Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50780 | −1.77328 | −0.886641 | − | 0.462459i | \(-0.846967\pi\) | ||||
−0.886641 | + | 0.462459i | \(0.846967\pi\) | |||||||
\(3\) | 2.09202 | 1.20783 | 0.603914 | − | 0.797050i | \(-0.293607\pi\) | ||||
0.603914 | + | 0.797050i | \(0.293607\pi\) | |||||||
\(4\) | 4.28906 | 2.14453 | ||||||||
\(5\) | −3.15733 | −1.41200 | −0.706001 | − | 0.708210i | \(-0.749503\pi\) | ||||
−0.706001 | + | 0.708210i | \(0.749503\pi\) | |||||||
\(6\) | −5.24636 | −2.14182 | ||||||||
\(7\) | −2.77421 | −1.04855 | −0.524277 | − | 0.851548i | \(-0.675664\pi\) | ||||
−0.524277 | + | 0.851548i | \(0.675664\pi\) | |||||||
\(8\) | −5.74049 | −2.02957 | ||||||||
\(9\) | 1.37654 | 0.458848 | ||||||||
\(10\) | 7.91796 | 2.50388 | ||||||||
\(11\) | 2.37154 | 0.715046 | 0.357523 | − | 0.933904i | \(-0.383621\pi\) | ||||
0.357523 | + | 0.933904i | \(0.383621\pi\) | |||||||
\(12\) | 8.97279 | 2.59022 | ||||||||
\(13\) | 1.38971 | 0.385437 | 0.192718 | − | 0.981254i | \(-0.438270\pi\) | ||||
0.192718 | + | 0.981254i | \(0.438270\pi\) | |||||||
\(14\) | 6.95717 | 1.85938 | ||||||||
\(15\) | −6.60520 | −1.70546 | ||||||||
\(16\) | 5.81789 | 1.45447 | ||||||||
\(17\) | −2.15703 | −0.523158 | −0.261579 | − | 0.965182i | \(-0.584243\pi\) | ||||
−0.261579 | + | 0.965182i | \(0.584243\pi\) | |||||||
\(18\) | −3.45210 | −0.813667 | ||||||||
\(19\) | −2.24645 | −0.515371 | −0.257685 | − | 0.966229i | \(-0.582960\pi\) | ||||
−0.257685 | + | 0.966229i | \(0.582960\pi\) | |||||||
\(20\) | −13.5420 | −3.02808 | ||||||||
\(21\) | −5.80370 | −1.26647 | ||||||||
\(22\) | −5.94735 | −1.26798 | ||||||||
\(23\) | 5.80938 | 1.21134 | 0.605669 | − | 0.795716i | \(-0.292905\pi\) | ||||
0.605669 | + | 0.795716i | \(0.292905\pi\) | |||||||
\(24\) | −12.0092 | −2.45137 | ||||||||
\(25\) | 4.96876 | 0.993752 | ||||||||
\(26\) | −3.48512 | −0.683488 | ||||||||
\(27\) | −3.39630 | −0.653618 | ||||||||
\(28\) | −11.8987 | −2.24865 | ||||||||
\(29\) | −4.81200 | −0.893566 | −0.446783 | − | 0.894642i | \(-0.647430\pi\) | ||||
−0.446783 | + | 0.894642i | \(0.647430\pi\) | |||||||
\(30\) | 16.5645 | 3.02425 | ||||||||
\(31\) | −5.81211 | −1.04389 | −0.521943 | − | 0.852981i | \(-0.674793\pi\) | ||||
−0.521943 | + | 0.852981i | \(0.674793\pi\) | |||||||
\(32\) | −3.10911 | −0.549618 | ||||||||
\(33\) | 4.96131 | 0.863653 | ||||||||
\(34\) | 5.40941 | 0.927706 | ||||||||
\(35\) | 8.75911 | 1.48056 | ||||||||
\(36\) | 5.90408 | 0.984013 | ||||||||
\(37\) | −9.46646 | −1.55628 | −0.778138 | − | 0.628093i | \(-0.783836\pi\) | ||||
−0.778138 | + | 0.628093i | \(0.783836\pi\) | |||||||
\(38\) | 5.63364 | 0.913897 | ||||||||
\(39\) | 2.90730 | 0.465541 | ||||||||
\(40\) | 18.1247 | 2.86576 | ||||||||
\(41\) | 8.95246 | 1.39814 | 0.699069 | − | 0.715054i | \(-0.253598\pi\) | ||||
0.699069 | + | 0.715054i | \(0.253598\pi\) | |||||||
\(42\) | 14.5545 | 2.24581 | ||||||||
\(43\) | 0.699540 | 0.106679 | 0.0533394 | − | 0.998576i | \(-0.483013\pi\) | ||||
0.0533394 | + | 0.998576i | \(0.483013\pi\) | |||||||
\(44\) | 10.1717 | 1.53344 | ||||||||
\(45\) | −4.34621 | −0.647895 | ||||||||
\(46\) | −14.5687 | −2.14804 | ||||||||
\(47\) | 11.6297 | 1.69637 | 0.848183 | − | 0.529703i | \(-0.177697\pi\) | ||||
0.848183 | + | 0.529703i | \(0.177697\pi\) | |||||||
\(48\) | 12.1711 | 1.75675 | ||||||||
\(49\) | 0.696251 | 0.0994644 | ||||||||
\(50\) | −12.4607 | −1.76220 | ||||||||
\(51\) | −4.51256 | −0.631885 | ||||||||
\(52\) | 5.96055 | 0.826579 | ||||||||
\(53\) | 5.27972 | 0.725225 | 0.362612 | − | 0.931940i | \(-0.381885\pi\) | ||||
0.362612 | + | 0.931940i | \(0.381885\pi\) | |||||||
\(54\) | 8.51724 | 1.15905 | ||||||||
\(55\) | −7.48775 | −1.00965 | ||||||||
\(56\) | 15.9253 | 2.12811 | ||||||||
\(57\) | −4.69961 | −0.622479 | ||||||||
\(58\) | 12.0675 | 1.58454 | ||||||||
\(59\) | −8.25919 | −1.07525 | −0.537627 | − | 0.843183i | \(-0.680679\pi\) | ||||
−0.537627 | + | 0.843183i | \(0.680679\pi\) | |||||||
\(60\) | −28.3301 | −3.65740 | ||||||||
\(61\) | −0.889360 | −0.113871 | −0.0569355 | − | 0.998378i | \(-0.518133\pi\) | ||||
−0.0569355 | + | 0.998378i | \(0.518133\pi\) | |||||||
\(62\) | 14.5756 | 1.85110 | ||||||||
\(63\) | −3.81883 | −0.481127 | ||||||||
\(64\) | −3.83875 | −0.479844 | ||||||||
\(65\) | −4.38778 | −0.544238 | ||||||||
\(66\) | −12.4420 | −1.53150 | ||||||||
\(67\) | 8.64543 | 1.05621 | 0.528103 | − | 0.849180i | \(-0.322903\pi\) | ||||
0.528103 | + | 0.849180i | \(0.322903\pi\) | |||||||
\(68\) | −9.25164 | −1.12193 | ||||||||
\(69\) | 12.1533 | 1.46309 | ||||||||
\(70\) | −21.9661 | −2.62545 | ||||||||
\(71\) | −5.37954 | −0.638433 | −0.319217 | − | 0.947682i | \(-0.603420\pi\) | ||||
−0.319217 | + | 0.947682i | \(0.603420\pi\) | |||||||
\(72\) | −7.90204 | −0.931265 | ||||||||
\(73\) | −15.2353 | −1.78316 | −0.891579 | − | 0.452866i | \(-0.850402\pi\) | ||||
−0.891579 | + | 0.452866i | \(0.850402\pi\) | |||||||
\(74\) | 23.7400 | 2.75972 | ||||||||
\(75\) | 10.3947 | 1.20028 | ||||||||
\(76\) | −9.63514 | −1.10523 | ||||||||
\(77\) | −6.57916 | −0.749764 | ||||||||
\(78\) | −7.29093 | −0.825535 | ||||||||
\(79\) | 13.3694 | 1.50417 | 0.752086 | − | 0.659065i | \(-0.229048\pi\) | ||||
0.752086 | + | 0.659065i | \(0.229048\pi\) | |||||||
\(80\) | −18.3690 | −2.05372 | ||||||||
\(81\) | −11.2348 | −1.24831 | ||||||||
\(82\) | −22.4510 | −2.47929 | ||||||||
\(83\) | −10.6453 | −1.16847 | −0.584237 | − | 0.811583i | \(-0.698606\pi\) | ||||
−0.584237 | + | 0.811583i | \(0.698606\pi\) | |||||||
\(84\) | −24.8924 | −2.71598 | ||||||||
\(85\) | 6.81048 | 0.738700 | ||||||||
\(86\) | −1.75431 | −0.189172 | ||||||||
\(87\) | −10.0668 | −1.07927 | ||||||||
\(88\) | −13.6138 | −1.45124 | ||||||||
\(89\) | 3.24014 | 0.343454 | 0.171727 | − | 0.985145i | \(-0.445065\pi\) | ||||
0.171727 | + | 0.985145i | \(0.445065\pi\) | |||||||
\(90\) | 10.8994 | 1.14890 | ||||||||
\(91\) | −3.85535 | −0.404151 | ||||||||
\(92\) | 24.9167 | 2.59775 | ||||||||
\(93\) | −12.1590 | −1.26083 | ||||||||
\(94\) | −29.1649 | −3.00813 | ||||||||
\(95\) | 7.09279 | 0.727705 | ||||||||
\(96\) | −6.50432 | −0.663844 | ||||||||
\(97\) | −8.37419 | −0.850270 | −0.425135 | − | 0.905130i | \(-0.639773\pi\) | ||||
−0.425135 | + | 0.905130i | \(0.639773\pi\) | |||||||
\(98\) | −1.74606 | −0.176378 | ||||||||
\(99\) | 3.26453 | 0.328098 | ||||||||
\(100\) | 21.3113 | 2.13113 | ||||||||
\(101\) | 11.1897 | 1.11341 | 0.556707 | − | 0.830709i | \(-0.312064\pi\) | ||||
0.556707 | + | 0.830709i | \(0.312064\pi\) | |||||||
\(102\) | 11.3166 | 1.12051 | ||||||||
\(103\) | 16.5627 | 1.63198 | 0.815988 | − | 0.578069i | \(-0.196194\pi\) | ||||
0.815988 | + | 0.578069i | \(0.196194\pi\) | |||||||
\(104\) | −7.97763 | −0.782271 | ||||||||
\(105\) | 18.3242 | 1.78826 | ||||||||
\(106\) | −13.2405 | −1.28603 | ||||||||
\(107\) | −16.9325 | −1.63692 | −0.818461 | − | 0.574562i | \(-0.805173\pi\) | ||||
−0.818461 | + | 0.574562i | \(0.805173\pi\) | |||||||
\(108\) | −14.5669 | −1.40170 | ||||||||
\(109\) | 3.76552 | 0.360671 | 0.180336 | − | 0.983605i | \(-0.442282\pi\) | ||||
0.180336 | + | 0.983605i | \(0.442282\pi\) | |||||||
\(110\) | 18.7778 | 1.79039 | ||||||||
\(111\) | −19.8040 | −1.87971 | ||||||||
\(112\) | −16.1401 | −1.52509 | ||||||||
\(113\) | 8.84687 | 0.832244 | 0.416122 | − | 0.909309i | \(-0.363389\pi\) | ||||
0.416122 | + | 0.909309i | \(0.363389\pi\) | |||||||
\(114\) | 11.7857 | 1.10383 | ||||||||
\(115\) | −18.3421 | −1.71041 | ||||||||
\(116\) | −20.6389 | −1.91628 | ||||||||
\(117\) | 1.91300 | 0.176857 | ||||||||
\(118\) | 20.7124 | 1.90673 | ||||||||
\(119\) | 5.98407 | 0.548559 | ||||||||
\(120\) | 37.9171 | 3.46134 | ||||||||
\(121\) | −5.37579 | −0.488709 | ||||||||
\(122\) | 2.23034 | 0.201925 | ||||||||
\(123\) | 18.7287 | 1.68871 | ||||||||
\(124\) | −24.9285 | −2.23864 | ||||||||
\(125\) | 0.0986302 | 0.00882176 | ||||||||
\(126\) | 9.57685 | 0.853173 | ||||||||
\(127\) | 10.3795 | 0.921036 | 0.460518 | − | 0.887650i | \(-0.347664\pi\) | ||||
0.460518 | + | 0.887650i | \(0.347664\pi\) | |||||||
\(128\) | 15.8450 | 1.40052 | ||||||||
\(129\) | 1.46345 | 0.128850 | ||||||||
\(130\) | 11.0037 | 0.965086 | ||||||||
\(131\) | 12.5787 | 1.09901 | 0.549505 | − | 0.835490i | \(-0.314816\pi\) | ||||
0.549505 | + | 0.835490i | \(0.314816\pi\) | |||||||
\(132\) | 21.2793 | 1.85213 | ||||||||
\(133\) | 6.23212 | 0.540394 | ||||||||
\(134\) | −21.6810 | −1.87295 | ||||||||
\(135\) | 10.7233 | 0.922911 | ||||||||
\(136\) | 12.3824 | 1.06179 | ||||||||
\(137\) | −18.2136 | −1.55609 | −0.778046 | − | 0.628208i | \(-0.783789\pi\) | ||||
−0.778046 | + | 0.628208i | \(0.783789\pi\) | |||||||
\(138\) | −30.4781 | −2.59447 | ||||||||
\(139\) | 10.0012 | 0.848291 | 0.424146 | − | 0.905594i | \(-0.360574\pi\) | ||||
0.424146 | + | 0.905594i | \(0.360574\pi\) | |||||||
\(140\) | 37.5683 | 3.17510 | ||||||||
\(141\) | 24.3296 | 2.04892 | ||||||||
\(142\) | 13.4908 | 1.13212 | ||||||||
\(143\) | 3.29576 | 0.275605 | ||||||||
\(144\) | 8.00858 | 0.667382 | ||||||||
\(145\) | 15.1931 | 1.26172 | ||||||||
\(146\) | 38.2071 | 3.16204 | ||||||||
\(147\) | 1.45657 | 0.120136 | ||||||||
\(148\) | −40.6022 | −3.33748 | ||||||||
\(149\) | 23.0912 | 1.89170 | 0.945851 | − | 0.324600i | \(-0.105230\pi\) | ||||
0.945851 | + | 0.324600i | \(0.105230\pi\) | |||||||
\(150\) | −26.0679 | −2.12844 | ||||||||
\(151\) | −10.4148 | −0.847548 | −0.423774 | − | 0.905768i | \(-0.639295\pi\) | ||||
−0.423774 | + | 0.905768i | \(0.639295\pi\) | |||||||
\(152\) | 12.8957 | 1.04598 | ||||||||
\(153\) | −2.96925 | −0.240050 | ||||||||
\(154\) | 16.4992 | 1.32954 | ||||||||
\(155\) | 18.3508 | 1.47397 | ||||||||
\(156\) | 12.4696 | 0.998366 | ||||||||
\(157\) | −4.71576 | −0.376358 | −0.188179 | − | 0.982135i | \(-0.560259\pi\) | ||||
−0.188179 | + | 0.982135i | \(0.560259\pi\) | |||||||
\(158\) | −33.5277 | −2.66732 | ||||||||
\(159\) | 11.0453 | 0.875947 | ||||||||
\(160\) | 9.81650 | 0.776062 | ||||||||
\(161\) | −16.1164 | −1.27015 | ||||||||
\(162\) | 28.1745 | 2.21360 | ||||||||
\(163\) | 1.42115 | 0.111313 | 0.0556564 | − | 0.998450i | \(-0.482275\pi\) | ||||
0.0556564 | + | 0.998450i | \(0.482275\pi\) | |||||||
\(164\) | 38.3976 | 2.99835 | ||||||||
\(165\) | −15.6645 | −1.21948 | ||||||||
\(166\) | 26.6963 | 2.07203 | ||||||||
\(167\) | 17.8972 | 1.38493 | 0.692464 | − | 0.721452i | \(-0.256525\pi\) | ||||
0.692464 | + | 0.721452i | \(0.256525\pi\) | |||||||
\(168\) | 33.3161 | 2.57039 | ||||||||
\(169\) | −11.0687 | −0.851439 | ||||||||
\(170\) | −17.0793 | −1.30992 | ||||||||
\(171\) | −3.09234 | −0.236477 | ||||||||
\(172\) | 3.00037 | 0.228776 | ||||||||
\(173\) | 19.0733 | 1.45012 | 0.725059 | − | 0.688686i | \(-0.241812\pi\) | ||||
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(174\) | 25.2455 | 1.91386 | ||||||||
\(175\) | −13.7844 | −1.04200 | ||||||||
\(176\) | 13.7974 | 1.04001 | ||||||||
\(177\) | −17.2784 | −1.29872 | ||||||||
\(178\) | −8.12562 | −0.609041 | ||||||||
\(179\) | 14.9133 | 1.11467 | 0.557337 | − | 0.830286i | \(-0.311823\pi\) | ||||
0.557337 | + | 0.830286i | \(0.311823\pi\) | |||||||
\(180\) | −18.6411 | −1.38943 | ||||||||
\(181\) | −3.64367 | −0.270832 | −0.135416 | − | 0.990789i | \(-0.543237\pi\) | ||||
−0.135416 | + | 0.990789i | \(0.543237\pi\) | |||||||
\(182\) | 9.66845 | 0.716673 | ||||||||
\(183\) | −1.86056 | −0.137536 | ||||||||
\(184\) | −33.3487 | −2.45850 | ||||||||
\(185\) | 29.8888 | 2.19747 | ||||||||
\(186\) | 30.4924 | 2.23581 | ||||||||
\(187\) | −5.11550 | −0.374082 | ||||||||
\(188\) | 49.8804 | 3.63790 | ||||||||
\(189\) | 9.42205 | 0.685354 | ||||||||
\(190\) | −17.7873 | −1.29043 | ||||||||
\(191\) | 8.60635 | 0.622734 | 0.311367 | − | 0.950290i | \(-0.399213\pi\) | ||||
0.311367 | + | 0.950290i | \(0.399213\pi\) | |||||||
\(192\) | −8.03075 | −0.579569 | ||||||||
\(193\) | 20.6861 | 1.48902 | 0.744509 | − | 0.667612i | \(-0.232684\pi\) | ||||
0.744509 | + | 0.667612i | \(0.232684\pi\) | |||||||
\(194\) | 21.0008 | 1.50777 | ||||||||
\(195\) | −9.17933 | −0.657345 | ||||||||
\(196\) | 2.98626 | 0.213304 | ||||||||
\(197\) | 19.4813 | 1.38798 | 0.693992 | − | 0.719983i | \(-0.255850\pi\) | ||||
0.693992 | + | 0.719983i | \(0.255850\pi\) | |||||||
\(198\) | −8.18679 | −0.581810 | ||||||||
\(199\) | −3.70541 | −0.262670 | −0.131335 | − | 0.991338i | \(-0.541926\pi\) | ||||
−0.131335 | + | 0.991338i | \(0.541926\pi\) | |||||||
\(200\) | −28.5231 | −2.01689 | ||||||||
\(201\) | 18.0864 | 1.27572 | ||||||||
\(202\) | −28.0615 | −1.97440 | ||||||||
\(203\) | 13.3495 | 0.936952 | ||||||||
\(204\) | −19.3546 | −1.35509 | ||||||||
\(205\) | −28.2659 | −1.97418 | ||||||||
\(206\) | −41.5360 | −2.89395 | ||||||||
\(207\) | 7.99687 | 0.555821 | ||||||||
\(208\) | 8.08518 | 0.560607 | ||||||||
\(209\) | −5.32754 | −0.368514 | ||||||||
\(210\) | −45.9535 | −3.17109 | ||||||||
\(211\) | −5.77506 | −0.397571 | −0.198786 | − | 0.980043i | \(-0.563700\pi\) | ||||
−0.198786 | + | 0.980043i | \(0.563700\pi\) | |||||||
\(212\) | 22.6450 | 1.55526 | ||||||||
\(213\) | −11.2541 | −0.771118 | ||||||||
\(214\) | 42.4632 | 2.90273 | ||||||||
\(215\) | −2.20868 | −0.150631 | ||||||||
\(216\) | 19.4964 | 1.32656 | ||||||||
\(217\) | 16.1240 | 1.09457 | ||||||||
\(218\) | −9.44316 | −0.639572 | ||||||||
\(219\) | −31.8725 | −2.15375 | ||||||||
\(220\) | −32.1154 | −2.16522 | ||||||||
\(221\) | −2.99766 | −0.201644 | ||||||||
\(222\) | 49.6645 | 3.33326 | ||||||||
\(223\) | 3.59749 | 0.240906 | 0.120453 | − | 0.992719i | \(-0.461565\pi\) | ||||
0.120453 | + | 0.992719i | \(0.461565\pi\) | |||||||
\(224\) | 8.62533 | 0.576304 | ||||||||
\(225\) | 6.83972 | 0.455981 | ||||||||
\(226\) | −22.1862 | −1.47580 | ||||||||
\(227\) | 8.91046 | 0.591408 | 0.295704 | − | 0.955280i | \(-0.404446\pi\) | ||||
0.295704 | + | 0.955280i | \(0.404446\pi\) | |||||||
\(228\) | −20.1569 | −1.33492 | ||||||||
\(229\) | −18.7226 | −1.23723 | −0.618613 | − | 0.785696i | \(-0.712305\pi\) | ||||
−0.618613 | + | 0.785696i | \(0.712305\pi\) | |||||||
\(230\) | 45.9984 | 3.03305 | ||||||||
\(231\) | −13.7637 | −0.905586 | ||||||||
\(232\) | 27.6233 | 1.81356 | ||||||||
\(233\) | 13.3786 | 0.876463 | 0.438231 | − | 0.898862i | \(-0.355605\pi\) | ||||
0.438231 | + | 0.898862i | \(0.355605\pi\) | |||||||
\(234\) | −4.79742 | −0.313617 | ||||||||
\(235\) | −36.7188 | −2.39527 | ||||||||
\(236\) | −35.4241 | −2.30591 | ||||||||
\(237\) | 27.9690 | 1.81678 | ||||||||
\(238\) | −15.0068 | −0.972750 | ||||||||
\(239\) | −16.4951 | −1.06698 | −0.533491 | − | 0.845806i | \(-0.679120\pi\) | ||||
−0.533491 | + | 0.845806i | \(0.679120\pi\) | |||||||
\(240\) | −38.4283 | −2.48054 | ||||||||
\(241\) | −0.552647 | −0.0355991 | −0.0177996 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177996 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(242\) | 13.4814 | 0.866618 | ||||||||
\(243\) | −13.3144 | −0.854121 | ||||||||
\(244\) | −3.81452 | −0.244199 | ||||||||
\(245\) | −2.19830 | −0.140444 | ||||||||
\(246\) | −46.9678 | −2.99456 | ||||||||
\(247\) | −3.12191 | −0.198643 | ||||||||
\(248\) | 33.3644 | 2.11864 | ||||||||
\(249\) | −22.2702 | −1.41132 | ||||||||
\(250\) | −0.247345 | −0.0156435 | ||||||||
\(251\) | −0.564031 | −0.0356013 | −0.0178007 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0178007 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(252\) | −16.3792 | −1.03179 | ||||||||
\(253\) | 13.7772 | 0.866163 | ||||||||
\(254\) | −26.0298 | −1.63326 | ||||||||
\(255\) | 14.2477 | 0.892223 | ||||||||
\(256\) | −32.0587 | −2.00367 | ||||||||
\(257\) | −20.0823 | −1.25270 | −0.626350 | − | 0.779542i | \(-0.715452\pi\) | ||||
−0.626350 | + | 0.779542i | \(0.715452\pi\) | |||||||
\(258\) | −3.67004 | −0.228487 | ||||||||
\(259\) | 26.2620 | 1.63184 | ||||||||
\(260\) | −18.8194 | −1.16713 | ||||||||
\(261\) | −6.62393 | −0.410011 | ||||||||
\(262\) | −31.5450 | −1.94885 | ||||||||
\(263\) | −6.87332 | −0.423827 | −0.211914 | − | 0.977288i | \(-0.567970\pi\) | ||||
−0.211914 | + | 0.977288i | \(0.567970\pi\) | |||||||
\(264\) | −28.4804 | −1.75284 | ||||||||
\(265\) | −16.6698 | −1.02402 | ||||||||
\(266\) | −15.6289 | −0.958270 | ||||||||
\(267\) | 6.77844 | 0.414834 | ||||||||
\(268\) | 37.0807 | 2.26507 | ||||||||
\(269\) | −0.918070 | −0.0559757 | −0.0279879 | − | 0.999608i | \(-0.508910\pi\) | ||||
−0.0279879 | + | 0.999608i | \(0.508910\pi\) | |||||||
\(270\) | −26.8918 | −1.63658 | ||||||||
\(271\) | 24.9286 | 1.51431 | 0.757153 | − | 0.653237i | \(-0.226590\pi\) | ||||
0.757153 | + | 0.653237i | \(0.226590\pi\) | |||||||
\(272\) | −12.5494 | −0.760918 | ||||||||
\(273\) | −8.06547 | −0.488145 | ||||||||
\(274\) | 45.6760 | 2.75939 | ||||||||
\(275\) | 11.7836 | 0.710579 | ||||||||
\(276\) | 52.1263 | 3.13763 | ||||||||
\(277\) | 16.5526 | 0.994548 | 0.497274 | − | 0.867594i | \(-0.334334\pi\) | ||||
0.497274 | + | 0.867594i | \(0.334334\pi\) | |||||||
\(278\) | −25.0810 | −1.50426 | ||||||||
\(279\) | −8.00063 | −0.478985 | ||||||||
\(280\) | −50.2816 | −3.00490 | ||||||||
\(281\) | −3.90216 | −0.232784 | −0.116392 | − | 0.993203i | \(-0.537133\pi\) | ||||
−0.116392 | + | 0.993203i | \(0.537133\pi\) | |||||||
\(282\) | −61.0136 | −3.63331 | ||||||||
\(283\) | 12.3796 | 0.735889 | 0.367945 | − | 0.929848i | \(-0.380062\pi\) | ||||
0.367945 | + | 0.929848i | \(0.380062\pi\) | |||||||
\(284\) | −23.0731 | −1.36914 | ||||||||
\(285\) | 14.8383 | 0.878942 | ||||||||
\(286\) | −8.26509 | −0.488725 | ||||||||
\(287\) | −24.8360 | −1.46602 | ||||||||
\(288\) | −4.27983 | −0.252191 | ||||||||
\(289\) | −12.3472 | −0.726306 | ||||||||
\(290\) | −38.1012 | −2.23738 | ||||||||
\(291\) | −17.5190 | −1.02698 | ||||||||
\(292\) | −65.3451 | −3.82403 | ||||||||
\(293\) | 13.0448 | 0.762087 | 0.381044 | − | 0.924557i | \(-0.375565\pi\) | ||||
0.381044 | + | 0.924557i | \(0.375565\pi\) | |||||||
\(294\) | −3.65278 | −0.213035 | ||||||||
\(295\) | 26.0770 | 1.51826 | ||||||||
\(296\) | 54.3421 | 3.15857 | ||||||||
\(297\) | −8.05446 | −0.467367 | ||||||||
\(298\) | −57.9080 | −3.35452 | ||||||||
\(299\) | 8.07336 | 0.466894 | ||||||||
\(300\) | 44.5836 | 2.57404 | ||||||||
\(301\) | −1.94067 | −0.111858 | ||||||||
\(302\) | 26.1183 | 1.50294 | ||||||||
\(303\) | 23.4090 | 1.34481 | ||||||||
\(304\) | −13.0696 | −0.749592 | ||||||||
\(305\) | 2.80801 | 0.160786 | ||||||||
\(306\) | 7.44629 | 0.425676 | ||||||||
\(307\) | 7.91892 | 0.451957 | 0.225978 | − | 0.974132i | \(-0.427442\pi\) | ||||
0.225978 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(308\) | −28.2184 | −1.60789 | ||||||||
\(309\) | 34.6496 | 1.97115 | ||||||||
\(310\) | −46.0200 | −2.61376 | ||||||||
\(311\) | 25.7388 | 1.45951 | 0.729757 | − | 0.683707i | \(-0.239633\pi\) | ||||
0.729757 | + | 0.683707i | \(0.239633\pi\) | |||||||
\(312\) | −16.6893 | −0.944848 | ||||||||
\(313\) | 32.2311 | 1.82181 | 0.910904 | − | 0.412618i | \(-0.135385\pi\) | ||||
0.910904 | + | 0.412618i | \(0.135385\pi\) | |||||||
\(314\) | 11.8262 | 0.667390 | ||||||||
\(315\) | 12.0573 | 0.679353 | ||||||||
\(316\) | 57.3420 | 3.22574 | ||||||||
\(317\) | −7.07935 | −0.397616 | −0.198808 | − | 0.980038i | \(-0.563707\pi\) | ||||
−0.198808 | + | 0.980038i | \(0.563707\pi\) | |||||||
\(318\) | −27.6993 | −1.55330 | ||||||||
\(319\) | −11.4119 | −0.638941 | ||||||||
\(320\) | 12.1202 | 0.677541 | ||||||||
\(321\) | −35.4230 | −1.97712 | ||||||||
\(322\) | 40.4168 | 2.25234 | ||||||||
\(323\) | 4.84567 | 0.269620 | ||||||||
\(324\) | −48.1865 | −2.67703 | ||||||||
\(325\) | 6.90514 | 0.383028 | ||||||||
\(326\) | −3.56395 | −0.197389 | ||||||||
\(327\) | 7.87754 | 0.435629 | ||||||||
\(328\) | −51.3915 | −2.83762 | ||||||||
\(329\) | −32.2632 | −1.77873 | ||||||||
\(330\) | 39.2834 | 2.16248 | ||||||||
\(331\) | 17.3309 | 0.952593 | 0.476296 | − | 0.879285i | \(-0.341979\pi\) | ||||
0.476296 | + | 0.879285i | \(0.341979\pi\) | |||||||
\(332\) | −45.6583 | −2.50583 | ||||||||
\(333\) | −13.0310 | −0.714095 | ||||||||
\(334\) | −44.8826 | −2.45587 | ||||||||
\(335\) | −27.2965 | −1.49137 | ||||||||
\(336\) | −33.7653 | −1.84205 | ||||||||
\(337\) | 26.9371 | 1.46736 | 0.733680 | − | 0.679495i | \(-0.237801\pi\) | ||||
0.733680 | + | 0.679495i | \(0.237801\pi\) | |||||||
\(338\) | 27.7581 | 1.50984 | ||||||||
\(339\) | 18.5078 | 1.00521 | ||||||||
\(340\) | 29.2105 | 1.58416 | ||||||||
\(341\) | −13.7837 | −0.746427 | ||||||||
\(342\) | 7.75496 | 0.419340 | ||||||||
\(343\) | 17.4879 | 0.944260 | ||||||||
\(344\) | −4.01570 | −0.216512 | ||||||||
\(345\) | −38.3721 | −2.06589 | ||||||||
\(346\) | −47.8321 | −2.57147 | ||||||||
\(347\) | −31.5841 | −1.69552 | −0.847762 | − | 0.530377i | \(-0.822050\pi\) | ||||
−0.847762 | + | 0.530377i | \(0.822050\pi\) | |||||||
\(348\) | −43.1771 | −2.31453 | ||||||||
\(349\) | −28.6483 | −1.53351 | −0.766755 | − | 0.641940i | \(-0.778130\pi\) | ||||
−0.766755 | + | 0.641940i | \(0.778130\pi\) | |||||||
\(350\) | 34.5685 | 1.84776 | ||||||||
\(351\) | −4.71988 | −0.251928 | ||||||||
\(352\) | −7.37338 | −0.393002 | ||||||||
\(353\) | −2.01142 | −0.107057 | −0.0535284 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535284 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(354\) | 43.3307 | 2.30300 | ||||||||
\(355\) | 16.9850 | 0.901470 | ||||||||
\(356\) | 13.8971 | 0.736547 | ||||||||
\(357\) | 12.5188 | 0.662565 | ||||||||
\(358\) | −37.3996 | −1.97663 | ||||||||
\(359\) | −2.60987 | −0.137744 | −0.0688719 | − | 0.997626i | \(-0.521940\pi\) | ||||
−0.0688719 | + | 0.997626i | \(0.521940\pi\) | |||||||
\(360\) | 24.9494 | 1.31495 | ||||||||
\(361\) | −13.9535 | −0.734393 | ||||||||
\(362\) | 9.13759 | 0.480261 | ||||||||
\(363\) | −11.2463 | −0.590276 | ||||||||
\(364\) | −16.5358 | −0.866713 | ||||||||
\(365\) | 48.1029 | 2.51782 | ||||||||
\(366\) | 4.66591 | 0.243891 | ||||||||
\(367\) | 11.7850 | 0.615170 | 0.307585 | − | 0.951521i | \(-0.400479\pi\) | ||||
0.307585 | + | 0.951521i | \(0.400479\pi\) | |||||||
\(368\) | 33.7983 | 1.76186 | ||||||||
\(369\) | 12.3235 | 0.641534 | ||||||||
\(370\) | −74.9550 | −3.89673 | ||||||||
\(371\) | −14.6470 | −0.760437 | ||||||||
\(372\) | −52.1508 | −2.70389 | ||||||||
\(373\) | 7.35336 | 0.380743 | 0.190371 | − | 0.981712i | \(-0.439031\pi\) | ||||
0.190371 | + | 0.981712i | \(0.439031\pi\) | |||||||
\(374\) | 12.8286 | 0.663353 | ||||||||
\(375\) | 0.206336 | 0.0106552 | ||||||||
\(376\) | −66.7602 | −3.44289 | ||||||||
\(377\) | −6.68729 | −0.344413 | ||||||||
\(378\) | −23.6286 | −1.21533 | ||||||||
\(379\) | 32.8343 | 1.68658 | 0.843292 | − | 0.537455i | \(-0.180614\pi\) | ||||
0.843292 | + | 0.537455i | \(0.180614\pi\) | |||||||
\(380\) | 30.4214 | 1.56058 | ||||||||
\(381\) | 21.7142 | 1.11245 | ||||||||
\(382\) | −21.5830 | −1.10428 | ||||||||
\(383\) | 20.5396 | 1.04952 | 0.524761 | − | 0.851249i | \(-0.324155\pi\) | ||||
0.524761 | + | 0.851249i | \(0.324155\pi\) | |||||||
\(384\) | 33.1481 | 1.69158 | ||||||||
\(385\) | 20.7726 | 1.05867 | ||||||||
\(386\) | −51.8766 | −2.64045 | ||||||||
\(387\) | 0.962948 | 0.0489494 | ||||||||
\(388\) | −35.9174 | −1.82343 | ||||||||
\(389\) | 24.5090 | 1.24266 | 0.621329 | − | 0.783550i | \(-0.286593\pi\) | ||||
0.621329 | + | 0.783550i | \(0.286593\pi\) | |||||||
\(390\) | 23.0199 | 1.16566 | ||||||||
\(391\) | −12.5310 | −0.633721 | ||||||||
\(392\) | −3.99682 | −0.201870 | ||||||||
\(393\) | 26.3150 | 1.32742 | ||||||||
\(394\) | −48.8551 | −2.46129 | ||||||||
\(395\) | −42.2116 | −2.12390 | ||||||||
\(396\) | 14.0018 | 0.703615 | ||||||||
\(397\) | 21.6119 | 1.08467 | 0.542334 | − | 0.840163i | \(-0.317541\pi\) | ||||
0.542334 | + | 0.840163i | \(0.317541\pi\) | |||||||
\(398\) | 9.29243 | 0.465787 | ||||||||
\(399\) | 13.0377 | 0.652702 | ||||||||
\(400\) | 28.9077 | 1.44538 | ||||||||
\(401\) | −19.5420 | −0.975881 | −0.487940 | − | 0.872877i | \(-0.662252\pi\) | ||||
−0.487940 | + | 0.872877i | \(0.662252\pi\) | |||||||
\(402\) | −45.3571 | −2.26220 | ||||||||
\(403\) | −8.07715 | −0.402352 | ||||||||
\(404\) | 47.9932 | 2.38775 | ||||||||
\(405\) | 35.4719 | 1.76261 | ||||||||
\(406\) | −33.4779 | −1.66148 | ||||||||
\(407\) | −22.4501 | −1.11281 | ||||||||
\(408\) | 25.9043 | 1.28245 | ||||||||
\(409\) | 5.64928 | 0.279339 | 0.139670 | − | 0.990198i | \(-0.455396\pi\) | ||||
0.139670 | + | 0.990198i | \(0.455396\pi\) | |||||||
\(410\) | 70.8852 | 3.50077 | ||||||||
\(411\) | −38.1032 | −1.87949 | ||||||||
\(412\) | 71.0385 | 3.49982 | ||||||||
\(413\) | 22.9127 | 1.12746 | ||||||||
\(414\) | −20.0545 | −0.985627 | ||||||||
\(415\) | 33.6108 | 1.64989 | ||||||||
\(416\) | −4.32076 | −0.211843 | ||||||||
\(417\) | 20.9227 | 1.02459 | ||||||||
\(418\) | 13.3604 | 0.653479 | ||||||||
\(419\) | 16.0956 | 0.786321 | 0.393160 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393160 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(420\) | 78.5937 | 3.83498 | ||||||||
\(421\) | 17.2086 | 0.838698 | 0.419349 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419349 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(422\) | 14.4827 | 0.705006 | ||||||||
\(423\) | 16.0088 | 0.778374 | ||||||||
\(424\) | −30.3082 | −1.47189 | ||||||||
\(425\) | −10.7178 | −0.519889 | ||||||||
\(426\) | 28.2230 | 1.36741 | ||||||||
\(427\) | 2.46727 | 0.119400 | ||||||||
\(428\) | −72.6243 | −3.51043 | ||||||||
\(429\) | 6.89479 | 0.332883 | ||||||||
\(430\) | 5.53893 | 0.267111 | ||||||||
\(431\) | −18.2825 | −0.880635 | −0.440318 | − | 0.897842i | \(-0.645134\pi\) | ||||
−0.440318 | + | 0.897842i | \(0.645134\pi\) | |||||||
\(432\) | −19.7593 | −0.950669 | ||||||||
\(433\) | 5.90112 | 0.283590 | 0.141795 | − | 0.989896i | \(-0.454713\pi\) | ||||
0.141795 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(434\) | −40.4358 | −1.94098 | ||||||||
\(435\) | 31.7843 | 1.52394 | ||||||||
\(436\) | 16.1505 | 0.773470 | ||||||||
\(437\) | −13.0505 | −0.624288 | ||||||||
\(438\) | 79.9299 | 3.81920 | ||||||||
\(439\) | −13.0195 | −0.621387 | −0.310693 | − | 0.950510i | \(-0.600561\pi\) | ||||
−0.310693 | + | 0.950510i | \(0.600561\pi\) | |||||||
\(440\) | 42.9834 | 2.04915 | ||||||||
\(441\) | 0.958420 | 0.0456390 | ||||||||
\(442\) | 7.51752 | 0.357572 | ||||||||
\(443\) | 13.8135 | 0.656301 | 0.328151 | − | 0.944625i | \(-0.393575\pi\) | ||||
0.328151 | + | 0.944625i | \(0.393575\pi\) | |||||||
\(444\) | −84.9405 | −4.03110 | ||||||||
\(445\) | −10.2302 | −0.484959 | ||||||||
\(446\) | −9.02178 | −0.427194 | ||||||||
\(447\) | 48.3072 | 2.28485 | ||||||||
\(448\) | 10.6495 | 0.503142 | ||||||||
\(449\) | −6.45993 | −0.304863 | −0.152431 | − | 0.988314i | \(-0.548710\pi\) | ||||
−0.152431 | + | 0.988314i | \(0.548710\pi\) | |||||||
\(450\) | −17.1526 | −0.808584 | ||||||||
\(451\) | 21.2311 | 0.999734 | ||||||||
\(452\) | 37.9447 | 1.78477 | ||||||||
\(453\) | −21.7881 | −1.02369 | ||||||||
\(454\) | −22.3456 | −1.04873 | ||||||||
\(455\) | 12.1726 | 0.570662 | ||||||||
\(456\) | 26.9781 | 1.26336 | ||||||||
\(457\) | 22.0973 | 1.03367 | 0.516835 | − | 0.856085i | \(-0.327110\pi\) | ||||
0.516835 | + | 0.856085i | \(0.327110\pi\) | |||||||
\(458\) | 46.9526 | 2.19395 | ||||||||
\(459\) | 7.32594 | 0.341945 | ||||||||
\(460\) | −78.6705 | −3.66803 | ||||||||
\(461\) | −6.55784 | −0.305429 | −0.152714 | − | 0.988270i | \(-0.548801\pi\) | ||||
−0.152714 | + | 0.988270i | \(0.548801\pi\) | |||||||
\(462\) | 34.5166 | 1.60586 | ||||||||
\(463\) | −18.2710 | −0.849124 | −0.424562 | − | 0.905399i | \(-0.639572\pi\) | ||||
−0.424562 | + | 0.905399i | \(0.639572\pi\) | |||||||
\(464\) | −27.9957 | −1.29967 | ||||||||
\(465\) | 38.3902 | 1.78030 | ||||||||
\(466\) | −33.5509 | −1.55422 | ||||||||
\(467\) | 24.9818 | 1.15602 | 0.578010 | − | 0.816030i | \(-0.303830\pi\) | ||||
0.578010 | + | 0.816030i | \(0.303830\pi\) | |||||||
\(468\) | 8.20496 | 0.379274 | ||||||||
\(469\) | −23.9842 | −1.10749 | ||||||||
\(470\) | 92.0835 | 4.24749 | ||||||||
\(471\) | −9.86546 | −0.454576 | ||||||||
\(472\) | 47.4118 | 2.18230 | ||||||||
\(473\) | 1.65899 | 0.0762803 | ||||||||
\(474\) | −70.1406 | −3.22167 | ||||||||
\(475\) | −11.1621 | −0.512151 | ||||||||
\(476\) | 25.6660 | 1.17640 | ||||||||
\(477\) | 7.26776 | 0.332768 | ||||||||
\(478\) | 41.3665 | 1.89206 | ||||||||
\(479\) | −20.5003 | −0.936683 | −0.468341 | − | 0.883548i | \(-0.655148\pi\) | ||||
−0.468341 | + | 0.883548i | \(0.655148\pi\) | |||||||
\(480\) | 20.5363 | 0.937350 | ||||||||
\(481\) | −13.1556 | −0.599846 | ||||||||
\(482\) | 1.38593 | 0.0631273 | ||||||||
\(483\) | −33.7159 | −1.53413 | ||||||||
\(484\) | −23.0571 | −1.04805 | ||||||||
\(485\) | 26.4401 | 1.20058 | ||||||||
\(486\) | 33.3899 | 1.51460 | ||||||||
\(487\) | −7.00703 | −0.317519 | −0.158759 | − | 0.987317i | \(-0.550749\pi\) | ||||
−0.158759 | + | 0.987317i | \(0.550749\pi\) | |||||||
\(488\) | 5.10536 | 0.231109 | ||||||||
\(489\) | 2.97307 | 0.134447 | ||||||||
\(490\) | 5.51288 | 0.249047 | ||||||||
\(491\) | −8.72994 | −0.393977 | −0.196988 | − | 0.980406i | \(-0.563116\pi\) | ||||
−0.196988 | + | 0.980406i | \(0.563116\pi\) | |||||||
\(492\) | 80.3285 | 3.62149 | ||||||||
\(493\) | 10.3797 | 0.467476 | ||||||||
\(494\) | 7.82913 | 0.352249 | ||||||||
\(495\) | −10.3072 | −0.463275 | ||||||||
\(496\) | −33.8142 | −1.51830 | ||||||||
\(497\) | 14.9240 | 0.669432 | ||||||||
\(498\) | 55.8491 | 2.50266 | ||||||||
\(499\) | 13.3535 | 0.597784 | 0.298892 | − | 0.954287i | \(-0.403383\pi\) | ||||
0.298892 | + | 0.954287i | \(0.403383\pi\) | |||||||
\(500\) | 0.423031 | 0.0189185 | ||||||||
\(501\) | 37.4413 | 1.67276 | ||||||||
\(502\) | 1.41448 | 0.0631312 | ||||||||
\(503\) | 32.4448 | 1.44664 | 0.723321 | − | 0.690511i | \(-0.242614\pi\) | ||||
0.723321 | + | 0.690511i | \(0.242614\pi\) | |||||||
\(504\) | 21.9219 | 0.976481 | ||||||||
\(505\) | −35.3296 | −1.57214 | ||||||||
\(506\) | −34.5504 | −1.53595 | ||||||||
\(507\) | −23.1559 | −1.02839 | ||||||||
\(508\) | 44.5184 | 1.97519 | ||||||||
\(509\) | −25.9994 | −1.15240 | −0.576201 | − | 0.817308i | \(-0.695466\pi\) | ||||
−0.576201 | + | 0.817308i | \(0.695466\pi\) | |||||||
\(510\) | −35.7303 | −1.58216 | ||||||||
\(511\) | 42.2660 | 1.86974 | ||||||||
\(512\) | 48.7066 | 2.15255 | ||||||||
\(513\) | 7.62961 | 0.336856 | ||||||||
\(514\) | 50.3624 | 2.22139 | ||||||||
\(515\) | −52.2941 | −2.30435 | ||||||||
\(516\) | 6.27682 | 0.276322 | ||||||||
\(517\) | 27.5803 | 1.21298 | ||||||||
\(518\) | −65.8597 | −2.89371 | ||||||||
\(519\) | 39.9018 | 1.75149 | ||||||||
\(520\) | 25.1880 | 1.10457 | ||||||||
\(521\) | −13.9201 | −0.609851 | −0.304926 | − | 0.952376i | \(-0.598632\pi\) | ||||
−0.304926 | + | 0.952376i | \(0.598632\pi\) | |||||||
\(522\) | 16.6115 | 0.727065 | ||||||||
\(523\) | −40.3251 | −1.76329 | −0.881646 | − | 0.471912i | \(-0.843564\pi\) | ||||
−0.881646 | + | 0.471912i | \(0.843564\pi\) | |||||||
\(524\) | 53.9509 | 2.35686 | ||||||||
\(525\) | −28.8372 | −1.25856 | ||||||||
\(526\) | 17.2369 | 0.751565 | ||||||||
\(527\) | 12.5369 | 0.546117 | ||||||||
\(528\) | 28.8643 | 1.25616 | ||||||||
\(529\) | 10.7489 | 0.467342 | ||||||||
\(530\) | 41.8046 | 1.81587 | ||||||||
\(531\) | −11.3691 | −0.493379 | ||||||||
\(532\) | 26.7299 | 1.15889 | ||||||||
\(533\) | 12.4413 | 0.538894 | ||||||||
\(534\) | −16.9990 | −0.735617 | ||||||||
\(535\) | 53.4614 | 2.31134 | ||||||||
\(536\) | −49.6290 | −2.14365 | ||||||||
\(537\) | 31.1990 | 1.34633 | ||||||||
\(538\) | 2.30233 | 0.0992607 | ||||||||
\(539\) | 1.65119 | 0.0711216 | ||||||||
\(540\) | 45.9926 | 1.97921 | ||||||||
\(541\) | −12.4075 | −0.533438 | −0.266719 | − | 0.963774i | \(-0.585940\pi\) | ||||
−0.266719 | + | 0.963774i | \(0.585940\pi\) | |||||||
\(542\) | −62.5160 | −2.68529 | ||||||||
\(543\) | −7.62262 | −0.327118 | ||||||||
\(544\) | 6.70646 | 0.287537 | ||||||||
\(545\) | −11.8890 | −0.509269 | ||||||||
\(546\) | 20.2266 | 0.865618 | ||||||||
\(547\) | 7.89112 | 0.337400 | 0.168700 | − | 0.985667i | \(-0.446043\pi\) | ||||
0.168700 | + | 0.985667i | \(0.446043\pi\) | |||||||
\(548\) | −78.1191 | −3.33708 | ||||||||
\(549\) | −1.22424 | −0.0522495 | ||||||||
\(550\) | −29.5510 | −1.26006 | ||||||||
\(551\) | 10.8099 | 0.460518 | ||||||||
\(552\) | −69.7661 | −2.96944 | ||||||||
\(553\) | −37.0895 | −1.57721 | ||||||||
\(554\) | −41.5105 | −1.76361 | ||||||||
\(555\) | 62.5279 | 2.65416 | ||||||||
\(556\) | 42.8957 | 1.81918 | ||||||||
\(557\) | 36.0448 | 1.52727 | 0.763633 | − | 0.645651i | \(-0.223414\pi\) | ||||
0.763633 | + | 0.645651i | \(0.223414\pi\) | |||||||
\(558\) | 20.0640 | 0.849375 | ||||||||
\(559\) | 0.972159 | 0.0411179 | ||||||||
\(560\) | 50.9595 | 2.15343 | ||||||||
\(561\) | −10.7017 | −0.451827 | ||||||||
\(562\) | 9.78584 | 0.412791 | ||||||||
\(563\) | 2.45029 | 0.103268 | 0.0516338 | − | 0.998666i | \(-0.483557\pi\) | ||||
0.0516338 | + | 0.998666i | \(0.483557\pi\) | |||||||
\(564\) | 104.351 | 4.39396 | ||||||||
\(565\) | −27.9325 | −1.17513 | ||||||||
\(566\) | −31.0455 | −1.30494 | ||||||||
\(567\) | 31.1676 | 1.30892 | ||||||||
\(568\) | 30.8812 | 1.29575 | ||||||||
\(569\) | 5.27470 | 0.221127 | 0.110563 | − | 0.993869i | \(-0.464734\pi\) | ||||
0.110563 | + | 0.993869i | \(0.464734\pi\) | |||||||
\(570\) | −37.2114 | −1.55861 | ||||||||
\(571\) | −23.9847 | −1.00373 | −0.501863 | − | 0.864947i | \(-0.667352\pi\) | ||||
−0.501863 | + | 0.864947i | \(0.667352\pi\) | |||||||
\(572\) | 14.1357 | 0.591043 | ||||||||
\(573\) | 18.0046 | 0.752155 | ||||||||
\(574\) | 62.2837 | 2.59967 | ||||||||
\(575\) | 28.8654 | 1.20377 | ||||||||
\(576\) | −5.28422 | −0.220176 | ||||||||
\(577\) | −0.512046 | −0.0213168 | −0.0106584 | − | 0.999943i | \(-0.503393\pi\) | ||||
−0.0106584 | + | 0.999943i | \(0.503393\pi\) | |||||||
\(578\) | 30.9643 | 1.28794 | ||||||||
\(579\) | 43.2757 | 1.79848 | ||||||||
\(580\) | 65.1640 | 2.70579 | ||||||||
\(581\) | 29.5323 | 1.22521 | ||||||||
\(582\) | 43.9340 | 1.82112 | ||||||||
\(583\) | 12.5211 | 0.518569 | ||||||||
\(584\) | 87.4581 | 3.61904 | ||||||||
\(585\) | −6.03998 | −0.249722 | ||||||||
\(586\) | −32.7138 | −1.35140 | ||||||||
\(587\) | 9.95942 | 0.411069 | 0.205535 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205535 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(588\) | 6.24731 | 0.257635 | ||||||||
\(589\) | 13.0566 | 0.537988 | ||||||||
\(590\) | −65.3959 | −2.69231 | ||||||||
\(591\) | 40.7552 | 1.67645 | ||||||||
\(592\) | −55.0748 | −2.26356 | ||||||||
\(593\) | −13.1422 | −0.539685 | −0.269843 | − | 0.962904i | \(-0.586972\pi\) | ||||
−0.269843 | + | 0.962904i | \(0.586972\pi\) | |||||||
\(594\) | 20.1990 | 0.828774 | ||||||||
\(595\) | −18.8937 | −0.774567 | ||||||||
\(596\) | 99.0393 | 4.05681 | ||||||||
\(597\) | −7.75179 | −0.317260 | ||||||||
\(598\) | −20.2464 | −0.827935 | ||||||||
\(599\) | 35.1687 | 1.43695 | 0.718477 | − | 0.695551i | \(-0.244839\pi\) | ||||
0.718477 | + | 0.695551i | \(0.244839\pi\) | |||||||
\(600\) | −59.6709 | −2.43606 | ||||||||
\(601\) | 44.5769 | 1.81833 | 0.909165 | − | 0.416437i | \(-0.136721\pi\) | ||||
0.909165 | + | 0.416437i | \(0.136721\pi\) | |||||||
\(602\) | 4.86682 | 0.198357 | ||||||||
\(603\) | 11.9008 | 0.484639 | ||||||||
\(604\) | −44.6699 | −1.81759 | ||||||||
\(605\) | 16.9732 | 0.690058 | ||||||||
\(606\) | −58.7051 | −2.38473 | ||||||||
\(607\) | −5.26537 | −0.213715 | −0.106857 | − | 0.994274i | \(-0.534079\pi\) | ||||
−0.106857 | + | 0.994274i | \(0.534079\pi\) | |||||||
\(608\) | 6.98445 | 0.283257 | ||||||||
\(609\) | 27.9274 | 1.13168 | ||||||||
\(610\) | −7.04192 | −0.285119 | ||||||||
\(611\) | 16.1619 | 0.653841 | ||||||||
\(612\) | −12.7353 | −0.514794 | ||||||||
\(613\) | −20.1333 | −0.813174 | −0.406587 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406587 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(614\) | −19.8591 | −0.801447 | ||||||||
\(615\) | −59.1328 | −2.38447 | ||||||||
\(616\) | 37.7676 | 1.52170 | ||||||||
\(617\) | −41.5701 | −1.67355 | −0.836775 | − | 0.547547i | \(-0.815562\pi\) | ||||
−0.836775 | + | 0.547547i | \(0.815562\pi\) | |||||||
\(618\) | −86.8942 | −3.49540 | ||||||||
\(619\) | 22.1384 | 0.889816 | 0.444908 | − | 0.895576i | \(-0.353236\pi\) | ||||
0.444908 | + | 0.895576i | \(0.353236\pi\) | |||||||
\(620\) | 78.7075 | 3.16097 | ||||||||
\(621\) | −19.7304 | −0.791753 | ||||||||
\(622\) | −64.5477 | −2.58813 | ||||||||
\(623\) | −8.98884 | −0.360130 | ||||||||
\(624\) | 16.9144 | 0.677116 | ||||||||
\(625\) | −25.1552 | −1.00621 | ||||||||
\(626\) | −80.8291 | −3.23058 | ||||||||
\(627\) | −11.1453 | −0.445101 | ||||||||
\(628\) | −20.2261 | −0.807111 | ||||||||
\(629\) | 20.4195 | 0.814178 | ||||||||
\(630\) | −30.2373 | −1.20468 | ||||||||
\(631\) | −9.18693 | −0.365726 | −0.182863 | − | 0.983138i | \(-0.558536\pi\) | ||||
−0.182863 | + | 0.983138i | \(0.558536\pi\) | |||||||
\(632\) | −76.7468 | −3.05282 | ||||||||
\(633\) | −12.0815 | −0.480198 | ||||||||
\(634\) | 17.7536 | 0.705085 | ||||||||
\(635\) | −32.7717 | −1.30051 | ||||||||
\(636\) | 47.3738 | 1.87849 | ||||||||
\(637\) | 0.967587 | 0.0383372 | ||||||||
\(638\) | 28.6186 | 1.13302 | ||||||||
\(639\) | −7.40517 | −0.292944 | ||||||||
\(640\) | −50.0281 | −1.97753 | ||||||||
\(641\) | −43.6865 | −1.72551 | −0.862756 | − | 0.505620i | \(-0.831264\pi\) | ||||
−0.862756 | + | 0.505620i | \(0.831264\pi\) | |||||||
\(642\) | 88.8339 | 3.50599 | ||||||||
\(643\) | −3.46349 | −0.136587 | −0.0682933 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682933 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(644\) | −69.1243 | −2.72388 | ||||||||
\(645\) | −4.62060 | −0.181936 | ||||||||
\(646\) | −12.1520 | −0.478112 | ||||||||
\(647\) | −14.0554 | −0.552573 | −0.276286 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276286 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(648\) | 64.4930 | 2.53353 | ||||||||
\(649\) | −19.5870 | −0.768857 | ||||||||
\(650\) | −17.3167 | −0.679217 | ||||||||
\(651\) | 33.7318 | 1.32205 | ||||||||
\(652\) | 6.09538 | 0.238713 | ||||||||
\(653\) | 7.76287 | 0.303785 | 0.151892 | − | 0.988397i | \(-0.451463\pi\) | ||||
0.151892 | + | 0.988397i | \(0.451463\pi\) | |||||||
\(654\) | −19.7553 | −0.772493 | ||||||||
\(655\) | −39.7153 | −1.55181 | ||||||||
\(656\) | 52.0844 | 2.03355 | ||||||||
\(657\) | −20.9721 | −0.818199 | ||||||||
\(658\) | 80.9097 | 3.15419 | ||||||||
\(659\) | 28.1715 | 1.09741 | 0.548703 | − | 0.836018i | \(-0.315122\pi\) | ||||
0.548703 | + | 0.836018i | \(0.315122\pi\) | |||||||
\(660\) | −67.1860 | −2.61521 | ||||||||
\(661\) | −43.4156 | −1.68867 | −0.844336 | − | 0.535813i | \(-0.820005\pi\) | ||||
−0.844336 | + | 0.535813i | \(0.820005\pi\) | |||||||
\(662\) | −43.4624 | −1.68922 | ||||||||
\(663\) | −6.27115 | −0.243551 | ||||||||
\(664\) | 61.1093 | 2.37150 | ||||||||
\(665\) | −19.6769 | −0.763037 | ||||||||
\(666\) | 32.6791 | 1.26629 | ||||||||
\(667\) | −27.9547 | −1.08241 | ||||||||
\(668\) | 76.7622 | 2.97002 | ||||||||
\(669\) | 7.52602 | 0.290973 | ||||||||
\(670\) | 68.4541 | 2.64461 | ||||||||
\(671\) | −2.10915 | −0.0814230 | ||||||||
\(672\) | 18.0444 | 0.696076 | ||||||||
\(673\) | −33.7929 | −1.30262 | −0.651311 | − | 0.758811i | \(-0.725781\pi\) | ||||
−0.651311 | + | 0.758811i | \(0.725781\pi\) | |||||||
\(674\) | −67.5529 | −2.60204 | ||||||||
\(675\) | −16.8754 | −0.649535 | ||||||||
\(676\) | −47.4743 | −1.82593 | ||||||||
\(677\) | 1.09918 | 0.0422450 | 0.0211225 | − | 0.999777i | \(-0.493276\pi\) | ||||
0.0211225 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(678\) | −46.4139 | −1.78252 | ||||||||
\(679\) | 23.2318 | 0.891554 | ||||||||
\(680\) | −39.0955 | −1.49924 | ||||||||
\(681\) | 18.6408 | 0.714319 | ||||||||
\(682\) | 34.5666 | 1.32362 | ||||||||
\(683\) | 38.5124 | 1.47364 | 0.736819 | − | 0.676090i | \(-0.236327\pi\) | ||||
0.736819 | + | 0.676090i | \(0.236327\pi\) | |||||||
\(684\) | −13.2632 | −0.507131 | ||||||||
\(685\) | 57.5064 | 2.19721 | ||||||||
\(686\) | −43.8562 | −1.67444 | ||||||||
\(687\) | −39.1681 | −1.49436 | ||||||||
\(688\) | 4.06985 | 0.155161 | ||||||||
\(689\) | 7.33728 | 0.279528 | ||||||||
\(690\) | 96.2296 | 3.66340 | ||||||||
\(691\) | −41.0331 | −1.56097 | −0.780486 | − | 0.625173i | \(-0.785028\pi\) | ||||
−0.780486 | + | 0.625173i | \(0.785028\pi\) | |||||||
\(692\) | 81.8066 | 3.10982 | ||||||||
\(693\) | −9.05650 | −0.344028 | ||||||||
\(694\) | 79.2066 | 3.00664 | ||||||||
\(695\) | −31.5772 | −1.19779 | ||||||||
\(696\) | 57.7884 | 2.19046 | ||||||||
\(697\) | −19.3108 | −0.731447 | ||||||||
\(698\) | 71.8443 | 2.71935 | ||||||||
\(699\) | 27.9883 | 1.05862 | ||||||||
\(700\) | −59.1220 | −2.23460 | ||||||||
\(701\) | 2.98726 | 0.112827 | 0.0564136 | − | 0.998407i | \(-0.482033\pi\) | ||||
0.0564136 | + | 0.998407i | \(0.482033\pi\) | |||||||
\(702\) | 11.8365 | 0.446740 | ||||||||
\(703\) | 21.2659 | 0.802059 | ||||||||
\(704\) | −9.10376 | −0.343111 | ||||||||
\(705\) | −76.8165 | −2.89308 | ||||||||
\(706\) | 5.04423 | 0.189842 | ||||||||
\(707\) | −31.0425 | −1.16747 | ||||||||
\(708\) | −74.1079 | −2.78515 | ||||||||
\(709\) | −9.26225 | −0.347851 | −0.173926 | − | 0.984759i | \(-0.555645\pi\) | ||||
−0.173926 | + | 0.984759i | \(0.555645\pi\) | |||||||
\(710\) | −42.5949 | −1.59856 | ||||||||
\(711\) | 18.4035 | 0.690187 | ||||||||
\(712\) | −18.6000 | −0.697065 | ||||||||
\(713\) | −33.7647 | −1.26450 | ||||||||
\(714\) | −31.3946 | −1.17491 | ||||||||
\(715\) | −10.4058 | −0.389155 | ||||||||
\(716\) | 63.9641 | 2.39045 | ||||||||
\(717\) | −34.5082 | −1.28873 | ||||||||
\(718\) | 6.54503 | 0.244258 | ||||||||
\(719\) | 29.0064 | 1.08176 | 0.540878 | − | 0.841101i | \(-0.318092\pi\) | ||||
0.540878 | + | 0.841101i | \(0.318092\pi\) | |||||||
\(720\) | −25.2858 | −0.942345 | ||||||||
\(721\) | −45.9485 | −1.71121 | ||||||||
\(722\) | 34.9925 | 1.30229 | ||||||||
\(723\) | −1.15615 | −0.0429976 | ||||||||
\(724\) | −15.6279 | −0.580806 | ||||||||
\(725\) | −23.9097 | −0.887983 | ||||||||
\(726\) | 28.2034 | 1.04673 | ||||||||
\(727\) | 30.2062 | 1.12029 | 0.560143 | − | 0.828396i | \(-0.310746\pi\) | ||||
0.560143 | + | 0.828396i | \(0.310746\pi\) | |||||||
\(728\) | 22.1316 | 0.820252 | ||||||||
\(729\) | 5.85023 | 0.216675 | ||||||||
\(730\) | −120.633 | −4.46481 | ||||||||
\(731\) | −1.50893 | −0.0558099 | ||||||||
\(732\) | −7.98004 | −0.294951 | ||||||||
\(733\) | 49.4928 | 1.82806 | 0.914030 | − | 0.405647i | \(-0.132954\pi\) | ||||
0.914030 | + | 0.405647i | \(0.132954\pi\) | |||||||
\(734\) | −29.5543 | −1.09087 | ||||||||
\(735\) | −4.59888 | −0.169632 | ||||||||
\(736\) | −18.0620 | −0.665774 | ||||||||
\(737\) | 20.5030 | 0.755237 | ||||||||
\(738\) | −30.9048 | −1.13762 | ||||||||
\(739\) | 40.1038 | 1.47524 | 0.737620 | − | 0.675216i | \(-0.235949\pi\) | ||||
0.737620 | + | 0.675216i | \(0.235949\pi\) | |||||||
\(740\) | 128.195 | 4.71253 | ||||||||
\(741\) | −6.53110 | −0.239926 | ||||||||
\(742\) | 36.7319 | 1.34847 | ||||||||
\(743\) | 1.42235 | 0.0521810 | 0.0260905 | − | 0.999660i | \(-0.491694\pi\) | ||||
0.0260905 | + | 0.999660i | \(0.491694\pi\) | |||||||
\(744\) | 69.7989 | 2.55895 | ||||||||
\(745\) | −72.9066 | −2.67109 | ||||||||
\(746\) | −18.4407 | −0.675164 | ||||||||
\(747\) | −14.6537 | −0.536152 | ||||||||
\(748\) | −21.9406 | −0.802230 | ||||||||
\(749\) | 46.9742 | 1.71640 | ||||||||
\(750\) | −0.517450 | −0.0188946 | ||||||||
\(751\) | −17.5781 | −0.641435 | −0.320718 | − | 0.947175i | \(-0.603924\pi\) | ||||
−0.320718 | + | 0.947175i | \(0.603924\pi\) | |||||||
\(752\) | 67.6603 | 2.46732 | ||||||||
\(753\) | −1.17996 | −0.0430003 | ||||||||
\(754\) | 16.7704 | 0.610741 | ||||||||
\(755\) | 32.8832 | 1.19674 | ||||||||
\(756\) | 40.4117 | 1.46976 | ||||||||
\(757\) | −14.6288 | −0.531694 | −0.265847 | − | 0.964015i | \(-0.585652\pi\) | ||||
−0.265847 | + | 0.964015i | \(0.585652\pi\) | |||||||
\(758\) | −82.3418 | −2.99079 | ||||||||
\(759\) | 28.8221 | 1.04618 | ||||||||
\(760\) | −40.7161 | −1.47693 | ||||||||
\(761\) | −30.4598 | −1.10417 | −0.552083 | − | 0.833789i | \(-0.686167\pi\) | ||||
−0.552083 | + | 0.833789i | \(0.686167\pi\) | |||||||
\(762\) | −54.4549 | −1.97269 | ||||||||
\(763\) | −10.4463 | −0.378183 | ||||||||
\(764\) | 36.9131 | 1.33547 | ||||||||
\(765\) | 9.37493 | 0.338951 | ||||||||
\(766\) | −51.5091 | −1.86110 | ||||||||
\(767\) | −11.4779 | −0.414442 | ||||||||
\(768\) | −67.0674 | −2.42008 | ||||||||
\(769\) | 2.36118 | 0.0851465 | 0.0425732 | − | 0.999093i | \(-0.486444\pi\) | ||||
0.0425732 | + | 0.999093i | \(0.486444\pi\) | |||||||
\(770\) | −52.0935 | −1.87732 | ||||||||
\(771\) | −42.0126 | −1.51305 | ||||||||
\(772\) | 88.7238 | 3.19324 | ||||||||
\(773\) | −6.65925 | −0.239516 | −0.119758 | − | 0.992803i | \(-0.538212\pi\) | ||||
−0.119758 | + | 0.992803i | \(0.538212\pi\) | |||||||
\(774\) | −2.41488 | −0.0868011 | ||||||||
\(775\) | −28.8790 | −1.03736 | ||||||||
\(776\) | 48.0720 | 1.72568 | ||||||||
\(777\) | 54.9405 | 1.97098 | ||||||||
\(778\) | −61.4637 | −2.20358 | ||||||||
\(779\) | −20.1112 | −0.720560 | ||||||||
\(780\) | −39.3706 | −1.40970 | ||||||||
\(781\) | −12.7578 | −0.456510 | ||||||||
\(782\) | 31.4253 | 1.12377 | ||||||||
\(783\) | 16.3430 | 0.584051 | ||||||||
\(784\) | 4.05071 | 0.144668 | ||||||||
\(785\) | 14.8892 | 0.531419 | ||||||||
\(786\) | −65.9927 | −2.35388 | ||||||||
\(787\) | 36.1520 | 1.28868 | 0.644340 | − | 0.764739i | \(-0.277132\pi\) | ||||
0.644340 | + | 0.764739i | \(0.277132\pi\) | |||||||
\(788\) | 83.5563 | 2.97657 | ||||||||
\(789\) | −14.3791 | −0.511910 | ||||||||
\(790\) | 105.858 | 3.76627 | ||||||||
\(791\) | −24.5431 | −0.872652 | ||||||||
\(792\) | −18.7400 | −0.665897 | ||||||||
\(793\) | −1.23595 | −0.0438900 | ||||||||
\(794\) | −54.1982 | −1.92342 | ||||||||
\(795\) | −34.8736 | −1.23684 | ||||||||
\(796\) | −15.8927 | −0.563302 | ||||||||
\(797\) | 43.1287 | 1.52770 | 0.763848 | − | 0.645397i | \(-0.223308\pi\) | ||||
0.763848 | + | 0.645397i | \(0.223308\pi\) | |||||||
\(798\) | −32.6960 | −1.15743 | ||||||||
\(799\) | −25.0857 | −0.887467 | ||||||||
\(800\) | −15.4484 | −0.546184 | ||||||||
\(801\) | 4.46020 | 0.157593 | ||||||||
\(802\) | 49.0074 | 1.73051 | ||||||||
\(803\) | −36.1311 | −1.27504 | ||||||||
\(804\) | 77.5736 | 2.73581 | ||||||||
\(805\) | 50.8850 | 1.79346 | ||||||||
\(806\) | 20.2559 | 0.713483 | ||||||||
\(807\) | −1.92062 | −0.0676090 | ||||||||
\(808\) | −64.2343 | −2.25975 | ||||||||
\(809\) | 7.77831 | 0.273471 | 0.136735 | − | 0.990608i | \(-0.456339\pi\) | ||||
0.136735 | + | 0.990608i | \(0.456339\pi\) | |||||||
\(810\) | −88.9564 | −3.12561 | ||||||||
\(811\) | −14.6808 | −0.515514 | −0.257757 | − | 0.966210i | \(-0.582983\pi\) | ||||
−0.257757 | + | 0.966210i | \(0.582983\pi\) | |||||||
\(812\) | 57.2568 | 2.00932 | ||||||||
\(813\) | 52.1512 | 1.82902 | ||||||||
\(814\) | 56.3003 | 1.97333 | ||||||||
\(815\) | −4.48704 | −0.157174 | ||||||||
\(816\) | −26.2536 | −0.919058 | ||||||||
\(817\) | −1.57148 | −0.0549791 | ||||||||
\(818\) | −14.1673 | −0.495347 | ||||||||
\(819\) | −5.30707 | −0.185444 | ||||||||
\(820\) | −121.234 | −4.23368 | ||||||||
\(821\) | −21.2187 | −0.740538 | −0.370269 | − | 0.928924i | \(-0.620735\pi\) | ||||
−0.370269 | + | 0.928924i | \(0.620735\pi\) | |||||||
\(822\) | 95.5551 | 3.33287 | ||||||||
\(823\) | −53.2220 | −1.85520 | −0.927601 | − | 0.373572i | \(-0.878133\pi\) | ||||
−0.927601 | + | 0.373572i | \(0.878133\pi\) | |||||||
\(824\) | −95.0783 | −3.31221 | ||||||||
\(825\) | 24.6516 | 0.858257 | ||||||||
\(826\) | −57.4605 | −1.99931 | ||||||||
\(827\) | −14.3032 | −0.497372 | −0.248686 | − | 0.968584i | \(-0.579999\pi\) | ||||
−0.248686 | + | 0.968584i | \(0.579999\pi\) | |||||||
\(828\) | 34.2990 | 1.19197 | ||||||||
\(829\) | 17.1601 | 0.595994 | 0.297997 | − | 0.954567i | \(-0.403682\pi\) | ||||
0.297997 | + | 0.954567i | \(0.403682\pi\) | |||||||
\(830\) | −84.2891 | −2.92572 | ||||||||
\(831\) | 34.6283 | 1.20124 | ||||||||
\(832\) | −5.33476 | −0.184950 | ||||||||
\(833\) | −1.50184 | −0.0520356 | ||||||||
\(834\) | −52.4700 | −1.81689 | ||||||||
\(835\) | −56.5075 | −1.95552 | ||||||||
\(836\) | −22.8501 | −0.790288 | ||||||||
\(837\) | 19.7397 | 0.682303 | ||||||||
\(838\) | −40.3645 | −1.39437 | ||||||||
\(839\) | 17.0657 | 0.589173 | 0.294586 | − | 0.955625i | \(-0.404818\pi\) | ||||
0.294586 | + | 0.955625i | \(0.404818\pi\) | |||||||
\(840\) | −105.190 | −3.62940 | ||||||||
\(841\) | −5.84465 | −0.201540 | ||||||||
\(842\) | −43.1558 | −1.48725 | ||||||||
\(843\) | −8.16340 | −0.281163 | ||||||||
\(844\) | −24.7695 | −0.852603 | ||||||||
\(845\) | 34.9476 | 1.20223 | ||||||||
\(846\) | −40.1469 | −1.38028 | ||||||||
\(847\) | 14.9136 | 0.512437 | ||||||||
\(848\) | 30.7168 | 1.05482 | ||||||||
\(849\) | 25.8983 | 0.888827 | ||||||||
\(850\) | 26.8781 | 0.921910 | ||||||||
\(851\) | −54.9942 | −1.88518 | ||||||||
\(852\) | −48.2694 | −1.65368 | ||||||||
\(853\) | 15.9210 | 0.545124 | 0.272562 | − | 0.962138i | \(-0.412129\pi\) | ||||
0.272562 | + | 0.962138i | \(0.412129\pi\) | |||||||
\(854\) | −6.18743 | −0.211729 | ||||||||
\(855\) | 9.76354 | 0.333906 | ||||||||
\(856\) | 97.2007 | 3.32225 | ||||||||
\(857\) | −3.76849 | −0.128729 | −0.0643645 | − | 0.997926i | \(-0.520502\pi\) | ||||
−0.0643645 | + | 0.997926i | \(0.520502\pi\) | |||||||
\(858\) | −17.2907 | −0.590296 | ||||||||
\(859\) | −31.0748 | −1.06026 | −0.530129 | − | 0.847917i | \(-0.677856\pi\) | ||||
−0.530129 | + | 0.847917i | \(0.677856\pi\) | |||||||
\(860\) | −9.47316 | −0.323032 | ||||||||
\(861\) | −51.9574 | −1.77070 | ||||||||
\(862\) | 45.8487 | 1.56161 | ||||||||
\(863\) | −47.5457 | −1.61847 | −0.809237 | − | 0.587482i | \(-0.800119\pi\) | ||||
−0.809237 | + | 0.587482i | \(0.800119\pi\) | |||||||
\(864\) | 10.5595 | 0.359240 | ||||||||
\(865\) | −60.2209 | −2.04757 | ||||||||
\(866\) | −14.7988 | −0.502885 | ||||||||
\(867\) | −25.8306 | −0.877253 | ||||||||
\(868\) | 69.1568 | 2.34734 | ||||||||
\(869\) | 31.7060 | 1.07555 | ||||||||
\(870\) | −79.7085 | −2.70237 | ||||||||
\(871\) | 12.0146 | 0.407101 | ||||||||
\(872\) | −21.6159 | −0.732008 | ||||||||
\(873\) | −11.5274 | −0.390145 | ||||||||
\(874\) | 32.7279 | 1.10704 | ||||||||
\(875\) | −0.273621 | −0.00925008 | ||||||||
\(876\) | −136.703 | −4.61877 | ||||||||
\(877\) | −25.7216 | −0.868556 | −0.434278 | − | 0.900779i | \(-0.642997\pi\) | ||||
−0.434278 | + | 0.900779i | \(0.642997\pi\) | |||||||
\(878\) | 32.6503 | 1.10189 | ||||||||
\(879\) | 27.2900 | 0.920470 | ||||||||
\(880\) | −43.5629 | −1.46850 | ||||||||
\(881\) | −10.6114 | −0.357506 | −0.178753 | − | 0.983894i | \(-0.557206\pi\) | ||||
−0.178753 | + | 0.983894i | \(0.557206\pi\) | |||||||
\(882\) | −2.40352 | −0.0809309 | ||||||||
\(883\) | 33.4492 | 1.12566 | 0.562828 | − | 0.826574i | \(-0.309713\pi\) | ||||
0.562828 | + | 0.826574i | \(0.309713\pi\) | |||||||
\(884\) | −12.8571 | −0.432431 | ||||||||
\(885\) | 54.5536 | 1.83380 | ||||||||
\(886\) | −34.6416 | −1.16381 | ||||||||
\(887\) | 20.5714 | 0.690720 | 0.345360 | − | 0.938470i | \(-0.387757\pi\) | ||||
0.345360 | + | 0.938470i | \(0.387757\pi\) | |||||||
\(888\) | 113.685 | 3.81501 | ||||||||
\(889\) | −28.7951 | −0.965755 | ||||||||
\(890\) | 25.6553 | 0.859968 | ||||||||
\(891\) | −26.6437 | −0.892597 | ||||||||
\(892\) | 15.4298 | 0.516629 | ||||||||
\(893\) | −26.1255 | −0.874257 | ||||||||
\(894\) | −121.145 | −4.05168 | ||||||||
\(895\) | −47.0863 | −1.57392 | ||||||||
\(896\) | −43.9575 | −1.46852 | ||||||||
\(897\) | 16.8896 | 0.563928 | ||||||||
\(898\) | 16.2002 | 0.540608 | ||||||||
\(899\) | 27.9679 | 0.932781 | ||||||||
\(900\) | 29.3359 | 0.977865 | ||||||||
\(901\) | −11.3885 | −0.379407 | ||||||||
\(902\) | −53.2434 | −1.77281 | ||||||||
\(903\) | −4.05992 | −0.135106 | ||||||||
\(904\) | −50.7854 | −1.68910 | ||||||||
\(905\) | 11.5043 | 0.382415 | ||||||||
\(906\) | 54.6401 | 1.81530 | ||||||||
\(907\) | 20.4540 | 0.679164 | 0.339582 | − | 0.940577i | \(-0.389714\pi\) | ||||
0.339582 | + | 0.940577i | \(0.389714\pi\) | |||||||
\(908\) | 38.2174 | 1.26829 | ||||||||
\(909\) | 15.4031 | 0.510888 | ||||||||
\(910\) | −30.5265 | −1.01194 | ||||||||
\(911\) | −47.9509 | −1.58868 | −0.794342 | − | 0.607470i | \(-0.792184\pi\) | ||||
−0.794342 | + | 0.607470i | \(0.792184\pi\) | |||||||
\(912\) | −27.3418 | −0.905378 | ||||||||
\(913\) | −25.2458 | −0.835513 | ||||||||
\(914\) | −55.4157 | −1.83299 | ||||||||
\(915\) | 5.87441 | 0.194202 | ||||||||
\(916\) | −80.3024 | −2.65326 | ||||||||
\(917\) | −34.8961 | −1.15237 | ||||||||
\(918\) | −18.3720 | −0.606366 | ||||||||
\(919\) | 30.1172 | 0.993473 | 0.496737 | − | 0.867901i | \(-0.334531\pi\) | ||||
0.496737 | + | 0.867901i | \(0.334531\pi\) | |||||||
\(920\) | 105.293 | 3.47141 | ||||||||
\(921\) | 16.5665 | 0.545886 | ||||||||
\(922\) | 16.4457 | 0.541611 | ||||||||
\(923\) | −7.47600 | −0.246076 | ||||||||
\(924\) | −59.0334 | −1.94206 | ||||||||
\(925\) | −47.0366 | −1.54655 | ||||||||
\(926\) | 45.8199 | 1.50574 | ||||||||
\(927\) | 22.7993 | 0.748829 | ||||||||
\(928\) | 14.9610 | 0.491120 | ||||||||
\(929\) | 16.9454 | 0.555960 | 0.277980 | − | 0.960587i | \(-0.410335\pi\) | ||||
0.277980 | + | 0.960587i | \(0.410335\pi\) | |||||||
\(930\) | −96.2748 | −3.15698 | ||||||||
\(931\) | −1.56409 | −0.0512610 | ||||||||
\(932\) | 57.3817 | 1.87960 | ||||||||
\(933\) | 53.8461 | 1.76284 | ||||||||
\(934\) | −62.6493 | −2.04995 | ||||||||
\(935\) | 16.1513 | 0.528205 | ||||||||
\(936\) | −10.9816 | −0.358943 | ||||||||
\(937\) | 14.3314 | 0.468188 | 0.234094 | − | 0.972214i | \(-0.424788\pi\) | ||||
0.234094 | + | 0.972214i | \(0.424788\pi\) | |||||||
\(938\) | 60.1477 | 1.96389 | ||||||||
\(939\) | 67.4280 | 2.20043 | ||||||||
\(940\) | −157.489 | −5.13673 | ||||||||
\(941\) | −13.2249 | −0.431121 | −0.215560 | − | 0.976491i | \(-0.569158\pi\) | ||||
−0.215560 | + | 0.976491i | \(0.569158\pi\) | |||||||
\(942\) | 24.7406 | 0.806092 | ||||||||
\(943\) | 52.0082 | 1.69362 | ||||||||
\(944\) | −48.0510 | −1.56393 | ||||||||
\(945\) | −29.7486 | −0.967721 | ||||||||
\(946\) | −4.16041 | −0.135267 | ||||||||
\(947\) | 20.4653 | 0.665031 | 0.332516 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332516 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(948\) | 119.961 | 3.89614 | ||||||||
\(949\) | −21.1727 | −0.687294 | ||||||||
\(950\) | 27.9922 | 0.908187 | ||||||||
\(951\) | −14.8101 | −0.480252 | ||||||||
\(952\) | −34.3515 | −1.11334 | ||||||||
\(953\) | 2.88689 | 0.0935154 | 0.0467577 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467577 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(954\) | −18.2261 | −0.590091 | ||||||||
\(955\) | −27.1731 | −0.879302 | ||||||||
\(956\) | −70.7486 | −2.28817 | ||||||||
\(957\) | −23.8738 | −0.771731 | ||||||||
\(958\) | 51.4106 | 1.66100 | ||||||||
\(959\) | 50.5283 | 1.63164 | ||||||||
\(960\) | 25.3558 | 0.818354 | ||||||||
\(961\) | 2.78060 | 0.0896968 | ||||||||
\(962\) | 32.9917 | 1.06370 | ||||||||
\(963\) | −23.3083 | −0.751099 | ||||||||
\(964\) | −2.37034 | −0.0763434 | ||||||||
\(965\) | −65.3129 | −2.10250 | ||||||||
\(966\) | 84.5527 | 2.72044 | ||||||||
\(967\) | 6.95913 | 0.223791 | 0.111895 | − | 0.993720i | \(-0.464308\pi\) | ||||
0.111895 | + | 0.993720i | \(0.464308\pi\) | |||||||
\(968\) | 30.8597 | 0.991868 | ||||||||
\(969\) | 10.1372 | 0.325655 | ||||||||
\(970\) | −66.3065 | −2.12897 | ||||||||
\(971\) | 30.7141 | 0.985663 | 0.492832 | − | 0.870125i | \(-0.335962\pi\) | ||||
0.492832 | + | 0.870125i | \(0.335962\pi\) | |||||||
\(972\) | −57.1063 | −1.83169 | ||||||||
\(973\) | −27.7455 | −0.889479 | ||||||||
\(974\) | 17.5722 | 0.563050 | ||||||||
\(975\) | 14.4457 | 0.462632 | ||||||||
\(976\) | −5.17420 | −0.165622 | ||||||||
\(977\) | 7.14575 | 0.228613 | 0.114306 | − | 0.993446i | \(-0.463535\pi\) | ||||
0.114306 | + | 0.993446i | \(0.463535\pi\) | |||||||
\(978\) | −7.45585 | −0.238412 | ||||||||
\(979\) | 7.68413 | 0.245586 | ||||||||
\(980\) | −9.42861 | −0.301186 | ||||||||
\(981\) | 5.18340 | 0.165493 | ||||||||
\(982\) | 21.8929 | 0.698632 | ||||||||
\(983\) | 13.2992 | 0.424180 | 0.212090 | − | 0.977250i | \(-0.431973\pi\) | ||||
0.212090 | + | 0.977250i | \(0.431973\pi\) | |||||||
\(984\) | −107.512 | −3.42736 | ||||||||
\(985\) | −61.5089 | −1.95984 | ||||||||
\(986\) | −26.0301 | −0.828967 | ||||||||
\(987\) | −67.4953 | −2.14840 | ||||||||
\(988\) | −13.3901 | −0.425995 | ||||||||
\(989\) | 4.06389 | 0.129224 | ||||||||
\(990\) | 25.8484 | 0.821517 | ||||||||
\(991\) | 25.1327 | 0.798366 | 0.399183 | − | 0.916871i | \(-0.369294\pi\) | ||||
0.399183 | + | 0.916871i | \(0.369294\pi\) | |||||||
\(992\) | 18.0705 | 0.573738 | ||||||||
\(993\) | 36.2566 | 1.15057 | ||||||||
\(994\) | −37.4263 | −1.18709 | ||||||||
\(995\) | 11.6992 | 0.370890 | ||||||||
\(996\) | −95.5181 | −3.02661 | ||||||||
\(997\) | 46.1536 | 1.46170 | 0.730850 | − | 0.682538i | \(-0.239124\pi\) | ||||
0.730850 | + | 0.682538i | \(0.239124\pi\) | |||||||
\(998\) | −33.4878 | −1.06004 | ||||||||
\(999\) | 32.1509 | 1.01721 |
(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 | 4027.2.a.c.1.12 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.c.1.12 | ✓ | 174 | 1.1 | even | 1 | trivial |