Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.07554 | 1.46763 | 0.733815 | − | 0.679349i | \(-0.237738\pi\) | ||||
0.733815 | + | 0.679349i | \(0.237738\pi\) | |||||||
\(3\) | −2.88027 | −1.66293 | −0.831464 | − | 0.555579i | \(-0.812497\pi\) | ||||
−0.831464 | + | 0.555579i | \(0.812497\pi\) | |||||||
\(4\) | 2.30788 | 1.15394 | ||||||||
\(5\) | −3.62707 | −1.62208 | −0.811038 | − | 0.584994i | \(-0.801097\pi\) | ||||
−0.811038 | + | 0.584994i | \(0.801097\pi\) | |||||||
\(6\) | −5.97813 | −2.44056 | ||||||||
\(7\) | −5.05987 | −1.91245 | −0.956225 | − | 0.292631i | \(-0.905469\pi\) | ||||
−0.956225 | + | 0.292631i | \(0.905469\pi\) | |||||||
\(8\) | 0.639017 | 0.225927 | ||||||||
\(9\) | 5.29598 | 1.76533 | ||||||||
\(10\) | −7.52814 | −2.38061 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −6.64733 | −1.91892 | ||||||||
\(13\) | 0.599325 | 0.166223 | 0.0831115 | − | 0.996540i | \(-0.473514\pi\) | ||||
0.0831115 | + | 0.996540i | \(0.473514\pi\) | |||||||
\(14\) | −10.5020 | −2.80677 | ||||||||
\(15\) | 10.4470 | 2.69739 | ||||||||
\(16\) | −3.28945 | −0.822363 | ||||||||
\(17\) | −3.13619 | −0.760638 | −0.380319 | − | 0.924855i | \(-0.624186\pi\) | ||||
−0.380319 | + | 0.924855i | \(0.624186\pi\) | |||||||
\(18\) | 10.9920 | 2.59085 | ||||||||
\(19\) | 3.58210 | 0.821791 | 0.410896 | − | 0.911682i | \(-0.365216\pi\) | ||||
0.410896 | + | 0.911682i | \(0.365216\pi\) | |||||||
\(20\) | −8.37084 | −1.87178 | ||||||||
\(21\) | 14.5738 | 3.18027 | ||||||||
\(22\) | 2.07554 | 0.442507 | ||||||||
\(23\) | 6.21835 | 1.29662 | 0.648308 | − | 0.761378i | \(-0.275477\pi\) | ||||
0.648308 | + | 0.761378i | \(0.275477\pi\) | |||||||
\(24\) | −1.84055 | −0.375700 | ||||||||
\(25\) | 8.15564 | 1.63113 | ||||||||
\(26\) | 1.24393 | 0.243954 | ||||||||
\(27\) | −6.61305 | −1.27268 | ||||||||
\(28\) | −11.6776 | −2.20685 | ||||||||
\(29\) | 1.58591 | 0.294497 | 0.147248 | − | 0.989100i | \(-0.452958\pi\) | ||||
0.147248 | + | 0.989100i | \(0.452958\pi\) | |||||||
\(30\) | 21.6831 | 3.95878 | ||||||||
\(31\) | −1.68617 | −0.302845 | −0.151422 | − | 0.988469i | \(-0.548385\pi\) | ||||
−0.151422 | + | 0.988469i | \(0.548385\pi\) | |||||||
\(32\) | −8.10543 | −1.43285 | ||||||||
\(33\) | −2.88027 | −0.501391 | ||||||||
\(34\) | −6.50930 | −1.11634 | ||||||||
\(35\) | 18.3525 | 3.10214 | ||||||||
\(36\) | 12.2225 | 2.03708 | ||||||||
\(37\) | 0.605232 | 0.0994995 | 0.0497497 | − | 0.998762i | \(-0.484158\pi\) | ||||
0.0497497 | + | 0.998762i | \(0.484158\pi\) | |||||||
\(38\) | 7.43481 | 1.20609 | ||||||||
\(39\) | −1.72622 | −0.276417 | ||||||||
\(40\) | −2.31776 | −0.366470 | ||||||||
\(41\) | −10.4360 | −1.62983 | −0.814916 | − | 0.579579i | \(-0.803217\pi\) | ||||
−0.814916 | + | 0.579579i | \(0.803217\pi\) | |||||||
\(42\) | 30.2486 | 4.66746 | ||||||||
\(43\) | 0.0776603 | 0.0118431 | 0.00592154 | − | 0.999982i | \(-0.498115\pi\) | ||||
0.00592154 | + | 0.999982i | \(0.498115\pi\) | |||||||
\(44\) | 2.30788 | 0.347926 | ||||||||
\(45\) | −19.2089 | −2.86349 | ||||||||
\(46\) | 12.9065 | 1.90295 | ||||||||
\(47\) | −2.17142 | −0.316734 | −0.158367 | − | 0.987380i | \(-0.550623\pi\) | ||||
−0.158367 | + | 0.987380i | \(0.550623\pi\) | |||||||
\(48\) | 9.47452 | 1.36753 | ||||||||
\(49\) | 18.6023 | 2.65747 | ||||||||
\(50\) | 16.9274 | 2.39389 | ||||||||
\(51\) | 9.03309 | 1.26489 | ||||||||
\(52\) | 1.38317 | 0.191811 | ||||||||
\(53\) | −0.650569 | −0.0893625 | −0.0446813 | − | 0.999001i | \(-0.514227\pi\) | ||||
−0.0446813 | + | 0.999001i | \(0.514227\pi\) | |||||||
\(54\) | −13.7257 | −1.86783 | ||||||||
\(55\) | −3.62707 | −0.489074 | ||||||||
\(56\) | −3.23334 | −0.432074 | ||||||||
\(57\) | −10.3174 | −1.36658 | ||||||||
\(58\) | 3.29163 | 0.432213 | ||||||||
\(59\) | 12.5623 | 1.63547 | 0.817737 | − | 0.575592i | \(-0.195228\pi\) | ||||
0.817737 | + | 0.575592i | \(0.195228\pi\) | |||||||
\(60\) | 24.1103 | 3.11263 | ||||||||
\(61\) | −10.8256 | −1.38608 | −0.693038 | − | 0.720901i | \(-0.743728\pi\) | ||||
−0.693038 | + | 0.720901i | \(0.743728\pi\) | |||||||
\(62\) | −3.49971 | −0.444464 | ||||||||
\(63\) | −26.7970 | −3.37610 | ||||||||
\(64\) | −10.2443 | −1.28053 | ||||||||
\(65\) | −2.17380 | −0.269626 | ||||||||
\(66\) | −5.97813 | −0.735857 | ||||||||
\(67\) | −13.6832 | −1.67167 | −0.835836 | − | 0.548980i | \(-0.815016\pi\) | ||||
−0.835836 | + | 0.548980i | \(0.815016\pi\) | |||||||
\(68\) | −7.23795 | −0.877731 | ||||||||
\(69\) | −17.9106 | −2.15618 | ||||||||
\(70\) | 38.0914 | 4.55279 | ||||||||
\(71\) | 15.3074 | 1.81666 | 0.908330 | − | 0.418255i | \(-0.137358\pi\) | ||||
0.908330 | + | 0.418255i | \(0.137358\pi\) | |||||||
\(72\) | 3.38422 | 0.398835 | ||||||||
\(73\) | 9.83072 | 1.15060 | 0.575299 | − | 0.817943i | \(-0.304886\pi\) | ||||
0.575299 | + | 0.817943i | \(0.304886\pi\) | |||||||
\(74\) | 1.25618 | 0.146028 | ||||||||
\(75\) | −23.4905 | −2.71245 | ||||||||
\(76\) | 8.26707 | 0.948297 | ||||||||
\(77\) | −5.05987 | −0.576626 | ||||||||
\(78\) | −3.58285 | −0.405678 | ||||||||
\(79\) | 1.02929 | 0.115804 | 0.0579021 | − | 0.998322i | \(-0.481559\pi\) | ||||
0.0579021 | + | 0.998322i | \(0.481559\pi\) | |||||||
\(80\) | 11.9311 | 1.33393 | ||||||||
\(81\) | 3.15947 | 0.351052 | ||||||||
\(82\) | −21.6604 | −2.39199 | ||||||||
\(83\) | −3.03240 | −0.332850 | −0.166425 | − | 0.986054i | \(-0.553222\pi\) | ||||
−0.166425 | + | 0.986054i | \(0.553222\pi\) | |||||||
\(84\) | 33.6346 | 3.66984 | ||||||||
\(85\) | 11.3752 | 1.23381 | ||||||||
\(86\) | 0.161187 | 0.0173813 | ||||||||
\(87\) | −4.56787 | −0.489727 | ||||||||
\(88\) | 0.639017 | 0.0681195 | ||||||||
\(89\) | −7.74657 | −0.821135 | −0.410567 | − | 0.911830i | \(-0.634669\pi\) | ||||
−0.410567 | + | 0.911830i | \(0.634669\pi\) | |||||||
\(90\) | −39.8689 | −4.20255 | ||||||||
\(91\) | −3.03251 | −0.317893 | ||||||||
\(92\) | 14.3512 | 1.49622 | ||||||||
\(93\) | 4.85663 | 0.503609 | ||||||||
\(94\) | −4.50687 | −0.464849 | ||||||||
\(95\) | −12.9925 | −1.33301 | ||||||||
\(96\) | 23.3459 | 2.38273 | ||||||||
\(97\) | −7.34334 | −0.745603 | −0.372801 | − | 0.927911i | \(-0.621603\pi\) | ||||
−0.372801 | + | 0.927911i | \(0.621603\pi\) | |||||||
\(98\) | 38.6098 | 3.90018 | ||||||||
\(99\) | 5.29598 | 0.532266 | ||||||||
\(100\) | 18.8222 | 1.88222 | ||||||||
\(101\) | 19.8066 | 1.97083 | 0.985416 | − | 0.170165i | \(-0.0544300\pi\) | ||||
0.985416 | + | 0.170165i | \(0.0544300\pi\) | |||||||
\(102\) | 18.7486 | 1.85639 | ||||||||
\(103\) | 8.56496 | 0.843931 | 0.421966 | − | 0.906612i | \(-0.361340\pi\) | ||||
0.421966 | + | 0.906612i | \(0.361340\pi\) | |||||||
\(104\) | 0.382979 | 0.0375542 | ||||||||
\(105\) | −52.8602 | −5.15863 | ||||||||
\(106\) | −1.35028 | −0.131151 | ||||||||
\(107\) | 1.50416 | 0.145413 | 0.0727065 | − | 0.997353i | \(-0.476836\pi\) | ||||
0.0727065 | + | 0.997353i | \(0.476836\pi\) | |||||||
\(108\) | −15.2621 | −1.46860 | ||||||||
\(109\) | 4.72854 | 0.452912 | 0.226456 | − | 0.974021i | \(-0.427286\pi\) | ||||
0.226456 | + | 0.974021i | \(0.427286\pi\) | |||||||
\(110\) | −7.52814 | −0.717780 | ||||||||
\(111\) | −1.74323 | −0.165460 | ||||||||
\(112\) | 16.6442 | 1.57273 | ||||||||
\(113\) | −17.8995 | −1.68385 | −0.841923 | − | 0.539597i | \(-0.818576\pi\) | ||||
−0.841923 | + | 0.539597i | \(0.818576\pi\) | |||||||
\(114\) | −21.4143 | −2.00563 | ||||||||
\(115\) | −22.5544 | −2.10321 | ||||||||
\(116\) | 3.66010 | 0.339832 | ||||||||
\(117\) | 3.17402 | 0.293438 | ||||||||
\(118\) | 26.0736 | 2.40027 | ||||||||
\(119\) | 15.8687 | 1.45468 | ||||||||
\(120\) | 6.67579 | 0.609413 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −22.4690 | −2.03425 | ||||||||
\(123\) | 30.0586 | 2.71029 | ||||||||
\(124\) | −3.89147 | −0.349464 | ||||||||
\(125\) | −11.4457 | −1.02374 | ||||||||
\(126\) | −55.6183 | −4.95487 | ||||||||
\(127\) | 22.0619 | 1.95768 | 0.978839 | − | 0.204634i | \(-0.0656004\pi\) | ||||
0.978839 | + | 0.204634i | \(0.0656004\pi\) | |||||||
\(128\) | −5.05157 | −0.446500 | ||||||||
\(129\) | −0.223683 | −0.0196942 | ||||||||
\(130\) | −4.51181 | −0.395712 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −6.64733 | −0.578576 | ||||||||
\(133\) | −18.1250 | −1.57163 | ||||||||
\(134\) | −28.4001 | −2.45340 | ||||||||
\(135\) | 23.9860 | 2.06439 | ||||||||
\(136\) | −2.00408 | −0.171849 | ||||||||
\(137\) | 18.1008 | 1.54646 | 0.773229 | − | 0.634127i | \(-0.218641\pi\) | ||||
0.773229 | + | 0.634127i | \(0.218641\pi\) | |||||||
\(138\) | −37.1741 | −3.16447 | ||||||||
\(139\) | 6.83730 | 0.579932 | 0.289966 | − | 0.957037i | \(-0.406356\pi\) | ||||
0.289966 | + | 0.957037i | \(0.406356\pi\) | |||||||
\(140\) | 42.3554 | 3.57968 | ||||||||
\(141\) | 6.25428 | 0.526706 | ||||||||
\(142\) | 31.7713 | 2.66618 | ||||||||
\(143\) | 0.599325 | 0.0501181 | ||||||||
\(144\) | −17.4209 | −1.45174 | ||||||||
\(145\) | −5.75222 | −0.477696 | ||||||||
\(146\) | 20.4041 | 1.68865 | ||||||||
\(147\) | −53.5797 | −4.41918 | ||||||||
\(148\) | 1.39680 | 0.114816 | ||||||||
\(149\) | −1.95100 | −0.159832 | −0.0799161 | − | 0.996802i | \(-0.525465\pi\) | ||||
−0.0799161 | + | 0.996802i | \(0.525465\pi\) | |||||||
\(150\) | −48.7555 | −3.98087 | ||||||||
\(151\) | 7.09464 | 0.577353 | 0.288677 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288677 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(152\) | 2.28903 | 0.185665 | ||||||||
\(153\) | −16.6092 | −1.34277 | ||||||||
\(154\) | −10.5020 | −0.846273 | ||||||||
\(155\) | 6.11585 | 0.491237 | ||||||||
\(156\) | −3.98391 | −0.318968 | ||||||||
\(157\) | 4.14969 | 0.331182 | 0.165591 | − | 0.986195i | \(-0.447047\pi\) | ||||
0.165591 | + | 0.986195i | \(0.447047\pi\) | |||||||
\(158\) | 2.13634 | 0.169958 | ||||||||
\(159\) | 1.87382 | 0.148603 | ||||||||
\(160\) | 29.3990 | 2.32419 | ||||||||
\(161\) | −31.4640 | −2.47971 | ||||||||
\(162\) | 6.55762 | 0.515215 | ||||||||
\(163\) | −13.9793 | −1.09494 | −0.547472 | − | 0.836824i | \(-0.684410\pi\) | ||||
−0.547472 | + | 0.836824i | \(0.684410\pi\) | |||||||
\(164\) | −24.0851 | −1.88073 | ||||||||
\(165\) | 10.4470 | 0.813295 | ||||||||
\(166\) | −6.29389 | −0.488500 | ||||||||
\(167\) | 11.5905 | 0.896904 | 0.448452 | − | 0.893807i | \(-0.351976\pi\) | ||||
0.448452 | + | 0.893807i | \(0.351976\pi\) | |||||||
\(168\) | 9.31292 | 0.718507 | ||||||||
\(169\) | −12.6408 | −0.972370 | ||||||||
\(170\) | 23.6097 | 1.81078 | ||||||||
\(171\) | 18.9708 | 1.45073 | ||||||||
\(172\) | 0.179231 | 0.0136662 | ||||||||
\(173\) | −11.7666 | −0.894600 | −0.447300 | − | 0.894384i | \(-0.647614\pi\) | ||||
−0.447300 | + | 0.894384i | \(0.647614\pi\) | |||||||
\(174\) | −9.48081 | −0.718738 | ||||||||
\(175\) | −41.2665 | −3.11945 | ||||||||
\(176\) | −3.28945 | −0.247952 | ||||||||
\(177\) | −36.1829 | −2.71967 | ||||||||
\(178\) | −16.0783 | −1.20512 | ||||||||
\(179\) | −11.0446 | −0.825509 | −0.412754 | − | 0.910842i | \(-0.635433\pi\) | ||||
−0.412754 | + | 0.910842i | \(0.635433\pi\) | |||||||
\(180\) | −44.3318 | −3.30430 | ||||||||
\(181\) | −17.9824 | −1.33662 | −0.668311 | − | 0.743882i | \(-0.732982\pi\) | ||||
−0.668311 | + | 0.743882i | \(0.732982\pi\) | |||||||
\(182\) | −6.29410 | −0.466550 | ||||||||
\(183\) | 31.1807 | 2.30494 | ||||||||
\(184\) | 3.97363 | 0.292940 | ||||||||
\(185\) | −2.19522 | −0.161396 | ||||||||
\(186\) | 10.0801 | 0.739111 | ||||||||
\(187\) | −3.13619 | −0.229341 | ||||||||
\(188\) | −5.01137 | −0.365492 | ||||||||
\(189\) | 33.4612 | 2.43394 | ||||||||
\(190\) | −26.9666 | −1.95636 | ||||||||
\(191\) | 17.6166 | 1.27469 | 0.637345 | − | 0.770579i | \(-0.280033\pi\) | ||||
0.637345 | + | 0.770579i | \(0.280033\pi\) | |||||||
\(192\) | 29.5063 | 2.12944 | ||||||||
\(193\) | 9.99634 | 0.719552 | 0.359776 | − | 0.933039i | \(-0.382853\pi\) | ||||
0.359776 | + | 0.933039i | \(0.382853\pi\) | |||||||
\(194\) | −15.2414 | −1.09427 | ||||||||
\(195\) | 6.26113 | 0.448369 | ||||||||
\(196\) | 42.9318 | 3.06656 | ||||||||
\(197\) | −10.6889 | −0.761552 | −0.380776 | − | 0.924667i | \(-0.624343\pi\) | ||||
−0.380776 | + | 0.924667i | \(0.624343\pi\) | |||||||
\(198\) | 10.9920 | 0.781170 | ||||||||
\(199\) | 9.24682 | 0.655490 | 0.327745 | − | 0.944766i | \(-0.393711\pi\) | ||||
0.327745 | + | 0.944766i | \(0.393711\pi\) | |||||||
\(200\) | 5.21160 | 0.368516 | ||||||||
\(201\) | 39.4114 | 2.77987 | ||||||||
\(202\) | 41.1095 | 2.89245 | ||||||||
\(203\) | −8.02452 | −0.563211 | ||||||||
\(204\) | 20.8473 | 1.45960 | ||||||||
\(205\) | 37.8522 | 2.64371 | ||||||||
\(206\) | 17.7770 | 1.23858 | ||||||||
\(207\) | 32.9323 | 2.28895 | ||||||||
\(208\) | −1.97145 | −0.136696 | ||||||||
\(209\) | 3.58210 | 0.247779 | ||||||||
\(210\) | −109.714 | −7.57097 | ||||||||
\(211\) | 19.4129 | 1.33644 | 0.668220 | − | 0.743963i | \(-0.267056\pi\) | ||||
0.668220 | + | 0.743963i | \(0.267056\pi\) | |||||||
\(212\) | −1.50143 | −0.103119 | ||||||||
\(213\) | −44.0896 | −3.02097 | ||||||||
\(214\) | 3.12196 | 0.213413 | ||||||||
\(215\) | −0.281679 | −0.0192104 | ||||||||
\(216\) | −4.22586 | −0.287533 | ||||||||
\(217\) | 8.53179 | 0.579175 | ||||||||
\(218\) | 9.81428 | 0.664707 | ||||||||
\(219\) | −28.3152 | −1.91336 | ||||||||
\(220\) | −8.37084 | −0.564362 | ||||||||
\(221\) | −1.87960 | −0.126436 | ||||||||
\(222\) | −3.61816 | −0.242835 | ||||||||
\(223\) | 1.53370 | 0.102704 | 0.0513519 | − | 0.998681i | \(-0.483647\pi\) | ||||
0.0513519 | + | 0.998681i | \(0.483647\pi\) | |||||||
\(224\) | 41.0124 | 2.74026 | ||||||||
\(225\) | 43.1921 | 2.87947 | ||||||||
\(226\) | −37.1513 | −2.47126 | ||||||||
\(227\) | −1.49973 | −0.0995409 | −0.0497704 | − | 0.998761i | \(-0.515849\pi\) | ||||
−0.0497704 | + | 0.998761i | \(0.515849\pi\) | |||||||
\(228\) | −23.8114 | −1.57695 | ||||||||
\(229\) | 4.15251 | 0.274405 | 0.137203 | − | 0.990543i | \(-0.456189\pi\) | ||||
0.137203 | + | 0.990543i | \(0.456189\pi\) | |||||||
\(230\) | −46.8126 | −3.08673 | ||||||||
\(231\) | 14.5738 | 0.958886 | ||||||||
\(232\) | 1.01343 | 0.0665347 | ||||||||
\(233\) | 16.0967 | 1.05453 | 0.527266 | − | 0.849700i | \(-0.323217\pi\) | ||||
0.527266 | + | 0.849700i | \(0.323217\pi\) | |||||||
\(234\) | 6.58781 | 0.430658 | ||||||||
\(235\) | 7.87589 | 0.513766 | ||||||||
\(236\) | 28.9923 | 1.88724 | ||||||||
\(237\) | −2.96464 | −0.192574 | ||||||||
\(238\) | 32.9362 | 2.13494 | ||||||||
\(239\) | 11.9835 | 0.775147 | 0.387573 | − | 0.921839i | \(-0.373313\pi\) | ||||
0.387573 | + | 0.921839i | \(0.373313\pi\) | |||||||
\(240\) | −34.3648 | −2.21824 | ||||||||
\(241\) | 20.3342 | 1.30984 | 0.654920 | − | 0.755698i | \(-0.272702\pi\) | ||||
0.654920 | + | 0.755698i | \(0.272702\pi\) | |||||||
\(242\) | 2.07554 | 0.133421 | ||||||||
\(243\) | 10.7390 | 0.688909 | ||||||||
\(244\) | −24.9842 | −1.59945 | ||||||||
\(245\) | −67.4718 | −4.31061 | ||||||||
\(246\) | 62.3879 | 3.97771 | ||||||||
\(247\) | 2.14685 | 0.136601 | ||||||||
\(248\) | −1.07749 | −0.0684207 | ||||||||
\(249\) | 8.73416 | 0.553505 | ||||||||
\(250\) | −23.7561 | −1.50247 | ||||||||
\(251\) | 0.584210 | 0.0368750 | 0.0184375 | − | 0.999830i | \(-0.494131\pi\) | ||||
0.0184375 | + | 0.999830i | \(0.494131\pi\) | |||||||
\(252\) | −61.8442 | −3.89582 | ||||||||
\(253\) | 6.21835 | 0.390944 | ||||||||
\(254\) | 45.7904 | 2.87315 | ||||||||
\(255\) | −32.7637 | −2.05174 | ||||||||
\(256\) | 10.0038 | 0.625238 | ||||||||
\(257\) | −21.9099 | −1.36670 | −0.683352 | − | 0.730089i | \(-0.739479\pi\) | ||||
−0.683352 | + | 0.730089i | \(0.739479\pi\) | |||||||
\(258\) | −0.464263 | −0.0289038 | ||||||||
\(259\) | −3.06239 | −0.190288 | ||||||||
\(260\) | −5.01686 | −0.311132 | ||||||||
\(261\) | 8.39897 | 0.519883 | ||||||||
\(262\) | −2.07554 | −0.128227 | ||||||||
\(263\) | −9.59178 | −0.591455 | −0.295727 | − | 0.955272i | \(-0.595562\pi\) | ||||
−0.295727 | + | 0.955272i | \(0.595562\pi\) | |||||||
\(264\) | −1.84055 | −0.113278 | ||||||||
\(265\) | 2.35966 | 0.144953 | ||||||||
\(266\) | −37.6192 | −2.30658 | ||||||||
\(267\) | 22.3122 | 1.36549 | ||||||||
\(268\) | −31.5792 | −1.92901 | ||||||||
\(269\) | 25.2765 | 1.54113 | 0.770567 | − | 0.637359i | \(-0.219973\pi\) | ||||
0.770567 | + | 0.637359i | \(0.219973\pi\) | |||||||
\(270\) | 49.7840 | 3.02976 | ||||||||
\(271\) | −6.16044 | −0.374220 | −0.187110 | − | 0.982339i | \(-0.559912\pi\) | ||||
−0.187110 | + | 0.982339i | \(0.559912\pi\) | |||||||
\(272\) | 10.3163 | 0.625520 | ||||||||
\(273\) | 8.73446 | 0.528633 | ||||||||
\(274\) | 37.5690 | 2.26963 | ||||||||
\(275\) | 8.15564 | 0.491804 | ||||||||
\(276\) | −41.3354 | −2.48810 | ||||||||
\(277\) | −8.89641 | −0.534534 | −0.267267 | − | 0.963623i | \(-0.586121\pi\) | ||||
−0.267267 | + | 0.963623i | \(0.586121\pi\) | |||||||
\(278\) | 14.1911 | 0.851126 | ||||||||
\(279\) | −8.92991 | −0.534620 | ||||||||
\(280\) | 11.7276 | 0.700856 | ||||||||
\(281\) | 15.8974 | 0.948360 | 0.474180 | − | 0.880428i | \(-0.342745\pi\) | ||||
0.474180 | + | 0.880428i | \(0.342745\pi\) | |||||||
\(282\) | 12.9810 | 0.773009 | ||||||||
\(283\) | −31.7367 | −1.88655 | −0.943277 | − | 0.332007i | \(-0.892274\pi\) | ||||
−0.943277 | + | 0.332007i | \(0.892274\pi\) | |||||||
\(284\) | 35.3277 | 2.09632 | ||||||||
\(285\) | 37.4221 | 2.21669 | ||||||||
\(286\) | 1.24393 | 0.0735549 | ||||||||
\(287\) | 52.8049 | 3.11697 | ||||||||
\(288\) | −42.9262 | −2.52945 | ||||||||
\(289\) | −7.16430 | −0.421430 | ||||||||
\(290\) | −11.9390 | −0.701081 | ||||||||
\(291\) | 21.1508 | 1.23988 | ||||||||
\(292\) | 22.6881 | 1.32772 | ||||||||
\(293\) | 10.0739 | 0.588524 | 0.294262 | − | 0.955725i | \(-0.404926\pi\) | ||||
0.294262 | + | 0.955725i | \(0.404926\pi\) | |||||||
\(294\) | −111.207 | −6.48572 | ||||||||
\(295\) | −45.5644 | −2.65286 | ||||||||
\(296\) | 0.386753 | 0.0224796 | ||||||||
\(297\) | −6.61305 | −0.383728 | ||||||||
\(298\) | −4.04939 | −0.234575 | ||||||||
\(299\) | 3.72682 | 0.215527 | ||||||||
\(300\) | −54.2132 | −3.13000 | ||||||||
\(301\) | −0.392951 | −0.0226493 | ||||||||
\(302\) | 14.7252 | 0.847342 | ||||||||
\(303\) | −57.0485 | −3.27735 | ||||||||
\(304\) | −11.7832 | −0.675810 | ||||||||
\(305\) | 39.2652 | 2.24832 | ||||||||
\(306\) | −34.4731 | −1.97070 | ||||||||
\(307\) | 26.5321 | 1.51427 | 0.757135 | − | 0.653259i | \(-0.226599\pi\) | ||||
0.757135 | + | 0.653259i | \(0.226599\pi\) | |||||||
\(308\) | −11.6776 | −0.665391 | ||||||||
\(309\) | −24.6694 | −1.40340 | ||||||||
\(310\) | 12.6937 | 0.720954 | ||||||||
\(311\) | −11.8642 | −0.672758 | −0.336379 | − | 0.941727i | \(-0.609202\pi\) | ||||
−0.336379 | + | 0.941727i | \(0.609202\pi\) | |||||||
\(312\) | −1.10309 | −0.0624499 | ||||||||
\(313\) | 2.21275 | 0.125072 | 0.0625362 | − | 0.998043i | \(-0.480081\pi\) | ||||
0.0625362 | + | 0.998043i | \(0.480081\pi\) | |||||||
\(314\) | 8.61287 | 0.486052 | ||||||||
\(315\) | 97.1945 | 5.47629 | ||||||||
\(316\) | 2.37548 | 0.133631 | ||||||||
\(317\) | −4.67660 | −0.262664 | −0.131332 | − | 0.991338i | \(-0.541925\pi\) | ||||
−0.131332 | + | 0.991338i | \(0.541925\pi\) | |||||||
\(318\) | 3.88919 | 0.218095 | ||||||||
\(319\) | 1.58591 | 0.0887941 | ||||||||
\(320\) | 37.1567 | 2.07712 | ||||||||
\(321\) | −4.33241 | −0.241811 | ||||||||
\(322\) | −65.3050 | −3.63930 | ||||||||
\(323\) | −11.2342 | −0.625086 | ||||||||
\(324\) | 7.29168 | 0.405093 | ||||||||
\(325\) | 4.88788 | 0.271131 | ||||||||
\(326\) | −29.0147 | −1.60697 | ||||||||
\(327\) | −13.6195 | −0.753159 | ||||||||
\(328\) | −6.66879 | −0.368223 | ||||||||
\(329\) | 10.9871 | 0.605738 | ||||||||
\(330\) | 21.6831 | 1.19362 | ||||||||
\(331\) | −25.5661 | −1.40524 | −0.702620 | − | 0.711565i | \(-0.747987\pi\) | ||||
−0.702620 | + | 0.711565i | \(0.747987\pi\) | |||||||
\(332\) | −6.99842 | −0.384088 | ||||||||
\(333\) | 3.20529 | 0.175649 | ||||||||
\(334\) | 24.0567 | 1.31632 | ||||||||
\(335\) | 49.6300 | 2.71158 | ||||||||
\(336\) | −47.9398 | −2.61533 | ||||||||
\(337\) | −1.59339 | −0.0867976 | −0.0433988 | − | 0.999058i | \(-0.513819\pi\) | ||||
−0.0433988 | + | 0.999058i | \(0.513819\pi\) | |||||||
\(338\) | −26.2365 | −1.42708 | ||||||||
\(339\) | 51.5556 | 2.80011 | ||||||||
\(340\) | 26.2526 | 1.42375 | ||||||||
\(341\) | −1.68617 | −0.0913111 | ||||||||
\(342\) | 39.3746 | 2.12914 | ||||||||
\(343\) | −58.7060 | −3.16983 | ||||||||
\(344\) | 0.0496263 | 0.00267567 | ||||||||
\(345\) | 64.9628 | 3.49748 | ||||||||
\(346\) | −24.4221 | −1.31294 | ||||||||
\(347\) | 25.0492 | 1.34471 | 0.672356 | − | 0.740228i | \(-0.265283\pi\) | ||||
0.672356 | + | 0.740228i | \(0.265283\pi\) | |||||||
\(348\) | −10.5421 | −0.565115 | ||||||||
\(349\) | 9.93581 | 0.531852 | 0.265926 | − | 0.963993i | \(-0.414322\pi\) | ||||
0.265926 | + | 0.963993i | \(0.414322\pi\) | |||||||
\(350\) | −85.6503 | −4.57820 | ||||||||
\(351\) | −3.96337 | −0.211549 | ||||||||
\(352\) | −8.10543 | −0.432021 | ||||||||
\(353\) | 12.0578 | 0.641771 | 0.320885 | − | 0.947118i | \(-0.396020\pi\) | ||||
0.320885 | + | 0.947118i | \(0.396020\pi\) | |||||||
\(354\) | −75.0992 | −3.99148 | ||||||||
\(355\) | −55.5212 | −2.94676 | ||||||||
\(356\) | −17.8781 | −0.947540 | ||||||||
\(357\) | −45.7063 | −2.41903 | ||||||||
\(358\) | −22.9235 | −1.21154 | ||||||||
\(359\) | 24.1797 | 1.27615 | 0.638077 | − | 0.769972i | \(-0.279730\pi\) | ||||
0.638077 | + | 0.769972i | \(0.279730\pi\) | |||||||
\(360\) | −12.2748 | −0.646940 | ||||||||
\(361\) | −6.16853 | −0.324659 | ||||||||
\(362\) | −37.3233 | −1.96167 | ||||||||
\(363\) | −2.88027 | −0.151175 | ||||||||
\(364\) | −6.99866 | −0.366830 | ||||||||
\(365\) | −35.6567 | −1.86636 | ||||||||
\(366\) | 64.7169 | 3.38281 | ||||||||
\(367\) | 2.94826 | 0.153898 | 0.0769490 | − | 0.997035i | \(-0.475482\pi\) | ||||
0.0769490 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(368\) | −20.4550 | −1.06629 | ||||||||
\(369\) | −55.2689 | −2.87719 | ||||||||
\(370\) | −4.55627 | −0.236869 | ||||||||
\(371\) | 3.29179 | 0.170901 | ||||||||
\(372\) | 11.2085 | 0.581134 | ||||||||
\(373\) | −29.6265 | −1.53400 | −0.767002 | − | 0.641645i | \(-0.778252\pi\) | ||||
−0.767002 | + | 0.641645i | \(0.778252\pi\) | |||||||
\(374\) | −6.50930 | −0.336588 | ||||||||
\(375\) | 32.9668 | 1.70240 | ||||||||
\(376\) | −1.38757 | −0.0715587 | ||||||||
\(377\) | 0.950479 | 0.0489521 | ||||||||
\(378\) | 69.4501 | 3.57213 | ||||||||
\(379\) | 0.0207330 | 0.00106498 | 0.000532491 | − | 1.00000i | \(-0.499831\pi\) | ||||
0.000532491 | 1.00000i | \(0.499831\pi\) | ||||||||
\(380\) | −29.9852 | −1.53821 | ||||||||
\(381\) | −63.5443 | −3.25547 | ||||||||
\(382\) | 36.5639 | 1.87077 | ||||||||
\(383\) | 21.6673 | 1.10715 | 0.553573 | − | 0.832801i | \(-0.313264\pi\) | ||||
0.553573 | + | 0.832801i | \(0.313264\pi\) | |||||||
\(384\) | 14.5499 | 0.742496 | ||||||||
\(385\) | 18.3525 | 0.935330 | ||||||||
\(386\) | 20.7478 | 1.05604 | ||||||||
\(387\) | 0.411287 | 0.0209069 | ||||||||
\(388\) | −16.9475 | −0.860381 | ||||||||
\(389\) | −4.78430 | −0.242573 | −0.121287 | − | 0.992618i | \(-0.538702\pi\) | ||||
−0.121287 | + | 0.992618i | \(0.538702\pi\) | |||||||
\(390\) | 12.9952 | 0.658040 | ||||||||
\(391\) | −19.5019 | −0.986255 | ||||||||
\(392\) | 11.8872 | 0.600393 | ||||||||
\(393\) | 2.88027 | 0.145291 | ||||||||
\(394\) | −22.1853 | −1.11768 | ||||||||
\(395\) | −3.73331 | −0.187843 | ||||||||
\(396\) | 12.2225 | 0.614203 | ||||||||
\(397\) | 25.9260 | 1.30119 | 0.650596 | − | 0.759424i | \(-0.274519\pi\) | ||||
0.650596 | + | 0.759424i | \(0.274519\pi\) | |||||||
\(398\) | 19.1922 | 0.962017 | ||||||||
\(399\) | 52.2049 | 2.61351 | ||||||||
\(400\) | −26.8276 | −1.34138 | ||||||||
\(401\) | 12.7727 | 0.637840 | 0.318920 | − | 0.947782i | \(-0.396680\pi\) | ||||
0.318920 | + | 0.947782i | \(0.396680\pi\) | |||||||
\(402\) | 81.8001 | 4.07982 | ||||||||
\(403\) | −1.01056 | −0.0503397 | ||||||||
\(404\) | 45.7113 | 2.27422 | ||||||||
\(405\) | −11.4596 | −0.569433 | ||||||||
\(406\) | −16.6552 | −0.826585 | ||||||||
\(407\) | 0.605232 | 0.0300002 | ||||||||
\(408\) | 5.77230 | 0.285772 | ||||||||
\(409\) | −21.3764 | −1.05699 | −0.528497 | − | 0.848935i | \(-0.677244\pi\) | ||||
−0.528497 | + | 0.848935i | \(0.677244\pi\) | |||||||
\(410\) | 78.5638 | 3.87999 | ||||||||
\(411\) | −52.1353 | −2.57165 | ||||||||
\(412\) | 19.7669 | 0.973846 | ||||||||
\(413\) | −63.5637 | −3.12776 | ||||||||
\(414\) | 68.3523 | 3.35933 | ||||||||
\(415\) | 10.9987 | 0.539907 | ||||||||
\(416\) | −4.85779 | −0.238173 | ||||||||
\(417\) | −19.6933 | −0.964384 | ||||||||
\(418\) | 7.43481 | 0.363649 | ||||||||
\(419\) | −20.2058 | −0.987117 | −0.493558 | − | 0.869713i | \(-0.664304\pi\) | ||||
−0.493558 | + | 0.869713i | \(0.664304\pi\) | |||||||
\(420\) | −121.995 | −5.95275 | ||||||||
\(421\) | −16.3870 | −0.798652 | −0.399326 | − | 0.916809i | \(-0.630756\pi\) | ||||
−0.399326 | + | 0.916809i | \(0.630756\pi\) | |||||||
\(422\) | 40.2924 | 1.96140 | ||||||||
\(423\) | −11.4998 | −0.559139 | ||||||||
\(424\) | −0.415725 | −0.0201894 | ||||||||
\(425\) | −25.5776 | −1.24070 | ||||||||
\(426\) | −91.5099 | −4.43367 | ||||||||
\(427\) | 54.7761 | 2.65080 | ||||||||
\(428\) | 3.47143 | 0.167798 | ||||||||
\(429\) | −1.72622 | −0.0833428 | ||||||||
\(430\) | −0.584637 | −0.0281937 | ||||||||
\(431\) | 23.0721 | 1.11135 | 0.555673 | − | 0.831401i | \(-0.312461\pi\) | ||||
0.555673 | + | 0.831401i | \(0.312461\pi\) | |||||||
\(432\) | 21.7533 | 1.04661 | ||||||||
\(433\) | −36.0195 | −1.73099 | −0.865494 | − | 0.500920i | \(-0.832995\pi\) | ||||
−0.865494 | + | 0.500920i | \(0.832995\pi\) | |||||||
\(434\) | 17.7081 | 0.850016 | ||||||||
\(435\) | 16.5680 | 0.794374 | ||||||||
\(436\) | 10.9129 | 0.522633 | ||||||||
\(437\) | 22.2748 | 1.06555 | ||||||||
\(438\) | −58.7694 | −2.80811 | ||||||||
\(439\) | 20.5470 | 0.980654 | 0.490327 | − | 0.871538i | \(-0.336877\pi\) | ||||
0.490327 | + | 0.871538i | \(0.336877\pi\) | |||||||
\(440\) | −2.31776 | −0.110495 | ||||||||
\(441\) | 98.5173 | 4.69130 | ||||||||
\(442\) | −3.90119 | −0.185561 | ||||||||
\(443\) | −15.5511 | −0.738854 | −0.369427 | − | 0.929260i | \(-0.620446\pi\) | ||||
−0.369427 | + | 0.929260i | \(0.620446\pi\) | |||||||
\(444\) | −4.02317 | −0.190931 | ||||||||
\(445\) | 28.0974 | 1.33194 | ||||||||
\(446\) | 3.18325 | 0.150731 | ||||||||
\(447\) | 5.61942 | 0.265789 | ||||||||
\(448\) | 51.8347 | 2.44896 | ||||||||
\(449\) | 0.180417 | 0.00851440 | 0.00425720 | − | 0.999991i | \(-0.498645\pi\) | ||||
0.00425720 | + | 0.999991i | \(0.498645\pi\) | |||||||
\(450\) | 89.6471 | 4.22601 | ||||||||
\(451\) | −10.4360 | −0.491413 | ||||||||
\(452\) | −41.3100 | −1.94306 | ||||||||
\(453\) | −20.4345 | −0.960097 | ||||||||
\(454\) | −3.11276 | −0.146089 | ||||||||
\(455\) | 10.9991 | 0.515647 | ||||||||
\(456\) | −6.59303 | −0.308747 | ||||||||
\(457\) | 13.4260 | 0.628040 | 0.314020 | − | 0.949416i | \(-0.398324\pi\) | ||||
0.314020 | + | 0.949416i | \(0.398324\pi\) | |||||||
\(458\) | 8.61871 | 0.402726 | ||||||||
\(459\) | 20.7398 | 0.968051 | ||||||||
\(460\) | −52.0528 | −2.42698 | ||||||||
\(461\) | 1.01035 | 0.0470567 | 0.0235284 | − | 0.999723i | \(-0.492510\pi\) | ||||
0.0235284 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(462\) | 30.2486 | 1.40729 | ||||||||
\(463\) | 4.58674 | 0.213164 | 0.106582 | − | 0.994304i | \(-0.466009\pi\) | ||||
0.106582 | + | 0.994304i | \(0.466009\pi\) | |||||||
\(464\) | −5.21679 | −0.242183 | ||||||||
\(465\) | −17.6153 | −0.816891 | ||||||||
\(466\) | 33.4095 | 1.54766 | ||||||||
\(467\) | −8.75168 | −0.404979 | −0.202490 | − | 0.979284i | \(-0.564903\pi\) | ||||
−0.202490 | + | 0.979284i | \(0.564903\pi\) | |||||||
\(468\) | 7.32525 | 0.338610 | ||||||||
\(469\) | 69.2353 | 3.19699 | ||||||||
\(470\) | 16.3468 | 0.754019 | ||||||||
\(471\) | −11.9523 | −0.550731 | ||||||||
\(472\) | 8.02754 | 0.369497 | ||||||||
\(473\) | 0.0776603 | 0.00357082 | ||||||||
\(474\) | −6.15323 | −0.282627 | ||||||||
\(475\) | 29.2144 | 1.34045 | ||||||||
\(476\) | 36.6231 | 1.67862 | ||||||||
\(477\) | −3.44540 | −0.157754 | ||||||||
\(478\) | 24.8722 | 1.13763 | ||||||||
\(479\) | 38.4992 | 1.75907 | 0.879536 | − | 0.475832i | \(-0.157853\pi\) | ||||
0.879536 | + | 0.475832i | \(0.157853\pi\) | |||||||
\(480\) | −84.6771 | −3.86496 | ||||||||
\(481\) | 0.362731 | 0.0165391 | ||||||||
\(482\) | 42.2045 | 1.92236 | ||||||||
\(483\) | 90.6251 | 4.12358 | ||||||||
\(484\) | 2.30788 | 0.104904 | ||||||||
\(485\) | 26.6348 | 1.20942 | ||||||||
\(486\) | 22.2893 | 1.01106 | ||||||||
\(487\) | 18.8334 | 0.853422 | 0.426711 | − | 0.904388i | \(-0.359672\pi\) | ||||
0.426711 | + | 0.904388i | \(0.359672\pi\) | |||||||
\(488\) | −6.91775 | −0.313152 | ||||||||
\(489\) | 40.2642 | 1.82081 | ||||||||
\(490\) | −140.041 | −6.32639 | ||||||||
\(491\) | 13.9059 | 0.627566 | 0.313783 | − | 0.949495i | \(-0.398404\pi\) | ||||
0.313783 | + | 0.949495i | \(0.398404\pi\) | |||||||
\(492\) | 69.3716 | 3.12751 | ||||||||
\(493\) | −4.97373 | −0.224006 | ||||||||
\(494\) | 4.45587 | 0.200479 | ||||||||
\(495\) | −19.2089 | −0.863376 | ||||||||
\(496\) | 5.54657 | 0.249048 | ||||||||
\(497\) | −77.4536 | −3.47427 | ||||||||
\(498\) | 18.1281 | 0.812340 | ||||||||
\(499\) | 12.3494 | 0.552836 | 0.276418 | − | 0.961038i | \(-0.410853\pi\) | ||||
0.276418 | + | 0.961038i | \(0.410853\pi\) | |||||||
\(500\) | −26.4154 | −1.18133 | ||||||||
\(501\) | −33.3840 | −1.49149 | ||||||||
\(502\) | 1.21255 | 0.0541189 | ||||||||
\(503\) | −28.0862 | −1.25230 | −0.626150 | − | 0.779703i | \(-0.715370\pi\) | ||||
−0.626150 | + | 0.779703i | \(0.715370\pi\) | |||||||
\(504\) | −17.1237 | −0.762752 | ||||||||
\(505\) | −71.8400 | −3.19684 | ||||||||
\(506\) | 12.9065 | 0.573762 | ||||||||
\(507\) | 36.4090 | 1.61698 | ||||||||
\(508\) | 50.9162 | 2.25904 | ||||||||
\(509\) | 32.1680 | 1.42582 | 0.712911 | − | 0.701255i | \(-0.247376\pi\) | ||||
0.712911 | + | 0.701255i | \(0.247376\pi\) | |||||||
\(510\) | −68.0024 | −3.01120 | ||||||||
\(511\) | −49.7422 | −2.20046 | ||||||||
\(512\) | 30.8665 | 1.36412 | ||||||||
\(513\) | −23.6887 | −1.04588 | ||||||||
\(514\) | −45.4750 | −2.00582 | ||||||||
\(515\) | −31.0657 | −1.36892 | ||||||||
\(516\) | −0.516233 | −0.0227259 | ||||||||
\(517\) | −2.17142 | −0.0954989 | ||||||||
\(518\) | −6.35613 | −0.279272 | ||||||||
\(519\) | 33.8911 | 1.48766 | ||||||||
\(520\) | −1.38909 | −0.0609158 | ||||||||
\(521\) | 28.3236 | 1.24088 | 0.620439 | − | 0.784255i | \(-0.286954\pi\) | ||||
0.620439 | + | 0.784255i | \(0.286954\pi\) | |||||||
\(522\) | 17.4324 | 0.762996 | ||||||||
\(523\) | 28.0700 | 1.22741 | 0.613707 | − | 0.789534i | \(-0.289677\pi\) | ||||
0.613707 | + | 0.789534i | \(0.289677\pi\) | |||||||
\(524\) | −2.30788 | −0.100820 | ||||||||
\(525\) | 118.859 | 5.18742 | ||||||||
\(526\) | −19.9082 | −0.868037 | ||||||||
\(527\) | 5.28814 | 0.230355 | ||||||||
\(528\) | 9.47452 | 0.412326 | ||||||||
\(529\) | 15.6679 | 0.681212 | ||||||||
\(530\) | 4.89758 | 0.212737 | ||||||||
\(531\) | 66.5298 | 2.88715 | ||||||||
\(532\) | −41.8303 | −1.81357 | ||||||||
\(533\) | −6.25457 | −0.270915 | ||||||||
\(534\) | 46.3100 | 2.00403 | ||||||||
\(535\) | −5.45571 | −0.235871 | ||||||||
\(536\) | −8.74382 | −0.377675 | ||||||||
\(537\) | 31.8114 | 1.37276 | ||||||||
\(538\) | 52.4624 | 2.26182 | ||||||||
\(539\) | 18.6023 | 0.801257 | ||||||||
\(540\) | 55.3568 | 2.38218 | ||||||||
\(541\) | 2.37442 | 0.102084 | 0.0510420 | − | 0.998697i | \(-0.483746\pi\) | ||||
0.0510420 | + | 0.998697i | \(0.483746\pi\) | |||||||
\(542\) | −12.7863 | −0.549217 | ||||||||
\(543\) | 51.7943 | 2.22271 | ||||||||
\(544\) | 25.4202 | 1.08988 | ||||||||
\(545\) | −17.1507 | −0.734657 | ||||||||
\(546\) | 18.1287 | 0.775839 | ||||||||
\(547\) | −35.7363 | −1.52797 | −0.763987 | − | 0.645231i | \(-0.776761\pi\) | ||||
−0.763987 | + | 0.645231i | \(0.776761\pi\) | |||||||
\(548\) | 41.7745 | 1.78452 | ||||||||
\(549\) | −57.3322 | −2.44688 | ||||||||
\(550\) | 16.9274 | 0.721786 | ||||||||
\(551\) | 5.68091 | 0.242015 | ||||||||
\(552\) | −11.4452 | −0.487138 | ||||||||
\(553\) | −5.20807 | −0.221470 | ||||||||
\(554\) | −18.4649 | −0.784498 | ||||||||
\(555\) | 6.32283 | 0.268389 | ||||||||
\(556\) | 15.7797 | 0.669206 | ||||||||
\(557\) | −12.6279 | −0.535059 | −0.267530 | − | 0.963550i | \(-0.586207\pi\) | ||||
−0.267530 | + | 0.963550i | \(0.586207\pi\) | |||||||
\(558\) | −18.5344 | −0.784624 | ||||||||
\(559\) | 0.0465438 | 0.00196859 | ||||||||
\(560\) | −60.3697 | −2.55108 | ||||||||
\(561\) | 9.03309 | 0.381377 | ||||||||
\(562\) | 32.9958 | 1.39184 | ||||||||
\(563\) | −15.0992 | −0.636354 | −0.318177 | − | 0.948031i | \(-0.603071\pi\) | ||||
−0.318177 | + | 0.948031i | \(0.603071\pi\) | |||||||
\(564\) | 14.4341 | 0.607787 | ||||||||
\(565\) | 64.9229 | 2.73133 | ||||||||
\(566\) | −65.8710 | −2.76876 | ||||||||
\(567\) | −15.9865 | −0.671370 | ||||||||
\(568\) | 9.78172 | 0.410432 | ||||||||
\(569\) | −29.9217 | −1.25438 | −0.627191 | − | 0.778866i | \(-0.715795\pi\) | ||||
−0.627191 | + | 0.778866i | \(0.715795\pi\) | |||||||
\(570\) | 77.6712 | 3.25329 | ||||||||
\(571\) | −39.6674 | −1.66003 | −0.830015 | − | 0.557740i | \(-0.811668\pi\) | ||||
−0.830015 | + | 0.557740i | \(0.811668\pi\) | |||||||
\(572\) | 1.38317 | 0.0578333 | ||||||||
\(573\) | −50.7405 | −2.11972 | ||||||||
\(574\) | 109.599 | 4.57456 | ||||||||
\(575\) | 50.7146 | 2.11495 | ||||||||
\(576\) | −54.2535 | −2.26056 | ||||||||
\(577\) | 9.08201 | 0.378089 | 0.189044 | − | 0.981969i | \(-0.439461\pi\) | ||||
0.189044 | + | 0.981969i | \(0.439461\pi\) | |||||||
\(578\) | −14.8698 | −0.618503 | ||||||||
\(579\) | −28.7922 | −1.19656 | ||||||||
\(580\) | −13.2754 | −0.551232 | ||||||||
\(581\) | 15.3436 | 0.636559 | ||||||||
\(582\) | 43.8995 | 1.81969 | ||||||||
\(583\) | −0.650569 | −0.0269438 | ||||||||
\(584\) | 6.28200 | 0.259951 | ||||||||
\(585\) | −11.5124 | −0.475978 | ||||||||
\(586\) | 20.9088 | 0.863736 | ||||||||
\(587\) | −36.2095 | −1.49453 | −0.747264 | − | 0.664527i | \(-0.768633\pi\) | ||||
−0.747264 | + | 0.664527i | \(0.768633\pi\) | |||||||
\(588\) | −123.655 | −5.09946 | ||||||||
\(589\) | −6.04003 | −0.248875 | ||||||||
\(590\) | −94.5709 | −3.89342 | ||||||||
\(591\) | 30.7869 | 1.26641 | ||||||||
\(592\) | −1.99088 | −0.0818246 | ||||||||
\(593\) | 13.6094 | 0.558871 | 0.279435 | − | 0.960164i | \(-0.409853\pi\) | ||||
0.279435 | + | 0.960164i | \(0.409853\pi\) | |||||||
\(594\) | −13.7257 | −0.563172 | ||||||||
\(595\) | −57.5570 | −2.35961 | ||||||||
\(596\) | −4.50268 | −0.184437 | ||||||||
\(597\) | −26.6334 | −1.09003 | ||||||||
\(598\) | 7.73517 | 0.316314 | ||||||||
\(599\) | −40.8257 | −1.66809 | −0.834047 | − | 0.551694i | \(-0.813982\pi\) | ||||
−0.834047 | + | 0.551694i | \(0.813982\pi\) | |||||||
\(600\) | −15.0108 | −0.612814 | ||||||||
\(601\) | −13.9254 | −0.568029 | −0.284015 | − | 0.958820i | \(-0.591666\pi\) | ||||
−0.284015 | + | 0.958820i | \(0.591666\pi\) | |||||||
\(602\) | −0.815586 | −0.0332408 | ||||||||
\(603\) | −72.4661 | −2.95105 | ||||||||
\(604\) | 16.3736 | 0.666231 | ||||||||
\(605\) | −3.62707 | −0.147461 | ||||||||
\(606\) | −118.407 | −4.80994 | ||||||||
\(607\) | 15.5306 | 0.630368 | 0.315184 | − | 0.949031i | \(-0.397934\pi\) | ||||
0.315184 | + | 0.949031i | \(0.397934\pi\) | |||||||
\(608\) | −29.0345 | −1.17750 | ||||||||
\(609\) | 23.1128 | 0.936578 | ||||||||
\(610\) | 81.4966 | 3.29970 | ||||||||
\(611\) | −1.30139 | −0.0526485 | ||||||||
\(612\) | −38.3321 | −1.54948 | ||||||||
\(613\) | −9.02158 | −0.364378 | −0.182189 | − | 0.983264i | \(-0.558318\pi\) | ||||
−0.182189 | + | 0.983264i | \(0.558318\pi\) | |||||||
\(614\) | 55.0686 | 2.22239 | ||||||||
\(615\) | −109.025 | −4.39630 | ||||||||
\(616\) | −3.23334 | −0.130275 | ||||||||
\(617\) | 17.7311 | 0.713827 | 0.356914 | − | 0.934137i | \(-0.383829\pi\) | ||||
0.356914 | + | 0.934137i | \(0.383829\pi\) | |||||||
\(618\) | −51.2025 | −2.05967 | ||||||||
\(619\) | 29.7961 | 1.19760 | 0.598802 | − | 0.800897i | \(-0.295643\pi\) | ||||
0.598802 | + | 0.800897i | \(0.295643\pi\) | |||||||
\(620\) | 14.1146 | 0.566858 | ||||||||
\(621\) | −41.1223 | −1.65018 | ||||||||
\(622\) | −24.6247 | −0.987360 | ||||||||
\(623\) | 39.1966 | 1.57038 | ||||||||
\(624\) | 5.67832 | 0.227315 | ||||||||
\(625\) | 0.736272 | 0.0294509 | ||||||||
\(626\) | 4.59267 | 0.183560 | ||||||||
\(627\) | −10.3174 | −0.412039 | ||||||||
\(628\) | 9.57699 | 0.382164 | ||||||||
\(629\) | −1.89812 | −0.0756831 | ||||||||
\(630\) | 201.731 | 8.03717 | ||||||||
\(631\) | 10.9697 | 0.436696 | 0.218348 | − | 0.975871i | \(-0.429933\pi\) | ||||
0.218348 | + | 0.975871i | \(0.429933\pi\) | |||||||
\(632\) | 0.657734 | 0.0261633 | ||||||||
\(633\) | −55.9146 | −2.22240 | ||||||||
\(634\) | −9.70648 | −0.385493 | ||||||||
\(635\) | −80.0201 | −3.17550 | ||||||||
\(636\) | 4.32454 | 0.171479 | ||||||||
\(637\) | 11.1488 | 0.441732 | ||||||||
\(638\) | 3.29163 | 0.130317 | ||||||||
\(639\) | 81.0679 | 3.20700 | ||||||||
\(640\) | 18.3224 | 0.724256 | ||||||||
\(641\) | 40.1623 | 1.58632 | 0.793158 | − | 0.609016i | \(-0.208436\pi\) | ||||
0.793158 | + | 0.609016i | \(0.208436\pi\) | |||||||
\(642\) | −8.99210 | −0.354890 | ||||||||
\(643\) | 20.2220 | 0.797476 | 0.398738 | − | 0.917065i | \(-0.369448\pi\) | ||||
0.398738 | + | 0.917065i | \(0.369448\pi\) | |||||||
\(644\) | −72.6152 | −2.86144 | ||||||||
\(645\) | 0.811314 | 0.0319454 | ||||||||
\(646\) | −23.3170 | −0.917395 | ||||||||
\(647\) | 19.8737 | 0.781315 | 0.390658 | − | 0.920536i | \(-0.372248\pi\) | ||||
0.390658 | + | 0.920536i | \(0.372248\pi\) | |||||||
\(648\) | 2.01896 | 0.0793121 | ||||||||
\(649\) | 12.5623 | 0.493114 | ||||||||
\(650\) | 10.1450 | 0.397920 | ||||||||
\(651\) | −24.5739 | −0.963127 | ||||||||
\(652\) | −32.2626 | −1.26350 | ||||||||
\(653\) | −31.5604 | −1.23505 | −0.617527 | − | 0.786550i | \(-0.711865\pi\) | ||||
−0.617527 | + | 0.786550i | \(0.711865\pi\) | |||||||
\(654\) | −28.2678 | −1.10536 | ||||||||
\(655\) | 3.62707 | 0.141721 | ||||||||
\(656\) | 34.3288 | 1.34031 | ||||||||
\(657\) | 52.0633 | 2.03118 | ||||||||
\(658\) | 22.8042 | 0.889000 | ||||||||
\(659\) | 30.4814 | 1.18739 | 0.593694 | − | 0.804691i | \(-0.297669\pi\) | ||||
0.593694 | + | 0.804691i | \(0.297669\pi\) | |||||||
\(660\) | 24.1103 | 0.938493 | ||||||||
\(661\) | 36.8905 | 1.43487 | 0.717436 | − | 0.696624i | \(-0.245315\pi\) | ||||
0.717436 | + | 0.696624i | \(0.245315\pi\) | |||||||
\(662\) | −53.0636 | −2.06237 | ||||||||
\(663\) | 5.41376 | 0.210253 | ||||||||
\(664\) | −1.93776 | −0.0751996 | ||||||||
\(665\) | 65.7406 | 2.54931 | ||||||||
\(666\) | 6.65273 | 0.257788 | ||||||||
\(667\) | 9.86177 | 0.381849 | ||||||||
\(668\) | 26.7496 | 1.03497 | ||||||||
\(669\) | −4.41746 | −0.170789 | ||||||||
\(670\) | 103.009 | 3.97959 | ||||||||
\(671\) | −10.8256 | −0.417918 | ||||||||
\(672\) | −118.127 | −4.55685 | ||||||||
\(673\) | 47.7316 | 1.83992 | 0.919958 | − | 0.392017i | \(-0.128222\pi\) | ||||
0.919958 | + | 0.392017i | \(0.128222\pi\) | |||||||
\(674\) | −3.30715 | −0.127387 | ||||||||
\(675\) | −53.9337 | −2.07591 | ||||||||
\(676\) | −29.1735 | −1.12206 | ||||||||
\(677\) | −21.6364 | −0.831555 | −0.415777 | − | 0.909466i | \(-0.636490\pi\) | ||||
−0.415777 | + | 0.909466i | \(0.636490\pi\) | |||||||
\(678\) | 107.006 | 4.10953 | ||||||||
\(679\) | 37.1563 | 1.42593 | ||||||||
\(680\) | 7.26894 | 0.278751 | ||||||||
\(681\) | 4.31965 | 0.165529 | ||||||||
\(682\) | −3.49971 | −0.134011 | ||||||||
\(683\) | −31.0578 | −1.18840 | −0.594198 | − | 0.804319i | \(-0.702530\pi\) | ||||
−0.594198 | + | 0.804319i | \(0.702530\pi\) | |||||||
\(684\) | 43.7822 | 1.67405 | ||||||||
\(685\) | −65.6529 | −2.50847 | ||||||||
\(686\) | −121.847 | −4.65213 | ||||||||
\(687\) | −11.9604 | −0.456316 | ||||||||
\(688\) | −0.255460 | −0.00973931 | ||||||||
\(689\) | −0.389903 | −0.0148541 | ||||||||
\(690\) | 134.833 | 5.13301 | ||||||||
\(691\) | 6.36017 | 0.241952 | 0.120976 | − | 0.992655i | \(-0.461398\pi\) | ||||
0.120976 | + | 0.992655i | \(0.461398\pi\) | |||||||
\(692\) | −27.1560 | −1.03231 | ||||||||
\(693\) | −26.7970 | −1.01793 | ||||||||
\(694\) | 51.9907 | 1.97354 | ||||||||
\(695\) | −24.7994 | −0.940693 | ||||||||
\(696\) | −2.91895 | −0.110642 | ||||||||
\(697\) | 32.7293 | 1.23971 | ||||||||
\(698\) | 20.6222 | 0.780562 | ||||||||
\(699\) | −46.3630 | −1.75361 | ||||||||
\(700\) | −95.2381 | −3.59966 | ||||||||
\(701\) | 29.4627 | 1.11279 | 0.556395 | − | 0.830918i | \(-0.312184\pi\) | ||||
0.556395 | + | 0.830918i | \(0.312184\pi\) | |||||||
\(702\) | −8.22615 | −0.310476 | ||||||||
\(703\) | 2.16800 | 0.0817678 | ||||||||
\(704\) | −10.2443 | −0.386096 | ||||||||
\(705\) | −22.6847 | −0.854356 | ||||||||
\(706\) | 25.0264 | 0.941882 | ||||||||
\(707\) | −100.219 | −3.76912 | ||||||||
\(708\) | −83.5058 | −3.13834 | ||||||||
\(709\) | −19.6700 | −0.738723 | −0.369361 | − | 0.929286i | \(-0.620424\pi\) | ||||
−0.369361 | + | 0.929286i | \(0.620424\pi\) | |||||||
\(710\) | −115.237 | −4.32475 | ||||||||
\(711\) | 5.45110 | 0.204432 | ||||||||
\(712\) | −4.95019 | −0.185516 | ||||||||
\(713\) | −10.4852 | −0.392673 | ||||||||
\(714\) | −94.8653 | −3.55025 | ||||||||
\(715\) | −2.17380 | −0.0812954 | ||||||||
\(716\) | −25.4895 | −0.952588 | ||||||||
\(717\) | −34.5157 | −1.28901 | ||||||||
\(718\) | 50.1860 | 1.87292 | ||||||||
\(719\) | 13.4191 | 0.500447 | 0.250224 | − | 0.968188i | \(-0.419496\pi\) | ||||
0.250224 | + | 0.968188i | \(0.419496\pi\) | |||||||
\(720\) | 63.1867 | 2.35483 | ||||||||
\(721\) | −43.3376 | −1.61398 | ||||||||
\(722\) | −12.8031 | −0.476480 | ||||||||
\(723\) | −58.5681 | −2.17817 | ||||||||
\(724\) | −41.5012 | −1.54238 | ||||||||
\(725\) | 12.9341 | 0.480362 | ||||||||
\(726\) | −5.97813 | −0.221869 | ||||||||
\(727\) | −23.7914 | −0.882373 | −0.441186 | − | 0.897415i | \(-0.645442\pi\) | ||||
−0.441186 | + | 0.897415i | \(0.645442\pi\) | |||||||
\(728\) | −1.93783 | −0.0718206 | ||||||||
\(729\) | −40.4097 | −1.49666 | ||||||||
\(730\) | −74.0071 | −2.73912 | ||||||||
\(731\) | −0.243557 | −0.00900830 | ||||||||
\(732\) | 71.9613 | 2.65977 | ||||||||
\(733\) | −35.5237 | −1.31210 | −0.656049 | − | 0.754718i | \(-0.727774\pi\) | ||||
−0.656049 | + | 0.754718i | \(0.727774\pi\) | |||||||
\(734\) | 6.11924 | 0.225865 | ||||||||
\(735\) | 194.337 | 7.16824 | ||||||||
\(736\) | −50.4024 | −1.85786 | ||||||||
\(737\) | −13.6832 | −0.504028 | ||||||||
\(738\) | −114.713 | −4.22265 | ||||||||
\(739\) | −15.1272 | −0.556462 | −0.278231 | − | 0.960514i | \(-0.589748\pi\) | ||||
−0.278231 | + | 0.960514i | \(0.589748\pi\) | |||||||
\(740\) | −5.06630 | −0.186241 | ||||||||
\(741\) | −6.18351 | −0.227157 | ||||||||
\(742\) | 6.83226 | 0.250820 | ||||||||
\(743\) | 46.1710 | 1.69385 | 0.846925 | − | 0.531713i | \(-0.178451\pi\) | ||||
0.846925 | + | 0.531713i | \(0.178451\pi\) | |||||||
\(744\) | 3.10347 | 0.113779 | ||||||||
\(745\) | 7.07642 | 0.259260 | ||||||||
\(746\) | −61.4912 | −2.25135 | ||||||||
\(747\) | −16.0596 | −0.587588 | ||||||||
\(748\) | −7.23795 | −0.264646 | ||||||||
\(749\) | −7.61088 | −0.278095 | ||||||||
\(750\) | 68.4241 | 2.49850 | ||||||||
\(751\) | −14.2430 | −0.519736 | −0.259868 | − | 0.965644i | \(-0.583679\pi\) | ||||
−0.259868 | + | 0.965644i | \(0.583679\pi\) | |||||||
\(752\) | 7.14278 | 0.260470 | ||||||||
\(753\) | −1.68269 | −0.0613205 | ||||||||
\(754\) | 1.97276 | 0.0718437 | ||||||||
\(755\) | −25.7328 | −0.936511 | ||||||||
\(756\) | 77.2244 | 2.80862 | ||||||||
\(757\) | 7.19531 | 0.261518 | 0.130759 | − | 0.991414i | \(-0.458259\pi\) | ||||
0.130759 | + | 0.991414i | \(0.458259\pi\) | |||||||
\(758\) | 0.0430322 | 0.00156300 | ||||||||
\(759\) | −17.9106 | −0.650112 | ||||||||
\(760\) | −8.30246 | −0.301162 | ||||||||
\(761\) | −2.94531 | −0.106767 | −0.0533837 | − | 0.998574i | \(-0.517001\pi\) | ||||
−0.0533837 | + | 0.998574i | \(0.517001\pi\) | |||||||
\(762\) | −131.889 | −4.77783 | ||||||||
\(763\) | −23.9258 | −0.866171 | ||||||||
\(764\) | 40.6569 | 1.47091 | ||||||||
\(765\) | 60.2428 | 2.17808 | ||||||||
\(766\) | 44.9714 | 1.62488 | ||||||||
\(767\) | 7.52892 | 0.271853 | ||||||||
\(768\) | −28.8137 | −1.03972 | ||||||||
\(769\) | 31.7843 | 1.14617 | 0.573086 | − | 0.819495i | \(-0.305746\pi\) | ||||
0.573086 | + | 0.819495i | \(0.305746\pi\) | |||||||
\(770\) | 38.0914 | 1.37272 | ||||||||
\(771\) | 63.1066 | 2.27273 | ||||||||
\(772\) | 23.0703 | 0.830320 | ||||||||
\(773\) | 6.99225 | 0.251494 | 0.125747 | − | 0.992062i | \(-0.459867\pi\) | ||||
0.125747 | + | 0.992062i | \(0.459867\pi\) | |||||||
\(774\) | 0.853644 | 0.0306836 | ||||||||
\(775\) | −13.7518 | −0.493978 | ||||||||
\(776\) | −4.69252 | −0.168452 | ||||||||
\(777\) | 8.82053 | 0.316435 | ||||||||
\(778\) | −9.93001 | −0.356008 | ||||||||
\(779\) | −37.3829 | −1.33938 | ||||||||
\(780\) | 14.4499 | 0.517391 | ||||||||
\(781\) | 15.3074 | 0.547743 | ||||||||
\(782\) | −40.4771 | −1.44746 | ||||||||
\(783\) | −10.4877 | −0.374801 | ||||||||
\(784\) | −61.1913 | −2.18540 | ||||||||
\(785\) | −15.0512 | −0.537201 | ||||||||
\(786\) | 5.97813 | 0.213233 | ||||||||
\(787\) | 30.0445 | 1.07097 | 0.535486 | − | 0.844544i | \(-0.320128\pi\) | ||||
0.535486 | + | 0.844544i | \(0.320128\pi\) | |||||||
\(788\) | −24.6687 | −0.878785 | ||||||||
\(789\) | 27.6270 | 0.983546 | ||||||||
\(790\) | −7.74864 | −0.275684 | ||||||||
\(791\) | 90.5693 | 3.22027 | ||||||||
\(792\) | 3.38422 | 0.120253 | ||||||||
\(793\) | −6.48806 | −0.230398 | ||||||||
\(794\) | 53.8106 | 1.90967 | ||||||||
\(795\) | −6.79647 | −0.241046 | ||||||||
\(796\) | 21.3405 | 0.756396 | ||||||||
\(797\) | 42.2552 | 1.49675 | 0.748377 | − | 0.663273i | \(-0.230833\pi\) | ||||
0.748377 | + | 0.663273i | \(0.230833\pi\) | |||||||
\(798\) | 108.354 | 3.83567 | ||||||||
\(799\) | 6.80999 | 0.240920 | ||||||||
\(800\) | −66.1050 | −2.33716 | ||||||||
\(801\) | −41.0257 | −1.44957 | ||||||||
\(802\) | 26.5104 | 0.936113 | ||||||||
\(803\) | 9.83072 | 0.346919 | ||||||||
\(804\) | 90.9568 | 3.20780 | ||||||||
\(805\) | 114.122 | 4.02228 | ||||||||
\(806\) | −2.09747 | −0.0738801 | ||||||||
\(807\) | −72.8032 | −2.56279 | ||||||||
\(808\) | 12.6568 | 0.445264 | ||||||||
\(809\) | 14.6690 | 0.515734 | 0.257867 | − | 0.966180i | \(-0.416980\pi\) | ||||
0.257867 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(810\) | −23.7849 | −0.835718 | ||||||||
\(811\) | −9.66211 | −0.339283 | −0.169641 | − | 0.985506i | \(-0.554261\pi\) | ||||
−0.169641 | + | 0.985506i | \(0.554261\pi\) | |||||||
\(812\) | −18.5196 | −0.649911 | ||||||||
\(813\) | 17.7438 | 0.622301 | ||||||||
\(814\) | 1.25618 | 0.0440292 | ||||||||
\(815\) | 50.7039 | 1.77608 | ||||||||
\(816\) | −29.7139 | −1.04019 | ||||||||
\(817\) | 0.278187 | 0.00973254 | ||||||||
\(818\) | −44.3676 | −1.55128 | ||||||||
\(819\) | −16.0601 | −0.561186 | ||||||||
\(820\) | 87.3582 | 3.05068 | ||||||||
\(821\) | 11.0306 | 0.384971 | 0.192486 | − | 0.981300i | \(-0.438345\pi\) | ||||
0.192486 | + | 0.981300i | \(0.438345\pi\) | |||||||
\(822\) | −108.209 | −3.77423 | ||||||||
\(823\) | −7.76970 | −0.270835 | −0.135417 | − | 0.990789i | \(-0.543238\pi\) | ||||
−0.135417 | + | 0.990789i | \(0.543238\pi\) | |||||||
\(824\) | 5.47316 | 0.190667 | ||||||||
\(825\) | −23.4905 | −0.817834 | ||||||||
\(826\) | −131.929 | −4.59040 | ||||||||
\(827\) | 56.4825 | 1.96409 | 0.982044 | − | 0.188653i | \(-0.0604123\pi\) | ||||
0.982044 | + | 0.188653i | \(0.0604123\pi\) | |||||||
\(828\) | 76.0037 | 2.64131 | ||||||||
\(829\) | −29.3697 | −1.02005 | −0.510026 | − | 0.860159i | \(-0.670364\pi\) | ||||
−0.510026 | + | 0.860159i | \(0.670364\pi\) | |||||||
\(830\) | 22.8284 | 0.792384 | ||||||||
\(831\) | 25.6241 | 0.888891 | ||||||||
\(832\) | −6.13965 | −0.212854 | ||||||||
\(833\) | −58.3403 | −2.02137 | ||||||||
\(834\) | −40.8743 | −1.41536 | ||||||||
\(835\) | −42.0397 | −1.45485 | ||||||||
\(836\) | 8.26707 | 0.285922 | ||||||||
\(837\) | 11.1507 | 0.385425 | ||||||||
\(838\) | −41.9380 | −1.44872 | ||||||||
\(839\) | 22.8663 | 0.789432 | 0.394716 | − | 0.918803i | \(-0.370843\pi\) | ||||
0.394716 | + | 0.918803i | \(0.370843\pi\) | |||||||
\(840\) | −33.7786 | −1.16547 | ||||||||
\(841\) | −26.4849 | −0.913272 | ||||||||
\(842\) | −34.0119 | −1.17213 | ||||||||
\(843\) | −45.7889 | −1.57705 | ||||||||
\(844\) | 44.8027 | 1.54217 | ||||||||
\(845\) | 45.8491 | 1.57726 | ||||||||
\(846\) | −23.8683 | −0.820610 | ||||||||
\(847\) | −5.05987 | −0.173859 | ||||||||
\(848\) | 2.14001 | 0.0734884 | ||||||||
\(849\) | 91.4105 | 3.13720 | ||||||||
\(850\) | −53.0875 | −1.82089 | ||||||||
\(851\) | 3.76354 | 0.129013 | ||||||||
\(852\) | −101.754 | −3.48602 | ||||||||
\(853\) | −19.9206 | −0.682067 | −0.341033 | − | 0.940051i | \(-0.610777\pi\) | ||||
−0.341033 | + | 0.940051i | \(0.610777\pi\) | |||||||
\(854\) | 113.690 | 3.89040 | ||||||||
\(855\) | −68.8083 | −2.35319 | ||||||||
\(856\) | 0.961187 | 0.0328527 | ||||||||
\(857\) | 3.07747 | 0.105124 | 0.0525622 | − | 0.998618i | \(-0.483261\pi\) | ||||
0.0525622 | + | 0.998618i | \(0.483261\pi\) | |||||||
\(858\) | −3.58285 | −0.122316 | ||||||||
\(859\) | −21.9826 | −0.750035 | −0.375018 | − | 0.927018i | \(-0.622363\pi\) | ||||
−0.375018 | + | 0.927018i | \(0.622363\pi\) | |||||||
\(860\) | −0.650082 | −0.0221676 | ||||||||
\(861\) | −152.092 | −5.18330 | ||||||||
\(862\) | 47.8872 | 1.63105 | ||||||||
\(863\) | 44.5908 | 1.51789 | 0.758944 | − | 0.651156i | \(-0.225716\pi\) | ||||
0.758944 | + | 0.651156i | \(0.225716\pi\) | |||||||
\(864\) | 53.6017 | 1.82357 | ||||||||
\(865\) | 42.6784 | 1.45111 | ||||||||
\(866\) | −74.7600 | −2.54045 | ||||||||
\(867\) | 20.6352 | 0.700807 | ||||||||
\(868\) | 19.6903 | 0.668334 | ||||||||
\(869\) | 1.02929 | 0.0349163 | ||||||||
\(870\) | 34.3876 | 1.16585 | ||||||||
\(871\) | −8.20070 | −0.277870 | ||||||||
\(872\) | 3.02162 | 0.102325 | ||||||||
\(873\) | −38.8902 | −1.31623 | ||||||||
\(874\) | 46.2323 | 1.56383 | ||||||||
\(875\) | 57.9139 | 1.95785 | ||||||||
\(876\) | −65.3480 | −2.20790 | ||||||||
\(877\) | 19.8995 | 0.671958 | 0.335979 | − | 0.941869i | \(-0.390933\pi\) | ||||
0.335979 | + | 0.941869i | \(0.390933\pi\) | |||||||
\(878\) | 42.6462 | 1.43924 | ||||||||
\(879\) | −29.0156 | −0.978673 | ||||||||
\(880\) | 11.9311 | 0.402196 | ||||||||
\(881\) | 38.9192 | 1.31122 | 0.655611 | − | 0.755099i | \(-0.272411\pi\) | ||||
0.655611 | + | 0.755099i | \(0.272411\pi\) | |||||||
\(882\) | 204.477 | 6.88509 | ||||||||
\(883\) | 21.5851 | 0.726397 | 0.363198 | − | 0.931712i | \(-0.381685\pi\) | ||||
0.363198 | + | 0.931712i | \(0.381685\pi\) | |||||||
\(884\) | −4.33789 | −0.145899 | ||||||||
\(885\) | 131.238 | 4.41152 | ||||||||
\(886\) | −32.2770 | −1.08437 | ||||||||
\(887\) | −7.59618 | −0.255055 | −0.127527 | − | 0.991835i | \(-0.540704\pi\) | ||||
−0.127527 | + | 0.991835i | \(0.540704\pi\) | |||||||
\(888\) | −1.11396 | −0.0373819 | ||||||||
\(889\) | −111.630 | −3.74396 | ||||||||
\(890\) | 58.3173 | 1.95480 | ||||||||
\(891\) | 3.15947 | 0.105846 | ||||||||
\(892\) | 3.53959 | 0.118514 | ||||||||
\(893\) | −7.77825 | −0.260289 | ||||||||
\(894\) | 11.6633 | 0.390081 | ||||||||
\(895\) | 40.0594 | 1.33904 | ||||||||
\(896\) | 25.5603 | 0.853909 | ||||||||
\(897\) | −10.7343 | −0.358406 | ||||||||
\(898\) | 0.374463 | 0.0124960 | ||||||||
\(899\) | −2.67412 | −0.0891868 | ||||||||
\(900\) | 99.6822 | 3.32274 | ||||||||
\(901\) | 2.04031 | 0.0679725 | ||||||||
\(902\) | −21.6604 | −0.721212 | ||||||||
\(903\) | 1.13181 | 0.0376641 | ||||||||
\(904\) | −11.4381 | −0.380426 | ||||||||
\(905\) | 65.2235 | 2.16810 | ||||||||
\(906\) | −42.4127 | −1.40907 | ||||||||
\(907\) | −19.1778 | −0.636788 | −0.318394 | − | 0.947958i | \(-0.603144\pi\) | ||||
−0.318394 | + | 0.947958i | \(0.603144\pi\) | |||||||
\(908\) | −3.46121 | −0.114864 | ||||||||
\(909\) | 104.895 | 3.47916 | ||||||||
\(910\) | 22.8292 | 0.756779 | ||||||||
\(911\) | −52.0752 | −1.72533 | −0.862665 | − | 0.505776i | \(-0.831206\pi\) | ||||
−0.862665 | + | 0.505776i | \(0.831206\pi\) | |||||||
\(912\) | 33.9387 | 1.12382 | ||||||||
\(913\) | −3.03240 | −0.100358 | ||||||||
\(914\) | 27.8662 | 0.921731 | ||||||||
\(915\) | −113.095 | −3.73879 | ||||||||
\(916\) | 9.58348 | 0.316647 | ||||||||
\(917\) | 5.05987 | 0.167092 | ||||||||
\(918\) | 43.0464 | 1.42074 | ||||||||
\(919\) | −25.4213 | −0.838570 | −0.419285 | − | 0.907855i | \(-0.637719\pi\) | ||||
−0.419285 | + | 0.907855i | \(0.637719\pi\) | |||||||
\(920\) | −14.4126 | −0.475171 | ||||||||
\(921\) | −76.4199 | −2.51812 | ||||||||
\(922\) | 2.09703 | 0.0690619 | ||||||||
\(923\) | 9.17414 | 0.301970 | ||||||||
\(924\) | 33.6346 | 1.10650 | ||||||||
\(925\) | 4.93605 | 0.162296 | ||||||||
\(926\) | 9.51999 | 0.312846 | ||||||||
\(927\) | 45.3599 | 1.48981 | ||||||||
\(928\) | −12.8545 | −0.421970 | ||||||||
\(929\) | −42.7304 | −1.40194 | −0.700969 | − | 0.713192i | \(-0.747249\pi\) | ||||
−0.700969 | + | 0.713192i | \(0.747249\pi\) | |||||||
\(930\) | −36.5614 | −1.19889 | ||||||||
\(931\) | 66.6353 | 2.18388 | ||||||||
\(932\) | 37.1493 | 1.21687 | ||||||||
\(933\) | 34.1722 | 1.11875 | ||||||||
\(934\) | −18.1645 | −0.594360 | ||||||||
\(935\) | 11.3752 | 0.372008 | ||||||||
\(936\) | 2.02825 | 0.0662955 | ||||||||
\(937\) | 20.6902 | 0.675921 | 0.337960 | − | 0.941160i | \(-0.390263\pi\) | ||||
0.337960 | + | 0.941160i | \(0.390263\pi\) | |||||||
\(938\) | 143.701 | 4.69200 | ||||||||
\(939\) | −6.37334 | −0.207986 | ||||||||
\(940\) | 18.1766 | 0.592856 | ||||||||
\(941\) | 21.3223 | 0.695089 | 0.347544 | − | 0.937664i | \(-0.387016\pi\) | ||||
0.347544 | + | 0.937664i | \(0.387016\pi\) | |||||||
\(942\) | −24.8074 | −0.808269 | ||||||||
\(943\) | −64.8948 | −2.11326 | ||||||||
\(944\) | −41.3231 | −1.34495 | ||||||||
\(945\) | −121.366 | −3.94804 | ||||||||
\(946\) | 0.161187 | 0.00524065 | ||||||||
\(947\) | −12.7588 | −0.414604 | −0.207302 | − | 0.978277i | \(-0.566468\pi\) | ||||
−0.207302 | + | 0.978277i | \(0.566468\pi\) | |||||||
\(948\) | −6.84203 | −0.222219 | ||||||||
\(949\) | 5.89180 | 0.191256 | ||||||||
\(950\) | 60.6357 | 1.96728 | ||||||||
\(951\) | 13.4699 | 0.436791 | ||||||||
\(952\) | 10.1404 | 0.328652 | ||||||||
\(953\) | 1.98491 | 0.0642974 | 0.0321487 | − | 0.999483i | \(-0.489765\pi\) | ||||
0.0321487 | + | 0.999483i | \(0.489765\pi\) | |||||||
\(954\) | −7.15108 | −0.231525 | ||||||||
\(955\) | −63.8965 | −2.06764 | ||||||||
\(956\) | 27.6564 | 0.894473 | ||||||||
\(957\) | −4.56787 | −0.147658 | ||||||||
\(958\) | 79.9067 | 2.58167 | ||||||||
\(959\) | −91.5878 | −2.95752 | ||||||||
\(960\) | −107.021 | −3.45410 | ||||||||
\(961\) | −28.1568 | −0.908285 | ||||||||
\(962\) | 0.752863 | 0.0242733 | ||||||||
\(963\) | 7.96603 | 0.256702 | ||||||||
\(964\) | 46.9289 | 1.51148 | ||||||||
\(965\) | −36.2574 | −1.16717 | ||||||||
\(966\) | 188.096 | 6.05190 | ||||||||
\(967\) | 43.8337 | 1.40960 | 0.704799 | − | 0.709407i | \(-0.251037\pi\) | ||||
0.704799 | + | 0.709407i | \(0.251037\pi\) | |||||||
\(968\) | 0.639017 | 0.0205388 | ||||||||
\(969\) | 32.3575 | 1.03947 | ||||||||
\(970\) | 55.2817 | 1.77499 | ||||||||
\(971\) | −28.8723 | −0.926555 | −0.463277 | − | 0.886213i | \(-0.653327\pi\) | ||||
−0.463277 | + | 0.886213i | \(0.653327\pi\) | |||||||
\(972\) | 24.7844 | 0.794959 | ||||||||
\(973\) | −34.5958 | −1.10909 | ||||||||
\(974\) | 39.0895 | 1.25251 | ||||||||
\(975\) | −14.0784 | −0.450871 | ||||||||
\(976\) | 35.6103 | 1.13986 | ||||||||
\(977\) | 61.5281 | 1.96846 | 0.984229 | − | 0.176897i | \(-0.0566061\pi\) | ||||
0.984229 | + | 0.176897i | \(0.0566061\pi\) | |||||||
\(978\) | 83.5702 | 2.67228 | ||||||||
\(979\) | −7.74657 | −0.247581 | ||||||||
\(980\) | −155.717 | −4.97419 | ||||||||
\(981\) | 25.0422 | 0.799537 | ||||||||
\(982\) | 28.8624 | 0.921035 | ||||||||
\(983\) | 4.64930 | 0.148290 | 0.0741448 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741448 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(984\) | 19.2080 | 0.612327 | ||||||||
\(985\) | 38.7694 | 1.23529 | ||||||||
\(986\) | −10.3232 | −0.328757 | ||||||||
\(987\) | −31.6459 | −1.00730 | ||||||||
\(988\) | 4.95466 | 0.157629 | ||||||||
\(989\) | 0.482919 | 0.0153559 | ||||||||
\(990\) | −39.8689 | −1.26712 | ||||||||
\(991\) | 43.7093 | 1.38847 | 0.694235 | − | 0.719748i | \(-0.255743\pi\) | ||||
0.694235 | + | 0.719748i | \(0.255743\pi\) | |||||||
\(992\) | 13.6671 | 0.433931 | ||||||||
\(993\) | 73.6374 | 2.33681 | ||||||||
\(994\) | −160.758 | −5.09895 | ||||||||
\(995\) | −33.5389 | −1.06325 | ||||||||
\(996\) | 20.1574 | 0.638711 | ||||||||
\(997\) | −32.7113 | −1.03598 | −0.517988 | − | 0.855388i | \(-0.673319\pi\) | ||||
−0.517988 | + | 0.855388i | \(0.673319\pi\) | |||||||
\(998\) | 25.6317 | 0.811359 | ||||||||
\(999\) | −4.00243 | −0.126631 |
(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 | 1441.2.a.e.1.22 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.e.1.22 | ✓ | 28 | 1.1 | even | 1 | trivial |