Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.522212 | 0.369260 | 0.184630 | − | 0.982808i | \(-0.440891\pi\) | ||||
0.184630 | + | 0.982808i | \(0.440891\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.72729 | −0.863647 | ||||||||
\(5\) | −2.49100 | −1.11401 | −0.557005 | − | 0.830509i | \(-0.688050\pi\) | ||||
−0.557005 | + | 0.830509i | \(0.688050\pi\) | |||||||
\(6\) | −0.522212 | −0.213192 | ||||||||
\(7\) | 5.20591 | 1.96765 | 0.983824 | − | 0.179138i | \(-0.0573309\pi\) | ||||
0.983824 | + | 0.179138i | \(0.0573309\pi\) | |||||||
\(8\) | −1.94644 | −0.688170 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.30083 | −0.411359 | ||||||||
\(11\) | 3.79213 | 1.14337 | 0.571684 | − | 0.820474i | \(-0.306290\pi\) | ||||
0.571684 | + | 0.820474i | \(0.306290\pi\) | |||||||
\(12\) | 1.72729 | 0.498627 | ||||||||
\(13\) | 1.98902 | 0.551655 | 0.275828 | − | 0.961207i | \(-0.411048\pi\) | ||||
0.275828 | + | 0.961207i | \(0.411048\pi\) | |||||||
\(14\) | 2.71859 | 0.726574 | ||||||||
\(15\) | 2.49100 | 0.643174 | ||||||||
\(16\) | 2.43813 | 0.609533 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.522212 | 0.123087 | ||||||||
\(19\) | −4.44935 | −1.02075 | −0.510375 | − | 0.859952i | \(-0.670493\pi\) | ||||
−0.510375 | + | 0.859952i | \(0.670493\pi\) | |||||||
\(20\) | 4.30269 | 0.962112 | ||||||||
\(21\) | −5.20591 | −1.13602 | ||||||||
\(22\) | 1.98030 | 0.422200 | ||||||||
\(23\) | 1.01413 | 0.211461 | 0.105731 | − | 0.994395i | \(-0.466282\pi\) | ||||
0.105731 | + | 0.994395i | \(0.466282\pi\) | |||||||
\(24\) | 1.94644 | 0.397315 | ||||||||
\(25\) | 1.20509 | 0.241019 | ||||||||
\(26\) | 1.03869 | 0.203704 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −8.99213 | −1.69935 | ||||||||
\(29\) | −8.84805 | −1.64304 | −0.821521 | − | 0.570179i | \(-0.806874\pi\) | ||||
−0.821521 | + | 0.570179i | \(0.806874\pi\) | |||||||
\(30\) | 1.30083 | 0.237498 | ||||||||
\(31\) | −7.21004 | −1.29496 | −0.647481 | − | 0.762082i | \(-0.724177\pi\) | ||||
−0.647481 | + | 0.762082i | \(0.724177\pi\) | |||||||
\(32\) | 5.16610 | 0.913246 | ||||||||
\(33\) | −3.79213 | −0.660124 | ||||||||
\(34\) | −0.522212 | −0.0895587 | ||||||||
\(35\) | −12.9679 | −2.19198 | ||||||||
\(36\) | −1.72729 | −0.287882 | ||||||||
\(37\) | −11.2380 | −1.84751 | −0.923757 | − | 0.382979i | \(-0.874898\pi\) | ||||
−0.923757 | + | 0.382979i | \(0.874898\pi\) | |||||||
\(38\) | −2.32350 | −0.376922 | ||||||||
\(39\) | −1.98902 | −0.318498 | ||||||||
\(40\) | 4.84859 | 0.766629 | ||||||||
\(41\) | 3.60771 | 0.563429 | 0.281715 | − | 0.959498i | \(-0.409097\pi\) | ||||
0.281715 | + | 0.959498i | \(0.409097\pi\) | |||||||
\(42\) | −2.71859 | −0.419487 | ||||||||
\(43\) | 3.48456 | 0.531390 | 0.265695 | − | 0.964057i | \(-0.414399\pi\) | ||||
0.265695 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(44\) | −6.55012 | −0.987467 | ||||||||
\(45\) | −2.49100 | −0.371337 | ||||||||
\(46\) | 0.529593 | 0.0780842 | ||||||||
\(47\) | −0.328790 | −0.0479590 | −0.0239795 | − | 0.999712i | \(-0.507634\pi\) | ||||
−0.0239795 | + | 0.999712i | \(0.507634\pi\) | |||||||
\(48\) | −2.43813 | −0.351914 | ||||||||
\(49\) | 20.1015 | 2.87164 | ||||||||
\(50\) | 0.629315 | 0.0889986 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.43562 | −0.476435 | ||||||||
\(53\) | 7.74323 | 1.06361 | 0.531807 | − | 0.846865i | \(-0.321513\pi\) | ||||
0.531807 | + | 0.846865i | \(0.321513\pi\) | |||||||
\(54\) | −0.522212 | −0.0710641 | ||||||||
\(55\) | −9.44620 | −1.27372 | ||||||||
\(56\) | −10.1330 | −1.35408 | ||||||||
\(57\) | 4.44935 | 0.589330 | ||||||||
\(58\) | −4.62056 | −0.606709 | ||||||||
\(59\) | 9.57031 | 1.24595 | 0.622974 | − | 0.782242i | \(-0.285924\pi\) | ||||
0.622974 | + | 0.782242i | \(0.285924\pi\) | |||||||
\(60\) | −4.30269 | −0.555475 | ||||||||
\(61\) | −4.50698 | −0.577060 | −0.288530 | − | 0.957471i | \(-0.593166\pi\) | ||||
−0.288530 | + | 0.957471i | \(0.593166\pi\) | |||||||
\(62\) | −3.76517 | −0.478178 | ||||||||
\(63\) | 5.20591 | 0.655883 | ||||||||
\(64\) | −2.17846 | −0.272308 | ||||||||
\(65\) | −4.95466 | −0.614549 | ||||||||
\(66\) | −1.98030 | −0.243757 | ||||||||
\(67\) | 1.51522 | 0.185114 | 0.0925568 | − | 0.995707i | \(-0.470496\pi\) | ||||
0.0925568 | + | 0.995707i | \(0.470496\pi\) | |||||||
\(68\) | 1.72729 | 0.209465 | ||||||||
\(69\) | −1.01413 | −0.122087 | ||||||||
\(70\) | −6.77201 | −0.809410 | ||||||||
\(71\) | 0.798424 | 0.0947556 | 0.0473778 | − | 0.998877i | \(-0.484914\pi\) | ||||
0.0473778 | + | 0.998877i | \(0.484914\pi\) | |||||||
\(72\) | −1.94644 | −0.229390 | ||||||||
\(73\) | −2.42446 | −0.283761 | −0.141881 | − | 0.989884i | \(-0.545315\pi\) | ||||
−0.141881 | + | 0.989884i | \(0.545315\pi\) | |||||||
\(74\) | −5.86862 | −0.682213 | ||||||||
\(75\) | −1.20509 | −0.139152 | ||||||||
\(76\) | 7.68533 | 0.881568 | ||||||||
\(77\) | 19.7415 | 2.24975 | ||||||||
\(78\) | −1.03869 | −0.117609 | ||||||||
\(79\) | −0.0708311 | −0.00796912 | −0.00398456 | − | 0.999992i | \(-0.501268\pi\) | ||||
−0.00398456 | + | 0.999992i | \(0.501268\pi\) | |||||||
\(80\) | −6.07340 | −0.679026 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.88399 | 0.208052 | ||||||||
\(83\) | −6.45036 | −0.708019 | −0.354010 | − | 0.935242i | \(-0.615182\pi\) | ||||
−0.354010 | + | 0.935242i | \(0.615182\pi\) | |||||||
\(84\) | 8.99213 | 0.981122 | ||||||||
\(85\) | 2.49100 | 0.270187 | ||||||||
\(86\) | 1.81968 | 0.196221 | ||||||||
\(87\) | 8.84805 | 0.948610 | ||||||||
\(88\) | −7.38114 | −0.786832 | ||||||||
\(89\) | −9.71172 | −1.02944 | −0.514720 | − | 0.857358i | \(-0.672104\pi\) | ||||
−0.514720 | + | 0.857358i | \(0.672104\pi\) | |||||||
\(90\) | −1.30083 | −0.137120 | ||||||||
\(91\) | 10.3547 | 1.08546 | ||||||||
\(92\) | −1.75171 | −0.182628 | ||||||||
\(93\) | 7.21004 | 0.747647 | ||||||||
\(94\) | −0.171698 | −0.0177093 | ||||||||
\(95\) | 11.0833 | 1.13713 | ||||||||
\(96\) | −5.16610 | −0.527263 | ||||||||
\(97\) | 6.02464 | 0.611710 | 0.305855 | − | 0.952078i | \(-0.401058\pi\) | ||||
0.305855 | + | 0.952078i | \(0.401058\pi\) | |||||||
\(98\) | 10.4972 | 1.06038 | ||||||||
\(99\) | 3.79213 | 0.381123 | ||||||||
\(100\) | −2.08155 | −0.208155 | ||||||||
\(101\) | 16.1285 | 1.60485 | 0.802424 | − | 0.596754i | \(-0.203543\pi\) | ||||
0.802424 | + | 0.596754i | \(0.203543\pi\) | |||||||
\(102\) | 0.522212 | 0.0517067 | ||||||||
\(103\) | −11.4708 | −1.13025 | −0.565125 | − | 0.825005i | \(-0.691172\pi\) | ||||
−0.565125 | + | 0.825005i | \(0.691172\pi\) | |||||||
\(104\) | −3.87151 | −0.379633 | ||||||||
\(105\) | 12.9679 | 1.26554 | ||||||||
\(106\) | 4.04361 | 0.392750 | ||||||||
\(107\) | 18.1871 | 1.75821 | 0.879107 | − | 0.476625i | \(-0.158140\pi\) | ||||
0.879107 | + | 0.476625i | \(0.158140\pi\) | |||||||
\(108\) | 1.72729 | 0.166209 | ||||||||
\(109\) | −16.0166 | −1.53411 | −0.767054 | − | 0.641583i | \(-0.778278\pi\) | ||||
−0.767054 | + | 0.641583i | \(0.778278\pi\) | |||||||
\(110\) | −4.93292 | −0.470336 | ||||||||
\(111\) | 11.2380 | 1.06666 | ||||||||
\(112\) | 12.6927 | 1.19935 | ||||||||
\(113\) | −16.9067 | −1.59044 | −0.795222 | − | 0.606318i | \(-0.792646\pi\) | ||||
−0.795222 | + | 0.606318i | \(0.792646\pi\) | |||||||
\(114\) | 2.32350 | 0.217616 | ||||||||
\(115\) | −2.52621 | −0.235570 | ||||||||
\(116\) | 15.2832 | 1.41901 | ||||||||
\(117\) | 1.98902 | 0.183885 | ||||||||
\(118\) | 4.99773 | 0.460079 | ||||||||
\(119\) | −5.20591 | −0.477225 | ||||||||
\(120\) | −4.84859 | −0.442613 | ||||||||
\(121\) | 3.38022 | 0.307292 | ||||||||
\(122\) | −2.35360 | −0.213085 | ||||||||
\(123\) | −3.60771 | −0.325296 | ||||||||
\(124\) | 12.4539 | 1.11839 | ||||||||
\(125\) | 9.45312 | 0.845513 | ||||||||
\(126\) | 2.71859 | 0.242191 | ||||||||
\(127\) | 6.58334 | 0.584177 | 0.292089 | − | 0.956391i | \(-0.405650\pi\) | ||||
0.292089 | + | 0.956391i | \(0.405650\pi\) | |||||||
\(128\) | −11.4698 | −1.01380 | ||||||||
\(129\) | −3.48456 | −0.306798 | ||||||||
\(130\) | −2.58738 | −0.226928 | ||||||||
\(131\) | −9.63710 | −0.841997 | −0.420999 | − | 0.907061i | \(-0.638320\pi\) | ||||
−0.420999 | + | 0.907061i | \(0.638320\pi\) | |||||||
\(132\) | 6.55012 | 0.570114 | ||||||||
\(133\) | −23.1629 | −2.00848 | ||||||||
\(134\) | 0.791266 | 0.0683550 | ||||||||
\(135\) | 2.49100 | 0.214391 | ||||||||
\(136\) | 1.94644 | 0.166906 | ||||||||
\(137\) | −14.6891 | −1.25498 | −0.627489 | − | 0.778625i | \(-0.715917\pi\) | ||||
−0.627489 | + | 0.778625i | \(0.715917\pi\) | |||||||
\(138\) | −0.529593 | −0.0450819 | ||||||||
\(139\) | −0.760234 | −0.0644822 | −0.0322411 | − | 0.999480i | \(-0.510264\pi\) | ||||
−0.0322411 | + | 0.999480i | \(0.510264\pi\) | |||||||
\(140\) | 22.3994 | 1.89310 | ||||||||
\(141\) | 0.328790 | 0.0276891 | ||||||||
\(142\) | 0.416947 | 0.0349894 | ||||||||
\(143\) | 7.54262 | 0.630745 | ||||||||
\(144\) | 2.43813 | 0.203178 | ||||||||
\(145\) | 22.0405 | 1.83036 | ||||||||
\(146\) | −1.26608 | −0.104782 | ||||||||
\(147\) | −20.1015 | −1.65794 | ||||||||
\(148\) | 19.4113 | 1.59560 | ||||||||
\(149\) | −2.99363 | −0.245248 | −0.122624 | − | 0.992453i | \(-0.539131\pi\) | ||||
−0.122624 | + | 0.992453i | \(0.539131\pi\) | |||||||
\(150\) | −0.629315 | −0.0513834 | ||||||||
\(151\) | −2.14812 | −0.174812 | −0.0874058 | − | 0.996173i | \(-0.527858\pi\) | ||||
−0.0874058 | + | 0.996173i | \(0.527858\pi\) | |||||||
\(152\) | 8.66038 | 0.702450 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 10.3092 | 0.830742 | ||||||||
\(155\) | 17.9602 | 1.44260 | ||||||||
\(156\) | 3.43562 | 0.275070 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −0.0369889 | −0.00294268 | ||||||||
\(159\) | −7.74323 | −0.614078 | ||||||||
\(160\) | −12.8688 | −1.01737 | ||||||||
\(161\) | 5.27948 | 0.416081 | ||||||||
\(162\) | 0.522212 | 0.0410289 | ||||||||
\(163\) | −6.26047 | −0.490358 | −0.245179 | − | 0.969478i | \(-0.578847\pi\) | ||||
−0.245179 | + | 0.969478i | \(0.578847\pi\) | |||||||
\(164\) | −6.23157 | −0.486604 | ||||||||
\(165\) | 9.44620 | 0.735385 | ||||||||
\(166\) | −3.36846 | −0.261443 | ||||||||
\(167\) | −11.7678 | −0.910621 | −0.455311 | − | 0.890333i | \(-0.650472\pi\) | ||||
−0.455311 | + | 0.890333i | \(0.650472\pi\) | |||||||
\(168\) | 10.1330 | 0.781777 | ||||||||
\(169\) | −9.04380 | −0.695677 | ||||||||
\(170\) | 1.30083 | 0.0997693 | ||||||||
\(171\) | −4.44935 | −0.340250 | ||||||||
\(172\) | −6.01886 | −0.458934 | ||||||||
\(173\) | 19.4467 | 1.47850 | 0.739252 | − | 0.673429i | \(-0.235179\pi\) | ||||
0.739252 | + | 0.673429i | \(0.235179\pi\) | |||||||
\(174\) | 4.62056 | 0.350284 | ||||||||
\(175\) | 6.27361 | 0.474240 | ||||||||
\(176\) | 9.24571 | 0.696922 | ||||||||
\(177\) | −9.57031 | −0.719349 | ||||||||
\(178\) | −5.07158 | −0.380131 | ||||||||
\(179\) | 21.8141 | 1.63047 | 0.815233 | − | 0.579133i | \(-0.196609\pi\) | ||||
0.815233 | + | 0.579133i | \(0.196609\pi\) | |||||||
\(180\) | 4.30269 | 0.320704 | ||||||||
\(181\) | 11.0565 | 0.821823 | 0.410912 | − | 0.911675i | \(-0.365210\pi\) | ||||
0.410912 | + | 0.911675i | \(0.365210\pi\) | |||||||
\(182\) | 5.40733 | 0.400818 | ||||||||
\(183\) | 4.50698 | 0.333165 | ||||||||
\(184\) | −1.97395 | −0.145521 | ||||||||
\(185\) | 27.9939 | 2.05815 | ||||||||
\(186\) | 3.76517 | 0.276076 | ||||||||
\(187\) | −3.79213 | −0.277308 | ||||||||
\(188\) | 0.567917 | 0.0414196 | ||||||||
\(189\) | −5.20591 | −0.378674 | ||||||||
\(190\) | 5.78785 | 0.419895 | ||||||||
\(191\) | −8.95026 | −0.647618 | −0.323809 | − | 0.946122i | \(-0.604964\pi\) | ||||
−0.323809 | + | 0.946122i | \(0.604964\pi\) | |||||||
\(192\) | 2.17846 | 0.157217 | ||||||||
\(193\) | 6.05971 | 0.436187 | 0.218094 | − | 0.975928i | \(-0.430016\pi\) | ||||
0.218094 | + | 0.975928i | \(0.430016\pi\) | |||||||
\(194\) | 3.14614 | 0.225880 | ||||||||
\(195\) | 4.95466 | 0.354810 | ||||||||
\(196\) | −34.7211 | −2.48008 | ||||||||
\(197\) | 8.51967 | 0.607001 | 0.303501 | − | 0.952831i | \(-0.401845\pi\) | ||||
0.303501 | + | 0.952831i | \(0.401845\pi\) | |||||||
\(198\) | 1.98030 | 0.140733 | ||||||||
\(199\) | −4.14330 | −0.293710 | −0.146855 | − | 0.989158i | \(-0.546915\pi\) | ||||
−0.146855 | + | 0.989158i | \(0.546915\pi\) | |||||||
\(200\) | −2.34564 | −0.165862 | ||||||||
\(201\) | −1.51522 | −0.106875 | ||||||||
\(202\) | 8.42252 | 0.592606 | ||||||||
\(203\) | −46.0621 | −3.23293 | ||||||||
\(204\) | −1.72729 | −0.120935 | ||||||||
\(205\) | −8.98681 | −0.627666 | ||||||||
\(206\) | −5.99019 | −0.417356 | ||||||||
\(207\) | 1.01413 | 0.0704871 | ||||||||
\(208\) | 4.84950 | 0.336252 | ||||||||
\(209\) | −16.8725 | −1.16709 | ||||||||
\(210\) | 6.77201 | 0.467313 | ||||||||
\(211\) | −21.8940 | −1.50725 | −0.753623 | − | 0.657307i | \(-0.771695\pi\) | ||||
−0.753623 | + | 0.657307i | \(0.771695\pi\) | |||||||
\(212\) | −13.3748 | −0.918588 | ||||||||
\(213\) | −0.798424 | −0.0547071 | ||||||||
\(214\) | 9.49753 | 0.649238 | ||||||||
\(215\) | −8.68005 | −0.591974 | ||||||||
\(216\) | 1.94644 | 0.132438 | ||||||||
\(217\) | −37.5348 | −2.54803 | ||||||||
\(218\) | −8.36404 | −0.566485 | ||||||||
\(219\) | 2.42446 | 0.163830 | ||||||||
\(220\) | 16.3164 | 1.10005 | ||||||||
\(221\) | −1.98902 | −0.133796 | ||||||||
\(222\) | 5.86862 | 0.393876 | ||||||||
\(223\) | −18.6656 | −1.24994 | −0.624971 | − | 0.780648i | \(-0.714889\pi\) | ||||
−0.624971 | + | 0.780648i | \(0.714889\pi\) | |||||||
\(224\) | 26.8942 | 1.79695 | ||||||||
\(225\) | 1.20509 | 0.0803396 | ||||||||
\(226\) | −8.82887 | −0.587287 | ||||||||
\(227\) | 6.96732 | 0.462437 | 0.231219 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231219 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(228\) | −7.68533 | −0.508973 | ||||||||
\(229\) | −10.7510 | −0.710444 | −0.355222 | − | 0.934782i | \(-0.615595\pi\) | ||||
−0.355222 | + | 0.934782i | \(0.615595\pi\) | |||||||
\(230\) | −1.31922 | −0.0869866 | ||||||||
\(231\) | −19.7415 | −1.29889 | ||||||||
\(232\) | 17.2222 | 1.13069 | ||||||||
\(233\) | −21.1681 | −1.38677 | −0.693385 | − | 0.720568i | \(-0.743881\pi\) | ||||
−0.693385 | + | 0.720568i | \(0.743881\pi\) | |||||||
\(234\) | 1.03869 | 0.0679014 | ||||||||
\(235\) | 0.819017 | 0.0534268 | ||||||||
\(236\) | −16.5307 | −1.07606 | ||||||||
\(237\) | 0.0708311 | 0.00460097 | ||||||||
\(238\) | −2.71859 | −0.176220 | ||||||||
\(239\) | −19.0843 | −1.23446 | −0.617229 | − | 0.786784i | \(-0.711745\pi\) | ||||
−0.617229 | + | 0.786784i | \(0.711745\pi\) | |||||||
\(240\) | 6.07340 | 0.392036 | ||||||||
\(241\) | −20.0543 | −1.29181 | −0.645907 | − | 0.763416i | \(-0.723521\pi\) | ||||
−0.645907 | + | 0.763416i | \(0.723521\pi\) | |||||||
\(242\) | 1.76519 | 0.113471 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.78488 | 0.498376 | ||||||||
\(245\) | −50.0728 | −3.19903 | ||||||||
\(246\) | −1.88399 | −0.120119 | ||||||||
\(247\) | −8.84984 | −0.563102 | ||||||||
\(248\) | 14.0339 | 0.891154 | ||||||||
\(249\) | 6.45036 | 0.408775 | ||||||||
\(250\) | 4.93654 | 0.312214 | ||||||||
\(251\) | 16.9195 | 1.06795 | 0.533975 | − | 0.845501i | \(-0.320698\pi\) | ||||
0.533975 | + | 0.845501i | \(0.320698\pi\) | |||||||
\(252\) | −8.99213 | −0.566451 | ||||||||
\(253\) | 3.84572 | 0.241778 | ||||||||
\(254\) | 3.43790 | 0.215713 | ||||||||
\(255\) | −2.49100 | −0.155993 | ||||||||
\(256\) | −1.63276 | −0.102047 | ||||||||
\(257\) | 4.62699 | 0.288623 | 0.144312 | − | 0.989532i | \(-0.453903\pi\) | ||||
0.144312 | + | 0.989532i | \(0.453903\pi\) | |||||||
\(258\) | −1.81968 | −0.113288 | ||||||||
\(259\) | −58.5039 | −3.63526 | ||||||||
\(260\) | 8.55815 | 0.530754 | ||||||||
\(261\) | −8.84805 | −0.547680 | ||||||||
\(262\) | −5.03261 | −0.310916 | ||||||||
\(263\) | −11.4847 | −0.708178 | −0.354089 | − | 0.935212i | \(-0.615209\pi\) | ||||
−0.354089 | + | 0.935212i | \(0.615209\pi\) | |||||||
\(264\) | 7.38114 | 0.454278 | ||||||||
\(265\) | −19.2884 | −1.18488 | ||||||||
\(266\) | −12.0959 | −0.741650 | ||||||||
\(267\) | 9.71172 | 0.594348 | ||||||||
\(268\) | −2.61723 | −0.159873 | ||||||||
\(269\) | 26.0351 | 1.58739 | 0.793695 | − | 0.608316i | \(-0.208155\pi\) | ||||
0.793695 | + | 0.608316i | \(0.208155\pi\) | |||||||
\(270\) | 1.30083 | 0.0791661 | ||||||||
\(271\) | −21.6310 | −1.31399 | −0.656996 | − | 0.753894i | \(-0.728173\pi\) | ||||
−0.656996 | + | 0.753894i | \(0.728173\pi\) | |||||||
\(272\) | −2.43813 | −0.147834 | ||||||||
\(273\) | −10.3547 | −0.626692 | ||||||||
\(274\) | −7.67085 | −0.463413 | ||||||||
\(275\) | 4.56987 | 0.275573 | ||||||||
\(276\) | 1.75171 | 0.105440 | ||||||||
\(277\) | −13.8130 | −0.829942 | −0.414971 | − | 0.909835i | \(-0.636208\pi\) | ||||
−0.414971 | + | 0.909835i | \(0.636208\pi\) | |||||||
\(278\) | −0.397004 | −0.0238107 | ||||||||
\(279\) | −7.21004 | −0.431654 | ||||||||
\(280\) | 25.2413 | 1.50846 | ||||||||
\(281\) | −10.6326 | −0.634286 | −0.317143 | − | 0.948378i | \(-0.602724\pi\) | ||||
−0.317143 | + | 0.948378i | \(0.602724\pi\) | |||||||
\(282\) | 0.171698 | 0.0102245 | ||||||||
\(283\) | 18.4505 | 1.09677 | 0.548385 | − | 0.836226i | \(-0.315243\pi\) | ||||
0.548385 | + | 0.836226i | \(0.315243\pi\) | |||||||
\(284\) | −1.37911 | −0.0818354 | ||||||||
\(285\) | −11.0833 | −0.656520 | ||||||||
\(286\) | 3.93885 | 0.232909 | ||||||||
\(287\) | 18.7814 | 1.10863 | ||||||||
\(288\) | 5.16610 | 0.304415 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 11.5098 | 0.675880 | ||||||||
\(291\) | −6.02464 | −0.353171 | ||||||||
\(292\) | 4.18775 | 0.245069 | ||||||||
\(293\) | 18.0697 | 1.05564 | 0.527820 | − | 0.849356i | \(-0.323010\pi\) | ||||
0.527820 | + | 0.849356i | \(0.323010\pi\) | |||||||
\(294\) | −10.4972 | −0.612211 | ||||||||
\(295\) | −23.8397 | −1.38800 | ||||||||
\(296\) | 21.8741 | 1.27140 | ||||||||
\(297\) | −3.79213 | −0.220041 | ||||||||
\(298\) | −1.56331 | −0.0905601 | ||||||||
\(299\) | 2.01713 | 0.116654 | ||||||||
\(300\) | 2.08155 | 0.120178 | ||||||||
\(301\) | 18.1403 | 1.04559 | ||||||||
\(302\) | −1.12178 | −0.0645510 | ||||||||
\(303\) | −16.1285 | −0.926559 | ||||||||
\(304\) | −10.8481 | −0.622181 | ||||||||
\(305\) | 11.2269 | 0.642850 | ||||||||
\(306\) | −0.522212 | −0.0298529 | ||||||||
\(307\) | −25.7624 | −1.47034 | −0.735170 | − | 0.677883i | \(-0.762898\pi\) | ||||
−0.735170 | + | 0.677883i | \(0.762898\pi\) | |||||||
\(308\) | −34.0993 | −1.94299 | ||||||||
\(309\) | 11.4708 | 0.652550 | ||||||||
\(310\) | 9.37906 | 0.532695 | ||||||||
\(311\) | −1.44216 | −0.0817771 | −0.0408886 | − | 0.999164i | \(-0.513019\pi\) | ||||
−0.0408886 | + | 0.999164i | \(0.513019\pi\) | |||||||
\(312\) | 3.87151 | 0.219181 | ||||||||
\(313\) | −19.1869 | −1.08451 | −0.542253 | − | 0.840215i | \(-0.682429\pi\) | ||||
−0.542253 | + | 0.840215i | \(0.682429\pi\) | |||||||
\(314\) | −0.522212 | −0.0294702 | ||||||||
\(315\) | −12.9679 | −0.730660 | ||||||||
\(316\) | 0.122346 | 0.00688251 | ||||||||
\(317\) | 16.6819 | 0.936950 | 0.468475 | − | 0.883477i | \(-0.344804\pi\) | ||||
0.468475 | + | 0.883477i | \(0.344804\pi\) | |||||||
\(318\) | −4.04361 | −0.226755 | ||||||||
\(319\) | −33.5529 | −1.87860 | ||||||||
\(320\) | 5.42656 | 0.303354 | ||||||||
\(321\) | −18.1871 | −1.01510 | ||||||||
\(322\) | 2.75701 | 0.153642 | ||||||||
\(323\) | 4.44935 | 0.247568 | ||||||||
\(324\) | −1.72729 | −0.0959608 | ||||||||
\(325\) | 2.39696 | 0.132959 | ||||||||
\(326\) | −3.26929 | −0.181069 | ||||||||
\(327\) | 16.0166 | 0.885717 | ||||||||
\(328\) | −7.02218 | −0.387735 | ||||||||
\(329\) | −1.71165 | −0.0943664 | ||||||||
\(330\) | 4.93292 | 0.271548 | ||||||||
\(331\) | −4.91999 | −0.270427 | −0.135213 | − | 0.990816i | \(-0.543172\pi\) | ||||
−0.135213 | + | 0.990816i | \(0.543172\pi\) | |||||||
\(332\) | 11.1417 | 0.611479 | ||||||||
\(333\) | −11.2380 | −0.615838 | ||||||||
\(334\) | −6.14530 | −0.336256 | ||||||||
\(335\) | −3.77442 | −0.206218 | ||||||||
\(336\) | −12.6927 | −0.692443 | ||||||||
\(337\) | −14.7265 | −0.802205 | −0.401102 | − | 0.916033i | \(-0.631373\pi\) | ||||
−0.401102 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(338\) | −4.72278 | −0.256886 | ||||||||
\(339\) | 16.9067 | 0.918243 | ||||||||
\(340\) | −4.30269 | −0.233346 | ||||||||
\(341\) | −27.3414 | −1.48062 | ||||||||
\(342\) | −2.32350 | −0.125641 | ||||||||
\(343\) | 68.2050 | 3.68272 | ||||||||
\(344\) | −6.78248 | −0.365687 | ||||||||
\(345\) | 2.52621 | 0.136006 | ||||||||
\(346\) | 10.1553 | 0.545952 | ||||||||
\(347\) | −1.32420 | −0.0710867 | −0.0355434 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355434 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(348\) | −15.2832 | −0.819264 | ||||||||
\(349\) | 1.58381 | 0.0847795 | 0.0423897 | − | 0.999101i | \(-0.486503\pi\) | ||||
0.0423897 | + | 0.999101i | \(0.486503\pi\) | |||||||
\(350\) | 3.27616 | 0.175118 | ||||||||
\(351\) | −1.98902 | −0.106166 | ||||||||
\(352\) | 19.5905 | 1.04418 | ||||||||
\(353\) | 0.214568 | 0.0114203 | 0.00571016 | − | 0.999984i | \(-0.498182\pi\) | ||||
0.00571016 | + | 0.999984i | \(0.498182\pi\) | |||||||
\(354\) | −4.99773 | −0.265627 | ||||||||
\(355\) | −1.98888 | −0.105559 | ||||||||
\(356\) | 16.7750 | 0.889073 | ||||||||
\(357\) | 5.20591 | 0.275526 | ||||||||
\(358\) | 11.3916 | 0.602066 | ||||||||
\(359\) | −0.503239 | −0.0265599 | −0.0132800 | − | 0.999912i | \(-0.504227\pi\) | ||||
−0.0132800 | + | 0.999912i | \(0.504227\pi\) | |||||||
\(360\) | 4.84859 | 0.255543 | ||||||||
\(361\) | 0.796677 | 0.0419304 | ||||||||
\(362\) | 5.77384 | 0.303466 | ||||||||
\(363\) | −3.38022 | −0.177415 | ||||||||
\(364\) | −17.8855 | −0.937457 | ||||||||
\(365\) | 6.03933 | 0.316113 | ||||||||
\(366\) | 2.35360 | 0.123025 | ||||||||
\(367\) | 17.4872 | 0.912826 | 0.456413 | − | 0.889768i | \(-0.349134\pi\) | ||||
0.456413 | + | 0.889768i | \(0.349134\pi\) | |||||||
\(368\) | 2.47259 | 0.128893 | ||||||||
\(369\) | 3.60771 | 0.187810 | ||||||||
\(370\) | 14.6187 | 0.759992 | ||||||||
\(371\) | 40.3106 | 2.09282 | ||||||||
\(372\) | −12.4539 | −0.645703 | ||||||||
\(373\) | 21.3453 | 1.10522 | 0.552610 | − | 0.833440i | \(-0.313632\pi\) | ||||
0.552610 | + | 0.833440i | \(0.313632\pi\) | |||||||
\(374\) | −1.98030 | −0.102399 | ||||||||
\(375\) | −9.45312 | −0.488157 | ||||||||
\(376\) | 0.639970 | 0.0330039 | ||||||||
\(377\) | −17.5989 | −0.906392 | ||||||||
\(378\) | −2.71859 | −0.139829 | ||||||||
\(379\) | −37.6086 | −1.93182 | −0.965912 | − | 0.258870i | \(-0.916650\pi\) | ||||
−0.965912 | + | 0.258870i | \(0.916650\pi\) | |||||||
\(380\) | −19.1442 | −0.982075 | ||||||||
\(381\) | −6.58334 | −0.337275 | ||||||||
\(382\) | −4.67394 | −0.239139 | ||||||||
\(383\) | 7.85675 | 0.401461 | 0.200731 | − | 0.979646i | \(-0.435668\pi\) | ||||
0.200731 | + | 0.979646i | \(0.435668\pi\) | |||||||
\(384\) | 11.4698 | 0.585317 | ||||||||
\(385\) | −49.1760 | −2.50624 | ||||||||
\(386\) | 3.16445 | 0.161066 | ||||||||
\(387\) | 3.48456 | 0.177130 | ||||||||
\(388\) | −10.4063 | −0.528302 | ||||||||
\(389\) | −31.0418 | −1.57388 | −0.786940 | − | 0.617029i | \(-0.788336\pi\) | ||||
−0.786940 | + | 0.617029i | \(0.788336\pi\) | |||||||
\(390\) | 2.58738 | 0.131017 | ||||||||
\(391\) | −1.01413 | −0.0512869 | ||||||||
\(392\) | −39.1263 | −1.97618 | ||||||||
\(393\) | 9.63710 | 0.486127 | ||||||||
\(394\) | 4.44908 | 0.224141 | ||||||||
\(395\) | 0.176440 | 0.00887768 | ||||||||
\(396\) | −6.55012 | −0.329156 | ||||||||
\(397\) | 4.96984 | 0.249429 | 0.124714 | − | 0.992193i | \(-0.460199\pi\) | ||||
0.124714 | + | 0.992193i | \(0.460199\pi\) | |||||||
\(398\) | −2.16368 | −0.108455 | ||||||||
\(399\) | 23.1629 | 1.15959 | ||||||||
\(400\) | 2.93818 | 0.146909 | ||||||||
\(401\) | 15.5267 | 0.775367 | 0.387684 | − | 0.921793i | \(-0.373275\pi\) | ||||
0.387684 | + | 0.921793i | \(0.373275\pi\) | |||||||
\(402\) | −0.791266 | −0.0394648 | ||||||||
\(403\) | −14.3409 | −0.714372 | ||||||||
\(404\) | −27.8587 | −1.38602 | ||||||||
\(405\) | −2.49100 | −0.123779 | ||||||||
\(406\) | −24.0542 | −1.19379 | ||||||||
\(407\) | −42.6159 | −2.11239 | ||||||||
\(408\) | −1.94644 | −0.0963631 | ||||||||
\(409\) | 21.7623 | 1.07607 | 0.538037 | − | 0.842921i | \(-0.319166\pi\) | ||||
0.538037 | + | 0.842921i | \(0.319166\pi\) | |||||||
\(410\) | −4.69302 | −0.231772 | ||||||||
\(411\) | 14.6891 | 0.724562 | ||||||||
\(412\) | 19.8134 | 0.976138 | ||||||||
\(413\) | 49.8221 | 2.45159 | ||||||||
\(414\) | 0.529593 | 0.0260281 | ||||||||
\(415\) | 16.0679 | 0.788741 | ||||||||
\(416\) | 10.2755 | 0.503797 | ||||||||
\(417\) | 0.760234 | 0.0372288 | ||||||||
\(418\) | −8.81102 | −0.430961 | ||||||||
\(419\) | 29.1199 | 1.42260 | 0.711299 | − | 0.702889i | \(-0.248107\pi\) | ||||
0.711299 | + | 0.702889i | \(0.248107\pi\) | |||||||
\(420\) | −22.3994 | −1.09298 | ||||||||
\(421\) | 29.3418 | 1.43003 | 0.715017 | − | 0.699107i | \(-0.246419\pi\) | ||||
0.715017 | + | 0.699107i | \(0.246419\pi\) | |||||||
\(422\) | −11.4333 | −0.556565 | ||||||||
\(423\) | −0.328790 | −0.0159863 | ||||||||
\(424\) | −15.0717 | −0.731948 | ||||||||
\(425\) | −1.20509 | −0.0584556 | ||||||||
\(426\) | −0.416947 | −0.0202012 | ||||||||
\(427\) | −23.4629 | −1.13545 | ||||||||
\(428\) | −31.4145 | −1.51848 | ||||||||
\(429\) | −7.54262 | −0.364161 | ||||||||
\(430\) | −4.53283 | −0.218592 | ||||||||
\(431\) | −2.24604 | −0.108188 | −0.0540940 | − | 0.998536i | \(-0.517227\pi\) | ||||
−0.0540940 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(432\) | −2.43813 | −0.117305 | ||||||||
\(433\) | 2.63146 | 0.126460 | 0.0632298 | − | 0.997999i | \(-0.479860\pi\) | ||||
0.0632298 | + | 0.997999i | \(0.479860\pi\) | |||||||
\(434\) | −19.6011 | −0.940885 | ||||||||
\(435\) | −22.0405 | −1.05676 | ||||||||
\(436\) | 27.6653 | 1.32493 | ||||||||
\(437\) | −4.51223 | −0.215849 | ||||||||
\(438\) | 1.26608 | 0.0604957 | ||||||||
\(439\) | −33.1159 | −1.58053 | −0.790267 | − | 0.612762i | \(-0.790058\pi\) | ||||
−0.790267 | + | 0.612762i | \(0.790058\pi\) | |||||||
\(440\) | 18.3864 | 0.876539 | ||||||||
\(441\) | 20.1015 | 0.957213 | ||||||||
\(442\) | −1.03869 | −0.0494055 | ||||||||
\(443\) | −20.3229 | −0.965572 | −0.482786 | − | 0.875738i | \(-0.660375\pi\) | ||||
−0.482786 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(444\) | −19.4113 | −0.921220 | ||||||||
\(445\) | 24.1919 | 1.14681 | ||||||||
\(446\) | −9.74742 | −0.461554 | ||||||||
\(447\) | 2.99363 | 0.141594 | ||||||||
\(448\) | −11.3409 | −0.535806 | ||||||||
\(449\) | −19.2412 | −0.908047 | −0.454023 | − | 0.890990i | \(-0.650012\pi\) | ||||
−0.454023 | + | 0.890990i | \(0.650012\pi\) | |||||||
\(450\) | 0.629315 | 0.0296662 | ||||||||
\(451\) | 13.6809 | 0.644208 | ||||||||
\(452\) | 29.2028 | 1.37358 | ||||||||
\(453\) | 2.14812 | 0.100928 | ||||||||
\(454\) | 3.63842 | 0.170760 | ||||||||
\(455\) | −25.7935 | −1.20922 | ||||||||
\(456\) | −8.66038 | −0.405560 | ||||||||
\(457\) | 33.2178 | 1.55387 | 0.776933 | − | 0.629584i | \(-0.216775\pi\) | ||||
0.776933 | + | 0.629584i | \(0.216775\pi\) | |||||||
\(458\) | −5.61429 | −0.262338 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 4.36350 | 0.203449 | ||||||||
\(461\) | 11.3985 | 0.530883 | 0.265441 | − | 0.964127i | \(-0.414482\pi\) | ||||
0.265441 | + | 0.964127i | \(0.414482\pi\) | |||||||
\(462\) | −10.3092 | −0.479629 | ||||||||
\(463\) | 24.7190 | 1.14879 | 0.574395 | − | 0.818578i | \(-0.305237\pi\) | ||||
0.574395 | + | 0.818578i | \(0.305237\pi\) | |||||||
\(464\) | −21.5727 | −1.00149 | ||||||||
\(465\) | −17.9602 | −0.832886 | ||||||||
\(466\) | −11.0543 | −0.512078 | ||||||||
\(467\) | −12.7157 | −0.588413 | −0.294207 | − | 0.955742i | \(-0.595055\pi\) | ||||
−0.294207 | + | 0.955742i | \(0.595055\pi\) | |||||||
\(468\) | −3.43562 | −0.158812 | ||||||||
\(469\) | 7.88809 | 0.364238 | ||||||||
\(470\) | 0.427701 | 0.0197284 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −18.6280 | −0.857424 | ||||||||
\(473\) | 13.2139 | 0.607575 | ||||||||
\(474\) | 0.0369889 | 0.00169896 | ||||||||
\(475\) | −5.36188 | −0.246020 | ||||||||
\(476\) | 8.99213 | 0.412154 | ||||||||
\(477\) | 7.74323 | 0.354538 | ||||||||
\(478\) | −9.96604 | −0.455836 | ||||||||
\(479\) | −29.0324 | −1.32652 | −0.663262 | − | 0.748387i | \(-0.730829\pi\) | ||||
−0.663262 | + | 0.748387i | \(0.730829\pi\) | |||||||
\(480\) | 12.8688 | 0.587377 | ||||||||
\(481\) | −22.3526 | −1.01919 | ||||||||
\(482\) | −10.4726 | −0.477015 | ||||||||
\(483\) | −5.27948 | −0.240225 | ||||||||
\(484\) | −5.83863 | −0.265392 | ||||||||
\(485\) | −15.0074 | −0.681451 | ||||||||
\(486\) | −0.522212 | −0.0236880 | ||||||||
\(487\) | −16.4916 | −0.747306 | −0.373653 | − | 0.927568i | \(-0.621895\pi\) | ||||
−0.373653 | + | 0.927568i | \(0.621895\pi\) | |||||||
\(488\) | 8.77256 | 0.397115 | ||||||||
\(489\) | 6.26047 | 0.283108 | ||||||||
\(490\) | −26.1486 | −1.18128 | ||||||||
\(491\) | −21.8575 | −0.986416 | −0.493208 | − | 0.869912i | \(-0.664176\pi\) | ||||
−0.493208 | + | 0.869912i | \(0.664176\pi\) | |||||||
\(492\) | 6.23157 | 0.280941 | ||||||||
\(493\) | 8.84805 | 0.398496 | ||||||||
\(494\) | −4.62150 | −0.207931 | ||||||||
\(495\) | −9.44620 | −0.424575 | ||||||||
\(496\) | −17.5790 | −0.789323 | ||||||||
\(497\) | 4.15652 | 0.186446 | ||||||||
\(498\) | 3.36846 | 0.150944 | ||||||||
\(499\) | 7.19177 | 0.321948 | 0.160974 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160974 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(500\) | −16.3283 | −0.730225 | ||||||||
\(501\) | 11.7678 | 0.525747 | ||||||||
\(502\) | 8.83557 | 0.394351 | ||||||||
\(503\) | −43.3914 | −1.93473 | −0.967364 | − | 0.253390i | \(-0.918454\pi\) | ||||
−0.967364 | + | 0.253390i | \(0.918454\pi\) | |||||||
\(504\) | −10.1330 | −0.451359 | ||||||||
\(505\) | −40.1762 | −1.78782 | ||||||||
\(506\) | 2.00828 | 0.0892790 | ||||||||
\(507\) | 9.04380 | 0.401649 | ||||||||
\(508\) | −11.3714 | −0.504523 | ||||||||
\(509\) | 0.935730 | 0.0414755 | 0.0207378 | − | 0.999785i | \(-0.493398\pi\) | ||||
0.0207378 | + | 0.999785i | \(0.493398\pi\) | |||||||
\(510\) | −1.30083 | −0.0576018 | ||||||||
\(511\) | −12.6215 | −0.558342 | ||||||||
\(512\) | 22.0870 | 0.976117 | ||||||||
\(513\) | 4.44935 | 0.196443 | ||||||||
\(514\) | 2.41627 | 0.106577 | ||||||||
\(515\) | 28.5738 | 1.25911 | ||||||||
\(516\) | 6.01886 | 0.264966 | ||||||||
\(517\) | −1.24681 | −0.0548348 | ||||||||
\(518\) | −30.5515 | −1.34235 | ||||||||
\(519\) | −19.4467 | −0.853615 | ||||||||
\(520\) | 9.64394 | 0.422915 | ||||||||
\(521\) | −17.3502 | −0.760125 | −0.380062 | − | 0.924961i | \(-0.624097\pi\) | ||||
−0.380062 | + | 0.924961i | \(0.624097\pi\) | |||||||
\(522\) | −4.62056 | −0.202236 | ||||||||
\(523\) | 17.7575 | 0.776480 | 0.388240 | − | 0.921558i | \(-0.373083\pi\) | ||||
0.388240 | + | 0.921558i | \(0.373083\pi\) | |||||||
\(524\) | 16.6461 | 0.727189 | ||||||||
\(525\) | −6.27361 | −0.273803 | ||||||||
\(526\) | −5.99746 | −0.261502 | ||||||||
\(527\) | 7.21004 | 0.314074 | ||||||||
\(528\) | −9.24571 | −0.402368 | ||||||||
\(529\) | −21.9715 | −0.955284 | ||||||||
\(530\) | −10.0727 | −0.437528 | ||||||||
\(531\) | 9.57031 | 0.415316 | ||||||||
\(532\) | 40.0091 | 1.73461 | ||||||||
\(533\) | 7.17580 | 0.310819 | ||||||||
\(534\) | 5.07158 | 0.219469 | ||||||||
\(535\) | −45.3041 | −1.95867 | ||||||||
\(536\) | −2.94928 | −0.127390 | ||||||||
\(537\) | −21.8141 | −0.941350 | ||||||||
\(538\) | 13.5959 | 0.586160 | ||||||||
\(539\) | 76.2273 | 3.28334 | ||||||||
\(540\) | −4.30269 | −0.185158 | ||||||||
\(541\) | 0.123900 | 0.00532689 | 0.00266345 | − | 0.999996i | \(-0.499152\pi\) | ||||
0.00266345 | + | 0.999996i | \(0.499152\pi\) | |||||||
\(542\) | −11.2960 | −0.485205 | ||||||||
\(543\) | −11.0565 | −0.474480 | ||||||||
\(544\) | −5.16610 | −0.221495 | ||||||||
\(545\) | 39.8973 | 1.70901 | ||||||||
\(546\) | −5.40733 | −0.231412 | ||||||||
\(547\) | −38.8959 | −1.66307 | −0.831533 | − | 0.555475i | \(-0.812537\pi\) | ||||
−0.831533 | + | 0.555475i | \(0.812537\pi\) | |||||||
\(548\) | 25.3725 | 1.08386 | ||||||||
\(549\) | −4.50698 | −0.192353 | ||||||||
\(550\) | 2.38644 | 0.101758 | ||||||||
\(551\) | 39.3680 | 1.67713 | ||||||||
\(552\) | 1.97395 | 0.0840168 | ||||||||
\(553\) | −0.368740 | −0.0156804 | ||||||||
\(554\) | −7.21331 | −0.306464 | ||||||||
\(555\) | −27.9939 | −1.18827 | ||||||||
\(556\) | 1.31315 | 0.0556899 | ||||||||
\(557\) | 20.3271 | 0.861289 | 0.430644 | − | 0.902522i | \(-0.358286\pi\) | ||||
0.430644 | + | 0.902522i | \(0.358286\pi\) | |||||||
\(558\) | −3.76517 | −0.159393 | ||||||||
\(559\) | 6.93086 | 0.293144 | ||||||||
\(560\) | −31.6175 | −1.33608 | ||||||||
\(561\) | 3.79213 | 0.160104 | ||||||||
\(562\) | −5.55246 | −0.234217 | ||||||||
\(563\) | 0.687516 | 0.0289753 | 0.0144877 | − | 0.999895i | \(-0.495388\pi\) | ||||
0.0144877 | + | 0.999895i | \(0.495388\pi\) | |||||||
\(564\) | −0.567917 | −0.0239136 | ||||||||
\(565\) | 42.1145 | 1.77177 | ||||||||
\(566\) | 9.63509 | 0.404993 | ||||||||
\(567\) | 5.20591 | 0.218628 | ||||||||
\(568\) | −1.55408 | −0.0652079 | ||||||||
\(569\) | −13.4798 | −0.565104 | −0.282552 | − | 0.959252i | \(-0.591181\pi\) | ||||
−0.282552 | + | 0.959252i | \(0.591181\pi\) | |||||||
\(570\) | −5.78785 | −0.242427 | ||||||||
\(571\) | −33.1731 | −1.38825 | −0.694125 | − | 0.719854i | \(-0.744209\pi\) | ||||
−0.694125 | + | 0.719854i | \(0.744209\pi\) | |||||||
\(572\) | −13.0283 | −0.544741 | ||||||||
\(573\) | 8.95026 | 0.373903 | ||||||||
\(574\) | 9.80788 | 0.409373 | ||||||||
\(575\) | 1.22212 | 0.0509661 | ||||||||
\(576\) | −2.17846 | −0.0907693 | ||||||||
\(577\) | 18.5904 | 0.773928 | 0.386964 | − | 0.922095i | \(-0.373524\pi\) | ||||
0.386964 | + | 0.922095i | \(0.373524\pi\) | |||||||
\(578\) | 0.522212 | 0.0217212 | ||||||||
\(579\) | −6.05971 | −0.251833 | ||||||||
\(580\) | −38.0704 | −1.58079 | ||||||||
\(581\) | −33.5800 | −1.39313 | ||||||||
\(582\) | −3.14614 | −0.130412 | ||||||||
\(583\) | 29.3633 | 1.21610 | ||||||||
\(584\) | 4.71906 | 0.195276 | ||||||||
\(585\) | −4.95466 | −0.204850 | ||||||||
\(586\) | 9.43620 | 0.389806 | ||||||||
\(587\) | −48.0234 | −1.98214 | −0.991068 | − | 0.133355i | \(-0.957425\pi\) | ||||
−0.991068 | + | 0.133355i | \(0.957425\pi\) | |||||||
\(588\) | 34.7211 | 1.43188 | ||||||||
\(589\) | 32.0800 | 1.32183 | ||||||||
\(590\) | −12.4494 | −0.512532 | ||||||||
\(591\) | −8.51967 | −0.350452 | ||||||||
\(592\) | −27.3997 | −1.12612 | ||||||||
\(593\) | −39.2854 | −1.61326 | −0.806628 | − | 0.591059i | \(-0.798710\pi\) | ||||
−0.806628 | + | 0.591059i | \(0.798710\pi\) | |||||||
\(594\) | −1.98030 | −0.0812525 | ||||||||
\(595\) | 12.9679 | 0.531633 | ||||||||
\(596\) | 5.17088 | 0.211807 | ||||||||
\(597\) | 4.14330 | 0.169574 | ||||||||
\(598\) | 1.05337 | 0.0430755 | ||||||||
\(599\) | −9.01560 | −0.368367 | −0.184184 | − | 0.982892i | \(-0.558964\pi\) | ||||
−0.184184 | + | 0.982892i | \(0.558964\pi\) | |||||||
\(600\) | 2.34564 | 0.0957604 | ||||||||
\(601\) | 43.2024 | 1.76226 | 0.881132 | − | 0.472871i | \(-0.156782\pi\) | ||||
0.881132 | + | 0.472871i | \(0.156782\pi\) | |||||||
\(602\) | 9.47309 | 0.386094 | ||||||||
\(603\) | 1.51522 | 0.0617045 | ||||||||
\(604\) | 3.71044 | 0.150976 | ||||||||
\(605\) | −8.42013 | −0.342327 | ||||||||
\(606\) | −8.42252 | −0.342141 | ||||||||
\(607\) | 14.1323 | 0.573610 | 0.286805 | − | 0.957989i | \(-0.407407\pi\) | ||||
0.286805 | + | 0.957989i | \(0.407407\pi\) | |||||||
\(608\) | −22.9858 | −0.932196 | ||||||||
\(609\) | 46.0621 | 1.86653 | ||||||||
\(610\) | 5.86283 | 0.237379 | ||||||||
\(611\) | −0.653971 | −0.0264568 | ||||||||
\(612\) | 1.72729 | 0.0698217 | ||||||||
\(613\) | 4.12819 | 0.166736 | 0.0833681 | − | 0.996519i | \(-0.473432\pi\) | ||||
0.0833681 | + | 0.996519i | \(0.473432\pi\) | |||||||
\(614\) | −13.4535 | −0.542938 | ||||||||
\(615\) | 8.98681 | 0.362383 | ||||||||
\(616\) | −38.4255 | −1.54821 | ||||||||
\(617\) | 20.8254 | 0.838399 | 0.419199 | − | 0.907894i | \(-0.362311\pi\) | ||||
0.419199 | + | 0.907894i | \(0.362311\pi\) | |||||||
\(618\) | 5.99019 | 0.240961 | ||||||||
\(619\) | −13.7296 | −0.551840 | −0.275920 | − | 0.961181i | \(-0.588982\pi\) | ||||
−0.275920 | + | 0.961181i | \(0.588982\pi\) | |||||||
\(620\) | −31.0226 | −1.24590 | ||||||||
\(621\) | −1.01413 | −0.0406957 | ||||||||
\(622\) | −0.753112 | −0.0301970 | ||||||||
\(623\) | −50.5583 | −2.02558 | ||||||||
\(624\) | −4.84950 | −0.194135 | ||||||||
\(625\) | −29.5732 | −1.18293 | ||||||||
\(626\) | −10.0196 | −0.400465 | ||||||||
\(627\) | 16.8725 | 0.673822 | ||||||||
\(628\) | 1.72729 | 0.0689265 | ||||||||
\(629\) | 11.2380 | 0.448088 | ||||||||
\(630\) | −6.77201 | −0.269803 | ||||||||
\(631\) | −11.2146 | −0.446445 | −0.223222 | − | 0.974768i | \(-0.571658\pi\) | ||||
−0.223222 | + | 0.974768i | \(0.571658\pi\) | |||||||
\(632\) | 0.137868 | 0.00548411 | ||||||||
\(633\) | 21.8940 | 0.870209 | ||||||||
\(634\) | 8.71150 | 0.345978 | ||||||||
\(635\) | −16.3991 | −0.650779 | ||||||||
\(636\) | 13.3748 | 0.530347 | ||||||||
\(637\) | 39.9822 | 1.58415 | ||||||||
\(638\) | −17.5217 | −0.693693 | ||||||||
\(639\) | 0.798424 | 0.0315852 | ||||||||
\(640\) | 28.5714 | 1.12938 | ||||||||
\(641\) | 12.7651 | 0.504189 | 0.252095 | − | 0.967703i | \(-0.418881\pi\) | ||||
0.252095 | + | 0.967703i | \(0.418881\pi\) | |||||||
\(642\) | −9.49753 | −0.374838 | ||||||||
\(643\) | −35.8234 | −1.41274 | −0.706369 | − | 0.707843i | \(-0.749668\pi\) | ||||
−0.706369 | + | 0.707843i | \(0.749668\pi\) | |||||||
\(644\) | −9.11921 | −0.359347 | ||||||||
\(645\) | 8.68005 | 0.341777 | ||||||||
\(646\) | 2.32350 | 0.0914170 | ||||||||
\(647\) | 40.8681 | 1.60669 | 0.803346 | − | 0.595512i | \(-0.203051\pi\) | ||||
0.803346 | + | 0.595512i | \(0.203051\pi\) | |||||||
\(648\) | −1.94644 | −0.0764634 | ||||||||
\(649\) | 36.2918 | 1.42458 | ||||||||
\(650\) | 1.25172 | 0.0490965 | ||||||||
\(651\) | 37.5348 | 1.47111 | ||||||||
\(652\) | 10.8137 | 0.423496 | ||||||||
\(653\) | −4.36228 | −0.170709 | −0.0853547 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853547 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(654\) | 8.36404 | 0.327060 | ||||||||
\(655\) | 24.0060 | 0.937994 | ||||||||
\(656\) | 8.79607 | 0.343429 | ||||||||
\(657\) | −2.42446 | −0.0945870 | ||||||||
\(658\) | −0.893846 | −0.0348457 | ||||||||
\(659\) | −18.8712 | −0.735116 | −0.367558 | − | 0.930001i | \(-0.619806\pi\) | ||||
−0.367558 | + | 0.930001i | \(0.619806\pi\) | |||||||
\(660\) | −16.3164 | −0.635113 | ||||||||
\(661\) | 14.0194 | 0.545290 | 0.272645 | − | 0.962115i | \(-0.412102\pi\) | ||||
0.272645 | + | 0.962115i | \(0.412102\pi\) | |||||||
\(662\) | −2.56928 | −0.0998578 | ||||||||
\(663\) | 1.98902 | 0.0772472 | ||||||||
\(664\) | 12.5552 | 0.487238 | ||||||||
\(665\) | 57.6988 | 2.23746 | ||||||||
\(666\) | −5.86862 | −0.227404 | ||||||||
\(667\) | −8.97309 | −0.347440 | ||||||||
\(668\) | 20.3265 | 0.786455 | ||||||||
\(669\) | 18.6656 | 0.721655 | ||||||||
\(670\) | −1.97105 | −0.0761482 | ||||||||
\(671\) | −17.0910 | −0.659792 | ||||||||
\(672\) | −26.8942 | −1.03747 | ||||||||
\(673\) | 15.3836 | 0.592994 | 0.296497 | − | 0.955034i | \(-0.404181\pi\) | ||||
0.296497 | + | 0.955034i | \(0.404181\pi\) | |||||||
\(674\) | −7.69037 | −0.296222 | ||||||||
\(675\) | −1.20509 | −0.0463841 | ||||||||
\(676\) | 15.6213 | 0.600819 | ||||||||
\(677\) | −6.08494 | −0.233863 | −0.116932 | − | 0.993140i | \(-0.537306\pi\) | ||||
−0.116932 | + | 0.993140i | \(0.537306\pi\) | |||||||
\(678\) | 8.82887 | 0.339071 | ||||||||
\(679\) | 31.3637 | 1.20363 | ||||||||
\(680\) | −4.84859 | −0.185935 | ||||||||
\(681\) | −6.96732 | −0.266988 | ||||||||
\(682\) | −14.2780 | −0.546733 | ||||||||
\(683\) | 15.3846 | 0.588674 | 0.294337 | − | 0.955702i | \(-0.404901\pi\) | ||||
0.294337 | + | 0.955702i | \(0.404901\pi\) | |||||||
\(684\) | 7.68533 | 0.293856 | ||||||||
\(685\) | 36.5907 | 1.39806 | ||||||||
\(686\) | 35.6175 | 1.35988 | ||||||||
\(687\) | 10.7510 | 0.410175 | ||||||||
\(688\) | 8.49582 | 0.323900 | ||||||||
\(689\) | 15.4015 | 0.586749 | ||||||||
\(690\) | 1.31922 | 0.0502217 | ||||||||
\(691\) | 24.9157 | 0.947839 | 0.473920 | − | 0.880568i | \(-0.342839\pi\) | ||||
0.473920 | + | 0.880568i | \(0.342839\pi\) | |||||||
\(692\) | −33.5901 | −1.27691 | ||||||||
\(693\) | 19.7415 | 0.749916 | ||||||||
\(694\) | −0.691513 | −0.0262495 | ||||||||
\(695\) | 1.89374 | 0.0718338 | ||||||||
\(696\) | −17.2222 | −0.652805 | ||||||||
\(697\) | −3.60771 | −0.136652 | ||||||||
\(698\) | 0.827086 | 0.0313057 | ||||||||
\(699\) | 21.1681 | 0.800652 | ||||||||
\(700\) | −10.8364 | −0.409576 | ||||||||
\(701\) | −11.0105 | −0.415861 | −0.207930 | − | 0.978144i | \(-0.566673\pi\) | ||||
−0.207930 | + | 0.978144i | \(0.566673\pi\) | |||||||
\(702\) | −1.03869 | −0.0392029 | ||||||||
\(703\) | 50.0017 | 1.88585 | ||||||||
\(704\) | −8.26101 | −0.311349 | ||||||||
\(705\) | −0.819017 | −0.0308460 | ||||||||
\(706\) | 0.112050 | 0.00421707 | ||||||||
\(707\) | 83.9636 | 3.15778 | ||||||||
\(708\) | 16.5307 | 0.621263 | ||||||||
\(709\) | 8.85382 | 0.332512 | 0.166256 | − | 0.986083i | \(-0.446832\pi\) | ||||
0.166256 | + | 0.986083i | \(0.446832\pi\) | |||||||
\(710\) | −1.03862 | −0.0389786 | ||||||||
\(711\) | −0.0708311 | −0.00265637 | ||||||||
\(712\) | 18.9033 | 0.708430 | ||||||||
\(713\) | −7.31194 | −0.273834 | ||||||||
\(714\) | 2.71859 | 0.101741 | ||||||||
\(715\) | −18.7887 | −0.702657 | ||||||||
\(716\) | −37.6795 | −1.40815 | ||||||||
\(717\) | 19.0843 | 0.712715 | ||||||||
\(718\) | −0.262798 | −0.00980752 | ||||||||
\(719\) | 1.50252 | 0.0560346 | 0.0280173 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280173 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(720\) | −6.07340 | −0.226342 | ||||||||
\(721\) | −59.7159 | −2.22394 | ||||||||
\(722\) | 0.416034 | 0.0154832 | ||||||||
\(723\) | 20.0543 | 0.745829 | ||||||||
\(724\) | −19.0978 | −0.709765 | ||||||||
\(725\) | −10.6627 | −0.396004 | ||||||||
\(726\) | −1.76519 | −0.0655124 | ||||||||
\(727\) | −8.16987 | −0.303004 | −0.151502 | − | 0.988457i | \(-0.548411\pi\) | ||||
−0.151502 | + | 0.988457i | \(0.548411\pi\) | |||||||
\(728\) | −20.1547 | −0.746983 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.15381 | 0.116728 | ||||||||
\(731\) | −3.48456 | −0.128881 | ||||||||
\(732\) | −7.78488 | −0.287737 | ||||||||
\(733\) | −49.6438 | −1.83363 | −0.916817 | − | 0.399307i | \(-0.869251\pi\) | ||||
−0.916817 | + | 0.399307i | \(0.869251\pi\) | |||||||
\(734\) | 9.13205 | 0.337070 | ||||||||
\(735\) | 50.0728 | 1.84696 | ||||||||
\(736\) | 5.23911 | 0.193116 | ||||||||
\(737\) | 5.74590 | 0.211653 | ||||||||
\(738\) | 1.88399 | 0.0693506 | ||||||||
\(739\) | −14.2807 | −0.525324 | −0.262662 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262662 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(740\) | −48.3536 | −1.77751 | ||||||||
\(741\) | 8.84984 | 0.325107 | ||||||||
\(742\) | 21.0507 | 0.772794 | ||||||||
\(743\) | −30.7706 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(744\) | −14.0339 | −0.514508 | ||||||||
\(745\) | 7.45713 | 0.273208 | ||||||||
\(746\) | 11.1468 | 0.408113 | ||||||||
\(747\) | −6.45036 | −0.236006 | ||||||||
\(748\) | 6.55012 | 0.239496 | ||||||||
\(749\) | 94.6803 | 3.45954 | ||||||||
\(750\) | −4.93654 | −0.180257 | ||||||||
\(751\) | −33.7472 | −1.23145 | −0.615727 | − | 0.787960i | \(-0.711138\pi\) | ||||
−0.615727 | + | 0.787960i | \(0.711138\pi\) | |||||||
\(752\) | −0.801635 | −0.0292326 | ||||||||
\(753\) | −16.9195 | −0.616581 | ||||||||
\(754\) | −9.19039 | −0.334694 | ||||||||
\(755\) | 5.35098 | 0.194742 | ||||||||
\(756\) | 8.99213 | 0.327041 | ||||||||
\(757\) | −1.48260 | −0.0538862 | −0.0269431 | − | 0.999637i | \(-0.508577\pi\) | ||||
−0.0269431 | + | 0.999637i | \(0.508577\pi\) | |||||||
\(758\) | −19.6397 | −0.713345 | ||||||||
\(759\) | −3.84572 | −0.139591 | ||||||||
\(760\) | −21.5730 | −0.782536 | ||||||||
\(761\) | −29.5931 | −1.07275 | −0.536374 | − | 0.843980i | \(-0.680206\pi\) | ||||
−0.536374 | + | 0.843980i | \(0.680206\pi\) | |||||||
\(762\) | −3.43790 | −0.124542 | ||||||||
\(763\) | −83.3807 | −3.01858 | ||||||||
\(764\) | 15.4597 | 0.559314 | ||||||||
\(765\) | 2.49100 | 0.0900624 | ||||||||
\(766\) | 4.10289 | 0.148244 | ||||||||
\(767\) | 19.0355 | 0.687334 | ||||||||
\(768\) | 1.63276 | 0.0589170 | ||||||||
\(769\) | −14.9783 | −0.540131 | −0.270065 | − | 0.962842i | \(-0.587045\pi\) | ||||
−0.270065 | + | 0.962842i | \(0.587045\pi\) | |||||||
\(770\) | −25.6803 | −0.925455 | ||||||||
\(771\) | −4.62699 | −0.166637 | ||||||||
\(772\) | −10.4669 | −0.376712 | ||||||||
\(773\) | −20.1276 | −0.723940 | −0.361970 | − | 0.932190i | \(-0.617896\pi\) | ||||
−0.361970 | + | 0.932190i | \(0.617896\pi\) | |||||||
\(774\) | 1.81968 | 0.0654071 | ||||||||
\(775\) | −8.68878 | −0.312110 | ||||||||
\(776\) | −11.7266 | −0.420961 | ||||||||
\(777\) | 58.5039 | 2.09882 | ||||||||
\(778\) | −16.2104 | −0.581171 | ||||||||
\(779\) | −16.0519 | −0.575120 | ||||||||
\(780\) | −8.55815 | −0.306431 | ||||||||
\(781\) | 3.02773 | 0.108341 | ||||||||
\(782\) | −0.529593 | −0.0189382 | ||||||||
\(783\) | 8.84805 | 0.316203 | ||||||||
\(784\) | 49.0101 | 1.75036 | ||||||||
\(785\) | 2.49100 | 0.0889077 | ||||||||
\(786\) | 5.03261 | 0.179507 | ||||||||
\(787\) | −5.71390 | −0.203679 | −0.101839 | − | 0.994801i | \(-0.532473\pi\) | ||||
−0.101839 | + | 0.994801i | \(0.532473\pi\) | |||||||
\(788\) | −14.7160 | −0.524235 | ||||||||
\(789\) | 11.4847 | 0.408867 | ||||||||
\(790\) | 0.0921394 | 0.00327817 | ||||||||
\(791\) | −88.0145 | −3.12943 | ||||||||
\(792\) | −7.38114 | −0.262277 | ||||||||
\(793\) | −8.96447 | −0.318338 | ||||||||
\(794\) | 2.59531 | 0.0921041 | ||||||||
\(795\) | 19.2884 | 0.684090 | ||||||||
\(796\) | 7.15669 | 0.253662 | ||||||||
\(797\) | 14.2418 | 0.504470 | 0.252235 | − | 0.967666i | \(-0.418834\pi\) | ||||
0.252235 | + | 0.967666i | \(0.418834\pi\) | |||||||
\(798\) | 12.0959 | 0.428192 | ||||||||
\(799\) | 0.328790 | 0.0116318 | ||||||||
\(800\) | 6.22564 | 0.220110 | ||||||||
\(801\) | −9.71172 | −0.343147 | ||||||||
\(802\) | 8.10824 | 0.286312 | ||||||||
\(803\) | −9.19384 | −0.324444 | ||||||||
\(804\) | 2.61723 | 0.0923026 | ||||||||
\(805\) | −13.1512 | −0.463519 | ||||||||
\(806\) | −7.48901 | −0.263789 | ||||||||
\(807\) | −26.0351 | −0.916480 | ||||||||
\(808\) | −31.3932 | −1.10441 | ||||||||
\(809\) | −26.6439 | −0.936751 | −0.468375 | − | 0.883530i | \(-0.655160\pi\) | ||||
−0.468375 | + | 0.883530i | \(0.655160\pi\) | |||||||
\(810\) | −1.30083 | −0.0457066 | ||||||||
\(811\) | 42.3718 | 1.48788 | 0.743938 | − | 0.668249i | \(-0.232956\pi\) | ||||
0.743938 | + | 0.668249i | \(0.232956\pi\) | |||||||
\(812\) | 79.5628 | 2.79211 | ||||||||
\(813\) | 21.6310 | 0.758634 | ||||||||
\(814\) | −22.2545 | −0.780021 | ||||||||
\(815\) | 15.5948 | 0.546264 | ||||||||
\(816\) | 2.43813 | 0.0853517 | ||||||||
\(817\) | −15.5040 | −0.542417 | ||||||||
\(818\) | 11.3645 | 0.397351 | ||||||||
\(819\) | 10.3547 | 0.361821 | ||||||||
\(820\) | 15.5229 | 0.542082 | ||||||||
\(821\) | −11.9910 | −0.418488 | −0.209244 | − | 0.977863i | \(-0.567100\pi\) | ||||
−0.209244 | + | 0.977863i | \(0.567100\pi\) | |||||||
\(822\) | 7.67085 | 0.267552 | ||||||||
\(823\) | −39.3510 | −1.37169 | −0.685845 | − | 0.727748i | \(-0.740567\pi\) | ||||
−0.685845 | + | 0.727748i | \(0.740567\pi\) | |||||||
\(824\) | 22.3272 | 0.777805 | ||||||||
\(825\) | −4.56987 | −0.159102 | ||||||||
\(826\) | 26.0177 | 0.905273 | ||||||||
\(827\) | 27.0540 | 0.940759 | 0.470379 | − | 0.882464i | \(-0.344117\pi\) | ||||
0.470379 | + | 0.882464i | \(0.344117\pi\) | |||||||
\(828\) | −1.75171 | −0.0608760 | ||||||||
\(829\) | −27.6852 | −0.961546 | −0.480773 | − | 0.876845i | \(-0.659644\pi\) | ||||
−0.480773 | + | 0.876845i | \(0.659644\pi\) | |||||||
\(830\) | 8.39084 | 0.291250 | ||||||||
\(831\) | 13.8130 | 0.479167 | ||||||||
\(832\) | −4.33301 | −0.150220 | ||||||||
\(833\) | −20.1015 | −0.696475 | ||||||||
\(834\) | 0.397004 | 0.0137471 | ||||||||
\(835\) | 29.3137 | 1.01444 | ||||||||
\(836\) | 29.1437 | 1.00796 | ||||||||
\(837\) | 7.21004 | 0.249216 | ||||||||
\(838\) | 15.2068 | 0.525309 | ||||||||
\(839\) | 3.36480 | 0.116166 | 0.0580829 | − | 0.998312i | \(-0.481501\pi\) | ||||
0.0580829 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(840\) | −25.2413 | −0.870907 | ||||||||
\(841\) | 49.2879 | 1.69958 | ||||||||
\(842\) | 15.3227 | 0.528054 | ||||||||
\(843\) | 10.6326 | 0.366205 | ||||||||
\(844\) | 37.8174 | 1.30173 | ||||||||
\(845\) | 22.5281 | 0.774991 | ||||||||
\(846\) | −0.171698 | −0.00590311 | ||||||||
\(847\) | 17.5971 | 0.604643 | ||||||||
\(848\) | 18.8790 | 0.648309 | ||||||||
\(849\) | −18.4505 | −0.633220 | ||||||||
\(850\) | −0.629315 | −0.0215853 | ||||||||
\(851\) | −11.3968 | −0.390678 | ||||||||
\(852\) | 1.37911 | 0.0472477 | ||||||||
\(853\) | −32.7232 | −1.12042 | −0.560210 | − | 0.828350i | \(-0.689280\pi\) | ||||
−0.560210 | + | 0.828350i | \(0.689280\pi\) | |||||||
\(854\) | −12.2526 | −0.419276 | ||||||||
\(855\) | 11.0833 | 0.379042 | ||||||||
\(856\) | −35.4001 | −1.20995 | ||||||||
\(857\) | −40.0228 | −1.36715 | −0.683576 | − | 0.729880i | \(-0.739576\pi\) | ||||
−0.683576 | + | 0.729880i | \(0.739576\pi\) | |||||||
\(858\) | −3.93885 | −0.134470 | ||||||||
\(859\) | −45.8602 | −1.56473 | −0.782364 | − | 0.622821i | \(-0.785986\pi\) | ||||
−0.782364 | + | 0.622821i | \(0.785986\pi\) | |||||||
\(860\) | 14.9930 | 0.511257 | ||||||||
\(861\) | −18.7814 | −0.640068 | ||||||||
\(862\) | −1.17291 | −0.0399495 | ||||||||
\(863\) | 3.56646 | 0.121404 | 0.0607018 | − | 0.998156i | \(-0.480666\pi\) | ||||
0.0607018 | + | 0.998156i | \(0.480666\pi\) | |||||||
\(864\) | −5.16610 | −0.175754 | ||||||||
\(865\) | −48.4417 | −1.64707 | ||||||||
\(866\) | 1.37418 | 0.0466965 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 64.8337 | 2.20060 | ||||||||
\(869\) | −0.268600 | −0.00911165 | ||||||||
\(870\) | −11.5098 | −0.390220 | ||||||||
\(871\) | 3.01380 | 0.102119 | ||||||||
\(872\) | 31.1753 | 1.05573 | ||||||||
\(873\) | 6.02464 | 0.203903 | ||||||||
\(874\) | −2.35634 | −0.0797044 | ||||||||
\(875\) | 49.2121 | 1.66367 | ||||||||
\(876\) | −4.18775 | −0.141491 | ||||||||
\(877\) | 27.2368 | 0.919722 | 0.459861 | − | 0.887991i | \(-0.347899\pi\) | ||||
0.459861 | + | 0.887991i | \(0.347899\pi\) | |||||||
\(878\) | −17.2935 | −0.583628 | ||||||||
\(879\) | −18.0697 | −0.609474 | ||||||||
\(880\) | −23.0311 | −0.776378 | ||||||||
\(881\) | 6.92647 | 0.233359 | 0.116679 | − | 0.993170i | \(-0.462775\pi\) | ||||
0.116679 | + | 0.993170i | \(0.462775\pi\) | |||||||
\(882\) | 10.4972 | 0.353460 | ||||||||
\(883\) | −7.49222 | −0.252133 | −0.126067 | − | 0.992022i | \(-0.540235\pi\) | ||||
−0.126067 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(884\) | 3.43562 | 0.115553 | ||||||||
\(885\) | 23.8397 | 0.801362 | ||||||||
\(886\) | −10.6129 | −0.356547 | ||||||||
\(887\) | 16.3091 | 0.547605 | 0.273803 | − | 0.961786i | \(-0.411719\pi\) | ||||
0.273803 | + | 0.961786i | \(0.411719\pi\) | |||||||
\(888\) | −21.8741 | −0.734046 | ||||||||
\(889\) | 34.2723 | 1.14945 | ||||||||
\(890\) | 12.6333 | 0.423470 | ||||||||
\(891\) | 3.79213 | 0.127041 | ||||||||
\(892\) | 32.2410 | 1.07951 | ||||||||
\(893\) | 1.46290 | 0.0489541 | ||||||||
\(894\) | 1.56331 | 0.0522849 | ||||||||
\(895\) | −54.3391 | −1.81636 | ||||||||
\(896\) | −59.7108 | −1.99480 | ||||||||
\(897\) | −2.01713 | −0.0673500 | ||||||||
\(898\) | −10.0480 | −0.335305 | ||||||||
\(899\) | 63.7948 | 2.12768 | ||||||||
\(900\) | −2.08155 | −0.0693851 | ||||||||
\(901\) | −7.74323 | −0.257965 | ||||||||
\(902\) | 7.14433 | 0.237880 | ||||||||
\(903\) | −18.1403 | −0.603671 | ||||||||
\(904\) | 32.9078 | 1.09450 | ||||||||
\(905\) | −27.5418 | −0.915520 | ||||||||
\(906\) | 1.12178 | 0.0372685 | ||||||||
\(907\) | −5.00073 | −0.166047 | −0.0830233 | − | 0.996548i | \(-0.526458\pi\) | ||||
−0.0830233 | + | 0.996548i | \(0.526458\pi\) | |||||||
\(908\) | −12.0346 | −0.399383 | ||||||||
\(909\) | 16.1285 | 0.534949 | ||||||||
\(910\) | −13.4697 | −0.446515 | ||||||||
\(911\) | −9.84715 | −0.326251 | −0.163125 | − | 0.986605i | \(-0.552158\pi\) | ||||
−0.163125 | + | 0.986605i | \(0.552158\pi\) | |||||||
\(912\) | 10.8481 | 0.359216 | ||||||||
\(913\) | −24.4606 | −0.809527 | ||||||||
\(914\) | 17.3468 | 0.573780 | ||||||||
\(915\) | −11.2269 | −0.371150 | ||||||||
\(916\) | 18.5701 | 0.613573 | ||||||||
\(917\) | −50.1698 | −1.65675 | ||||||||
\(918\) | 0.522212 | 0.0172356 | ||||||||
\(919\) | 26.6248 | 0.878270 | 0.439135 | − | 0.898421i | \(-0.355285\pi\) | ||||
0.439135 | + | 0.898421i | \(0.355285\pi\) | |||||||
\(920\) | 4.91711 | 0.162112 | ||||||||
\(921\) | 25.7624 | 0.848901 | ||||||||
\(922\) | 5.95245 | 0.196034 | ||||||||
\(923\) | 1.58808 | 0.0522724 | ||||||||
\(924\) | 34.0993 | 1.12178 | ||||||||
\(925\) | −13.5428 | −0.445286 | ||||||||
\(926\) | 12.9086 | 0.424202 | ||||||||
\(927\) | −11.4708 | −0.376750 | ||||||||
\(928\) | −45.7099 | −1.50050 | ||||||||
\(929\) | −23.4936 | −0.770799 | −0.385399 | − | 0.922750i | \(-0.625936\pi\) | ||||
−0.385399 | + | 0.922750i | \(0.625936\pi\) | |||||||
\(930\) | −9.37906 | −0.307551 | ||||||||
\(931\) | −89.4384 | −2.93122 | ||||||||
\(932\) | 36.5636 | 1.19768 | ||||||||
\(933\) | 1.44216 | 0.0472141 | ||||||||
\(934\) | −6.64031 | −0.217277 | ||||||||
\(935\) | 9.44620 | 0.308924 | ||||||||
\(936\) | −3.87151 | −0.126544 | ||||||||
\(937\) | 9.16463 | 0.299396 | 0.149698 | − | 0.988732i | \(-0.452170\pi\) | ||||
0.149698 | + | 0.988732i | \(0.452170\pi\) | |||||||
\(938\) | 4.11926 | 0.134499 | ||||||||
\(939\) | 19.1869 | 0.626140 | ||||||||
\(940\) | −1.41468 | −0.0461419 | ||||||||
\(941\) | 33.1940 | 1.08209 | 0.541046 | − | 0.840993i | \(-0.318028\pi\) | ||||
0.541046 | + | 0.840993i | \(0.318028\pi\) | |||||||
\(942\) | 0.522212 | 0.0170146 | ||||||||
\(943\) | 3.65869 | 0.119143 | ||||||||
\(944\) | 23.3337 | 0.759447 | ||||||||
\(945\) | 12.9679 | 0.421847 | ||||||||
\(946\) | 6.90046 | 0.224353 | ||||||||
\(947\) | 39.4199 | 1.28097 | 0.640487 | − | 0.767969i | \(-0.278733\pi\) | ||||
0.640487 | + | 0.767969i | \(0.278733\pi\) | |||||||
\(948\) | −0.122346 | −0.00397362 | ||||||||
\(949\) | −4.82229 | −0.156538 | ||||||||
\(950\) | −2.80004 | −0.0908453 | ||||||||
\(951\) | −16.6819 | −0.540948 | ||||||||
\(952\) | 10.1330 | 0.328412 | ||||||||
\(953\) | −20.3173 | −0.658141 | −0.329070 | − | 0.944305i | \(-0.606735\pi\) | ||||
−0.329070 | + | 0.944305i | \(0.606735\pi\) | |||||||
\(954\) | 4.04361 | 0.130917 | ||||||||
\(955\) | 22.2951 | 0.721453 | ||||||||
\(956\) | 32.9641 | 1.06614 | ||||||||
\(957\) | 33.5529 | 1.08461 | ||||||||
\(958\) | −15.1611 | −0.489832 | ||||||||
\(959\) | −76.4703 | −2.46936 | ||||||||
\(960\) | −5.42656 | −0.175141 | ||||||||
\(961\) | 20.9847 | 0.676927 | ||||||||
\(962\) | −11.6728 | −0.376346 | ||||||||
\(963\) | 18.1871 | 0.586071 | ||||||||
\(964\) | 34.6398 | 1.11567 | ||||||||
\(965\) | −15.0947 | −0.485917 | ||||||||
\(966\) | −2.75701 | −0.0887053 | ||||||||
\(967\) | 50.5603 | 1.62591 | 0.812955 | − | 0.582327i | \(-0.197858\pi\) | ||||
0.812955 | + | 0.582327i | \(0.197858\pi\) | |||||||
\(968\) | −6.57939 | −0.211470 | ||||||||
\(969\) | −4.44935 | −0.142934 | ||||||||
\(970\) | −7.83705 | −0.251633 | ||||||||
\(971\) | −36.0127 | −1.15570 | −0.577851 | − | 0.816142i | \(-0.696109\pi\) | ||||
−0.577851 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(972\) | 1.72729 | 0.0554030 | ||||||||
\(973\) | −3.95771 | −0.126878 | ||||||||
\(974\) | −8.61213 | −0.275950 | ||||||||
\(975\) | −2.39696 | −0.0767640 | ||||||||
\(976\) | −10.9886 | −0.351737 | ||||||||
\(977\) | −16.9909 | −0.543589 | −0.271794 | − | 0.962355i | \(-0.587617\pi\) | ||||
−0.271794 | + | 0.962355i | \(0.587617\pi\) | |||||||
\(978\) | 3.26929 | 0.104541 | ||||||||
\(979\) | −36.8281 | −1.17703 | ||||||||
\(980\) | 86.4905 | 2.76284 | ||||||||
\(981\) | −16.0166 | −0.511369 | ||||||||
\(982\) | −11.4143 | −0.364244 | ||||||||
\(983\) | 11.7320 | 0.374192 | 0.187096 | − | 0.982342i | \(-0.440092\pi\) | ||||
0.187096 | + | 0.982342i | \(0.440092\pi\) | |||||||
\(984\) | 7.02218 | 0.223859 | ||||||||
\(985\) | −21.2225 | −0.676206 | ||||||||
\(986\) | 4.62056 | 0.147149 | ||||||||
\(987\) | 1.71165 | 0.0544825 | ||||||||
\(988\) | 15.2863 | 0.486321 | ||||||||
\(989\) | 3.53381 | 0.112368 | ||||||||
\(990\) | −4.93292 | −0.156779 | ||||||||
\(991\) | −29.8970 | −0.949709 | −0.474855 | − | 0.880064i | \(-0.657499\pi\) | ||||
−0.474855 | + | 0.880064i | \(0.657499\pi\) | |||||||
\(992\) | −37.2478 | −1.18262 | ||||||||
\(993\) | 4.91999 | 0.156131 | ||||||||
\(994\) | 2.17059 | 0.0688469 | ||||||||
\(995\) | 10.3210 | 0.327196 | ||||||||
\(996\) | −11.1417 | −0.353037 | ||||||||
\(997\) | 47.7503 | 1.51227 | 0.756133 | − | 0.654417i | \(-0.227086\pi\) | ||||
0.756133 | + | 0.654417i | \(0.227086\pi\) | |||||||
\(998\) | 3.75563 | 0.118882 | ||||||||
\(999\) | 11.2380 | 0.355554 |
(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 | 8007.2.a.f.1.29 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.29 | ✓ | 48 | 1.1 | even | 1 | trivial |