Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8038,2,Mod(1,8038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.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: | \(64.1837531447\) |
Analytic rank: | \(1\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8038.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.71506 | −1.56754 | −0.783769 | − | 0.621052i | \(-0.786706\pi\) | ||||
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.98033 | −1.33284 | −0.666422 | − | 0.745575i | \(-0.732175\pi\) | ||||
−0.666422 | + | 0.745575i | \(0.732175\pi\) | |||||||
\(6\) | 2.71506 | 1.10842 | ||||||||
\(7\) | 3.18004 | 1.20194 | 0.600971 | − | 0.799271i | \(-0.294781\pi\) | ||||
0.600971 | + | 0.799271i | \(0.294781\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.37153 | 1.45718 | ||||||||
\(10\) | 2.98033 | 0.942463 | ||||||||
\(11\) | −4.66208 | −1.40567 | −0.702836 | − | 0.711352i | \(-0.748083\pi\) | ||||
−0.702836 | + | 0.711352i | \(0.748083\pi\) | |||||||
\(12\) | −2.71506 | −0.783769 | ||||||||
\(13\) | −0.206957 | −0.0573995 | −0.0286998 | − | 0.999588i | \(-0.509137\pi\) | ||||
−0.0286998 | + | 0.999588i | \(0.509137\pi\) | |||||||
\(14\) | −3.18004 | −0.849902 | ||||||||
\(15\) | 8.09177 | 2.08929 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.33338 | −0.808463 | −0.404231 | − | 0.914657i | \(-0.632461\pi\) | ||||
−0.404231 | + | 0.914657i | \(0.632461\pi\) | |||||||
\(18\) | −4.37153 | −1.03038 | ||||||||
\(19\) | −4.88581 | −1.12088 | −0.560440 | − | 0.828195i | \(-0.689368\pi\) | ||||
−0.560440 | + | 0.828195i | \(0.689368\pi\) | |||||||
\(20\) | −2.98033 | −0.666422 | ||||||||
\(21\) | −8.63399 | −1.88409 | ||||||||
\(22\) | 4.66208 | 0.993960 | ||||||||
\(23\) | 7.91913 | 1.65125 | 0.825626 | − | 0.564217i | \(-0.190822\pi\) | ||||
0.825626 | + | 0.564217i | \(0.190822\pi\) | |||||||
\(24\) | 2.71506 | 0.554209 | ||||||||
\(25\) | 3.88237 | 0.776474 | ||||||||
\(26\) | 0.206957 | 0.0405876 | ||||||||
\(27\) | −3.72379 | −0.716644 | ||||||||
\(28\) | 3.18004 | 0.600971 | ||||||||
\(29\) | −1.80448 | −0.335084 | −0.167542 | − | 0.985865i | \(-0.553583\pi\) | ||||
−0.167542 | + | 0.985865i | \(0.553583\pi\) | |||||||
\(30\) | −8.09177 | −1.47735 | ||||||||
\(31\) | 5.19137 | 0.932398 | 0.466199 | − | 0.884680i | \(-0.345623\pi\) | ||||
0.466199 | + | 0.884680i | \(0.345623\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 12.6578 | 2.20344 | ||||||||
\(34\) | 3.33338 | 0.571669 | ||||||||
\(35\) | −9.47758 | −1.60200 | ||||||||
\(36\) | 4.37153 | 0.728589 | ||||||||
\(37\) | −0.280897 | −0.0461791 | −0.0230896 | − | 0.999733i | \(-0.507350\pi\) | ||||
−0.0230896 | + | 0.999733i | \(0.507350\pi\) | |||||||
\(38\) | 4.88581 | 0.792582 | ||||||||
\(39\) | 0.561900 | 0.0899759 | ||||||||
\(40\) | 2.98033 | 0.471232 | ||||||||
\(41\) | 5.18280 | 0.809418 | 0.404709 | − | 0.914446i | \(-0.367373\pi\) | ||||
0.404709 | + | 0.914446i | \(0.367373\pi\) | |||||||
\(42\) | 8.63399 | 1.33225 | ||||||||
\(43\) | −0.889927 | −0.135713 | −0.0678563 | − | 0.997695i | \(-0.521616\pi\) | ||||
−0.0678563 | + | 0.997695i | \(0.521616\pi\) | |||||||
\(44\) | −4.66208 | −0.702836 | ||||||||
\(45\) | −13.0286 | −1.94219 | ||||||||
\(46\) | −7.91913 | −1.16761 | ||||||||
\(47\) | −11.9910 | −1.74906 | −0.874530 | − | 0.484971i | \(-0.838830\pi\) | ||||
−0.874530 | + | 0.484971i | \(0.838830\pi\) | |||||||
\(48\) | −2.71506 | −0.391885 | ||||||||
\(49\) | 3.11267 | 0.444667 | ||||||||
\(50\) | −3.88237 | −0.549050 | ||||||||
\(51\) | 9.05031 | 1.26730 | ||||||||
\(52\) | −0.206957 | −0.0286998 | ||||||||
\(53\) | −6.17248 | −0.847855 | −0.423928 | − | 0.905696i | \(-0.639349\pi\) | ||||
−0.423928 | + | 0.905696i | \(0.639349\pi\) | |||||||
\(54\) | 3.72379 | 0.506744 | ||||||||
\(55\) | 13.8946 | 1.87354 | ||||||||
\(56\) | −3.18004 | −0.424951 | ||||||||
\(57\) | 13.2652 | 1.75702 | ||||||||
\(58\) | 1.80448 | 0.236940 | ||||||||
\(59\) | −10.4000 | −1.35396 | −0.676981 | − | 0.736001i | \(-0.736712\pi\) | ||||
−0.676981 | + | 0.736001i | \(0.736712\pi\) | |||||||
\(60\) | 8.09177 | 1.04464 | ||||||||
\(61\) | 6.51902 | 0.834675 | 0.417337 | − | 0.908752i | \(-0.362963\pi\) | ||||
0.417337 | + | 0.908752i | \(0.362963\pi\) | |||||||
\(62\) | −5.19137 | −0.659305 | ||||||||
\(63\) | 13.9017 | 1.75144 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.616800 | 0.0765046 | ||||||||
\(66\) | −12.6578 | −1.55807 | ||||||||
\(67\) | 4.53232 | 0.553711 | 0.276856 | − | 0.960912i | \(-0.410708\pi\) | ||||
0.276856 | + | 0.960912i | \(0.410708\pi\) | |||||||
\(68\) | −3.33338 | −0.404231 | ||||||||
\(69\) | −21.5009 | −2.58840 | ||||||||
\(70\) | 9.47758 | 1.13279 | ||||||||
\(71\) | 1.72059 | 0.204197 | 0.102098 | − | 0.994774i | \(-0.467444\pi\) | ||||
0.102098 | + | 0.994774i | \(0.467444\pi\) | |||||||
\(72\) | −4.37153 | −0.515190 | ||||||||
\(73\) | 11.0021 | 1.28770 | 0.643848 | − | 0.765153i | \(-0.277337\pi\) | ||||
0.643848 | + | 0.765153i | \(0.277337\pi\) | |||||||
\(74\) | 0.280897 | 0.0326536 | ||||||||
\(75\) | −10.5409 | −1.21715 | ||||||||
\(76\) | −4.88581 | −0.560440 | ||||||||
\(77\) | −14.8256 | −1.68954 | ||||||||
\(78\) | −0.561900 | −0.0636226 | ||||||||
\(79\) | 5.85921 | 0.659212 | 0.329606 | − | 0.944118i | \(-0.393084\pi\) | ||||
0.329606 | + | 0.944118i | \(0.393084\pi\) | |||||||
\(80\) | −2.98033 | −0.333211 | ||||||||
\(81\) | −3.00429 | −0.333810 | ||||||||
\(82\) | −5.18280 | −0.572345 | ||||||||
\(83\) | 8.19014 | 0.898984 | 0.449492 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449492 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(84\) | −8.63399 | −0.942046 | ||||||||
\(85\) | 9.93456 | 1.07755 | ||||||||
\(86\) | 0.889927 | 0.0959633 | ||||||||
\(87\) | 4.89927 | 0.525257 | ||||||||
\(88\) | 4.66208 | 0.496980 | ||||||||
\(89\) | −9.24870 | −0.980360 | −0.490180 | − | 0.871621i | \(-0.663069\pi\) | ||||
−0.490180 | + | 0.871621i | \(0.663069\pi\) | |||||||
\(90\) | 13.0286 | 1.37334 | ||||||||
\(91\) | −0.658131 | −0.0689909 | ||||||||
\(92\) | 7.91913 | 0.825626 | ||||||||
\(93\) | −14.0949 | −1.46157 | ||||||||
\(94\) | 11.9910 | 1.23677 | ||||||||
\(95\) | 14.5613 | 1.49396 | ||||||||
\(96\) | 2.71506 | 0.277104 | ||||||||
\(97\) | 8.00436 | 0.812719 | 0.406360 | − | 0.913713i | \(-0.366798\pi\) | ||||
0.406360 | + | 0.913713i | \(0.366798\pi\) | |||||||
\(98\) | −3.11267 | −0.314427 | ||||||||
\(99\) | −20.3805 | −2.04831 | ||||||||
\(100\) | 3.88237 | 0.388237 | ||||||||
\(101\) | 1.16145 | 0.115569 | 0.0577844 | − | 0.998329i | \(-0.481596\pi\) | ||||
0.0577844 | + | 0.998329i | \(0.481596\pi\) | |||||||
\(102\) | −9.05031 | −0.896114 | ||||||||
\(103\) | −14.4312 | −1.42195 | −0.710973 | − | 0.703220i | \(-0.751745\pi\) | ||||
−0.710973 | + | 0.703220i | \(0.751745\pi\) | |||||||
\(104\) | 0.206957 | 0.0202938 | ||||||||
\(105\) | 25.7322 | 2.51120 | ||||||||
\(106\) | 6.17248 | 0.599524 | ||||||||
\(107\) | −6.01878 | −0.581857 | −0.290929 | − | 0.956745i | \(-0.593964\pi\) | ||||
−0.290929 | + | 0.956745i | \(0.593964\pi\) | |||||||
\(108\) | −3.72379 | −0.358322 | ||||||||
\(109\) | 2.77808 | 0.266092 | 0.133046 | − | 0.991110i | \(-0.457524\pi\) | ||||
0.133046 | + | 0.991110i | \(0.457524\pi\) | |||||||
\(110\) | −13.8946 | −1.32479 | ||||||||
\(111\) | 0.762650 | 0.0723875 | ||||||||
\(112\) | 3.18004 | 0.300486 | ||||||||
\(113\) | 9.98211 | 0.939037 | 0.469519 | − | 0.882923i | \(-0.344427\pi\) | ||||
0.469519 | + | 0.882923i | \(0.344427\pi\) | |||||||
\(114\) | −13.2652 | −1.24240 | ||||||||
\(115\) | −23.6016 | −2.20086 | ||||||||
\(116\) | −1.80448 | −0.167542 | ||||||||
\(117\) | −0.904719 | −0.0836413 | ||||||||
\(118\) | 10.4000 | 0.957396 | ||||||||
\(119\) | −10.6003 | −0.971726 | ||||||||
\(120\) | −8.09177 | −0.738674 | ||||||||
\(121\) | 10.7350 | 0.975912 | ||||||||
\(122\) | −6.51902 | −0.590204 | ||||||||
\(123\) | −14.0716 | −1.26879 | ||||||||
\(124\) | 5.19137 | 0.466199 | ||||||||
\(125\) | 3.33091 | 0.297925 | ||||||||
\(126\) | −13.9017 | −1.23846 | ||||||||
\(127\) | 18.2806 | 1.62214 | 0.811071 | − | 0.584948i | \(-0.198885\pi\) | ||||
0.811071 | + | 0.584948i | \(0.198885\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.41620 | 0.212735 | ||||||||
\(130\) | −0.616800 | −0.0540969 | ||||||||
\(131\) | −11.4382 | −0.999357 | −0.499679 | − | 0.866211i | \(-0.666549\pi\) | ||||
−0.499679 | + | 0.866211i | \(0.666549\pi\) | |||||||
\(132\) | 12.6578 | 1.10172 | ||||||||
\(133\) | −15.5371 | −1.34723 | ||||||||
\(134\) | −4.53232 | −0.391533 | ||||||||
\(135\) | 11.0981 | 0.955175 | ||||||||
\(136\) | 3.33338 | 0.285835 | ||||||||
\(137\) | 17.7954 | 1.52037 | 0.760184 | − | 0.649708i | \(-0.225109\pi\) | ||||
0.760184 | + | 0.649708i | \(0.225109\pi\) | |||||||
\(138\) | 21.5009 | 1.83028 | ||||||||
\(139\) | 8.20329 | 0.695794 | 0.347897 | − | 0.937533i | \(-0.386896\pi\) | ||||
0.347897 | + | 0.937533i | \(0.386896\pi\) | |||||||
\(140\) | −9.47758 | −0.801001 | ||||||||
\(141\) | 32.5561 | 2.74172 | ||||||||
\(142\) | −1.72059 | −0.144389 | ||||||||
\(143\) | 0.964850 | 0.0806848 | ||||||||
\(144\) | 4.37153 | 0.364294 | ||||||||
\(145\) | 5.37795 | 0.446614 | ||||||||
\(146\) | −11.0021 | −0.910539 | ||||||||
\(147\) | −8.45107 | −0.697032 | ||||||||
\(148\) | −0.280897 | −0.0230896 | ||||||||
\(149\) | 0.563397 | 0.0461553 | 0.0230777 | − | 0.999734i | \(-0.492654\pi\) | ||||
0.0230777 | + | 0.999734i | \(0.492654\pi\) | |||||||
\(150\) | 10.5409 | 0.860657 | ||||||||
\(151\) | −11.8749 | −0.966368 | −0.483184 | − | 0.875519i | \(-0.660520\pi\) | ||||
−0.483184 | + | 0.875519i | \(0.660520\pi\) | |||||||
\(152\) | 4.88581 | 0.396291 | ||||||||
\(153\) | −14.5720 | −1.17807 | ||||||||
\(154\) | 14.8256 | 1.19468 | ||||||||
\(155\) | −15.4720 | −1.24274 | ||||||||
\(156\) | 0.561900 | 0.0449880 | ||||||||
\(157\) | −18.7754 | −1.49844 | −0.749219 | − | 0.662322i | \(-0.769571\pi\) | ||||
−0.749219 | + | 0.662322i | \(0.769571\pi\) | |||||||
\(158\) | −5.85921 | −0.466134 | ||||||||
\(159\) | 16.7586 | 1.32905 | ||||||||
\(160\) | 2.98033 | 0.235616 | ||||||||
\(161\) | 25.1832 | 1.98471 | ||||||||
\(162\) | 3.00429 | 0.236040 | ||||||||
\(163\) | 5.27573 | 0.413227 | 0.206614 | − | 0.978423i | \(-0.433756\pi\) | ||||
0.206614 | + | 0.978423i | \(0.433756\pi\) | |||||||
\(164\) | 5.18280 | 0.404709 | ||||||||
\(165\) | −37.7245 | −2.93685 | ||||||||
\(166\) | −8.19014 | −0.635678 | ||||||||
\(167\) | 9.39964 | 0.727366 | 0.363683 | − | 0.931523i | \(-0.381519\pi\) | ||||
0.363683 | + | 0.931523i | \(0.381519\pi\) | |||||||
\(168\) | 8.63399 | 0.666127 | ||||||||
\(169\) | −12.9572 | −0.996705 | ||||||||
\(170\) | −9.93456 | −0.761946 | ||||||||
\(171\) | −21.3585 | −1.63332 | ||||||||
\(172\) | −0.889927 | −0.0678563 | ||||||||
\(173\) | −3.38774 | −0.257565 | −0.128782 | − | 0.991673i | \(-0.541107\pi\) | ||||
−0.128782 | + | 0.991673i | \(0.541107\pi\) | |||||||
\(174\) | −4.89927 | −0.371413 | ||||||||
\(175\) | 12.3461 | 0.933277 | ||||||||
\(176\) | −4.66208 | −0.351418 | ||||||||
\(177\) | 28.2365 | 2.12239 | ||||||||
\(178\) | 9.24870 | 0.693219 | ||||||||
\(179\) | 12.7495 | 0.952943 | 0.476472 | − | 0.879190i | \(-0.341916\pi\) | ||||
0.476472 | + | 0.879190i | \(0.341916\pi\) | |||||||
\(180\) | −13.0286 | −0.971096 | ||||||||
\(181\) | 8.33225 | 0.619331 | 0.309666 | − | 0.950846i | \(-0.399783\pi\) | ||||
0.309666 | + | 0.950846i | \(0.399783\pi\) | |||||||
\(182\) | 0.658131 | 0.0487839 | ||||||||
\(183\) | −17.6995 | −1.30838 | ||||||||
\(184\) | −7.91913 | −0.583806 | ||||||||
\(185\) | 0.837164 | 0.0615496 | ||||||||
\(186\) | 14.0949 | 1.03349 | ||||||||
\(187\) | 15.5405 | 1.13643 | ||||||||
\(188\) | −11.9910 | −0.874530 | ||||||||
\(189\) | −11.8418 | −0.861365 | ||||||||
\(190\) | −14.5613 | −1.05639 | ||||||||
\(191\) | 15.5119 | 1.12240 | 0.561201 | − | 0.827679i | \(-0.310339\pi\) | ||||
0.561201 | + | 0.827679i | \(0.310339\pi\) | |||||||
\(192\) | −2.71506 | −0.195942 | ||||||||
\(193\) | 20.2688 | 1.45898 | 0.729491 | − | 0.683990i | \(-0.239757\pi\) | ||||
0.729491 | + | 0.683990i | \(0.239757\pi\) | |||||||
\(194\) | −8.00436 | −0.574679 | ||||||||
\(195\) | −1.67465 | −0.119924 | ||||||||
\(196\) | 3.11267 | 0.222333 | ||||||||
\(197\) | 19.8796 | 1.41636 | 0.708181 | − | 0.706030i | \(-0.249516\pi\) | ||||
0.708181 | + | 0.706030i | \(0.249516\pi\) | |||||||
\(198\) | 20.3805 | 1.44838 | ||||||||
\(199\) | −1.66224 | −0.117833 | −0.0589164 | − | 0.998263i | \(-0.518765\pi\) | ||||
−0.0589164 | + | 0.998263i | \(0.518765\pi\) | |||||||
\(200\) | −3.88237 | −0.274525 | ||||||||
\(201\) | −12.3055 | −0.867964 | ||||||||
\(202\) | −1.16145 | −0.0817194 | ||||||||
\(203\) | −5.73832 | −0.402751 | ||||||||
\(204\) | 9.05031 | 0.633648 | ||||||||
\(205\) | −15.4465 | −1.07883 | ||||||||
\(206\) | 14.4312 | 1.00547 | ||||||||
\(207\) | 34.6187 | 2.40617 | ||||||||
\(208\) | −0.206957 | −0.0143499 | ||||||||
\(209\) | 22.7780 | 1.57559 | ||||||||
\(210\) | −25.7322 | −1.77569 | ||||||||
\(211\) | 3.03770 | 0.209124 | 0.104562 | − | 0.994518i | \(-0.466656\pi\) | ||||
0.104562 | + | 0.994518i | \(0.466656\pi\) | |||||||
\(212\) | −6.17248 | −0.423928 | ||||||||
\(213\) | −4.67151 | −0.320086 | ||||||||
\(214\) | 6.01878 | 0.411435 | ||||||||
\(215\) | 2.65228 | 0.180884 | ||||||||
\(216\) | 3.72379 | 0.253372 | ||||||||
\(217\) | 16.5088 | 1.12069 | ||||||||
\(218\) | −2.77808 | −0.188155 | ||||||||
\(219\) | −29.8713 | −2.01851 | ||||||||
\(220\) | 13.8946 | 0.936771 | ||||||||
\(221\) | 0.689865 | 0.0464054 | ||||||||
\(222\) | −0.762650 | −0.0511857 | ||||||||
\(223\) | −10.3577 | −0.693602 | −0.346801 | − | 0.937939i | \(-0.612732\pi\) | ||||
−0.346801 | + | 0.937939i | \(0.612732\pi\) | |||||||
\(224\) | −3.18004 | −0.212475 | ||||||||
\(225\) | 16.9719 | 1.13146 | ||||||||
\(226\) | −9.98211 | −0.664000 | ||||||||
\(227\) | 6.77101 | 0.449408 | 0.224704 | − | 0.974427i | \(-0.427859\pi\) | ||||
0.224704 | + | 0.974427i | \(0.427859\pi\) | |||||||
\(228\) | 13.2652 | 0.878512 | ||||||||
\(229\) | 7.30024 | 0.482413 | 0.241207 | − | 0.970474i | \(-0.422457\pi\) | ||||
0.241207 | + | 0.970474i | \(0.422457\pi\) | |||||||
\(230\) | 23.6016 | 1.55625 | ||||||||
\(231\) | 40.2524 | 2.64841 | ||||||||
\(232\) | 1.80448 | 0.118470 | ||||||||
\(233\) | −25.5717 | −1.67526 | −0.837628 | − | 0.546241i | \(-0.816058\pi\) | ||||
−0.837628 | + | 0.546241i | \(0.816058\pi\) | |||||||
\(234\) | 0.904719 | 0.0591433 | ||||||||
\(235\) | 35.7370 | 2.33122 | ||||||||
\(236\) | −10.4000 | −0.676981 | ||||||||
\(237\) | −15.9081 | −1.03334 | ||||||||
\(238\) | 10.6003 | 0.687114 | ||||||||
\(239\) | 19.1259 | 1.23715 | 0.618575 | − | 0.785726i | \(-0.287710\pi\) | ||||
0.618575 | + | 0.785726i | \(0.287710\pi\) | |||||||
\(240\) | 8.09177 | 0.522321 | ||||||||
\(241\) | −6.79789 | −0.437891 | −0.218945 | − | 0.975737i | \(-0.570262\pi\) | ||||
−0.218945 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(242\) | −10.7350 | −0.690074 | ||||||||
\(243\) | 19.3282 | 1.23990 | ||||||||
\(244\) | 6.51902 | 0.417337 | ||||||||
\(245\) | −9.27678 | −0.592671 | ||||||||
\(246\) | 14.0716 | 0.897173 | ||||||||
\(247\) | 1.01115 | 0.0643380 | ||||||||
\(248\) | −5.19137 | −0.329652 | ||||||||
\(249\) | −22.2367 | −1.40919 | ||||||||
\(250\) | −3.33091 | −0.210665 | ||||||||
\(251\) | 13.4974 | 0.851948 | 0.425974 | − | 0.904735i | \(-0.359932\pi\) | ||||
0.425974 | + | 0.904735i | \(0.359932\pi\) | |||||||
\(252\) | 13.9017 | 0.875722 | ||||||||
\(253\) | −36.9197 | −2.32112 | ||||||||
\(254\) | −18.2806 | −1.14703 | ||||||||
\(255\) | −26.9729 | −1.68911 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.4986 | −1.15391 | −0.576955 | − | 0.816776i | \(-0.695759\pi\) | ||||
−0.576955 | + | 0.816776i | \(0.695759\pi\) | |||||||
\(258\) | −2.41620 | −0.150426 | ||||||||
\(259\) | −0.893263 | −0.0555046 | ||||||||
\(260\) | 0.616800 | 0.0382523 | ||||||||
\(261\) | −7.88835 | −0.488276 | ||||||||
\(262\) | 11.4382 | 0.706652 | ||||||||
\(263\) | 20.5832 | 1.26922 | 0.634609 | − | 0.772834i | \(-0.281161\pi\) | ||||
0.634609 | + | 0.772834i | \(0.281161\pi\) | |||||||
\(264\) | −12.6578 | −0.779035 | ||||||||
\(265\) | 18.3960 | 1.13006 | ||||||||
\(266\) | 15.5371 | 0.952639 | ||||||||
\(267\) | 25.1108 | 1.53675 | ||||||||
\(268\) | 4.53232 | 0.276856 | ||||||||
\(269\) | 30.4811 | 1.85847 | 0.929234 | − | 0.369491i | \(-0.120468\pi\) | ||||
0.929234 | + | 0.369491i | \(0.120468\pi\) | |||||||
\(270\) | −11.0981 | −0.675411 | ||||||||
\(271\) | −2.74238 | −0.166588 | −0.0832938 | − | 0.996525i | \(-0.526544\pi\) | ||||
−0.0832938 | + | 0.996525i | \(0.526544\pi\) | |||||||
\(272\) | −3.33338 | −0.202116 | ||||||||
\(273\) | 1.78686 | 0.108146 | ||||||||
\(274\) | −17.7954 | −1.07506 | ||||||||
\(275\) | −18.0999 | −1.09147 | ||||||||
\(276\) | −21.5009 | −1.29420 | ||||||||
\(277\) | 7.80451 | 0.468928 | 0.234464 | − | 0.972125i | \(-0.424667\pi\) | ||||
0.234464 | + | 0.972125i | \(0.424667\pi\) | |||||||
\(278\) | −8.20329 | −0.492001 | ||||||||
\(279\) | 22.6943 | 1.35867 | ||||||||
\(280\) | 9.47758 | 0.566394 | ||||||||
\(281\) | −13.6091 | −0.811853 | −0.405927 | − | 0.913906i | \(-0.633051\pi\) | ||||
−0.405927 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(282\) | −32.5561 | −1.93869 | ||||||||
\(283\) | 8.78731 | 0.522351 | 0.261176 | − | 0.965291i | \(-0.415890\pi\) | ||||
0.261176 | + | 0.965291i | \(0.415890\pi\) | |||||||
\(284\) | 1.72059 | 0.102098 | ||||||||
\(285\) | −39.5348 | −2.34184 | ||||||||
\(286\) | −0.964850 | −0.0570528 | ||||||||
\(287\) | 16.4815 | 0.972874 | ||||||||
\(288\) | −4.37153 | −0.257595 | ||||||||
\(289\) | −5.88860 | −0.346388 | ||||||||
\(290\) | −5.37795 | −0.315804 | ||||||||
\(291\) | −21.7323 | −1.27397 | ||||||||
\(292\) | 11.0021 | 0.643848 | ||||||||
\(293\) | −3.65314 | −0.213419 | −0.106709 | − | 0.994290i | \(-0.534031\pi\) | ||||
−0.106709 | + | 0.994290i | \(0.534031\pi\) | |||||||
\(294\) | 8.45107 | 0.492876 | ||||||||
\(295\) | 30.9954 | 1.80462 | ||||||||
\(296\) | 0.280897 | 0.0163268 | ||||||||
\(297\) | 17.3606 | 1.00737 | ||||||||
\(298\) | −0.563397 | −0.0326367 | ||||||||
\(299\) | −1.63892 | −0.0947811 | ||||||||
\(300\) | −10.5409 | −0.608577 | ||||||||
\(301\) | −2.83001 | −0.163119 | ||||||||
\(302\) | 11.8749 | 0.683325 | ||||||||
\(303\) | −3.15341 | −0.181158 | ||||||||
\(304\) | −4.88581 | −0.280220 | ||||||||
\(305\) | −19.4288 | −1.11249 | ||||||||
\(306\) | 14.5720 | 0.833024 | ||||||||
\(307\) | −12.2995 | −0.701968 | −0.350984 | − | 0.936381i | \(-0.614153\pi\) | ||||
−0.350984 | + | 0.936381i | \(0.614153\pi\) | |||||||
\(308\) | −14.8256 | −0.844768 | ||||||||
\(309\) | 39.1815 | 2.22895 | ||||||||
\(310\) | 15.4720 | 0.878751 | ||||||||
\(311\) | 31.9397 | 1.81113 | 0.905566 | − | 0.424206i | \(-0.139447\pi\) | ||||
0.905566 | + | 0.424206i | \(0.139447\pi\) | |||||||
\(312\) | −0.561900 | −0.0318113 | ||||||||
\(313\) | 26.3933 | 1.49184 | 0.745918 | − | 0.666038i | \(-0.232011\pi\) | ||||
0.745918 | + | 0.666038i | \(0.232011\pi\) | |||||||
\(314\) | 18.7754 | 1.05956 | ||||||||
\(315\) | −41.4315 | −2.33440 | ||||||||
\(316\) | 5.85921 | 0.329606 | ||||||||
\(317\) | 19.1032 | 1.07294 | 0.536470 | − | 0.843919i | \(-0.319757\pi\) | ||||
0.536470 | + | 0.843919i | \(0.319757\pi\) | |||||||
\(318\) | −16.7586 | −0.939778 | ||||||||
\(319\) | 8.41264 | 0.471018 | ||||||||
\(320\) | −2.98033 | −0.166606 | ||||||||
\(321\) | 16.3413 | 0.912084 | ||||||||
\(322\) | −25.1832 | −1.40340 | ||||||||
\(323\) | 16.2862 | 0.906190 | ||||||||
\(324\) | −3.00429 | −0.166905 | ||||||||
\(325\) | −0.803483 | −0.0445692 | ||||||||
\(326\) | −5.27573 | −0.292196 | ||||||||
\(327\) | −7.54264 | −0.417109 | ||||||||
\(328\) | −5.18280 | −0.286172 | ||||||||
\(329\) | −38.1317 | −2.10227 | ||||||||
\(330\) | 37.7245 | 2.07667 | ||||||||
\(331\) | 33.7805 | 1.85674 | 0.928371 | − | 0.371655i | \(-0.121209\pi\) | ||||
0.928371 | + | 0.371655i | \(0.121209\pi\) | |||||||
\(332\) | 8.19014 | 0.449492 | ||||||||
\(333\) | −1.22795 | −0.0672912 | ||||||||
\(334\) | −9.39964 | −0.514326 | ||||||||
\(335\) | −13.5078 | −0.738011 | ||||||||
\(336\) | −8.63399 | −0.471023 | ||||||||
\(337\) | −34.1726 | −1.86150 | −0.930751 | − | 0.365653i | \(-0.880846\pi\) | ||||
−0.930751 | + | 0.365653i | \(0.880846\pi\) | |||||||
\(338\) | 12.9572 | 0.704777 | ||||||||
\(339\) | −27.1020 | −1.47198 | ||||||||
\(340\) | 9.93456 | 0.538777 | ||||||||
\(341\) | −24.2026 | −1.31065 | ||||||||
\(342\) | 21.3585 | 1.15493 | ||||||||
\(343\) | −12.3619 | −0.667479 | ||||||||
\(344\) | 0.889927 | 0.0479817 | ||||||||
\(345\) | 64.0798 | 3.44994 | ||||||||
\(346\) | 3.38774 | 0.182126 | ||||||||
\(347\) | −25.1976 | −1.35268 | −0.676338 | − | 0.736591i | \(-0.736434\pi\) | ||||
−0.676338 | + | 0.736591i | \(0.736434\pi\) | |||||||
\(348\) | 4.89927 | 0.262628 | ||||||||
\(349\) | 9.19423 | 0.492156 | 0.246078 | − | 0.969250i | \(-0.420858\pi\) | ||||
0.246078 | + | 0.969250i | \(0.420858\pi\) | |||||||
\(350\) | −12.3461 | −0.659927 | ||||||||
\(351\) | 0.770664 | 0.0411350 | ||||||||
\(352\) | 4.66208 | 0.248490 | ||||||||
\(353\) | −6.61158 | −0.351899 | −0.175949 | − | 0.984399i | \(-0.556300\pi\) | ||||
−0.175949 | + | 0.984399i | \(0.556300\pi\) | |||||||
\(354\) | −28.2365 | −1.50075 | ||||||||
\(355\) | −5.12793 | −0.272162 | ||||||||
\(356\) | −9.24870 | −0.490180 | ||||||||
\(357\) | 28.7804 | 1.52322 | ||||||||
\(358\) | −12.7495 | −0.673832 | ||||||||
\(359\) | −3.95873 | −0.208934 | −0.104467 | − | 0.994528i | \(-0.533314\pi\) | ||||
−0.104467 | + | 0.994528i | \(0.533314\pi\) | |||||||
\(360\) | 13.0286 | 0.686668 | ||||||||
\(361\) | 4.87110 | 0.256374 | ||||||||
\(362\) | −8.33225 | −0.437933 | ||||||||
\(363\) | −29.1462 | −1.52978 | ||||||||
\(364\) | −0.658131 | −0.0344955 | ||||||||
\(365\) | −32.7898 | −1.71630 | ||||||||
\(366\) | 17.6995 | 0.925168 | ||||||||
\(367\) | −21.0053 | −1.09647 | −0.548233 | − | 0.836325i | \(-0.684699\pi\) | ||||
−0.548233 | + | 0.836325i | \(0.684699\pi\) | |||||||
\(368\) | 7.91913 | 0.412813 | ||||||||
\(369\) | 22.6568 | 1.17947 | ||||||||
\(370\) | −0.837164 | −0.0435221 | ||||||||
\(371\) | −19.6287 | −1.01907 | ||||||||
\(372\) | −14.0949 | −0.730785 | ||||||||
\(373\) | −12.4902 | −0.646716 | −0.323358 | − | 0.946277i | \(-0.604812\pi\) | ||||
−0.323358 | + | 0.946277i | \(0.604812\pi\) | |||||||
\(374\) | −15.5405 | −0.803579 | ||||||||
\(375\) | −9.04360 | −0.467009 | ||||||||
\(376\) | 11.9910 | 0.618386 | ||||||||
\(377\) | 0.373450 | 0.0192336 | ||||||||
\(378\) | 11.8418 | 0.609077 | ||||||||
\(379\) | 14.1273 | 0.725672 | 0.362836 | − | 0.931853i | \(-0.381809\pi\) | ||||
0.362836 | + | 0.931853i | \(0.381809\pi\) | |||||||
\(380\) | 14.5613 | 0.746980 | ||||||||
\(381\) | −49.6329 | −2.54277 | ||||||||
\(382\) | −15.5119 | −0.793658 | ||||||||
\(383\) | −34.1908 | −1.74707 | −0.873534 | − | 0.486763i | \(-0.838177\pi\) | ||||
−0.873534 | + | 0.486763i | \(0.838177\pi\) | |||||||
\(384\) | 2.71506 | 0.138552 | ||||||||
\(385\) | 44.1853 | 2.25189 | ||||||||
\(386\) | −20.2688 | −1.03166 | ||||||||
\(387\) | −3.89035 | −0.197757 | ||||||||
\(388\) | 8.00436 | 0.406360 | ||||||||
\(389\) | −16.7005 | −0.846750 | −0.423375 | − | 0.905954i | \(-0.639155\pi\) | ||||
−0.423375 | + | 0.905954i | \(0.639155\pi\) | |||||||
\(390\) | 1.67465 | 0.0847990 | ||||||||
\(391\) | −26.3974 | −1.33498 | ||||||||
\(392\) | −3.11267 | −0.157213 | ||||||||
\(393\) | 31.0553 | 1.56653 | ||||||||
\(394\) | −19.8796 | −1.00152 | ||||||||
\(395\) | −17.4624 | −0.878628 | ||||||||
\(396\) | −20.3805 | −1.02416 | ||||||||
\(397\) | 3.64414 | 0.182894 | 0.0914472 | − | 0.995810i | \(-0.470851\pi\) | ||||
0.0914472 | + | 0.995810i | \(0.470851\pi\) | |||||||
\(398\) | 1.66224 | 0.0833204 | ||||||||
\(399\) | 42.1840 | 2.11184 | ||||||||
\(400\) | 3.88237 | 0.194119 | ||||||||
\(401\) | −19.8567 | −0.991597 | −0.495799 | − | 0.868438i | \(-0.665125\pi\) | ||||
−0.495799 | + | 0.868438i | \(0.665125\pi\) | |||||||
\(402\) | 12.3055 | 0.613743 | ||||||||
\(403\) | −1.07439 | −0.0535192 | ||||||||
\(404\) | 1.16145 | 0.0577844 | ||||||||
\(405\) | 8.95379 | 0.444917 | ||||||||
\(406\) | 5.73832 | 0.284788 | ||||||||
\(407\) | 1.30956 | 0.0649126 | ||||||||
\(408\) | −9.05031 | −0.448057 | ||||||||
\(409\) | −18.5685 | −0.918152 | −0.459076 | − | 0.888397i | \(-0.651819\pi\) | ||||
−0.459076 | + | 0.888397i | \(0.651819\pi\) | |||||||
\(410\) | 15.4465 | 0.762847 | ||||||||
\(411\) | −48.3156 | −2.38323 | ||||||||
\(412\) | −14.4312 | −0.710973 | ||||||||
\(413\) | −33.0724 | −1.62738 | ||||||||
\(414\) | −34.6187 | −1.70142 | ||||||||
\(415\) | −24.4093 | −1.19821 | ||||||||
\(416\) | 0.206957 | 0.0101469 | ||||||||
\(417\) | −22.2724 | −1.09068 | ||||||||
\(418\) | −22.7780 | −1.11411 | ||||||||
\(419\) | −14.9158 | −0.728684 | −0.364342 | − | 0.931265i | \(-0.618706\pi\) | ||||
−0.364342 | + | 0.931265i | \(0.618706\pi\) | |||||||
\(420\) | 25.7322 | 1.25560 | ||||||||
\(421\) | −25.5757 | −1.24648 | −0.623242 | − | 0.782029i | \(-0.714185\pi\) | ||||
−0.623242 | + | 0.782029i | \(0.714185\pi\) | |||||||
\(422\) | −3.03770 | −0.147873 | ||||||||
\(423\) | −52.4188 | −2.54869 | ||||||||
\(424\) | 6.17248 | 0.299762 | ||||||||
\(425\) | −12.9414 | −0.627750 | ||||||||
\(426\) | 4.67151 | 0.226335 | ||||||||
\(427\) | 20.7307 | 1.00323 | ||||||||
\(428\) | −6.01878 | −0.290929 | ||||||||
\(429\) | −2.61962 | −0.126477 | ||||||||
\(430\) | −2.65228 | −0.127904 | ||||||||
\(431\) | −2.65323 | −0.127802 | −0.0639009 | − | 0.997956i | \(-0.520354\pi\) | ||||
−0.0639009 | + | 0.997956i | \(0.520354\pi\) | |||||||
\(432\) | −3.72379 | −0.179161 | ||||||||
\(433\) | −12.7148 | −0.611035 | −0.305517 | − | 0.952187i | \(-0.598829\pi\) | ||||
−0.305517 | + | 0.952187i | \(0.598829\pi\) | |||||||
\(434\) | −16.5088 | −0.792447 | ||||||||
\(435\) | −14.6014 | −0.700085 | ||||||||
\(436\) | 2.77808 | 0.133046 | ||||||||
\(437\) | −38.6913 | −1.85086 | ||||||||
\(438\) | 29.8713 | 1.42730 | ||||||||
\(439\) | −10.0130 | −0.477896 | −0.238948 | − | 0.971032i | \(-0.576803\pi\) | ||||
−0.238948 | + | 0.971032i | \(0.576803\pi\) | |||||||
\(440\) | −13.8946 | −0.662397 | ||||||||
\(441\) | 13.6071 | 0.647958 | ||||||||
\(442\) | −0.689865 | −0.0328135 | ||||||||
\(443\) | 15.6462 | 0.743376 | 0.371688 | − | 0.928358i | \(-0.378779\pi\) | ||||
0.371688 | + | 0.928358i | \(0.378779\pi\) | |||||||
\(444\) | 0.762650 | 0.0361938 | ||||||||
\(445\) | 27.5642 | 1.30667 | ||||||||
\(446\) | 10.3577 | 0.490451 | ||||||||
\(447\) | −1.52966 | −0.0723502 | ||||||||
\(448\) | 3.18004 | 0.150243 | ||||||||
\(449\) | 1.71080 | 0.0807377 | 0.0403689 | − | 0.999185i | \(-0.487147\pi\) | ||||
0.0403689 | + | 0.999185i | \(0.487147\pi\) | |||||||
\(450\) | −16.9719 | −0.800064 | ||||||||
\(451\) | −24.1627 | −1.13778 | ||||||||
\(452\) | 9.98211 | 0.469519 | ||||||||
\(453\) | 32.2411 | 1.51482 | ||||||||
\(454\) | −6.77101 | −0.317779 | ||||||||
\(455\) | 1.96145 | 0.0919542 | ||||||||
\(456\) | −13.2652 | −0.621202 | ||||||||
\(457\) | −28.2034 | −1.31930 | −0.659649 | − | 0.751574i | \(-0.729295\pi\) | ||||
−0.659649 | + | 0.751574i | \(0.729295\pi\) | |||||||
\(458\) | −7.30024 | −0.341118 | ||||||||
\(459\) | 12.4128 | 0.579380 | ||||||||
\(460\) | −23.6016 | −1.10043 | ||||||||
\(461\) | 19.2700 | 0.897495 | 0.448748 | − | 0.893659i | \(-0.351870\pi\) | ||||
0.448748 | + | 0.893659i | \(0.351870\pi\) | |||||||
\(462\) | −40.2524 | −1.87271 | ||||||||
\(463\) | −32.2347 | −1.49807 | −0.749037 | − | 0.662528i | \(-0.769484\pi\) | ||||
−0.749037 | + | 0.662528i | \(0.769484\pi\) | |||||||
\(464\) | −1.80448 | −0.0837709 | ||||||||
\(465\) | 42.0074 | 1.94805 | ||||||||
\(466\) | 25.5717 | 1.18458 | ||||||||
\(467\) | −32.8624 | −1.52069 | −0.760346 | − | 0.649518i | \(-0.774971\pi\) | ||||
−0.760346 | + | 0.649518i | \(0.774971\pi\) | |||||||
\(468\) | −0.904719 | −0.0418206 | ||||||||
\(469\) | 14.4130 | 0.665529 | ||||||||
\(470\) | −35.7370 | −1.64842 | ||||||||
\(471\) | 50.9762 | 2.34886 | ||||||||
\(472\) | 10.4000 | 0.478698 | ||||||||
\(473\) | 4.14892 | 0.190767 | ||||||||
\(474\) | 15.9081 | 0.730682 | ||||||||
\(475\) | −18.9685 | −0.870335 | ||||||||
\(476\) | −10.6003 | −0.485863 | ||||||||
\(477\) | −26.9832 | −1.23548 | ||||||||
\(478\) | −19.1259 | −0.874797 | ||||||||
\(479\) | −4.90869 | −0.224284 | −0.112142 | − | 0.993692i | \(-0.535771\pi\) | ||||
−0.112142 | + | 0.993692i | \(0.535771\pi\) | |||||||
\(480\) | −8.09177 | −0.369337 | ||||||||
\(481\) | 0.0581335 | 0.00265066 | ||||||||
\(482\) | 6.79789 | 0.309636 | ||||||||
\(483\) | −68.3737 | −3.11111 | ||||||||
\(484\) | 10.7350 | 0.487956 | ||||||||
\(485\) | −23.8556 | −1.08323 | ||||||||
\(486\) | −19.3282 | −0.876745 | ||||||||
\(487\) | 7.40585 | 0.335591 | 0.167795 | − | 0.985822i | \(-0.446335\pi\) | ||||
0.167795 | + | 0.985822i | \(0.446335\pi\) | |||||||
\(488\) | −6.51902 | −0.295102 | ||||||||
\(489\) | −14.3239 | −0.647750 | ||||||||
\(490\) | 9.27678 | 0.419082 | ||||||||
\(491\) | −19.5284 | −0.881305 | −0.440652 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(492\) | −14.0716 | −0.634397 | ||||||||
\(493\) | 6.01501 | 0.270903 | ||||||||
\(494\) | −1.01115 | −0.0454938 | ||||||||
\(495\) | 60.7405 | 2.73008 | ||||||||
\(496\) | 5.19137 | 0.233099 | ||||||||
\(497\) | 5.47156 | 0.245433 | ||||||||
\(498\) | 22.2367 | 0.996450 | ||||||||
\(499\) | 33.7657 | 1.51156 | 0.755780 | − | 0.654825i | \(-0.227258\pi\) | ||||
0.755780 | + | 0.654825i | \(0.227258\pi\) | |||||||
\(500\) | 3.33091 | 0.148963 | ||||||||
\(501\) | −25.5206 | −1.14017 | ||||||||
\(502\) | −13.4974 | −0.602418 | ||||||||
\(503\) | −10.8833 | −0.485262 | −0.242631 | − | 0.970119i | \(-0.578010\pi\) | ||||
−0.242631 | + | 0.970119i | \(0.578010\pi\) | |||||||
\(504\) | −13.9017 | −0.619229 | ||||||||
\(505\) | −3.46151 | −0.154035 | ||||||||
\(506\) | 36.9197 | 1.64128 | ||||||||
\(507\) | 35.1795 | 1.56237 | ||||||||
\(508\) | 18.2806 | 0.811071 | ||||||||
\(509\) | 21.2484 | 0.941821 | 0.470910 | − | 0.882181i | \(-0.343926\pi\) | ||||
0.470910 | + | 0.882181i | \(0.343926\pi\) | |||||||
\(510\) | 26.9729 | 1.19438 | ||||||||
\(511\) | 34.9871 | 1.54774 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 18.1937 | 0.803273 | ||||||||
\(514\) | 18.4986 | 0.815938 | ||||||||
\(515\) | 43.0097 | 1.89523 | ||||||||
\(516\) | 2.41620 | 0.106367 | ||||||||
\(517\) | 55.9028 | 2.45860 | ||||||||
\(518\) | 0.893263 | 0.0392477 | ||||||||
\(519\) | 9.19790 | 0.403743 | ||||||||
\(520\) | −0.616800 | −0.0270485 | ||||||||
\(521\) | −5.68808 | −0.249199 | −0.124600 | − | 0.992207i | \(-0.539765\pi\) | ||||
−0.124600 | + | 0.992207i | \(0.539765\pi\) | |||||||
\(522\) | 7.88835 | 0.345264 | ||||||||
\(523\) | 32.8650 | 1.43709 | 0.718543 | − | 0.695483i | \(-0.244810\pi\) | ||||
0.718543 | + | 0.695483i | \(0.244810\pi\) | |||||||
\(524\) | −11.4382 | −0.499679 | ||||||||
\(525\) | −33.5204 | −1.46295 | ||||||||
\(526\) | −20.5832 | −0.897472 | ||||||||
\(527\) | −17.3048 | −0.753809 | ||||||||
\(528\) | 12.6578 | 0.550861 | ||||||||
\(529\) | 39.7126 | 1.72664 | ||||||||
\(530\) | −18.3960 | −0.799073 | ||||||||
\(531\) | −45.4639 | −1.97296 | ||||||||
\(532\) | −15.5371 | −0.673617 | ||||||||
\(533\) | −1.07262 | −0.0464602 | ||||||||
\(534\) | −25.1108 | −1.08665 | ||||||||
\(535\) | 17.9380 | 0.775525 | ||||||||
\(536\) | −4.53232 | −0.195766 | ||||||||
\(537\) | −34.6156 | −1.49378 | ||||||||
\(538\) | −30.4811 | −1.31414 | ||||||||
\(539\) | −14.5115 | −0.625055 | ||||||||
\(540\) | 11.0981 | 0.477588 | ||||||||
\(541\) | −21.9527 | −0.943818 | −0.471909 | − | 0.881647i | \(-0.656435\pi\) | ||||
−0.471909 | + | 0.881647i | \(0.656435\pi\) | |||||||
\(542\) | 2.74238 | 0.117795 | ||||||||
\(543\) | −22.6225 | −0.970826 | ||||||||
\(544\) | 3.33338 | 0.142917 | ||||||||
\(545\) | −8.27959 | −0.354659 | ||||||||
\(546\) | −1.78686 | −0.0764707 | ||||||||
\(547\) | 15.5043 | 0.662917 | 0.331458 | − | 0.943470i | \(-0.392459\pi\) | ||||
0.331458 | + | 0.943470i | \(0.392459\pi\) | |||||||
\(548\) | 17.7954 | 0.760184 | ||||||||
\(549\) | 28.4981 | 1.21627 | ||||||||
\(550\) | 18.0999 | 0.771784 | ||||||||
\(551\) | 8.81634 | 0.375589 | ||||||||
\(552\) | 21.5009 | 0.915139 | ||||||||
\(553\) | 18.6325 | 0.792336 | ||||||||
\(554\) | −7.80451 | −0.331582 | ||||||||
\(555\) | −2.27295 | −0.0964813 | ||||||||
\(556\) | 8.20329 | 0.347897 | ||||||||
\(557\) | 17.1437 | 0.726404 | 0.363202 | − | 0.931710i | \(-0.381684\pi\) | ||||
0.363202 | + | 0.931710i | \(0.381684\pi\) | |||||||
\(558\) | −22.6943 | −0.960725 | ||||||||
\(559\) | 0.184177 | 0.00778984 | ||||||||
\(560\) | −9.47758 | −0.400501 | ||||||||
\(561\) | −42.1933 | −1.78140 | ||||||||
\(562\) | 13.6091 | 0.574067 | ||||||||
\(563\) | 26.8191 | 1.13029 | 0.565146 | − | 0.824991i | \(-0.308820\pi\) | ||||
0.565146 | + | 0.824991i | \(0.308820\pi\) | |||||||
\(564\) | 32.5561 | 1.37086 | ||||||||
\(565\) | −29.7500 | −1.25159 | ||||||||
\(566\) | −8.78731 | −0.369358 | ||||||||
\(567\) | −9.55378 | −0.401221 | ||||||||
\(568\) | −1.72059 | −0.0721945 | ||||||||
\(569\) | −38.3653 | −1.60836 | −0.804179 | − | 0.594387i | \(-0.797395\pi\) | ||||
−0.804179 | + | 0.594387i | \(0.797395\pi\) | |||||||
\(570\) | 39.5348 | 1.65593 | ||||||||
\(571\) | 14.9750 | 0.626683 | 0.313341 | − | 0.949641i | \(-0.398552\pi\) | ||||
0.313341 | + | 0.949641i | \(0.398552\pi\) | |||||||
\(572\) | 0.964850 | 0.0403424 | ||||||||
\(573\) | −42.1157 | −1.75941 | ||||||||
\(574\) | −16.4815 | −0.687926 | ||||||||
\(575\) | 30.7450 | 1.28215 | ||||||||
\(576\) | 4.37153 | 0.182147 | ||||||||
\(577\) | −37.3763 | −1.55600 | −0.777998 | − | 0.628266i | \(-0.783765\pi\) | ||||
−0.777998 | + | 0.628266i | \(0.783765\pi\) | |||||||
\(578\) | 5.88860 | 0.244933 | ||||||||
\(579\) | −55.0310 | −2.28701 | ||||||||
\(580\) | 5.37795 | 0.223307 | ||||||||
\(581\) | 26.0450 | 1.08053 | ||||||||
\(582\) | 21.7323 | 0.900832 | ||||||||
\(583\) | 28.7766 | 1.19181 | ||||||||
\(584\) | −11.0021 | −0.455269 | ||||||||
\(585\) | 2.69636 | 0.111481 | ||||||||
\(586\) | 3.65314 | 0.150910 | ||||||||
\(587\) | −45.1867 | −1.86506 | −0.932528 | − | 0.361097i | \(-0.882402\pi\) | ||||
−0.932528 | + | 0.361097i | \(0.882402\pi\) | |||||||
\(588\) | −8.45107 | −0.348516 | ||||||||
\(589\) | −25.3640 | −1.04511 | ||||||||
\(590\) | −30.9954 | −1.27606 | ||||||||
\(591\) | −53.9742 | −2.22020 | ||||||||
\(592\) | −0.280897 | −0.0115448 | ||||||||
\(593\) | −16.1582 | −0.663536 | −0.331768 | − | 0.943361i | \(-0.607645\pi\) | ||||
−0.331768 | + | 0.943361i | \(0.607645\pi\) | |||||||
\(594\) | −17.3606 | −0.712315 | ||||||||
\(595\) | 31.5923 | 1.29516 | ||||||||
\(596\) | 0.563397 | 0.0230777 | ||||||||
\(597\) | 4.51307 | 0.184707 | ||||||||
\(598\) | 1.63892 | 0.0670203 | ||||||||
\(599\) | 11.3198 | 0.462516 | 0.231258 | − | 0.972892i | \(-0.425716\pi\) | ||||
0.231258 | + | 0.972892i | \(0.425716\pi\) | |||||||
\(600\) | 10.5409 | 0.430329 | ||||||||
\(601\) | 3.30959 | 0.135001 | 0.0675005 | − | 0.997719i | \(-0.478498\pi\) | ||||
0.0675005 | + | 0.997719i | \(0.478498\pi\) | |||||||
\(602\) | 2.83001 | 0.115342 | ||||||||
\(603\) | 19.8132 | 0.806856 | ||||||||
\(604\) | −11.8749 | −0.483184 | ||||||||
\(605\) | −31.9940 | −1.30074 | ||||||||
\(606\) | 3.15341 | 0.128098 | ||||||||
\(607\) | −40.5505 | −1.64590 | −0.822948 | − | 0.568117i | \(-0.807672\pi\) | ||||
−0.822948 | + | 0.568117i | \(0.807672\pi\) | |||||||
\(608\) | 4.88581 | 0.198146 | ||||||||
\(609\) | 15.5799 | 0.631328 | ||||||||
\(610\) | 19.4288 | 0.786650 | ||||||||
\(611\) | 2.48161 | 0.100395 | ||||||||
\(612\) | −14.5720 | −0.589037 | ||||||||
\(613\) | 30.2864 | 1.22325 | 0.611627 | − | 0.791146i | \(-0.290515\pi\) | ||||
0.611627 | + | 0.791146i | \(0.290515\pi\) | |||||||
\(614\) | 12.2995 | 0.496366 | ||||||||
\(615\) | 41.9380 | 1.69110 | ||||||||
\(616\) | 14.8256 | 0.597341 | ||||||||
\(617\) | −38.4514 | −1.54799 | −0.773997 | − | 0.633189i | \(-0.781746\pi\) | ||||
−0.773997 | + | 0.633189i | \(0.781746\pi\) | |||||||
\(618\) | −39.1815 | −1.57611 | ||||||||
\(619\) | −42.1015 | −1.69220 | −0.846102 | − | 0.533021i | \(-0.821057\pi\) | ||||
−0.846102 | + | 0.533021i | \(0.821057\pi\) | |||||||
\(620\) | −15.4720 | −0.621371 | ||||||||
\(621\) | −29.4892 | −1.18336 | ||||||||
\(622\) | −31.9397 | −1.28066 | ||||||||
\(623\) | −29.4113 | −1.17834 | ||||||||
\(624\) | 0.561900 | 0.0224940 | ||||||||
\(625\) | −29.3391 | −1.17356 | ||||||||
\(626\) | −26.3933 | −1.05489 | ||||||||
\(627\) | −61.8437 | −2.46980 | ||||||||
\(628\) | −18.7754 | −0.749219 | ||||||||
\(629\) | 0.936334 | 0.0373341 | ||||||||
\(630\) | 41.4315 | 1.65067 | ||||||||
\(631\) | 31.5677 | 1.25669 | 0.628345 | − | 0.777935i | \(-0.283733\pi\) | ||||
0.628345 | + | 0.777935i | \(0.283733\pi\) | |||||||
\(632\) | −5.85921 | −0.233067 | ||||||||
\(633\) | −8.24752 | −0.327810 | ||||||||
\(634\) | −19.1032 | −0.758684 | ||||||||
\(635\) | −54.4823 | −2.16206 | ||||||||
\(636\) | 16.7586 | 0.664523 | ||||||||
\(637\) | −0.644188 | −0.0255236 | ||||||||
\(638\) | −8.41264 | −0.333060 | ||||||||
\(639\) | 7.52163 | 0.297551 | ||||||||
\(640\) | 2.98033 | 0.117808 | ||||||||
\(641\) | −8.82845 | −0.348703 | −0.174351 | − | 0.984683i | \(-0.555783\pi\) | ||||
−0.174351 | + | 0.984683i | \(0.555783\pi\) | |||||||
\(642\) | −16.3413 | −0.644941 | ||||||||
\(643\) | −24.2926 | −0.958006 | −0.479003 | − | 0.877813i | \(-0.659002\pi\) | ||||
−0.479003 | + | 0.877813i | \(0.659002\pi\) | |||||||
\(644\) | 25.1832 | 0.992356 | ||||||||
\(645\) | −7.20108 | −0.283542 | ||||||||
\(646\) | −16.2862 | −0.640773 | ||||||||
\(647\) | −11.9308 | −0.469047 | −0.234524 | − | 0.972110i | \(-0.575353\pi\) | ||||
−0.234524 | + | 0.972110i | \(0.575353\pi\) | |||||||
\(648\) | 3.00429 | 0.118020 | ||||||||
\(649\) | 48.4856 | 1.90323 | ||||||||
\(650\) | 0.803483 | 0.0315152 | ||||||||
\(651\) | −44.8223 | −1.75672 | ||||||||
\(652\) | 5.27573 | 0.206614 | ||||||||
\(653\) | −22.6933 | −0.888056 | −0.444028 | − | 0.896013i | \(-0.646451\pi\) | ||||
−0.444028 | + | 0.896013i | \(0.646451\pi\) | |||||||
\(654\) | 7.54264 | 0.294941 | ||||||||
\(655\) | 34.0895 | 1.33199 | ||||||||
\(656\) | 5.18280 | 0.202354 | ||||||||
\(657\) | 48.0960 | 1.87640 | ||||||||
\(658\) | 38.1317 | 1.48653 | ||||||||
\(659\) | 1.43771 | 0.0560053 | 0.0280026 | − | 0.999608i | \(-0.491085\pi\) | ||||
0.0280026 | + | 0.999608i | \(0.491085\pi\) | |||||||
\(660\) | −37.7245 | −1.46842 | ||||||||
\(661\) | −0.449770 | −0.0174940 | −0.00874701 | − | 0.999962i | \(-0.502784\pi\) | ||||
−0.00874701 | + | 0.999962i | \(0.502784\pi\) | |||||||
\(662\) | −33.7805 | −1.31291 | ||||||||
\(663\) | −1.87302 | −0.0727422 | ||||||||
\(664\) | −8.19014 | −0.317839 | ||||||||
\(665\) | 46.3056 | 1.79565 | ||||||||
\(666\) | 1.22795 | 0.0475820 | ||||||||
\(667\) | −14.2899 | −0.553308 | ||||||||
\(668\) | 9.39964 | 0.363683 | ||||||||
\(669\) | 28.1217 | 1.08725 | ||||||||
\(670\) | 13.5078 | 0.521852 | ||||||||
\(671\) | −30.3922 | −1.17328 | ||||||||
\(672\) | 8.63399 | 0.333064 | ||||||||
\(673\) | −6.07289 | −0.234093 | −0.117046 | − | 0.993126i | \(-0.537343\pi\) | ||||
−0.117046 | + | 0.993126i | \(0.537343\pi\) | |||||||
\(674\) | 34.1726 | 1.31628 | ||||||||
\(675\) | −14.4571 | −0.556456 | ||||||||
\(676\) | −12.9572 | −0.498353 | ||||||||
\(677\) | 31.6368 | 1.21590 | 0.607950 | − | 0.793976i | \(-0.291992\pi\) | ||||
0.607950 | + | 0.793976i | \(0.291992\pi\) | |||||||
\(678\) | 27.1020 | 1.04085 | ||||||||
\(679\) | 25.4542 | 0.976842 | ||||||||
\(680\) | −9.93456 | −0.380973 | ||||||||
\(681\) | −18.3837 | −0.704464 | ||||||||
\(682\) | 24.2026 | 0.926766 | ||||||||
\(683\) | −4.71850 | −0.180548 | −0.0902742 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902742 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(684\) | −21.3585 | −0.816661 | ||||||||
\(685\) | −53.0363 | −2.02641 | ||||||||
\(686\) | 12.3619 | 0.471979 | ||||||||
\(687\) | −19.8206 | −0.756201 | ||||||||
\(688\) | −0.889927 | −0.0339282 | ||||||||
\(689\) | 1.27744 | 0.0486665 | ||||||||
\(690\) | −64.0798 | −2.43947 | ||||||||
\(691\) | −1.92218 | −0.0731232 | −0.0365616 | − | 0.999331i | \(-0.511641\pi\) | ||||
−0.0365616 | + | 0.999331i | \(0.511641\pi\) | |||||||
\(692\) | −3.38774 | −0.128782 | ||||||||
\(693\) | −64.8107 | −2.46196 | ||||||||
\(694\) | 25.1976 | 0.956487 | ||||||||
\(695\) | −24.4485 | −0.927386 | ||||||||
\(696\) | −4.89927 | −0.185706 | ||||||||
\(697\) | −17.2762 | −0.654384 | ||||||||
\(698\) | −9.19423 | −0.348007 | ||||||||
\(699\) | 69.4285 | 2.62603 | ||||||||
\(700\) | 12.3461 | 0.466639 | ||||||||
\(701\) | −4.67864 | −0.176710 | −0.0883549 | − | 0.996089i | \(-0.528161\pi\) | ||||
−0.0883549 | + | 0.996089i | \(0.528161\pi\) | |||||||
\(702\) | −0.770664 | −0.0290868 | ||||||||
\(703\) | 1.37241 | 0.0517613 | ||||||||
\(704\) | −4.66208 | −0.175709 | ||||||||
\(705\) | −97.0280 | −3.65429 | ||||||||
\(706\) | 6.61158 | 0.248830 | ||||||||
\(707\) | 3.69346 | 0.138907 | ||||||||
\(708\) | 28.2365 | 1.06119 | ||||||||
\(709\) | 20.9711 | 0.787587 | 0.393794 | − | 0.919199i | \(-0.371162\pi\) | ||||
0.393794 | + | 0.919199i | \(0.371162\pi\) | |||||||
\(710\) | 5.12793 | 0.192448 | ||||||||
\(711\) | 25.6137 | 0.960590 | ||||||||
\(712\) | 9.24870 | 0.346610 | ||||||||
\(713\) | 41.1111 | 1.53962 | ||||||||
\(714\) | −28.7804 | −1.07708 | ||||||||
\(715\) | −2.87557 | −0.107540 | ||||||||
\(716\) | 12.7495 | 0.476472 | ||||||||
\(717\) | −51.9278 | −1.93928 | ||||||||
\(718\) | 3.95873 | 0.147738 | ||||||||
\(719\) | −33.4944 | −1.24913 | −0.624565 | − | 0.780973i | \(-0.714724\pi\) | ||||
−0.624565 | + | 0.780973i | \(0.714724\pi\) | |||||||
\(720\) | −13.0286 | −0.485548 | ||||||||
\(721\) | −45.8917 | −1.70910 | ||||||||
\(722\) | −4.87110 | −0.181284 | ||||||||
\(723\) | 18.4567 | 0.686411 | ||||||||
\(724\) | 8.33225 | 0.309666 | ||||||||
\(725\) | −7.00566 | −0.260184 | ||||||||
\(726\) | 29.1462 | 1.08172 | ||||||||
\(727\) | 16.2573 | 0.602950 | 0.301475 | − | 0.953474i | \(-0.402521\pi\) | ||||
0.301475 | + | 0.953474i | \(0.402521\pi\) | |||||||
\(728\) | 0.658131 | 0.0243920 | ||||||||
\(729\) | −43.4643 | −1.60979 | ||||||||
\(730\) | 32.7898 | 1.21361 | ||||||||
\(731\) | 2.96646 | 0.109719 | ||||||||
\(732\) | −17.6995 | −0.654192 | ||||||||
\(733\) | −11.0712 | −0.408925 | −0.204462 | − | 0.978874i | \(-0.565545\pi\) | ||||
−0.204462 | + | 0.978874i | \(0.565545\pi\) | |||||||
\(734\) | 21.0053 | 0.775319 | ||||||||
\(735\) | 25.1870 | 0.929035 | ||||||||
\(736\) | −7.91913 | −0.291903 | ||||||||
\(737\) | −21.1301 | −0.778336 | ||||||||
\(738\) | −22.6568 | −0.834008 | ||||||||
\(739\) | 0.171298 | 0.00630131 | 0.00315065 | − | 0.999995i | \(-0.498997\pi\) | ||||
0.00315065 | + | 0.999995i | \(0.498997\pi\) | |||||||
\(740\) | 0.837164 | 0.0307748 | ||||||||
\(741\) | −2.74533 | −0.100852 | ||||||||
\(742\) | 19.6287 | 0.720594 | ||||||||
\(743\) | −38.9687 | −1.42962 | −0.714811 | − | 0.699318i | \(-0.753487\pi\) | ||||
−0.714811 | + | 0.699318i | \(0.753487\pi\) | |||||||
\(744\) | 14.0949 | 0.516743 | ||||||||
\(745\) | −1.67911 | −0.0615179 | ||||||||
\(746\) | 12.4902 | 0.457297 | ||||||||
\(747\) | 35.8035 | 1.30998 | ||||||||
\(748\) | 15.5405 | 0.568216 | ||||||||
\(749\) | −19.1400 | −0.699359 | ||||||||
\(750\) | 9.04360 | 0.330226 | ||||||||
\(751\) | 12.3065 | 0.449070 | 0.224535 | − | 0.974466i | \(-0.427914\pi\) | ||||
0.224535 | + | 0.974466i | \(0.427914\pi\) | |||||||
\(752\) | −11.9910 | −0.437265 | ||||||||
\(753\) | −36.6462 | −1.33546 | ||||||||
\(754\) | −0.373450 | −0.0136002 | ||||||||
\(755\) | 35.3912 | 1.28802 | ||||||||
\(756\) | −11.8418 | −0.430683 | ||||||||
\(757\) | −2.40537 | −0.0874246 | −0.0437123 | − | 0.999044i | \(-0.513918\pi\) | ||||
−0.0437123 | + | 0.999044i | \(0.513918\pi\) | |||||||
\(758\) | −14.1273 | −0.513127 | ||||||||
\(759\) | 100.239 | 3.63844 | ||||||||
\(760\) | −14.5613 | −0.528195 | ||||||||
\(761\) | −15.1862 | −0.550501 | −0.275251 | − | 0.961373i | \(-0.588761\pi\) | ||||
−0.275251 | + | 0.961373i | \(0.588761\pi\) | |||||||
\(762\) | 49.6329 | 1.79801 | ||||||||
\(763\) | 8.83441 | 0.319827 | ||||||||
\(764\) | 15.5119 | 0.561201 | ||||||||
\(765\) | 43.4293 | 1.57019 | ||||||||
\(766\) | 34.1908 | 1.23536 | ||||||||
\(767\) | 2.15235 | 0.0777167 | ||||||||
\(768\) | −2.71506 | −0.0979712 | ||||||||
\(769\) | 15.8385 | 0.571151 | 0.285576 | − | 0.958356i | \(-0.407815\pi\) | ||||
0.285576 | + | 0.958356i | \(0.407815\pi\) | |||||||
\(770\) | −44.1853 | −1.59233 | ||||||||
\(771\) | 50.2247 | 1.80880 | ||||||||
\(772\) | 20.2688 | 0.729491 | ||||||||
\(773\) | 24.4928 | 0.880944 | 0.440472 | − | 0.897766i | \(-0.354811\pi\) | ||||
0.440472 | + | 0.897766i | \(0.354811\pi\) | |||||||
\(774\) | 3.89035 | 0.139836 | ||||||||
\(775\) | 20.1548 | 0.723983 | ||||||||
\(776\) | −8.00436 | −0.287340 | ||||||||
\(777\) | 2.42526 | 0.0870057 | ||||||||
\(778\) | 16.7005 | 0.598743 | ||||||||
\(779\) | −25.3222 | −0.907261 | ||||||||
\(780\) | −1.67465 | −0.0599620 | ||||||||
\(781\) | −8.02155 | −0.287034 | ||||||||
\(782\) | 26.3974 | 0.943971 | ||||||||
\(783\) | 6.71951 | 0.240136 | ||||||||
\(784\) | 3.11267 | 0.111167 | ||||||||
\(785\) | 55.9568 | 1.99719 | ||||||||
\(786\) | −31.0553 | −1.10770 | ||||||||
\(787\) | −43.5080 | −1.55089 | −0.775446 | − | 0.631413i | \(-0.782475\pi\) | ||||
−0.775446 | + | 0.631413i | \(0.782475\pi\) | |||||||
\(788\) | 19.8796 | 0.708181 | ||||||||
\(789\) | −55.8847 | −1.98955 | ||||||||
\(790\) | 17.4624 | 0.621284 | ||||||||
\(791\) | 31.7435 | 1.12867 | ||||||||
\(792\) | 20.3805 | 0.724188 | ||||||||
\(793\) | −1.34916 | −0.0479099 | ||||||||
\(794\) | −3.64414 | −0.129326 | ||||||||
\(795\) | −49.9463 | −1.77141 | ||||||||
\(796\) | −1.66224 | −0.0589164 | ||||||||
\(797\) | 0.437157 | 0.0154849 | 0.00774245 | − | 0.999970i | \(-0.497535\pi\) | ||||
0.00774245 | + | 0.999970i | \(0.497535\pi\) | |||||||
\(798\) | −42.1840 | −1.49330 | ||||||||
\(799\) | 39.9704 | 1.41405 | ||||||||
\(800\) | −3.88237 | −0.137263 | ||||||||
\(801\) | −40.4310 | −1.42856 | ||||||||
\(802\) | 19.8567 | 0.701165 | ||||||||
\(803\) | −51.2926 | −1.81008 | ||||||||
\(804\) | −12.3055 | −0.433982 | ||||||||
\(805\) | −75.0542 | −2.64531 | ||||||||
\(806\) | 1.07439 | 0.0378438 | ||||||||
\(807\) | −82.7580 | −2.91322 | ||||||||
\(808\) | −1.16145 | −0.0408597 | ||||||||
\(809\) | −20.4158 | −0.717783 | −0.358891 | − | 0.933379i | \(-0.616845\pi\) | ||||
−0.358891 | + | 0.933379i | \(0.616845\pi\) | |||||||
\(810\) | −8.95379 | −0.314604 | ||||||||
\(811\) | −7.47920 | −0.262630 | −0.131315 | − | 0.991341i | \(-0.541920\pi\) | ||||
−0.131315 | + | 0.991341i | \(0.541920\pi\) | |||||||
\(812\) | −5.73832 | −0.201376 | ||||||||
\(813\) | 7.44571 | 0.261133 | ||||||||
\(814\) | −1.30956 | −0.0459002 | ||||||||
\(815\) | −15.7234 | −0.550768 | ||||||||
\(816\) | 9.05031 | 0.316824 | ||||||||
\(817\) | 4.34801 | 0.152118 | ||||||||
\(818\) | 18.5685 | 0.649231 | ||||||||
\(819\) | −2.87704 | −0.100532 | ||||||||
\(820\) | −15.4465 | −0.539414 | ||||||||
\(821\) | −34.6098 | −1.20789 | −0.603945 | − | 0.797026i | \(-0.706405\pi\) | ||||
−0.603945 | + | 0.797026i | \(0.706405\pi\) | |||||||
\(822\) | 48.3156 | 1.68520 | ||||||||
\(823\) | 8.69650 | 0.303141 | 0.151570 | − | 0.988446i | \(-0.451567\pi\) | ||||
0.151570 | + | 0.988446i | \(0.451567\pi\) | |||||||
\(824\) | 14.4312 | 0.502734 | ||||||||
\(825\) | 49.1424 | 1.71092 | ||||||||
\(826\) | 33.0724 | 1.15073 | ||||||||
\(827\) | −23.8248 | −0.828470 | −0.414235 | − | 0.910170i | \(-0.635951\pi\) | ||||
−0.414235 | + | 0.910170i | \(0.635951\pi\) | |||||||
\(828\) | 34.6187 | 1.20308 | ||||||||
\(829\) | −21.9911 | −0.763781 | −0.381890 | − | 0.924208i | \(-0.624727\pi\) | ||||
−0.381890 | + | 0.924208i | \(0.624727\pi\) | |||||||
\(830\) | 24.4093 | 0.847260 | ||||||||
\(831\) | −21.1897 | −0.735062 | ||||||||
\(832\) | −0.206957 | −0.00717494 | ||||||||
\(833\) | −10.3757 | −0.359496 | ||||||||
\(834\) | 22.2724 | 0.771231 | ||||||||
\(835\) | −28.0140 | −0.969466 | ||||||||
\(836\) | 22.7780 | 0.787795 | ||||||||
\(837\) | −19.3316 | −0.668197 | ||||||||
\(838\) | 14.9158 | 0.515257 | ||||||||
\(839\) | 57.0136 | 1.96833 | 0.984165 | − | 0.177257i | \(-0.0567225\pi\) | ||||
0.984165 | + | 0.177257i | \(0.0567225\pi\) | |||||||
\(840\) | −25.7322 | −0.887844 | ||||||||
\(841\) | −25.7438 | −0.887719 | ||||||||
\(842\) | 25.5757 | 0.881398 | ||||||||
\(843\) | 36.9496 | 1.27261 | ||||||||
\(844\) | 3.03770 | 0.104562 | ||||||||
\(845\) | 38.6166 | 1.32845 | ||||||||
\(846\) | 52.4188 | 1.80220 | ||||||||
\(847\) | 34.1379 | 1.17299 | ||||||||
\(848\) | −6.17248 | −0.211964 | ||||||||
\(849\) | −23.8580 | −0.818806 | ||||||||
\(850\) | 12.9414 | 0.443886 | ||||||||
\(851\) | −2.22446 | −0.0762534 | ||||||||
\(852\) | −4.67151 | −0.160043 | ||||||||
\(853\) | 54.1597 | 1.85439 | 0.927196 | − | 0.374575i | \(-0.122211\pi\) | ||||
0.927196 | + | 0.374575i | \(0.122211\pi\) | |||||||
\(854\) | −20.7307 | −0.709392 | ||||||||
\(855\) | 63.6553 | 2.17697 | ||||||||
\(856\) | 6.01878 | 0.205718 | ||||||||
\(857\) | −54.2068 | −1.85167 | −0.925835 | − | 0.377929i | \(-0.876636\pi\) | ||||
−0.925835 | + | 0.377929i | \(0.876636\pi\) | |||||||
\(858\) | 2.61962 | 0.0894325 | ||||||||
\(859\) | 30.7914 | 1.05059 | 0.525295 | − | 0.850920i | \(-0.323955\pi\) | ||||
0.525295 | + | 0.850920i | \(0.323955\pi\) | |||||||
\(860\) | 2.65228 | 0.0904419 | ||||||||
\(861\) | −44.7483 | −1.52502 | ||||||||
\(862\) | 2.65323 | 0.0903695 | ||||||||
\(863\) | 6.74771 | 0.229695 | 0.114847 | − | 0.993383i | \(-0.463362\pi\) | ||||
0.114847 | + | 0.993383i | \(0.463362\pi\) | |||||||
\(864\) | 3.72379 | 0.126686 | ||||||||
\(865\) | 10.0966 | 0.343294 | ||||||||
\(866\) | 12.7148 | 0.432067 | ||||||||
\(867\) | 15.9879 | 0.542977 | ||||||||
\(868\) | 16.5088 | 0.560345 | ||||||||
\(869\) | −27.3161 | −0.926636 | ||||||||
\(870\) | 14.6014 | 0.495035 | ||||||||
\(871\) | −0.937995 | −0.0317827 | ||||||||
\(872\) | −2.77808 | −0.0940776 | ||||||||
\(873\) | 34.9913 | 1.18428 | ||||||||
\(874\) | 38.6913 | 1.30875 | ||||||||
\(875\) | 10.5924 | 0.358089 | ||||||||
\(876\) | −29.8713 | −1.00926 | ||||||||
\(877\) | −3.33844 | −0.112731 | −0.0563655 | − | 0.998410i | \(-0.517951\pi\) | ||||
−0.0563655 | + | 0.998410i | \(0.517951\pi\) | |||||||
\(878\) | 10.0130 | 0.337923 | ||||||||
\(879\) | 9.91847 | 0.334542 | ||||||||
\(880\) | 13.8946 | 0.468385 | ||||||||
\(881\) | 10.0319 | 0.337985 | 0.168992 | − | 0.985617i | \(-0.445949\pi\) | ||||
0.168992 | + | 0.985617i | \(0.445949\pi\) | |||||||
\(882\) | −13.6071 | −0.458176 | ||||||||
\(883\) | −3.32455 | −0.111880 | −0.0559400 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559400 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(884\) | 0.689865 | 0.0232027 | ||||||||
\(885\) | −84.1542 | −2.82881 | ||||||||
\(886\) | −15.6462 | −0.525646 | ||||||||
\(887\) | 43.8304 | 1.47168 | 0.735841 | − | 0.677155i | \(-0.236787\pi\) | ||||
0.735841 | + | 0.677155i | \(0.236787\pi\) | |||||||
\(888\) | −0.762650 | −0.0255929 | ||||||||
\(889\) | 58.1331 | 1.94972 | ||||||||
\(890\) | −27.5642 | −0.923954 | ||||||||
\(891\) | 14.0063 | 0.469228 | ||||||||
\(892\) | −10.3577 | −0.346801 | ||||||||
\(893\) | 58.5855 | 1.96049 | ||||||||
\(894\) | 1.52966 | 0.0511594 | ||||||||
\(895\) | −37.9978 | −1.27012 | ||||||||
\(896\) | −3.18004 | −0.106238 | ||||||||
\(897\) | 4.44976 | 0.148573 | ||||||||
\(898\) | −1.71080 | −0.0570902 | ||||||||
\(899\) | −9.36773 | −0.312431 | ||||||||
\(900\) | 16.9719 | 0.565730 | ||||||||
\(901\) | 20.5752 | 0.685459 | ||||||||
\(902\) | 24.1627 | 0.804529 | ||||||||
\(903\) | 7.68363 | 0.255695 | ||||||||
\(904\) | −9.98211 | −0.332000 | ||||||||
\(905\) | −24.8329 | −0.825472 | ||||||||
\(906\) | −32.2411 | −1.07114 | ||||||||
\(907\) | −12.2466 | −0.406641 | −0.203321 | − | 0.979112i | \(-0.565173\pi\) | ||||
−0.203321 | + | 0.979112i | \(0.565173\pi\) | |||||||
\(908\) | 6.77101 | 0.224704 | ||||||||
\(909\) | 5.07732 | 0.168404 | ||||||||
\(910\) | −1.96145 | −0.0650214 | ||||||||
\(911\) | 33.0019 | 1.09340 | 0.546701 | − | 0.837328i | \(-0.315883\pi\) | ||||
0.546701 | + | 0.837328i | \(0.315883\pi\) | |||||||
\(912\) | 13.2652 | 0.439256 | ||||||||
\(913\) | −38.1831 | −1.26368 | ||||||||
\(914\) | 28.2034 | 0.932884 | ||||||||
\(915\) | 52.7504 | 1.74387 | ||||||||
\(916\) | 7.30024 | 0.241207 | ||||||||
\(917\) | −36.3738 | −1.20117 | ||||||||
\(918\) | −12.4128 | −0.409683 | ||||||||
\(919\) | 20.4217 | 0.673649 | 0.336825 | − | 0.941567i | \(-0.390647\pi\) | ||||
0.336825 | + | 0.941567i | \(0.390647\pi\) | |||||||
\(920\) | 23.6016 | 0.778123 | ||||||||
\(921\) | 33.3938 | 1.10036 | ||||||||
\(922\) | −19.2700 | −0.634625 | ||||||||
\(923\) | −0.356088 | −0.0117208 | ||||||||
\(924\) | 40.2524 | 1.32421 | ||||||||
\(925\) | −1.09054 | −0.0358569 | ||||||||
\(926\) | 32.2347 | 1.05930 | ||||||||
\(927\) | −63.0864 | −2.07203 | ||||||||
\(928\) | 1.80448 | 0.0592350 | ||||||||
\(929\) | −3.02829 | −0.0993551 | −0.0496775 | − | 0.998765i | \(-0.515819\pi\) | ||||
−0.0496775 | + | 0.998765i | \(0.515819\pi\) | |||||||
\(930\) | −42.0074 | −1.37748 | ||||||||
\(931\) | −15.2079 | −0.498418 | ||||||||
\(932\) | −25.5717 | −0.837628 | ||||||||
\(933\) | −86.7180 | −2.83902 | ||||||||
\(934\) | 32.8624 | 1.07529 | ||||||||
\(935\) | −46.3158 | −1.51469 | ||||||||
\(936\) | 0.904719 | 0.0295717 | ||||||||
\(937\) | −5.39320 | −0.176188 | −0.0880941 | − | 0.996112i | \(-0.528078\pi\) | ||||
−0.0880941 | + | 0.996112i | \(0.528078\pi\) | |||||||
\(938\) | −14.4130 | −0.470600 | ||||||||
\(939\) | −71.6592 | −2.33851 | ||||||||
\(940\) | 35.7370 | 1.16561 | ||||||||
\(941\) | −12.8638 | −0.419347 | −0.209674 | − | 0.977771i | \(-0.567240\pi\) | ||||
−0.209674 | + | 0.977771i | \(0.567240\pi\) | |||||||
\(942\) | −50.9762 | −1.66090 | ||||||||
\(943\) | 41.0433 | 1.33655 | ||||||||
\(944\) | −10.4000 | −0.338490 | ||||||||
\(945\) | 35.2925 | 1.14807 | ||||||||
\(946\) | −4.14892 | −0.134893 | ||||||||
\(947\) | 10.8217 | 0.351657 | 0.175828 | − | 0.984421i | \(-0.443740\pi\) | ||||
0.175828 | + | 0.984421i | \(0.443740\pi\) | |||||||
\(948\) | −15.9081 | −0.516671 | ||||||||
\(949\) | −2.27696 | −0.0739131 | ||||||||
\(950\) | 18.9685 | 0.615420 | ||||||||
\(951\) | −51.8662 | −1.68188 | ||||||||
\(952\) | 10.6003 | 0.343557 | ||||||||
\(953\) | −10.2430 | −0.331803 | −0.165902 | − | 0.986142i | \(-0.553053\pi\) | ||||
−0.165902 | + | 0.986142i | \(0.553053\pi\) | |||||||
\(954\) | 26.9832 | 0.873613 | ||||||||
\(955\) | −46.2306 | −1.49599 | ||||||||
\(956\) | 19.1259 | 0.618575 | ||||||||
\(957\) | −22.8408 | −0.738338 | ||||||||
\(958\) | 4.90869 | 0.158593 | ||||||||
\(959\) | 56.5902 | 1.82739 | ||||||||
\(960\) | 8.09177 | 0.261161 | ||||||||
\(961\) | −4.04966 | −0.130634 | ||||||||
\(962\) | −0.0581335 | −0.00187430 | ||||||||
\(963\) | −26.3113 | −0.847870 | ||||||||
\(964\) | −6.79789 | −0.218945 | ||||||||
\(965\) | −60.4078 | −1.94460 | ||||||||
\(966\) | 68.3737 | 2.19989 | ||||||||
\(967\) | −10.7481 | −0.345635 | −0.172818 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172818 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(968\) | −10.7350 | −0.345037 | ||||||||
\(969\) | −44.2180 | −1.42049 | ||||||||
\(970\) | 23.8556 | 0.765958 | ||||||||
\(971\) | −30.7645 | −0.987280 | −0.493640 | − | 0.869666i | \(-0.664334\pi\) | ||||
−0.493640 | + | 0.869666i | \(0.664334\pi\) | |||||||
\(972\) | 19.3282 | 0.619952 | ||||||||
\(973\) | 26.0868 | 0.836305 | ||||||||
\(974\) | −7.40585 | −0.237299 | ||||||||
\(975\) | 2.18150 | 0.0698640 | ||||||||
\(976\) | 6.51902 | 0.208669 | ||||||||
\(977\) | 27.7488 | 0.887764 | 0.443882 | − | 0.896085i | \(-0.353601\pi\) | ||||
0.443882 | + | 0.896085i | \(0.353601\pi\) | |||||||
\(978\) | 14.3239 | 0.458028 | ||||||||
\(979\) | 43.1182 | 1.37806 | ||||||||
\(980\) | −9.27678 | −0.296336 | ||||||||
\(981\) | 12.1445 | 0.387743 | ||||||||
\(982\) | 19.5284 | 0.623177 | ||||||||
\(983\) | 18.6357 | 0.594388 | 0.297194 | − | 0.954817i | \(-0.403949\pi\) | ||||
0.297194 | + | 0.954817i | \(0.403949\pi\) | |||||||
\(984\) | 14.0716 | 0.448586 | ||||||||
\(985\) | −59.2478 | −1.88779 | ||||||||
\(986\) | −6.01501 | −0.191557 | ||||||||
\(987\) | 103.530 | 3.29539 | ||||||||
\(988\) | 1.01115 | 0.0321690 | ||||||||
\(989\) | −7.04745 | −0.224096 | ||||||||
\(990\) | −60.7405 | −1.93046 | ||||||||
\(991\) | 12.5523 | 0.398736 | 0.199368 | − | 0.979925i | \(-0.436111\pi\) | ||||
0.199368 | + | 0.979925i | \(0.436111\pi\) | |||||||
\(992\) | −5.19137 | −0.164826 | ||||||||
\(993\) | −91.7159 | −2.91052 | ||||||||
\(994\) | −5.47156 | −0.173547 | ||||||||
\(995\) | 4.95401 | 0.157053 | ||||||||
\(996\) | −22.2367 | −0.704597 | ||||||||
\(997\) | −18.7170 | −0.592774 | −0.296387 | − | 0.955068i | \(-0.595782\pi\) | ||||
−0.296387 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(998\) | −33.7657 | −1.06883 | ||||||||
\(999\) | 1.04600 | 0.0330940 |
(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 | 8038.2.a.c.1.10 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8038.2.a.c.1.10 | ✓ | 84 | 1.1 | even | 1 | trivial |