ||||||||
\(268\) | 13.4210 | 0.819816 | ||||||||
\(269\) | −13.5901 | −0.828602 | −0.414301 | − | 0.910140i | \(-0.635974\pi\) | ||||
−0.414301 | + | 0.910140i | \(0.635974\pi\) | |||||||
\(270\) | 0.366544 | 0.0223071 | ||||||||
\(271\) | −6.73699 | −0.409243 | −0.204621 | − | 0.978841i | \(-0.565596\pi\) | ||||
−0.204621 | + | 0.978841i | \(0.565596\pi\) | |||||||
\(272\) | 4.28009 | 0.259519 | ||||||||
\(273\) | −0.269965 | −0.0163391 | ||||||||
\(274\) | 6.06546 | 0.366428 | ||||||||
\(275\) | 0.645973 | 0.0389537 | ||||||||
\(276\) | −1.66164 | −0.100019 | ||||||||
\(277\) | −13.9821 | −0.840100 | −0.420050 | − | 0.907501i | \(-0.637987\pi\) | ||||
−0.420050 | + | 0.907501i | \(0.637987\pi\) | |||||||
\(278\) | −3.01603 | −0.180890 | ||||||||
\(279\) | −0.806891 | −0.0483073 | ||||||||
\(280\) | −0.00702635 | −0.000419905 0 | ||||||||
\(281\) | −20.2562 | −1.20838 | −0.604191 | − | 0.796840i | \(-0.706503\pi\) | ||||
−0.604191 | + | 0.796840i | \(0.706503\pi\) | |||||||
\(282\) | 0.453988 | 0.0270346 | ||||||||
\(283\) | −29.7323 | −1.76740 | −0.883700 | − | 0.468054i | \(-0.844955\pi\) | ||||
−0.883700 | + | 0.468054i | \(0.844955\pi\) | |||||||
\(284\) | 3.25184 | 0.192961 | ||||||||
\(285\) | 0.539902 | 0.0319810 | ||||||||
\(286\) | −0.203645 | −0.0120418 | ||||||||
\(287\) | −0.0978395 | −0.00577528 | ||||||||
\(288\) | 0.238964 | 0.0140811 | ||||||||
\(289\) | 1.31917 | 0.0775981 | ||||||||
\(290\) | 0.407282 | 0.0239164 | ||||||||
\(291\) | 18.0884 | 1.06036 | ||||||||
\(292\) | 2.62561 | 0.153652 | ||||||||
\(293\) | −11.4793 | −0.670630 | −0.335315 | − | 0.942106i | \(-0.608843\pi\) | ||||
−0.335315 | + | 0.942106i | \(0.608843\pi\) | |||||||
\(294\) | 11.6138 | 0.677329 | ||||||||
\(295\) | −0.641337 | −0.0373401 | ||||||||
\(296\) | 6.98679 | 0.406099 | ||||||||
\(297\) | 0.695969 | 0.0403842 | ||||||||
\(298\) | −22.4253 | −1.29906 | ||||||||
\(299\) | 1.57480 | 0.0910732 | ||||||||
\(300\) | −8.30048 | −0.479228 | ||||||||
\(301\) | −1.34621 | −0.0775944 | ||||||||
\(302\) | 0.552905 | 0.0318161 | ||||||||
\(303\) | 3.18435 | 0.182936 | ||||||||
\(304\) | 4.77084 | 0.273627 | ||||||||
\(305\) | −0.337329 | −0.0193154 | ||||||||
\(306\) | 1.02279 | 0.0584688 | ||||||||
\(307\) | −31.7828 | −1.81394 | −0.906969 | − | 0.421197i | \(-0.861610\pi\) | ||||
−0.906969 | + | 0.421197i | \(0.861610\pi\) | |||||||
\(308\) | −0.0133412 | −0.000760183 0 | ||||||||
\(309\) | 10.3361 | 0.587997 | ||||||||
\(310\) | −0.229967 | −0.0130613 | ||||||||
\(311\) | 15.1847 | 0.861045 | 0.430522 | − | 0.902580i | \(-0.358329\pi\) | ||||
0.430522 | + | 0.902580i | \(0.358329\pi\) | |||||||
\(312\) | 2.61675 | 0.148144 | ||||||||
\(313\) | 15.3439 | 0.867289 | 0.433644 | − | 0.901084i | \(-0.357227\pi\) | ||||
0.433644 | + | 0.901084i | \(0.357227\pi\) | |||||||
\(314\) | 1.07714 | 0.0607868 | ||||||||
\(315\) | −0.00167904 | −9.46034e−5 0 | ||||||||
\(316\) | 2.17954 | 0.122609 | ||||||||
\(317\) | −4.79810 | −0.269488 | −0.134744 | − | 0.990880i | \(-0.543021\pi\) | ||||
−0.134744 | + | 0.990880i | \(0.543021\pi\) | |||||||
\(318\) | 5.29063 | 0.296684 | ||||||||
\(319\) | 0.773321 | 0.0432976 | ||||||||
\(320\) | 0.0681057 | 0.00380723 | ||||||||
\(321\) | 11.2344 | 0.627044 | ||||||||
\(322\) | 0.103168 | 0.00574934 | ||||||||
\(323\) | 20.4196 | 1.13618 | ||||||||
\(324\) | −8.22600 | −0.457000 | ||||||||
\(325\) | 7.86671 | 0.436367 | ||||||||
\(326\) | −1.63737 | −0.0906858 | ||||||||
\(327\) | −8.35370 | −0.461960 | ||||||||
\(328\) | 0.948349 | 0.0523638 | ||||||||
\(329\) | −0.0281873 | −0.00155402 | ||||||||
\(330\) | 0.0146342 | 0.000805583 0 | ||||||||
\(331\) | −22.3587 | −1.22895 | −0.614474 | − | 0.788937i | \(-0.710632\pi\) | ||||
−0.614474 | + | 0.788937i | \(0.710632\pi\) | |||||||
\(332\) | −2.80733 | −0.154072 | ||||||||
\(333\) | 1.66959 | 0.0914930 | ||||||||
\(334\) | −8.65968 | −0.473837 | ||||||||
\(335\) | 0.914046 | 0.0499396 | ||||||||
\(336\) | 0.171428 | 0.00935217 | ||||||||
\(337\) | 1.67063 | 0.0910050 | 0.0455025 | − | 0.998964i | \(-0.485511\pi\) | ||||
0.0455025 | + | 0.998964i | \(0.485511\pi\) | |||||||
\(338\) | 10.5200 | 0.572212 | ||||||||
\(339\) | −32.0120 | −1.73865 | ||||||||
\(340\) | 0.291499 | 0.0158087 | ||||||||
\(341\) | −0.436647 | −0.0236458 | ||||||||
\(342\) | 1.14006 | 0.0616473 | ||||||||
\(343\) | −1.44326 | −0.0779286 | ||||||||
\(344\) | 13.0487 | 0.703540 | ||||||||
\(345\) | −0.113167 | −0.00609271 | ||||||||
\(346\) | 19.0933 | 1.02646 | ||||||||
\(347\) | 17.1821 | 0.922381 | 0.461191 | − | 0.887301i | \(-0.347422\pi\) | ||||
0.461191 | + | 0.887301i | \(0.347422\pi\) | |||||||
\(348\) | −9.93683 | −0.532670 | ||||||||
\(349\) | −8.12701 | −0.435029 | −0.217514 | − | 0.976057i | \(-0.569795\pi\) | ||||
−0.217514 | + | 0.976057i | \(0.569795\pi\) | |||||||
\(350\) | 0.515363 | 0.0275473 | ||||||||
\(351\) | 8.47556 | 0.452392 | ||||||||
\(352\) | 0.129315 | 0.00689249 | ||||||||
\(353\) | −5.53155 | −0.294415 | −0.147207 | − | 0.989106i | \(-0.547029\pi\) | ||||
−0.147207 | + | 0.989106i | \(0.547029\pi\) | |||||||
\(354\) | 15.6473 | 0.831644 | ||||||||
\(355\) | 0.221469 | 0.0117544 | ||||||||
\(356\) | 8.53563 | 0.452388 | ||||||||
\(357\) | 0.733728 | 0.0388330 | ||||||||
\(358\) | 19.5982 | 1.03580 | ||||||||
\(359\) | −18.6210 | −0.982781 | −0.491390 | − | 0.870939i | \(-0.663511\pi\) | ||||
−0.491390 | + | 0.870939i | \(0.663511\pi\) | |||||||
\(360\) | 0.0162748 | 0.000857758 0 | ||||||||
\(361\) | 3.76093 | 0.197944 | ||||||||
\(362\) | 16.7947 | 0.882712 | ||||||||
\(363\) | −18.2502 | −0.957888 | ||||||||
\(364\) | −0.162470 | −0.00851572 | ||||||||
\(365\) | 0.178819 | 0.00935982 | ||||||||
\(366\) | 8.23011 | 0.430195 | ||||||||
\(367\) | −0.636508 | −0.0332254 | −0.0166127 | − | 0.999862i | \(-0.505288\pi\) | ||||
−0.0166127 | + | 0.999862i | \(0.505288\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0.226621 | 0.0117974 | ||||||||
\(370\) | 0.475841 | 0.0247378 | ||||||||
\(371\) | −0.328486 | −0.0170542 | ||||||||
\(372\) | 5.61072 | 0.290902 | ||||||||
\(373\) | 33.1785 | 1.71792 | 0.858960 | − | 0.512043i | \(-0.171111\pi\) | ||||
0.858960 | + | 0.512043i | \(0.171111\pi\) | |||||||
\(374\) | 0.553478 | 0.0286197 | ||||||||
\(375\) | −1.13115 | −0.0584121 | ||||||||
\(376\) | 0.273217 | 0.0140901 | ||||||||
\(377\) | 9.41755 | 0.485029 | ||||||||
\(378\) | 0.555249 | 0.0285589 | ||||||||
\(379\) | −9.59012 | −0.492611 | −0.246306 | − | 0.969192i | \(-0.579217\pi\) | ||||
−0.246306 | + | 0.969192i | \(0.579217\pi\) | |||||||
\(380\) | 0.324922 | 0.0166681 | ||||||||
\(381\) | 6.44164 | 0.330015 | ||||||||
\(382\) | −22.5027 | −1.15134 | ||||||||
\(383\) | 35.3604 | 1.80683 | 0.903415 | − | 0.428768i | \(-0.141052\pi\) | ||||
0.903415 | + | 0.428768i | \(0.141052\pi\) | |||||||
\(384\) | −1.66164 | −0.0847950 | ||||||||
\(385\) | −0.000908610 0 | −4.63070e−5 0 | ||||||||
\(386\) | −1.78146 | −0.0906739 | ||||||||
\(387\) | 3.11817 | 0.158506 | ||||||||
\(388\) | 10.8859 | 0.552646 | ||||||||
\(389\) | 2.45355 | 0.124400 | 0.0621998 | − | 0.998064i | \(-0.480188\pi\) | ||||
0.0621998 | + | 0.998064i | \(0.480188\pi\) | |||||||
\(390\) | 0.178216 | 0.00902430 | ||||||||
\(391\) | −4.28009 | −0.216453 | ||||||||
\(392\) | 6.98936 | 0.353016 | ||||||||
\(393\) | −1.66164 | −0.0838185 | ||||||||
\(394\) | 6.52172 | 0.328559 | ||||||||
\(395\) | 0.148439 | 0.00746880 | ||||||||
\(396\) | 0.0309015 | 0.00155286 | ||||||||
\(397\) | −11.0341 | −0.553784 | −0.276892 | − | 0.960901i | \(-0.589304\pi\) | ||||
−0.276892 | + | 0.960901i | \(0.589304\pi\) | |||||||
\(398\) | 15.2926 | 0.766548 | ||||||||
\(399\) | 0.817856 | 0.0409440 | ||||||||
\(400\) | −4.99536 | −0.249768 | ||||||||
\(401\) | −37.7797 | −1.88663 | −0.943314 | − | 0.331902i | \(-0.892310\pi\) | ||||
−0.943314 | + | 0.331902i | \(0.892310\pi\) | |||||||
\(402\) | −22.3008 | −1.11226 | ||||||||
\(403\) | −5.31752 | −0.264884 | ||||||||
\(404\) | 1.91639 | 0.0953442 | ||||||||
\(405\) | −0.560238 | −0.0278385 | ||||||||
\(406\) | 0.616961 | 0.0306193 | ||||||||
\(407\) | 0.903494 | 0.0447846 | ||||||||
\(408\) | −7.11195 | −0.352094 | ||||||||
\(409\) | −13.9430 | −0.689436 | −0.344718 | − | 0.938706i | \(-0.612025\pi\) | ||||
−0.344718 | + | 0.938706i | \(0.612025\pi\) | |||||||
\(410\) | 0.0645880 | 0.00318977 | ||||||||
\(411\) | −10.0786 | −0.497140 | ||||||||
\(412\) | 6.22040 | 0.306457 | ||||||||
\(413\) | −0.971513 | −0.0478050 | ||||||||
\(414\) | −0.238964 | −0.0117444 | ||||||||
\(415\) | −0.191195 | −0.00938540 | ||||||||
\(416\) | 1.57480 | 0.0772111 | ||||||||
\(417\) | 5.01155 | 0.245417 | ||||||||
\(418\) | 0.616940 | 0.0301755 | ||||||||
\(419\) | 11.1923 | 0.546782 | 0.273391 | − | 0.961903i | \(-0.411855\pi\) | ||||
0.273391 | + | 0.961903i | \(0.411855\pi\) | |||||||
\(420\) | 0.0116752 | 0.000569693 0 | ||||||||
\(421\) | 29.4705 | 1.43630 | 0.718152 | − | 0.695887i | \(-0.244988\pi\) | ||||
0.718152 | + | 0.695887i | \(0.244988\pi\) | |||||||
\(422\) | 22.3879 | 1.08982 | ||||||||
\(423\) | 0.0652891 | 0.00317446 | ||||||||
\(424\) | 3.18399 | 0.154628 | ||||||||
\(425\) | −21.3806 | −1.03711 | ||||||||
\(426\) | −5.40337 | −0.261794 | ||||||||
\(427\) | −0.510994 | −0.0247287 | ||||||||
\(428\) | 6.76105 | 0.326808 | ||||||||
\(429\) | 0.338384 | 0.0163373 | ||||||||
\(430\) | 0.888693 | 0.0428566 | ||||||||
\(431\) | −21.7821 | −1.04921 | −0.524605 | − | 0.851346i | \(-0.675787\pi\) | ||||
−0.524605 | + | 0.851346i | \(0.675787\pi\) | |||||||
\(432\) | −5.38198 | −0.258941 | ||||||||
\(433\) | −3.14831 | −0.151298 | −0.0756491 | − | 0.997134i | \(-0.524103\pi\) | ||||
−0.0756491 | + | 0.997134i | \(0.524103\pi\) | |||||||
\(434\) | −0.348360 | −0.0167218 | ||||||||
\(435\) | −0.676755 | −0.0324479 | ||||||||
\(436\) | −5.02739 | −0.240768 | ||||||||
\(437\) | −4.77084 | −0.228220 | ||||||||
\(438\) | −4.36281 | −0.208463 | ||||||||
\(439\) | 9.32482 | 0.445049 | 0.222525 | − | 0.974927i | \(-0.428570\pi\) | ||||
0.222525 | + | 0.974927i | \(0.428570\pi\) | |||||||
\(440\) | 0.00880707 | 0.000419861 0 | ||||||||
\(441\) | 1.67020 | 0.0795335 | ||||||||
\(442\) | 6.74030 | 0.320603 | ||||||||
\(443\) | −37.2152 | −1.76815 | −0.884074 | − | 0.467347i | \(-0.845210\pi\) | ||||
−0.884074 | + | 0.467347i | \(0.845210\pi\) | |||||||
\(444\) | −11.6095 | −0.550963 | ||||||||
\(445\) | 0.581326 | 0.0275575 | ||||||||
\(446\) | 24.0032 | 1.13659 | ||||||||
\(447\) | 37.2627 | 1.76246 | ||||||||
\(448\) | 0.103168 | 0.00487424 | ||||||||
\(449\) | 16.4776 | 0.777624 | 0.388812 | − | 0.921317i | \(-0.372886\pi\) | ||||
0.388812 | + | 0.921317i | \(0.372886\pi\) | |||||||
\(450\) | −1.19371 | −0.0562721 | ||||||||
\(451\) | 0.122635 | 0.00577468 | ||||||||
\(452\) | −19.2653 | −0.906164 | ||||||||
\(453\) | −0.918728 | −0.0431656 | ||||||||
\(454\) | −15.5676 | −0.730624 | ||||||||
\(455\) | −0.0110651 | −0.000518741 0 | ||||||||
\(456\) | −7.92741 | −0.371235 | ||||||||
\(457\) | −12.2407 | −0.572596 | −0.286298 | − | 0.958141i | \(-0.592425\pi\) | ||||
−0.286298 | + | 0.958141i | \(0.592425\pi\) | |||||||
\(458\) | 11.0634 | 0.516957 | ||||||||
\(459\) | −23.0354 | −1.07520 | ||||||||
\(460\) | −0.0681057 | −0.00317545 | ||||||||
\(461\) | −6.20618 | −0.289051 | −0.144525 | − | 0.989501i | \(-0.546166\pi\) | ||||
−0.144525 | + | 0.989501i | \(0.546166\pi\) | |||||||
\(462\) | 0.0221682 | 0.00103136 | ||||||||
\(463\) | 36.9146 | 1.71557 | 0.857785 | − | 0.514009i | \(-0.171840\pi\) | ||||
0.857785 | + | 0.514009i | \(0.171840\pi\) | |||||||
\(464\) | −5.98015 | −0.277621 | ||||||||
\(465\) | 0.382122 | 0.0177205 | ||||||||
\(466\) | 15.7481 | 0.729517 | ||||||||
\(467\) | −0.590865 | −0.0273420 | −0.0136710 | − | 0.999907i | \(-0.504352\pi\) | ||||
−0.0136710 | + | 0.999907i | \(0.504352\pi\) | |||||||
\(468\) | 0.376321 | 0.0173954 | ||||||||
\(469\) | 1.38462 | 0.0639357 | ||||||||
\(470\) | 0.0186077 | 0.000858308 0 | ||||||||
\(471\) | −1.78982 | −0.0824707 | ||||||||
\(472\) | 9.41679 | 0.433443 | ||||||||
\(473\) | 1.68739 | 0.0775863 | ||||||||
\(474\) | −3.62161 | −0.166346 | ||||||||
\(475\) | −23.8321 | −1.09349 | ||||||||
\(476\) | 0.441569 | 0.0202393 | ||||||||
\(477\) | 0.760858 | 0.0348373 | ||||||||
\(478\) | −19.4788 | −0.890939 | ||||||||
\(479\) | 43.2955 | 1.97822 | 0.989111 | − | 0.147172i | \(-0.0470172\pi\) | ||||
0.989111 | + | 0.147172i | \(0.0470172\pi\) | |||||||
\(480\) | −0.113167 | −0.00516534 | ||||||||
\(481\) | 11.0028 | 0.501685 | ||||||||
\(482\) | −25.5974 | −1.16593 | ||||||||
\(483\) | −0.171428 | −0.00780025 | ||||||||
\(484\) | −10.9833 | −0.499240 | ||||||||
\(485\) | 0.741390 | 0.0336648 | ||||||||
\(486\) | −2.47731 | −0.112373 | ||||||||
\(487\) | −12.0357 | −0.545391 | −0.272695 | − | 0.962100i | \(-0.587915\pi\) | ||||
−0.272695 | + | 0.962100i | \(0.587915\pi\) | |||||||
\(488\) | 4.95302 | 0.224212 | ||||||||
\(489\) | 2.72072 | 0.123035 | ||||||||
\(490\) | 0.476015 | 0.0215042 | ||||||||
\(491\) | 18.9412 | 0.854803 | 0.427402 | − | 0.904062i | \(-0.359429\pi\) | ||||
0.427402 | + | 0.904062i | \(0.359429\pi\) | |||||||
\(492\) | −1.57581 | −0.0710431 | ||||||||
\(493\) | −25.5956 | −1.15277 | ||||||||
\(494\) | 7.51313 | 0.338032 | ||||||||
\(495\) | 0.00210457 | 9.45935e−5 0 | ||||||||
\(496\) | 3.37662 | 0.151615 | ||||||||
\(497\) | 0.335486 | 0.0150486 | ||||||||
\(498\) | 4.66476 | 0.209033 | ||||||||
\(499\) | −0.580220 | −0.0259742 | −0.0129871 | − | 0.999916i | \(-0.504134\pi\) | ||||
−0.0129871 | + | 0.999916i | \(0.504134\pi\) | |||||||
\(500\) | −0.680742 | −0.0304437 | ||||||||
\(501\) | 14.3892 | 0.642864 | ||||||||
\(502\) | 27.2530 | 1.21636 | ||||||||
\(503\) | 7.21164 | 0.321551 | 0.160775 | − | 0.986991i | \(-0.448601\pi\) | ||||
0.160775 | + | 0.986991i | \(0.448601\pi\) | |||||||
\(504\) | 0.0246535 | 0.00109815 | ||||||||
\(505\) | 0.130517 | 0.00580795 | ||||||||
\(506\) | −0.129315 | −0.00574874 | ||||||||
\(507\) | −17.4804 | −0.776332 | ||||||||
\(508\) | 3.87668 | 0.172000 | ||||||||
\(509\) | 37.1143 | 1.64506 | 0.822531 | − | 0.568720i | \(-0.192561\pi\) | ||||
0.822531 | + | 0.568720i | \(0.192561\pi\) | |||||||
\(510\) | −0.484365 | −0.0214480 | ||||||||
\(511\) | 0.270879 | 0.0119830 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −25.6766 | −1.13365 | ||||||||
\(514\) | −26.7783 | −1.18114 | ||||||||
\(515\) | 0.423645 | 0.0186680 | ||||||||
\(516\) | −21.6822 | −0.954507 | ||||||||
\(517\) | 0.0353310 | 0.00155386 | ||||||||
\(518\) | 0.720815 | 0.0316708 | ||||||||
\(519\) | −31.7261 | −1.39262 | ||||||||
\(520\) | 0.107253 | 0.00470336 | ||||||||
\(521\) | −13.1708 | −0.577023 | −0.288511 | − | 0.957476i | \(-0.593160\pi\) | ||||
−0.288511 | + | 0.957476i | \(0.593160\pi\) | |||||||
\(522\) | −1.42904 | −0.0625474 | ||||||||
\(523\) | 7.06875 | 0.309095 | 0.154547 | − | 0.987985i | \(-0.450608\pi\) | ||||
0.154547 | + | 0.987985i | \(0.450608\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −0.856345 | −0.0373740 | ||||||||
\(526\) | −19.4072 | −0.846195 | ||||||||
\(527\) | 14.4523 | 0.629550 | ||||||||
\(528\) | −0.214874 | −0.00935119 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.216848 | 0.00941927 | ||||||||
\(531\) | 2.25027 | 0.0976535 | ||||||||
\(532\) | 0.492199 | 0.0213395 | ||||||||
\(533\) | 1.49346 | 0.0646890 | ||||||||
\(534\) | −14.1831 | −0.613764 | ||||||||
\(535\) | 0.460467 | 0.0199077 | ||||||||
\(536\) | −13.4210 | −0.579698 | ||||||||
\(537\) | −32.5651 | −1.40529 | ||||||||
\(538\) | 13.5901 | 0.585910 | ||||||||
\(539\) | 0.903826 | 0.0389305 | ||||||||
\(540\) | −0.366544 | −0.0157735 | ||||||||
\(541\) | −35.2227 | −1.51434 | −0.757171 | − | 0.653216i | \(-0.773419\pi\) | ||||
−0.757171 | + | 0.653216i | \(0.773419\pi\) | |||||||
\(542\) | 6.73699 | 0.289378 | ||||||||
\(543\) | −27.9068 | −1.19759 | ||||||||
\(544\) | −4.28009 | −0.183507 | ||||||||
\(545\) | −0.342394 | −0.0146666 | ||||||||
\(546\) | 0.269965 | 0.0115535 | ||||||||
\(547\) | 28.8398 | 1.23310 | 0.616550 | − | 0.787316i | \(-0.288530\pi\) | ||||
0.616550 | + | 0.787316i | \(0.288530\pi\) | |||||||
\(548\) | −6.06546 | −0.259104 | ||||||||
\(549\) | 1.18359 | 0.0505145 | ||||||||
\(550\) | −0.645973 | −0.0275444 | ||||||||
\(551\) | −28.5303 | −1.21543 | ||||||||
\(552\) | 1.66164 | 0.0707239 | ||||||||
\(553\) | 0.224860 | 0.00956200 | ||||||||
\(554\) | 13.9821 | 0.594040 | ||||||||
\(555\) | −0.790674 | −0.0335622 | ||||||||
\(556\) | 3.01603 | 0.127908 | ||||||||
\(557\) | −35.4117 | −1.50044 | −0.750221 | − | 0.661188i | \(-0.770053\pi\) | ||||
−0.750221 | + | 0.661188i | \(0.770053\pi\) | |||||||
\(558\) | 0.806891 | 0.0341584 | ||||||||
\(559\) | 20.5492 | 0.869137 | ||||||||
\(560\) | 0.00702635 | 0.000296917 0 | ||||||||
\(561\) | −0.919680 | −0.0388289 | ||||||||
\(562\) | 20.2562 | 0.854454 | ||||||||
\(563\) | −1.28144 | −0.0540063 | −0.0270032 | − | 0.999635i | \(-0.508596\pi\) | ||||
−0.0270032 | + | 0.999635i | \(0.508596\pi\) | |||||||
\(564\) | −0.453988 | −0.0191163 | ||||||||
\(565\) | −1.31208 | −0.0551996 | ||||||||
\(566\) | 29.7323 | 1.24974 | ||||||||
\(567\) | −0.848662 | −0.0356405 | ||||||||
\(568\) | −3.25184 | −0.136444 | ||||||||
\(569\) | −10.2066 | −0.427885 | −0.213942 | − | 0.976846i | \(-0.568631\pi\) | ||||
−0.213942 | + | 0.976846i | \(0.568631\pi\) | |||||||
\(570\) | −0.539902 | −0.0226140 | ||||||||
\(571\) | −10.3662 | −0.433811 | −0.216905 | − | 0.976193i | \(-0.569596\pi\) | ||||
−0.216905 | + | 0.976193i | \(0.569596\pi\) | |||||||
\(572\) | 0.203645 | 0.00851483 | ||||||||
\(573\) | 37.3912 | 1.56204 | ||||||||
\(574\) | 0.0978395 | 0.00408374 | ||||||||
\(575\) | 4.99536 | 0.208321 | ||||||||
\(576\) | −0.238964 | −0.00995683 | ||||||||
\(577\) | −1.27987 | −0.0532816 | −0.0266408 | − | 0.999645i | \(-0.508481\pi\) | ||||
−0.0266408 | + | 0.999645i | \(0.508481\pi\) | |||||||
\(578\) | −1.31917 | −0.0548701 | ||||||||
\(579\) | 2.96014 | 0.123019 | ||||||||
\(580\) | −0.407282 | −0.0169115 | ||||||||
\(581\) | −0.289627 | −0.0120157 | ||||||||
\(582\) | −18.0884 | −0.749787 | ||||||||
\(583\) | 0.411736 | 0.0170524 | ||||||||
\(584\) | −2.62561 | −0.108648 | ||||||||
\(585\) | 0.0256296 | 0.00105965 | ||||||||
\(586\) | 11.4793 | 0.474207 | ||||||||
\(587\) | 6.05942 | 0.250099 | 0.125050 | − | 0.992150i | \(-0.460091\pi\) | ||||
0.125050 | + | 0.992150i | \(0.460091\pi\) | |||||||
\(588\) | −11.6138 | −0.478944 | ||||||||
\(589\) | 16.1093 | 0.663774 | ||||||||
\(590\) | 0.641337 | 0.0264034 | ||||||||
\(591\) | −10.8367 | −0.445763 | ||||||||
\(592\) | −6.98679 | −0.287155 | ||||||||
\(593\) | 23.2391 | 0.954317 | 0.477159 | − | 0.878817i | \(-0.341667\pi\) | ||||
0.477159 | + | 0.878817i | \(0.341667\pi\) | |||||||
\(594\) | −0.695969 | −0.0285560 | ||||||||
\(595\) | 0.0300734 | 0.00123289 | ||||||||
\(596\) | 22.4253 | 0.918576 | ||||||||
\(597\) | −25.4107 | −1.03999 | ||||||||
\(598\) | −1.57480 | −0.0643985 | ||||||||
\(599\) | 3.34062 | 0.136494 | 0.0682470 | − | 0.997668i | \(-0.478259\pi\) | ||||
0.0682470 | + | 0.997668i | \(0.478259\pi\) | |||||||
\(600\) | 8.30048 | 0.338865 | ||||||||
\(601\) | −7.25587 | −0.295973 | −0.147987 | − | 0.988989i | \(-0.547279\pi\) | ||||
−0.147987 | + | 0.988989i | \(0.547279\pi\) | |||||||
\(602\) | 1.34621 | 0.0548676 | ||||||||
\(603\) | −3.20713 | −0.130604 | ||||||||
\(604\) | −0.552905 | −0.0224974 | ||||||||
\(605\) | −0.748024 | −0.0304115 | ||||||||
\(606\) | −3.18435 | −0.129355 | ||||||||
\(607\) | −19.8661 | −0.806341 | −0.403171 | − | 0.915125i | \(-0.632092\pi\) | ||||
−0.403171 | + | 0.915125i | \(0.632092\pi\) | |||||||
\(608\) | −4.77084 | −0.193483 | ||||||||
\(609\) | −1.02517 | −0.0415418 | ||||||||
\(610\) | 0.337329 | 0.0136580 | ||||||||
\(611\) | 0.430263 | 0.0174066 | ||||||||
\(612\) | −1.02279 | −0.0413437 | ||||||||
\(613\) | −36.8621 | −1.48885 | −0.744423 | − | 0.667708i | \(-0.767275\pi\) | ||||
−0.744423 | + | 0.667708i | \(0.767275\pi\) | |||||||
\(614\) | 31.7828 | 1.28265 | ||||||||
\(615\) | −0.107322 | −0.00432763 | ||||||||
\(616\) | 0.0133412 | 0.000537531 0 | ||||||||
\(617\) | 14.6106 | 0.588199 | 0.294099 | − | 0.955775i | \(-0.404980\pi\) | ||||
0.294099 | + | 0.955775i | \(0.404980\pi\) | |||||||
\(618\) | −10.3361 | −0.415777 | ||||||||
\(619\) | 45.0525 | 1.81081 | 0.905406 | − | 0.424548i | \(-0.139567\pi\) | ||||
0.905406 | + | 0.424548i | \(0.139567\pi\) | |||||||
\(620\) | 0.229967 | 0.00923571 | ||||||||
\(621\) | 5.38198 | 0.215971 | ||||||||
\(622\) | −15.1847 | −0.608850 | ||||||||
\(623\) | 0.880606 | 0.0352807 | ||||||||
\(624\) | −2.61675 | −0.104754 | ||||||||
\(625\) | 24.9304 | 0.997218 | ||||||||
\(626\) | −15.3439 | −0.613266 | ||||||||
\(627\) | −1.02513 | −0.0409397 | ||||||||
\(628\) | −1.07714 | −0.0429828 | ||||||||
\(629\) | −29.9041 | −1.19235 | ||||||||
\(630\) | 0.00167904 | 6.68947e−5 0 | ||||||||
\(631\) | −32.0164 | −1.27455 | −0.637277 | − | 0.770635i | \(-0.719939\pi\) | ||||
−0.637277 | + | 0.770635i | \(0.719939\pi\) | |||||||
\(632\) | −2.17954 | −0.0866976 | ||||||||
\(633\) | −37.2005 | −1.47859 | ||||||||
\(634\) | 4.79810 | 0.190557 | ||||||||
\(635\) | 0.264024 | 0.0104775 | ||||||||
\(636\) | −5.29063 | −0.209787 | ||||||||
\(637\) | 11.0069 | 0.436108 | ||||||||
\(638\) | −0.773321 | −0.0306161 | ||||||||
\(639\) | −0.777072 | −0.0307405 | ||||||||
\(640\) | −0.0681057 | −0.00269212 | ||||||||
\(641\) | 27.6756 | 1.09312 | 0.546560 | − | 0.837420i | \(-0.315937\pi\) | ||||
0.546560 | + | 0.837420i | \(0.315937\pi\) | |||||||
\(642\) | −11.2344 | −0.443387 | ||||||||
\(643\) | −27.7603 | −1.09476 | −0.547380 | − | 0.836884i | \(-0.684375\pi\) | ||||
−0.547380 | + | 0.836884i | \(0.684375\pi\) | |||||||
\(644\) | −0.103168 | −0.00406540 | ||||||||
\(645\) | −1.47668 | −0.0581444 | ||||||||
\(646\) | −20.4196 | −0.803400 | ||||||||
\(647\) | −42.4703 | −1.66968 | −0.834839 | − | 0.550494i | \(-0.814439\pi\) | ||||
−0.834839 | + | 0.550494i | \(0.814439\pi\) | |||||||
\(648\) | 8.22600 | 0.323148 | ||||||||
\(649\) | 1.21773 | 0.0478000 | ||||||||
\(650\) | −7.86671 | −0.308558 | ||||||||
\(651\) | 0.578848 | 0.0226868 | ||||||||
\(652\) | 1.63737 | 0.0641245 | ||||||||
\(653\) | 28.3733 | 1.11033 | 0.555167 | − | 0.831739i | \(-0.312654\pi\) | ||||
0.555167 | + | 0.831739i | \(0.312654\pi\) | |||||||
\(654\) | 8.35370 | 0.326655 | ||||||||
\(655\) | −0.0681057 | −0.00266111 | ||||||||
\(656\) | −0.948349 | −0.0370268 | ||||||||
\(657\) | −0.627426 | −0.0244782 | ||||||||
\(658\) | 0.0281873 | 0.00109886 | ||||||||
\(659\) | 35.1529 | 1.36936 | 0.684682 | − | 0.728842i | \(-0.259941\pi\) | ||||
0.684682 | + | 0.728842i | \(0.259941\pi\) | |||||||
\(660\) | −0.0146342 | −0.000569634 0 | ||||||||
\(661\) | −38.5901 | −1.50098 | −0.750490 | − | 0.660882i | \(-0.770182\pi\) | ||||
−0.750490 | + | 0.660882i | \(0.770182\pi\) | |||||||
\(662\) | 22.3587 | 0.868997 | ||||||||
\(663\) | −11.1999 | −0.434969 | ||||||||
\(664\) | 2.80733 | 0.108945 | ||||||||
\(665\) | 0.0335216 | 0.00129991 | ||||||||
\(666\) | −1.66959 | −0.0646953 | ||||||||
\(667\) | 5.98015 | 0.231552 | ||||||||
\(668\) | 8.65968 | 0.335053 | ||||||||
\(669\) | −39.8846 | −1.54203 | ||||||||
\(670\) | −0.914046 | −0.0353127 | ||||||||
\(671\) | 0.640497 | 0.0247261 | ||||||||
\(672\) | −0.171428 | −0.00661298 | ||||||||
\(673\) | 3.22933 | 0.124482 | 0.0622409 | − | 0.998061i | \(-0.480175\pi\) | ||||
0.0622409 | + | 0.998061i | \(0.480175\pi\) | |||||||
\(674\) | −1.67063 | −0.0643502 | ||||||||
\(675\) | 26.8849 | 1.03480 | ||||||||
\(676\) | −10.5200 | −0.404615 | ||||||||
\(677\) | 35.9550 | 1.38186 | 0.690932 | − | 0.722920i | \(-0.257201\pi\) | ||||
0.690932 | + | 0.722920i | \(0.257201\pi\) | |||||||
\(678\) | 32.0120 | 1.22941 | ||||||||
\(679\) | 1.12308 | 0.0430997 | ||||||||
\(680\) | −0.291499 | −0.0111785 | ||||||||
\(681\) | 25.8677 | 0.991253 | ||||||||
\(682\) | 0.436647 | 0.0167201 | ||||||||
\(683\) | 37.3860 | 1.43053 | 0.715267 | − | 0.698851i | \(-0.246305\pi\) | ||||
0.715267 | + | 0.698851i | \(0.246305\pi\) | |||||||
\(684\) | −1.14006 | −0.0435912 | ||||||||
\(685\) | −0.413093 | −0.0157835 | ||||||||
\(686\) | 1.44326 | 0.0551038 | ||||||||
\(687\) | −18.3833 | −0.701366 | ||||||||
\(688\) | −13.0487 | −0.497478 | ||||||||
\(689\) | 5.01415 | 0.191024 | ||||||||
\(690\) | 0.113167 | 0.00430819 | ||||||||
\(691\) | 19.8892 | 0.756622 | 0.378311 | − | 0.925679i | \(-0.376505\pi\) | ||||
0.378311 | + | 0.925679i | \(0.376505\pi\) | |||||||
\(692\) | −19.0933 | −0.725817 | ||||||||
\(693\) | 0.00318806 | 0.000121104 0 | ||||||||
\(694\) | −17.1821 | −0.652222 | ||||||||
\(695\) | 0.205409 | 0.00779161 | ||||||||
\(696\) | 9.93683 | 0.376655 | ||||||||
\(697\) | −4.05902 | −0.153746 | ||||||||
\(698\) | 8.12701 | 0.307612 | ||||||||
\(699\) | −26.1676 | −0.989750 | ||||||||
\(700\) | −0.515363 | −0.0194789 | ||||||||
\(701\) | −2.15357 | −0.0813393 | −0.0406696 | − | 0.999173i | \(-0.512949\pi\) | ||||
−0.0406696 | + | 0.999173i | \(0.512949\pi\) | |||||||
\(702\) | −8.47556 | −0.319889 | ||||||||
\(703\) | −33.3329 | −1.25717 | ||||||||
\(704\) | −0.129315 | −0.00487373 | ||||||||
\(705\) | −0.0309192 | −0.00116448 | ||||||||
\(706\) | 5.53155 | 0.208183 | ||||||||
\(707\) | 0.197711 | 0.00743569 | ||||||||
\(708\) | −15.6473 | −0.588061 | ||||||||
\(709\) | 40.9246 | 1.53696 | 0.768478 | − | 0.639876i | \(-0.221014\pi\) | ||||
0.768478 | + | 0.639876i | \(0.221014\pi\) | |||||||
\(710\) | −0.221469 | −0.00831158 | ||||||||
\(711\) | −0.520832 | −0.0195327 | ||||||||
\(712\) | −8.53563 | −0.319886 | ||||||||
\(713\) | −3.37662 | −0.126456 | ||||||||
\(714\) | −0.733728 | −0.0274591 | ||||||||
\(715\) | 0.0138694 | 0.000518686 0 | ||||||||
\(716\) | −19.5982 | −0.732419 | ||||||||
\(717\) | 32.3667 | 1.20876 | ||||||||
\(718\) | 18.6210 | 0.694931 | ||||||||
\(719\) | −23.6341 | −0.881403 | −0.440701 | − | 0.897654i | \(-0.645270\pi\) | ||||
−0.440701 | + | 0.897654i | \(0.645270\pi\) | |||||||
\(720\) | −0.0162748 | −0.000606527 0 | ||||||||
\(721\) | 0.641748 | 0.0238999 | ||||||||
\(722\) | −3.76093 | −0.139967 | ||||||||
\(723\) | 42.5335 | 1.58184 | ||||||||
\(724\) | −16.7947 | −0.624172 | ||||||||
\(725\) | 29.8730 | 1.10946 | ||||||||
\(726\) | 18.2502 | 0.677329 | ||||||||
\(727\) | 3.72667 | 0.138215 | 0.0691073 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691073 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(728\) | 0.162470 | 0.00602152 | ||||||||
\(729\) | 28.7944 | 1.06646 | ||||||||
\(730\) | −0.178819 | −0.00661839 | ||||||||
\(731\) | −55.8497 | −2.06568 | ||||||||
\(732\) | −8.23011 | −0.304194 | ||||||||
\(733\) | 38.1577 | 1.40939 | 0.704693 | − | 0.709513i | \(-0.251085\pi\) | ||||
0.704693 | + | 0.709513i | \(0.251085\pi\) | |||||||
\(734\) | 0.636508 | 0.0234939 | ||||||||
\(735\) | −0.790964 | −0.0291752 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −1.73553 | −0.0639290 | ||||||||
\(738\) | −0.226621 | −0.00834204 | ||||||||
\(739\) | 49.8362 | 1.83325 | 0.916626 | − | 0.399745i | \(-0.130901\pi\) | ||||
0.916626 | + | 0.399745i | \(0.130901\pi\) | |||||||
\(740\) | −0.475841 | −0.0174922 | ||||||||
\(741\) | −12.4841 | −0.458615 | ||||||||
\(742\) | 0.328486 | 0.0120591 | ||||||||
\(743\) | 42.5633 | 1.56150 | 0.780748 | − | 0.624847i | \(-0.214838\pi\) | ||||
0.780748 | + | 0.624847i | \(0.214838\pi\) | |||||||
\(744\) | −5.61072 | −0.205699 | ||||||||
\(745\) | 1.52729 | 0.0559556 | ||||||||
\(746\) | −33.1785 | −1.21475 | ||||||||
\(747\) | 0.670850 | 0.0245451 | ||||||||
\(748\) | −0.553478 | −0.0202372 | ||||||||
\(749\) | 0.697526 | 0.0254870 | ||||||||
\(750\) | 1.13115 | 0.0413036 | ||||||||
\(751\) | 41.8799 | 1.52822 | 0.764110 | − | 0.645086i | \(-0.223179\pi\) | ||||
0.764110 | + | 0.645086i | \(0.223179\pi\) | |||||||
\(752\) | −0.273217 | −0.00996321 | ||||||||
\(753\) | −45.2846 | −1.65026 | ||||||||
\(754\) | −9.41755 | −0.342967 | ||||||||
\(755\) | −0.0376560 | −0.00137044 | ||||||||
\(756\) | −0.555249 | −0.0201942 | ||||||||
\(757\) | 11.9595 | 0.434676 | 0.217338 | − | 0.976096i | \(-0.430263\pi\) | ||||
0.217338 | + | 0.976096i | \(0.430263\pi\) | |||||||
\(758\) | 9.59012 | 0.348329 | ||||||||
\(759\) | 0.214874 | 0.00779943 | ||||||||
\(760\) | −0.324922 | −0.0117862 | ||||||||
\(761\) | 26.5509 | 0.962468 | 0.481234 | − | 0.876592i | \(-0.340189\pi\) | ||||
0.481234 | + | 0.876592i | \(0.340189\pi\) | |||||||
\(762\) | −6.44164 | −0.233356 | ||||||||
\(763\) | −0.518667 | −0.0187770 | ||||||||
\(764\) | 22.5027 | 0.814118 | ||||||||
\(765\) | −0.0696577 | −0.00251848 | ||||||||
\(766\) | −35.3604 | −1.27762 | ||||||||
\(767\) | 14.8296 | 0.535465 | ||||||||
\(768\) | 1.66164 | 0.0599591 | ||||||||
\(769\) | 33.0702 | 1.19254 | 0.596271 | − | 0.802783i | \(-0.296648\pi\) | ||||
0.596271 | + | 0.802783i | \(0.296648\pi\) | |||||||
\(770\) | 0.000908610 0 | 3.27440e−5 0 | ||||||||
\(771\) | 44.4958 | 1.60248 | ||||||||
\(772\) | 1.78146 | 0.0641161 | ||||||||
\(773\) | −12.6664 | −0.455580 | −0.227790 | − | 0.973710i | \(-0.573150\pi\) | ||||
−0.227790 | + | 0.973710i | \(0.573150\pi\) | |||||||
\(774\) | −3.11817 | −0.112080 | ||||||||
\(775\) | −16.8675 | −0.605897 | ||||||||
\(776\) | −10.8859 | −0.390780 | ||||||||
\(777\) | −1.19773 | −0.0429684 | ||||||||
\(778\) | −2.45355 | −0.0879639 | ||||||||
\(779\) | −4.52442 | −0.162104 | ||||||||
\(780\) | −0.178216 | −0.00638115 | ||||||||
\(781\) | −0.420510 | −0.0150470 | ||||||||
\(782\) | 4.28009 | 0.153056 | ||||||||
\(783\) | 32.1850 | 1.15020 | ||||||||
\(784\) | −6.98936 | −0.249620 | ||||||||
\(785\) | −0.0733598 | −0.00261832 | ||||||||
\(786\) | 1.66164 | 0.0592686 | ||||||||
\(787\) | −27.5283 | −0.981277 | −0.490638 | − | 0.871363i | \(-0.663236\pi\) | ||||
−0.490638 | + | 0.871363i | \(0.663236\pi\) | |||||||
\(788\) | −6.52172 | −0.232327 | ||||||||
\(789\) | 32.2477 | 1.14805 | ||||||||
\(790\) | −0.148439 | −0.00528124 | ||||||||
\(791\) | −1.98757 | −0.0706698 | ||||||||
\(792\) | −0.0309015 | −0.00109804 | ||||||||
\(793\) | 7.80002 | 0.276987 | ||||||||
\(794\) | 11.0341 | 0.391584 | ||||||||
\(795\) | −0.360322 | −0.0127793 | ||||||||
\(796\) | −15.2926 | −0.542031 | ||||||||
\(797\) | −19.3932 | −0.686943 | −0.343471 | − | 0.939163i | \(-0.611603\pi\) | ||||
−0.343471 | + | 0.939163i | \(0.611603\pi\) | |||||||
\(798\) | −0.817856 | −0.0289518 | ||||||||
\(799\) | −1.16939 | −0.0413702 | ||||||||
\(800\) | 4.99536 | 0.176613 | ||||||||
\(801\) | −2.03971 | −0.0720695 | ||||||||
\(802\) | 37.7797 | 1.33405 | ||||||||
\(803\) | −0.339530 | −0.0119817 | ||||||||
\(804\) | 22.3008 | 0.786488 | ||||||||
\(805\) | −0.00702635 | −0.000247646 0 | ||||||||
\(806\) | 5.31752 | 0.187301 | ||||||||
\(807\) | −22.5818 | −0.794917 | ||||||||
\(808\) | −1.91639 | −0.0674185 | ||||||||
\(809\) | 25.2514 | 0.887793 | 0.443897 | − | 0.896078i | \(-0.353596\pi\) | ||||
0.443897 | + | 0.896078i | \(0.353596\pi\) | |||||||
\(810\) | 0.560238 | 0.0196848 | ||||||||
\(811\) | −13.1333 | −0.461171 | −0.230585 | − | 0.973052i | \(-0.574064\pi\) | ||||
−0.230585 | + | 0.973052i | \(0.574064\pi\) | |||||||
\(812\) | −0.616961 | −0.0216511 | ||||||||
\(813\) | −11.1944 | −0.392605 | ||||||||
\(814\) | −0.903494 | −0.0316675 | ||||||||
\(815\) | 0.111515 | 0.00390619 | ||||||||
\(816\) | 7.11195 | 0.248968 | ||||||||
\(817\) | −62.2534 | −2.17797 | ||||||||
\(818\) | 13.9430 | 0.487505 | ||||||||
\(819\) | 0.0388244 | 0.00135663 | ||||||||
\(820\) | −0.0645880 | −0.00225551 | ||||||||
\(821\) | 29.2836 | 1.02200 | 0.511002 | − | 0.859580i | \(-0.329275\pi\) | ||||
0.511002 | + | 0.859580i | \(0.329275\pi\) | |||||||
\(822\) | 10.0786 | 0.351531 | ||||||||
\(823\) | 5.77425 | 0.201278 | 0.100639 | − | 0.994923i | \(-0.467911\pi\) | ||||
0.100639 | + | 0.994923i | \(0.467911\pi\) | |||||||
\(824\) | −6.22040 | −0.216698 | ||||||||
\(825\) | 1.07337 | 0.0373701 | ||||||||
\(826\) | 0.971513 | 0.0338033 | ||||||||
\(827\) | −33.2577 | −1.15649 | −0.578243 | − | 0.815865i | \(-0.696261\pi\) | ||||
−0.578243 | + | 0.815865i | \(0.696261\pi\) | |||||||
\(828\) | 0.238964 | 0.00830457 | ||||||||
\(829\) | −1.22601 | −0.0425810 | −0.0212905 | − | 0.999773i | \(-0.506777\pi\) | ||||
−0.0212905 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(830\) | 0.191195 | 0.00663648 | ||||||||
\(831\) | −23.2331 | −0.805947 | ||||||||
\(832\) | −1.57480 | −0.0545965 | ||||||||
\(833\) | −29.9151 | −1.03650 | ||||||||
\(834\) | −5.01155 | −0.173536 | ||||||||
\(835\) | 0.589774 | 0.0204100 | ||||||||
\(836\) | −0.616940 | −0.0213373 | ||||||||
\(837\) | −18.1729 | −0.628148 | ||||||||
\(838\) | −11.1923 | −0.386633 | ||||||||
\(839\) | 4.38282 | 0.151312 | 0.0756558 | − | 0.997134i | \(-0.475895\pi\) | ||||
0.0756558 | + | 0.997134i | \(0.475895\pi\) | |||||||
\(840\) | −0.0116752 | −0.000402834 0 | ||||||||
\(841\) | 6.76216 | 0.233178 | ||||||||
\(842\) | −29.4705 | −1.01562 | ||||||||
\(843\) | −33.6584 | −1.15926 | ||||||||
\(844\) | −22.3879 | −0.770622 | ||||||||
\(845\) | −0.716472 | −0.0246474 | ||||||||
\(846\) | −0.0652891 | −0.00224468 | ||||||||
\(847\) | −1.13313 | −0.0389346 | ||||||||
\(848\) | −3.18399 | −0.109339 | ||||||||
\(849\) | −49.4042 | −1.69555 | ||||||||
\(850\) | 21.3806 | 0.733348 | ||||||||
\(851\) | 6.98679 | 0.239504 | ||||||||
\(852\) | 5.40337 | 0.185117 | ||||||||
\(853\) | −52.5689 | −1.79993 | −0.899963 | − | 0.435967i | \(-0.856407\pi\) | ||||
−0.899963 | + | 0.435967i | \(0.856407\pi\) | |||||||
\(854\) | 0.510994 | 0.0174858 | ||||||||
\(855\) | −0.0776446 | −0.00265539 | ||||||||
\(856\) | −6.76105 | −0.231088 | ||||||||
\(857\) | −45.6787 | −1.56035 | −0.780177 | − | 0.625559i | \(-0.784871\pi\) | ||||
−0.780177 | + | 0.625559i | \(0.784871\pi\) | |||||||
\(858\) | −0.338384 | −0.0115522 | ||||||||
\(859\) | −48.5674 | −1.65710 | −0.828548 | − | 0.559917i | \(-0.810833\pi\) | ||||
−0.828548 | + | 0.559917i | \(0.810833\pi\) | |||||||
\(860\) | −0.888693 | −0.0303042 | ||||||||
\(861\) | −0.162574 | −0.00554050 | ||||||||
\(862\) | 21.7821 | 0.741903 | ||||||||
\(863\) | −22.1014 | −0.752340 | −0.376170 | − | 0.926551i | \(-0.622759\pi\) | ||||
−0.376170 | + | 0.926551i | \(0.622759\pi\) | |||||||
\(864\) | 5.38198 | 0.183099 | ||||||||
\(865\) | −1.30036 | −0.0442136 | ||||||||
\(866\) | 3.14831 | 0.106984 | ||||||||
\(867\) | 2.19198 | 0.0744434 | ||||||||
\(868\) | 0.348360 | 0.0118241 | ||||||||
\(869\) | −0.281847 | −0.00956100 | ||||||||
\(870\) | 0.676755 | 0.0229442 | ||||||||
\(871\) | −21.1354 | −0.716145 | ||||||||
\(872\) | 5.02739 | 0.170249 | ||||||||
\(873\) | −2.60133 | −0.0880417 | ||||||||
\(874\) | 4.77084 | 0.161376 | ||||||||
\(875\) | −0.0702309 | −0.00237424 | ||||||||
\(876\) | 4.36281 | 0.147406 | ||||||||
\(877\) | −7.44859 | −0.251521 | −0.125760 | − | 0.992061i | \(-0.540137\pi\) | ||||
−0.125760 | + | 0.992061i | \(0.540137\pi\) | |||||||
\(878\) | −9.32482 | −0.314697 | ||||||||
\(879\) | −19.0745 | −0.643366 | ||||||||
\(880\) | −0.00880707 | −0.000296886 0 | ||||||||
\(881\) | −16.1167 | −0.542984 | −0.271492 | − | 0.962441i | \(-0.587517\pi\) | ||||
−0.271492 | + | 0.962441i | \(0.587517\pi\) | |||||||
\(882\) | −1.67020 | −0.0562387 | ||||||||
\(883\) | 44.4679 | 1.49646 | 0.748232 | − | 0.663437i | \(-0.230903\pi\) | ||||
0.748232 | + | 0.663437i | \(0.230903\pi\) | |||||||
\(884\) | −6.74030 | −0.226701 | ||||||||
\(885\) | −1.06567 | −0.0358221 | ||||||||
\(886\) | 37.2152 | 1.25027 | ||||||||
\(887\) | −47.7750 | −1.60413 | −0.802063 | − | 0.597239i | \(-0.796264\pi\) | ||||
−0.802063 | + | 0.597239i | \(0.796264\pi\) | |||||||
\(888\) | 11.6095 | 0.389590 | ||||||||
\(889\) | 0.399950 | 0.0134139 | ||||||||
\(890\) | −0.581326 | −0.0194861 | ||||||||
\(891\) | 1.06374 | 0.0356367 | ||||||||
\(892\) | −24.0032 | −0.803687 | ||||||||
\(893\) | −1.30348 | −0.0436192 | ||||||||
\(894\) | −37.2627 | −1.24625 | ||||||||
\(895\) | −1.33475 | −0.0446158 | ||||||||
\(896\) | −0.103168 | −0.00344661 | ||||||||
\(897\) | 2.61675 | 0.0873707 | ||||||||
\(898\) | −16.4776 | −0.549863 | ||||||||
\(899\) | −20.1927 | −0.673464 | ||||||||
\(900\) | 1.19371 | 0.0397904 | ||||||||
\(901\) | −13.6277 | −0.454006 | ||||||||
\(902\) | −0.122635 | −0.00408331 | ||||||||
\(903\) | −2.23692 | −0.0744399 | ||||||||
\(904\) | 19.2653 | 0.640755 | ||||||||
\(905\) | −1.14382 | −0.0380218 | ||||||||
\(906\) | 0.918728 | 0.0305227 | ||||||||
\(907\) | 7.52431 | 0.249840 | 0.124920 | − | 0.992167i | \(-0.460133\pi\) | ||||
0.124920 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(908\) | 15.5676 | 0.516629 | ||||||||
\(909\) | −0.457949 | −0.0151892 | ||||||||
\(910\) | 0.0110651 | 0.000366805 0 | ||||||||
\(911\) | −6.23744 | −0.206656 | −0.103328 | − | 0.994647i | \(-0.532949\pi\) | ||||
−0.103328 | + | 0.994647i | \(0.532949\pi\) | |||||||
\(912\) | 7.92741 | 0.262503 | ||||||||
\(913\) | 0.363028 | 0.0120145 | ||||||||
\(914\) | 12.2407 | 0.404886 | ||||||||
\(915\) | −0.560518 | −0.0185301 | ||||||||
\(916\) | −11.0634 | −0.365544 | ||||||||
\(917\) | −0.103168 | −0.00340691 | ||||||||
\(918\) | 23.0354 | 0.760280 | ||||||||
\(919\) | −0.685114 | −0.0225998 | −0.0112999 | − | 0.999936i | \(-0.503597\pi\) | ||||
−0.0112999 | + | 0.999936i | \(0.503597\pi\) | |||||||
\(920\) | 0.0681057 | 0.00224538 | ||||||||
\(921\) | −52.8114 | −1.74019 | ||||||||
\(922\) | 6.20618 | 0.204390 | ||||||||
\(923\) | −5.12101 | −0.168560 | ||||||||
\(924\) | −0.0221682 | −0.000729279 0 | ||||||||
\(925\) | 34.9015 | 1.14756 | ||||||||
\(926\) | −36.9146 | −1.21309 | ||||||||
\(927\) | −1.48645 | −0.0488215 | ||||||||
\(928\) | 5.98015 | 0.196308 | ||||||||
\(929\) | −34.1747 | −1.12124 | −0.560618 | − | 0.828075i | \(-0.689436\pi\) | ||||
−0.560618 | + | 0.828075i | \(0.689436\pi\) | |||||||
\(930\) | −0.382122 | −0.0125303 | ||||||||
\(931\) | −33.3451 | −1.09284 | ||||||||
\(932\) | −15.7481 | −0.515846 | ||||||||
\(933\) | 25.2314 | 0.826040 | ||||||||
\(934\) | 0.590865 | 0.0193337 | ||||||||
\(935\) | −0.0376951 | −0.00123276 | ||||||||
\(936\) | −0.376321 | −0.0123004 | ||||||||
\(937\) | 5.66657 | 0.185119 | 0.0925593 | − | 0.995707i | \(-0.470495\pi\) | ||||
0.0925593 | + | 0.995707i | \(0.470495\pi\) | |||||||
\(938\) | −1.38462 | −0.0452094 | ||||||||
\(939\) | 25.4960 | 0.832030 | ||||||||
\(940\) | −0.0186077 | −0.000606915 0 | ||||||||
\(941\) | 38.6785 | 1.26088 | 0.630441 | − | 0.776237i | \(-0.282874\pi\) | ||||
0.630441 | + | 0.776237i | \(0.282874\pi\) | |||||||
\(942\) | 1.78982 | 0.0583156 | ||||||||
\(943\) | 0.948349 | 0.0308825 | ||||||||
\(944\) | −9.41679 | −0.306490 | ||||||||
\(945\) | −0.0378157 | −0.00123014 | ||||||||
\(946\) | −1.68739 | −0.0548618 | ||||||||
\(947\) | 39.6055 | 1.28700 | 0.643502 | − | 0.765444i | \(-0.277481\pi\) | ||||
0.643502 | + | 0.765444i | \(0.277481\pi\) | |||||||
\(948\) | 3.62161 | 0.117624 | ||||||||
\(949\) | −4.13482 | −0.134222 | ||||||||
\(950\) | 23.8321 | 0.773215 | ||||||||
\(951\) | −7.97269 | −0.258532 | ||||||||
\(952\) | −0.441569 | −0.0143113 | ||||||||
\(953\) | 0.252656 | 0.00818434 | 0.00409217 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409217 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(954\) | −0.760858 | −0.0246337 | ||||||||
\(955\) | 1.53256 | 0.0495925 | ||||||||
\(956\) | 19.4788 | 0.629989 | ||||||||
\(957\) | 1.28498 | 0.0415374 | ||||||||
\(958\) | −43.2955 | −1.39881 | ||||||||
\(959\) | −0.625763 | −0.0202069 | ||||||||
\(960\) | 0.113167 | 0.00365245 | ||||||||
\(961\) | −19.5984 | −0.632207 | ||||||||
\(962\) | −11.0028 | −0.354745 | ||||||||
\(963\) | −1.61565 | −0.0520635 | ||||||||
\(964\) | 25.5974 | 0.824435 | ||||||||
\(965\) | 0.121328 | 0.00390567 | ||||||||
\(966\) | 0.171428 | 0.00551561 | ||||||||
\(967\) | −29.7690 | −0.957307 | −0.478654 | − | 0.878004i | \(-0.658875\pi\) | ||||
−0.478654 | + | 0.878004i | \(0.658875\pi\) | |||||||
\(968\) | 10.9833 | 0.353016 | ||||||||
\(969\) | 33.9300 | 1.08999 | ||||||||
\(970\) | −0.741390 | −0.0238046 | ||||||||
\(971\) | −29.7422 | −0.954473 | −0.477237 | − | 0.878775i | \(-0.658362\pi\) | ||||
−0.477237 | + | 0.878775i | \(0.658362\pi\) | |||||||
\(972\) | 2.47731 | 0.0794598 | ||||||||
\(973\) | 0.311159 | 0.00997529 | ||||||||
\(974\) | 12.0357 | 0.385649 | ||||||||
\(975\) | 13.0716 | 0.418627 | ||||||||
\(976\) | −4.95302 | −0.158542 | ||||||||
\(977\) | 29.8376 | 0.954589 | 0.477295 | − | 0.878743i | \(-0.341617\pi\) | ||||
0.477295 | + | 0.878743i | \(0.341617\pi\) | |||||||
\(978\) | −2.72072 | −0.0869991 | ||||||||
\(979\) | −1.10378 | −0.0352770 | ||||||||
\(980\) | −0.476015 | −0.0152058 | ||||||||
\(981\) | 1.20136 | 0.0383566 | ||||||||
\(982\) | −18.9412 | −0.604437 | ||||||||
\(983\) | 50.5612 | 1.61265 | 0.806325 | − | 0.591472i | \(-0.201453\pi\) | ||||
0.806325 | + | 0.591472i | \(0.201453\pi\) | |||||||
\(984\) | 1.57581 | 0.0502350 | ||||||||
\(985\) | −0.444166 | −0.0141523 | ||||||||
\(986\) | 25.5956 | 0.815129 | ||||||||
\(987\) | −0.0468371 | −0.00149084 | ||||||||
\(988\) | −7.51313 | −0.239025 | ||||||||
\(989\) | 13.0487 | 0.414925 | ||||||||
\(990\) | −0.00210457 | −6.68877e−5 0 | ||||||||
\(991\) | 35.9668 | 1.14252 | 0.571261 | − | 0.820768i | \(-0.306454\pi\) | ||||
0.571261 | + | 0.820768i | \(0.306454\pi\) | |||||||
\(992\) | −3.37662 | −0.107208 | ||||||||
\(993\) | −37.1521 | −1.17899 | ||||||||
\(994\) | −0.335486 | −0.0106410 | ||||||||
\(995\) | −1.04151 | −0.0330182 | ||||||||
\(996\) | −4.66476 | −0.147808 | ||||||||
\(997\) | −14.8725 | −0.471017 | −0.235509 | − | 0.971872i | \(-0.575676\pi\) | ||||
−0.235509 | + | 0.971872i | \(0.575676\pi\) | |||||||
\(998\) | 0.580220 | 0.0183665 | ||||||||
\(999\) | 37.6028 | 1.18970 |
(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 | 6026.2.a.h.1.18 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.18 | ✓ | 24 | 1.1 | even | 1 | trivial |