Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53428 | −1.79201 | −0.896003 | − | 0.444048i | \(-0.853542\pi\) | ||||
−0.896003 | + | 0.444048i | \(0.853542\pi\) | |||||||
\(3\) | −2.04027 | −1.17795 | −0.588974 | − | 0.808152i | \(-0.700468\pi\) | ||||
−0.588974 | + | 0.808152i | \(0.700468\pi\) | |||||||
\(4\) | 4.42257 | 2.21129 | ||||||||
\(5\) | −2.47983 | −1.10901 | −0.554507 | − | 0.832179i | \(-0.687093\pi\) | ||||
−0.554507 | + | 0.832179i | \(0.687093\pi\) | |||||||
\(6\) | 5.17061 | 2.11089 | ||||||||
\(7\) | −0.629929 | −0.238091 | −0.119045 | − | 0.992889i | \(-0.537983\pi\) | ||||
−0.119045 | + | 0.992889i | \(0.537983\pi\) | |||||||
\(8\) | −6.13948 | −2.17063 | ||||||||
\(9\) | 1.16269 | 0.387562 | ||||||||
\(10\) | 6.28458 | 1.98736 | ||||||||
\(11\) | 0.0387158 | 0.0116732 | 0.00583662 | − | 0.999983i | \(-0.498142\pi\) | ||||
0.00583662 | + | 0.999983i | \(0.498142\pi\) | |||||||
\(12\) | −9.02323 | −2.60478 | ||||||||
\(13\) | −2.09282 | −0.580443 | −0.290221 | − | 0.956960i | \(-0.593729\pi\) | ||||
−0.290221 | + | 0.956960i | \(0.593729\pi\) | |||||||
\(14\) | 1.59642 | 0.426660 | ||||||||
\(15\) | 5.05951 | 1.30636 | ||||||||
\(16\) | 6.71401 | 1.67850 | ||||||||
\(17\) | 1.11384 | 0.270145 | 0.135073 | − | 0.990836i | \(-0.456873\pi\) | ||||
0.135073 | + | 0.990836i | \(0.456873\pi\) | |||||||
\(18\) | −2.94657 | −0.694514 | ||||||||
\(19\) | −4.51218 | −1.03517 | −0.517583 | − | 0.855633i | \(-0.673168\pi\) | ||||
−0.517583 | + | 0.855633i | \(0.673168\pi\) | |||||||
\(20\) | −10.9672 | −2.45235 | ||||||||
\(21\) | 1.28522 | 0.280459 | ||||||||
\(22\) | −0.0981165 | −0.0209185 | ||||||||
\(23\) | 4.29752 | 0.896096 | 0.448048 | − | 0.894010i | \(-0.352119\pi\) | ||||
0.448048 | + | 0.894010i | \(0.352119\pi\) | |||||||
\(24\) | 12.5262 | 2.55689 | ||||||||
\(25\) | 1.14956 | 0.229912 | ||||||||
\(26\) | 5.30378 | 1.04016 | ||||||||
\(27\) | 3.74861 | 0.721420 | ||||||||
\(28\) | −2.78591 | −0.526487 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −12.8222 | −2.34101 | ||||||||
\(31\) | −9.00294 | −1.61698 | −0.808488 | − | 0.588513i | \(-0.799714\pi\) | ||||
−0.808488 | + | 0.588513i | \(0.799714\pi\) | |||||||
\(32\) | −4.73622 | −0.837253 | ||||||||
\(33\) | −0.0789904 | −0.0137505 | ||||||||
\(34\) | −2.82278 | −0.484102 | ||||||||
\(35\) | 1.56212 | 0.264046 | ||||||||
\(36\) | 5.14207 | 0.857011 | ||||||||
\(37\) | 0.632125 | 0.103921 | 0.0519603 | − | 0.998649i | \(-0.483453\pi\) | ||||
0.0519603 | + | 0.998649i | \(0.483453\pi\) | |||||||
\(38\) | 11.4351 | 1.85502 | ||||||||
\(39\) | 4.26990 | 0.683732 | ||||||||
\(40\) | 15.2249 | 2.40726 | ||||||||
\(41\) | 6.59466 | 1.02991 | 0.514956 | − | 0.857217i | \(-0.327808\pi\) | ||||
0.514956 | + | 0.857217i | \(0.327808\pi\) | |||||||
\(42\) | −3.25712 | −0.502584 | ||||||||
\(43\) | −0.733209 | −0.111813 | −0.0559067 | − | 0.998436i | \(-0.517805\pi\) | ||||
−0.0559067 | + | 0.998436i | \(0.517805\pi\) | |||||||
\(44\) | 0.171223 | 0.0258129 | ||||||||
\(45\) | −2.88327 | −0.429812 | ||||||||
\(46\) | −10.8911 | −1.60581 | ||||||||
\(47\) | 2.09354 | 0.305374 | 0.152687 | − | 0.988275i | \(-0.451207\pi\) | ||||
0.152687 | + | 0.988275i | \(0.451207\pi\) | |||||||
\(48\) | −13.6984 | −1.97719 | ||||||||
\(49\) | −6.60319 | −0.943313 | ||||||||
\(50\) | −2.91330 | −0.412003 | ||||||||
\(51\) | −2.27253 | −0.318217 | ||||||||
\(52\) | −9.25563 | −1.28353 | ||||||||
\(53\) | −5.00250 | −0.687147 | −0.343573 | − | 0.939126i | \(-0.611637\pi\) | ||||
−0.343573 | + | 0.939126i | \(0.611637\pi\) | |||||||
\(54\) | −9.50002 | −1.29279 | ||||||||
\(55\) | −0.0960085 | −0.0129458 | ||||||||
\(56\) | 3.86744 | 0.516808 | ||||||||
\(57\) | 9.20606 | 1.21937 | ||||||||
\(58\) | 2.53428 | 0.332767 | ||||||||
\(59\) | 7.01828 | 0.913702 | 0.456851 | − | 0.889543i | \(-0.348977\pi\) | ||||
0.456851 | + | 0.889543i | \(0.348977\pi\) | |||||||
\(60\) | 22.3761 | 2.88874 | ||||||||
\(61\) | 8.02767 | 1.02784 | 0.513919 | − | 0.857839i | \(-0.328193\pi\) | ||||
0.513919 | + | 0.857839i | \(0.328193\pi\) | |||||||
\(62\) | 22.8160 | 2.89763 | ||||||||
\(63\) | −0.732410 | −0.0922750 | ||||||||
\(64\) | −1.42512 | −0.178140 | ||||||||
\(65\) | 5.18983 | 0.643719 | ||||||||
\(66\) | 0.200184 | 0.0246409 | ||||||||
\(67\) | 9.08801 | 1.11028 | 0.555138 | − | 0.831758i | \(-0.312665\pi\) | ||||
0.555138 | + | 0.831758i | \(0.312665\pi\) | |||||||
\(68\) | 4.92603 | 0.597369 | ||||||||
\(69\) | −8.76810 | −1.05555 | ||||||||
\(70\) | −3.95884 | −0.473172 | ||||||||
\(71\) | −7.30583 | −0.867042 | −0.433521 | − | 0.901143i | \(-0.642729\pi\) | ||||
−0.433521 | + | 0.901143i | \(0.642729\pi\) | |||||||
\(72\) | −7.13829 | −0.841256 | ||||||||
\(73\) | 1.15403 | 0.135069 | 0.0675347 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675347 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(74\) | −1.60198 | −0.186227 | ||||||||
\(75\) | −2.34540 | −0.270824 | ||||||||
\(76\) | −19.9555 | −2.28905 | ||||||||
\(77\) | −0.0243882 | −0.00277929 | ||||||||
\(78\) | −10.8211 | −1.22525 | ||||||||
\(79\) | −8.00526 | −0.900662 | −0.450331 | − | 0.892862i | \(-0.648694\pi\) | ||||
−0.450331 | + | 0.892862i | \(0.648694\pi\) | |||||||
\(80\) | −16.6496 | −1.86148 | ||||||||
\(81\) | −11.1362 | −1.23736 | ||||||||
\(82\) | −16.7127 | −1.84561 | ||||||||
\(83\) | 7.30793 | 0.802150 | 0.401075 | − | 0.916045i | \(-0.368637\pi\) | ||||
0.401075 | + | 0.916045i | \(0.368637\pi\) | |||||||
\(84\) | 5.68399 | 0.620175 | ||||||||
\(85\) | −2.76213 | −0.299595 | ||||||||
\(86\) | 1.85816 | 0.200370 | ||||||||
\(87\) | 2.04027 | 0.218740 | ||||||||
\(88\) | −0.237695 | −0.0253383 | ||||||||
\(89\) | −0.395426 | −0.0419150 | −0.0209575 | − | 0.999780i | \(-0.506671\pi\) | ||||
−0.0209575 | + | 0.999780i | \(0.506671\pi\) | |||||||
\(90\) | 7.30700 | 0.770226 | ||||||||
\(91\) | 1.31833 | 0.138198 | ||||||||
\(92\) | 19.0061 | 1.98152 | ||||||||
\(93\) | 18.3684 | 1.90471 | ||||||||
\(94\) | −5.30562 | −0.547233 | ||||||||
\(95\) | 11.1895 | 1.14801 | ||||||||
\(96\) | 9.66315 | 0.986241 | ||||||||
\(97\) | 15.2066 | 1.54399 | 0.771997 | − | 0.635627i | \(-0.219258\pi\) | ||||
0.771997 | + | 0.635627i | \(0.219258\pi\) | |||||||
\(98\) | 16.7343 | 1.69042 | ||||||||
\(99\) | 0.0450143 | 0.00452411 | ||||||||
\(100\) | 5.08401 | 0.508401 | ||||||||
\(101\) | −6.72285 | −0.668948 | −0.334474 | − | 0.942405i | \(-0.608559\pi\) | ||||
−0.334474 | + | 0.942405i | \(0.608559\pi\) | |||||||
\(102\) | 5.75922 | 0.570248 | ||||||||
\(103\) | −1.70519 | −0.168018 | −0.0840088 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840088 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(104\) | 12.8488 | 1.25993 | ||||||||
\(105\) | −3.18714 | −0.311033 | ||||||||
\(106\) | 12.6777 | 1.23137 | ||||||||
\(107\) | −2.03038 | −0.196284 | −0.0981420 | − | 0.995172i | \(-0.531290\pi\) | ||||
−0.0981420 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(108\) | 16.5785 | 1.59527 | ||||||||
\(109\) | −0.0254372 | −0.00243644 | −0.00121822 | − | 0.999999i | \(-0.500388\pi\) | ||||
−0.00121822 | + | 0.999999i | \(0.500388\pi\) | |||||||
\(110\) | 0.243312 | 0.0231989 | ||||||||
\(111\) | −1.28970 | −0.122413 | ||||||||
\(112\) | −4.22935 | −0.399636 | ||||||||
\(113\) | 10.3511 | 0.973753 | 0.486876 | − | 0.873471i | \(-0.338136\pi\) | ||||
0.486876 | + | 0.873471i | \(0.338136\pi\) | |||||||
\(114\) | −23.3307 | −2.18512 | ||||||||
\(115\) | −10.6571 | −0.993783 | ||||||||
\(116\) | −4.42257 | −0.410626 | ||||||||
\(117\) | −2.43329 | −0.224958 | ||||||||
\(118\) | −17.7863 | −1.63736 | ||||||||
\(119\) | −0.701639 | −0.0643192 | ||||||||
\(120\) | −31.0628 | −2.83563 | ||||||||
\(121\) | −10.9985 | −0.999864 | ||||||||
\(122\) | −20.3444 | −1.84189 | ||||||||
\(123\) | −13.4549 | −1.21318 | ||||||||
\(124\) | −39.8162 | −3.57560 | ||||||||
\(125\) | 9.54844 | 0.854039 | ||||||||
\(126\) | 1.85613 | 0.165357 | ||||||||
\(127\) | 15.8767 | 1.40883 | 0.704413 | − | 0.709790i | \(-0.251210\pi\) | ||||
0.704413 | + | 0.709790i | \(0.251210\pi\) | |||||||
\(128\) | 13.0841 | 1.15648 | ||||||||
\(129\) | 1.49594 | 0.131710 | ||||||||
\(130\) | −13.1525 | −1.15355 | ||||||||
\(131\) | 15.7505 | 1.37613 | 0.688064 | − | 0.725650i | \(-0.258461\pi\) | ||||
0.688064 | + | 0.725650i | \(0.258461\pi\) | |||||||
\(132\) | −0.349341 | −0.0304062 | ||||||||
\(133\) | 2.84236 | 0.246464 | ||||||||
\(134\) | −23.0316 | −1.98962 | ||||||||
\(135\) | −9.29591 | −0.800065 | ||||||||
\(136\) | −6.83839 | −0.586387 | ||||||||
\(137\) | 9.04429 | 0.772706 | 0.386353 | − | 0.922351i | \(-0.373735\pi\) | ||||
0.386353 | + | 0.922351i | \(0.373735\pi\) | |||||||
\(138\) | 22.2208 | 1.89156 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 6.90858 | 0.583881 | ||||||||
\(141\) | −4.27138 | −0.359715 | ||||||||
\(142\) | 18.5150 | 1.55375 | ||||||||
\(143\) | −0.0810249 | −0.00677565 | ||||||||
\(144\) | 7.80629 | 0.650524 | ||||||||
\(145\) | 2.47983 | 0.205939 | ||||||||
\(146\) | −2.92464 | −0.242045 | ||||||||
\(147\) | 13.4723 | 1.11117 | ||||||||
\(148\) | 2.79562 | 0.229798 | ||||||||
\(149\) | 12.6443 | 1.03586 | 0.517932 | − | 0.855422i | \(-0.326702\pi\) | ||||
0.517932 | + | 0.855422i | \(0.326702\pi\) | |||||||
\(150\) | 5.94391 | 0.485318 | ||||||||
\(151\) | 11.5787 | 0.942262 | 0.471131 | − | 0.882063i | \(-0.343846\pi\) | ||||
0.471131 | + | 0.882063i | \(0.343846\pi\) | |||||||
\(152\) | 27.7025 | 2.24697 | ||||||||
\(153\) | 1.29505 | 0.104698 | ||||||||
\(154\) | 0.0618065 | 0.00498051 | ||||||||
\(155\) | 22.3258 | 1.79325 | ||||||||
\(156\) | 18.8840 | 1.51193 | ||||||||
\(157\) | −5.42291 | −0.432795 | −0.216398 | − | 0.976305i | \(-0.569431\pi\) | ||||
−0.216398 | + | 0.976305i | \(0.569431\pi\) | |||||||
\(158\) | 20.2876 | 1.61399 | ||||||||
\(159\) | 10.2064 | 0.809423 | ||||||||
\(160\) | 11.7450 | 0.928525 | ||||||||
\(161\) | −2.70714 | −0.213352 | ||||||||
\(162\) | 28.2223 | 2.21735 | ||||||||
\(163\) | −8.88009 | −0.695543 | −0.347771 | − | 0.937579i | \(-0.613061\pi\) | ||||
−0.347771 | + | 0.937579i | \(0.613061\pi\) | |||||||
\(164\) | 29.1653 | 2.27743 | ||||||||
\(165\) | 0.195883 | 0.0152495 | ||||||||
\(166\) | −18.5203 | −1.43746 | ||||||||
\(167\) | −13.1561 | −1.01805 | −0.509024 | − | 0.860752i | \(-0.669994\pi\) | ||||
−0.509024 | + | 0.860752i | \(0.669994\pi\) | |||||||
\(168\) | −7.89060 | −0.608773 | ||||||||
\(169\) | −8.62012 | −0.663086 | ||||||||
\(170\) | 7.00001 | 0.536876 | ||||||||
\(171\) | −5.24626 | −0.401191 | ||||||||
\(172\) | −3.24267 | −0.247251 | ||||||||
\(173\) | 19.2022 | 1.45992 | 0.729960 | − | 0.683490i | \(-0.239539\pi\) | ||||
0.729960 | + | 0.683490i | \(0.239539\pi\) | |||||||
\(174\) | −5.17061 | −0.391983 | ||||||||
\(175\) | −0.724140 | −0.0547399 | ||||||||
\(176\) | 0.259938 | 0.0195936 | ||||||||
\(177\) | −14.3192 | −1.07629 | ||||||||
\(178\) | 1.00212 | 0.0751120 | ||||||||
\(179\) | −2.91749 | −0.218064 | −0.109032 | − | 0.994038i | \(-0.534775\pi\) | ||||
−0.109032 | + | 0.994038i | \(0.534775\pi\) | |||||||
\(180\) | −12.7515 | −0.950437 | ||||||||
\(181\) | 15.8412 | 1.17747 | 0.588733 | − | 0.808327i | \(-0.299627\pi\) | ||||
0.588733 | + | 0.808327i | \(0.299627\pi\) | |||||||
\(182\) | −3.34101 | −0.247652 | ||||||||
\(183\) | −16.3786 | −1.21074 | ||||||||
\(184\) | −26.3846 | −1.94510 | ||||||||
\(185\) | −1.56756 | −0.115249 | ||||||||
\(186\) | −46.5507 | −3.41326 | ||||||||
\(187\) | 0.0431231 | 0.00315347 | ||||||||
\(188\) | 9.25884 | 0.675270 | ||||||||
\(189\) | −2.36136 | −0.171763 | ||||||||
\(190\) | −28.3572 | −2.05725 | ||||||||
\(191\) | −0.0385705 | −0.00279086 | −0.00139543 | − | 0.999999i | \(-0.500444\pi\) | ||||
−0.00139543 | + | 0.999999i | \(0.500444\pi\) | |||||||
\(192\) | 2.90762 | 0.209839 | ||||||||
\(193\) | −11.6336 | −0.837403 | −0.418701 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418701 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(194\) | −38.5377 | −2.76685 | ||||||||
\(195\) | −10.5886 | −0.758268 | ||||||||
\(196\) | −29.2031 | −2.08593 | ||||||||
\(197\) | 17.5139 | 1.24781 | 0.623906 | − | 0.781499i | \(-0.285545\pi\) | ||||
0.623906 | + | 0.781499i | \(0.285545\pi\) | |||||||
\(198\) | −0.114079 | −0.00810723 | ||||||||
\(199\) | 20.0932 | 1.42437 | 0.712186 | − | 0.701991i | \(-0.247705\pi\) | ||||
0.712186 | + | 0.701991i | \(0.247705\pi\) | |||||||
\(200\) | −7.05769 | −0.499054 | ||||||||
\(201\) | −18.5420 | −1.30785 | ||||||||
\(202\) | 17.0376 | 1.19876 | ||||||||
\(203\) | 0.629929 | 0.0442124 | ||||||||
\(204\) | −10.0504 | −0.703670 | ||||||||
\(205\) | −16.3536 | −1.14219 | ||||||||
\(206\) | 4.32144 | 0.301089 | ||||||||
\(207\) | 4.99668 | 0.347293 | ||||||||
\(208\) | −14.0512 | −0.974274 | ||||||||
\(209\) | −0.174693 | −0.0120837 | ||||||||
\(210\) | 8.07709 | 0.557372 | ||||||||
\(211\) | 1.68594 | 0.116065 | 0.0580325 | − | 0.998315i | \(-0.481517\pi\) | ||||
0.0580325 | + | 0.998315i | \(0.481517\pi\) | |||||||
\(212\) | −22.1239 | −1.51948 | ||||||||
\(213\) | 14.9058 | 1.02133 | ||||||||
\(214\) | 5.14555 | 0.351742 | ||||||||
\(215\) | 1.81823 | 0.124002 | ||||||||
\(216\) | −23.0145 | −1.56594 | ||||||||
\(217\) | 5.67122 | 0.384987 | ||||||||
\(218\) | 0.0644650 | 0.00436612 | ||||||||
\(219\) | −2.35453 | −0.159105 | ||||||||
\(220\) | −0.424605 | −0.0286268 | ||||||||
\(221\) | −2.33106 | −0.156804 | ||||||||
\(222\) | 3.26847 | 0.219365 | ||||||||
\(223\) | −6.69856 | −0.448569 | −0.224284 | − | 0.974524i | \(-0.572004\pi\) | ||||
−0.224284 | + | 0.974524i | \(0.572004\pi\) | |||||||
\(224\) | 2.98348 | 0.199342 | ||||||||
\(225\) | 1.33658 | 0.0891051 | ||||||||
\(226\) | −26.2327 | −1.74497 | ||||||||
\(227\) | 0.666704 | 0.0442507 | 0.0221254 | − | 0.999755i | \(-0.492957\pi\) | ||||
0.0221254 | + | 0.999755i | \(0.492957\pi\) | |||||||
\(228\) | 40.7145 | 2.69638 | ||||||||
\(229\) | 24.7669 | 1.63665 | 0.818323 | − | 0.574759i | \(-0.194904\pi\) | ||||
0.818323 | + | 0.574759i | \(0.194904\pi\) | |||||||
\(230\) | 27.0082 | 1.78086 | ||||||||
\(231\) | 0.0497584 | 0.00327386 | ||||||||
\(232\) | 6.13948 | 0.403076 | ||||||||
\(233\) | −7.46473 | −0.489031 | −0.244515 | − | 0.969645i | \(-0.578629\pi\) | ||||
−0.244515 | + | 0.969645i | \(0.578629\pi\) | |||||||
\(234\) | 6.16664 | 0.403126 | ||||||||
\(235\) | −5.19163 | −0.338664 | ||||||||
\(236\) | 31.0388 | 2.02046 | ||||||||
\(237\) | 16.3329 | 1.06093 | ||||||||
\(238\) | 1.77815 | 0.115260 | ||||||||
\(239\) | 15.1859 | 0.982297 | 0.491148 | − | 0.871076i | \(-0.336577\pi\) | ||||
0.491148 | + | 0.871076i | \(0.336577\pi\) | |||||||
\(240\) | 33.9696 | 2.19273 | ||||||||
\(241\) | −25.0731 | −1.61510 | −0.807549 | − | 0.589801i | \(-0.799206\pi\) | ||||
−0.807549 | + | 0.589801i | \(0.799206\pi\) | |||||||
\(242\) | 27.8733 | 1.79176 | ||||||||
\(243\) | 11.4750 | 0.736124 | ||||||||
\(244\) | 35.5030 | 2.27284 | ||||||||
\(245\) | 16.3748 | 1.04615 | ||||||||
\(246\) | 34.0984 | 2.17403 | ||||||||
\(247\) | 9.44317 | 0.600855 | ||||||||
\(248\) | 55.2734 | 3.50986 | ||||||||
\(249\) | −14.9101 | −0.944891 | ||||||||
\(250\) | −24.1984 | −1.53044 | ||||||||
\(251\) | −2.13311 | −0.134640 | −0.0673202 | − | 0.997731i | \(-0.521445\pi\) | ||||
−0.0673202 | + | 0.997731i | \(0.521445\pi\) | |||||||
\(252\) | −3.23914 | −0.204047 | ||||||||
\(253\) | 0.166382 | 0.0104603 | ||||||||
\(254\) | −40.2359 | −2.52463 | ||||||||
\(255\) | 5.63548 | 0.352907 | ||||||||
\(256\) | −30.3085 | −1.89428 | ||||||||
\(257\) | −0.832643 | −0.0519388 | −0.0259694 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259694 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(258\) | −3.79113 | −0.236026 | ||||||||
\(259\) | −0.398194 | −0.0247426 | ||||||||
\(260\) | 22.9524 | 1.42345 | ||||||||
\(261\) | −1.16269 | −0.0719685 | ||||||||
\(262\) | −39.9162 | −2.46603 | ||||||||
\(263\) | 19.2457 | 1.18674 | 0.593371 | − | 0.804929i | \(-0.297797\pi\) | ||||
0.593371 | + | 0.804929i | \(0.297797\pi\) | |||||||
\(264\) | 0.484960 | 0.0298472 | ||||||||
\(265\) | 12.4054 | 0.762055 | ||||||||
\(266\) | −7.20333 | −0.441664 | ||||||||
\(267\) | 0.806774 | 0.0493738 | ||||||||
\(268\) | 40.1924 | 2.45514 | ||||||||
\(269\) | −5.86704 | −0.357719 | −0.178860 | − | 0.983875i | \(-0.557241\pi\) | ||||
−0.178860 | + | 0.983875i | \(0.557241\pi\) | |||||||
\(270\) | 23.5584 | 1.43372 | ||||||||
\(271\) | 4.41421 | 0.268144 | 0.134072 | − | 0.990972i | \(-0.457195\pi\) | ||||
0.134072 | + | 0.990972i | \(0.457195\pi\) | |||||||
\(272\) | 7.47832 | 0.453440 | ||||||||
\(273\) | −2.68974 | −0.162790 | ||||||||
\(274\) | −22.9208 | −1.38469 | ||||||||
\(275\) | 0.0445060 | 0.00268381 | ||||||||
\(276\) | −38.7775 | −2.33413 | ||||||||
\(277\) | −8.35250 | −0.501853 | −0.250927 | − | 0.968006i | \(-0.580735\pi\) | ||||
−0.250927 | + | 0.968006i | \(0.580735\pi\) | |||||||
\(278\) | 2.53428 | 0.151996 | ||||||||
\(279\) | −10.4676 | −0.626679 | ||||||||
\(280\) | −9.59059 | −0.573147 | ||||||||
\(281\) | 0.482945 | 0.0288101 | 0.0144050 | − | 0.999896i | \(-0.495415\pi\) | ||||
0.0144050 | + | 0.999896i | \(0.495415\pi\) | |||||||
\(282\) | 10.8249 | 0.644612 | ||||||||
\(283\) | −9.14175 | −0.543421 | −0.271710 | − | 0.962379i | \(-0.587589\pi\) | ||||
−0.271710 | + | 0.962379i | \(0.587589\pi\) | |||||||
\(284\) | −32.3106 | −1.91728 | ||||||||
\(285\) | −22.8295 | −1.35230 | ||||||||
\(286\) | 0.205340 | 0.0121420 | ||||||||
\(287\) | −4.15417 | −0.245213 | ||||||||
\(288\) | −5.50674 | −0.324488 | ||||||||
\(289\) | −15.7594 | −0.927021 | ||||||||
\(290\) | −6.28458 | −0.369043 | ||||||||
\(291\) | −31.0255 | −1.81874 | ||||||||
\(292\) | 5.10379 | 0.298677 | ||||||||
\(293\) | 9.06814 | 0.529767 | 0.264883 | − | 0.964280i | \(-0.414667\pi\) | ||||
0.264883 | + | 0.964280i | \(0.414667\pi\) | |||||||
\(294\) | −34.1425 | −1.99123 | ||||||||
\(295\) | −17.4041 | −1.01331 | ||||||||
\(296\) | −3.88092 | −0.225574 | ||||||||
\(297\) | 0.145130 | 0.00842131 | ||||||||
\(298\) | −32.0443 | −1.85627 | ||||||||
\(299\) | −8.99393 | −0.520132 | ||||||||
\(300\) | −10.3727 | −0.598870 | ||||||||
\(301\) | 0.461870 | 0.0266217 | ||||||||
\(302\) | −29.3437 | −1.68854 | ||||||||
\(303\) | 13.7164 | 0.787986 | ||||||||
\(304\) | −30.2948 | −1.73753 | ||||||||
\(305\) | −19.9073 | −1.13989 | ||||||||
\(306\) | −3.28201 | −0.187620 | ||||||||
\(307\) | 22.1343 | 1.26327 | 0.631635 | − | 0.775266i | \(-0.282384\pi\) | ||||
0.631635 | + | 0.775266i | \(0.282384\pi\) | |||||||
\(308\) | −0.107859 | −0.00614581 | ||||||||
\(309\) | 3.47905 | 0.197916 | ||||||||
\(310\) | −56.5797 | −3.21351 | ||||||||
\(311\) | −29.3636 | −1.66505 | −0.832527 | − | 0.553984i | \(-0.813107\pi\) | ||||
−0.832527 | + | 0.553984i | \(0.813107\pi\) | |||||||
\(312\) | −26.2150 | −1.48413 | ||||||||
\(313\) | −17.3492 | −0.980636 | −0.490318 | − | 0.871544i | \(-0.663119\pi\) | ||||
−0.490318 | + | 0.871544i | \(0.663119\pi\) | |||||||
\(314\) | 13.7432 | 0.775572 | ||||||||
\(315\) | 1.81625 | 0.102334 | ||||||||
\(316\) | −35.4039 | −1.99162 | ||||||||
\(317\) | 3.38474 | 0.190106 | 0.0950531 | − | 0.995472i | \(-0.469698\pi\) | ||||
0.0950531 | + | 0.995472i | \(0.469698\pi\) | |||||||
\(318\) | −25.8660 | −1.45049 | ||||||||
\(319\) | −0.0387158 | −0.00216767 | ||||||||
\(320\) | 3.53405 | 0.197559 | ||||||||
\(321\) | 4.14251 | 0.231212 | ||||||||
\(322\) | 6.86064 | 0.382329 | ||||||||
\(323\) | −5.02584 | −0.279645 | ||||||||
\(324\) | −49.2507 | −2.73615 | ||||||||
\(325\) | −2.40581 | −0.133451 | ||||||||
\(326\) | 22.5046 | 1.24642 | ||||||||
\(327\) | 0.0518987 | 0.00287000 | ||||||||
\(328\) | −40.4877 | −2.23556 | ||||||||
\(329\) | −1.31878 | −0.0727068 | ||||||||
\(330\) | −0.496422 | −0.0273271 | ||||||||
\(331\) | 18.9850 | 1.04351 | 0.521756 | − | 0.853095i | \(-0.325277\pi\) | ||||
0.521756 | + | 0.853095i | \(0.325277\pi\) | |||||||
\(332\) | 32.3199 | 1.77378 | ||||||||
\(333\) | 0.734963 | 0.0402757 | ||||||||
\(334\) | 33.3412 | 1.82435 | ||||||||
\(335\) | −22.5367 | −1.23131 | ||||||||
\(336\) | 8.62900 | 0.470751 | ||||||||
\(337\) | 2.41583 | 0.131599 | 0.0657993 | − | 0.997833i | \(-0.479040\pi\) | ||||
0.0657993 | + | 0.997833i | \(0.479040\pi\) | |||||||
\(338\) | 21.8458 | 1.18825 | ||||||||
\(339\) | −21.1191 | −1.14703 | ||||||||
\(340\) | −12.2157 | −0.662491 | ||||||||
\(341\) | −0.348556 | −0.0188753 | ||||||||
\(342\) | 13.2955 | 0.718937 | ||||||||
\(343\) | 8.56905 | 0.462685 | ||||||||
\(344\) | 4.50152 | 0.242706 | ||||||||
\(345\) | 21.7434 | 1.17062 | ||||||||
\(346\) | −48.6638 | −2.61618 | ||||||||
\(347\) | −25.9390 | −1.39248 | −0.696239 | − | 0.717810i | \(-0.745145\pi\) | ||||
−0.696239 | + | 0.717810i | \(0.745145\pi\) | |||||||
\(348\) | 9.02323 | 0.483696 | ||||||||
\(349\) | −17.1162 | −0.916207 | −0.458103 | − | 0.888899i | \(-0.651471\pi\) | ||||
−0.458103 | + | 0.888899i | \(0.651471\pi\) | |||||||
\(350\) | 1.83517 | 0.0980942 | ||||||||
\(351\) | −7.84515 | −0.418743 | ||||||||
\(352\) | −0.183366 | −0.00977345 | ||||||||
\(353\) | −34.2932 | −1.82524 | −0.912620 | − | 0.408808i | \(-0.865944\pi\) | ||||
−0.912620 | + | 0.408808i | \(0.865944\pi\) | |||||||
\(354\) | 36.2887 | 1.92872 | ||||||||
\(355\) | 18.1172 | 0.961562 | ||||||||
\(356\) | −1.74880 | −0.0926862 | ||||||||
\(357\) | 1.43153 | 0.0757647 | ||||||||
\(358\) | 7.39375 | 0.390772 | ||||||||
\(359\) | −15.3319 | −0.809188 | −0.404594 | − | 0.914496i | \(-0.632587\pi\) | ||||
−0.404594 | + | 0.914496i | \(0.632587\pi\) | |||||||
\(360\) | 17.7017 | 0.932964 | ||||||||
\(361\) | 1.35981 | 0.0715690 | ||||||||
\(362\) | −40.1460 | −2.11003 | ||||||||
\(363\) | 22.4399 | 1.17779 | ||||||||
\(364\) | 5.83039 | 0.305596 | ||||||||
\(365\) | −2.86181 | −0.149794 | ||||||||
\(366\) | 41.5079 | 2.16965 | ||||||||
\(367\) | 12.8028 | 0.668300 | 0.334150 | − | 0.942520i | \(-0.391551\pi\) | ||||
0.334150 | + | 0.942520i | \(0.391551\pi\) | |||||||
\(368\) | 28.8536 | 1.50410 | ||||||||
\(369\) | 7.66752 | 0.399155 | ||||||||
\(370\) | 3.97264 | 0.206528 | ||||||||
\(371\) | 3.15122 | 0.163603 | ||||||||
\(372\) | 81.2356 | 4.21187 | ||||||||
\(373\) | −7.55022 | −0.390935 | −0.195468 | − | 0.980710i | \(-0.562622\pi\) | ||||
−0.195468 | + | 0.980710i | \(0.562622\pi\) | |||||||
\(374\) | −0.109286 | −0.00565104 | ||||||||
\(375\) | −19.4814 | −1.00601 | ||||||||
\(376\) | −12.8532 | −0.662856 | ||||||||
\(377\) | 2.09282 | 0.107786 | ||||||||
\(378\) | 5.98434 | 0.307801 | ||||||||
\(379\) | −19.0391 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(380\) | 49.4862 | 2.53859 | ||||||||
\(381\) | −32.3926 | −1.65953 | ||||||||
\(382\) | 0.0977485 | 0.00500125 | ||||||||
\(383\) | 21.0226 | 1.07420 | 0.537102 | − | 0.843517i | \(-0.319519\pi\) | ||||
0.537102 | + | 0.843517i | \(0.319519\pi\) | |||||||
\(384\) | −26.6950 | −1.36227 | ||||||||
\(385\) | 0.0604785 | 0.00308227 | ||||||||
\(386\) | 29.4827 | 1.50063 | ||||||||
\(387\) | −0.852492 | −0.0433346 | ||||||||
\(388\) | 67.2522 | 3.41421 | ||||||||
\(389\) | 14.8273 | 0.751773 | 0.375886 | − | 0.926666i | \(-0.377338\pi\) | ||||
0.375886 | + | 0.926666i | \(0.377338\pi\) | |||||||
\(390\) | 26.8346 | 1.35882 | ||||||||
\(391\) | 4.78675 | 0.242076 | ||||||||
\(392\) | 40.5401 | 2.04759 | ||||||||
\(393\) | −32.1352 | −1.62101 | ||||||||
\(394\) | −44.3851 | −2.23609 | ||||||||
\(395\) | 19.8517 | 0.998847 | ||||||||
\(396\) | 0.199079 | 0.0100041 | ||||||||
\(397\) | −2.20756 | −0.110794 | −0.0553972 | − | 0.998464i | \(-0.517643\pi\) | ||||
−0.0553972 | + | 0.998464i | \(0.517643\pi\) | |||||||
\(398\) | −50.9219 | −2.55248 | ||||||||
\(399\) | −5.79917 | −0.290321 | ||||||||
\(400\) | 7.71814 | 0.385907 | ||||||||
\(401\) | −16.5629 | −0.827112 | −0.413556 | − | 0.910479i | \(-0.635713\pi\) | ||||
−0.413556 | + | 0.910479i | \(0.635713\pi\) | |||||||
\(402\) | 46.9905 | 2.34367 | ||||||||
\(403\) | 18.8415 | 0.938562 | ||||||||
\(404\) | −29.7323 | −1.47924 | ||||||||
\(405\) | 27.6159 | 1.37225 | ||||||||
\(406\) | −1.59642 | −0.0792288 | ||||||||
\(407\) | 0.0244732 | 0.00121309 | ||||||||
\(408\) | 13.9521 | 0.690733 | ||||||||
\(409\) | −13.5897 | −0.671968 | −0.335984 | − | 0.941868i | \(-0.609069\pi\) | ||||
−0.335984 | + | 0.941868i | \(0.609069\pi\) | |||||||
\(410\) | 41.4447 | 2.04681 | ||||||||
\(411\) | −18.4528 | −0.910208 | ||||||||
\(412\) | −7.54134 | −0.371535 | ||||||||
\(413\) | −4.42102 | −0.217544 | ||||||||
\(414\) | −12.6630 | −0.622351 | ||||||||
\(415\) | −18.1224 | −0.889595 | ||||||||
\(416\) | 9.91203 | 0.485977 | ||||||||
\(417\) | 2.04027 | 0.0999123 | ||||||||
\(418\) | 0.442720 | 0.0216541 | ||||||||
\(419\) | −17.9232 | −0.875604 | −0.437802 | − | 0.899071i | \(-0.644243\pi\) | ||||
−0.437802 | + | 0.899071i | \(0.644243\pi\) | |||||||
\(420\) | −14.0953 | −0.687782 | ||||||||
\(421\) | 7.35827 | 0.358620 | 0.179310 | − | 0.983793i | \(-0.442613\pi\) | ||||
0.179310 | + | 0.983793i | \(0.442613\pi\) | |||||||
\(422\) | −4.27265 | −0.207989 | ||||||||
\(423\) | 2.43413 | 0.118352 | ||||||||
\(424\) | 30.7128 | 1.49154 | ||||||||
\(425\) | 1.28042 | 0.0621096 | ||||||||
\(426\) | −37.7756 | −1.83023 | ||||||||
\(427\) | −5.05686 | −0.244719 | ||||||||
\(428\) | −8.97950 | −0.434040 | ||||||||
\(429\) | 0.165312 | 0.00798136 | ||||||||
\(430\) | −4.60791 | −0.222213 | ||||||||
\(431\) | −13.8655 | −0.667880 | −0.333940 | − | 0.942594i | \(-0.608378\pi\) | ||||
−0.333940 | + | 0.942594i | \(0.608378\pi\) | |||||||
\(432\) | 25.1682 | 1.21090 | ||||||||
\(433\) | 0.389905 | 0.0187377 | 0.00936883 | − | 0.999956i | \(-0.497018\pi\) | ||||
0.00936883 | + | 0.999956i | \(0.497018\pi\) | |||||||
\(434\) | −14.3724 | −0.689899 | ||||||||
\(435\) | −5.05951 | −0.242585 | ||||||||
\(436\) | −0.112498 | −0.00538767 | ||||||||
\(437\) | −19.3912 | −0.927608 | ||||||||
\(438\) | 5.96705 | 0.285117 | ||||||||
\(439\) | −23.8276 | −1.13723 | −0.568615 | − | 0.822604i | \(-0.692521\pi\) | ||||
−0.568615 | + | 0.822604i | \(0.692521\pi\) | |||||||
\(440\) | 0.589442 | 0.0281005 | ||||||||
\(441\) | −7.67744 | −0.365592 | ||||||||
\(442\) | 5.90755 | 0.280994 | ||||||||
\(443\) | −28.7945 | −1.36807 | −0.684035 | − | 0.729450i | \(-0.739776\pi\) | ||||
−0.684035 | + | 0.729450i | \(0.739776\pi\) | |||||||
\(444\) | −5.70381 | −0.270691 | ||||||||
\(445\) | 0.980589 | 0.0464844 | ||||||||
\(446\) | 16.9760 | 0.803838 | ||||||||
\(447\) | −25.7978 | −1.22019 | ||||||||
\(448\) | 0.897722 | 0.0424134 | ||||||||
\(449\) | 4.27392 | 0.201699 | 0.100849 | − | 0.994902i | \(-0.467844\pi\) | ||||
0.100849 | + | 0.994902i | \(0.467844\pi\) | |||||||
\(450\) | −3.38726 | −0.159677 | ||||||||
\(451\) | 0.255317 | 0.0120224 | ||||||||
\(452\) | 45.7786 | 2.15325 | ||||||||
\(453\) | −23.6236 | −1.10994 | ||||||||
\(454\) | −1.68962 | −0.0792976 | ||||||||
\(455\) | −3.26922 | −0.153264 | ||||||||
\(456\) | −56.5204 | −2.64681 | ||||||||
\(457\) | −36.6346 | −1.71369 | −0.856847 | − | 0.515571i | \(-0.827580\pi\) | ||||
−0.856847 | + | 0.515571i | \(0.827580\pi\) | |||||||
\(458\) | −62.7664 | −2.93288 | ||||||||
\(459\) | 4.17534 | 0.194888 | ||||||||
\(460\) | −47.1319 | −2.19754 | ||||||||
\(461\) | 23.5352 | 1.09614 | 0.548072 | − | 0.836431i | \(-0.315362\pi\) | ||||
0.548072 | + | 0.836431i | \(0.315362\pi\) | |||||||
\(462\) | −0.126102 | −0.00586678 | ||||||||
\(463\) | −18.5748 | −0.863242 | −0.431621 | − | 0.902055i | \(-0.642058\pi\) | ||||
−0.431621 | + | 0.902055i | \(0.642058\pi\) | |||||||
\(464\) | −6.71401 | −0.311690 | ||||||||
\(465\) | −45.5505 | −2.11235 | ||||||||
\(466\) | 18.9177 | 0.876347 | ||||||||
\(467\) | −0.0296519 | −0.00137212 | −0.000686062 | − | 1.00000i | \(-0.500218\pi\) | ||||
−0.000686062 | 1.00000i | \(0.500218\pi\) | ||||||||
\(468\) | −10.7614 | −0.497446 | ||||||||
\(469\) | −5.72480 | −0.264347 | ||||||||
\(470\) | 13.1570 | 0.606889 | ||||||||
\(471\) | 11.0642 | 0.509811 | ||||||||
\(472\) | −43.0885 | −1.98331 | ||||||||
\(473\) | −0.0283867 | −0.00130522 | ||||||||
\(474\) | −41.3921 | −1.90120 | ||||||||
\(475\) | −5.18702 | −0.237997 | ||||||||
\(476\) | −3.10305 | −0.142228 | ||||||||
\(477\) | −5.81634 | −0.266312 | ||||||||
\(478\) | −38.4854 | −1.76028 | ||||||||
\(479\) | −11.5808 | −0.529142 | −0.264571 | − | 0.964366i | \(-0.585230\pi\) | ||||
−0.264571 | + | 0.964366i | \(0.585230\pi\) | |||||||
\(480\) | −23.9630 | −1.09375 | ||||||||
\(481\) | −1.32292 | −0.0603200 | ||||||||
\(482\) | 63.5421 | 2.89426 | ||||||||
\(483\) | 5.52328 | 0.251318 | ||||||||
\(484\) | −48.6417 | −2.21099 | ||||||||
\(485\) | −37.7097 | −1.71231 | ||||||||
\(486\) | −29.0809 | −1.31914 | ||||||||
\(487\) | 8.42949 | 0.381977 | 0.190988 | − | 0.981592i | \(-0.438831\pi\) | ||||
0.190988 | + | 0.981592i | \(0.438831\pi\) | |||||||
\(488\) | −49.2857 | −2.23106 | ||||||||
\(489\) | 18.1178 | 0.819313 | ||||||||
\(490\) | −41.4983 | −1.87470 | ||||||||
\(491\) | −20.8335 | −0.940204 | −0.470102 | − | 0.882612i | \(-0.655783\pi\) | ||||
−0.470102 | + | 0.882612i | \(0.655783\pi\) | |||||||
\(492\) | −59.5051 | −2.68270 | ||||||||
\(493\) | −1.11384 | −0.0501648 | ||||||||
\(494\) | −23.9316 | −1.07674 | ||||||||
\(495\) | −0.111628 | −0.00501730 | ||||||||
\(496\) | −60.4458 | −2.71410 | ||||||||
\(497\) | 4.60216 | 0.206435 | ||||||||
\(498\) | 37.7864 | 1.69325 | ||||||||
\(499\) | 27.9109 | 1.24947 | 0.624733 | − | 0.780839i | \(-0.285208\pi\) | ||||
0.624733 | + | 0.780839i | \(0.285208\pi\) | |||||||
\(500\) | 42.2287 | 1.88852 | ||||||||
\(501\) | 26.8419 | 1.19921 | ||||||||
\(502\) | 5.40589 | 0.241277 | ||||||||
\(503\) | −6.43258 | −0.286815 | −0.143407 | − | 0.989664i | \(-0.545806\pi\) | ||||
−0.143407 | + | 0.989664i | \(0.545806\pi\) | |||||||
\(504\) | 4.49662 | 0.200295 | ||||||||
\(505\) | 16.6715 | 0.741873 | ||||||||
\(506\) | −0.421658 | −0.0187450 | ||||||||
\(507\) | 17.5873 | 0.781081 | ||||||||
\(508\) | 70.2157 | 3.11532 | ||||||||
\(509\) | −28.7881 | −1.27601 | −0.638005 | − | 0.770033i | \(-0.720240\pi\) | ||||
−0.638005 | + | 0.770033i | \(0.720240\pi\) | |||||||
\(510\) | −14.2819 | −0.632412 | ||||||||
\(511\) | −0.726959 | −0.0321588 | ||||||||
\(512\) | 50.6420 | 2.23808 | ||||||||
\(513\) | −16.9144 | −0.746790 | ||||||||
\(514\) | 2.11015 | 0.0930747 | ||||||||
\(515\) | 4.22859 | 0.186334 | ||||||||
\(516\) | 6.61591 | 0.291249 | ||||||||
\(517\) | 0.0810530 | 0.00356471 | ||||||||
\(518\) | 1.00913 | 0.0443388 | ||||||||
\(519\) | −39.1777 | −1.71971 | ||||||||
\(520\) | −31.8628 | −1.39728 | ||||||||
\(521\) | −25.5383 | −1.11885 | −0.559426 | − | 0.828880i | \(-0.688979\pi\) | ||||
−0.559426 | + | 0.828880i | \(0.688979\pi\) | |||||||
\(522\) | 2.94657 | 0.128968 | ||||||||
\(523\) | 19.6507 | 0.859264 | 0.429632 | − | 0.903004i | \(-0.358643\pi\) | ||||
0.429632 | + | 0.903004i | \(0.358643\pi\) | |||||||
\(524\) | 69.6578 | 3.04301 | ||||||||
\(525\) | 1.47744 | 0.0644807 | ||||||||
\(526\) | −48.7741 | −2.12665 | ||||||||
\(527\) | −10.0278 | −0.436819 | ||||||||
\(528\) | −0.530342 | −0.0230802 | ||||||||
\(529\) | −4.53128 | −0.197012 | ||||||||
\(530\) | −31.4386 | −1.36561 | ||||||||
\(531\) | 8.16006 | 0.354116 | ||||||||
\(532\) | 12.5705 | 0.545002 | ||||||||
\(533\) | −13.8014 | −0.597805 | ||||||||
\(534\) | −2.04459 | −0.0884781 | ||||||||
\(535\) | 5.03499 | 0.217682 | ||||||||
\(536\) | −55.7956 | −2.41000 | ||||||||
\(537\) | 5.95247 | 0.256868 | ||||||||
\(538\) | 14.8687 | 0.641036 | ||||||||
\(539\) | −0.255647 | −0.0110115 | ||||||||
\(540\) | −41.1119 | −1.76917 | ||||||||
\(541\) | −31.3091 | −1.34608 | −0.673042 | − | 0.739604i | \(-0.735013\pi\) | ||||
−0.673042 | + | 0.739604i | \(0.735013\pi\) | |||||||
\(542\) | −11.1868 | −0.480516 | ||||||||
\(543\) | −32.3202 | −1.38699 | ||||||||
\(544\) | −5.27538 | −0.226180 | ||||||||
\(545\) | 0.0630800 | 0.00270205 | ||||||||
\(546\) | 6.81654 | 0.291721 | ||||||||
\(547\) | −42.1175 | −1.80082 | −0.900408 | − | 0.435046i | \(-0.856732\pi\) | ||||
−0.900408 | + | 0.435046i | \(0.856732\pi\) | |||||||
\(548\) | 39.9991 | 1.70867 | ||||||||
\(549\) | 9.33367 | 0.398351 | ||||||||
\(550\) | −0.112791 | −0.00480941 | ||||||||
\(551\) | 4.51218 | 0.192226 | ||||||||
\(552\) | 53.8315 | 2.29122 | ||||||||
\(553\) | 5.04275 | 0.214439 | ||||||||
\(554\) | 21.1676 | 0.899324 | ||||||||
\(555\) | 3.19824 | 0.135758 | ||||||||
\(556\) | −4.42257 | −0.187559 | ||||||||
\(557\) | −14.1445 | −0.599324 | −0.299662 | − | 0.954045i | \(-0.596874\pi\) | ||||
−0.299662 | + | 0.954045i | \(0.596874\pi\) | |||||||
\(558\) | 26.5278 | 1.12301 | ||||||||
\(559\) | 1.53447 | 0.0649012 | ||||||||
\(560\) | 10.4881 | 0.443202 | ||||||||
\(561\) | −0.0879826 | −0.00371463 | ||||||||
\(562\) | −1.22392 | −0.0516279 | ||||||||
\(563\) | −40.2579 | −1.69667 | −0.848333 | − | 0.529463i | \(-0.822393\pi\) | ||||
−0.848333 | + | 0.529463i | \(0.822393\pi\) | |||||||
\(564\) | −18.8905 | −0.795433 | ||||||||
\(565\) | −25.6691 | −1.07991 | ||||||||
\(566\) | 23.1677 | 0.973813 | ||||||||
\(567\) | 7.01503 | 0.294604 | ||||||||
\(568\) | 44.8540 | 1.88203 | ||||||||
\(569\) | 25.9081 | 1.08613 | 0.543063 | − | 0.839692i | \(-0.317265\pi\) | ||||
0.543063 | + | 0.839692i | \(0.317265\pi\) | |||||||
\(570\) | 57.8562 | 2.42333 | ||||||||
\(571\) | 18.2387 | 0.763267 | 0.381633 | − | 0.924314i | \(-0.375362\pi\) | ||||
0.381633 | + | 0.924314i | \(0.375362\pi\) | |||||||
\(572\) | −0.358339 | −0.0149829 | ||||||||
\(573\) | 0.0786941 | 0.00328749 | ||||||||
\(574\) | 10.5278 | 0.439423 | ||||||||
\(575\) | 4.94025 | 0.206023 | ||||||||
\(576\) | −1.65696 | −0.0690402 | ||||||||
\(577\) | 21.0699 | 0.877152 | 0.438576 | − | 0.898694i | \(-0.355483\pi\) | ||||
0.438576 | + | 0.898694i | \(0.355483\pi\) | |||||||
\(578\) | 39.9386 | 1.66123 | ||||||||
\(579\) | 23.7356 | 0.986417 | ||||||||
\(580\) | 10.9672 | 0.455389 | ||||||||
\(581\) | −4.60348 | −0.190984 | ||||||||
\(582\) | 78.6272 | 3.25920 | ||||||||
\(583\) | −0.193676 | −0.00802123 | ||||||||
\(584\) | −7.08516 | −0.293186 | ||||||||
\(585\) | 6.03415 | 0.249481 | ||||||||
\(586\) | −22.9812 | −0.949345 | ||||||||
\(587\) | −10.7856 | −0.445170 | −0.222585 | − | 0.974913i | \(-0.571449\pi\) | ||||
−0.222585 | + | 0.974913i | \(0.571449\pi\) | |||||||
\(588\) | 59.5821 | 2.45712 | ||||||||
\(589\) | 40.6229 | 1.67384 | ||||||||
\(590\) | 44.1069 | 1.81585 | ||||||||
\(591\) | −35.7330 | −1.46986 | ||||||||
\(592\) | 4.24409 | 0.174431 | ||||||||
\(593\) | −1.13587 | −0.0466445 | −0.0233223 | − | 0.999728i | \(-0.507424\pi\) | ||||
−0.0233223 | + | 0.999728i | \(0.507424\pi\) | |||||||
\(594\) | −0.367800 | −0.0150910 | ||||||||
\(595\) | 1.73995 | 0.0713308 | ||||||||
\(596\) | 55.9205 | 2.29059 | ||||||||
\(597\) | −40.9955 | −1.67784 | ||||||||
\(598\) | 22.7931 | 0.932080 | ||||||||
\(599\) | 0.647277 | 0.0264470 | 0.0132235 | − | 0.999913i | \(-0.495791\pi\) | ||||
0.0132235 | + | 0.999913i | \(0.495791\pi\) | |||||||
\(600\) | 14.3996 | 0.587860 | ||||||||
\(601\) | −1.18958 | −0.0485239 | −0.0242619 | − | 0.999706i | \(-0.507724\pi\) | ||||
−0.0242619 | + | 0.999706i | \(0.507724\pi\) | |||||||
\(602\) | −1.17051 | −0.0477063 | ||||||||
\(603\) | 10.5665 | 0.430301 | ||||||||
\(604\) | 51.2077 | 2.08361 | ||||||||
\(605\) | 27.2744 | 1.10886 | ||||||||
\(606\) | −34.7612 | −1.41208 | ||||||||
\(607\) | 7.41191 | 0.300840 | 0.150420 | − | 0.988622i | \(-0.451937\pi\) | ||||
0.150420 | + | 0.988622i | \(0.451937\pi\) | |||||||
\(608\) | 21.3707 | 0.866696 | ||||||||
\(609\) | −1.28522 | −0.0520799 | ||||||||
\(610\) | 50.4506 | 2.04268 | ||||||||
\(611\) | −4.38140 | −0.177252 | ||||||||
\(612\) | 5.72743 | 0.231518 | ||||||||
\(613\) | −18.7227 | −0.756203 | −0.378102 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378102 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(614\) | −56.0945 | −2.26379 | ||||||||
\(615\) | 33.3658 | 1.34544 | ||||||||
\(616\) | 0.149731 | 0.00603282 | ||||||||
\(617\) | −24.1954 | −0.974071 | −0.487035 | − | 0.873382i | \(-0.661922\pi\) | ||||
−0.487035 | + | 0.873382i | \(0.661922\pi\) | |||||||
\(618\) | −8.81688 | −0.354667 | ||||||||
\(619\) | 27.6196 | 1.11012 | 0.555062 | − | 0.831809i | \(-0.312694\pi\) | ||||
0.555062 | + | 0.831809i | \(0.312694\pi\) | |||||||
\(620\) | 98.7373 | 3.96539 | ||||||||
\(621\) | 16.1097 | 0.646461 | ||||||||
\(622\) | 74.4155 | 2.98379 | ||||||||
\(623\) | 0.249090 | 0.00997959 | ||||||||
\(624\) | 28.6682 | 1.14764 | ||||||||
\(625\) | −29.4263 | −1.17705 | ||||||||
\(626\) | 43.9678 | 1.75731 | ||||||||
\(627\) | 0.356419 | 0.0142340 | ||||||||
\(628\) | −23.9832 | −0.957035 | ||||||||
\(629\) | 0.704085 | 0.0280737 | ||||||||
\(630\) | −4.60289 | −0.183384 | ||||||||
\(631\) | 22.2756 | 0.886777 | 0.443389 | − | 0.896329i | \(-0.353776\pi\) | ||||
0.443389 | + | 0.896329i | \(0.353776\pi\) | |||||||
\(632\) | 49.1481 | 1.95501 | ||||||||
\(633\) | −3.43977 | −0.136719 | ||||||||
\(634\) | −8.57789 | −0.340671 | ||||||||
\(635\) | −39.3714 | −1.56241 | ||||||||
\(636\) | 45.1387 | 1.78987 | ||||||||
\(637\) | 13.8193 | 0.547539 | ||||||||
\(638\) | 0.0981165 | 0.00388447 | ||||||||
\(639\) | −8.49439 | −0.336033 | ||||||||
\(640\) | −32.4463 | −1.28255 | ||||||||
\(641\) | 11.9095 | 0.470397 | 0.235199 | − | 0.971947i | \(-0.424426\pi\) | ||||
0.235199 | + | 0.971947i | \(0.424426\pi\) | |||||||
\(642\) | −10.4983 | −0.414334 | ||||||||
\(643\) | 25.5380 | 1.00712 | 0.503561 | − | 0.863960i | \(-0.332023\pi\) | ||||
0.503561 | + | 0.863960i | \(0.332023\pi\) | |||||||
\(644\) | −11.9725 | −0.471783 | ||||||||
\(645\) | −3.70968 | −0.146069 | ||||||||
\(646\) | 12.7369 | 0.501126 | ||||||||
\(647\) | 19.0558 | 0.749162 | 0.374581 | − | 0.927194i | \(-0.377787\pi\) | ||||
0.374581 | + | 0.927194i | \(0.377787\pi\) | |||||||
\(648\) | 68.3706 | 2.68585 | ||||||||
\(649\) | 0.271718 | 0.0106659 | ||||||||
\(650\) | 6.09700 | 0.239144 | ||||||||
\(651\) | −11.5708 | −0.453495 | ||||||||
\(652\) | −39.2729 | −1.53804 | ||||||||
\(653\) | −14.2224 | −0.556564 | −0.278282 | − | 0.960499i | \(-0.589765\pi\) | ||||
−0.278282 | + | 0.960499i | \(0.589765\pi\) | |||||||
\(654\) | −0.131526 | −0.00514306 | ||||||||
\(655\) | −39.0586 | −1.52614 | ||||||||
\(656\) | 44.2766 | 1.72871 | ||||||||
\(657\) | 1.34178 | 0.0523478 | ||||||||
\(658\) | 3.34216 | 0.130291 | ||||||||
\(659\) | 0.462001 | 0.0179970 | 0.00899851 | − | 0.999960i | \(-0.497136\pi\) | ||||
0.00899851 | + | 0.999960i | \(0.497136\pi\) | |||||||
\(660\) | 0.866306 | 0.0337209 | ||||||||
\(661\) | 0.698548 | 0.0271703 | 0.0135852 | − | 0.999908i | \(-0.495676\pi\) | ||||
0.0135852 | + | 0.999908i | \(0.495676\pi\) | |||||||
\(662\) | −48.1134 | −1.86998 | ||||||||
\(663\) | 4.75598 | 0.184707 | ||||||||
\(664\) | −44.8669 | −1.74117 | ||||||||
\(665\) | −7.04856 | −0.273332 | ||||||||
\(666\) | −1.86260 | −0.0721744 | ||||||||
\(667\) | −4.29752 | −0.166401 | ||||||||
\(668\) | −58.1837 | −2.25120 | ||||||||
\(669\) | 13.6668 | 0.528391 | ||||||||
\(670\) | 57.1143 | 2.20652 | ||||||||
\(671\) | 0.310797 | 0.0119982 | ||||||||
\(672\) | −6.08710 | −0.234815 | ||||||||
\(673\) | −26.7501 | −1.03114 | −0.515571 | − | 0.856847i | \(-0.672420\pi\) | ||||
−0.515571 | + | 0.856847i | \(0.672420\pi\) | |||||||
\(674\) | −6.12239 | −0.235826 | ||||||||
\(675\) | 4.30924 | 0.165863 | ||||||||
\(676\) | −38.1231 | −1.46627 | ||||||||
\(677\) | −15.5018 | −0.595784 | −0.297892 | − | 0.954600i | \(-0.596284\pi\) | ||||
−0.297892 | + | 0.954600i | \(0.596284\pi\) | |||||||
\(678\) | 53.5216 | 2.05549 | ||||||||
\(679\) | −9.57906 | −0.367611 | ||||||||
\(680\) | 16.9580 | 0.650311 | ||||||||
\(681\) | −1.36025 | −0.0521251 | ||||||||
\(682\) | 0.883337 | 0.0338247 | ||||||||
\(683\) | 45.6589 | 1.74709 | 0.873545 | − | 0.486743i | \(-0.161815\pi\) | ||||
0.873545 | + | 0.486743i | \(0.161815\pi\) | |||||||
\(684\) | −23.2020 | −0.887149 | ||||||||
\(685\) | −22.4283 | −0.856942 | ||||||||
\(686\) | −21.7164 | −0.829134 | ||||||||
\(687\) | −50.5312 | −1.92788 | ||||||||
\(688\) | −4.92277 | −0.187679 | ||||||||
\(689\) | 10.4693 | 0.398849 | ||||||||
\(690\) | −55.1038 | −2.09777 | ||||||||
\(691\) | 11.0375 | 0.419888 | 0.209944 | − | 0.977713i | \(-0.432672\pi\) | ||||
0.209944 | + | 0.977713i | \(0.432672\pi\) | |||||||
\(692\) | 84.9233 | 3.22830 | ||||||||
\(693\) | −0.0283558 | −0.00107715 | ||||||||
\(694\) | 65.7367 | 2.49533 | ||||||||
\(695\) | 2.47983 | 0.0940653 | ||||||||
\(696\) | −12.5262 | −0.474803 | ||||||||
\(697\) | 7.34538 | 0.278226 | ||||||||
\(698\) | 43.3771 | 1.64185 | ||||||||
\(699\) | 15.2300 | 0.576053 | ||||||||
\(700\) | −3.20256 | −0.121046 | ||||||||
\(701\) | 47.3794 | 1.78950 | 0.894748 | − | 0.446571i | \(-0.147355\pi\) | ||||
0.894748 | + | 0.446571i | \(0.147355\pi\) | |||||||
\(702\) | 19.8818 | 0.750390 | ||||||||
\(703\) | −2.85226 | −0.107575 | ||||||||
\(704\) | −0.0551745 | −0.00207947 | ||||||||
\(705\) | 10.5923 | 0.398929 | ||||||||
\(706\) | 86.9084 | 3.27084 | ||||||||
\(707\) | 4.23492 | 0.159270 | ||||||||
\(708\) | −63.3275 | −2.37999 | ||||||||
\(709\) | −29.2500 | −1.09851 | −0.549253 | − | 0.835656i | \(-0.685088\pi\) | ||||
−0.549253 | + | 0.835656i | \(0.685088\pi\) | |||||||
\(710\) | −45.9141 | −1.72313 | ||||||||
\(711\) | −9.30761 | −0.349063 | ||||||||
\(712\) | 2.42771 | 0.0909822 | ||||||||
\(713\) | −38.6904 | −1.44897 | ||||||||
\(714\) | −3.62790 | −0.135771 | ||||||||
\(715\) | 0.200928 | 0.00751428 | ||||||||
\(716\) | −12.9028 | −0.482202 | ||||||||
\(717\) | −30.9834 | −1.15709 | ||||||||
\(718\) | 38.8554 | 1.45007 | ||||||||
\(719\) | −19.4417 | −0.725052 | −0.362526 | − | 0.931974i | \(-0.618086\pi\) | ||||
−0.362526 | + | 0.931974i | \(0.618086\pi\) | |||||||
\(720\) | −19.3583 | −0.721440 | ||||||||
\(721\) | 1.07415 | 0.0400035 | ||||||||
\(722\) | −3.44614 | −0.128252 | ||||||||
\(723\) | 51.1557 | 1.90250 | ||||||||
\(724\) | 70.0588 | 2.60372 | ||||||||
\(725\) | −1.14956 | −0.0426935 | ||||||||
\(726\) | −56.8689 | −2.11060 | ||||||||
\(727\) | 16.1524 | 0.599059 | 0.299529 | − | 0.954087i | \(-0.403170\pi\) | ||||
0.299529 | + | 0.954087i | \(0.403170\pi\) | |||||||
\(728\) | −8.09383 | −0.299977 | ||||||||
\(729\) | 9.99654 | 0.370242 | ||||||||
\(730\) | 7.25262 | 0.268431 | ||||||||
\(731\) | −0.816676 | −0.0302059 | ||||||||
\(732\) | −72.4355 | −2.67729 | ||||||||
\(733\) | 11.2349 | 0.414972 | 0.207486 | − | 0.978238i | \(-0.433472\pi\) | ||||
0.207486 | + | 0.978238i | \(0.433472\pi\) | |||||||
\(734\) | −32.4458 | −1.19760 | ||||||||
\(735\) | −33.4089 | −1.23231 | ||||||||
\(736\) | −20.3540 | −0.750259 | ||||||||
\(737\) | 0.351849 | 0.0129605 | ||||||||
\(738\) | −19.4316 | −0.715289 | ||||||||
\(739\) | 1.20092 | 0.0441764 | 0.0220882 | − | 0.999756i | \(-0.492969\pi\) | ||||
0.0220882 | + | 0.999756i | \(0.492969\pi\) | |||||||
\(740\) | −6.93266 | −0.254850 | ||||||||
\(741\) | −19.2666 | −0.707776 | ||||||||
\(742\) | −7.98608 | −0.293178 | ||||||||
\(743\) | 25.1822 | 0.923845 | 0.461922 | − | 0.886920i | \(-0.347160\pi\) | ||||
0.461922 | + | 0.886920i | \(0.347160\pi\) | |||||||
\(744\) | −112.772 | −4.13444 | ||||||||
\(745\) | −31.3558 | −1.14879 | ||||||||
\(746\) | 19.1344 | 0.700559 | ||||||||
\(747\) | 8.49684 | 0.310883 | ||||||||
\(748\) | 0.190715 | 0.00697323 | ||||||||
\(749\) | 1.27899 | 0.0467334 | ||||||||
\(750\) | 49.3712 | 1.80278 | ||||||||
\(751\) | −0.808800 | −0.0295135 | −0.0147568 | − | 0.999891i | \(-0.504697\pi\) | ||||
−0.0147568 | + | 0.999891i | \(0.504697\pi\) | |||||||
\(752\) | 14.0561 | 0.512571 | ||||||||
\(753\) | 4.35210 | 0.158599 | ||||||||
\(754\) | −5.30378 | −0.193152 | ||||||||
\(755\) | −28.7132 | −1.04498 | ||||||||
\(756\) | −10.4433 | −0.379818 | ||||||||
\(757\) | 39.3734 | 1.43105 | 0.715525 | − | 0.698587i | \(-0.246187\pi\) | ||||
0.715525 | + | 0.698587i | \(0.246187\pi\) | |||||||
\(758\) | 48.2503 | 1.75253 | ||||||||
\(759\) | −0.339463 | −0.0123217 | ||||||||
\(760\) | −68.6974 | −2.49192 | ||||||||
\(761\) | −10.7107 | −0.388264 | −0.194132 | − | 0.980975i | \(-0.562189\pi\) | ||||
−0.194132 | + | 0.980975i | \(0.562189\pi\) | |||||||
\(762\) | 82.0920 | 2.97388 | ||||||||
\(763\) | 0.0160236 | 0.000580095 0 | ||||||||
\(764\) | −0.170581 | −0.00617140 | ||||||||
\(765\) | −3.21149 | −0.116112 | ||||||||
\(766\) | −53.2772 | −1.92498 | ||||||||
\(767\) | −14.6880 | −0.530351 | ||||||||
\(768\) | 61.8374 | 2.23136 | ||||||||
\(769\) | 46.2157 | 1.66658 | 0.833291 | − | 0.552834i | \(-0.186454\pi\) | ||||
0.833291 | + | 0.552834i | \(0.186454\pi\) | |||||||
\(770\) | −0.153270 | −0.00552345 | ||||||||
\(771\) | 1.69881 | 0.0611812 | ||||||||
\(772\) | −51.4503 | −1.85174 | ||||||||
\(773\) | 40.0454 | 1.44033 | 0.720166 | − | 0.693802i | \(-0.244066\pi\) | ||||
0.720166 | + | 0.693802i | \(0.244066\pi\) | |||||||
\(774\) | 2.16045 | 0.0776559 | ||||||||
\(775\) | −10.3494 | −0.371762 | ||||||||
\(776\) | −93.3604 | −3.35144 | ||||||||
\(777\) | 0.812422 | 0.0291455 | ||||||||
\(778\) | −37.5765 | −1.34718 | ||||||||
\(779\) | −29.7563 | −1.06613 | ||||||||
\(780\) | −46.8290 | −1.67675 | ||||||||
\(781\) | −0.282851 | −0.0101212 | ||||||||
\(782\) | −12.1310 | −0.433802 | ||||||||
\(783\) | −3.74861 | −0.133964 | ||||||||
\(784\) | −44.3339 | −1.58335 | ||||||||
\(785\) | 13.4479 | 0.479976 | ||||||||
\(786\) | 81.4396 | 2.90486 | ||||||||
\(787\) | 47.6121 | 1.69719 | 0.848593 | − | 0.529046i | \(-0.177450\pi\) | ||||
0.848593 | + | 0.529046i | \(0.177450\pi\) | |||||||
\(788\) | 77.4564 | 2.75927 | ||||||||
\(789\) | −39.2664 | −1.39792 | ||||||||
\(790\) | −50.3097 | −1.78994 | ||||||||
\(791\) | −6.52048 | −0.231842 | ||||||||
\(792\) | −0.276364 | −0.00982018 | ||||||||
\(793\) | −16.8004 | −0.596601 | ||||||||
\(794\) | 5.59458 | 0.198544 | ||||||||
\(795\) | −25.3102 | −0.897661 | ||||||||
\(796\) | 88.8638 | 3.14969 | ||||||||
\(797\) | 33.2123 | 1.17644 | 0.588220 | − | 0.808701i | \(-0.299829\pi\) | ||||
0.588220 | + | 0.808701i | \(0.299829\pi\) | |||||||
\(798\) | 14.6967 | 0.520258 | ||||||||
\(799\) | 2.33187 | 0.0824955 | ||||||||
\(800\) | −5.44456 | −0.192494 | ||||||||
\(801\) | −0.459756 | −0.0162447 | ||||||||
\(802\) | 41.9751 | 1.48219 | ||||||||
\(803\) | 0.0446792 | 0.00157670 | ||||||||
\(804\) | −82.0032 | −2.89203 | ||||||||
\(805\) | 6.71324 | 0.236611 | ||||||||
\(806\) | −47.7496 | −1.68191 | ||||||||
\(807\) | 11.9703 | 0.421375 | ||||||||
\(808\) | 41.2748 | 1.45204 | ||||||||
\(809\) | 22.2372 | 0.781819 | 0.390910 | − | 0.920429i | \(-0.372161\pi\) | ||||
0.390910 | + | 0.920429i | \(0.372161\pi\) | |||||||
\(810\) | −69.9865 | −2.45908 | ||||||||
\(811\) | 7.63656 | 0.268156 | 0.134078 | − | 0.990971i | \(-0.457193\pi\) | ||||
0.134078 | + | 0.990971i | \(0.457193\pi\) | |||||||
\(812\) | 2.78591 | 0.0977662 | ||||||||
\(813\) | −9.00617 | −0.315860 | ||||||||
\(814\) | −0.0620219 | −0.00217387 | ||||||||
\(815\) | 22.0211 | 0.771366 | ||||||||
\(816\) | −15.2578 | −0.534129 | ||||||||
\(817\) | 3.30837 | 0.115745 | ||||||||
\(818\) | 34.4401 | 1.20417 | ||||||||
\(819\) | 1.53280 | 0.0535604 | ||||||||
\(820\) | −72.3251 | −2.52570 | ||||||||
\(821\) | −36.3186 | −1.26753 | −0.633765 | − | 0.773526i | \(-0.718491\pi\) | ||||
−0.633765 | + | 0.773526i | \(0.718491\pi\) | |||||||
\(822\) | 46.7645 | 1.63110 | ||||||||
\(823\) | −45.5195 | −1.58671 | −0.793356 | − | 0.608758i | \(-0.791668\pi\) | ||||
−0.793356 | + | 0.608758i | \(0.791668\pi\) | |||||||
\(824\) | 10.4690 | 0.364705 | ||||||||
\(825\) | −0.0908041 | −0.00316139 | ||||||||
\(826\) | 11.2041 | 0.389840 | ||||||||
\(827\) | −39.0261 | −1.35707 | −0.678535 | − | 0.734568i | \(-0.737385\pi\) | ||||
−0.678535 | + | 0.734568i | \(0.737385\pi\) | |||||||
\(828\) | 22.0982 | 0.767964 | ||||||||
\(829\) | −33.5883 | −1.16657 | −0.583286 | − | 0.812267i | \(-0.698233\pi\) | ||||
−0.583286 | + | 0.812267i | \(0.698233\pi\) | |||||||
\(830\) | 45.9273 | 1.59416 | ||||||||
\(831\) | 17.0413 | 0.591157 | ||||||||
\(832\) | 2.98251 | 0.103400 | ||||||||
\(833\) | −7.35489 | −0.254832 | ||||||||
\(834\) | −5.17061 | −0.179043 | ||||||||
\(835\) | 32.6248 | 1.12903 | ||||||||
\(836\) | −0.772591 | −0.0267206 | ||||||||
\(837\) | −33.7485 | −1.16652 | ||||||||
\(838\) | 45.4223 | 1.56909 | ||||||||
\(839\) | 47.7165 | 1.64736 | 0.823679 | − | 0.567057i | \(-0.191918\pi\) | ||||
0.823679 | + | 0.567057i | \(0.191918\pi\) | |||||||
\(840\) | 19.5674 | 0.675138 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −18.6479 | −0.642649 | ||||||||
\(843\) | −0.985336 | −0.0339368 | ||||||||
\(844\) | 7.45620 | 0.256653 | ||||||||
\(845\) | 21.3764 | 0.735372 | ||||||||
\(846\) | −6.16877 | −0.212087 | ||||||||
\(847\) | 6.92828 | 0.238058 | ||||||||
\(848\) | −33.5868 | −1.15338 | ||||||||
\(849\) | 18.6516 | 0.640121 | ||||||||
\(850\) | −3.24495 | −0.111301 | ||||||||
\(851\) | 2.71657 | 0.0931229 | ||||||||
\(852\) | 65.9222 | 2.25846 | ||||||||
\(853\) | −38.0888 | −1.30414 | −0.652068 | − | 0.758161i | \(-0.726098\pi\) | ||||
−0.652068 | + | 0.758161i | \(0.726098\pi\) | |||||||
\(854\) | 12.8155 | 0.438538 | ||||||||
\(855\) | 13.0098 | 0.444927 | ||||||||
\(856\) | 12.4655 | 0.426061 | ||||||||
\(857\) | 4.47298 | 0.152794 | 0.0763970 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763970 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(858\) | −0.418948 | −0.0143026 | ||||||||
\(859\) | −32.3534 | −1.10388 | −0.551942 | − | 0.833883i | \(-0.686113\pi\) | ||||
−0.551942 | + | 0.833883i | \(0.686113\pi\) | |||||||
\(860\) | 8.04127 | 0.274205 | ||||||||
\(861\) | 8.47561 | 0.288848 | ||||||||
\(862\) | 35.1392 | 1.19684 | ||||||||
\(863\) | 7.89144 | 0.268628 | 0.134314 | − | 0.990939i | \(-0.457117\pi\) | ||||
0.134314 | + | 0.990939i | \(0.457117\pi\) | |||||||
\(864\) | −17.7542 | −0.604011 | ||||||||
\(865\) | −47.6183 | −1.61907 | ||||||||
\(866\) | −0.988129 | −0.0335780 | ||||||||
\(867\) | 32.1533 | 1.09198 | ||||||||
\(868\) | 25.0814 | 0.851317 | ||||||||
\(869\) | −0.309930 | −0.0105136 | ||||||||
\(870\) | 12.8222 | 0.434714 | ||||||||
\(871\) | −19.0195 | −0.644452 | ||||||||
\(872\) | 0.156171 | 0.00528862 | ||||||||
\(873\) | 17.6805 | 0.598394 | ||||||||
\(874\) | 49.1428 | 1.66228 | ||||||||
\(875\) | −6.01484 | −0.203339 | ||||||||
\(876\) | −10.4131 | −0.351826 | ||||||||
\(877\) | −51.8770 | −1.75176 | −0.875881 | − | 0.482527i | \(-0.839719\pi\) | ||||
−0.875881 | + | 0.482527i | \(0.839719\pi\) | |||||||
\(878\) | 60.3858 | 2.03792 | ||||||||
\(879\) | −18.5014 | −0.624038 | ||||||||
\(880\) | −0.644602 | −0.0217295 | ||||||||
\(881\) | −31.5281 | −1.06221 | −0.531105 | − | 0.847306i | \(-0.678223\pi\) | ||||
−0.531105 | + | 0.847306i | \(0.678223\pi\) | |||||||
\(882\) | 19.4568 | 0.655144 | ||||||||
\(883\) | 58.7926 | 1.97853 | 0.989265 | − | 0.146135i | \(-0.0466833\pi\) | ||||
0.989265 | + | 0.146135i | \(0.0466833\pi\) | |||||||
\(884\) | −10.3093 | −0.346739 | ||||||||
\(885\) | 35.5091 | 1.19362 | ||||||||
\(886\) | 72.9734 | 2.45159 | ||||||||
\(887\) | 1.69885 | 0.0570417 | 0.0285208 | − | 0.999593i | \(-0.490920\pi\) | ||||
0.0285208 | + | 0.999593i | \(0.490920\pi\) | |||||||
\(888\) | 7.91810 | 0.265714 | ||||||||
\(889\) | −10.0012 | −0.335429 | ||||||||
\(890\) | −2.48509 | −0.0833003 | ||||||||
\(891\) | −0.431147 | −0.0144440 | ||||||||
\(892\) | −29.6249 | −0.991914 | ||||||||
\(893\) | −9.44644 | −0.316113 | ||||||||
\(894\) | 65.3788 | 2.18660 | ||||||||
\(895\) | 7.23489 | 0.241836 | ||||||||
\(896\) | −8.24204 | −0.275347 | ||||||||
\(897\) | 18.3500 | 0.612689 | ||||||||
\(898\) | −10.8313 | −0.361446 | ||||||||
\(899\) | 9.00294 | 0.300265 | ||||||||
\(900\) | 5.91111 | 0.197037 | ||||||||
\(901\) | −5.57198 | −0.185630 | ||||||||
\(902\) | −0.647045 | −0.0215442 | ||||||||
\(903\) | −0.942337 | −0.0313590 | ||||||||
\(904\) | −63.5506 | −2.11366 | ||||||||
\(905\) | −39.2835 | −1.30583 | ||||||||
\(906\) | 59.8689 | 1.98901 | ||||||||
\(907\) | −40.5913 | −1.34781 | −0.673906 | − | 0.738817i | \(-0.735385\pi\) | ||||
−0.673906 | + | 0.738817i | \(0.735385\pi\) | |||||||
\(908\) | 2.94855 | 0.0978510 | ||||||||
\(909\) | −7.81656 | −0.259259 | ||||||||
\(910\) | 8.28513 | 0.274649 | ||||||||
\(911\) | 4.06313 | 0.134617 | 0.0673087 | − | 0.997732i | \(-0.478559\pi\) | ||||
0.0673087 | + | 0.997732i | \(0.478559\pi\) | |||||||
\(912\) | 61.8096 | 2.04672 | ||||||||
\(913\) | 0.282932 | 0.00936368 | ||||||||
\(914\) | 92.8423 | 3.07095 | ||||||||
\(915\) | 40.6161 | 1.34273 | ||||||||
\(916\) | 109.534 | 3.61909 | ||||||||
\(917\) | −9.92170 | −0.327643 | ||||||||
\(918\) | −10.5815 | −0.349241 | ||||||||
\(919\) | −5.19417 | −0.171340 | −0.0856699 | − | 0.996324i | \(-0.527303\pi\) | ||||
−0.0856699 | + | 0.996324i | \(0.527303\pi\) | |||||||
\(920\) | 65.4292 | 2.15714 | ||||||||
\(921\) | −45.1598 | −1.48807 | ||||||||
\(922\) | −59.6448 | −1.96430 | ||||||||
\(923\) | 15.2898 | 0.503268 | ||||||||
\(924\) | 0.220060 | 0.00723945 | ||||||||
\(925\) | 0.726664 | 0.0238926 | ||||||||
\(926\) | 47.0736 | 1.54694 | ||||||||
\(927\) | −1.98261 | −0.0651173 | ||||||||
\(928\) | 4.73622 | 0.155474 | ||||||||
\(929\) | 14.1571 | 0.464478 | 0.232239 | − | 0.972659i | \(-0.425395\pi\) | ||||
0.232239 | + | 0.972659i | \(0.425395\pi\) | |||||||
\(930\) | 115.438 | 3.78535 | ||||||||
\(931\) | 29.7948 | 0.976485 | ||||||||
\(932\) | −33.0133 | −1.08139 | ||||||||
\(933\) | 59.9095 | 1.96135 | ||||||||
\(934\) | 0.0751461 | 0.00245886 | ||||||||
\(935\) | −0.106938 | −0.00349724 | ||||||||
\(936\) | 14.9391 | 0.488301 | ||||||||
\(937\) | −6.43455 | −0.210207 | −0.105104 | − | 0.994461i | \(-0.533517\pi\) | ||||
−0.105104 | + | 0.994461i | \(0.533517\pi\) | |||||||
\(938\) | 14.5082 | 0.473711 | ||||||||
\(939\) | 35.3970 | 1.15514 | ||||||||
\(940\) | −22.9603 | −0.748884 | ||||||||
\(941\) | 7.80257 | 0.254357 | 0.127178 | − | 0.991880i | \(-0.459408\pi\) | ||||
0.127178 | + | 0.991880i | \(0.459408\pi\) | |||||||
\(942\) | −28.0397 | −0.913584 | ||||||||
\(943\) | 28.3407 | 0.922900 | ||||||||
\(944\) | 47.1208 | 1.53365 | ||||||||
\(945\) | 5.85577 | 0.190488 | ||||||||
\(946\) | 0.0719399 | 0.00233897 | ||||||||
\(947\) | 45.6451 | 1.48327 | 0.741633 | − | 0.670806i | \(-0.234051\pi\) | ||||
0.741633 | + | 0.670806i | \(0.234051\pi\) | |||||||
\(948\) | 72.2333 | 2.34603 | ||||||||
\(949\) | −2.41518 | −0.0784000 | ||||||||
\(950\) | 13.1454 | 0.426492 | ||||||||
\(951\) | −6.90578 | −0.223935 | ||||||||
\(952\) | 4.30770 | 0.139613 | ||||||||
\(953\) | −41.0425 | −1.32950 | −0.664748 | − | 0.747067i | \(-0.731461\pi\) | ||||
−0.664748 | + | 0.747067i | \(0.731461\pi\) | |||||||
\(954\) | 14.7402 | 0.477233 | ||||||||
\(955\) | 0.0956483 | 0.00309511 | ||||||||
\(956\) | 67.1609 | 2.17214 | ||||||||
\(957\) | 0.0789904 | 0.00255340 | ||||||||
\(958\) | 29.3491 | 0.948227 | ||||||||
\(959\) | −5.69726 | −0.183974 | ||||||||
\(960\) | −7.21040 | −0.232715 | ||||||||
\(961\) | 50.0529 | 1.61461 | ||||||||
\(962\) | 3.35265 | 0.108094 | ||||||||
\(963\) | −2.36069 | −0.0760723 | ||||||||
\(964\) | −110.887 | −3.57144 | ||||||||
\(965\) | 28.8493 | 0.928691 | ||||||||
\(966\) | −13.9975 | −0.450363 | ||||||||
\(967\) | 2.07805 | 0.0668255 | 0.0334128 | − | 0.999442i | \(-0.489362\pi\) | ||||
0.0334128 | + | 0.999442i | \(0.489362\pi\) | |||||||
\(968\) | 67.5251 | 2.17034 | ||||||||
\(969\) | 10.2541 | 0.329408 | ||||||||
\(970\) | 95.5670 | 3.06847 | ||||||||
\(971\) | −28.5806 | −0.917195 | −0.458598 | − | 0.888644i | \(-0.651648\pi\) | ||||
−0.458598 | + | 0.888644i | \(0.651648\pi\) | |||||||
\(972\) | 50.7492 | 1.62778 | ||||||||
\(973\) | 0.629929 | 0.0201946 | ||||||||
\(974\) | −21.3627 | −0.684504 | ||||||||
\(975\) | 4.90850 | 0.157198 | ||||||||
\(976\) | 53.8978 | 1.72523 | ||||||||
\(977\) | 11.8580 | 0.379371 | 0.189685 | − | 0.981845i | \(-0.439253\pi\) | ||||
0.189685 | + | 0.981845i | \(0.439253\pi\) | |||||||
\(978\) | −45.9155 | −1.46821 | ||||||||
\(979\) | −0.0153092 | −0.000489284 0 | ||||||||
\(980\) | 72.4187 | 2.31333 | ||||||||
\(981\) | −0.0295755 | −0.000944273 0 | ||||||||
\(982\) | 52.7980 | 1.68485 | ||||||||
\(983\) | 14.4929 | 0.462252 | 0.231126 | − | 0.972924i | \(-0.425759\pi\) | ||||
0.231126 | + | 0.972924i | \(0.425759\pi\) | |||||||
\(984\) | 82.6058 | 2.63338 | ||||||||
\(985\) | −43.4315 | −1.38384 | ||||||||
\(986\) | 2.82278 | 0.0898956 | ||||||||
\(987\) | 2.69067 | 0.0856449 | ||||||||
\(988\) | 41.7631 | 1.32866 | ||||||||
\(989\) | −3.15098 | −0.100195 | ||||||||
\(990\) | 0.282896 | 0.00899103 | ||||||||
\(991\) | −6.11159 | −0.194141 | −0.0970706 | − | 0.995278i | \(-0.530947\pi\) | ||||
−0.0970706 | + | 0.995278i | \(0.530947\pi\) | |||||||
\(992\) | 42.6399 | 1.35382 | ||||||||
\(993\) | −38.7345 | −1.22920 | ||||||||
\(994\) | −11.6631 | −0.369933 | ||||||||
\(995\) | −49.8278 | −1.57965 | ||||||||
\(996\) | −65.9411 | −2.08942 | ||||||||
\(997\) | 12.8682 | 0.407540 | 0.203770 | − | 0.979019i | \(-0.434681\pi\) | ||||
0.203770 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(998\) | −70.7341 | −2.23905 | ||||||||
\(999\) | 2.36959 | 0.0749705 |
(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 | 4031.2.a.c.1.3 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.3 | ✓ | 61 | 1.1 | even | 1 | trivial |