Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.58 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.53639 | 1.79350 | 0.896751 | − | 0.442536i | \(-0.145921\pi\) | ||||
0.896751 | + | 0.442536i | \(0.145921\pi\) | |||||||
\(3\) | 3.11385 | 1.79778 | 0.898892 | − | 0.438171i | \(-0.144374\pi\) | ||||
0.898892 | + | 0.438171i | \(0.144374\pi\) | |||||||
\(4\) | 4.43329 | 2.21665 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 7.89795 | 3.22433 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 6.17179 | 2.18206 | ||||||||
\(9\) | 6.69607 | 2.23202 | ||||||||
\(10\) | −2.53639 | −0.802078 | ||||||||
\(11\) | 0.694118 | 0.209284 | 0.104642 | − | 0.994510i | \(-0.466630\pi\) | ||||
0.104642 | + | 0.994510i | \(0.466630\pi\) | |||||||
\(12\) | 13.8046 | 3.98505 | ||||||||
\(13\) | 6.89482 | 1.91228 | 0.956139 | − | 0.292914i | \(-0.0946249\pi\) | ||||
0.956139 | + | 0.292914i | \(0.0946249\pi\) | |||||||
\(14\) | −2.53639 | −0.677880 | ||||||||
\(15\) | −3.11385 | −0.803993 | ||||||||
\(16\) | 6.78751 | 1.69688 | ||||||||
\(17\) | −1.07371 | −0.260414 | −0.130207 | − | 0.991487i | \(-0.541564\pi\) | ||||
−0.130207 | + | 0.991487i | \(0.541564\pi\) | |||||||
\(18\) | 16.9839 | 4.00314 | ||||||||
\(19\) | −6.93839 | −1.59178 | −0.795888 | − | 0.605444i | \(-0.792996\pi\) | ||||
−0.795888 | + | 0.605444i | \(0.792996\pi\) | |||||||
\(20\) | −4.43329 | −0.991315 | ||||||||
\(21\) | −3.11385 | −0.679498 | ||||||||
\(22\) | 1.76056 | 0.375352 | ||||||||
\(23\) | −6.40773 | −1.33610 | −0.668052 | − | 0.744115i | \(-0.732872\pi\) | ||||
−0.668052 | + | 0.744115i | \(0.732872\pi\) | |||||||
\(24\) | 19.2180 | 3.92287 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 17.4880 | 3.42967 | ||||||||
\(27\) | 11.5090 | 2.21491 | ||||||||
\(28\) | −4.43329 | −0.837814 | ||||||||
\(29\) | 8.17452 | 1.51797 | 0.758986 | − | 0.651107i | \(-0.225695\pi\) | ||||
0.758986 | + | 0.651107i | \(0.225695\pi\) | |||||||
\(30\) | −7.89795 | −1.44196 | ||||||||
\(31\) | −3.45726 | −0.620942 | −0.310471 | − | 0.950583i | \(-0.600487\pi\) | ||||
−0.310471 | + | 0.950583i | \(0.600487\pi\) | |||||||
\(32\) | 4.87221 | 0.861294 | ||||||||
\(33\) | 2.16138 | 0.376248 | ||||||||
\(34\) | −2.72336 | −0.467053 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 29.6857 | 4.94761 | ||||||||
\(37\) | 3.20904 | 0.527562 | 0.263781 | − | 0.964583i | \(-0.415030\pi\) | ||||
0.263781 | + | 0.964583i | \(0.415030\pi\) | |||||||
\(38\) | −17.5985 | −2.85485 | ||||||||
\(39\) | 21.4694 | 3.43786 | ||||||||
\(40\) | −6.17179 | −0.975846 | ||||||||
\(41\) | 12.4117 | 1.93838 | 0.969189 | − | 0.246317i | \(-0.0792204\pi\) | ||||
0.969189 | + | 0.246317i | \(0.0792204\pi\) | |||||||
\(42\) | −7.89795 | −1.21868 | ||||||||
\(43\) | 3.20569 | 0.488863 | 0.244431 | − | 0.969667i | \(-0.421399\pi\) | ||||
0.244431 | + | 0.969667i | \(0.421399\pi\) | |||||||
\(44\) | 3.07723 | 0.463909 | ||||||||
\(45\) | −6.69607 | −0.998192 | ||||||||
\(46\) | −16.2525 | −2.39630 | ||||||||
\(47\) | −7.35044 | −1.07217 | −0.536086 | − | 0.844163i | \(-0.680098\pi\) | ||||
−0.536086 | + | 0.844163i | \(0.680098\pi\) | |||||||
\(48\) | 21.1353 | 3.05062 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.53639 | 0.358700 | ||||||||
\(51\) | −3.34339 | −0.468168 | ||||||||
\(52\) | 30.5667 | 4.23885 | ||||||||
\(53\) | −4.64026 | −0.637388 | −0.318694 | − | 0.947858i | \(-0.603244\pi\) | ||||
−0.318694 | + | 0.947858i | \(0.603244\pi\) | |||||||
\(54\) | 29.1914 | 3.97245 | ||||||||
\(55\) | −0.694118 | −0.0935948 | ||||||||
\(56\) | −6.17179 | −0.824741 | ||||||||
\(57\) | −21.6051 | −2.86167 | ||||||||
\(58\) | 20.7338 | 2.72248 | ||||||||
\(59\) | 4.98998 | 0.649640 | 0.324820 | − | 0.945776i | \(-0.394696\pi\) | ||||
0.324820 | + | 0.945776i | \(0.394696\pi\) | |||||||
\(60\) | −13.8046 | −1.78217 | ||||||||
\(61\) | 8.72134 | 1.11665 | 0.558326 | − | 0.829621i | \(-0.311444\pi\) | ||||
0.558326 | + | 0.829621i | \(0.311444\pi\) | |||||||
\(62\) | −8.76897 | −1.11366 | ||||||||
\(63\) | −6.69607 | −0.843626 | ||||||||
\(64\) | −1.21717 | −0.152146 | ||||||||
\(65\) | −6.89482 | −0.855197 | ||||||||
\(66\) | 5.48211 | 0.674801 | ||||||||
\(67\) | 1.23346 | 0.150692 | 0.0753458 | − | 0.997157i | \(-0.475994\pi\) | ||||
0.0753458 | + | 0.997157i | \(0.475994\pi\) | |||||||
\(68\) | −4.76009 | −0.577246 | ||||||||
\(69\) | −19.9527 | −2.40203 | ||||||||
\(70\) | 2.53639 | 0.303157 | ||||||||
\(71\) | −6.96428 | −0.826508 | −0.413254 | − | 0.910616i | \(-0.635608\pi\) | ||||
−0.413254 | + | 0.910616i | \(0.635608\pi\) | |||||||
\(72\) | 41.3268 | 4.87041 | ||||||||
\(73\) | −0.707397 | −0.0827946 | −0.0413973 | − | 0.999143i | \(-0.513181\pi\) | ||||
−0.0413973 | + | 0.999143i | \(0.513181\pi\) | |||||||
\(74\) | 8.13938 | 0.946184 | ||||||||
\(75\) | 3.11385 | 0.359557 | ||||||||
\(76\) | −30.7599 | −3.52841 | ||||||||
\(77\) | −0.694118 | −0.0791020 | ||||||||
\(78\) | 54.4549 | 6.16581 | ||||||||
\(79\) | −10.5072 | −1.18215 | −0.591075 | − | 0.806616i | \(-0.701296\pi\) | ||||
−0.591075 | + | 0.806616i | \(0.701296\pi\) | |||||||
\(80\) | −6.78751 | −0.758867 | ||||||||
\(81\) | 15.7492 | 1.74991 | ||||||||
\(82\) | 31.4809 | 3.47648 | ||||||||
\(83\) | 4.46033 | 0.489584 | 0.244792 | − | 0.969576i | \(-0.421280\pi\) | ||||
0.244792 | + | 0.969576i | \(0.421280\pi\) | |||||||
\(84\) | −13.8046 | −1.50621 | ||||||||
\(85\) | 1.07371 | 0.116461 | ||||||||
\(86\) | 8.13089 | 0.876776 | ||||||||
\(87\) | 25.4543 | 2.72898 | ||||||||
\(88\) | 4.28395 | 0.456671 | ||||||||
\(89\) | −10.6281 | −1.12657 | −0.563287 | − | 0.826261i | \(-0.690464\pi\) | ||||
−0.563287 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(90\) | −16.9839 | −1.79026 | ||||||||
\(91\) | −6.89482 | −0.722773 | ||||||||
\(92\) | −28.4074 | −2.96167 | ||||||||
\(93\) | −10.7654 | −1.11632 | ||||||||
\(94\) | −18.6436 | −1.92294 | ||||||||
\(95\) | 6.93839 | 0.711864 | ||||||||
\(96\) | 15.1713 | 1.54842 | ||||||||
\(97\) | 16.7029 | 1.69592 | 0.847961 | − | 0.530059i | \(-0.177830\pi\) | ||||
0.847961 | + | 0.530059i | \(0.177830\pi\) | |||||||
\(98\) | 2.53639 | 0.256214 | ||||||||
\(99\) | 4.64786 | 0.467128 | ||||||||
\(100\) | 4.43329 | 0.443329 | ||||||||
\(101\) | −19.0840 | −1.89893 | −0.949465 | − | 0.313874i | \(-0.898373\pi\) | ||||
−0.949465 | + | 0.313874i | \(0.898373\pi\) | |||||||
\(102\) | −8.48015 | −0.839660 | ||||||||
\(103\) | −3.71668 | −0.366215 | −0.183108 | − | 0.983093i | \(-0.558616\pi\) | ||||
−0.183108 | + | 0.983093i | \(0.558616\pi\) | |||||||
\(104\) | 42.5534 | 4.17270 | ||||||||
\(105\) | 3.11385 | 0.303881 | ||||||||
\(106\) | −11.7695 | −1.14316 | ||||||||
\(107\) | −13.6558 | −1.32015 | −0.660077 | − | 0.751198i | \(-0.729476\pi\) | ||||
−0.660077 | + | 0.751198i | \(0.729476\pi\) | |||||||
\(108\) | 51.0229 | 4.90968 | ||||||||
\(109\) | 0.0225205 | 0.00215707 | 0.00107853 | − | 0.999999i | \(-0.499657\pi\) | ||||
0.00107853 | + | 0.999999i | \(0.499657\pi\) | |||||||
\(110\) | −1.76056 | −0.167862 | ||||||||
\(111\) | 9.99246 | 0.948443 | ||||||||
\(112\) | −6.78751 | −0.641359 | ||||||||
\(113\) | −9.15269 | −0.861013 | −0.430506 | − | 0.902588i | \(-0.641665\pi\) | ||||
−0.430506 | + | 0.902588i | \(0.641665\pi\) | |||||||
\(114\) | −54.7991 | −5.13241 | ||||||||
\(115\) | 6.40773 | 0.597524 | ||||||||
\(116\) | 36.2401 | 3.36481 | ||||||||
\(117\) | 46.1682 | 4.26825 | ||||||||
\(118\) | 12.6566 | 1.16513 | ||||||||
\(119\) | 1.07371 | 0.0984272 | ||||||||
\(120\) | −19.2180 | −1.75436 | ||||||||
\(121\) | −10.5182 | −0.956200 | ||||||||
\(122\) | 22.1207 | 2.00272 | ||||||||
\(123\) | 38.6481 | 3.48478 | ||||||||
\(124\) | −15.3270 | −1.37641 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −16.9839 | −1.51304 | ||||||||
\(127\) | 7.14187 | 0.633738 | 0.316869 | − | 0.948469i | \(-0.397368\pi\) | ||||
0.316869 | + | 0.948469i | \(0.397368\pi\) | |||||||
\(128\) | −12.8316 | −1.13417 | ||||||||
\(129\) | 9.98204 | 0.878869 | ||||||||
\(130\) | −17.4880 | −1.53380 | ||||||||
\(131\) | −2.62484 | −0.229333 | −0.114667 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114667 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(132\) | 9.58203 | 0.834009 | ||||||||
\(133\) | 6.93839 | 0.601635 | ||||||||
\(134\) | 3.12855 | 0.270265 | ||||||||
\(135\) | −11.5090 | −0.990539 | ||||||||
\(136\) | −6.62674 | −0.568238 | ||||||||
\(137\) | −3.40028 | −0.290506 | −0.145253 | − | 0.989395i | \(-0.546400\pi\) | ||||
−0.145253 | + | 0.989395i | \(0.546400\pi\) | |||||||
\(138\) | −50.6080 | −4.30804 | ||||||||
\(139\) | 15.1275 | 1.28310 | 0.641548 | − | 0.767083i | \(-0.278292\pi\) | ||||
0.641548 | + | 0.767083i | \(0.278292\pi\) | |||||||
\(140\) | 4.43329 | 0.374682 | ||||||||
\(141\) | −22.8882 | −1.92753 | ||||||||
\(142\) | −17.6642 | −1.48234 | ||||||||
\(143\) | 4.78581 | 0.400210 | ||||||||
\(144\) | 45.4497 | 3.78747 | ||||||||
\(145\) | −8.17452 | −0.678857 | ||||||||
\(146\) | −1.79424 | −0.148492 | ||||||||
\(147\) | 3.11385 | 0.256826 | ||||||||
\(148\) | 14.2266 | 1.16942 | ||||||||
\(149\) | 2.39105 | 0.195883 | 0.0979414 | − | 0.995192i | \(-0.468774\pi\) | ||||
0.0979414 | + | 0.995192i | \(0.468774\pi\) | |||||||
\(150\) | 7.89795 | 0.644865 | ||||||||
\(151\) | 13.7810 | 1.12148 | 0.560742 | − | 0.827991i | \(-0.310516\pi\) | ||||
0.560742 | + | 0.827991i | \(0.310516\pi\) | |||||||
\(152\) | −42.8223 | −3.47335 | ||||||||
\(153\) | −7.18967 | −0.581250 | ||||||||
\(154\) | −1.76056 | −0.141870 | ||||||||
\(155\) | 3.45726 | 0.277694 | ||||||||
\(156\) | 95.1803 | 7.62052 | ||||||||
\(157\) | −14.4724 | −1.15503 | −0.577513 | − | 0.816382i | \(-0.695977\pi\) | ||||
−0.577513 | + | 0.816382i | \(0.695977\pi\) | |||||||
\(158\) | −26.6504 | −2.12019 | ||||||||
\(159\) | −14.4491 | −1.14589 | ||||||||
\(160\) | −4.87221 | −0.385182 | ||||||||
\(161\) | 6.40773 | 0.505000 | ||||||||
\(162\) | 39.9461 | 3.13846 | ||||||||
\(163\) | −11.3530 | −0.889236 | −0.444618 | − | 0.895720i | \(-0.646661\pi\) | ||||
−0.444618 | + | 0.895720i | \(0.646661\pi\) | |||||||
\(164\) | 55.0246 | 4.29670 | ||||||||
\(165\) | −2.16138 | −0.168263 | ||||||||
\(166\) | 11.3131 | 0.878070 | ||||||||
\(167\) | −23.9335 | −1.85203 | −0.926014 | − | 0.377489i | \(-0.876788\pi\) | ||||
−0.926014 | + | 0.377489i | \(0.876788\pi\) | |||||||
\(168\) | −19.2180 | −1.48270 | ||||||||
\(169\) | 34.5385 | 2.65681 | ||||||||
\(170\) | 2.72336 | 0.208872 | ||||||||
\(171\) | −46.4600 | −3.55288 | ||||||||
\(172\) | 14.2118 | 1.08364 | ||||||||
\(173\) | 22.1259 | 1.68220 | 0.841101 | − | 0.540879i | \(-0.181908\pi\) | ||||
0.841101 | + | 0.540879i | \(0.181908\pi\) | |||||||
\(174\) | 64.5620 | 4.89443 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 4.71133 | 0.355130 | ||||||||
\(177\) | 15.5381 | 1.16791 | ||||||||
\(178\) | −26.9570 | −2.02051 | ||||||||
\(179\) | −13.2390 | −0.989526 | −0.494763 | − | 0.869028i | \(-0.664745\pi\) | ||||
−0.494763 | + | 0.869028i | \(0.664745\pi\) | |||||||
\(180\) | −29.6857 | −2.21264 | ||||||||
\(181\) | −24.5051 | −1.82145 | −0.910724 | − | 0.413015i | \(-0.864476\pi\) | ||||
−0.910724 | + | 0.413015i | \(0.864476\pi\) | |||||||
\(182\) | −17.4880 | −1.29629 | ||||||||
\(183\) | 27.1569 | 2.00750 | ||||||||
\(184\) | −39.5472 | −2.91546 | ||||||||
\(185\) | −3.20904 | −0.235933 | ||||||||
\(186\) | −27.3053 | −2.00212 | ||||||||
\(187\) | −0.745284 | −0.0545006 | ||||||||
\(188\) | −32.5867 | −2.37663 | ||||||||
\(189\) | −11.5090 | −0.837158 | ||||||||
\(190\) | 17.5985 | 1.27673 | ||||||||
\(191\) | −6.29692 | −0.455629 | −0.227814 | − | 0.973705i | \(-0.573158\pi\) | ||||
−0.227814 | + | 0.973705i | \(0.573158\pi\) | |||||||
\(192\) | −3.79008 | −0.273526 | ||||||||
\(193\) | 9.76342 | 0.702787 | 0.351393 | − | 0.936228i | \(-0.385708\pi\) | ||||
0.351393 | + | 0.936228i | \(0.385708\pi\) | |||||||
\(194\) | 42.3651 | 3.04164 | ||||||||
\(195\) | −21.4694 | −1.53746 | ||||||||
\(196\) | 4.43329 | 0.316664 | ||||||||
\(197\) | 9.83007 | 0.700364 | 0.350182 | − | 0.936682i | \(-0.386120\pi\) | ||||
0.350182 | + | 0.936682i | \(0.386120\pi\) | |||||||
\(198\) | 11.7888 | 0.837794 | ||||||||
\(199\) | 11.5793 | 0.820836 | 0.410418 | − | 0.911898i | \(-0.365383\pi\) | ||||
0.410418 | + | 0.911898i | \(0.365383\pi\) | |||||||
\(200\) | 6.17179 | 0.436412 | ||||||||
\(201\) | 3.84082 | 0.270911 | ||||||||
\(202\) | −48.4045 | −3.40573 | ||||||||
\(203\) | −8.17452 | −0.573739 | ||||||||
\(204\) | −14.8222 | −1.03776 | ||||||||
\(205\) | −12.4117 | −0.866869 | ||||||||
\(206\) | −9.42696 | −0.656807 | ||||||||
\(207\) | −42.9066 | −2.98222 | ||||||||
\(208\) | 46.7986 | 3.24490 | ||||||||
\(209\) | −4.81606 | −0.333134 | ||||||||
\(210\) | 7.89795 | 0.545011 | ||||||||
\(211\) | −28.9280 | −1.99149 | −0.995744 | − | 0.0921609i | \(-0.970623\pi\) | ||||
−0.995744 | + | 0.0921609i | \(0.970623\pi\) | |||||||
\(212\) | −20.5716 | −1.41286 | ||||||||
\(213\) | −21.6857 | −1.48588 | ||||||||
\(214\) | −34.6364 | −2.36770 | ||||||||
\(215\) | −3.20569 | −0.218626 | ||||||||
\(216\) | 71.0313 | 4.83307 | ||||||||
\(217\) | 3.45726 | 0.234694 | ||||||||
\(218\) | 0.0571207 | 0.00386870 | ||||||||
\(219\) | −2.20273 | −0.148847 | ||||||||
\(220\) | −3.07723 | −0.207467 | ||||||||
\(221\) | −7.40306 | −0.497984 | ||||||||
\(222\) | 25.3448 | 1.70103 | ||||||||
\(223\) | −16.2888 | −1.09078 | −0.545389 | − | 0.838183i | \(-0.683618\pi\) | ||||
−0.545389 | + | 0.838183i | \(0.683618\pi\) | |||||||
\(224\) | −4.87221 | −0.325538 | ||||||||
\(225\) | 6.69607 | 0.446405 | ||||||||
\(226\) | −23.2148 | −1.54423 | ||||||||
\(227\) | 9.63959 | 0.639802 | 0.319901 | − | 0.947451i | \(-0.396350\pi\) | ||||
0.319901 | + | 0.947451i | \(0.396350\pi\) | |||||||
\(228\) | −95.7819 | −6.34331 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 16.2525 | 1.07166 | ||||||||
\(231\) | −2.16138 | −0.142208 | ||||||||
\(232\) | 50.4515 | 3.31230 | ||||||||
\(233\) | 8.65226 | 0.566829 | 0.283414 | − | 0.958998i | \(-0.408533\pi\) | ||||
0.283414 | + | 0.958998i | \(0.408533\pi\) | |||||||
\(234\) | 117.101 | 7.65511 | ||||||||
\(235\) | 7.35044 | 0.479490 | ||||||||
\(236\) | 22.1221 | 1.44002 | ||||||||
\(237\) | −32.7178 | −2.12525 | ||||||||
\(238\) | 2.72336 | 0.176529 | ||||||||
\(239\) | 20.5627 | 1.33009 | 0.665046 | − | 0.746803i | \(-0.268412\pi\) | ||||
0.665046 | + | 0.746803i | \(0.268412\pi\) | |||||||
\(240\) | −21.1353 | −1.36428 | ||||||||
\(241\) | 0.271703 | 0.0175019 | 0.00875096 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875096 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(242\) | −26.6783 | −1.71495 | ||||||||
\(243\) | 14.5135 | 0.931042 | ||||||||
\(244\) | 38.6643 | 2.47523 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 98.0269 | 6.24997 | ||||||||
\(247\) | −47.8389 | −3.04392 | ||||||||
\(248\) | −21.3375 | −1.35493 | ||||||||
\(249\) | 13.8888 | 0.880167 | ||||||||
\(250\) | −2.53639 | −0.160416 | ||||||||
\(251\) | −9.97546 | −0.629646 | −0.314823 | − | 0.949150i | \(-0.601945\pi\) | ||||
−0.314823 | + | 0.949150i | \(0.601945\pi\) | |||||||
\(252\) | −29.6857 | −1.87002 | ||||||||
\(253\) | −4.44772 | −0.279626 | ||||||||
\(254\) | 18.1146 | 1.13661 | ||||||||
\(255\) | 3.34339 | 0.209371 | ||||||||
\(256\) | −30.1118 | −1.88199 | ||||||||
\(257\) | 4.57395 | 0.285315 | 0.142657 | − | 0.989772i | \(-0.454435\pi\) | ||||
0.142657 | + | 0.989772i | \(0.454435\pi\) | |||||||
\(258\) | 25.3184 | 1.57625 | ||||||||
\(259\) | −3.20904 | −0.199400 | ||||||||
\(260\) | −30.5667 | −1.89567 | ||||||||
\(261\) | 54.7372 | 3.38815 | ||||||||
\(262\) | −6.65763 | −0.411310 | ||||||||
\(263\) | −4.40317 | −0.271511 | −0.135755 | − | 0.990742i | \(-0.543346\pi\) | ||||
−0.135755 | + | 0.990742i | \(0.543346\pi\) | |||||||
\(264\) | 13.3396 | 0.820995 | ||||||||
\(265\) | 4.64026 | 0.285049 | ||||||||
\(266\) | 17.5985 | 1.07903 | ||||||||
\(267\) | −33.0943 | −2.02534 | ||||||||
\(268\) | 5.46831 | 0.334030 | ||||||||
\(269\) | 29.2799 | 1.78523 | 0.892613 | − | 0.450824i | \(-0.148870\pi\) | ||||
0.892613 | + | 0.450824i | \(0.148870\pi\) | |||||||
\(270\) | −29.1914 | −1.77653 | ||||||||
\(271\) | −14.4079 | −0.875219 | −0.437610 | − | 0.899165i | \(-0.644175\pi\) | ||||
−0.437610 | + | 0.899165i | \(0.644175\pi\) | |||||||
\(272\) | −7.28785 | −0.441891 | ||||||||
\(273\) | −21.4694 | −1.29939 | ||||||||
\(274\) | −8.62446 | −0.521023 | ||||||||
\(275\) | 0.694118 | 0.0418569 | ||||||||
\(276\) | −88.4563 | −5.32444 | ||||||||
\(277\) | 16.4969 | 0.991202 | 0.495601 | − | 0.868550i | \(-0.334948\pi\) | ||||
0.495601 | + | 0.868550i | \(0.334948\pi\) | |||||||
\(278\) | 38.3693 | 2.30124 | ||||||||
\(279\) | −23.1501 | −1.38596 | ||||||||
\(280\) | 6.17179 | 0.368835 | ||||||||
\(281\) | −19.2992 | −1.15129 | −0.575647 | − | 0.817698i | \(-0.695250\pi\) | ||||
−0.575647 | + | 0.817698i | \(0.695250\pi\) | |||||||
\(282\) | −58.0535 | −3.45703 | ||||||||
\(283\) | 4.38026 | 0.260380 | 0.130190 | − | 0.991489i | \(-0.458441\pi\) | ||||
0.130190 | + | 0.991489i | \(0.458441\pi\) | |||||||
\(284\) | −30.8747 | −1.83208 | ||||||||
\(285\) | 21.6051 | 1.27978 | ||||||||
\(286\) | 12.1387 | 0.717777 | ||||||||
\(287\) | −12.4117 | −0.732638 | ||||||||
\(288\) | 32.6247 | 1.92243 | ||||||||
\(289\) | −15.8471 | −0.932185 | ||||||||
\(290\) | −20.7338 | −1.21753 | ||||||||
\(291\) | 52.0103 | 3.04890 | ||||||||
\(292\) | −3.13610 | −0.183526 | ||||||||
\(293\) | −9.28530 | −0.542453 | −0.271227 | − | 0.962516i | \(-0.587429\pi\) | ||||
−0.271227 | + | 0.962516i | \(0.587429\pi\) | |||||||
\(294\) | 7.89795 | 0.460618 | ||||||||
\(295\) | −4.98998 | −0.290528 | ||||||||
\(296\) | 19.8055 | 1.15117 | ||||||||
\(297\) | 7.98861 | 0.463546 | ||||||||
\(298\) | 6.06466 | 0.351316 | ||||||||
\(299\) | −44.1801 | −2.55500 | ||||||||
\(300\) | 13.8046 | 0.797010 | ||||||||
\(301\) | −3.20569 | −0.184773 | ||||||||
\(302\) | 34.9541 | 2.01138 | ||||||||
\(303\) | −59.4248 | −3.41386 | ||||||||
\(304\) | −47.0944 | −2.70105 | ||||||||
\(305\) | −8.72134 | −0.499382 | ||||||||
\(306\) | −18.2358 | −1.04247 | ||||||||
\(307\) | 11.9072 | 0.679580 | 0.339790 | − | 0.940501i | \(-0.389644\pi\) | ||||
0.339790 | + | 0.940501i | \(0.389644\pi\) | |||||||
\(308\) | −3.07723 | −0.175341 | ||||||||
\(309\) | −11.5732 | −0.658375 | ||||||||
\(310\) | 8.76897 | 0.498044 | ||||||||
\(311\) | 9.34999 | 0.530189 | 0.265095 | − | 0.964222i | \(-0.414597\pi\) | ||||
0.265095 | + | 0.964222i | \(0.414597\pi\) | |||||||
\(312\) | 132.505 | 7.50161 | ||||||||
\(313\) | −3.30987 | −0.187085 | −0.0935423 | − | 0.995615i | \(-0.529819\pi\) | ||||
−0.0935423 | + | 0.995615i | \(0.529819\pi\) | |||||||
\(314\) | −36.7078 | −2.07154 | ||||||||
\(315\) | 6.69607 | 0.377281 | ||||||||
\(316\) | −46.5814 | −2.62041 | ||||||||
\(317\) | −0.410312 | −0.0230454 | −0.0115227 | − | 0.999934i | \(-0.503668\pi\) | ||||
−0.0115227 | + | 0.999934i | \(0.503668\pi\) | |||||||
\(318\) | −36.6485 | −2.05515 | ||||||||
\(319\) | 5.67408 | 0.317688 | ||||||||
\(320\) | 1.21717 | 0.0680418 | ||||||||
\(321\) | −42.5221 | −2.37335 | ||||||||
\(322\) | 16.2525 | 0.905718 | ||||||||
\(323\) | 7.44985 | 0.414521 | ||||||||
\(324\) | 69.8207 | 3.87893 | ||||||||
\(325\) | 6.89482 | 0.382456 | ||||||||
\(326\) | −28.7957 | −1.59485 | ||||||||
\(327\) | 0.0701253 | 0.00387794 | ||||||||
\(328\) | 76.6023 | 4.22966 | ||||||||
\(329\) | 7.35044 | 0.405243 | ||||||||
\(330\) | −5.48211 | −0.301780 | ||||||||
\(331\) | 3.36690 | 0.185061 | 0.0925307 | − | 0.995710i | \(-0.470504\pi\) | ||||
0.0925307 | + | 0.995710i | \(0.470504\pi\) | |||||||
\(332\) | 19.7739 | 1.08524 | ||||||||
\(333\) | 21.4879 | 1.17753 | ||||||||
\(334\) | −60.7047 | −3.32162 | ||||||||
\(335\) | −1.23346 | −0.0673913 | ||||||||
\(336\) | −21.1353 | −1.15303 | ||||||||
\(337\) | −18.9603 | −1.03283 | −0.516415 | − | 0.856338i | \(-0.672734\pi\) | ||||
−0.516415 | + | 0.856338i | \(0.672734\pi\) | |||||||
\(338\) | 87.6032 | 4.76499 | ||||||||
\(339\) | −28.5001 | −1.54791 | ||||||||
\(340\) | 4.76009 | 0.258152 | ||||||||
\(341\) | −2.39974 | −0.129953 | ||||||||
\(342\) | −117.841 | −6.37210 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 19.7848 | 1.06673 | ||||||||
\(345\) | 19.9527 | 1.07422 | ||||||||
\(346\) | 56.1200 | 3.01703 | ||||||||
\(347\) | 2.04321 | 0.109685 | 0.0548427 | − | 0.998495i | \(-0.482534\pi\) | ||||
0.0548427 | + | 0.998495i | \(0.482534\pi\) | |||||||
\(348\) | 112.846 | 6.04919 | ||||||||
\(349\) | −17.4134 | −0.932116 | −0.466058 | − | 0.884754i | \(-0.654326\pi\) | ||||
−0.466058 | + | 0.884754i | \(0.654326\pi\) | |||||||
\(350\) | −2.53639 | −0.135576 | ||||||||
\(351\) | 79.3526 | 4.23553 | ||||||||
\(352\) | 3.38189 | 0.180255 | ||||||||
\(353\) | 16.3755 | 0.871578 | 0.435789 | − | 0.900049i | \(-0.356469\pi\) | ||||
0.435789 | + | 0.900049i | \(0.356469\pi\) | |||||||
\(354\) | 39.4107 | 2.09465 | ||||||||
\(355\) | 6.96428 | 0.369626 | ||||||||
\(356\) | −47.1174 | −2.49722 | ||||||||
\(357\) | 3.34339 | 0.176951 | ||||||||
\(358\) | −33.5792 | −1.77472 | ||||||||
\(359\) | 18.7159 | 0.987789 | 0.493894 | − | 0.869522i | \(-0.335573\pi\) | ||||
0.493894 | + | 0.869522i | \(0.335573\pi\) | |||||||
\(360\) | −41.3268 | −2.17811 | ||||||||
\(361\) | 29.1413 | 1.53375 | ||||||||
\(362\) | −62.1546 | −3.26677 | ||||||||
\(363\) | −32.7521 | −1.71904 | ||||||||
\(364\) | −30.5667 | −1.60213 | ||||||||
\(365\) | 0.707397 | 0.0370269 | ||||||||
\(366\) | 68.8807 | 3.60045 | ||||||||
\(367\) | 7.13403 | 0.372394 | 0.186197 | − | 0.982512i | \(-0.440384\pi\) | ||||
0.186197 | + | 0.982512i | \(0.440384\pi\) | |||||||
\(368\) | −43.4925 | −2.26720 | ||||||||
\(369\) | 83.1095 | 4.32651 | ||||||||
\(370\) | −8.13938 | −0.423146 | ||||||||
\(371\) | 4.64026 | 0.240910 | ||||||||
\(372\) | −47.7262 | −2.47449 | ||||||||
\(373\) | −10.4582 | −0.541504 | −0.270752 | − | 0.962649i | \(-0.587272\pi\) | ||||
−0.270752 | + | 0.962649i | \(0.587272\pi\) | |||||||
\(374\) | −1.89033 | −0.0977468 | ||||||||
\(375\) | −3.11385 | −0.160799 | ||||||||
\(376\) | −45.3654 | −2.33954 | ||||||||
\(377\) | 56.3618 | 2.90278 | ||||||||
\(378\) | −29.1914 | −1.50144 | ||||||||
\(379\) | −10.0073 | −0.514042 | −0.257021 | − | 0.966406i | \(-0.582741\pi\) | ||||
−0.257021 | + | 0.966406i | \(0.582741\pi\) | |||||||
\(380\) | 30.7599 | 1.57795 | ||||||||
\(381\) | 22.2387 | 1.13932 | ||||||||
\(382\) | −15.9715 | −0.817171 | ||||||||
\(383\) | −12.0370 | −0.615061 | −0.307531 | − | 0.951538i | \(-0.599503\pi\) | ||||
−0.307531 | + | 0.951538i | \(0.599503\pi\) | |||||||
\(384\) | −39.9558 | −2.03899 | ||||||||
\(385\) | 0.694118 | 0.0353755 | ||||||||
\(386\) | 24.7639 | 1.26045 | ||||||||
\(387\) | 21.4655 | 1.09115 | ||||||||
\(388\) | 74.0488 | 3.75926 | ||||||||
\(389\) | 6.24817 | 0.316795 | 0.158397 | − | 0.987375i | \(-0.449367\pi\) | ||||
0.158397 | + | 0.987375i | \(0.449367\pi\) | |||||||
\(390\) | −54.4549 | −2.75743 | ||||||||
\(391\) | 6.88007 | 0.347940 | ||||||||
\(392\) | 6.17179 | 0.311723 | ||||||||
\(393\) | −8.17336 | −0.412292 | ||||||||
\(394\) | 24.9329 | 1.25610 | ||||||||
\(395\) | 10.5072 | 0.528674 | ||||||||
\(396\) | 20.6053 | 1.03546 | ||||||||
\(397\) | 23.2972 | 1.16925 | 0.584626 | − | 0.811303i | \(-0.301241\pi\) | ||||
0.584626 | + | 0.811303i | \(0.301241\pi\) | |||||||
\(398\) | 29.3697 | 1.47217 | ||||||||
\(399\) | 21.6051 | 1.08161 | ||||||||
\(400\) | 6.78751 | 0.339375 | ||||||||
\(401\) | −12.8957 | −0.643980 | −0.321990 | − | 0.946743i | \(-0.604352\pi\) | ||||
−0.321990 | + | 0.946743i | \(0.604352\pi\) | |||||||
\(402\) | 9.74184 | 0.485879 | ||||||||
\(403\) | −23.8372 | −1.18741 | ||||||||
\(404\) | −84.6050 | −4.20926 | ||||||||
\(405\) | −15.7492 | −0.782583 | ||||||||
\(406\) | −20.7338 | −1.02900 | ||||||||
\(407\) | 2.22745 | 0.110411 | ||||||||
\(408\) | −20.6347 | −1.02157 | ||||||||
\(409\) | 12.4018 | 0.613230 | 0.306615 | − | 0.951834i | \(-0.400804\pi\) | ||||
0.306615 | + | 0.951834i | \(0.400804\pi\) | |||||||
\(410\) | −31.4809 | −1.55473 | ||||||||
\(411\) | −10.5880 | −0.522267 | ||||||||
\(412\) | −16.4771 | −0.811770 | ||||||||
\(413\) | −4.98998 | −0.245541 | ||||||||
\(414\) | −108.828 | −5.34861 | ||||||||
\(415\) | −4.46033 | −0.218949 | ||||||||
\(416\) | 33.5930 | 1.64703 | ||||||||
\(417\) | 47.1048 | 2.30673 | ||||||||
\(418\) | −12.2154 | −0.597476 | ||||||||
\(419\) | 25.4805 | 1.24481 | 0.622403 | − | 0.782697i | \(-0.286156\pi\) | ||||
0.622403 | + | 0.782697i | \(0.286156\pi\) | |||||||
\(420\) | 13.8046 | 0.673597 | ||||||||
\(421\) | 15.8522 | 0.772591 | 0.386296 | − | 0.922375i | \(-0.373754\pi\) | ||||
0.386296 | + | 0.922375i | \(0.373754\pi\) | |||||||
\(422\) | −73.3729 | −3.57174 | ||||||||
\(423\) | −49.2191 | −2.39311 | ||||||||
\(424\) | −28.6387 | −1.39082 | ||||||||
\(425\) | −1.07371 | −0.0520828 | ||||||||
\(426\) | −55.0036 | −2.66493 | ||||||||
\(427\) | −8.72134 | −0.422055 | ||||||||
\(428\) | −60.5401 | −2.92631 | ||||||||
\(429\) | 14.9023 | 0.719490 | ||||||||
\(430\) | −8.13089 | −0.392106 | ||||||||
\(431\) | 27.1499 | 1.30776 | 0.653881 | − | 0.756597i | \(-0.273140\pi\) | ||||
0.653881 | + | 0.756597i | \(0.273140\pi\) | |||||||
\(432\) | 78.1176 | 3.75843 | ||||||||
\(433\) | 37.4869 | 1.80150 | 0.900752 | − | 0.434335i | \(-0.143016\pi\) | ||||
0.900752 | + | 0.434335i | \(0.143016\pi\) | |||||||
\(434\) | 8.76897 | 0.420924 | ||||||||
\(435\) | −25.4543 | −1.22044 | ||||||||
\(436\) | 0.0998398 | 0.00478146 | ||||||||
\(437\) | 44.4593 | 2.12678 | ||||||||
\(438\) | −5.58699 | −0.266957 | ||||||||
\(439\) | 27.6510 | 1.31971 | 0.659855 | − | 0.751393i | \(-0.270618\pi\) | ||||
0.659855 | + | 0.751393i | \(0.270618\pi\) | |||||||
\(440\) | −4.28395 | −0.204229 | ||||||||
\(441\) | 6.69607 | 0.318861 | ||||||||
\(442\) | −18.7771 | −0.893135 | ||||||||
\(443\) | 16.4609 | 0.782080 | 0.391040 | − | 0.920374i | \(-0.372115\pi\) | ||||
0.391040 | + | 0.920374i | \(0.372115\pi\) | |||||||
\(444\) | 44.2995 | 2.10236 | ||||||||
\(445\) | 10.6281 | 0.503819 | ||||||||
\(446\) | −41.3148 | −1.95631 | ||||||||
\(447\) | 7.44539 | 0.352155 | ||||||||
\(448\) | 1.21717 | 0.0575058 | ||||||||
\(449\) | −33.9770 | −1.60347 | −0.801737 | − | 0.597677i | \(-0.796091\pi\) | ||||
−0.801737 | + | 0.597677i | \(0.796091\pi\) | |||||||
\(450\) | 16.9839 | 0.800628 | ||||||||
\(451\) | 8.61516 | 0.405672 | ||||||||
\(452\) | −40.5766 | −1.90856 | ||||||||
\(453\) | 42.9121 | 2.01619 | ||||||||
\(454\) | 24.4498 | 1.14749 | ||||||||
\(455\) | 6.89482 | 0.323234 | ||||||||
\(456\) | −133.342 | −6.24433 | ||||||||
\(457\) | 8.90711 | 0.416657 | 0.208328 | − | 0.978059i | \(-0.433198\pi\) | ||||
0.208328 | + | 0.978059i | \(0.433198\pi\) | |||||||
\(458\) | 2.53639 | 0.118518 | ||||||||
\(459\) | −12.3574 | −0.576794 | ||||||||
\(460\) | 28.4074 | 1.32450 | ||||||||
\(461\) | 0.253730 | 0.0118174 | 0.00590870 | − | 0.999983i | \(-0.498119\pi\) | ||||
0.00590870 | + | 0.999983i | \(0.498119\pi\) | |||||||
\(462\) | −5.48211 | −0.255051 | ||||||||
\(463\) | −22.3456 | −1.03849 | −0.519244 | − | 0.854626i | \(-0.673786\pi\) | ||||
−0.519244 | + | 0.854626i | \(0.673786\pi\) | |||||||
\(464\) | 55.4847 | 2.57581 | ||||||||
\(465\) | 10.7654 | 0.499233 | ||||||||
\(466\) | 21.9456 | 1.01661 | ||||||||
\(467\) | 35.9456 | 1.66337 | 0.831683 | − | 0.555251i | \(-0.187378\pi\) | ||||
0.831683 | + | 0.555251i | \(0.187378\pi\) | |||||||
\(468\) | 204.677 | 9.46120 | ||||||||
\(469\) | −1.23346 | −0.0569560 | ||||||||
\(470\) | 18.6436 | 0.859966 | ||||||||
\(471\) | −45.0650 | −2.07649 | ||||||||
\(472\) | 30.7971 | 1.41755 | ||||||||
\(473\) | 2.22512 | 0.102311 | ||||||||
\(474\) | −82.9853 | −3.81164 | ||||||||
\(475\) | −6.93839 | −0.318355 | ||||||||
\(476\) | 4.76009 | 0.218178 | ||||||||
\(477\) | −31.0715 | −1.42267 | ||||||||
\(478\) | 52.1552 | 2.38552 | ||||||||
\(479\) | −14.2792 | −0.652434 | −0.326217 | − | 0.945295i | \(-0.605774\pi\) | ||||
−0.326217 | + | 0.945295i | \(0.605774\pi\) | |||||||
\(480\) | −15.1713 | −0.692474 | ||||||||
\(481\) | 22.1257 | 1.00885 | ||||||||
\(482\) | 0.689145 | 0.0313897 | ||||||||
\(483\) | 19.9527 | 0.907880 | ||||||||
\(484\) | −46.6303 | −2.11956 | ||||||||
\(485\) | −16.7029 | −0.758439 | ||||||||
\(486\) | 36.8120 | 1.66983 | ||||||||
\(487\) | −2.74442 | −0.124361 | −0.0621807 | − | 0.998065i | \(-0.519805\pi\) | ||||
−0.0621807 | + | 0.998065i | \(0.519805\pi\) | |||||||
\(488\) | 53.8263 | 2.43660 | ||||||||
\(489\) | −35.3516 | −1.59865 | ||||||||
\(490\) | −2.53639 | −0.114583 | ||||||||
\(491\) | −9.75967 | −0.440448 | −0.220224 | − | 0.975449i | \(-0.570679\pi\) | ||||
−0.220224 | + | 0.975449i | \(0.570679\pi\) | |||||||
\(492\) | 171.339 | 7.72454 | ||||||||
\(493\) | −8.77710 | −0.395301 | ||||||||
\(494\) | −121.338 | −5.45927 | ||||||||
\(495\) | −4.64786 | −0.208906 | ||||||||
\(496\) | −23.4662 | −1.05366 | ||||||||
\(497\) | 6.96428 | 0.312391 | ||||||||
\(498\) | 35.2275 | 1.57858 | ||||||||
\(499\) | −13.3965 | −0.599709 | −0.299854 | − | 0.953985i | \(-0.596938\pi\) | ||||
−0.299854 | + | 0.953985i | \(0.596938\pi\) | |||||||
\(500\) | −4.43329 | −0.198263 | ||||||||
\(501\) | −74.5253 | −3.32955 | ||||||||
\(502\) | −25.3017 | −1.12927 | ||||||||
\(503\) | −38.5846 | −1.72040 | −0.860201 | − | 0.509954i | \(-0.829662\pi\) | ||||
−0.860201 | + | 0.509954i | \(0.829662\pi\) | |||||||
\(504\) | −41.3268 | −1.84084 | ||||||||
\(505\) | 19.0840 | 0.849227 | ||||||||
\(506\) | −11.2812 | −0.501509 | ||||||||
\(507\) | 107.548 | 4.77636 | ||||||||
\(508\) | 31.6620 | 1.40477 | ||||||||
\(509\) | 22.6354 | 1.00329 | 0.501647 | − | 0.865072i | \(-0.332728\pi\) | ||||
0.501647 | + | 0.865072i | \(0.332728\pi\) | |||||||
\(510\) | 8.48015 | 0.375507 | ||||||||
\(511\) | 0.707397 | 0.0312934 | ||||||||
\(512\) | −50.7120 | −2.24118 | ||||||||
\(513\) | −79.8541 | −3.52564 | ||||||||
\(514\) | 11.6013 | 0.511713 | ||||||||
\(515\) | 3.71668 | 0.163776 | ||||||||
\(516\) | 44.2533 | 1.94814 | ||||||||
\(517\) | −5.10207 | −0.224389 | ||||||||
\(518\) | −8.13938 | −0.357624 | ||||||||
\(519\) | 68.8968 | 3.02423 | ||||||||
\(520\) | −42.5534 | −1.86609 | ||||||||
\(521\) | 13.9472 | 0.611037 | 0.305518 | − | 0.952186i | \(-0.401170\pi\) | ||||
0.305518 | + | 0.952186i | \(0.401170\pi\) | |||||||
\(522\) | 138.835 | 6.07665 | ||||||||
\(523\) | 5.46489 | 0.238963 | 0.119482 | − | 0.992836i | \(-0.461877\pi\) | ||||
0.119482 | + | 0.992836i | \(0.461877\pi\) | |||||||
\(524\) | −11.6367 | −0.508351 | ||||||||
\(525\) | −3.11385 | −0.135900 | ||||||||
\(526\) | −11.1682 | −0.486955 | ||||||||
\(527\) | 3.71211 | 0.161702 | ||||||||
\(528\) | 14.6704 | 0.638446 | ||||||||
\(529\) | 18.0590 | 0.785174 | ||||||||
\(530\) | 11.7695 | 0.511235 | ||||||||
\(531\) | 33.4133 | 1.45001 | ||||||||
\(532\) | 30.7599 | 1.33361 | ||||||||
\(533\) | 85.5762 | 3.70672 | ||||||||
\(534\) | −83.9401 | −3.63244 | ||||||||
\(535\) | 13.6558 | 0.590391 | ||||||||
\(536\) | 7.61268 | 0.328818 | ||||||||
\(537\) | −41.2242 | −1.77895 | ||||||||
\(538\) | 74.2653 | 3.20181 | ||||||||
\(539\) | 0.694118 | 0.0298978 | ||||||||
\(540\) | −51.0229 | −2.19568 | ||||||||
\(541\) | 12.4275 | 0.534300 | 0.267150 | − | 0.963655i | \(-0.413918\pi\) | ||||
0.267150 | + | 0.963655i | \(0.413918\pi\) | |||||||
\(542\) | −36.5442 | −1.56971 | ||||||||
\(543\) | −76.3052 | −3.27457 | ||||||||
\(544\) | −5.23136 | −0.224293 | ||||||||
\(545\) | −0.0225205 | −0.000964670 0 | ||||||||
\(546\) | −54.4549 | −2.33046 | ||||||||
\(547\) | −26.3836 | −1.12808 | −0.564040 | − | 0.825748i | \(-0.690754\pi\) | ||||
−0.564040 | + | 0.825748i | \(0.690754\pi\) | |||||||
\(548\) | −15.0745 | −0.643949 | ||||||||
\(549\) | 58.3987 | 2.49240 | ||||||||
\(550\) | 1.76056 | 0.0750703 | ||||||||
\(551\) | −56.7180 | −2.41627 | ||||||||
\(552\) | −123.144 | −5.24136 | ||||||||
\(553\) | 10.5072 | 0.446811 | ||||||||
\(554\) | 41.8426 | 1.77772 | ||||||||
\(555\) | −9.99246 | −0.424156 | ||||||||
\(556\) | 67.0646 | 2.84417 | ||||||||
\(557\) | −35.8380 | −1.51850 | −0.759252 | − | 0.650797i | \(-0.774435\pi\) | ||||
−0.759252 | + | 0.650797i | \(0.774435\pi\) | |||||||
\(558\) | −58.7177 | −2.48572 | ||||||||
\(559\) | 22.1026 | 0.934841 | ||||||||
\(560\) | 6.78751 | 0.286825 | ||||||||
\(561\) | −2.32070 | −0.0979802 | ||||||||
\(562\) | −48.9504 | −2.06485 | ||||||||
\(563\) | 28.7783 | 1.21286 | 0.606430 | − | 0.795137i | \(-0.292601\pi\) | ||||
0.606430 | + | 0.795137i | \(0.292601\pi\) | |||||||
\(564\) | −101.470 | −4.27266 | ||||||||
\(565\) | 9.15269 | 0.385057 | ||||||||
\(566\) | 11.1101 | 0.466991 | ||||||||
\(567\) | −15.7492 | −0.661403 | ||||||||
\(568\) | −42.9821 | −1.80349 | ||||||||
\(569\) | 19.2339 | 0.806327 | 0.403164 | − | 0.915128i | \(-0.367911\pi\) | ||||
0.403164 | + | 0.915128i | \(0.367911\pi\) | |||||||
\(570\) | 54.7991 | 2.29528 | ||||||||
\(571\) | 4.18337 | 0.175068 | 0.0875342 | − | 0.996162i | \(-0.472101\pi\) | ||||
0.0875342 | + | 0.996162i | \(0.472101\pi\) | |||||||
\(572\) | 21.2169 | 0.887124 | ||||||||
\(573\) | −19.6077 | −0.819122 | ||||||||
\(574\) | −31.4809 | −1.31399 | ||||||||
\(575\) | −6.40773 | −0.267221 | ||||||||
\(576\) | −8.15025 | −0.339594 | ||||||||
\(577\) | 23.3122 | 0.970501 | 0.485251 | − | 0.874375i | \(-0.338728\pi\) | ||||
0.485251 | + | 0.874375i | \(0.338728\pi\) | |||||||
\(578\) | −40.1946 | −1.67187 | ||||||||
\(579\) | 30.4019 | 1.26346 | ||||||||
\(580\) | −36.2401 | −1.50479 | ||||||||
\(581\) | −4.46033 | −0.185046 | ||||||||
\(582\) | 131.919 | 5.46820 | ||||||||
\(583\) | −3.22088 | −0.133395 | ||||||||
\(584\) | −4.36591 | −0.180663 | ||||||||
\(585\) | −46.1682 | −1.90882 | ||||||||
\(586\) | −23.5512 | −0.972891 | ||||||||
\(587\) | 7.83786 | 0.323503 | 0.161752 | − | 0.986832i | \(-0.448286\pi\) | ||||
0.161752 | + | 0.986832i | \(0.448286\pi\) | |||||||
\(588\) | 13.8046 | 0.569293 | ||||||||
\(589\) | 23.9878 | 0.988401 | ||||||||
\(590\) | −12.6566 | −0.521062 | ||||||||
\(591\) | 30.6094 | 1.25910 | ||||||||
\(592\) | 21.7814 | 0.895209 | ||||||||
\(593\) | −34.7711 | −1.42788 | −0.713939 | − | 0.700208i | \(-0.753091\pi\) | ||||
−0.713939 | + | 0.700208i | \(0.753091\pi\) | |||||||
\(594\) | 20.2623 | 0.831371 | ||||||||
\(595\) | −1.07371 | −0.0440180 | ||||||||
\(596\) | 10.6002 | 0.434203 | ||||||||
\(597\) | 36.0563 | 1.47569 | ||||||||
\(598\) | −112.058 | −4.58240 | ||||||||
\(599\) | −45.6310 | −1.86443 | −0.932217 | − | 0.361900i | \(-0.882128\pi\) | ||||
−0.932217 | + | 0.361900i | \(0.882128\pi\) | |||||||
\(600\) | 19.2180 | 0.784574 | ||||||||
\(601\) | −31.1708 | −1.27148 | −0.635742 | − | 0.771902i | \(-0.719306\pi\) | ||||
−0.635742 | + | 0.771902i | \(0.719306\pi\) | |||||||
\(602\) | −8.13089 | −0.331390 | ||||||||
\(603\) | 8.25936 | 0.336347 | ||||||||
\(604\) | 61.0954 | 2.48593 | ||||||||
\(605\) | 10.5182 | 0.427626 | ||||||||
\(606\) | −150.725 | −6.12277 | ||||||||
\(607\) | −22.3766 | −0.908237 | −0.454119 | − | 0.890941i | \(-0.650046\pi\) | ||||
−0.454119 | + | 0.890941i | \(0.650046\pi\) | |||||||
\(608\) | −33.8053 | −1.37099 | ||||||||
\(609\) | −25.4543 | −1.03146 | ||||||||
\(610\) | −22.1207 | −0.895643 | ||||||||
\(611\) | −50.6799 | −2.05029 | ||||||||
\(612\) | −31.8739 | −1.28843 | ||||||||
\(613\) | 39.7573 | 1.60578 | 0.802891 | − | 0.596126i | \(-0.203294\pi\) | ||||
0.802891 | + | 0.596126i | \(0.203294\pi\) | |||||||
\(614\) | 30.2013 | 1.21883 | ||||||||
\(615\) | −38.6481 | −1.55844 | ||||||||
\(616\) | −4.28395 | −0.172605 | ||||||||
\(617\) | −34.8823 | −1.40431 | −0.702155 | − | 0.712024i | \(-0.747779\pi\) | ||||
−0.702155 | + | 0.712024i | \(0.747779\pi\) | |||||||
\(618\) | −29.3541 | −1.18080 | ||||||||
\(619\) | −16.6609 | −0.669659 | −0.334829 | − | 0.942279i | \(-0.608679\pi\) | ||||
−0.334829 | + | 0.942279i | \(0.608679\pi\) | |||||||
\(620\) | 15.3270 | 0.615549 | ||||||||
\(621\) | −73.7467 | −2.95935 | ||||||||
\(622\) | 23.7153 | 0.950895 | ||||||||
\(623\) | 10.6281 | 0.425805 | ||||||||
\(624\) | 145.724 | 5.83363 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.39512 | −0.335537 | ||||||||
\(627\) | −14.9965 | −0.598902 | ||||||||
\(628\) | −64.1605 | −2.56028 | ||||||||
\(629\) | −3.44559 | −0.137385 | ||||||||
\(630\) | 16.9839 | 0.676654 | ||||||||
\(631\) | 36.1944 | 1.44088 | 0.720438 | − | 0.693519i | \(-0.243941\pi\) | ||||
0.720438 | + | 0.693519i | \(0.243941\pi\) | |||||||
\(632\) | −64.8482 | −2.57952 | ||||||||
\(633\) | −90.0776 | −3.58026 | ||||||||
\(634\) | −1.04071 | −0.0413320 | ||||||||
\(635\) | −7.14187 | −0.283416 | ||||||||
\(636\) | −64.0570 | −2.54002 | ||||||||
\(637\) | 6.89482 | 0.273183 | ||||||||
\(638\) | 14.3917 | 0.569773 | ||||||||
\(639\) | −46.6333 | −1.84479 | ||||||||
\(640\) | 12.8316 | 0.507215 | ||||||||
\(641\) | −41.5036 | −1.63929 | −0.819647 | − | 0.572869i | \(-0.805830\pi\) | ||||
−0.819647 | + | 0.572869i | \(0.805830\pi\) | |||||||
\(642\) | −107.853 | −4.25661 | ||||||||
\(643\) | 10.9258 | 0.430873 | 0.215436 | − | 0.976518i | \(-0.430883\pi\) | ||||
0.215436 | + | 0.976518i | \(0.430883\pi\) | |||||||
\(644\) | 28.4074 | 1.11941 | ||||||||
\(645\) | −9.98204 | −0.393042 | ||||||||
\(646\) | 18.8958 | 0.743443 | ||||||||
\(647\) | −24.0338 | −0.944866 | −0.472433 | − | 0.881367i | \(-0.656624\pi\) | ||||
−0.472433 | + | 0.881367i | \(0.656624\pi\) | |||||||
\(648\) | 97.2006 | 3.81840 | ||||||||
\(649\) | 3.46363 | 0.135960 | ||||||||
\(650\) | 17.4880 | 0.685935 | ||||||||
\(651\) | 10.7654 | 0.421929 | ||||||||
\(652\) | −50.3312 | −1.97112 | ||||||||
\(653\) | −44.6154 | −1.74594 | −0.872968 | − | 0.487778i | \(-0.837807\pi\) | ||||
−0.872968 | + | 0.487778i | \(0.837807\pi\) | |||||||
\(654\) | 0.177866 | 0.00695509 | ||||||||
\(655\) | 2.62484 | 0.102561 | ||||||||
\(656\) | 84.2444 | 3.28919 | ||||||||
\(657\) | −4.73678 | −0.184799 | ||||||||
\(658\) | 18.6436 | 0.726804 | ||||||||
\(659\) | 32.1860 | 1.25379 | 0.626894 | − | 0.779105i | \(-0.284326\pi\) | ||||
0.626894 | + | 0.779105i | \(0.284326\pi\) | |||||||
\(660\) | −9.58203 | −0.372980 | ||||||||
\(661\) | −26.9824 | −1.04949 | −0.524747 | − | 0.851258i | \(-0.675840\pi\) | ||||
−0.524747 | + | 0.851258i | \(0.675840\pi\) | |||||||
\(662\) | 8.53978 | 0.331908 | ||||||||
\(663\) | −23.0520 | −0.895267 | ||||||||
\(664\) | 27.5282 | 1.06830 | ||||||||
\(665\) | −6.93839 | −0.269059 | ||||||||
\(666\) | 54.5019 | 2.11190 | ||||||||
\(667\) | −52.3801 | −2.02817 | ||||||||
\(668\) | −106.104 | −4.10529 | ||||||||
\(669\) | −50.7209 | −1.96098 | ||||||||
\(670\) | −3.12855 | −0.120866 | ||||||||
\(671\) | 6.05363 | 0.233698 | ||||||||
\(672\) | −15.1713 | −0.585247 | ||||||||
\(673\) | 33.5732 | 1.29415 | 0.647076 | − | 0.762426i | \(-0.275992\pi\) | ||||
0.647076 | + | 0.762426i | \(0.275992\pi\) | |||||||
\(674\) | −48.0907 | −1.85238 | ||||||||
\(675\) | 11.5090 | 0.442982 | ||||||||
\(676\) | 153.119 | 5.88920 | ||||||||
\(677\) | 28.8307 | 1.10805 | 0.554026 | − | 0.832499i | \(-0.313091\pi\) | ||||
0.554026 | + | 0.832499i | \(0.313091\pi\) | |||||||
\(678\) | −72.2875 | −2.77619 | ||||||||
\(679\) | −16.7029 | −0.640998 | ||||||||
\(680\) | 6.62674 | 0.254124 | ||||||||
\(681\) | 30.0162 | 1.15022 | ||||||||
\(682\) | −6.08670 | −0.233072 | ||||||||
\(683\) | 10.7047 | 0.409602 | 0.204801 | − | 0.978804i | \(-0.434345\pi\) | ||||
0.204801 | + | 0.978804i | \(0.434345\pi\) | |||||||
\(684\) | −205.971 | −7.87549 | ||||||||
\(685\) | 3.40028 | 0.129918 | ||||||||
\(686\) | −2.53639 | −0.0968400 | ||||||||
\(687\) | 3.11385 | 0.118801 | ||||||||
\(688\) | 21.7586 | 0.829540 | ||||||||
\(689\) | −31.9937 | −1.21886 | ||||||||
\(690\) | 50.6080 | 1.92661 | ||||||||
\(691\) | −6.28528 | −0.239103 | −0.119552 | − | 0.992828i | \(-0.538146\pi\) | ||||
−0.119552 | + | 0.992828i | \(0.538146\pi\) | |||||||
\(692\) | 98.0906 | 3.72885 | ||||||||
\(693\) | −4.64786 | −0.176558 | ||||||||
\(694\) | 5.18239 | 0.196721 | ||||||||
\(695\) | −15.1275 | −0.573818 | ||||||||
\(696\) | 157.098 | 5.95480 | ||||||||
\(697\) | −13.3266 | −0.504781 | ||||||||
\(698\) | −44.1671 | −1.67175 | ||||||||
\(699\) | 26.9419 | 1.01904 | ||||||||
\(700\) | −4.43329 | −0.167563 | ||||||||
\(701\) | 45.0514 | 1.70157 | 0.850783 | − | 0.525516i | \(-0.176128\pi\) | ||||
0.850783 | + | 0.525516i | \(0.176128\pi\) | |||||||
\(702\) | 201.269 | 7.59642 | ||||||||
\(703\) | −22.2655 | −0.839761 | ||||||||
\(704\) | −0.844858 | −0.0318418 | ||||||||
\(705\) | 22.8882 | 0.862019 | ||||||||
\(706\) | 41.5346 | 1.56318 | ||||||||
\(707\) | 19.0840 | 0.717728 | ||||||||
\(708\) | 68.8848 | 2.58885 | ||||||||
\(709\) | 14.3281 | 0.538104 | 0.269052 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269052 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(710\) | 17.6642 | 0.662924 | ||||||||
\(711\) | −70.3569 | −2.63859 | ||||||||
\(712\) | −65.5943 | −2.45825 | ||||||||
\(713\) | 22.1532 | 0.829643 | ||||||||
\(714\) | 8.48015 | 0.317362 | ||||||||
\(715\) | −4.78581 | −0.178979 | ||||||||
\(716\) | −58.6922 | −2.19343 | ||||||||
\(717\) | 64.0293 | 2.39122 | ||||||||
\(718\) | 47.4710 | 1.77160 | ||||||||
\(719\) | −32.2886 | −1.20416 | −0.602081 | − | 0.798435i | \(-0.705662\pi\) | ||||
−0.602081 | + | 0.798435i | \(0.705662\pi\) | |||||||
\(720\) | −45.4497 | −1.69381 | ||||||||
\(721\) | 3.71668 | 0.138416 | ||||||||
\(722\) | 73.9137 | 2.75078 | ||||||||
\(723\) | 0.846042 | 0.0314647 | ||||||||
\(724\) | −108.638 | −4.03751 | ||||||||
\(725\) | 8.17452 | 0.303594 | ||||||||
\(726\) | −83.0723 | −3.08310 | ||||||||
\(727\) | 14.2026 | 0.526744 | 0.263372 | − | 0.964694i | \(-0.415165\pi\) | ||||
0.263372 | + | 0.964694i | \(0.415165\pi\) | |||||||
\(728\) | −42.5534 | −1.57713 | ||||||||
\(729\) | −2.05458 | −0.0760954 | ||||||||
\(730\) | 1.79424 | 0.0664077 | ||||||||
\(731\) | −3.44199 | −0.127307 | ||||||||
\(732\) | 120.395 | 4.44992 | ||||||||
\(733\) | −2.19744 | −0.0811642 | −0.0405821 | − | 0.999176i | \(-0.512921\pi\) | ||||
−0.0405821 | + | 0.999176i | \(0.512921\pi\) | |||||||
\(734\) | 18.0947 | 0.667888 | ||||||||
\(735\) | −3.11385 | −0.114856 | ||||||||
\(736\) | −31.2198 | −1.15078 | ||||||||
\(737\) | 0.856168 | 0.0315374 | ||||||||
\(738\) | 210.798 | 7.75960 | ||||||||
\(739\) | −25.9961 | −0.956283 | −0.478141 | − | 0.878283i | \(-0.658689\pi\) | ||||
−0.478141 | + | 0.878283i | \(0.658689\pi\) | |||||||
\(740\) | −14.2266 | −0.522980 | ||||||||
\(741\) | −148.963 | −5.47230 | ||||||||
\(742\) | 11.7695 | 0.432073 | ||||||||
\(743\) | −8.73693 | −0.320527 | −0.160263 | − | 0.987074i | \(-0.551234\pi\) | ||||
−0.160263 | + | 0.987074i | \(0.551234\pi\) | |||||||
\(744\) | −66.4418 | −2.43587 | ||||||||
\(745\) | −2.39105 | −0.0876014 | ||||||||
\(746\) | −26.5261 | −0.971189 | ||||||||
\(747\) | 29.8667 | 1.09276 | ||||||||
\(748\) | −3.30406 | −0.120808 | ||||||||
\(749\) | 13.6558 | 0.498971 | ||||||||
\(750\) | −7.89795 | −0.288393 | ||||||||
\(751\) | 31.8729 | 1.16306 | 0.581530 | − | 0.813525i | \(-0.302454\pi\) | ||||
0.581530 | + | 0.813525i | \(0.302454\pi\) | |||||||
\(752\) | −49.8912 | −1.81934 | ||||||||
\(753\) | −31.0621 | −1.13197 | ||||||||
\(754\) | 142.956 | 5.20614 | ||||||||
\(755\) | −13.7810 | −0.501543 | ||||||||
\(756\) | −51.0229 | −1.85568 | ||||||||
\(757\) | −27.4187 | −0.996548 | −0.498274 | − | 0.867020i | \(-0.666033\pi\) | ||||
−0.498274 | + | 0.867020i | \(0.666033\pi\) | |||||||
\(758\) | −25.3825 | −0.921934 | ||||||||
\(759\) | −13.8495 | −0.502706 | ||||||||
\(760\) | 42.8223 | 1.55333 | ||||||||
\(761\) | 2.80527 | 0.101691 | 0.0508455 | − | 0.998707i | \(-0.483808\pi\) | ||||
0.0508455 | + | 0.998707i | \(0.483808\pi\) | |||||||
\(762\) | 56.4061 | 2.04338 | ||||||||
\(763\) | −0.0225205 | −0.000815295 0 | ||||||||
\(764\) | −27.9161 | −1.00997 | ||||||||
\(765\) | 7.18967 | 0.259943 | ||||||||
\(766\) | −30.5305 | −1.10311 | ||||||||
\(767\) | 34.4050 | 1.24229 | ||||||||
\(768\) | −93.7636 | −3.38340 | ||||||||
\(769\) | 35.1929 | 1.26909 | 0.634544 | − | 0.772886i | \(-0.281188\pi\) | ||||
0.634544 | + | 0.772886i | \(0.281188\pi\) | |||||||
\(770\) | 1.76056 | 0.0634460 | ||||||||
\(771\) | 14.2426 | 0.512934 | ||||||||
\(772\) | 43.2841 | 1.55783 | ||||||||
\(773\) | −41.9774 | −1.50982 | −0.754910 | − | 0.655828i | \(-0.772320\pi\) | ||||
−0.754910 | + | 0.655828i | \(0.772320\pi\) | |||||||
\(774\) | 54.4450 | 1.95699 | ||||||||
\(775\) | −3.45726 | −0.124188 | ||||||||
\(776\) | 103.087 | 3.70060 | ||||||||
\(777\) | −9.99246 | −0.358478 | ||||||||
\(778\) | 15.8478 | 0.568172 | ||||||||
\(779\) | −86.1171 | −3.08546 | ||||||||
\(780\) | −95.1803 | −3.40800 | ||||||||
\(781\) | −4.83403 | −0.172975 | ||||||||
\(782\) | 17.4506 | 0.624031 | ||||||||
\(783\) | 94.0808 | 3.36217 | ||||||||
\(784\) | 6.78751 | 0.242411 | ||||||||
\(785\) | 14.4724 | 0.516543 | ||||||||
\(786\) | −20.7309 | −0.739445 | ||||||||
\(787\) | 19.3395 | 0.689377 | 0.344689 | − | 0.938717i | \(-0.387985\pi\) | ||||
0.344689 | + | 0.938717i | \(0.387985\pi\) | |||||||
\(788\) | 43.5796 | 1.55246 | ||||||||
\(789\) | −13.7108 | −0.488118 | ||||||||
\(790\) | 26.6504 | 0.948177 | ||||||||
\(791\) | 9.15269 | 0.325432 | ||||||||
\(792\) | 28.6856 | 1.01930 | ||||||||
\(793\) | 60.1320 | 2.13535 | ||||||||
\(794\) | 59.0908 | 2.09706 | ||||||||
\(795\) | 14.4491 | 0.512456 | ||||||||
\(796\) | 51.3345 | 1.81950 | ||||||||
\(797\) | 28.6379 | 1.01441 | 0.507203 | − | 0.861827i | \(-0.330680\pi\) | ||||
0.507203 | + | 0.861827i | \(0.330680\pi\) | |||||||
\(798\) | 54.7991 | 1.93987 | ||||||||
\(799\) | 7.89227 | 0.279209 | ||||||||
\(800\) | 4.87221 | 0.172259 | ||||||||
\(801\) | −71.1664 | −2.51454 | ||||||||
\(802\) | −32.7086 | −1.15498 | ||||||||
\(803\) | −0.491017 | −0.0173276 | ||||||||
\(804\) | 17.0275 | 0.600513 | ||||||||
\(805\) | −6.40773 | −0.225843 | ||||||||
\(806\) | −60.4604 | −2.12963 | ||||||||
\(807\) | 91.1732 | 3.20945 | ||||||||
\(808\) | −117.783 | −4.14357 | ||||||||
\(809\) | 51.2405 | 1.80152 | 0.900760 | − | 0.434317i | \(-0.143010\pi\) | ||||
0.900760 | + | 0.434317i | \(0.143010\pi\) | |||||||
\(810\) | −39.9461 | −1.40356 | ||||||||
\(811\) | −21.6619 | −0.760652 | −0.380326 | − | 0.924852i | \(-0.624188\pi\) | ||||
−0.380326 | + | 0.924852i | \(0.624188\pi\) | |||||||
\(812\) | −36.2401 | −1.27178 | ||||||||
\(813\) | −44.8642 | −1.57345 | ||||||||
\(814\) | 5.64969 | 0.198021 | ||||||||
\(815\) | 11.3530 | 0.397678 | ||||||||
\(816\) | −22.6933 | −0.794423 | ||||||||
\(817\) | −22.2423 | −0.778160 | ||||||||
\(818\) | 31.4559 | 1.09983 | ||||||||
\(819\) | −46.1682 | −1.61325 | ||||||||
\(820\) | −55.0246 | −1.92154 | ||||||||
\(821\) | 44.4385 | 1.55091 | 0.775457 | − | 0.631400i | \(-0.217520\pi\) | ||||
0.775457 | + | 0.631400i | \(0.217520\pi\) | |||||||
\(822\) | −26.8553 | −0.936686 | ||||||||
\(823\) | −45.4173 | −1.58315 | −0.791574 | − | 0.611073i | \(-0.790738\pi\) | ||||
−0.791574 | + | 0.611073i | \(0.790738\pi\) | |||||||
\(824\) | −22.9386 | −0.799103 | ||||||||
\(825\) | 2.16138 | 0.0752496 | ||||||||
\(826\) | −12.6566 | −0.440378 | ||||||||
\(827\) | 5.27897 | 0.183568 | 0.0917840 | − | 0.995779i | \(-0.470743\pi\) | ||||
0.0917840 | + | 0.995779i | \(0.470743\pi\) | |||||||
\(828\) | −190.218 | −6.61052 | ||||||||
\(829\) | −5.27399 | −0.183173 | −0.0915866 | − | 0.995797i | \(-0.529194\pi\) | ||||
−0.0915866 | + | 0.995797i | \(0.529194\pi\) | |||||||
\(830\) | −11.3131 | −0.392685 | ||||||||
\(831\) | 51.3688 | 1.78197 | ||||||||
\(832\) | −8.39215 | −0.290945 | ||||||||
\(833\) | −1.07371 | −0.0372020 | ||||||||
\(834\) | 119.476 | 4.13712 | ||||||||
\(835\) | 23.9335 | 0.828252 | ||||||||
\(836\) | −21.3510 | −0.738440 | ||||||||
\(837\) | −39.7897 | −1.37533 | ||||||||
\(838\) | 64.6287 | 2.23256 | ||||||||
\(839\) | −9.41643 | −0.325091 | −0.162546 | − | 0.986701i | \(-0.551970\pi\) | ||||
−0.162546 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(840\) | 19.2180 | 0.663086 | ||||||||
\(841\) | 37.8228 | 1.30424 | ||||||||
\(842\) | 40.2075 | 1.38564 | ||||||||
\(843\) | −60.0949 | −2.06978 | ||||||||
\(844\) | −128.247 | −4.41443 | ||||||||
\(845\) | −34.5385 | −1.18816 | ||||||||
\(846\) | −124.839 | −4.29205 | ||||||||
\(847\) | 10.5182 | 0.361410 | ||||||||
\(848\) | −31.4958 | −1.08157 | ||||||||
\(849\) | 13.6395 | 0.468106 | ||||||||
\(850\) | −2.72336 | −0.0934106 | ||||||||
\(851\) | −20.5626 | −0.704878 | ||||||||
\(852\) | −96.1392 | −3.29368 | ||||||||
\(853\) | 25.9727 | 0.889287 | 0.444643 | − | 0.895708i | \(-0.353330\pi\) | ||||
0.444643 | + | 0.895708i | \(0.353330\pi\) | |||||||
\(854\) | −22.1207 | −0.756956 | ||||||||
\(855\) | 46.4600 | 1.58890 | ||||||||
\(856\) | −84.2806 | −2.88065 | ||||||||
\(857\) | 36.0150 | 1.23025 | 0.615125 | − | 0.788429i | \(-0.289105\pi\) | ||||
0.615125 | + | 0.788429i | \(0.289105\pi\) | |||||||
\(858\) | 37.7981 | 1.29041 | ||||||||
\(859\) | 5.11809 | 0.174627 | 0.0873134 | − | 0.996181i | \(-0.472172\pi\) | ||||
0.0873134 | + | 0.996181i | \(0.472172\pi\) | |||||||
\(860\) | −14.2118 | −0.484617 | ||||||||
\(861\) | −38.6481 | −1.31712 | ||||||||
\(862\) | 68.8627 | 2.34547 | ||||||||
\(863\) | −30.1432 | −1.02609 | −0.513043 | − | 0.858363i | \(-0.671482\pi\) | ||||
−0.513043 | + | 0.858363i | \(0.671482\pi\) | |||||||
\(864\) | 56.0744 | 1.90769 | ||||||||
\(865\) | −22.1259 | −0.752303 | ||||||||
\(866\) | 95.0814 | 3.23100 | ||||||||
\(867\) | −49.3456 | −1.67587 | ||||||||
\(868\) | 15.3270 | 0.520234 | ||||||||
\(869\) | −7.29322 | −0.247406 | ||||||||
\(870\) | −64.5620 | −2.18886 | ||||||||
\(871\) | 8.50450 | 0.288164 | ||||||||
\(872\) | 0.138992 | 0.00470685 | ||||||||
\(873\) | 111.844 | 3.78534 | ||||||||
\(874\) | 112.766 | 3.81438 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −9.76535 | −0.329941 | ||||||||
\(877\) | −4.50267 | −0.152044 | −0.0760221 | − | 0.997106i | \(-0.524222\pi\) | ||||
−0.0760221 | + | 0.997106i | \(0.524222\pi\) | |||||||
\(878\) | 70.1338 | 2.36690 | ||||||||
\(879\) | −28.9131 | −0.975213 | ||||||||
\(880\) | −4.71133 | −0.158819 | ||||||||
\(881\) | −5.48375 | −0.184752 | −0.0923761 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923761 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(882\) | 16.9839 | 0.571877 | ||||||||
\(883\) | −1.62232 | −0.0545954 | −0.0272977 | − | 0.999627i | \(-0.508690\pi\) | ||||
−0.0272977 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(884\) | −32.8200 | −1.10385 | ||||||||
\(885\) | −15.5381 | −0.522306 | ||||||||
\(886\) | 41.7513 | 1.40266 | ||||||||
\(887\) | 3.13140 | 0.105142 | 0.0525710 | − | 0.998617i | \(-0.483258\pi\) | ||||
0.0525710 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(888\) | 61.6714 | 2.06956 | ||||||||
\(889\) | −7.14187 | −0.239531 | ||||||||
\(890\) | 26.9570 | 0.903601 | ||||||||
\(891\) | 10.9318 | 0.366228 | ||||||||
\(892\) | −72.2130 | −2.41787 | ||||||||
\(893\) | 51.0002 | 1.70666 | ||||||||
\(894\) | 18.8844 | 0.631590 | ||||||||
\(895\) | 13.2390 | 0.442530 | ||||||||
\(896\) | 12.8316 | 0.428675 | ||||||||
\(897\) | −137.570 | −4.59334 | ||||||||
\(898\) | −86.1791 | −2.87583 | ||||||||
\(899\) | −28.2614 | −0.942572 | ||||||||
\(900\) | 29.6857 | 0.989522 | ||||||||
\(901\) | 4.98231 | 0.165985 | ||||||||
\(902\) | 21.8515 | 0.727574 | ||||||||
\(903\) | −9.98204 | −0.332181 | ||||||||
\(904\) | −56.4885 | −1.87878 | ||||||||
\(905\) | 24.5051 | 0.814577 | ||||||||
\(906\) | 108.842 | 3.61603 | ||||||||
\(907\) | 41.6263 | 1.38218 | 0.691090 | − | 0.722769i | \(-0.257131\pi\) | ||||
0.691090 | + | 0.722769i | \(0.257131\pi\) | |||||||
\(908\) | 42.7351 | 1.41821 | ||||||||
\(909\) | −127.788 | −4.23846 | ||||||||
\(910\) | 17.4880 | 0.579721 | ||||||||
\(911\) | −19.8906 | −0.659004 | −0.329502 | − | 0.944155i | \(-0.606881\pi\) | ||||
−0.329502 | + | 0.944155i | \(0.606881\pi\) | |||||||
\(912\) | −146.645 | −4.85590 | ||||||||
\(913\) | 3.09599 | 0.102462 | ||||||||
\(914\) | 22.5919 | 0.747275 | ||||||||
\(915\) | −27.1569 | −0.897781 | ||||||||
\(916\) | 4.43329 | 0.146480 | ||||||||
\(917\) | 2.62484 | 0.0866798 | ||||||||
\(918\) | −31.3432 | −1.03448 | ||||||||
\(919\) | −43.0877 | −1.42133 | −0.710667 | − | 0.703529i | \(-0.751607\pi\) | ||||
−0.710667 | + | 0.703529i | \(0.751607\pi\) | |||||||
\(920\) | 39.5472 | 1.30383 | ||||||||
\(921\) | 37.0773 | 1.22174 | ||||||||
\(922\) | 0.643560 | 0.0211945 | ||||||||
\(923\) | −48.0174 | −1.58051 | ||||||||
\(924\) | −9.58203 | −0.315226 | ||||||||
\(925\) | 3.20904 | 0.105512 | ||||||||
\(926\) | −56.6772 | −1.86253 | ||||||||
\(927\) | −24.8871 | −0.817401 | ||||||||
\(928\) | 39.8280 | 1.30742 | ||||||||
\(929\) | −20.6800 | −0.678490 | −0.339245 | − | 0.940698i | \(-0.610172\pi\) | ||||
−0.339245 | + | 0.940698i | \(0.610172\pi\) | |||||||
\(930\) | 27.3053 | 0.895375 | ||||||||
\(931\) | −6.93839 | −0.227397 | ||||||||
\(932\) | 38.3580 | 1.25646 | ||||||||
\(933\) | 29.1145 | 0.953166 | ||||||||
\(934\) | 91.1723 | 2.98325 | ||||||||
\(935\) | 0.745284 | 0.0243734 | ||||||||
\(936\) | 284.940 | 9.31357 | ||||||||
\(937\) | 35.2520 | 1.15163 | 0.575816 | − | 0.817579i | \(-0.304684\pi\) | ||||
0.575816 | + | 0.817579i | \(0.304684\pi\) | |||||||
\(938\) | −3.12855 | −0.102151 | ||||||||
\(939\) | −10.3064 | −0.336338 | ||||||||
\(940\) | 32.5867 | 1.06286 | ||||||||
\(941\) | 38.6480 | 1.25989 | 0.629945 | − | 0.776640i | \(-0.283077\pi\) | ||||
0.629945 | + | 0.776640i | \(0.283077\pi\) | |||||||
\(942\) | −114.303 | −3.72418 | ||||||||
\(943\) | −79.5307 | −2.58988 | ||||||||
\(944\) | 33.8696 | 1.10236 | ||||||||
\(945\) | 11.5090 | 0.374389 | ||||||||
\(946\) | 5.64379 | 0.183495 | ||||||||
\(947\) | 49.5153 | 1.60903 | 0.804516 | − | 0.593932i | \(-0.202425\pi\) | ||||
0.804516 | + | 0.593932i | \(0.202425\pi\) | |||||||
\(948\) | −145.048 | −4.71093 | ||||||||
\(949\) | −4.87737 | −0.158326 | ||||||||
\(950\) | −17.5985 | −0.570970 | ||||||||
\(951\) | −1.27765 | −0.0414306 | ||||||||
\(952\) | 6.62674 | 0.214774 | ||||||||
\(953\) | 28.4065 | 0.920176 | 0.460088 | − | 0.887873i | \(-0.347818\pi\) | ||||
0.460088 | + | 0.887873i | \(0.347818\pi\) | |||||||
\(954\) | −78.8096 | −2.55155 | ||||||||
\(955\) | 6.29692 | 0.203763 | ||||||||
\(956\) | 91.1606 | 2.94834 | ||||||||
\(957\) | 17.6682 | 0.571133 | ||||||||
\(958\) | −36.2177 | −1.17014 | ||||||||
\(959\) | 3.40028 | 0.109801 | ||||||||
\(960\) | 3.79008 | 0.122324 | ||||||||
\(961\) | −19.0474 | −0.614431 | ||||||||
\(962\) | 56.1195 | 1.80937 | ||||||||
\(963\) | −91.4401 | −2.94661 | ||||||||
\(964\) | 1.20454 | 0.0387956 | ||||||||
\(965\) | −9.76342 | −0.314296 | ||||||||
\(966\) | 50.6080 | 1.62828 | ||||||||
\(967\) | 0.0613950 | 0.00197433 | 0.000987166 | − | 1.00000i | \(-0.499686\pi\) | ||||
0.000987166 | 1.00000i | \(0.499686\pi\) | ||||||||
\(968\) | −64.9162 | −2.08648 | ||||||||
\(969\) | 23.1977 | 0.745218 | ||||||||
\(970\) | −42.3651 | −1.36026 | ||||||||
\(971\) | −3.13614 | −0.100643 | −0.0503217 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503217 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(972\) | 64.3427 | 2.06379 | ||||||||
\(973\) | −15.1275 | −0.484965 | ||||||||
\(974\) | −6.96092 | −0.223042 | ||||||||
\(975\) | 21.4694 | 0.687572 | ||||||||
\(976\) | 59.1962 | 1.89482 | ||||||||
\(977\) | −58.3101 | −1.86551 | −0.932753 | − | 0.360517i | \(-0.882600\pi\) | ||||
−0.932753 | + | 0.360517i | \(0.882600\pi\) | |||||||
\(978\) | −89.6655 | −2.86719 | ||||||||
\(979\) | −7.37714 | −0.235774 | ||||||||
\(980\) | −4.43329 | −0.141616 | ||||||||
\(981\) | 0.150799 | 0.00481463 | ||||||||
\(982\) | −24.7544 | −0.789944 | ||||||||
\(983\) | 6.56017 | 0.209237 | 0.104618 | − | 0.994512i | \(-0.466638\pi\) | ||||
0.104618 | + | 0.994512i | \(0.466638\pi\) | |||||||
\(984\) | 238.528 | 7.60400 | ||||||||
\(985\) | −9.83007 | −0.313212 | ||||||||
\(986\) | −22.2622 | −0.708973 | ||||||||
\(987\) | 22.8882 | 0.728539 | ||||||||
\(988\) | −212.084 | −6.74729 | ||||||||
\(989\) | −20.5412 | −0.653172 | ||||||||
\(990\) | −11.7888 | −0.374673 | ||||||||
\(991\) | −43.4062 | −1.37884 | −0.689422 | − | 0.724360i | \(-0.742135\pi\) | ||||
−0.689422 | + | 0.724360i | \(0.742135\pi\) | |||||||
\(992\) | −16.8445 | −0.534813 | ||||||||
\(993\) | 10.4840 | 0.332700 | ||||||||
\(994\) | 17.6642 | 0.560273 | ||||||||
\(995\) | −11.5793 | −0.367089 | ||||||||
\(996\) | 61.5731 | 1.95102 | ||||||||
\(997\) | −27.4582 | −0.869611 | −0.434805 | − | 0.900524i | \(-0.643183\pi\) | ||||
−0.434805 | + | 0.900524i | \(0.643183\pi\) | |||||||
\(998\) | −33.9787 | −1.07558 | ||||||||
\(999\) | 36.9329 | 1.16850 |
(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 | 8015.2.a.l.1.58 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.58 | ✓ | 62 | 1.1 | even | 1 | trivial |