Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61585 | −1.84969 | −0.924844 | − | 0.380346i | \(-0.875805\pi\) | ||||
−0.924844 | + | 0.380346i | \(0.875805\pi\) | |||||||
\(3\) | 1.81779 | 1.04950 | 0.524750 | − | 0.851257i | \(-0.324159\pi\) | ||||
0.524750 | + | 0.851257i | \(0.324159\pi\) | |||||||
\(4\) | 4.84270 | 2.42135 | ||||||||
\(5\) | 3.74717 | 1.67579 | 0.837894 | − | 0.545834i | \(-0.183787\pi\) | ||||
0.837894 | + | 0.545834i | \(0.183787\pi\) | |||||||
\(6\) | −4.75507 | −1.94125 | ||||||||
\(7\) | 0.406260 | 0.153552 | 0.0767760 | − | 0.997048i | \(-0.475537\pi\) | ||||
0.0767760 | + | 0.997048i | \(0.475537\pi\) | |||||||
\(8\) | −7.43608 | −2.62905 | ||||||||
\(9\) | 0.304348 | 0.101449 | ||||||||
\(10\) | −9.80206 | −3.09968 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 8.80299 | 2.54120 | ||||||||
\(13\) | −3.01331 | −0.835742 | −0.417871 | − | 0.908506i | \(-0.637224\pi\) | ||||
−0.417871 | + | 0.908506i | \(0.637224\pi\) | |||||||
\(14\) | −1.06272 | −0.284023 | ||||||||
\(15\) | 6.81156 | 1.75874 | ||||||||
\(16\) | 9.76632 | 2.44158 | ||||||||
\(17\) | −6.49061 | −1.57420 | −0.787102 | − | 0.616823i | \(-0.788419\pi\) | ||||
−0.787102 | + | 0.616823i | \(0.788419\pi\) | |||||||
\(18\) | −0.796131 | −0.187650 | ||||||||
\(19\) | −1.64413 | −0.377190 | −0.188595 | − | 0.982055i | \(-0.560393\pi\) | ||||
−0.188595 | + | 0.982055i | \(0.560393\pi\) | |||||||
\(20\) | 18.1464 | 4.05766 | ||||||||
\(21\) | 0.738494 | 0.161153 | ||||||||
\(22\) | −2.61585 | −0.557702 | ||||||||
\(23\) | −1.93831 | −0.404165 | −0.202082 | − | 0.979369i | \(-0.564771\pi\) | ||||
−0.202082 | + | 0.979369i | \(0.564771\pi\) | |||||||
\(24\) | −13.5172 | −2.75919 | ||||||||
\(25\) | 9.04131 | 1.80826 | ||||||||
\(26\) | 7.88239 | 1.54586 | ||||||||
\(27\) | −4.90012 | −0.943028 | ||||||||
\(28\) | 1.96740 | 0.371803 | ||||||||
\(29\) | −7.98224 | −1.48227 | −0.741133 | − | 0.671359i | \(-0.765711\pi\) | ||||
−0.741133 | + | 0.671359i | \(0.765711\pi\) | |||||||
\(30\) | −17.8181 | −3.25312 | ||||||||
\(31\) | −2.09748 | −0.376719 | −0.188360 | − | 0.982100i | \(-0.560317\pi\) | ||||
−0.188360 | + | 0.982100i | \(0.560317\pi\) | |||||||
\(32\) | −10.6751 | −1.88711 | ||||||||
\(33\) | 1.81779 | 0.316436 | ||||||||
\(34\) | 16.9785 | 2.91179 | ||||||||
\(35\) | 1.52233 | 0.257320 | ||||||||
\(36\) | 1.47387 | 0.245644 | ||||||||
\(37\) | −4.51913 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(38\) | 4.30082 | 0.697684 | ||||||||
\(39\) | −5.47756 | −0.877111 | ||||||||
\(40\) | −27.8643 | −4.40573 | ||||||||
\(41\) | 8.72483 | 1.36259 | 0.681295 | − | 0.732009i | \(-0.261417\pi\) | ||||
0.681295 | + | 0.732009i | \(0.261417\pi\) | |||||||
\(42\) | −1.93179 | −0.298082 | ||||||||
\(43\) | −11.3450 | −1.73009 | −0.865046 | − | 0.501693i | \(-0.832711\pi\) | ||||
−0.865046 | + | 0.501693i | \(0.832711\pi\) | |||||||
\(44\) | 4.84270 | 0.730064 | ||||||||
\(45\) | 1.14045 | 0.170008 | ||||||||
\(46\) | 5.07033 | 0.747579 | ||||||||
\(47\) | −1.52918 | −0.223054 | −0.111527 | − | 0.993761i | \(-0.535574\pi\) | ||||
−0.111527 | + | 0.993761i | \(0.535574\pi\) | |||||||
\(48\) | 17.7531 | 2.56244 | ||||||||
\(49\) | −6.83495 | −0.976422 | ||||||||
\(50\) | −23.6508 | −3.34472 | ||||||||
\(51\) | −11.7985 | −1.65213 | ||||||||
\(52\) | −14.5926 | −2.02362 | ||||||||
\(53\) | −5.40672 | −0.742671 | −0.371335 | − | 0.928499i | \(-0.621100\pi\) | ||||
−0.371335 | + | 0.928499i | \(0.621100\pi\) | |||||||
\(54\) | 12.8180 | 1.74431 | ||||||||
\(55\) | 3.74717 | 0.505269 | ||||||||
\(56\) | −3.02098 | −0.403696 | ||||||||
\(57\) | −2.98868 | −0.395861 | ||||||||
\(58\) | 20.8804 | 2.74173 | ||||||||
\(59\) | 5.97599 | 0.778008 | 0.389004 | − | 0.921236i | \(-0.372819\pi\) | ||||
0.389004 | + | 0.921236i | \(0.372819\pi\) | |||||||
\(60\) | 32.9863 | 4.25852 | ||||||||
\(61\) | 13.7626 | 1.76212 | 0.881062 | − | 0.473001i | \(-0.156829\pi\) | ||||
0.881062 | + | 0.473001i | \(0.156829\pi\) | |||||||
\(62\) | 5.48671 | 0.696813 | ||||||||
\(63\) | 0.123645 | 0.0155778 | ||||||||
\(64\) | 8.39191 | 1.04899 | ||||||||
\(65\) | −11.2914 | −1.40053 | ||||||||
\(66\) | −4.75507 | −0.585308 | ||||||||
\(67\) | 7.92550 | 0.968254 | 0.484127 | − | 0.874998i | \(-0.339137\pi\) | ||||
0.484127 | + | 0.874998i | \(0.339137\pi\) | |||||||
\(68\) | −31.4320 | −3.81170 | ||||||||
\(69\) | −3.52343 | −0.424171 | ||||||||
\(70\) | −3.98219 | −0.475962 | ||||||||
\(71\) | 12.1603 | 1.44316 | 0.721581 | − | 0.692330i | \(-0.243416\pi\) | ||||
0.721581 | + | 0.692330i | \(0.243416\pi\) | |||||||
\(72\) | −2.26316 | −0.266716 | ||||||||
\(73\) | −6.94597 | −0.812964 | −0.406482 | − | 0.913659i | \(-0.633245\pi\) | ||||
−0.406482 | + | 0.913659i | \(0.633245\pi\) | |||||||
\(74\) | 11.8214 | 1.37421 | ||||||||
\(75\) | 16.4352 | 1.89777 | ||||||||
\(76\) | −7.96204 | −0.913309 | ||||||||
\(77\) | 0.406260 | 0.0462976 | ||||||||
\(78\) | 14.3285 | 1.62238 | ||||||||
\(79\) | 7.28573 | 0.819709 | 0.409854 | − | 0.912151i | \(-0.365580\pi\) | ||||
0.409854 | + | 0.912151i | \(0.365580\pi\) | |||||||
\(80\) | 36.5961 | 4.09157 | ||||||||
\(81\) | −9.82042 | −1.09116 | ||||||||
\(82\) | −22.8229 | −2.52037 | ||||||||
\(83\) | 8.02259 | 0.880594 | 0.440297 | − | 0.897852i | \(-0.354873\pi\) | ||||
0.440297 | + | 0.897852i | \(0.354873\pi\) | |||||||
\(84\) | 3.57630 | 0.390207 | ||||||||
\(85\) | −24.3214 | −2.63803 | ||||||||
\(86\) | 29.6768 | 3.20013 | ||||||||
\(87\) | −14.5100 | −1.55564 | ||||||||
\(88\) | −7.43608 | −0.792689 | ||||||||
\(89\) | 0.679834 | 0.0720622 | 0.0360311 | − | 0.999351i | \(-0.488528\pi\) | ||||
0.0360311 | + | 0.999351i | \(0.488528\pi\) | |||||||
\(90\) | −2.98324 | −0.314461 | ||||||||
\(91\) | −1.22419 | −0.128330 | ||||||||
\(92\) | −9.38663 | −0.978623 | ||||||||
\(93\) | −3.81278 | −0.395366 | ||||||||
\(94\) | 4.00012 | 0.412581 | ||||||||
\(95\) | −6.16086 | −0.632090 | ||||||||
\(96\) | −19.4051 | −1.98052 | ||||||||
\(97\) | −14.7354 | −1.49616 | −0.748079 | − | 0.663610i | \(-0.769024\pi\) | ||||
−0.748079 | + | 0.663610i | \(0.769024\pi\) | |||||||
\(98\) | 17.8792 | 1.80608 | ||||||||
\(99\) | 0.304348 | 0.0305881 | ||||||||
\(100\) | 43.7843 | 4.37843 | ||||||||
\(101\) | −10.0124 | −0.996272 | −0.498136 | − | 0.867099i | \(-0.665982\pi\) | ||||
−0.498136 | + | 0.867099i | \(0.665982\pi\) | |||||||
\(102\) | 30.8633 | 3.05592 | ||||||||
\(103\) | 6.17742 | 0.608679 | 0.304340 | − | 0.952564i | \(-0.401564\pi\) | ||||
0.304340 | + | 0.952564i | \(0.401564\pi\) | |||||||
\(104\) | 22.4072 | 2.19721 | ||||||||
\(105\) | 2.76727 | 0.270058 | ||||||||
\(106\) | 14.1432 | 1.37371 | ||||||||
\(107\) | −14.5630 | −1.40786 | −0.703931 | − | 0.710268i | \(-0.748574\pi\) | ||||
−0.703931 | + | 0.710268i | \(0.748574\pi\) | |||||||
\(108\) | −23.7298 | −2.28340 | ||||||||
\(109\) | 1.69123 | 0.161991 | 0.0809954 | − | 0.996714i | \(-0.474190\pi\) | ||||
0.0809954 | + | 0.996714i | \(0.474190\pi\) | |||||||
\(110\) | −9.80206 | −0.934590 | ||||||||
\(111\) | −8.21481 | −0.779715 | ||||||||
\(112\) | 3.96767 | 0.374909 | ||||||||
\(113\) | −10.6778 | −1.00448 | −0.502242 | − | 0.864727i | \(-0.667491\pi\) | ||||
−0.502242 | + | 0.864727i | \(0.667491\pi\) | |||||||
\(114\) | 7.81797 | 0.732220 | ||||||||
\(115\) | −7.26317 | −0.677294 | ||||||||
\(116\) | −38.6556 | −3.58908 | ||||||||
\(117\) | −0.917096 | −0.0847856 | ||||||||
\(118\) | −15.6323 | −1.43907 | ||||||||
\(119\) | −2.63688 | −0.241722 | ||||||||
\(120\) | −50.6513 | −4.62381 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −36.0010 | −3.25938 | ||||||||
\(123\) | 15.8599 | 1.43004 | ||||||||
\(124\) | −10.1575 | −0.912168 | ||||||||
\(125\) | 15.1435 | 1.35448 | ||||||||
\(126\) | −0.323436 | −0.0288140 | ||||||||
\(127\) | 8.81146 | 0.781891 | 0.390945 | − | 0.920414i | \(-0.372148\pi\) | ||||
0.390945 | + | 0.920414i | \(0.372148\pi\) | |||||||
\(128\) | −0.601782 | −0.0531905 | ||||||||
\(129\) | −20.6227 | −1.81573 | ||||||||
\(130\) | 29.5367 | 2.59054 | ||||||||
\(131\) | −7.45255 | −0.651132 | −0.325566 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325566 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(132\) | 8.80299 | 0.766202 | ||||||||
\(133\) | −0.667946 | −0.0579183 | ||||||||
\(134\) | −20.7320 | −1.79097 | ||||||||
\(135\) | −18.3616 | −1.58031 | ||||||||
\(136\) | 48.2647 | 4.13866 | ||||||||
\(137\) | 21.5751 | 1.84329 | 0.921644 | − | 0.388037i | \(-0.126847\pi\) | ||||
0.921644 | + | 0.388037i | \(0.126847\pi\) | |||||||
\(138\) | 9.21677 | 0.784584 | ||||||||
\(139\) | 13.6880 | 1.16100 | 0.580501 | − | 0.814260i | \(-0.302857\pi\) | ||||
0.580501 | + | 0.814260i | \(0.302857\pi\) | |||||||
\(140\) | 7.37217 | 0.623062 | ||||||||
\(141\) | −2.77973 | −0.234095 | ||||||||
\(142\) | −31.8096 | −2.66940 | ||||||||
\(143\) | −3.01331 | −0.251986 | ||||||||
\(144\) | 2.97236 | 0.247697 | ||||||||
\(145\) | −29.9108 | −2.48396 | ||||||||
\(146\) | 18.1696 | 1.50373 | ||||||||
\(147\) | −12.4245 | −1.02475 | ||||||||
\(148\) | −21.8848 | −1.79892 | ||||||||
\(149\) | 3.22940 | 0.264563 | 0.132281 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132281 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(150\) | −42.9920 | −3.51028 | ||||||||
\(151\) | 3.62504 | 0.295002 | 0.147501 | − | 0.989062i | \(-0.452877\pi\) | ||||
0.147501 | + | 0.989062i | \(0.452877\pi\) | |||||||
\(152\) | 12.2259 | 0.991653 | ||||||||
\(153\) | −1.97540 | −0.159702 | ||||||||
\(154\) | −1.06272 | −0.0856362 | ||||||||
\(155\) | −7.85963 | −0.631301 | ||||||||
\(156\) | −26.5262 | −2.12379 | ||||||||
\(157\) | −20.4077 | −1.62871 | −0.814355 | − | 0.580367i | \(-0.802909\pi\) | ||||
−0.814355 | + | 0.580367i | \(0.802909\pi\) | |||||||
\(158\) | −19.0584 | −1.51621 | ||||||||
\(159\) | −9.82827 | −0.779433 | ||||||||
\(160\) | −40.0015 | −3.16240 | ||||||||
\(161\) | −0.787456 | −0.0620603 | ||||||||
\(162\) | 25.6888 | 2.01830 | ||||||||
\(163\) | −18.9494 | −1.48423 | −0.742114 | − | 0.670273i | \(-0.766177\pi\) | ||||
−0.742114 | + | 0.670273i | \(0.766177\pi\) | |||||||
\(164\) | 42.2517 | 3.29931 | ||||||||
\(165\) | 6.81156 | 0.530279 | ||||||||
\(166\) | −20.9859 | −1.62883 | ||||||||
\(167\) | −12.6749 | −0.980816 | −0.490408 | − | 0.871493i | \(-0.663152\pi\) | ||||
−0.490408 | + | 0.871493i | \(0.663152\pi\) | |||||||
\(168\) | −5.49151 | −0.423679 | ||||||||
\(169\) | −3.91995 | −0.301535 | ||||||||
\(170\) | 63.6213 | 4.87953 | ||||||||
\(171\) | −0.500389 | −0.0382657 | ||||||||
\(172\) | −54.9403 | −4.18916 | ||||||||
\(173\) | 11.1155 | 0.845096 | 0.422548 | − | 0.906340i | \(-0.361136\pi\) | ||||
0.422548 | + | 0.906340i | \(0.361136\pi\) | |||||||
\(174\) | 37.9561 | 2.87744 | ||||||||
\(175\) | 3.67312 | 0.277662 | ||||||||
\(176\) | 9.76632 | 0.736164 | ||||||||
\(177\) | 10.8631 | 0.816519 | ||||||||
\(178\) | −1.77835 | −0.133293 | ||||||||
\(179\) | −15.8713 | −1.18628 | −0.593139 | − | 0.805100i | \(-0.702112\pi\) | ||||
−0.593139 | + | 0.805100i | \(0.702112\pi\) | |||||||
\(180\) | 5.52283 | 0.411648 | ||||||||
\(181\) | −23.4620 | −1.74392 | −0.871959 | − | 0.489579i | \(-0.837150\pi\) | ||||
−0.871959 | + | 0.489579i | \(0.837150\pi\) | |||||||
\(182\) | 3.20230 | 0.237370 | ||||||||
\(183\) | 25.0175 | 1.84935 | ||||||||
\(184\) | 14.4134 | 1.06257 | ||||||||
\(185\) | −16.9340 | −1.24501 | ||||||||
\(186\) | 9.97367 | 0.731305 | ||||||||
\(187\) | −6.49061 | −0.474640 | ||||||||
\(188\) | −7.40537 | −0.540092 | ||||||||
\(189\) | −1.99072 | −0.144804 | ||||||||
\(190\) | 16.1159 | 1.16917 | ||||||||
\(191\) | −14.7215 | −1.06521 | −0.532606 | − | 0.846363i | \(-0.678787\pi\) | ||||
−0.532606 | + | 0.846363i | \(0.678787\pi\) | |||||||
\(192\) | 15.2547 | 1.10091 | ||||||||
\(193\) | −14.9958 | −1.07942 | −0.539712 | − | 0.841850i | \(-0.681467\pi\) | ||||
−0.539712 | + | 0.841850i | \(0.681467\pi\) | |||||||
\(194\) | 38.5458 | 2.76743 | ||||||||
\(195\) | −20.5254 | −1.46985 | ||||||||
\(196\) | −33.0996 | −2.36426 | ||||||||
\(197\) | −13.9415 | −0.993293 | −0.496647 | − | 0.867953i | \(-0.665436\pi\) | ||||
−0.496647 | + | 0.867953i | \(0.665436\pi\) | |||||||
\(198\) | −0.796131 | −0.0565785 | ||||||||
\(199\) | −20.9879 | −1.48779 | −0.743895 | − | 0.668296i | \(-0.767024\pi\) | ||||
−0.743895 | + | 0.668296i | \(0.767024\pi\) | |||||||
\(200\) | −67.2319 | −4.75402 | ||||||||
\(201\) | 14.4069 | 1.01618 | ||||||||
\(202\) | 26.1910 | 1.84279 | ||||||||
\(203\) | −3.24287 | −0.227605 | ||||||||
\(204\) | −57.1367 | −4.00037 | ||||||||
\(205\) | 32.6935 | 2.28341 | ||||||||
\(206\) | −16.1592 | −1.12587 | ||||||||
\(207\) | −0.589920 | −0.0410023 | ||||||||
\(208\) | −29.4290 | −2.04053 | ||||||||
\(209\) | −1.64413 | −0.113727 | ||||||||
\(210\) | −7.23877 | −0.499522 | ||||||||
\(211\) | −10.0528 | −0.692063 | −0.346032 | − | 0.938223i | \(-0.612471\pi\) | ||||
−0.346032 | + | 0.938223i | \(0.612471\pi\) | |||||||
\(212\) | −26.1831 | −1.79826 | ||||||||
\(213\) | 22.1048 | 1.51460 | ||||||||
\(214\) | 38.0948 | 2.60411 | ||||||||
\(215\) | −42.5116 | −2.89927 | ||||||||
\(216\) | 36.4377 | 2.47927 | ||||||||
\(217\) | −0.852124 | −0.0578459 | ||||||||
\(218\) | −4.42402 | −0.299633 | ||||||||
\(219\) | −12.6263 | −0.853206 | ||||||||
\(220\) | 18.1464 | 1.22343 | ||||||||
\(221\) | 19.5582 | 1.31563 | ||||||||
\(222\) | 21.4887 | 1.44223 | ||||||||
\(223\) | 15.5038 | 1.03821 | 0.519105 | − | 0.854711i | \(-0.326266\pi\) | ||||
0.519105 | + | 0.854711i | \(0.326266\pi\) | |||||||
\(224\) | −4.33687 | −0.289770 | ||||||||
\(225\) | 2.75171 | 0.183447 | ||||||||
\(226\) | 27.9316 | 1.85798 | ||||||||
\(227\) | 19.0306 | 1.26310 | 0.631552 | − | 0.775333i | \(-0.282418\pi\) | ||||
0.631552 | + | 0.775333i | \(0.282418\pi\) | |||||||
\(228\) | −14.4733 | −0.958517 | ||||||||
\(229\) | −11.7134 | −0.774045 | −0.387023 | − | 0.922070i | \(-0.626496\pi\) | ||||
−0.387023 | + | 0.922070i | \(0.626496\pi\) | |||||||
\(230\) | 18.9994 | 1.25278 | ||||||||
\(231\) | 0.738494 | 0.0485894 | ||||||||
\(232\) | 59.3566 | 3.89695 | ||||||||
\(233\) | 29.3282 | 1.92135 | 0.960677 | − | 0.277669i | \(-0.0895617\pi\) | ||||
0.960677 | + | 0.277669i | \(0.0895617\pi\) | |||||||
\(234\) | 2.39899 | 0.156827 | ||||||||
\(235\) | −5.73012 | −0.373792 | ||||||||
\(236\) | 28.9399 | 1.88383 | ||||||||
\(237\) | 13.2439 | 0.860284 | ||||||||
\(238\) | 6.89768 | 0.447110 | ||||||||
\(239\) | −19.7215 | −1.27568 | −0.637840 | − | 0.770169i | \(-0.720172\pi\) | ||||
−0.637840 | + | 0.770169i | \(0.720172\pi\) | |||||||
\(240\) | 66.5239 | 4.29410 | ||||||||
\(241\) | 5.17290 | 0.333216 | 0.166608 | − | 0.986023i | \(-0.446719\pi\) | ||||
0.166608 | + | 0.986023i | \(0.446719\pi\) | |||||||
\(242\) | −2.61585 | −0.168154 | ||||||||
\(243\) | −3.15106 | −0.202141 | ||||||||
\(244\) | 66.6482 | 4.26672 | ||||||||
\(245\) | −25.6118 | −1.63627 | ||||||||
\(246\) | −41.4872 | −2.64513 | ||||||||
\(247\) | 4.95429 | 0.315234 | ||||||||
\(248\) | 15.5971 | 0.990414 | ||||||||
\(249\) | 14.5834 | 0.924183 | ||||||||
\(250\) | −39.6132 | −2.50536 | ||||||||
\(251\) | −26.9332 | −1.70001 | −0.850004 | − | 0.526777i | \(-0.823400\pi\) | ||||
−0.850004 | + | 0.526777i | \(0.823400\pi\) | |||||||
\(252\) | 0.598773 | 0.0377192 | ||||||||
\(253\) | −1.93831 | −0.121860 | ||||||||
\(254\) | −23.0495 | −1.44625 | ||||||||
\(255\) | −44.2112 | −2.76861 | ||||||||
\(256\) | −15.2096 | −0.950602 | ||||||||
\(257\) | 12.4718 | 0.777969 | 0.388984 | − | 0.921244i | \(-0.372826\pi\) | ||||
0.388984 | + | 0.921244i | \(0.372826\pi\) | |||||||
\(258\) | 53.9461 | 3.35854 | ||||||||
\(259\) | −1.83594 | −0.114080 | ||||||||
\(260\) | −54.6808 | −3.39116 | ||||||||
\(261\) | −2.42938 | −0.150375 | ||||||||
\(262\) | 19.4948 | 1.20439 | ||||||||
\(263\) | −22.5282 | −1.38915 | −0.694575 | − | 0.719420i | \(-0.744408\pi\) | ||||
−0.694575 | + | 0.719420i | \(0.744408\pi\) | |||||||
\(264\) | −13.5172 | −0.831927 | ||||||||
\(265\) | −20.2599 | −1.24456 | ||||||||
\(266\) | 1.74725 | 0.107131 | ||||||||
\(267\) | 1.23579 | 0.0756293 | ||||||||
\(268\) | 38.3808 | 2.34448 | ||||||||
\(269\) | 3.54782 | 0.216314 | 0.108157 | − | 0.994134i | \(-0.465505\pi\) | ||||
0.108157 | + | 0.994134i | \(0.465505\pi\) | |||||||
\(270\) | 48.0313 | 2.92309 | ||||||||
\(271\) | 20.4190 | 1.24037 | 0.620183 | − | 0.784457i | \(-0.287058\pi\) | ||||
0.620183 | + | 0.784457i | \(0.287058\pi\) | |||||||
\(272\) | −63.3894 | −3.84354 | ||||||||
\(273\) | −2.22531 | −0.134682 | ||||||||
\(274\) | −56.4374 | −3.40951 | ||||||||
\(275\) | 9.04131 | 0.545212 | ||||||||
\(276\) | −17.0629 | −1.02706 | ||||||||
\(277\) | 9.98239 | 0.599784 | 0.299892 | − | 0.953973i | \(-0.403049\pi\) | ||||
0.299892 | + | 0.953973i | \(0.403049\pi\) | |||||||
\(278\) | −35.8058 | −2.14749 | ||||||||
\(279\) | −0.638365 | −0.0382179 | ||||||||
\(280\) | −11.3202 | −0.676509 | ||||||||
\(281\) | −4.16711 | −0.248589 | −0.124294 | − | 0.992245i | \(-0.539667\pi\) | ||||
−0.124294 | + | 0.992245i | \(0.539667\pi\) | |||||||
\(282\) | 7.27137 | 0.433004 | ||||||||
\(283\) | −21.9093 | −1.30237 | −0.651187 | − | 0.758917i | \(-0.725729\pi\) | ||||
−0.651187 | + | 0.758917i | \(0.725729\pi\) | |||||||
\(284\) | 58.8887 | 3.49440 | ||||||||
\(285\) | −11.1991 | −0.663379 | ||||||||
\(286\) | 7.88239 | 0.466095 | ||||||||
\(287\) | 3.54455 | 0.209228 | ||||||||
\(288\) | −3.24895 | −0.191446 | ||||||||
\(289\) | 25.1280 | 1.47812 | ||||||||
\(290\) | 78.2424 | 4.59455 | ||||||||
\(291\) | −26.7859 | −1.57022 | ||||||||
\(292\) | −33.6372 | −1.96847 | ||||||||
\(293\) | 1.15469 | 0.0674579 | 0.0337289 | − | 0.999431i | \(-0.489262\pi\) | ||||
0.0337289 | + | 0.999431i | \(0.489262\pi\) | |||||||
\(294\) | 32.5007 | 1.89548 | ||||||||
\(295\) | 22.3931 | 1.30378 | ||||||||
\(296\) | 33.6046 | 1.95323 | ||||||||
\(297\) | −4.90012 | −0.284334 | ||||||||
\(298\) | −8.44764 | −0.489359 | ||||||||
\(299\) | 5.84072 | 0.337777 | ||||||||
\(300\) | 79.5906 | 4.59516 | ||||||||
\(301\) | −4.60901 | −0.265659 | ||||||||
\(302\) | −9.48258 | −0.545661 | ||||||||
\(303\) | −18.2004 | −1.04559 | ||||||||
\(304\) | −16.0571 | −0.920940 | ||||||||
\(305\) | 51.5710 | 2.95294 | ||||||||
\(306\) | 5.16737 | 0.295399 | ||||||||
\(307\) | −28.8157 | −1.64460 | −0.822299 | − | 0.569055i | \(-0.807309\pi\) | ||||
−0.822299 | + | 0.569055i | \(0.807309\pi\) | |||||||
\(308\) | 1.96740 | 0.112103 | ||||||||
\(309\) | 11.2292 | 0.638809 | ||||||||
\(310\) | 20.5597 | 1.16771 | ||||||||
\(311\) | 7.02554 | 0.398382 | 0.199191 | − | 0.979961i | \(-0.436169\pi\) | ||||
0.199191 | + | 0.979961i | \(0.436169\pi\) | |||||||
\(312\) | 40.7316 | 2.30597 | ||||||||
\(313\) | 6.40546 | 0.362058 | 0.181029 | − | 0.983478i | \(-0.442057\pi\) | ||||
0.181029 | + | 0.983478i | \(0.442057\pi\) | |||||||
\(314\) | 53.3835 | 3.01261 | ||||||||
\(315\) | 0.463318 | 0.0261050 | ||||||||
\(316\) | 35.2826 | 1.98480 | ||||||||
\(317\) | −11.0741 | −0.621983 | −0.310992 | − | 0.950413i | \(-0.600661\pi\) | ||||
−0.310992 | + | 0.950413i | \(0.600661\pi\) | |||||||
\(318\) | 25.7093 | 1.44171 | ||||||||
\(319\) | −7.98224 | −0.446920 | ||||||||
\(320\) | 31.4459 | 1.75788 | ||||||||
\(321\) | −26.4725 | −1.47755 | ||||||||
\(322\) | 2.05987 | 0.114792 | ||||||||
\(323\) | 10.6714 | 0.593774 | ||||||||
\(324\) | −47.5573 | −2.64207 | ||||||||
\(325\) | −27.2443 | −1.51124 | ||||||||
\(326\) | 49.5688 | 2.74536 | ||||||||
\(327\) | 3.07430 | 0.170009 | ||||||||
\(328\) | −64.8786 | −3.58232 | ||||||||
\(329\) | −0.621246 | −0.0342504 | ||||||||
\(330\) | −17.8181 | −0.980852 | ||||||||
\(331\) | 11.9337 | 0.655935 | 0.327968 | − | 0.944689i | \(-0.393636\pi\) | ||||
0.327968 | + | 0.944689i | \(0.393636\pi\) | |||||||
\(332\) | 38.8510 | 2.13223 | ||||||||
\(333\) | −1.37539 | −0.0753708 | ||||||||
\(334\) | 33.1558 | 1.81420 | ||||||||
\(335\) | 29.6982 | 1.62259 | ||||||||
\(336\) | 7.21237 | 0.393467 | ||||||||
\(337\) | −28.8855 | −1.57349 | −0.786746 | − | 0.617277i | \(-0.788236\pi\) | ||||
−0.786746 | + | 0.617277i | \(0.788236\pi\) | |||||||
\(338\) | 10.2540 | 0.557745 | ||||||||
\(339\) | −19.4100 | −1.05421 | ||||||||
\(340\) | −117.781 | −6.38759 | ||||||||
\(341\) | −2.09748 | −0.113585 | ||||||||
\(342\) | 1.30895 | 0.0707797 | ||||||||
\(343\) | −5.62059 | −0.303483 | ||||||||
\(344\) | 84.3622 | 4.54850 | ||||||||
\(345\) | −13.2029 | −0.710820 | ||||||||
\(346\) | −29.0766 | −1.56317 | ||||||||
\(347\) | 32.1910 | 1.72810 | 0.864051 | − | 0.503405i | \(-0.167920\pi\) | ||||
0.864051 | + | 0.503405i | \(0.167920\pi\) | |||||||
\(348\) | −70.2676 | −3.76674 | ||||||||
\(349\) | 14.0774 | 0.753547 | 0.376774 | − | 0.926305i | \(-0.377033\pi\) | ||||
0.376774 | + | 0.926305i | \(0.377033\pi\) | |||||||
\(350\) | −9.60836 | −0.513589 | ||||||||
\(351\) | 14.7656 | 0.788129 | ||||||||
\(352\) | −10.6751 | −0.568985 | ||||||||
\(353\) | 28.4325 | 1.51331 | 0.756656 | − | 0.653813i | \(-0.226832\pi\) | ||||
0.756656 | + | 0.653813i | \(0.226832\pi\) | |||||||
\(354\) | −28.4162 | −1.51031 | ||||||||
\(355\) | 45.5668 | 2.41843 | ||||||||
\(356\) | 3.29223 | 0.174488 | ||||||||
\(357\) | −4.79328 | −0.253687 | ||||||||
\(358\) | 41.5171 | 2.19425 | ||||||||
\(359\) | 27.0917 | 1.42984 | 0.714922 | − | 0.699204i | \(-0.246462\pi\) | ||||
0.714922 | + | 0.699204i | \(0.246462\pi\) | |||||||
\(360\) | −8.48045 | −0.446959 | ||||||||
\(361\) | −16.2968 | −0.857728 | ||||||||
\(362\) | 61.3732 | 3.22570 | ||||||||
\(363\) | 1.81779 | 0.0954091 | ||||||||
\(364\) | −5.92837 | −0.310731 | ||||||||
\(365\) | −26.0278 | −1.36235 | ||||||||
\(366\) | −65.4422 | −3.42072 | ||||||||
\(367\) | 23.6316 | 1.23356 | 0.616781 | − | 0.787135i | \(-0.288437\pi\) | ||||
0.616781 | + | 0.787135i | \(0.288437\pi\) | |||||||
\(368\) | −18.9301 | −0.986800 | ||||||||
\(369\) | 2.65539 | 0.138234 | ||||||||
\(370\) | 44.2968 | 2.30288 | ||||||||
\(371\) | −2.19654 | −0.114039 | ||||||||
\(372\) | −18.4641 | −0.957320 | ||||||||
\(373\) | −16.8513 | −0.872528 | −0.436264 | − | 0.899819i | \(-0.643699\pi\) | ||||
−0.436264 | + | 0.899819i | \(0.643699\pi\) | |||||||
\(374\) | 16.9785 | 0.877937 | ||||||||
\(375\) | 27.5276 | 1.42152 | ||||||||
\(376\) | 11.3711 | 0.586422 | ||||||||
\(377\) | 24.0530 | 1.23879 | ||||||||
\(378\) | 5.20744 | 0.267842 | ||||||||
\(379\) | 24.9236 | 1.28024 | 0.640120 | − | 0.768275i | \(-0.278885\pi\) | ||||
0.640120 | + | 0.768275i | \(0.278885\pi\) | |||||||
\(380\) | −29.8352 | −1.53051 | ||||||||
\(381\) | 16.0174 | 0.820594 | ||||||||
\(382\) | 38.5094 | 1.97031 | ||||||||
\(383\) | 32.0931 | 1.63988 | 0.819940 | − | 0.572450i | \(-0.194007\pi\) | ||||
0.819940 | + | 0.572450i | \(0.194007\pi\) | |||||||
\(384\) | −1.09391 | −0.0558234 | ||||||||
\(385\) | 1.52233 | 0.0775850 | ||||||||
\(386\) | 39.2269 | 1.99660 | ||||||||
\(387\) | −3.45282 | −0.175517 | ||||||||
\(388\) | −71.3593 | −3.62272 | ||||||||
\(389\) | −1.60480 | −0.0813666 | −0.0406833 | − | 0.999172i | \(-0.512953\pi\) | ||||
−0.0406833 | + | 0.999172i | \(0.512953\pi\) | |||||||
\(390\) | 53.6914 | 2.71877 | ||||||||
\(391\) | 12.5808 | 0.636237 | ||||||||
\(392\) | 50.8253 | 2.56706 | ||||||||
\(393\) | −13.5471 | −0.683363 | ||||||||
\(394\) | 36.4690 | 1.83728 | ||||||||
\(395\) | 27.3009 | 1.37366 | ||||||||
\(396\) | 1.47387 | 0.0740646 | ||||||||
\(397\) | 12.0859 | 0.606575 | 0.303288 | − | 0.952899i | \(-0.401916\pi\) | ||||
0.303288 | + | 0.952899i | \(0.401916\pi\) | |||||||
\(398\) | 54.9012 | 2.75195 | ||||||||
\(399\) | −1.21418 | −0.0607852 | ||||||||
\(400\) | 88.3003 | 4.41502 | ||||||||
\(401\) | 14.8137 | 0.739761 | 0.369880 | − | 0.929079i | \(-0.379399\pi\) | ||||
0.369880 | + | 0.929079i | \(0.379399\pi\) | |||||||
\(402\) | −37.6863 | −1.87962 | ||||||||
\(403\) | 6.32037 | 0.314840 | ||||||||
\(404\) | −48.4871 | −2.41232 | ||||||||
\(405\) | −36.7988 | −1.82855 | ||||||||
\(406\) | 8.48287 | 0.420998 | ||||||||
\(407\) | −4.51913 | −0.224005 | ||||||||
\(408\) | 87.7349 | 4.34353 | ||||||||
\(409\) | −25.8299 | −1.27721 | −0.638603 | − | 0.769537i | \(-0.720487\pi\) | ||||
−0.638603 | + | 0.769537i | \(0.720487\pi\) | |||||||
\(410\) | −85.5214 | −4.22360 | ||||||||
\(411\) | 39.2190 | 1.93453 | ||||||||
\(412\) | 29.9154 | 1.47382 | ||||||||
\(413\) | 2.42781 | 0.119465 | ||||||||
\(414\) | 1.54314 | 0.0758414 | ||||||||
\(415\) | 30.0621 | 1.47569 | ||||||||
\(416\) | 32.1674 | 1.57714 | ||||||||
\(417\) | 24.8819 | 1.21847 | ||||||||
\(418\) | 4.30082 | 0.210360 | ||||||||
\(419\) | 15.4141 | 0.753027 | 0.376514 | − | 0.926411i | \(-0.377123\pi\) | ||||
0.376514 | + | 0.926411i | \(0.377123\pi\) | |||||||
\(420\) | 13.4010 | 0.653904 | ||||||||
\(421\) | 29.8792 | 1.45622 | 0.728112 | − | 0.685458i | \(-0.240398\pi\) | ||||
0.728112 | + | 0.685458i | \(0.240398\pi\) | |||||||
\(422\) | 26.2967 | 1.28010 | ||||||||
\(423\) | −0.465404 | −0.0226287 | ||||||||
\(424\) | 40.2049 | 1.95252 | ||||||||
\(425\) | −58.6836 | −2.84657 | ||||||||
\(426\) | −57.8230 | −2.80154 | ||||||||
\(427\) | 5.59121 | 0.270578 | ||||||||
\(428\) | −70.5244 | −3.40893 | ||||||||
\(429\) | −5.47756 | −0.264459 | ||||||||
\(430\) | 111.204 | 5.36274 | ||||||||
\(431\) | −4.02678 | −0.193963 | −0.0969816 | − | 0.995286i | \(-0.530919\pi\) | ||||
−0.0969816 | + | 0.995286i | \(0.530919\pi\) | |||||||
\(432\) | −47.8561 | −2.30248 | ||||||||
\(433\) | −10.3919 | −0.499403 | −0.249701 | − | 0.968323i | \(-0.580332\pi\) | ||||
−0.249701 | + | 0.968323i | \(0.580332\pi\) | |||||||
\(434\) | 2.22903 | 0.106997 | ||||||||
\(435\) | −54.3715 | −2.60692 | ||||||||
\(436\) | 8.19013 | 0.392236 | ||||||||
\(437\) | 3.18683 | 0.152447 | ||||||||
\(438\) | 33.0285 | 1.57816 | ||||||||
\(439\) | −27.2829 | −1.30214 | −0.651071 | − | 0.759017i | \(-0.725680\pi\) | ||||
−0.651071 | + | 0.759017i | \(0.725680\pi\) | |||||||
\(440\) | −27.8643 | −1.32838 | ||||||||
\(441\) | −2.08021 | −0.0990574 | ||||||||
\(442\) | −51.1615 | −2.43350 | ||||||||
\(443\) | −23.9806 | −1.13935 | −0.569676 | − | 0.821870i | \(-0.692931\pi\) | ||||
−0.569676 | + | 0.821870i | \(0.692931\pi\) | |||||||
\(444\) | −39.7818 | −1.88796 | ||||||||
\(445\) | 2.54746 | 0.120761 | ||||||||
\(446\) | −40.5556 | −1.92036 | ||||||||
\(447\) | 5.87036 | 0.277659 | ||||||||
\(448\) | 3.40930 | 0.161074 | ||||||||
\(449\) | −4.78234 | −0.225692 | −0.112846 | − | 0.993612i | \(-0.535997\pi\) | ||||
−0.112846 | + | 0.993612i | \(0.535997\pi\) | |||||||
\(450\) | −7.19807 | −0.339320 | ||||||||
\(451\) | 8.72483 | 0.410836 | ||||||||
\(452\) | −51.7094 | −2.43221 | ||||||||
\(453\) | 6.58955 | 0.309604 | ||||||||
\(454\) | −49.7813 | −2.33635 | ||||||||
\(455\) | −4.58725 | −0.215053 | ||||||||
\(456\) | 22.2241 | 1.04074 | ||||||||
\(457\) | −4.10829 | −0.192178 | −0.0960889 | − | 0.995373i | \(-0.530633\pi\) | ||||
−0.0960889 | + | 0.995373i | \(0.530633\pi\) | |||||||
\(458\) | 30.6406 | 1.43174 | ||||||||
\(459\) | 31.8048 | 1.48452 | ||||||||
\(460\) | −35.1733 | −1.63996 | ||||||||
\(461\) | 13.1908 | 0.614357 | 0.307179 | − | 0.951652i | \(-0.400615\pi\) | ||||
0.307179 | + | 0.951652i | \(0.400615\pi\) | |||||||
\(462\) | −1.93179 | −0.0898752 | ||||||||
\(463\) | −36.4953 | −1.69608 | −0.848039 | − | 0.529933i | \(-0.822217\pi\) | ||||
−0.848039 | + | 0.529933i | \(0.822217\pi\) | |||||||
\(464\) | −77.9571 | −3.61907 | ||||||||
\(465\) | −14.2871 | −0.662550 | ||||||||
\(466\) | −76.7183 | −3.55391 | ||||||||
\(467\) | 3.68289 | 0.170424 | 0.0852118 | − | 0.996363i | \(-0.472843\pi\) | ||||
0.0852118 | + | 0.996363i | \(0.472843\pi\) | |||||||
\(468\) | −4.44122 | −0.205295 | ||||||||
\(469\) | 3.21982 | 0.148677 | ||||||||
\(470\) | 14.9892 | 0.691398 | ||||||||
\(471\) | −37.0968 | −1.70933 | ||||||||
\(472\) | −44.4380 | −2.04542 | ||||||||
\(473\) | −11.3450 | −0.521642 | ||||||||
\(474\) | −34.6441 | −1.59126 | ||||||||
\(475\) | −14.8651 | −0.682059 | ||||||||
\(476\) | −12.7696 | −0.585293 | ||||||||
\(477\) | −1.64553 | −0.0753435 | ||||||||
\(478\) | 51.5886 | 2.35961 | ||||||||
\(479\) | −8.83130 | −0.403512 | −0.201756 | − | 0.979436i | \(-0.564665\pi\) | ||||
−0.201756 | + | 0.979436i | \(0.564665\pi\) | |||||||
\(480\) | −72.7142 | −3.31893 | ||||||||
\(481\) | 13.6175 | 0.620906 | ||||||||
\(482\) | −13.5315 | −0.616345 | ||||||||
\(483\) | −1.43143 | −0.0651322 | ||||||||
\(484\) | 4.84270 | 0.220123 | ||||||||
\(485\) | −55.2163 | −2.50724 | ||||||||
\(486\) | 8.24272 | 0.373898 | ||||||||
\(487\) | −36.8666 | −1.67059 | −0.835293 | − | 0.549805i | \(-0.814702\pi\) | ||||
−0.835293 | + | 0.549805i | \(0.814702\pi\) | |||||||
\(488\) | −102.340 | −4.63272 | ||||||||
\(489\) | −34.4459 | −1.55770 | ||||||||
\(490\) | 66.9966 | 3.02660 | ||||||||
\(491\) | 23.7402 | 1.07138 | 0.535690 | − | 0.844415i | \(-0.320052\pi\) | ||||
0.535690 | + | 0.844415i | \(0.320052\pi\) | |||||||
\(492\) | 76.8046 | 3.46262 | ||||||||
\(493\) | 51.8096 | 2.33339 | ||||||||
\(494\) | −12.9597 | −0.583084 | ||||||||
\(495\) | 1.14045 | 0.0512592 | ||||||||
\(496\) | −20.4847 | −0.919790 | ||||||||
\(497\) | 4.94025 | 0.221600 | ||||||||
\(498\) | −38.1480 | −1.70945 | ||||||||
\(499\) | 31.8301 | 1.42491 | 0.712455 | − | 0.701718i | \(-0.247583\pi\) | ||||
0.712455 | + | 0.701718i | \(0.247583\pi\) | |||||||
\(500\) | 73.3353 | 3.27966 | ||||||||
\(501\) | −23.0403 | −1.02937 | ||||||||
\(502\) | 70.4533 | 3.14448 | ||||||||
\(503\) | −1.69168 | −0.0754281 | −0.0377141 | − | 0.999289i | \(-0.512008\pi\) | ||||
−0.0377141 | + | 0.999289i | \(0.512008\pi\) | |||||||
\(504\) | −0.919431 | −0.0409547 | ||||||||
\(505\) | −37.5182 | −1.66954 | ||||||||
\(506\) | 5.07033 | 0.225403 | ||||||||
\(507\) | −7.12564 | −0.316461 | ||||||||
\(508\) | 42.6712 | 1.89323 | ||||||||
\(509\) | 38.9738 | 1.72748 | 0.863742 | − | 0.503934i | \(-0.168115\pi\) | ||||
0.863742 | + | 0.503934i | \(0.168115\pi\) | |||||||
\(510\) | 115.650 | 5.12107 | ||||||||
\(511\) | −2.82187 | −0.124832 | ||||||||
\(512\) | 40.9898 | 1.81151 | ||||||||
\(513\) | 8.05645 | 0.355701 | ||||||||
\(514\) | −32.6244 | −1.43900 | ||||||||
\(515\) | 23.1479 | 1.02002 | ||||||||
\(516\) | −99.8697 | −4.39652 | ||||||||
\(517\) | −1.52918 | −0.0672534 | ||||||||
\(518\) | 4.80256 | 0.211012 | ||||||||
\(519\) | 20.2056 | 0.886928 | ||||||||
\(520\) | 83.9638 | 3.68206 | ||||||||
\(521\) | −31.2559 | −1.36935 | −0.684674 | − | 0.728850i | \(-0.740055\pi\) | ||||
−0.684674 | + | 0.728850i | \(0.740055\pi\) | |||||||
\(522\) | 6.35491 | 0.278147 | ||||||||
\(523\) | −6.31710 | −0.276228 | −0.138114 | − | 0.990416i | \(-0.544104\pi\) | ||||
−0.138114 | + | 0.990416i | \(0.544104\pi\) | |||||||
\(524\) | −36.0904 | −1.57662 | ||||||||
\(525\) | 6.67696 | 0.291406 | ||||||||
\(526\) | 58.9306 | 2.56950 | ||||||||
\(527\) | 13.6139 | 0.593032 | ||||||||
\(528\) | 17.7531 | 0.772604 | ||||||||
\(529\) | −19.2430 | −0.836651 | ||||||||
\(530\) | 52.9970 | 2.30204 | ||||||||
\(531\) | 1.81878 | 0.0789284 | ||||||||
\(532\) | −3.23466 | −0.140240 | ||||||||
\(533\) | −26.2906 | −1.13877 | ||||||||
\(534\) | −3.23265 | −0.139891 | ||||||||
\(535\) | −54.5703 | −2.35928 | ||||||||
\(536\) | −58.9347 | −2.54559 | ||||||||
\(537\) | −28.8507 | −1.24500 | ||||||||
\(538\) | −9.28057 | −0.400114 | ||||||||
\(539\) | −6.83495 | −0.294402 | ||||||||
\(540\) | −88.9197 | −3.82649 | ||||||||
\(541\) | −21.8392 | −0.938942 | −0.469471 | − | 0.882948i | \(-0.655555\pi\) | ||||
−0.469471 | + | 0.882948i | \(0.655555\pi\) | |||||||
\(542\) | −53.4131 | −2.29429 | ||||||||
\(543\) | −42.6489 | −1.83024 | ||||||||
\(544\) | 69.2880 | 2.97070 | ||||||||
\(545\) | 6.33735 | 0.271462 | ||||||||
\(546\) | 5.82110 | 0.249120 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 104.482 | 4.46324 | ||||||||
\(549\) | 4.18863 | 0.178766 | ||||||||
\(550\) | −23.6508 | −1.00847 | ||||||||
\(551\) | 13.1239 | 0.559096 | ||||||||
\(552\) | 26.2005 | 1.11517 | ||||||||
\(553\) | 2.95990 | 0.125868 | ||||||||
\(554\) | −26.1125 | −1.10941 | ||||||||
\(555\) | −30.7823 | −1.30664 | ||||||||
\(556\) | 66.2869 | 2.81119 | ||||||||
\(557\) | 34.1731 | 1.44796 | 0.723980 | − | 0.689821i | \(-0.242311\pi\) | ||||
0.723980 | + | 0.689821i | \(0.242311\pi\) | |||||||
\(558\) | 1.66987 | 0.0706913 | ||||||||
\(559\) | 34.1859 | 1.44591 | ||||||||
\(560\) | 14.8675 | 0.628268 | ||||||||
\(561\) | −11.7985 | −0.498135 | ||||||||
\(562\) | 10.9006 | 0.459812 | ||||||||
\(563\) | −1.24870 | −0.0526264 | −0.0263132 | − | 0.999654i | \(-0.508377\pi\) | ||||
−0.0263132 | + | 0.999654i | \(0.508377\pi\) | |||||||
\(564\) | −13.4614 | −0.566827 | ||||||||
\(565\) | −40.0116 | −1.68330 | ||||||||
\(566\) | 57.3116 | 2.40899 | ||||||||
\(567\) | −3.98964 | −0.167549 | ||||||||
\(568\) | −90.4250 | −3.79415 | ||||||||
\(569\) | −8.39342 | −0.351870 | −0.175935 | − | 0.984402i | \(-0.556295\pi\) | ||||
−0.175935 | + | 0.984402i | \(0.556295\pi\) | |||||||
\(570\) | 29.2953 | 1.22704 | ||||||||
\(571\) | −13.9183 | −0.582465 | −0.291232 | − | 0.956652i | \(-0.594065\pi\) | ||||
−0.291232 | + | 0.956652i | \(0.594065\pi\) | |||||||
\(572\) | −14.5926 | −0.610145 | ||||||||
\(573\) | −26.7606 | −1.11794 | ||||||||
\(574\) | −9.27204 | −0.387007 | ||||||||
\(575\) | −17.5248 | −0.730836 | ||||||||
\(576\) | 2.55406 | 0.106419 | ||||||||
\(577\) | 11.6473 | 0.484883 | 0.242441 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242441 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(578\) | −65.7311 | −2.73405 | ||||||||
\(579\) | −27.2592 | −1.13285 | ||||||||
\(580\) | −144.849 | −6.01453 | ||||||||
\(581\) | 3.25926 | 0.135217 | ||||||||
\(582\) | 70.0680 | 2.90441 | ||||||||
\(583\) | −5.40672 | −0.223924 | ||||||||
\(584\) | 51.6508 | 2.13733 | ||||||||
\(585\) | −3.43652 | −0.142083 | ||||||||
\(586\) | −3.02051 | −0.124776 | ||||||||
\(587\) | 24.8707 | 1.02653 | 0.513263 | − | 0.858232i | \(-0.328437\pi\) | ||||
0.513263 | + | 0.858232i | \(0.328437\pi\) | |||||||
\(588\) | −60.1680 | −2.48129 | ||||||||
\(589\) | 3.44854 | 0.142095 | ||||||||
\(590\) | −58.5770 | −2.41158 | ||||||||
\(591\) | −25.3427 | −1.04246 | ||||||||
\(592\) | −44.1352 | −1.81395 | ||||||||
\(593\) | 42.3587 | 1.73946 | 0.869732 | − | 0.493524i | \(-0.164292\pi\) | ||||
0.869732 | + | 0.493524i | \(0.164292\pi\) | |||||||
\(594\) | 12.8180 | 0.525929 | ||||||||
\(595\) | −9.88083 | −0.405075 | ||||||||
\(596\) | 15.6390 | 0.640599 | ||||||||
\(597\) | −38.1515 | −1.56144 | ||||||||
\(598\) | −15.2785 | −0.624783 | ||||||||
\(599\) | −21.5127 | −0.878987 | −0.439494 | − | 0.898246i | \(-0.644842\pi\) | ||||
−0.439494 | + | 0.898246i | \(0.644842\pi\) | |||||||
\(600\) | −122.213 | −4.98934 | ||||||||
\(601\) | 22.6113 | 0.922335 | 0.461168 | − | 0.887313i | \(-0.347431\pi\) | ||||
0.461168 | + | 0.887313i | \(0.347431\pi\) | |||||||
\(602\) | 12.0565 | 0.491386 | ||||||||
\(603\) | 2.41211 | 0.0982288 | ||||||||
\(604\) | 17.5550 | 0.714302 | ||||||||
\(605\) | 3.74717 | 0.152344 | ||||||||
\(606\) | 47.6097 | 1.93401 | ||||||||
\(607\) | −10.9909 | −0.446107 | −0.223054 | − | 0.974806i | \(-0.571603\pi\) | ||||
−0.223054 | + | 0.974806i | \(0.571603\pi\) | |||||||
\(608\) | 17.5513 | 0.711800 | ||||||||
\(609\) | −5.89484 | −0.238871 | ||||||||
\(610\) | −134.902 | −5.46203 | ||||||||
\(611\) | 4.60791 | 0.186416 | ||||||||
\(612\) | −9.56629 | −0.386694 | ||||||||
\(613\) | −8.53005 | −0.344526 | −0.172263 | − | 0.985051i | \(-0.555108\pi\) | ||||
−0.172263 | + | 0.985051i | \(0.555108\pi\) | |||||||
\(614\) | 75.3777 | 3.04200 | ||||||||
\(615\) | 59.4298 | 2.39644 | ||||||||
\(616\) | −3.02098 | −0.121719 | ||||||||
\(617\) | −22.1586 | −0.892074 | −0.446037 | − | 0.895015i | \(-0.647165\pi\) | ||||
−0.446037 | + | 0.895015i | \(0.647165\pi\) | |||||||
\(618\) | −29.3740 | −1.18160 | ||||||||
\(619\) | −25.0431 | −1.00657 | −0.503283 | − | 0.864122i | \(-0.667875\pi\) | ||||
−0.503283 | + | 0.864122i | \(0.667875\pi\) | |||||||
\(620\) | −38.0618 | −1.52860 | ||||||||
\(621\) | 9.49793 | 0.381139 | ||||||||
\(622\) | −18.3778 | −0.736883 | ||||||||
\(623\) | 0.276189 | 0.0110653 | ||||||||
\(624\) | −53.4956 | −2.14154 | ||||||||
\(625\) | 11.5387 | 0.461550 | ||||||||
\(626\) | −16.7557 | −0.669694 | ||||||||
\(627\) | −2.98868 | −0.119357 | ||||||||
\(628\) | −98.8282 | −3.94367 | ||||||||
\(629\) | 29.3319 | 1.16954 | ||||||||
\(630\) | −1.21197 | −0.0482861 | ||||||||
\(631\) | 8.28732 | 0.329913 | 0.164956 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164956 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(632\) | −54.1773 | −2.15506 | ||||||||
\(633\) | −18.2738 | −0.726320 | ||||||||
\(634\) | 28.9682 | 1.15048 | ||||||||
\(635\) | 33.0181 | 1.31028 | ||||||||
\(636\) | −47.5953 | −1.88728 | ||||||||
\(637\) | 20.5958 | 0.816037 | ||||||||
\(638\) | 20.8804 | 0.826662 | ||||||||
\(639\) | 3.70097 | 0.146408 | ||||||||
\(640\) | −2.25498 | −0.0891359 | ||||||||
\(641\) | 19.8980 | 0.785925 | 0.392963 | − | 0.919554i | \(-0.371450\pi\) | ||||
0.392963 | + | 0.919554i | \(0.371450\pi\) | |||||||
\(642\) | 69.2482 | 2.73301 | ||||||||
\(643\) | 18.0543 | 0.711994 | 0.355997 | − | 0.934487i | \(-0.384141\pi\) | ||||
0.355997 | + | 0.934487i | \(0.384141\pi\) | |||||||
\(644\) | −3.81341 | −0.150270 | ||||||||
\(645\) | −77.2770 | −3.04278 | ||||||||
\(646\) | −27.9149 | −1.09830 | ||||||||
\(647\) | −16.6657 | −0.655196 | −0.327598 | − | 0.944817i | \(-0.606239\pi\) | ||||
−0.327598 | + | 0.944817i | \(0.606239\pi\) | |||||||
\(648\) | 73.0254 | 2.86871 | ||||||||
\(649\) | 5.97599 | 0.234578 | ||||||||
\(650\) | 71.2671 | 2.79533 | ||||||||
\(651\) | −1.54898 | −0.0607093 | ||||||||
\(652\) | −91.7660 | −3.59384 | ||||||||
\(653\) | 6.26686 | 0.245241 | 0.122621 | − | 0.992454i | \(-0.460870\pi\) | ||||
0.122621 | + | 0.992454i | \(0.460870\pi\) | |||||||
\(654\) | −8.04193 | −0.314464 | ||||||||
\(655\) | −27.9260 | −1.09116 | ||||||||
\(656\) | 85.2095 | 3.32687 | ||||||||
\(657\) | −2.11399 | −0.0824747 | ||||||||
\(658\) | 1.62509 | 0.0633526 | ||||||||
\(659\) | 19.3921 | 0.755409 | 0.377704 | − | 0.925926i | \(-0.376714\pi\) | ||||
0.377704 | + | 0.925926i | \(0.376714\pi\) | |||||||
\(660\) | 32.9863 | 1.28399 | ||||||||
\(661\) | 25.2995 | 0.984035 | 0.492018 | − | 0.870585i | \(-0.336260\pi\) | ||||
0.492018 | + | 0.870585i | \(0.336260\pi\) | |||||||
\(662\) | −31.2168 | −1.21328 | ||||||||
\(663\) | 35.5527 | 1.38075 | ||||||||
\(664\) | −59.6567 | −2.31513 | ||||||||
\(665\) | −2.50291 | −0.0970587 | ||||||||
\(666\) | 3.59782 | 0.139413 | ||||||||
\(667\) | 15.4720 | 0.599079 | ||||||||
\(668\) | −61.3809 | −2.37490 | ||||||||
\(669\) | 28.1825 | 1.08960 | ||||||||
\(670\) | −77.6863 | −3.00128 | ||||||||
\(671\) | 13.7626 | 0.531300 | ||||||||
\(672\) | −7.88351 | −0.304113 | ||||||||
\(673\) | −20.5174 | −0.790888 | −0.395444 | − | 0.918490i | \(-0.629409\pi\) | ||||
−0.395444 | + | 0.918490i | \(0.629409\pi\) | |||||||
\(674\) | 75.5602 | 2.91047 | ||||||||
\(675\) | −44.3035 | −1.70524 | ||||||||
\(676\) | −18.9831 | −0.730121 | ||||||||
\(677\) | −2.52438 | −0.0970197 | −0.0485099 | − | 0.998823i | \(-0.515447\pi\) | ||||
−0.0485099 | + | 0.998823i | \(0.515447\pi\) | |||||||
\(678\) | 50.7737 | 1.94995 | ||||||||
\(679\) | −5.98643 | −0.229738 | ||||||||
\(680\) | 180.856 | 6.93552 | ||||||||
\(681\) | 34.5936 | 1.32563 | ||||||||
\(682\) | 5.48671 | 0.210097 | ||||||||
\(683\) | −15.0787 | −0.576969 | −0.288484 | − | 0.957485i | \(-0.593151\pi\) | ||||
−0.288484 | + | 0.957485i | \(0.593151\pi\) | |||||||
\(684\) | −2.42323 | −0.0926546 | ||||||||
\(685\) | 80.8458 | 3.08896 | ||||||||
\(686\) | 14.7026 | 0.561350 | ||||||||
\(687\) | −21.2925 | −0.812360 | ||||||||
\(688\) | −110.799 | −4.22416 | ||||||||
\(689\) | 16.2921 | 0.620681 | ||||||||
\(690\) | 34.5368 | 1.31480 | ||||||||
\(691\) | 9.48717 | 0.360909 | 0.180455 | − | 0.983583i | \(-0.442243\pi\) | ||||
0.180455 | + | 0.983583i | \(0.442243\pi\) | |||||||
\(692\) | 53.8290 | 2.04627 | ||||||||
\(693\) | 0.123645 | 0.00469687 | ||||||||
\(694\) | −84.2069 | −3.19645 | ||||||||
\(695\) | 51.2913 | 1.94559 | ||||||||
\(696\) | 107.898 | 4.08985 | ||||||||
\(697\) | −56.6295 | −2.14499 | ||||||||
\(698\) | −36.8245 | −1.39383 | ||||||||
\(699\) | 53.3124 | 2.01646 | ||||||||
\(700\) | 17.7878 | 0.672317 | ||||||||
\(701\) | 14.7547 | 0.557279 | 0.278639 | − | 0.960396i | \(-0.410117\pi\) | ||||
0.278639 | + | 0.960396i | \(0.410117\pi\) | |||||||
\(702\) | −38.6246 | −1.45779 | ||||||||
\(703\) | 7.43005 | 0.280230 | ||||||||
\(704\) | 8.39191 | 0.316282 | ||||||||
\(705\) | −10.4161 | −0.392294 | ||||||||
\(706\) | −74.3754 | −2.79916 | ||||||||
\(707\) | −4.06764 | −0.152980 | ||||||||
\(708\) | 52.6066 | 1.97708 | ||||||||
\(709\) | −19.5306 | −0.733486 | −0.366743 | − | 0.930322i | \(-0.619527\pi\) | ||||
−0.366743 | + | 0.930322i | \(0.619527\pi\) | |||||||
\(710\) | −119.196 | −4.47335 | ||||||||
\(711\) | 2.21740 | 0.0831590 | ||||||||
\(712\) | −5.05530 | −0.189455 | ||||||||
\(713\) | 4.06556 | 0.152257 | ||||||||
\(714\) | 12.5385 | 0.469242 | ||||||||
\(715\) | −11.2914 | −0.422275 | ||||||||
\(716\) | −76.8600 | −2.87239 | ||||||||
\(717\) | −35.8495 | −1.33882 | ||||||||
\(718\) | −70.8679 | −2.64477 | ||||||||
\(719\) | 9.80130 | 0.365527 | 0.182763 | − | 0.983157i | \(-0.441496\pi\) | ||||
0.182763 | + | 0.983157i | \(0.441496\pi\) | |||||||
\(720\) | 11.1380 | 0.415087 | ||||||||
\(721\) | 2.50964 | 0.0934639 | ||||||||
\(722\) | 42.6301 | 1.58653 | ||||||||
\(723\) | 9.40322 | 0.349710 | ||||||||
\(724\) | −113.619 | −4.22263 | ||||||||
\(725\) | −72.1699 | −2.68032 | ||||||||
\(726\) | −4.75507 | −0.176477 | ||||||||
\(727\) | −37.1944 | −1.37947 | −0.689733 | − | 0.724064i | \(-0.742272\pi\) | ||||
−0.689733 | + | 0.724064i | \(0.742272\pi\) | |||||||
\(728\) | 9.10317 | 0.337386 | ||||||||
\(729\) | 23.7333 | 0.879011 | ||||||||
\(730\) | 68.0848 | 2.51993 | ||||||||
\(731\) | 73.6358 | 2.72352 | ||||||||
\(732\) | 121.152 | 4.47792 | ||||||||
\(733\) | −39.2717 | −1.45054 | −0.725268 | − | 0.688467i | \(-0.758284\pi\) | ||||
−0.725268 | + | 0.688467i | \(0.758284\pi\) | |||||||
\(734\) | −61.8169 | −2.28170 | ||||||||
\(735\) | −46.5567 | −1.71727 | ||||||||
\(736\) | 20.6916 | 0.762704 | ||||||||
\(737\) | 7.92550 | 0.291940 | ||||||||
\(738\) | −6.94611 | −0.255690 | ||||||||
\(739\) | 4.69533 | 0.172720 | 0.0863602 | − | 0.996264i | \(-0.472476\pi\) | ||||
0.0863602 | + | 0.996264i | \(0.472476\pi\) | |||||||
\(740\) | −82.0060 | −3.01460 | ||||||||
\(741\) | 9.00584 | 0.330838 | ||||||||
\(742\) | 5.74582 | 0.210936 | ||||||||
\(743\) | 41.5704 | 1.52507 | 0.762535 | − | 0.646947i | \(-0.223954\pi\) | ||||
0.762535 | + | 0.646947i | \(0.223954\pi\) | |||||||
\(744\) | 28.3521 | 1.03944 | ||||||||
\(745\) | 12.1011 | 0.443351 | ||||||||
\(746\) | 44.0806 | 1.61391 | ||||||||
\(747\) | 2.44166 | 0.0893358 | ||||||||
\(748\) | −31.4320 | −1.14927 | ||||||||
\(749\) | −5.91639 | −0.216180 | ||||||||
\(750\) | −72.0083 | −2.62937 | ||||||||
\(751\) | 14.5781 | 0.531963 | 0.265981 | − | 0.963978i | \(-0.414304\pi\) | ||||
0.265981 | + | 0.963978i | \(0.414304\pi\) | |||||||
\(752\) | −14.9345 | −0.544605 | ||||||||
\(753\) | −48.9588 | −1.78416 | ||||||||
\(754\) | −62.9191 | −2.29138 | ||||||||
\(755\) | 13.5837 | 0.494360 | ||||||||
\(756\) | −9.64047 | −0.350621 | ||||||||
\(757\) | 37.7246 | 1.37112 | 0.685562 | − | 0.728014i | \(-0.259557\pi\) | ||||
0.685562 | + | 0.728014i | \(0.259557\pi\) | |||||||
\(758\) | −65.1965 | −2.36804 | ||||||||
\(759\) | −3.52343 | −0.127892 | ||||||||
\(760\) | 45.8126 | 1.66180 | ||||||||
\(761\) | −31.0762 | −1.12651 | −0.563256 | − | 0.826282i | \(-0.690452\pi\) | ||||
−0.563256 | + | 0.826282i | \(0.690452\pi\) | |||||||
\(762\) | −41.8991 | −1.51784 | ||||||||
\(763\) | 0.687081 | 0.0248740 | ||||||||
\(764\) | −71.2919 | −2.57925 | ||||||||
\(765\) | −7.40218 | −0.267627 | ||||||||
\(766\) | −83.9508 | −3.03327 | ||||||||
\(767\) | −18.0075 | −0.650214 | ||||||||
\(768\) | −27.6479 | −0.997657 | ||||||||
\(769\) | 4.40830 | 0.158967 | 0.0794837 | − | 0.996836i | \(-0.474673\pi\) | ||||
0.0794837 | + | 0.996836i | \(0.474673\pi\) | |||||||
\(770\) | −3.98219 | −0.143508 | ||||||||
\(771\) | 22.6710 | 0.816478 | ||||||||
\(772\) | −72.6203 | −2.61366 | ||||||||
\(773\) | 24.8597 | 0.894142 | 0.447071 | − | 0.894498i | \(-0.352467\pi\) | ||||
0.447071 | + | 0.894498i | \(0.352467\pi\) | |||||||
\(774\) | 9.03208 | 0.324651 | ||||||||
\(775\) | −18.9640 | −0.681207 | ||||||||
\(776\) | 109.574 | 3.93348 | ||||||||
\(777\) | −3.33735 | −0.119727 | ||||||||
\(778\) | 4.19792 | 0.150503 | ||||||||
\(779\) | −14.3448 | −0.513956 | ||||||||
\(780\) | −99.3981 | −3.55902 | ||||||||
\(781\) | 12.1603 | 0.435130 | ||||||||
\(782\) | −32.9095 | −1.17684 | ||||||||
\(783\) | 39.1139 | 1.39782 | ||||||||
\(784\) | −66.7523 | −2.38401 | ||||||||
\(785\) | −76.4711 | −2.72937 | ||||||||
\(786\) | 35.4374 | 1.26401 | ||||||||
\(787\) | 23.9191 | 0.852625 | 0.426313 | − | 0.904576i | \(-0.359812\pi\) | ||||
0.426313 | + | 0.904576i | \(0.359812\pi\) | |||||||
\(788\) | −67.5146 | −2.40511 | ||||||||
\(789\) | −40.9515 | −1.45791 | ||||||||
\(790\) | −71.4152 | −2.54084 | ||||||||
\(791\) | −4.33797 | −0.154241 | ||||||||
\(792\) | −2.26316 | −0.0804178 | ||||||||
\(793\) | −41.4711 | −1.47268 | ||||||||
\(794\) | −31.6150 | −1.12198 | ||||||||
\(795\) | −36.8282 | −1.30616 | ||||||||
\(796\) | −101.638 | −3.60246 | ||||||||
\(797\) | 47.5946 | 1.68589 | 0.842944 | − | 0.538002i | \(-0.180821\pi\) | ||||
0.842944 | + | 0.538002i | \(0.180821\pi\) | |||||||
\(798\) | 3.17613 | 0.112434 | ||||||||
\(799\) | 9.92533 | 0.351133 | ||||||||
\(800\) | −96.5170 | −3.41239 | ||||||||
\(801\) | 0.206906 | 0.00731067 | ||||||||
\(802\) | −38.7505 | −1.36833 | ||||||||
\(803\) | −6.94597 | −0.245118 | ||||||||
\(804\) | 69.7681 | 2.46053 | ||||||||
\(805\) | −2.95074 | −0.104000 | ||||||||
\(806\) | −16.5332 | −0.582356 | ||||||||
\(807\) | 6.44917 | 0.227022 | ||||||||
\(808\) | 74.4531 | 2.61925 | ||||||||
\(809\) | −51.6584 | −1.81621 | −0.908107 | − | 0.418739i | \(-0.862472\pi\) | ||||
−0.908107 | + | 0.418739i | \(0.862472\pi\) | |||||||
\(810\) | 96.2603 | 3.38224 | ||||||||
\(811\) | 43.9447 | 1.54311 | 0.771554 | − | 0.636163i | \(-0.219480\pi\) | ||||
0.771554 | + | 0.636163i | \(0.219480\pi\) | |||||||
\(812\) | −15.7042 | −0.551110 | ||||||||
\(813\) | 37.1174 | 1.30176 | ||||||||
\(814\) | 11.8214 | 0.414339 | ||||||||
\(815\) | −71.0066 | −2.48725 | ||||||||
\(816\) | −115.228 | −4.03380 | ||||||||
\(817\) | 18.6527 | 0.652574 | ||||||||
\(818\) | 67.5672 | 2.36243 | ||||||||
\(819\) | −0.372580 | −0.0130190 | ||||||||
\(820\) | 158.325 | 5.52893 | ||||||||
\(821\) | −1.53166 | −0.0534553 | −0.0267277 | − | 0.999643i | \(-0.508509\pi\) | ||||
−0.0267277 | + | 0.999643i | \(0.508509\pi\) | |||||||
\(822\) | −102.591 | −3.57828 | ||||||||
\(823\) | 9.87643 | 0.344271 | 0.172135 | − | 0.985073i | \(-0.444933\pi\) | ||||
0.172135 | + | 0.985073i | \(0.444933\pi\) | |||||||
\(824\) | −45.9358 | −1.60025 | ||||||||
\(825\) | 16.4352 | 0.572199 | ||||||||
\(826\) | −6.35079 | −0.220972 | ||||||||
\(827\) | 25.3600 | 0.881854 | 0.440927 | − | 0.897543i | \(-0.354650\pi\) | ||||
0.440927 | + | 0.897543i | \(0.354650\pi\) | |||||||
\(828\) | −2.85680 | −0.0992808 | ||||||||
\(829\) | −2.02393 | −0.0702940 | −0.0351470 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351470 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(830\) | −78.6380 | −2.72956 | ||||||||
\(831\) | 18.1459 | 0.629473 | ||||||||
\(832\) | −25.2874 | −0.876684 | ||||||||
\(833\) | 44.3630 | 1.53709 | ||||||||
\(834\) | −65.0874 | −2.25379 | ||||||||
\(835\) | −47.4952 | −1.64364 | ||||||||
\(836\) | −7.96204 | −0.275373 | ||||||||
\(837\) | 10.2779 | 0.355257 | ||||||||
\(838\) | −40.3210 | −1.39287 | ||||||||
\(839\) | 19.3795 | 0.669053 | 0.334526 | − | 0.942386i | \(-0.391424\pi\) | ||||
0.334526 | + | 0.942386i | \(0.391424\pi\) | |||||||
\(840\) | −20.5776 | −0.709996 | ||||||||
\(841\) | 34.7162 | 1.19711 | ||||||||
\(842\) | −78.1597 | −2.69356 | ||||||||
\(843\) | −7.57491 | −0.260894 | ||||||||
\(844\) | −48.6827 | −1.67573 | ||||||||
\(845\) | −14.6887 | −0.505308 | ||||||||
\(846\) | 1.21743 | 0.0418561 | ||||||||
\(847\) | 0.406260 | 0.0139593 | ||||||||
\(848\) | −52.8038 | −1.81329 | ||||||||
\(849\) | −39.8265 | −1.36684 | ||||||||
\(850\) | 153.508 | 5.26527 | ||||||||
\(851\) | 8.75945 | 0.300270 | ||||||||
\(852\) | 107.047 | 3.66737 | ||||||||
\(853\) | 15.7500 | 0.539270 | 0.269635 | − | 0.962963i | \(-0.413097\pi\) | ||||
0.269635 | + | 0.962963i | \(0.413097\pi\) | |||||||
\(854\) | −14.6258 | −0.500484 | ||||||||
\(855\) | −1.87505 | −0.0641252 | ||||||||
\(856\) | 108.292 | 3.70135 | ||||||||
\(857\) | −15.5489 | −0.531139 | −0.265570 | − | 0.964092i | \(-0.585560\pi\) | ||||
−0.265570 | + | 0.964092i | \(0.585560\pi\) | |||||||
\(858\) | 14.3285 | 0.489167 | ||||||||
\(859\) | −35.3732 | −1.20692 | −0.603458 | − | 0.797394i | \(-0.706211\pi\) | ||||
−0.603458 | + | 0.797394i | \(0.706211\pi\) | |||||||
\(860\) | −205.871 | −7.02013 | ||||||||
\(861\) | 6.44324 | 0.219585 | ||||||||
\(862\) | 10.5335 | 0.358772 | ||||||||
\(863\) | −38.9298 | −1.32519 | −0.662593 | − | 0.748980i | \(-0.730544\pi\) | ||||
−0.662593 | + | 0.748980i | \(0.730544\pi\) | |||||||
\(864\) | 52.3093 | 1.77960 | ||||||||
\(865\) | 41.6517 | 1.41620 | ||||||||
\(866\) | 27.1837 | 0.923740 | ||||||||
\(867\) | 45.6773 | 1.55128 | ||||||||
\(868\) | −4.12658 | −0.140065 | ||||||||
\(869\) | 7.28573 | 0.247151 | ||||||||
\(870\) | 142.228 | 4.82198 | ||||||||
\(871\) | −23.8820 | −0.809211 | ||||||||
\(872\) | −12.5762 | −0.425882 | ||||||||
\(873\) | −4.48471 | −0.151784 | ||||||||
\(874\) | −8.33629 | −0.281979 | ||||||||
\(875\) | 6.15220 | 0.207982 | ||||||||
\(876\) | −61.1453 | −2.06591 | ||||||||
\(877\) | −32.0277 | −1.08150 | −0.540750 | − | 0.841184i | \(-0.681859\pi\) | ||||
−0.540750 | + | 0.841184i | \(0.681859\pi\) | |||||||
\(878\) | 71.3681 | 2.40856 | ||||||||
\(879\) | 2.09898 | 0.0707970 | ||||||||
\(880\) | 36.5961 | 1.23365 | ||||||||
\(881\) | 50.3338 | 1.69579 | 0.847895 | − | 0.530165i | \(-0.177870\pi\) | ||||
0.847895 | + | 0.530165i | \(0.177870\pi\) | |||||||
\(882\) | 5.44152 | 0.183225 | ||||||||
\(883\) | 31.8313 | 1.07121 | 0.535604 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535604 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(884\) | 94.7145 | 3.18559 | ||||||||
\(885\) | 40.7058 | 1.36831 | ||||||||
\(886\) | 62.7297 | 2.10745 | ||||||||
\(887\) | −0.781354 | −0.0262353 | −0.0131177 | − | 0.999914i | \(-0.504176\pi\) | ||||
−0.0131177 | + | 0.999914i | \(0.504176\pi\) | |||||||
\(888\) | 61.0860 | 2.04991 | ||||||||
\(889\) | 3.57975 | 0.120061 | ||||||||
\(890\) | −6.66377 | −0.223370 | ||||||||
\(891\) | −9.82042 | −0.328996 | ||||||||
\(892\) | 75.0800 | 2.51387 | ||||||||
\(893\) | 2.51418 | 0.0841339 | ||||||||
\(894\) | −15.3560 | −0.513582 | ||||||||
\(895\) | −59.4726 | −1.98795 | ||||||||
\(896\) | −0.244480 | −0.00816750 | ||||||||
\(897\) | 10.6172 | 0.354497 | ||||||||
\(898\) | 12.5099 | 0.417461 | ||||||||
\(899\) | 16.7426 | 0.558397 | ||||||||
\(900\) | 13.3257 | 0.444189 | ||||||||
\(901\) | 35.0929 | 1.16911 | ||||||||
\(902\) | −22.8229 | −0.759920 | ||||||||
\(903\) | −8.37820 | −0.278809 | ||||||||
\(904\) | 79.4011 | 2.64084 | ||||||||
\(905\) | −87.9162 | −2.92243 | ||||||||
\(906\) | −17.2373 | −0.572671 | ||||||||
\(907\) | −46.6003 | −1.54734 | −0.773669 | − | 0.633591i | \(-0.781580\pi\) | ||||
−0.773669 | + | 0.633591i | \(0.781580\pi\) | |||||||
\(908\) | 92.1594 | 3.05842 | ||||||||
\(909\) | −3.04726 | −0.101071 | ||||||||
\(910\) | 11.9996 | 0.397782 | ||||||||
\(911\) | −15.8917 | −0.526514 | −0.263257 | − | 0.964726i | \(-0.584797\pi\) | ||||
−0.263257 | + | 0.964726i | \(0.584797\pi\) | |||||||
\(912\) | −29.1885 | −0.966526 | ||||||||
\(913\) | 8.02259 | 0.265509 | ||||||||
\(914\) | 10.7467 | 0.355469 | ||||||||
\(915\) | 93.7450 | 3.09911 | ||||||||
\(916\) | −56.7246 | −1.87423 | ||||||||
\(917\) | −3.02767 | −0.0999826 | ||||||||
\(918\) | −83.1966 | −2.74590 | ||||||||
\(919\) | −18.5713 | −0.612611 | −0.306306 | − | 0.951933i | \(-0.599093\pi\) | ||||
−0.306306 | + | 0.951933i | \(0.599093\pi\) | |||||||
\(920\) | 54.0095 | 1.78064 | ||||||||
\(921\) | −52.3808 | −1.72601 | ||||||||
\(922\) | −34.5052 | −1.13637 | ||||||||
\(923\) | −36.6428 | −1.20611 | ||||||||
\(924\) | 3.57630 | 0.117652 | ||||||||
\(925\) | −40.8588 | −1.34343 | ||||||||
\(926\) | 95.4663 | 3.13722 | ||||||||
\(927\) | 1.88009 | 0.0617501 | ||||||||
\(928\) | 85.2113 | 2.79720 | ||||||||
\(929\) | −26.5792 | −0.872035 | −0.436018 | − | 0.899938i | \(-0.643611\pi\) | ||||
−0.436018 | + | 0.899938i | \(0.643611\pi\) | |||||||
\(930\) | 37.3731 | 1.22551 | ||||||||
\(931\) | 11.2376 | 0.368297 | ||||||||
\(932\) | 142.028 | 4.65227 | ||||||||
\(933\) | 12.7709 | 0.418102 | ||||||||
\(934\) | −9.63389 | −0.315231 | ||||||||
\(935\) | −24.3214 | −0.795396 | ||||||||
\(936\) | 6.81960 | 0.222906 | ||||||||
\(937\) | 3.86062 | 0.126121 | 0.0630605 | − | 0.998010i | \(-0.479914\pi\) | ||||
0.0630605 | + | 0.998010i | \(0.479914\pi\) | |||||||
\(938\) | −8.42257 | −0.275007 | ||||||||
\(939\) | 11.6438 | 0.379980 | ||||||||
\(940\) | −27.7492 | −0.905080 | ||||||||
\(941\) | 25.4012 | 0.828055 | 0.414028 | − | 0.910264i | \(-0.364122\pi\) | ||||
0.414028 | + | 0.910264i | \(0.364122\pi\) | |||||||
\(942\) | 97.0398 | 3.16173 | ||||||||
\(943\) | −16.9114 | −0.550711 | ||||||||
\(944\) | 58.3635 | 1.89957 | ||||||||
\(945\) | −7.45959 | −0.242660 | ||||||||
\(946\) | 29.6768 | 0.964876 | ||||||||
\(947\) | 10.1398 | 0.329499 | 0.164750 | − | 0.986335i | \(-0.447318\pi\) | ||||
0.164750 | + | 0.986335i | \(0.447318\pi\) | |||||||
\(948\) | 64.1362 | 2.08305 | ||||||||
\(949\) | 20.9304 | 0.679429 | ||||||||
\(950\) | 38.8850 | 1.26160 | ||||||||
\(951\) | −20.1303 | −0.652771 | ||||||||
\(952\) | 19.6080 | 0.635500 | ||||||||
\(953\) | 55.5328 | 1.79888 | 0.899441 | − | 0.437041i | \(-0.143974\pi\) | ||||
0.899441 | + | 0.437041i | \(0.143974\pi\) | |||||||
\(954\) | 4.30446 | 0.139362 | ||||||||
\(955\) | −55.1641 | −1.78507 | ||||||||
\(956\) | −95.5054 | −3.08886 | ||||||||
\(957\) | −14.5100 | −0.469042 | ||||||||
\(958\) | 23.1014 | 0.746372 | ||||||||
\(959\) | 8.76512 | 0.283040 | ||||||||
\(960\) | 57.1620 | 1.84490 | ||||||||
\(961\) | −26.6006 | −0.858083 | ||||||||
\(962\) | −35.6215 | −1.14848 | ||||||||
\(963\) | −4.43224 | −0.142827 | ||||||||
\(964\) | 25.0508 | 0.806831 | ||||||||
\(965\) | −56.1920 | −1.80888 | ||||||||
\(966\) | 3.74441 | 0.120474 | ||||||||
\(967\) | 35.4343 | 1.13949 | 0.569745 | − | 0.821821i | \(-0.307042\pi\) | ||||
0.569745 | + | 0.821821i | \(0.307042\pi\) | |||||||
\(968\) | −7.43608 | −0.239005 | ||||||||
\(969\) | 19.3984 | 0.623166 | ||||||||
\(970\) | 144.438 | 4.63762 | ||||||||
\(971\) | 21.8054 | 0.699770 | 0.349885 | − | 0.936793i | \(-0.386221\pi\) | ||||
0.349885 | + | 0.936793i | \(0.386221\pi\) | |||||||
\(972\) | −15.2596 | −0.489453 | ||||||||
\(973\) | 5.56089 | 0.178274 | ||||||||
\(974\) | 96.4377 | 3.09006 | ||||||||
\(975\) | −49.5243 | −1.58605 | ||||||||
\(976\) | 134.410 | 4.30237 | ||||||||
\(977\) | −26.0413 | −0.833136 | −0.416568 | − | 0.909104i | \(-0.636767\pi\) | ||||
−0.416568 | + | 0.909104i | \(0.636767\pi\) | |||||||
\(978\) | 90.1055 | 2.88126 | ||||||||
\(979\) | 0.679834 | 0.0217276 | ||||||||
\(980\) | −124.030 | −3.96199 | ||||||||
\(981\) | 0.514724 | 0.0164339 | ||||||||
\(982\) | −62.1009 | −1.98172 | ||||||||
\(983\) | 23.9811 | 0.764877 | 0.382439 | − | 0.923981i | \(-0.375084\pi\) | ||||
0.382439 | + | 0.923981i | \(0.375084\pi\) | |||||||
\(984\) | −117.935 | −3.75964 | ||||||||
\(985\) | −52.2414 | −1.66455 | ||||||||
\(986\) | −135.526 | −4.31604 | ||||||||
\(987\) | −1.12929 | −0.0359458 | ||||||||
\(988\) | 23.9921 | 0.763291 | ||||||||
\(989\) | 21.9900 | 0.699242 | ||||||||
\(990\) | −2.98324 | −0.0948136 | ||||||||
\(991\) | 10.5877 | 0.336329 | 0.168165 | − | 0.985759i | \(-0.446216\pi\) | ||||
0.168165 | + | 0.985759i | \(0.446216\pi\) | |||||||
\(992\) | 22.3909 | 0.710911 | ||||||||
\(993\) | 21.6929 | 0.688404 | ||||||||
\(994\) | −12.9230 | −0.409892 | ||||||||
\(995\) | −78.6452 | −2.49322 | ||||||||
\(996\) | 70.6228 | 2.23777 | ||||||||
\(997\) | 19.7017 | 0.623959 | 0.311979 | − | 0.950089i | \(-0.399008\pi\) | ||||
0.311979 | + | 0.950089i | \(0.399008\pi\) | |||||||
\(998\) | −83.2629 | −2.63564 | ||||||||
\(999\) | 22.1443 | 0.700613 |
(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 | 6017.2.a.c.1.6 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.6 | ✓ | 106 | 1.1 | even | 1 | trivial |