Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,4,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(85.0217523183\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.81294 | −1.70163 | −0.850816 | − | 0.525464i | \(-0.823892\pi\) | ||||
−0.850816 | + | 0.525464i | \(0.823892\pi\) | |||||||
\(3\) | 2.88277 | 0.554790 | 0.277395 | − | 0.960756i | \(-0.410529\pi\) | ||||
0.277395 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(4\) | 15.1644 | 1.89555 | ||||||||
\(5\) | −12.4285 | −1.11164 | −0.555821 | − | 0.831302i | \(-0.687596\pi\) | ||||
−0.555821 | + | 0.831302i | \(0.687596\pi\) | |||||||
\(6\) | −13.8746 | −0.944048 | ||||||||
\(7\) | −12.7070 | −0.686112 | −0.343056 | − | 0.939315i | \(-0.611462\pi\) | ||||
−0.343056 | + | 0.939315i | \(0.611462\pi\) | |||||||
\(8\) | −34.4818 | −1.52389 | ||||||||
\(9\) | −18.6896 | −0.692208 | ||||||||
\(10\) | 59.8178 | 1.89160 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 43.7155 | 1.05163 | ||||||||
\(13\) | 69.0410 | 1.47296 | 0.736482 | − | 0.676457i | \(-0.236485\pi\) | ||||
0.736482 | + | 0.676457i | \(0.236485\pi\) | |||||||
\(14\) | 61.1579 | 1.16751 | ||||||||
\(15\) | −35.8286 | −0.616728 | ||||||||
\(16\) | 44.6437 | 0.697558 | ||||||||
\(17\) | −79.5521 | −1.13495 | −0.567477 | − | 0.823389i | \(-0.692080\pi\) | ||||
−0.567477 | + | 0.823389i | \(0.692080\pi\) | |||||||
\(18\) | 89.9520 | 1.17788 | ||||||||
\(19\) | 112.287 | 1.35581 | 0.677904 | − | 0.735151i | \(-0.262889\pi\) | ||||
0.677904 | + | 0.735151i | \(0.262889\pi\) | |||||||
\(20\) | −188.471 | −2.10717 | ||||||||
\(21\) | −36.6313 | −0.380648 | ||||||||
\(22\) | −52.9423 | −0.513061 | ||||||||
\(23\) | −122.870 | −1.11392 | −0.556961 | − | 0.830539i | \(-0.688033\pi\) | ||||
−0.556961 | + | 0.830539i | \(0.688033\pi\) | |||||||
\(24\) | −99.4032 | −0.845442 | ||||||||
\(25\) | 29.4683 | 0.235747 | ||||||||
\(26\) | −332.290 | −2.50644 | ||||||||
\(27\) | −131.713 | −0.938820 | ||||||||
\(28\) | −192.694 | −1.30056 | ||||||||
\(29\) | −146.473 | −0.937910 | −0.468955 | − | 0.883222i | \(-0.655369\pi\) | ||||
−0.468955 | + | 0.883222i | \(0.655369\pi\) | |||||||
\(30\) | 172.441 | 1.04944 | ||||||||
\(31\) | 198.735 | 1.15142 | 0.575709 | − | 0.817655i | \(-0.304726\pi\) | ||||
0.575709 | + | 0.817655i | \(0.304726\pi\) | |||||||
\(32\) | 60.9869 | 0.336908 | ||||||||
\(33\) | 31.7105 | 0.167275 | ||||||||
\(34\) | 382.879 | 1.93127 | ||||||||
\(35\) | 157.929 | 0.762711 | ||||||||
\(36\) | −283.417 | −1.31211 | ||||||||
\(37\) | 265.049 | 1.17767 | 0.588836 | − | 0.808253i | \(-0.299586\pi\) | ||||
0.588836 | + | 0.808253i | \(0.299586\pi\) | |||||||
\(38\) | −540.429 | −2.30708 | ||||||||
\(39\) | 199.030 | 0.817186 | ||||||||
\(40\) | 428.558 | 1.69402 | ||||||||
\(41\) | 26.8558 | 0.102297 | 0.0511484 | − | 0.998691i | \(-0.483712\pi\) | ||||
0.0511484 | + | 0.998691i | \(0.483712\pi\) | |||||||
\(42\) | 176.304 | 0.647723 | ||||||||
\(43\) | −6.45965 | −0.0229090 | −0.0114545 | − | 0.999934i | \(-0.503646\pi\) | ||||
−0.0114545 | + | 0.999934i | \(0.503646\pi\) | |||||||
\(44\) | 166.808 | 0.571530 | ||||||||
\(45\) | 232.284 | 0.769487 | ||||||||
\(46\) | 591.366 | 1.89548 | ||||||||
\(47\) | 495.176 | 1.53678 | 0.768392 | − | 0.639979i | \(-0.221057\pi\) | ||||
0.768392 | + | 0.639979i | \(0.221057\pi\) | |||||||
\(48\) | 128.698 | 0.386998 | ||||||||
\(49\) | −181.533 | −0.529250 | ||||||||
\(50\) | −141.829 | −0.401154 | ||||||||
\(51\) | −229.331 | −0.629661 | ||||||||
\(52\) | 1046.97 | 2.79208 | ||||||||
\(53\) | −5.15724 | −0.0133661 | −0.00668303 | − | 0.999978i | \(-0.502127\pi\) | ||||
−0.00668303 | + | 0.999978i | \(0.502127\pi\) | |||||||
\(54\) | 633.926 | 1.59753 | ||||||||
\(55\) | −136.714 | −0.335173 | ||||||||
\(56\) | 438.159 | 1.04556 | ||||||||
\(57\) | 323.697 | 0.752188 | ||||||||
\(58\) | 704.967 | 1.59598 | ||||||||
\(59\) | 108.052 | 0.238426 | 0.119213 | − | 0.992869i | \(-0.461963\pi\) | ||||
0.119213 | + | 0.992869i | \(0.461963\pi\) | |||||||
\(60\) | −543.320 | −1.16904 | ||||||||
\(61\) | 109.201 | 0.229210 | 0.114605 | − | 0.993411i | \(-0.463440\pi\) | ||||
0.114605 | + | 0.993411i | \(0.463440\pi\) | |||||||
\(62\) | −956.502 | −1.95929 | ||||||||
\(63\) | 237.488 | 0.474932 | ||||||||
\(64\) | −650.676 | −1.27085 | ||||||||
\(65\) | −858.079 | −1.63741 | ||||||||
\(66\) | −152.621 | −0.284641 | ||||||||
\(67\) | 269.510 | 0.491431 | 0.245715 | − | 0.969342i | \(-0.420977\pi\) | ||||
0.245715 | + | 0.969342i | \(0.420977\pi\) | |||||||
\(68\) | −1206.36 | −2.15136 | ||||||||
\(69\) | −354.207 | −0.617992 | ||||||||
\(70\) | −760.103 | −1.29785 | ||||||||
\(71\) | −33.3057 | −0.0556713 | −0.0278356 | − | 0.999613i | \(-0.508862\pi\) | ||||
−0.0278356 | + | 0.999613i | \(0.508862\pi\) | |||||||
\(72\) | 644.452 | 1.05485 | ||||||||
\(73\) | −481.037 | −0.771249 | −0.385624 | − | 0.922656i | \(-0.626014\pi\) | ||||
−0.385624 | + | 0.922656i | \(0.626014\pi\) | |||||||
\(74\) | −1275.67 | −2.00396 | ||||||||
\(75\) | 84.9505 | 0.130790 | ||||||||
\(76\) | 1702.76 | 2.57000 | ||||||||
\(77\) | −139.777 | −0.206871 | ||||||||
\(78\) | −957.918 | −1.39055 | ||||||||
\(79\) | 694.397 | 0.988934 | 0.494467 | − | 0.869196i | \(-0.335363\pi\) | ||||
0.494467 | + | 0.869196i | \(0.335363\pi\) | |||||||
\(80\) | −554.856 | −0.775434 | ||||||||
\(81\) | 124.921 | 0.171360 | ||||||||
\(82\) | −129.255 | −0.174071 | ||||||||
\(83\) | 1483.15 | 1.96141 | 0.980706 | − | 0.195490i | \(-0.0626298\pi\) | ||||
0.980706 | + | 0.195490i | \(0.0626298\pi\) | |||||||
\(84\) | −555.492 | −0.721537 | ||||||||
\(85\) | 988.715 | 1.26166 | ||||||||
\(86\) | 31.0899 | 0.0389827 | ||||||||
\(87\) | −422.249 | −0.520343 | ||||||||
\(88\) | −379.300 | −0.459472 | ||||||||
\(89\) | −1242.93 | −1.48034 | −0.740170 | − | 0.672420i | \(-0.765255\pi\) | ||||
−0.740170 | + | 0.672420i | \(0.765255\pi\) | |||||||
\(90\) | −1117.97 | −1.30938 | ||||||||
\(91\) | −877.303 | −1.01062 | ||||||||
\(92\) | −1863.25 | −2.11149 | ||||||||
\(93\) | 572.909 | 0.638795 | ||||||||
\(94\) | −2383.25 | −2.61504 | ||||||||
\(95\) | −1395.56 | −1.50717 | ||||||||
\(96\) | 175.811 | 0.186913 | ||||||||
\(97\) | −994.914 | −1.04142 | −0.520712 | − | 0.853732i | \(-0.674334\pi\) | ||||
−0.520712 | + | 0.853732i | \(0.674334\pi\) | |||||||
\(98\) | 873.707 | 0.900589 | ||||||||
\(99\) | −205.586 | −0.208709 | ||||||||
\(100\) | 446.869 | 0.446869 | ||||||||
\(101\) | 1093.92 | 1.07772 | 0.538858 | − | 0.842396i | \(-0.318856\pi\) | ||||
0.538858 | + | 0.842396i | \(0.318856\pi\) | |||||||
\(102\) | 1103.75 | 1.07145 | ||||||||
\(103\) | 722.486 | 0.691152 | 0.345576 | − | 0.938391i | \(-0.387684\pi\) | ||||
0.345576 | + | 0.938391i | \(0.387684\pi\) | |||||||
\(104\) | −2380.66 | −2.24464 | ||||||||
\(105\) | 455.274 | 0.423144 | ||||||||
\(106\) | 24.8215 | 0.0227441 | ||||||||
\(107\) | −1371.36 | −1.23901 | −0.619505 | − | 0.784993i | \(-0.712667\pi\) | ||||
−0.619505 | + | 0.784993i | \(0.712667\pi\) | |||||||
\(108\) | −1997.35 | −1.77958 | ||||||||
\(109\) | 592.866 | 0.520975 | 0.260488 | − | 0.965477i | \(-0.416117\pi\) | ||||
0.260488 | + | 0.965477i | \(0.416117\pi\) | |||||||
\(110\) | 657.995 | 0.570340 | ||||||||
\(111\) | 764.078 | 0.653361 | ||||||||
\(112\) | −567.287 | −0.478603 | ||||||||
\(113\) | 327.515 | 0.272655 | 0.136327 | − | 0.990664i | \(-0.456470\pi\) | ||||
0.136327 | + | 0.990664i | \(0.456470\pi\) | |||||||
\(114\) | −1557.94 | −1.27995 | ||||||||
\(115\) | 1527.09 | 1.23828 | ||||||||
\(116\) | −2221.18 | −1.77786 | ||||||||
\(117\) | −1290.35 | −1.01960 | ||||||||
\(118\) | −520.047 | −0.405714 | ||||||||
\(119\) | 1010.87 | 0.778705 | ||||||||
\(120\) | 1235.44 | 0.939828 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −525.580 | −0.390031 | ||||||||
\(123\) | 77.4191 | 0.0567532 | ||||||||
\(124\) | 3013.70 | 2.18257 | ||||||||
\(125\) | 1187.32 | 0.849576 | ||||||||
\(126\) | −1143.02 | −0.808160 | ||||||||
\(127\) | 23.2120 | 0.0162184 | 0.00810919 | − | 0.999967i | \(-0.497419\pi\) | ||||
0.00810919 | + | 0.999967i | \(0.497419\pi\) | |||||||
\(128\) | 2643.77 | 1.82561 | ||||||||
\(129\) | −18.6217 | −0.0127097 | ||||||||
\(130\) | 4129.88 | 2.78627 | ||||||||
\(131\) | −131.000 | −0.0873704 | ||||||||
\(132\) | 480.871 | 0.317079 | ||||||||
\(133\) | −1426.82 | −0.930236 | ||||||||
\(134\) | −1297.13 | −0.836234 | ||||||||
\(135\) | 1637.00 | 1.04363 | ||||||||
\(136\) | 2743.10 | 1.72955 | ||||||||
\(137\) | −9.30853 | −0.00580498 | −0.00290249 | − | 0.999996i | \(-0.500924\pi\) | ||||
−0.00290249 | + | 0.999996i | \(0.500924\pi\) | |||||||
\(138\) | 1704.78 | 1.05160 | ||||||||
\(139\) | −1774.82 | −1.08301 | −0.541506 | − | 0.840697i | \(-0.682146\pi\) | ||||
−0.541506 | + | 0.840697i | \(0.682146\pi\) | |||||||
\(140\) | 2394.90 | 1.44576 | ||||||||
\(141\) | 1427.48 | 0.852592 | ||||||||
\(142\) | 160.298 | 0.0947320 | ||||||||
\(143\) | 759.451 | 0.444116 | ||||||||
\(144\) | −834.374 | −0.482855 | ||||||||
\(145\) | 1820.45 | 1.04262 | ||||||||
\(146\) | 2315.20 | 1.31238 | ||||||||
\(147\) | −523.318 | −0.293623 | ||||||||
\(148\) | 4019.31 | 2.23234 | ||||||||
\(149\) | −842.339 | −0.463135 | −0.231567 | − | 0.972819i | \(-0.574385\pi\) | ||||
−0.231567 | + | 0.972819i | \(0.574385\pi\) | |||||||
\(150\) | −408.862 | −0.222556 | ||||||||
\(151\) | −2773.37 | −1.49466 | −0.747331 | − | 0.664452i | \(-0.768665\pi\) | ||||
−0.747331 | + | 0.664452i | \(0.768665\pi\) | |||||||
\(152\) | −3871.85 | −2.06611 | ||||||||
\(153\) | 1486.80 | 0.785624 | ||||||||
\(154\) | 672.737 | 0.352017 | ||||||||
\(155\) | −2469.99 | −1.27996 | ||||||||
\(156\) | 3018.17 | 1.54902 | ||||||||
\(157\) | −2130.05 | −1.08278 | −0.541391 | − | 0.840771i | \(-0.682102\pi\) | ||||
−0.541391 | + | 0.840771i | \(0.682102\pi\) | |||||||
\(158\) | −3342.09 | −1.68280 | ||||||||
\(159\) | −14.8671 | −0.00741535 | ||||||||
\(160\) | −757.977 | −0.374521 | ||||||||
\(161\) | 1561.31 | 0.764275 | ||||||||
\(162\) | −601.239 | −0.291591 | ||||||||
\(163\) | 3457.25 | 1.66130 | 0.830652 | − | 0.556792i | \(-0.187968\pi\) | ||||
0.830652 | + | 0.556792i | \(0.187968\pi\) | |||||||
\(164\) | 407.252 | 0.193909 | ||||||||
\(165\) | −394.115 | −0.185950 | ||||||||
\(166\) | −7138.32 | −3.33760 | ||||||||
\(167\) | 1359.97 | 0.630167 | 0.315083 | − | 0.949064i | \(-0.397968\pi\) | ||||
0.315083 | + | 0.949064i | \(0.397968\pi\) | |||||||
\(168\) | 1263.11 | 0.580068 | ||||||||
\(169\) | 2569.67 | 1.16962 | ||||||||
\(170\) | −4758.63 | −2.14688 | ||||||||
\(171\) | −2098.60 | −0.938501 | ||||||||
\(172\) | −97.9567 | −0.0434252 | ||||||||
\(173\) | −967.698 | −0.425276 | −0.212638 | − | 0.977131i | \(-0.568206\pi\) | ||||
−0.212638 | + | 0.977131i | \(0.568206\pi\) | |||||||
\(174\) | 2032.26 | 0.885433 | ||||||||
\(175\) | −374.453 | −0.161749 | ||||||||
\(176\) | 491.081 | 0.210322 | ||||||||
\(177\) | 311.489 | 0.132276 | ||||||||
\(178\) | 5982.14 | 2.51899 | ||||||||
\(179\) | −3121.28 | −1.30333 | −0.651663 | − | 0.758509i | \(-0.725928\pi\) | ||||
−0.651663 | + | 0.758509i | \(0.725928\pi\) | |||||||
\(180\) | 3522.45 | 1.45860 | ||||||||
\(181\) | 673.200 | 0.276456 | 0.138228 | − | 0.990400i | \(-0.455859\pi\) | ||||
0.138228 | + | 0.990400i | \(0.455859\pi\) | |||||||
\(182\) | 4222.41 | 1.71970 | ||||||||
\(183\) | 314.803 | 0.127163 | ||||||||
\(184\) | 4236.78 | 1.69750 | ||||||||
\(185\) | −3294.17 | −1.30915 | ||||||||
\(186\) | −2757.38 | −1.08699 | ||||||||
\(187\) | −875.073 | −0.342201 | ||||||||
\(188\) | 7509.05 | 2.91305 | ||||||||
\(189\) | 1673.67 | 0.644136 | ||||||||
\(190\) | 6716.74 | 2.56465 | ||||||||
\(191\) | 2224.34 | 0.842658 | 0.421329 | − | 0.906908i | \(-0.361564\pi\) | ||||
0.421329 | + | 0.906908i | \(0.361564\pi\) | |||||||
\(192\) | −1875.75 | −0.705056 | ||||||||
\(193\) | −1442.29 | −0.537918 | −0.268959 | − | 0.963152i | \(-0.586680\pi\) | ||||
−0.268959 | + | 0.963152i | \(0.586680\pi\) | |||||||
\(194\) | 4788.46 | 1.77212 | ||||||||
\(195\) | −2473.65 | −0.908418 | ||||||||
\(196\) | −2752.84 | −1.00322 | ||||||||
\(197\) | 1557.92 | 0.563438 | 0.281719 | − | 0.959497i | \(-0.409095\pi\) | ||||
0.281719 | + | 0.959497i | \(0.409095\pi\) | |||||||
\(198\) | 989.472 | 0.355145 | ||||||||
\(199\) | 2261.71 | 0.805671 | 0.402835 | − | 0.915272i | \(-0.368025\pi\) | ||||
0.402835 | + | 0.915272i | \(0.368025\pi\) | |||||||
\(200\) | −1016.12 | −0.359253 | ||||||||
\(201\) | 776.936 | 0.272641 | ||||||||
\(202\) | −5264.99 | −1.83388 | ||||||||
\(203\) | 1861.23 | 0.643512 | ||||||||
\(204\) | −3477.66 | −1.19355 | ||||||||
\(205\) | −333.778 | −0.113717 | ||||||||
\(206\) | −3477.28 | −1.17609 | ||||||||
\(207\) | 2296.39 | 0.771065 | ||||||||
\(208\) | 3082.25 | 1.02748 | ||||||||
\(209\) | 1235.15 | 0.408791 | ||||||||
\(210\) | −2191.20 | −0.720036 | ||||||||
\(211\) | 3227.11 | 1.05291 | 0.526454 | − | 0.850204i | \(-0.323521\pi\) | ||||
0.526454 | + | 0.850204i | \(0.323521\pi\) | |||||||
\(212\) | −78.2064 | −0.0253360 | ||||||||
\(213\) | −96.0128 | −0.0308859 | ||||||||
\(214\) | 6600.26 | 2.10834 | ||||||||
\(215\) | 80.2840 | 0.0254666 | ||||||||
\(216\) | 4541.70 | 1.43066 | ||||||||
\(217\) | −2525.33 | −0.790001 | ||||||||
\(218\) | −2853.43 | −0.886508 | ||||||||
\(219\) | −1386.72 | −0.427881 | ||||||||
\(220\) | −2073.18 | −0.635336 | ||||||||
\(221\) | −5492.36 | −1.67175 | ||||||||
\(222\) | −3677.46 | −1.11178 | ||||||||
\(223\) | 1205.99 | 0.362150 | 0.181075 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181075 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(224\) | −774.959 | −0.231157 | ||||||||
\(225\) | −550.752 | −0.163186 | ||||||||
\(226\) | −1576.31 | −0.463958 | ||||||||
\(227\) | −2479.50 | −0.724979 | −0.362490 | − | 0.931988i | \(-0.618073\pi\) | ||||
−0.362490 | + | 0.931988i | \(0.618073\pi\) | |||||||
\(228\) | 4908.67 | 1.42581 | ||||||||
\(229\) | −3428.15 | −0.989250 | −0.494625 | − | 0.869106i | \(-0.664695\pi\) | ||||
−0.494625 | + | 0.869106i | \(0.664695\pi\) | |||||||
\(230\) | −7349.81 | −2.10710 | ||||||||
\(231\) | −402.945 | −0.114770 | ||||||||
\(232\) | 5050.66 | 1.42928 | ||||||||
\(233\) | −1951.25 | −0.548630 | −0.274315 | − | 0.961640i | \(-0.588451\pi\) | ||||
−0.274315 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(234\) | 6210.38 | 1.73498 | ||||||||
\(235\) | −6154.31 | −1.70835 | ||||||||
\(236\) | 1638.54 | 0.451949 | ||||||||
\(237\) | 2001.79 | 0.548651 | ||||||||
\(238\) | −4865.24 | −1.32507 | ||||||||
\(239\) | −4077.36 | −1.10352 | −0.551762 | − | 0.834002i | \(-0.686044\pi\) | ||||
−0.551762 | + | 0.834002i | \(0.686044\pi\) | |||||||
\(240\) | −1599.52 | −0.430203 | ||||||||
\(241\) | −3335.97 | −0.891653 | −0.445827 | − | 0.895119i | \(-0.647090\pi\) | ||||
−0.445827 | + | 0.895119i | \(0.647090\pi\) | |||||||
\(242\) | −582.366 | −0.154694 | ||||||||
\(243\) | 3916.37 | 1.03389 | ||||||||
\(244\) | 1655.97 | 0.434479 | ||||||||
\(245\) | 2256.19 | 0.588336 | ||||||||
\(246\) | −372.614 | −0.0965731 | ||||||||
\(247\) | 7752.39 | 1.99706 | ||||||||
\(248\) | −6852.76 | −1.75464 | ||||||||
\(249\) | 4275.59 | 1.08817 | ||||||||
\(250\) | −5714.49 | −1.44566 | ||||||||
\(251\) | 5700.17 | 1.43343 | 0.716717 | − | 0.697365i | \(-0.245644\pi\) | ||||
0.716717 | + | 0.697365i | \(0.245644\pi\) | |||||||
\(252\) | 3601.37 | 0.900258 | ||||||||
\(253\) | −1351.57 | −0.335860 | ||||||||
\(254\) | −111.718 | −0.0275977 | ||||||||
\(255\) | 2850.24 | 0.699957 | ||||||||
\(256\) | −7518.90 | −1.83567 | ||||||||
\(257\) | 957.717 | 0.232454 | 0.116227 | − | 0.993223i | \(-0.462920\pi\) | ||||
0.116227 | + | 0.993223i | \(0.462920\pi\) | |||||||
\(258\) | 89.6252 | 0.0216272 | ||||||||
\(259\) | −3367.98 | −0.808015 | ||||||||
\(260\) | −13012.2 | −3.10379 | ||||||||
\(261\) | 2737.53 | 0.649229 | ||||||||
\(262\) | 630.495 | 0.148672 | ||||||||
\(263\) | −3477.86 | −0.815414 | −0.407707 | − | 0.913113i | \(-0.633672\pi\) | ||||
−0.407707 | + | 0.913113i | \(0.633672\pi\) | |||||||
\(264\) | −1093.44 | −0.254910 | ||||||||
\(265\) | 64.0969 | 0.0148583 | ||||||||
\(266\) | 6867.22 | 1.58292 | ||||||||
\(267\) | −3583.08 | −0.821277 | ||||||||
\(268\) | 4086.95 | 0.931531 | ||||||||
\(269\) | −7097.25 | −1.60865 | −0.804326 | − | 0.594189i | \(-0.797473\pi\) | ||||
−0.804326 | + | 0.594189i | \(0.797473\pi\) | |||||||
\(270\) | −7878.77 | −1.77588 | ||||||||
\(271\) | −7743.09 | −1.73564 | −0.867821 | − | 0.496877i | \(-0.834480\pi\) | ||||
−0.867821 | + | 0.496877i | \(0.834480\pi\) | |||||||
\(272\) | −3551.50 | −0.791696 | ||||||||
\(273\) | −2529.07 | −0.560681 | ||||||||
\(274\) | 44.8014 | 0.00987793 | ||||||||
\(275\) | 324.152 | 0.0710803 | ||||||||
\(276\) | −5371.33 | −1.17143 | ||||||||
\(277\) | −1739.02 | −0.377212 | −0.188606 | − | 0.982053i | \(-0.560397\pi\) | ||||
−0.188606 | + | 0.982053i | \(0.560397\pi\) | |||||||
\(278\) | 8542.12 | 1.84289 | ||||||||
\(279\) | −3714.29 | −0.797020 | ||||||||
\(280\) | −5445.68 | −1.16229 | ||||||||
\(281\) | −6087.61 | −1.29237 | −0.646186 | − | 0.763180i | \(-0.723637\pi\) | ||||
−0.646186 | + | 0.763180i | \(0.723637\pi\) | |||||||
\(282\) | −6870.38 | −1.45080 | ||||||||
\(283\) | −7485.51 | −1.57232 | −0.786161 | − | 0.618021i | \(-0.787935\pi\) | ||||
−0.786161 | + | 0.618021i | \(0.787935\pi\) | |||||||
\(284\) | −505.061 | −0.105528 | ||||||||
\(285\) | −4023.08 | −0.836164 | ||||||||
\(286\) | −3655.19 | −0.755721 | ||||||||
\(287\) | −341.256 | −0.0701871 | ||||||||
\(288\) | −1139.82 | −0.233211 | ||||||||
\(289\) | 1415.53 | 0.288119 | ||||||||
\(290\) | −8761.70 | −1.77416 | ||||||||
\(291\) | −2868.11 | −0.577772 | ||||||||
\(292\) | −7294.64 | −1.46194 | ||||||||
\(293\) | −5674.34 | −1.13139 | −0.565697 | − | 0.824613i | \(-0.691393\pi\) | ||||
−0.565697 | + | 0.824613i | \(0.691393\pi\) | |||||||
\(294\) | 2518.70 | 0.499638 | ||||||||
\(295\) | −1342.92 | −0.265044 | ||||||||
\(296\) | −9139.38 | −1.79465 | ||||||||
\(297\) | −1448.84 | −0.283065 | ||||||||
\(298\) | 4054.13 | 0.788085 | ||||||||
\(299\) | −8483.08 | −1.64077 | ||||||||
\(300\) | 1288.22 | 0.247919 | ||||||||
\(301\) | 82.0826 | 0.0157182 | ||||||||
\(302\) | 13348.1 | 2.54336 | ||||||||
\(303\) | 3153.53 | 0.597907 | ||||||||
\(304\) | 5012.90 | 0.945754 | ||||||||
\(305\) | −1357.21 | −0.254799 | ||||||||
\(306\) | −7155.87 | −1.33684 | ||||||||
\(307\) | −972.535 | −0.180800 | −0.0903999 | − | 0.995906i | \(-0.528815\pi\) | ||||
−0.0903999 | + | 0.995906i | \(0.528815\pi\) | |||||||
\(308\) | −2119.63 | −0.392133 | ||||||||
\(309\) | 2082.76 | 0.383444 | ||||||||
\(310\) | 11887.9 | 2.17803 | ||||||||
\(311\) | 1657.27 | 0.302171 | 0.151086 | − | 0.988521i | \(-0.451723\pi\) | ||||
0.151086 | + | 0.988521i | \(0.451723\pi\) | |||||||
\(312\) | −6862.90 | −1.24531 | ||||||||
\(313\) | −4397.59 | −0.794143 | −0.397071 | − | 0.917788i | \(-0.629973\pi\) | ||||
−0.397071 | + | 0.917788i | \(0.629973\pi\) | |||||||
\(314\) | 10251.8 | 1.84250 | ||||||||
\(315\) | −2951.63 | −0.527954 | ||||||||
\(316\) | 10530.1 | 1.87457 | ||||||||
\(317\) | 540.436 | 0.0957537 | 0.0478768 | − | 0.998853i | \(-0.484754\pi\) | ||||
0.0478768 | + | 0.998853i | \(0.484754\pi\) | |||||||
\(318\) | 71.5547 | 0.0126182 | ||||||||
\(319\) | −1611.21 | −0.282791 | ||||||||
\(320\) | 8086.95 | 1.41273 | ||||||||
\(321\) | −3953.31 | −0.687390 | ||||||||
\(322\) | −7514.48 | −1.30051 | ||||||||
\(323\) | −8932.64 | −1.53878 | ||||||||
\(324\) | 1894.36 | 0.324821 | ||||||||
\(325\) | 2034.52 | 0.347247 | ||||||||
\(326\) | −16639.5 | −2.82693 | ||||||||
\(327\) | 1709.10 | 0.289032 | ||||||||
\(328\) | −926.036 | −0.155890 | ||||||||
\(329\) | −6292.19 | −1.05441 | ||||||||
\(330\) | 1896.85 | 0.316419 | ||||||||
\(331\) | 9335.25 | 1.55019 | 0.775093 | − | 0.631847i | \(-0.217703\pi\) | ||||
0.775093 | + | 0.631847i | \(0.217703\pi\) | |||||||
\(332\) | 22491.1 | 3.71795 | ||||||||
\(333\) | −4953.67 | −0.815194 | ||||||||
\(334\) | −6545.47 | −1.07231 | ||||||||
\(335\) | −3349.61 | −0.546295 | ||||||||
\(336\) | −1635.36 | −0.265524 | ||||||||
\(337\) | −8699.39 | −1.40619 | −0.703095 | − | 0.711096i | \(-0.748199\pi\) | ||||
−0.703095 | + | 0.711096i | \(0.748199\pi\) | |||||||
\(338\) | −12367.6 | −1.99027 | ||||||||
\(339\) | 944.151 | 0.151266 | ||||||||
\(340\) | 14993.3 | 2.39154 | ||||||||
\(341\) | 2186.09 | 0.347165 | ||||||||
\(342\) | 10100.4 | 1.59698 | ||||||||
\(343\) | 6665.22 | 1.04924 | ||||||||
\(344\) | 222.741 | 0.0349109 | ||||||||
\(345\) | 4402.27 | 0.686986 | ||||||||
\(346\) | 4657.47 | 0.723663 | ||||||||
\(347\) | −9167.24 | −1.41822 | −0.709111 | − | 0.705097i | \(-0.750903\pi\) | ||||
−0.709111 | + | 0.705097i | \(0.750903\pi\) | |||||||
\(348\) | −6403.15 | −0.986337 | ||||||||
\(349\) | −4725.44 | −0.724777 | −0.362389 | − | 0.932027i | \(-0.618039\pi\) | ||||
−0.362389 | + | 0.932027i | \(0.618039\pi\) | |||||||
\(350\) | 1802.22 | 0.275237 | ||||||||
\(351\) | −9093.59 | −1.38285 | ||||||||
\(352\) | 670.856 | 0.101582 | ||||||||
\(353\) | 4341.29 | 0.654570 | 0.327285 | − | 0.944926i | \(-0.393866\pi\) | ||||
0.327285 | + | 0.944926i | \(0.393866\pi\) | |||||||
\(354\) | −1499.18 | −0.225086 | ||||||||
\(355\) | 413.941 | 0.0618865 | ||||||||
\(356\) | −18848.3 | −2.80606 | ||||||||
\(357\) | 2914.10 | 0.432018 | ||||||||
\(358\) | 15022.5 | 2.21778 | ||||||||
\(359\) | 1253.74 | 0.184317 | 0.0921585 | − | 0.995744i | \(-0.470623\pi\) | ||||
0.0921585 | + | 0.995744i | \(0.470623\pi\) | |||||||
\(360\) | −8009.59 | −1.17262 | ||||||||
\(361\) | 5749.31 | 0.838213 | ||||||||
\(362\) | −3240.07 | −0.470426 | ||||||||
\(363\) | 348.816 | 0.0504355 | ||||||||
\(364\) | −13303.8 | −1.91568 | ||||||||
\(365\) | 5978.59 | 0.857352 | ||||||||
\(366\) | −1515.13 | −0.216385 | ||||||||
\(367\) | 1426.36 | 0.202875 | 0.101438 | − | 0.994842i | \(-0.467656\pi\) | ||||
0.101438 | + | 0.994842i | \(0.467656\pi\) | |||||||
\(368\) | −5485.38 | −0.777025 | ||||||||
\(369\) | −501.924 | −0.0708107 | ||||||||
\(370\) | 15854.7 | 2.22769 | ||||||||
\(371\) | 65.5329 | 0.00917061 | ||||||||
\(372\) | 8687.82 | 1.21087 | ||||||||
\(373\) | 856.823 | 0.118940 | 0.0594700 | − | 0.998230i | \(-0.481059\pi\) | ||||
0.0594700 | + | 0.998230i | \(0.481059\pi\) | |||||||
\(374\) | 4211.67 | 0.582301 | ||||||||
\(375\) | 3422.77 | 0.471336 | ||||||||
\(376\) | −17074.6 | −2.34190 | ||||||||
\(377\) | −10112.7 | −1.38151 | ||||||||
\(378\) | −8055.28 | −1.09608 | ||||||||
\(379\) | 7789.36 | 1.05571 | 0.527853 | − | 0.849336i | \(-0.322997\pi\) | ||||
0.527853 | + | 0.849336i | \(0.322997\pi\) | |||||||
\(380\) | −21162.8 | −2.85692 | ||||||||
\(381\) | 66.9150 | 0.00899780 | ||||||||
\(382\) | −10705.6 | −1.43389 | ||||||||
\(383\) | 2844.39 | 0.379482 | 0.189741 | − | 0.981834i | \(-0.439235\pi\) | ||||
0.189741 | + | 0.981834i | \(0.439235\pi\) | |||||||
\(384\) | 7621.39 | 1.01283 | ||||||||
\(385\) | 1737.22 | 0.229966 | ||||||||
\(386\) | 6941.65 | 0.915338 | ||||||||
\(387\) | 120.728 | 0.0158578 | ||||||||
\(388\) | −15087.3 | −1.97407 | ||||||||
\(389\) | −5069.27 | −0.660725 | −0.330363 | − | 0.943854i | \(-0.607171\pi\) | ||||
−0.330363 | + | 0.943854i | \(0.607171\pi\) | |||||||
\(390\) | 11905.5 | 1.54579 | ||||||||
\(391\) | 9774.57 | 1.26425 | ||||||||
\(392\) | 6259.58 | 0.806522 | ||||||||
\(393\) | −377.643 | −0.0484722 | ||||||||
\(394\) | −7498.18 | −0.958764 | ||||||||
\(395\) | −8630.34 | −1.09934 | ||||||||
\(396\) | −3117.58 | −0.395617 | ||||||||
\(397\) | 2861.62 | 0.361764 | 0.180882 | − | 0.983505i | \(-0.442105\pi\) | ||||
0.180882 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(398\) | −10885.5 | −1.37095 | ||||||||
\(399\) | −4113.21 | −0.516086 | ||||||||
\(400\) | 1315.58 | 0.164447 | ||||||||
\(401\) | −3081.80 | −0.383785 | −0.191892 | − | 0.981416i | \(-0.561462\pi\) | ||||
−0.191892 | + | 0.981416i | \(0.561462\pi\) | |||||||
\(402\) | −3739.35 | −0.463934 | ||||||||
\(403\) | 13720.9 | 1.69600 | ||||||||
\(404\) | 16588.7 | 2.04287 | ||||||||
\(405\) | −1552.59 | −0.190491 | ||||||||
\(406\) | −8958.00 | −1.09502 | ||||||||
\(407\) | 2915.54 | 0.355081 | ||||||||
\(408\) | 7907.73 | 0.959537 | ||||||||
\(409\) | 490.037 | 0.0592440 | 0.0296220 | − | 0.999561i | \(-0.490570\pi\) | ||||
0.0296220 | + | 0.999561i | \(0.490570\pi\) | |||||||
\(410\) | 1606.45 | 0.193505 | ||||||||
\(411\) | −26.8344 | −0.00322054 | ||||||||
\(412\) | 10956.1 | 1.31011 | ||||||||
\(413\) | −1373.01 | −0.163587 | ||||||||
\(414\) | −11052.4 | −1.31207 | ||||||||
\(415\) | −18433.4 | −2.18039 | ||||||||
\(416\) | 4210.60 | 0.496254 | ||||||||
\(417\) | −5116.42 | −0.600844 | ||||||||
\(418\) | −5944.72 | −0.695612 | ||||||||
\(419\) | 807.157 | 0.0941103 | 0.0470552 | − | 0.998892i | \(-0.485016\pi\) | ||||
0.0470552 | + | 0.998892i | \(0.485016\pi\) | |||||||
\(420\) | 6903.95 | 0.802091 | ||||||||
\(421\) | −13416.7 | −1.55318 | −0.776589 | − | 0.630007i | \(-0.783052\pi\) | ||||
−0.776589 | + | 0.630007i | \(0.783052\pi\) | |||||||
\(422\) | −15531.9 | −1.79166 | ||||||||
\(423\) | −9254.65 | −1.06377 | ||||||||
\(424\) | 177.831 | 0.0203685 | ||||||||
\(425\) | −2344.27 | −0.267562 | ||||||||
\(426\) | 462.104 | 0.0525564 | ||||||||
\(427\) | −1387.62 | −0.157264 | ||||||||
\(428\) | −20795.8 | −2.34860 | ||||||||
\(429\) | 2189.33 | 0.246391 | ||||||||
\(430\) | −386.402 | −0.0433348 | ||||||||
\(431\) | −14006.6 | −1.56537 | −0.782685 | − | 0.622418i | \(-0.786150\pi\) | ||||
−0.782685 | + | 0.622418i | \(0.786150\pi\) | |||||||
\(432\) | −5880.15 | −0.654882 | ||||||||
\(433\) | −1046.71 | −0.116170 | −0.0580852 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580852 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(434\) | 12154.2 | 1.34429 | ||||||||
\(435\) | 5247.94 | 0.578435 | ||||||||
\(436\) | 8990.46 | 0.987534 | ||||||||
\(437\) | −13796.7 | −1.51026 | ||||||||
\(438\) | 6674.21 | 0.728096 | ||||||||
\(439\) | 11960.3 | 1.30030 | 0.650151 | − | 0.759805i | \(-0.274706\pi\) | ||||
0.650151 | + | 0.759805i | \(0.274706\pi\) | |||||||
\(440\) | 4714.14 | 0.510768 | ||||||||
\(441\) | 3392.78 | 0.366351 | ||||||||
\(442\) | 26434.4 | 2.84470 | ||||||||
\(443\) | −57.0715 | −0.00612087 | −0.00306044 | − | 0.999995i | \(-0.500974\pi\) | ||||
−0.00306044 | + | 0.999995i | \(0.500974\pi\) | |||||||
\(444\) | 11586.8 | 1.23848 | ||||||||
\(445\) | 15447.8 | 1.64561 | ||||||||
\(446\) | −5804.38 | −0.616245 | ||||||||
\(447\) | −2428.27 | −0.256943 | ||||||||
\(448\) | 8268.12 | 0.871947 | ||||||||
\(449\) | 15533.0 | 1.63263 | 0.816314 | − | 0.577609i | \(-0.196014\pi\) | ||||
0.816314 | + | 0.577609i | \(0.196014\pi\) | |||||||
\(450\) | 2650.74 | 0.277682 | ||||||||
\(451\) | 295.414 | 0.0308436 | ||||||||
\(452\) | 4966.56 | 0.516830 | ||||||||
\(453\) | −7995.01 | −0.829223 | ||||||||
\(454\) | 11933.7 | 1.23365 | ||||||||
\(455\) | 10903.6 | 1.12345 | ||||||||
\(456\) | −11161.7 | −1.14626 | ||||||||
\(457\) | 8667.99 | 0.887246 | 0.443623 | − | 0.896213i | \(-0.353693\pi\) | ||||
0.443623 | + | 0.896213i | \(0.353693\pi\) | |||||||
\(458\) | 16499.5 | 1.68334 | ||||||||
\(459\) | 10478.0 | 1.06552 | ||||||||
\(460\) | 23157.5 | 2.34722 | ||||||||
\(461\) | −11264.1 | −1.13801 | −0.569005 | − | 0.822334i | \(-0.692671\pi\) | ||||
−0.569005 | + | 0.822334i | \(0.692671\pi\) | |||||||
\(462\) | 1939.35 | 0.195296 | ||||||||
\(463\) | −17534.4 | −1.76003 | −0.880015 | − | 0.474946i | \(-0.842468\pi\) | ||||
−0.880015 | + | 0.474946i | \(0.842468\pi\) | |||||||
\(464\) | −6539.11 | −0.654247 | ||||||||
\(465\) | −7120.42 | −0.710111 | ||||||||
\(466\) | 9391.26 | 0.933566 | ||||||||
\(467\) | 496.301 | 0.0491779 | 0.0245889 | − | 0.999698i | \(-0.492172\pi\) | ||||
0.0245889 | + | 0.999698i | \(0.492172\pi\) | |||||||
\(468\) | −19567.4 | −1.93270 | ||||||||
\(469\) | −3424.65 | −0.337177 | ||||||||
\(470\) | 29620.3 | 2.90699 | ||||||||
\(471\) | −6140.46 | −0.600717 | ||||||||
\(472\) | −3725.82 | −0.363336 | ||||||||
\(473\) | −71.0562 | −0.00690733 | ||||||||
\(474\) | −9634.50 | −0.933602 | ||||||||
\(475\) | 3308.90 | 0.319627 | ||||||||
\(476\) | 15329.2 | 1.47607 | ||||||||
\(477\) | 96.3868 | 0.00925209 | ||||||||
\(478\) | 19624.1 | 1.87779 | ||||||||
\(479\) | −20243.2 | −1.93097 | −0.965485 | − | 0.260458i | \(-0.916126\pi\) | ||||
−0.965485 | + | 0.260458i | \(0.916126\pi\) | |||||||
\(480\) | −2185.08 | −0.207781 | ||||||||
\(481\) | 18299.3 | 1.73467 | ||||||||
\(482\) | 16055.8 | 1.51727 | ||||||||
\(483\) | 4500.89 | 0.424012 | ||||||||
\(484\) | 1834.89 | 0.172323 | ||||||||
\(485\) | 12365.3 | 1.15769 | ||||||||
\(486\) | −18849.2 | −1.75930 | ||||||||
\(487\) | 3880.42 | 0.361065 | 0.180532 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180532 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(488\) | −3765.46 | −0.349292 | ||||||||
\(489\) | 9966.47 | 0.921675 | ||||||||
\(490\) | −10858.9 | −1.00113 | ||||||||
\(491\) | −3238.53 | −0.297664 | −0.148832 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148832 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(492\) | 1174.01 | 0.107579 | ||||||||
\(493\) | 11652.3 | 1.06448 | ||||||||
\(494\) | −37311.8 | −3.39825 | ||||||||
\(495\) | 2555.13 | 0.232009 | ||||||||
\(496\) | 8872.29 | 0.803180 | ||||||||
\(497\) | 423.215 | 0.0381967 | ||||||||
\(498\) | −20578.2 | −1.85167 | ||||||||
\(499\) | −6473.71 | −0.580768 | −0.290384 | − | 0.956910i | \(-0.593783\pi\) | ||||
−0.290384 | + | 0.956910i | \(0.593783\pi\) | |||||||
\(500\) | 18005.0 | 1.61041 | ||||||||
\(501\) | 3920.49 | 0.349610 | ||||||||
\(502\) | −27434.6 | −2.43917 | ||||||||
\(503\) | 5199.63 | 0.460915 | 0.230457 | − | 0.973082i | \(-0.425978\pi\) | ||||
0.230457 | + | 0.973082i | \(0.425978\pi\) | |||||||
\(504\) | −8189.03 | −0.723747 | ||||||||
\(505\) | −13595.9 | −1.19803 | ||||||||
\(506\) | 6505.03 | 0.571510 | ||||||||
\(507\) | 7407.76 | 0.648896 | ||||||||
\(508\) | 351.996 | 0.0307428 | ||||||||
\(509\) | −4993.37 | −0.434827 | −0.217414 | − | 0.976080i | \(-0.569762\pi\) | ||||
−0.217414 | + | 0.976080i | \(0.569762\pi\) | |||||||
\(510\) | −13718.0 | −1.19107 | ||||||||
\(511\) | 6112.53 | 0.529163 | ||||||||
\(512\) | 15037.9 | 1.29802 | ||||||||
\(513\) | −14789.6 | −1.27286 | ||||||||
\(514\) | −4609.44 | −0.395552 | ||||||||
\(515\) | −8979.44 | −0.768313 | ||||||||
\(516\) | −282.387 | −0.0240919 | ||||||||
\(517\) | 5446.94 | 0.463358 | ||||||||
\(518\) | 16209.9 | 1.37494 | ||||||||
\(519\) | −2789.66 | −0.235939 | ||||||||
\(520\) | 29588.1 | 2.49524 | ||||||||
\(521\) | −8412.30 | −0.707389 | −0.353694 | − | 0.935361i | \(-0.615075\pi\) | ||||
−0.353694 | + | 0.935361i | \(0.615075\pi\) | |||||||
\(522\) | −13175.6 | −1.10475 | ||||||||
\(523\) | 4110.76 | 0.343692 | 0.171846 | − | 0.985124i | \(-0.445027\pi\) | ||||
0.171846 | + | 0.985124i | \(0.445027\pi\) | |||||||
\(524\) | −1986.54 | −0.165615 | ||||||||
\(525\) | −1079.46 | −0.0897365 | ||||||||
\(526\) | 16738.7 | 1.38753 | ||||||||
\(527\) | −15809.8 | −1.30681 | ||||||||
\(528\) | 1415.68 | 0.116684 | ||||||||
\(529\) | 2930.06 | 0.240820 | ||||||||
\(530\) | −308.494 | −0.0252833 | ||||||||
\(531\) | −2019.45 | −0.165041 | ||||||||
\(532\) | −21636.9 | −1.76331 | ||||||||
\(533\) | 1854.15 | 0.150680 | ||||||||
\(534\) | 17245.2 | 1.39751 | ||||||||
\(535\) | 17043.9 | 1.37733 | ||||||||
\(536\) | −9293.19 | −0.748889 | ||||||||
\(537\) | −8997.94 | −0.723072 | ||||||||
\(538\) | 34158.7 | 2.73733 | ||||||||
\(539\) | −1996.86 | −0.159575 | ||||||||
\(540\) | 24824.1 | 1.97825 | ||||||||
\(541\) | −5569.83 | −0.442635 | −0.221318 | − | 0.975202i | \(-0.571036\pi\) | ||||
−0.221318 | + | 0.975202i | \(0.571036\pi\) | |||||||
\(542\) | 37267.0 | 2.95342 | ||||||||
\(543\) | 1940.68 | 0.153375 | ||||||||
\(544\) | −4851.63 | −0.382375 | ||||||||
\(545\) | −7368.46 | −0.579138 | ||||||||
\(546\) | 12172.2 | 0.954073 | ||||||||
\(547\) | −10562.9 | −0.825658 | −0.412829 | − | 0.910809i | \(-0.635459\pi\) | ||||
−0.412829 | + | 0.910809i | \(0.635459\pi\) | |||||||
\(548\) | −141.158 | −0.0110036 | ||||||||
\(549\) | −2040.93 | −0.158661 | ||||||||
\(550\) | −1560.12 | −0.120952 | ||||||||
\(551\) | −16447.0 | −1.27163 | ||||||||
\(552\) | 12213.7 | 0.941755 | ||||||||
\(553\) | −8823.69 | −0.678520 | ||||||||
\(554\) | 8369.80 | 0.641875 | ||||||||
\(555\) | −9496.36 | −0.726303 | ||||||||
\(556\) | −26914.1 | −2.05290 | ||||||||
\(557\) | −12272.7 | −0.933596 | −0.466798 | − | 0.884364i | \(-0.654592\pi\) | ||||
−0.466798 | + | 0.884364i | \(0.654592\pi\) | |||||||
\(558\) | 17876.7 | 1.35623 | ||||||||
\(559\) | −445.981 | −0.0337442 | ||||||||
\(560\) | 7050.54 | 0.532035 | ||||||||
\(561\) | −2522.64 | −0.189850 | ||||||||
\(562\) | 29299.3 | 2.19914 | ||||||||
\(563\) | −7340.77 | −0.549514 | −0.274757 | − | 0.961514i | \(-0.588597\pi\) | ||||
−0.274757 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(564\) | 21646.9 | 1.61613 | ||||||||
\(565\) | −4070.52 | −0.303094 | ||||||||
\(566\) | 36027.3 | 2.67551 | ||||||||
\(567\) | −1587.37 | −0.117572 | ||||||||
\(568\) | 1148.44 | 0.0848372 | ||||||||
\(569\) | 22051.9 | 1.62471 | 0.812356 | − | 0.583161i | \(-0.198184\pi\) | ||||
0.812356 | + | 0.583161i | \(0.198184\pi\) | |||||||
\(570\) | 19362.8 | 1.42284 | ||||||||
\(571\) | −11672.6 | −0.855485 | −0.427742 | − | 0.903901i | \(-0.640691\pi\) | ||||
−0.427742 | + | 0.903901i | \(0.640691\pi\) | |||||||
\(572\) | 11516.6 | 0.841843 | ||||||||
\(573\) | 6412.27 | 0.467498 | ||||||||
\(574\) | 1642.44 | 0.119433 | ||||||||
\(575\) | −3620.78 | −0.262603 | ||||||||
\(576\) | 12160.9 | 0.879694 | ||||||||
\(577\) | −17850.3 | −1.28790 | −0.643950 | − | 0.765068i | \(-0.722705\pi\) | ||||
−0.643950 | + | 0.765068i | \(0.722705\pi\) | |||||||
\(578\) | −6812.86 | −0.490273 | ||||||||
\(579\) | −4157.79 | −0.298431 | ||||||||
\(580\) | 27606.0 | 1.97634 | ||||||||
\(581\) | −18846.4 | −1.34575 | ||||||||
\(582\) | 13804.0 | 0.983155 | ||||||||
\(583\) | −56.7296 | −0.00403002 | ||||||||
\(584\) | 16587.0 | 1.17530 | ||||||||
\(585\) | 16037.2 | 1.13343 | ||||||||
\(586\) | 27310.3 | 1.92522 | ||||||||
\(587\) | −876.228 | −0.0616112 | −0.0308056 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308056 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(588\) | −7935.80 | −0.556576 | ||||||||
\(589\) | 22315.3 | 1.56110 | ||||||||
\(590\) | 6463.42 | 0.451008 | ||||||||
\(591\) | 4491.13 | 0.312590 | ||||||||
\(592\) | 11832.8 | 0.821495 | ||||||||
\(593\) | 1897.12 | 0.131375 | 0.0656877 | − | 0.997840i | \(-0.479076\pi\) | ||||
0.0656877 | + | 0.997840i | \(0.479076\pi\) | |||||||
\(594\) | 6973.19 | 0.481672 | ||||||||
\(595\) | −12563.6 | −0.865641 | ||||||||
\(596\) | −12773.6 | −0.877895 | ||||||||
\(597\) | 6520.00 | 0.446978 | ||||||||
\(598\) | 40828.6 | 2.79198 | ||||||||
\(599\) | −20724.9 | −1.41368 | −0.706841 | − | 0.707373i | \(-0.749880\pi\) | ||||
−0.706841 | + | 0.707373i | \(0.749880\pi\) | |||||||
\(600\) | −2929.25 | −0.199310 | ||||||||
\(601\) | −2916.81 | −0.197969 | −0.0989844 | − | 0.995089i | \(-0.531559\pi\) | ||||
−0.0989844 | + | 0.995089i | \(0.531559\pi\) | |||||||
\(602\) | −395.059 | −0.0267465 | ||||||||
\(603\) | −5037.04 | −0.340172 | ||||||||
\(604\) | −42056.5 | −2.83320 | ||||||||
\(605\) | −1503.85 | −0.101058 | ||||||||
\(606\) | −15177.8 | −1.01742 | ||||||||
\(607\) | 27913.0 | 1.86648 | 0.933241 | − | 0.359250i | \(-0.116968\pi\) | ||||
0.933241 | + | 0.359250i | \(0.116968\pi\) | |||||||
\(608\) | 6848.02 | 0.456783 | ||||||||
\(609\) | 5365.51 | 0.357014 | ||||||||
\(610\) | 6532.19 | 0.433575 | ||||||||
\(611\) | 34187.5 | 2.26363 | ||||||||
\(612\) | 22546.4 | 1.48919 | ||||||||
\(613\) | −318.939 | −0.0210144 | −0.0105072 | − | 0.999945i | \(-0.503345\pi\) | ||||
−0.0105072 | + | 0.999945i | \(0.503345\pi\) | |||||||
\(614\) | 4680.76 | 0.307655 | ||||||||
\(615\) | −962.206 | −0.0630892 | ||||||||
\(616\) | 4819.75 | 0.315249 | ||||||||
\(617\) | −16978.6 | −1.10784 | −0.553918 | − | 0.832572i | \(-0.686868\pi\) | ||||
−0.553918 | + | 0.832572i | \(0.686868\pi\) | |||||||
\(618\) | −10024.2 | −0.652481 | ||||||||
\(619\) | 26132.1 | 1.69683 | 0.848414 | − | 0.529333i | \(-0.177558\pi\) | ||||
0.848414 | + | 0.529333i | \(0.177558\pi\) | |||||||
\(620\) | −37455.9 | −2.42623 | ||||||||
\(621\) | 16183.6 | 1.04577 | ||||||||
\(622\) | −7976.35 | −0.514184 | ||||||||
\(623\) | 15793.9 | 1.01568 | ||||||||
\(624\) | 8885.43 | 0.570035 | ||||||||
\(625\) | −18440.2 | −1.18017 | ||||||||
\(626\) | 21165.4 | 1.35134 | ||||||||
\(627\) | 3560.67 | 0.226793 | ||||||||
\(628\) | −32301.0 | −2.05247 | ||||||||
\(629\) | −21085.2 | −1.33660 | ||||||||
\(630\) | 14206.0 | 0.898384 | ||||||||
\(631\) | 29730.0 | 1.87565 | 0.937823 | − | 0.347113i | \(-0.112838\pi\) | ||||
0.937823 | + | 0.347113i | \(0.112838\pi\) | |||||||
\(632\) | −23944.1 | −1.50703 | ||||||||
\(633\) | 9303.04 | 0.584143 | ||||||||
\(634\) | −2601.09 | −0.162937 | ||||||||
\(635\) | −288.491 | −0.0180290 | ||||||||
\(636\) | −225.451 | −0.0140562 | ||||||||
\(637\) | −12533.2 | −0.779567 | ||||||||
\(638\) | 7754.64 | 0.481205 | ||||||||
\(639\) | 622.471 | 0.0385361 | ||||||||
\(640\) | −32858.2 | −2.02943 | ||||||||
\(641\) | 5481.24 | 0.337747 | 0.168874 | − | 0.985638i | \(-0.445987\pi\) | ||||
0.168874 | + | 0.985638i | \(0.445987\pi\) | |||||||
\(642\) | 19027.1 | 1.16969 | ||||||||
\(643\) | 25418.2 | 1.55893 | 0.779467 | − | 0.626443i | \(-0.215490\pi\) | ||||
0.779467 | + | 0.626443i | \(0.215490\pi\) | |||||||
\(644\) | 23676.3 | 1.44872 | ||||||||
\(645\) | 231.441 | 0.0141286 | ||||||||
\(646\) | 42992.3 | 2.61843 | ||||||||
\(647\) | −12725.8 | −0.773267 | −0.386633 | − | 0.922234i | \(-0.626362\pi\) | ||||
−0.386633 | + | 0.922234i | \(0.626362\pi\) | |||||||
\(648\) | −4307.51 | −0.261135 | ||||||||
\(649\) | 1188.57 | 0.0718882 | ||||||||
\(650\) | −9792.05 | −0.590886 | ||||||||
\(651\) | −7279.94 | −0.438285 | ||||||||
\(652\) | 52427.1 | 3.14908 | ||||||||
\(653\) | 15378.7 | 0.921617 | 0.460808 | − | 0.887500i | \(-0.347560\pi\) | ||||
0.460808 | + | 0.887500i | \(0.347560\pi\) | |||||||
\(654\) | −8225.79 | −0.491826 | ||||||||
\(655\) | 1628.14 | 0.0971246 | ||||||||
\(656\) | 1198.94 | 0.0713579 | ||||||||
\(657\) | 8990.40 | 0.533865 | ||||||||
\(658\) | 30283.9 | 1.79421 | ||||||||
\(659\) | 3097.56 | 0.183101 | 0.0915507 | − | 0.995800i | \(-0.470818\pi\) | ||||
0.0915507 | + | 0.995800i | \(0.470818\pi\) | |||||||
\(660\) | −5976.52 | −0.352478 | ||||||||
\(661\) | −22527.3 | −1.32558 | −0.662792 | − | 0.748803i | \(-0.730629\pi\) | ||||
−0.662792 | + | 0.748803i | \(0.730629\pi\) | |||||||
\(662\) | −44930.0 | −2.63785 | ||||||||
\(663\) | −15833.2 | −0.927468 | ||||||||
\(664\) | −51141.8 | −2.98898 | ||||||||
\(665\) | 17733.3 | 1.03409 | ||||||||
\(666\) | 23841.7 | 1.38716 | ||||||||
\(667\) | 17997.2 | 1.04476 | ||||||||
\(668\) | 20623.2 | 1.19451 | ||||||||
\(669\) | 3476.61 | 0.200917 | ||||||||
\(670\) | 16121.5 | 0.929593 | ||||||||
\(671\) | 1201.22 | 0.0691094 | ||||||||
\(672\) | −2234.03 | −0.128243 | ||||||||
\(673\) | 6391.49 | 0.366083 | 0.183041 | − | 0.983105i | \(-0.441406\pi\) | ||||
0.183041 | + | 0.983105i | \(0.441406\pi\) | |||||||
\(674\) | 41869.6 | 2.39282 | ||||||||
\(675\) | −3881.36 | −0.221324 | ||||||||
\(676\) | 38967.4 | 2.21708 | ||||||||
\(677\) | −19747.0 | −1.12103 | −0.560517 | − | 0.828143i | \(-0.689398\pi\) | ||||
−0.560517 | + | 0.828143i | \(0.689398\pi\) | |||||||
\(678\) | −4544.14 | −0.257399 | ||||||||
\(679\) | 12642.3 | 0.714534 | ||||||||
\(680\) | −34092.7 | −1.92264 | ||||||||
\(681\) | −7147.84 | −0.402211 | ||||||||
\(682\) | −10521.5 | −0.590748 | ||||||||
\(683\) | 17156.1 | 0.961144 | 0.480572 | − | 0.876955i | \(-0.340429\pi\) | ||||
0.480572 | + | 0.876955i | \(0.340429\pi\) | |||||||
\(684\) | −31823.9 | −1.77897 | ||||||||
\(685\) | 115.691 | 0.00645305 | ||||||||
\(686\) | −32079.3 | −1.78541 | ||||||||
\(687\) | −9882.57 | −0.548826 | ||||||||
\(688\) | −288.383 | −0.0159804 | ||||||||
\(689\) | −356.061 | −0.0196877 | ||||||||
\(690\) | −21187.9 | −1.16900 | ||||||||
\(691\) | −5754.63 | −0.316811 | −0.158405 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158405 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(692\) | −14674.6 | −0.806132 | ||||||||
\(693\) | 2612.37 | 0.143197 | ||||||||
\(694\) | 44121.4 | 2.41329 | ||||||||
\(695\) | 22058.5 | 1.20392 | ||||||||
\(696\) | 14559.9 | 0.792949 | ||||||||
\(697\) | −2136.43 | −0.116102 | ||||||||
\(698\) | 22743.3 | 1.23330 | ||||||||
\(699\) | −5625.02 | −0.304374 | ||||||||
\(700\) | −5678.36 | −0.306603 | ||||||||
\(701\) | −34405.6 | −1.85375 | −0.926877 | − | 0.375366i | \(-0.877517\pi\) | ||||
−0.926877 | + | 0.375366i | \(0.877517\pi\) | |||||||
\(702\) | 43766.9 | 2.35310 | ||||||||
\(703\) | 29761.5 | 1.59670 | ||||||||
\(704\) | −7157.44 | −0.383176 | ||||||||
\(705\) | −17741.5 | −0.947777 | ||||||||
\(706\) | −20894.4 | −1.11384 | ||||||||
\(707\) | −13900.4 | −0.739435 | ||||||||
\(708\) | 4723.54 | 0.250737 | ||||||||
\(709\) | −5247.78 | −0.277976 | −0.138988 | − | 0.990294i | \(-0.544385\pi\) | ||||
−0.138988 | + | 0.990294i | \(0.544385\pi\) | |||||||
\(710\) | −1992.27 | −0.105308 | ||||||||
\(711\) | −12978.0 | −0.684548 | ||||||||
\(712\) | 42858.4 | 2.25588 | ||||||||
\(713\) | −24418.6 | −1.28259 | ||||||||
\(714\) | −14025.4 | −0.735135 | ||||||||
\(715\) | −9438.86 | −0.493697 | ||||||||
\(716\) | −47332.3 | −2.47052 | ||||||||
\(717\) | −11754.1 | −0.612224 | ||||||||
\(718\) | −6034.17 | −0.313640 | ||||||||
\(719\) | −11261.5 | −0.584122 | −0.292061 | − | 0.956400i | \(-0.594341\pi\) | ||||
−0.292061 | + | 0.956400i | \(0.594341\pi\) | |||||||
\(720\) | 10370.0 | 0.536762 | ||||||||
\(721\) | −9180.61 | −0.474208 | ||||||||
\(722\) | −27671.1 | −1.42633 | ||||||||
\(723\) | −9616.83 | −0.494680 | ||||||||
\(724\) | 10208.7 | 0.524036 | ||||||||
\(725\) | −4316.32 | −0.221109 | ||||||||
\(726\) | −1678.83 | −0.0858226 | ||||||||
\(727\) | 20408.8 | 1.04115 | 0.520577 | − | 0.853815i | \(-0.325717\pi\) | ||||
0.520577 | + | 0.853815i | \(0.325717\pi\) | |||||||
\(728\) | 30251.0 | 1.54008 | ||||||||
\(729\) | 7917.12 | 0.402231 | ||||||||
\(730\) | −28774.6 | −1.45890 | ||||||||
\(731\) | 513.879 | 0.0260007 | ||||||||
\(732\) | 4773.80 | 0.241045 | ||||||||
\(733\) | 16343.4 | 0.823543 | 0.411772 | − | 0.911287i | \(-0.364910\pi\) | ||||
0.411772 | + | 0.911287i | \(0.364910\pi\) | |||||||
\(734\) | −6864.96 | −0.345219 | ||||||||
\(735\) | 6504.07 | 0.326403 | ||||||||
\(736\) | −7493.47 | −0.375289 | ||||||||
\(737\) | 2964.61 | 0.148172 | ||||||||
\(738\) | 2415.73 | 0.120494 | ||||||||
\(739\) | 20458.1 | 1.01836 | 0.509178 | − | 0.860662i | \(-0.329950\pi\) | ||||
0.509178 | + | 0.860662i | \(0.329950\pi\) | |||||||
\(740\) | −49954.2 | −2.48156 | ||||||||
\(741\) | 22348.4 | 1.10795 | ||||||||
\(742\) | −315.406 | −0.0156050 | ||||||||
\(743\) | 31227.7 | 1.54190 | 0.770952 | − | 0.636894i | \(-0.219781\pi\) | ||||
0.770952 | + | 0.636894i | \(0.219781\pi\) | |||||||
\(744\) | −19754.9 | −0.973456 | ||||||||
\(745\) | 10469.0 | 0.514840 | ||||||||
\(746\) | −4123.84 | −0.202392 | ||||||||
\(747\) | −27719.6 | −1.35770 | ||||||||
\(748\) | −13269.9 | −0.648660 | ||||||||
\(749\) | 17425.8 | 0.850100 | ||||||||
\(750\) | −16473.6 | −0.802040 | ||||||||
\(751\) | −10031.8 | −0.487436 | −0.243718 | − | 0.969846i | \(-0.578367\pi\) | ||||
−0.243718 | + | 0.969846i | \(0.578367\pi\) | |||||||
\(752\) | 22106.5 | 1.07200 | ||||||||
\(753\) | 16432.3 | 0.795254 | ||||||||
\(754\) | 48671.7 | 2.35082 | ||||||||
\(755\) | 34468.9 | 1.66153 | ||||||||
\(756\) | 25380.2 | 1.22099 | ||||||||
\(757\) | −38647.7 | −1.85558 | −0.927790 | − | 0.373102i | \(-0.878294\pi\) | ||||
−0.927790 | + | 0.373102i | \(0.878294\pi\) | |||||||
\(758\) | −37489.7 | −1.79642 | ||||||||
\(759\) | −3896.27 | −0.186332 | ||||||||
\(760\) | 48121.4 | 2.29677 | ||||||||
\(761\) | −489.763 | −0.0233297 | −0.0116649 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116649 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(762\) | −322.058 | −0.0153109 | ||||||||
\(763\) | −7533.54 | −0.357447 | ||||||||
\(764\) | 33730.8 | 1.59730 | ||||||||
\(765\) | −18478.7 | −0.873332 | ||||||||
\(766\) | −13689.9 | −0.645738 | ||||||||
\(767\) | 7460.01 | 0.351193 | ||||||||
\(768\) | −21675.3 | −1.01841 | ||||||||
\(769\) | −674.895 | −0.0316481 | −0.0158240 | − | 0.999875i | \(-0.505037\pi\) | ||||
−0.0158240 | + | 0.999875i | \(0.505037\pi\) | |||||||
\(770\) | −8361.13 | −0.391317 | ||||||||
\(771\) | 2760.88 | 0.128963 | ||||||||
\(772\) | −21871.4 | −1.01965 | ||||||||
\(773\) | 30397.0 | 1.41437 | 0.707183 | − | 0.707030i | \(-0.249966\pi\) | ||||
0.707183 | + | 0.707030i | \(0.249966\pi\) | |||||||
\(774\) | −581.059 | −0.0269841 | ||||||||
\(775\) | 5856.40 | 0.271443 | ||||||||
\(776\) | 34306.4 | 1.58702 | ||||||||
\(777\) | −9709.11 | −0.448279 | ||||||||
\(778\) | 24398.1 | 1.12431 | ||||||||
\(779\) | 3015.55 | 0.138695 | ||||||||
\(780\) | −37511.4 | −1.72195 | ||||||||
\(781\) | −366.363 | −0.0167855 | ||||||||
\(782\) | −47044.4 | −2.15128 | ||||||||
\(783\) | 19292.4 | 0.880529 | ||||||||
\(784\) | −8104.30 | −0.369183 | ||||||||
\(785\) | 26473.4 | 1.20367 | ||||||||
\(786\) | 1817.57 | 0.0824819 | ||||||||
\(787\) | −5662.68 | −0.256484 | −0.128242 | − | 0.991743i | \(-0.540933\pi\) | ||||
−0.128242 | + | 0.991743i | \(0.540933\pi\) | |||||||
\(788\) | 23624.9 | 1.06802 | ||||||||
\(789\) | −10025.9 | −0.452384 | ||||||||
\(790\) | 41537.3 | 1.87067 | ||||||||
\(791\) | −4161.72 | −0.187072 | ||||||||
\(792\) | 7088.97 | 0.318050 | ||||||||
\(793\) | 7539.38 | 0.337618 | ||||||||
\(794\) | −13772.8 | −0.615590 | ||||||||
\(795\) | 184.777 | 0.00824322 | ||||||||
\(796\) | 34297.5 | 1.52719 | ||||||||
\(797\) | −26107.2 | −1.16031 | −0.580153 | − | 0.814507i | \(-0.697007\pi\) | ||||
−0.580153 | + | 0.814507i | \(0.697007\pi\) | |||||||
\(798\) | 19796.6 | 0.878187 | ||||||||
\(799\) | −39392.3 | −1.74418 | ||||||||
\(800\) | 1797.18 | 0.0794250 | ||||||||
\(801\) | 23229.9 | 1.02470 | ||||||||
\(802\) | 14832.5 | 0.653060 | ||||||||
\(803\) | −5291.41 | −0.232540 | ||||||||
\(804\) | 11781.8 | 0.516804 | ||||||||
\(805\) | −19404.7 | −0.849599 | ||||||||
\(806\) | −66037.9 | −2.88596 | ||||||||
\(807\) | −20459.8 | −0.892464 | ||||||||
\(808\) | −37720.4 | −1.64233 | ||||||||
\(809\) | 28202.3 | 1.22564 | 0.612818 | − | 0.790224i | \(-0.290036\pi\) | ||||
0.612818 | + | 0.790224i | \(0.290036\pi\) | |||||||
\(810\) | 7472.52 | 0.324145 | ||||||||
\(811\) | −18137.7 | −0.785327 | −0.392663 | − | 0.919682i | \(-0.628446\pi\) | ||||
−0.392663 | + | 0.919682i | \(0.628446\pi\) | |||||||
\(812\) | 28224.5 | 1.21981 | ||||||||
\(813\) | −22321.6 | −0.962917 | ||||||||
\(814\) | −14032.3 | −0.604218 | ||||||||
\(815\) | −42968.5 | −1.84677 | ||||||||
\(816\) | −10238.2 | −0.439225 | ||||||||
\(817\) | −725.333 | −0.0310602 | ||||||||
\(818\) | −2358.52 | −0.100811 | ||||||||
\(819\) | 16396.5 | 0.699558 | ||||||||
\(820\) | −5061.54 | −0.215557 | ||||||||
\(821\) | −12795.3 | −0.543920 | −0.271960 | − | 0.962309i | \(-0.587672\pi\) | ||||
−0.271960 | + | 0.962309i | \(0.587672\pi\) | |||||||
\(822\) | 129.152 | 0.00548018 | ||||||||
\(823\) | −16164.3 | −0.684631 | −0.342315 | − | 0.939585i | \(-0.611211\pi\) | ||||
−0.342315 | + | 0.939585i | \(0.611211\pi\) | |||||||
\(824\) | −24912.6 | −1.05324 | ||||||||
\(825\) | 934.456 | 0.0394346 | ||||||||
\(826\) | 6608.22 | 0.278365 | ||||||||
\(827\) | −5621.29 | −0.236362 | −0.118181 | − | 0.992992i | \(-0.537706\pi\) | ||||
−0.118181 | + | 0.992992i | \(0.537706\pi\) | |||||||
\(828\) | 34823.4 | 1.46159 | ||||||||
\(829\) | −39059.8 | −1.63643 | −0.818217 | − | 0.574910i | \(-0.805037\pi\) | ||||
−0.818217 | + | 0.574910i | \(0.805037\pi\) | |||||||
\(830\) | 88718.9 | 3.71021 | ||||||||
\(831\) | −5013.20 | −0.209273 | ||||||||
\(832\) | −44923.4 | −1.87192 | ||||||||
\(833\) | 14441.3 | 0.600674 | ||||||||
\(834\) | 24625.0 | 1.02242 | ||||||||
\(835\) | −16902.5 | −0.700519 | ||||||||
\(836\) | 18730.4 | 0.774884 | ||||||||
\(837\) | −26176.0 | −1.08097 | ||||||||
\(838\) | −3884.80 | −0.160141 | ||||||||
\(839\) | −8129.04 | −0.334500 | −0.167250 | − | 0.985915i | \(-0.553489\pi\) | ||||
−0.167250 | + | 0.985915i | \(0.553489\pi\) | |||||||
\(840\) | −15698.7 | −0.644827 | ||||||||
\(841\) | −2934.58 | −0.120324 | ||||||||
\(842\) | 64573.6 | 2.64294 | ||||||||
\(843\) | −17549.2 | −0.716995 | ||||||||
\(844\) | 48937.2 | 1.99584 | ||||||||
\(845\) | −31937.2 | −1.30020 | ||||||||
\(846\) | 44542.1 | 1.81015 | ||||||||
\(847\) | −1537.54 | −0.0623738 | ||||||||
\(848\) | −230.238 | −0.00932360 | ||||||||
\(849\) | −21579.0 | −0.872309 | ||||||||
\(850\) | 11282.8 | 0.455291 | ||||||||
\(851\) | −32566.6 | −1.31183 | ||||||||
\(852\) | −1455.98 | −0.0585457 | ||||||||
\(853\) | −36159.4 | −1.45144 | −0.725719 | − | 0.687992i | \(-0.758493\pi\) | ||||
−0.725719 | + | 0.687992i | \(0.758493\pi\) | |||||||
\(854\) | 6678.53 | 0.267605 | ||||||||
\(855\) | 26082.5 | 1.04328 | ||||||||
\(856\) | 47286.9 | 1.88812 | ||||||||
\(857\) | 40431.4 | 1.61157 | 0.805783 | − | 0.592211i | \(-0.201745\pi\) | ||||
0.805783 | + | 0.592211i | \(0.201745\pi\) | |||||||
\(858\) | −10537.1 | −0.419266 | ||||||||
\(859\) | −31565.4 | −1.25378 | −0.626891 | − | 0.779107i | \(-0.715673\pi\) | ||||
−0.626891 | + | 0.779107i | \(0.715673\pi\) | |||||||
\(860\) | 1217.46 | 0.0482732 | ||||||||
\(861\) | −983.763 | −0.0389391 | ||||||||
\(862\) | 67412.9 | 2.66368 | ||||||||
\(863\) | 40280.1 | 1.58882 | 0.794410 | − | 0.607382i | \(-0.207780\pi\) | ||||
0.794410 | + | 0.607382i | \(0.207780\pi\) | |||||||
\(864\) | −8032.76 | −0.316296 | ||||||||
\(865\) | 12027.1 | 0.472754 | ||||||||
\(866\) | 5037.76 | 0.197679 | ||||||||
\(867\) | 4080.65 | 0.159846 | ||||||||
\(868\) | −38295.0 | −1.49749 | ||||||||
\(869\) | 7638.37 | 0.298175 | ||||||||
\(870\) | −25258.0 | −0.984284 | ||||||||
\(871\) | 18607.2 | 0.723860 | ||||||||
\(872\) | −20443.1 | −0.793911 | ||||||||
\(873\) | 18594.6 | 0.720882 | ||||||||
\(874\) | 66402.6 | 2.56991 | ||||||||
\(875\) | −15087.2 | −0.582904 | ||||||||
\(876\) | −21028.8 | −0.811070 | ||||||||
\(877\) | 73.3545 | 0.00282441 | 0.00141220 | − | 0.999999i | \(-0.499550\pi\) | ||||
0.00141220 | + | 0.999999i | \(0.499550\pi\) | |||||||
\(878\) | −57564.1 | −2.21263 | ||||||||
\(879\) | −16357.8 | −0.627686 | ||||||||
\(880\) | −6103.41 | −0.233802 | ||||||||
\(881\) | −23041.7 | −0.881153 | −0.440576 | − | 0.897715i | \(-0.645226\pi\) | ||||
−0.440576 | + | 0.897715i | \(0.645226\pi\) | |||||||
\(882\) | −16329.2 | −0.623395 | ||||||||
\(883\) | −5593.41 | −0.213175 | −0.106587 | − | 0.994303i | \(-0.533992\pi\) | ||||
−0.106587 | + | 0.994303i | \(0.533992\pi\) | |||||||
\(884\) | −83288.3 | −3.16888 | ||||||||
\(885\) | −3871.35 | −0.147044 | ||||||||
\(886\) | 274.682 | 0.0104155 | ||||||||
\(887\) | 36177.4 | 1.36947 | 0.684734 | − | 0.728793i | \(-0.259918\pi\) | ||||
0.684734 | + | 0.728793i | \(0.259918\pi\) | |||||||
\(888\) | −26346.8 | −0.995653 | ||||||||
\(889\) | −294.955 | −0.0111276 | ||||||||
\(890\) | −74349.2 | −2.80022 | ||||||||
\(891\) | 1374.14 | 0.0516670 | ||||||||
\(892\) | 18288.2 | 0.686472 | ||||||||
\(893\) | 55601.7 | 2.08358 | ||||||||
\(894\) | 11687.1 | 0.437222 | ||||||||
\(895\) | 38792.9 | 1.44883 | ||||||||
\(896\) | −33594.3 | −1.25258 | ||||||||
\(897\) | −24454.8 | −0.910281 | ||||||||
\(898\) | −74759.6 | −2.77813 | ||||||||
\(899\) | −29109.4 | −1.07993 | ||||||||
\(900\) | −8351.82 | −0.309327 | ||||||||
\(901\) | 410.269 | 0.0151699 | ||||||||
\(902\) | −1421.81 | −0.0524845 | ||||||||
\(903\) | 236.626 | 0.00872028 | ||||||||
\(904\) | −11293.3 | −0.415497 | ||||||||
\(905\) | −8366.88 | −0.307320 | ||||||||
\(906\) | 38479.5 | 1.41103 | ||||||||
\(907\) | 372.408 | 0.0136335 | 0.00681675 | − | 0.999977i | \(-0.497830\pi\) | ||||
0.00681675 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(908\) | −37600.1 | −1.37423 | ||||||||
\(909\) | −20445.0 | −0.746004 | ||||||||
\(910\) | −52478.3 | −1.91169 | ||||||||
\(911\) | −10956.7 | −0.398476 | −0.199238 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199238 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(912\) | 14451.0 | 0.524695 | ||||||||
\(913\) | 16314.7 | 0.591388 | ||||||||
\(914\) | −41718.5 | −1.50977 | ||||||||
\(915\) | −3912.54 | −0.141360 | ||||||||
\(916\) | −51985.8 | −1.87517 | ||||||||
\(917\) | 1664.61 | 0.0599459 | ||||||||
\(918\) | −50430.1 | −1.81312 | ||||||||
\(919\) | −16477.5 | −0.591452 | −0.295726 | − | 0.955273i | \(-0.595561\pi\) | ||||
−0.295726 | + | 0.955273i | \(0.595561\pi\) | |||||||
\(920\) | −52657.0 | −1.88701 | ||||||||
\(921\) | −2803.60 | −0.100306 | ||||||||
\(922\) | 54213.5 | 1.93647 | ||||||||
\(923\) | −2299.46 | −0.0820018 | ||||||||
\(924\) | −6110.41 | −0.217552 | ||||||||
\(925\) | 7810.57 | 0.277632 | ||||||||
\(926\) | 84392.2 | 2.99492 | ||||||||
\(927\) | −13503.0 | −0.478421 | ||||||||
\(928\) | −8932.95 | −0.315990 | ||||||||
\(929\) | 22853.7 | 0.807111 | 0.403556 | − | 0.914955i | \(-0.367774\pi\) | ||||
0.403556 | + | 0.914955i | \(0.367774\pi\) | |||||||
\(930\) | 34270.2 | 1.20835 | ||||||||
\(931\) | −20383.7 | −0.717561 | ||||||||
\(932\) | −29589.6 | −1.03995 | ||||||||
\(933\) | 4777.54 | 0.167642 | ||||||||
\(934\) | −2388.67 | −0.0836826 | ||||||||
\(935\) | 10875.9 | 0.380405 | ||||||||
\(936\) | 44493.6 | 1.55376 | ||||||||
\(937\) | −23823.3 | −0.830602 | −0.415301 | − | 0.909684i | \(-0.636324\pi\) | ||||
−0.415301 | + | 0.909684i | \(0.636324\pi\) | |||||||
\(938\) | 16482.7 | 0.573750 | ||||||||
\(939\) | −12677.3 | −0.440583 | ||||||||
\(940\) | −93326.4 | −3.23827 | ||||||||
\(941\) | −13339.6 | −0.462124 | −0.231062 | − | 0.972939i | \(-0.574220\pi\) | ||||
−0.231062 | + | 0.972939i | \(0.574220\pi\) | |||||||
\(942\) | 29553.7 | 1.02220 | ||||||||
\(943\) | −3299.77 | −0.113951 | ||||||||
\(944\) | 4823.83 | 0.166316 | ||||||||
\(945\) | −20801.3 | −0.716048 | ||||||||
\(946\) | 341.989 | 0.0117537 | ||||||||
\(947\) | −14119.9 | −0.484514 | −0.242257 | − | 0.970212i | \(-0.577888\pi\) | ||||
−0.242257 | + | 0.970212i | \(0.577888\pi\) | |||||||
\(948\) | 30355.9 | 1.03999 | ||||||||
\(949\) | −33211.3 | −1.13602 | ||||||||
\(950\) | −15925.5 | −0.543887 | ||||||||
\(951\) | 1557.96 | 0.0531232 | ||||||||
\(952\) | −34856.5 | −1.18667 | ||||||||
\(953\) | 25335.3 | 0.861167 | 0.430584 | − | 0.902551i | \(-0.358308\pi\) | ||||
0.430584 | + | 0.902551i | \(0.358308\pi\) | |||||||
\(954\) | −463.904 | −0.0157436 | ||||||||
\(955\) | −27645.3 | −0.936734 | ||||||||
\(956\) | −61830.7 | −2.09178 | ||||||||
\(957\) | −4644.74 | −0.156889 | ||||||||
\(958\) | 97429.3 | 3.28580 | ||||||||
\(959\) | 118.283 | 0.00398286 | ||||||||
\(960\) | 23312.8 | 0.783769 | ||||||||
\(961\) | 9704.77 | 0.325762 | ||||||||
\(962\) | −88073.4 | −2.95177 | ||||||||
\(963\) | 25630.1 | 0.857653 | ||||||||
\(964\) | −50587.9 | −1.69017 | ||||||||
\(965\) | 17925.5 | 0.597972 | ||||||||
\(966\) | −21662.5 | −0.721512 | ||||||||
\(967\) | 21854.1 | 0.726764 | 0.363382 | − | 0.931640i | \(-0.381622\pi\) | ||||
0.363382 | + | 0.931640i | \(0.381622\pi\) | |||||||
\(968\) | −4172.30 | −0.138536 | ||||||||
\(969\) | −25750.8 | −0.853699 | ||||||||
\(970\) | −59513.5 | −1.96996 | ||||||||
\(971\) | 23044.6 | 0.761622 | 0.380811 | − | 0.924653i | \(-0.375645\pi\) | ||||
0.380811 | + | 0.924653i | \(0.375645\pi\) | |||||||
\(972\) | 59389.3 | 1.95979 | ||||||||
\(973\) | 22552.6 | 0.743068 | ||||||||
\(974\) | −18676.2 | −0.614399 | ||||||||
\(975\) | 5865.07 | 0.192649 | ||||||||
\(976\) | 4875.16 | 0.159887 | ||||||||
\(977\) | 59011.4 | 1.93239 | 0.966193 | − | 0.257820i | \(-0.0830042\pi\) | ||||
0.966193 | + | 0.257820i | \(0.0830042\pi\) | |||||||
\(978\) | −47968.0 | −1.56835 | ||||||||
\(979\) | −13672.2 | −0.446339 | ||||||||
\(980\) | 34213.7 | 1.11522 | ||||||||
\(981\) | −11080.4 | −0.360623 | ||||||||
\(982\) | 15586.9 | 0.506514 | ||||||||
\(983\) | −4203.76 | −0.136398 | −0.0681989 | − | 0.997672i | \(-0.521725\pi\) | ||||
−0.0681989 | + | 0.997672i | \(0.521725\pi\) | |||||||
\(984\) | −2669.55 | −0.0864860 | ||||||||
\(985\) | −19362.7 | −0.626341 | ||||||||
\(986\) | −56081.6 | −1.81136 | ||||||||
\(987\) | −18139.0 | −0.584974 | ||||||||
\(988\) | 117560. | 3.78552 | ||||||||
\(989\) | 793.698 | 0.0255188 | ||||||||
\(990\) | −12297.7 | −0.394794 | ||||||||
\(991\) | 25120.7 | 0.805233 | 0.402616 | − | 0.915369i | \(-0.368101\pi\) | ||||
0.402616 | + | 0.915369i | \(0.368101\pi\) | |||||||
\(992\) | 12120.3 | 0.387922 | ||||||||
\(993\) | 26911.4 | 0.860028 | ||||||||
\(994\) | −2036.91 | −0.0649968 | ||||||||
\(995\) | −28109.8 | −0.895617 | ||||||||
\(996\) | 64836.8 | 2.06268 | ||||||||
\(997\) | −24088.4 | −0.765182 | −0.382591 | − | 0.923918i | \(-0.624968\pi\) | ||||
−0.382591 | + | 0.923918i | \(0.624968\pi\) | |||||||
\(998\) | 31157.6 | 0.988252 | ||||||||
\(999\) | −34910.4 | −1.10562 |
(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 | 1441.4.a.b.1.10 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.4.a.b.1.10 | ✓ | 79 | 1.1 | even | 1 | trivial |