Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.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: | \(48.1418073786\) |
Analytic rank: | \(1\) |
Dimension: | \(234\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80022 | −1.98005 | −0.990026 | − | 0.140886i | \(-0.955005\pi\) | ||||
−0.990026 | + | 0.140886i | \(0.955005\pi\) | |||||||
\(3\) | 1.58457 | 0.914852 | 0.457426 | − | 0.889248i | \(-0.348771\pi\) | ||||
0.457426 | + | 0.889248i | \(0.348771\pi\) | |||||||
\(4\) | 5.84121 | 2.92060 | ||||||||
\(5\) | 4.15609 | 1.85866 | 0.929329 | − | 0.369252i | \(-0.120386\pi\) | ||||
0.929329 | + | 0.369252i | \(0.120386\pi\) | |||||||
\(6\) | −4.43714 | −1.81145 | ||||||||
\(7\) | −3.16901 | −1.19777 | −0.598887 | − | 0.800833i | \(-0.704390\pi\) | ||||
−0.598887 | + | 0.800833i | \(0.704390\pi\) | |||||||
\(8\) | −10.7562 | −3.80290 | ||||||||
\(9\) | −0.489138 | −0.163046 | ||||||||
\(10\) | −11.6379 | −3.68024 | ||||||||
\(11\) | −2.40992 | −0.726618 | −0.363309 | − | 0.931669i | \(-0.618353\pi\) | ||||
−0.363309 | + | 0.931669i | \(0.618353\pi\) | |||||||
\(12\) | 9.25580 | 2.67192 | ||||||||
\(13\) | −1.53495 | −0.425719 | −0.212860 | − | 0.977083i | \(-0.568278\pi\) | ||||
−0.212860 | + | 0.977083i | \(0.568278\pi\) | |||||||
\(14\) | 8.87392 | 2.37166 | ||||||||
\(15\) | 6.58561 | 1.70040 | ||||||||
\(16\) | 18.4373 | 4.60932 | ||||||||
\(17\) | 2.66666 | 0.646761 | 0.323381 | − | 0.946269i | \(-0.395181\pi\) | ||||
0.323381 | + | 0.946269i | \(0.395181\pi\) | |||||||
\(18\) | 1.36969 | 0.322840 | ||||||||
\(19\) | −0.944943 | −0.216785 | −0.108392 | − | 0.994108i | \(-0.534570\pi\) | ||||
−0.108392 | + | 0.994108i | \(0.534570\pi\) | |||||||
\(20\) | 24.2766 | 5.42841 | ||||||||
\(21\) | −5.02152 | −1.09579 | ||||||||
\(22\) | 6.74830 | 1.43874 | ||||||||
\(23\) | 3.96705 | 0.827186 | 0.413593 | − | 0.910462i | \(-0.364274\pi\) | ||||
0.413593 | + | 0.910462i | \(0.364274\pi\) | |||||||
\(24\) | −17.0440 | −3.47909 | ||||||||
\(25\) | 12.2731 | 2.45461 | ||||||||
\(26\) | 4.29820 | 0.842946 | ||||||||
\(27\) | −5.52878 | −1.06401 | ||||||||
\(28\) | −18.5109 | −3.49823 | ||||||||
\(29\) | −4.07587 | −0.756870 | −0.378435 | − | 0.925628i | \(-0.623538\pi\) | ||||
−0.378435 | + | 0.925628i | \(0.623538\pi\) | |||||||
\(30\) | −18.4411 | −3.36687 | ||||||||
\(31\) | −1.89498 | −0.340348 | −0.170174 | − | 0.985414i | \(-0.554433\pi\) | ||||
−0.170174 | + | 0.985414i | \(0.554433\pi\) | |||||||
\(32\) | −30.1160 | −5.32380 | ||||||||
\(33\) | −3.81869 | −0.664748 | ||||||||
\(34\) | −7.46724 | −1.28062 | ||||||||
\(35\) | −13.1707 | −2.22625 | ||||||||
\(36\) | −2.85716 | −0.476193 | ||||||||
\(37\) | 6.09196 | 1.00151 | 0.500756 | − | 0.865589i | \(-0.333055\pi\) | ||||
0.500756 | + | 0.865589i | \(0.333055\pi\) | |||||||
\(38\) | 2.64605 | 0.429245 | ||||||||
\(39\) | −2.43224 | −0.389470 | ||||||||
\(40\) | −44.7038 | −7.06828 | ||||||||
\(41\) | 7.62325 | 1.19055 | 0.595276 | − | 0.803521i | \(-0.297043\pi\) | ||||
0.595276 | + | 0.803521i | \(0.297043\pi\) | |||||||
\(42\) | 14.0613 | 2.16971 | ||||||||
\(43\) | −10.2910 | −1.56936 | −0.784680 | − | 0.619901i | \(-0.787173\pi\) | ||||
−0.784680 | + | 0.619901i | \(0.787173\pi\) | |||||||
\(44\) | −14.0768 | −2.12216 | ||||||||
\(45\) | −2.03290 | −0.303047 | ||||||||
\(46\) | −11.1086 | −1.63787 | ||||||||
\(47\) | −4.33913 | −0.632927 | −0.316463 | − | 0.948605i | \(-0.602495\pi\) | ||||
−0.316463 | + | 0.948605i | \(0.602495\pi\) | |||||||
\(48\) | 29.2152 | 4.21685 | ||||||||
\(49\) | 3.04265 | 0.434664 | ||||||||
\(50\) | −34.3672 | −4.86026 | ||||||||
\(51\) | 4.22552 | 0.591691 | ||||||||
\(52\) | −8.96598 | −1.24336 | ||||||||
\(53\) | −8.34417 | −1.14616 | −0.573080 | − | 0.819500i | \(-0.694251\pi\) | ||||
−0.573080 | + | 0.819500i | \(0.694251\pi\) | |||||||
\(54\) | 15.4818 | 2.10680 | ||||||||
\(55\) | −10.0158 | −1.35054 | ||||||||
\(56\) | 34.0866 | 4.55501 | ||||||||
\(57\) | −1.49733 | −0.198326 | ||||||||
\(58\) | 11.4133 | 1.49864 | ||||||||
\(59\) | −10.3895 | −1.35260 | −0.676299 | − | 0.736627i | \(-0.736417\pi\) | ||||
−0.676299 | + | 0.736627i | \(0.736417\pi\) | |||||||
\(60\) | 38.4679 | 4.96619 | ||||||||
\(61\) | −6.02046 | −0.770841 | −0.385420 | − | 0.922741i | \(-0.625944\pi\) | ||||
−0.385420 | + | 0.922741i | \(0.625944\pi\) | |||||||
\(62\) | 5.30635 | 0.673907 | ||||||||
\(63\) | 1.55009 | 0.195292 | ||||||||
\(64\) | 47.4567 | 5.93208 | ||||||||
\(65\) | −6.37940 | −0.791267 | ||||||||
\(66\) | 10.6931 | 1.31624 | ||||||||
\(67\) | 14.1657 | 1.73061 | 0.865306 | − | 0.501244i | \(-0.167124\pi\) | ||||
0.865306 | + | 0.501244i | \(0.167124\pi\) | |||||||
\(68\) | 15.5765 | 1.88893 | ||||||||
\(69\) | 6.28606 | 0.756753 | ||||||||
\(70\) | 36.8808 | 4.40810 | ||||||||
\(71\) | −12.8144 | −1.52079 | −0.760394 | − | 0.649461i | \(-0.774994\pi\) | ||||
−0.760394 | + | 0.649461i | \(0.774994\pi\) | |||||||
\(72\) | 5.26128 | 0.620047 | ||||||||
\(73\) | −1.30315 | −0.152523 | −0.0762614 | − | 0.997088i | \(-0.524298\pi\) | ||||
−0.0762614 | + | 0.997088i | \(0.524298\pi\) | |||||||
\(74\) | −17.0588 | −1.98304 | ||||||||
\(75\) | 19.4475 | 2.24561 | ||||||||
\(76\) | −5.51961 | −0.633143 | ||||||||
\(77\) | 7.63707 | 0.870325 | ||||||||
\(78\) | 6.81080 | 0.771171 | ||||||||
\(79\) | −8.54427 | −0.961306 | −0.480653 | − | 0.876911i | \(-0.659600\pi\) | ||||
−0.480653 | + | 0.876911i | \(0.659600\pi\) | |||||||
\(80\) | 76.6270 | 8.56716 | ||||||||
\(81\) | −7.29333 | −0.810370 | ||||||||
\(82\) | −21.3468 | −2.35736 | ||||||||
\(83\) | 2.18827 | 0.240194 | 0.120097 | − | 0.992762i | \(-0.461679\pi\) | ||||
0.120097 | + | 0.992762i | \(0.461679\pi\) | |||||||
\(84\) | −29.3318 | −3.20036 | ||||||||
\(85\) | 11.0829 | 1.20211 | ||||||||
\(86\) | 28.8170 | 3.10741 | ||||||||
\(87\) | −6.45850 | −0.692424 | ||||||||
\(88\) | 25.9216 | 2.76325 | ||||||||
\(89\) | 4.24721 | 0.450204 | 0.225102 | − | 0.974335i | \(-0.427729\pi\) | ||||
0.225102 | + | 0.974335i | \(0.427729\pi\) | |||||||
\(90\) | 5.69256 | 0.600049 | ||||||||
\(91\) | 4.86429 | 0.509916 | ||||||||
\(92\) | 23.1723 | 2.41588 | ||||||||
\(93\) | −3.00272 | −0.311368 | ||||||||
\(94\) | 12.1505 | 1.25323 | ||||||||
\(95\) | −3.92727 | −0.402929 | ||||||||
\(96\) | −47.7209 | −4.87049 | ||||||||
\(97\) | −8.88506 | −0.902141 | −0.451071 | − | 0.892488i | \(-0.648958\pi\) | ||||
−0.451071 | + | 0.892488i | \(0.648958\pi\) | |||||||
\(98\) | −8.52007 | −0.860657 | ||||||||
\(99\) | 1.17878 | 0.118472 | ||||||||
\(100\) | 71.6895 | 7.16895 | ||||||||
\(101\) | −2.08529 | −0.207494 | −0.103747 | − | 0.994604i | \(-0.533083\pi\) | ||||
−0.103747 | + | 0.994604i | \(0.533083\pi\) | |||||||
\(102\) | −11.8324 | −1.17158 | ||||||||
\(103\) | 9.16272 | 0.902829 | 0.451415 | − | 0.892314i | \(-0.350920\pi\) | ||||
0.451415 | + | 0.892314i | \(0.350920\pi\) | |||||||
\(104\) | 16.5103 | 1.61897 | ||||||||
\(105\) | −20.8699 | −2.03669 | ||||||||
\(106\) | 23.3655 | 2.26945 | ||||||||
\(107\) | −8.28976 | −0.801402 | −0.400701 | − | 0.916209i | \(-0.631233\pi\) | ||||
−0.400701 | + | 0.916209i | \(0.631233\pi\) | |||||||
\(108\) | −32.2948 | −3.10757 | ||||||||
\(109\) | −9.63887 | −0.923236 | −0.461618 | − | 0.887079i | \(-0.652731\pi\) | ||||
−0.461618 | + | 0.887079i | \(0.652731\pi\) | |||||||
\(110\) | 28.0465 | 2.67413 | ||||||||
\(111\) | 9.65313 | 0.916235 | ||||||||
\(112\) | −58.4280 | −5.52093 | ||||||||
\(113\) | 1.36810 | 0.128700 | 0.0643498 | − | 0.997927i | \(-0.479503\pi\) | ||||
0.0643498 | + | 0.997927i | \(0.479503\pi\) | |||||||
\(114\) | 4.19284 | 0.392696 | ||||||||
\(115\) | 16.4874 | 1.53746 | ||||||||
\(116\) | −23.8080 | −2.21052 | ||||||||
\(117\) | 0.750804 | 0.0694119 | ||||||||
\(118\) | 29.0928 | 2.67821 | ||||||||
\(119\) | −8.45070 | −0.774674 | ||||||||
\(120\) | −70.8362 | −6.46643 | ||||||||
\(121\) | −5.19228 | −0.472026 | ||||||||
\(122\) | 16.8586 | 1.52630 | ||||||||
\(123\) | 12.0796 | 1.08918 | ||||||||
\(124\) | −11.0690 | −0.994022 | ||||||||
\(125\) | 30.2275 | 2.70363 | ||||||||
\(126\) | −4.34058 | −0.386689 | ||||||||
\(127\) | 3.54613 | 0.314668 | 0.157334 | − | 0.987545i | \(-0.449710\pi\) | ||||
0.157334 | + | 0.987545i | \(0.449710\pi\) | |||||||
\(128\) | −72.6569 | −6.42203 | ||||||||
\(129\) | −16.3068 | −1.43573 | ||||||||
\(130\) | 17.8637 | 1.56675 | ||||||||
\(131\) | −11.0650 | −0.966753 | −0.483376 | − | 0.875413i | \(-0.660590\pi\) | ||||
−0.483376 | + | 0.875413i | \(0.660590\pi\) | |||||||
\(132\) | −22.3057 | −1.94147 | ||||||||
\(133\) | 2.99454 | 0.259659 | ||||||||
\(134\) | −39.6669 | −3.42670 | ||||||||
\(135\) | −22.9781 | −1.97764 | ||||||||
\(136\) | −28.6832 | −2.45956 | ||||||||
\(137\) | 14.9137 | 1.27417 | 0.637083 | − | 0.770795i | \(-0.280141\pi\) | ||||
0.637083 | + | 0.770795i | \(0.280141\pi\) | |||||||
\(138\) | −17.6023 | −1.49841 | ||||||||
\(139\) | 0.889659 | 0.0754599 | 0.0377300 | − | 0.999288i | \(-0.487987\pi\) | ||||
0.0377300 | + | 0.999288i | \(0.487987\pi\) | |||||||
\(140\) | −76.9328 | −6.50201 | ||||||||
\(141\) | −6.87565 | −0.579034 | ||||||||
\(142\) | 35.8831 | 3.01124 | ||||||||
\(143\) | 3.69911 | 0.309335 | ||||||||
\(144\) | −9.01839 | −0.751532 | ||||||||
\(145\) | −16.9397 | −1.40676 | ||||||||
\(146\) | 3.64911 | 0.302003 | ||||||||
\(147\) | 4.82129 | 0.397653 | ||||||||
\(148\) | 35.5844 | 2.92502 | ||||||||
\(149\) | 23.9969 | 1.96591 | 0.982953 | − | 0.183855i | \(-0.0588578\pi\) | ||||
0.982953 | + | 0.183855i | \(0.0588578\pi\) | |||||||
\(150\) | −54.4573 | −4.44642 | ||||||||
\(151\) | −16.2702 | −1.32405 | −0.662023 | − | 0.749483i | \(-0.730302\pi\) | ||||
−0.662023 | + | 0.749483i | \(0.730302\pi\) | |||||||
\(152\) | 10.1640 | 0.824410 | ||||||||
\(153\) | −1.30437 | −0.105452 | ||||||||
\(154\) | −21.3854 | −1.72329 | ||||||||
\(155\) | −7.87569 | −0.632591 | ||||||||
\(156\) | −14.2072 | −1.13749 | ||||||||
\(157\) | −5.33212 | −0.425550 | −0.212775 | − | 0.977101i | \(-0.568250\pi\) | ||||
−0.212775 | + | 0.977101i | \(0.568250\pi\) | |||||||
\(158\) | 23.9258 | 1.90344 | ||||||||
\(159\) | −13.2219 | −1.04857 | ||||||||
\(160\) | −125.165 | −9.89513 | ||||||||
\(161\) | −12.5716 | −0.990783 | ||||||||
\(162\) | 20.4229 | 1.60457 | ||||||||
\(163\) | −13.6210 | −1.06688 | −0.533439 | − | 0.845838i | \(-0.679101\pi\) | ||||
−0.533439 | + | 0.845838i | \(0.679101\pi\) | |||||||
\(164\) | 44.5290 | 3.47713 | ||||||||
\(165\) | −15.8708 | −1.23554 | ||||||||
\(166\) | −6.12762 | −0.475596 | ||||||||
\(167\) | 6.17812 | 0.478078 | 0.239039 | − | 0.971010i | \(-0.423168\pi\) | ||||
0.239039 | + | 0.971010i | \(0.423168\pi\) | |||||||
\(168\) | 54.0126 | 4.16716 | ||||||||
\(169\) | −10.6439 | −0.818763 | ||||||||
\(170\) | −31.0345 | −2.38024 | ||||||||
\(171\) | 0.462208 | 0.0353459 | ||||||||
\(172\) | −60.1118 | −4.58348 | ||||||||
\(173\) | 19.8825 | 1.51164 | 0.755818 | − | 0.654782i | \(-0.227240\pi\) | ||||
0.755818 | + | 0.654782i | \(0.227240\pi\) | |||||||
\(174\) | 18.0852 | 1.37103 | ||||||||
\(175\) | −38.8935 | −2.94007 | ||||||||
\(176\) | −44.4324 | −3.34922 | ||||||||
\(177\) | −16.4629 | −1.23743 | ||||||||
\(178\) | −11.8931 | −0.891426 | ||||||||
\(179\) | −23.7272 | −1.77345 | −0.886727 | − | 0.462294i | \(-0.847026\pi\) | ||||
−0.886727 | + | 0.462294i | \(0.847026\pi\) | |||||||
\(180\) | −11.8746 | −0.885080 | ||||||||
\(181\) | −17.0985 | −1.27092 | −0.635462 | − | 0.772132i | \(-0.719191\pi\) | ||||
−0.635462 | + | 0.772132i | \(0.719191\pi\) | |||||||
\(182\) | −13.6210 | −1.00966 | ||||||||
\(183\) | −9.53984 | −0.705205 | ||||||||
\(184\) | −42.6704 | −3.14570 | ||||||||
\(185\) | 25.3187 | 1.86147 | ||||||||
\(186\) | 8.40828 | 0.616525 | ||||||||
\(187\) | −6.42645 | −0.469949 | ||||||||
\(188\) | −25.3458 | −1.84853 | ||||||||
\(189\) | 17.5208 | 1.27445 | ||||||||
\(190\) | 10.9972 | 0.797820 | ||||||||
\(191\) | −18.0860 | −1.30866 | −0.654328 | − | 0.756211i | \(-0.727048\pi\) | ||||
−0.654328 | + | 0.756211i | \(0.727048\pi\) | |||||||
\(192\) | 75.1984 | 5.42698 | ||||||||
\(193\) | 1.42737 | 0.102745 | 0.0513723 | − | 0.998680i | \(-0.483641\pi\) | ||||
0.0513723 | + | 0.998680i | \(0.483641\pi\) | |||||||
\(194\) | 24.8801 | 1.78629 | ||||||||
\(195\) | −10.1086 | −0.723892 | ||||||||
\(196\) | 17.7727 | 1.26948 | ||||||||
\(197\) | 1.19023 | 0.0848006 | 0.0424003 | − | 0.999101i | \(-0.486500\pi\) | ||||
0.0424003 | + | 0.999101i | \(0.486500\pi\) | |||||||
\(198\) | −3.30085 | −0.234581 | ||||||||
\(199\) | 14.6131 | 1.03589 | 0.517947 | − | 0.855413i | \(-0.326697\pi\) | ||||
0.517947 | + | 0.855413i | \(0.326697\pi\) | |||||||
\(200\) | −132.012 | −9.33463 | ||||||||
\(201\) | 22.4465 | 1.58325 | ||||||||
\(202\) | 5.83926 | 0.410849 | ||||||||
\(203\) | 12.9165 | 0.906560 | ||||||||
\(204\) | 24.6821 | 1.72809 | ||||||||
\(205\) | 31.6829 | 2.21283 | ||||||||
\(206\) | −25.6576 | −1.78765 | ||||||||
\(207\) | −1.94043 | −0.134870 | ||||||||
\(208\) | −28.3004 | −1.96228 | ||||||||
\(209\) | 2.27724 | 0.157520 | ||||||||
\(210\) | 58.4402 | 4.03276 | ||||||||
\(211\) | 4.10287 | 0.282453 | 0.141227 | − | 0.989977i | \(-0.454895\pi\) | ||||
0.141227 | + | 0.989977i | \(0.454895\pi\) | |||||||
\(212\) | −48.7400 | −3.34748 | ||||||||
\(213\) | −20.3053 | −1.39130 | ||||||||
\(214\) | 23.2131 | 1.58682 | ||||||||
\(215\) | −42.7702 | −2.91690 | ||||||||
\(216\) | 59.4688 | 4.04634 | ||||||||
\(217\) | 6.00521 | 0.407660 | ||||||||
\(218\) | 26.9909 | 1.82806 | ||||||||
\(219\) | −2.06494 | −0.139536 | ||||||||
\(220\) | −58.5046 | −3.94438 | ||||||||
\(221\) | −4.09320 | −0.275339 | ||||||||
\(222\) | −27.0309 | −1.81419 | ||||||||
\(223\) | 2.45016 | 0.164075 | 0.0820375 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820375 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(224\) | 95.4380 | 6.37672 | ||||||||
\(225\) | −6.00322 | −0.400215 | ||||||||
\(226\) | −3.83097 | −0.254832 | ||||||||
\(227\) | 10.0421 | 0.666517 | 0.333258 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333258 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(228\) | −8.74621 | −0.579232 | ||||||||
\(229\) | 14.2599 | 0.942323 | 0.471162 | − | 0.882047i | \(-0.343835\pi\) | ||||
0.471162 | + | 0.882047i | \(0.343835\pi\) | |||||||
\(230\) | −46.1683 | −3.04424 | ||||||||
\(231\) | 12.1015 | 0.796219 | ||||||||
\(232\) | 43.8409 | 2.87830 | ||||||||
\(233\) | 28.1392 | 1.84346 | 0.921730 | − | 0.387833i | \(-0.126776\pi\) | ||||
0.921730 | + | 0.387833i | \(0.126776\pi\) | |||||||
\(234\) | −2.10241 | −0.137439 | ||||||||
\(235\) | −18.0338 | −1.17640 | ||||||||
\(236\) | −60.6872 | −3.95040 | ||||||||
\(237\) | −13.5390 | −0.879452 | ||||||||
\(238\) | 23.6638 | 1.53389 | ||||||||
\(239\) | 23.3841 | 1.51259 | 0.756295 | − | 0.654231i | \(-0.227007\pi\) | ||||
0.756295 | + | 0.654231i | \(0.227007\pi\) | |||||||
\(240\) | 121.421 | 7.83768 | ||||||||
\(241\) | −12.4228 | −0.800224 | −0.400112 | − | 0.916466i | \(-0.631029\pi\) | ||||
−0.400112 | + | 0.916466i | \(0.631029\pi\) | |||||||
\(242\) | 14.5395 | 0.934635 | ||||||||
\(243\) | 5.02956 | 0.322647 | ||||||||
\(244\) | −35.1668 | −2.25132 | ||||||||
\(245\) | 12.6455 | 0.807892 | ||||||||
\(246\) | −33.8254 | −2.15663 | ||||||||
\(247\) | 1.45044 | 0.0922895 | ||||||||
\(248\) | 20.3828 | 1.29431 | ||||||||
\(249\) | 3.46746 | 0.219742 | ||||||||
\(250\) | −84.6434 | −5.35332 | ||||||||
\(251\) | −4.61670 | −0.291404 | −0.145702 | − | 0.989329i | \(-0.546544\pi\) | ||||
−0.145702 | + | 0.989329i | \(0.546544\pi\) | |||||||
\(252\) | 9.05437 | 0.570372 | ||||||||
\(253\) | −9.56027 | −0.601049 | ||||||||
\(254\) | −9.92993 | −0.623059 | ||||||||
\(255\) | 17.5616 | 1.09975 | ||||||||
\(256\) | 108.542 | 6.78386 | ||||||||
\(257\) | −24.7242 | −1.54225 | −0.771126 | − | 0.636682i | \(-0.780306\pi\) | ||||
−0.771126 | + | 0.636682i | \(0.780306\pi\) | |||||||
\(258\) | 45.6625 | 2.84282 | ||||||||
\(259\) | −19.3055 | −1.19959 | ||||||||
\(260\) | −37.2634 | −2.31098 | ||||||||
\(261\) | 1.99366 | 0.123405 | ||||||||
\(262\) | 30.9844 | 1.91422 | ||||||||
\(263\) | −8.62048 | −0.531562 | −0.265781 | − | 0.964033i | \(-0.585630\pi\) | ||||
−0.265781 | + | 0.964033i | \(0.585630\pi\) | |||||||
\(264\) | 41.0746 | 2.52797 | ||||||||
\(265\) | −34.6791 | −2.13032 | ||||||||
\(266\) | −8.38535 | −0.514139 | ||||||||
\(267\) | 6.73000 | 0.411870 | ||||||||
\(268\) | 82.7446 | 5.05443 | ||||||||
\(269\) | 2.08517 | 0.127135 | 0.0635674 | − | 0.997978i | \(-0.479752\pi\) | ||||
0.0635674 | + | 0.997978i | \(0.479752\pi\) | |||||||
\(270\) | 64.3437 | 3.91583 | ||||||||
\(271\) | 0.910909 | 0.0553338 | 0.0276669 | − | 0.999617i | \(-0.491192\pi\) | ||||
0.0276669 | + | 0.999617i | \(0.491192\pi\) | |||||||
\(272\) | 49.1661 | 2.98113 | ||||||||
\(273\) | 7.70780 | 0.466497 | ||||||||
\(274\) | −41.7617 | −2.52291 | ||||||||
\(275\) | −29.5771 | −1.78357 | ||||||||
\(276\) | 36.7182 | 2.21018 | ||||||||
\(277\) | −27.9806 | −1.68119 | −0.840595 | − | 0.541664i | \(-0.817794\pi\) | ||||
−0.840595 | + | 0.541664i | \(0.817794\pi\) | |||||||
\(278\) | −2.49124 | −0.149415 | ||||||||
\(279\) | 0.926906 | 0.0554924 | ||||||||
\(280\) | 141.667 | 8.46621 | ||||||||
\(281\) | 8.36709 | 0.499139 | 0.249569 | − | 0.968357i | \(-0.419711\pi\) | ||||
0.249569 | + | 0.968357i | \(0.419711\pi\) | |||||||
\(282\) | 19.2533 | 1.14652 | ||||||||
\(283\) | 2.03596 | 0.121025 | 0.0605126 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605126 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(284\) | −74.8516 | −4.44162 | ||||||||
\(285\) | −6.22303 | −0.368620 | ||||||||
\(286\) | −10.3583 | −0.612500 | ||||||||
\(287\) | −24.1582 | −1.42601 | ||||||||
\(288\) | 14.7309 | 0.868026 | ||||||||
\(289\) | −9.88890 | −0.581700 | ||||||||
\(290\) | 47.4347 | 2.78546 | ||||||||
\(291\) | −14.0790 | −0.825326 | ||||||||
\(292\) | −7.61200 | −0.445458 | ||||||||
\(293\) | 19.1136 | 1.11663 | 0.558315 | − | 0.829629i | \(-0.311448\pi\) | ||||
0.558315 | + | 0.829629i | \(0.311448\pi\) | |||||||
\(294\) | −13.5006 | −0.787374 | ||||||||
\(295\) | −43.1797 | −2.51402 | ||||||||
\(296\) | −65.5264 | −3.80864 | ||||||||
\(297\) | 13.3239 | 0.773133 | ||||||||
\(298\) | −67.1966 | −3.89260 | ||||||||
\(299\) | −6.08923 | −0.352149 | ||||||||
\(300\) | 113.597 | 6.55853 | ||||||||
\(301\) | 32.6123 | 1.87974 | ||||||||
\(302\) | 45.5599 | 2.62168 | ||||||||
\(303\) | −3.30429 | −0.189826 | ||||||||
\(304\) | −17.4222 | −0.999232 | ||||||||
\(305\) | −25.0216 | −1.43273 | ||||||||
\(306\) | 3.65251 | 0.208800 | ||||||||
\(307\) | −7.56381 | −0.431690 | −0.215845 | − | 0.976428i | \(-0.569251\pi\) | ||||
−0.215845 | + | 0.976428i | \(0.569251\pi\) | |||||||
\(308\) | 44.6097 | 2.54188 | ||||||||
\(309\) | 14.5190 | 0.825955 | ||||||||
\(310\) | 22.0536 | 1.25256 | ||||||||
\(311\) | 13.6171 | 0.772156 | 0.386078 | − | 0.922466i | \(-0.373830\pi\) | ||||
0.386078 | + | 0.922466i | \(0.373830\pi\) | |||||||
\(312\) | 26.1617 | 1.48111 | ||||||||
\(313\) | −5.07688 | −0.286962 | −0.143481 | − | 0.989653i | \(-0.545830\pi\) | ||||
−0.143481 | + | 0.989653i | \(0.545830\pi\) | |||||||
\(314\) | 14.9311 | 0.842610 | ||||||||
\(315\) | 6.44229 | 0.362982 | ||||||||
\(316\) | −49.9089 | −2.80759 | ||||||||
\(317\) | −19.3200 | −1.08512 | −0.542561 | − | 0.840017i | \(-0.682545\pi\) | ||||
−0.542561 | + | 0.840017i | \(0.682545\pi\) | |||||||
\(318\) | 37.0242 | 2.07621 | ||||||||
\(319\) | 9.82252 | 0.549956 | ||||||||
\(320\) | 197.234 | 11.0257 | ||||||||
\(321\) | −13.1357 | −0.733164 | ||||||||
\(322\) | 35.2033 | 1.96180 | ||||||||
\(323\) | −2.51985 | −0.140208 | ||||||||
\(324\) | −42.6019 | −2.36677 | ||||||||
\(325\) | −18.8386 | −1.04498 | ||||||||
\(326\) | 38.1417 | 2.11247 | ||||||||
\(327\) | −15.2735 | −0.844624 | ||||||||
\(328\) | −81.9973 | −4.52755 | ||||||||
\(329\) | 13.7508 | 0.758104 | ||||||||
\(330\) | 44.4417 | 2.44643 | ||||||||
\(331\) | −25.4491 | −1.39881 | −0.699404 | − | 0.714726i | \(-0.746551\pi\) | ||||
−0.699404 | + | 0.714726i | \(0.746551\pi\) | |||||||
\(332\) | 12.7821 | 0.701510 | ||||||||
\(333\) | −2.97981 | −0.163293 | ||||||||
\(334\) | −17.3001 | −0.946618 | ||||||||
\(335\) | 58.8737 | 3.21662 | ||||||||
\(336\) | −92.5833 | −5.05083 | ||||||||
\(337\) | −31.1263 | −1.69556 | −0.847778 | − | 0.530352i | \(-0.822060\pi\) | ||||
−0.847778 | + | 0.530352i | \(0.822060\pi\) | |||||||
\(338\) | 29.8053 | 1.62119 | ||||||||
\(339\) | 2.16784 | 0.117741 | ||||||||
\(340\) | 64.7375 | 3.51088 | ||||||||
\(341\) | 4.56675 | 0.247303 | ||||||||
\(342\) | −1.29428 | −0.0699868 | ||||||||
\(343\) | 12.5409 | 0.677145 | ||||||||
\(344\) | 110.692 | 5.96811 | ||||||||
\(345\) | 26.1254 | 1.40655 | ||||||||
\(346\) | −55.6752 | −2.99312 | ||||||||
\(347\) | −2.83749 | −0.152324 | −0.0761622 | − | 0.997095i | \(-0.524267\pi\) | ||||
−0.0761622 | + | 0.997095i | \(0.524267\pi\) | |||||||
\(348\) | −37.7254 | −2.02230 | ||||||||
\(349\) | 34.0585 | 1.82311 | 0.911554 | − | 0.411181i | \(-0.134883\pi\) | ||||
0.911554 | + | 0.411181i | \(0.134883\pi\) | |||||||
\(350\) | 108.910 | 5.82149 | ||||||||
\(351\) | 8.48642 | 0.452972 | ||||||||
\(352\) | 72.5771 | 3.86837 | ||||||||
\(353\) | 20.2474 | 1.07766 | 0.538831 | − | 0.842414i | \(-0.318866\pi\) | ||||
0.538831 | + | 0.842414i | \(0.318866\pi\) | |||||||
\(354\) | 46.0996 | 2.45017 | ||||||||
\(355\) | −53.2577 | −2.82663 | ||||||||
\(356\) | 24.8089 | 1.31487 | ||||||||
\(357\) | −13.3907 | −0.708712 | ||||||||
\(358\) | 66.4412 | 3.51153 | ||||||||
\(359\) | −17.8457 | −0.941857 | −0.470929 | − | 0.882171i | \(-0.656081\pi\) | ||||
−0.470929 | + | 0.882171i | \(0.656081\pi\) | |||||||
\(360\) | 21.8663 | 1.15246 | ||||||||
\(361\) | −18.1071 | −0.953004 | ||||||||
\(362\) | 47.8796 | 2.51650 | ||||||||
\(363\) | −8.22753 | −0.431834 | ||||||||
\(364\) | 28.4133 | 1.48926 | ||||||||
\(365\) | −5.41602 | −0.283488 | ||||||||
\(366\) | 26.7136 | 1.39634 | ||||||||
\(367\) | 0.0381163 | 0.00198966 | 0.000994828 | − | 1.00000i | \(-0.499683\pi\) | ||||
0.000994828 | 1.00000i | \(0.499683\pi\) | ||||||||
\(368\) | 73.1416 | 3.81277 | ||||||||
\(369\) | −3.72883 | −0.194115 | ||||||||
\(370\) | −70.8978 | −3.68580 | ||||||||
\(371\) | 26.4428 | 1.37284 | ||||||||
\(372\) | −17.5395 | −0.909383 | ||||||||
\(373\) | −21.3659 | −1.10629 | −0.553143 | − | 0.833087i | \(-0.686572\pi\) | ||||
−0.553143 | + | 0.833087i | \(0.686572\pi\) | |||||||
\(374\) | 17.9954 | 0.930522 | ||||||||
\(375\) | 47.8975 | 2.47342 | ||||||||
\(376\) | 46.6726 | 2.40695 | ||||||||
\(377\) | 6.25627 | 0.322214 | ||||||||
\(378\) | −49.0620 | −2.52348 | ||||||||
\(379\) | 18.1989 | 0.934813 | 0.467407 | − | 0.884043i | \(-0.345188\pi\) | ||||
0.467407 | + | 0.884043i | \(0.345188\pi\) | |||||||
\(380\) | −22.9400 | −1.17680 | ||||||||
\(381\) | 5.61909 | 0.287875 | ||||||||
\(382\) | 50.6446 | 2.59121 | ||||||||
\(383\) | −2.63328 | −0.134554 | −0.0672771 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672771 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(384\) | −115.130 | −5.87520 | ||||||||
\(385\) | 31.7403 | 1.61764 | ||||||||
\(386\) | −3.99695 | −0.203439 | ||||||||
\(387\) | 5.03371 | 0.255878 | ||||||||
\(388\) | −51.8995 | −2.63480 | ||||||||
\(389\) | −16.4654 | −0.834828 | −0.417414 | − | 0.908716i | \(-0.637064\pi\) | ||||
−0.417414 | + | 0.908716i | \(0.637064\pi\) | |||||||
\(390\) | 28.3063 | 1.43334 | ||||||||
\(391\) | 10.5788 | 0.534992 | ||||||||
\(392\) | −32.7274 | −1.65298 | ||||||||
\(393\) | −17.5333 | −0.884436 | ||||||||
\(394\) | −3.33291 | −0.167909 | ||||||||
\(395\) | −35.5107 | −1.78674 | ||||||||
\(396\) | 6.88553 | 0.346011 | ||||||||
\(397\) | −16.0457 | −0.805312 | −0.402656 | − | 0.915351i | \(-0.631913\pi\) | ||||
−0.402656 | + | 0.915351i | \(0.631913\pi\) | |||||||
\(398\) | −40.9198 | −2.05112 | ||||||||
\(399\) | 4.74506 | 0.237550 | ||||||||
\(400\) | 226.282 | 11.3141 | ||||||||
\(401\) | 36.5715 | 1.82629 | 0.913147 | − | 0.407631i | \(-0.133645\pi\) | ||||
0.913147 | + | 0.407631i | \(0.133645\pi\) | |||||||
\(402\) | −62.8550 | −3.13492 | ||||||||
\(403\) | 2.90870 | 0.144893 | ||||||||
\(404\) | −12.1806 | −0.606008 | ||||||||
\(405\) | −30.3117 | −1.50620 | ||||||||
\(406\) | −36.1689 | −1.79503 | ||||||||
\(407\) | −14.6811 | −0.727717 | ||||||||
\(408\) | −45.4505 | −2.25014 | ||||||||
\(409\) | −26.9493 | −1.33255 | −0.666277 | − | 0.745704i | \(-0.732113\pi\) | ||||
−0.666277 | + | 0.745704i | \(0.732113\pi\) | |||||||
\(410\) | −88.7190 | −4.38152 | ||||||||
\(411\) | 23.6318 | 1.16567 | ||||||||
\(412\) | 53.5213 | 2.63681 | ||||||||
\(413\) | 32.9245 | 1.62011 | ||||||||
\(414\) | 5.43363 | 0.267049 | ||||||||
\(415\) | 9.09463 | 0.446438 | ||||||||
\(416\) | 46.2266 | 2.26645 | ||||||||
\(417\) | 1.40973 | 0.0690346 | ||||||||
\(418\) | −6.37676 | −0.311897 | ||||||||
\(419\) | −24.2233 | −1.18338 | −0.591692 | − | 0.806164i | \(-0.701540\pi\) | ||||
−0.591692 | + | 0.806164i | \(0.701540\pi\) | |||||||
\(420\) | −121.905 | −5.94837 | ||||||||
\(421\) | −31.2057 | −1.52087 | −0.760437 | − | 0.649412i | \(-0.775015\pi\) | ||||
−0.760437 | + | 0.649412i | \(0.775015\pi\) | |||||||
\(422\) | −11.4889 | −0.559272 | ||||||||
\(423\) | 2.12243 | 0.103196 | ||||||||
\(424\) | 89.7516 | 4.35872 | ||||||||
\(425\) | 32.7281 | 1.58755 | ||||||||
\(426\) | 56.8592 | 2.75484 | ||||||||
\(427\) | 19.0789 | 0.923293 | ||||||||
\(428\) | −48.4222 | −2.34058 | ||||||||
\(429\) | 5.86150 | 0.282996 | ||||||||
\(430\) | 119.766 | 5.77562 | ||||||||
\(431\) | −7.63410 | −0.367722 | −0.183861 | − | 0.982952i | \(-0.558860\pi\) | ||||
−0.183861 | + | 0.982952i | \(0.558860\pi\) | |||||||
\(432\) | −101.936 | −4.90439 | ||||||||
\(433\) | 14.3854 | 0.691319 | 0.345659 | − | 0.938360i | \(-0.387655\pi\) | ||||
0.345659 | + | 0.938360i | \(0.387655\pi\) | |||||||
\(434\) | −16.8159 | −0.807188 | ||||||||
\(435\) | −26.8421 | −1.28698 | ||||||||
\(436\) | −56.3026 | −2.69641 | ||||||||
\(437\) | −3.74863 | −0.179321 | ||||||||
\(438\) | 5.78228 | 0.276288 | ||||||||
\(439\) | −16.0142 | −0.764314 | −0.382157 | − | 0.924097i | \(-0.624819\pi\) | ||||
−0.382157 | + | 0.924097i | \(0.624819\pi\) | |||||||
\(440\) | 107.732 | 5.13595 | ||||||||
\(441\) | −1.48828 | −0.0708703 | ||||||||
\(442\) | 11.4619 | 0.545185 | ||||||||
\(443\) | −25.3818 | −1.20593 | −0.602963 | − | 0.797769i | \(-0.706013\pi\) | ||||
−0.602963 | + | 0.797769i | \(0.706013\pi\) | |||||||
\(444\) | 56.3860 | 2.67596 | ||||||||
\(445\) | 17.6518 | 0.836775 | ||||||||
\(446\) | −6.86099 | −0.324877 | ||||||||
\(447\) | 38.0248 | 1.79851 | ||||||||
\(448\) | −150.391 | −7.10530 | ||||||||
\(449\) | −18.6471 | −0.880012 | −0.440006 | − | 0.897995i | \(-0.645024\pi\) | ||||
−0.440006 | + | 0.897995i | \(0.645024\pi\) | |||||||
\(450\) | 16.8103 | 0.792446 | ||||||||
\(451\) | −18.3714 | −0.865077 | ||||||||
\(452\) | 7.99134 | 0.375881 | ||||||||
\(453\) | −25.7812 | −1.21131 | ||||||||
\(454\) | −28.1200 | −1.31974 | ||||||||
\(455\) | 20.2164 | 0.947759 | ||||||||
\(456\) | 16.1056 | 0.754213 | ||||||||
\(457\) | −8.02070 | −0.375193 | −0.187596 | − | 0.982246i | \(-0.560070\pi\) | ||||
−0.187596 | + | 0.982246i | \(0.560070\pi\) | |||||||
\(458\) | −39.9309 | −1.86585 | ||||||||
\(459\) | −14.7434 | −0.688163 | ||||||||
\(460\) | 96.3063 | 4.49030 | ||||||||
\(461\) | −37.1778 | −1.73154 | −0.865772 | − | 0.500439i | \(-0.833172\pi\) | ||||
−0.865772 | + | 0.500439i | \(0.833172\pi\) | |||||||
\(462\) | −33.8867 | −1.57655 | ||||||||
\(463\) | 29.2413 | 1.35896 | 0.679480 | − | 0.733694i | \(-0.262205\pi\) | ||||
0.679480 | + | 0.733694i | \(0.262205\pi\) | |||||||
\(464\) | −75.1480 | −3.48866 | ||||||||
\(465\) | −12.4796 | −0.578727 | ||||||||
\(466\) | −78.7958 | −3.65015 | ||||||||
\(467\) | −7.67520 | −0.355166 | −0.177583 | − | 0.984106i | \(-0.556828\pi\) | ||||
−0.177583 | + | 0.984106i | \(0.556828\pi\) | |||||||
\(468\) | 4.38560 | 0.202725 | ||||||||
\(469\) | −44.8912 | −2.07288 | ||||||||
\(470\) | 50.4985 | 2.32932 | ||||||||
\(471\) | −8.44912 | −0.389315 | ||||||||
\(472\) | 111.752 | 5.14379 | ||||||||
\(473\) | 24.8004 | 1.14033 | ||||||||
\(474\) | 37.9121 | 1.74136 | ||||||||
\(475\) | −11.5973 | −0.532123 | ||||||||
\(476\) | −49.3623 | −2.26252 | ||||||||
\(477\) | 4.08145 | 0.186877 | ||||||||
\(478\) | −65.4805 | −2.99501 | ||||||||
\(479\) | −4.49479 | −0.205372 | −0.102686 | − | 0.994714i | \(-0.532744\pi\) | ||||
−0.102686 | + | 0.994714i | \(0.532744\pi\) | |||||||
\(480\) | −198.332 | −9.05258 | ||||||||
\(481\) | −9.35086 | −0.426363 | ||||||||
\(482\) | 34.7866 | 1.58448 | ||||||||
\(483\) | −19.9206 | −0.906420 | ||||||||
\(484\) | −30.3292 | −1.37860 | ||||||||
\(485\) | −36.9271 | −1.67677 | ||||||||
\(486\) | −14.0839 | −0.638857 | ||||||||
\(487\) | 4.45775 | 0.202000 | 0.101000 | − | 0.994886i | \(-0.467796\pi\) | ||||
0.101000 | + | 0.994886i | \(0.467796\pi\) | |||||||
\(488\) | 64.7573 | 2.93143 | ||||||||
\(489\) | −21.5834 | −0.976035 | ||||||||
\(490\) | −35.4102 | −1.59967 | ||||||||
\(491\) | 22.4757 | 1.01431 | 0.507157 | − | 0.861854i | \(-0.330697\pi\) | ||||
0.507157 | + | 0.861854i | \(0.330697\pi\) | |||||||
\(492\) | 70.5593 | 3.18106 | ||||||||
\(493\) | −10.8690 | −0.489514 | ||||||||
\(494\) | −4.06155 | −0.182738 | ||||||||
\(495\) | 4.89913 | 0.220200 | ||||||||
\(496\) | −34.9383 | −1.56877 | ||||||||
\(497\) | 40.6090 | 1.82156 | ||||||||
\(498\) | −9.70965 | −0.435100 | ||||||||
\(499\) | −11.5710 | −0.517988 | −0.258994 | − | 0.965879i | \(-0.583391\pi\) | ||||
−0.258994 | + | 0.965879i | \(0.583391\pi\) | |||||||
\(500\) | 176.565 | 7.89622 | ||||||||
\(501\) | 9.78967 | 0.437370 | ||||||||
\(502\) | 12.9278 | 0.576994 | ||||||||
\(503\) | 31.2981 | 1.39551 | 0.697756 | − | 0.716336i | \(-0.254182\pi\) | ||||
0.697756 | + | 0.716336i | \(0.254182\pi\) | |||||||
\(504\) | −16.6731 | −0.742677 | ||||||||
\(505\) | −8.66664 | −0.385661 | ||||||||
\(506\) | 26.7708 | 1.19011 | ||||||||
\(507\) | −16.8660 | −0.749047 | ||||||||
\(508\) | 20.7137 | 0.919022 | ||||||||
\(509\) | 15.9515 | 0.707039 | 0.353520 | − | 0.935427i | \(-0.384985\pi\) | ||||
0.353520 | + | 0.935427i | \(0.384985\pi\) | |||||||
\(510\) | −49.1763 | −2.17756 | ||||||||
\(511\) | 4.12971 | 0.182688 | ||||||||
\(512\) | −158.626 | −7.01036 | ||||||||
\(513\) | 5.22439 | 0.230662 | ||||||||
\(514\) | 69.2331 | 3.05374 | ||||||||
\(515\) | 38.0811 | 1.67805 | ||||||||
\(516\) | −95.2513 | −4.19320 | ||||||||
\(517\) | 10.4570 | 0.459896 | ||||||||
\(518\) | 54.0596 | 2.37524 | ||||||||
\(519\) | 31.5051 | 1.38292 | ||||||||
\(520\) | 68.6181 | 3.00910 | ||||||||
\(521\) | 11.8797 | 0.520458 | 0.260229 | − | 0.965547i | \(-0.416202\pi\) | ||||
0.260229 | + | 0.965547i | \(0.416202\pi\) | |||||||
\(522\) | −5.58269 | −0.244348 | ||||||||
\(523\) | −40.5952 | −1.77510 | −0.887552 | − | 0.460707i | \(-0.847596\pi\) | ||||
−0.887552 | + | 0.460707i | \(0.847596\pi\) | |||||||
\(524\) | −64.6329 | −2.82350 | ||||||||
\(525\) | −61.6295 | −2.68973 | ||||||||
\(526\) | 24.1392 | 1.05252 | ||||||||
\(527\) | −5.05327 | −0.220124 | ||||||||
\(528\) | −70.4063 | −3.06404 | ||||||||
\(529\) | −7.26254 | −0.315763 | ||||||||
\(530\) | 97.1089 | 4.21814 | ||||||||
\(531\) | 5.08190 | 0.220536 | ||||||||
\(532\) | 17.4917 | 0.758362 | ||||||||
\(533\) | −11.7013 | −0.506841 | ||||||||
\(534\) | −18.8455 | −0.815523 | ||||||||
\(535\) | −34.4530 | −1.48953 | ||||||||
\(536\) | −152.369 | −6.58133 | ||||||||
\(537\) | −37.5974 | −1.62245 | ||||||||
\(538\) | −5.83891 | −0.251734 | ||||||||
\(539\) | −7.33254 | −0.315835 | ||||||||
\(540\) | −134.220 | −5.77590 | ||||||||
\(541\) | −17.2817 | −0.742999 | −0.371500 | − | 0.928433i | \(-0.621156\pi\) | ||||
−0.371500 | + | 0.928433i | \(0.621156\pi\) | |||||||
\(542\) | −2.55074 | −0.109564 | ||||||||
\(543\) | −27.0938 | −1.16271 | ||||||||
\(544\) | −80.3092 | −3.44323 | ||||||||
\(545\) | −40.0600 | −1.71598 | ||||||||
\(546\) | −21.5835 | −0.923689 | ||||||||
\(547\) | 36.1947 | 1.54757 | 0.773786 | − | 0.633447i | \(-0.218361\pi\) | ||||
0.773786 | + | 0.633447i | \(0.218361\pi\) | |||||||
\(548\) | 87.1142 | 3.72133 | ||||||||
\(549\) | 2.94484 | 0.125683 | ||||||||
\(550\) | 82.8223 | 3.53155 | ||||||||
\(551\) | 3.85147 | 0.164078 | ||||||||
\(552\) | −67.6142 | −2.87785 | ||||||||
\(553\) | 27.0769 | 1.15143 | ||||||||
\(554\) | 78.3516 | 3.32884 | ||||||||
\(555\) | 40.1193 | 1.70297 | ||||||||
\(556\) | 5.19669 | 0.220389 | ||||||||
\(557\) | −33.0969 | −1.40236 | −0.701180 | − | 0.712985i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712985i | \(0.747343\pi\) | |||||||
\(558\) | −2.59554 | −0.109878 | ||||||||
\(559\) | 15.7962 | 0.668107 | ||||||||
\(560\) | −242.832 | −10.2615 | ||||||||
\(561\) | −10.1832 | −0.429933 | ||||||||
\(562\) | −23.4297 | −0.988321 | ||||||||
\(563\) | −3.67137 | −0.154730 | −0.0773648 | − | 0.997003i | \(-0.524651\pi\) | ||||
−0.0773648 | + | 0.997003i | \(0.524651\pi\) | |||||||
\(564\) | −40.1621 | −1.69113 | ||||||||
\(565\) | 5.68593 | 0.239209 | ||||||||
\(566\) | −5.70113 | −0.239636 | ||||||||
\(567\) | 23.1127 | 0.970640 | ||||||||
\(568\) | 137.834 | 5.78340 | ||||||||
\(569\) | 33.9810 | 1.42456 | 0.712279 | − | 0.701896i | \(-0.247663\pi\) | ||||
0.712279 | + | 0.701896i | \(0.247663\pi\) | |||||||
\(570\) | 17.4258 | 0.729887 | ||||||||
\(571\) | 31.7629 | 1.32923 | 0.664617 | − | 0.747184i | \(-0.268595\pi\) | ||||
0.664617 | + | 0.747184i | \(0.268595\pi\) | |||||||
\(572\) | 21.6073 | 0.903446 | ||||||||
\(573\) | −28.6585 | −1.19723 | ||||||||
\(574\) | 67.6482 | 2.82358 | ||||||||
\(575\) | 48.6878 | 2.03042 | ||||||||
\(576\) | −23.2129 | −0.967203 | ||||||||
\(577\) | 5.10203 | 0.212400 | 0.106200 | − | 0.994345i | \(-0.466132\pi\) | ||||
0.106200 | + | 0.994345i | \(0.466132\pi\) | |||||||
\(578\) | 27.6911 | 1.15180 | ||||||||
\(579\) | 2.26177 | 0.0939960 | ||||||||
\(580\) | −98.9481 | −4.10860 | ||||||||
\(581\) | −6.93465 | −0.287698 | ||||||||
\(582\) | 39.4242 | 1.63419 | ||||||||
\(583\) | 20.1088 | 0.832821 | ||||||||
\(584\) | 14.0170 | 0.580028 | ||||||||
\(585\) | 3.12041 | 0.129013 | ||||||||
\(586\) | −53.5223 | −2.21099 | ||||||||
\(587\) | 0.917702 | 0.0378776 | 0.0189388 | − | 0.999821i | \(-0.493971\pi\) | ||||
0.0189388 | + | 0.999821i | \(0.493971\pi\) | |||||||
\(588\) | 28.1621 | 1.16139 | ||||||||
\(589\) | 1.79065 | 0.0737823 | ||||||||
\(590\) | 120.912 | 4.97788 | ||||||||
\(591\) | 1.88601 | 0.0775800 | ||||||||
\(592\) | 112.319 | 4.61629 | ||||||||
\(593\) | −28.4587 | −1.16866 | −0.584329 | − | 0.811517i | \(-0.698642\pi\) | ||||
−0.584329 | + | 0.811517i | \(0.698642\pi\) | |||||||
\(594\) | −37.3099 | −1.53084 | ||||||||
\(595\) | −35.1218 | −1.43985 | ||||||||
\(596\) | 140.171 | 5.74163 | ||||||||
\(597\) | 23.1554 | 0.947689 | ||||||||
\(598\) | 17.0512 | 0.697273 | ||||||||
\(599\) | −42.1401 | −1.72180 | −0.860899 | − | 0.508776i | \(-0.830098\pi\) | ||||
−0.860899 | + | 0.508776i | \(0.830098\pi\) | |||||||
\(600\) | −209.182 | −8.53980 | ||||||||
\(601\) | −7.85375 | −0.320361 | −0.160181 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160181 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(602\) | −91.3214 | −3.72198 | ||||||||
\(603\) | −6.92897 | −0.282169 | ||||||||
\(604\) | −95.0374 | −3.86702 | ||||||||
\(605\) | −21.5796 | −0.877335 | ||||||||
\(606\) | 9.25271 | 0.375866 | ||||||||
\(607\) | −20.9818 | −0.851627 | −0.425813 | − | 0.904811i | \(-0.640012\pi\) | ||||
−0.425813 | + | 0.904811i | \(0.640012\pi\) | |||||||
\(608\) | 28.4579 | 1.15412 | ||||||||
\(609\) | 20.4671 | 0.829368 | ||||||||
\(610\) | 70.0657 | 2.83688 | ||||||||
\(611\) | 6.66036 | 0.269449 | ||||||||
\(612\) | −7.61908 | −0.307983 | ||||||||
\(613\) | −21.3216 | −0.861170 | −0.430585 | − | 0.902550i | \(-0.641693\pi\) | ||||
−0.430585 | + | 0.902550i | \(0.641693\pi\) | |||||||
\(614\) | 21.1803 | 0.854768 | ||||||||
\(615\) | 50.2038 | 2.02441 | ||||||||
\(616\) | −82.1460 | −3.30976 | ||||||||
\(617\) | 26.3587 | 1.06116 | 0.530580 | − | 0.847635i | \(-0.321974\pi\) | ||||
0.530580 | + | 0.847635i | \(0.321974\pi\) | |||||||
\(618\) | −40.6562 | −1.63543 | ||||||||
\(619\) | 48.1962 | 1.93717 | 0.968585 | − | 0.248683i | \(-0.0799976\pi\) | ||||
0.968585 | + | 0.248683i | \(0.0799976\pi\) | |||||||
\(620\) | −46.0036 | −1.84755 | ||||||||
\(621\) | −21.9329 | −0.880139 | ||||||||
\(622\) | −38.1308 | −1.52891 | ||||||||
\(623\) | −13.4595 | −0.539242 | ||||||||
\(624\) | −44.8439 | −1.79519 | ||||||||
\(625\) | 64.2627 | 2.57051 | ||||||||
\(626\) | 14.2164 | 0.568200 | ||||||||
\(627\) | 3.60844 | 0.144107 | ||||||||
\(628\) | −31.1460 | −1.24286 | ||||||||
\(629\) | 16.2452 | 0.647739 | ||||||||
\(630\) | −18.0398 | −0.718723 | ||||||||
\(631\) | −24.4686 | −0.974078 | −0.487039 | − | 0.873380i | \(-0.661923\pi\) | ||||
−0.487039 | + | 0.873380i | \(0.661923\pi\) | |||||||
\(632\) | 91.9040 | 3.65575 | ||||||||
\(633\) | 6.50129 | 0.258403 | ||||||||
\(634\) | 54.1003 | 2.14860 | ||||||||
\(635\) | 14.7380 | 0.584861 | ||||||||
\(636\) | −77.2320 | −3.06245 | ||||||||
\(637\) | −4.67032 | −0.185045 | ||||||||
\(638\) | −27.5052 | −1.08894 | ||||||||
\(639\) | 6.26801 | 0.247959 | ||||||||
\(640\) | −301.968 | −11.9364 | ||||||||
\(641\) | 25.0756 | 0.990425 | 0.495213 | − | 0.868772i | \(-0.335090\pi\) | ||||
0.495213 | + | 0.868772i | \(0.335090\pi\) | |||||||
\(642\) | 36.7828 | 1.45170 | ||||||||
\(643\) | −26.4733 | −1.04400 | −0.522002 | − | 0.852944i | \(-0.674815\pi\) | ||||
−0.522002 | + | 0.852944i | \(0.674815\pi\) | |||||||
\(644\) | −73.4335 | −2.89368 | ||||||||
\(645\) | −67.7724 | −2.66854 | ||||||||
\(646\) | 7.05611 | 0.277619 | ||||||||
\(647\) | 40.1364 | 1.57792 | 0.788961 | − | 0.614443i | \(-0.210619\pi\) | ||||
0.788961 | + | 0.614443i | \(0.210619\pi\) | |||||||
\(648\) | 78.4486 | 3.08175 | ||||||||
\(649\) | 25.0379 | 0.982823 | ||||||||
\(650\) | 52.7520 | 2.06911 | ||||||||
\(651\) | 9.51568 | 0.372949 | ||||||||
\(652\) | −79.5630 | −3.11593 | ||||||||
\(653\) | −38.5453 | −1.50840 | −0.754198 | − | 0.656647i | \(-0.771974\pi\) | ||||
−0.754198 | + | 0.656647i | \(0.771974\pi\) | |||||||
\(654\) | 42.7690 | 1.67240 | ||||||||
\(655\) | −45.9871 | −1.79686 | ||||||||
\(656\) | 140.552 | 5.48764 | ||||||||
\(657\) | 0.637423 | 0.0248682 | ||||||||
\(658\) | −38.5051 | −1.50108 | ||||||||
\(659\) | 9.13115 | 0.355699 | 0.177850 | − | 0.984058i | \(-0.443086\pi\) | ||||
0.177850 | + | 0.984058i | \(0.443086\pi\) | |||||||
\(660\) | −92.7046 | −3.60852 | ||||||||
\(661\) | 45.4593 | 1.76816 | 0.884082 | − | 0.467333i | \(-0.154785\pi\) | ||||
0.884082 | + | 0.467333i | \(0.154785\pi\) | |||||||
\(662\) | 71.2629 | 2.76971 | ||||||||
\(663\) | −6.48597 | −0.251894 | ||||||||
\(664\) | −23.5375 | −0.913431 | ||||||||
\(665\) | 12.4456 | 0.482618 | ||||||||
\(666\) | 8.34411 | 0.323328 | ||||||||
\(667\) | −16.1692 | −0.626073 | ||||||||
\(668\) | 36.0877 | 1.39628 | ||||||||
\(669\) | 3.88245 | 0.150104 | ||||||||
\(670\) | −164.859 | −6.36907 | ||||||||
\(671\) | 14.5088 | 0.560107 | ||||||||
\(672\) | 151.228 | 5.83375 | ||||||||
\(673\) | 27.5067 | 1.06031 | 0.530153 | − | 0.847902i | \(-0.322135\pi\) | ||||
0.530153 | + | 0.847902i | \(0.322135\pi\) | |||||||
\(674\) | 87.1602 | 3.35729 | ||||||||
\(675\) | −67.8551 | −2.61174 | ||||||||
\(676\) | −62.1734 | −2.39128 | ||||||||
\(677\) | 35.9310 | 1.38094 | 0.690470 | − | 0.723361i | \(-0.257404\pi\) | ||||
0.690470 | + | 0.723361i | \(0.257404\pi\) | |||||||
\(678\) | −6.07043 | −0.233134 | ||||||||
\(679\) | 28.1569 | 1.08056 | ||||||||
\(680\) | −119.210 | −4.57149 | ||||||||
\(681\) | 15.9124 | 0.609764 | ||||||||
\(682\) | −12.7879 | −0.489673 | ||||||||
\(683\) | −34.6240 | −1.32485 | −0.662426 | − | 0.749128i | \(-0.730473\pi\) | ||||
−0.662426 | + | 0.749128i | \(0.730473\pi\) | |||||||
\(684\) | 2.69985 | 0.103231 | ||||||||
\(685\) | 61.9828 | 2.36824 | ||||||||
\(686\) | −35.1172 | −1.34078 | ||||||||
\(687\) | 22.5959 | 0.862086 | ||||||||
\(688\) | −189.738 | −7.23369 | ||||||||
\(689\) | 12.8079 | 0.487942 | ||||||||
\(690\) | −73.1568 | −2.78503 | ||||||||
\(691\) | −39.9579 | −1.52007 | −0.760034 | − | 0.649883i | \(-0.774818\pi\) | ||||
−0.760034 | + | 0.649883i | \(0.774818\pi\) | |||||||
\(692\) | 116.138 | 4.41489 | ||||||||
\(693\) | −3.73558 | −0.141903 | ||||||||
\(694\) | 7.94558 | 0.301610 | ||||||||
\(695\) | 3.69750 | 0.140254 | ||||||||
\(696\) | 69.4690 | 2.63322 | ||||||||
\(697\) | 20.3287 | 0.770003 | ||||||||
\(698\) | −95.3710 | −3.60985 | ||||||||
\(699\) | 44.5885 | 1.68649 | ||||||||
\(700\) | −227.185 | −8.58679 | ||||||||
\(701\) | 14.7487 | 0.557051 | 0.278525 | − | 0.960429i | \(-0.410154\pi\) | ||||
0.278525 | + | 0.960429i | \(0.410154\pi\) | |||||||
\(702\) | −23.7638 | −0.896907 | ||||||||
\(703\) | −5.75655 | −0.217113 | ||||||||
\(704\) | −114.367 | −4.31036 | ||||||||
\(705\) | −28.5758 | −1.07623 | ||||||||
\(706\) | −56.6971 | −2.13383 | ||||||||
\(707\) | 6.60831 | 0.248531 | ||||||||
\(708\) | −96.1632 | −3.61403 | ||||||||
\(709\) | −21.6850 | −0.814398 | −0.407199 | − | 0.913340i | \(-0.633494\pi\) | ||||
−0.407199 | + | 0.913340i | \(0.633494\pi\) | |||||||
\(710\) | 149.133 | 5.59687 | ||||||||
\(711\) | 4.17933 | 0.156737 | ||||||||
\(712\) | −45.6839 | −1.71208 | ||||||||
\(713\) | −7.51746 | −0.281531 | ||||||||
\(714\) | 37.4969 | 1.40329 | ||||||||
\(715\) | 15.3738 | 0.574949 | ||||||||
\(716\) | −138.595 | −5.17955 | ||||||||
\(717\) | 37.0537 | 1.38380 | ||||||||
\(718\) | 49.9717 | 1.86493 | ||||||||
\(719\) | −12.8348 | −0.478659 | −0.239329 | − | 0.970938i | \(-0.576928\pi\) | ||||
−0.239329 | + | 0.970938i | \(0.576928\pi\) | |||||||
\(720\) | −37.4812 | −1.39684 | ||||||||
\(721\) | −29.0368 | −1.08139 | ||||||||
\(722\) | 50.7037 | 1.88700 | ||||||||
\(723\) | −19.6848 | −0.732086 | ||||||||
\(724\) | −99.8762 | −3.71187 | ||||||||
\(725\) | −50.0234 | −1.85782 | ||||||||
\(726\) | 23.0389 | 0.855053 | ||||||||
\(727\) | 4.45180 | 0.165108 | 0.0825541 | − | 0.996587i | \(-0.473692\pi\) | ||||
0.0825541 | + | 0.996587i | \(0.473692\pi\) | |||||||
\(728\) | −52.3213 | −1.93916 | ||||||||
\(729\) | 29.8497 | 1.10554 | ||||||||
\(730\) | 15.1660 | 0.561320 | ||||||||
\(731\) | −27.4426 | −1.01500 | ||||||||
\(732\) | −55.7242 | −2.05962 | ||||||||
\(733\) | 39.0592 | 1.44269 | 0.721343 | − | 0.692578i | \(-0.243525\pi\) | ||||
0.721343 | + | 0.692578i | \(0.243525\pi\) | |||||||
\(734\) | −0.106734 | −0.00393962 | ||||||||
\(735\) | 20.0377 | 0.739101 | ||||||||
\(736\) | −119.472 | −4.40378 | ||||||||
\(737\) | −34.1381 | −1.25749 | ||||||||
\(738\) | 10.4415 | 0.384358 | ||||||||
\(739\) | −5.96033 | −0.219254 | −0.109627 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109627 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(740\) | 147.892 | 5.43661 | ||||||||
\(741\) | 2.29833 | 0.0844312 | ||||||||
\(742\) | −74.0455 | −2.71830 | ||||||||
\(743\) | −24.5069 | −0.899071 | −0.449536 | − | 0.893262i | \(-0.648411\pi\) | ||||
−0.449536 | + | 0.893262i | \(0.648411\pi\) | |||||||
\(744\) | 32.2979 | 1.18410 | ||||||||
\(745\) | 99.7334 | 3.65395 | ||||||||
\(746\) | 59.8292 | 2.19050 | ||||||||
\(747\) | −1.07037 | −0.0391626 | ||||||||
\(748\) | −37.5382 | −1.37253 | ||||||||
\(749\) | 26.2704 | 0.959899 | ||||||||
\(750\) | −134.123 | −4.89750 | ||||||||
\(751\) | −20.9152 | −0.763208 | −0.381604 | − | 0.924326i | \(-0.624628\pi\) | ||||
−0.381604 | + | 0.924326i | \(0.624628\pi\) | |||||||
\(752\) | −80.0018 | −2.91737 | ||||||||
\(753\) | −7.31549 | −0.266591 | ||||||||
\(754\) | −17.5189 | −0.638000 | ||||||||
\(755\) | −67.6202 | −2.46095 | ||||||||
\(756\) | 102.343 | 3.72216 | ||||||||
\(757\) | −52.5682 | −1.91062 | −0.955311 | − | 0.295602i | \(-0.904480\pi\) | ||||
−0.955311 | + | 0.295602i | \(0.904480\pi\) | |||||||
\(758\) | −50.9608 | −1.85098 | ||||||||
\(759\) | −15.1489 | −0.549871 | ||||||||
\(760\) | 42.2425 | 1.53230 | ||||||||
\(761\) | 12.9860 | 0.470743 | 0.235371 | − | 0.971905i | \(-0.424369\pi\) | ||||
0.235371 | + | 0.971905i | \(0.424369\pi\) | |||||||
\(762\) | −15.7347 | −0.570007 | ||||||||
\(763\) | 30.5457 | 1.10583 | ||||||||
\(764\) | −105.644 | −3.82206 | ||||||||
\(765\) | −5.42107 | −0.195999 | ||||||||
\(766\) | 7.37375 | 0.266424 | ||||||||
\(767\) | 15.9474 | 0.575827 | ||||||||
\(768\) | 171.992 | 6.20623 | ||||||||
\(769\) | −17.4010 | −0.627495 | −0.313747 | − | 0.949507i | \(-0.601584\pi\) | ||||
−0.313747 | + | 0.949507i | \(0.601584\pi\) | |||||||
\(770\) | −88.8798 | −3.20301 | ||||||||
\(771\) | −39.1772 | −1.41093 | ||||||||
\(772\) | 8.33758 | 0.300076 | ||||||||
\(773\) | 35.3180 | 1.27030 | 0.635151 | − | 0.772388i | \(-0.280938\pi\) | ||||
0.635151 | + | 0.772388i | \(0.280938\pi\) | |||||||
\(774\) | −14.0955 | −0.506652 | ||||||||
\(775\) | −23.2572 | −0.835422 | ||||||||
\(776\) | 95.5696 | 3.43075 | ||||||||
\(777\) | −30.5909 | −1.09744 | ||||||||
\(778\) | 46.1066 | 1.65300 | ||||||||
\(779\) | −7.20354 | −0.258094 | ||||||||
\(780\) | −59.0464 | −2.11420 | ||||||||
\(781\) | 30.8817 | 1.10503 | ||||||||
\(782\) | −29.6229 | −1.05931 | ||||||||
\(783\) | 22.5346 | 0.805321 | ||||||||
\(784\) | 56.0982 | 2.00351 | ||||||||
\(785\) | −22.1608 | −0.790951 | ||||||||
\(786\) | 49.0969 | 1.75123 | ||||||||
\(787\) | 45.9012 | 1.63620 | 0.818100 | − | 0.575076i | \(-0.195027\pi\) | ||||
0.818100 | + | 0.575076i | \(0.195027\pi\) | |||||||
\(788\) | 6.95240 | 0.247669 | ||||||||
\(789\) | −13.6598 | −0.486300 | ||||||||
\(790\) | 99.4377 | 3.53784 | ||||||||
\(791\) | −4.33552 | −0.154153 | ||||||||
\(792\) | −12.6793 | −0.450538 | ||||||||
\(793\) | 9.24112 | 0.328162 | ||||||||
\(794\) | 44.9315 | 1.59456 | ||||||||
\(795\) | −54.9514 | −1.94893 | ||||||||
\(796\) | 85.3580 | 3.02544 | ||||||||
\(797\) | −8.50110 | −0.301125 | −0.150562 | − | 0.988601i | \(-0.548108\pi\) | ||||
−0.150562 | + | 0.988601i | \(0.548108\pi\) | |||||||
\(798\) | −13.2872 | −0.470361 | ||||||||
\(799\) | −11.5710 | −0.409353 | ||||||||
\(800\) | −369.615 | −13.0679 | ||||||||
\(801\) | −2.07747 | −0.0734039 | ||||||||
\(802\) | −102.408 | −3.61615 | ||||||||
\(803\) | 3.14050 | 0.110826 | ||||||||
\(804\) | 131.115 | 4.62406 | ||||||||
\(805\) | −52.2488 | −1.84153 | ||||||||
\(806\) | −8.14499 | −0.286895 | ||||||||
\(807\) | 3.30409 | 0.116310 | ||||||||
\(808\) | 22.4298 | 0.789078 | ||||||||
\(809\) | −15.3275 | −0.538888 | −0.269444 | − | 0.963016i | \(-0.586840\pi\) | ||||
−0.269444 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(810\) | 84.8793 | 2.98236 | ||||||||
\(811\) | 13.9925 | 0.491342 | 0.245671 | − | 0.969353i | \(-0.420992\pi\) | ||||
0.245671 | + | 0.969353i | \(0.420992\pi\) | |||||||
\(812\) | 75.4479 | 2.64770 | ||||||||
\(813\) | 1.44340 | 0.0506222 | ||||||||
\(814\) | 41.1103 | 1.44092 | ||||||||
\(815\) | −56.6100 | −1.98296 | ||||||||
\(816\) | 77.9071 | 2.72729 | ||||||||
\(817\) | 9.72439 | 0.340213 | ||||||||
\(818\) | 75.4637 | 2.63853 | ||||||||
\(819\) | −2.37931 | −0.0831398 | ||||||||
\(820\) | 185.066 | 6.46280 | ||||||||
\(821\) | 35.9363 | 1.25418 | 0.627092 | − | 0.778945i | \(-0.284245\pi\) | ||||
0.627092 | + | 0.778945i | \(0.284245\pi\) | |||||||
\(822\) | −66.1743 | −2.30809 | ||||||||
\(823\) | 28.7272 | 1.00137 | 0.500684 | − | 0.865630i | \(-0.333082\pi\) | ||||
0.500684 | + | 0.865630i | \(0.333082\pi\) | |||||||
\(824\) | −98.5561 | −3.43337 | ||||||||
\(825\) | −46.8670 | −1.63170 | ||||||||
\(826\) | −92.1956 | −3.20790 | ||||||||
\(827\) | −10.6041 | −0.368741 | −0.184370 | − | 0.982857i | \(-0.559025\pi\) | ||||
−0.184370 | + | 0.982857i | \(0.559025\pi\) | |||||||
\(828\) | −11.3345 | −0.393900 | ||||||||
\(829\) | −8.66659 | −0.301003 | −0.150502 | − | 0.988610i | \(-0.548089\pi\) | ||||
−0.150502 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(830\) | −25.4669 | −0.883970 | ||||||||
\(831\) | −44.3372 | −1.53804 | ||||||||
\(832\) | −72.8437 | −2.52540 | ||||||||
\(833\) | 8.11372 | 0.281124 | ||||||||
\(834\) | −3.94754 | −0.136692 | ||||||||
\(835\) | 25.6768 | 0.888583 | ||||||||
\(836\) | 13.3018 | 0.460053 | ||||||||
\(837\) | 10.4769 | 0.362135 | ||||||||
\(838\) | 67.8304 | 2.34316 | ||||||||
\(839\) | 38.8286 | 1.34051 | 0.670256 | − | 0.742130i | \(-0.266185\pi\) | ||||
0.670256 | + | 0.742130i | \(0.266185\pi\) | |||||||
\(840\) | 224.481 | 7.74533 | ||||||||
\(841\) | −12.3873 | −0.427148 | ||||||||
\(842\) | 87.3827 | 3.01141 | ||||||||
\(843\) | 13.2582 | 0.456638 | ||||||||
\(844\) | 23.9657 | 0.824935 | ||||||||
\(845\) | −44.2371 | −1.52180 | ||||||||
\(846\) | −5.94327 | −0.204334 | ||||||||
\(847\) | 16.4544 | 0.565380 | ||||||||
\(848\) | −153.844 | −5.28302 | ||||||||
\(849\) | 3.22612 | 0.110720 | ||||||||
\(850\) | −91.6458 | −3.14343 | ||||||||
\(851\) | 24.1671 | 0.828437 | ||||||||
\(852\) | −118.608 | −4.06343 | ||||||||
\(853\) | −41.0465 | −1.40540 | −0.702702 | − | 0.711484i | \(-0.748023\pi\) | ||||
−0.702702 | + | 0.711484i | \(0.748023\pi\) | |||||||
\(854\) | −53.4251 | −1.82817 | ||||||||
\(855\) | 1.92098 | 0.0656960 | ||||||||
\(856\) | 89.1664 | 3.04765 | ||||||||
\(857\) | 24.2998 | 0.830066 | 0.415033 | − | 0.909806i | \(-0.363770\pi\) | ||||
0.415033 | + | 0.909806i | \(0.363770\pi\) | |||||||
\(858\) | −16.4135 | −0.560347 | ||||||||
\(859\) | −14.5945 | −0.497959 | −0.248979 | − | 0.968509i | \(-0.580095\pi\) | ||||
−0.248979 | + | 0.968509i | \(0.580095\pi\) | |||||||
\(860\) | −249.830 | −8.51912 | ||||||||
\(861\) | −38.2804 | −1.30459 | ||||||||
\(862\) | 21.3771 | 0.728108 | ||||||||
\(863\) | −10.8256 | −0.368507 | −0.184253 | − | 0.982879i | \(-0.558987\pi\) | ||||
−0.184253 | + | 0.982879i | \(0.558987\pi\) | |||||||
\(864\) | 166.505 | 5.66461 | ||||||||
\(865\) | 82.6332 | 2.80961 | ||||||||
\(866\) | −40.2822 | −1.36885 | ||||||||
\(867\) | −15.6697 | −0.532169 | ||||||||
\(868\) | 35.0777 | 1.19061 | ||||||||
\(869\) | 20.5910 | 0.698503 | ||||||||
\(870\) | 75.1636 | 2.54829 | ||||||||
\(871\) | −21.7436 | −0.736755 | ||||||||
\(872\) | 103.678 | 3.51097 | ||||||||
\(873\) | 4.34602 | 0.147091 | ||||||||
\(874\) | 10.4970 | 0.355066 | ||||||||
\(875\) | −95.7913 | −3.23834 | ||||||||
\(876\) | −12.0617 | −0.407528 | ||||||||
\(877\) | 26.9718 | 0.910772 | 0.455386 | − | 0.890294i | \(-0.349501\pi\) | ||||
0.455386 | + | 0.890294i | \(0.349501\pi\) | |||||||
\(878\) | 44.8431 | 1.51338 | ||||||||
\(879\) | 30.2869 | 1.02155 | ||||||||
\(880\) | −184.665 | −6.22506 | ||||||||
\(881\) | 54.1135 | 1.82313 | 0.911565 | − | 0.411155i | \(-0.134874\pi\) | ||||
0.911565 | + | 0.411155i | \(0.134874\pi\) | |||||||
\(882\) | 4.16749 | 0.140327 | ||||||||
\(883\) | −23.2584 | −0.782709 | −0.391355 | − | 0.920240i | \(-0.627993\pi\) | ||||
−0.391355 | + | 0.920240i | \(0.627993\pi\) | |||||||
\(884\) | −23.9093 | −0.804155 | ||||||||
\(885\) | −68.4212 | −2.29995 | ||||||||
\(886\) | 71.0745 | 2.38779 | ||||||||
\(887\) | 7.35789 | 0.247054 | 0.123527 | − | 0.992341i | \(-0.460579\pi\) | ||||
0.123527 | + | 0.992341i | \(0.460579\pi\) | |||||||
\(888\) | −103.831 | −3.48434 | ||||||||
\(889\) | −11.2377 | −0.376902 | ||||||||
\(890\) | −49.4288 | −1.65686 | ||||||||
\(891\) | 17.5763 | 0.588830 | ||||||||
\(892\) | 14.3119 | 0.479198 | ||||||||
\(893\) | 4.10023 | 0.137209 | ||||||||
\(894\) | −106.478 | −3.56115 | ||||||||
\(895\) | −98.6122 | −3.29624 | ||||||||
\(896\) | 230.251 | 7.69214 | ||||||||
\(897\) | −9.64881 | −0.322164 | ||||||||
\(898\) | 52.2160 | 1.74247 | ||||||||
\(899\) | 7.72368 | 0.257599 | ||||||||
\(900\) | −35.0661 | −1.16887 | ||||||||
\(901\) | −22.2511 | −0.741291 | ||||||||
\(902\) | 51.4440 | 1.71290 | ||||||||
\(903\) | 51.6764 | 1.71968 | ||||||||
\(904\) | −14.7155 | −0.489431 | ||||||||
\(905\) | −71.0630 | −2.36222 | ||||||||
\(906\) | 72.1929 | 2.39845 | ||||||||
\(907\) | 27.4997 | 0.913112 | 0.456556 | − | 0.889695i | \(-0.349083\pi\) | ||||
0.456556 | + | 0.889695i | \(0.349083\pi\) | |||||||
\(908\) | 58.6579 | 1.94663 | ||||||||
\(909\) | 1.01999 | 0.0338311 | ||||||||
\(910\) | −56.6103 | −1.87661 | ||||||||
\(911\) | 18.1112 | 0.600052 | 0.300026 | − | 0.953931i | \(-0.403005\pi\) | ||||
0.300026 | + | 0.953931i | \(0.403005\pi\) | |||||||
\(912\) | −27.6067 | −0.914149 | ||||||||
\(913\) | −5.27355 | −0.174529 | ||||||||
\(914\) | 22.4597 | 0.742901 | ||||||||
\(915\) | −39.6484 | −1.31074 | ||||||||
\(916\) | 83.2953 | 2.75215 | ||||||||
\(917\) | 35.0651 | 1.15795 | ||||||||
\(918\) | 41.2847 | 1.36260 | ||||||||
\(919\) | −22.8862 | −0.754944 | −0.377472 | − | 0.926021i | \(-0.623207\pi\) | ||||
−0.377472 | + | 0.926021i | \(0.623207\pi\) | |||||||
\(920\) | −177.342 | −5.84679 | ||||||||
\(921\) | −11.9854 | −0.394932 | ||||||||
\(922\) | 104.106 | 3.42855 | ||||||||
\(923\) | 19.6695 | 0.647429 | ||||||||
\(924\) | 70.6872 | 2.32544 | ||||||||
\(925\) | 74.7670 | 2.45832 | ||||||||
\(926\) | −81.8821 | −2.69081 | ||||||||
\(927\) | −4.48184 | −0.147203 | ||||||||
\(928\) | 122.749 | 4.02943 | ||||||||
\(929\) | 27.5905 | 0.905215 | 0.452607 | − | 0.891710i | \(-0.350494\pi\) | ||||
0.452607 | + | 0.891710i | \(0.350494\pi\) | |||||||
\(930\) | 34.9455 | 1.14591 | ||||||||
\(931\) | −2.87513 | −0.0942286 | ||||||||
\(932\) | 164.367 | 5.38402 | ||||||||
\(933\) | 21.5773 | 0.706408 | ||||||||
\(934\) | 21.4922 | 0.703246 | ||||||||
\(935\) | −26.7089 | −0.873474 | ||||||||
\(936\) | −8.07581 | −0.263966 | ||||||||
\(937\) | 1.20405 | 0.0393347 | 0.0196673 | − | 0.999807i | \(-0.493739\pi\) | ||||
0.0196673 | + | 0.999807i | \(0.493739\pi\) | |||||||
\(938\) | 125.705 | 4.10441 | ||||||||
\(939\) | −8.04467 | −0.262528 | ||||||||
\(940\) | −105.339 | −3.43578 | ||||||||
\(941\) | −20.0826 | −0.654674 | −0.327337 | − | 0.944908i | \(-0.606151\pi\) | ||||
−0.327337 | + | 0.944908i | \(0.606151\pi\) | |||||||
\(942\) | 23.6594 | 0.770863 | ||||||||
\(943\) | 30.2418 | 0.984809 | ||||||||
\(944\) | −191.554 | −6.23456 | ||||||||
\(945\) | 72.8179 | 2.36877 | ||||||||
\(946\) | −69.4466 | −2.25790 | ||||||||
\(947\) | 25.0019 | 0.812453 | 0.406226 | − | 0.913772i | \(-0.366844\pi\) | ||||
0.406226 | + | 0.913772i | \(0.366844\pi\) | |||||||
\(948\) | −79.0841 | −2.56853 | ||||||||
\(949\) | 2.00028 | 0.0649318 | ||||||||
\(950\) | 32.4751 | 1.05363 | ||||||||
\(951\) | −30.6140 | −0.992726 | ||||||||
\(952\) | 90.8975 | 2.94600 | ||||||||
\(953\) | −4.66080 | −0.150978 | −0.0754890 | − | 0.997147i | \(-0.524052\pi\) | ||||
−0.0754890 | + | 0.997147i | \(0.524052\pi\) | |||||||
\(954\) | −11.4289 | −0.370026 | ||||||||
\(955\) | −75.1669 | −2.43234 | ||||||||
\(956\) | 136.591 | 4.41768 | ||||||||
\(957\) | 15.5645 | 0.503128 | ||||||||
\(958\) | 12.5864 | 0.406648 | ||||||||
\(959\) | −47.2618 | −1.52616 | ||||||||
\(960\) | 312.531 | 10.0869 | ||||||||
\(961\) | −27.4091 | −0.884163 | ||||||||
\(962\) | 26.1844 | 0.844220 | ||||||||
\(963\) | 4.05484 | 0.130665 | ||||||||
\(964\) | −72.5642 | −2.33714 | ||||||||
\(965\) | 5.93228 | 0.190967 | ||||||||
\(966\) | 55.7820 | 1.79476 | ||||||||
\(967\) | 25.5256 | 0.820848 | 0.410424 | − | 0.911895i | \(-0.365381\pi\) | ||||
0.410424 | + | 0.911895i | \(0.365381\pi\) | |||||||
\(968\) | 55.8493 | 1.79506 | ||||||||
\(969\) | −3.99287 | −0.128270 | ||||||||
\(970\) | 103.404 | 3.32010 | ||||||||
\(971\) | 25.0419 | 0.803634 | 0.401817 | − | 0.915720i | \(-0.368379\pi\) | ||||
0.401817 | + | 0.915720i | \(0.368379\pi\) | |||||||
\(972\) | 29.3787 | 0.942323 | ||||||||
\(973\) | −2.81934 | −0.0903840 | ||||||||
\(974\) | −12.4827 | −0.399970 | ||||||||
\(975\) | −29.8510 | −0.955998 | ||||||||
\(976\) | −111.001 | −3.55305 | ||||||||
\(977\) | 18.4826 | 0.591310 | 0.295655 | − | 0.955295i | \(-0.404462\pi\) | ||||
0.295655 | + | 0.955295i | \(0.404462\pi\) | |||||||
\(978\) | 60.4382 | 1.93260 | ||||||||
\(979\) | −10.2354 | −0.327126 | ||||||||
\(980\) | 73.8651 | 2.35953 | ||||||||
\(981\) | 4.71474 | 0.150530 | ||||||||
\(982\) | −62.9368 | −2.00839 | ||||||||
\(983\) | 10.8244 | 0.345243 | 0.172622 | − | 0.984988i | \(-0.444776\pi\) | ||||
0.172622 | + | 0.984988i | \(0.444776\pi\) | |||||||
\(984\) | −129.931 | −4.14203 | ||||||||
\(985\) | 4.94671 | 0.157615 | ||||||||
\(986\) | 30.4355 | 0.969263 | ||||||||
\(987\) | 21.7890 | 0.693553 | ||||||||
\(988\) | 8.47234 | 0.269541 | ||||||||
\(989\) | −40.8248 | −1.29815 | ||||||||
\(990\) | −13.7186 | −0.436006 | ||||||||
\(991\) | −4.43497 | −0.140882 | −0.0704408 | − | 0.997516i | \(-0.522441\pi\) | ||||
−0.0704408 | + | 0.997516i | \(0.522441\pi\) | |||||||
\(992\) | 57.0691 | 1.81195 | ||||||||
\(993\) | −40.3259 | −1.27970 | ||||||||
\(994\) | −113.714 | −3.60679 | ||||||||
\(995\) | 60.7332 | 1.92537 | ||||||||
\(996\) | 20.2542 | 0.641778 | ||||||||
\(997\) | 23.1085 | 0.731852 | 0.365926 | − | 0.930644i | \(-0.380752\pi\) | ||||
0.365926 | + | 0.930644i | \(0.380752\pi\) | |||||||
\(998\) | 32.4012 | 1.02564 | ||||||||
\(999\) | −33.6811 | −1.06562 |
(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 | 6029.2.a.a.1.1 | ✓ | 234 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6029.2.a.a.1.1 | ✓ | 234 | 1.1 | even | 1 | trivial |