Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.563182\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.563182 | −0.398230 | −0.199115 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199115 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.68283 | −0.841413 | ||||||||
\(5\) | −1.59433 | −0.713005 | −0.356503 | − | 0.934294i | \(-0.616031\pi\) | ||||
−0.356503 | + | 0.934294i | \(0.616031\pi\) | |||||||
\(6\) | −0.563182 | −0.229918 | ||||||||
\(7\) | 4.95339 | 1.87221 | 0.936104 | − | 0.351724i | \(-0.114405\pi\) | ||||
0.936104 | + | 0.351724i | \(0.114405\pi\) | |||||||
\(8\) | 2.07410 | 0.733306 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.897897 | 0.283940 | ||||||||
\(11\) | −0.616624 | −0.185919 | −0.0929596 | − | 0.995670i | \(-0.529633\pi\) | ||||
−0.0929596 | + | 0.995670i | \(0.529633\pi\) | |||||||
\(12\) | −1.68283 | −0.485790 | ||||||||
\(13\) | 6.48438 | 1.79844 | 0.899221 | − | 0.437494i | \(-0.144134\pi\) | ||||
0.899221 | + | 0.437494i | \(0.144134\pi\) | |||||||
\(14\) | −2.78966 | −0.745569 | ||||||||
\(15\) | −1.59433 | −0.411654 | ||||||||
\(16\) | 2.19756 | 0.549389 | ||||||||
\(17\) | −1.67611 | −0.406516 | −0.203258 | − | 0.979125i | \(-0.565153\pi\) | ||||
−0.203258 | + | 0.979125i | \(0.565153\pi\) | |||||||
\(18\) | −0.563182 | −0.132743 | ||||||||
\(19\) | 2.69708 | 0.618753 | 0.309376 | − | 0.950940i | \(-0.399880\pi\) | ||||
0.309376 | + | 0.950940i | \(0.399880\pi\) | |||||||
\(20\) | 2.68298 | 0.599932 | ||||||||
\(21\) | 4.95339 | 1.08092 | ||||||||
\(22\) | 0.347272 | 0.0740386 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.07410 | 0.423374 | ||||||||
\(25\) | −2.45812 | −0.491624 | ||||||||
\(26\) | −3.65188 | −0.716193 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −8.33570 | −1.57530 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0.897897 | 0.163933 | ||||||||
\(31\) | −3.94303 | −0.708188 | −0.354094 | − | 0.935210i | \(-0.615211\pi\) | ||||
−0.354094 | + | 0.935210i | \(0.615211\pi\) | |||||||
\(32\) | −5.38583 | −0.952089 | ||||||||
\(33\) | −0.616624 | −0.107341 | ||||||||
\(34\) | 0.943955 | 0.161887 | ||||||||
\(35\) | −7.89733 | −1.33489 | ||||||||
\(36\) | −1.68283 | −0.280471 | ||||||||
\(37\) | 5.81974 | 0.956759 | 0.478379 | − | 0.878153i | \(-0.341224\pi\) | ||||
0.478379 | + | 0.878153i | \(0.341224\pi\) | |||||||
\(38\) | −1.51895 | −0.246406 | ||||||||
\(39\) | 6.48438 | 1.03833 | ||||||||
\(40\) | −3.30680 | −0.522851 | ||||||||
\(41\) | −6.01020 | −0.938636 | −0.469318 | − | 0.883029i | \(-0.655500\pi\) | ||||
−0.469318 | + | 0.883029i | \(0.655500\pi\) | |||||||
\(42\) | −2.78966 | −0.430454 | ||||||||
\(43\) | 0.472349 | 0.0720326 | 0.0360163 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360163 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(44\) | 1.03767 | 0.156435 | ||||||||
\(45\) | −1.59433 | −0.237668 | ||||||||
\(46\) | 0.563182 | 0.0830367 | ||||||||
\(47\) | 4.27730 | 0.623909 | 0.311954 | − | 0.950097i | \(-0.399016\pi\) | ||||
0.311954 | + | 0.950097i | \(0.399016\pi\) | |||||||
\(48\) | 2.19756 | 0.317190 | ||||||||
\(49\) | 17.5361 | 2.50516 | ||||||||
\(50\) | 1.38437 | 0.195779 | ||||||||
\(51\) | −1.67611 | −0.234702 | ||||||||
\(52\) | −10.9121 | −1.51323 | ||||||||
\(53\) | −7.82304 | −1.07458 | −0.537288 | − | 0.843399i | \(-0.680551\pi\) | ||||
−0.537288 | + | 0.843399i | \(0.680551\pi\) | |||||||
\(54\) | −0.563182 | −0.0766394 | ||||||||
\(55\) | 0.983101 | 0.132561 | ||||||||
\(56\) | 10.2738 | 1.37290 | ||||||||
\(57\) | 2.69708 | 0.357237 | ||||||||
\(58\) | 0.563182 | 0.0739494 | ||||||||
\(59\) | 11.6621 | 1.51827 | 0.759137 | − | 0.650930i | \(-0.225621\pi\) | ||||
0.759137 | + | 0.650930i | \(0.225621\pi\) | |||||||
\(60\) | 2.68298 | 0.346371 | ||||||||
\(61\) | 10.3582 | 1.32623 | 0.663115 | − | 0.748517i | \(-0.269234\pi\) | ||||
0.663115 | + | 0.748517i | \(0.269234\pi\) | |||||||
\(62\) | 2.22064 | 0.282022 | ||||||||
\(63\) | 4.95339 | 0.624069 | ||||||||
\(64\) | −1.36191 | −0.170239 | ||||||||
\(65\) | −10.3382 | −1.28230 | ||||||||
\(66\) | 0.347272 | 0.0427462 | ||||||||
\(67\) | −6.36345 | −0.777420 | −0.388710 | − | 0.921360i | \(-0.627079\pi\) | ||||
−0.388710 | + | 0.921360i | \(0.627079\pi\) | |||||||
\(68\) | 2.82060 | 0.342048 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 4.44764 | 0.531594 | ||||||||
\(71\) | 8.81789 | 1.04649 | 0.523246 | − | 0.852182i | \(-0.324721\pi\) | ||||
0.523246 | + | 0.852182i | \(0.324721\pi\) | |||||||
\(72\) | 2.07410 | 0.244435 | ||||||||
\(73\) | −2.13920 | −0.250375 | −0.125187 | − | 0.992133i | \(-0.539953\pi\) | ||||
−0.125187 | + | 0.992133i | \(0.539953\pi\) | |||||||
\(74\) | −3.27757 | −0.381010 | ||||||||
\(75\) | −2.45812 | −0.283839 | ||||||||
\(76\) | −4.53872 | −0.520626 | ||||||||
\(77\) | −3.05438 | −0.348079 | ||||||||
\(78\) | −3.65188 | −0.413494 | ||||||||
\(79\) | −11.9951 | −1.34956 | −0.674780 | − | 0.738019i | \(-0.735761\pi\) | ||||
−0.674780 | + | 0.738019i | \(0.735761\pi\) | |||||||
\(80\) | −3.50362 | −0.391717 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.38484 | 0.373793 | ||||||||
\(83\) | 10.2126 | 1.12098 | 0.560490 | − | 0.828161i | \(-0.310613\pi\) | ||||
0.560490 | + | 0.828161i | \(0.310613\pi\) | |||||||
\(84\) | −8.33570 | −0.909500 | ||||||||
\(85\) | 2.67227 | 0.289848 | ||||||||
\(86\) | −0.266019 | −0.0286855 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −1.27894 | −0.136336 | ||||||||
\(89\) | −6.30439 | −0.668264 | −0.334132 | − | 0.942526i | \(-0.608443\pi\) | ||||
−0.334132 | + | 0.942526i | \(0.608443\pi\) | |||||||
\(90\) | 0.897897 | 0.0946466 | ||||||||
\(91\) | 32.1197 | 3.36706 | ||||||||
\(92\) | 1.68283 | 0.175447 | ||||||||
\(93\) | −3.94303 | −0.408873 | ||||||||
\(94\) | −2.40890 | −0.248459 | ||||||||
\(95\) | −4.30003 | −0.441174 | ||||||||
\(96\) | −5.38583 | −0.549689 | ||||||||
\(97\) | 11.9110 | 1.20938 | 0.604691 | − | 0.796461i | \(-0.293297\pi\) | ||||
0.604691 | + | 0.796461i | \(0.293297\pi\) | |||||||
\(98\) | −9.87603 | −0.997630 | ||||||||
\(99\) | −0.616624 | −0.0619731 | ||||||||
\(100\) | 4.13659 | 0.413659 | ||||||||
\(101\) | 4.59685 | 0.457404 | 0.228702 | − | 0.973496i | \(-0.426552\pi\) | ||||
0.228702 | + | 0.973496i | \(0.426552\pi\) | |||||||
\(102\) | 0.943955 | 0.0934655 | ||||||||
\(103\) | 4.58092 | 0.451372 | 0.225686 | − | 0.974200i | \(-0.427538\pi\) | ||||
0.225686 | + | 0.974200i | \(0.427538\pi\) | |||||||
\(104\) | 13.4493 | 1.31881 | ||||||||
\(105\) | −7.89733 | −0.770701 | ||||||||
\(106\) | 4.40579 | 0.427929 | ||||||||
\(107\) | 9.04500 | 0.874413 | 0.437207 | − | 0.899361i | \(-0.355968\pi\) | ||||
0.437207 | + | 0.899361i | \(0.355968\pi\) | |||||||
\(108\) | −1.68283 | −0.161930 | ||||||||
\(109\) | −16.0639 | −1.53864 | −0.769320 | − | 0.638864i | \(-0.779405\pi\) | ||||
−0.769320 | + | 0.638864i | \(0.779405\pi\) | |||||||
\(110\) | −0.553665 | −0.0527899 | ||||||||
\(111\) | 5.81974 | 0.552385 | ||||||||
\(112\) | 10.8854 | 1.02857 | ||||||||
\(113\) | 18.3897 | 1.72996 | 0.864978 | − | 0.501809i | \(-0.167332\pi\) | ||||
0.864978 | + | 0.501809i | \(0.167332\pi\) | |||||||
\(114\) | −1.51895 | −0.142262 | ||||||||
\(115\) | 1.59433 | 0.148672 | ||||||||
\(116\) | 1.68283 | 0.156246 | ||||||||
\(117\) | 6.48438 | 0.599481 | ||||||||
\(118\) | −6.56788 | −0.604622 | ||||||||
\(119\) | −8.30243 | −0.761083 | ||||||||
\(120\) | −3.30680 | −0.301868 | ||||||||
\(121\) | −10.6198 | −0.965434 | ||||||||
\(122\) | −5.83355 | −0.528144 | ||||||||
\(123\) | −6.01020 | −0.541922 | ||||||||
\(124\) | 6.63543 | 0.595879 | ||||||||
\(125\) | 11.8907 | 1.06354 | ||||||||
\(126\) | −2.78966 | −0.248523 | ||||||||
\(127\) | 4.34065 | 0.385171 | 0.192585 | − | 0.981280i | \(-0.438313\pi\) | ||||
0.192585 | + | 0.981280i | \(0.438313\pi\) | |||||||
\(128\) | 11.5387 | 1.01988 | ||||||||
\(129\) | 0.472349 | 0.0415880 | ||||||||
\(130\) | 5.82230 | 0.510650 | ||||||||
\(131\) | 14.2331 | 1.24355 | 0.621776 | − | 0.783195i | \(-0.286411\pi\) | ||||
0.621776 | + | 0.783195i | \(0.286411\pi\) | |||||||
\(132\) | 1.03767 | 0.0903177 | ||||||||
\(133\) | 13.3597 | 1.15843 | ||||||||
\(134\) | 3.58378 | 0.309592 | ||||||||
\(135\) | −1.59433 | −0.137218 | ||||||||
\(136\) | −3.47642 | −0.298101 | ||||||||
\(137\) | 10.4871 | 0.895977 | 0.447988 | − | 0.894039i | \(-0.352141\pi\) | ||||
0.447988 | + | 0.894039i | \(0.352141\pi\) | |||||||
\(138\) | 0.563182 | 0.0479412 | ||||||||
\(139\) | −19.5982 | −1.66230 | −0.831151 | − | 0.556047i | \(-0.812317\pi\) | ||||
−0.831151 | + | 0.556047i | \(0.812317\pi\) | |||||||
\(140\) | 13.2898 | 1.12320 | ||||||||
\(141\) | 4.27730 | 0.360214 | ||||||||
\(142\) | −4.96608 | −0.416744 | ||||||||
\(143\) | −3.99842 | −0.334365 | ||||||||
\(144\) | 2.19756 | 0.183130 | ||||||||
\(145\) | 1.59433 | 0.132402 | ||||||||
\(146\) | 1.20476 | 0.0997067 | ||||||||
\(147\) | 17.5361 | 1.44635 | ||||||||
\(148\) | −9.79360 | −0.805029 | ||||||||
\(149\) | −6.73460 | −0.551720 | −0.275860 | − | 0.961198i | \(-0.588963\pi\) | ||||
−0.275860 | + | 0.961198i | \(0.588963\pi\) | |||||||
\(150\) | 1.38437 | 0.113033 | ||||||||
\(151\) | 4.73376 | 0.385228 | 0.192614 | − | 0.981275i | \(-0.438304\pi\) | ||||
0.192614 | + | 0.981275i | \(0.438304\pi\) | |||||||
\(152\) | 5.59402 | 0.453735 | ||||||||
\(153\) | −1.67611 | −0.135505 | ||||||||
\(154\) | 1.72017 | 0.138616 | ||||||||
\(155\) | 6.28648 | 0.504942 | ||||||||
\(156\) | −10.9121 | −0.873665 | ||||||||
\(157\) | 21.3212 | 1.70162 | 0.850810 | − | 0.525473i | \(-0.176112\pi\) | ||||
0.850810 | + | 0.525473i | \(0.176112\pi\) | |||||||
\(158\) | 6.75545 | 0.537435 | ||||||||
\(159\) | −7.82304 | −0.620407 | ||||||||
\(160\) | 8.58677 | 0.678844 | ||||||||
\(161\) | −4.95339 | −0.390382 | ||||||||
\(162\) | −0.563182 | −0.0442478 | ||||||||
\(163\) | 4.09507 | 0.320750 | 0.160375 | − | 0.987056i | \(-0.448730\pi\) | ||||
0.160375 | + | 0.987056i | \(0.448730\pi\) | |||||||
\(164\) | 10.1141 | 0.789780 | ||||||||
\(165\) | 0.983101 | 0.0765343 | ||||||||
\(166\) | −5.75156 | −0.446408 | ||||||||
\(167\) | −10.3928 | −0.804217 | −0.402108 | − | 0.915592i | \(-0.631723\pi\) | ||||
−0.402108 | + | 0.915592i | \(0.631723\pi\) | |||||||
\(168\) | 10.2738 | 0.792644 | ||||||||
\(169\) | 29.0471 | 2.23440 | ||||||||
\(170\) | −1.50497 | −0.115426 | ||||||||
\(171\) | 2.69708 | 0.206251 | ||||||||
\(172\) | −0.794882 | −0.0606091 | ||||||||
\(173\) | −4.60624 | −0.350206 | −0.175103 | − | 0.984550i | \(-0.556026\pi\) | ||||
−0.175103 | + | 0.984550i | \(0.556026\pi\) | |||||||
\(174\) | 0.563182 | 0.0426947 | ||||||||
\(175\) | −12.1760 | −0.920422 | ||||||||
\(176\) | −1.35507 | −0.102142 | ||||||||
\(177\) | 11.6621 | 0.876576 | ||||||||
\(178\) | 3.55052 | 0.266123 | ||||||||
\(179\) | −25.3247 | −1.89286 | −0.946430 | − | 0.322910i | \(-0.895339\pi\) | ||||
−0.946430 | + | 0.322910i | \(0.895339\pi\) | |||||||
\(180\) | 2.68298 | 0.199977 | ||||||||
\(181\) | −22.1243 | −1.64449 | −0.822245 | − | 0.569134i | \(-0.807279\pi\) | ||||
−0.822245 | + | 0.569134i | \(0.807279\pi\) | |||||||
\(182\) | −18.0892 | −1.34086 | ||||||||
\(183\) | 10.3582 | 0.765699 | ||||||||
\(184\) | −2.07410 | −0.152905 | ||||||||
\(185\) | −9.27857 | −0.682174 | ||||||||
\(186\) | 2.22064 | 0.162825 | ||||||||
\(187\) | 1.03353 | 0.0755792 | ||||||||
\(188\) | −7.19796 | −0.524965 | ||||||||
\(189\) | 4.95339 | 0.360306 | ||||||||
\(190\) | 2.42170 | 0.175689 | ||||||||
\(191\) | −20.9666 | −1.51709 | −0.758545 | − | 0.651620i | \(-0.774090\pi\) | ||||
−0.758545 | + | 0.651620i | \(0.774090\pi\) | |||||||
\(192\) | −1.36191 | −0.0982874 | ||||||||
\(193\) | 20.7423 | 1.49306 | 0.746530 | − | 0.665351i | \(-0.231718\pi\) | ||||
0.746530 | + | 0.665351i | \(0.231718\pi\) | |||||||
\(194\) | −6.70807 | −0.481612 | ||||||||
\(195\) | −10.3382 | −0.740335 | ||||||||
\(196\) | −29.5102 | −2.10787 | ||||||||
\(197\) | −22.2579 | −1.58581 | −0.792906 | − | 0.609344i | \(-0.791433\pi\) | ||||
−0.792906 | + | 0.609344i | \(0.791433\pi\) | |||||||
\(198\) | 0.347272 | 0.0246795 | ||||||||
\(199\) | 0.316336 | 0.0224245 | 0.0112122 | − | 0.999937i | \(-0.496431\pi\) | ||||
0.0112122 | + | 0.999937i | \(0.496431\pi\) | |||||||
\(200\) | −5.09839 | −0.360511 | ||||||||
\(201\) | −6.36345 | −0.448843 | ||||||||
\(202\) | −2.58887 | −0.182152 | ||||||||
\(203\) | −4.95339 | −0.347660 | ||||||||
\(204\) | 2.82060 | 0.197482 | ||||||||
\(205\) | 9.58223 | 0.669252 | ||||||||
\(206\) | −2.57989 | −0.179750 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 14.2498 | 0.988044 | ||||||||
\(209\) | −1.66308 | −0.115038 | ||||||||
\(210\) | 4.44764 | 0.306916 | ||||||||
\(211\) | −0.730479 | −0.0502883 | −0.0251441 | − | 0.999684i | \(-0.508004\pi\) | ||||
−0.0251441 | + | 0.999684i | \(0.508004\pi\) | |||||||
\(212\) | 13.1648 | 0.904163 | ||||||||
\(213\) | 8.81789 | 0.604192 | ||||||||
\(214\) | −5.09398 | −0.348217 | ||||||||
\(215\) | −0.753079 | −0.0513596 | ||||||||
\(216\) | 2.07410 | 0.141125 | ||||||||
\(217\) | −19.5314 | −1.32588 | ||||||||
\(218\) | 9.04688 | 0.612732 | ||||||||
\(219\) | −2.13920 | −0.144554 | ||||||||
\(220\) | −1.65439 | −0.111539 | ||||||||
\(221\) | −10.8685 | −0.731096 | ||||||||
\(222\) | −3.27757 | −0.219976 | ||||||||
\(223\) | −0.992801 | −0.0664829 | −0.0332414 | − | 0.999447i | \(-0.510583\pi\) | ||||
−0.0332414 | + | 0.999447i | \(0.510583\pi\) | |||||||
\(224\) | −26.6781 | −1.78251 | ||||||||
\(225\) | −2.45812 | −0.163875 | ||||||||
\(226\) | −10.3567 | −0.688920 | ||||||||
\(227\) | −6.80592 | −0.451725 | −0.225862 | − | 0.974159i | \(-0.572520\pi\) | ||||
−0.225862 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(228\) | −4.53872 | −0.300584 | ||||||||
\(229\) | 16.5937 | 1.09654 | 0.548272 | − | 0.836300i | \(-0.315286\pi\) | ||||
0.548272 | + | 0.836300i | \(0.315286\pi\) | |||||||
\(230\) | −0.897897 | −0.0592056 | ||||||||
\(231\) | −3.05438 | −0.200964 | ||||||||
\(232\) | −2.07410 | −0.136171 | ||||||||
\(233\) | 25.8874 | 1.69594 | 0.847971 | − | 0.530042i | \(-0.177824\pi\) | ||||
0.847971 | + | 0.530042i | \(0.177824\pi\) | |||||||
\(234\) | −3.65188 | −0.238731 | ||||||||
\(235\) | −6.81942 | −0.444850 | ||||||||
\(236\) | −19.6253 | −1.27750 | ||||||||
\(237\) | −11.9951 | −0.779168 | ||||||||
\(238\) | 4.67578 | 0.303086 | ||||||||
\(239\) | 6.18941 | 0.400360 | 0.200180 | − | 0.979759i | \(-0.435847\pi\) | ||||
0.200180 | + | 0.979759i | \(0.435847\pi\) | |||||||
\(240\) | −3.50362 | −0.226158 | ||||||||
\(241\) | 20.6273 | 1.32872 | 0.664360 | − | 0.747413i | \(-0.268704\pi\) | ||||
0.664360 | + | 0.747413i | \(0.268704\pi\) | |||||||
\(242\) | 5.98087 | 0.384465 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −17.4310 | −1.11591 | ||||||||
\(245\) | −27.9583 | −1.78619 | ||||||||
\(246\) | 3.38484 | 0.215809 | ||||||||
\(247\) | 17.4889 | 1.11279 | ||||||||
\(248\) | −8.17824 | −0.519319 | ||||||||
\(249\) | 10.2126 | 0.647198 | ||||||||
\(250\) | −6.69662 | −0.423531 | ||||||||
\(251\) | −16.1608 | −1.02006 | −0.510029 | − | 0.860157i | \(-0.670365\pi\) | ||||
−0.510029 | + | 0.860157i | \(0.670365\pi\) | |||||||
\(252\) | −8.33570 | −0.525100 | ||||||||
\(253\) | 0.616624 | 0.0387668 | ||||||||
\(254\) | −2.44458 | −0.153386 | ||||||||
\(255\) | 2.67227 | 0.167344 | ||||||||
\(256\) | −3.77454 | −0.235909 | ||||||||
\(257\) | −7.71144 | −0.481026 | −0.240513 | − | 0.970646i | \(-0.577316\pi\) | ||||
−0.240513 | + | 0.970646i | \(0.577316\pi\) | |||||||
\(258\) | −0.266019 | −0.0165616 | ||||||||
\(259\) | 28.8275 | 1.79125 | ||||||||
\(260\) | 17.3974 | 1.07894 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −8.01583 | −0.495220 | ||||||||
\(263\) | −3.66457 | −0.225967 | −0.112984 | − | 0.993597i | \(-0.536041\pi\) | ||||
−0.112984 | + | 0.993597i | \(0.536041\pi\) | |||||||
\(264\) | −1.27894 | −0.0787134 | ||||||||
\(265\) | 12.4725 | 0.766179 | ||||||||
\(266\) | −7.52394 | −0.461323 | ||||||||
\(267\) | −6.30439 | −0.385823 | ||||||||
\(268\) | 10.7086 | 0.654131 | ||||||||
\(269\) | 18.5829 | 1.13302 | 0.566510 | − | 0.824055i | \(-0.308293\pi\) | ||||
0.566510 | + | 0.824055i | \(0.308293\pi\) | |||||||
\(270\) | 0.897897 | 0.0546443 | ||||||||
\(271\) | −11.7264 | −0.712326 | −0.356163 | − | 0.934424i | \(-0.615915\pi\) | ||||
−0.356163 | + | 0.934424i | \(0.615915\pi\) | |||||||
\(272\) | −3.68334 | −0.223336 | ||||||||
\(273\) | 32.1197 | 1.94397 | ||||||||
\(274\) | −5.90617 | −0.356805 | ||||||||
\(275\) | 1.51574 | 0.0914023 | ||||||||
\(276\) | 1.68283 | 0.101294 | ||||||||
\(277\) | −25.5590 | −1.53569 | −0.767846 | − | 0.640634i | \(-0.778672\pi\) | ||||
−0.767846 | + | 0.640634i | \(0.778672\pi\) | |||||||
\(278\) | 11.0374 | 0.661978 | ||||||||
\(279\) | −3.94303 | −0.236063 | ||||||||
\(280\) | −16.3799 | −0.978885 | ||||||||
\(281\) | −7.56252 | −0.451142 | −0.225571 | − | 0.974227i | \(-0.572425\pi\) | ||||
−0.225571 | + | 0.974227i | \(0.572425\pi\) | |||||||
\(282\) | −2.40890 | −0.143448 | ||||||||
\(283\) | 15.6951 | 0.932980 | 0.466490 | − | 0.884527i | \(-0.345518\pi\) | ||||
0.466490 | + | 0.884527i | \(0.345518\pi\) | |||||||
\(284\) | −14.8390 | −0.880531 | ||||||||
\(285\) | −4.30003 | −0.254712 | ||||||||
\(286\) | 2.25184 | 0.133154 | ||||||||
\(287\) | −29.7709 | −1.75732 | ||||||||
\(288\) | −5.38583 | −0.317363 | ||||||||
\(289\) | −14.1907 | −0.834744 | ||||||||
\(290\) | −0.897897 | −0.0527263 | ||||||||
\(291\) | 11.9110 | 0.698236 | ||||||||
\(292\) | 3.59991 | 0.210669 | ||||||||
\(293\) | 27.4297 | 1.60246 | 0.801229 | − | 0.598358i | \(-0.204180\pi\) | ||||
0.801229 | + | 0.598358i | \(0.204180\pi\) | |||||||
\(294\) | −9.87603 | −0.575982 | ||||||||
\(295\) | −18.5932 | −1.08254 | ||||||||
\(296\) | 12.0707 | 0.701596 | ||||||||
\(297\) | −0.616624 | −0.0357802 | ||||||||
\(298\) | 3.79281 | 0.219711 | ||||||||
\(299\) | −6.48438 | −0.375001 | ||||||||
\(300\) | 4.13659 | 0.238826 | ||||||||
\(301\) | 2.33973 | 0.134860 | ||||||||
\(302\) | −2.66597 | −0.153409 | ||||||||
\(303\) | 4.59685 | 0.264082 | ||||||||
\(304\) | 5.92698 | 0.339936 | ||||||||
\(305\) | −16.5143 | −0.945609 | ||||||||
\(306\) | 0.943955 | 0.0539623 | ||||||||
\(307\) | 12.9197 | 0.737365 | 0.368683 | − | 0.929555i | \(-0.379809\pi\) | ||||
0.368683 | + | 0.929555i | \(0.379809\pi\) | |||||||
\(308\) | 5.14000 | 0.292878 | ||||||||
\(309\) | 4.58092 | 0.260600 | ||||||||
\(310\) | −3.54043 | −0.201083 | ||||||||
\(311\) | −3.77938 | −0.214309 | −0.107155 | − | 0.994242i | \(-0.534174\pi\) | ||||
−0.107155 | + | 0.994242i | \(0.534174\pi\) | |||||||
\(312\) | 13.4493 | 0.761414 | ||||||||
\(313\) | 4.35313 | 0.246054 | 0.123027 | − | 0.992403i | \(-0.460740\pi\) | ||||
0.123027 | + | 0.992403i | \(0.460740\pi\) | |||||||
\(314\) | −12.0077 | −0.677636 | ||||||||
\(315\) | −7.89733 | −0.444964 | ||||||||
\(316\) | 20.1857 | 1.13554 | ||||||||
\(317\) | 0.496952 | 0.0279116 | 0.0139558 | − | 0.999903i | \(-0.495558\pi\) | ||||
0.0139558 | + | 0.999903i | \(0.495558\pi\) | |||||||
\(318\) | 4.40579 | 0.247065 | ||||||||
\(319\) | 0.616624 | 0.0345243 | ||||||||
\(320\) | 2.17133 | 0.121381 | ||||||||
\(321\) | 9.04500 | 0.504843 | ||||||||
\(322\) | 2.78966 | 0.155462 | ||||||||
\(323\) | −4.52060 | −0.251533 | ||||||||
\(324\) | −1.68283 | −0.0934903 | ||||||||
\(325\) | −15.9394 | −0.884157 | ||||||||
\(326\) | −2.30627 | −0.127732 | ||||||||
\(327\) | −16.0639 | −0.888334 | ||||||||
\(328\) | −12.4658 | −0.688307 | ||||||||
\(329\) | 21.1872 | 1.16809 | ||||||||
\(330\) | −0.553665 | −0.0304782 | ||||||||
\(331\) | −5.64763 | −0.310422 | −0.155211 | − | 0.987881i | \(-0.549606\pi\) | ||||
−0.155211 | + | 0.987881i | \(0.549606\pi\) | |||||||
\(332\) | −17.1861 | −0.943207 | ||||||||
\(333\) | 5.81974 | 0.318920 | ||||||||
\(334\) | 5.85302 | 0.320263 | ||||||||
\(335\) | 10.1454 | 0.554304 | ||||||||
\(336\) | 10.8854 | 0.593845 | ||||||||
\(337\) | −7.46517 | −0.406654 | −0.203327 | − | 0.979111i | \(-0.565175\pi\) | ||||
−0.203327 | + | 0.979111i | \(0.565175\pi\) | |||||||
\(338\) | −16.3588 | −0.889803 | ||||||||
\(339\) | 18.3897 | 0.998791 | ||||||||
\(340\) | −4.49696 | −0.243882 | ||||||||
\(341\) | 2.43137 | 0.131666 | ||||||||
\(342\) | −1.51895 | −0.0821352 | ||||||||
\(343\) | 52.1896 | 2.81797 | ||||||||
\(344\) | 0.979700 | 0.0528219 | ||||||||
\(345\) | 1.59433 | 0.0858357 | ||||||||
\(346\) | 2.59415 | 0.139462 | ||||||||
\(347\) | 14.1931 | 0.761923 | 0.380961 | − | 0.924591i | \(-0.375593\pi\) | ||||
0.380961 | + | 0.924591i | \(0.375593\pi\) | |||||||
\(348\) | 1.68283 | 0.0902089 | ||||||||
\(349\) | −18.3724 | −0.983455 | −0.491727 | − | 0.870749i | \(-0.663634\pi\) | ||||
−0.491727 | + | 0.870749i | \(0.663634\pi\) | |||||||
\(350\) | 6.85732 | 0.366539 | ||||||||
\(351\) | 6.48438 | 0.346110 | ||||||||
\(352\) | 3.32103 | 0.177012 | ||||||||
\(353\) | −29.4962 | −1.56992 | −0.784962 | − | 0.619544i | \(-0.787318\pi\) | ||||
−0.784962 | + | 0.619544i | \(0.787318\pi\) | |||||||
\(354\) | −6.56788 | −0.349079 | ||||||||
\(355\) | −14.0586 | −0.746154 | ||||||||
\(356\) | 10.6092 | 0.562286 | ||||||||
\(357\) | −8.30243 | −0.439411 | ||||||||
\(358\) | 14.2624 | 0.753793 | ||||||||
\(359\) | 1.45373 | 0.0767248 | 0.0383624 | − | 0.999264i | \(-0.487786\pi\) | ||||
0.0383624 | + | 0.999264i | \(0.487786\pi\) | |||||||
\(360\) | −3.30680 | −0.174284 | ||||||||
\(361\) | −11.7258 | −0.617145 | ||||||||
\(362\) | 12.4600 | 0.654885 | ||||||||
\(363\) | −10.6198 | −0.557394 | ||||||||
\(364\) | −54.0518 | −2.83309 | ||||||||
\(365\) | 3.41059 | 0.178518 | ||||||||
\(366\) | −5.83355 | −0.304924 | ||||||||
\(367\) | −10.1531 | −0.529990 | −0.264995 | − | 0.964250i | \(-0.585370\pi\) | ||||
−0.264995 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(368\) | −2.19756 | −0.114555 | ||||||||
\(369\) | −6.01020 | −0.312879 | ||||||||
\(370\) | 5.22552 | 0.271662 | ||||||||
\(371\) | −38.7506 | −2.01183 | ||||||||
\(372\) | 6.63543 | 0.344031 | ||||||||
\(373\) | 10.0893 | 0.522406 | 0.261203 | − | 0.965284i | \(-0.415881\pi\) | ||||
0.261203 | + | 0.965284i | \(0.415881\pi\) | |||||||
\(374\) | −0.582065 | −0.0300979 | ||||||||
\(375\) | 11.8907 | 0.614032 | ||||||||
\(376\) | 8.87156 | 0.457516 | ||||||||
\(377\) | −6.48438 | −0.333962 | ||||||||
\(378\) | −2.78966 | −0.143485 | ||||||||
\(379\) | −14.5482 | −0.747293 | −0.373646 | − | 0.927571i | \(-0.621893\pi\) | ||||
−0.373646 | + | 0.927571i | \(0.621893\pi\) | |||||||
\(380\) | 7.23620 | 0.371209 | ||||||||
\(381\) | 4.34065 | 0.222378 | ||||||||
\(382\) | 11.8080 | 0.604151 | ||||||||
\(383\) | 14.7357 | 0.752960 | 0.376480 | − | 0.926425i | \(-0.377134\pi\) | ||||
0.376480 | + | 0.926425i | \(0.377134\pi\) | |||||||
\(384\) | 11.5387 | 0.588830 | ||||||||
\(385\) | 4.86969 | 0.248182 | ||||||||
\(386\) | −11.6817 | −0.594581 | ||||||||
\(387\) | 0.472349 | 0.0240109 | ||||||||
\(388\) | −20.0442 | −1.01759 | ||||||||
\(389\) | −5.48698 | −0.278201 | −0.139101 | − | 0.990278i | \(-0.544421\pi\) | ||||
−0.139101 | + | 0.990278i | \(0.544421\pi\) | |||||||
\(390\) | 5.82230 | 0.294824 | ||||||||
\(391\) | 1.67611 | 0.0847645 | ||||||||
\(392\) | 36.3717 | 1.83705 | ||||||||
\(393\) | 14.2331 | 0.717965 | ||||||||
\(394\) | 12.5353 | 0.631518 | ||||||||
\(395\) | 19.1242 | 0.962243 | ||||||||
\(396\) | 1.03767 | 0.0521450 | ||||||||
\(397\) | −8.85454 | −0.444397 | −0.222198 | − | 0.975002i | \(-0.571323\pi\) | ||||
−0.222198 | + | 0.975002i | \(0.571323\pi\) | |||||||
\(398\) | −0.178155 | −0.00893009 | ||||||||
\(399\) | 13.3597 | 0.668822 | ||||||||
\(400\) | −5.40185 | −0.270093 | ||||||||
\(401\) | −1.93901 | −0.0968298 | −0.0484149 | − | 0.998827i | \(-0.515417\pi\) | ||||
−0.0484149 | + | 0.998827i | \(0.515417\pi\) | |||||||
\(402\) | 3.58378 | 0.178743 | ||||||||
\(403\) | −25.5681 | −1.27364 | ||||||||
\(404\) | −7.73571 | −0.384866 | ||||||||
\(405\) | −1.59433 | −0.0792228 | ||||||||
\(406\) | 2.78966 | 0.138449 | ||||||||
\(407\) | −3.58859 | −0.177880 | ||||||||
\(408\) | −3.47642 | −0.172109 | ||||||||
\(409\) | 6.64781 | 0.328713 | 0.164357 | − | 0.986401i | \(-0.447445\pi\) | ||||
0.164357 | + | 0.986401i | \(0.447445\pi\) | |||||||
\(410\) | −5.39654 | −0.266516 | ||||||||
\(411\) | 10.4871 | 0.517292 | ||||||||
\(412\) | −7.70890 | −0.379790 | ||||||||
\(413\) | 57.7669 | 2.84253 | ||||||||
\(414\) | 0.563182 | 0.0276789 | ||||||||
\(415\) | −16.2823 | −0.799264 | ||||||||
\(416\) | −34.9237 | −1.71228 | ||||||||
\(417\) | −19.5982 | −0.959730 | ||||||||
\(418\) | 0.936620 | 0.0458116 | ||||||||
\(419\) | 0.802297 | 0.0391948 | 0.0195974 | − | 0.999808i | \(-0.493762\pi\) | ||||
0.0195974 | + | 0.999808i | \(0.493762\pi\) | |||||||
\(420\) | 13.2898 | 0.648478 | ||||||||
\(421\) | 21.2976 | 1.03798 | 0.518990 | − | 0.854781i | \(-0.326308\pi\) | ||||
0.518990 | + | 0.854781i | \(0.326308\pi\) | |||||||
\(422\) | 0.411393 | 0.0200263 | ||||||||
\(423\) | 4.27730 | 0.207970 | ||||||||
\(424\) | −16.2258 | −0.787993 | ||||||||
\(425\) | 4.12008 | 0.199853 | ||||||||
\(426\) | −4.96608 | −0.240607 | ||||||||
\(427\) | 51.3082 | 2.48298 | ||||||||
\(428\) | −15.2212 | −0.735743 | ||||||||
\(429\) | −3.99842 | −0.193046 | ||||||||
\(430\) | 0.424121 | 0.0204529 | ||||||||
\(431\) | −21.0438 | −1.01364 | −0.506822 | − | 0.862051i | \(-0.669180\pi\) | ||||
−0.506822 | + | 0.862051i | \(0.669180\pi\) | |||||||
\(432\) | 2.19756 | 0.105730 | ||||||||
\(433\) | 3.07000 | 0.147535 | 0.0737675 | − | 0.997275i | \(-0.476498\pi\) | ||||
0.0737675 | + | 0.997275i | \(0.476498\pi\) | |||||||
\(434\) | 10.9997 | 0.528003 | ||||||||
\(435\) | 1.59433 | 0.0764422 | ||||||||
\(436\) | 27.0327 | 1.29463 | ||||||||
\(437\) | −2.69708 | −0.129019 | ||||||||
\(438\) | 1.20476 | 0.0575657 | ||||||||
\(439\) | 22.8075 | 1.08854 | 0.544271 | − | 0.838909i | \(-0.316806\pi\) | ||||
0.544271 | + | 0.838909i | \(0.316806\pi\) | |||||||
\(440\) | 2.03905 | 0.0972080 | ||||||||
\(441\) | 17.5361 | 0.835053 | ||||||||
\(442\) | 6.12096 | 0.291144 | ||||||||
\(443\) | 1.82887 | 0.0868922 | 0.0434461 | − | 0.999056i | \(-0.486166\pi\) | ||||
0.0434461 | + | 0.999056i | \(0.486166\pi\) | |||||||
\(444\) | −9.79360 | −0.464784 | ||||||||
\(445\) | 10.0513 | 0.476476 | ||||||||
\(446\) | 0.559128 | 0.0264755 | ||||||||
\(447\) | −6.73460 | −0.318536 | ||||||||
\(448\) | −6.74608 | −0.318722 | ||||||||
\(449\) | 32.1557 | 1.51752 | 0.758760 | − | 0.651371i | \(-0.225806\pi\) | ||||
0.758760 | + | 0.651371i | \(0.225806\pi\) | |||||||
\(450\) | 1.38437 | 0.0652598 | ||||||||
\(451\) | 3.70604 | 0.174510 | ||||||||
\(452\) | −30.9466 | −1.45561 | ||||||||
\(453\) | 4.73376 | 0.222411 | ||||||||
\(454\) | 3.83297 | 0.179890 | ||||||||
\(455\) | −51.2093 | −2.40073 | ||||||||
\(456\) | 5.59402 | 0.261964 | ||||||||
\(457\) | −17.6731 | −0.826714 | −0.413357 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413357 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(458\) | −9.34528 | −0.436676 | ||||||||
\(459\) | −1.67611 | −0.0782341 | ||||||||
\(460\) | −2.68298 | −0.125094 | ||||||||
\(461\) | 35.1978 | 1.63932 | 0.819662 | − | 0.572848i | \(-0.194161\pi\) | ||||
0.819662 | + | 0.572848i | \(0.194161\pi\) | |||||||
\(462\) | 1.72017 | 0.0800297 | ||||||||
\(463\) | −9.53381 | −0.443074 | −0.221537 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221537 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(464\) | −2.19756 | −0.102019 | ||||||||
\(465\) | 6.28648 | 0.291528 | ||||||||
\(466\) | −14.5793 | −0.675375 | ||||||||
\(467\) | −20.9801 | −0.970841 | −0.485421 | − | 0.874281i | \(-0.661333\pi\) | ||||
−0.485421 | + | 0.874281i | \(0.661333\pi\) | |||||||
\(468\) | −10.9121 | −0.504411 | ||||||||
\(469\) | −31.5207 | −1.45549 | ||||||||
\(470\) | 3.84058 | 0.177153 | ||||||||
\(471\) | 21.3212 | 0.982431 | ||||||||
\(472\) | 24.1884 | 1.11336 | ||||||||
\(473\) | −0.291262 | −0.0133922 | ||||||||
\(474\) | 6.75545 | 0.310288 | ||||||||
\(475\) | −6.62974 | −0.304194 | ||||||||
\(476\) | 13.9716 | 0.640385 | ||||||||
\(477\) | −7.82304 | −0.358192 | ||||||||
\(478\) | −3.48577 | −0.159435 | ||||||||
\(479\) | −29.5362 | −1.34954 | −0.674772 | − | 0.738027i | \(-0.735758\pi\) | ||||
−0.674772 | + | 0.738027i | \(0.735758\pi\) | |||||||
\(480\) | 8.58677 | 0.391931 | ||||||||
\(481\) | 37.7374 | 1.72068 | ||||||||
\(482\) | −11.6169 | −0.529136 | ||||||||
\(483\) | −4.95339 | −0.225387 | ||||||||
\(484\) | 17.8712 | 0.812329 | ||||||||
\(485\) | −18.9901 | −0.862295 | ||||||||
\(486\) | −0.563182 | −0.0255465 | ||||||||
\(487\) | −4.69157 | −0.212595 | −0.106298 | − | 0.994334i | \(-0.533900\pi\) | ||||
−0.106298 | + | 0.994334i | \(0.533900\pi\) | |||||||
\(488\) | 21.4839 | 0.972532 | ||||||||
\(489\) | 4.09507 | 0.185185 | ||||||||
\(490\) | 15.7456 | 0.711315 | ||||||||
\(491\) | −17.4315 | −0.786674 | −0.393337 | − | 0.919394i | \(-0.628679\pi\) | ||||
−0.393337 | + | 0.919394i | \(0.628679\pi\) | |||||||
\(492\) | 10.1141 | 0.455980 | ||||||||
\(493\) | 1.67611 | 0.0754882 | ||||||||
\(494\) | −9.84942 | −0.443147 | ||||||||
\(495\) | 0.983101 | 0.0441871 | ||||||||
\(496\) | −8.66502 | −0.389071 | ||||||||
\(497\) | 43.6785 | 1.95925 | ||||||||
\(498\) | −5.75156 | −0.257734 | ||||||||
\(499\) | 9.04617 | 0.404962 | 0.202481 | − | 0.979286i | \(-0.435100\pi\) | ||||
0.202481 | + | 0.979286i | \(0.435100\pi\) | |||||||
\(500\) | −20.0100 | −0.894872 | ||||||||
\(501\) | −10.3928 | −0.464315 | ||||||||
\(502\) | 9.10145 | 0.406217 | ||||||||
\(503\) | 25.7136 | 1.14651 | 0.573255 | − | 0.819377i | \(-0.305680\pi\) | ||||
0.573255 | + | 0.819377i | \(0.305680\pi\) | |||||||
\(504\) | 10.2738 | 0.457633 | ||||||||
\(505\) | −7.32889 | −0.326131 | ||||||||
\(506\) | −0.347272 | −0.0154381 | ||||||||
\(507\) | 29.0471 | 1.29003 | ||||||||
\(508\) | −7.30456 | −0.324088 | ||||||||
\(509\) | −10.4056 | −0.461220 | −0.230610 | − | 0.973046i | \(-0.574072\pi\) | ||||
−0.230610 | + | 0.973046i | \(0.574072\pi\) | |||||||
\(510\) | −1.50497 | −0.0666413 | ||||||||
\(511\) | −10.5963 | −0.468753 | ||||||||
\(512\) | −20.9516 | −0.925937 | ||||||||
\(513\) | 2.69708 | 0.119079 | ||||||||
\(514\) | 4.34294 | 0.191559 | ||||||||
\(515\) | −7.30349 | −0.321830 | ||||||||
\(516\) | −0.794882 | −0.0349927 | ||||||||
\(517\) | −2.63749 | −0.115997 | ||||||||
\(518\) | −16.2351 | −0.713329 | ||||||||
\(519\) | −4.60624 | −0.202191 | ||||||||
\(520\) | −21.4425 | −0.940317 | ||||||||
\(521\) | −44.3130 | −1.94139 | −0.970693 | − | 0.240323i | \(-0.922747\pi\) | ||||
−0.970693 | + | 0.240323i | \(0.922747\pi\) | |||||||
\(522\) | 0.563182 | 0.0246498 | ||||||||
\(523\) | 2.54821 | 0.111425 | 0.0557127 | − | 0.998447i | \(-0.482257\pi\) | ||||
0.0557127 | + | 0.998447i | \(0.482257\pi\) | |||||||
\(524\) | −23.9518 | −1.04634 | ||||||||
\(525\) | −12.1760 | −0.531406 | ||||||||
\(526\) | 2.06382 | 0.0899869 | ||||||||
\(527\) | 6.60894 | 0.287890 | ||||||||
\(528\) | −1.35507 | −0.0589717 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −7.02428 | −0.305115 | ||||||||
\(531\) | 11.6621 | 0.506092 | ||||||||
\(532\) | −22.4821 | −0.974721 | ||||||||
\(533\) | −38.9724 | −1.68808 | ||||||||
\(534\) | 3.55052 | 0.153646 | ||||||||
\(535\) | −14.4207 | −0.623461 | ||||||||
\(536\) | −13.1984 | −0.570086 | ||||||||
\(537\) | −25.3247 | −1.09284 | ||||||||
\(538\) | −10.4656 | −0.451203 | ||||||||
\(539\) | −10.8132 | −0.465757 | ||||||||
\(540\) | 2.68298 | 0.115457 | ||||||||
\(541\) | −9.57940 | −0.411851 | −0.205925 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205925 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(542\) | 6.60408 | 0.283670 | ||||||||
\(543\) | −22.1243 | −0.949447 | ||||||||
\(544\) | 9.02724 | 0.387040 | ||||||||
\(545\) | 25.6111 | 1.09706 | ||||||||
\(546\) | −18.0892 | −0.774147 | ||||||||
\(547\) | 7.62918 | 0.326200 | 0.163100 | − | 0.986610i | \(-0.447851\pi\) | ||||
0.163100 | + | 0.986610i | \(0.447851\pi\) | |||||||
\(548\) | −17.6480 | −0.753887 | ||||||||
\(549\) | 10.3582 | 0.442077 | ||||||||
\(550\) | −0.853635 | −0.0363991 | ||||||||
\(551\) | −2.69708 | −0.114899 | ||||||||
\(552\) | −2.07410 | −0.0882796 | ||||||||
\(553\) | −59.4167 | −2.52665 | ||||||||
\(554\) | 14.3944 | 0.611559 | ||||||||
\(555\) | −9.27857 | −0.393853 | ||||||||
\(556\) | 32.9804 | 1.39868 | ||||||||
\(557\) | −29.7588 | −1.26092 | −0.630460 | − | 0.776222i | \(-0.717134\pi\) | ||||
−0.630460 | + | 0.776222i | \(0.717134\pi\) | |||||||
\(558\) | 2.22064 | 0.0940073 | ||||||||
\(559\) | 3.06289 | 0.129546 | ||||||||
\(560\) | −17.3548 | −0.733375 | ||||||||
\(561\) | 1.03353 | 0.0436357 | ||||||||
\(562\) | 4.25907 | 0.179658 | ||||||||
\(563\) | 35.5508 | 1.49829 | 0.749145 | − | 0.662407i | \(-0.230465\pi\) | ||||
0.749145 | + | 0.662407i | \(0.230465\pi\) | |||||||
\(564\) | −7.19796 | −0.303089 | ||||||||
\(565\) | −29.3192 | −1.23347 | ||||||||
\(566\) | −8.83923 | −0.371540 | ||||||||
\(567\) | 4.95339 | 0.208023 | ||||||||
\(568\) | 18.2892 | 0.767398 | ||||||||
\(569\) | −16.4596 | −0.690023 | −0.345011 | − | 0.938599i | \(-0.612125\pi\) | ||||
−0.345011 | + | 0.938599i | \(0.612125\pi\) | |||||||
\(570\) | 2.42170 | 0.101434 | ||||||||
\(571\) | −32.1451 | −1.34523 | −0.672616 | − | 0.739992i | \(-0.734829\pi\) | ||||
−0.672616 | + | 0.739992i | \(0.734829\pi\) | |||||||
\(572\) | 6.72865 | 0.281339 | ||||||||
\(573\) | −20.9666 | −0.875893 | ||||||||
\(574\) | 16.7664 | 0.699818 | ||||||||
\(575\) | 2.45812 | 0.102511 | ||||||||
\(576\) | −1.36191 | −0.0567463 | ||||||||
\(577\) | −22.2212 | −0.925080 | −0.462540 | − | 0.886598i | \(-0.653062\pi\) | ||||
−0.462540 | + | 0.886598i | \(0.653062\pi\) | |||||||
\(578\) | 7.99192 | 0.332420 | ||||||||
\(579\) | 20.7423 | 0.862019 | ||||||||
\(580\) | −2.68298 | −0.111405 | ||||||||
\(581\) | 50.5871 | 2.09871 | ||||||||
\(582\) | −6.70807 | −0.278059 | ||||||||
\(583\) | 4.82387 | 0.199784 | ||||||||
\(584\) | −4.43692 | −0.183601 | ||||||||
\(585\) | −10.3382 | −0.427433 | ||||||||
\(586\) | −15.4479 | −0.638146 | ||||||||
\(587\) | 8.38053 | 0.345902 | 0.172951 | − | 0.984930i | \(-0.444670\pi\) | ||||
0.172951 | + | 0.984930i | \(0.444670\pi\) | |||||||
\(588\) | −29.5102 | −1.21698 | ||||||||
\(589\) | −10.6347 | −0.438193 | ||||||||
\(590\) | 10.4714 | 0.431099 | ||||||||
\(591\) | −22.2579 | −0.915569 | ||||||||
\(592\) | 12.7892 | 0.525633 | ||||||||
\(593\) | 41.5343 | 1.70561 | 0.852805 | − | 0.522230i | \(-0.174900\pi\) | ||||
0.852805 | + | 0.522230i | \(0.174900\pi\) | |||||||
\(594\) | 0.347272 | 0.0142487 | ||||||||
\(595\) | 13.2368 | 0.542656 | ||||||||
\(596\) | 11.3332 | 0.464224 | ||||||||
\(597\) | 0.316336 | 0.0129468 | ||||||||
\(598\) | 3.65188 | 0.149337 | ||||||||
\(599\) | −41.6783 | −1.70293 | −0.851465 | − | 0.524412i | \(-0.824285\pi\) | ||||
−0.851465 | + | 0.524412i | \(0.824285\pi\) | |||||||
\(600\) | −5.09839 | −0.208141 | ||||||||
\(601\) | −15.7600 | −0.642862 | −0.321431 | − | 0.946933i | \(-0.604164\pi\) | ||||
−0.321431 | + | 0.946933i | \(0.604164\pi\) | |||||||
\(602\) | −1.31770 | −0.0537052 | ||||||||
\(603\) | −6.36345 | −0.259140 | ||||||||
\(604\) | −7.96609 | −0.324136 | ||||||||
\(605\) | 16.9314 | 0.688359 | ||||||||
\(606\) | −2.58887 | −0.105165 | ||||||||
\(607\) | −28.2457 | −1.14646 | −0.573229 | − | 0.819395i | \(-0.694309\pi\) | ||||
−0.573229 | + | 0.819395i | \(0.694309\pi\) | |||||||
\(608\) | −14.5260 | −0.589107 | ||||||||
\(609\) | −4.95339 | −0.200722 | ||||||||
\(610\) | 9.30058 | 0.376570 | ||||||||
\(611\) | 27.7356 | 1.12206 | ||||||||
\(612\) | 2.82060 | 0.114016 | ||||||||
\(613\) | 37.9241 | 1.53174 | 0.765870 | − | 0.642996i | \(-0.222309\pi\) | ||||
0.765870 | + | 0.642996i | \(0.222309\pi\) | |||||||
\(614\) | −7.27613 | −0.293641 | ||||||||
\(615\) | 9.58223 | 0.386393 | ||||||||
\(616\) | −6.33510 | −0.255249 | ||||||||
\(617\) | 12.9445 | 0.521128 | 0.260564 | − | 0.965457i | \(-0.416092\pi\) | ||||
0.260564 | + | 0.965457i | \(0.416092\pi\) | |||||||
\(618\) | −2.57989 | −0.103779 | ||||||||
\(619\) | −44.2979 | −1.78048 | −0.890242 | − | 0.455487i | \(-0.849465\pi\) | ||||
−0.890242 | + | 0.455487i | \(0.849465\pi\) | |||||||
\(620\) | −10.5790 | −0.424865 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 2.12848 | 0.0853443 | ||||||||
\(623\) | −31.2281 | −1.25113 | ||||||||
\(624\) | 14.2498 | 0.570448 | ||||||||
\(625\) | −6.66705 | −0.266682 | ||||||||
\(626\) | −2.45161 | −0.0979859 | ||||||||
\(627\) | −1.66308 | −0.0664172 | ||||||||
\(628\) | −35.8800 | −1.43177 | ||||||||
\(629\) | −9.75452 | −0.388938 | ||||||||
\(630\) | 4.44764 | 0.177198 | ||||||||
\(631\) | 1.21447 | 0.0483474 | 0.0241737 | − | 0.999708i | \(-0.492305\pi\) | ||||
0.0241737 | + | 0.999708i | \(0.492305\pi\) | |||||||
\(632\) | −24.8791 | −0.989639 | ||||||||
\(633\) | −0.730479 | −0.0290340 | ||||||||
\(634\) | −0.279875 | −0.0111152 | ||||||||
\(635\) | −6.92042 | −0.274629 | ||||||||
\(636\) | 13.1648 | 0.522019 | ||||||||
\(637\) | 113.711 | 4.50539 | ||||||||
\(638\) | −0.347272 | −0.0137486 | ||||||||
\(639\) | 8.81789 | 0.348830 | ||||||||
\(640\) | −18.3964 | −0.727182 | ||||||||
\(641\) | −41.6001 | −1.64310 | −0.821552 | − | 0.570134i | \(-0.806891\pi\) | ||||
−0.821552 | + | 0.570134i | \(0.806891\pi\) | |||||||
\(642\) | −5.09398 | −0.201043 | ||||||||
\(643\) | −33.3387 | −1.31475 | −0.657374 | − | 0.753564i | \(-0.728333\pi\) | ||||
−0.657374 | + | 0.753564i | \(0.728333\pi\) | |||||||
\(644\) | 8.33570 | 0.328473 | ||||||||
\(645\) | −0.753079 | −0.0296525 | ||||||||
\(646\) | 2.54592 | 0.100168 | ||||||||
\(647\) | −16.2174 | −0.637570 | −0.318785 | − | 0.947827i | \(-0.603275\pi\) | ||||
−0.318785 | + | 0.947827i | \(0.603275\pi\) | |||||||
\(648\) | 2.07410 | 0.0814784 | ||||||||
\(649\) | −7.19113 | −0.282276 | ||||||||
\(650\) | 8.97677 | 0.352098 | ||||||||
\(651\) | −19.5314 | −0.765495 | ||||||||
\(652\) | −6.89128 | −0.269883 | ||||||||
\(653\) | −19.3624 | −0.757708 | −0.378854 | − | 0.925456i | \(-0.623682\pi\) | ||||
−0.378854 | + | 0.925456i | \(0.623682\pi\) | |||||||
\(654\) | 9.04688 | 0.353761 | ||||||||
\(655\) | −22.6922 | −0.886659 | ||||||||
\(656\) | −13.2078 | −0.515676 | ||||||||
\(657\) | −2.13920 | −0.0834583 | ||||||||
\(658\) | −11.9322 | −0.465167 | ||||||||
\(659\) | −29.7211 | −1.15777 | −0.578885 | − | 0.815409i | \(-0.696512\pi\) | ||||
−0.578885 | + | 0.815409i | \(0.696512\pi\) | |||||||
\(660\) | −1.65439 | −0.0643970 | ||||||||
\(661\) | 16.5459 | 0.643562 | 0.321781 | − | 0.946814i | \(-0.395719\pi\) | ||||
0.321781 | + | 0.946814i | \(0.395719\pi\) | |||||||
\(662\) | 3.18065 | 0.123619 | ||||||||
\(663\) | −10.8685 | −0.422099 | ||||||||
\(664\) | 21.1820 | 0.822021 | ||||||||
\(665\) | −21.2997 | −0.825969 | ||||||||
\(666\) | −3.27757 | −0.127003 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 17.4892 | 0.676679 | ||||||||
\(669\) | −0.992801 | −0.0383839 | ||||||||
\(670\) | −5.71372 | −0.220740 | ||||||||
\(671\) | −6.38711 | −0.246572 | ||||||||
\(672\) | −26.6781 | −1.02913 | ||||||||
\(673\) | −34.0750 | −1.31349 | −0.656746 | − | 0.754112i | \(-0.728068\pi\) | ||||
−0.656746 | + | 0.754112i | \(0.728068\pi\) | |||||||
\(674\) | 4.20425 | 0.161942 | ||||||||
\(675\) | −2.45812 | −0.0946131 | ||||||||
\(676\) | −48.8813 | −1.88005 | ||||||||
\(677\) | −20.9027 | −0.803357 | −0.401678 | − | 0.915781i | \(-0.631573\pi\) | ||||
−0.401678 | + | 0.915781i | \(0.631573\pi\) | |||||||
\(678\) | −10.3567 | −0.397748 | ||||||||
\(679\) | 59.0000 | 2.26421 | ||||||||
\(680\) | 5.54255 | 0.212547 | ||||||||
\(681\) | −6.80592 | −0.260803 | ||||||||
\(682\) | −1.36930 | −0.0524333 | ||||||||
\(683\) | 47.7573 | 1.82738 | 0.913692 | − | 0.406408i | \(-0.133219\pi\) | ||||
0.913692 | + | 0.406408i | \(0.133219\pi\) | |||||||
\(684\) | −4.53872 | −0.173542 | ||||||||
\(685\) | −16.7199 | −0.638836 | ||||||||
\(686\) | −29.3922 | −1.12220 | ||||||||
\(687\) | 16.5937 | 0.633090 | ||||||||
\(688\) | 1.03801 | 0.0395739 | ||||||||
\(689\) | −50.7275 | −1.93256 | ||||||||
\(690\) | −0.897897 | −0.0341823 | ||||||||
\(691\) | −0.154264 | −0.00586849 | −0.00293424 | − | 0.999996i | \(-0.500934\pi\) | ||||
−0.00293424 | + | 0.999996i | \(0.500934\pi\) | |||||||
\(692\) | 7.75150 | 0.294668 | ||||||||
\(693\) | −3.05438 | −0.116026 | ||||||||
\(694\) | −7.99327 | −0.303420 | ||||||||
\(695\) | 31.2460 | 1.18523 | ||||||||
\(696\) | −2.07410 | −0.0786186 | ||||||||
\(697\) | 10.0738 | 0.381571 | ||||||||
\(698\) | 10.3470 | 0.391641 | ||||||||
\(699\) | 25.8874 | 0.979153 | ||||||||
\(700\) | 20.4901 | 0.774455 | ||||||||
\(701\) | −30.8317 | −1.16450 | −0.582248 | − | 0.813011i | \(-0.697827\pi\) | ||||
−0.582248 | + | 0.813011i | \(0.697827\pi\) | |||||||
\(702\) | −3.65188 | −0.137831 | ||||||||
\(703\) | 15.6963 | 0.591997 | ||||||||
\(704\) | 0.839787 | 0.0316507 | ||||||||
\(705\) | −6.81942 | −0.256834 | ||||||||
\(706\) | 16.6117 | 0.625191 | ||||||||
\(707\) | 22.7700 | 0.856355 | ||||||||
\(708\) | −19.6253 | −0.737563 | ||||||||
\(709\) | −3.56458 | −0.133871 | −0.0669353 | − | 0.997757i | \(-0.521322\pi\) | ||||
−0.0669353 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(710\) | 7.91756 | 0.297141 | ||||||||
\(711\) | −11.9951 | −0.449853 | ||||||||
\(712\) | −13.0759 | −0.490042 | ||||||||
\(713\) | 3.94303 | 0.147667 | ||||||||
\(714\) | 4.67578 | 0.174987 | ||||||||
\(715\) | 6.37480 | 0.238404 | ||||||||
\(716\) | 42.6171 | 1.59268 | ||||||||
\(717\) | 6.18941 | 0.231148 | ||||||||
\(718\) | −0.818713 | −0.0305541 | ||||||||
\(719\) | 20.9959 | 0.783016 | 0.391508 | − | 0.920175i | \(-0.371954\pi\) | ||||
0.391508 | + | 0.920175i | \(0.371954\pi\) | |||||||
\(720\) | −3.50362 | −0.130572 | ||||||||
\(721\) | 22.6911 | 0.845062 | ||||||||
\(722\) | 6.60374 | 0.245766 | ||||||||
\(723\) | 20.6273 | 0.767137 | ||||||||
\(724\) | 37.2314 | 1.38370 | ||||||||
\(725\) | 2.45812 | 0.0912923 | ||||||||
\(726\) | 5.98087 | 0.221971 | ||||||||
\(727\) | 19.3196 | 0.716524 | 0.358262 | − | 0.933621i | \(-0.383369\pi\) | ||||
0.358262 | + | 0.933621i | \(0.383369\pi\) | |||||||
\(728\) | 66.6195 | 2.46908 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.92078 | −0.0710914 | ||||||||
\(731\) | −0.791709 | −0.0292824 | ||||||||
\(732\) | −17.4310 | −0.644269 | ||||||||
\(733\) | 0.320498 | 0.0118379 | 0.00591893 | − | 0.999982i | \(-0.498116\pi\) | ||||
0.00591893 | + | 0.999982i | \(0.498116\pi\) | |||||||
\(734\) | 5.71807 | 0.211058 | ||||||||
\(735\) | −27.9583 | −1.03126 | ||||||||
\(736\) | 5.38583 | 0.198524 | ||||||||
\(737\) | 3.92386 | 0.144537 | ||||||||
\(738\) | 3.38484 | 0.124598 | ||||||||
\(739\) | −29.9692 | −1.10243 | −0.551217 | − | 0.834362i | \(-0.685837\pi\) | ||||
−0.551217 | + | 0.834362i | \(0.685837\pi\) | |||||||
\(740\) | 15.6142 | 0.573990 | ||||||||
\(741\) | 17.4889 | 0.642470 | ||||||||
\(742\) | 21.8236 | 0.801171 | ||||||||
\(743\) | 14.3052 | 0.524808 | 0.262404 | − | 0.964958i | \(-0.415485\pi\) | ||||
0.262404 | + | 0.964958i | \(0.415485\pi\) | |||||||
\(744\) | −8.17824 | −0.299829 | ||||||||
\(745\) | 10.7372 | 0.393379 | ||||||||
\(746\) | −5.68214 | −0.208038 | ||||||||
\(747\) | 10.2126 | 0.373660 | ||||||||
\(748\) | −1.73925 | −0.0635933 | ||||||||
\(749\) | 44.8035 | 1.63708 | ||||||||
\(750\) | −6.69662 | −0.244526 | ||||||||
\(751\) | 40.9102 | 1.49283 | 0.746417 | − | 0.665479i | \(-0.231773\pi\) | ||||
0.746417 | + | 0.665479i | \(0.231773\pi\) | |||||||
\(752\) | 9.39961 | 0.342769 | ||||||||
\(753\) | −16.1608 | −0.588931 | ||||||||
\(754\) | 3.65188 | 0.132994 | ||||||||
\(755\) | −7.54716 | −0.274669 | ||||||||
\(756\) | −8.33570 | −0.303167 | ||||||||
\(757\) | −6.22635 | −0.226300 | −0.113150 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113150 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(758\) | 8.19331 | 0.297594 | ||||||||
\(759\) | 0.616624 | 0.0223820 | ||||||||
\(760\) | −8.91870 | −0.323515 | ||||||||
\(761\) | −13.1589 | −0.477011 | −0.238505 | − | 0.971141i | \(-0.576657\pi\) | ||||
−0.238505 | + | 0.971141i | \(0.576657\pi\) | |||||||
\(762\) | −2.44458 | −0.0885577 | ||||||||
\(763\) | −79.5707 | −2.88065 | ||||||||
\(764\) | 35.2832 | 1.27650 | ||||||||
\(765\) | 2.67227 | 0.0966161 | ||||||||
\(766\) | −8.29889 | −0.299851 | ||||||||
\(767\) | 75.6214 | 2.73053 | ||||||||
\(768\) | −3.77454 | −0.136202 | ||||||||
\(769\) | 15.8580 | 0.571854 | 0.285927 | − | 0.958251i | \(-0.407698\pi\) | ||||
0.285927 | + | 0.958251i | \(0.407698\pi\) | |||||||
\(770\) | −2.74252 | −0.0988336 | ||||||||
\(771\) | −7.71144 | −0.277721 | ||||||||
\(772\) | −34.9056 | −1.25628 | ||||||||
\(773\) | 25.0338 | 0.900402 | 0.450201 | − | 0.892927i | \(-0.351352\pi\) | ||||
0.450201 | + | 0.892927i | \(0.351352\pi\) | |||||||
\(774\) | −0.266019 | −0.00956184 | ||||||||
\(775\) | 9.69243 | 0.348162 | ||||||||
\(776\) | 24.7047 | 0.886846 | ||||||||
\(777\) | 28.8275 | 1.03418 | ||||||||
\(778\) | 3.09017 | 0.110788 | ||||||||
\(779\) | −16.2100 | −0.580783 | ||||||||
\(780\) | 17.3974 | 0.622928 | ||||||||
\(781\) | −5.43733 | −0.194563 | ||||||||
\(782\) | −0.943955 | −0.0337558 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 38.5366 | 1.37631 | ||||||||
\(785\) | −33.9931 | −1.21326 | ||||||||
\(786\) | −8.01583 | −0.285915 | ||||||||
\(787\) | −22.1812 | −0.790674 | −0.395337 | − | 0.918536i | \(-0.629372\pi\) | ||||
−0.395337 | + | 0.918536i | \(0.629372\pi\) | |||||||
\(788\) | 37.4562 | 1.33432 | ||||||||
\(789\) | −3.66457 | −0.130462 | ||||||||
\(790\) | −10.7704 | −0.383194 | ||||||||
\(791\) | 91.0914 | 3.23884 | ||||||||
\(792\) | −1.27894 | −0.0454452 | ||||||||
\(793\) | 67.1664 | 2.38515 | ||||||||
\(794\) | 4.98672 | 0.176972 | ||||||||
\(795\) | 12.4725 | 0.442353 | ||||||||
\(796\) | −0.532338 | −0.0188682 | ||||||||
\(797\) | −30.2552 | −1.07169 | −0.535846 | − | 0.844315i | \(-0.680007\pi\) | ||||
−0.535846 | + | 0.844315i | \(0.680007\pi\) | |||||||
\(798\) | −7.52394 | −0.266345 | ||||||||
\(799\) | −7.16923 | −0.253629 | ||||||||
\(800\) | 13.2390 | 0.468069 | ||||||||
\(801\) | −6.30439 | −0.222755 | ||||||||
\(802\) | 1.09202 | 0.0385605 | ||||||||
\(803\) | 1.31908 | 0.0465495 | ||||||||
\(804\) | 10.7086 | 0.377663 | ||||||||
\(805\) | 7.89733 | 0.278344 | ||||||||
\(806\) | 14.3995 | 0.507200 | ||||||||
\(807\) | 18.5829 | 0.654150 | ||||||||
\(808\) | 9.53434 | 0.335417 | ||||||||
\(809\) | −32.5292 | −1.14367 | −0.571833 | − | 0.820370i | \(-0.693767\pi\) | ||||
−0.571833 | + | 0.820370i | \(0.693767\pi\) | |||||||
\(810\) | 0.897897 | 0.0315489 | ||||||||
\(811\) | −17.2748 | −0.606599 | −0.303300 | − | 0.952895i | \(-0.598088\pi\) | ||||
−0.303300 | + | 0.952895i | \(0.598088\pi\) | |||||||
\(812\) | 8.33570 | 0.292526 | ||||||||
\(813\) | −11.7264 | −0.411262 | ||||||||
\(814\) | 2.02103 | 0.0708371 | ||||||||
\(815\) | −6.52888 | −0.228697 | ||||||||
\(816\) | −3.68334 | −0.128943 | ||||||||
\(817\) | 1.27396 | 0.0445703 | ||||||||
\(818\) | −3.74393 | −0.130903 | ||||||||
\(819\) | 32.1197 | 1.12235 | ||||||||
\(820\) | −16.1252 | −0.563117 | ||||||||
\(821\) | 11.3961 | 0.397728 | 0.198864 | − | 0.980027i | \(-0.436275\pi\) | ||||
0.198864 | + | 0.980027i | \(0.436275\pi\) | |||||||
\(822\) | −5.90617 | −0.206001 | ||||||||
\(823\) | 16.8758 | 0.588255 | 0.294128 | − | 0.955766i | \(-0.404971\pi\) | ||||
0.294128 | + | 0.955766i | \(0.404971\pi\) | |||||||
\(824\) | 9.50130 | 0.330993 | ||||||||
\(825\) | 1.51574 | 0.0527712 | ||||||||
\(826\) | −32.5333 | −1.13198 | ||||||||
\(827\) | −45.9867 | −1.59911 | −0.799557 | − | 0.600590i | \(-0.794932\pi\) | ||||
−0.799557 | + | 0.600590i | \(0.794932\pi\) | |||||||
\(828\) | 1.68283 | 0.0584822 | ||||||||
\(829\) | −53.2178 | −1.84833 | −0.924165 | − | 0.381995i | \(-0.875237\pi\) | ||||
−0.924165 | + | 0.381995i | \(0.875237\pi\) | |||||||
\(830\) | 9.16987 | 0.318291 | ||||||||
\(831\) | −25.5590 | −0.886633 | ||||||||
\(832\) | −8.83114 | −0.306165 | ||||||||
\(833\) | −29.3925 | −1.01839 | ||||||||
\(834\) | 11.0374 | 0.382193 | ||||||||
\(835\) | 16.5695 | 0.573411 | ||||||||
\(836\) | 2.79868 | 0.0967945 | ||||||||
\(837\) | −3.94303 | −0.136291 | ||||||||
\(838\) | −0.451839 | −0.0156085 | ||||||||
\(839\) | 13.5867 | 0.469064 | 0.234532 | − | 0.972108i | \(-0.424644\pi\) | ||||
0.234532 | + | 0.972108i | \(0.424644\pi\) | |||||||
\(840\) | −16.3799 | −0.565159 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −11.9944 | −0.413354 | ||||||||
\(843\) | −7.56252 | −0.260467 | ||||||||
\(844\) | 1.22927 | 0.0423132 | ||||||||
\(845\) | −46.3107 | −1.59314 | ||||||||
\(846\) | −2.40890 | −0.0828197 | ||||||||
\(847\) | −52.6039 | −1.80749 | ||||||||
\(848\) | −17.1916 | −0.590361 | ||||||||
\(849\) | 15.6951 | 0.538656 | ||||||||
\(850\) | −2.32035 | −0.0795875 | ||||||||
\(851\) | −5.81974 | −0.199498 | ||||||||
\(852\) | −14.8390 | −0.508375 | ||||||||
\(853\) | −6.73050 | −0.230448 | −0.115224 | − | 0.993340i | \(-0.536759\pi\) | ||||
−0.115224 | + | 0.993340i | \(0.536759\pi\) | |||||||
\(854\) | −28.8959 | −0.988796 | ||||||||
\(855\) | −4.30003 | −0.147058 | ||||||||
\(856\) | 18.7603 | 0.641212 | ||||||||
\(857\) | 35.0261 | 1.19647 | 0.598234 | − | 0.801321i | \(-0.295869\pi\) | ||||
0.598234 | + | 0.801321i | \(0.295869\pi\) | |||||||
\(858\) | 2.25184 | 0.0768766 | ||||||||
\(859\) | 1.65393 | 0.0564314 | 0.0282157 | − | 0.999602i | \(-0.491017\pi\) | ||||
0.0282157 | + | 0.999602i | \(0.491017\pi\) | |||||||
\(860\) | 1.26730 | 0.0432146 | ||||||||
\(861\) | −29.7709 | −1.01459 | ||||||||
\(862\) | 11.8515 | 0.403663 | ||||||||
\(863\) | 31.4926 | 1.07202 | 0.536010 | − | 0.844212i | \(-0.319931\pi\) | ||||
0.536010 | + | 0.844212i | \(0.319931\pi\) | |||||||
\(864\) | −5.38583 | −0.183230 | ||||||||
\(865\) | 7.34385 | 0.249698 | ||||||||
\(866\) | −1.72897 | −0.0587528 | ||||||||
\(867\) | −14.1907 | −0.481940 | ||||||||
\(868\) | 32.8679 | 1.11561 | ||||||||
\(869\) | 7.39650 | 0.250909 | ||||||||
\(870\) | −0.897897 | −0.0304415 | ||||||||
\(871\) | −41.2630 | −1.39814 | ||||||||
\(872\) | −33.3181 | −1.12829 | ||||||||
\(873\) | 11.9110 | 0.403127 | ||||||||
\(874\) | 1.51895 | 0.0513791 | ||||||||
\(875\) | 58.8993 | 1.99116 | ||||||||
\(876\) | 3.59991 | 0.121630 | ||||||||
\(877\) | 42.2692 | 1.42733 | 0.713665 | − | 0.700487i | \(-0.247034\pi\) | ||||
0.713665 | + | 0.700487i | \(0.247034\pi\) | |||||||
\(878\) | −12.8448 | −0.433490 | ||||||||
\(879\) | 27.4297 | 0.925179 | ||||||||
\(880\) | 2.16042 | 0.0728277 | ||||||||
\(881\) | −32.5253 | −1.09581 | −0.547903 | − | 0.836542i | \(-0.684574\pi\) | ||||
−0.547903 | + | 0.836542i | \(0.684574\pi\) | |||||||
\(882\) | −9.87603 | −0.332543 | ||||||||
\(883\) | −20.9256 | −0.704202 | −0.352101 | − | 0.935962i | \(-0.614533\pi\) | ||||
−0.352101 | + | 0.935962i | \(0.614533\pi\) | |||||||
\(884\) | 18.2898 | 0.615154 | ||||||||
\(885\) | −18.5932 | −0.625003 | ||||||||
\(886\) | −1.02999 | −0.0346031 | ||||||||
\(887\) | 3.39320 | 0.113933 | 0.0569663 | − | 0.998376i | \(-0.481857\pi\) | ||||
0.0569663 | + | 0.998376i | \(0.481857\pi\) | |||||||
\(888\) | 12.0707 | 0.405067 | ||||||||
\(889\) | 21.5010 | 0.721119 | ||||||||
\(890\) | −5.66069 | −0.189747 | ||||||||
\(891\) | −0.616624 | −0.0206577 | ||||||||
\(892\) | 1.67071 | 0.0559395 | ||||||||
\(893\) | 11.5362 | 0.386045 | ||||||||
\(894\) | 3.79281 | 0.126850 | ||||||||
\(895\) | 40.3759 | 1.34962 | ||||||||
\(896\) | 57.1555 | 1.90943 | ||||||||
\(897\) | −6.48438 | −0.216507 | ||||||||
\(898\) | −18.1095 | −0.604321 | ||||||||
\(899\) | 3.94303 | 0.131507 | ||||||||
\(900\) | 4.13659 | 0.137886 | ||||||||
\(901\) | 13.1123 | 0.436833 | ||||||||
\(902\) | −2.08717 | −0.0694953 | ||||||||
\(903\) | 2.33973 | 0.0778614 | ||||||||
\(904\) | 38.1421 | 1.26859 | ||||||||
\(905\) | 35.2735 | 1.17253 | ||||||||
\(906\) | −2.66597 | −0.0885708 | ||||||||
\(907\) | 46.3463 | 1.53890 | 0.769452 | − | 0.638704i | \(-0.220529\pi\) | ||||
0.769452 | + | 0.638704i | \(0.220529\pi\) | |||||||
\(908\) | 11.4532 | 0.380087 | ||||||||
\(909\) | 4.59685 | 0.152468 | ||||||||
\(910\) | 28.8402 | 0.956042 | ||||||||
\(911\) | 34.0270 | 1.12737 | 0.563683 | − | 0.825991i | \(-0.309384\pi\) | ||||
0.563683 | + | 0.825991i | \(0.309384\pi\) | |||||||
\(912\) | 5.92698 | 0.196262 | ||||||||
\(913\) | −6.29735 | −0.208412 | ||||||||
\(914\) | 9.95319 | 0.329222 | ||||||||
\(915\) | −16.5143 | −0.545948 | ||||||||
\(916\) | −27.9243 | −0.922646 | ||||||||
\(917\) | 70.5022 | 2.32819 | ||||||||
\(918\) | 0.943955 | 0.0311552 | ||||||||
\(919\) | 8.92150 | 0.294293 | 0.147147 | − | 0.989115i | \(-0.452991\pi\) | ||||
0.147147 | + | 0.989115i | \(0.452991\pi\) | |||||||
\(920\) | 3.30680 | 0.109022 | ||||||||
\(921\) | 12.9197 | 0.425718 | ||||||||
\(922\) | −19.8227 | −0.652827 | ||||||||
\(923\) | 57.1785 | 1.88205 | ||||||||
\(924\) | 5.14000 | 0.169093 | ||||||||
\(925\) | −14.3056 | −0.470365 | ||||||||
\(926\) | 5.36927 | 0.176445 | ||||||||
\(927\) | 4.58092 | 0.150457 | ||||||||
\(928\) | 5.38583 | 0.176798 | ||||||||
\(929\) | −3.51706 | −0.115391 | −0.0576955 | − | 0.998334i | \(-0.518375\pi\) | ||||
−0.0576955 | + | 0.998334i | \(0.518375\pi\) | |||||||
\(930\) | −3.54043 | −0.116095 | ||||||||
\(931\) | 47.2963 | 1.55007 | ||||||||
\(932\) | −43.5641 | −1.42699 | ||||||||
\(933\) | −3.77938 | −0.123731 | ||||||||
\(934\) | 11.8156 | 0.386618 | ||||||||
\(935\) | −1.64779 | −0.0538883 | ||||||||
\(936\) | 13.4493 | 0.439603 | ||||||||
\(937\) | 16.7996 | 0.548819 | 0.274409 | − | 0.961613i | \(-0.411518\pi\) | ||||
0.274409 | + | 0.961613i | \(0.411518\pi\) | |||||||
\(938\) | 17.7519 | 0.579620 | ||||||||
\(939\) | 4.35313 | 0.142059 | ||||||||
\(940\) | 11.4759 | 0.374303 | ||||||||
\(941\) | 2.96990 | 0.0968159 | 0.0484080 | − | 0.998828i | \(-0.484585\pi\) | ||||
0.0484080 | + | 0.998828i | \(0.484585\pi\) | |||||||
\(942\) | −12.0077 | −0.391233 | ||||||||
\(943\) | 6.01020 | 0.195719 | ||||||||
\(944\) | 25.6281 | 0.834123 | ||||||||
\(945\) | −7.89733 | −0.256900 | ||||||||
\(946\) | 0.164034 | 0.00533319 | ||||||||
\(947\) | −25.1490 | −0.817233 | −0.408617 | − | 0.912706i | \(-0.633989\pi\) | ||||
−0.408617 | + | 0.912706i | \(0.633989\pi\) | |||||||
\(948\) | 20.1857 | 0.655602 | ||||||||
\(949\) | −13.8714 | −0.450285 | ||||||||
\(950\) | 3.73375 | 0.121139 | ||||||||
\(951\) | 0.496952 | 0.0161148 | ||||||||
\(952\) | −17.2201 | −0.558106 | ||||||||
\(953\) | −0.976881 | −0.0316443 | −0.0158221 | − | 0.999875i | \(-0.505037\pi\) | ||||
−0.0158221 | + | 0.999875i | \(0.505037\pi\) | |||||||
\(954\) | 4.40579 | 0.142643 | ||||||||
\(955\) | 33.4276 | 1.08169 | ||||||||
\(956\) | −10.4157 | −0.336868 | ||||||||
\(957\) | 0.616624 | 0.0199326 | ||||||||
\(958\) | 16.6343 | 0.537428 | ||||||||
\(959\) | 51.9469 | 1.67745 | ||||||||
\(960\) | 2.17133 | 0.0700794 | ||||||||
\(961\) | −15.4525 | −0.498469 | ||||||||
\(962\) | −21.2530 | −0.685224 | ||||||||
\(963\) | 9.04500 | 0.291471 | ||||||||
\(964\) | −34.7121 | −1.11800 | ||||||||
\(965\) | −33.0700 | −1.06456 | ||||||||
\(966\) | 2.78966 | 0.0897559 | ||||||||
\(967\) | −50.3884 | −1.62038 | −0.810191 | − | 0.586166i | \(-0.800637\pi\) | ||||
−0.810191 | + | 0.586166i | \(0.800637\pi\) | |||||||
\(968\) | −22.0265 | −0.707958 | ||||||||
\(969\) | −4.52060 | −0.145223 | ||||||||
\(970\) | 10.6949 | 0.343391 | ||||||||
\(971\) | 47.9179 | 1.53776 | 0.768879 | − | 0.639394i | \(-0.220815\pi\) | ||||
0.768879 | + | 0.639394i | \(0.220815\pi\) | |||||||
\(972\) | −1.68283 | −0.0539767 | ||||||||
\(973\) | −97.0779 | −3.11217 | ||||||||
\(974\) | 2.64221 | 0.0846617 | ||||||||
\(975\) | −15.9394 | −0.510468 | ||||||||
\(976\) | 22.7627 | 0.728616 | ||||||||
\(977\) | 25.9762 | 0.831053 | 0.415527 | − | 0.909581i | \(-0.363597\pi\) | ||||
0.415527 | + | 0.909581i | \(0.363597\pi\) | |||||||
\(978\) | −2.30627 | −0.0737463 | ||||||||
\(979\) | 3.88744 | 0.124243 | ||||||||
\(980\) | 47.0490 | 1.50293 | ||||||||
\(981\) | −16.0639 | −0.512880 | ||||||||
\(982\) | 9.81712 | 0.313277 | ||||||||
\(983\) | 50.0104 | 1.59509 | 0.797543 | − | 0.603263i | \(-0.206133\pi\) | ||||
0.797543 | + | 0.603263i | \(0.206133\pi\) | |||||||
\(984\) | −12.4658 | −0.397394 | ||||||||
\(985\) | 35.4865 | 1.13069 | ||||||||
\(986\) | −0.943955 | −0.0300616 | ||||||||
\(987\) | 21.1872 | 0.674395 | ||||||||
\(988\) | −29.4307 | −0.936317 | ||||||||
\(989\) | −0.472349 | −0.0150198 | ||||||||
\(990\) | −0.553665 | −0.0175966 | ||||||||
\(991\) | −47.1683 | −1.49835 | −0.749176 | − | 0.662371i | \(-0.769550\pi\) | ||||
−0.749176 | + | 0.662371i | \(0.769550\pi\) | |||||||
\(992\) | 21.2365 | 0.674258 | ||||||||
\(993\) | −5.64763 | −0.179222 | ||||||||
\(994\) | −24.5989 | −0.780231 | ||||||||
\(995\) | −0.504343 | −0.0159888 | ||||||||
\(996\) | −17.1861 | −0.544561 | ||||||||
\(997\) | −5.86063 | −0.185608 | −0.0928040 | − | 0.995684i | \(-0.529583\pi\) | ||||
−0.0928040 | + | 0.995684i | \(0.529583\pi\) | |||||||
\(998\) | −5.09464 | −0.161268 | ||||||||
\(999\) | 5.81974 | 0.184128 |
(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 | 2001.2.a.n.1.7 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.r.1.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.n.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.r.1.10 | 16 | 3.2 | odd | 2 |