Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54054 | −1.79643 | −0.898215 | − | 0.439556i | \(-0.855136\pi\) | ||||
−0.898215 | + | 0.439556i | \(0.855136\pi\) | |||||||
\(3\) | 2.90668 | 1.67817 | 0.839087 | − | 0.543997i | \(-0.183090\pi\) | ||||
0.839087 | + | 0.543997i | \(0.183090\pi\) | |||||||
\(4\) | 4.45432 | 2.22716 | ||||||||
\(5\) | −2.39844 | −1.07262 | −0.536309 | − | 0.844022i | \(-0.680182\pi\) | ||||
−0.536309 | + | 0.844022i | \(0.680182\pi\) | |||||||
\(6\) | −7.38453 | −3.01472 | ||||||||
\(7\) | 0.864832 | 0.326876 | 0.163438 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163438 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(8\) | −6.23529 | −2.20451 | ||||||||
\(9\) | 5.44881 | 1.81627 | ||||||||
\(10\) | 6.09333 | 1.92688 | ||||||||
\(11\) | 0.754457 | 0.227477 | 0.113739 | − | 0.993511i | \(-0.463717\pi\) | ||||
0.113739 | + | 0.993511i | \(0.463717\pi\) | |||||||
\(12\) | 12.9473 | 3.73756 | ||||||||
\(13\) | 6.48536 | 1.79871 | 0.899357 | − | 0.437215i | \(-0.144035\pi\) | ||||
0.899357 | + | 0.437215i | \(0.144035\pi\) | |||||||
\(14\) | −2.19714 | −0.587209 | ||||||||
\(15\) | −6.97152 | −1.80004 | ||||||||
\(16\) | 6.93234 | 1.73308 | ||||||||
\(17\) | −2.24253 | −0.543894 | −0.271947 | − | 0.962312i | \(-0.587668\pi\) | ||||
−0.271947 | + | 0.962312i | \(0.587668\pi\) | |||||||
\(18\) | −13.8429 | −3.26280 | ||||||||
\(19\) | 4.96611 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(20\) | −10.6834 | −2.38889 | ||||||||
\(21\) | 2.51379 | 0.548554 | ||||||||
\(22\) | −1.91672 | −0.408647 | ||||||||
\(23\) | −5.99611 | −1.25028 | −0.625138 | − | 0.780514i | \(-0.714957\pi\) | ||||
−0.625138 | + | 0.780514i | \(0.714957\pi\) | |||||||
\(24\) | −18.1240 | −3.69955 | ||||||||
\(25\) | 0.752537 | 0.150507 | ||||||||
\(26\) | −16.4763 | −3.23126 | ||||||||
\(27\) | 7.11791 | 1.36984 | ||||||||
\(28\) | 3.85224 | 0.728005 | ||||||||
\(29\) | −8.64730 | −1.60576 | −0.802882 | − | 0.596138i | \(-0.796701\pi\) | ||||
−0.802882 | + | 0.596138i | \(0.796701\pi\) | |||||||
\(30\) | 17.7114 | 3.23364 | ||||||||
\(31\) | −4.93301 | −0.885996 | −0.442998 | − | 0.896523i | \(-0.646085\pi\) | ||||
−0.442998 | + | 0.896523i | \(0.646085\pi\) | |||||||
\(32\) | −5.14127 | −0.908857 | ||||||||
\(33\) | 2.19297 | 0.381747 | ||||||||
\(34\) | 5.69724 | 0.977068 | ||||||||
\(35\) | −2.07425 | −0.350612 | ||||||||
\(36\) | 24.2707 | 4.04512 | ||||||||
\(37\) | −8.49641 | −1.39680 | −0.698400 | − | 0.715707i | \(-0.746104\pi\) | ||||
−0.698400 | + | 0.715707i | \(0.746104\pi\) | |||||||
\(38\) | −12.6166 | −2.04668 | ||||||||
\(39\) | 18.8509 | 3.01856 | ||||||||
\(40\) | 14.9550 | 2.36459 | ||||||||
\(41\) | 7.04999 | 1.10102 | 0.550512 | − | 0.834827i | \(-0.314433\pi\) | ||||
0.550512 | + | 0.834827i | \(0.314433\pi\) | |||||||
\(42\) | −6.38638 | −0.985440 | ||||||||
\(43\) | −4.93997 | −0.753338 | −0.376669 | − | 0.926348i | \(-0.622931\pi\) | ||||
−0.376669 | + | 0.926348i | \(0.622931\pi\) | |||||||
\(44\) | 3.36059 | 0.506629 | ||||||||
\(45\) | −13.0687 | −1.94816 | ||||||||
\(46\) | 15.2333 | 2.24603 | ||||||||
\(47\) | −3.26788 | −0.476669 | −0.238335 | − | 0.971183i | \(-0.576601\pi\) | ||||
−0.238335 | + | 0.971183i | \(0.576601\pi\) | |||||||
\(48\) | 20.1501 | 2.90842 | ||||||||
\(49\) | −6.25207 | −0.893152 | ||||||||
\(50\) | −1.91185 | −0.270376 | ||||||||
\(51\) | −6.51834 | −0.912750 | ||||||||
\(52\) | 28.8879 | 4.00603 | ||||||||
\(53\) | −3.16355 | −0.434548 | −0.217274 | − | 0.976111i | \(-0.569716\pi\) | ||||
−0.217274 | + | 0.976111i | \(0.569716\pi\) | |||||||
\(54\) | −18.0833 | −2.46083 | ||||||||
\(55\) | −1.80952 | −0.243996 | ||||||||
\(56\) | −5.39248 | −0.720600 | ||||||||
\(57\) | 14.4349 | 1.91195 | ||||||||
\(58\) | 21.9688 | 2.88464 | ||||||||
\(59\) | −8.33643 | −1.08531 | −0.542655 | − | 0.839956i | \(-0.682581\pi\) | ||||
−0.542655 | + | 0.839956i | \(0.682581\pi\) | |||||||
\(60\) | −31.0534 | −4.00898 | ||||||||
\(61\) | 7.09924 | 0.908964 | 0.454482 | − | 0.890756i | \(-0.349824\pi\) | ||||
0.454482 | + | 0.890756i | \(0.349824\pi\) | |||||||
\(62\) | 12.5325 | 1.59163 | ||||||||
\(63\) | 4.71230 | 0.593694 | ||||||||
\(64\) | −0.803098 | −0.100387 | ||||||||
\(65\) | −15.5548 | −1.92933 | ||||||||
\(66\) | −5.57131 | −0.685781 | ||||||||
\(67\) | −5.01430 | −0.612595 | −0.306297 | − | 0.951936i | \(-0.599090\pi\) | ||||
−0.306297 | + | 0.951936i | \(0.599090\pi\) | |||||||
\(68\) | −9.98897 | −1.21134 | ||||||||
\(69\) | −17.4288 | −2.09818 | ||||||||
\(70\) | 5.26971 | 0.629851 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −33.9749 | −4.00398 | ||||||||
\(73\) | −6.83649 | −0.800151 | −0.400076 | − | 0.916482i | \(-0.631016\pi\) | ||||
−0.400076 | + | 0.916482i | \(0.631016\pi\) | |||||||
\(74\) | 21.5854 | 2.50925 | ||||||||
\(75\) | 2.18739 | 0.252578 | ||||||||
\(76\) | 22.1206 | 2.53741 | ||||||||
\(77\) | 0.652478 | 0.0743568 | ||||||||
\(78\) | −47.8913 | −5.42262 | ||||||||
\(79\) | 14.1403 | 1.59091 | 0.795456 | − | 0.606012i | \(-0.207232\pi\) | ||||
0.795456 | + | 0.606012i | \(0.207232\pi\) | |||||||
\(80\) | −16.6268 | −1.85894 | ||||||||
\(81\) | 4.34308 | 0.482565 | ||||||||
\(82\) | −17.9108 | −1.97791 | ||||||||
\(83\) | −10.5939 | −1.16283 | −0.581414 | − | 0.813608i | \(-0.697500\pi\) | ||||
−0.581414 | + | 0.813608i | \(0.697500\pi\) | |||||||
\(84\) | 11.1972 | 1.22172 | ||||||||
\(85\) | 5.37859 | 0.583390 | ||||||||
\(86\) | 12.5502 | 1.35332 | ||||||||
\(87\) | −25.1350 | −2.69475 | ||||||||
\(88\) | −4.70426 | −0.501476 | ||||||||
\(89\) | −16.5313 | −1.75231 | −0.876157 | − | 0.482026i | \(-0.839901\pi\) | ||||
−0.876157 | + | 0.482026i | \(0.839901\pi\) | |||||||
\(90\) | 33.2014 | 3.49974 | ||||||||
\(91\) | 5.60874 | 0.587956 | ||||||||
\(92\) | −26.7086 | −2.78457 | ||||||||
\(93\) | −14.3387 | −1.48686 | ||||||||
\(94\) | 8.30216 | 0.856303 | ||||||||
\(95\) | −11.9109 | −1.22204 | ||||||||
\(96\) | −14.9440 | −1.52522 | ||||||||
\(97\) | −4.88962 | −0.496466 | −0.248233 | − | 0.968700i | \(-0.579850\pi\) | ||||
−0.248233 | + | 0.968700i | \(0.579850\pi\) | |||||||
\(98\) | 15.8836 | 1.60449 | ||||||||
\(99\) | 4.11089 | 0.413160 | ||||||||
\(100\) | 3.35204 | 0.335204 | ||||||||
\(101\) | 0.330137 | 0.0328498 | 0.0164249 | − | 0.999865i | \(-0.494772\pi\) | ||||
0.0164249 | + | 0.999865i | \(0.494772\pi\) | |||||||
\(102\) | 16.5601 | 1.63969 | ||||||||
\(103\) | −13.0320 | −1.28409 | −0.642043 | − | 0.766669i | \(-0.721913\pi\) | ||||
−0.642043 | + | 0.766669i | \(0.721913\pi\) | |||||||
\(104\) | −40.4381 | −3.96528 | ||||||||
\(105\) | −6.02919 | −0.588389 | ||||||||
\(106\) | 8.03712 | 0.780634 | ||||||||
\(107\) | −11.6794 | −1.12909 | −0.564545 | − | 0.825402i | \(-0.690948\pi\) | ||||
−0.564545 | + | 0.825402i | \(0.690948\pi\) | |||||||
\(108\) | 31.7055 | 3.05086 | ||||||||
\(109\) | −6.88946 | −0.659891 | −0.329945 | − | 0.944000i | \(-0.607030\pi\) | ||||
−0.329945 | + | 0.944000i | \(0.607030\pi\) | |||||||
\(110\) | 4.59716 | 0.438322 | ||||||||
\(111\) | −24.6964 | −2.34407 | ||||||||
\(112\) | 5.99531 | 0.566503 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | −36.6724 | −3.43468 | ||||||||
\(115\) | 14.3813 | 1.34107 | ||||||||
\(116\) | −38.5179 | −3.57629 | ||||||||
\(117\) | 35.3375 | 3.26695 | ||||||||
\(118\) | 21.1790 | 1.94968 | ||||||||
\(119\) | −1.93941 | −0.177786 | ||||||||
\(120\) | 43.4695 | 3.96820 | ||||||||
\(121\) | −10.4308 | −0.948254 | ||||||||
\(122\) | −18.0359 | −1.63289 | ||||||||
\(123\) | 20.4921 | 1.84771 | ||||||||
\(124\) | −21.9732 | −1.97325 | ||||||||
\(125\) | 10.1873 | 0.911180 | ||||||||
\(126\) | −11.9718 | −1.06653 | ||||||||
\(127\) | 8.16770 | 0.724766 | 0.362383 | − | 0.932029i | \(-0.381963\pi\) | ||||
0.362383 | + | 0.932029i | \(0.381963\pi\) | |||||||
\(128\) | 12.3228 | 1.08920 | ||||||||
\(129\) | −14.3589 | −1.26423 | ||||||||
\(130\) | 39.5174 | 3.46591 | ||||||||
\(131\) | 11.8604 | 1.03625 | 0.518125 | − | 0.855305i | \(-0.326630\pi\) | ||||
0.518125 | + | 0.855305i | \(0.326630\pi\) | |||||||
\(132\) | 9.76818 | 0.850211 | ||||||||
\(133\) | 4.29485 | 0.372411 | ||||||||
\(134\) | 12.7390 | 1.10048 | ||||||||
\(135\) | −17.0719 | −1.46932 | ||||||||
\(136\) | 13.9829 | 1.19902 | ||||||||
\(137\) | 12.2080 | 1.04300 | 0.521501 | − | 0.853251i | \(-0.325372\pi\) | ||||
0.521501 | + | 0.853251i | \(0.325372\pi\) | |||||||
\(138\) | 44.2785 | 3.76924 | ||||||||
\(139\) | −15.7167 | −1.33307 | −0.666535 | − | 0.745474i | \(-0.732223\pi\) | ||||
−0.666535 | + | 0.745474i | \(0.732223\pi\) | |||||||
\(140\) | −9.23938 | −0.780870 | ||||||||
\(141\) | −9.49869 | −0.799934 | ||||||||
\(142\) | 2.54054 | 0.213197 | ||||||||
\(143\) | 4.89292 | 0.409167 | ||||||||
\(144\) | 37.7730 | 3.14775 | ||||||||
\(145\) | 20.7401 | 1.72237 | ||||||||
\(146\) | 17.3684 | 1.43742 | ||||||||
\(147\) | −18.1728 | −1.49887 | ||||||||
\(148\) | −37.8457 | −3.11090 | ||||||||
\(149\) | −8.87057 | −0.726706 | −0.363353 | − | 0.931652i | \(-0.618368\pi\) | ||||
−0.363353 | + | 0.931652i | \(0.618368\pi\) | |||||||
\(150\) | −5.55713 | −0.453738 | ||||||||
\(151\) | 0.285061 | 0.0231980 | 0.0115990 | − | 0.999933i | \(-0.496308\pi\) | ||||
0.0115990 | + | 0.999933i | \(0.496308\pi\) | |||||||
\(152\) | −30.9651 | −2.51160 | ||||||||
\(153\) | −12.2191 | −0.987859 | ||||||||
\(154\) | −1.65764 | −0.133577 | ||||||||
\(155\) | 11.8316 | 0.950334 | ||||||||
\(156\) | 83.9679 | 6.72281 | ||||||||
\(157\) | 13.3021 | 1.06163 | 0.530813 | − | 0.847489i | \(-0.321887\pi\) | ||||
0.530813 | + | 0.847489i | \(0.321887\pi\) | |||||||
\(158\) | −35.9240 | −2.85796 | ||||||||
\(159\) | −9.19545 | −0.729247 | ||||||||
\(160\) | 12.3311 | 0.974855 | ||||||||
\(161\) | −5.18563 | −0.408685 | ||||||||
\(162\) | −11.0338 | −0.866894 | ||||||||
\(163\) | −1.14068 | −0.0893453 | −0.0446727 | − | 0.999002i | \(-0.514224\pi\) | ||||
−0.0446727 | + | 0.999002i | \(0.514224\pi\) | |||||||
\(164\) | 31.4029 | 2.45216 | ||||||||
\(165\) | −5.25971 | −0.409468 | ||||||||
\(166\) | 26.9141 | 2.08894 | ||||||||
\(167\) | −14.8599 | −1.14990 | −0.574948 | − | 0.818190i | \(-0.694978\pi\) | ||||
−0.574948 | + | 0.818190i | \(0.694978\pi\) | |||||||
\(168\) | −15.6742 | −1.20929 | ||||||||
\(169\) | 29.0598 | 2.23537 | ||||||||
\(170\) | −13.6645 | −1.04802 | ||||||||
\(171\) | 27.0594 | 2.06928 | ||||||||
\(172\) | −22.0042 | −1.67781 | ||||||||
\(173\) | 23.3696 | 1.77676 | 0.888380 | − | 0.459108i | \(-0.151831\pi\) | ||||
0.888380 | + | 0.459108i | \(0.151831\pi\) | |||||||
\(174\) | 63.8563 | 4.84093 | ||||||||
\(175\) | 0.650818 | 0.0491972 | ||||||||
\(176\) | 5.23015 | 0.394237 | ||||||||
\(177\) | −24.2314 | −1.82134 | ||||||||
\(178\) | 41.9983 | 3.14791 | ||||||||
\(179\) | 8.44406 | 0.631138 | 0.315569 | − | 0.948903i | \(-0.397805\pi\) | ||||
0.315569 | + | 0.948903i | \(0.397805\pi\) | |||||||
\(180\) | −58.2120 | −4.33887 | ||||||||
\(181\) | −10.2294 | −0.760349 | −0.380174 | − | 0.924915i | \(-0.624136\pi\) | ||||
−0.380174 | + | 0.924915i | \(0.624136\pi\) | |||||||
\(182\) | −14.2492 | −1.05622 | ||||||||
\(183\) | 20.6352 | 1.52540 | ||||||||
\(184\) | 37.3875 | 2.75624 | ||||||||
\(185\) | 20.3782 | 1.49823 | ||||||||
\(186\) | 36.4280 | 2.67103 | ||||||||
\(187\) | −1.69189 | −0.123724 | ||||||||
\(188\) | −14.5562 | −1.06162 | ||||||||
\(189\) | 6.15579 | 0.447768 | ||||||||
\(190\) | 30.2602 | 2.19530 | ||||||||
\(191\) | −1.65633 | −0.119848 | −0.0599238 | − | 0.998203i | \(-0.519086\pi\) | ||||
−0.0599238 | + | 0.998203i | \(0.519086\pi\) | |||||||
\(192\) | −2.33435 | −0.168467 | ||||||||
\(193\) | −14.3713 | −1.03447 | −0.517233 | − | 0.855845i | \(-0.673038\pi\) | ||||
−0.517233 | + | 0.855845i | \(0.673038\pi\) | |||||||
\(194\) | 12.4223 | 0.891866 | ||||||||
\(195\) | −45.2128 | −3.23775 | ||||||||
\(196\) | −27.8487 | −1.98919 | ||||||||
\(197\) | 21.7851 | 1.55213 | 0.776063 | − | 0.630655i | \(-0.217214\pi\) | ||||
0.776063 | + | 0.630655i | \(0.217214\pi\) | |||||||
\(198\) | −10.4439 | −0.742213 | ||||||||
\(199\) | 19.1160 | 1.35510 | 0.677548 | − | 0.735478i | \(-0.263042\pi\) | ||||
0.677548 | + | 0.735478i | \(0.263042\pi\) | |||||||
\(200\) | −4.69229 | −0.331795 | ||||||||
\(201\) | −14.5750 | −1.02804 | ||||||||
\(202\) | −0.838724 | −0.0590124 | ||||||||
\(203\) | −7.47846 | −0.524885 | ||||||||
\(204\) | −29.0348 | −2.03284 | ||||||||
\(205\) | −16.9090 | −1.18098 | ||||||||
\(206\) | 33.1084 | 2.30677 | ||||||||
\(207\) | −32.6717 | −2.27084 | ||||||||
\(208\) | 44.9587 | 3.11732 | ||||||||
\(209\) | 3.74671 | 0.259166 | ||||||||
\(210\) | 15.3174 | 1.05700 | ||||||||
\(211\) | 7.51634 | 0.517446 | 0.258723 | − | 0.965952i | \(-0.416698\pi\) | ||||
0.258723 | + | 0.965952i | \(0.416698\pi\) | |||||||
\(212\) | −14.0915 | −0.967807 | ||||||||
\(213\) | −2.90668 | −0.199163 | ||||||||
\(214\) | 29.6719 | 2.02833 | ||||||||
\(215\) | 11.8482 | 0.808044 | ||||||||
\(216\) | −44.3822 | −3.01983 | ||||||||
\(217\) | −4.26623 | −0.289610 | ||||||||
\(218\) | 17.5029 | 1.18545 | ||||||||
\(219\) | −19.8715 | −1.34279 | ||||||||
\(220\) | −8.06020 | −0.543418 | ||||||||
\(221\) | −14.5436 | −0.978310 | ||||||||
\(222\) | 62.7420 | 4.21097 | ||||||||
\(223\) | −20.3650 | −1.36374 | −0.681872 | − | 0.731472i | \(-0.738834\pi\) | ||||
−0.681872 | + | 0.731472i | \(0.738834\pi\) | |||||||
\(224\) | −4.44633 | −0.297083 | ||||||||
\(225\) | 4.10043 | 0.273362 | ||||||||
\(226\) | 2.54054 | 0.168994 | ||||||||
\(227\) | −29.9297 | −1.98650 | −0.993251 | − | 0.115988i | \(-0.962997\pi\) | ||||
−0.993251 | + | 0.115988i | \(0.962997\pi\) | |||||||
\(228\) | 64.2977 | 4.25822 | ||||||||
\(229\) | 16.7831 | 1.10906 | 0.554529 | − | 0.832164i | \(-0.312898\pi\) | ||||
0.554529 | + | 0.832164i | \(0.312898\pi\) | |||||||
\(230\) | −36.5363 | −2.40913 | ||||||||
\(231\) | 1.89655 | 0.124784 | ||||||||
\(232\) | 53.9185 | 3.53992 | ||||||||
\(233\) | −3.47543 | −0.227683 | −0.113841 | − | 0.993499i | \(-0.536316\pi\) | ||||
−0.113841 | + | 0.993499i | \(0.536316\pi\) | |||||||
\(234\) | −89.7761 | −5.86885 | ||||||||
\(235\) | 7.83783 | 0.511283 | ||||||||
\(236\) | −37.1331 | −2.41716 | ||||||||
\(237\) | 41.1015 | 2.66983 | ||||||||
\(238\) | 4.92715 | 0.319380 | ||||||||
\(239\) | 11.5586 | 0.747667 | 0.373833 | − | 0.927496i | \(-0.378043\pi\) | ||||
0.373833 | + | 0.927496i | \(0.378043\pi\) | |||||||
\(240\) | −48.3289 | −3.11962 | ||||||||
\(241\) | 8.44147 | 0.543763 | 0.271881 | − | 0.962331i | \(-0.412354\pi\) | ||||
0.271881 | + | 0.962331i | \(0.412354\pi\) | |||||||
\(242\) | 26.4998 | 1.70347 | ||||||||
\(243\) | −8.72976 | −0.560014 | ||||||||
\(244\) | 31.6223 | 2.02441 | ||||||||
\(245\) | 14.9952 | 0.958010 | ||||||||
\(246\) | −52.0609 | −3.31928 | ||||||||
\(247\) | 32.2070 | 2.04928 | ||||||||
\(248\) | 30.7588 | 1.95318 | ||||||||
\(249\) | −30.7930 | −1.95143 | ||||||||
\(250\) | −25.8812 | −1.63687 | ||||||||
\(251\) | 26.1640 | 1.65146 | 0.825728 | − | 0.564069i | \(-0.190765\pi\) | ||||
0.825728 | + | 0.564069i | \(0.190765\pi\) | |||||||
\(252\) | 20.9901 | 1.32225 | ||||||||
\(253\) | −4.52381 | −0.284409 | ||||||||
\(254\) | −20.7503 | −1.30199 | ||||||||
\(255\) | 15.6339 | 0.979031 | ||||||||
\(256\) | −29.7004 | −1.85628 | ||||||||
\(257\) | −2.86796 | −0.178899 | −0.0894493 | − | 0.995991i | \(-0.528511\pi\) | ||||
−0.0894493 | + | 0.995991i | \(0.528511\pi\) | |||||||
\(258\) | 36.4794 | 2.27111 | ||||||||
\(259\) | −7.34796 | −0.456580 | ||||||||
\(260\) | −69.2859 | −4.29693 | ||||||||
\(261\) | −47.1175 | −2.91650 | ||||||||
\(262\) | −30.1318 | −1.86155 | ||||||||
\(263\) | 19.4056 | 1.19660 | 0.598302 | − | 0.801271i | \(-0.295842\pi\) | ||||
0.598302 | + | 0.801271i | \(0.295842\pi\) | |||||||
\(264\) | −13.6738 | −0.841564 | ||||||||
\(265\) | 7.58761 | 0.466103 | ||||||||
\(266\) | −10.9112 | −0.669010 | ||||||||
\(267\) | −48.0512 | −2.94069 | ||||||||
\(268\) | −22.3353 | −1.36435 | ||||||||
\(269\) | 3.76334 | 0.229455 | 0.114728 | − | 0.993397i | \(-0.463401\pi\) | ||||
0.114728 | + | 0.993397i | \(0.463401\pi\) | |||||||
\(270\) | 43.3718 | 2.63952 | ||||||||
\(271\) | 31.2409 | 1.89775 | 0.948874 | − | 0.315655i | \(-0.102224\pi\) | ||||
0.948874 | + | 0.315655i | \(0.102224\pi\) | |||||||
\(272\) | −15.5460 | −0.942615 | ||||||||
\(273\) | 16.3028 | 0.986693 | ||||||||
\(274\) | −31.0149 | −1.87368 | ||||||||
\(275\) | 0.567757 | 0.0342370 | ||||||||
\(276\) | −77.6335 | −4.67299 | ||||||||
\(277\) | −0.856384 | −0.0514551 | −0.0257276 | − | 0.999669i | \(-0.508190\pi\) | ||||
−0.0257276 | + | 0.999669i | \(0.508190\pi\) | |||||||
\(278\) | 39.9288 | 2.39477 | ||||||||
\(279\) | −26.8791 | −1.60921 | ||||||||
\(280\) | 12.9336 | 0.772928 | ||||||||
\(281\) | −30.3893 | −1.81287 | −0.906436 | − | 0.422343i | \(-0.861208\pi\) | ||||
−0.906436 | + | 0.422343i | \(0.861208\pi\) | |||||||
\(282\) | 24.1318 | 1.43703 | ||||||||
\(283\) | 2.57768 | 0.153227 | 0.0766136 | − | 0.997061i | \(-0.475589\pi\) | ||||
0.0766136 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(284\) | −4.45432 | −0.264315 | ||||||||
\(285\) | −34.6213 | −2.05079 | ||||||||
\(286\) | −12.4306 | −0.735039 | ||||||||
\(287\) | 6.09706 | 0.359898 | ||||||||
\(288\) | −28.0138 | −1.65073 | ||||||||
\(289\) | −11.9710 | −0.704179 | ||||||||
\(290\) | −52.6909 | −3.09412 | ||||||||
\(291\) | −14.2126 | −0.833157 | ||||||||
\(292\) | −30.4519 | −1.78207 | ||||||||
\(293\) | −12.5610 | −0.733819 | −0.366909 | − | 0.930257i | \(-0.619584\pi\) | ||||
−0.366909 | + | 0.930257i | \(0.619584\pi\) | |||||||
\(294\) | 46.1686 | 2.69261 | ||||||||
\(295\) | 19.9945 | 1.16412 | ||||||||
\(296\) | 52.9776 | 3.07926 | ||||||||
\(297\) | 5.37016 | 0.311608 | ||||||||
\(298\) | 22.5360 | 1.30548 | ||||||||
\(299\) | −38.8869 | −2.24889 | ||||||||
\(300\) | 9.74332 | 0.562531 | ||||||||
\(301\) | −4.27224 | −0.246248 | ||||||||
\(302\) | −0.724208 | −0.0416735 | ||||||||
\(303\) | 0.959603 | 0.0551278 | ||||||||
\(304\) | 34.4267 | 1.97451 | ||||||||
\(305\) | −17.0271 | −0.974971 | ||||||||
\(306\) | 31.0432 | 1.77462 | ||||||||
\(307\) | −18.2335 | −1.04064 | −0.520319 | − | 0.853972i | \(-0.674187\pi\) | ||||
−0.520319 | + | 0.853972i | \(0.674187\pi\) | |||||||
\(308\) | 2.90635 | 0.165605 | ||||||||
\(309\) | −37.8800 | −2.15492 | ||||||||
\(310\) | −30.0585 | −1.70721 | ||||||||
\(311\) | 13.5981 | 0.771080 | 0.385540 | − | 0.922691i | \(-0.374015\pi\) | ||||
0.385540 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(312\) | −117.541 | −6.65443 | ||||||||
\(313\) | 26.4258 | 1.49367 | 0.746836 | − | 0.665008i | \(-0.231572\pi\) | ||||
0.746836 | + | 0.665008i | \(0.231572\pi\) | |||||||
\(314\) | −33.7945 | −1.90714 | ||||||||
\(315\) | −11.3022 | −0.636807 | ||||||||
\(316\) | 62.9856 | 3.54322 | ||||||||
\(317\) | 4.07511 | 0.228881 | 0.114440 | − | 0.993430i | \(-0.463493\pi\) | ||||
0.114440 | + | 0.993430i | \(0.463493\pi\) | |||||||
\(318\) | 23.3614 | 1.31004 | ||||||||
\(319\) | −6.52402 | −0.365275 | ||||||||
\(320\) | 1.92619 | 0.107677 | ||||||||
\(321\) | −33.9483 | −1.89481 | ||||||||
\(322\) | 13.1743 | 0.734174 | ||||||||
\(323\) | −11.1367 | −0.619661 | ||||||||
\(324\) | 19.3455 | 1.07475 | ||||||||
\(325\) | 4.88047 | 0.270720 | ||||||||
\(326\) | 2.89795 | 0.160503 | ||||||||
\(327\) | −20.0255 | −1.10741 | ||||||||
\(328\) | −43.9588 | −2.42722 | ||||||||
\(329\) | −2.82617 | −0.155812 | ||||||||
\(330\) | 13.3625 | 0.735580 | ||||||||
\(331\) | −26.2802 | −1.44449 | −0.722246 | − | 0.691636i | \(-0.756890\pi\) | ||||
−0.722246 | + | 0.691636i | \(0.756890\pi\) | |||||||
\(332\) | −47.1885 | −2.58981 | ||||||||
\(333\) | −46.2953 | −2.53697 | ||||||||
\(334\) | 37.7522 | 2.06571 | ||||||||
\(335\) | 12.0265 | 0.657080 | ||||||||
\(336\) | 17.4265 | 0.950691 | ||||||||
\(337\) | 10.9635 | 0.597221 | 0.298610 | − | 0.954375i | \(-0.403477\pi\) | ||||
0.298610 | + | 0.954375i | \(0.403477\pi\) | |||||||
\(338\) | −73.8276 | −4.01569 | ||||||||
\(339\) | −2.90668 | −0.157869 | ||||||||
\(340\) | 23.9580 | 1.29930 | ||||||||
\(341\) | −3.72175 | −0.201544 | ||||||||
\(342\) | −68.7453 | −3.71732 | ||||||||
\(343\) | −11.4608 | −0.618825 | ||||||||
\(344\) | 30.8022 | 1.66074 | ||||||||
\(345\) | 41.8020 | 2.25055 | ||||||||
\(346\) | −59.3714 | −3.19183 | ||||||||
\(347\) | 22.7537 | 1.22148 | 0.610742 | − | 0.791829i | \(-0.290871\pi\) | ||||
0.610742 | + | 0.791829i | \(0.290871\pi\) | |||||||
\(348\) | −111.959 | −6.00165 | ||||||||
\(349\) | −0.317408 | −0.0169904 | −0.00849522 | − | 0.999964i | \(-0.502704\pi\) | ||||
−0.00849522 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(350\) | −1.65343 | −0.0883793 | ||||||||
\(351\) | 46.1622 | 2.46395 | ||||||||
\(352\) | −3.87887 | −0.206744 | ||||||||
\(353\) | 0.242761 | 0.0129209 | 0.00646044 | − | 0.999979i | \(-0.497944\pi\) | ||||
0.00646044 | + | 0.999979i | \(0.497944\pi\) | |||||||
\(354\) | 61.5606 | 3.27191 | ||||||||
\(355\) | 2.39844 | 0.127296 | ||||||||
\(356\) | −73.6357 | −3.90268 | ||||||||
\(357\) | −5.63726 | −0.298356 | ||||||||
\(358\) | −21.4524 | −1.13380 | ||||||||
\(359\) | 22.6126 | 1.19345 | 0.596723 | − | 0.802448i | \(-0.296469\pi\) | ||||
0.596723 | + | 0.802448i | \(0.296469\pi\) | |||||||
\(360\) | 81.4869 | 4.29474 | ||||||||
\(361\) | 5.66224 | 0.298013 | ||||||||
\(362\) | 25.9883 | 1.36591 | ||||||||
\(363\) | −30.3190 | −1.59134 | ||||||||
\(364\) | 24.9831 | 1.30947 | ||||||||
\(365\) | 16.3970 | 0.858256 | ||||||||
\(366\) | −52.4246 | −2.74028 | ||||||||
\(367\) | −14.7954 | −0.772315 | −0.386157 | − | 0.922433i | \(-0.626198\pi\) | ||||
−0.386157 | + | 0.922433i | \(0.626198\pi\) | |||||||
\(368\) | −41.5671 | −2.16683 | ||||||||
\(369\) | 38.4141 | 1.99976 | ||||||||
\(370\) | −51.7714 | −2.69147 | ||||||||
\(371\) | −2.73594 | −0.142043 | ||||||||
\(372\) | −63.8692 | −3.31147 | ||||||||
\(373\) | −0.958361 | −0.0496221 | −0.0248110 | − | 0.999692i | \(-0.507898\pi\) | ||||
−0.0248110 | + | 0.999692i | \(0.507898\pi\) | |||||||
\(374\) | 4.29832 | 0.222261 | ||||||||
\(375\) | 29.6113 | 1.52912 | ||||||||
\(376\) | 20.3762 | 1.05082 | ||||||||
\(377\) | −56.0808 | −2.88831 | ||||||||
\(378\) | −15.6390 | −0.804384 | ||||||||
\(379\) | −9.34743 | −0.480145 | −0.240073 | − | 0.970755i | \(-0.577171\pi\) | ||||
−0.240073 | + | 0.970755i | \(0.577171\pi\) | |||||||
\(380\) | −53.0551 | −2.72167 | ||||||||
\(381\) | 23.7409 | 1.21628 | ||||||||
\(382\) | 4.20796 | 0.215298 | ||||||||
\(383\) | 38.4182 | 1.96308 | 0.981540 | − | 0.191258i | \(-0.0612567\pi\) | ||||
0.981540 | + | 0.191258i | \(0.0612567\pi\) | |||||||
\(384\) | 35.8186 | 1.82786 | ||||||||
\(385\) | −1.56493 | −0.0797564 | ||||||||
\(386\) | 36.5107 | 1.85835 | ||||||||
\(387\) | −26.9169 | −1.36827 | ||||||||
\(388\) | −21.7800 | −1.10571 | ||||||||
\(389\) | −34.7673 | −1.76277 | −0.881387 | − | 0.472395i | \(-0.843390\pi\) | ||||
−0.881387 | + | 0.472395i | \(0.843390\pi\) | |||||||
\(390\) | 114.865 | 5.81640 | ||||||||
\(391\) | 13.4465 | 0.680018 | ||||||||
\(392\) | 38.9835 | 1.96896 | ||||||||
\(393\) | 34.4745 | 1.73901 | ||||||||
\(394\) | −55.3459 | −2.78829 | ||||||||
\(395\) | −33.9148 | −1.70644 | ||||||||
\(396\) | 18.3112 | 0.920174 | ||||||||
\(397\) | 4.52356 | 0.227031 | 0.113515 | − | 0.993536i | \(-0.463789\pi\) | ||||
0.113515 | + | 0.993536i | \(0.463789\pi\) | |||||||
\(398\) | −48.5649 | −2.43434 | ||||||||
\(399\) | 12.4838 | 0.624970 | ||||||||
\(400\) | 5.21684 | 0.260842 | ||||||||
\(401\) | −9.81605 | −0.490190 | −0.245095 | − | 0.969499i | \(-0.578819\pi\) | ||||
−0.245095 | + | 0.969499i | \(0.578819\pi\) | |||||||
\(402\) | 37.0283 | 1.84680 | ||||||||
\(403\) | −31.9924 | −1.59365 | ||||||||
\(404\) | 1.47054 | 0.0731619 | ||||||||
\(405\) | −10.4166 | −0.517607 | ||||||||
\(406\) | 18.9993 | 0.942920 | ||||||||
\(407\) | −6.41017 | −0.317740 | ||||||||
\(408\) | 40.6437 | 2.01216 | ||||||||
\(409\) | 2.47050 | 0.122158 | 0.0610792 | − | 0.998133i | \(-0.480546\pi\) | ||||
0.0610792 | + | 0.998133i | \(0.480546\pi\) | |||||||
\(410\) | 42.9580 | 2.12154 | ||||||||
\(411\) | 35.4848 | 1.75034 | ||||||||
\(412\) | −58.0489 | −2.85987 | ||||||||
\(413\) | −7.20961 | −0.354762 | ||||||||
\(414\) | 83.0036 | 4.07940 | ||||||||
\(415\) | 25.4088 | 1.24727 | ||||||||
\(416\) | −33.3430 | −1.63477 | ||||||||
\(417\) | −45.6834 | −2.23712 | ||||||||
\(418\) | −9.51866 | −0.465573 | ||||||||
\(419\) | 6.53790 | 0.319397 | 0.159699 | − | 0.987166i | \(-0.448948\pi\) | ||||
0.159699 | + | 0.987166i | \(0.448948\pi\) | |||||||
\(420\) | −26.8560 | −1.31044 | ||||||||
\(421\) | −2.94410 | −0.143487 | −0.0717433 | − | 0.997423i | \(-0.522856\pi\) | ||||
−0.0717433 | + | 0.997423i | \(0.522856\pi\) | |||||||
\(422\) | −19.0955 | −0.929555 | ||||||||
\(423\) | −17.8060 | −0.865760 | ||||||||
\(424\) | 19.7257 | 0.957964 | ||||||||
\(425\) | −1.68759 | −0.0818601 | ||||||||
\(426\) | 7.38453 | 0.357782 | ||||||||
\(427\) | 6.13965 | 0.297118 | ||||||||
\(428\) | −52.0238 | −2.51467 | ||||||||
\(429\) | 14.2222 | 0.686653 | ||||||||
\(430\) | −30.1009 | −1.45159 | ||||||||
\(431\) | −28.1340 | −1.35517 | −0.677583 | − | 0.735446i | \(-0.736973\pi\) | ||||
−0.677583 | + | 0.735446i | \(0.736973\pi\) | |||||||
\(432\) | 49.3438 | 2.37405 | ||||||||
\(433\) | 6.35756 | 0.305525 | 0.152762 | − | 0.988263i | \(-0.451183\pi\) | ||||
0.152762 | + | 0.988263i | \(0.451183\pi\) | |||||||
\(434\) | 10.8385 | 0.520265 | ||||||||
\(435\) | 60.2848 | 2.89044 | ||||||||
\(436\) | −30.6879 | −1.46968 | ||||||||
\(437\) | −29.7774 | −1.42444 | ||||||||
\(438\) | 50.4843 | 2.41223 | ||||||||
\(439\) | −22.3173 | −1.06515 | −0.532573 | − | 0.846384i | \(-0.678775\pi\) | ||||
−0.532573 | + | 0.846384i | \(0.678775\pi\) | |||||||
\(440\) | 11.2829 | 0.537891 | ||||||||
\(441\) | −34.0663 | −1.62221 | ||||||||
\(442\) | 36.9486 | 1.75747 | ||||||||
\(443\) | 4.82135 | 0.229069 | 0.114535 | − | 0.993419i | \(-0.463462\pi\) | ||||
0.114535 | + | 0.993419i | \(0.463462\pi\) | |||||||
\(444\) | −110.006 | −5.22063 | ||||||||
\(445\) | 39.6494 | 1.87956 | ||||||||
\(446\) | 51.7381 | 2.44987 | ||||||||
\(447\) | −25.7840 | −1.21954 | ||||||||
\(448\) | −0.694544 | −0.0328141 | ||||||||
\(449\) | −38.1210 | −1.79904 | −0.899520 | − | 0.436879i | \(-0.856084\pi\) | ||||
−0.899520 | + | 0.436879i | \(0.856084\pi\) | |||||||
\(450\) | −10.4173 | −0.491076 | ||||||||
\(451\) | 5.31891 | 0.250458 | ||||||||
\(452\) | −4.45432 | −0.209514 | ||||||||
\(453\) | 0.828583 | 0.0389302 | ||||||||
\(454\) | 76.0374 | 3.56861 | ||||||||
\(455\) | −13.4523 | −0.630652 | ||||||||
\(456\) | −90.0059 | −4.21491 | ||||||||
\(457\) | −26.5710 | −1.24294 | −0.621469 | − | 0.783438i | \(-0.713464\pi\) | ||||
−0.621469 | + | 0.783438i | \(0.713464\pi\) | |||||||
\(458\) | −42.6381 | −1.99235 | ||||||||
\(459\) | −15.9622 | −0.745049 | ||||||||
\(460\) | 64.0592 | 2.98677 | ||||||||
\(461\) | 36.1197 | 1.68226 | 0.841130 | − | 0.540832i | \(-0.181891\pi\) | ||||
0.841130 | + | 0.540832i | \(0.181891\pi\) | |||||||
\(462\) | −4.81825 | −0.224165 | ||||||||
\(463\) | 34.7042 | 1.61284 | 0.806422 | − | 0.591341i | \(-0.201401\pi\) | ||||
0.806422 | + | 0.591341i | \(0.201401\pi\) | |||||||
\(464\) | −59.9460 | −2.78292 | ||||||||
\(465\) | 34.3906 | 1.59483 | ||||||||
\(466\) | 8.82944 | 0.409016 | ||||||||
\(467\) | 19.4347 | 0.899330 | 0.449665 | − | 0.893197i | \(-0.351543\pi\) | ||||
0.449665 | + | 0.893197i | \(0.351543\pi\) | |||||||
\(468\) | 157.404 | 7.27602 | ||||||||
\(469\) | −4.33653 | −0.200242 | ||||||||
\(470\) | −19.9123 | −0.918485 | ||||||||
\(471\) | 38.6651 | 1.78159 | ||||||||
\(472\) | 51.9801 | 2.39258 | ||||||||
\(473\) | −3.72699 | −0.171367 | ||||||||
\(474\) | −104.420 | −4.79616 | ||||||||
\(475\) | 3.73718 | 0.171474 | ||||||||
\(476\) | −8.63878 | −0.395958 | ||||||||
\(477\) | −17.2376 | −0.789255 | ||||||||
\(478\) | −29.3652 | −1.34313 | ||||||||
\(479\) | −3.85665 | −0.176215 | −0.0881074 | − | 0.996111i | \(-0.528082\pi\) | ||||
−0.0881074 | + | 0.996111i | \(0.528082\pi\) | |||||||
\(480\) | 35.8425 | 1.63598 | ||||||||
\(481\) | −55.1022 | −2.51244 | ||||||||
\(482\) | −21.4459 | −0.976832 | ||||||||
\(483\) | −15.0730 | −0.685845 | ||||||||
\(484\) | −46.4621 | −2.11191 | ||||||||
\(485\) | 11.7275 | 0.532518 | ||||||||
\(486\) | 22.1783 | 1.00603 | ||||||||
\(487\) | −7.97250 | −0.361268 | −0.180634 | − | 0.983550i | \(-0.557815\pi\) | ||||
−0.180634 | + | 0.983550i | \(0.557815\pi\) | |||||||
\(488\) | −44.2658 | −2.00382 | ||||||||
\(489\) | −3.31561 | −0.149937 | ||||||||
\(490\) | −38.0959 | −1.72100 | ||||||||
\(491\) | −28.8480 | −1.30189 | −0.650947 | − | 0.759123i | \(-0.725628\pi\) | ||||
−0.650947 | + | 0.759123i | \(0.725628\pi\) | |||||||
\(492\) | 91.2784 | 4.11515 | ||||||||
\(493\) | 19.3919 | 0.873366 | ||||||||
\(494\) | −81.8230 | −3.68139 | ||||||||
\(495\) | −9.85974 | −0.443163 | ||||||||
\(496\) | −34.1973 | −1.53551 | ||||||||
\(497\) | −0.864832 | −0.0387930 | ||||||||
\(498\) | 78.2308 | 3.50560 | ||||||||
\(499\) | 24.4070 | 1.09261 | 0.546303 | − | 0.837588i | \(-0.316035\pi\) | ||||
0.546303 | + | 0.837588i | \(0.316035\pi\) | |||||||
\(500\) | 45.3775 | 2.02935 | ||||||||
\(501\) | −43.1931 | −1.92973 | ||||||||
\(502\) | −66.4705 | −2.96672 | ||||||||
\(503\) | 11.8602 | 0.528821 | 0.264411 | − | 0.964410i | \(-0.414823\pi\) | ||||
0.264411 | + | 0.964410i | \(0.414823\pi\) | |||||||
\(504\) | −29.3826 | −1.30880 | ||||||||
\(505\) | −0.791815 | −0.0352353 | ||||||||
\(506\) | 11.4929 | 0.510922 | ||||||||
\(507\) | 84.4677 | 3.75134 | ||||||||
\(508\) | 36.3816 | 1.61417 | ||||||||
\(509\) | 33.7485 | 1.49587 | 0.747937 | − | 0.663769i | \(-0.231044\pi\) | ||||
0.747937 | + | 0.663769i | \(0.231044\pi\) | |||||||
\(510\) | −39.7184 | −1.75876 | ||||||||
\(511\) | −5.91242 | −0.261550 | ||||||||
\(512\) | 50.8093 | 2.24547 | ||||||||
\(513\) | 35.3483 | 1.56067 | ||||||||
\(514\) | 7.28616 | 0.321379 | ||||||||
\(515\) | 31.2566 | 1.37733 | ||||||||
\(516\) | −63.9593 | −2.81565 | ||||||||
\(517\) | −2.46547 | −0.108431 | ||||||||
\(518\) | 18.6678 | 0.820214 | ||||||||
\(519\) | 67.9281 | 2.98171 | ||||||||
\(520\) | 96.9885 | 4.25323 | ||||||||
\(521\) | 0.416514 | 0.0182478 | 0.00912391 | − | 0.999958i | \(-0.497096\pi\) | ||||
0.00912391 | + | 0.999958i | \(0.497096\pi\) | |||||||
\(522\) | 119.704 | 5.23929 | ||||||||
\(523\) | 28.6460 | 1.25260 | 0.626302 | − | 0.779580i | \(-0.284568\pi\) | ||||
0.626302 | + | 0.779580i | \(0.284568\pi\) | |||||||
\(524\) | 52.8301 | 2.30790 | ||||||||
\(525\) | 1.89172 | 0.0825615 | ||||||||
\(526\) | −49.3007 | −2.14961 | ||||||||
\(527\) | 11.0625 | 0.481888 | ||||||||
\(528\) | 15.2024 | 0.661599 | ||||||||
\(529\) | 12.9534 | 0.563191 | ||||||||
\(530\) | −19.2766 | −0.837322 | ||||||||
\(531\) | −45.4236 | −1.97122 | ||||||||
\(532\) | 19.1306 | 0.829418 | ||||||||
\(533\) | 45.7217 | 1.98043 | ||||||||
\(534\) | 122.076 | 5.28274 | ||||||||
\(535\) | 28.0124 | 1.21108 | ||||||||
\(536\) | 31.2657 | 1.35047 | ||||||||
\(537\) | 24.5442 | 1.05916 | ||||||||
\(538\) | −9.56091 | −0.412200 | ||||||||
\(539\) | −4.71691 | −0.203172 | ||||||||
\(540\) | −76.0438 | −3.27240 | ||||||||
\(541\) | 7.92150 | 0.340572 | 0.170286 | − | 0.985395i | \(-0.445531\pi\) | ||||
0.170286 | + | 0.985395i | \(0.445531\pi\) | |||||||
\(542\) | −79.3686 | −3.40917 | ||||||||
\(543\) | −29.7338 | −1.27600 | ||||||||
\(544\) | 11.5295 | 0.494322 | ||||||||
\(545\) | 16.5240 | 0.707810 | ||||||||
\(546\) | −41.4179 | −1.77252 | ||||||||
\(547\) | −18.3996 | −0.786710 | −0.393355 | − | 0.919387i | \(-0.628686\pi\) | ||||
−0.393355 | + | 0.919387i | \(0.628686\pi\) | |||||||
\(548\) | 54.3784 | 2.32293 | ||||||||
\(549\) | 38.6824 | 1.65092 | ||||||||
\(550\) | −1.44241 | −0.0615044 | ||||||||
\(551\) | −42.9435 | −1.82945 | ||||||||
\(552\) | 108.674 | 4.62546 | ||||||||
\(553\) | 12.2290 | 0.520030 | ||||||||
\(554\) | 2.17567 | 0.0924355 | ||||||||
\(555\) | 59.2329 | 2.51429 | ||||||||
\(556\) | −70.0071 | −2.96896 | ||||||||
\(557\) | 19.2630 | 0.816199 | 0.408100 | − | 0.912937i | \(-0.366192\pi\) | ||||
0.408100 | + | 0.912937i | \(0.366192\pi\) | |||||||
\(558\) | 68.2872 | 2.89083 | ||||||||
\(559\) | −32.0375 | −1.35504 | ||||||||
\(560\) | −14.3794 | −0.607641 | ||||||||
\(561\) | −4.91780 | −0.207630 | ||||||||
\(562\) | 77.2050 | 3.25670 | ||||||||
\(563\) | −19.5573 | −0.824243 | −0.412121 | − | 0.911129i | \(-0.635212\pi\) | ||||
−0.412121 | + | 0.911129i | \(0.635212\pi\) | |||||||
\(564\) | −42.3102 | −1.78158 | ||||||||
\(565\) | 2.39844 | 0.100903 | ||||||||
\(566\) | −6.54869 | −0.275262 | ||||||||
\(567\) | 3.75604 | 0.157739 | ||||||||
\(568\) | 6.23529 | 0.261627 | ||||||||
\(569\) | 47.1227 | 1.97549 | 0.987743 | − | 0.156088i | \(-0.0498883\pi\) | ||||
0.987743 | + | 0.156088i | \(0.0498883\pi\) | |||||||
\(570\) | 87.9567 | 3.68410 | ||||||||
\(571\) | 28.1737 | 1.17903 | 0.589516 | − | 0.807757i | \(-0.299319\pi\) | ||||
0.589516 | + | 0.807757i | \(0.299319\pi\) | |||||||
\(572\) | 21.7946 | 0.911280 | ||||||||
\(573\) | −4.81442 | −0.201125 | ||||||||
\(574\) | −15.4898 | −0.646531 | ||||||||
\(575\) | −4.51230 | −0.188176 | ||||||||
\(576\) | −4.37592 | −0.182330 | ||||||||
\(577\) | 6.97596 | 0.290413 | 0.145206 | − | 0.989401i | \(-0.453615\pi\) | ||||
0.145206 | + | 0.989401i | \(0.453615\pi\) | |||||||
\(578\) | 30.4129 | 1.26501 | ||||||||
\(579\) | −41.7727 | −1.73601 | ||||||||
\(580\) | 92.3830 | 3.83599 | ||||||||
\(581\) | −9.16191 | −0.380100 | ||||||||
\(582\) | 36.1076 | 1.49671 | ||||||||
\(583\) | −2.38676 | −0.0988497 | ||||||||
\(584\) | 42.6275 | 1.76394 | ||||||||
\(585\) | −84.7549 | −3.50419 | ||||||||
\(586\) | 31.9116 | 1.31825 | ||||||||
\(587\) | 13.2436 | 0.546622 | 0.273311 | − | 0.961926i | \(-0.411881\pi\) | ||||
0.273311 | + | 0.961926i | \(0.411881\pi\) | |||||||
\(588\) | −80.9474 | −3.33821 | ||||||||
\(589\) | −24.4979 | −1.00942 | ||||||||
\(590\) | −50.7966 | −2.09126 | ||||||||
\(591\) | 63.3225 | 2.60474 | ||||||||
\(592\) | −58.9000 | −2.42077 | ||||||||
\(593\) | −13.3338 | −0.547554 | −0.273777 | − | 0.961793i | \(-0.588273\pi\) | ||||
−0.273777 | + | 0.961793i | \(0.588273\pi\) | |||||||
\(594\) | −13.6431 | −0.559782 | ||||||||
\(595\) | 4.65158 | 0.190696 | ||||||||
\(596\) | −39.5124 | −1.61849 | ||||||||
\(597\) | 55.5641 | 2.27409 | ||||||||
\(598\) | 98.7936 | 4.03997 | ||||||||
\(599\) | 19.9071 | 0.813384 | 0.406692 | − | 0.913565i | \(-0.366682\pi\) | ||||
0.406692 | + | 0.913565i | \(0.366682\pi\) | |||||||
\(600\) | −13.6390 | −0.556809 | ||||||||
\(601\) | −36.2171 | −1.47733 | −0.738664 | − | 0.674074i | \(-0.764543\pi\) | ||||
−0.738664 | + | 0.674074i | \(0.764543\pi\) | |||||||
\(602\) | 10.8538 | 0.442367 | ||||||||
\(603\) | −27.3220 | −1.11264 | ||||||||
\(604\) | 1.26975 | 0.0516656 | ||||||||
\(605\) | 25.0177 | 1.01711 | ||||||||
\(606\) | −2.43791 | −0.0990332 | ||||||||
\(607\) | 5.59905 | 0.227258 | 0.113629 | − | 0.993523i | \(-0.463752\pi\) | ||||
0.113629 | + | 0.993523i | \(0.463752\pi\) | |||||||
\(608\) | −25.5321 | −1.03546 | ||||||||
\(609\) | −21.7375 | −0.880849 | ||||||||
\(610\) | 43.2580 | 1.75147 | ||||||||
\(611\) | −21.1934 | −0.857392 | ||||||||
\(612\) | −54.4280 | −2.20012 | ||||||||
\(613\) | 19.2666 | 0.778171 | 0.389085 | − | 0.921202i | \(-0.372791\pi\) | ||||
0.389085 | + | 0.921202i | \(0.372791\pi\) | |||||||
\(614\) | 46.3228 | 1.86943 | ||||||||
\(615\) | −49.1492 | −1.98189 | ||||||||
\(616\) | −4.06839 | −0.163920 | ||||||||
\(617\) | −20.9597 | −0.843806 | −0.421903 | − | 0.906641i | \(-0.638638\pi\) | ||||
−0.421903 | + | 0.906641i | \(0.638638\pi\) | |||||||
\(618\) | 96.2356 | 3.87116 | ||||||||
\(619\) | 19.0538 | 0.765839 | 0.382919 | − | 0.923782i | \(-0.374919\pi\) | ||||
0.382919 | + | 0.923782i | \(0.374919\pi\) | |||||||
\(620\) | 52.7016 | 2.11655 | ||||||||
\(621\) | −42.6798 | −1.71268 | ||||||||
\(622\) | −34.5466 | −1.38519 | ||||||||
\(623\) | −14.2968 | −0.572789 | ||||||||
\(624\) | 130.681 | 5.23141 | ||||||||
\(625\) | −28.1964 | −1.12785 | ||||||||
\(626\) | −67.1356 | −2.68328 | ||||||||
\(627\) | 10.8905 | 0.434925 | ||||||||
\(628\) | 59.2519 | 2.36441 | ||||||||
\(629\) | 19.0535 | 0.759712 | ||||||||
\(630\) | 28.7136 | 1.14398 | ||||||||
\(631\) | −37.7621 | −1.50329 | −0.751643 | − | 0.659570i | \(-0.770738\pi\) | ||||
−0.751643 | + | 0.659570i | \(0.770738\pi\) | |||||||
\(632\) | −88.1691 | −3.50718 | ||||||||
\(633\) | 21.8476 | 0.868365 | ||||||||
\(634\) | −10.3530 | −0.411168 | ||||||||
\(635\) | −19.5898 | −0.777396 | ||||||||
\(636\) | −40.9595 | −1.62415 | ||||||||
\(637\) | −40.5469 | −1.60653 | ||||||||
\(638\) | 16.5745 | 0.656191 | ||||||||
\(639\) | −5.44881 | −0.215552 | ||||||||
\(640\) | −29.5556 | −1.16829 | ||||||||
\(641\) | 28.1792 | 1.11301 | 0.556507 | − | 0.830843i | \(-0.312141\pi\) | ||||
0.556507 | + | 0.830843i | \(0.312141\pi\) | |||||||
\(642\) | 86.2469 | 3.40389 | ||||||||
\(643\) | −12.1599 | −0.479539 | −0.239770 | − | 0.970830i | \(-0.577072\pi\) | ||||
−0.239770 | + | 0.970830i | \(0.577072\pi\) | |||||||
\(644\) | −23.0985 | −0.910207 | ||||||||
\(645\) | 34.4391 | 1.35604 | ||||||||
\(646\) | 28.2931 | 1.11318 | ||||||||
\(647\) | −21.0256 | −0.826600 | −0.413300 | − | 0.910595i | \(-0.635624\pi\) | ||||
−0.413300 | + | 0.910595i | \(0.635624\pi\) | |||||||
\(648\) | −27.0804 | −1.06382 | ||||||||
\(649\) | −6.28948 | −0.246883 | ||||||||
\(650\) | −12.3990 | −0.486329 | ||||||||
\(651\) | −12.4006 | −0.486017 | ||||||||
\(652\) | −5.08098 | −0.198986 | ||||||||
\(653\) | −22.2896 | −0.872258 | −0.436129 | − | 0.899884i | \(-0.643651\pi\) | ||||
−0.436129 | + | 0.899884i | \(0.643651\pi\) | |||||||
\(654\) | 50.8755 | 1.98939 | ||||||||
\(655\) | −28.4466 | −1.11150 | ||||||||
\(656\) | 48.8729 | 1.90817 | ||||||||
\(657\) | −37.2507 | −1.45329 | ||||||||
\(658\) | 7.17998 | 0.279905 | ||||||||
\(659\) | 1.40781 | 0.0548406 | 0.0274203 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274203 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(660\) | −23.4284 | −0.911951 | ||||||||
\(661\) | −21.5702 | −0.838983 | −0.419491 | − | 0.907759i | \(-0.637792\pi\) | ||||
−0.419491 | + | 0.907759i | \(0.637792\pi\) | |||||||
\(662\) | 66.7659 | 2.59493 | ||||||||
\(663\) | −42.2737 | −1.64178 | ||||||||
\(664\) | 66.0559 | 2.56346 | ||||||||
\(665\) | −10.3010 | −0.399454 | ||||||||
\(666\) | 117.615 | 4.55748 | ||||||||
\(667\) | 51.8502 | 2.00765 | ||||||||
\(668\) | −66.1910 | −2.56101 | ||||||||
\(669\) | −59.1947 | −2.28860 | ||||||||
\(670\) | −30.5538 | −1.18040 | ||||||||
\(671\) | 5.35607 | 0.206769 | ||||||||
\(672\) | −12.9241 | −0.498557 | ||||||||
\(673\) | −22.2535 | −0.857810 | −0.428905 | − | 0.903349i | \(-0.641101\pi\) | ||||
−0.428905 | + | 0.903349i | \(0.641101\pi\) | |||||||
\(674\) | −27.8532 | −1.07286 | ||||||||
\(675\) | 5.35649 | 0.206171 | ||||||||
\(676\) | 129.442 | 4.97853 | ||||||||
\(677\) | 32.1078 | 1.23400 | 0.617002 | − | 0.786962i | \(-0.288347\pi\) | ||||
0.617002 | + | 0.786962i | \(0.288347\pi\) | |||||||
\(678\) | 7.38453 | 0.283601 | ||||||||
\(679\) | −4.22870 | −0.162283 | ||||||||
\(680\) | −33.5371 | −1.28609 | ||||||||
\(681\) | −86.9960 | −3.33370 | ||||||||
\(682\) | 9.45523 | 0.362059 | ||||||||
\(683\) | −46.4116 | −1.77589 | −0.887946 | − | 0.459948i | \(-0.847868\pi\) | ||||
−0.887946 | + | 0.459948i | \(0.847868\pi\) | |||||||
\(684\) | 120.531 | 4.60862 | ||||||||
\(685\) | −29.2803 | −1.11874 | ||||||||
\(686\) | 29.1166 | 1.11168 | ||||||||
\(687\) | 48.7832 | 1.86119 | ||||||||
\(688\) | −34.2455 | −1.30560 | ||||||||
\(689\) | −20.5168 | −0.781627 | ||||||||
\(690\) | −106.200 | −4.04295 | ||||||||
\(691\) | 16.1404 | 0.614011 | 0.307006 | − | 0.951708i | \(-0.400673\pi\) | ||||
0.307006 | + | 0.951708i | \(0.400673\pi\) | |||||||
\(692\) | 104.096 | 3.95713 | ||||||||
\(693\) | 3.55523 | 0.135052 | ||||||||
\(694\) | −57.8067 | −2.19431 | ||||||||
\(695\) | 37.6956 | 1.42987 | ||||||||
\(696\) | 156.724 | 5.94060 | ||||||||
\(697\) | −15.8098 | −0.598841 | ||||||||
\(698\) | 0.806385 | 0.0305221 | ||||||||
\(699\) | −10.1020 | −0.382091 | ||||||||
\(700\) | 2.89895 | 0.109570 | ||||||||
\(701\) | −34.6658 | −1.30931 | −0.654655 | − | 0.755928i | \(-0.727186\pi\) | ||||
−0.654655 | + | 0.755928i | \(0.727186\pi\) | |||||||
\(702\) | −117.277 | −4.42632 | ||||||||
\(703\) | −42.1941 | −1.59138 | ||||||||
\(704\) | −0.605903 | −0.0228358 | ||||||||
\(705\) | 22.7821 | 0.858023 | ||||||||
\(706\) | −0.616744 | −0.0232115 | ||||||||
\(707\) | 0.285513 | 0.0107378 | ||||||||
\(708\) | −107.934 | −4.05642 | ||||||||
\(709\) | −44.7348 | −1.68005 | −0.840025 | − | 0.542548i | \(-0.817460\pi\) | ||||
−0.840025 | + | 0.542548i | \(0.817460\pi\) | |||||||
\(710\) | −6.09333 | −0.228679 | ||||||||
\(711\) | 77.0479 | 2.88952 | ||||||||
\(712\) | 103.077 | 3.86299 | ||||||||
\(713\) | 29.5789 | 1.10774 | ||||||||
\(714\) | 14.3217 | 0.535975 | ||||||||
\(715\) | −11.7354 | −0.438879 | ||||||||
\(716\) | 37.6125 | 1.40565 | ||||||||
\(717\) | 33.5973 | 1.25472 | ||||||||
\(718\) | −57.4480 | −2.14394 | ||||||||
\(719\) | 9.88601 | 0.368686 | 0.184343 | − | 0.982862i | \(-0.440984\pi\) | ||||
0.184343 | + | 0.982862i | \(0.440984\pi\) | |||||||
\(720\) | −90.5964 | −3.37633 | ||||||||
\(721\) | −11.2705 | −0.419736 | ||||||||
\(722\) | −14.3851 | −0.535359 | ||||||||
\(723\) | 24.5367 | 0.912529 | ||||||||
\(724\) | −45.5653 | −1.69342 | ||||||||
\(725\) | −6.50741 | −0.241679 | ||||||||
\(726\) | 77.0265 | 2.85872 | ||||||||
\(727\) | −9.14325 | −0.339104 | −0.169552 | − | 0.985521i | \(-0.554232\pi\) | ||||
−0.169552 | + | 0.985521i | \(0.554232\pi\) | |||||||
\(728\) | −34.9721 | −1.29615 | ||||||||
\(729\) | −38.4039 | −1.42237 | ||||||||
\(730\) | −41.6570 | −1.54180 | ||||||||
\(731\) | 11.0780 | 0.409736 | ||||||||
\(732\) | 91.9160 | 3.39731 | ||||||||
\(733\) | 13.3708 | 0.493860 | 0.246930 | − | 0.969033i | \(-0.420578\pi\) | ||||
0.246930 | + | 0.969033i | \(0.420578\pi\) | |||||||
\(734\) | 37.5883 | 1.38741 | ||||||||
\(735\) | 43.5864 | 1.60771 | ||||||||
\(736\) | 30.8276 | 1.13632 | ||||||||
\(737\) | −3.78308 | −0.139351 | ||||||||
\(738\) | −97.5923 | −3.59242 | ||||||||
\(739\) | −37.1917 | −1.36812 | −0.684059 | − | 0.729426i | \(-0.739787\pi\) | ||||
−0.684059 | + | 0.729426i | \(0.739787\pi\) | |||||||
\(740\) | 90.7709 | 3.33680 | ||||||||
\(741\) | 93.6155 | 3.43905 | ||||||||
\(742\) | 6.95076 | 0.255170 | ||||||||
\(743\) | −49.7980 | −1.82691 | −0.913456 | − | 0.406938i | \(-0.866597\pi\) | ||||
−0.913456 | + | 0.406938i | \(0.866597\pi\) | |||||||
\(744\) | 89.4061 | 3.27779 | ||||||||
\(745\) | 21.2756 | 0.779477 | ||||||||
\(746\) | 2.43475 | 0.0891426 | ||||||||
\(747\) | −57.7240 | −2.11201 | ||||||||
\(748\) | −7.53624 | −0.275552 | ||||||||
\(749\) | −10.1007 | −0.369072 | ||||||||
\(750\) | −75.2285 | −2.74696 | ||||||||
\(751\) | 37.8541 | 1.38131 | 0.690657 | − | 0.723182i | \(-0.257321\pi\) | ||||
0.690657 | + | 0.723182i | \(0.257321\pi\) | |||||||
\(752\) | −22.6540 | −0.826108 | ||||||||
\(753\) | 76.0504 | 2.77143 | ||||||||
\(754\) | 142.475 | 5.18865 | ||||||||
\(755\) | −0.683704 | −0.0248825 | ||||||||
\(756\) | 27.4199 | 0.997252 | ||||||||
\(757\) | −12.4834 | −0.453718 | −0.226859 | − | 0.973928i | \(-0.572846\pi\) | ||||
−0.226859 | + | 0.973928i | \(0.572846\pi\) | |||||||
\(758\) | 23.7475 | 0.862547 | ||||||||
\(759\) | −13.1493 | −0.477289 | ||||||||
\(760\) | 74.2682 | 2.69399 | ||||||||
\(761\) | 2.55387 | 0.0925777 | 0.0462888 | − | 0.998928i | \(-0.485261\pi\) | ||||
0.0462888 | + | 0.998928i | \(0.485261\pi\) | |||||||
\(762\) | −60.3146 | −2.18497 | ||||||||
\(763\) | −5.95823 | −0.215702 | ||||||||
\(764\) | −7.37781 | −0.266920 | ||||||||
\(765\) | 29.3069 | 1.05959 | ||||||||
\(766\) | −97.6029 | −3.52654 | ||||||||
\(767\) | −54.0647 | −1.95216 | ||||||||
\(768\) | −86.3297 | −3.11515 | ||||||||
\(769\) | −10.8952 | −0.392893 | −0.196446 | − | 0.980515i | \(-0.562940\pi\) | ||||
−0.196446 | + | 0.980515i | \(0.562940\pi\) | |||||||
\(770\) | 3.97577 | 0.143277 | ||||||||
\(771\) | −8.33626 | −0.300223 | ||||||||
\(772\) | −64.0142 | −2.30392 | ||||||||
\(773\) | −12.1555 | −0.437202 | −0.218601 | − | 0.975814i | \(-0.570149\pi\) | ||||
−0.218601 | + | 0.975814i | \(0.570149\pi\) | |||||||
\(774\) | 68.3835 | 2.45799 | ||||||||
\(775\) | −3.71228 | −0.133349 | ||||||||
\(776\) | 30.4882 | 1.09446 | ||||||||
\(777\) | −21.3582 | −0.766221 | ||||||||
\(778\) | 88.3277 | 3.16670 | ||||||||
\(779\) | 35.0110 | 1.25440 | ||||||||
\(780\) | −201.392 | −7.21100 | ||||||||
\(781\) | −0.754457 | −0.0269966 | ||||||||
\(782\) | −34.1613 | −1.22161 | ||||||||
\(783\) | −61.5507 | −2.19964 | ||||||||
\(784\) | −43.3414 | −1.54791 | ||||||||
\(785\) | −31.9044 | −1.13872 | ||||||||
\(786\) | −87.5837 | −3.12401 | ||||||||
\(787\) | −27.3912 | −0.976391 | −0.488195 | − | 0.872734i | \(-0.662345\pi\) | ||||
−0.488195 | + | 0.872734i | \(0.662345\pi\) | |||||||
\(788\) | 97.0380 | 3.45683 | ||||||||
\(789\) | 56.4061 | 2.00811 | ||||||||
\(790\) | 86.1618 | 3.06550 | ||||||||
\(791\) | −0.864832 | −0.0307499 | ||||||||
\(792\) | −25.6326 | −0.910815 | ||||||||
\(793\) | 46.0411 | 1.63497 | ||||||||
\(794\) | −11.4923 | −0.407845 | ||||||||
\(795\) | 22.0548 | 0.782202 | ||||||||
\(796\) | 85.1488 | 3.01802 | ||||||||
\(797\) | −18.7348 | −0.663619 | −0.331809 | − | 0.943346i | \(-0.607659\pi\) | ||||
−0.331809 | + | 0.943346i | \(0.607659\pi\) | |||||||
\(798\) | −31.7155 | −1.12271 | ||||||||
\(799\) | 7.32833 | 0.259258 | ||||||||
\(800\) | −3.86899 | −0.136790 | ||||||||
\(801\) | −90.0759 | −3.18267 | ||||||||
\(802\) | 24.9380 | 0.880592 | ||||||||
\(803\) | −5.15784 | −0.182016 | ||||||||
\(804\) | −64.9217 | −2.28961 | ||||||||
\(805\) | 12.4374 | 0.438362 | ||||||||
\(806\) | 81.2777 | 2.86289 | ||||||||
\(807\) | 10.9388 | 0.385066 | ||||||||
\(808\) | −2.05850 | −0.0724178 | ||||||||
\(809\) | 17.0279 | 0.598670 | 0.299335 | − | 0.954148i | \(-0.403235\pi\) | ||||
0.299335 | + | 0.954148i | \(0.403235\pi\) | |||||||
\(810\) | 26.4639 | 0.929846 | ||||||||
\(811\) | −11.0296 | −0.387300 | −0.193650 | − | 0.981071i | \(-0.562033\pi\) | ||||
−0.193650 | + | 0.981071i | \(0.562033\pi\) | |||||||
\(812\) | −33.3115 | −1.16900 | ||||||||
\(813\) | 90.8073 | 3.18475 | ||||||||
\(814\) | 16.2853 | 0.570798 | ||||||||
\(815\) | 2.73587 | 0.0958333 | ||||||||
\(816\) | −45.1873 | −1.58187 | ||||||||
\(817\) | −24.5324 | −0.858281 | ||||||||
\(818\) | −6.27640 | −0.219449 | ||||||||
\(819\) | 30.5610 | 1.06789 | ||||||||
\(820\) | −75.3182 | −2.63023 | ||||||||
\(821\) | −17.6725 | −0.616775 | −0.308387 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308387 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(822\) | −90.1505 | −3.14436 | ||||||||
\(823\) | 6.30855 | 0.219902 | 0.109951 | − | 0.993937i | \(-0.464931\pi\) | ||||
0.109951 | + | 0.993937i | \(0.464931\pi\) | |||||||
\(824\) | 81.2586 | 2.83078 | ||||||||
\(825\) | 1.65029 | 0.0574557 | ||||||||
\(826\) | 18.3163 | 0.637304 | ||||||||
\(827\) | −42.7669 | −1.48715 | −0.743576 | − | 0.668652i | \(-0.766872\pi\) | ||||
−0.743576 | + | 0.668652i | \(0.766872\pi\) | |||||||
\(828\) | −145.530 | −5.05752 | ||||||||
\(829\) | −0.0991423 | −0.00344335 | −0.00172168 | − | 0.999999i | \(-0.500548\pi\) | ||||
−0.00172168 | + | 0.999999i | \(0.500548\pi\) | |||||||
\(830\) | −64.5520 | −2.24063 | ||||||||
\(831\) | −2.48924 | −0.0863507 | ||||||||
\(832\) | −5.20837 | −0.180568 | ||||||||
\(833\) | 14.0205 | 0.485780 | ||||||||
\(834\) | 116.060 | 4.01884 | ||||||||
\(835\) | 35.6408 | 1.23340 | ||||||||
\(836\) | 16.6891 | 0.577204 | ||||||||
\(837\) | −35.1128 | −1.21367 | ||||||||
\(838\) | −16.6098 | −0.573775 | ||||||||
\(839\) | 27.3247 | 0.943352 | 0.471676 | − | 0.881772i | \(-0.343649\pi\) | ||||
0.471676 | + | 0.881772i | \(0.343649\pi\) | |||||||
\(840\) | 37.5938 | 1.29711 | ||||||||
\(841\) | 45.7759 | 1.57848 | ||||||||
\(842\) | 7.47959 | 0.257764 | ||||||||
\(843\) | −88.3320 | −3.04232 | ||||||||
\(844\) | 33.4802 | 1.15244 | ||||||||
\(845\) | −69.6984 | −2.39770 | ||||||||
\(846\) | 45.2369 | 1.55528 | ||||||||
\(847\) | −9.02088 | −0.309961 | ||||||||
\(848\) | −21.9308 | −0.753108 | ||||||||
\(849\) | 7.49250 | 0.257142 | ||||||||
\(850\) | 4.28738 | 0.147056 | ||||||||
\(851\) | 50.9454 | 1.74639 | ||||||||
\(852\) | −12.9473 | −0.443567 | ||||||||
\(853\) | −25.1711 | −0.861843 | −0.430921 | − | 0.902389i | \(-0.641811\pi\) | ||||
−0.430921 | + | 0.902389i | \(0.641811\pi\) | |||||||
\(854\) | −15.5980 | −0.533752 | ||||||||
\(855\) | −64.9004 | −2.21955 | ||||||||
\(856\) | 72.8245 | 2.48909 | ||||||||
\(857\) | −38.0878 | −1.30105 | −0.650527 | − | 0.759483i | \(-0.725452\pi\) | ||||
−0.650527 | + | 0.759483i | \(0.725452\pi\) | |||||||
\(858\) | −36.1319 | −1.23352 | ||||||||
\(859\) | 9.06000 | 0.309123 | 0.154562 | − | 0.987983i | \(-0.450604\pi\) | ||||
0.154562 | + | 0.987983i | \(0.450604\pi\) | |||||||
\(860\) | 52.7759 | 1.79964 | ||||||||
\(861\) | 17.7222 | 0.603971 | ||||||||
\(862\) | 71.4754 | 2.43446 | ||||||||
\(863\) | 49.0771 | 1.67060 | 0.835302 | − | 0.549791i | \(-0.185293\pi\) | ||||
0.835302 | + | 0.549791i | \(0.185293\pi\) | |||||||
\(864\) | −36.5951 | −1.24499 | ||||||||
\(865\) | −56.0508 | −1.90578 | ||||||||
\(866\) | −16.1516 | −0.548854 | ||||||||
\(867\) | −34.7960 | −1.18174 | ||||||||
\(868\) | −19.0032 | −0.645009 | ||||||||
\(869\) | 10.6683 | 0.361896 | ||||||||
\(870\) | −153.156 | −5.19247 | ||||||||
\(871\) | −32.5195 | −1.10188 | ||||||||
\(872\) | 42.9578 | 1.45473 | ||||||||
\(873\) | −26.6426 | −0.901716 | ||||||||
\(874\) | 75.6504 | 2.55891 | ||||||||
\(875\) | 8.81031 | 0.297843 | ||||||||
\(876\) | −88.5142 | −2.99062 | ||||||||
\(877\) | −12.3218 | −0.416077 | −0.208039 | − | 0.978121i | \(-0.566708\pi\) | ||||
−0.208039 | + | 0.978121i | \(0.566708\pi\) | |||||||
\(878\) | 56.6978 | 1.91346 | ||||||||
\(879\) | −36.5107 | −1.23148 | ||||||||
\(880\) | −12.5442 | −0.422866 | ||||||||
\(881\) | 12.5558 | 0.423017 | 0.211508 | − | 0.977376i | \(-0.432162\pi\) | ||||
0.211508 | + | 0.977376i | \(0.432162\pi\) | |||||||
\(882\) | 86.5467 | 2.91418 | ||||||||
\(883\) | −3.19155 | −0.107404 | −0.0537021 | − | 0.998557i | \(-0.517102\pi\) | ||||
−0.0537021 | + | 0.998557i | \(0.517102\pi\) | |||||||
\(884\) | −64.7820 | −2.17885 | ||||||||
\(885\) | 58.1176 | 1.95360 | ||||||||
\(886\) | −12.2488 | −0.411507 | ||||||||
\(887\) | 26.5796 | 0.892454 | 0.446227 | − | 0.894920i | \(-0.352767\pi\) | ||||
0.446227 | + | 0.894920i | \(0.352767\pi\) | |||||||
\(888\) | 153.989 | 5.16753 | ||||||||
\(889\) | 7.06369 | 0.236908 | ||||||||
\(890\) | −100.731 | −3.37650 | ||||||||
\(891\) | 3.27667 | 0.109773 | ||||||||
\(892\) | −90.7124 | −3.03728 | ||||||||
\(893\) | −16.2286 | −0.543071 | ||||||||
\(894\) | 65.5051 | 2.19082 | ||||||||
\(895\) | −20.2526 | −0.676970 | ||||||||
\(896\) | 10.6572 | 0.356031 | ||||||||
\(897\) | −113.032 | −3.77403 | ||||||||
\(898\) | 96.8477 | 3.23185 | ||||||||
\(899\) | 42.6573 | 1.42270 | ||||||||
\(900\) | 18.2646 | 0.608821 | ||||||||
\(901\) | 7.09438 | 0.236348 | ||||||||
\(902\) | −13.5129 | −0.449930 | ||||||||
\(903\) | −12.4181 | −0.413247 | ||||||||
\(904\) | 6.23529 | 0.207383 | ||||||||
\(905\) | 24.5348 | 0.815563 | ||||||||
\(906\) | −2.10504 | −0.0699354 | ||||||||
\(907\) | 37.1566 | 1.23376 | 0.616882 | − | 0.787056i | \(-0.288395\pi\) | ||||
0.616882 | + | 0.787056i | \(0.288395\pi\) | |||||||
\(908\) | −133.316 | −4.42426 | ||||||||
\(909\) | 1.79885 | 0.0596642 | ||||||||
\(910\) | 34.1759 | 1.13292 | ||||||||
\(911\) | −48.6415 | −1.61156 | −0.805782 | − | 0.592212i | \(-0.798255\pi\) | ||||
−0.805782 | + | 0.592212i | \(0.798255\pi\) | |||||||
\(912\) | 100.068 | 3.31357 | ||||||||
\(913\) | −7.99262 | −0.264517 | ||||||||
\(914\) | 67.5046 | 2.23285 | ||||||||
\(915\) | −49.4925 | −1.63617 | ||||||||
\(916\) | 74.7573 | 2.47005 | ||||||||
\(917\) | 10.2573 | 0.338725 | ||||||||
\(918\) | 40.5524 | 1.33843 | ||||||||
\(919\) | 26.8077 | 0.884303 | 0.442152 | − | 0.896940i | \(-0.354215\pi\) | ||||
0.442152 | + | 0.896940i | \(0.354215\pi\) | |||||||
\(920\) | −89.6719 | −2.95640 | ||||||||
\(921\) | −52.9989 | −1.74637 | ||||||||
\(922\) | −91.7633 | −3.02206 | ||||||||
\(923\) | −6.48536 | −0.213468 | ||||||||
\(924\) | 8.44783 | 0.277913 | ||||||||
\(925\) | −6.39386 | −0.210229 | ||||||||
\(926\) | −88.1674 | −2.89736 | ||||||||
\(927\) | −71.0091 | −2.33225 | ||||||||
\(928\) | 44.4581 | 1.45941 | ||||||||
\(929\) | −9.69227 | −0.317993 | −0.158997 | − | 0.987279i | \(-0.550826\pi\) | ||||
−0.158997 | + | 0.987279i | \(0.550826\pi\) | |||||||
\(930\) | −87.3706 | −2.86499 | ||||||||
\(931\) | −31.0484 | −1.01757 | ||||||||
\(932\) | −15.4807 | −0.507086 | ||||||||
\(933\) | 39.5255 | 1.29401 | ||||||||
\(934\) | −49.3745 | −1.61558 | ||||||||
\(935\) | 4.05792 | 0.132708 | ||||||||
\(936\) | −220.339 | −7.20202 | ||||||||
\(937\) | −1.30603 | −0.0426661 | −0.0213330 | − | 0.999772i | \(-0.506791\pi\) | ||||
−0.0213330 | + | 0.999772i | \(0.506791\pi\) | |||||||
\(938\) | 11.0171 | 0.359721 | ||||||||
\(939\) | 76.8113 | 2.50664 | ||||||||
\(940\) | 34.9122 | 1.13871 | ||||||||
\(941\) | 29.9934 | 0.977756 | 0.488878 | − | 0.872352i | \(-0.337406\pi\) | ||||
0.488878 | + | 0.872352i | \(0.337406\pi\) | |||||||
\(942\) | −98.2300 | −3.20051 | ||||||||
\(943\) | −42.2726 | −1.37658 | ||||||||
\(944\) | −57.7909 | −1.88093 | ||||||||
\(945\) | −14.7643 | −0.480284 | ||||||||
\(946\) | 9.46856 | 0.307849 | ||||||||
\(947\) | 33.7358 | 1.09627 | 0.548134 | − | 0.836391i | \(-0.315338\pi\) | ||||
0.548134 | + | 0.836391i | \(0.315338\pi\) | |||||||
\(948\) | 183.079 | 5.94613 | ||||||||
\(949\) | −44.3371 | −1.43924 | ||||||||
\(950\) | −9.49444 | −0.308040 | ||||||||
\(951\) | 11.8450 | 0.384102 | ||||||||
\(952\) | 12.0928 | 0.391930 | ||||||||
\(953\) | 42.9836 | 1.39238 | 0.696188 | − | 0.717860i | \(-0.254878\pi\) | ||||
0.696188 | + | 0.717860i | \(0.254878\pi\) | |||||||
\(954\) | 43.7927 | 1.41784 | ||||||||
\(955\) | 3.97261 | 0.128551 | ||||||||
\(956\) | 51.4859 | 1.66517 | ||||||||
\(957\) | −18.9633 | −0.612995 | ||||||||
\(958\) | 9.79796 | 0.316558 | ||||||||
\(959\) | 10.5579 | 0.340932 | ||||||||
\(960\) | 5.59881 | 0.180701 | ||||||||
\(961\) | −6.66536 | −0.215012 | ||||||||
\(962\) | 139.989 | 4.51343 | ||||||||
\(963\) | −63.6388 | −2.05073 | ||||||||
\(964\) | 37.6010 | 1.21105 | ||||||||
\(965\) | 34.4687 | 1.10959 | ||||||||
\(966\) | 38.2935 | 1.23207 | ||||||||
\(967\) | −29.1721 | −0.938112 | −0.469056 | − | 0.883168i | \(-0.655406\pi\) | ||||
−0.469056 | + | 0.883168i | \(0.655406\pi\) | |||||||
\(968\) | 65.0391 | 2.09043 | ||||||||
\(969\) | −32.3708 | −1.03990 | ||||||||
\(970\) | −29.7941 | −0.956631 | ||||||||
\(971\) | 45.3244 | 1.45453 | 0.727265 | − | 0.686357i | \(-0.240791\pi\) | ||||
0.727265 | + | 0.686357i | \(0.240791\pi\) | |||||||
\(972\) | −38.8851 | −1.24724 | ||||||||
\(973\) | −13.5923 | −0.435748 | ||||||||
\(974\) | 20.2544 | 0.648993 | ||||||||
\(975\) | 14.1860 | 0.454315 | ||||||||
\(976\) | 49.2143 | 1.57531 | ||||||||
\(977\) | −39.5448 | −1.26515 | −0.632575 | − | 0.774499i | \(-0.718002\pi\) | ||||
−0.632575 | + | 0.774499i | \(0.718002\pi\) | |||||||
\(978\) | 8.42343 | 0.269351 | ||||||||
\(979\) | −12.4721 | −0.398612 | ||||||||
\(980\) | 66.7936 | 2.13364 | ||||||||
\(981\) | −37.5394 | −1.19854 | ||||||||
\(982\) | 73.2895 | 2.33876 | ||||||||
\(983\) | −28.2671 | −0.901580 | −0.450790 | − | 0.892630i | \(-0.648858\pi\) | ||||
−0.450790 | + | 0.892630i | \(0.648858\pi\) | |||||||
\(984\) | −127.774 | −4.07329 | ||||||||
\(985\) | −52.2504 | −1.66484 | ||||||||
\(986\) | −49.2657 | −1.56894 | ||||||||
\(987\) | −8.21477 | −0.261479 | ||||||||
\(988\) | 143.460 | 4.56408 | ||||||||
\(989\) | 29.6206 | 0.941881 | ||||||||
\(990\) | 25.0490 | 0.796110 | ||||||||
\(991\) | −29.2232 | −0.928305 | −0.464153 | − | 0.885755i | \(-0.653641\pi\) | ||||
−0.464153 | + | 0.885755i | \(0.653641\pi\) | |||||||
\(992\) | 25.3620 | 0.805243 | ||||||||
\(993\) | −76.3883 | −2.42411 | ||||||||
\(994\) | 2.19714 | 0.0696889 | ||||||||
\(995\) | −45.8486 | −1.45350 | ||||||||
\(996\) | −137.162 | −4.34614 | ||||||||
\(997\) | −26.4138 | −0.836535 | −0.418267 | − | 0.908324i | \(-0.637363\pi\) | ||||
−0.418267 | + | 0.908324i | \(0.637363\pi\) | |||||||
\(998\) | −62.0068 | −1.96279 | ||||||||
\(999\) | −60.4766 | −1.91340 |
(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 | 8023.2.a.c.1.13 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.13 | ✓ | 158 | 1.1 | even | 1 | trivial |