Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.65 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16719 | 1.53244 | 0.766218 | − | 0.642580i | \(-0.222136\pi\) | ||||
0.766218 | + | 0.642580i | \(0.222136\pi\) | |||||||
\(3\) | 2.87932 | 1.66238 | 0.831189 | − | 0.555990i | \(-0.187661\pi\) | ||||
0.831189 | + | 0.555990i | \(0.187661\pi\) | |||||||
\(4\) | 2.69672 | 1.34836 | ||||||||
\(5\) | −4.25842 | −1.90442 | −0.952211 | − | 0.305442i | \(-0.901196\pi\) | ||||
−0.952211 | + | 0.305442i | \(0.901196\pi\) | |||||||
\(6\) | 6.24005 | 2.54749 | ||||||||
\(7\) | −1.70968 | −0.646198 | −0.323099 | − | 0.946365i | \(-0.604725\pi\) | ||||
−0.323099 | + | 0.946365i | \(0.604725\pi\) | |||||||
\(8\) | 1.50993 | 0.533842 | ||||||||
\(9\) | 5.29050 | 1.76350 | ||||||||
\(10\) | −9.22881 | −2.91840 | ||||||||
\(11\) | −4.00730 | −1.20825 | −0.604123 | − | 0.796891i | \(-0.706476\pi\) | ||||
−0.604123 | + | 0.796891i | \(0.706476\pi\) | |||||||
\(12\) | 7.76474 | 2.24149 | ||||||||
\(13\) | −2.63185 | −0.729945 | −0.364972 | − | 0.931018i | \(-0.618922\pi\) | ||||
−0.364972 | + | 0.931018i | \(0.618922\pi\) | |||||||
\(14\) | −3.70520 | −0.990258 | ||||||||
\(15\) | −12.2614 | −3.16587 | ||||||||
\(16\) | −2.12113 | −0.530282 | ||||||||
\(17\) | 4.14067 | 1.00426 | 0.502130 | − | 0.864792i | \(-0.332550\pi\) | ||||
0.502130 | + | 0.864792i | \(0.332550\pi\) | |||||||
\(18\) | 11.4655 | 2.70245 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −11.4838 | −2.56785 | ||||||||
\(21\) | −4.92272 | −1.07423 | ||||||||
\(22\) | −8.68458 | −1.85156 | ||||||||
\(23\) | −5.04807 | −1.05260 | −0.526298 | − | 0.850300i | \(-0.676420\pi\) | ||||
−0.526298 | + | 0.850300i | \(0.676420\pi\) | |||||||
\(24\) | 4.34759 | 0.887448 | ||||||||
\(25\) | 13.1341 | 2.62682 | ||||||||
\(26\) | −5.70373 | −1.11859 | ||||||||
\(27\) | 6.59508 | 1.26922 | ||||||||
\(28\) | −4.61053 | −0.871309 | ||||||||
\(29\) | −8.96525 | −1.66481 | −0.832403 | − | 0.554171i | \(-0.813035\pi\) | ||||
−0.832403 | + | 0.554171i | \(0.813035\pi\) | |||||||
\(30\) | −26.5727 | −4.85149 | ||||||||
\(31\) | 2.22075 | 0.398859 | 0.199429 | − | 0.979912i | \(-0.436091\pi\) | ||||
0.199429 | + | 0.979912i | \(0.436091\pi\) | |||||||
\(32\) | −7.61676 | −1.34647 | ||||||||
\(33\) | −11.5383 | −2.00856 | ||||||||
\(34\) | 8.97362 | 1.53896 | ||||||||
\(35\) | 7.28053 | 1.23063 | ||||||||
\(36\) | 14.2670 | 2.37783 | ||||||||
\(37\) | −7.33592 | −1.20602 | −0.603009 | − | 0.797735i | \(-0.706032\pi\) | ||||
−0.603009 | + | 0.797735i | \(0.706032\pi\) | |||||||
\(38\) | 2.16719 | 0.351565 | ||||||||
\(39\) | −7.57795 | −1.21344 | ||||||||
\(40\) | −6.42993 | −1.01666 | ||||||||
\(41\) | −8.62721 | −1.34734 | −0.673672 | − | 0.739031i | \(-0.735284\pi\) | ||||
−0.673672 | + | 0.739031i | \(0.735284\pi\) | |||||||
\(42\) | −10.6685 | −1.64618 | ||||||||
\(43\) | 6.93765 | 1.05798 | 0.528991 | − | 0.848628i | \(-0.322571\pi\) | ||||
0.528991 | + | 0.848628i | \(0.322571\pi\) | |||||||
\(44\) | −10.8066 | −1.62915 | ||||||||
\(45\) | −22.5291 | −3.35844 | ||||||||
\(46\) | −10.9401 | −1.61304 | ||||||||
\(47\) | −5.46855 | −0.797671 | −0.398835 | − | 0.917023i | \(-0.630585\pi\) | ||||
−0.398835 | + | 0.917023i | \(0.630585\pi\) | |||||||
\(48\) | −6.10741 | −0.881529 | ||||||||
\(49\) | −4.07700 | −0.582428 | ||||||||
\(50\) | 28.4641 | 4.02544 | ||||||||
\(51\) | 11.9223 | 1.66946 | ||||||||
\(52\) | −7.09738 | −0.984230 | ||||||||
\(53\) | 3.24590 | 0.445859 | 0.222929 | − | 0.974835i | \(-0.428438\pi\) | ||||
0.222929 | + | 0.974835i | \(0.428438\pi\) | |||||||
\(54\) | 14.2928 | 1.94500 | ||||||||
\(55\) | 17.0647 | 2.30101 | ||||||||
\(56\) | −2.58150 | −0.344968 | ||||||||
\(57\) | 2.87932 | 0.381376 | ||||||||
\(58\) | −19.4294 | −2.55121 | ||||||||
\(59\) | 9.54293 | 1.24238 | 0.621192 | − | 0.783659i | \(-0.286649\pi\) | ||||
0.621192 | + | 0.783659i | \(0.286649\pi\) | |||||||
\(60\) | −33.0655 | −4.26873 | ||||||||
\(61\) | −2.66329 | −0.340999 | −0.170500 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170500 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(62\) | 4.81279 | 0.611225 | ||||||||
\(63\) | −9.04505 | −1.13957 | ||||||||
\(64\) | −12.2647 | −1.53309 | ||||||||
\(65\) | 11.2075 | 1.39012 | ||||||||
\(66\) | −25.0057 | −3.07799 | ||||||||
\(67\) | 6.98673 | 0.853565 | 0.426783 | − | 0.904354i | \(-0.359647\pi\) | ||||
0.426783 | + | 0.904354i | \(0.359647\pi\) | |||||||
\(68\) | 11.1662 | 1.35411 | ||||||||
\(69\) | −14.5350 | −1.74981 | ||||||||
\(70\) | 15.7783 | 1.88587 | ||||||||
\(71\) | 3.65784 | 0.434105 | 0.217053 | − | 0.976160i | \(-0.430356\pi\) | ||||
0.217053 | + | 0.976160i | \(0.430356\pi\) | |||||||
\(72\) | 7.98830 | 0.941431 | ||||||||
\(73\) | −2.97541 | −0.348246 | −0.174123 | − | 0.984724i | \(-0.555709\pi\) | ||||
−0.174123 | + | 0.984724i | \(0.555709\pi\) | |||||||
\(74\) | −15.8983 | −1.84814 | ||||||||
\(75\) | 37.8173 | 4.36677 | ||||||||
\(76\) | 2.69672 | 0.309335 | ||||||||
\(77\) | 6.85119 | 0.780766 | ||||||||
\(78\) | −16.4229 | −1.85953 | ||||||||
\(79\) | 14.4890 | 1.63014 | 0.815071 | − | 0.579361i | \(-0.196698\pi\) | ||||
0.815071 | + | 0.579361i | \(0.196698\pi\) | |||||||
\(80\) | 9.03265 | 1.00988 | ||||||||
\(81\) | 3.11786 | 0.346429 | ||||||||
\(82\) | −18.6968 | −2.06472 | ||||||||
\(83\) | 1.38732 | 0.152278 | 0.0761391 | − | 0.997097i | \(-0.475741\pi\) | ||||
0.0761391 | + | 0.997097i | \(0.475741\pi\) | |||||||
\(84\) | −13.2752 | −1.44844 | ||||||||
\(85\) | −17.6327 | −1.91253 | ||||||||
\(86\) | 15.0352 | 1.62129 | ||||||||
\(87\) | −25.8139 | −2.76754 | ||||||||
\(88\) | −6.05076 | −0.645013 | ||||||||
\(89\) | −13.4196 | −1.42248 | −0.711238 | − | 0.702952i | \(-0.751865\pi\) | ||||
−0.711238 | + | 0.702952i | \(0.751865\pi\) | |||||||
\(90\) | −48.8250 | −5.14660 | ||||||||
\(91\) | 4.49963 | 0.471689 | ||||||||
\(92\) | −13.6132 | −1.41928 | ||||||||
\(93\) | 6.39426 | 0.663053 | ||||||||
\(94\) | −11.8514 | −1.22238 | ||||||||
\(95\) | −4.25842 | −0.436904 | ||||||||
\(96\) | −21.9311 | −2.23834 | ||||||||
\(97\) | −0.983902 | −0.0999001 | −0.0499501 | − | 0.998752i | \(-0.515906\pi\) | ||||
−0.0499501 | + | 0.998752i | \(0.515906\pi\) | |||||||
\(98\) | −8.83564 | −0.892534 | ||||||||
\(99\) | −21.2006 | −2.13074 | ||||||||
\(100\) | 35.4191 | 3.54191 | ||||||||
\(101\) | −9.86814 | −0.981917 | −0.490958 | − | 0.871183i | \(-0.663353\pi\) | ||||
−0.490958 | + | 0.871183i | \(0.663353\pi\) | |||||||
\(102\) | 25.8380 | 2.55834 | ||||||||
\(103\) | 0.571976 | 0.0563584 | 0.0281792 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281792 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(104\) | −3.97393 | −0.389676 | ||||||||
\(105\) | 20.9630 | 2.04578 | ||||||||
\(106\) | 7.03449 | 0.683250 | ||||||||
\(107\) | 7.45932 | 0.721120 | 0.360560 | − | 0.932736i | \(-0.382586\pi\) | ||||
0.360560 | + | 0.932736i | \(0.382586\pi\) | |||||||
\(108\) | 17.7851 | 1.71137 | ||||||||
\(109\) | 7.75355 | 0.742656 | 0.371328 | − | 0.928502i | \(-0.378903\pi\) | ||||
0.371328 | + | 0.928502i | \(0.378903\pi\) | |||||||
\(110\) | 36.9826 | 3.52615 | ||||||||
\(111\) | −21.1225 | −2.00486 | ||||||||
\(112\) | 3.62645 | 0.342667 | ||||||||
\(113\) | −6.98163 | −0.656776 | −0.328388 | − | 0.944543i | \(-0.606505\pi\) | ||||
−0.328388 | + | 0.944543i | \(0.606505\pi\) | |||||||
\(114\) | 6.24005 | 0.584434 | ||||||||
\(115\) | 21.4968 | 2.00458 | ||||||||
\(116\) | −24.1768 | −2.24476 | ||||||||
\(117\) | −13.9238 | −1.28726 | ||||||||
\(118\) | 20.6814 | 1.90387 | ||||||||
\(119\) | −7.07921 | −0.648950 | ||||||||
\(120\) | −18.5138 | −1.69007 | ||||||||
\(121\) | 5.05842 | 0.459857 | ||||||||
\(122\) | −5.77186 | −0.522560 | ||||||||
\(123\) | −24.8405 | −2.23979 | ||||||||
\(124\) | 5.98875 | 0.537806 | ||||||||
\(125\) | −34.6384 | −3.09815 | ||||||||
\(126\) | −19.6024 | −1.74632 | ||||||||
\(127\) | 8.38454 | 0.744007 | 0.372004 | − | 0.928231i | \(-0.378671\pi\) | ||||
0.372004 | + | 0.928231i | \(0.378671\pi\) | |||||||
\(128\) | −11.3465 | −1.00290 | ||||||||
\(129\) | 19.9757 | 1.75876 | ||||||||
\(130\) | 24.2889 | 2.13027 | ||||||||
\(131\) | 12.6908 | 1.10880 | 0.554401 | − | 0.832250i | \(-0.312948\pi\) | ||||
0.554401 | + | 0.832250i | \(0.312948\pi\) | |||||||
\(132\) | −31.1156 | −2.70827 | ||||||||
\(133\) | −1.70968 | −0.148248 | ||||||||
\(134\) | 15.1416 | 1.30803 | ||||||||
\(135\) | −28.0846 | −2.41714 | ||||||||
\(136\) | 6.25214 | 0.536116 | ||||||||
\(137\) | −9.74542 | −0.832608 | −0.416304 | − | 0.909226i | \(-0.636675\pi\) | ||||
−0.416304 | + | 0.909226i | \(0.636675\pi\) | |||||||
\(138\) | −31.5002 | −2.68147 | ||||||||
\(139\) | 11.7380 | 0.995605 | 0.497802 | − | 0.867291i | \(-0.334140\pi\) | ||||
0.497802 | + | 0.867291i | \(0.334140\pi\) | |||||||
\(140\) | 19.6336 | 1.65934 | ||||||||
\(141\) | −15.7457 | −1.32603 | ||||||||
\(142\) | 7.92724 | 0.665239 | ||||||||
\(143\) | 10.5466 | 0.881953 | ||||||||
\(144\) | −11.2218 | −0.935152 | ||||||||
\(145\) | 38.1778 | 3.17049 | ||||||||
\(146\) | −6.44830 | −0.533665 | ||||||||
\(147\) | −11.7390 | −0.968215 | ||||||||
\(148\) | −19.7829 | −1.62615 | ||||||||
\(149\) | 7.15271 | 0.585973 | 0.292986 | − | 0.956117i | \(-0.405351\pi\) | ||||
0.292986 | + | 0.956117i | \(0.405351\pi\) | |||||||
\(150\) | 81.9574 | 6.69179 | ||||||||
\(151\) | 0.483583 | 0.0393535 | 0.0196767 | − | 0.999806i | \(-0.493736\pi\) | ||||
0.0196767 | + | 0.999806i | \(0.493736\pi\) | |||||||
\(152\) | 1.50993 | 0.122472 | ||||||||
\(153\) | 21.9062 | 1.77101 | ||||||||
\(154\) | 14.8479 | 1.19647 | ||||||||
\(155\) | −9.45688 | −0.759595 | ||||||||
\(156\) | −20.4357 | −1.63616 | ||||||||
\(157\) | 13.3796 | 1.06781 | 0.533905 | − | 0.845544i | \(-0.320724\pi\) | ||||
0.533905 | + | 0.845544i | \(0.320724\pi\) | |||||||
\(158\) | 31.4005 | 2.49809 | ||||||||
\(159\) | 9.34599 | 0.741185 | ||||||||
\(160\) | 32.4353 | 2.56424 | ||||||||
\(161\) | 8.63058 | 0.680185 | ||||||||
\(162\) | 6.75701 | 0.530880 | ||||||||
\(163\) | −8.68627 | −0.680361 | −0.340181 | − | 0.940360i | \(-0.610488\pi\) | ||||
−0.340181 | + | 0.940360i | \(0.610488\pi\) | |||||||
\(164\) | −23.2652 | −1.81671 | ||||||||
\(165\) | 49.1349 | 3.82514 | ||||||||
\(166\) | 3.00659 | 0.233357 | ||||||||
\(167\) | 3.05375 | 0.236306 | 0.118153 | − | 0.992995i | \(-0.462303\pi\) | ||||
0.118153 | + | 0.992995i | \(0.462303\pi\) | |||||||
\(168\) | −7.43298 | −0.573467 | ||||||||
\(169\) | −6.07335 | −0.467180 | ||||||||
\(170\) | −38.2134 | −2.93084 | ||||||||
\(171\) | 5.29050 | 0.404574 | ||||||||
\(172\) | 18.7089 | 1.42654 | ||||||||
\(173\) | −20.1828 | −1.53447 | −0.767234 | − | 0.641367i | \(-0.778367\pi\) | ||||
−0.767234 | + | 0.641367i | \(0.778367\pi\) | |||||||
\(174\) | −55.9436 | −4.24107 | ||||||||
\(175\) | −22.4551 | −1.69745 | ||||||||
\(176\) | 8.49999 | 0.640711 | ||||||||
\(177\) | 27.4772 | 2.06531 | ||||||||
\(178\) | −29.0829 | −2.17985 | ||||||||
\(179\) | −21.7815 | −1.62802 | −0.814012 | − | 0.580848i | \(-0.802721\pi\) | ||||
−0.814012 | + | 0.580848i | \(0.802721\pi\) | |||||||
\(180\) | −60.7548 | −4.52840 | ||||||||
\(181\) | 15.1678 | 1.12742 | 0.563708 | − | 0.825974i | \(-0.309375\pi\) | ||||
0.563708 | + | 0.825974i | \(0.309375\pi\) | |||||||
\(182\) | 9.75156 | 0.722833 | ||||||||
\(183\) | −7.66847 | −0.566869 | ||||||||
\(184\) | −7.62225 | −0.561920 | ||||||||
\(185\) | 31.2394 | 2.29676 | ||||||||
\(186\) | 13.8576 | 1.01609 | ||||||||
\(187\) | −16.5929 | −1.21339 | ||||||||
\(188\) | −14.7472 | −1.07555 | ||||||||
\(189\) | −11.2755 | −0.820169 | ||||||||
\(190\) | −9.22881 | −0.669528 | ||||||||
\(191\) | 9.92944 | 0.718469 | 0.359234 | − | 0.933247i | \(-0.383038\pi\) | ||||
0.359234 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(192\) | −35.3141 | −2.54858 | ||||||||
\(193\) | −4.68227 | −0.337037 | −0.168519 | − | 0.985698i | \(-0.553898\pi\) | ||||
−0.168519 | + | 0.985698i | \(0.553898\pi\) | |||||||
\(194\) | −2.13231 | −0.153091 | ||||||||
\(195\) | 32.2701 | 2.31091 | ||||||||
\(196\) | −10.9945 | −0.785324 | ||||||||
\(197\) | 12.3738 | 0.881599 | 0.440799 | − | 0.897606i | \(-0.354695\pi\) | ||||
0.440799 | + | 0.897606i | \(0.354695\pi\) | |||||||
\(198\) | −45.9458 | −3.26522 | ||||||||
\(199\) | −18.3056 | −1.29765 | −0.648825 | − | 0.760938i | \(-0.724739\pi\) | ||||
−0.648825 | + | 0.760938i | \(0.724739\pi\) | |||||||
\(200\) | 19.8316 | 1.40231 | ||||||||
\(201\) | 20.1171 | 1.41895 | ||||||||
\(202\) | −21.3862 | −1.50472 | ||||||||
\(203\) | 15.3277 | 1.07579 | ||||||||
\(204\) | 32.1512 | 2.25103 | ||||||||
\(205\) | 36.7382 | 2.56591 | ||||||||
\(206\) | 1.23958 | 0.0863657 | ||||||||
\(207\) | −26.7068 | −1.85625 | ||||||||
\(208\) | 5.58250 | 0.387077 | ||||||||
\(209\) | −4.00730 | −0.277190 | ||||||||
\(210\) | 45.4308 | 3.13502 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 8.75329 | 0.601179 | ||||||||
\(213\) | 10.5321 | 0.721647 | ||||||||
\(214\) | 16.1658 | 1.10507 | ||||||||
\(215\) | −29.5434 | −2.01484 | ||||||||
\(216\) | 9.95813 | 0.677565 | ||||||||
\(217\) | −3.79677 | −0.257742 | ||||||||
\(218\) | 16.8034 | 1.13807 | ||||||||
\(219\) | −8.56718 | −0.578916 | ||||||||
\(220\) | 46.0189 | 3.10259 | ||||||||
\(221\) | −10.8976 | −0.733054 | ||||||||
\(222\) | −45.7765 | −3.07231 | ||||||||
\(223\) | −16.3037 | −1.09178 | −0.545888 | − | 0.837858i | \(-0.683808\pi\) | ||||
−0.545888 | + | 0.837858i | \(0.683808\pi\) | |||||||
\(224\) | 13.0222 | 0.870084 | ||||||||
\(225\) | 69.4859 | 4.63240 | ||||||||
\(226\) | −15.1305 | −1.00647 | ||||||||
\(227\) | 22.6846 | 1.50563 | 0.752815 | − | 0.658232i | \(-0.228696\pi\) | ||||
0.752815 | + | 0.658232i | \(0.228696\pi\) | |||||||
\(228\) | 7.76474 | 0.514232 | ||||||||
\(229\) | −18.3444 | −1.21223 | −0.606116 | − | 0.795376i | \(-0.707273\pi\) | ||||
−0.606116 | + | 0.795376i | \(0.707273\pi\) | |||||||
\(230\) | 46.5877 | 3.07190 | ||||||||
\(231\) | 19.7268 | 1.29793 | ||||||||
\(232\) | −13.5369 | −0.888744 | ||||||||
\(233\) | 17.4259 | 1.14161 | 0.570805 | − | 0.821086i | \(-0.306631\pi\) | ||||
0.570805 | + | 0.821086i | \(0.306631\pi\) | |||||||
\(234\) | −30.1756 | −1.97264 | ||||||||
\(235\) | 23.2874 | 1.51910 | ||||||||
\(236\) | 25.7346 | 1.67518 | ||||||||
\(237\) | 41.7185 | 2.70991 | ||||||||
\(238\) | −15.3420 | −0.994475 | ||||||||
\(239\) | −29.6240 | −1.91622 | −0.958110 | − | 0.286402i | \(-0.907541\pi\) | ||||
−0.958110 | + | 0.286402i | \(0.907541\pi\) | |||||||
\(240\) | 26.0079 | 1.67880 | ||||||||
\(241\) | −21.8992 | −1.41065 | −0.705327 | − | 0.708882i | \(-0.749200\pi\) | ||||
−0.705327 | + | 0.708882i | \(0.749200\pi\) | |||||||
\(242\) | 10.9626 | 0.704701 | ||||||||
\(243\) | −10.8079 | −0.693327 | ||||||||
\(244\) | −7.18215 | −0.459790 | ||||||||
\(245\) | 17.3615 | 1.10919 | ||||||||
\(246\) | −53.8342 | −3.43234 | ||||||||
\(247\) | −2.63185 | −0.167461 | ||||||||
\(248\) | 3.35319 | 0.212928 | ||||||||
\(249\) | 3.99454 | 0.253144 | ||||||||
\(250\) | −75.0681 | −4.74772 | ||||||||
\(251\) | 14.9288 | 0.942299 | 0.471150 | − | 0.882053i | \(-0.343839\pi\) | ||||
0.471150 | + | 0.882053i | \(0.343839\pi\) | |||||||
\(252\) | −24.3920 | −1.53655 | ||||||||
\(253\) | 20.2291 | 1.27179 | ||||||||
\(254\) | 18.1709 | 1.14014 | ||||||||
\(255\) | −50.7702 | −3.17935 | ||||||||
\(256\) | −0.0606190 | −0.00378869 | ||||||||
\(257\) | −12.5660 | −0.783843 | −0.391922 | − | 0.919999i | \(-0.628190\pi\) | ||||
−0.391922 | + | 0.919999i | \(0.628190\pi\) | |||||||
\(258\) | 43.2912 | 2.69519 | ||||||||
\(259\) | 12.5421 | 0.779326 | ||||||||
\(260\) | 30.2236 | 1.87439 | ||||||||
\(261\) | −47.4306 | −2.93588 | ||||||||
\(262\) | 27.5034 | 1.69917 | ||||||||
\(263\) | 16.7367 | 1.03203 | 0.516014 | − | 0.856580i | \(-0.327415\pi\) | ||||
0.516014 | + | 0.856580i | \(0.327415\pi\) | |||||||
\(264\) | −17.4221 | −1.07225 | ||||||||
\(265\) | −13.8224 | −0.849103 | ||||||||
\(266\) | −3.70520 | −0.227181 | ||||||||
\(267\) | −38.6394 | −2.36469 | ||||||||
\(268\) | 18.8413 | 1.15091 | ||||||||
\(269\) | −8.52905 | −0.520026 | −0.260013 | − | 0.965605i | \(-0.583727\pi\) | ||||
−0.260013 | + | 0.965605i | \(0.583727\pi\) | |||||||
\(270\) | −60.8647 | −3.70411 | ||||||||
\(271\) | 9.43623 | 0.573210 | 0.286605 | − | 0.958049i | \(-0.407473\pi\) | ||||
0.286605 | + | 0.958049i | \(0.407473\pi\) | |||||||
\(272\) | −8.78289 | −0.532541 | ||||||||
\(273\) | 12.9559 | 0.784125 | ||||||||
\(274\) | −21.1202 | −1.27592 | ||||||||
\(275\) | −52.6322 | −3.17384 | ||||||||
\(276\) | −39.1969 | −2.35938 | ||||||||
\(277\) | −7.66038 | −0.460267 | −0.230134 | − | 0.973159i | \(-0.573916\pi\) | ||||
−0.230134 | + | 0.973159i | \(0.573916\pi\) | |||||||
\(278\) | 25.4385 | 1.52570 | ||||||||
\(279\) | 11.7489 | 0.703387 | ||||||||
\(280\) | 10.9931 | 0.656964 | ||||||||
\(281\) | −12.9359 | −0.771694 | −0.385847 | − | 0.922563i | \(-0.626091\pi\) | ||||
−0.385847 | + | 0.922563i | \(0.626091\pi\) | |||||||
\(282\) | −34.1240 | −2.03206 | ||||||||
\(283\) | −28.4112 | −1.68887 | −0.844435 | − | 0.535657i | \(-0.820064\pi\) | ||||
−0.844435 | + | 0.535657i | \(0.820064\pi\) | |||||||
\(284\) | 9.86418 | 0.585331 | ||||||||
\(285\) | −12.2614 | −0.726300 | ||||||||
\(286\) | 22.8566 | 1.35154 | ||||||||
\(287\) | 14.7498 | 0.870651 | ||||||||
\(288\) | −40.2965 | −2.37449 | ||||||||
\(289\) | 0.145128 | 0.00853695 | ||||||||
\(290\) | 82.7386 | 4.85858 | ||||||||
\(291\) | −2.83297 | −0.166072 | ||||||||
\(292\) | −8.02387 | −0.469562 | ||||||||
\(293\) | 5.53292 | 0.323237 | 0.161618 | − | 0.986853i | \(-0.448329\pi\) | ||||
0.161618 | + | 0.986853i | \(0.448329\pi\) | |||||||
\(294\) | −25.4406 | −1.48373 | ||||||||
\(295\) | −40.6377 | −2.36602 | ||||||||
\(296\) | −11.0768 | −0.643823 | ||||||||
\(297\) | −26.4284 | −1.53353 | ||||||||
\(298\) | 15.5013 | 0.897966 | ||||||||
\(299\) | 13.2858 | 0.768336 | ||||||||
\(300\) | 101.983 | 5.88798 | ||||||||
\(301\) | −11.8612 | −0.683665 | ||||||||
\(302\) | 1.04802 | 0.0603067 | ||||||||
\(303\) | −28.4136 | −1.63232 | ||||||||
\(304\) | −2.12113 | −0.121655 | ||||||||
\(305\) | 11.3414 | 0.649406 | ||||||||
\(306\) | 47.4749 | 2.71396 | ||||||||
\(307\) | 18.8491 | 1.07577 | 0.537887 | − | 0.843017i | \(-0.319223\pi\) | ||||
0.537887 | + | 0.843017i | \(0.319223\pi\) | |||||||
\(308\) | 18.4758 | 1.05275 | ||||||||
\(309\) | 1.64690 | 0.0936890 | ||||||||
\(310\) | −20.4949 | −1.16403 | ||||||||
\(311\) | 26.6786 | 1.51280 | 0.756402 | − | 0.654107i | \(-0.226955\pi\) | ||||
0.756402 | + | 0.654107i | \(0.226955\pi\) | |||||||
\(312\) | −11.4422 | −0.647788 | ||||||||
\(313\) | 13.6310 | 0.770468 | 0.385234 | − | 0.922819i | \(-0.374121\pi\) | ||||
0.385234 | + | 0.922819i | \(0.374121\pi\) | |||||||
\(314\) | 28.9962 | 1.63635 | ||||||||
\(315\) | 38.5176 | 2.17022 | ||||||||
\(316\) | 39.0729 | 2.19802 | ||||||||
\(317\) | −29.6563 | −1.66567 | −0.832833 | − | 0.553524i | \(-0.813283\pi\) | ||||
−0.832833 | + | 0.553524i | \(0.813283\pi\) | |||||||
\(318\) | 20.2546 | 1.13582 | ||||||||
\(319\) | 35.9264 | 2.01149 | ||||||||
\(320\) | 52.2283 | 2.91965 | ||||||||
\(321\) | 21.4778 | 1.19877 | ||||||||
\(322\) | 18.7041 | 1.04234 | ||||||||
\(323\) | 4.14067 | 0.230393 | ||||||||
\(324\) | 8.40801 | 0.467112 | ||||||||
\(325\) | −34.5670 | −1.91743 | ||||||||
\(326\) | −18.8248 | −1.04261 | ||||||||
\(327\) | 22.3250 | 1.23457 | ||||||||
\(328\) | −13.0265 | −0.719269 | ||||||||
\(329\) | 9.34947 | 0.515453 | ||||||||
\(330\) | 106.485 | 5.86179 | ||||||||
\(331\) | 8.17521 | 0.449350 | 0.224675 | − | 0.974434i | \(-0.427868\pi\) | ||||
0.224675 | + | 0.974434i | \(0.427868\pi\) | |||||||
\(332\) | 3.74122 | 0.205326 | ||||||||
\(333\) | −38.8106 | −2.12681 | ||||||||
\(334\) | 6.61806 | 0.362124 | ||||||||
\(335\) | −29.7524 | −1.62555 | ||||||||
\(336\) | 10.4417 | 0.569642 | ||||||||
\(337\) | 10.9093 | 0.594265 | 0.297132 | − | 0.954836i | \(-0.403970\pi\) | ||||
0.297132 | + | 0.954836i | \(0.403970\pi\) | |||||||
\(338\) | −13.1621 | −0.715924 | ||||||||
\(339\) | −20.1024 | −1.09181 | ||||||||
\(340\) | −47.5505 | −2.57879 | ||||||||
\(341\) | −8.89921 | −0.481919 | ||||||||
\(342\) | 11.4655 | 0.619985 | ||||||||
\(343\) | 18.9381 | 1.02256 | ||||||||
\(344\) | 10.4754 | 0.564795 | ||||||||
\(345\) | 61.8961 | 3.33238 | ||||||||
\(346\) | −43.7400 | −2.35147 | ||||||||
\(347\) | −9.01824 | −0.484125 | −0.242062 | − | 0.970261i | \(-0.577824\pi\) | ||||
−0.242062 | + | 0.970261i | \(0.577824\pi\) | |||||||
\(348\) | −69.6128 | −3.73164 | ||||||||
\(349\) | −14.3748 | −0.769464 | −0.384732 | − | 0.923028i | \(-0.625706\pi\) | ||||
−0.384732 | + | 0.923028i | \(0.625706\pi\) | |||||||
\(350\) | −48.6645 | −2.60123 | ||||||||
\(351\) | −17.3573 | −0.926463 | ||||||||
\(352\) | 30.5226 | 1.62686 | ||||||||
\(353\) | −24.7876 | −1.31931 | −0.659656 | − | 0.751568i | \(-0.729298\pi\) | ||||
−0.659656 | + | 0.751568i | \(0.729298\pi\) | |||||||
\(354\) | 59.5483 | 3.16496 | ||||||||
\(355\) | −15.5766 | −0.826720 | ||||||||
\(356\) | −36.1890 | −1.91801 | ||||||||
\(357\) | −20.3833 | −1.07880 | ||||||||
\(358\) | −47.2047 | −2.49484 | ||||||||
\(359\) | 30.2455 | 1.59630 | 0.798149 | − | 0.602460i | \(-0.205813\pi\) | ||||
0.798149 | + | 0.602460i | \(0.205813\pi\) | |||||||
\(360\) | −34.0175 | −1.79288 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 32.8716 | 1.72769 | ||||||||
\(363\) | 14.5648 | 0.764456 | ||||||||
\(364\) | 12.1342 | 0.636007 | ||||||||
\(365\) | 12.6706 | 0.663207 | ||||||||
\(366\) | −16.6190 | −0.868691 | ||||||||
\(367\) | −20.1918 | −1.05400 | −0.527001 | − | 0.849864i | \(-0.676684\pi\) | ||||
−0.527001 | + | 0.849864i | \(0.676684\pi\) | |||||||
\(368\) | 10.7076 | 0.558172 | ||||||||
\(369\) | −45.6422 | −2.37604 | ||||||||
\(370\) | 67.7018 | 3.51965 | ||||||||
\(371\) | −5.54945 | −0.288113 | ||||||||
\(372\) | 17.2435 | 0.894036 | ||||||||
\(373\) | −10.6876 | −0.553384 | −0.276692 | − | 0.960959i | \(-0.589238\pi\) | ||||
−0.276692 | + | 0.960959i | \(0.589238\pi\) | |||||||
\(374\) | −35.9600 | −1.85945 | ||||||||
\(375\) | −99.7351 | −5.15030 | ||||||||
\(376\) | −8.25716 | −0.425830 | ||||||||
\(377\) | 23.5952 | 1.21522 | ||||||||
\(378\) | −24.4361 | −1.25686 | ||||||||
\(379\) | 14.9681 | 0.768861 | 0.384431 | − | 0.923154i | \(-0.374398\pi\) | ||||
0.384431 | + | 0.923154i | \(0.374398\pi\) | |||||||
\(380\) | −11.4838 | −0.589105 | ||||||||
\(381\) | 24.1418 | 1.23682 | ||||||||
\(382\) | 21.5190 | 1.10101 | ||||||||
\(383\) | −1.34642 | −0.0687988 | −0.0343994 | − | 0.999408i | \(-0.510952\pi\) | ||||
−0.0343994 | + | 0.999408i | \(0.510952\pi\) | |||||||
\(384\) | −32.6703 | −1.66720 | ||||||||
\(385\) | −29.1752 | −1.48691 | ||||||||
\(386\) | −10.1474 | −0.516488 | ||||||||
\(387\) | 36.7036 | 1.86575 | ||||||||
\(388\) | −2.65331 | −0.134702 | ||||||||
\(389\) | −15.1422 | −0.767739 | −0.383870 | − | 0.923387i | \(-0.625409\pi\) | ||||
−0.383870 | + | 0.923387i | \(0.625409\pi\) | |||||||
\(390\) | 69.9355 | 3.54132 | ||||||||
\(391\) | −20.9024 | −1.05708 | ||||||||
\(392\) | −6.15600 | −0.310925 | ||||||||
\(393\) | 36.5409 | 1.84325 | ||||||||
\(394\) | 26.8165 | 1.35099 | ||||||||
\(395\) | −61.7003 | −3.10448 | ||||||||
\(396\) | −57.1721 | −2.87301 | ||||||||
\(397\) | −24.7214 | −1.24073 | −0.620365 | − | 0.784314i | \(-0.713015\pi\) | ||||
−0.620365 | + | 0.784314i | \(0.713015\pi\) | |||||||
\(398\) | −39.6717 | −1.98856 | ||||||||
\(399\) | −4.92272 | −0.246444 | ||||||||
\(400\) | −27.8591 | −1.39296 | ||||||||
\(401\) | −1.13303 | −0.0565806 | −0.0282903 | − | 0.999600i | \(-0.509006\pi\) | ||||
−0.0282903 | + | 0.999600i | \(0.509006\pi\) | |||||||
\(402\) | 43.5975 | 2.17445 | ||||||||
\(403\) | −5.84469 | −0.291145 | ||||||||
\(404\) | −26.6116 | −1.32398 | ||||||||
\(405\) | −13.2771 | −0.659747 | ||||||||
\(406\) | 33.2181 | 1.64859 | ||||||||
\(407\) | 29.3972 | 1.45716 | ||||||||
\(408\) | 18.0019 | 0.891228 | ||||||||
\(409\) | −11.7058 | −0.578817 | −0.289409 | − | 0.957206i | \(-0.593459\pi\) | ||||
−0.289409 | + | 0.957206i | \(0.593459\pi\) | |||||||
\(410\) | 79.6188 | 3.93209 | ||||||||
\(411\) | −28.0602 | −1.38411 | ||||||||
\(412\) | 1.54246 | 0.0759915 | ||||||||
\(413\) | −16.3153 | −0.802826 | ||||||||
\(414\) | −57.8788 | −2.84459 | ||||||||
\(415\) | −5.90779 | −0.290002 | ||||||||
\(416\) | 20.0462 | 0.982846 | ||||||||
\(417\) | 33.7975 | 1.65507 | ||||||||
\(418\) | −8.68458 | −0.424777 | ||||||||
\(419\) | 13.4807 | 0.658577 | 0.329289 | − | 0.944229i | \(-0.393191\pi\) | ||||
0.329289 | + | 0.944229i | \(0.393191\pi\) | |||||||
\(420\) | 56.5314 | 2.75845 | ||||||||
\(421\) | 22.2022 | 1.08207 | 0.541036 | − | 0.841000i | \(-0.318032\pi\) | ||||
0.541036 | + | 0.841000i | \(0.318032\pi\) | |||||||
\(422\) | 2.16719 | 0.105497 | ||||||||
\(423\) | −28.9314 | −1.40669 | ||||||||
\(424\) | 4.90110 | 0.238018 | ||||||||
\(425\) | 54.3840 | 2.63801 | ||||||||
\(426\) | 22.8251 | 1.10588 | ||||||||
\(427\) | 4.55337 | 0.220353 | ||||||||
\(428\) | 20.1157 | 0.972330 | ||||||||
\(429\) | 30.3671 | 1.46614 | ||||||||
\(430\) | −64.0262 | −3.08762 | ||||||||
\(431\) | −37.5740 | −1.80988 | −0.904939 | − | 0.425542i | \(-0.860084\pi\) | ||||
−0.904939 | + | 0.425542i | \(0.860084\pi\) | |||||||
\(432\) | −13.9890 | −0.673046 | ||||||||
\(433\) | 21.1055 | 1.01426 | 0.507132 | − | 0.861868i | \(-0.330706\pi\) | ||||
0.507132 | + | 0.861868i | \(0.330706\pi\) | |||||||
\(434\) | −8.22833 | −0.394973 | ||||||||
\(435\) | 109.926 | 5.27055 | ||||||||
\(436\) | 20.9092 | 1.00137 | ||||||||
\(437\) | −5.04807 | −0.241482 | ||||||||
\(438\) | −18.5667 | −0.887152 | ||||||||
\(439\) | 27.9490 | 1.33393 | 0.666965 | − | 0.745089i | \(-0.267593\pi\) | ||||
0.666965 | + | 0.745089i | \(0.267593\pi\) | |||||||
\(440\) | 25.7666 | 1.22838 | ||||||||
\(441\) | −21.5693 | −1.02711 | ||||||||
\(442\) | −23.6173 | −1.12336 | ||||||||
\(443\) | 2.46109 | 0.116930 | 0.0584648 | − | 0.998289i | \(-0.481379\pi\) | ||||
0.0584648 | + | 0.998289i | \(0.481379\pi\) | |||||||
\(444\) | −56.9615 | −2.70327 | ||||||||
\(445\) | 57.1463 | 2.70899 | ||||||||
\(446\) | −35.3333 | −1.67308 | ||||||||
\(447\) | 20.5949 | 0.974107 | ||||||||
\(448\) | 20.9688 | 0.990681 | ||||||||
\(449\) | 14.3210 | 0.675851 | 0.337925 | − | 0.941173i | \(-0.390275\pi\) | ||||
0.337925 | + | 0.941173i | \(0.390275\pi\) | |||||||
\(450\) | 150.589 | 7.09885 | ||||||||
\(451\) | 34.5718 | 1.62792 | ||||||||
\(452\) | −18.8275 | −0.885572 | ||||||||
\(453\) | 1.39239 | 0.0654203 | ||||||||
\(454\) | 49.1619 | 2.30728 | ||||||||
\(455\) | −19.1613 | −0.898295 | ||||||||
\(456\) | 4.34759 | 0.203594 | ||||||||
\(457\) | −0.831442 | −0.0388932 | −0.0194466 | − | 0.999811i | \(-0.506190\pi\) | ||||
−0.0194466 | + | 0.999811i | \(0.506190\pi\) | |||||||
\(458\) | −39.7558 | −1.85767 | ||||||||
\(459\) | 27.3080 | 1.27463 | ||||||||
\(460\) | 57.9709 | 2.70291 | ||||||||
\(461\) | 33.1750 | 1.54511 | 0.772557 | − | 0.634946i | \(-0.218978\pi\) | ||||
0.772557 | + | 0.634946i | \(0.218978\pi\) | |||||||
\(462\) | 42.7518 | 1.98899 | ||||||||
\(463\) | −20.3065 | −0.943724 | −0.471862 | − | 0.881672i | \(-0.656418\pi\) | ||||
−0.471862 | + | 0.881672i | \(0.656418\pi\) | |||||||
\(464\) | 19.0165 | 0.882817 | ||||||||
\(465\) | −27.2294 | −1.26273 | ||||||||
\(466\) | 37.7653 | 1.74944 | ||||||||
\(467\) | −10.5297 | −0.487257 | −0.243629 | − | 0.969869i | \(-0.578338\pi\) | ||||
−0.243629 | + | 0.969869i | \(0.578338\pi\) | |||||||
\(468\) | −37.5487 | −1.73569 | ||||||||
\(469\) | −11.9451 | −0.551572 | ||||||||
\(470\) | 50.4682 | 2.32793 | ||||||||
\(471\) | 38.5242 | 1.77510 | ||||||||
\(472\) | 14.4092 | 0.663237 | ||||||||
\(473\) | −27.8012 | −1.27830 | ||||||||
\(474\) | 90.4121 | 4.15277 | ||||||||
\(475\) | 13.1341 | 0.602634 | ||||||||
\(476\) | −19.0907 | −0.875020 | ||||||||
\(477\) | 17.1724 | 0.786271 | ||||||||
\(478\) | −64.2010 | −2.93648 | ||||||||
\(479\) | −34.6808 | −1.58461 | −0.792303 | − | 0.610128i | \(-0.791118\pi\) | ||||
−0.792303 | + | 0.610128i | \(0.791118\pi\) | |||||||
\(480\) | 93.3918 | 4.26273 | ||||||||
\(481\) | 19.3071 | 0.880326 | ||||||||
\(482\) | −47.4599 | −2.16174 | ||||||||
\(483\) | 24.8502 | 1.13072 | ||||||||
\(484\) | 13.6412 | 0.620053 | ||||||||
\(485\) | 4.18986 | 0.190252 | ||||||||
\(486\) | −23.4228 | −1.06248 | ||||||||
\(487\) | −15.9807 | −0.724154 | −0.362077 | − | 0.932148i | \(-0.617932\pi\) | ||||
−0.362077 | + | 0.932148i | \(0.617932\pi\) | |||||||
\(488\) | −4.02139 | −0.182040 | ||||||||
\(489\) | −25.0106 | −1.13102 | ||||||||
\(490\) | 37.6258 | 1.69976 | ||||||||
\(491\) | −21.4119 | −0.966306 | −0.483153 | − | 0.875536i | \(-0.660508\pi\) | ||||
−0.483153 | + | 0.875536i | \(0.660508\pi\) | |||||||
\(492\) | −66.9880 | −3.02005 | ||||||||
\(493\) | −37.1221 | −1.67190 | ||||||||
\(494\) | −5.70373 | −0.256623 | ||||||||
\(495\) | 90.2809 | 4.05783 | ||||||||
\(496\) | −4.71050 | −0.211508 | ||||||||
\(497\) | −6.25373 | −0.280518 | ||||||||
\(498\) | 8.65695 | 0.387927 | ||||||||
\(499\) | −14.4330 | −0.646112 | −0.323056 | − | 0.946380i | \(-0.604710\pi\) | ||||
−0.323056 | + | 0.946380i | \(0.604710\pi\) | |||||||
\(500\) | −93.4102 | −4.17743 | ||||||||
\(501\) | 8.79272 | 0.392830 | ||||||||
\(502\) | 32.3537 | 1.44401 | ||||||||
\(503\) | 14.5977 | 0.650881 | 0.325440 | − | 0.945563i | \(-0.394487\pi\) | ||||
0.325440 | + | 0.945563i | \(0.394487\pi\) | |||||||
\(504\) | −13.6574 | −0.608351 | ||||||||
\(505\) | 42.0226 | 1.86998 | ||||||||
\(506\) | 43.8404 | 1.94894 | ||||||||
\(507\) | −17.4871 | −0.776630 | ||||||||
\(508\) | 22.6108 | 1.00319 | ||||||||
\(509\) | 26.4523 | 1.17248 | 0.586240 | − | 0.810138i | \(-0.300608\pi\) | ||||
0.586240 | + | 0.810138i | \(0.300608\pi\) | |||||||
\(510\) | −110.029 | −4.87216 | ||||||||
\(511\) | 5.08701 | 0.225036 | ||||||||
\(512\) | 22.5617 | 0.997094 | ||||||||
\(513\) | 6.59508 | 0.291180 | ||||||||
\(514\) | −27.2329 | −1.20119 | ||||||||
\(515\) | −2.43571 | −0.107330 | ||||||||
\(516\) | 53.8690 | 2.37145 | ||||||||
\(517\) | 21.9141 | 0.963782 | ||||||||
\(518\) | 27.1811 | 1.19427 | ||||||||
\(519\) | −58.1127 | −2.55086 | ||||||||
\(520\) | 16.9226 | 0.742107 | ||||||||
\(521\) | −14.3554 | −0.628921 | −0.314460 | − | 0.949271i | \(-0.601824\pi\) | ||||
−0.314460 | + | 0.949271i | \(0.601824\pi\) | |||||||
\(522\) | −102.791 | −4.49905 | ||||||||
\(523\) | −25.3097 | −1.10672 | −0.553359 | − | 0.832943i | \(-0.686654\pi\) | ||||
−0.553359 | + | 0.832943i | \(0.686654\pi\) | |||||||
\(524\) | 34.2236 | 1.49507 | ||||||||
\(525\) | −64.6555 | −2.82180 | ||||||||
\(526\) | 36.2716 | 1.58152 | ||||||||
\(527\) | 9.19539 | 0.400557 | ||||||||
\(528\) | 24.4742 | 1.06510 | ||||||||
\(529\) | 2.48300 | 0.107956 | ||||||||
\(530\) | −29.9558 | −1.30120 | ||||||||
\(531\) | 50.4868 | 2.19094 | ||||||||
\(532\) | −4.61053 | −0.199892 | ||||||||
\(533\) | 22.7055 | 0.983486 | ||||||||
\(534\) | −83.7390 | −3.62374 | ||||||||
\(535\) | −31.7649 | −1.37332 | ||||||||
\(536\) | 10.5495 | 0.455669 | ||||||||
\(537\) | −62.7159 | −2.70639 | ||||||||
\(538\) | −18.4841 | −0.796906 | ||||||||
\(539\) | 16.3377 | 0.703716 | ||||||||
\(540\) | −75.7363 | −3.25917 | ||||||||
\(541\) | 37.4827 | 1.61151 | 0.805754 | − | 0.592250i | \(-0.201760\pi\) | ||||
0.805754 | + | 0.592250i | \(0.201760\pi\) | |||||||
\(542\) | 20.4501 | 0.878408 | ||||||||
\(543\) | 43.6730 | 1.87419 | ||||||||
\(544\) | −31.5385 | −1.35220 | ||||||||
\(545\) | −33.0179 | −1.41433 | ||||||||
\(546\) | 28.0779 | 1.20162 | ||||||||
\(547\) | −42.8872 | −1.83372 | −0.916862 | − | 0.399203i | \(-0.869287\pi\) | ||||
−0.916862 | + | 0.399203i | \(0.869287\pi\) | |||||||
\(548\) | −26.2807 | −1.12266 | ||||||||
\(549\) | −14.0901 | −0.601352 | ||||||||
\(550\) | −114.064 | −4.86371 | ||||||||
\(551\) | −8.96525 | −0.381933 | ||||||||
\(552\) | −21.9469 | −0.934123 | ||||||||
\(553\) | −24.7716 | −1.05339 | ||||||||
\(554\) | −16.6015 | −0.705331 | ||||||||
\(555\) | 89.9482 | 3.81809 | ||||||||
\(556\) | 31.6542 | 1.34244 | ||||||||
\(557\) | −21.4499 | −0.908863 | −0.454432 | − | 0.890782i | \(-0.650158\pi\) | ||||
−0.454432 | + | 0.890782i | \(0.650158\pi\) | |||||||
\(558\) | 25.4621 | 1.07790 | ||||||||
\(559\) | −18.2589 | −0.772268 | ||||||||
\(560\) | −15.4429 | −0.652583 | ||||||||
\(561\) | −47.7763 | −2.01712 | ||||||||
\(562\) | −28.0347 | −1.18257 | ||||||||
\(563\) | −3.36460 | −0.141801 | −0.0709005 | − | 0.997483i | \(-0.522587\pi\) | ||||
−0.0709005 | + | 0.997483i | \(0.522587\pi\) | |||||||
\(564\) | −42.4619 | −1.78797 | ||||||||
\(565\) | 29.7307 | 1.25078 | ||||||||
\(566\) | −61.5726 | −2.58809 | ||||||||
\(567\) | −5.33054 | −0.223862 | ||||||||
\(568\) | 5.52310 | 0.231744 | ||||||||
\(569\) | 40.1048 | 1.68128 | 0.840640 | − | 0.541595i | \(-0.182179\pi\) | ||||
0.840640 | + | 0.541595i | \(0.182179\pi\) | |||||||
\(570\) | −26.5727 | −1.11301 | ||||||||
\(571\) | −8.77625 | −0.367275 | −0.183637 | − | 0.982994i | \(-0.558787\pi\) | ||||
−0.183637 | + | 0.982994i | \(0.558787\pi\) | |||||||
\(572\) | 28.4413 | 1.18919 | ||||||||
\(573\) | 28.5900 | 1.19437 | ||||||||
\(574\) | 31.9656 | 1.33422 | ||||||||
\(575\) | −66.3019 | −2.76498 | ||||||||
\(576\) | −64.8865 | −2.70361 | ||||||||
\(577\) | −32.3697 | −1.34757 | −0.673784 | − | 0.738928i | \(-0.735332\pi\) | ||||
−0.673784 | + | 0.738928i | \(0.735332\pi\) | |||||||
\(578\) | 0.314521 | 0.0130823 | ||||||||
\(579\) | −13.4818 | −0.560283 | ||||||||
\(580\) | 102.955 | 4.27497 | ||||||||
\(581\) | −2.37187 | −0.0984019 | ||||||||
\(582\) | −6.13959 | −0.254494 | ||||||||
\(583\) | −13.0073 | −0.538707 | ||||||||
\(584\) | −4.49268 | −0.185908 | ||||||||
\(585\) | 59.2934 | 2.45148 | ||||||||
\(586\) | 11.9909 | 0.495340 | ||||||||
\(587\) | 9.09005 | 0.375186 | 0.187593 | − | 0.982247i | \(-0.439931\pi\) | ||||
0.187593 | + | 0.982247i | \(0.439931\pi\) | |||||||
\(588\) | −31.6568 | −1.30550 | ||||||||
\(589\) | 2.22075 | 0.0915044 | ||||||||
\(590\) | −88.0698 | −3.62578 | ||||||||
\(591\) | 35.6282 | 1.46555 | ||||||||
\(592\) | 15.5604 | 0.639529 | ||||||||
\(593\) | −20.4309 | −0.838996 | −0.419498 | − | 0.907756i | \(-0.637794\pi\) | ||||
−0.419498 | + | 0.907756i | \(0.637794\pi\) | |||||||
\(594\) | −57.2755 | −2.35004 | ||||||||
\(595\) | 30.1462 | 1.23588 | ||||||||
\(596\) | 19.2889 | 0.790103 | ||||||||
\(597\) | −52.7077 | −2.15718 | ||||||||
\(598\) | 28.7928 | 1.17743 | ||||||||
\(599\) | −18.5797 | −0.759147 | −0.379573 | − | 0.925162i | \(-0.623929\pi\) | ||||
−0.379573 | + | 0.925162i | \(0.623929\pi\) | |||||||
\(600\) | 57.1017 | 2.33117 | ||||||||
\(601\) | 17.2954 | 0.705493 | 0.352746 | − | 0.935719i | \(-0.385248\pi\) | ||||
0.352746 | + | 0.935719i | \(0.385248\pi\) | |||||||
\(602\) | −25.7054 | −1.04767 | ||||||||
\(603\) | 36.9633 | 1.50526 | ||||||||
\(604\) | 1.30409 | 0.0530627 | ||||||||
\(605\) | −21.5409 | −0.875761 | ||||||||
\(606\) | −61.5776 | −2.50142 | ||||||||
\(607\) | 24.4841 | 0.993778 | 0.496889 | − | 0.867814i | \(-0.334476\pi\) | ||||
0.496889 | + | 0.867814i | \(0.334476\pi\) | |||||||
\(608\) | −7.61676 | −0.308901 | ||||||||
\(609\) | 44.1334 | 1.78838 | ||||||||
\(610\) | 24.5790 | 0.995174 | ||||||||
\(611\) | 14.3924 | 0.582256 | ||||||||
\(612\) | 59.0749 | 2.38796 | ||||||||
\(613\) | −29.0335 | −1.17265 | −0.586326 | − | 0.810075i | \(-0.699426\pi\) | ||||
−0.586326 | + | 0.810075i | \(0.699426\pi\) | |||||||
\(614\) | 40.8496 | 1.64855 | ||||||||
\(615\) | 105.781 | 4.26551 | ||||||||
\(616\) | 10.3449 | 0.416806 | ||||||||
\(617\) | −28.1947 | −1.13508 | −0.567538 | − | 0.823347i | \(-0.692104\pi\) | ||||
−0.567538 | + | 0.823347i | \(0.692104\pi\) | |||||||
\(618\) | 3.56915 | 0.143572 | ||||||||
\(619\) | 45.9958 | 1.84873 | 0.924364 | − | 0.381512i | \(-0.124597\pi\) | ||||
0.924364 | + | 0.381512i | \(0.124597\pi\) | |||||||
\(620\) | −25.5026 | −1.02421 | ||||||||
\(621\) | −33.2924 | −1.33598 | ||||||||
\(622\) | 57.8177 | 2.31828 | ||||||||
\(623\) | 22.9432 | 0.919201 | ||||||||
\(624\) | 16.0738 | 0.643468 | ||||||||
\(625\) | 81.8342 | 3.27337 | ||||||||
\(626\) | 29.5409 | 1.18069 | ||||||||
\(627\) | −11.5383 | −0.460795 | ||||||||
\(628\) | 36.0811 | 1.43979 | ||||||||
\(629\) | −30.3756 | −1.21115 | ||||||||
\(630\) | 83.4750 | 3.32573 | ||||||||
\(631\) | 0.940049 | 0.0374228 | 0.0187114 | − | 0.999825i | \(-0.494044\pi\) | ||||
0.0187114 | + | 0.999825i | \(0.494044\pi\) | |||||||
\(632\) | 21.8775 | 0.870239 | ||||||||
\(633\) | 2.87932 | 0.114443 | ||||||||
\(634\) | −64.2710 | −2.55253 | ||||||||
\(635\) | −35.7048 | −1.41690 | ||||||||
\(636\) | 25.2036 | 0.999386 | ||||||||
\(637\) | 10.7301 | 0.425140 | ||||||||
\(638\) | 77.8595 | 3.08249 | ||||||||
\(639\) | 19.3518 | 0.765544 | ||||||||
\(640\) | 48.3182 | 1.90994 | ||||||||
\(641\) | −29.3880 | −1.16076 | −0.580379 | − | 0.814347i | \(-0.697095\pi\) | ||||
−0.580379 | + | 0.814347i | \(0.697095\pi\) | |||||||
\(642\) | 46.5465 | 1.83704 | ||||||||
\(643\) | −11.6452 | −0.459242 | −0.229621 | − | 0.973280i | \(-0.573749\pi\) | ||||
−0.229621 | + | 0.973280i | \(0.573749\pi\) | |||||||
\(644\) | 23.2743 | 0.917135 | ||||||||
\(645\) | −85.0649 | −3.34943 | ||||||||
\(646\) | 8.97362 | 0.353063 | ||||||||
\(647\) | 40.9315 | 1.60918 | 0.804591 | − | 0.593829i | \(-0.202384\pi\) | ||||
0.804591 | + | 0.593829i | \(0.202384\pi\) | |||||||
\(648\) | 4.70777 | 0.184939 | ||||||||
\(649\) | −38.2413 | −1.50110 | ||||||||
\(650\) | −74.9134 | −2.93835 | ||||||||
\(651\) | −10.9321 | −0.428464 | ||||||||
\(652\) | −23.4245 | −0.917373 | ||||||||
\(653\) | 26.5609 | 1.03941 | 0.519704 | − | 0.854346i | \(-0.326042\pi\) | ||||
0.519704 | + | 0.854346i | \(0.326042\pi\) | |||||||
\(654\) | 48.3825 | 1.89191 | ||||||||
\(655\) | −54.0428 | −2.11162 | ||||||||
\(656\) | 18.2994 | 0.714472 | ||||||||
\(657\) | −15.7414 | −0.614131 | ||||||||
\(658\) | 20.2621 | 0.789899 | ||||||||
\(659\) | −29.1176 | −1.13426 | −0.567130 | − | 0.823628i | \(-0.691946\pi\) | ||||
−0.567130 | + | 0.823628i | \(0.691946\pi\) | |||||||
\(660\) | 132.503 | 5.15768 | ||||||||
\(661\) | −34.2846 | −1.33352 | −0.666759 | − | 0.745274i | \(-0.732319\pi\) | ||||
−0.666759 | + | 0.745274i | \(0.732319\pi\) | |||||||
\(662\) | 17.7173 | 0.688601 | ||||||||
\(663\) | −31.3778 | −1.21861 | ||||||||
\(664\) | 2.09476 | 0.0812926 | ||||||||
\(665\) | 7.28053 | 0.282327 | ||||||||
\(666\) | −84.1101 | −3.25920 | ||||||||
\(667\) | 45.2572 | 1.75237 | ||||||||
\(668\) | 8.23511 | 0.318626 | ||||||||
\(669\) | −46.9436 | −1.81494 | ||||||||
\(670\) | −64.4792 | −2.49105 | ||||||||
\(671\) | 10.6726 | 0.412011 | ||||||||
\(672\) | 37.4952 | 1.44641 | ||||||||
\(673\) | −42.7027 | −1.64607 | −0.823033 | − | 0.567993i | \(-0.807720\pi\) | ||||
−0.823033 | + | 0.567993i | \(0.807720\pi\) | |||||||
\(674\) | 23.6424 | 0.910673 | ||||||||
\(675\) | 86.6204 | 3.33402 | ||||||||
\(676\) | −16.3781 | −0.629928 | ||||||||
\(677\) | −16.4776 | −0.633286 | −0.316643 | − | 0.948545i | \(-0.602556\pi\) | ||||
−0.316643 | + | 0.948545i | \(0.602556\pi\) | |||||||
\(678\) | −43.5657 | −1.67313 | ||||||||
\(679\) | 1.68216 | 0.0645553 | ||||||||
\(680\) | −26.6242 | −1.02099 | ||||||||
\(681\) | 65.3163 | 2.50292 | ||||||||
\(682\) | −19.2863 | −0.738510 | ||||||||
\(683\) | 32.2742 | 1.23494 | 0.617468 | − | 0.786596i | \(-0.288158\pi\) | ||||
0.617468 | + | 0.786596i | \(0.288158\pi\) | |||||||
\(684\) | 14.2670 | 0.545513 | ||||||||
\(685\) | 41.5001 | 1.58564 | ||||||||
\(686\) | 41.0425 | 1.56701 | ||||||||
\(687\) | −52.8194 | −2.01519 | ||||||||
\(688\) | −14.7156 | −0.561029 | ||||||||
\(689\) | −8.54273 | −0.325452 | ||||||||
\(690\) | 134.141 | 5.10666 | ||||||||
\(691\) | −0.935249 | −0.0355786 | −0.0177893 | − | 0.999842i | \(-0.505663\pi\) | ||||
−0.0177893 | + | 0.999842i | \(0.505663\pi\) | |||||||
\(692\) | −54.4274 | −2.06902 | ||||||||
\(693\) | 36.2462 | 1.37688 | ||||||||
\(694\) | −19.5443 | −0.741890 | ||||||||
\(695\) | −49.9853 | −1.89605 | ||||||||
\(696\) | −38.9772 | −1.47743 | ||||||||
\(697\) | −35.7224 | −1.35308 | ||||||||
\(698\) | −31.1529 | −1.17915 | ||||||||
\(699\) | 50.1748 | 1.89779 | ||||||||
\(700\) | −60.5552 | −2.28877 | ||||||||
\(701\) | −18.2432 | −0.689036 | −0.344518 | − | 0.938780i | \(-0.611958\pi\) | ||||
−0.344518 | + | 0.938780i | \(0.611958\pi\) | |||||||
\(702\) | −37.6166 | −1.41975 | ||||||||
\(703\) | −7.33592 | −0.276679 | ||||||||
\(704\) | 49.1484 | 1.85235 | ||||||||
\(705\) | 67.0519 | 2.52532 | ||||||||
\(706\) | −53.7196 | −2.02176 | ||||||||
\(707\) | 16.8714 | 0.634513 | ||||||||
\(708\) | 74.0983 | 2.78478 | ||||||||
\(709\) | 41.1922 | 1.54701 | 0.773503 | − | 0.633793i | \(-0.218503\pi\) | ||||
0.773503 | + | 0.633793i | \(0.218503\pi\) | |||||||
\(710\) | −33.7575 | −1.26690 | ||||||||
\(711\) | 76.6541 | 2.87475 | ||||||||
\(712\) | −20.2627 | −0.759378 | ||||||||
\(713\) | −11.2105 | −0.419837 | ||||||||
\(714\) | −44.1746 | −1.65319 | ||||||||
\(715\) | −44.9119 | −1.67961 | ||||||||
\(716\) | −58.7386 | −2.19517 | ||||||||
\(717\) | −85.2971 | −3.18548 | ||||||||
\(718\) | 65.5479 | 2.44623 | ||||||||
\(719\) | 47.8093 | 1.78299 | 0.891493 | − | 0.453035i | \(-0.149659\pi\) | ||||
0.891493 | + | 0.453035i | \(0.149659\pi\) | |||||||
\(720\) | 47.7872 | 1.78092 | ||||||||
\(721\) | −0.977895 | −0.0364187 | ||||||||
\(722\) | 2.16719 | 0.0806546 | ||||||||
\(723\) | −63.0550 | −2.34504 | ||||||||
\(724\) | 40.9034 | 1.52016 | ||||||||
\(725\) | −117.751 | −4.37315 | ||||||||
\(726\) | 31.5648 | 1.17148 | ||||||||
\(727\) | 0.453591 | 0.0168228 | 0.00841138 | − | 0.999965i | \(-0.497323\pi\) | ||||
0.00841138 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(728\) | 6.79414 | 0.251808 | ||||||||
\(729\) | −40.4730 | −1.49900 | ||||||||
\(730\) | 27.4595 | 1.01632 | ||||||||
\(731\) | 28.7265 | 1.06249 | ||||||||
\(732\) | −20.6797 | −0.764345 | ||||||||
\(733\) | 23.3673 | 0.863090 | 0.431545 | − | 0.902091i | \(-0.357969\pi\) | ||||
0.431545 | + | 0.902091i | \(0.357969\pi\) | |||||||
\(734\) | −43.7595 | −1.61519 | ||||||||
\(735\) | 49.9895 | 1.84389 | ||||||||
\(736\) | 38.4499 | 1.41728 | ||||||||
\(737\) | −27.9979 | −1.03132 | ||||||||
\(738\) | −98.9154 | −3.64113 | ||||||||
\(739\) | 29.2472 | 1.07588 | 0.537938 | − | 0.842985i | \(-0.319204\pi\) | ||||
0.537938 | + | 0.842985i | \(0.319204\pi\) | |||||||
\(740\) | 84.2440 | 3.09687 | ||||||||
\(741\) | −7.57795 | −0.278383 | ||||||||
\(742\) | −12.0267 | −0.441515 | ||||||||
\(743\) | −35.9322 | −1.31822 | −0.659112 | − | 0.752045i | \(-0.729068\pi\) | ||||
−0.659112 | + | 0.752045i | \(0.729068\pi\) | |||||||
\(744\) | 9.65491 | 0.353966 | ||||||||
\(745\) | −30.4592 | −1.11594 | ||||||||
\(746\) | −23.1621 | −0.848026 | ||||||||
\(747\) | 7.33962 | 0.268542 | ||||||||
\(748\) | −44.7464 | −1.63609 | ||||||||
\(749\) | −12.7530 | −0.465986 | ||||||||
\(750\) | −216.145 | −7.89251 | ||||||||
\(751\) | −47.5286 | −1.73434 | −0.867172 | − | 0.498009i | \(-0.834065\pi\) | ||||
−0.867172 | + | 0.498009i | \(0.834065\pi\) | |||||||
\(752\) | 11.5995 | 0.422990 | ||||||||
\(753\) | 42.9849 | 1.56646 | ||||||||
\(754\) | 51.1354 | 1.86224 | ||||||||
\(755\) | −2.05930 | −0.0749456 | ||||||||
\(756\) | −30.4068 | −1.10589 | ||||||||
\(757\) | 44.2924 | 1.60984 | 0.804918 | − | 0.593387i | \(-0.202209\pi\) | ||||
0.804918 | + | 0.593387i | \(0.202209\pi\) | |||||||
\(758\) | 32.4388 | 1.17823 | ||||||||
\(759\) | 58.2461 | 2.11420 | ||||||||
\(760\) | −6.42993 | −0.233238 | ||||||||
\(761\) | −23.3740 | −0.847307 | −0.423653 | − | 0.905824i | \(-0.639253\pi\) | ||||
−0.423653 | + | 0.905824i | \(0.639253\pi\) | |||||||
\(762\) | 52.3199 | 1.89535 | ||||||||
\(763\) | −13.2561 | −0.479903 | ||||||||
\(764\) | 26.7769 | 0.968756 | ||||||||
\(765\) | −93.2856 | −3.37275 | ||||||||
\(766\) | −2.91795 | −0.105430 | ||||||||
\(767\) | −25.1156 | −0.906871 | ||||||||
\(768\) | −0.174542 | −0.00629823 | ||||||||
\(769\) | 24.4875 | 0.883041 | 0.441521 | − | 0.897251i | \(-0.354439\pi\) | ||||
0.441521 | + | 0.897251i | \(0.354439\pi\) | |||||||
\(770\) | −63.2283 | −2.27859 | ||||||||
\(771\) | −36.1814 | −1.30304 | ||||||||
\(772\) | −12.6268 | −0.454448 | ||||||||
\(773\) | 23.5308 | 0.846343 | 0.423171 | − | 0.906050i | \(-0.360917\pi\) | ||||
0.423171 | + | 0.906050i | \(0.360917\pi\) | |||||||
\(774\) | 79.5438 | 2.85914 | ||||||||
\(775\) | 29.1676 | 1.04773 | ||||||||
\(776\) | −1.48563 | −0.0533309 | ||||||||
\(777\) | 36.1126 | 1.29553 | ||||||||
\(778\) | −32.8160 | −1.17651 | ||||||||
\(779\) | −8.62721 | −0.309102 | ||||||||
\(780\) | 87.0235 | 3.11594 | ||||||||
\(781\) | −14.6580 | −0.524506 | ||||||||
\(782\) | −45.2995 | −1.61991 | ||||||||
\(783\) | −59.1265 | −2.11301 | ||||||||
\(784\) | 8.64783 | 0.308851 | ||||||||
\(785\) | −56.9760 | −2.03356 | ||||||||
\(786\) | 79.1912 | 2.82466 | ||||||||
\(787\) | 22.5911 | 0.805287 | 0.402644 | − | 0.915357i | \(-0.368091\pi\) | ||||
0.402644 | + | 0.915357i | \(0.368091\pi\) | |||||||
\(788\) | 33.3688 | 1.18871 | ||||||||
\(789\) | 48.1903 | 1.71562 | ||||||||
\(790\) | −133.716 | −4.75741 | ||||||||
\(791\) | 11.9363 | 0.424408 | ||||||||
\(792\) | −32.0115 | −1.13748 | ||||||||
\(793\) | 7.00939 | 0.248911 | ||||||||
\(794\) | −53.5759 | −1.90134 | ||||||||
\(795\) | −39.7991 | −1.41153 | ||||||||
\(796\) | −49.3651 | −1.74970 | ||||||||
\(797\) | 11.7605 | 0.416577 | 0.208289 | − | 0.978067i | \(-0.433211\pi\) | ||||
0.208289 | + | 0.978067i | \(0.433211\pi\) | |||||||
\(798\) | −10.6685 | −0.377660 | ||||||||
\(799\) | −22.6435 | −0.801068 | ||||||||
\(800\) | −100.039 | −3.53693 | ||||||||
\(801\) | −70.9964 | −2.50853 | ||||||||
\(802\) | −2.45549 | −0.0867062 | ||||||||
\(803\) | 11.9234 | 0.420767 | ||||||||
\(804\) | 54.2501 | 1.91325 | ||||||||
\(805\) | −36.7526 | −1.29536 | ||||||||
\(806\) | −12.6666 | −0.446161 | ||||||||
\(807\) | −24.5579 | −0.864479 | ||||||||
\(808\) | −14.9002 | −0.524189 | ||||||||
\(809\) | −49.8893 | −1.75401 | −0.877006 | − | 0.480479i | \(-0.840463\pi\) | ||||
−0.877006 | + | 0.480479i | \(0.840463\pi\) | |||||||
\(810\) | −28.7741 | −1.01102 | ||||||||
\(811\) | −48.6349 | −1.70780 | −0.853900 | − | 0.520437i | \(-0.825769\pi\) | ||||
−0.853900 | + | 0.520437i | \(0.825769\pi\) | |||||||
\(812\) | 41.3346 | 1.45056 | ||||||||
\(813\) | 27.1699 | 0.952891 | ||||||||
\(814\) | 63.7094 | 2.23301 | ||||||||
\(815\) | 36.9898 | 1.29569 | ||||||||
\(816\) | −25.2888 | −0.885284 | ||||||||
\(817\) | 6.93765 | 0.242718 | ||||||||
\(818\) | −25.3688 | −0.887000 | ||||||||
\(819\) | 23.8053 | 0.831823 | ||||||||
\(820\) | 99.0729 | 3.45977 | ||||||||
\(821\) | −25.0945 | −0.875806 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(822\) | −60.8119 | −2.12106 | ||||||||
\(823\) | −48.1808 | −1.67948 | −0.839738 | − | 0.542992i | \(-0.817291\pi\) | ||||
−0.839738 | + | 0.542992i | \(0.817291\pi\) | |||||||
\(824\) | 0.863646 | 0.0300865 | ||||||||
\(825\) | −151.545 | −5.27613 | ||||||||
\(826\) | −35.3585 | −1.23028 | ||||||||
\(827\) | −46.7300 | −1.62496 | −0.812481 | − | 0.582988i | \(-0.801883\pi\) | ||||
−0.812481 | + | 0.582988i | \(0.801883\pi\) | |||||||
\(828\) | −72.0208 | −2.50290 | ||||||||
\(829\) | −32.1946 | −1.11817 | −0.559083 | − | 0.829112i | \(-0.688847\pi\) | ||||
−0.559083 | + | 0.829112i | \(0.688847\pi\) | |||||||
\(830\) | −12.8033 | −0.444410 | ||||||||
\(831\) | −22.0567 | −0.765138 | ||||||||
\(832\) | 32.2790 | 1.11907 | ||||||||
\(833\) | −16.8815 | −0.584909 | ||||||||
\(834\) | 73.2457 | 2.53629 | ||||||||
\(835\) | −13.0041 | −0.450026 | ||||||||
\(836\) | −10.8066 | −0.373753 | ||||||||
\(837\) | 14.6460 | 0.506240 | ||||||||
\(838\) | 29.2154 | 1.00923 | ||||||||
\(839\) | −38.0886 | −1.31496 | −0.657482 | − | 0.753470i | \(-0.728378\pi\) | ||||
−0.657482 | + | 0.753470i | \(0.728378\pi\) | |||||||
\(840\) | 31.6527 | 1.09212 | ||||||||
\(841\) | 51.3758 | 1.77158 | ||||||||
\(842\) | 48.1165 | 1.65821 | ||||||||
\(843\) | −37.2467 | −1.28285 | ||||||||
\(844\) | 2.69672 | 0.0928251 | ||||||||
\(845\) | 25.8628 | 0.889708 | ||||||||
\(846\) | −62.6998 | −2.15566 | ||||||||
\(847\) | −8.64828 | −0.297159 | ||||||||
\(848\) | −6.88497 | −0.236431 | ||||||||
\(849\) | −81.8050 | −2.80754 | ||||||||
\(850\) | 117.861 | 4.04258 | ||||||||
\(851\) | 37.0322 | 1.26945 | ||||||||
\(852\) | 28.4021 | 0.973041 | ||||||||
\(853\) | 8.25536 | 0.282658 | 0.141329 | − | 0.989963i | \(-0.454862\pi\) | ||||
0.141329 | + | 0.989963i | \(0.454862\pi\) | |||||||
\(854\) | 9.86803 | 0.337677 | ||||||||
\(855\) | −22.5291 | −0.770480 | ||||||||
\(856\) | 11.2631 | 0.384964 | ||||||||
\(857\) | −14.7310 | −0.503201 | −0.251600 | − | 0.967831i | \(-0.580957\pi\) | ||||
−0.251600 | + | 0.967831i | \(0.580957\pi\) | |||||||
\(858\) | 65.8114 | 2.24676 | ||||||||
\(859\) | −36.6395 | −1.25012 | −0.625061 | − | 0.780576i | \(-0.714926\pi\) | ||||
−0.625061 | + | 0.780576i | \(0.714926\pi\) | |||||||
\(860\) | −79.6704 | −2.71674 | ||||||||
\(861\) | 42.4693 | 1.44735 | ||||||||
\(862\) | −81.4302 | −2.77352 | ||||||||
\(863\) | −9.39637 | −0.319856 | −0.159928 | − | 0.987129i | \(-0.551126\pi\) | ||||
−0.159928 | + | 0.987129i | \(0.551126\pi\) | |||||||
\(864\) | −50.2331 | −1.70897 | ||||||||
\(865\) | 85.9466 | 2.92227 | ||||||||
\(866\) | 45.7396 | 1.55430 | ||||||||
\(867\) | 0.417871 | 0.0141916 | ||||||||
\(868\) | −10.2388 | −0.347529 | ||||||||
\(869\) | −58.0618 | −1.96961 | ||||||||
\(870\) | 238.231 | 8.07679 | ||||||||
\(871\) | −18.3881 | −0.623056 | ||||||||
\(872\) | 11.7074 | 0.396461 | ||||||||
\(873\) | −5.20533 | −0.176174 | ||||||||
\(874\) | −10.9401 | −0.370056 | ||||||||
\(875\) | 59.2206 | 2.00202 | ||||||||
\(876\) | −23.1033 | −0.780589 | ||||||||
\(877\) | −26.1174 | −0.881920 | −0.440960 | − | 0.897527i | \(-0.645362\pi\) | ||||
−0.440960 | + | 0.897527i | \(0.645362\pi\) | |||||||
\(878\) | 60.5708 | 2.04416 | ||||||||
\(879\) | 15.9311 | 0.537341 | ||||||||
\(880\) | −36.1965 | −1.22018 | ||||||||
\(881\) | −29.0872 | −0.979974 | −0.489987 | − | 0.871730i | \(-0.662998\pi\) | ||||
−0.489987 | + | 0.871730i | \(0.662998\pi\) | |||||||
\(882\) | −46.7449 | −1.57398 | ||||||||
\(883\) | 54.4577 | 1.83265 | 0.916324 | − | 0.400437i | \(-0.131142\pi\) | ||||
0.916324 | + | 0.400437i | \(0.131142\pi\) | |||||||
\(884\) | −29.3879 | −0.988422 | ||||||||
\(885\) | −117.009 | −3.93322 | ||||||||
\(886\) | 5.33365 | 0.179187 | ||||||||
\(887\) | −40.3775 | −1.35574 | −0.677872 | − | 0.735180i | \(-0.737098\pi\) | ||||
−0.677872 | + | 0.735180i | \(0.737098\pi\) | |||||||
\(888\) | −31.8935 | −1.07028 | ||||||||
\(889\) | −14.3349 | −0.480776 | ||||||||
\(890\) | 123.847 | 4.15136 | ||||||||
\(891\) | −12.4942 | −0.418571 | ||||||||
\(892\) | −43.9666 | −1.47211 | ||||||||
\(893\) | −5.46855 | −0.182998 | ||||||||
\(894\) | 44.6332 | 1.49276 | ||||||||
\(895\) | 92.7546 | 3.10044 | ||||||||
\(896\) | 19.3989 | 0.648072 | ||||||||
\(897\) | 38.2540 | 1.27727 | ||||||||
\(898\) | 31.0364 | 1.03570 | ||||||||
\(899\) | −19.9096 | −0.664022 | ||||||||
\(900\) | 187.384 | 6.24615 | ||||||||
\(901\) | 13.4402 | 0.447758 | ||||||||
\(902\) | 74.9237 | 2.49469 | ||||||||
\(903\) | −34.1521 | −1.13651 | ||||||||
\(904\) | −10.5418 | −0.350615 | ||||||||
\(905\) | −64.5909 | −2.14707 | ||||||||
\(906\) | 3.01758 | 0.100252 | ||||||||
\(907\) | −7.48800 | −0.248635 | −0.124318 | − | 0.992242i | \(-0.539674\pi\) | ||||
−0.124318 | + | 0.992242i | \(0.539674\pi\) | |||||||
\(908\) | 61.1741 | 2.03013 | ||||||||
\(909\) | −52.2074 | −1.73161 | ||||||||
\(910\) | −41.5262 | −1.37658 | ||||||||
\(911\) | −30.2244 | −1.00138 | −0.500690 | − | 0.865627i | \(-0.666920\pi\) | ||||
−0.500690 | + | 0.865627i | \(0.666920\pi\) | |||||||
\(912\) | −6.10741 | −0.202237 | ||||||||
\(913\) | −5.55941 | −0.183989 | ||||||||
\(914\) | −1.80190 | −0.0596014 | ||||||||
\(915\) | 32.6555 | 1.07956 | ||||||||
\(916\) | −49.4698 | −1.63453 | ||||||||
\(917\) | −21.6972 | −0.716505 | ||||||||
\(918\) | 59.1817 | 1.95329 | ||||||||
\(919\) | 34.0006 | 1.12158 | 0.560788 | − | 0.827959i | \(-0.310498\pi\) | ||||
0.560788 | + | 0.827959i | \(0.310498\pi\) | |||||||
\(920\) | 32.4587 | 1.07013 | ||||||||
\(921\) | 54.2726 | 1.78834 | ||||||||
\(922\) | 71.8966 | 2.36779 | ||||||||
\(923\) | −9.62689 | −0.316873 | ||||||||
\(924\) | 53.1977 | 1.75008 | ||||||||
\(925\) | −96.3507 | −3.16799 | ||||||||
\(926\) | −44.0081 | −1.44620 | ||||||||
\(927\) | 3.02603 | 0.0993880 | ||||||||
\(928\) | 68.2862 | 2.24160 | ||||||||
\(929\) | 22.5268 | 0.739082 | 0.369541 | − | 0.929214i | \(-0.379515\pi\) | ||||
0.369541 | + | 0.929214i | \(0.379515\pi\) | |||||||
\(930\) | −59.0114 | −1.93506 | ||||||||
\(931\) | −4.07700 | −0.133618 | ||||||||
\(932\) | 46.9929 | 1.53930 | ||||||||
\(933\) | 76.8163 | 2.51485 | ||||||||
\(934\) | −22.8199 | −0.746691 | ||||||||
\(935\) | 70.6594 | 2.31081 | ||||||||
\(936\) | −21.0240 | −0.687192 | ||||||||
\(937\) | 21.1318 | 0.690345 | 0.345172 | − | 0.938539i | \(-0.387820\pi\) | ||||
0.345172 | + | 0.938539i | \(0.387820\pi\) | |||||||
\(938\) | −25.8873 | −0.845249 | ||||||||
\(939\) | 39.2479 | 1.28081 | ||||||||
\(940\) | 62.7996 | 2.04830 | ||||||||
\(941\) | 2.99282 | 0.0975632 | 0.0487816 | − | 0.998809i | \(-0.484466\pi\) | ||||
0.0487816 | + | 0.998809i | \(0.484466\pi\) | |||||||
\(942\) | 83.4894 | 2.72023 | ||||||||
\(943\) | 43.5507 | 1.41821 | ||||||||
\(944\) | −20.2418 | −0.658814 | ||||||||
\(945\) | 48.0156 | 1.56195 | ||||||||
\(946\) | −60.2506 | −1.95892 | ||||||||
\(947\) | −17.4832 | −0.568129 | −0.284065 | − | 0.958805i | \(-0.591683\pi\) | ||||
−0.284065 | + | 0.958805i | \(0.591683\pi\) | |||||||
\(948\) | 112.503 | 3.65394 | ||||||||
\(949\) | 7.83086 | 0.254200 | ||||||||
\(950\) | 28.4641 | 0.923498 | ||||||||
\(951\) | −85.3901 | −2.76897 | ||||||||
\(952\) | −10.6892 | −0.346437 | ||||||||
\(953\) | 2.09617 | 0.0679017 | 0.0339509 | − | 0.999424i | \(-0.489191\pi\) | ||||
0.0339509 | + | 0.999424i | \(0.489191\pi\) | |||||||
\(954\) | 37.2159 | 1.20491 | ||||||||
\(955\) | −42.2837 | −1.36827 | ||||||||
\(956\) | −79.8878 | −2.58376 | ||||||||
\(957\) | 103.444 | 3.34386 | ||||||||
\(958\) | −75.1600 | −2.42831 | ||||||||
\(959\) | 16.6615 | 0.538029 | ||||||||
\(960\) | 150.382 | 4.85357 | ||||||||
\(961\) | −26.0683 | −0.840912 | ||||||||
\(962\) | 41.8421 | 1.34904 | ||||||||
\(963\) | 39.4635 | 1.27169 | ||||||||
\(964\) | −59.0562 | −1.90207 | ||||||||
\(965\) | 19.9390 | 0.641860 | ||||||||
\(966\) | 53.8552 | 1.73276 | ||||||||
\(967\) | 22.9660 | 0.738535 | 0.369268 | − | 0.929323i | \(-0.379609\pi\) | ||||
0.369268 | + | 0.929323i | \(0.379609\pi\) | |||||||
\(968\) | 7.63789 | 0.245491 | ||||||||
\(969\) | 11.9223 | 0.383000 | ||||||||
\(970\) | 9.08024 | 0.291549 | ||||||||
\(971\) | 32.5638 | 1.04502 | 0.522511 | − | 0.852633i | \(-0.324996\pi\) | ||||
0.522511 | + | 0.852633i | \(0.324996\pi\) | |||||||
\(972\) | −29.1459 | −0.934856 | ||||||||
\(973\) | −20.0682 | −0.643358 | ||||||||
\(974\) | −34.6332 | −1.10972 | ||||||||
\(975\) | −99.5296 | −3.18750 | ||||||||
\(976\) | 5.64918 | 0.180826 | ||||||||
\(977\) | −30.0208 | −0.960450 | −0.480225 | − | 0.877145i | \(-0.659445\pi\) | ||||
−0.480225 | + | 0.877145i | \(0.659445\pi\) | |||||||
\(978\) | −54.2027 | −1.73321 | ||||||||
\(979\) | 53.7763 | 1.71870 | ||||||||
\(980\) | 46.8193 | 1.49559 | ||||||||
\(981\) | 41.0202 | 1.30967 | ||||||||
\(982\) | −46.4037 | −1.48080 | ||||||||
\(983\) | 46.4133 | 1.48035 | 0.740177 | − | 0.672412i | \(-0.234742\pi\) | ||||
0.740177 | + | 0.672412i | \(0.234742\pi\) | |||||||
\(984\) | −37.5075 | −1.19570 | ||||||||
\(985\) | −52.6929 | −1.67894 | ||||||||
\(986\) | −80.4508 | −2.56208 | ||||||||
\(987\) | 26.9201 | 0.856878 | ||||||||
\(988\) | −7.09738 | −0.225798 | ||||||||
\(989\) | −35.0217 | −1.11363 | ||||||||
\(990\) | 195.656 | 6.21836 | ||||||||
\(991\) | 54.3961 | 1.72795 | 0.863974 | − | 0.503536i | \(-0.167968\pi\) | ||||
0.863974 | + | 0.503536i | \(0.167968\pi\) | |||||||
\(992\) | −16.9149 | −0.537050 | ||||||||
\(993\) | 23.5391 | 0.746990 | ||||||||
\(994\) | −13.5530 | −0.429876 | ||||||||
\(995\) | 77.9528 | 2.47127 | ||||||||
\(996\) | 10.7722 | 0.341330 | ||||||||
\(997\) | −42.4442 | −1.34422 | −0.672111 | − | 0.740451i | \(-0.734612\pi\) | ||||
−0.672111 | + | 0.740451i | \(0.734612\pi\) | |||||||
\(998\) | −31.2792 | −0.990125 | ||||||||
\(999\) | −48.3809 | −1.53070 |
(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 | 4009.2.a.c.1.65 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.65 | ✓ | 71 | 1.1 | even | 1 | trivial |