Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48664 | −1.75832 | −0.879161 | − | 0.476524i | \(-0.841896\pi\) | ||||
−0.879161 | + | 0.476524i | \(0.841896\pi\) | |||||||
\(3\) | 3.28438 | 1.89624 | 0.948120 | − | 0.317914i | \(-0.102982\pi\) | ||||
0.948120 | + | 0.317914i | \(0.102982\pi\) | |||||||
\(4\) | 4.18340 | 2.09170 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −8.16709 | −3.33420 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −5.42933 | −1.91956 | ||||||||
\(9\) | 7.78717 | 2.59572 | ||||||||
\(10\) | 2.48664 | 0.786346 | ||||||||
\(11\) | −3.56103 | −1.07369 | −0.536846 | − | 0.843680i | \(-0.680384\pi\) | ||||
−0.536846 | + | 0.843680i | \(0.680384\pi\) | |||||||
\(12\) | 13.7399 | 3.96636 | ||||||||
\(13\) | 1.97454 | 0.547638 | 0.273819 | − | 0.961781i | \(-0.411713\pi\) | ||||
0.273819 | + | 0.961781i | \(0.411713\pi\) | |||||||
\(14\) | 2.48664 | 0.664583 | ||||||||
\(15\) | −3.28438 | −0.848024 | ||||||||
\(16\) | 5.13402 | 1.28350 | ||||||||
\(17\) | −7.88010 | −1.91121 | −0.955603 | − | 0.294657i | \(-0.904795\pi\) | ||||
−0.955603 | + | 0.294657i | \(0.904795\pi\) | |||||||
\(18\) | −19.3639 | −4.56412 | ||||||||
\(19\) | −2.56746 | −0.589015 | −0.294507 | − | 0.955649i | \(-0.595156\pi\) | ||||
−0.294507 | + | 0.955649i | \(0.595156\pi\) | |||||||
\(20\) | −4.18340 | −0.935436 | ||||||||
\(21\) | −3.28438 | −0.716711 | ||||||||
\(22\) | 8.85502 | 1.88790 | ||||||||
\(23\) | 1.14897 | 0.239576 | 0.119788 | − | 0.992799i | \(-0.461779\pi\) | ||||
0.119788 | + | 0.992799i | \(0.461779\pi\) | |||||||
\(24\) | −17.8320 | −3.63994 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.90997 | −0.962924 | ||||||||
\(27\) | 15.7229 | 3.02587 | ||||||||
\(28\) | −4.18340 | −0.790588 | ||||||||
\(29\) | 1.72372 | 0.320086 | 0.160043 | − | 0.987110i | \(-0.448837\pi\) | ||||
0.160043 | + | 0.987110i | \(0.448837\pi\) | |||||||
\(30\) | 8.16709 | 1.49110 | ||||||||
\(31\) | 6.82699 | 1.22616 | 0.613082 | − | 0.790019i | \(-0.289930\pi\) | ||||
0.613082 | + | 0.790019i | \(0.289930\pi\) | |||||||
\(32\) | −1.90781 | −0.337256 | ||||||||
\(33\) | −11.6958 | −2.03598 | ||||||||
\(34\) | 19.5950 | 3.36052 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 32.5768 | 5.42947 | ||||||||
\(37\) | 7.16654 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(38\) | 6.38435 | 1.03568 | ||||||||
\(39\) | 6.48514 | 1.03845 | ||||||||
\(40\) | 5.42933 | 0.858452 | ||||||||
\(41\) | −3.32254 | −0.518894 | −0.259447 | − | 0.965757i | \(-0.583540\pi\) | ||||
−0.259447 | + | 0.965757i | \(0.583540\pi\) | |||||||
\(42\) | 8.16709 | 1.26021 | ||||||||
\(43\) | −4.87597 | −0.743578 | −0.371789 | − | 0.928317i | \(-0.621256\pi\) | ||||
−0.371789 | + | 0.928317i | \(0.621256\pi\) | |||||||
\(44\) | −14.8972 | −2.24584 | ||||||||
\(45\) | −7.78717 | −1.16084 | ||||||||
\(46\) | −2.85707 | −0.421252 | ||||||||
\(47\) | 3.93309 | 0.573700 | 0.286850 | − | 0.957976i | \(-0.407392\pi\) | ||||
0.286850 | + | 0.957976i | \(0.407392\pi\) | |||||||
\(48\) | 16.8621 | 2.43383 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.48664 | −0.351665 | ||||||||
\(51\) | −25.8813 | −3.62410 | ||||||||
\(52\) | 8.26027 | 1.14549 | ||||||||
\(53\) | −3.77441 | −0.518456 | −0.259228 | − | 0.965816i | \(-0.583468\pi\) | ||||
−0.259228 | + | 0.965816i | \(0.583468\pi\) | |||||||
\(54\) | −39.0973 | −5.32046 | ||||||||
\(55\) | 3.56103 | 0.480170 | ||||||||
\(56\) | 5.42933 | 0.725525 | ||||||||
\(57\) | −8.43251 | −1.11691 | ||||||||
\(58\) | −4.28627 | −0.562815 | ||||||||
\(59\) | 6.42701 | 0.836725 | 0.418363 | − | 0.908280i | \(-0.362604\pi\) | ||||
0.418363 | + | 0.908280i | \(0.362604\pi\) | |||||||
\(60\) | −13.7399 | −1.77381 | ||||||||
\(61\) | −14.5197 | −1.85905 | −0.929526 | − | 0.368756i | \(-0.879784\pi\) | ||||
−0.929526 | + | 0.368756i | \(0.879784\pi\) | |||||||
\(62\) | −16.9763 | −2.15599 | ||||||||
\(63\) | −7.78717 | −0.981091 | ||||||||
\(64\) | −5.52400 | −0.690499 | ||||||||
\(65\) | −1.97454 | −0.244911 | ||||||||
\(66\) | 29.0833 | 3.57990 | ||||||||
\(67\) | 9.79842 | 1.19707 | 0.598534 | − | 0.801097i | \(-0.295750\pi\) | ||||
0.598534 | + | 0.801097i | \(0.295750\pi\) | |||||||
\(68\) | −32.9656 | −3.99767 | ||||||||
\(69\) | 3.77364 | 0.454293 | ||||||||
\(70\) | −2.48664 | −0.297211 | ||||||||
\(71\) | 10.8647 | 1.28940 | 0.644702 | − | 0.764434i | \(-0.276982\pi\) | ||||
0.644702 | + | 0.764434i | \(0.276982\pi\) | |||||||
\(72\) | −42.2791 | −4.98264 | ||||||||
\(73\) | 10.4860 | 1.22729 | 0.613644 | − | 0.789583i | \(-0.289703\pi\) | ||||
0.613644 | + | 0.789583i | \(0.289703\pi\) | |||||||
\(74\) | −17.8206 | −2.07161 | ||||||||
\(75\) | 3.28438 | 0.379248 | ||||||||
\(76\) | −10.7407 | −1.23204 | ||||||||
\(77\) | 3.56103 | 0.405817 | ||||||||
\(78\) | −16.1262 | −1.82594 | ||||||||
\(79\) | 9.78565 | 1.10097 | 0.550486 | − | 0.834844i | \(-0.314442\pi\) | ||||
0.550486 | + | 0.834844i | \(0.314442\pi\) | |||||||
\(80\) | −5.13402 | −0.574000 | ||||||||
\(81\) | 28.2785 | 3.14206 | ||||||||
\(82\) | 8.26198 | 0.912383 | ||||||||
\(83\) | −2.98903 | −0.328088 | −0.164044 | − | 0.986453i | \(-0.552454\pi\) | ||||
−0.164044 | + | 0.986453i | \(0.552454\pi\) | |||||||
\(84\) | −13.7399 | −1.49914 | ||||||||
\(85\) | 7.88010 | 0.854717 | ||||||||
\(86\) | 12.1248 | 1.30745 | ||||||||
\(87\) | 5.66135 | 0.606960 | ||||||||
\(88\) | 19.3340 | 2.06101 | ||||||||
\(89\) | −1.05934 | −0.112289 | −0.0561447 | − | 0.998423i | \(-0.517881\pi\) | ||||
−0.0561447 | + | 0.998423i | \(0.517881\pi\) | |||||||
\(90\) | 19.3639 | 2.04114 | ||||||||
\(91\) | −1.97454 | −0.206988 | ||||||||
\(92\) | 4.80658 | 0.501121 | ||||||||
\(93\) | 22.4224 | 2.32510 | ||||||||
\(94\) | −9.78019 | −1.00875 | ||||||||
\(95\) | 2.56746 | 0.263415 | ||||||||
\(96\) | −6.26597 | −0.639518 | ||||||||
\(97\) | 8.30149 | 0.842889 | 0.421444 | − | 0.906854i | \(-0.361523\pi\) | ||||
0.421444 | + | 0.906854i | \(0.361523\pi\) | |||||||
\(98\) | −2.48664 | −0.251189 | ||||||||
\(99\) | −27.7304 | −2.78701 | ||||||||
\(100\) | 4.18340 | 0.418340 | ||||||||
\(101\) | −13.1811 | −1.31157 | −0.655785 | − | 0.754948i | \(-0.727662\pi\) | ||||
−0.655785 | + | 0.754948i | \(0.727662\pi\) | |||||||
\(102\) | 64.3575 | 6.37234 | ||||||||
\(103\) | 10.3389 | 1.01872 | 0.509359 | − | 0.860554i | \(-0.329883\pi\) | ||||
0.509359 | + | 0.860554i | \(0.329883\pi\) | |||||||
\(104\) | −10.7204 | −1.05122 | ||||||||
\(105\) | 3.28438 | 0.320523 | ||||||||
\(106\) | 9.38562 | 0.911612 | ||||||||
\(107\) | −1.21505 | −0.117463 | −0.0587316 | − | 0.998274i | \(-0.518706\pi\) | ||||
−0.0587316 | + | 0.998274i | \(0.518706\pi\) | |||||||
\(108\) | 65.7751 | 6.32922 | ||||||||
\(109\) | 2.28859 | 0.219207 | 0.109603 | − | 0.993975i | \(-0.465042\pi\) | ||||
0.109603 | + | 0.993975i | \(0.465042\pi\) | |||||||
\(110\) | −8.85502 | −0.844293 | ||||||||
\(111\) | 23.5377 | 2.23410 | ||||||||
\(112\) | −5.13402 | −0.485119 | ||||||||
\(113\) | −14.4375 | −1.35817 | −0.679084 | − | 0.734060i | \(-0.737623\pi\) | ||||
−0.679084 | + | 0.734060i | \(0.737623\pi\) | |||||||
\(114\) | 20.9686 | 1.96389 | ||||||||
\(115\) | −1.14897 | −0.107142 | ||||||||
\(116\) | 7.21100 | 0.669524 | ||||||||
\(117\) | 15.3761 | 1.42152 | ||||||||
\(118\) | −15.9817 | −1.47123 | ||||||||
\(119\) | 7.88010 | 0.722368 | ||||||||
\(120\) | 17.8320 | 1.62783 | ||||||||
\(121\) | 1.68096 | 0.152815 | ||||||||
\(122\) | 36.1052 | 3.26881 | ||||||||
\(123\) | −10.9125 | −0.983947 | ||||||||
\(124\) | 28.5600 | 2.56476 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 19.3639 | 1.72508 | ||||||||
\(127\) | 1.31794 | 0.116949 | 0.0584743 | − | 0.998289i | \(-0.481376\pi\) | ||||
0.0584743 | + | 0.998289i | \(0.481376\pi\) | |||||||
\(128\) | 17.5518 | 1.55138 | ||||||||
\(129\) | −16.0145 | −1.41000 | ||||||||
\(130\) | 4.90997 | 0.430633 | ||||||||
\(131\) | 18.2716 | 1.59640 | 0.798198 | − | 0.602395i | \(-0.205787\pi\) | ||||
0.798198 | + | 0.602395i | \(0.205787\pi\) | |||||||
\(132\) | −48.9282 | −4.25865 | ||||||||
\(133\) | 2.56746 | 0.222627 | ||||||||
\(134\) | −24.3652 | −2.10483 | ||||||||
\(135\) | −15.7229 | −1.35321 | ||||||||
\(136\) | 42.7837 | 3.66867 | ||||||||
\(137\) | −2.10301 | −0.179673 | −0.0898363 | − | 0.995957i | \(-0.528634\pi\) | ||||
−0.0898363 | + | 0.995957i | \(0.528634\pi\) | |||||||
\(138\) | −9.38371 | −0.798794 | ||||||||
\(139\) | −6.87366 | −0.583016 | −0.291508 | − | 0.956568i | \(-0.594157\pi\) | ||||
−0.291508 | + | 0.956568i | \(0.594157\pi\) | |||||||
\(140\) | 4.18340 | 0.353562 | ||||||||
\(141\) | 12.9178 | 1.08787 | ||||||||
\(142\) | −27.0167 | −2.26719 | ||||||||
\(143\) | −7.03139 | −0.587995 | ||||||||
\(144\) | 39.9795 | 3.33162 | ||||||||
\(145\) | −1.72372 | −0.143147 | ||||||||
\(146\) | −26.0748 | −2.15797 | ||||||||
\(147\) | 3.28438 | 0.270891 | ||||||||
\(148\) | 29.9805 | 2.46438 | ||||||||
\(149\) | −3.86043 | −0.316258 | −0.158129 | − | 0.987418i | \(-0.550546\pi\) | ||||
−0.158129 | + | 0.987418i | \(0.550546\pi\) | |||||||
\(150\) | −8.16709 | −0.666840 | ||||||||
\(151\) | 14.0677 | 1.14481 | 0.572406 | − | 0.819971i | \(-0.306010\pi\) | ||||
0.572406 | + | 0.819971i | \(0.306010\pi\) | |||||||
\(152\) | 13.9396 | 1.13065 | ||||||||
\(153\) | −61.3637 | −4.96096 | ||||||||
\(154\) | −8.85502 | −0.713558 | ||||||||
\(155\) | −6.82699 | −0.548357 | ||||||||
\(156\) | 27.1299 | 2.17213 | ||||||||
\(157\) | −0.799106 | −0.0637756 | −0.0318878 | − | 0.999491i | \(-0.510152\pi\) | ||||
−0.0318878 | + | 0.999491i | \(0.510152\pi\) | |||||||
\(158\) | −24.3334 | −1.93586 | ||||||||
\(159\) | −12.3966 | −0.983116 | ||||||||
\(160\) | 1.90781 | 0.150825 | ||||||||
\(161\) | −1.14897 | −0.0905512 | ||||||||
\(162\) | −70.3186 | −5.52475 | ||||||||
\(163\) | 7.01804 | 0.549695 | 0.274848 | − | 0.961488i | \(-0.411373\pi\) | ||||
0.274848 | + | 0.961488i | \(0.411373\pi\) | |||||||
\(164\) | −13.8995 | −1.08537 | ||||||||
\(165\) | 11.6958 | 0.910517 | ||||||||
\(166\) | 7.43264 | 0.576885 | ||||||||
\(167\) | 14.5887 | 1.12891 | 0.564454 | − | 0.825464i | \(-0.309087\pi\) | ||||
0.564454 | + | 0.825464i | \(0.309087\pi\) | |||||||
\(168\) | 17.8320 | 1.37577 | ||||||||
\(169\) | −9.10120 | −0.700093 | ||||||||
\(170\) | −19.5950 | −1.50287 | ||||||||
\(171\) | −19.9932 | −1.52892 | ||||||||
\(172\) | −20.3981 | −1.55534 | ||||||||
\(173\) | 18.1670 | 1.38121 | 0.690606 | − | 0.723232i | \(-0.257344\pi\) | ||||
0.690606 | + | 0.723232i | \(0.257344\pi\) | |||||||
\(174\) | −14.0778 | −1.06723 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −18.2824 | −1.37809 | ||||||||
\(177\) | 21.1088 | 1.58663 | ||||||||
\(178\) | 2.63419 | 0.197441 | ||||||||
\(179\) | 11.1634 | 0.834391 | 0.417196 | − | 0.908817i | \(-0.363013\pi\) | ||||
0.417196 | + | 0.908817i | \(0.363013\pi\) | |||||||
\(180\) | −32.5768 | −2.42813 | ||||||||
\(181\) | 0.368337 | 0.0273783 | 0.0136891 | − | 0.999906i | \(-0.495642\pi\) | ||||
0.0136891 | + | 0.999906i | \(0.495642\pi\) | |||||||
\(182\) | 4.90997 | 0.363951 | ||||||||
\(183\) | −47.6881 | −3.52521 | ||||||||
\(184\) | −6.23811 | −0.459880 | ||||||||
\(185\) | −7.16654 | −0.526895 | ||||||||
\(186\) | −55.7566 | −4.08828 | ||||||||
\(187\) | 28.0613 | 2.05205 | ||||||||
\(188\) | 16.4537 | 1.20001 | ||||||||
\(189\) | −15.7229 | −1.14367 | ||||||||
\(190\) | −6.38435 | −0.463169 | ||||||||
\(191\) | 13.0207 | 0.942144 | 0.471072 | − | 0.882095i | \(-0.343867\pi\) | ||||
0.471072 | + | 0.882095i | \(0.343867\pi\) | |||||||
\(192\) | −18.1429 | −1.30935 | ||||||||
\(193\) | 7.13123 | 0.513317 | 0.256659 | − | 0.966502i | \(-0.417378\pi\) | ||||
0.256659 | + | 0.966502i | \(0.417378\pi\) | |||||||
\(194\) | −20.6428 | −1.48207 | ||||||||
\(195\) | −6.48514 | −0.464410 | ||||||||
\(196\) | 4.18340 | 0.298814 | ||||||||
\(197\) | −6.90082 | −0.491663 | −0.245832 | − | 0.969313i | \(-0.579061\pi\) | ||||
−0.245832 | + | 0.969313i | \(0.579061\pi\) | |||||||
\(198\) | 68.9556 | 4.90046 | ||||||||
\(199\) | −12.6513 | −0.896830 | −0.448415 | − | 0.893825i | \(-0.648011\pi\) | ||||
−0.448415 | + | 0.893825i | \(0.648011\pi\) | |||||||
\(200\) | −5.42933 | −0.383912 | ||||||||
\(201\) | 32.1818 | 2.26993 | ||||||||
\(202\) | 32.7767 | 2.30616 | ||||||||
\(203\) | −1.72372 | −0.120981 | ||||||||
\(204\) | −108.272 | −7.58053 | ||||||||
\(205\) | 3.32254 | 0.232056 | ||||||||
\(206\) | −25.7091 | −1.79123 | ||||||||
\(207\) | 8.94719 | 0.621873 | ||||||||
\(208\) | 10.1373 | 0.702895 | ||||||||
\(209\) | 9.14280 | 0.632421 | ||||||||
\(210\) | −8.16709 | −0.563583 | ||||||||
\(211\) | 2.92960 | 0.201682 | 0.100841 | − | 0.994903i | \(-0.467847\pi\) | ||||
0.100841 | + | 0.994903i | \(0.467847\pi\) | |||||||
\(212\) | −15.7899 | −1.08445 | ||||||||
\(213\) | 35.6839 | 2.44502 | ||||||||
\(214\) | 3.02139 | 0.206538 | ||||||||
\(215\) | 4.87597 | 0.332538 | ||||||||
\(216\) | −85.3648 | −5.80834 | ||||||||
\(217\) | −6.82699 | −0.463446 | ||||||||
\(218\) | −5.69090 | −0.385436 | ||||||||
\(219\) | 34.4399 | 2.32723 | ||||||||
\(220\) | 14.8972 | 1.00437 | ||||||||
\(221\) | −15.5596 | −1.04665 | ||||||||
\(222\) | −58.5298 | −3.92826 | ||||||||
\(223\) | 13.4568 | 0.901131 | 0.450565 | − | 0.892743i | \(-0.351222\pi\) | ||||
0.450565 | + | 0.892743i | \(0.351222\pi\) | |||||||
\(224\) | 1.90781 | 0.127471 | ||||||||
\(225\) | 7.78717 | 0.519145 | ||||||||
\(226\) | 35.9010 | 2.38810 | ||||||||
\(227\) | 17.3492 | 1.15151 | 0.575753 | − | 0.817624i | \(-0.304709\pi\) | ||||
0.575753 | + | 0.817624i | \(0.304709\pi\) | |||||||
\(228\) | −35.2765 | −2.33625 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 2.85707 | 0.188390 | ||||||||
\(231\) | 11.6958 | 0.769527 | ||||||||
\(232\) | −9.35863 | −0.614424 | ||||||||
\(233\) | −21.6011 | −1.41513 | −0.707567 | − | 0.706646i | \(-0.750207\pi\) | ||||
−0.707567 | + | 0.706646i | \(0.750207\pi\) | |||||||
\(234\) | −38.2348 | −2.49949 | ||||||||
\(235\) | −3.93309 | −0.256566 | ||||||||
\(236\) | 26.8867 | 1.75018 | ||||||||
\(237\) | 32.1398 | 2.08771 | ||||||||
\(238\) | −19.5950 | −1.27016 | ||||||||
\(239\) | 24.5242 | 1.58634 | 0.793170 | − | 0.609000i | \(-0.208429\pi\) | ||||
0.793170 | + | 0.609000i | \(0.208429\pi\) | |||||||
\(240\) | −16.8621 | −1.08844 | ||||||||
\(241\) | 6.34370 | 0.408634 | 0.204317 | − | 0.978905i | \(-0.434503\pi\) | ||||
0.204317 | + | 0.978905i | \(0.434503\pi\) | |||||||
\(242\) | −4.17995 | −0.268697 | ||||||||
\(243\) | 45.7088 | 2.93222 | ||||||||
\(244\) | −60.7415 | −3.88858 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 27.1355 | 1.73010 | ||||||||
\(247\) | −5.06954 | −0.322567 | ||||||||
\(248\) | −37.0660 | −2.35369 | ||||||||
\(249\) | −9.81711 | −0.622134 | ||||||||
\(250\) | 2.48664 | 0.157269 | ||||||||
\(251\) | 1.35108 | 0.0852791 | 0.0426396 | − | 0.999091i | \(-0.486423\pi\) | ||||
0.0426396 | + | 0.999091i | \(0.486423\pi\) | |||||||
\(252\) | −32.5768 | −2.05215 | ||||||||
\(253\) | −4.09151 | −0.257231 | ||||||||
\(254\) | −3.27726 | −0.205633 | ||||||||
\(255\) | 25.8813 | 1.62075 | ||||||||
\(256\) | −32.5971 | −2.03732 | ||||||||
\(257\) | 3.56974 | 0.222674 | 0.111337 | − | 0.993783i | \(-0.464487\pi\) | ||||
0.111337 | + | 0.993783i | \(0.464487\pi\) | |||||||
\(258\) | 39.8225 | 2.47924 | ||||||||
\(259\) | −7.16654 | −0.445307 | ||||||||
\(260\) | −8.26027 | −0.512280 | ||||||||
\(261\) | 13.4229 | 0.830856 | ||||||||
\(262\) | −45.4349 | −2.80698 | ||||||||
\(263\) | 17.2626 | 1.06446 | 0.532230 | − | 0.846600i | \(-0.321354\pi\) | ||||
0.532230 | + | 0.846600i | \(0.321354\pi\) | |||||||
\(264\) | 63.5003 | 3.90818 | ||||||||
\(265\) | 3.77441 | 0.231860 | ||||||||
\(266\) | −6.38435 | −0.391450 | ||||||||
\(267\) | −3.47926 | −0.212928 | ||||||||
\(268\) | 40.9907 | 2.50391 | ||||||||
\(269\) | −15.6063 | −0.951535 | −0.475768 | − | 0.879571i | \(-0.657830\pi\) | ||||
−0.475768 | + | 0.879571i | \(0.657830\pi\) | |||||||
\(270\) | 39.0973 | 2.37938 | ||||||||
\(271\) | 28.5180 | 1.73235 | 0.866174 | − | 0.499743i | \(-0.166572\pi\) | ||||
0.866174 | + | 0.499743i | \(0.166572\pi\) | |||||||
\(272\) | −40.4566 | −2.45304 | ||||||||
\(273\) | −6.48514 | −0.392498 | ||||||||
\(274\) | 5.22945 | 0.315922 | ||||||||
\(275\) | −3.56103 | −0.214738 | ||||||||
\(276\) | 15.7866 | 0.950245 | ||||||||
\(277\) | 2.42119 | 0.145475 | 0.0727377 | − | 0.997351i | \(-0.476826\pi\) | ||||
0.0727377 | + | 0.997351i | \(0.476826\pi\) | |||||||
\(278\) | 17.0923 | 1.02513 | ||||||||
\(279\) | 53.1629 | 3.18278 | ||||||||
\(280\) | −5.42933 | −0.324465 | ||||||||
\(281\) | −13.5128 | −0.806107 | −0.403054 | − | 0.915176i | \(-0.632051\pi\) | ||||
−0.403054 | + | 0.915176i | \(0.632051\pi\) | |||||||
\(282\) | −32.1219 | −1.91283 | ||||||||
\(283\) | −2.24471 | −0.133434 | −0.0667171 | − | 0.997772i | \(-0.521253\pi\) | ||||
−0.0667171 | + | 0.997772i | \(0.521253\pi\) | |||||||
\(284\) | 45.4514 | 2.69704 | ||||||||
\(285\) | 8.43251 | 0.499499 | ||||||||
\(286\) | 17.4846 | 1.03388 | ||||||||
\(287\) | 3.32254 | 0.196124 | ||||||||
\(288\) | −14.8564 | −0.875423 | ||||||||
\(289\) | 45.0960 | 2.65271 | ||||||||
\(290\) | 4.28627 | 0.251699 | ||||||||
\(291\) | 27.2653 | 1.59832 | ||||||||
\(292\) | 43.8669 | 2.56712 | ||||||||
\(293\) | −12.3215 | −0.719830 | −0.359915 | − | 0.932985i | \(-0.617194\pi\) | ||||
−0.359915 | + | 0.932985i | \(0.617194\pi\) | |||||||
\(294\) | −8.16709 | −0.476314 | ||||||||
\(295\) | −6.42701 | −0.374195 | ||||||||
\(296\) | −38.9095 | −2.26157 | ||||||||
\(297\) | −55.9898 | −3.24886 | ||||||||
\(298\) | 9.59951 | 0.556084 | ||||||||
\(299\) | 2.26868 | 0.131201 | ||||||||
\(300\) | 13.7399 | 0.793272 | ||||||||
\(301\) | 4.87597 | 0.281046 | ||||||||
\(302\) | −34.9813 | −2.01295 | ||||||||
\(303\) | −43.2918 | −2.48705 | ||||||||
\(304\) | −13.1814 | −0.756003 | ||||||||
\(305\) | 14.5197 | 0.831394 | ||||||||
\(306\) | 152.590 | 8.72297 | ||||||||
\(307\) | 4.74010 | 0.270532 | 0.135266 | − | 0.990809i | \(-0.456811\pi\) | ||||
0.135266 | + | 0.990809i | \(0.456811\pi\) | |||||||
\(308\) | 14.8972 | 0.848848 | ||||||||
\(309\) | 33.9568 | 1.93173 | ||||||||
\(310\) | 16.9763 | 0.964189 | ||||||||
\(311\) | 5.08306 | 0.288234 | 0.144117 | − | 0.989561i | \(-0.453966\pi\) | ||||
0.144117 | + | 0.989561i | \(0.453966\pi\) | |||||||
\(312\) | −35.2099 | −1.99337 | ||||||||
\(313\) | 18.6127 | 1.05205 | 0.526027 | − | 0.850468i | \(-0.323681\pi\) | ||||
0.526027 | + | 0.850468i | \(0.323681\pi\) | |||||||
\(314\) | 1.98709 | 0.112138 | ||||||||
\(315\) | 7.78717 | 0.438757 | ||||||||
\(316\) | 40.9373 | 2.30290 | ||||||||
\(317\) | −14.6893 | −0.825031 | −0.412516 | − | 0.910950i | \(-0.635350\pi\) | ||||
−0.412516 | + | 0.910950i | \(0.635350\pi\) | |||||||
\(318\) | 30.8260 | 1.72864 | ||||||||
\(319\) | −6.13822 | −0.343674 | ||||||||
\(320\) | 5.52400 | 0.308801 | ||||||||
\(321\) | −3.99068 | −0.222738 | ||||||||
\(322\) | 2.85707 | 0.159218 | ||||||||
\(323\) | 20.2318 | 1.12573 | ||||||||
\(324\) | 118.300 | 6.57224 | ||||||||
\(325\) | 1.97454 | 0.109528 | ||||||||
\(326\) | −17.4514 | −0.966541 | ||||||||
\(327\) | 7.51659 | 0.415668 | ||||||||
\(328\) | 18.0392 | 0.996047 | ||||||||
\(329\) | −3.93309 | −0.216838 | ||||||||
\(330\) | −29.0833 | −1.60098 | ||||||||
\(331\) | −6.90169 | −0.379351 | −0.189676 | − | 0.981847i | \(-0.560744\pi\) | ||||
−0.189676 | + | 0.981847i | \(0.560744\pi\) | |||||||
\(332\) | −12.5043 | −0.686262 | ||||||||
\(333\) | 55.8071 | 3.05821 | ||||||||
\(334\) | −36.2769 | −1.98499 | ||||||||
\(335\) | −9.79842 | −0.535345 | ||||||||
\(336\) | −16.8621 | −0.919901 | ||||||||
\(337\) | 29.8381 | 1.62538 | 0.812691 | − | 0.582695i | \(-0.198002\pi\) | ||||
0.812691 | + | 0.582695i | \(0.198002\pi\) | |||||||
\(338\) | 22.6315 | 1.23099 | ||||||||
\(339\) | −47.4184 | −2.57541 | ||||||||
\(340\) | 32.9656 | 1.78781 | ||||||||
\(341\) | −24.3111 | −1.31652 | ||||||||
\(342\) | 49.7160 | 2.68833 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 26.4732 | 1.42734 | ||||||||
\(345\) | −3.77364 | −0.203166 | ||||||||
\(346\) | −45.1748 | −2.42861 | ||||||||
\(347\) | 16.2530 | 0.872506 | 0.436253 | − | 0.899824i | \(-0.356305\pi\) | ||||
0.436253 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(348\) | 23.6837 | 1.26958 | ||||||||
\(349\) | −32.7580 | −1.75350 | −0.876748 | − | 0.480950i | \(-0.840292\pi\) | ||||
−0.876748 | + | 0.480950i | \(0.840292\pi\) | |||||||
\(350\) | 2.48664 | 0.132917 | ||||||||
\(351\) | 31.0455 | 1.65708 | ||||||||
\(352\) | 6.79376 | 0.362109 | ||||||||
\(353\) | 3.94008 | 0.209709 | 0.104855 | − | 0.994488i | \(-0.466562\pi\) | ||||
0.104855 | + | 0.994488i | \(0.466562\pi\) | |||||||
\(354\) | −52.4900 | −2.78981 | ||||||||
\(355\) | −10.8647 | −0.576639 | ||||||||
\(356\) | −4.43162 | −0.234876 | ||||||||
\(357\) | 25.8813 | 1.36978 | ||||||||
\(358\) | −27.7594 | −1.46713 | ||||||||
\(359\) | 0.694703 | 0.0366650 | 0.0183325 | − | 0.999832i | \(-0.494164\pi\) | ||||
0.0183325 | + | 0.999832i | \(0.494164\pi\) | |||||||
\(360\) | 42.2791 | 2.22831 | ||||||||
\(361\) | −12.4082 | −0.653061 | ||||||||
\(362\) | −0.915923 | −0.0481399 | ||||||||
\(363\) | 5.52092 | 0.289773 | ||||||||
\(364\) | −8.26027 | −0.432956 | ||||||||
\(365\) | −10.4860 | −0.548860 | ||||||||
\(366\) | 118.583 | 6.19845 | ||||||||
\(367\) | 23.0002 | 1.20060 | 0.600300 | − | 0.799775i | \(-0.295048\pi\) | ||||
0.600300 | + | 0.799775i | \(0.295048\pi\) | |||||||
\(368\) | 5.89881 | 0.307497 | ||||||||
\(369\) | −25.8732 | −1.34691 | ||||||||
\(370\) | 17.8206 | 0.926451 | ||||||||
\(371\) | 3.77441 | 0.195958 | ||||||||
\(372\) | 93.8020 | 4.86341 | ||||||||
\(373\) | 33.5364 | 1.73645 | 0.868225 | − | 0.496171i | \(-0.165261\pi\) | ||||
0.868225 | + | 0.496171i | \(0.165261\pi\) | |||||||
\(374\) | −69.7785 | −3.60816 | ||||||||
\(375\) | −3.28438 | −0.169605 | ||||||||
\(376\) | −21.3540 | −1.10125 | ||||||||
\(377\) | 3.40354 | 0.175291 | ||||||||
\(378\) | 39.0973 | 2.01095 | ||||||||
\(379\) | −19.6980 | −1.01182 | −0.505909 | − | 0.862587i | \(-0.668843\pi\) | ||||
−0.505909 | + | 0.862587i | \(0.668843\pi\) | |||||||
\(380\) | 10.7407 | 0.550986 | ||||||||
\(381\) | 4.32863 | 0.221763 | ||||||||
\(382\) | −32.3778 | −1.65659 | ||||||||
\(383\) | 15.4538 | 0.789653 | 0.394826 | − | 0.918756i | \(-0.370805\pi\) | ||||
0.394826 | + | 0.918756i | \(0.370805\pi\) | |||||||
\(384\) | 57.6469 | 2.94178 | ||||||||
\(385\) | −3.56103 | −0.181487 | ||||||||
\(386\) | −17.7328 | −0.902577 | ||||||||
\(387\) | −37.9700 | −1.93012 | ||||||||
\(388\) | 34.7284 | 1.76307 | ||||||||
\(389\) | 9.61295 | 0.487396 | 0.243698 | − | 0.969851i | \(-0.421639\pi\) | ||||
0.243698 | + | 0.969851i | \(0.421639\pi\) | |||||||
\(390\) | 16.1262 | 0.816583 | ||||||||
\(391\) | −9.05397 | −0.457879 | ||||||||
\(392\) | −5.42933 | −0.274223 | ||||||||
\(393\) | 60.0109 | 3.02715 | ||||||||
\(394\) | 17.1599 | 0.864503 | ||||||||
\(395\) | −9.78565 | −0.492370 | ||||||||
\(396\) | −116.007 | −5.82958 | ||||||||
\(397\) | −32.2987 | −1.62103 | −0.810513 | − | 0.585720i | \(-0.800812\pi\) | ||||
−0.810513 | + | 0.585720i | \(0.800812\pi\) | |||||||
\(398\) | 31.4594 | 1.57692 | ||||||||
\(399\) | 8.43251 | 0.422154 | ||||||||
\(400\) | 5.13402 | 0.256701 | ||||||||
\(401\) | 1.02512 | 0.0511922 | 0.0255961 | − | 0.999672i | \(-0.491852\pi\) | ||||
0.0255961 | + | 0.999672i | \(0.491852\pi\) | |||||||
\(402\) | −80.0246 | −3.99126 | ||||||||
\(403\) | 13.4801 | 0.671494 | ||||||||
\(404\) | −55.1418 | −2.74341 | ||||||||
\(405\) | −28.2785 | −1.40517 | ||||||||
\(406\) | 4.28627 | 0.212724 | ||||||||
\(407\) | −25.5203 | −1.26499 | ||||||||
\(408\) | 140.518 | 6.95668 | ||||||||
\(409\) | 17.9055 | 0.885372 | 0.442686 | − | 0.896677i | \(-0.354026\pi\) | ||||
0.442686 | + | 0.896677i | \(0.354026\pi\) | |||||||
\(410\) | −8.26198 | −0.408030 | ||||||||
\(411\) | −6.90710 | −0.340702 | ||||||||
\(412\) | 43.2515 | 2.13085 | ||||||||
\(413\) | −6.42701 | −0.316252 | ||||||||
\(414\) | −22.2485 | −1.09345 | ||||||||
\(415\) | 2.98903 | 0.146726 | ||||||||
\(416\) | −3.76703 | −0.184694 | ||||||||
\(417\) | −22.5757 | −1.10554 | ||||||||
\(418\) | −22.7349 | −1.11200 | ||||||||
\(419\) | 32.0126 | 1.56392 | 0.781959 | − | 0.623330i | \(-0.214221\pi\) | ||||
0.781959 | + | 0.623330i | \(0.214221\pi\) | |||||||
\(420\) | 13.7399 | 0.670437 | ||||||||
\(421\) | −17.1113 | −0.833956 | −0.416978 | − | 0.908917i | \(-0.636911\pi\) | ||||
−0.416978 | + | 0.908917i | \(0.636911\pi\) | |||||||
\(422\) | −7.28487 | −0.354622 | ||||||||
\(423\) | 30.6276 | 1.48917 | ||||||||
\(424\) | 20.4925 | 0.995206 | ||||||||
\(425\) | −7.88010 | −0.382241 | ||||||||
\(426\) | −88.7330 | −4.29913 | ||||||||
\(427\) | 14.5197 | 0.702656 | ||||||||
\(428\) | −5.08303 | −0.245697 | ||||||||
\(429\) | −23.0938 | −1.11498 | ||||||||
\(430\) | −12.1248 | −0.584710 | ||||||||
\(431\) | 23.4068 | 1.12747 | 0.563734 | − | 0.825956i | \(-0.309364\pi\) | ||||
0.563734 | + | 0.825956i | \(0.309364\pi\) | |||||||
\(432\) | 80.7216 | 3.88372 | ||||||||
\(433\) | 20.4289 | 0.981748 | 0.490874 | − | 0.871231i | \(-0.336678\pi\) | ||||
0.490874 | + | 0.871231i | \(0.336678\pi\) | |||||||
\(434\) | 16.9763 | 0.814888 | ||||||||
\(435\) | −5.66135 | −0.271441 | ||||||||
\(436\) | 9.57406 | 0.458514 | ||||||||
\(437\) | −2.94992 | −0.141114 | ||||||||
\(438\) | −85.6397 | −4.09202 | ||||||||
\(439\) | −11.1468 | −0.532007 | −0.266004 | − | 0.963972i | \(-0.585703\pi\) | ||||
−0.266004 | + | 0.963972i | \(0.585703\pi\) | |||||||
\(440\) | −19.3340 | −0.921714 | ||||||||
\(441\) | 7.78717 | 0.370818 | ||||||||
\(442\) | 38.6911 | 1.84035 | ||||||||
\(443\) | −18.0499 | −0.857578 | −0.428789 | − | 0.903405i | \(-0.641060\pi\) | ||||
−0.428789 | + | 0.903405i | \(0.641060\pi\) | |||||||
\(444\) | 98.4674 | 4.67306 | ||||||||
\(445\) | 1.05934 | 0.0502173 | ||||||||
\(446\) | −33.4621 | −1.58448 | ||||||||
\(447\) | −12.6791 | −0.599702 | ||||||||
\(448\) | 5.52400 | 0.260984 | ||||||||
\(449\) | −7.74944 | −0.365719 | −0.182859 | − | 0.983139i | \(-0.558535\pi\) | ||||
−0.182859 | + | 0.983139i | \(0.558535\pi\) | |||||||
\(450\) | −19.3639 | −0.912824 | ||||||||
\(451\) | 11.8317 | 0.557132 | ||||||||
\(452\) | −60.3979 | −2.84088 | ||||||||
\(453\) | 46.2036 | 2.17084 | ||||||||
\(454\) | −43.1412 | −2.02472 | ||||||||
\(455\) | 1.97454 | 0.0925677 | ||||||||
\(456\) | 45.7829 | 2.14398 | ||||||||
\(457\) | 38.1423 | 1.78422 | 0.892111 | − | 0.451817i | \(-0.149224\pi\) | ||||
0.892111 | + | 0.451817i | \(0.149224\pi\) | |||||||
\(458\) | −2.48664 | −0.116193 | ||||||||
\(459\) | −123.898 | −5.78307 | ||||||||
\(460\) | −4.80658 | −0.224108 | ||||||||
\(461\) | −4.91934 | −0.229116 | −0.114558 | − | 0.993417i | \(-0.536545\pi\) | ||||
−0.114558 | + | 0.993417i | \(0.536545\pi\) | |||||||
\(462\) | −29.0833 | −1.35308 | ||||||||
\(463\) | −38.7665 | −1.80163 | −0.900815 | − | 0.434203i | \(-0.857030\pi\) | ||||
−0.900815 | + | 0.434203i | \(0.857030\pi\) | |||||||
\(464\) | 8.84959 | 0.410832 | ||||||||
\(465\) | −22.4224 | −1.03982 | ||||||||
\(466\) | 53.7142 | 2.48826 | ||||||||
\(467\) | −5.59374 | −0.258847 | −0.129424 | − | 0.991589i | \(-0.541313\pi\) | ||||
−0.129424 | + | 0.991589i | \(0.541313\pi\) | |||||||
\(468\) | 64.3241 | 2.97338 | ||||||||
\(469\) | −9.79842 | −0.452449 | ||||||||
\(470\) | 9.78019 | 0.451126 | ||||||||
\(471\) | −2.62457 | −0.120934 | ||||||||
\(472\) | −34.8944 | −1.60614 | ||||||||
\(473\) | 17.3635 | 0.798374 | ||||||||
\(474\) | −79.9203 | −3.67086 | ||||||||
\(475\) | −2.56746 | −0.117803 | ||||||||
\(476\) | 32.9656 | 1.51098 | ||||||||
\(477\) | −29.3920 | −1.34577 | ||||||||
\(478\) | −60.9830 | −2.78930 | ||||||||
\(479\) | −27.6797 | −1.26472 | −0.632360 | − | 0.774675i | \(-0.717913\pi\) | ||||
−0.632360 | + | 0.774675i | \(0.717913\pi\) | |||||||
\(480\) | 6.26597 | 0.286001 | ||||||||
\(481\) | 14.1506 | 0.645212 | ||||||||
\(482\) | −15.7745 | −0.718510 | ||||||||
\(483\) | −3.77364 | −0.171707 | ||||||||
\(484\) | 7.03213 | 0.319642 | ||||||||
\(485\) | −8.30149 | −0.376951 | ||||||||
\(486\) | −113.661 | −5.15579 | ||||||||
\(487\) | −39.0276 | −1.76851 | −0.884254 | − | 0.467007i | \(-0.845332\pi\) | ||||
−0.884254 | + | 0.467007i | \(0.845332\pi\) | |||||||
\(488\) | 78.8321 | 3.56856 | ||||||||
\(489\) | 23.0499 | 1.04235 | ||||||||
\(490\) | 2.48664 | 0.112335 | ||||||||
\(491\) | −33.5268 | −1.51304 | −0.756522 | − | 0.653968i | \(-0.773103\pi\) | ||||
−0.756522 | + | 0.653968i | \(0.773103\pi\) | |||||||
\(492\) | −45.6513 | −2.05812 | ||||||||
\(493\) | −13.5831 | −0.611751 | ||||||||
\(494\) | 12.6061 | 0.567177 | ||||||||
\(495\) | 27.7304 | 1.24639 | ||||||||
\(496\) | 35.0499 | 1.57379 | ||||||||
\(497\) | −10.8647 | −0.487349 | ||||||||
\(498\) | 24.4117 | 1.09391 | ||||||||
\(499\) | −24.6300 | −1.10259 | −0.551294 | − | 0.834311i | \(-0.685866\pi\) | ||||
−0.551294 | + | 0.834311i | \(0.685866\pi\) | |||||||
\(500\) | −4.18340 | −0.187087 | ||||||||
\(501\) | 47.9149 | 2.14068 | ||||||||
\(502\) | −3.35964 | −0.149948 | ||||||||
\(503\) | −4.35206 | −0.194049 | −0.0970244 | − | 0.995282i | \(-0.530932\pi\) | ||||
−0.0970244 | + | 0.995282i | \(0.530932\pi\) | |||||||
\(504\) | 42.2791 | 1.88326 | ||||||||
\(505\) | 13.1811 | 0.586552 | ||||||||
\(506\) | 10.1741 | 0.452295 | ||||||||
\(507\) | −29.8918 | −1.32754 | ||||||||
\(508\) | 5.51348 | 0.244621 | ||||||||
\(509\) | 13.5231 | 0.599400 | 0.299700 | − | 0.954033i | \(-0.403113\pi\) | ||||
0.299700 | + | 0.954033i | \(0.403113\pi\) | |||||||
\(510\) | −64.3575 | −2.84980 | ||||||||
\(511\) | −10.4860 | −0.463871 | ||||||||
\(512\) | 45.9538 | 2.03089 | ||||||||
\(513\) | −40.3679 | −1.78228 | ||||||||
\(514\) | −8.87666 | −0.391533 | ||||||||
\(515\) | −10.3389 | −0.455584 | ||||||||
\(516\) | −66.9952 | −2.94930 | ||||||||
\(517\) | −14.0059 | −0.615977 | ||||||||
\(518\) | 17.8206 | 0.782994 | ||||||||
\(519\) | 59.6674 | 2.61911 | ||||||||
\(520\) | 10.7204 | 0.470121 | ||||||||
\(521\) | 20.8328 | 0.912702 | 0.456351 | − | 0.889800i | \(-0.349156\pi\) | ||||
0.456351 | + | 0.889800i | \(0.349156\pi\) | |||||||
\(522\) | −33.3779 | −1.46091 | ||||||||
\(523\) | −4.14453 | −0.181228 | −0.0906138 | − | 0.995886i | \(-0.528883\pi\) | ||||
−0.0906138 | + | 0.995886i | \(0.528883\pi\) | |||||||
\(524\) | 76.4373 | 3.33918 | ||||||||
\(525\) | −3.28438 | −0.143342 | ||||||||
\(526\) | −42.9260 | −1.87166 | ||||||||
\(527\) | −53.7974 | −2.34345 | ||||||||
\(528\) | −60.0464 | −2.61318 | ||||||||
\(529\) | −21.6799 | −0.942603 | ||||||||
\(530\) | −9.38562 | −0.407685 | ||||||||
\(531\) | 50.0482 | 2.17191 | ||||||||
\(532\) | 10.7407 | 0.465668 | ||||||||
\(533\) | −6.56048 | −0.284166 | ||||||||
\(534\) | 8.65169 | 0.374395 | ||||||||
\(535\) | 1.21505 | 0.0525311 | ||||||||
\(536\) | −53.1989 | −2.29784 | ||||||||
\(537\) | 36.6648 | 1.58221 | ||||||||
\(538\) | 38.8074 | 1.67311 | ||||||||
\(539\) | −3.56103 | −0.153385 | ||||||||
\(540\) | −65.7751 | −2.83051 | ||||||||
\(541\) | 34.2434 | 1.47224 | 0.736120 | − | 0.676851i | \(-0.236656\pi\) | ||||
0.736120 | + | 0.676851i | \(0.236656\pi\) | |||||||
\(542\) | −70.9142 | −3.04603 | ||||||||
\(543\) | 1.20976 | 0.0519158 | ||||||||
\(544\) | 15.0337 | 0.644565 | ||||||||
\(545\) | −2.28859 | −0.0980322 | ||||||||
\(546\) | 16.1262 | 0.690139 | ||||||||
\(547\) | 18.1159 | 0.774581 | 0.387291 | − | 0.921958i | \(-0.373411\pi\) | ||||
0.387291 | + | 0.921958i | \(0.373411\pi\) | |||||||
\(548\) | −8.79774 | −0.375821 | ||||||||
\(549\) | −113.067 | −4.82559 | ||||||||
\(550\) | 8.85502 | 0.377579 | ||||||||
\(551\) | −4.42557 | −0.188536 | ||||||||
\(552\) | −20.4884 | −0.872042 | ||||||||
\(553\) | −9.78565 | −0.416128 | ||||||||
\(554\) | −6.02064 | −0.255793 | ||||||||
\(555\) | −23.5377 | −0.999118 | ||||||||
\(556\) | −28.7552 | −1.21949 | ||||||||
\(557\) | 24.4835 | 1.03740 | 0.518700 | − | 0.854957i | \(-0.326416\pi\) | ||||
0.518700 | + | 0.854957i | \(0.326416\pi\) | |||||||
\(558\) | −132.197 | −5.59636 | ||||||||
\(559\) | −9.62778 | −0.407212 | ||||||||
\(560\) | 5.13402 | 0.216952 | ||||||||
\(561\) | 92.1641 | 3.89117 | ||||||||
\(562\) | 33.6016 | 1.41740 | ||||||||
\(563\) | −14.5774 | −0.614366 | −0.307183 | − | 0.951650i | \(-0.599386\pi\) | ||||
−0.307183 | + | 0.951650i | \(0.599386\pi\) | |||||||
\(564\) | 54.0401 | 2.27550 | ||||||||
\(565\) | 14.4375 | 0.607391 | ||||||||
\(566\) | 5.58180 | 0.234620 | ||||||||
\(567\) | −28.2785 | −1.18759 | ||||||||
\(568\) | −58.9881 | −2.47508 | ||||||||
\(569\) | 31.7672 | 1.33175 | 0.665875 | − | 0.746064i | \(-0.268059\pi\) | ||||
0.665875 | + | 0.746064i | \(0.268059\pi\) | |||||||
\(570\) | −20.9686 | −0.878280 | ||||||||
\(571\) | −2.50021 | −0.104631 | −0.0523154 | − | 0.998631i | \(-0.516660\pi\) | ||||
−0.0523154 | + | 0.998631i | \(0.516660\pi\) | |||||||
\(572\) | −29.4151 | −1.22991 | ||||||||
\(573\) | 42.7649 | 1.78653 | ||||||||
\(574\) | −8.26198 | −0.344848 | ||||||||
\(575\) | 1.14897 | 0.0479152 | ||||||||
\(576\) | −43.0163 | −1.79235 | ||||||||
\(577\) | −13.6979 | −0.570253 | −0.285126 | − | 0.958490i | \(-0.592036\pi\) | ||||
−0.285126 | + | 0.958490i | \(0.592036\pi\) | |||||||
\(578\) | −112.138 | −4.66432 | ||||||||
\(579\) | 23.4217 | 0.973372 | ||||||||
\(580\) | −7.21100 | −0.299420 | ||||||||
\(581\) | 2.98903 | 0.124006 | ||||||||
\(582\) | −67.7990 | −2.81036 | ||||||||
\(583\) | 13.4408 | 0.556662 | ||||||||
\(584\) | −56.9317 | −2.35585 | ||||||||
\(585\) | −15.3761 | −0.635722 | ||||||||
\(586\) | 30.6392 | 1.26569 | ||||||||
\(587\) | −17.2091 | −0.710294 | −0.355147 | − | 0.934810i | \(-0.615569\pi\) | ||||
−0.355147 | + | 0.934810i | \(0.615569\pi\) | |||||||
\(588\) | 13.7399 | 0.566623 | ||||||||
\(589\) | −17.5280 | −0.722229 | ||||||||
\(590\) | 15.9817 | 0.657955 | ||||||||
\(591\) | −22.6649 | −0.932311 | ||||||||
\(592\) | 36.7931 | 1.51219 | ||||||||
\(593\) | −2.29597 | −0.0942843 | −0.0471422 | − | 0.998888i | \(-0.515011\pi\) | ||||
−0.0471422 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(594\) | 139.227 | 5.71254 | ||||||||
\(595\) | −7.88010 | −0.323053 | ||||||||
\(596\) | −16.1497 | −0.661517 | ||||||||
\(597\) | −41.5519 | −1.70060 | ||||||||
\(598\) | −5.64139 | −0.230694 | ||||||||
\(599\) | 30.5006 | 1.24622 | 0.623109 | − | 0.782135i | \(-0.285869\pi\) | ||||
0.623109 | + | 0.782135i | \(0.285869\pi\) | |||||||
\(600\) | −17.8320 | −0.727988 | ||||||||
\(601\) | 13.6138 | 0.555319 | 0.277659 | − | 0.960680i | \(-0.410441\pi\) | ||||
0.277659 | + | 0.960680i | \(0.410441\pi\) | |||||||
\(602\) | −12.1248 | −0.494170 | ||||||||
\(603\) | 76.3020 | 3.10726 | ||||||||
\(604\) | 58.8507 | 2.39460 | ||||||||
\(605\) | −1.68096 | −0.0683408 | ||||||||
\(606\) | 107.651 | 4.37304 | ||||||||
\(607\) | 35.7065 | 1.44928 | 0.724641 | − | 0.689127i | \(-0.242006\pi\) | ||||
0.724641 | + | 0.689127i | \(0.242006\pi\) | |||||||
\(608\) | 4.89821 | 0.198649 | ||||||||
\(609\) | −5.66135 | −0.229409 | ||||||||
\(610\) | −36.1052 | −1.46186 | ||||||||
\(611\) | 7.76603 | 0.314180 | ||||||||
\(612\) | −256.709 | −10.3768 | ||||||||
\(613\) | −28.0691 | −1.13370 | −0.566849 | − | 0.823822i | \(-0.691838\pi\) | ||||
−0.566849 | + | 0.823822i | \(0.691838\pi\) | |||||||
\(614\) | −11.7870 | −0.475683 | ||||||||
\(615\) | 10.9125 | 0.440035 | ||||||||
\(616\) | −19.3340 | −0.778990 | ||||||||
\(617\) | 38.2188 | 1.53863 | 0.769316 | − | 0.638869i | \(-0.220597\pi\) | ||||
0.769316 | + | 0.638869i | \(0.220597\pi\) | |||||||
\(618\) | −84.4384 | −3.39661 | ||||||||
\(619\) | 15.1355 | 0.608349 | 0.304174 | − | 0.952616i | \(-0.401619\pi\) | ||||
0.304174 | + | 0.952616i | \(0.401619\pi\) | |||||||
\(620\) | −28.5600 | −1.14700 | ||||||||
\(621\) | 18.0651 | 0.724927 | ||||||||
\(622\) | −12.6397 | −0.506808 | ||||||||
\(623\) | 1.05934 | 0.0424414 | ||||||||
\(624\) | 33.2948 | 1.33286 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −46.2832 | −1.84985 | ||||||||
\(627\) | 30.0285 | 1.19922 | ||||||||
\(628\) | −3.34298 | −0.133399 | ||||||||
\(629\) | −56.4731 | −2.25173 | ||||||||
\(630\) | −19.3639 | −0.771477 | ||||||||
\(631\) | 25.6019 | 1.01919 | 0.509597 | − | 0.860413i | \(-0.329794\pi\) | ||||
0.509597 | + | 0.860413i | \(0.329794\pi\) | |||||||
\(632\) | −53.1295 | −2.11338 | ||||||||
\(633\) | 9.62193 | 0.382437 | ||||||||
\(634\) | 36.5270 | 1.45067 | ||||||||
\(635\) | −1.31794 | −0.0523010 | ||||||||
\(636\) | −51.8600 | −2.05638 | ||||||||
\(637\) | 1.97454 | 0.0782340 | ||||||||
\(638\) | 15.2636 | 0.604290 | ||||||||
\(639\) | 84.6053 | 3.34693 | ||||||||
\(640\) | −17.5518 | −0.693797 | ||||||||
\(641\) | −33.4308 | −1.32044 | −0.660219 | − | 0.751073i | \(-0.729536\pi\) | ||||
−0.660219 | + | 0.751073i | \(0.729536\pi\) | |||||||
\(642\) | 9.92341 | 0.391646 | ||||||||
\(643\) | 40.1619 | 1.58383 | 0.791915 | − | 0.610632i | \(-0.209084\pi\) | ||||
0.791915 | + | 0.610632i | \(0.209084\pi\) | |||||||
\(644\) | −4.80658 | −0.189406 | ||||||||
\(645\) | 16.0145 | 0.630572 | ||||||||
\(646\) | −50.3093 | −1.97939 | ||||||||
\(647\) | −41.1155 | −1.61642 | −0.808209 | − | 0.588895i | \(-0.799563\pi\) | ||||
−0.808209 | + | 0.588895i | \(0.799563\pi\) | |||||||
\(648\) | −153.533 | −6.03136 | ||||||||
\(649\) | −22.8868 | −0.898385 | ||||||||
\(650\) | −4.90997 | −0.192585 | ||||||||
\(651\) | −22.4224 | −0.878805 | ||||||||
\(652\) | 29.3592 | 1.14980 | ||||||||
\(653\) | 17.9715 | 0.703280 | 0.351640 | − | 0.936135i | \(-0.385624\pi\) | ||||
0.351640 | + | 0.936135i | \(0.385624\pi\) | |||||||
\(654\) | −18.6911 | −0.730879 | ||||||||
\(655\) | −18.2716 | −0.713930 | ||||||||
\(656\) | −17.0580 | −0.666002 | ||||||||
\(657\) | 81.6559 | 3.18570 | ||||||||
\(658\) | 9.78019 | 0.381271 | ||||||||
\(659\) | −19.0812 | −0.743296 | −0.371648 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371648 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(660\) | 48.9282 | 1.90453 | ||||||||
\(661\) | −33.3225 | −1.29609 | −0.648047 | − | 0.761600i | \(-0.724414\pi\) | ||||
−0.648047 | + | 0.761600i | \(0.724414\pi\) | |||||||
\(662\) | 17.1620 | 0.667021 | ||||||||
\(663\) | −51.1035 | −1.98470 | ||||||||
\(664\) | 16.2284 | 0.629785 | ||||||||
\(665\) | −2.56746 | −0.0995617 | ||||||||
\(666\) | −138.772 | −5.37732 | ||||||||
\(667\) | 1.98049 | 0.0766850 | ||||||||
\(668\) | 61.0304 | 2.36134 | ||||||||
\(669\) | 44.1971 | 1.70876 | ||||||||
\(670\) | 24.3652 | 0.941309 | ||||||||
\(671\) | 51.7050 | 1.99605 | ||||||||
\(672\) | 6.26597 | 0.241715 | ||||||||
\(673\) | −9.94512 | −0.383356 | −0.191678 | − | 0.981458i | \(-0.561393\pi\) | ||||
−0.191678 | + | 0.981458i | \(0.561393\pi\) | |||||||
\(674\) | −74.1966 | −2.85795 | ||||||||
\(675\) | 15.7229 | 0.605175 | ||||||||
\(676\) | −38.0739 | −1.46438 | ||||||||
\(677\) | 21.5207 | 0.827107 | 0.413554 | − | 0.910480i | \(-0.364287\pi\) | ||||
0.413554 | + | 0.910480i | \(0.364287\pi\) | |||||||
\(678\) | 117.913 | 4.52841 | ||||||||
\(679\) | −8.30149 | −0.318582 | ||||||||
\(680\) | −42.7837 | −1.64068 | ||||||||
\(681\) | 56.9814 | 2.18353 | ||||||||
\(682\) | 60.4531 | 2.31487 | ||||||||
\(683\) | 8.63902 | 0.330563 | 0.165281 | − | 0.986246i | \(-0.447147\pi\) | ||||
0.165281 | + | 0.986246i | \(0.447147\pi\) | |||||||
\(684\) | −83.6396 | −3.19804 | ||||||||
\(685\) | 2.10301 | 0.0803520 | ||||||||
\(686\) | 2.48664 | 0.0949405 | ||||||||
\(687\) | 3.28438 | 0.125307 | ||||||||
\(688\) | −25.0333 | −0.954385 | ||||||||
\(689\) | −7.45272 | −0.283926 | ||||||||
\(690\) | 9.38371 | 0.357232 | ||||||||
\(691\) | −17.9794 | −0.683969 | −0.341984 | − | 0.939706i | \(-0.611099\pi\) | ||||
−0.341984 | + | 0.939706i | \(0.611099\pi\) | |||||||
\(692\) | 75.9997 | 2.88908 | ||||||||
\(693\) | 27.7304 | 1.05339 | ||||||||
\(694\) | −40.4154 | −1.53415 | ||||||||
\(695\) | 6.87366 | 0.260733 | ||||||||
\(696\) | −30.7373 | −1.16510 | ||||||||
\(697\) | 26.1820 | 0.991713 | ||||||||
\(698\) | 81.4575 | 3.08321 | ||||||||
\(699\) | −70.9462 | −2.68343 | ||||||||
\(700\) | −4.18340 | −0.158118 | ||||||||
\(701\) | −13.8650 | −0.523675 | −0.261837 | − | 0.965112i | \(-0.584328\pi\) | ||||
−0.261837 | + | 0.965112i | \(0.584328\pi\) | |||||||
\(702\) | −77.1990 | −2.91369 | ||||||||
\(703\) | −18.3998 | −0.693961 | ||||||||
\(704\) | 19.6711 | 0.741384 | ||||||||
\(705\) | −12.9178 | −0.486511 | ||||||||
\(706\) | −9.79756 | −0.368736 | ||||||||
\(707\) | 13.1811 | 0.495727 | ||||||||
\(708\) | 88.3063 | 3.31875 | ||||||||
\(709\) | −9.54439 | −0.358447 | −0.179224 | − | 0.983808i | \(-0.557359\pi\) | ||||
−0.179224 | + | 0.983808i | \(0.557359\pi\) | |||||||
\(710\) | 27.0167 | 1.01392 | ||||||||
\(711\) | 76.2025 | 2.85782 | ||||||||
\(712\) | 5.75148 | 0.215546 | ||||||||
\(713\) | 7.84398 | 0.293759 | ||||||||
\(714\) | −64.3575 | −2.40852 | ||||||||
\(715\) | 7.03139 | 0.262959 | ||||||||
\(716\) | 46.7009 | 1.74529 | ||||||||
\(717\) | 80.5469 | 3.00808 | ||||||||
\(718\) | −1.72748 | −0.0644690 | ||||||||
\(719\) | 0.192431 | 0.00717647 | 0.00358823 | − | 0.999994i | \(-0.498858\pi\) | ||||
0.00358823 | + | 0.999994i | \(0.498858\pi\) | |||||||
\(720\) | −39.9795 | −1.48995 | ||||||||
\(721\) | −10.3389 | −0.385039 | ||||||||
\(722\) | 30.8547 | 1.14829 | ||||||||
\(723\) | 20.8351 | 0.774867 | ||||||||
\(724\) | 1.54090 | 0.0572671 | ||||||||
\(725\) | 1.72372 | 0.0640173 | ||||||||
\(726\) | −13.7286 | −0.509515 | ||||||||
\(727\) | 50.2974 | 1.86543 | 0.932714 | − | 0.360618i | \(-0.117434\pi\) | ||||
0.932714 | + | 0.360618i | \(0.117434\pi\) | |||||||
\(728\) | 10.7204 | 0.397325 | ||||||||
\(729\) | 65.2896 | 2.41813 | ||||||||
\(730\) | 26.0748 | 0.965073 | ||||||||
\(731\) | 38.4231 | 1.42113 | ||||||||
\(732\) | −199.498 | −7.37367 | ||||||||
\(733\) | 37.8290 | 1.39724 | 0.698622 | − | 0.715491i | \(-0.253797\pi\) | ||||
0.698622 | + | 0.715491i | \(0.253797\pi\) | |||||||
\(734\) | −57.1933 | −2.11104 | ||||||||
\(735\) | −3.28438 | −0.121146 | ||||||||
\(736\) | −2.19200 | −0.0807984 | ||||||||
\(737\) | −34.8925 | −1.28528 | ||||||||
\(738\) | 64.3375 | 2.36829 | ||||||||
\(739\) | −37.0416 | −1.36260 | −0.681299 | − | 0.732005i | \(-0.738585\pi\) | ||||
−0.681299 | + | 0.732005i | \(0.738585\pi\) | |||||||
\(740\) | −29.9805 | −1.10210 | ||||||||
\(741\) | −16.6503 | −0.611664 | ||||||||
\(742\) | −9.38562 | −0.344557 | ||||||||
\(743\) | −46.8626 | −1.71922 | −0.859611 | − | 0.510949i | \(-0.829294\pi\) | ||||
−0.859611 | + | 0.510949i | \(0.829294\pi\) | |||||||
\(744\) | −121.739 | −4.46316 | ||||||||
\(745\) | 3.86043 | 0.141435 | ||||||||
\(746\) | −83.3931 | −3.05324 | ||||||||
\(747\) | −23.2761 | −0.851627 | ||||||||
\(748\) | 117.392 | 4.29226 | ||||||||
\(749\) | 1.21505 | 0.0443969 | ||||||||
\(750\) | 8.16709 | 0.298220 | ||||||||
\(751\) | −43.9175 | −1.60257 | −0.801286 | − | 0.598282i | \(-0.795850\pi\) | ||||
−0.801286 | + | 0.598282i | \(0.795850\pi\) | |||||||
\(752\) | 20.1925 | 0.736346 | ||||||||
\(753\) | 4.43745 | 0.161710 | ||||||||
\(754\) | −8.46340 | −0.308219 | ||||||||
\(755\) | −14.0677 | −0.511975 | ||||||||
\(756\) | −65.7751 | −2.39222 | ||||||||
\(757\) | −19.7190 | −0.716698 | −0.358349 | − | 0.933588i | \(-0.616660\pi\) | ||||
−0.358349 | + | 0.933588i | \(0.616660\pi\) | |||||||
\(758\) | 48.9819 | 1.77910 | ||||||||
\(759\) | −13.4381 | −0.487771 | ||||||||
\(760\) | −13.9396 | −0.505641 | ||||||||
\(761\) | −0.374516 | −0.0135762 | −0.00678809 | − | 0.999977i | \(-0.502161\pi\) | ||||
−0.00678809 | + | 0.999977i | \(0.502161\pi\) | |||||||
\(762\) | −10.7638 | −0.389930 | ||||||||
\(763\) | −2.28859 | −0.0828524 | ||||||||
\(764\) | 54.4707 | 1.97068 | ||||||||
\(765\) | 61.3637 | 2.21861 | ||||||||
\(766\) | −38.4281 | −1.38846 | ||||||||
\(767\) | 12.6904 | 0.458223 | ||||||||
\(768\) | −107.061 | −3.86325 | ||||||||
\(769\) | 33.6633 | 1.21393 | 0.606965 | − | 0.794729i | \(-0.292387\pi\) | ||||
0.606965 | + | 0.794729i | \(0.292387\pi\) | |||||||
\(770\) | 8.85502 | 0.319113 | ||||||||
\(771\) | 11.7244 | 0.422243 | ||||||||
\(772\) | 29.8328 | 1.07370 | ||||||||
\(773\) | −0.0785286 | −0.00282448 | −0.00141224 | − | 0.999999i | \(-0.500450\pi\) | ||||
−0.00141224 | + | 0.999999i | \(0.500450\pi\) | |||||||
\(774\) | 94.4179 | 3.39378 | ||||||||
\(775\) | 6.82699 | 0.245233 | ||||||||
\(776\) | −45.0715 | −1.61797 | ||||||||
\(777\) | −23.5377 | −0.844409 | ||||||||
\(778\) | −23.9040 | −0.857000 | ||||||||
\(779\) | 8.53048 | 0.305636 | ||||||||
\(780\) | −27.1299 | −0.971406 | ||||||||
\(781\) | −38.6896 | −1.38442 | ||||||||
\(782\) | 22.5140 | 0.805099 | ||||||||
\(783\) | 27.1018 | 0.968541 | ||||||||
\(784\) | 5.13402 | 0.183358 | ||||||||
\(785\) | 0.799106 | 0.0285213 | ||||||||
\(786\) | −149.226 | −5.32270 | ||||||||
\(787\) | −45.9656 | −1.63850 | −0.819249 | − | 0.573438i | \(-0.805609\pi\) | ||||
−0.819249 | + | 0.573438i | \(0.805609\pi\) | |||||||
\(788\) | −28.8689 | −1.02841 | ||||||||
\(789\) | 56.6971 | 2.01847 | ||||||||
\(790\) | 24.3334 | 0.865744 | ||||||||
\(791\) | 14.4375 | 0.513339 | ||||||||
\(792\) | 150.557 | 5.34982 | ||||||||
\(793\) | −28.6696 | −1.01809 | ||||||||
\(794\) | 80.3154 | 2.85029 | ||||||||
\(795\) | 12.3966 | 0.439663 | ||||||||
\(796\) | −52.9256 | −1.87590 | ||||||||
\(797\) | −17.8234 | −0.631338 | −0.315669 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315669 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(798\) | −20.9686 | −0.742282 | ||||||||
\(799\) | −30.9931 | −1.09646 | ||||||||
\(800\) | −1.90781 | −0.0674511 | ||||||||
\(801\) | −8.24923 | −0.291472 | ||||||||
\(802\) | −2.54912 | −0.0900125 | ||||||||
\(803\) | −37.3408 | −1.31773 | ||||||||
\(804\) | 134.629 | 4.74800 | ||||||||
\(805\) | 1.14897 | 0.0404957 | ||||||||
\(806\) | −33.5203 | −1.18070 | ||||||||
\(807\) | −51.2572 | −1.80434 | ||||||||
\(808\) | 71.5646 | 2.51763 | ||||||||
\(809\) | 36.6016 | 1.28685 | 0.643423 | − | 0.765511i | \(-0.277514\pi\) | ||||
0.643423 | + | 0.765511i | \(0.277514\pi\) | |||||||
\(810\) | 70.3186 | 2.47074 | ||||||||
\(811\) | 11.6237 | 0.408164 | 0.204082 | − | 0.978954i | \(-0.434579\pi\) | ||||
0.204082 | + | 0.978954i | \(0.434579\pi\) | |||||||
\(812\) | −7.21100 | −0.253056 | ||||||||
\(813\) | 93.6642 | 3.28495 | ||||||||
\(814\) | 63.4599 | 2.22427 | ||||||||
\(815\) | −7.01804 | −0.245831 | ||||||||
\(816\) | −132.875 | −4.65155 | ||||||||
\(817\) | 12.5188 | 0.437979 | ||||||||
\(818\) | −44.5247 | −1.55677 | ||||||||
\(819\) | −15.3761 | −0.537283 | ||||||||
\(820\) | 13.8995 | 0.485392 | ||||||||
\(821\) | −24.2189 | −0.845246 | −0.422623 | − | 0.906306i | \(-0.638890\pi\) | ||||
−0.422623 | + | 0.906306i | \(0.638890\pi\) | |||||||
\(822\) | 17.1755 | 0.599064 | ||||||||
\(823\) | −51.3024 | −1.78829 | −0.894144 | − | 0.447779i | \(-0.852215\pi\) | ||||
−0.894144 | + | 0.447779i | \(0.852215\pi\) | |||||||
\(824\) | −56.1331 | −1.95549 | ||||||||
\(825\) | −11.6958 | −0.407195 | ||||||||
\(826\) | 15.9817 | 0.556074 | ||||||||
\(827\) | −27.1158 | −0.942909 | −0.471455 | − | 0.881890i | \(-0.656271\pi\) | ||||
−0.471455 | + | 0.881890i | \(0.656271\pi\) | |||||||
\(828\) | 37.4297 | 1.30077 | ||||||||
\(829\) | −36.3908 | −1.26391 | −0.631953 | − | 0.775007i | \(-0.717746\pi\) | ||||
−0.631953 | + | 0.775007i | \(0.717746\pi\) | |||||||
\(830\) | −7.43264 | −0.257991 | ||||||||
\(831\) | 7.95213 | 0.275856 | ||||||||
\(832\) | −10.9073 | −0.378144 | ||||||||
\(833\) | −7.88010 | −0.273029 | ||||||||
\(834\) | 56.1378 | 1.94389 | ||||||||
\(835\) | −14.5887 | −0.504863 | ||||||||
\(836\) | 38.2480 | 1.32283 | ||||||||
\(837\) | 107.340 | 3.71022 | ||||||||
\(838\) | −79.6039 | −2.74987 | ||||||||
\(839\) | −55.0079 | −1.89908 | −0.949541 | − | 0.313643i | \(-0.898451\pi\) | ||||
−0.949541 | + | 0.313643i | \(0.898451\pi\) | |||||||
\(840\) | −17.8320 | −0.615262 | ||||||||
\(841\) | −26.0288 | −0.897545 | ||||||||
\(842\) | 42.5498 | 1.46636 | ||||||||
\(843\) | −44.3813 | −1.52857 | ||||||||
\(844\) | 12.2557 | 0.421858 | ||||||||
\(845\) | 9.10120 | 0.313091 | ||||||||
\(846\) | −76.1600 | −2.61843 | ||||||||
\(847\) | −1.68096 | −0.0577585 | ||||||||
\(848\) | −19.3779 | −0.665440 | ||||||||
\(849\) | −7.37249 | −0.253023 | ||||||||
\(850\) | 19.5950 | 0.672103 | ||||||||
\(851\) | 8.23411 | 0.282262 | ||||||||
\(852\) | 149.280 | 5.11424 | ||||||||
\(853\) | 22.3079 | 0.763808 | 0.381904 | − | 0.924202i | \(-0.375269\pi\) | ||||
0.381904 | + | 0.924202i | \(0.375269\pi\) | |||||||
\(854\) | −36.1052 | −1.23550 | ||||||||
\(855\) | 19.9932 | 0.683754 | ||||||||
\(856\) | 6.59690 | 0.225477 | ||||||||
\(857\) | −6.49791 | −0.221964 | −0.110982 | − | 0.993822i | \(-0.535400\pi\) | ||||
−0.110982 | + | 0.993822i | \(0.535400\pi\) | |||||||
\(858\) | 57.4260 | 1.96049 | ||||||||
\(859\) | 30.9448 | 1.05582 | 0.527911 | − | 0.849300i | \(-0.322976\pi\) | ||||
0.527911 | + | 0.849300i | \(0.322976\pi\) | |||||||
\(860\) | 20.3981 | 0.695570 | ||||||||
\(861\) | 10.9125 | 0.371897 | ||||||||
\(862\) | −58.2045 | −1.98245 | ||||||||
\(863\) | −42.5620 | −1.44883 | −0.724413 | − | 0.689366i | \(-0.757889\pi\) | ||||
−0.724413 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(864\) | −29.9963 | −1.02049 | ||||||||
\(865\) | −18.1670 | −0.617696 | ||||||||
\(866\) | −50.7993 | −1.72623 | ||||||||
\(867\) | 148.113 | 5.03017 | ||||||||
\(868\) | −28.5600 | −0.969390 | ||||||||
\(869\) | −34.8470 | −1.18210 | ||||||||
\(870\) | 14.0778 | 0.477281 | ||||||||
\(871\) | 19.3473 | 0.655560 | ||||||||
\(872\) | −12.4255 | −0.420780 | ||||||||
\(873\) | 64.6451 | 2.18791 | ||||||||
\(874\) | 7.33540 | 0.248124 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 144.076 | 4.86787 | ||||||||
\(877\) | −26.1764 | −0.883914 | −0.441957 | − | 0.897036i | \(-0.645716\pi\) | ||||
−0.441957 | + | 0.897036i | \(0.645716\pi\) | |||||||
\(878\) | 27.7181 | 0.935440 | ||||||||
\(879\) | −40.4686 | −1.36497 | ||||||||
\(880\) | 18.2824 | 0.616300 | ||||||||
\(881\) | −27.9158 | −0.940506 | −0.470253 | − | 0.882532i | \(-0.655837\pi\) | ||||
−0.470253 | + | 0.882532i | \(0.655837\pi\) | |||||||
\(882\) | −19.3639 | −0.652017 | ||||||||
\(883\) | −57.3263 | −1.92918 | −0.964591 | − | 0.263750i | \(-0.915041\pi\) | ||||
−0.964591 | + | 0.263750i | \(0.915041\pi\) | |||||||
\(884\) | −65.0918 | −2.18927 | ||||||||
\(885\) | −21.1088 | −0.709563 | ||||||||
\(886\) | 44.8838 | 1.50790 | ||||||||
\(887\) | 41.1089 | 1.38030 | 0.690152 | − | 0.723665i | \(-0.257544\pi\) | ||||
0.690152 | + | 0.723665i | \(0.257544\pi\) | |||||||
\(888\) | −127.794 | −4.28848 | ||||||||
\(889\) | −1.31794 | −0.0442024 | ||||||||
\(890\) | −2.63419 | −0.0882983 | ||||||||
\(891\) | −100.701 | −3.37360 | ||||||||
\(892\) | 56.2949 | 1.88489 | ||||||||
\(893\) | −10.0980 | −0.337918 | ||||||||
\(894\) | 31.5285 | 1.05447 | ||||||||
\(895\) | −11.1634 | −0.373151 | ||||||||
\(896\) | −17.5518 | −0.586365 | ||||||||
\(897\) | 7.45120 | 0.248788 | ||||||||
\(898\) | 19.2701 | 0.643051 | ||||||||
\(899\) | 11.7678 | 0.392478 | ||||||||
\(900\) | 32.5768 | 1.08589 | ||||||||
\(901\) | 29.7428 | 0.990876 | ||||||||
\(902\) | −29.4212 | −0.979618 | ||||||||
\(903\) | 16.0145 | 0.532931 | ||||||||
\(904\) | 78.3861 | 2.60708 | ||||||||
\(905\) | −0.368337 | −0.0122439 | ||||||||
\(906\) | −114.892 | −3.81703 | ||||||||
\(907\) | 43.6513 | 1.44942 | 0.724709 | − | 0.689055i | \(-0.241974\pi\) | ||||
0.724709 | + | 0.689055i | \(0.241974\pi\) | |||||||
\(908\) | 72.5785 | 2.40860 | ||||||||
\(909\) | −102.644 | −3.40447 | ||||||||
\(910\) | −4.90997 | −0.162764 | ||||||||
\(911\) | −57.6015 | −1.90842 | −0.954211 | − | 0.299135i | \(-0.903302\pi\) | ||||
−0.954211 | + | 0.299135i | \(0.903302\pi\) | |||||||
\(912\) | −43.2926 | −1.43356 | ||||||||
\(913\) | 10.6440 | 0.352266 | ||||||||
\(914\) | −94.8463 | −3.13724 | ||||||||
\(915\) | 47.6881 | 1.57652 | ||||||||
\(916\) | 4.18340 | 0.138223 | ||||||||
\(917\) | −18.2716 | −0.603381 | ||||||||
\(918\) | 308.090 | 10.1685 | ||||||||
\(919\) | −49.8054 | −1.64293 | −0.821464 | − | 0.570261i | \(-0.806842\pi\) | ||||
−0.821464 | + | 0.570261i | \(0.806842\pi\) | |||||||
\(920\) | 6.23811 | 0.205665 | ||||||||
\(921\) | 15.5683 | 0.512994 | ||||||||
\(922\) | 12.2326 | 0.402860 | ||||||||
\(923\) | 21.4528 | 0.706126 | ||||||||
\(924\) | 48.9282 | 1.60962 | ||||||||
\(925\) | 7.16654 | 0.235634 | ||||||||
\(926\) | 96.3984 | 3.16785 | ||||||||
\(927\) | 80.5105 | 2.64431 | ||||||||
\(928\) | −3.28852 | −0.107951 | ||||||||
\(929\) | 14.1498 | 0.464239 | 0.232120 | − | 0.972687i | \(-0.425434\pi\) | ||||
0.232120 | + | 0.972687i | \(0.425434\pi\) | |||||||
\(930\) | 55.7566 | 1.82833 | ||||||||
\(931\) | −2.56746 | −0.0841450 | ||||||||
\(932\) | −90.3659 | −2.96003 | ||||||||
\(933\) | 16.6947 | 0.546560 | ||||||||
\(934\) | 13.9096 | 0.455137 | ||||||||
\(935\) | −28.0613 | −0.917703 | ||||||||
\(936\) | −83.4817 | −2.72868 | ||||||||
\(937\) | 24.7070 | 0.807141 | 0.403571 | − | 0.914949i | \(-0.367769\pi\) | ||||
0.403571 | + | 0.914949i | \(0.367769\pi\) | |||||||
\(938\) | 24.3652 | 0.795552 | ||||||||
\(939\) | 61.1313 | 1.99494 | ||||||||
\(940\) | −16.4537 | −0.536659 | ||||||||
\(941\) | 12.9427 | 0.421920 | 0.210960 | − | 0.977495i | \(-0.432341\pi\) | ||||
0.210960 | + | 0.977495i | \(0.432341\pi\) | |||||||
\(942\) | 6.52637 | 0.212641 | ||||||||
\(943\) | −3.81749 | −0.124315 | ||||||||
\(944\) | 32.9964 | 1.07394 | ||||||||
\(945\) | 15.7229 | 0.511466 | ||||||||
\(946\) | −43.1768 | −1.40380 | ||||||||
\(947\) | 5.70726 | 0.185461 | 0.0927304 | − | 0.995691i | \(-0.470441\pi\) | ||||
0.0927304 | + | 0.995691i | \(0.470441\pi\) | |||||||
\(948\) | 134.454 | 4.36685 | ||||||||
\(949\) | 20.7049 | 0.672110 | ||||||||
\(950\) | 6.38435 | 0.207136 | ||||||||
\(951\) | −48.2452 | −1.56446 | ||||||||
\(952\) | −42.7837 | −1.38663 | ||||||||
\(953\) | −19.1077 | −0.618960 | −0.309480 | − | 0.950906i | \(-0.600155\pi\) | ||||
−0.309480 | + | 0.950906i | \(0.600155\pi\) | |||||||
\(954\) | 73.0875 | 2.36629 | ||||||||
\(955\) | −13.0207 | −0.421339 | ||||||||
\(956\) | 102.595 | 3.31815 | ||||||||
\(957\) | −20.1603 | −0.651689 | ||||||||
\(958\) | 68.8296 | 2.22378 | ||||||||
\(959\) | 2.10301 | 0.0679099 | ||||||||
\(960\) | 18.1429 | 0.585560 | ||||||||
\(961\) | 15.6078 | 0.503477 | ||||||||
\(962\) | −35.1875 | −1.13449 | ||||||||
\(963\) | −9.46179 | −0.304902 | ||||||||
\(964\) | 26.5382 | 0.854738 | ||||||||
\(965\) | −7.13123 | −0.229562 | ||||||||
\(966\) | 9.38371 | 0.301916 | ||||||||
\(967\) | 27.5502 | 0.885953 | 0.442977 | − | 0.896533i | \(-0.353922\pi\) | ||||
0.442977 | + | 0.896533i | \(0.353922\pi\) | |||||||
\(968\) | −9.12649 | −0.293336 | ||||||||
\(969\) | 66.4491 | 2.13465 | ||||||||
\(970\) | 20.6428 | 0.662802 | ||||||||
\(971\) | 40.5061 | 1.29990 | 0.649952 | − | 0.759975i | \(-0.274789\pi\) | ||||
0.649952 | + | 0.759975i | \(0.274789\pi\) | |||||||
\(972\) | 191.218 | 6.13332 | ||||||||
\(973\) | 6.87366 | 0.220359 | ||||||||
\(974\) | 97.0476 | 3.10961 | ||||||||
\(975\) | 6.48514 | 0.207691 | ||||||||
\(976\) | −74.5442 | −2.38610 | ||||||||
\(977\) | 55.3291 | 1.77014 | 0.885068 | − | 0.465462i | \(-0.154112\pi\) | ||||
0.885068 | + | 0.465462i | \(0.154112\pi\) | |||||||
\(978\) | −57.3169 | −1.83279 | ||||||||
\(979\) | 3.77233 | 0.120564 | ||||||||
\(980\) | −4.18340 | −0.133634 | ||||||||
\(981\) | 17.8216 | 0.569000 | ||||||||
\(982\) | 83.3693 | 2.66042 | ||||||||
\(983\) | 58.4717 | 1.86496 | 0.932478 | − | 0.361226i | \(-0.117642\pi\) | ||||
0.932478 | + | 0.361226i | \(0.117642\pi\) | |||||||
\(984\) | 59.2476 | 1.88874 | ||||||||
\(985\) | 6.90082 | 0.219878 | ||||||||
\(986\) | 33.7763 | 1.07566 | ||||||||
\(987\) | −12.9178 | −0.411177 | ||||||||
\(988\) | −21.2079 | −0.674713 | ||||||||
\(989\) | −5.60232 | −0.178143 | ||||||||
\(990\) | −68.9556 | −2.19155 | ||||||||
\(991\) | −43.8189 | −1.39195 | −0.695976 | − | 0.718065i | \(-0.745028\pi\) | ||||
−0.695976 | + | 0.718065i | \(0.745028\pi\) | |||||||
\(992\) | −13.0246 | −0.413531 | ||||||||
\(993\) | −22.6678 | −0.719340 | ||||||||
\(994\) | 27.0167 | 0.856916 | ||||||||
\(995\) | 12.6513 | 0.401075 | ||||||||
\(996\) | −41.0689 | −1.30132 | ||||||||
\(997\) | 7.19453 | 0.227853 | 0.113926 | − | 0.993489i | \(-0.463657\pi\) | ||||
0.113926 | + | 0.993489i | \(0.463657\pi\) | |||||||
\(998\) | 61.2460 | 1.93871 | ||||||||
\(999\) | 112.679 | 3.56500 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8015.2.a.l.1.4 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.4 | ✓ | 62 | 1.1 | even | 1 | trivial |