Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11064 | −0.785343 | −0.392671 | − | 0.919679i | \(-0.628449\pi\) | ||||
−0.392671 | + | 0.919679i | \(0.628449\pi\) | |||||||
\(3\) | 3.24263 | 1.87213 | 0.936067 | − | 0.351821i | \(-0.114438\pi\) | ||||
0.936067 | + | 0.351821i | \(0.114438\pi\) | |||||||
\(4\) | −0.766474 | −0.383237 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.60140 | −1.47027 | ||||||||
\(7\) | 2.31774 | 0.876021 | 0.438011 | − | 0.898970i | \(-0.355683\pi\) | ||||
0.438011 | + | 0.898970i | \(0.355683\pi\) | |||||||
\(8\) | 3.07256 | 1.08631 | ||||||||
\(9\) | 7.51466 | 2.50489 | ||||||||
\(10\) | −1.11064 | −0.351216 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.48539 | −0.717471 | ||||||||
\(13\) | −0.104355 | −0.0289430 | −0.0144715 | − | 0.999895i | \(-0.504607\pi\) | ||||
−0.0144715 | + | 0.999895i | \(0.504607\pi\) | |||||||
\(14\) | −2.57417 | −0.687977 | ||||||||
\(15\) | 3.24263 | 0.837244 | ||||||||
\(16\) | −1.87957 | −0.469892 | ||||||||
\(17\) | 3.59955 | 0.873019 | 0.436509 | − | 0.899700i | \(-0.356215\pi\) | ||||
0.436509 | + | 0.899700i | \(0.356215\pi\) | |||||||
\(18\) | −8.34610 | −1.96719 | ||||||||
\(19\) | 3.68931 | 0.846386 | 0.423193 | − | 0.906040i | \(-0.360909\pi\) | ||||
0.423193 | + | 0.906040i | \(0.360909\pi\) | |||||||
\(20\) | −0.766474 | −0.171389 | ||||||||
\(21\) | 7.51556 | 1.64003 | ||||||||
\(22\) | −1.11064 | −0.236790 | ||||||||
\(23\) | 7.11088 | 1.48272 | 0.741360 | − | 0.671107i | \(-0.234181\pi\) | ||||
0.741360 | + | 0.671107i | \(0.234181\pi\) | |||||||
\(24\) | 9.96319 | 2.03373 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.115901 | 0.0227301 | ||||||||
\(27\) | 14.6394 | 2.81735 | ||||||||
\(28\) | −1.77648 | −0.335724 | ||||||||
\(29\) | 4.35072 | 0.807908 | 0.403954 | − | 0.914779i | \(-0.367636\pi\) | ||||
0.403954 | + | 0.914779i | \(0.367636\pi\) | |||||||
\(30\) | −3.60140 | −0.657523 | ||||||||
\(31\) | 0.187969 | 0.0337602 | 0.0168801 | − | 0.999858i | \(-0.494627\pi\) | ||||
0.0168801 | + | 0.999858i | \(0.494627\pi\) | |||||||
\(32\) | −4.05760 | −0.717289 | ||||||||
\(33\) | 3.24263 | 0.564470 | ||||||||
\(34\) | −3.99781 | −0.685619 | ||||||||
\(35\) | 2.31774 | 0.391769 | ||||||||
\(36\) | −5.75979 | −0.959966 | ||||||||
\(37\) | −2.99014 | −0.491576 | −0.245788 | − | 0.969324i | \(-0.579047\pi\) | ||||
−0.245788 | + | 0.969324i | \(0.579047\pi\) | |||||||
\(38\) | −4.09750 | −0.664703 | ||||||||
\(39\) | −0.338386 | −0.0541851 | ||||||||
\(40\) | 3.07256 | 0.485815 | ||||||||
\(41\) | −9.01977 | −1.40865 | −0.704325 | − | 0.709877i | \(-0.748750\pi\) | ||||
−0.704325 | + | 0.709877i | \(0.748750\pi\) | |||||||
\(42\) | −8.34710 | −1.28799 | ||||||||
\(43\) | −5.30348 | −0.808773 | −0.404387 | − | 0.914588i | \(-0.632515\pi\) | ||||
−0.404387 | + | 0.914588i | \(0.632515\pi\) | |||||||
\(44\) | −0.766474 | −0.115550 | ||||||||
\(45\) | 7.51466 | 1.12022 | ||||||||
\(46\) | −7.89764 | −1.16444 | ||||||||
\(47\) | −12.0184 | −1.75306 | −0.876532 | − | 0.481344i | \(-0.840149\pi\) | ||||
−0.876532 | + | 0.481344i | \(0.840149\pi\) | |||||||
\(48\) | −6.09475 | −0.879701 | ||||||||
\(49\) | −1.62810 | −0.232586 | ||||||||
\(50\) | −1.11064 | −0.157069 | ||||||||
\(51\) | 11.6720 | 1.63441 | ||||||||
\(52\) | 0.0799857 | 0.0110920 | ||||||||
\(53\) | −12.2860 | −1.68762 | −0.843808 | − | 0.536646i | \(-0.819691\pi\) | ||||
−0.843808 | + | 0.536646i | \(0.819691\pi\) | |||||||
\(54\) | −16.2591 | −2.21258 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 7.12139 | 0.951635 | ||||||||
\(57\) | 11.9631 | 1.58455 | ||||||||
\(58\) | −4.83209 | −0.634484 | ||||||||
\(59\) | −4.26462 | −0.555206 | −0.277603 | − | 0.960696i | \(-0.589540\pi\) | ||||
−0.277603 | + | 0.960696i | \(0.589540\pi\) | |||||||
\(60\) | −2.48539 | −0.320863 | ||||||||
\(61\) | −0.802852 | −0.102795 | −0.0513973 | − | 0.998678i | \(-0.516367\pi\) | ||||
−0.0513973 | + | 0.998678i | \(0.516367\pi\) | |||||||
\(62\) | −0.208766 | −0.0265133 | ||||||||
\(63\) | 17.4170 | 2.19433 | ||||||||
\(64\) | 8.26568 | 1.03321 | ||||||||
\(65\) | −0.104355 | −0.0129437 | ||||||||
\(66\) | −3.60140 | −0.443302 | ||||||||
\(67\) | 6.84360 | 0.836079 | 0.418039 | − | 0.908429i | \(-0.362717\pi\) | ||||
0.418039 | + | 0.908429i | \(0.362717\pi\) | |||||||
\(68\) | −2.75896 | −0.334573 | ||||||||
\(69\) | 23.0580 | 2.77585 | ||||||||
\(70\) | −2.57417 | −0.307673 | ||||||||
\(71\) | −8.85756 | −1.05120 | −0.525600 | − | 0.850732i | \(-0.676159\pi\) | ||||
−0.525600 | + | 0.850732i | \(0.676159\pi\) | |||||||
\(72\) | 23.0893 | 2.72110 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 3.32098 | 0.386056 | ||||||||
\(75\) | 3.24263 | 0.374427 | ||||||||
\(76\) | −2.82776 | −0.324366 | ||||||||
\(77\) | 2.31774 | 0.264130 | ||||||||
\(78\) | 0.375826 | 0.0425539 | ||||||||
\(79\) | −4.89807 | −0.551076 | −0.275538 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275538 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(80\) | −1.87957 | −0.210142 | ||||||||
\(81\) | 24.9261 | 2.76957 | ||||||||
\(82\) | 10.0177 | 1.10627 | ||||||||
\(83\) | 8.39151 | 0.921088 | 0.460544 | − | 0.887637i | \(-0.347654\pi\) | ||||
0.460544 | + | 0.887637i | \(0.347654\pi\) | |||||||
\(84\) | −5.76048 | −0.628520 | ||||||||
\(85\) | 3.59955 | 0.390426 | ||||||||
\(86\) | 5.89027 | 0.635164 | ||||||||
\(87\) | 14.1078 | 1.51251 | ||||||||
\(88\) | 3.07256 | 0.327536 | ||||||||
\(89\) | 2.19724 | 0.232907 | 0.116454 | − | 0.993196i | \(-0.462847\pi\) | ||||
0.116454 | + | 0.993196i | \(0.462847\pi\) | |||||||
\(90\) | −8.34610 | −0.879756 | ||||||||
\(91\) | −0.241868 | −0.0253547 | ||||||||
\(92\) | −5.45030 | −0.568233 | ||||||||
\(93\) | 0.609514 | 0.0632037 | ||||||||
\(94\) | 13.3481 | 1.37676 | ||||||||
\(95\) | 3.68931 | 0.378515 | ||||||||
\(96\) | −13.1573 | −1.34286 | ||||||||
\(97\) | −0.769097 | −0.0780900 | −0.0390450 | − | 0.999237i | \(-0.512432\pi\) | ||||
−0.0390450 | + | 0.999237i | \(0.512432\pi\) | |||||||
\(98\) | 1.80824 | 0.182660 | ||||||||
\(99\) | 7.51466 | 0.755252 | ||||||||
\(100\) | −0.766474 | −0.0766474 | ||||||||
\(101\) | −12.0828 | −1.20229 | −0.601143 | − | 0.799141i | \(-0.705288\pi\) | ||||
−0.601143 | + | 0.799141i | \(0.705288\pi\) | |||||||
\(102\) | −12.9634 | −1.28357 | ||||||||
\(103\) | −2.23624 | −0.220344 | −0.110172 | − | 0.993913i | \(-0.535140\pi\) | ||||
−0.110172 | + | 0.993913i | \(0.535140\pi\) | |||||||
\(104\) | −0.320638 | −0.0314412 | ||||||||
\(105\) | 7.51556 | 0.733444 | ||||||||
\(106\) | 13.6454 | 1.32536 | ||||||||
\(107\) | 11.7229 | 1.13330 | 0.566649 | − | 0.823959i | \(-0.308239\pi\) | ||||
0.566649 | + | 0.823959i | \(0.308239\pi\) | |||||||
\(108\) | −11.2207 | −1.07971 | ||||||||
\(109\) | −6.69712 | −0.641468 | −0.320734 | − | 0.947169i | \(-0.603930\pi\) | ||||
−0.320734 | + | 0.947169i | \(0.603930\pi\) | |||||||
\(110\) | −1.11064 | −0.105896 | ||||||||
\(111\) | −9.69593 | −0.920297 | ||||||||
\(112\) | −4.35634 | −0.411636 | ||||||||
\(113\) | −10.6623 | −1.00302 | −0.501511 | − | 0.865151i | \(-0.667222\pi\) | ||||
−0.501511 | + | 0.865151i | \(0.667222\pi\) | |||||||
\(114\) | −13.2867 | −1.24441 | ||||||||
\(115\) | 7.11088 | 0.663093 | ||||||||
\(116\) | −3.33471 | −0.309620 | ||||||||
\(117\) | −0.784195 | −0.0724989 | ||||||||
\(118\) | 4.73647 | 0.436027 | ||||||||
\(119\) | 8.34280 | 0.764783 | ||||||||
\(120\) | 9.96319 | 0.909511 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.891681 | 0.0807290 | ||||||||
\(123\) | −29.2478 | −2.63718 | ||||||||
\(124\) | −0.144073 | −0.0129382 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −19.3440 | −1.72330 | ||||||||
\(127\) | −8.78544 | −0.779582 | −0.389791 | − | 0.920903i | \(-0.627453\pi\) | ||||
−0.389791 | + | 0.920903i | \(0.627453\pi\) | |||||||
\(128\) | −1.06501 | −0.0941347 | ||||||||
\(129\) | −17.1972 | −1.51413 | ||||||||
\(130\) | 0.115901 | 0.0101652 | ||||||||
\(131\) | 1.42501 | 0.124504 | 0.0622519 | − | 0.998060i | \(-0.480172\pi\) | ||||
0.0622519 | + | 0.998060i | \(0.480172\pi\) | |||||||
\(132\) | −2.48539 | −0.216326 | ||||||||
\(133\) | 8.55084 | 0.741452 | ||||||||
\(134\) | −7.60079 | −0.656608 | ||||||||
\(135\) | 14.6394 | 1.25996 | ||||||||
\(136\) | 11.0598 | 0.948373 | ||||||||
\(137\) | 1.06013 | 0.0905734 | 0.0452867 | − | 0.998974i | \(-0.485580\pi\) | ||||
0.0452867 | + | 0.998974i | \(0.485580\pi\) | |||||||
\(138\) | −25.6091 | −2.17999 | ||||||||
\(139\) | 3.28018 | 0.278221 | 0.139111 | − | 0.990277i | \(-0.455576\pi\) | ||||
0.139111 | + | 0.990277i | \(0.455576\pi\) | |||||||
\(140\) | −1.77648 | −0.150140 | ||||||||
\(141\) | −38.9712 | −3.28197 | ||||||||
\(142\) | 9.83758 | 0.825551 | ||||||||
\(143\) | −0.104355 | −0.00872663 | ||||||||
\(144\) | −14.1243 | −1.17703 | ||||||||
\(145\) | 4.35072 | 0.361307 | ||||||||
\(146\) | −1.11064 | −0.0919174 | ||||||||
\(147\) | −5.27934 | −0.435433 | ||||||||
\(148\) | 2.29187 | 0.188390 | ||||||||
\(149\) | 1.07627 | 0.0881711 | 0.0440856 | − | 0.999028i | \(-0.485963\pi\) | ||||
0.0440856 | + | 0.999028i | \(0.485963\pi\) | |||||||
\(150\) | −3.60140 | −0.294053 | ||||||||
\(151\) | 12.7304 | 1.03599 | 0.517994 | − | 0.855384i | \(-0.326679\pi\) | ||||
0.517994 | + | 0.855384i | \(0.326679\pi\) | |||||||
\(152\) | 11.3356 | 0.919442 | ||||||||
\(153\) | 27.0494 | 2.18681 | ||||||||
\(154\) | −2.57417 | −0.207433 | ||||||||
\(155\) | 0.187969 | 0.0150980 | ||||||||
\(156\) | 0.259364 | 0.0207657 | ||||||||
\(157\) | 16.1169 | 1.28627 | 0.643136 | − | 0.765752i | \(-0.277633\pi\) | ||||
0.643136 | + | 0.765752i | \(0.277633\pi\) | |||||||
\(158\) | 5.44000 | 0.432783 | ||||||||
\(159\) | −39.8391 | −3.15944 | ||||||||
\(160\) | −4.05760 | −0.320781 | ||||||||
\(161\) | 16.4811 | 1.29889 | ||||||||
\(162\) | −27.6840 | −2.17506 | ||||||||
\(163\) | −5.22058 | −0.408907 | −0.204454 | − | 0.978876i | \(-0.565542\pi\) | ||||
−0.204454 | + | 0.978876i | \(0.565542\pi\) | |||||||
\(164\) | 6.91342 | 0.539847 | ||||||||
\(165\) | 3.24263 | 0.252439 | ||||||||
\(166\) | −9.31997 | −0.723370 | ||||||||
\(167\) | 1.12152 | 0.0867855 | 0.0433928 | − | 0.999058i | \(-0.486183\pi\) | ||||
0.0433928 | + | 0.999058i | \(0.486183\pi\) | |||||||
\(168\) | 23.0920 | 1.78159 | ||||||||
\(169\) | −12.9891 | −0.999162 | ||||||||
\(170\) | −3.99781 | −0.306618 | ||||||||
\(171\) | 27.7239 | 2.12010 | ||||||||
\(172\) | 4.06498 | 0.309952 | ||||||||
\(173\) | −11.1407 | −0.847010 | −0.423505 | − | 0.905894i | \(-0.639200\pi\) | ||||
−0.423505 | + | 0.905894i | \(0.639200\pi\) | |||||||
\(174\) | −15.6687 | −1.18784 | ||||||||
\(175\) | 2.31774 | 0.175204 | ||||||||
\(176\) | −1.87957 | −0.141678 | ||||||||
\(177\) | −13.8286 | −1.03942 | ||||||||
\(178\) | −2.44035 | −0.182912 | ||||||||
\(179\) | 5.42469 | 0.405460 | 0.202730 | − | 0.979235i | \(-0.435019\pi\) | ||||
0.202730 | + | 0.979235i | \(0.435019\pi\) | |||||||
\(180\) | −5.75979 | −0.429310 | ||||||||
\(181\) | −24.4907 | −1.82038 | −0.910190 | − | 0.414191i | \(-0.864065\pi\) | ||||
−0.910190 | + | 0.414191i | \(0.864065\pi\) | |||||||
\(182\) | 0.268629 | 0.0199121 | ||||||||
\(183\) | −2.60335 | −0.192445 | ||||||||
\(184\) | 21.8486 | 1.61070 | ||||||||
\(185\) | −2.99014 | −0.219840 | ||||||||
\(186\) | −0.676952 | −0.0496365 | ||||||||
\(187\) | 3.59955 | 0.263225 | ||||||||
\(188\) | 9.21179 | 0.671839 | ||||||||
\(189\) | 33.9302 | 2.46806 | ||||||||
\(190\) | −4.09750 | −0.297264 | ||||||||
\(191\) | −5.73400 | −0.414898 | −0.207449 | − | 0.978246i | \(-0.566516\pi\) | ||||
−0.207449 | + | 0.978246i | \(0.566516\pi\) | |||||||
\(192\) | 26.8025 | 1.93431 | ||||||||
\(193\) | −6.13432 | −0.441558 | −0.220779 | − | 0.975324i | \(-0.570860\pi\) | ||||
−0.220779 | + | 0.975324i | \(0.570860\pi\) | |||||||
\(194\) | 0.854192 | 0.0613274 | ||||||||
\(195\) | −0.338386 | −0.0242323 | ||||||||
\(196\) | 1.24790 | 0.0891357 | ||||||||
\(197\) | 21.1772 | 1.50881 | 0.754406 | − | 0.656408i | \(-0.227925\pi\) | ||||
0.754406 | + | 0.656408i | \(0.227925\pi\) | |||||||
\(198\) | −8.34610 | −0.593131 | ||||||||
\(199\) | −15.3514 | −1.08823 | −0.544114 | − | 0.839011i | \(-0.683134\pi\) | ||||
−0.544114 | + | 0.839011i | \(0.683134\pi\) | |||||||
\(200\) | 3.07256 | 0.217263 | ||||||||
\(201\) | 22.1913 | 1.56525 | ||||||||
\(202\) | 13.4197 | 0.944207 | ||||||||
\(203\) | 10.0838 | 0.707745 | ||||||||
\(204\) | −8.94630 | −0.626366 | ||||||||
\(205\) | −9.01977 | −0.629968 | ||||||||
\(206\) | 2.48367 | 0.173045 | ||||||||
\(207\) | 53.4358 | 3.71405 | ||||||||
\(208\) | 0.196143 | 0.0136001 | ||||||||
\(209\) | 3.68931 | 0.255195 | ||||||||
\(210\) | −8.34710 | −0.576004 | ||||||||
\(211\) | −5.00689 | −0.344688 | −0.172344 | − | 0.985037i | \(-0.555134\pi\) | ||||
−0.172344 | + | 0.985037i | \(0.555134\pi\) | |||||||
\(212\) | 9.41692 | 0.646757 | ||||||||
\(213\) | −28.7218 | −1.96799 | ||||||||
\(214\) | −13.0200 | −0.890028 | ||||||||
\(215\) | −5.30348 | −0.361694 | ||||||||
\(216\) | 44.9804 | 3.06053 | ||||||||
\(217\) | 0.435662 | 0.0295747 | ||||||||
\(218\) | 7.43810 | 0.503772 | ||||||||
\(219\) | 3.24263 | 0.219117 | ||||||||
\(220\) | −0.766474 | −0.0516757 | ||||||||
\(221\) | −0.375632 | −0.0252678 | ||||||||
\(222\) | 10.7687 | 0.722748 | ||||||||
\(223\) | 1.46903 | 0.0983736 | 0.0491868 | − | 0.998790i | \(-0.484337\pi\) | ||||
0.0491868 | + | 0.998790i | \(0.484337\pi\) | |||||||
\(224\) | −9.40444 | −0.628360 | ||||||||
\(225\) | 7.51466 | 0.500977 | ||||||||
\(226\) | 11.8420 | 0.787716 | ||||||||
\(227\) | 14.8681 | 0.986829 | 0.493414 | − | 0.869794i | \(-0.335749\pi\) | ||||
0.493414 | + | 0.869794i | \(0.335749\pi\) | |||||||
\(228\) | −9.16939 | −0.607258 | ||||||||
\(229\) | −7.39386 | −0.488600 | −0.244300 | − | 0.969700i | \(-0.578558\pi\) | ||||
−0.244300 | + | 0.969700i | \(0.578558\pi\) | |||||||
\(230\) | −7.89764 | −0.520755 | ||||||||
\(231\) | 7.51556 | 0.494488 | ||||||||
\(232\) | 13.3678 | 0.877642 | ||||||||
\(233\) | −9.19061 | −0.602097 | −0.301048 | − | 0.953609i | \(-0.597337\pi\) | ||||
−0.301048 | + | 0.953609i | \(0.597337\pi\) | |||||||
\(234\) | 0.870960 | 0.0569364 | ||||||||
\(235\) | −12.0184 | −0.783994 | ||||||||
\(236\) | 3.26872 | 0.212776 | ||||||||
\(237\) | −15.8826 | −1.03169 | ||||||||
\(238\) | −9.26586 | −0.600617 | ||||||||
\(239\) | −17.5535 | −1.13544 | −0.567720 | − | 0.823222i | \(-0.692174\pi\) | ||||
−0.567720 | + | 0.823222i | \(0.692174\pi\) | |||||||
\(240\) | −6.09475 | −0.393414 | ||||||||
\(241\) | 13.9738 | 0.900133 | 0.450066 | − | 0.892995i | \(-0.351400\pi\) | ||||
0.450066 | + | 0.892995i | \(0.351400\pi\) | |||||||
\(242\) | −1.11064 | −0.0713948 | ||||||||
\(243\) | 36.9081 | 2.36766 | ||||||||
\(244\) | 0.615366 | 0.0393947 | ||||||||
\(245\) | −1.62810 | −0.104016 | ||||||||
\(246\) | 32.4838 | 2.07109 | ||||||||
\(247\) | −0.384999 | −0.0244969 | ||||||||
\(248\) | 0.577546 | 0.0366742 | ||||||||
\(249\) | 27.2106 | 1.72440 | ||||||||
\(250\) | −1.11064 | −0.0702432 | ||||||||
\(251\) | −15.8761 | −1.00209 | −0.501044 | − | 0.865422i | \(-0.667050\pi\) | ||||
−0.501044 | + | 0.865422i | \(0.667050\pi\) | |||||||
\(252\) | −13.3497 | −0.840950 | ||||||||
\(253\) | 7.11088 | 0.447057 | ||||||||
\(254\) | 9.75748 | 0.612239 | ||||||||
\(255\) | 11.6720 | 0.730930 | ||||||||
\(256\) | −15.3485 | −0.959281 | ||||||||
\(257\) | −10.8144 | −0.674583 | −0.337291 | − | 0.941400i | \(-0.609511\pi\) | ||||
−0.337291 | + | 0.941400i | \(0.609511\pi\) | |||||||
\(258\) | 19.1000 | 1.18911 | ||||||||
\(259\) | −6.93035 | −0.430631 | ||||||||
\(260\) | 0.0799857 | 0.00496050 | ||||||||
\(261\) | 32.6942 | 2.02372 | ||||||||
\(262\) | −1.58268 | −0.0977782 | ||||||||
\(263\) | 9.71885 | 0.599290 | 0.299645 | − | 0.954051i | \(-0.403132\pi\) | ||||
0.299645 | + | 0.954051i | \(0.403132\pi\) | |||||||
\(264\) | 9.96319 | 0.613192 | ||||||||
\(265\) | −12.2860 | −0.754725 | ||||||||
\(266\) | −9.49693 | −0.582294 | ||||||||
\(267\) | 7.12485 | 0.436034 | ||||||||
\(268\) | −5.24544 | −0.320416 | ||||||||
\(269\) | 14.9942 | 0.914212 | 0.457106 | − | 0.889412i | \(-0.348886\pi\) | ||||
0.457106 | + | 0.889412i | \(0.348886\pi\) | |||||||
\(270\) | −16.2591 | −0.989498 | ||||||||
\(271\) | 17.1807 | 1.04365 | 0.521827 | − | 0.853052i | \(-0.325251\pi\) | ||||
0.521827 | + | 0.853052i | \(0.325251\pi\) | |||||||
\(272\) | −6.76560 | −0.410225 | ||||||||
\(273\) | −0.784289 | −0.0474673 | ||||||||
\(274\) | −1.17743 | −0.0711312 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −17.6733 | −1.06381 | ||||||||
\(277\) | 21.3363 | 1.28198 | 0.640988 | − | 0.767551i | \(-0.278525\pi\) | ||||
0.640988 | + | 0.767551i | \(0.278525\pi\) | |||||||
\(278\) | −3.64310 | −0.218499 | ||||||||
\(279\) | 1.41252 | 0.0845655 | ||||||||
\(280\) | 7.12139 | 0.425584 | ||||||||
\(281\) | 5.93349 | 0.353962 | 0.176981 | − | 0.984214i | \(-0.443367\pi\) | ||||
0.176981 | + | 0.984214i | \(0.443367\pi\) | |||||||
\(282\) | 43.2831 | 2.57747 | ||||||||
\(283\) | 10.5608 | 0.627775 | 0.313888 | − | 0.949460i | \(-0.398368\pi\) | ||||
0.313888 | + | 0.949460i | \(0.398368\pi\) | |||||||
\(284\) | 6.78909 | 0.402858 | ||||||||
\(285\) | 11.9631 | 0.708631 | ||||||||
\(286\) | 0.115901 | 0.00685340 | ||||||||
\(287\) | −20.9054 | −1.23401 | ||||||||
\(288\) | −30.4915 | −1.79673 | ||||||||
\(289\) | −4.04325 | −0.237838 | ||||||||
\(290\) | −4.83209 | −0.283750 | ||||||||
\(291\) | −2.49390 | −0.146195 | ||||||||
\(292\) | −0.766474 | −0.0448545 | ||||||||
\(293\) | 17.5725 | 1.02660 | 0.513298 | − | 0.858211i | \(-0.328424\pi\) | ||||
0.513298 | + | 0.858211i | \(0.328424\pi\) | |||||||
\(294\) | 5.86346 | 0.341964 | ||||||||
\(295\) | −4.26462 | −0.248296 | ||||||||
\(296\) | −9.18740 | −0.534006 | ||||||||
\(297\) | 14.6394 | 0.849463 | ||||||||
\(298\) | −1.19535 | −0.0692445 | ||||||||
\(299\) | −0.742058 | −0.0429143 | ||||||||
\(300\) | −2.48539 | −0.143494 | ||||||||
\(301\) | −12.2921 | −0.708503 | ||||||||
\(302\) | −14.1390 | −0.813605 | ||||||||
\(303\) | −39.1802 | −2.25084 | ||||||||
\(304\) | −6.93431 | −0.397710 | ||||||||
\(305\) | −0.802852 | −0.0459712 | ||||||||
\(306\) | −30.0422 | −1.71740 | ||||||||
\(307\) | 28.5979 | 1.63217 | 0.816083 | − | 0.577935i | \(-0.196141\pi\) | ||||
0.816083 | + | 0.577935i | \(0.196141\pi\) | |||||||
\(308\) | −1.77648 | −0.101225 | ||||||||
\(309\) | −7.25132 | −0.412513 | ||||||||
\(310\) | −0.208766 | −0.0118571 | ||||||||
\(311\) | −7.86587 | −0.446033 | −0.223016 | − | 0.974815i | \(-0.571590\pi\) | ||||
−0.223016 | + | 0.974815i | \(0.571590\pi\) | |||||||
\(312\) | −1.03971 | −0.0588621 | ||||||||
\(313\) | −34.7967 | −1.96683 | −0.983414 | − | 0.181375i | \(-0.941945\pi\) | ||||
−0.983414 | + | 0.181375i | \(0.941945\pi\) | |||||||
\(314\) | −17.9002 | −1.01016 | ||||||||
\(315\) | 17.4170 | 0.981336 | ||||||||
\(316\) | 3.75425 | 0.211193 | ||||||||
\(317\) | 13.8673 | 0.778867 | 0.389434 | − | 0.921055i | \(-0.372671\pi\) | ||||
0.389434 | + | 0.921055i | \(0.372671\pi\) | |||||||
\(318\) | 44.2469 | 2.48124 | ||||||||
\(319\) | 4.35072 | 0.243593 | ||||||||
\(320\) | 8.26568 | 0.462065 | ||||||||
\(321\) | 38.0132 | 2.12169 | ||||||||
\(322\) | −18.3046 | −1.02008 | ||||||||
\(323\) | 13.2799 | 0.738911 | ||||||||
\(324\) | −19.1052 | −1.06140 | ||||||||
\(325\) | −0.104355 | −0.00578859 | ||||||||
\(326\) | 5.79819 | 0.321132 | ||||||||
\(327\) | −21.7163 | −1.20091 | ||||||||
\(328\) | −27.7138 | −1.53024 | ||||||||
\(329\) | −27.8555 | −1.53572 | ||||||||
\(330\) | −3.60140 | −0.198251 | ||||||||
\(331\) | −0.832550 | −0.0457611 | −0.0228806 | − | 0.999738i | \(-0.507284\pi\) | ||||
−0.0228806 | + | 0.999738i | \(0.507284\pi\) | |||||||
\(332\) | −6.43188 | −0.352995 | ||||||||
\(333\) | −22.4699 | −1.23134 | ||||||||
\(334\) | −1.24560 | −0.0681563 | ||||||||
\(335\) | 6.84360 | 0.373906 | ||||||||
\(336\) | −14.1260 | −0.770637 | ||||||||
\(337\) | −6.98939 | −0.380736 | −0.190368 | − | 0.981713i | \(-0.560968\pi\) | ||||
−0.190368 | + | 0.981713i | \(0.560968\pi\) | |||||||
\(338\) | 14.4263 | 0.784685 | ||||||||
\(339\) | −34.5738 | −1.87779 | ||||||||
\(340\) | −2.75896 | −0.149626 | ||||||||
\(341\) | 0.187969 | 0.0101791 | ||||||||
\(342\) | −30.7913 | −1.66501 | ||||||||
\(343\) | −19.9977 | −1.07977 | ||||||||
\(344\) | −16.2953 | −0.878582 | ||||||||
\(345\) | 23.0580 | 1.24140 | ||||||||
\(346\) | 12.3733 | 0.665193 | ||||||||
\(347\) | 17.4871 | 0.938755 | 0.469378 | − | 0.882998i | \(-0.344478\pi\) | ||||
0.469378 | + | 0.882998i | \(0.344478\pi\) | |||||||
\(348\) | −10.8132 | −0.579651 | ||||||||
\(349\) | 19.0408 | 1.01923 | 0.509616 | − | 0.860402i | \(-0.329788\pi\) | ||||
0.509616 | + | 0.860402i | \(0.329788\pi\) | |||||||
\(350\) | −2.57417 | −0.137595 | ||||||||
\(351\) | −1.52770 | −0.0815425 | ||||||||
\(352\) | −4.05760 | −0.216271 | ||||||||
\(353\) | 3.33126 | 0.177305 | 0.0886524 | − | 0.996063i | \(-0.471744\pi\) | ||||
0.0886524 | + | 0.996063i | \(0.471744\pi\) | |||||||
\(354\) | 15.3586 | 0.816301 | ||||||||
\(355\) | −8.85756 | −0.470111 | ||||||||
\(356\) | −1.68413 | −0.0892587 | ||||||||
\(357\) | 27.0526 | 1.43178 | ||||||||
\(358\) | −6.02489 | −0.318425 | ||||||||
\(359\) | 35.6412 | 1.88107 | 0.940535 | − | 0.339696i | \(-0.110324\pi\) | ||||
0.940535 | + | 0.339696i | \(0.110324\pi\) | |||||||
\(360\) | 23.0893 | 1.21691 | ||||||||
\(361\) | −5.38899 | −0.283631 | ||||||||
\(362\) | 27.2004 | 1.42962 | ||||||||
\(363\) | 3.24263 | 0.170194 | ||||||||
\(364\) | 0.185386 | 0.00971685 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 2.89139 | 0.151136 | ||||||||
\(367\) | 31.4974 | 1.64415 | 0.822075 | − | 0.569379i | \(-0.192816\pi\) | ||||
0.822075 | + | 0.569379i | \(0.192816\pi\) | |||||||
\(368\) | −13.3654 | −0.696719 | ||||||||
\(369\) | −67.7805 | −3.52851 | ||||||||
\(370\) | 3.32098 | 0.172649 | ||||||||
\(371\) | −28.4757 | −1.47839 | ||||||||
\(372\) | −0.467177 | −0.0242220 | ||||||||
\(373\) | −18.3239 | −0.948775 | −0.474388 | − | 0.880316i | \(-0.657331\pi\) | ||||
−0.474388 | + | 0.880316i | \(0.657331\pi\) | |||||||
\(374\) | −3.99781 | −0.206722 | ||||||||
\(375\) | 3.24263 | 0.167449 | ||||||||
\(376\) | −36.9273 | −1.90438 | ||||||||
\(377\) | −0.454021 | −0.0233832 | ||||||||
\(378\) | −37.6843 | −1.93827 | ||||||||
\(379\) | −26.1585 | −1.34367 | −0.671835 | − | 0.740701i | \(-0.734494\pi\) | ||||
−0.671835 | + | 0.740701i | \(0.734494\pi\) | |||||||
\(380\) | −2.82776 | −0.145061 | ||||||||
\(381\) | −28.4879 | −1.45948 | ||||||||
\(382\) | 6.36843 | 0.325837 | ||||||||
\(383\) | 21.8437 | 1.11616 | 0.558082 | − | 0.829786i | \(-0.311538\pi\) | ||||
0.558082 | + | 0.829786i | \(0.311538\pi\) | |||||||
\(384\) | −3.45344 | −0.176233 | ||||||||
\(385\) | 2.31774 | 0.118123 | ||||||||
\(386\) | 6.81304 | 0.346775 | ||||||||
\(387\) | −39.8538 | −2.02588 | ||||||||
\(388\) | 0.589493 | 0.0299270 | ||||||||
\(389\) | 21.6212 | 1.09624 | 0.548119 | − | 0.836401i | \(-0.315344\pi\) | ||||
0.548119 | + | 0.836401i | \(0.315344\pi\) | |||||||
\(390\) | 0.375826 | 0.0190307 | ||||||||
\(391\) | 25.5959 | 1.29444 | ||||||||
\(392\) | −5.00245 | −0.252662 | ||||||||
\(393\) | 4.62079 | 0.233088 | ||||||||
\(394\) | −23.5203 | −1.18493 | ||||||||
\(395\) | −4.89807 | −0.246449 | ||||||||
\(396\) | −5.75979 | −0.289441 | ||||||||
\(397\) | −23.7727 | −1.19312 | −0.596560 | − | 0.802569i | \(-0.703466\pi\) | ||||
−0.596560 | + | 0.802569i | \(0.703466\pi\) | |||||||
\(398\) | 17.0499 | 0.854632 | ||||||||
\(399\) | 27.7272 | 1.38810 | ||||||||
\(400\) | −1.87957 | −0.0939784 | ||||||||
\(401\) | 12.7742 | 0.637911 | 0.318955 | − | 0.947770i | \(-0.396668\pi\) | ||||
0.318955 | + | 0.947770i | \(0.396668\pi\) | |||||||
\(402\) | −24.6466 | −1.22926 | ||||||||
\(403\) | −0.0196156 | −0.000977121 0 | ||||||||
\(404\) | 9.26118 | 0.460761 | ||||||||
\(405\) | 24.9261 | 1.23859 | ||||||||
\(406\) | −11.1995 | −0.555822 | ||||||||
\(407\) | −2.99014 | −0.148216 | ||||||||
\(408\) | 35.8630 | 1.77548 | ||||||||
\(409\) | −19.0333 | −0.941136 | −0.470568 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470568 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(410\) | 10.0177 | 0.494741 | ||||||||
\(411\) | 3.43763 | 0.169566 | ||||||||
\(412\) | 1.71402 | 0.0844439 | ||||||||
\(413\) | −9.88426 | −0.486373 | ||||||||
\(414\) | −59.3481 | −2.91680 | ||||||||
\(415\) | 8.39151 | 0.411923 | ||||||||
\(416\) | 0.423432 | 0.0207605 | ||||||||
\(417\) | 10.6364 | 0.520867 | ||||||||
\(418\) | −4.09750 | −0.200415 | ||||||||
\(419\) | −27.3911 | −1.33814 | −0.669072 | − | 0.743198i | \(-0.733308\pi\) | ||||
−0.669072 | + | 0.743198i | \(0.733308\pi\) | |||||||
\(420\) | −5.76048 | −0.281083 | ||||||||
\(421\) | 15.2897 | 0.745176 | 0.372588 | − | 0.927997i | \(-0.378471\pi\) | ||||
0.372588 | + | 0.927997i | \(0.378471\pi\) | |||||||
\(422\) | 5.56086 | 0.270699 | ||||||||
\(423\) | −90.3142 | −4.39123 | ||||||||
\(424\) | −37.7496 | −1.83328 | ||||||||
\(425\) | 3.59955 | 0.174604 | ||||||||
\(426\) | 31.8996 | 1.54554 | ||||||||
\(427\) | −1.86080 | −0.0900504 | ||||||||
\(428\) | −8.98533 | −0.434322 | ||||||||
\(429\) | −0.338386 | −0.0163374 | ||||||||
\(430\) | 5.89027 | 0.284054 | ||||||||
\(431\) | −21.5046 | −1.03584 | −0.517919 | − | 0.855430i | \(-0.673293\pi\) | ||||
−0.517919 | + | 0.855430i | \(0.673293\pi\) | |||||||
\(432\) | −27.5157 | −1.32385 | ||||||||
\(433\) | 34.0633 | 1.63698 | 0.818489 | − | 0.574522i | \(-0.194812\pi\) | ||||
0.818489 | + | 0.574522i | \(0.194812\pi\) | |||||||
\(434\) | −0.483865 | −0.0232263 | ||||||||
\(435\) | 14.1078 | 0.676416 | ||||||||
\(436\) | 5.13317 | 0.245834 | ||||||||
\(437\) | 26.2342 | 1.25495 | ||||||||
\(438\) | −3.60140 | −0.172082 | ||||||||
\(439\) | −22.3758 | −1.06794 | −0.533968 | − | 0.845504i | \(-0.679300\pi\) | ||||
−0.533968 | + | 0.845504i | \(0.679300\pi\) | |||||||
\(440\) | 3.07256 | 0.146479 | ||||||||
\(441\) | −12.2347 | −0.582602 | ||||||||
\(442\) | 0.417193 | 0.0198438 | ||||||||
\(443\) | 10.8216 | 0.514147 | 0.257074 | − | 0.966392i | \(-0.417242\pi\) | ||||
0.257074 | + | 0.966392i | \(0.417242\pi\) | |||||||
\(444\) | 7.43168 | 0.352692 | ||||||||
\(445\) | 2.19724 | 0.104159 | ||||||||
\(446\) | −1.63157 | −0.0772569 | ||||||||
\(447\) | 3.48993 | 0.165068 | ||||||||
\(448\) | 19.1576 | 0.905114 | ||||||||
\(449\) | 34.7691 | 1.64085 | 0.820427 | − | 0.571751i | \(-0.193736\pi\) | ||||
0.820427 | + | 0.571751i | \(0.193736\pi\) | |||||||
\(450\) | −8.34610 | −0.393439 | ||||||||
\(451\) | −9.01977 | −0.424724 | ||||||||
\(452\) | 8.17236 | 0.384395 | ||||||||
\(453\) | 41.2801 | 1.93951 | ||||||||
\(454\) | −16.5131 | −0.774998 | ||||||||
\(455\) | −0.241868 | −0.0113389 | ||||||||
\(456\) | 36.7573 | 1.72132 | ||||||||
\(457\) | −19.5949 | −0.916612 | −0.458306 | − | 0.888795i | \(-0.651544\pi\) | ||||
−0.458306 | + | 0.888795i | \(0.651544\pi\) | |||||||
\(458\) | 8.21193 | 0.383718 | ||||||||
\(459\) | 52.6952 | 2.45960 | ||||||||
\(460\) | −5.45030 | −0.254122 | ||||||||
\(461\) | −8.50366 | −0.396055 | −0.198027 | − | 0.980196i | \(-0.563454\pi\) | ||||
−0.198027 | + | 0.980196i | \(0.563454\pi\) | |||||||
\(462\) | −8.34710 | −0.388342 | ||||||||
\(463\) | −1.52409 | −0.0708303 | −0.0354152 | − | 0.999373i | \(-0.511275\pi\) | ||||
−0.0354152 | + | 0.999373i | \(0.511275\pi\) | |||||||
\(464\) | −8.17747 | −0.379630 | ||||||||
\(465\) | 0.609514 | 0.0282655 | ||||||||
\(466\) | 10.2075 | 0.472852 | ||||||||
\(467\) | −8.67250 | −0.401315 | −0.200658 | − | 0.979661i | \(-0.564308\pi\) | ||||
−0.200658 | + | 0.979661i | \(0.564308\pi\) | |||||||
\(468\) | 0.601065 | 0.0277843 | ||||||||
\(469\) | 15.8617 | 0.732423 | ||||||||
\(470\) | 13.3481 | 0.615704 | ||||||||
\(471\) | 52.2613 | 2.40807 | ||||||||
\(472\) | −13.1033 | −0.603129 | ||||||||
\(473\) | −5.30348 | −0.243854 | ||||||||
\(474\) | 17.6399 | 0.810229 | ||||||||
\(475\) | 3.68931 | 0.169277 | ||||||||
\(476\) | −6.39454 | −0.293093 | ||||||||
\(477\) | −92.3253 | −4.22729 | ||||||||
\(478\) | 19.4956 | 0.891709 | ||||||||
\(479\) | −30.7065 | −1.40301 | −0.701507 | − | 0.712662i | \(-0.747489\pi\) | ||||
−0.701507 | + | 0.712662i | \(0.747489\pi\) | |||||||
\(480\) | −13.1573 | −0.600546 | ||||||||
\(481\) | 0.312037 | 0.0142277 | ||||||||
\(482\) | −15.5199 | −0.706912 | ||||||||
\(483\) | 53.4422 | 2.43171 | ||||||||
\(484\) | −0.766474 | −0.0348397 | ||||||||
\(485\) | −0.769097 | −0.0349229 | ||||||||
\(486\) | −40.9917 | −1.85942 | ||||||||
\(487\) | −5.66639 | −0.256768 | −0.128384 | − | 0.991725i | \(-0.540979\pi\) | ||||
−0.128384 | + | 0.991725i | \(0.540979\pi\) | |||||||
\(488\) | −2.46681 | −0.111667 | ||||||||
\(489\) | −16.9284 | −0.765529 | ||||||||
\(490\) | 1.80824 | 0.0816880 | ||||||||
\(491\) | 27.3569 | 1.23460 | 0.617300 | − | 0.786728i | \(-0.288227\pi\) | ||||
0.617300 | + | 0.786728i | \(0.288227\pi\) | |||||||
\(492\) | 22.4177 | 1.01067 | ||||||||
\(493\) | 15.6606 | 0.705319 | ||||||||
\(494\) | 0.427596 | 0.0192385 | ||||||||
\(495\) | 7.51466 | 0.337759 | ||||||||
\(496\) | −0.353301 | −0.0158637 | ||||||||
\(497\) | −20.5295 | −0.920873 | ||||||||
\(498\) | −30.2212 | −1.35425 | ||||||||
\(499\) | 2.61647 | 0.117129 | 0.0585647 | − | 0.998284i | \(-0.481348\pi\) | ||||
0.0585647 | + | 0.998284i | \(0.481348\pi\) | |||||||
\(500\) | −0.766474 | −0.0342778 | ||||||||
\(501\) | 3.63666 | 0.162474 | ||||||||
\(502\) | 17.6326 | 0.786982 | ||||||||
\(503\) | 14.7349 | 0.656996 | 0.328498 | − | 0.944505i | \(-0.393458\pi\) | ||||
0.328498 | + | 0.944505i | \(0.393458\pi\) | |||||||
\(504\) | 53.5148 | 2.38374 | ||||||||
\(505\) | −12.0828 | −0.537679 | ||||||||
\(506\) | −7.89764 | −0.351093 | ||||||||
\(507\) | −42.1189 | −1.87057 | ||||||||
\(508\) | 6.73381 | 0.298765 | ||||||||
\(509\) | 24.3139 | 1.07769 | 0.538847 | − | 0.842404i | \(-0.318860\pi\) | ||||
0.538847 | + | 0.842404i | \(0.318860\pi\) | |||||||
\(510\) | −12.9634 | −0.574030 | ||||||||
\(511\) | 2.31774 | 0.102531 | ||||||||
\(512\) | 19.1767 | 0.847499 | ||||||||
\(513\) | 54.0092 | 2.38457 | ||||||||
\(514\) | 12.0109 | 0.529778 | ||||||||
\(515\) | −2.23624 | −0.0985407 | ||||||||
\(516\) | 13.1812 | 0.580272 | ||||||||
\(517\) | −12.0184 | −0.528568 | ||||||||
\(518\) | 7.69714 | 0.338193 | ||||||||
\(519\) | −36.1251 | −1.58572 | ||||||||
\(520\) | −0.320638 | −0.0140609 | ||||||||
\(521\) | 18.4182 | 0.806917 | 0.403459 | − | 0.914998i | \(-0.367808\pi\) | ||||
0.403459 | + | 0.914998i | \(0.367808\pi\) | |||||||
\(522\) | −36.3115 | −1.58931 | ||||||||
\(523\) | 9.39261 | 0.410710 | 0.205355 | − | 0.978688i | \(-0.434165\pi\) | ||||
0.205355 | + | 0.978688i | \(0.434165\pi\) | |||||||
\(524\) | −1.09223 | −0.0477145 | ||||||||
\(525\) | 7.51556 | 0.328006 | ||||||||
\(526\) | −10.7942 | −0.470648 | ||||||||
\(527\) | 0.676603 | 0.0294733 | ||||||||
\(528\) | −6.09475 | −0.265240 | ||||||||
\(529\) | 27.5646 | 1.19846 | ||||||||
\(530\) | 13.6454 | 0.592717 | ||||||||
\(531\) | −32.0472 | −1.39073 | ||||||||
\(532\) | −6.55400 | −0.284152 | ||||||||
\(533\) | 0.941261 | 0.0407705 | ||||||||
\(534\) | −7.91316 | −0.342436 | ||||||||
\(535\) | 11.7229 | 0.506827 | ||||||||
\(536\) | 21.0274 | 0.908245 | ||||||||
\(537\) | 17.5903 | 0.759076 | ||||||||
\(538\) | −16.6532 | −0.717969 | ||||||||
\(539\) | −1.62810 | −0.0701274 | ||||||||
\(540\) | −11.2207 | −0.482862 | ||||||||
\(541\) | 26.4794 | 1.13844 | 0.569220 | − | 0.822185i | \(-0.307245\pi\) | ||||
0.569220 | + | 0.822185i | \(0.307245\pi\) | |||||||
\(542\) | −19.0816 | −0.819625 | ||||||||
\(543\) | −79.4144 | −3.40800 | ||||||||
\(544\) | −14.6055 | −0.626206 | ||||||||
\(545\) | −6.69712 | −0.286873 | ||||||||
\(546\) | 0.871064 | 0.0372781 | ||||||||
\(547\) | 23.5934 | 1.00878 | 0.504391 | − | 0.863475i | \(-0.331717\pi\) | ||||
0.504391 | + | 0.863475i | \(0.331717\pi\) | |||||||
\(548\) | −0.812566 | −0.0347111 | ||||||||
\(549\) | −6.03316 | −0.257489 | ||||||||
\(550\) | −1.11064 | −0.0473579 | ||||||||
\(551\) | 16.0511 | 0.683802 | ||||||||
\(552\) | 70.8470 | 3.01545 | ||||||||
\(553\) | −11.3524 | −0.482754 | ||||||||
\(554\) | −23.6970 | −1.00679 | ||||||||
\(555\) | −9.69593 | −0.411569 | ||||||||
\(556\) | −2.51417 | −0.106625 | ||||||||
\(557\) | −27.7533 | −1.17595 | −0.587973 | − | 0.808881i | \(-0.700074\pi\) | ||||
−0.587973 | + | 0.808881i | \(0.700074\pi\) | |||||||
\(558\) | −1.56881 | −0.0664129 | ||||||||
\(559\) | 0.553447 | 0.0234083 | ||||||||
\(560\) | −4.35634 | −0.184089 | ||||||||
\(561\) | 11.6720 | 0.492793 | ||||||||
\(562\) | −6.58998 | −0.277982 | ||||||||
\(563\) | −22.3231 | −0.940808 | −0.470404 | − | 0.882451i | \(-0.655892\pi\) | ||||
−0.470404 | + | 0.882451i | \(0.655892\pi\) | |||||||
\(564\) | 29.8704 | 1.25777 | ||||||||
\(565\) | −10.6623 | −0.448565 | ||||||||
\(566\) | −11.7293 | −0.493019 | ||||||||
\(567\) | 57.7722 | 2.42620 | ||||||||
\(568\) | −27.2154 | −1.14193 | ||||||||
\(569\) | 4.78450 | 0.200577 | 0.100288 | − | 0.994958i | \(-0.468023\pi\) | ||||
0.100288 | + | 0.994958i | \(0.468023\pi\) | |||||||
\(570\) | −13.2867 | −0.556518 | ||||||||
\(571\) | 17.6031 | 0.736668 | 0.368334 | − | 0.929693i | \(-0.379928\pi\) | ||||
0.368334 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(572\) | 0.0799857 | 0.00334437 | ||||||||
\(573\) | −18.5933 | −0.776745 | ||||||||
\(574\) | 23.2184 | 0.969119 | ||||||||
\(575\) | 7.11088 | 0.296544 | ||||||||
\(576\) | 62.1137 | 2.58807 | ||||||||
\(577\) | −19.6879 | −0.819616 | −0.409808 | − | 0.912172i | \(-0.634404\pi\) | ||||
−0.409808 | + | 0.912172i | \(0.634404\pi\) | |||||||
\(578\) | 4.49060 | 0.186784 | ||||||||
\(579\) | −19.8914 | −0.826656 | ||||||||
\(580\) | −3.33471 | −0.138466 | ||||||||
\(581\) | 19.4493 | 0.806893 | ||||||||
\(582\) | 2.76983 | 0.114813 | ||||||||
\(583\) | −12.2860 | −0.508835 | ||||||||
\(584\) | 3.07256 | 0.127144 | ||||||||
\(585\) | −0.784195 | −0.0324225 | ||||||||
\(586\) | −19.5167 | −0.806229 | ||||||||
\(587\) | −16.7400 | −0.690934 | −0.345467 | − | 0.938431i | \(-0.612279\pi\) | ||||
−0.345467 | + | 0.938431i | \(0.612279\pi\) | |||||||
\(588\) | 4.04648 | 0.166874 | ||||||||
\(589\) | 0.693476 | 0.0285742 | ||||||||
\(590\) | 4.73647 | 0.194997 | ||||||||
\(591\) | 68.6698 | 2.82470 | ||||||||
\(592\) | 5.62018 | 0.230988 | ||||||||
\(593\) | −34.5839 | −1.42019 | −0.710096 | − | 0.704105i | \(-0.751348\pi\) | ||||
−0.710096 | + | 0.704105i | \(0.751348\pi\) | |||||||
\(594\) | −16.2591 | −0.667119 | ||||||||
\(595\) | 8.34280 | 0.342021 | ||||||||
\(596\) | −0.824930 | −0.0337905 | ||||||||
\(597\) | −49.7788 | −2.03731 | ||||||||
\(598\) | 0.824161 | 0.0337024 | ||||||||
\(599\) | 1.02128 | 0.0417283 | 0.0208642 | − | 0.999782i | \(-0.493358\pi\) | ||||
0.0208642 | + | 0.999782i | \(0.493358\pi\) | |||||||
\(600\) | 9.96319 | 0.406745 | ||||||||
\(601\) | 36.9998 | 1.50925 | 0.754626 | − | 0.656156i | \(-0.227818\pi\) | ||||
0.754626 | + | 0.656156i | \(0.227818\pi\) | |||||||
\(602\) | 13.6521 | 0.556417 | ||||||||
\(603\) | 51.4273 | 2.09428 | ||||||||
\(604\) | −9.75755 | −0.397029 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 43.5151 | 1.76768 | ||||||||
\(607\) | −38.3325 | −1.55587 | −0.777934 | − | 0.628346i | \(-0.783732\pi\) | ||||
−0.777934 | + | 0.628346i | \(0.783732\pi\) | |||||||
\(608\) | −14.9697 | −0.607103 | ||||||||
\(609\) | 32.6981 | 1.32499 | ||||||||
\(610\) | 0.891681 | 0.0361031 | ||||||||
\(611\) | 1.25418 | 0.0507389 | ||||||||
\(612\) | −20.7327 | −0.838068 | ||||||||
\(613\) | −7.99889 | −0.323072 | −0.161536 | − | 0.986867i | \(-0.551645\pi\) | ||||
−0.161536 | + | 0.986867i | \(0.551645\pi\) | |||||||
\(614\) | −31.7620 | −1.28181 | ||||||||
\(615\) | −29.2478 | −1.17938 | ||||||||
\(616\) | 7.12139 | 0.286929 | ||||||||
\(617\) | 8.32067 | 0.334978 | 0.167489 | − | 0.985874i | \(-0.446434\pi\) | ||||
0.167489 | + | 0.985874i | \(0.446434\pi\) | |||||||
\(618\) | 8.05362 | 0.323964 | ||||||||
\(619\) | −3.23706 | −0.130108 | −0.0650541 | − | 0.997882i | \(-0.520722\pi\) | ||||
−0.0650541 | + | 0.997882i | \(0.520722\pi\) | |||||||
\(620\) | −0.144073 | −0.00578613 | ||||||||
\(621\) | 104.099 | 4.17734 | ||||||||
\(622\) | 8.73616 | 0.350288 | ||||||||
\(623\) | 5.09263 | 0.204032 | ||||||||
\(624\) | 0.636020 | 0.0254612 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 38.6467 | 1.54463 | ||||||||
\(627\) | 11.9631 | 0.477759 | ||||||||
\(628\) | −12.3532 | −0.492947 | ||||||||
\(629\) | −10.7632 | −0.429155 | ||||||||
\(630\) | −19.3440 | −0.770685 | ||||||||
\(631\) | −45.7667 | −1.82194 | −0.910972 | − | 0.412469i | \(-0.864667\pi\) | ||||
−0.910972 | + | 0.412469i | \(0.864667\pi\) | |||||||
\(632\) | −15.0496 | −0.598642 | ||||||||
\(633\) | −16.2355 | −0.645303 | ||||||||
\(634\) | −15.4016 | −0.611677 | ||||||||
\(635\) | −8.78544 | −0.348640 | ||||||||
\(636\) | 30.5356 | 1.21082 | ||||||||
\(637\) | 0.169901 | 0.00673174 | ||||||||
\(638\) | −4.83209 | −0.191304 | ||||||||
\(639\) | −66.5616 | −2.63313 | ||||||||
\(640\) | −1.06501 | −0.0420983 | ||||||||
\(641\) | −19.4579 | −0.768542 | −0.384271 | − | 0.923220i | \(-0.625547\pi\) | ||||
−0.384271 | + | 0.923220i | \(0.625547\pi\) | |||||||
\(642\) | −42.2190 | −1.66625 | ||||||||
\(643\) | −22.2063 | −0.875732 | −0.437866 | − | 0.899040i | \(-0.644266\pi\) | ||||
−0.437866 | + | 0.899040i | \(0.644266\pi\) | |||||||
\(644\) | −12.6324 | −0.497785 | ||||||||
\(645\) | −17.1972 | −0.677140 | ||||||||
\(646\) | −14.7492 | −0.580298 | ||||||||
\(647\) | 41.1684 | 1.61850 | 0.809249 | − | 0.587466i | \(-0.199874\pi\) | ||||
0.809249 | + | 0.587466i | \(0.199874\pi\) | |||||||
\(648\) | 76.5871 | 3.00863 | ||||||||
\(649\) | −4.26462 | −0.167401 | ||||||||
\(650\) | 0.115901 | 0.00454603 | ||||||||
\(651\) | 1.41269 | 0.0553678 | ||||||||
\(652\) | 4.00144 | 0.156708 | ||||||||
\(653\) | −27.1831 | −1.06376 | −0.531879 | − | 0.846820i | \(-0.678514\pi\) | ||||
−0.531879 | + | 0.846820i | \(0.678514\pi\) | |||||||
\(654\) | 24.1190 | 0.943129 | ||||||||
\(655\) | 1.42501 | 0.0556798 | ||||||||
\(656\) | 16.9533 | 0.661914 | ||||||||
\(657\) | 7.51466 | 0.293175 | ||||||||
\(658\) | 30.9374 | 1.20607 | ||||||||
\(659\) | −4.05460 | −0.157945 | −0.0789723 | − | 0.996877i | \(-0.525164\pi\) | ||||
−0.0789723 | + | 0.996877i | \(0.525164\pi\) | |||||||
\(660\) | −2.48539 | −0.0967438 | ||||||||
\(661\) | 25.5990 | 0.995686 | 0.497843 | − | 0.867267i | \(-0.334126\pi\) | ||||
0.497843 | + | 0.867267i | \(0.334126\pi\) | |||||||
\(662\) | 0.924665 | 0.0359381 | ||||||||
\(663\) | −1.21804 | −0.0473046 | ||||||||
\(664\) | 25.7835 | 1.00059 | ||||||||
\(665\) | 8.55084 | 0.331588 | ||||||||
\(666\) | 24.9560 | 0.967026 | ||||||||
\(667\) | 30.9374 | 1.19790 | ||||||||
\(668\) | −0.859613 | −0.0332594 | ||||||||
\(669\) | 4.76353 | 0.184169 | ||||||||
\(670\) | −7.60079 | −0.293644 | ||||||||
\(671\) | −0.802852 | −0.0309938 | ||||||||
\(672\) | −30.4951 | −1.17637 | ||||||||
\(673\) | 5.15543 | 0.198727 | 0.0993637 | − | 0.995051i | \(-0.468319\pi\) | ||||
0.0993637 | + | 0.995051i | \(0.468319\pi\) | |||||||
\(674\) | 7.76271 | 0.299009 | ||||||||
\(675\) | 14.6394 | 0.563470 | ||||||||
\(676\) | 9.95582 | 0.382916 | ||||||||
\(677\) | 30.3026 | 1.16462 | 0.582312 | − | 0.812965i | \(-0.302148\pi\) | ||||
0.582312 | + | 0.812965i | \(0.302148\pi\) | |||||||
\(678\) | 38.3991 | 1.47471 | ||||||||
\(679\) | −1.78256 | −0.0684085 | ||||||||
\(680\) | 11.0598 | 0.424125 | ||||||||
\(681\) | 48.2117 | 1.84748 | ||||||||
\(682\) | −0.208766 | −0.00799407 | ||||||||
\(683\) | 35.3348 | 1.35205 | 0.676024 | − | 0.736879i | \(-0.263701\pi\) | ||||
0.676024 | + | 0.736879i | \(0.263701\pi\) | |||||||
\(684\) | −21.2497 | −0.812501 | ||||||||
\(685\) | 1.06013 | 0.0405057 | ||||||||
\(686\) | 22.2102 | 0.847991 | ||||||||
\(687\) | −23.9756 | −0.914725 | ||||||||
\(688\) | 9.96825 | 0.380036 | ||||||||
\(689\) | 1.28211 | 0.0488446 | ||||||||
\(690\) | −25.6091 | −0.974923 | ||||||||
\(691\) | 28.4840 | 1.08358 | 0.541791 | − | 0.840513i | \(-0.317746\pi\) | ||||
0.541791 | + | 0.840513i | \(0.317746\pi\) | |||||||
\(692\) | 8.53905 | 0.324606 | ||||||||
\(693\) | 17.4170 | 0.661617 | ||||||||
\(694\) | −19.4219 | −0.737244 | ||||||||
\(695\) | 3.28018 | 0.124424 | ||||||||
\(696\) | 43.3470 | 1.64306 | ||||||||
\(697\) | −32.4671 | −1.22978 | ||||||||
\(698\) | −21.1475 | −0.800445 | ||||||||
\(699\) | −29.8018 | −1.12721 | ||||||||
\(700\) | −1.77648 | −0.0671448 | ||||||||
\(701\) | −25.7728 | −0.973424 | −0.486712 | − | 0.873562i | \(-0.661804\pi\) | ||||
−0.486712 | + | 0.873562i | \(0.661804\pi\) | |||||||
\(702\) | 1.69673 | 0.0640388 | ||||||||
\(703\) | −11.0316 | −0.416063 | ||||||||
\(704\) | 8.26568 | 0.311524 | ||||||||
\(705\) | −38.9712 | −1.46774 | ||||||||
\(706\) | −3.69983 | −0.139245 | ||||||||
\(707\) | −28.0048 | −1.05323 | ||||||||
\(708\) | 10.5993 | 0.398345 | ||||||||
\(709\) | 37.6115 | 1.41253 | 0.706265 | − | 0.707948i | \(-0.250379\pi\) | ||||
0.706265 | + | 0.707948i | \(0.250379\pi\) | |||||||
\(710\) | 9.83758 | 0.369198 | ||||||||
\(711\) | −36.8073 | −1.38038 | ||||||||
\(712\) | 6.75117 | 0.253011 | ||||||||
\(713\) | 1.33662 | 0.0500570 | ||||||||
\(714\) | −30.0458 | −1.12444 | ||||||||
\(715\) | −0.104355 | −0.00390267 | ||||||||
\(716\) | −4.15789 | −0.155387 | ||||||||
\(717\) | −56.9194 | −2.12570 | ||||||||
\(718\) | −39.5846 | −1.47728 | ||||||||
\(719\) | 16.3335 | 0.609137 | 0.304568 | − | 0.952490i | \(-0.401488\pi\) | ||||
0.304568 | + | 0.952490i | \(0.401488\pi\) | |||||||
\(720\) | −14.1243 | −0.526382 | ||||||||
\(721\) | −5.18302 | −0.193026 | ||||||||
\(722\) | 5.98524 | 0.222747 | ||||||||
\(723\) | 45.3119 | 1.68517 | ||||||||
\(724\) | 18.7715 | 0.697637 | ||||||||
\(725\) | 4.35072 | 0.161582 | ||||||||
\(726\) | −3.60140 | −0.133661 | ||||||||
\(727\) | −23.3093 | −0.864492 | −0.432246 | − | 0.901756i | \(-0.642279\pi\) | ||||
−0.432246 | + | 0.901756i | \(0.642279\pi\) | |||||||
\(728\) | −0.743155 | −0.0275431 | ||||||||
\(729\) | 44.9011 | 1.66300 | ||||||||
\(730\) | −1.11064 | −0.0411067 | ||||||||
\(731\) | −19.0901 | −0.706074 | ||||||||
\(732\) | 1.99540 | 0.0737522 | ||||||||
\(733\) | −50.1884 | −1.85375 | −0.926875 | − | 0.375371i | \(-0.877515\pi\) | ||||
−0.926875 | + | 0.375371i | \(0.877515\pi\) | |||||||
\(734\) | −34.9823 | −1.29122 | ||||||||
\(735\) | −5.27934 | −0.194732 | ||||||||
\(736\) | −28.8531 | −1.06354 | ||||||||
\(737\) | 6.84360 | 0.252087 | ||||||||
\(738\) | 75.2799 | 2.77109 | ||||||||
\(739\) | 39.1895 | 1.44161 | 0.720805 | − | 0.693138i | \(-0.243772\pi\) | ||||
0.720805 | + | 0.693138i | \(0.243772\pi\) | |||||||
\(740\) | 2.29187 | 0.0842507 | ||||||||
\(741\) | −1.24841 | −0.0458615 | ||||||||
\(742\) | 31.6264 | 1.16104 | ||||||||
\(743\) | 35.4247 | 1.29961 | 0.649803 | − | 0.760102i | \(-0.274851\pi\) | ||||
0.649803 | + | 0.760102i | \(0.274851\pi\) | |||||||
\(744\) | 1.87277 | 0.0686591 | ||||||||
\(745\) | 1.07627 | 0.0394313 | ||||||||
\(746\) | 20.3513 | 0.745114 | ||||||||
\(747\) | 63.0594 | 2.30722 | ||||||||
\(748\) | −2.75896 | −0.100878 | ||||||||
\(749\) | 27.1707 | 0.992794 | ||||||||
\(750\) | −3.60140 | −0.131505 | ||||||||
\(751\) | 18.1970 | 0.664019 | 0.332010 | − | 0.943276i | \(-0.392273\pi\) | ||||
0.332010 | + | 0.943276i | \(0.392273\pi\) | |||||||
\(752\) | 22.5894 | 0.823751 | ||||||||
\(753\) | −51.4802 | −1.87604 | ||||||||
\(754\) | 0.504254 | 0.0183639 | ||||||||
\(755\) | 12.7304 | 0.463308 | ||||||||
\(756\) | −26.0066 | −0.945852 | ||||||||
\(757\) | 8.91458 | 0.324006 | 0.162003 | − | 0.986790i | \(-0.448205\pi\) | ||||
0.162003 | + | 0.986790i | \(0.448205\pi\) | |||||||
\(758\) | 29.0527 | 1.05524 | ||||||||
\(759\) | 23.0580 | 0.836951 | ||||||||
\(760\) | 11.3356 | 0.411187 | ||||||||
\(761\) | 20.5297 | 0.744201 | 0.372100 | − | 0.928192i | \(-0.378638\pi\) | ||||
0.372100 | + | 0.928192i | \(0.378638\pi\) | |||||||
\(762\) | 31.6399 | 1.14619 | ||||||||
\(763\) | −15.5222 | −0.561940 | ||||||||
\(764\) | 4.39497 | 0.159004 | ||||||||
\(765\) | 27.0494 | 0.977973 | ||||||||
\(766\) | −24.2606 | −0.876570 | ||||||||
\(767\) | 0.445036 | 0.0160693 | ||||||||
\(768\) | −49.7695 | −1.79590 | ||||||||
\(769\) | 37.1119 | 1.33829 | 0.669145 | − | 0.743132i | \(-0.266660\pi\) | ||||
0.669145 | + | 0.743132i | \(0.266660\pi\) | |||||||
\(770\) | −2.57417 | −0.0927668 | ||||||||
\(771\) | −35.0671 | −1.26291 | ||||||||
\(772\) | 4.70180 | 0.169222 | ||||||||
\(773\) | −46.0364 | −1.65581 | −0.827907 | − | 0.560866i | \(-0.810468\pi\) | ||||
−0.827907 | + | 0.560866i | \(0.810468\pi\) | |||||||
\(774\) | 44.2634 | 1.59101 | ||||||||
\(775\) | 0.187969 | 0.00675204 | ||||||||
\(776\) | −2.36310 | −0.0848303 | ||||||||
\(777\) | −22.4726 | −0.806200 | ||||||||
\(778\) | −24.0134 | −0.860922 | ||||||||
\(779\) | −33.2767 | −1.19226 | ||||||||
\(780\) | 0.259364 | 0.00928673 | ||||||||
\(781\) | −8.85756 | −0.316948 | ||||||||
\(782\) | −28.4279 | −1.01658 | ||||||||
\(783\) | 63.6918 | 2.27616 | ||||||||
\(784\) | 3.06013 | 0.109291 | ||||||||
\(785\) | 16.1169 | 0.575238 | ||||||||
\(786\) | −5.13204 | −0.183054 | ||||||||
\(787\) | −45.1949 | −1.61102 | −0.805512 | − | 0.592580i | \(-0.798110\pi\) | ||||
−0.805512 | + | 0.592580i | \(0.798110\pi\) | |||||||
\(788\) | −16.2318 | −0.578233 | ||||||||
\(789\) | 31.5146 | 1.12195 | ||||||||
\(790\) | 5.44000 | 0.193547 | ||||||||
\(791\) | −24.7123 | −0.878669 | ||||||||
\(792\) | 23.0893 | 0.820441 | ||||||||
\(793\) | 0.0837819 | 0.00297518 | ||||||||
\(794\) | 26.4030 | 0.937007 | ||||||||
\(795\) | −39.8391 | −1.41295 | ||||||||
\(796\) | 11.7664 | 0.417050 | ||||||||
\(797\) | −46.4228 | −1.64438 | −0.822191 | − | 0.569212i | \(-0.807248\pi\) | ||||
−0.822191 | + | 0.569212i | \(0.807248\pi\) | |||||||
\(798\) | −30.7950 | −1.09013 | ||||||||
\(799\) | −43.2608 | −1.53046 | ||||||||
\(800\) | −4.05760 | −0.143458 | ||||||||
\(801\) | 16.5115 | 0.583406 | ||||||||
\(802\) | −14.1875 | −0.500979 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −17.0090 | −0.599863 | ||||||||
\(805\) | 16.4811 | 0.580883 | ||||||||
\(806\) | 0.0217859 | 0.000767375 0 | ||||||||
\(807\) | 48.6206 | 1.71153 | ||||||||
\(808\) | −37.1252 | −1.30606 | ||||||||
\(809\) | 22.3728 | 0.786584 | 0.393292 | − | 0.919414i | \(-0.371336\pi\) | ||||
0.393292 | + | 0.919414i | \(0.371336\pi\) | |||||||
\(810\) | −27.6840 | −0.972717 | ||||||||
\(811\) | 49.9496 | 1.75397 | 0.876984 | − | 0.480520i | \(-0.159552\pi\) | ||||
0.876984 | + | 0.480520i | \(0.159552\pi\) | |||||||
\(812\) | −7.72898 | −0.271234 | ||||||||
\(813\) | 55.7107 | 1.95386 | ||||||||
\(814\) | 3.32098 | 0.116400 | ||||||||
\(815\) | −5.22058 | −0.182869 | ||||||||
\(816\) | −21.9383 | −0.767996 | ||||||||
\(817\) | −19.5662 | −0.684534 | ||||||||
\(818\) | 21.1392 | 0.739114 | ||||||||
\(819\) | −1.81756 | −0.0635106 | ||||||||
\(820\) | 6.91342 | 0.241427 | ||||||||
\(821\) | 12.9215 | 0.450963 | 0.225482 | − | 0.974247i | \(-0.427604\pi\) | ||||
0.225482 | + | 0.974247i | \(0.427604\pi\) | |||||||
\(822\) | −3.81797 | −0.133167 | ||||||||
\(823\) | −30.8889 | −1.07672 | −0.538359 | − | 0.842715i | \(-0.680956\pi\) | ||||
−0.538359 | + | 0.842715i | \(0.680956\pi\) | |||||||
\(824\) | −6.87100 | −0.239363 | ||||||||
\(825\) | 3.24263 | 0.112894 | ||||||||
\(826\) | 10.9779 | 0.381969 | ||||||||
\(827\) | 22.0987 | 0.768446 | 0.384223 | − | 0.923240i | \(-0.374469\pi\) | ||||
0.384223 | + | 0.923240i | \(0.374469\pi\) | |||||||
\(828\) | −40.9572 | −1.42336 | ||||||||
\(829\) | −23.1793 | −0.805049 | −0.402525 | − | 0.915409i | \(-0.631867\pi\) | ||||
−0.402525 | + | 0.915409i | \(0.631867\pi\) | |||||||
\(830\) | −9.31997 | −0.323501 | ||||||||
\(831\) | 69.1859 | 2.40003 | ||||||||
\(832\) | −0.862567 | −0.0299041 | ||||||||
\(833\) | −5.86044 | −0.203052 | ||||||||
\(834\) | −11.8132 | −0.409059 | ||||||||
\(835\) | 1.12152 | 0.0388117 | ||||||||
\(836\) | −2.82776 | −0.0978002 | ||||||||
\(837\) | 2.75175 | 0.0951143 | ||||||||
\(838\) | 30.4217 | 1.05090 | ||||||||
\(839\) | 54.6105 | 1.88537 | 0.942683 | − | 0.333690i | \(-0.108294\pi\) | ||||
0.942683 | + | 0.333690i | \(0.108294\pi\) | |||||||
\(840\) | 23.0920 | 0.796751 | ||||||||
\(841\) | −10.0713 | −0.347285 | ||||||||
\(842\) | −16.9814 | −0.585218 | ||||||||
\(843\) | 19.2401 | 0.662665 | ||||||||
\(844\) | 3.83765 | 0.132097 | ||||||||
\(845\) | −12.9891 | −0.446839 | ||||||||
\(846\) | 100.307 | 3.44862 | ||||||||
\(847\) | 2.31774 | 0.0796383 | ||||||||
\(848\) | 23.0924 | 0.792997 | ||||||||
\(849\) | 34.2448 | 1.17528 | ||||||||
\(850\) | −3.99781 | −0.137124 | ||||||||
\(851\) | −21.2625 | −0.728870 | ||||||||
\(852\) | 22.0145 | 0.754205 | ||||||||
\(853\) | −44.7750 | −1.53307 | −0.766534 | − | 0.642204i | \(-0.778020\pi\) | ||||
−0.766534 | + | 0.642204i | \(0.778020\pi\) | |||||||
\(854\) | 2.06668 | 0.0707204 | ||||||||
\(855\) | 27.7239 | 0.948138 | ||||||||
\(856\) | 36.0194 | 1.23112 | ||||||||
\(857\) | 53.9241 | 1.84201 | 0.921006 | − | 0.389549i | \(-0.127369\pi\) | ||||
0.921006 | + | 0.389549i | \(0.127369\pi\) | |||||||
\(858\) | 0.375826 | 0.0128305 | ||||||||
\(859\) | 14.6892 | 0.501190 | 0.250595 | − | 0.968092i | \(-0.419374\pi\) | ||||
0.250595 | + | 0.968092i | \(0.419374\pi\) | |||||||
\(860\) | 4.06498 | 0.138615 | ||||||||
\(861\) | −67.7886 | −2.31023 | ||||||||
\(862\) | 23.8839 | 0.813488 | ||||||||
\(863\) | −13.7763 | −0.468952 | −0.234476 | − | 0.972122i | \(-0.575337\pi\) | ||||
−0.234476 | + | 0.972122i | \(0.575337\pi\) | |||||||
\(864\) | −59.4007 | −2.02085 | ||||||||
\(865\) | −11.1407 | −0.378795 | ||||||||
\(866\) | −37.8321 | −1.28559 | ||||||||
\(867\) | −13.1108 | −0.445265 | ||||||||
\(868\) | −0.333924 | −0.0113341 | ||||||||
\(869\) | −4.89807 | −0.166156 | ||||||||
\(870\) | −15.6687 | −0.531218 | ||||||||
\(871\) | −0.714166 | −0.0241986 | ||||||||
\(872\) | −20.5773 | −0.696836 | ||||||||
\(873\) | −5.77951 | −0.195607 | ||||||||
\(874\) | −29.1368 | −0.985568 | ||||||||
\(875\) | 2.31774 | 0.0783537 | ||||||||
\(876\) | −2.48539 | −0.0839737 | ||||||||
\(877\) | −12.2557 | −0.413844 | −0.206922 | − | 0.978357i | \(-0.566345\pi\) | ||||
−0.206922 | + | 0.978357i | \(0.566345\pi\) | |||||||
\(878\) | 24.8515 | 0.838696 | ||||||||
\(879\) | 56.9811 | 1.92192 | ||||||||
\(880\) | −1.87957 | −0.0633602 | ||||||||
\(881\) | −37.9263 | −1.27777 | −0.638885 | − | 0.769302i | \(-0.720604\pi\) | ||||
−0.638885 | + | 0.769302i | \(0.720604\pi\) | |||||||
\(882\) | 13.5883 | 0.457542 | ||||||||
\(883\) | 26.3489 | 0.886710 | 0.443355 | − | 0.896346i | \(-0.353788\pi\) | ||||
0.443355 | + | 0.896346i | \(0.353788\pi\) | |||||||
\(884\) | 0.287912 | 0.00968354 | ||||||||
\(885\) | −13.8286 | −0.464843 | ||||||||
\(886\) | −12.0189 | −0.403782 | ||||||||
\(887\) | 5.07689 | 0.170465 | 0.0852327 | − | 0.996361i | \(-0.472837\pi\) | ||||
0.0852327 | + | 0.996361i | \(0.472837\pi\) | |||||||
\(888\) | −29.7913 | −0.999732 | ||||||||
\(889\) | −20.3623 | −0.682930 | ||||||||
\(890\) | −2.44035 | −0.0818007 | ||||||||
\(891\) | 24.9261 | 0.835057 | ||||||||
\(892\) | −1.12597 | −0.0377004 | ||||||||
\(893\) | −44.3396 | −1.48377 | ||||||||
\(894\) | −3.87607 | −0.129635 | ||||||||
\(895\) | 5.42469 | 0.181327 | ||||||||
\(896\) | −2.46842 | −0.0824640 | ||||||||
\(897\) | −2.40622 | −0.0803414 | ||||||||
\(898\) | −38.6160 | −1.28863 | ||||||||
\(899\) | 0.817800 | 0.0272751 | ||||||||
\(900\) | −5.75979 | −0.191993 | ||||||||
\(901\) | −44.2241 | −1.47332 | ||||||||
\(902\) | 10.0177 | 0.333554 | ||||||||
\(903\) | −39.8586 | −1.32641 | ||||||||
\(904\) | −32.7605 | −1.08960 | ||||||||
\(905\) | −24.4907 | −0.814099 | ||||||||
\(906\) | −45.8474 | −1.52318 | ||||||||
\(907\) | −38.5702 | −1.28070 | −0.640351 | − | 0.768082i | \(-0.721211\pi\) | ||||
−0.640351 | + | 0.768082i | \(0.721211\pi\) | |||||||
\(908\) | −11.3960 | −0.378189 | ||||||||
\(909\) | −90.7984 | −3.01159 | ||||||||
\(910\) | 0.268629 | 0.00890496 | ||||||||
\(911\) | 48.1779 | 1.59621 | 0.798103 | − | 0.602521i | \(-0.205837\pi\) | ||||
0.798103 | + | 0.602521i | \(0.205837\pi\) | |||||||
\(912\) | −22.4854 | −0.744567 | ||||||||
\(913\) | 8.39151 | 0.277719 | ||||||||
\(914\) | 21.7629 | 0.719854 | ||||||||
\(915\) | −2.60335 | −0.0860642 | ||||||||
\(916\) | 5.66720 | 0.187250 | ||||||||
\(917\) | 3.30280 | 0.109068 | ||||||||
\(918\) | −58.5255 | −1.93163 | ||||||||
\(919\) | 18.8156 | 0.620671 | 0.310335 | − | 0.950627i | \(-0.399559\pi\) | ||||
0.310335 | + | 0.950627i | \(0.399559\pi\) | |||||||
\(920\) | 21.8486 | 0.720327 | ||||||||
\(921\) | 92.7323 | 3.05563 | ||||||||
\(922\) | 9.44452 | 0.311039 | ||||||||
\(923\) | 0.924334 | 0.0304248 | ||||||||
\(924\) | −5.76048 | −0.189506 | ||||||||
\(925\) | −2.99014 | −0.0983152 | ||||||||
\(926\) | 1.69272 | 0.0556261 | ||||||||
\(927\) | −16.8046 | −0.551936 | ||||||||
\(928\) | −17.6535 | −0.579503 | ||||||||
\(929\) | −55.5219 | −1.82162 | −0.910808 | − | 0.412830i | \(-0.864540\pi\) | ||||
−0.910808 | + | 0.412830i | \(0.864540\pi\) | |||||||
\(930\) | −0.676952 | −0.0221981 | ||||||||
\(931\) | −6.00658 | −0.196858 | ||||||||
\(932\) | 7.04437 | 0.230746 | ||||||||
\(933\) | −25.5061 | −0.835033 | ||||||||
\(934\) | 9.63204 | 0.315170 | ||||||||
\(935\) | 3.59955 | 0.117718 | ||||||||
\(936\) | −2.40949 | −0.0787566 | ||||||||
\(937\) | 2.30247 | 0.0752184 | 0.0376092 | − | 0.999293i | \(-0.488026\pi\) | ||||
0.0376092 | + | 0.999293i | \(0.488026\pi\) | |||||||
\(938\) | −17.6166 | −0.575203 | ||||||||
\(939\) | −112.833 | −3.68217 | ||||||||
\(940\) | 9.21179 | 0.300456 | ||||||||
\(941\) | −53.8253 | −1.75465 | −0.877327 | − | 0.479893i | \(-0.840676\pi\) | ||||
−0.877327 | + | 0.479893i | \(0.840676\pi\) | |||||||
\(942\) | −58.0436 | −1.89116 | ||||||||
\(943\) | −64.1384 | −2.08864 | ||||||||
\(944\) | 8.01565 | 0.260887 | ||||||||
\(945\) | 33.9302 | 1.10375 | ||||||||
\(946\) | 5.89027 | 0.191509 | ||||||||
\(947\) | 5.47100 | 0.177784 | 0.0888918 | − | 0.996041i | \(-0.471667\pi\) | ||||
0.0888918 | + | 0.996041i | \(0.471667\pi\) | |||||||
\(948\) | 12.1736 | 0.395381 | ||||||||
\(949\) | −0.104355 | −0.00338752 | ||||||||
\(950\) | −4.09750 | −0.132941 | ||||||||
\(951\) | 44.9667 | 1.45814 | ||||||||
\(952\) | 25.6338 | 0.830795 | ||||||||
\(953\) | −14.2194 | −0.460613 | −0.230307 | − | 0.973118i | \(-0.573973\pi\) | ||||
−0.230307 | + | 0.973118i | \(0.573973\pi\) | |||||||
\(954\) | 102.540 | 3.31987 | ||||||||
\(955\) | −5.73400 | −0.185548 | ||||||||
\(956\) | 13.4543 | 0.435143 | ||||||||
\(957\) | 14.1078 | 0.456039 | ||||||||
\(958\) | 34.1039 | 1.10185 | ||||||||
\(959\) | 2.45711 | 0.0793443 | ||||||||
\(960\) | 26.8025 | 0.865048 | ||||||||
\(961\) | −30.9647 | −0.998860 | ||||||||
\(962\) | −0.346562 | −0.0111736 | ||||||||
\(963\) | 88.0939 | 2.83879 | ||||||||
\(964\) | −10.7106 | −0.344964 | ||||||||
\(965\) | −6.13432 | −0.197471 | ||||||||
\(966\) | −59.3552 | −1.90972 | ||||||||
\(967\) | −27.1002 | −0.871484 | −0.435742 | − | 0.900072i | \(-0.643514\pi\) | ||||
−0.435742 | + | 0.900072i | \(0.643514\pi\) | |||||||
\(968\) | 3.07256 | 0.0987559 | ||||||||
\(969\) | 43.0617 | 1.38334 | ||||||||
\(970\) | 0.854192 | 0.0274264 | ||||||||
\(971\) | −28.0582 | −0.900431 | −0.450215 | − | 0.892920i | \(-0.648653\pi\) | ||||
−0.450215 | + | 0.892920i | \(0.648653\pi\) | |||||||
\(972\) | −28.2891 | −0.907375 | ||||||||
\(973\) | 7.60258 | 0.243728 | ||||||||
\(974\) | 6.29333 | 0.201651 | ||||||||
\(975\) | −0.338386 | −0.0108370 | ||||||||
\(976\) | 1.50902 | 0.0483024 | ||||||||
\(977\) | −17.0216 | −0.544569 | −0.272285 | − | 0.962217i | \(-0.587779\pi\) | ||||
−0.272285 | + | 0.962217i | \(0.587779\pi\) | |||||||
\(978\) | 18.8014 | 0.601203 | ||||||||
\(979\) | 2.19724 | 0.0702242 | ||||||||
\(980\) | 1.24790 | 0.0398627 | ||||||||
\(981\) | −50.3266 | −1.60680 | ||||||||
\(982\) | −30.3837 | −0.969584 | ||||||||
\(983\) | 33.1812 | 1.05832 | 0.529158 | − | 0.848523i | \(-0.322508\pi\) | ||||
0.529158 | + | 0.848523i | \(0.322508\pi\) | |||||||
\(984\) | −89.8656 | −2.86481 | ||||||||
\(985\) | 21.1772 | 0.674761 | ||||||||
\(986\) | −17.3933 | −0.553917 | ||||||||
\(987\) | −90.3250 | −2.87508 | ||||||||
\(988\) | 0.295092 | 0.00938813 | ||||||||
\(989\) | −37.7124 | −1.19918 | ||||||||
\(990\) | −8.34610 | −0.265256 | ||||||||
\(991\) | −59.5509 | −1.89170 | −0.945848 | − | 0.324610i | \(-0.894767\pi\) | ||||
−0.945848 | + | 0.324610i | \(0.894767\pi\) | |||||||
\(992\) | −0.762702 | −0.0242158 | ||||||||
\(993\) | −2.69965 | −0.0856709 | ||||||||
\(994\) | 22.8009 | 0.723201 | ||||||||
\(995\) | −15.3514 | −0.486671 | ||||||||
\(996\) | −20.8562 | −0.660854 | ||||||||
\(997\) | 11.7572 | 0.372355 | 0.186177 | − | 0.982516i | \(-0.440390\pi\) | ||||
0.186177 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(998\) | −2.90596 | −0.0919866 | ||||||||
\(999\) | −43.7738 | −1.38494 |
(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 | 4015.2.a.h.1.12 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.12 | ✓ | 37 | 1.1 | even | 1 | trivial |