Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.79 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77530 | 1.96243 | 0.981216 | − | 0.192914i | \(-0.0617938\pi\) | ||||
0.981216 | + | 0.192914i | \(0.0617938\pi\) | |||||||
\(3\) | 0.714201 | 0.412344 | 0.206172 | − | 0.978516i | \(-0.433899\pi\) | ||||
0.206172 | + | 0.978516i | \(0.433899\pi\) | |||||||
\(4\) | 5.70227 | 2.85114 | ||||||||
\(5\) | −2.27953 | −1.01944 | −0.509718 | − | 0.860341i | \(-0.670250\pi\) | ||||
−0.509718 | + | 0.860341i | \(0.670250\pi\) | |||||||
\(6\) | 1.98212 | 0.809197 | ||||||||
\(7\) | −4.78018 | −1.80674 | −0.903370 | − | 0.428863i | \(-0.858914\pi\) | ||||
−0.903370 | + | 0.428863i | \(0.858914\pi\) | |||||||
\(8\) | 10.2749 | 3.63273 | ||||||||
\(9\) | −2.48992 | −0.829972 | ||||||||
\(10\) | −6.32637 | −2.00057 | ||||||||
\(11\) | 2.27334 | 0.685437 | 0.342719 | − | 0.939438i | \(-0.388652\pi\) | ||||
0.342719 | + | 0.939438i | \(0.388652\pi\) | |||||||
\(12\) | 4.07257 | 1.17565 | ||||||||
\(13\) | −3.53419 | −0.980207 | −0.490104 | − | 0.871664i | \(-0.663041\pi\) | ||||
−0.490104 | + | 0.871664i | \(0.663041\pi\) | |||||||
\(14\) | −13.2664 | −3.54560 | ||||||||
\(15\) | −1.62804 | −0.420359 | ||||||||
\(16\) | 17.1114 | 4.27784 | ||||||||
\(17\) | −6.35164 | −1.54050 | −0.770249 | − | 0.637743i | \(-0.779868\pi\) | ||||
−0.770249 | + | 0.637743i | \(0.779868\pi\) | |||||||
\(18\) | −6.91026 | −1.62876 | ||||||||
\(19\) | −5.74978 | −1.31909 | −0.659545 | − | 0.751665i | \(-0.729251\pi\) | ||||
−0.659545 | + | 0.751665i | \(0.729251\pi\) | |||||||
\(20\) | −12.9985 | −2.90655 | ||||||||
\(21\) | −3.41401 | −0.744998 | ||||||||
\(22\) | 6.30919 | 1.34512 | ||||||||
\(23\) | 1.35354 | 0.282233 | 0.141117 | − | 0.989993i | \(-0.454931\pi\) | ||||
0.141117 | + | 0.989993i | \(0.454931\pi\) | |||||||
\(24\) | 7.33835 | 1.49793 | ||||||||
\(25\) | 0.196253 | 0.0392506 | ||||||||
\(26\) | −9.80842 | −1.92359 | ||||||||
\(27\) | −3.92090 | −0.754578 | ||||||||
\(28\) | −27.2579 | −5.15126 | ||||||||
\(29\) | −2.70705 | −0.502686 | −0.251343 | − | 0.967898i | \(-0.580872\pi\) | ||||
−0.251343 | + | 0.967898i | \(0.580872\pi\) | |||||||
\(30\) | −4.51830 | −0.824925 | ||||||||
\(31\) | 8.27203 | 1.48570 | 0.742850 | − | 0.669457i | \(-0.233473\pi\) | ||||
0.742850 | + | 0.669457i | \(0.233473\pi\) | |||||||
\(32\) | 26.9393 | 4.76225 | ||||||||
\(33\) | 1.62362 | 0.282636 | ||||||||
\(34\) | −17.6277 | −3.02312 | ||||||||
\(35\) | 10.8966 | 1.84186 | ||||||||
\(36\) | −14.1982 | −2.36636 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −15.9573 | −2.58862 | ||||||||
\(39\) | −2.52412 | −0.404183 | ||||||||
\(40\) | −23.4220 | −3.70334 | ||||||||
\(41\) | 7.35264 | 1.14829 | 0.574144 | − | 0.818754i | \(-0.305335\pi\) | ||||
0.574144 | + | 0.818754i | \(0.305335\pi\) | |||||||
\(42\) | −9.47489 | −1.46201 | ||||||||
\(43\) | 2.84117 | 0.433274 | 0.216637 | − | 0.976252i | \(-0.430491\pi\) | ||||
0.216637 | + | 0.976252i | \(0.430491\pi\) | |||||||
\(44\) | 12.9632 | 1.95428 | ||||||||
\(45\) | 5.67584 | 0.846104 | ||||||||
\(46\) | 3.75649 | 0.553864 | ||||||||
\(47\) | −7.58798 | −1.10682 | −0.553410 | − | 0.832909i | \(-0.686674\pi\) | ||||
−0.553410 | + | 0.832909i | \(0.686674\pi\) | |||||||
\(48\) | 12.2210 | 1.76394 | ||||||||
\(49\) | 15.8501 | 2.26431 | ||||||||
\(50\) | 0.544661 | 0.0770267 | ||||||||
\(51\) | −4.53635 | −0.635216 | ||||||||
\(52\) | −20.1529 | −2.79470 | ||||||||
\(53\) | −12.9859 | −1.78375 | −0.891875 | − | 0.452281i | \(-0.850610\pi\) | ||||
−0.891875 | + | 0.452281i | \(0.850610\pi\) | |||||||
\(54\) | −10.8817 | −1.48081 | ||||||||
\(55\) | −5.18214 | −0.698760 | ||||||||
\(56\) | −49.1159 | −6.56339 | ||||||||
\(57\) | −4.10650 | −0.543919 | ||||||||
\(58\) | −7.51286 | −0.986487 | ||||||||
\(59\) | 0.431054 | 0.0561185 | 0.0280592 | − | 0.999606i | \(-0.491067\pi\) | ||||
0.0280592 | + | 0.999606i | \(0.491067\pi\) | |||||||
\(60\) | −9.28354 | −1.19850 | ||||||||
\(61\) | −6.23767 | −0.798652 | −0.399326 | − | 0.916809i | \(-0.630756\pi\) | ||||
−0.399326 | + | 0.916809i | \(0.630756\pi\) | |||||||
\(62\) | 22.9573 | 2.91559 | ||||||||
\(63\) | 11.9023 | 1.49954 | ||||||||
\(64\) | 40.5419 | 5.06774 | ||||||||
\(65\) | 8.05628 | 0.999259 | ||||||||
\(66\) | 4.50603 | 0.554654 | ||||||||
\(67\) | 0.666623 | 0.0814409 | 0.0407205 | − | 0.999171i | \(-0.487035\pi\) | ||||
0.0407205 | + | 0.999171i | \(0.487035\pi\) | |||||||
\(68\) | −36.2188 | −4.39217 | ||||||||
\(69\) | 0.966702 | 0.116377 | ||||||||
\(70\) | 30.2412 | 3.61452 | ||||||||
\(71\) | 0.691721 | 0.0820922 | 0.0410461 | − | 0.999157i | \(-0.486931\pi\) | ||||
0.0410461 | + | 0.999157i | \(0.486931\pi\) | |||||||
\(72\) | −25.5837 | −3.01506 | ||||||||
\(73\) | −13.4129 | −1.56986 | −0.784931 | − | 0.619583i | \(-0.787302\pi\) | ||||
−0.784931 | + | 0.619583i | \(0.787302\pi\) | |||||||
\(74\) | −2.77530 | −0.322622 | ||||||||
\(75\) | 0.140164 | 0.0161848 | ||||||||
\(76\) | −32.7868 | −3.76090 | ||||||||
\(77\) | −10.8670 | −1.23841 | ||||||||
\(78\) | −7.00518 | −0.793181 | ||||||||
\(79\) | −5.41458 | −0.609188 | −0.304594 | − | 0.952482i | \(-0.598521\pi\) | ||||
−0.304594 | + | 0.952482i | \(0.598521\pi\) | |||||||
\(80\) | −39.0059 | −4.36099 | ||||||||
\(81\) | 4.66944 | 0.518826 | ||||||||
\(82\) | 20.4057 | 2.25344 | ||||||||
\(83\) | −1.29394 | −0.142028 | −0.0710141 | − | 0.997475i | \(-0.522624\pi\) | ||||
−0.0710141 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(84\) | −19.4676 | −2.12409 | ||||||||
\(85\) | 14.4787 | 1.57044 | ||||||||
\(86\) | 7.88508 | 0.850270 | ||||||||
\(87\) | −1.93338 | −0.207280 | ||||||||
\(88\) | 23.3583 | 2.49001 | ||||||||
\(89\) | 11.7089 | 1.24114 | 0.620571 | − | 0.784150i | \(-0.286901\pi\) | ||||
0.620571 | + | 0.784150i | \(0.286901\pi\) | |||||||
\(90\) | 15.7521 | 1.66042 | ||||||||
\(91\) | 16.8941 | 1.77098 | ||||||||
\(92\) | 7.71828 | 0.804686 | ||||||||
\(93\) | 5.90789 | 0.612620 | ||||||||
\(94\) | −21.0589 | −2.17206 | ||||||||
\(95\) | 13.1068 | 1.34473 | ||||||||
\(96\) | 19.2401 | 1.96368 | ||||||||
\(97\) | −11.9401 | −1.21233 | −0.606165 | − | 0.795339i | \(-0.707293\pi\) | ||||
−0.606165 | + | 0.795339i | \(0.707293\pi\) | |||||||
\(98\) | 43.9888 | 4.44354 | ||||||||
\(99\) | −5.66042 | −0.568894 | ||||||||
\(100\) | 1.11909 | 0.111909 | ||||||||
\(101\) | 18.0764 | 1.79867 | 0.899337 | − | 0.437257i | \(-0.144050\pi\) | ||||
0.899337 | + | 0.437257i | \(0.144050\pi\) | |||||||
\(102\) | −12.5897 | −1.24657 | ||||||||
\(103\) | 11.2106 | 1.10461 | 0.552304 | − | 0.833643i | \(-0.313749\pi\) | ||||
0.552304 | + | 0.833643i | \(0.313749\pi\) | |||||||
\(104\) | −36.3134 | −3.56083 | ||||||||
\(105\) | 7.78234 | 0.759478 | ||||||||
\(106\) | −36.0397 | −3.50049 | ||||||||
\(107\) | 7.70623 | 0.744989 | 0.372494 | − | 0.928034i | \(-0.378503\pi\) | ||||
0.372494 | + | 0.928034i | \(0.378503\pi\) | |||||||
\(108\) | −22.3581 | −2.15141 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −14.3820 | −1.37127 | ||||||||
\(111\) | −0.714201 | −0.0677890 | ||||||||
\(112\) | −81.7955 | −7.72895 | ||||||||
\(113\) | 2.59623 | 0.244232 | 0.122116 | − | 0.992516i | \(-0.461032\pi\) | ||||
0.122116 | + | 0.992516i | \(0.461032\pi\) | |||||||
\(114\) | −11.3967 | −1.06740 | ||||||||
\(115\) | −3.08544 | −0.287719 | ||||||||
\(116\) | −15.4363 | −1.43323 | ||||||||
\(117\) | 8.79983 | 0.813545 | ||||||||
\(118\) | 1.19630 | 0.110129 | ||||||||
\(119\) | 30.3620 | 2.78328 | ||||||||
\(120\) | −16.7280 | −1.52705 | ||||||||
\(121\) | −5.83193 | −0.530176 | ||||||||
\(122\) | −17.3114 | −1.56730 | ||||||||
\(123\) | 5.25126 | 0.473490 | ||||||||
\(124\) | 47.1694 | 4.23594 | ||||||||
\(125\) | 10.9503 | 0.979423 | ||||||||
\(126\) | 33.0323 | 2.94275 | ||||||||
\(127\) | −3.27414 | −0.290533 | −0.145266 | − | 0.989393i | \(-0.546404\pi\) | ||||
−0.145266 | + | 0.989393i | \(0.546404\pi\) | |||||||
\(128\) | 58.6371 | 5.18284 | ||||||||
\(129\) | 2.02916 | 0.178658 | ||||||||
\(130\) | 22.3586 | 1.96098 | ||||||||
\(131\) | −5.05540 | −0.441692 | −0.220846 | − | 0.975309i | \(-0.570882\pi\) | ||||
−0.220846 | + | 0.975309i | \(0.570882\pi\) | |||||||
\(132\) | 9.25833 | 0.805834 | ||||||||
\(133\) | 27.4850 | 2.38325 | ||||||||
\(134\) | 1.85008 | 0.159822 | ||||||||
\(135\) | 8.93781 | 0.769245 | ||||||||
\(136\) | −65.2625 | −5.59621 | ||||||||
\(137\) | −16.9417 | −1.44743 | −0.723714 | − | 0.690100i | \(-0.757567\pi\) | ||||
−0.723714 | + | 0.690100i | \(0.757567\pi\) | |||||||
\(138\) | 2.68289 | 0.228382 | ||||||||
\(139\) | 16.2835 | 1.38115 | 0.690573 | − | 0.723263i | \(-0.257359\pi\) | ||||
0.690573 | + | 0.723263i | \(0.257359\pi\) | |||||||
\(140\) | 62.1352 | 5.25138 | ||||||||
\(141\) | −5.41934 | −0.456391 | ||||||||
\(142\) | 1.91973 | 0.161100 | ||||||||
\(143\) | −8.03440 | −0.671871 | ||||||||
\(144\) | −42.6059 | −3.55049 | ||||||||
\(145\) | 6.17080 | 0.512457 | ||||||||
\(146\) | −37.2248 | −3.08075 | ||||||||
\(147\) | 11.3202 | 0.933673 | ||||||||
\(148\) | −5.70227 | −0.468724 | ||||||||
\(149\) | 2.89005 | 0.236762 | 0.118381 | − | 0.992968i | \(-0.462230\pi\) | ||||
0.118381 | + | 0.992968i | \(0.462230\pi\) | |||||||
\(150\) | 0.388997 | 0.0317615 | ||||||||
\(151\) | 16.1526 | 1.31448 | 0.657240 | − | 0.753682i | \(-0.271724\pi\) | ||||
0.657240 | + | 0.753682i | \(0.271724\pi\) | |||||||
\(152\) | −59.0784 | −4.79189 | ||||||||
\(153\) | 15.8151 | 1.27857 | ||||||||
\(154\) | −30.1591 | −2.43029 | ||||||||
\(155\) | −18.8563 | −1.51458 | ||||||||
\(156\) | −14.3932 | −1.15238 | ||||||||
\(157\) | −16.6431 | −1.32827 | −0.664134 | − | 0.747614i | \(-0.731199\pi\) | ||||
−0.664134 | + | 0.747614i | \(0.731199\pi\) | |||||||
\(158\) | −15.0271 | −1.19549 | ||||||||
\(159\) | −9.27454 | −0.735519 | ||||||||
\(160\) | −61.4090 | −4.85481 | ||||||||
\(161\) | −6.47018 | −0.509922 | ||||||||
\(162\) | 12.9591 | 1.01816 | ||||||||
\(163\) | 0.322726 | 0.0252779 | 0.0126389 | − | 0.999920i | \(-0.495977\pi\) | ||||
0.0126389 | + | 0.999920i | \(0.495977\pi\) | |||||||
\(164\) | 41.9267 | 3.27393 | ||||||||
\(165\) | −3.70109 | −0.288130 | ||||||||
\(166\) | −3.59107 | −0.278721 | ||||||||
\(167\) | −17.7694 | −1.37504 | −0.687521 | − | 0.726165i | \(-0.741301\pi\) | ||||
−0.687521 | + | 0.726165i | \(0.741301\pi\) | |||||||
\(168\) | −35.0786 | −2.70638 | ||||||||
\(169\) | −0.509521 | −0.0391939 | ||||||||
\(170\) | 40.1828 | 3.08188 | ||||||||
\(171\) | 14.3165 | 1.09481 | ||||||||
\(172\) | 16.2011 | 1.23532 | ||||||||
\(173\) | −3.73205 | −0.283743 | −0.141871 | − | 0.989885i | \(-0.545312\pi\) | ||||
−0.141871 | + | 0.989885i | \(0.545312\pi\) | |||||||
\(174\) | −5.36569 | −0.406772 | ||||||||
\(175\) | −0.938126 | −0.0709157 | ||||||||
\(176\) | 38.9000 | 2.93219 | ||||||||
\(177\) | 0.307859 | 0.0231401 | ||||||||
\(178\) | 32.4957 | 2.43566 | ||||||||
\(179\) | 23.6743 | 1.76950 | 0.884749 | − | 0.466067i | \(-0.154330\pi\) | ||||
0.884749 | + | 0.466067i | \(0.154330\pi\) | |||||||
\(180\) | 32.3652 | 2.41236 | ||||||||
\(181\) | −23.6607 | −1.75868 | −0.879341 | − | 0.476192i | \(-0.842017\pi\) | ||||
−0.879341 | + | 0.476192i | \(0.842017\pi\) | |||||||
\(182\) | 46.8860 | 3.47542 | ||||||||
\(183\) | −4.45495 | −0.329319 | ||||||||
\(184\) | 13.9075 | 1.02528 | ||||||||
\(185\) | 2.27953 | 0.167594 | ||||||||
\(186\) | 16.3962 | 1.20222 | ||||||||
\(187\) | −14.4394 | −1.05592 | ||||||||
\(188\) | −43.2687 | −3.15570 | ||||||||
\(189\) | 18.7426 | 1.36333 | ||||||||
\(190\) | 36.3752 | 2.63894 | ||||||||
\(191\) | −8.26889 | −0.598316 | −0.299158 | − | 0.954204i | \(-0.596706\pi\) | ||||
−0.299158 | + | 0.954204i | \(0.596706\pi\) | |||||||
\(192\) | 28.9551 | 2.08965 | ||||||||
\(193\) | −3.84462 | −0.276741 | −0.138371 | − | 0.990381i | \(-0.544187\pi\) | ||||
−0.138371 | + | 0.990381i | \(0.544187\pi\) | |||||||
\(194\) | −33.1372 | −2.37912 | ||||||||
\(195\) | 5.75380 | 0.412039 | ||||||||
\(196\) | 90.3818 | 6.45585 | ||||||||
\(197\) | 3.99863 | 0.284890 | 0.142445 | − | 0.989803i | \(-0.454504\pi\) | ||||
0.142445 | + | 0.989803i | \(0.454504\pi\) | |||||||
\(198\) | −15.7094 | −1.11642 | ||||||||
\(199\) | −0.637214 | −0.0451709 | −0.0225854 | − | 0.999745i | \(-0.507190\pi\) | ||||
−0.0225854 | + | 0.999745i | \(0.507190\pi\) | |||||||
\(200\) | 2.01648 | 0.142587 | ||||||||
\(201\) | 0.476102 | 0.0335817 | ||||||||
\(202\) | 50.1675 | 3.52977 | ||||||||
\(203\) | 12.9402 | 0.908223 | ||||||||
\(204\) | −25.8675 | −1.81109 | ||||||||
\(205\) | −16.7605 | −1.17061 | ||||||||
\(206\) | 31.1126 | 2.16772 | ||||||||
\(207\) | −3.37021 | −0.234246 | ||||||||
\(208\) | −60.4748 | −4.19317 | ||||||||
\(209\) | −13.0712 | −0.904153 | ||||||||
\(210\) | 21.5983 | 1.49042 | ||||||||
\(211\) | 2.06981 | 0.142492 | 0.0712460 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712460 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(212\) | −74.0492 | −5.08572 | ||||||||
\(213\) | 0.494028 | 0.0338502 | ||||||||
\(214\) | 21.3871 | 1.46199 | ||||||||
\(215\) | −6.47652 | −0.441695 | ||||||||
\(216\) | −40.2869 | −2.74118 | ||||||||
\(217\) | −39.5418 | −2.68427 | ||||||||
\(218\) | −2.77530 | −0.187967 | ||||||||
\(219\) | −9.57951 | −0.647323 | ||||||||
\(220\) | −29.5500 | −1.99226 | ||||||||
\(221\) | 22.4479 | 1.51001 | ||||||||
\(222\) | −1.98212 | −0.133031 | ||||||||
\(223\) | −6.48010 | −0.433940 | −0.216970 | − | 0.976178i | \(-0.569617\pi\) | ||||
−0.216970 | + | 0.976178i | \(0.569617\pi\) | |||||||
\(224\) | −128.775 | −8.60414 | ||||||||
\(225\) | −0.488654 | −0.0325769 | ||||||||
\(226\) | 7.20530 | 0.479289 | ||||||||
\(227\) | −21.5329 | −1.42919 | −0.714593 | − | 0.699540i | \(-0.753388\pi\) | ||||
−0.714593 | + | 0.699540i | \(0.753388\pi\) | |||||||
\(228\) | −23.4164 | −1.55079 | ||||||||
\(229\) | 2.52407 | 0.166795 | 0.0833977 | − | 0.996516i | \(-0.473423\pi\) | ||||
0.0833977 | + | 0.996516i | \(0.473423\pi\) | |||||||
\(230\) | −8.56302 | −0.564629 | ||||||||
\(231\) | −7.76120 | −0.510650 | ||||||||
\(232\) | −27.8147 | −1.82612 | ||||||||
\(233\) | −2.09896 | −0.137508 | −0.0687538 | − | 0.997634i | \(-0.521902\pi\) | ||||
−0.0687538 | + | 0.997634i | \(0.521902\pi\) | |||||||
\(234\) | 24.4221 | 1.59653 | ||||||||
\(235\) | 17.2970 | 1.12833 | ||||||||
\(236\) | 2.45799 | 0.160001 | ||||||||
\(237\) | −3.86710 | −0.251195 | ||||||||
\(238\) | 84.2635 | 5.46199 | ||||||||
\(239\) | 28.8245 | 1.86450 | 0.932252 | − | 0.361809i | \(-0.117841\pi\) | ||||
0.932252 | + | 0.361809i | \(0.117841\pi\) | |||||||
\(240\) | −27.8580 | −1.79823 | ||||||||
\(241\) | −9.11602 | −0.587215 | −0.293607 | − | 0.955926i | \(-0.594856\pi\) | ||||
−0.293607 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(242\) | −16.1853 | −1.04043 | ||||||||
\(243\) | 15.0976 | 0.968513 | ||||||||
\(244\) | −35.5689 | −2.27707 | ||||||||
\(245\) | −36.1309 | −2.30832 | ||||||||
\(246\) | 14.5738 | 0.929192 | ||||||||
\(247\) | 20.3208 | 1.29298 | ||||||||
\(248\) | 84.9944 | 5.39715 | ||||||||
\(249\) | −0.924133 | −0.0585645 | ||||||||
\(250\) | 30.3903 | 1.92205 | ||||||||
\(251\) | −10.9599 | −0.691781 | −0.345890 | − | 0.938275i | \(-0.612423\pi\) | ||||
−0.345890 | + | 0.938275i | \(0.612423\pi\) | |||||||
\(252\) | 67.8699 | 4.27540 | ||||||||
\(253\) | 3.07706 | 0.193453 | ||||||||
\(254\) | −9.08671 | −0.570151 | ||||||||
\(255\) | 10.3407 | 0.647562 | ||||||||
\(256\) | 81.6517 | 5.10323 | ||||||||
\(257\) | −31.1095 | −1.94056 | −0.970278 | − | 0.241991i | \(-0.922200\pi\) | ||||
−0.970278 | + | 0.241991i | \(0.922200\pi\) | |||||||
\(258\) | 5.63153 | 0.350604 | ||||||||
\(259\) | 4.78018 | 0.297026 | ||||||||
\(260\) | 45.9391 | 2.84902 | ||||||||
\(261\) | 6.74033 | 0.417216 | ||||||||
\(262\) | −14.0302 | −0.866791 | ||||||||
\(263\) | −3.26479 | −0.201316 | −0.100658 | − | 0.994921i | \(-0.532095\pi\) | ||||
−0.100658 | + | 0.994921i | \(0.532095\pi\) | |||||||
\(264\) | 16.6826 | 1.02674 | ||||||||
\(265\) | 29.6017 | 1.81842 | ||||||||
\(266\) | 76.2790 | 4.67697 | ||||||||
\(267\) | 8.36252 | 0.511778 | ||||||||
\(268\) | 3.80126 | 0.232199 | ||||||||
\(269\) | 3.18715 | 0.194324 | 0.0971621 | − | 0.995269i | \(-0.469023\pi\) | ||||
0.0971621 | + | 0.995269i | \(0.469023\pi\) | |||||||
\(270\) | 24.8051 | 1.50959 | ||||||||
\(271\) | −9.84695 | −0.598160 | −0.299080 | − | 0.954228i | \(-0.596680\pi\) | ||||
−0.299080 | + | 0.954228i | \(0.596680\pi\) | |||||||
\(272\) | −108.685 | −6.59001 | ||||||||
\(273\) | 12.0658 | 0.730253 | ||||||||
\(274\) | −47.0183 | −2.84048 | ||||||||
\(275\) | 0.446150 | 0.0269039 | ||||||||
\(276\) | 5.51240 | 0.331807 | ||||||||
\(277\) | 11.3928 | 0.684527 | 0.342264 | − | 0.939604i | \(-0.388806\pi\) | ||||
0.342264 | + | 0.939604i | \(0.388806\pi\) | |||||||
\(278\) | 45.1914 | 2.71040 | ||||||||
\(279\) | −20.5967 | −1.23309 | ||||||||
\(280\) | 111.961 | 6.69096 | ||||||||
\(281\) | 4.67462 | 0.278864 | 0.139432 | − | 0.990232i | \(-0.455472\pi\) | ||||
0.139432 | + | 0.990232i | \(0.455472\pi\) | |||||||
\(282\) | −15.0403 | −0.895635 | ||||||||
\(283\) | 20.4781 | 1.21730 | 0.608648 | − | 0.793440i | \(-0.291712\pi\) | ||||
0.608648 | + | 0.793440i | \(0.291712\pi\) | |||||||
\(284\) | 3.94438 | 0.234056 | ||||||||
\(285\) | 9.36088 | 0.554491 | ||||||||
\(286\) | −22.2979 | −1.31850 | ||||||||
\(287\) | −35.1469 | −2.07466 | ||||||||
\(288\) | −67.0767 | −3.95253 | ||||||||
\(289\) | 23.3433 | 1.37314 | ||||||||
\(290\) | 17.1258 | 1.00566 | ||||||||
\(291\) | −8.52761 | −0.499897 | ||||||||
\(292\) | −76.4841 | −4.47589 | ||||||||
\(293\) | −5.18021 | −0.302631 | −0.151316 | − | 0.988485i | \(-0.548351\pi\) | ||||
−0.151316 | + | 0.988485i | \(0.548351\pi\) | |||||||
\(294\) | 31.4169 | 1.83227 | ||||||||
\(295\) | −0.982601 | −0.0572092 | ||||||||
\(296\) | −10.2749 | −0.597217 | ||||||||
\(297\) | −8.91354 | −0.517216 | ||||||||
\(298\) | 8.02075 | 0.464630 | ||||||||
\(299\) | −4.78368 | −0.276647 | ||||||||
\(300\) | 0.799255 | 0.0461450 | ||||||||
\(301\) | −13.5813 | −0.782813 | ||||||||
\(302\) | 44.8282 | 2.57958 | ||||||||
\(303\) | 12.9102 | 0.741672 | ||||||||
\(304\) | −98.3866 | −5.64286 | ||||||||
\(305\) | 14.2189 | 0.814175 | ||||||||
\(306\) | 43.8915 | 2.50911 | ||||||||
\(307\) | 24.8472 | 1.41810 | 0.709052 | − | 0.705156i | \(-0.249123\pi\) | ||||
0.709052 | + | 0.705156i | \(0.249123\pi\) | |||||||
\(308\) | −61.9665 | −3.53087 | ||||||||
\(309\) | 8.00659 | 0.455479 | ||||||||
\(310\) | −52.3319 | −2.97225 | ||||||||
\(311\) | −9.91826 | −0.562413 | −0.281206 | − | 0.959647i | \(-0.590735\pi\) | ||||
−0.281206 | + | 0.959647i | \(0.590735\pi\) | |||||||
\(312\) | −25.9351 | −1.46829 | ||||||||
\(313\) | 24.4577 | 1.38243 | 0.691215 | − | 0.722649i | \(-0.257076\pi\) | ||||
0.691215 | + | 0.722649i | \(0.257076\pi\) | |||||||
\(314\) | −46.1897 | −2.60663 | ||||||||
\(315\) | −27.1315 | −1.52869 | ||||||||
\(316\) | −30.8754 | −1.73688 | ||||||||
\(317\) | −25.4916 | −1.43175 | −0.715875 | − | 0.698229i | \(-0.753972\pi\) | ||||
−0.715875 | + | 0.698229i | \(0.753972\pi\) | |||||||
\(318\) | −25.7396 | −1.44341 | ||||||||
\(319\) | −6.15404 | −0.344560 | ||||||||
\(320\) | −92.4164 | −5.16624 | ||||||||
\(321\) | 5.50379 | 0.307192 | ||||||||
\(322\) | −17.9567 | −1.00069 | ||||||||
\(323\) | 36.5205 | 2.03206 | ||||||||
\(324\) | 26.6264 | 1.47925 | ||||||||
\(325\) | −0.693595 | −0.0384738 | ||||||||
\(326\) | 0.895661 | 0.0496061 | ||||||||
\(327\) | −0.714201 | −0.0394954 | ||||||||
\(328\) | 75.5477 | 4.17142 | ||||||||
\(329\) | 36.2719 | 1.99974 | ||||||||
\(330\) | −10.2716 | −0.565434 | ||||||||
\(331\) | −23.1540 | −1.27266 | −0.636329 | − | 0.771418i | \(-0.719548\pi\) | ||||
−0.636329 | + | 0.771418i | \(0.719548\pi\) | |||||||
\(332\) | −7.37840 | −0.404942 | ||||||||
\(333\) | 2.48992 | 0.136447 | ||||||||
\(334\) | −49.3155 | −2.69842 | ||||||||
\(335\) | −1.51959 | −0.0830238 | ||||||||
\(336\) | −58.4184 | −3.18699 | ||||||||
\(337\) | 9.33003 | 0.508239 | 0.254119 | − | 0.967173i | \(-0.418214\pi\) | ||||
0.254119 | + | 0.967173i | \(0.418214\pi\) | |||||||
\(338\) | −1.41407 | −0.0769154 | ||||||||
\(339\) | 1.85423 | 0.100708 | ||||||||
\(340\) | 82.5618 | 4.47754 | ||||||||
\(341\) | 18.8051 | 1.01835 | ||||||||
\(342\) | 39.7325 | 2.14849 | ||||||||
\(343\) | −42.3053 | −2.28427 | ||||||||
\(344\) | 29.1927 | 1.57397 | ||||||||
\(345\) | −2.20363 | −0.118639 | ||||||||
\(346\) | −10.3576 | −0.556826 | ||||||||
\(347\) | 12.8462 | 0.689618 | 0.344809 | − | 0.938673i | \(-0.387944\pi\) | ||||
0.344809 | + | 0.938673i | \(0.387944\pi\) | |||||||
\(348\) | −11.0246 | −0.590983 | ||||||||
\(349\) | −31.8799 | −1.70649 | −0.853246 | − | 0.521508i | \(-0.825370\pi\) | ||||
−0.853246 | + | 0.521508i | \(0.825370\pi\) | |||||||
\(350\) | −2.60358 | −0.139167 | ||||||||
\(351\) | 13.8572 | 0.739643 | ||||||||
\(352\) | 61.2422 | 3.26422 | ||||||||
\(353\) | −32.1816 | −1.71285 | −0.856426 | − | 0.516269i | \(-0.827320\pi\) | ||||
−0.856426 | + | 0.516269i | \(0.827320\pi\) | |||||||
\(354\) | 0.854401 | 0.0454109 | ||||||||
\(355\) | −1.57680 | −0.0836878 | ||||||||
\(356\) | 66.7675 | 3.53867 | ||||||||
\(357\) | 21.6846 | 1.14767 | ||||||||
\(358\) | 65.7031 | 3.47252 | ||||||||
\(359\) | 5.62295 | 0.296768 | 0.148384 | − | 0.988930i | \(-0.452593\pi\) | ||||
0.148384 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(360\) | 58.3187 | 3.07367 | ||||||||
\(361\) | 14.0600 | 0.739998 | ||||||||
\(362\) | −65.6654 | −3.45129 | ||||||||
\(363\) | −4.16517 | −0.218615 | ||||||||
\(364\) | 96.3345 | 5.04930 | ||||||||
\(365\) | 30.5751 | 1.60037 | ||||||||
\(366\) | −12.3638 | −0.646267 | ||||||||
\(367\) | −15.5485 | −0.811624 | −0.405812 | − | 0.913957i | \(-0.633011\pi\) | ||||
−0.405812 | + | 0.913957i | \(0.633011\pi\) | |||||||
\(368\) | 23.1610 | 1.20735 | ||||||||
\(369\) | −18.3075 | −0.953048 | ||||||||
\(370\) | 6.32637 | 0.328892 | ||||||||
\(371\) | 62.0750 | 3.22277 | ||||||||
\(372\) | 33.6884 | 1.74666 | ||||||||
\(373\) | −8.46974 | −0.438546 | −0.219273 | − | 0.975663i | \(-0.570369\pi\) | ||||
−0.219273 | + | 0.975663i | \(0.570369\pi\) | |||||||
\(374\) | −40.0737 | −2.07216 | ||||||||
\(375\) | 7.82070 | 0.403859 | ||||||||
\(376\) | −77.9658 | −4.02078 | ||||||||
\(377\) | 9.56722 | 0.492737 | ||||||||
\(378\) | 52.0164 | 2.67543 | ||||||||
\(379\) | 21.3493 | 1.09664 | 0.548320 | − | 0.836269i | \(-0.315268\pi\) | ||||
0.548320 | + | 0.836269i | \(0.315268\pi\) | |||||||
\(380\) | 74.7385 | 3.83400 | ||||||||
\(381\) | −2.33839 | −0.119800 | ||||||||
\(382\) | −22.9486 | −1.17415 | ||||||||
\(383\) | 3.76037 | 0.192146 | 0.0960730 | − | 0.995374i | \(-0.469372\pi\) | ||||
0.0960730 | + | 0.995374i | \(0.469372\pi\) | |||||||
\(384\) | 41.8787 | 2.13711 | ||||||||
\(385\) | 24.7716 | 1.26248 | ||||||||
\(386\) | −10.6699 | −0.543086 | ||||||||
\(387\) | −7.07427 | −0.359605 | ||||||||
\(388\) | −68.0856 | −3.45652 | ||||||||
\(389\) | −11.8710 | −0.601885 | −0.300942 | − | 0.953642i | \(-0.597301\pi\) | ||||
−0.300942 | + | 0.953642i | \(0.597301\pi\) | |||||||
\(390\) | 15.9685 | 0.808597 | ||||||||
\(391\) | −8.59722 | −0.434780 | ||||||||
\(392\) | 162.859 | 8.22561 | ||||||||
\(393\) | −3.61057 | −0.182129 | ||||||||
\(394\) | 11.0974 | 0.559078 | ||||||||
\(395\) | 12.3427 | 0.621028 | ||||||||
\(396\) | −32.2773 | −1.62199 | ||||||||
\(397\) | −19.3858 | −0.972944 | −0.486472 | − | 0.873696i | \(-0.661717\pi\) | ||||
−0.486472 | + | 0.873696i | \(0.661717\pi\) | |||||||
\(398\) | −1.76846 | −0.0886448 | ||||||||
\(399\) | 19.6298 | 0.982719 | ||||||||
\(400\) | 3.35816 | 0.167908 | ||||||||
\(401\) | 37.5886 | 1.87709 | 0.938544 | − | 0.345160i | \(-0.112175\pi\) | ||||
0.938544 | + | 0.345160i | \(0.112175\pi\) | |||||||
\(402\) | 1.32133 | 0.0659017 | ||||||||
\(403\) | −29.2349 | −1.45629 | ||||||||
\(404\) | 103.077 | 5.12826 | ||||||||
\(405\) | −10.6441 | −0.528911 | ||||||||
\(406\) | 35.9129 | 1.78233 | ||||||||
\(407\) | −2.27334 | −0.112685 | ||||||||
\(408\) | −46.6105 | −2.30757 | ||||||||
\(409\) | −29.3979 | −1.45363 | −0.726816 | − | 0.686832i | \(-0.759001\pi\) | ||||
−0.726816 | + | 0.686832i | \(0.759001\pi\) | |||||||
\(410\) | −46.5155 | −2.29724 | ||||||||
\(411\) | −12.0998 | −0.596839 | ||||||||
\(412\) | 63.9256 | 3.14939 | ||||||||
\(413\) | −2.06052 | −0.101391 | ||||||||
\(414\) | −9.35334 | −0.459691 | ||||||||
\(415\) | 2.94957 | 0.144789 | ||||||||
\(416\) | −95.2086 | −4.66799 | ||||||||
\(417\) | 11.6297 | 0.569507 | ||||||||
\(418\) | −36.2764 | −1.77434 | ||||||||
\(419\) | 25.1072 | 1.22657 | 0.613283 | − | 0.789863i | \(-0.289848\pi\) | ||||
0.613283 | + | 0.789863i | \(0.289848\pi\) | |||||||
\(420\) | 44.3770 | 2.16538 | ||||||||
\(421\) | −16.0196 | −0.780746 | −0.390373 | − | 0.920657i | \(-0.627654\pi\) | ||||
−0.390373 | + | 0.920657i | \(0.627654\pi\) | |||||||
\(422\) | 5.74435 | 0.279631 | ||||||||
\(423\) | 18.8934 | 0.918630 | ||||||||
\(424\) | −133.429 | −6.47988 | ||||||||
\(425\) | −1.24653 | −0.0604656 | ||||||||
\(426\) | 1.37107 | 0.0664288 | ||||||||
\(427\) | 29.8172 | 1.44296 | ||||||||
\(428\) | 43.9430 | 2.12407 | ||||||||
\(429\) | −5.73818 | −0.277042 | ||||||||
\(430\) | −17.9743 | −0.866797 | ||||||||
\(431\) | −8.45458 | −0.407243 | −0.203621 | − | 0.979050i | \(-0.565271\pi\) | ||||
−0.203621 | + | 0.979050i | \(0.565271\pi\) | |||||||
\(432\) | −67.0921 | −3.22797 | ||||||||
\(433\) | −5.64365 | −0.271216 | −0.135608 | − | 0.990763i | \(-0.543299\pi\) | ||||
−0.135608 | + | 0.990763i | \(0.543299\pi\) | |||||||
\(434\) | −109.740 | −5.26770 | ||||||||
\(435\) | 4.40719 | 0.211309 | ||||||||
\(436\) | −5.70227 | −0.273089 | ||||||||
\(437\) | −7.78258 | −0.372291 | ||||||||
\(438\) | −26.5860 | −1.27033 | ||||||||
\(439\) | −11.2605 | −0.537433 | −0.268716 | − | 0.963219i | \(-0.586599\pi\) | ||||
−0.268716 | + | 0.963219i | \(0.586599\pi\) | |||||||
\(440\) | −53.2460 | −2.53840 | ||||||||
\(441\) | −39.4655 | −1.87931 | ||||||||
\(442\) | 62.2995 | 2.96329 | ||||||||
\(443\) | −4.74032 | −0.225219 | −0.112610 | − | 0.993639i | \(-0.535921\pi\) | ||||
−0.112610 | + | 0.993639i | \(0.535921\pi\) | |||||||
\(444\) | −4.07257 | −0.193276 | ||||||||
\(445\) | −26.6908 | −1.26527 | ||||||||
\(446\) | −17.9842 | −0.851577 | ||||||||
\(447\) | 2.06408 | 0.0976275 | ||||||||
\(448\) | −193.798 | −9.15608 | ||||||||
\(449\) | 3.26679 | 0.154169 | 0.0770847 | − | 0.997025i | \(-0.475439\pi\) | ||||
0.0770847 | + | 0.997025i | \(0.475439\pi\) | |||||||
\(450\) | −1.35616 | −0.0639300 | ||||||||
\(451\) | 16.7150 | 0.787080 | ||||||||
\(452\) | 14.8044 | 0.696340 | ||||||||
\(453\) | 11.5362 | 0.542018 | ||||||||
\(454\) | −59.7601 | −2.80468 | ||||||||
\(455\) | −38.5105 | −1.80540 | ||||||||
\(456\) | −42.1939 | −1.97591 | ||||||||
\(457\) | 20.6589 | 0.966381 | 0.483190 | − | 0.875515i | \(-0.339478\pi\) | ||||
0.483190 | + | 0.875515i | \(0.339478\pi\) | |||||||
\(458\) | 7.00505 | 0.327324 | ||||||||
\(459\) | 24.9042 | 1.16243 | ||||||||
\(460\) | −17.5940 | −0.820326 | ||||||||
\(461\) | −16.0370 | −0.746918 | −0.373459 | − | 0.927647i | \(-0.621828\pi\) | ||||
−0.373459 | + | 0.927647i | \(0.621828\pi\) | |||||||
\(462\) | −21.5396 | −1.00211 | ||||||||
\(463\) | −16.2860 | −0.756875 | −0.378438 | − | 0.925627i | \(-0.623539\pi\) | ||||
−0.378438 | + | 0.925627i | \(0.623539\pi\) | |||||||
\(464\) | −46.3213 | −2.15041 | ||||||||
\(465\) | −13.4672 | −0.624527 | ||||||||
\(466\) | −5.82524 | −0.269849 | ||||||||
\(467\) | 18.2679 | 0.845339 | 0.422670 | − | 0.906284i | \(-0.361093\pi\) | ||||
0.422670 | + | 0.906284i | \(0.361093\pi\) | |||||||
\(468\) | 50.1791 | 2.31953 | ||||||||
\(469\) | −3.18658 | −0.147142 | ||||||||
\(470\) | 48.0043 | 2.21428 | ||||||||
\(471\) | −11.8865 | −0.547703 | ||||||||
\(472\) | 4.42904 | 0.203863 | ||||||||
\(473\) | 6.45894 | 0.296982 | ||||||||
\(474\) | −10.7323 | −0.492953 | ||||||||
\(475\) | −1.12841 | −0.0517751 | ||||||||
\(476\) | 173.132 | 7.93551 | ||||||||
\(477\) | 32.3338 | 1.48046 | ||||||||
\(478\) | 79.9967 | 3.65896 | ||||||||
\(479\) | 24.5562 | 1.12200 | 0.561001 | − | 0.827815i | \(-0.310416\pi\) | ||||
0.561001 | + | 0.827815i | \(0.310416\pi\) | |||||||
\(480\) | −43.8584 | −2.00185 | ||||||||
\(481\) | 3.53419 | 0.161145 | ||||||||
\(482\) | −25.2997 | −1.15237 | ||||||||
\(483\) | −4.62101 | −0.210263 | ||||||||
\(484\) | −33.2553 | −1.51160 | ||||||||
\(485\) | 27.2177 | 1.23589 | ||||||||
\(486\) | 41.9004 | 1.90064 | ||||||||
\(487\) | −6.65037 | −0.301357 | −0.150679 | − | 0.988583i | \(-0.548146\pi\) | ||||
−0.150679 | + | 0.988583i | \(0.548146\pi\) | |||||||
\(488\) | −64.0915 | −2.90129 | ||||||||
\(489\) | 0.230491 | 0.0104232 | ||||||||
\(490\) | −100.274 | −4.52991 | ||||||||
\(491\) | −7.73292 | −0.348982 | −0.174491 | − | 0.984659i | \(-0.555828\pi\) | ||||
−0.174491 | + | 0.984659i | \(0.555828\pi\) | |||||||
\(492\) | 29.9441 | 1.34999 | ||||||||
\(493\) | 17.1942 | 0.774388 | ||||||||
\(494\) | 56.3962 | 2.53739 | ||||||||
\(495\) | 12.9031 | 0.579951 | ||||||||
\(496\) | 141.546 | 6.35560 | ||||||||
\(497\) | −3.30655 | −0.148319 | ||||||||
\(498\) | −2.56474 | −0.114929 | ||||||||
\(499\) | −24.9461 | −1.11674 | −0.558370 | − | 0.829592i | \(-0.688573\pi\) | ||||
−0.558370 | + | 0.829592i | \(0.688573\pi\) | |||||||
\(500\) | 62.4415 | 2.79247 | ||||||||
\(501\) | −12.6910 | −0.566990 | ||||||||
\(502\) | −30.4169 | −1.35757 | ||||||||
\(503\) | 0.704072 | 0.0313930 | 0.0156965 | − | 0.999877i | \(-0.495003\pi\) | ||||
0.0156965 | + | 0.999877i | \(0.495003\pi\) | |||||||
\(504\) | 122.295 | 5.44743 | ||||||||
\(505\) | −41.2058 | −1.83363 | ||||||||
\(506\) | 8.53976 | 0.379639 | ||||||||
\(507\) | −0.363900 | −0.0161614 | ||||||||
\(508\) | −18.6700 | −0.828349 | ||||||||
\(509\) | −6.52617 | −0.289267 | −0.144634 | − | 0.989485i | \(-0.546200\pi\) | ||||
−0.144634 | + | 0.989485i | \(0.546200\pi\) | |||||||
\(510\) | 28.6986 | 1.27080 | ||||||||
\(511\) | 64.1161 | 2.83633 | ||||||||
\(512\) | 109.333 | 4.83190 | ||||||||
\(513\) | 22.5443 | 0.995356 | ||||||||
\(514\) | −86.3381 | −3.80821 | ||||||||
\(515\) | −25.5548 | −1.12608 | ||||||||
\(516\) | 11.5709 | 0.509378 | ||||||||
\(517\) | −17.2500 | −0.758656 | ||||||||
\(518\) | 13.2664 | 0.582893 | ||||||||
\(519\) | −2.66544 | −0.117000 | ||||||||
\(520\) | 82.7776 | 3.63004 | ||||||||
\(521\) | 23.3605 | 1.02344 | 0.511721 | − | 0.859151i | \(-0.329008\pi\) | ||||
0.511721 | + | 0.859151i | \(0.329008\pi\) | |||||||
\(522\) | 18.7064 | 0.818757 | ||||||||
\(523\) | −44.8106 | −1.95943 | −0.979714 | − | 0.200398i | \(-0.935776\pi\) | ||||
−0.979714 | + | 0.200398i | \(0.935776\pi\) | |||||||
\(524\) | −28.8273 | −1.25933 | ||||||||
\(525\) | −0.670010 | −0.0292417 | ||||||||
\(526\) | −9.06077 | −0.395068 | ||||||||
\(527\) | −52.5410 | −2.28872 | ||||||||
\(528\) | 27.7824 | 1.20907 | ||||||||
\(529\) | −21.1679 | −0.920344 | ||||||||
\(530\) | 82.1536 | 3.56853 | ||||||||
\(531\) | −1.07329 | −0.0465768 | ||||||||
\(532\) | 156.727 | 6.79497 | ||||||||
\(533\) | −25.9856 | −1.12556 | ||||||||
\(534\) | 23.2085 | 1.00433 | ||||||||
\(535\) | −17.5666 | −0.759469 | ||||||||
\(536\) | 6.84949 | 0.295853 | ||||||||
\(537\) | 16.9082 | 0.729642 | ||||||||
\(538\) | 8.84530 | 0.381348 | ||||||||
\(539\) | 36.0327 | 1.55204 | ||||||||
\(540\) | 50.9659 | 2.19322 | ||||||||
\(541\) | 12.6920 | 0.545671 | 0.272835 | − | 0.962061i | \(-0.412039\pi\) | ||||
0.272835 | + | 0.962061i | \(0.412039\pi\) | |||||||
\(542\) | −27.3282 | −1.17385 | ||||||||
\(543\) | −16.8985 | −0.725183 | ||||||||
\(544\) | −171.109 | −7.33623 | ||||||||
\(545\) | 2.27953 | 0.0976443 | ||||||||
\(546\) | 33.4860 | 1.43307 | ||||||||
\(547\) | −29.0607 | −1.24255 | −0.621274 | − | 0.783593i | \(-0.713385\pi\) | ||||
−0.621274 | + | 0.783593i | \(0.713385\pi\) | |||||||
\(548\) | −96.6063 | −4.12682 | ||||||||
\(549\) | 15.5313 | 0.662859 | ||||||||
\(550\) | 1.23820 | 0.0527970 | ||||||||
\(551\) | 15.5649 | 0.663088 | ||||||||
\(552\) | 9.93277 | 0.422767 | ||||||||
\(553\) | 25.8827 | 1.10064 | ||||||||
\(554\) | 31.6184 | 1.34334 | ||||||||
\(555\) | 1.62804 | 0.0691065 | ||||||||
\(556\) | 92.8527 | 3.93783 | ||||||||
\(557\) | 39.5149 | 1.67430 | 0.837151 | − | 0.546972i | \(-0.184220\pi\) | ||||
0.837151 | + | 0.546972i | \(0.184220\pi\) | |||||||
\(558\) | −57.1619 | −2.41986 | ||||||||
\(559\) | −10.0412 | −0.424698 | ||||||||
\(560\) | 186.455 | 7.87917 | ||||||||
\(561\) | −10.3127 | −0.435401 | ||||||||
\(562\) | 12.9735 | 0.547252 | ||||||||
\(563\) | 33.5395 | 1.41352 | 0.706760 | − | 0.707454i | \(-0.250156\pi\) | ||||
0.706760 | + | 0.707454i | \(0.250156\pi\) | |||||||
\(564\) | −30.9026 | −1.30123 | ||||||||
\(565\) | −5.91817 | −0.248979 | ||||||||
\(566\) | 56.8328 | 2.38886 | ||||||||
\(567\) | −22.3208 | −0.937384 | ||||||||
\(568\) | 7.10737 | 0.298219 | ||||||||
\(569\) | −31.3312 | −1.31347 | −0.656735 | − | 0.754121i | \(-0.728063\pi\) | ||||
−0.656735 | + | 0.754121i | \(0.728063\pi\) | |||||||
\(570\) | 25.9792 | 1.08815 | ||||||||
\(571\) | 4.31388 | 0.180530 | 0.0902652 | − | 0.995918i | \(-0.471229\pi\) | ||||
0.0902652 | + | 0.995918i | \(0.471229\pi\) | |||||||
\(572\) | −45.8144 | −1.91560 | ||||||||
\(573\) | −5.90565 | −0.246712 | ||||||||
\(574\) | −97.5432 | −4.07137 | ||||||||
\(575\) | 0.265637 | 0.0110778 | ||||||||
\(576\) | −100.946 | −4.20608 | ||||||||
\(577\) | 17.2498 | 0.718118 | 0.359059 | − | 0.933315i | \(-0.383098\pi\) | ||||
0.359059 | + | 0.933315i | \(0.383098\pi\) | |||||||
\(578\) | 64.7846 | 2.69469 | ||||||||
\(579\) | −2.74583 | −0.114113 | ||||||||
\(580\) | 35.1876 | 1.46108 | ||||||||
\(581\) | 6.18527 | 0.256608 | ||||||||
\(582\) | −23.6667 | −0.981014 | ||||||||
\(583\) | −29.5214 | −1.22265 | ||||||||
\(584\) | −137.816 | −5.70288 | ||||||||
\(585\) | −20.0595 | −0.829357 | ||||||||
\(586\) | −14.3766 | −0.593893 | ||||||||
\(587\) | 0.501336 | 0.0206924 | 0.0103462 | − | 0.999946i | \(-0.496707\pi\) | ||||
0.0103462 | + | 0.999946i | \(0.496707\pi\) | |||||||
\(588\) | 64.5508 | 2.66203 | ||||||||
\(589\) | −47.5624 | −1.95977 | ||||||||
\(590\) | −2.72701 | −0.112269 | ||||||||
\(591\) | 2.85582 | 0.117473 | ||||||||
\(592\) | −17.1114 | −0.703273 | ||||||||
\(593\) | 41.5671 | 1.70696 | 0.853478 | − | 0.521128i | \(-0.174489\pi\) | ||||
0.853478 | + | 0.521128i | \(0.174489\pi\) | |||||||
\(594\) | −24.7377 | −1.01500 | ||||||||
\(595\) | −69.2110 | −2.83738 | ||||||||
\(596\) | 16.4799 | 0.675042 | ||||||||
\(597\) | −0.455099 | −0.0186260 | ||||||||
\(598\) | −13.2761 | −0.542901 | ||||||||
\(599\) | −36.8908 | −1.50732 | −0.753659 | − | 0.657265i | \(-0.771713\pi\) | ||||
−0.753659 | + | 0.657265i | \(0.771713\pi\) | |||||||
\(600\) | 1.44017 | 0.0587949 | ||||||||
\(601\) | 25.5938 | 1.04399 | 0.521997 | − | 0.852947i | \(-0.325187\pi\) | ||||
0.521997 | + | 0.852947i | \(0.325187\pi\) | |||||||
\(602\) | −37.6921 | −1.53622 | ||||||||
\(603\) | −1.65983 | −0.0675937 | ||||||||
\(604\) | 92.1065 | 3.74776 | ||||||||
\(605\) | 13.2941 | 0.540480 | ||||||||
\(606\) | 35.8297 | 1.45548 | ||||||||
\(607\) | 19.2017 | 0.779372 | 0.389686 | − | 0.920948i | \(-0.372584\pi\) | ||||
0.389686 | + | 0.920948i | \(0.372584\pi\) | |||||||
\(608\) | −154.895 | −6.28183 | ||||||||
\(609\) | 9.24189 | 0.374500 | ||||||||
\(610\) | 39.4618 | 1.59776 | ||||||||
\(611\) | 26.8173 | 1.08491 | ||||||||
\(612\) | 90.1818 | 3.64538 | ||||||||
\(613\) | −15.1564 | −0.612161 | −0.306080 | − | 0.952006i | \(-0.599018\pi\) | ||||
−0.306080 | + | 0.952006i | \(0.599018\pi\) | |||||||
\(614\) | 68.9584 | 2.78293 | ||||||||
\(615\) | −11.9704 | −0.482693 | ||||||||
\(616\) | −111.657 | −4.49879 | ||||||||
\(617\) | 8.14996 | 0.328105 | 0.164053 | − | 0.986452i | \(-0.447543\pi\) | ||||
0.164053 | + | 0.986452i | \(0.447543\pi\) | |||||||
\(618\) | 22.2207 | 0.893846 | ||||||||
\(619\) | 37.5309 | 1.50849 | 0.754246 | − | 0.656591i | \(-0.228002\pi\) | ||||
0.754246 | + | 0.656591i | \(0.228002\pi\) | |||||||
\(620\) | −107.524 | −4.31827 | ||||||||
\(621\) | −5.30711 | −0.212967 | ||||||||
\(622\) | −27.5261 | −1.10370 | ||||||||
\(623\) | −55.9708 | −2.24242 | ||||||||
\(624\) | −43.1912 | −1.72903 | ||||||||
\(625\) | −25.9428 | −1.03771 | ||||||||
\(626\) | 67.8774 | 2.71292 | ||||||||
\(627\) | −9.33546 | −0.372822 | ||||||||
\(628\) | −94.9037 | −3.78707 | ||||||||
\(629\) | 6.35164 | 0.253256 | ||||||||
\(630\) | −75.2981 | −2.99995 | ||||||||
\(631\) | −14.3127 | −0.569779 | −0.284890 | − | 0.958560i | \(-0.591957\pi\) | ||||
−0.284890 | + | 0.958560i | \(0.591957\pi\) | |||||||
\(632\) | −55.6343 | −2.21301 | ||||||||
\(633\) | 1.47826 | 0.0587557 | ||||||||
\(634\) | −70.7467 | −2.80971 | ||||||||
\(635\) | 7.46350 | 0.296180 | ||||||||
\(636\) | −52.8860 | −2.09707 | ||||||||
\(637\) | −56.0174 | −2.21949 | ||||||||
\(638\) | −17.0793 | −0.676175 | ||||||||
\(639\) | −1.72233 | −0.0681343 | ||||||||
\(640\) | −133.665 | −5.28358 | ||||||||
\(641\) | 5.64811 | 0.223087 | 0.111543 | − | 0.993760i | \(-0.464421\pi\) | ||||
0.111543 | + | 0.993760i | \(0.464421\pi\) | |||||||
\(642\) | 15.2747 | 0.602843 | ||||||||
\(643\) | −15.2476 | −0.601307 | −0.300653 | − | 0.953734i | \(-0.597205\pi\) | ||||
−0.300653 | + | 0.953734i | \(0.597205\pi\) | |||||||
\(644\) | −36.8948 | −1.45386 | ||||||||
\(645\) | −4.62554 | −0.182130 | ||||||||
\(646\) | 101.355 | 3.98777 | ||||||||
\(647\) | −1.55911 | −0.0612949 | −0.0306475 | − | 0.999530i | \(-0.509757\pi\) | ||||
−0.0306475 | + | 0.999530i | \(0.509757\pi\) | |||||||
\(648\) | 47.9780 | 1.88476 | ||||||||
\(649\) | 0.979932 | 0.0384657 | ||||||||
\(650\) | −1.92493 | −0.0755021 | ||||||||
\(651\) | −28.2408 | −1.10684 | ||||||||
\(652\) | 1.84027 | 0.0720707 | ||||||||
\(653\) | 22.7942 | 0.892007 | 0.446003 | − | 0.895031i | \(-0.352847\pi\) | ||||
0.446003 | + | 0.895031i | \(0.352847\pi\) | |||||||
\(654\) | −1.98212 | −0.0775070 | ||||||||
\(655\) | 11.5239 | 0.450277 | ||||||||
\(656\) | 125.814 | 4.91220 | ||||||||
\(657\) | 33.3970 | 1.30294 | ||||||||
\(658\) | 100.665 | 3.92434 | ||||||||
\(659\) | −38.2210 | −1.48888 | −0.744440 | − | 0.667689i | \(-0.767283\pi\) | ||||
−0.744440 | + | 0.667689i | \(0.767283\pi\) | |||||||
\(660\) | −21.1046 | −0.821497 | ||||||||
\(661\) | −30.1739 | −1.17363 | −0.586815 | − | 0.809721i | \(-0.699618\pi\) | ||||
−0.586815 | + | 0.809721i | \(0.699618\pi\) | |||||||
\(662\) | −64.2592 | −2.49750 | ||||||||
\(663\) | 16.0323 | 0.622643 | ||||||||
\(664\) | −13.2951 | −0.515950 | ||||||||
\(665\) | −62.6528 | −2.42957 | ||||||||
\(666\) | 6.91026 | 0.267767 | ||||||||
\(667\) | −3.66411 | −0.141875 | ||||||||
\(668\) | −101.326 | −3.92043 | ||||||||
\(669\) | −4.62810 | −0.178933 | ||||||||
\(670\) | −4.21730 | −0.162929 | ||||||||
\(671\) | −14.1803 | −0.547426 | ||||||||
\(672\) | −91.9712 | −3.54786 | ||||||||
\(673\) | 7.45780 | 0.287477 | 0.143739 | − | 0.989616i | \(-0.454088\pi\) | ||||
0.143739 | + | 0.989616i | \(0.454088\pi\) | |||||||
\(674\) | 25.8936 | 0.997384 | ||||||||
\(675\) | −0.769490 | −0.0296177 | ||||||||
\(676\) | −2.90543 | −0.111747 | ||||||||
\(677\) | 3.48593 | 0.133975 | 0.0669876 | − | 0.997754i | \(-0.478661\pi\) | ||||
0.0669876 | + | 0.997754i | \(0.478661\pi\) | |||||||
\(678\) | 5.14603 | 0.197632 | ||||||||
\(679\) | 57.0757 | 2.19036 | ||||||||
\(680\) | 148.768 | 5.70498 | ||||||||
\(681\) | −15.3788 | −0.589317 | ||||||||
\(682\) | 52.1898 | 1.99845 | ||||||||
\(683\) | −33.1191 | −1.26727 | −0.633634 | − | 0.773633i | \(-0.718438\pi\) | ||||
−0.633634 | + | 0.773633i | \(0.718438\pi\) | |||||||
\(684\) | 81.6364 | 3.12145 | ||||||||
\(685\) | 38.6191 | 1.47556 | ||||||||
\(686\) | −117.410 | −4.48272 | ||||||||
\(687\) | 1.80269 | 0.0687771 | ||||||||
\(688\) | 48.6163 | 1.85348 | ||||||||
\(689\) | 45.8946 | 1.74845 | ||||||||
\(690\) | −6.11572 | −0.232821 | ||||||||
\(691\) | −22.6571 | −0.861916 | −0.430958 | − | 0.902372i | \(-0.641824\pi\) | ||||
−0.430958 | + | 0.902372i | \(0.641824\pi\) | |||||||
\(692\) | −21.2812 | −0.808989 | ||||||||
\(693\) | 27.0579 | 1.02784 | ||||||||
\(694\) | 35.6519 | 1.35333 | ||||||||
\(695\) | −37.1186 | −1.40799 | ||||||||
\(696\) | −19.8653 | −0.752991 | ||||||||
\(697\) | −46.7013 | −1.76894 | ||||||||
\(698\) | −88.4762 | −3.34887 | ||||||||
\(699\) | −1.49908 | −0.0567004 | ||||||||
\(700\) | −5.34945 | −0.202190 | ||||||||
\(701\) | −32.2047 | −1.21635 | −0.608177 | − | 0.793802i | \(-0.708099\pi\) | ||||
−0.608177 | + | 0.793802i | \(0.708099\pi\) | |||||||
\(702\) | 38.4579 | 1.45150 | ||||||||
\(703\) | 5.74978 | 0.216857 | ||||||||
\(704\) | 92.1655 | 3.47362 | ||||||||
\(705\) | 12.3535 | 0.465261 | ||||||||
\(706\) | −89.3134 | −3.36136 | ||||||||
\(707\) | −86.4087 | −3.24973 | ||||||||
\(708\) | 1.75550 | 0.0659757 | ||||||||
\(709\) | 18.8350 | 0.707363 | 0.353682 | − | 0.935366i | \(-0.384930\pi\) | ||||
0.353682 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(710\) | −4.37609 | −0.164232 | ||||||||
\(711\) | 13.4819 | 0.505609 | ||||||||
\(712\) | 120.308 | 4.50874 | ||||||||
\(713\) | 11.1966 | 0.419314 | ||||||||
\(714\) | 60.1811 | 2.25222 | ||||||||
\(715\) | 18.3147 | 0.684929 | ||||||||
\(716\) | 134.997 | 5.04508 | ||||||||
\(717\) | 20.5865 | 0.768817 | ||||||||
\(718\) | 15.6053 | 0.582386 | ||||||||
\(719\) | −3.77422 | −0.140755 | −0.0703773 | − | 0.997520i | \(-0.522420\pi\) | ||||
−0.0703773 | + | 0.997520i | \(0.522420\pi\) | |||||||
\(720\) | 97.1214 | 3.61950 | ||||||||
\(721\) | −53.5885 | −1.99574 | ||||||||
\(722\) | 39.0205 | 1.45219 | ||||||||
\(723\) | −6.51067 | −0.242134 | ||||||||
\(724\) | −134.920 | −5.01425 | ||||||||
\(725\) | −0.531267 | −0.0197308 | ||||||||
\(726\) | −11.5596 | −0.429016 | ||||||||
\(727\) | −41.5073 | −1.53942 | −0.769710 | − | 0.638393i | \(-0.779599\pi\) | ||||
−0.769710 | + | 0.638393i | \(0.779599\pi\) | |||||||
\(728\) | 173.585 | 6.43348 | ||||||||
\(729\) | −3.22557 | −0.119466 | ||||||||
\(730\) | 84.8550 | 3.14063 | ||||||||
\(731\) | −18.0461 | −0.667458 | ||||||||
\(732\) | −25.4033 | −0.938934 | ||||||||
\(733\) | −10.2931 | −0.380185 | −0.190093 | − | 0.981766i | \(-0.560879\pi\) | ||||
−0.190093 | + | 0.981766i | \(0.560879\pi\) | |||||||
\(734\) | −43.1516 | −1.59276 | ||||||||
\(735\) | −25.8047 | −0.951820 | ||||||||
\(736\) | 36.4636 | 1.34406 | ||||||||
\(737\) | 1.51546 | 0.0558226 | ||||||||
\(738\) | −50.8086 | −1.87029 | ||||||||
\(739\) | 15.7578 | 0.579660 | 0.289830 | − | 0.957078i | \(-0.406401\pi\) | ||||
0.289830 | + | 0.957078i | \(0.406401\pi\) | |||||||
\(740\) | 12.9985 | 0.477834 | ||||||||
\(741\) | 14.5131 | 0.533153 | ||||||||
\(742\) | 172.276 | 6.32447 | ||||||||
\(743\) | 19.7268 | 0.723708 | 0.361854 | − | 0.932235i | \(-0.382144\pi\) | ||||
0.361854 | + | 0.932235i | \(0.382144\pi\) | |||||||
\(744\) | 60.7031 | 2.22548 | ||||||||
\(745\) | −6.58796 | −0.241364 | ||||||||
\(746\) | −23.5060 | −0.860617 | ||||||||
\(747\) | 3.22180 | 0.117880 | ||||||||
\(748\) | −82.3376 | −3.01056 | ||||||||
\(749\) | −36.8372 | −1.34600 | ||||||||
\(750\) | 21.7048 | 0.792546 | ||||||||
\(751\) | −15.4840 | −0.565019 | −0.282510 | − | 0.959264i | \(-0.591167\pi\) | ||||
−0.282510 | + | 0.959264i | \(0.591167\pi\) | |||||||
\(752\) | −129.841 | −4.73480 | ||||||||
\(753\) | −7.82755 | −0.285252 | ||||||||
\(754\) | 26.5519 | 0.966962 | ||||||||
\(755\) | −36.8203 | −1.34003 | ||||||||
\(756\) | 106.876 | 3.88703 | ||||||||
\(757\) | 4.68563 | 0.170302 | 0.0851511 | − | 0.996368i | \(-0.472863\pi\) | ||||
0.0851511 | + | 0.996368i | \(0.472863\pi\) | |||||||
\(758\) | 59.2506 | 2.15208 | ||||||||
\(759\) | 2.19764 | 0.0797693 | ||||||||
\(760\) | 134.671 | 4.88503 | ||||||||
\(761\) | 18.2788 | 0.662605 | 0.331303 | − | 0.943525i | \(-0.392512\pi\) | ||||
0.331303 | + | 0.943525i | \(0.392512\pi\) | |||||||
\(762\) | −6.48974 | −0.235098 | ||||||||
\(763\) | 4.78018 | 0.173054 | ||||||||
\(764\) | −47.1515 | −1.70588 | ||||||||
\(765\) | −36.0509 | −1.30342 | ||||||||
\(766\) | 10.4361 | 0.377073 | ||||||||
\(767\) | −1.52343 | −0.0550077 | ||||||||
\(768\) | 58.3157 | 2.10429 | ||||||||
\(769\) | −15.7087 | −0.566471 | −0.283236 | − | 0.959050i | \(-0.591408\pi\) | ||||
−0.283236 | + | 0.959050i | \(0.591408\pi\) | |||||||
\(770\) | 68.7485 | 2.47752 | ||||||||
\(771\) | −22.2184 | −0.800177 | ||||||||
\(772\) | −21.9230 | −0.789028 | ||||||||
\(773\) | 5.33431 | 0.191862 | 0.0959310 | − | 0.995388i | \(-0.469417\pi\) | ||||
0.0959310 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(774\) | −19.6332 | −0.705701 | ||||||||
\(775\) | 1.62341 | 0.0583147 | ||||||||
\(776\) | −122.683 | −4.40407 | ||||||||
\(777\) | 3.41401 | 0.122477 | ||||||||
\(778\) | −32.9456 | −1.18116 | ||||||||
\(779\) | −42.2760 | −1.51470 | ||||||||
\(780\) | 32.8098 | 1.17478 | ||||||||
\(781\) | 1.57252 | 0.0562691 | ||||||||
\(782\) | −23.8598 | −0.853226 | ||||||||
\(783\) | 10.6141 | 0.379316 | ||||||||
\(784\) | 271.218 | 9.68635 | ||||||||
\(785\) | 37.9385 | 1.35408 | ||||||||
\(786\) | −10.0204 | −0.357416 | ||||||||
\(787\) | 51.6176 | 1.83997 | 0.919985 | − | 0.391953i | \(-0.128201\pi\) | ||||
0.919985 | + | 0.391953i | \(0.128201\pi\) | |||||||
\(788\) | 22.8013 | 0.812261 | ||||||||
\(789\) | −2.33172 | −0.0830114 | ||||||||
\(790\) | 34.2546 | 1.21872 | ||||||||
\(791\) | −12.4104 | −0.441264 | ||||||||
\(792\) | −58.1603 | −2.06664 | ||||||||
\(793\) | 22.0451 | 0.782844 | ||||||||
\(794\) | −53.8013 | −1.90934 | ||||||||
\(795\) | 21.1416 | 0.749815 | ||||||||
\(796\) | −3.63357 | −0.128788 | ||||||||
\(797\) | −54.5486 | −1.93221 | −0.966105 | − | 0.258151i | \(-0.916887\pi\) | ||||
−0.966105 | + | 0.258151i | \(0.916887\pi\) | |||||||
\(798\) | 54.4785 | 1.92852 | ||||||||
\(799\) | 48.1961 | 1.70505 | ||||||||
\(800\) | 5.28693 | 0.186921 | ||||||||
\(801\) | −29.1542 | −1.03011 | ||||||||
\(802\) | 104.320 | 3.68366 | ||||||||
\(803\) | −30.4921 | −1.07604 | ||||||||
\(804\) | 2.71487 | 0.0957460 | ||||||||
\(805\) | 14.7490 | 0.519833 | ||||||||
\(806\) | −81.1356 | −2.85788 | ||||||||
\(807\) | 2.27627 | 0.0801285 | ||||||||
\(808\) | 185.734 | 6.53409 | ||||||||
\(809\) | 15.6349 | 0.549693 | 0.274846 | − | 0.961488i | \(-0.411373\pi\) | ||||
0.274846 | + | 0.961488i | \(0.411373\pi\) | |||||||
\(810\) | −29.5406 | −1.03795 | ||||||||
\(811\) | 39.6254 | 1.39143 | 0.695717 | − | 0.718316i | \(-0.255087\pi\) | ||||
0.695717 | + | 0.718316i | \(0.255087\pi\) | |||||||
\(812\) | 73.7885 | 2.58947 | ||||||||
\(813\) | −7.03270 | −0.246648 | ||||||||
\(814\) | −6.30919 | −0.221137 | ||||||||
\(815\) | −0.735664 | −0.0257692 | ||||||||
\(816\) | −77.6231 | −2.71735 | ||||||||
\(817\) | −16.3361 | −0.571527 | ||||||||
\(818\) | −81.5878 | −2.85265 | ||||||||
\(819\) | −42.0648 | −1.46986 | ||||||||
\(820\) | −95.5732 | −3.33756 | ||||||||
\(821\) | −34.7967 | −1.21441 | −0.607206 | − | 0.794545i | \(-0.707710\pi\) | ||||
−0.607206 | + | 0.794545i | \(0.707710\pi\) | |||||||
\(822\) | −33.5805 | −1.17125 | ||||||||
\(823\) | 42.2634 | 1.47321 | 0.736604 | − | 0.676324i | \(-0.236428\pi\) | ||||
0.736604 | + | 0.676324i | \(0.236428\pi\) | |||||||
\(824\) | 115.187 | 4.01274 | ||||||||
\(825\) | 0.318641 | 0.0110936 | ||||||||
\(826\) | −5.71855 | −0.198974 | ||||||||
\(827\) | −49.4228 | −1.71860 | −0.859300 | − | 0.511472i | \(-0.829101\pi\) | ||||
−0.859300 | + | 0.511472i | \(0.829101\pi\) | |||||||
\(828\) | −19.2179 | −0.667867 | ||||||||
\(829\) | −51.4919 | −1.78839 | −0.894193 | − | 0.447682i | \(-0.852250\pi\) | ||||
−0.894193 | + | 0.447682i | \(0.852250\pi\) | |||||||
\(830\) | 8.18594 | 0.284138 | ||||||||
\(831\) | 8.13675 | 0.282261 | ||||||||
\(832\) | −143.283 | −4.96743 | ||||||||
\(833\) | −100.674 | −3.48816 | ||||||||
\(834\) | 32.2758 | 1.11762 | ||||||||
\(835\) | 40.5060 | 1.40177 | ||||||||
\(836\) | −74.5355 | −2.57786 | ||||||||
\(837\) | −32.4338 | −1.12108 | ||||||||
\(838\) | 69.6799 | 2.40705 | ||||||||
\(839\) | 11.5186 | 0.397668 | 0.198834 | − | 0.980033i | \(-0.436285\pi\) | ||||
0.198834 | + | 0.980033i | \(0.436285\pi\) | |||||||
\(840\) | 79.9628 | 2.75898 | ||||||||
\(841\) | −21.6719 | −0.747306 | ||||||||
\(842\) | −44.4591 | −1.53216 | ||||||||
\(843\) | 3.33862 | 0.114988 | ||||||||
\(844\) | 11.8026 | 0.406264 | ||||||||
\(845\) | 1.16147 | 0.0399557 | ||||||||
\(846\) | 52.4349 | 1.80275 | ||||||||
\(847\) | 27.8777 | 0.957889 | ||||||||
\(848\) | −222.207 | −7.63061 | ||||||||
\(849\) | 14.6255 | 0.501945 | ||||||||
\(850\) | −3.45949 | −0.118660 | ||||||||
\(851\) | −1.35354 | −0.0463989 | ||||||||
\(852\) | 2.81708 | 0.0965117 | ||||||||
\(853\) | 7.90139 | 0.270539 | 0.135269 | − | 0.990809i | \(-0.456810\pi\) | ||||
0.135269 | + | 0.990809i | \(0.456810\pi\) | |||||||
\(854\) | 82.7516 | 2.83170 | ||||||||
\(855\) | −32.6348 | −1.11609 | ||||||||
\(856\) | 79.1808 | 2.70634 | ||||||||
\(857\) | 37.8937 | 1.29443 | 0.647213 | − | 0.762310i | \(-0.275935\pi\) | ||||
0.647213 | + | 0.762310i | \(0.275935\pi\) | |||||||
\(858\) | −15.9252 | −0.543676 | ||||||||
\(859\) | 51.8909 | 1.77049 | 0.885247 | − | 0.465121i | \(-0.153989\pi\) | ||||
0.885247 | + | 0.465121i | \(0.153989\pi\) | |||||||
\(860\) | −36.9309 | −1.25933 | ||||||||
\(861\) | −25.1020 | −0.855473 | ||||||||
\(862\) | −23.4640 | −0.799186 | ||||||||
\(863\) | −9.77648 | −0.332795 | −0.166398 | − | 0.986059i | \(-0.553214\pi\) | ||||
−0.166398 | + | 0.986059i | \(0.553214\pi\) | |||||||
\(864\) | −105.627 | −3.59349 | ||||||||
\(865\) | 8.50732 | 0.289258 | ||||||||
\(866\) | −15.6628 | −0.532244 | ||||||||
\(867\) | 16.6718 | 0.566205 | ||||||||
\(868\) | −225.478 | −7.65323 | ||||||||
\(869\) | −12.3092 | −0.417560 | ||||||||
\(870\) | 12.2313 | 0.414678 | ||||||||
\(871\) | −2.35597 | −0.0798290 | ||||||||
\(872\) | −10.2749 | −0.347952 | ||||||||
\(873\) | 29.7298 | 1.00620 | ||||||||
\(874\) | −21.5990 | −0.730596 | ||||||||
\(875\) | −52.3443 | −1.76956 | ||||||||
\(876\) | −54.6250 | −1.84561 | ||||||||
\(877\) | 29.4725 | 0.995216 | 0.497608 | − | 0.867402i | \(-0.334212\pi\) | ||||
0.497608 | + | 0.867402i | \(0.334212\pi\) | |||||||
\(878\) | −31.2511 | −1.05467 | ||||||||
\(879\) | −3.69971 | −0.124788 | ||||||||
\(880\) | −88.6736 | −2.98919 | ||||||||
\(881\) | −15.2632 | −0.514229 | −0.257114 | − | 0.966381i | \(-0.582772\pi\) | ||||
−0.257114 | + | 0.966381i | \(0.582772\pi\) | |||||||
\(882\) | −109.529 | −3.68802 | ||||||||
\(883\) | 37.0330 | 1.24626 | 0.623130 | − | 0.782118i | \(-0.285861\pi\) | ||||
0.623130 | + | 0.782118i | \(0.285861\pi\) | |||||||
\(884\) | 128.004 | 4.30524 | ||||||||
\(885\) | −0.701774 | −0.0235899 | ||||||||
\(886\) | −13.1558 | −0.441978 | ||||||||
\(887\) | −25.9964 | −0.872875 | −0.436437 | − | 0.899735i | \(-0.643760\pi\) | ||||
−0.436437 | + | 0.899735i | \(0.643760\pi\) | |||||||
\(888\) | −7.33835 | −0.246259 | ||||||||
\(889\) | 15.6510 | 0.524917 | ||||||||
\(890\) | −74.0750 | −2.48300 | ||||||||
\(891\) | 10.6152 | 0.355623 | ||||||||
\(892\) | −36.9513 | −1.23722 | ||||||||
\(893\) | 43.6292 | 1.45999 | ||||||||
\(894\) | 5.72843 | 0.191587 | ||||||||
\(895\) | −53.9662 | −1.80389 | ||||||||
\(896\) | −280.296 | −9.36404 | ||||||||
\(897\) | −3.41651 | −0.114074 | ||||||||
\(898\) | 9.06631 | 0.302547 | ||||||||
\(899\) | −22.3928 | −0.746841 | ||||||||
\(900\) | −2.78644 | −0.0928813 | ||||||||
\(901\) | 82.4818 | 2.74787 | ||||||||
\(902\) | 46.3892 | 1.54459 | ||||||||
\(903\) | −9.69978 | −0.322788 | ||||||||
\(904\) | 26.6760 | 0.887230 | ||||||||
\(905\) | 53.9352 | 1.79287 | ||||||||
\(906\) | 32.0164 | 1.06367 | ||||||||
\(907\) | −20.9225 | −0.694719 | −0.347359 | − | 0.937732i | \(-0.612922\pi\) | ||||
−0.347359 | + | 0.937732i | \(0.612922\pi\) | |||||||
\(908\) | −122.786 | −4.07481 | ||||||||
\(909\) | −45.0088 | −1.49285 | ||||||||
\(910\) | −106.878 | −3.54297 | ||||||||
\(911\) | −37.0236 | −1.22665 | −0.613324 | − | 0.789832i | \(-0.710168\pi\) | ||||
−0.613324 | + | 0.789832i | \(0.710168\pi\) | |||||||
\(912\) | −70.2678 | −2.32680 | ||||||||
\(913\) | −2.94156 | −0.0973515 | ||||||||
\(914\) | 57.3345 | 1.89646 | ||||||||
\(915\) | 10.1552 | 0.335720 | ||||||||
\(916\) | 14.3929 | 0.475556 | ||||||||
\(917\) | 24.1657 | 0.798023 | ||||||||
\(918\) | 69.1165 | 2.28118 | ||||||||
\(919\) | −28.5293 | −0.941096 | −0.470548 | − | 0.882374i | \(-0.655944\pi\) | ||||
−0.470548 | + | 0.882374i | \(0.655944\pi\) | |||||||
\(920\) | −31.7026 | −1.04520 | ||||||||
\(921\) | 17.7459 | 0.584747 | ||||||||
\(922\) | −44.5075 | −1.46578 | ||||||||
\(923\) | −2.44467 | −0.0804674 | ||||||||
\(924\) | −44.2565 | −1.45593 | ||||||||
\(925\) | −0.196253 | −0.00645276 | ||||||||
\(926\) | −45.1985 | −1.48532 | ||||||||
\(927\) | −27.9133 | −0.916794 | ||||||||
\(928\) | −72.9261 | −2.39392 | ||||||||
\(929\) | 14.9398 | 0.490158 | 0.245079 | − | 0.969503i | \(-0.421186\pi\) | ||||
0.245079 | + | 0.969503i | \(0.421186\pi\) | |||||||
\(930\) | −37.3755 | −1.22559 | ||||||||
\(931\) | −91.1348 | −2.98682 | ||||||||
\(932\) | −11.9689 | −0.392053 | ||||||||
\(933\) | −7.08363 | −0.231908 | ||||||||
\(934\) | 50.6990 | 1.65892 | ||||||||
\(935\) | 32.9151 | 1.07644 | ||||||||
\(936\) | 90.4175 | 2.95539 | ||||||||
\(937\) | 14.9470 | 0.488296 | 0.244148 | − | 0.969738i | \(-0.421492\pi\) | ||||
0.244148 | + | 0.969738i | \(0.421492\pi\) | |||||||
\(938\) | −8.84370 | −0.288757 | ||||||||
\(939\) | 17.4677 | 0.570037 | ||||||||
\(940\) | 98.6323 | 3.21703 | ||||||||
\(941\) | 17.3025 | 0.564046 | 0.282023 | − | 0.959408i | \(-0.408995\pi\) | ||||
0.282023 | + | 0.959408i | \(0.408995\pi\) | |||||||
\(942\) | −32.9887 | −1.07483 | ||||||||
\(943\) | 9.95211 | 0.324085 | ||||||||
\(944\) | 7.37593 | 0.240066 | ||||||||
\(945\) | −42.7244 | −1.38982 | ||||||||
\(946\) | 17.9255 | 0.582807 | ||||||||
\(947\) | 3.07936 | 0.100066 | 0.0500330 | − | 0.998748i | \(-0.484067\pi\) | ||||
0.0500330 | + | 0.998748i | \(0.484067\pi\) | |||||||
\(948\) | −22.0512 | −0.716191 | ||||||||
\(949\) | 47.4037 | 1.53879 | ||||||||
\(950\) | −3.13168 | −0.101605 | ||||||||
\(951\) | −18.2061 | −0.590373 | ||||||||
\(952\) | 311.967 | 10.1109 | ||||||||
\(953\) | 51.1464 | 1.65679 | 0.828397 | − | 0.560142i | \(-0.189253\pi\) | ||||
0.828397 | + | 0.560142i | \(0.189253\pi\) | |||||||
\(954\) | 89.7359 | 2.90531 | ||||||||
\(955\) | 18.8492 | 0.609945 | ||||||||
\(956\) | 164.365 | 5.31596 | ||||||||
\(957\) | −4.39522 | −0.142077 | ||||||||
\(958\) | 68.1508 | 2.20185 | ||||||||
\(959\) | 80.9845 | 2.61513 | ||||||||
\(960\) | −66.0039 | −2.13027 | ||||||||
\(961\) | 37.4265 | 1.20731 | ||||||||
\(962\) | 9.80842 | 0.316236 | ||||||||
\(963\) | −19.1879 | −0.618320 | ||||||||
\(964\) | −51.9821 | −1.67423 | ||||||||
\(965\) | 8.76391 | 0.282120 | ||||||||
\(966\) | −12.8247 | −0.412627 | ||||||||
\(967\) | −1.55344 | −0.0499554 | −0.0249777 | − | 0.999688i | \(-0.507951\pi\) | ||||
−0.0249777 | + | 0.999688i | \(0.507951\pi\) | |||||||
\(968\) | −59.9226 | −1.92598 | ||||||||
\(969\) | 26.0830 | 0.837906 | ||||||||
\(970\) | 75.5373 | 2.42536 | ||||||||
\(971\) | −13.2256 | −0.424431 | −0.212215 | − | 0.977223i | \(-0.568068\pi\) | ||||
−0.212215 | + | 0.977223i | \(0.568068\pi\) | |||||||
\(972\) | 86.0908 | 2.76136 | ||||||||
\(973\) | −77.8379 | −2.49537 | ||||||||
\(974\) | −18.4568 | −0.591393 | ||||||||
\(975\) | −0.495367 | −0.0158644 | ||||||||
\(976\) | −106.735 | −3.41651 | ||||||||
\(977\) | 20.7097 | 0.662560 | 0.331280 | − | 0.943532i | \(-0.392519\pi\) | ||||
0.331280 | + | 0.943532i | \(0.392519\pi\) | |||||||
\(978\) | 0.639682 | 0.0204548 | ||||||||
\(979\) | 26.6183 | 0.850726 | ||||||||
\(980\) | −206.028 | −6.58132 | ||||||||
\(981\) | 2.48992 | 0.0794969 | ||||||||
\(982\) | −21.4611 | −0.684853 | ||||||||
\(983\) | 45.0770 | 1.43773 | 0.718866 | − | 0.695149i | \(-0.244662\pi\) | ||||
0.718866 | + | 0.695149i | \(0.244662\pi\) | |||||||
\(984\) | 53.9562 | 1.72006 | ||||||||
\(985\) | −9.11498 | −0.290428 | ||||||||
\(986\) | 47.7190 | 1.51968 | ||||||||
\(987\) | 25.9054 | 0.824579 | ||||||||
\(988\) | 115.875 | 3.68647 | ||||||||
\(989\) | 3.84564 | 0.122284 | ||||||||
\(990\) | 35.8099 | 1.13811 | ||||||||
\(991\) | 39.5977 | 1.25786 | 0.628932 | − | 0.777461i | \(-0.283492\pi\) | ||||
0.628932 | + | 0.777461i | \(0.283492\pi\) | |||||||
\(992\) | 222.843 | 7.07527 | ||||||||
\(993\) | −16.5366 | −0.524773 | ||||||||
\(994\) | −9.17667 | −0.291066 | ||||||||
\(995\) | 1.45255 | 0.0460489 | ||||||||
\(996\) | −5.26966 | −0.166975 | ||||||||
\(997\) | 25.1944 | 0.797915 | 0.398957 | − | 0.916969i | \(-0.369372\pi\) | ||||
0.398957 | + | 0.916969i | \(0.369372\pi\) | |||||||
\(998\) | −69.2328 | −2.19153 | ||||||||
\(999\) | 3.92090 | 0.124052 |
(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 | 4033.2.a.d.1.79 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.79 | ✓ | 79 | 1.1 | even | 1 | trivial |