Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53517 | −1.79263 | −0.896317 | − | 0.443414i | \(-0.853767\pi\) | ||||
−0.896317 | + | 0.443414i | \(0.853767\pi\) | |||||||
\(3\) | 1.42230 | 0.821163 | 0.410581 | − | 0.911824i | \(-0.365326\pi\) | ||||
0.410581 | + | 0.911824i | \(0.365326\pi\) | |||||||
\(4\) | 4.42707 | 2.21354 | ||||||||
\(5\) | −0.780530 | −0.349064 | −0.174532 | − | 0.984652i | \(-0.555841\pi\) | ||||
−0.174532 | + | 0.984652i | \(0.555841\pi\) | |||||||
\(6\) | −3.60576 | −1.47204 | ||||||||
\(7\) | 3.78955 | 1.43232 | 0.716158 | − | 0.697938i | \(-0.245899\pi\) | ||||
0.716158 | + | 0.697938i | \(0.245899\pi\) | |||||||
\(8\) | −6.15303 | −2.17543 | ||||||||
\(9\) | −0.977076 | −0.325692 | ||||||||
\(10\) | 1.97877 | 0.625743 | ||||||||
\(11\) | 2.96223 | 0.893145 | 0.446572 | − | 0.894748i | \(-0.352645\pi\) | ||||
0.446572 | + | 0.894748i | \(0.352645\pi\) | |||||||
\(12\) | 6.29660 | 1.81767 | ||||||||
\(13\) | 1.57830 | 0.437742 | 0.218871 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218871 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(14\) | −9.60715 | −2.56762 | ||||||||
\(15\) | −1.11014 | −0.286638 | ||||||||
\(16\) | 6.74482 | 1.68620 | ||||||||
\(17\) | 2.53935 | 0.615882 | 0.307941 | − | 0.951405i | \(-0.400360\pi\) | ||||
0.307941 | + | 0.951405i | \(0.400360\pi\) | |||||||
\(18\) | 2.47705 | 0.583846 | ||||||||
\(19\) | −7.71279 | −1.76944 | −0.884718 | − | 0.466127i | \(-0.845649\pi\) | ||||
−0.884718 | + | 0.466127i | \(0.845649\pi\) | |||||||
\(20\) | −3.45546 | −0.772665 | ||||||||
\(21\) | 5.38986 | 1.17616 | ||||||||
\(22\) | −7.50974 | −1.60108 | ||||||||
\(23\) | −4.09240 | −0.853324 | −0.426662 | − | 0.904411i | \(-0.640311\pi\) | ||||
−0.426662 | + | 0.904411i | \(0.640311\pi\) | |||||||
\(24\) | −8.75143 | −1.78638 | ||||||||
\(25\) | −4.39077 | −0.878155 | ||||||||
\(26\) | −4.00126 | −0.784711 | ||||||||
\(27\) | −5.65658 | −1.08861 | ||||||||
\(28\) | 16.7766 | 3.17048 | ||||||||
\(29\) | −0.435120 | −0.0807997 | −0.0403999 | − | 0.999184i | \(-0.512863\pi\) | ||||
−0.0403999 | + | 0.999184i | \(0.512863\pi\) | |||||||
\(30\) | 2.81440 | 0.513837 | ||||||||
\(31\) | −1.49375 | −0.268286 | −0.134143 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134143 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(32\) | −4.79318 | −0.847323 | ||||||||
\(33\) | 4.21316 | 0.733417 | ||||||||
\(34\) | −6.43767 | −1.10405 | ||||||||
\(35\) | −2.95786 | −0.499969 | ||||||||
\(36\) | −4.32558 | −0.720931 | ||||||||
\(37\) | −0.989655 | −0.162698 | −0.0813491 | − | 0.996686i | \(-0.525923\pi\) | ||||
−0.0813491 | + | 0.996686i | \(0.525923\pi\) | |||||||
\(38\) | 19.5532 | 3.17195 | ||||||||
\(39\) | 2.24481 | 0.359457 | ||||||||
\(40\) | 4.80263 | 0.759362 | ||||||||
\(41\) | 12.0832 | 1.88708 | 0.943540 | − | 0.331259i | \(-0.107473\pi\) | ||||
0.943540 | + | 0.331259i | \(0.107473\pi\) | |||||||
\(42\) | −13.6642 | −2.10843 | ||||||||
\(43\) | −0.490917 | −0.0748642 | −0.0374321 | − | 0.999299i | \(-0.511918\pi\) | ||||
−0.0374321 | + | 0.999299i | \(0.511918\pi\) | |||||||
\(44\) | 13.1140 | 1.97701 | ||||||||
\(45\) | 0.762637 | 0.113687 | ||||||||
\(46\) | 10.3749 | 1.52970 | ||||||||
\(47\) | −4.41763 | −0.644378 | −0.322189 | − | 0.946675i | \(-0.604419\pi\) | ||||
−0.322189 | + | 0.946675i | \(0.604419\pi\) | |||||||
\(48\) | 9.59313 | 1.38465 | ||||||||
\(49\) | 7.36070 | 1.05153 | ||||||||
\(50\) | 11.1313 | 1.57421 | ||||||||
\(51\) | 3.61170 | 0.505739 | ||||||||
\(52\) | 6.98725 | 0.968957 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 14.3404 | 1.95148 | ||||||||
\(55\) | −2.31211 | −0.311764 | ||||||||
\(56\) | −23.3172 | −3.11590 | ||||||||
\(57\) | −10.9699 | −1.45299 | ||||||||
\(58\) | 1.10310 | 0.144844 | ||||||||
\(59\) | 8.60279 | 1.11999 | 0.559994 | − | 0.828497i | \(-0.310803\pi\) | ||||
0.559994 | + | 0.828497i | \(0.310803\pi\) | |||||||
\(60\) | −4.91469 | −0.634483 | ||||||||
\(61\) | −9.88072 | −1.26510 | −0.632548 | − | 0.774521i | \(-0.717991\pi\) | ||||
−0.632548 | + | 0.774521i | \(0.717991\pi\) | |||||||
\(62\) | 3.78691 | 0.480939 | ||||||||
\(63\) | −3.70268 | −0.466494 | ||||||||
\(64\) | −1.33813 | −0.167266 | ||||||||
\(65\) | −1.23191 | −0.152800 | ||||||||
\(66\) | −10.6811 | −1.31475 | ||||||||
\(67\) | 3.59744 | 0.439497 | 0.219748 | − | 0.975557i | \(-0.429476\pi\) | ||||
0.219748 | + | 0.975557i | \(0.429476\pi\) | |||||||
\(68\) | 11.2419 | 1.36328 | ||||||||
\(69\) | −5.82060 | −0.700718 | ||||||||
\(70\) | 7.49866 | 0.896262 | ||||||||
\(71\) | −10.9407 | −1.29843 | −0.649213 | − | 0.760607i | \(-0.724902\pi\) | ||||
−0.649213 | + | 0.760607i | \(0.724902\pi\) | |||||||
\(72\) | 6.01198 | 0.708518 | ||||||||
\(73\) | −14.3983 | −1.68519 | −0.842595 | − | 0.538548i | \(-0.818973\pi\) | ||||
−0.842595 | + | 0.538548i | \(0.818973\pi\) | |||||||
\(74\) | 2.50894 | 0.291658 | ||||||||
\(75\) | −6.24498 | −0.721108 | ||||||||
\(76\) | −34.1451 | −3.91671 | ||||||||
\(77\) | 11.2255 | 1.27927 | ||||||||
\(78\) | −5.69097 | −0.644375 | ||||||||
\(79\) | −14.4925 | −1.63053 | −0.815267 | − | 0.579085i | \(-0.803410\pi\) | ||||
−0.815267 | + | 0.579085i | \(0.803410\pi\) | |||||||
\(80\) | −5.26453 | −0.588593 | ||||||||
\(81\) | −5.11410 | −0.568233 | ||||||||
\(82\) | −30.6329 | −3.38284 | ||||||||
\(83\) | 4.85792 | 0.533226 | 0.266613 | − | 0.963804i | \(-0.414095\pi\) | ||||
0.266613 | + | 0.963804i | \(0.414095\pi\) | |||||||
\(84\) | 23.8613 | 2.60348 | ||||||||
\(85\) | −1.98204 | −0.214982 | ||||||||
\(86\) | 1.24456 | 0.134204 | ||||||||
\(87\) | −0.618869 | −0.0663497 | ||||||||
\(88\) | −18.2267 | −1.94297 | ||||||||
\(89\) | −2.41218 | −0.255690 | −0.127845 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127845 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(90\) | −1.93341 | −0.203800 | ||||||||
\(91\) | 5.98105 | 0.626985 | ||||||||
\(92\) | −18.1173 | −1.88886 | ||||||||
\(93\) | −2.12456 | −0.220306 | ||||||||
\(94\) | 11.1994 | 1.15513 | ||||||||
\(95\) | 6.02006 | 0.617645 | ||||||||
\(96\) | −6.81732 | −0.695790 | ||||||||
\(97\) | 4.04116 | 0.410318 | 0.205159 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205159 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(98\) | −18.6606 | −1.88501 | ||||||||
\(99\) | −2.89432 | −0.290890 | ||||||||
\(100\) | −19.4383 | −1.94383 | ||||||||
\(101\) | −15.3894 | −1.53130 | −0.765650 | − | 0.643257i | \(-0.777583\pi\) | ||||
−0.765650 | + | 0.643257i | \(0.777583\pi\) | |||||||
\(102\) | −9.15627 | −0.906606 | ||||||||
\(103\) | 2.16277 | 0.213104 | 0.106552 | − | 0.994307i | \(-0.466019\pi\) | ||||
0.106552 | + | 0.994307i | \(0.466019\pi\) | |||||||
\(104\) | −9.71134 | −0.952275 | ||||||||
\(105\) | −4.20695 | −0.410556 | ||||||||
\(106\) | 2.53517 | 0.246237 | ||||||||
\(107\) | 12.7260 | 1.23026 | 0.615132 | − | 0.788424i | \(-0.289103\pi\) | ||||
0.615132 | + | 0.788424i | \(0.289103\pi\) | |||||||
\(108\) | −25.0421 | −2.40967 | ||||||||
\(109\) | −2.19302 | −0.210053 | −0.105027 | − | 0.994469i | \(-0.533493\pi\) | ||||
−0.105027 | + | 0.994469i | \(0.533493\pi\) | |||||||
\(110\) | 5.86157 | 0.558879 | ||||||||
\(111\) | −1.40758 | −0.133602 | ||||||||
\(112\) | 25.5598 | 2.41518 | ||||||||
\(113\) | 6.09623 | 0.573485 | 0.286742 | − | 0.958008i | \(-0.407428\pi\) | ||||
0.286742 | + | 0.958008i | \(0.407428\pi\) | |||||||
\(114\) | 27.8104 | 2.60469 | ||||||||
\(115\) | 3.19424 | 0.297864 | ||||||||
\(116\) | −1.92631 | −0.178853 | ||||||||
\(117\) | −1.54212 | −0.142569 | ||||||||
\(118\) | −21.8095 | −2.00773 | ||||||||
\(119\) | 9.62299 | 0.882138 | ||||||||
\(120\) | 6.83075 | 0.623559 | ||||||||
\(121\) | −2.22522 | −0.202293 | ||||||||
\(122\) | 25.0493 | 2.26785 | ||||||||
\(123\) | 17.1859 | 1.54960 | ||||||||
\(124\) | −6.61295 | −0.593861 | ||||||||
\(125\) | 7.32978 | 0.655595 | ||||||||
\(126\) | 9.38691 | 0.836252 | ||||||||
\(127\) | −20.5673 | −1.82506 | −0.912528 | − | 0.409014i | \(-0.865873\pi\) | ||||
−0.912528 | + | 0.409014i | \(0.865873\pi\) | |||||||
\(128\) | 12.9787 | 1.14717 | ||||||||
\(129\) | −0.698229 | −0.0614756 | ||||||||
\(130\) | 3.12310 | 0.273914 | ||||||||
\(131\) | −16.6749 | −1.45689 | −0.728446 | − | 0.685104i | \(-0.759757\pi\) | ||||
−0.728446 | + | 0.685104i | \(0.759757\pi\) | |||||||
\(132\) | 18.6520 | 1.62344 | ||||||||
\(133\) | −29.2280 | −2.53439 | ||||||||
\(134\) | −9.12011 | −0.787857 | ||||||||
\(135\) | 4.41513 | 0.379994 | ||||||||
\(136\) | −15.6247 | −1.33981 | ||||||||
\(137\) | 0.202869 | 0.0173323 | 0.00866613 | − | 0.999962i | \(-0.497241\pi\) | ||||
0.00866613 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(138\) | 14.7562 | 1.25613 | ||||||||
\(139\) | 14.4046 | 1.22178 | 0.610891 | − | 0.791715i | \(-0.290811\pi\) | ||||
0.610891 | + | 0.791715i | \(0.290811\pi\) | |||||||
\(140\) | −13.0947 | −1.10670 | ||||||||
\(141\) | −6.28318 | −0.529139 | ||||||||
\(142\) | 27.7366 | 2.32760 | ||||||||
\(143\) | 4.67528 | 0.390967 | ||||||||
\(144\) | −6.59020 | −0.549183 | ||||||||
\(145\) | 0.339624 | 0.0282043 | ||||||||
\(146\) | 36.5020 | 3.02093 | ||||||||
\(147\) | 10.4691 | 0.863476 | ||||||||
\(148\) | −4.38127 | −0.360138 | ||||||||
\(149\) | −3.90790 | −0.320148 | −0.160074 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160074 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(150\) | 15.8321 | 1.29268 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 47.4570 | 3.84927 | ||||||||
\(153\) | −2.48114 | −0.200588 | ||||||||
\(154\) | −28.4585 | −2.29325 | ||||||||
\(155\) | 1.16592 | 0.0936489 | ||||||||
\(156\) | 9.93793 | 0.795672 | ||||||||
\(157\) | 16.1979 | 1.29274 | 0.646368 | − | 0.763026i | \(-0.276287\pi\) | ||||
0.646368 | + | 0.763026i | \(0.276287\pi\) | |||||||
\(158\) | 36.7409 | 2.92295 | ||||||||
\(159\) | −1.42230 | −0.112795 | ||||||||
\(160\) | 3.74122 | 0.295769 | ||||||||
\(161\) | −15.5084 | −1.22223 | ||||||||
\(162\) | 12.9651 | 1.01863 | ||||||||
\(163\) | −13.8251 | −1.08287 | −0.541433 | − | 0.840744i | \(-0.682118\pi\) | ||||
−0.541433 | + | 0.840744i | \(0.682118\pi\) | |||||||
\(164\) | 53.4932 | 4.17712 | ||||||||
\(165\) | −3.28850 | −0.256009 | ||||||||
\(166\) | −12.3156 | −0.955879 | ||||||||
\(167\) | −7.81948 | −0.605089 | −0.302545 | − | 0.953135i | \(-0.597836\pi\) | ||||
−0.302545 | + | 0.953135i | \(0.597836\pi\) | |||||||
\(168\) | −33.1640 | −2.55866 | ||||||||
\(169\) | −10.5090 | −0.808382 | ||||||||
\(170\) | 5.02479 | 0.385384 | ||||||||
\(171\) | 7.53598 | 0.576291 | ||||||||
\(172\) | −2.17333 | −0.165714 | ||||||||
\(173\) | −22.6389 | −1.72120 | −0.860602 | − | 0.509277i | \(-0.829913\pi\) | ||||
−0.860602 | + | 0.509277i | \(0.829913\pi\) | |||||||
\(174\) | 1.56894 | 0.118941 | ||||||||
\(175\) | −16.6391 | −1.25779 | ||||||||
\(176\) | 19.9797 | 1.50602 | ||||||||
\(177\) | 12.2357 | 0.919693 | ||||||||
\(178\) | 6.11527 | 0.458359 | ||||||||
\(179\) | −17.3408 | −1.29611 | −0.648056 | − | 0.761592i | \(-0.724418\pi\) | ||||
−0.648056 | + | 0.761592i | \(0.724418\pi\) | |||||||
\(180\) | 3.37625 | 0.251651 | ||||||||
\(181\) | −10.8386 | −0.805624 | −0.402812 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402812 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(182\) | −15.1630 | −1.12395 | ||||||||
\(183\) | −14.0533 | −1.03885 | ||||||||
\(184\) | 25.1807 | 1.85634 | ||||||||
\(185\) | 0.772455 | 0.0567920 | ||||||||
\(186\) | 5.38611 | 0.394929 | ||||||||
\(187\) | 7.52212 | 0.550072 | ||||||||
\(188\) | −19.5572 | −1.42635 | ||||||||
\(189\) | −21.4359 | −1.55923 | ||||||||
\(190\) | −15.2619 | −1.10721 | ||||||||
\(191\) | 17.6961 | 1.28045 | 0.640224 | − | 0.768188i | \(-0.278842\pi\) | ||||
0.640224 | + | 0.768188i | \(0.278842\pi\) | |||||||
\(192\) | −1.90321 | −0.137352 | ||||||||
\(193\) | 17.8255 | 1.28310 | 0.641552 | − | 0.767079i | \(-0.278291\pi\) | ||||
0.641552 | + | 0.767079i | \(0.278291\pi\) | |||||||
\(194\) | −10.2450 | −0.735550 | ||||||||
\(195\) | −1.75214 | −0.125473 | ||||||||
\(196\) | 32.5863 | 2.32760 | ||||||||
\(197\) | −0.546629 | −0.0389457 | −0.0194728 | − | 0.999810i | \(-0.506199\pi\) | ||||
−0.0194728 | + | 0.999810i | \(0.506199\pi\) | |||||||
\(198\) | 7.33758 | 0.521459 | ||||||||
\(199\) | 3.54426 | 0.251246 | 0.125623 | − | 0.992078i | \(-0.459907\pi\) | ||||
0.125623 | + | 0.992078i | \(0.459907\pi\) | |||||||
\(200\) | 27.0166 | 1.91036 | ||||||||
\(201\) | 5.11662 | 0.360898 | ||||||||
\(202\) | 39.0146 | 2.74506 | ||||||||
\(203\) | −1.64891 | −0.115731 | ||||||||
\(204\) | 15.9893 | 1.11947 | ||||||||
\(205\) | −9.43130 | −0.658711 | ||||||||
\(206\) | −5.48298 | −0.382018 | ||||||||
\(207\) | 3.99858 | 0.277921 | ||||||||
\(208\) | 10.6454 | 0.738123 | ||||||||
\(209\) | −22.8470 | −1.58036 | ||||||||
\(210\) | 10.6653 | 0.735977 | ||||||||
\(211\) | −3.04660 | −0.209737 | −0.104868 | − | 0.994486i | \(-0.533442\pi\) | ||||
−0.104868 | + | 0.994486i | \(0.533442\pi\) | |||||||
\(212\) | −4.42707 | −0.304053 | ||||||||
\(213\) | −15.5610 | −1.06622 | ||||||||
\(214\) | −32.2624 | −2.20541 | ||||||||
\(215\) | 0.383176 | 0.0261324 | ||||||||
\(216\) | 34.8051 | 2.36819 | ||||||||
\(217\) | −5.66066 | −0.384270 | ||||||||
\(218\) | 5.55967 | 0.376549 | ||||||||
\(219\) | −20.4786 | −1.38381 | ||||||||
\(220\) | −10.2359 | −0.690101 | ||||||||
\(221\) | 4.00785 | 0.269597 | ||||||||
\(222\) | 3.56845 | 0.239499 | ||||||||
\(223\) | −5.88157 | −0.393859 | −0.196929 | − | 0.980418i | \(-0.563097\pi\) | ||||
−0.196929 | + | 0.980418i | \(0.563097\pi\) | |||||||
\(224\) | −18.1640 | −1.21363 | ||||||||
\(225\) | 4.29012 | 0.286008 | ||||||||
\(226\) | −15.4549 | −1.02805 | ||||||||
\(227\) | 10.2859 | 0.682696 | 0.341348 | − | 0.939937i | \(-0.389116\pi\) | ||||
0.341348 | + | 0.939937i | \(0.389116\pi\) | |||||||
\(228\) | −48.5644 | −3.21625 | ||||||||
\(229\) | −0.407756 | −0.0269453 | −0.0134726 | − | 0.999909i | \(-0.504289\pi\) | ||||
−0.0134726 | + | 0.999909i | \(0.504289\pi\) | |||||||
\(230\) | −8.09793 | −0.533962 | ||||||||
\(231\) | 15.9660 | 1.05048 | ||||||||
\(232\) | 2.67731 | 0.175774 | ||||||||
\(233\) | −18.0135 | −1.18010 | −0.590052 | − | 0.807365i | \(-0.700893\pi\) | ||||
−0.590052 | + | 0.807365i | \(0.700893\pi\) | |||||||
\(234\) | 3.90953 | 0.255574 | ||||||||
\(235\) | 3.44809 | 0.224929 | ||||||||
\(236\) | 38.0852 | 2.47913 | ||||||||
\(237\) | −20.6126 | −1.33893 | ||||||||
\(238\) | −24.3959 | −1.58135 | ||||||||
\(239\) | 26.3806 | 1.70642 | 0.853211 | − | 0.521567i | \(-0.174652\pi\) | ||||
0.853211 | + | 0.521567i | \(0.174652\pi\) | |||||||
\(240\) | −7.48772 | −0.483330 | ||||||||
\(241\) | −29.4002 | −1.89383 | −0.946916 | − | 0.321482i | \(-0.895819\pi\) | ||||
−0.946916 | + | 0.321482i | \(0.895819\pi\) | |||||||
\(242\) | 5.64131 | 0.362637 | ||||||||
\(243\) | 9.69598 | 0.621997 | ||||||||
\(244\) | −43.7427 | −2.80034 | ||||||||
\(245\) | −5.74525 | −0.367050 | ||||||||
\(246\) | −43.5691 | −2.77786 | ||||||||
\(247\) | −12.1731 | −0.774556 | ||||||||
\(248\) | 9.19111 | 0.583636 | ||||||||
\(249\) | 6.90939 | 0.437865 | ||||||||
\(250\) | −18.5822 | −1.17524 | ||||||||
\(251\) | 13.3300 | 0.841381 | 0.420690 | − | 0.907204i | \(-0.361788\pi\) | ||||
0.420690 | + | 0.907204i | \(0.361788\pi\) | |||||||
\(252\) | −16.3920 | −1.03260 | ||||||||
\(253\) | −12.1226 | −0.762142 | ||||||||
\(254\) | 52.1416 | 3.27166 | ||||||||
\(255\) | −2.81904 | −0.176535 | ||||||||
\(256\) | −30.2270 | −1.88919 | ||||||||
\(257\) | 16.5338 | 1.03135 | 0.515676 | − | 0.856784i | \(-0.327541\pi\) | ||||
0.515676 | + | 0.856784i | \(0.327541\pi\) | |||||||
\(258\) | 1.77013 | 0.110203 | ||||||||
\(259\) | −3.75035 | −0.233035 | ||||||||
\(260\) | −5.45376 | −0.338228 | ||||||||
\(261\) | 0.425145 | 0.0263158 | ||||||||
\(262\) | 42.2736 | 2.61167 | ||||||||
\(263\) | −23.6621 | −1.45907 | −0.729534 | − | 0.683945i | \(-0.760263\pi\) | ||||
−0.729534 | + | 0.683945i | \(0.760263\pi\) | |||||||
\(264\) | −25.9237 | −1.59549 | ||||||||
\(265\) | 0.780530 | 0.0479476 | ||||||||
\(266\) | 74.0979 | 4.54323 | ||||||||
\(267\) | −3.43083 | −0.209963 | ||||||||
\(268\) | 15.9261 | 0.972842 | ||||||||
\(269\) | 17.9531 | 1.09462 | 0.547311 | − | 0.836930i | \(-0.315652\pi\) | ||||
0.547311 | + | 0.836930i | \(0.315652\pi\) | |||||||
\(270\) | −11.1931 | −0.681189 | ||||||||
\(271\) | 18.4020 | 1.11784 | 0.558922 | − | 0.829220i | \(-0.311215\pi\) | ||||
0.558922 | + | 0.829220i | \(0.311215\pi\) | |||||||
\(272\) | 17.1274 | 1.03850 | ||||||||
\(273\) | 8.50682 | 0.514856 | ||||||||
\(274\) | −0.514307 | −0.0310704 | ||||||||
\(275\) | −13.0065 | −0.784319 | ||||||||
\(276\) | −25.7682 | −1.55106 | ||||||||
\(277\) | 1.14262 | 0.0686532 | 0.0343266 | − | 0.999411i | \(-0.489071\pi\) | ||||
0.0343266 | + | 0.999411i | \(0.489071\pi\) | |||||||
\(278\) | −36.5180 | −2.19021 | ||||||||
\(279\) | 1.45951 | 0.0873786 | ||||||||
\(280\) | 18.1998 | 1.08765 | ||||||||
\(281\) | 6.49174 | 0.387265 | 0.193632 | − | 0.981074i | \(-0.437973\pi\) | ||||
0.193632 | + | 0.981074i | \(0.437973\pi\) | |||||||
\(282\) | 15.9289 | 0.948552 | ||||||||
\(283\) | −13.5329 | −0.804446 | −0.402223 | − | 0.915542i | \(-0.631762\pi\) | ||||
−0.402223 | + | 0.915542i | \(0.631762\pi\) | |||||||
\(284\) | −48.4354 | −2.87411 | ||||||||
\(285\) | 8.56231 | 0.507187 | ||||||||
\(286\) | −11.8526 | −0.700860 | ||||||||
\(287\) | 45.7899 | 2.70289 | ||||||||
\(288\) | 4.68330 | 0.275966 | ||||||||
\(289\) | −10.5517 | −0.620689 | ||||||||
\(290\) | −0.861004 | −0.0505599 | ||||||||
\(291\) | 5.74773 | 0.336938 | ||||||||
\(292\) | −63.7422 | −3.73023 | ||||||||
\(293\) | −0.789509 | −0.0461236 | −0.0230618 | − | 0.999734i | \(-0.507341\pi\) | ||||
−0.0230618 | + | 0.999734i | \(0.507341\pi\) | |||||||
\(294\) | −26.5409 | −1.54790 | ||||||||
\(295\) | −6.71474 | −0.390947 | ||||||||
\(296\) | 6.08938 | 0.353938 | ||||||||
\(297\) | −16.7561 | −0.972285 | ||||||||
\(298\) | 9.90717 | 0.573907 | ||||||||
\(299\) | −6.45904 | −0.373536 | ||||||||
\(300\) | −27.6470 | −1.59620 | ||||||||
\(301\) | −1.86036 | −0.107229 | ||||||||
\(302\) | 2.53517 | 0.145882 | ||||||||
\(303\) | −21.8882 | −1.25745 | ||||||||
\(304\) | −52.0214 | −2.98363 | ||||||||
\(305\) | 7.71220 | 0.441599 | ||||||||
\(306\) | 6.29009 | 0.359581 | ||||||||
\(307\) | 7.19759 | 0.410788 | 0.205394 | − | 0.978679i | \(-0.434152\pi\) | ||||
0.205394 | + | 0.978679i | \(0.434152\pi\) | |||||||
\(308\) | 49.6961 | 2.83170 | ||||||||
\(309\) | 3.07610 | 0.174993 | ||||||||
\(310\) | −2.95580 | −0.167878 | ||||||||
\(311\) | −17.1788 | −0.974122 | −0.487061 | − | 0.873368i | \(-0.661931\pi\) | ||||
−0.487061 | + | 0.873368i | \(0.661931\pi\) | |||||||
\(312\) | −13.8124 | −0.781972 | ||||||||
\(313\) | 0.710526 | 0.0401613 | 0.0200806 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200806 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(314\) | −41.0645 | −2.31740 | ||||||||
\(315\) | 2.89005 | 0.162836 | ||||||||
\(316\) | −64.1593 | −3.60924 | ||||||||
\(317\) | 7.16933 | 0.402670 | 0.201335 | − | 0.979522i | \(-0.435472\pi\) | ||||
0.201335 | + | 0.979522i | \(0.435472\pi\) | |||||||
\(318\) | 3.60576 | 0.202201 | ||||||||
\(319\) | −1.28892 | −0.0721659 | ||||||||
\(320\) | 1.04445 | 0.0583864 | ||||||||
\(321\) | 18.1001 | 1.01025 | ||||||||
\(322\) | 39.3163 | 2.19101 | ||||||||
\(323\) | −19.5855 | −1.08976 | ||||||||
\(324\) | −22.6405 | −1.25780 | ||||||||
\(325\) | −6.92996 | −0.384405 | ||||||||
\(326\) | 35.0490 | 1.94118 | ||||||||
\(327\) | −3.11912 | −0.172488 | ||||||||
\(328\) | −74.3483 | −4.10520 | ||||||||
\(329\) | −16.7408 | −0.922952 | ||||||||
\(330\) | 8.33689 | 0.458931 | ||||||||
\(331\) | 18.1768 | 0.999088 | 0.499544 | − | 0.866288i | \(-0.333501\pi\) | ||||
0.499544 | + | 0.866288i | \(0.333501\pi\) | |||||||
\(332\) | 21.5064 | 1.18031 | ||||||||
\(333\) | 0.966968 | 0.0529895 | ||||||||
\(334\) | 19.8237 | 1.08470 | ||||||||
\(335\) | −2.80791 | −0.153412 | ||||||||
\(336\) | 36.3536 | 1.98325 | ||||||||
\(337\) | 7.47309 | 0.407085 | 0.203543 | − | 0.979066i | \(-0.434754\pi\) | ||||
0.203543 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(338\) | 26.6420 | 1.44913 | ||||||||
\(339\) | 8.67063 | 0.470924 | ||||||||
\(340\) | −8.77462 | −0.475871 | ||||||||
\(341\) | −4.42483 | −0.239618 | ||||||||
\(342\) | −19.1050 | −1.03308 | ||||||||
\(343\) | 1.36689 | 0.0738053 | ||||||||
\(344\) | 3.02063 | 0.162861 | ||||||||
\(345\) | 4.54315 | 0.244595 | ||||||||
\(346\) | 57.3934 | 3.08549 | ||||||||
\(347\) | 10.6215 | 0.570191 | 0.285096 | − | 0.958499i | \(-0.407975\pi\) | ||||
0.285096 | + | 0.958499i | \(0.407975\pi\) | |||||||
\(348\) | −2.73978 | −0.146868 | ||||||||
\(349\) | −23.1081 | −1.23695 | −0.618475 | − | 0.785804i | \(-0.712249\pi\) | ||||
−0.618475 | + | 0.785804i | \(0.712249\pi\) | |||||||
\(350\) | 42.1828 | 2.25477 | ||||||||
\(351\) | −8.92778 | −0.476530 | ||||||||
\(352\) | −14.1985 | −0.756781 | ||||||||
\(353\) | −0.312466 | −0.0166309 | −0.00831545 | − | 0.999965i | \(-0.502647\pi\) | ||||
−0.00831545 | + | 0.999965i | \(0.502647\pi\) | |||||||
\(354\) | −31.0196 | −1.64867 | ||||||||
\(355\) | 8.53957 | 0.453233 | ||||||||
\(356\) | −10.6789 | −0.565980 | ||||||||
\(357\) | 13.6867 | 0.724379 | ||||||||
\(358\) | 43.9618 | 2.32346 | ||||||||
\(359\) | −18.1619 | −0.958547 | −0.479274 | − | 0.877665i | \(-0.659100\pi\) | ||||
−0.479274 | + | 0.877665i | \(0.659100\pi\) | |||||||
\(360\) | −4.69253 | −0.247318 | ||||||||
\(361\) | 40.4871 | 2.13090 | ||||||||
\(362\) | 27.4776 | 1.44419 | ||||||||
\(363\) | −3.16492 | −0.166115 | ||||||||
\(364\) | 26.4785 | 1.38785 | ||||||||
\(365\) | 11.2383 | 0.588238 | ||||||||
\(366\) | 35.6275 | 1.86228 | ||||||||
\(367\) | −4.23375 | −0.221000 | −0.110500 | − | 0.993876i | \(-0.535245\pi\) | ||||
−0.110500 | + | 0.993876i | \(0.535245\pi\) | |||||||
\(368\) | −27.6025 | −1.43888 | ||||||||
\(369\) | −11.8062 | −0.614607 | ||||||||
\(370\) | −1.95830 | −0.101807 | ||||||||
\(371\) | −3.78955 | −0.196744 | ||||||||
\(372\) | −9.40557 | −0.487656 | ||||||||
\(373\) | −1.42926 | −0.0740044 | −0.0370022 | − | 0.999315i | \(-0.511781\pi\) | ||||
−0.0370022 | + | 0.999315i | \(0.511781\pi\) | |||||||
\(374\) | −19.0698 | −0.986077 | ||||||||
\(375\) | 10.4251 | 0.538350 | ||||||||
\(376\) | 27.1818 | 1.40180 | ||||||||
\(377\) | −0.686750 | −0.0353694 | ||||||||
\(378\) | 54.3436 | 2.79513 | ||||||||
\(379\) | 8.98996 | 0.461783 | 0.230892 | − | 0.972979i | \(-0.425836\pi\) | ||||
0.230892 | + | 0.972979i | \(0.425836\pi\) | |||||||
\(380\) | 26.6513 | 1.36718 | ||||||||
\(381\) | −29.2528 | −1.49867 | ||||||||
\(382\) | −44.8627 | −2.29537 | ||||||||
\(383\) | 20.8480 | 1.06528 | 0.532642 | − | 0.846341i | \(-0.321199\pi\) | ||||
0.532642 | + | 0.846341i | \(0.321199\pi\) | |||||||
\(384\) | 18.4596 | 0.942012 | ||||||||
\(385\) | −8.76184 | −0.446545 | ||||||||
\(386\) | −45.1905 | −2.30014 | ||||||||
\(387\) | 0.479663 | 0.0243827 | ||||||||
\(388\) | 17.8905 | 0.908253 | ||||||||
\(389\) | 27.1287 | 1.37548 | 0.687740 | − | 0.725957i | \(-0.258603\pi\) | ||||
0.687740 | + | 0.725957i | \(0.258603\pi\) | |||||||
\(390\) | 4.44197 | 0.224928 | ||||||||
\(391\) | −10.3920 | −0.525547 | ||||||||
\(392\) | −45.2906 | −2.28752 | ||||||||
\(393\) | −23.7166 | −1.19634 | ||||||||
\(394\) | 1.38580 | 0.0698153 | ||||||||
\(395\) | 11.3118 | 0.569160 | ||||||||
\(396\) | −12.8134 | −0.643895 | ||||||||
\(397\) | −33.3046 | −1.67151 | −0.835755 | − | 0.549102i | \(-0.814970\pi\) | ||||
−0.835755 | + | 0.549102i | \(0.814970\pi\) | |||||||
\(398\) | −8.98529 | −0.450392 | ||||||||
\(399\) | −41.5709 | −2.08115 | ||||||||
\(400\) | −29.6150 | −1.48075 | ||||||||
\(401\) | −20.8965 | −1.04352 | −0.521759 | − | 0.853093i | \(-0.674724\pi\) | ||||
−0.521759 | + | 0.853093i | \(0.674724\pi\) | |||||||
\(402\) | −12.9715 | −0.646959 | ||||||||
\(403\) | −2.35759 | −0.117440 | ||||||||
\(404\) | −68.1299 | −3.38959 | ||||||||
\(405\) | 3.99170 | 0.198349 | ||||||||
\(406\) | 4.18026 | 0.207463 | ||||||||
\(407\) | −2.93158 | −0.145313 | ||||||||
\(408\) | −22.2229 | −1.10020 | ||||||||
\(409\) | 33.2954 | 1.64635 | 0.823175 | − | 0.567788i | \(-0.192201\pi\) | ||||
0.823175 | + | 0.567788i | \(0.192201\pi\) | |||||||
\(410\) | 23.9099 | 1.18083 | ||||||||
\(411\) | 0.288540 | 0.0142326 | ||||||||
\(412\) | 9.57474 | 0.471714 | ||||||||
\(413\) | 32.6007 | 1.60418 | ||||||||
\(414\) | −10.1371 | −0.498210 | ||||||||
\(415\) | −3.79175 | −0.186130 | ||||||||
\(416\) | −7.56508 | −0.370909 | ||||||||
\(417\) | 20.4876 | 1.00328 | ||||||||
\(418\) | 57.9210 | 2.83301 | ||||||||
\(419\) | 9.14241 | 0.446636 | 0.223318 | − | 0.974746i | \(-0.428311\pi\) | ||||
0.223318 | + | 0.974746i | \(0.428311\pi\) | |||||||
\(420\) | −18.6245 | −0.908781 | ||||||||
\(421\) | −7.30262 | −0.355908 | −0.177954 | − | 0.984039i | \(-0.556948\pi\) | ||||
−0.177954 | + | 0.984039i | \(0.556948\pi\) | |||||||
\(422\) | 7.72364 | 0.375981 | ||||||||
\(423\) | 4.31636 | 0.209869 | ||||||||
\(424\) | 6.15303 | 0.298818 | ||||||||
\(425\) | −11.1497 | −0.540840 | ||||||||
\(426\) | 39.4496 | 1.91134 | ||||||||
\(427\) | −37.4435 | −1.81202 | ||||||||
\(428\) | 56.3387 | 2.72323 | ||||||||
\(429\) | 6.64963 | 0.321047 | ||||||||
\(430\) | −0.971414 | −0.0468457 | ||||||||
\(431\) | −12.7117 | −0.612299 | −0.306150 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306150 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(432\) | −38.1526 | −1.83562 | ||||||||
\(433\) | 20.0799 | 0.964977 | 0.482489 | − | 0.875902i | \(-0.339733\pi\) | ||||
0.482489 | + | 0.875902i | \(0.339733\pi\) | |||||||
\(434\) | 14.3507 | 0.688856 | ||||||||
\(435\) | 0.483046 | 0.0231603 | ||||||||
\(436\) | −9.70866 | −0.464961 | ||||||||
\(437\) | 31.5638 | 1.50990 | ||||||||
\(438\) | 51.9166 | 2.48067 | ||||||||
\(439\) | 3.28138 | 0.156612 | 0.0783058 | − | 0.996929i | \(-0.475049\pi\) | ||||
0.0783058 | + | 0.996929i | \(0.475049\pi\) | |||||||
\(440\) | 14.2265 | 0.678220 | ||||||||
\(441\) | −7.19196 | −0.342474 | ||||||||
\(442\) | −10.1606 | −0.483290 | ||||||||
\(443\) | −27.5654 | −1.30967 | −0.654837 | − | 0.755771i | \(-0.727263\pi\) | ||||
−0.654837 | + | 0.755771i | \(0.727263\pi\) | |||||||
\(444\) | −6.23146 | −0.295732 | ||||||||
\(445\) | 1.88278 | 0.0892522 | ||||||||
\(446\) | 14.9108 | 0.706045 | ||||||||
\(447\) | −5.55819 | −0.262893 | ||||||||
\(448\) | −5.07090 | −0.239578 | ||||||||
\(449\) | −40.6193 | −1.91694 | −0.958471 | − | 0.285191i | \(-0.907943\pi\) | ||||
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(450\) | −10.8762 | −0.512707 | ||||||||
\(451\) | 35.7932 | 1.68543 | ||||||||
\(452\) | 26.9884 | 1.26943 | ||||||||
\(453\) | −1.42230 | −0.0668253 | ||||||||
\(454\) | −26.0764 | −1.22382 | ||||||||
\(455\) | −4.66839 | −0.218858 | ||||||||
\(456\) | 67.4979 | 3.16088 | ||||||||
\(457\) | 24.3174 | 1.13752 | 0.568761 | − | 0.822503i | \(-0.307423\pi\) | ||||
0.568761 | + | 0.822503i | \(0.307423\pi\) | |||||||
\(458\) | 1.03373 | 0.0483030 | ||||||||
\(459\) | −14.3640 | −0.670455 | ||||||||
\(460\) | 14.1411 | 0.659334 | ||||||||
\(461\) | −12.8419 | −0.598107 | −0.299053 | − | 0.954236i | \(-0.596671\pi\) | ||||
−0.299053 | + | 0.954236i | \(0.596671\pi\) | |||||||
\(462\) | −40.4764 | −1.88313 | ||||||||
\(463\) | 21.3933 | 0.994230 | 0.497115 | − | 0.867685i | \(-0.334393\pi\) | ||||
0.497115 | + | 0.867685i | \(0.334393\pi\) | |||||||
\(464\) | −2.93481 | −0.136245 | ||||||||
\(465\) | 1.65828 | 0.0769010 | ||||||||
\(466\) | 45.6672 | 2.11549 | ||||||||
\(467\) | 7.86624 | 0.364006 | 0.182003 | − | 0.983298i | \(-0.441742\pi\) | ||||
0.182003 | + | 0.983298i | \(0.441742\pi\) | |||||||
\(468\) | −6.82707 | −0.315582 | ||||||||
\(469\) | 13.6327 | 0.629498 | ||||||||
\(470\) | −8.74149 | −0.403215 | ||||||||
\(471\) | 23.0382 | 1.06155 | ||||||||
\(472\) | −52.9333 | −2.43645 | ||||||||
\(473\) | −1.45421 | −0.0668645 | ||||||||
\(474\) | 52.2564 | 2.40022 | ||||||||
\(475\) | 33.8651 | 1.55384 | ||||||||
\(476\) | 42.6017 | 1.95264 | ||||||||
\(477\) | 0.977076 | 0.0447372 | ||||||||
\(478\) | −66.8793 | −3.05899 | ||||||||
\(479\) | 12.3114 | 0.562521 | 0.281261 | − | 0.959631i | \(-0.409247\pi\) | ||||
0.281261 | + | 0.959631i | \(0.409247\pi\) | |||||||
\(480\) | 5.32112 | 0.242875 | ||||||||
\(481\) | −1.56197 | −0.0712198 | ||||||||
\(482\) | 74.5343 | 3.39495 | ||||||||
\(483\) | −22.0575 | −1.00365 | ||||||||
\(484\) | −9.85121 | −0.447782 | ||||||||
\(485\) | −3.15425 | −0.143227 | ||||||||
\(486\) | −24.5809 | −1.11501 | ||||||||
\(487\) | −2.12100 | −0.0961115 | −0.0480558 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480558 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(488\) | 60.7964 | 2.75212 | ||||||||
\(489\) | −19.6634 | −0.889210 | ||||||||
\(490\) | 14.5652 | 0.657987 | ||||||||
\(491\) | 5.02536 | 0.226791 | 0.113396 | − | 0.993550i | \(-0.463827\pi\) | ||||
0.113396 | + | 0.993550i | \(0.463827\pi\) | |||||||
\(492\) | 76.0832 | 3.43009 | ||||||||
\(493\) | −1.10492 | −0.0497631 | ||||||||
\(494\) | 30.8608 | 1.38850 | ||||||||
\(495\) | 2.25910 | 0.101539 | ||||||||
\(496\) | −10.0751 | −0.452385 | ||||||||
\(497\) | −41.4605 | −1.85976 | ||||||||
\(498\) | −17.5165 | −0.784932 | ||||||||
\(499\) | −22.1075 | −0.989669 | −0.494834 | − | 0.868987i | \(-0.664771\pi\) | ||||
−0.494834 | + | 0.868987i | \(0.664771\pi\) | |||||||
\(500\) | 32.4495 | 1.45118 | ||||||||
\(501\) | −11.1216 | −0.496877 | ||||||||
\(502\) | −33.7937 | −1.50829 | ||||||||
\(503\) | 14.5539 | 0.648929 | 0.324464 | − | 0.945898i | \(-0.394816\pi\) | ||||
0.324464 | + | 0.945898i | \(0.394816\pi\) | |||||||
\(504\) | 22.7827 | 1.01482 | ||||||||
\(505\) | 12.0119 | 0.534521 | ||||||||
\(506\) | 30.7328 | 1.36624 | ||||||||
\(507\) | −14.9469 | −0.663813 | ||||||||
\(508\) | −91.0531 | −4.03983 | ||||||||
\(509\) | 1.43602 | 0.0636503 | 0.0318252 | − | 0.999493i | \(-0.489868\pi\) | ||||
0.0318252 | + | 0.999493i | \(0.489868\pi\) | |||||||
\(510\) | 7.14674 | 0.316463 | ||||||||
\(511\) | −54.5630 | −2.41372 | ||||||||
\(512\) | 50.6730 | 2.23945 | ||||||||
\(513\) | 43.6280 | 1.92622 | ||||||||
\(514\) | −41.9160 | −1.84884 | ||||||||
\(515\) | −1.68811 | −0.0743869 | ||||||||
\(516\) | −3.09111 | −0.136079 | ||||||||
\(517\) | −13.0860 | −0.575522 | ||||||||
\(518\) | 9.50776 | 0.417747 | ||||||||
\(519\) | −32.1992 | −1.41339 | ||||||||
\(520\) | 7.57999 | 0.332404 | ||||||||
\(521\) | −38.2031 | −1.67371 | −0.836854 | − | 0.547426i | \(-0.815608\pi\) | ||||
−0.836854 | + | 0.547426i | \(0.815608\pi\) | |||||||
\(522\) | −1.07781 | −0.0471746 | ||||||||
\(523\) | 2.65160 | 0.115946 | 0.0579731 | − | 0.998318i | \(-0.481536\pi\) | ||||
0.0579731 | + | 0.998318i | \(0.481536\pi\) | |||||||
\(524\) | −73.8209 | −3.22488 | ||||||||
\(525\) | −23.6657 | −1.03285 | ||||||||
\(526\) | 59.9874 | 2.61557 | ||||||||
\(527\) | −3.79316 | −0.165233 | ||||||||
\(528\) | 28.4170 | 1.23669 | ||||||||
\(529\) | −6.25227 | −0.271838 | ||||||||
\(530\) | −1.97877 | −0.0859524 | ||||||||
\(531\) | −8.40558 | −0.364771 | ||||||||
\(532\) | −129.395 | −5.60996 | ||||||||
\(533\) | 19.0709 | 0.826054 | ||||||||
\(534\) | 8.69773 | 0.376387 | ||||||||
\(535\) | −9.93299 | −0.429440 | ||||||||
\(536\) | −22.1351 | −0.956093 | ||||||||
\(537\) | −24.6638 | −1.06432 | ||||||||
\(538\) | −45.5142 | −1.96225 | ||||||||
\(539\) | 21.8041 | 0.939167 | ||||||||
\(540\) | 19.5461 | 0.841130 | ||||||||
\(541\) | 21.7655 | 0.935774 | 0.467887 | − | 0.883788i | \(-0.345016\pi\) | ||||
0.467887 | + | 0.883788i | \(0.345016\pi\) | |||||||
\(542\) | −46.6522 | −2.00388 | ||||||||
\(543\) | −15.4156 | −0.661548 | ||||||||
\(544\) | −12.1716 | −0.521851 | ||||||||
\(545\) | 1.71172 | 0.0733220 | ||||||||
\(546\) | −21.5662 | −0.922949 | ||||||||
\(547\) | 14.0132 | 0.599161 | 0.299580 | − | 0.954071i | \(-0.403153\pi\) | ||||
0.299580 | + | 0.954071i | \(0.403153\pi\) | |||||||
\(548\) | 0.898115 | 0.0383656 | ||||||||
\(549\) | 9.65421 | 0.412032 | ||||||||
\(550\) | 32.9735 | 1.40600 | ||||||||
\(551\) | 3.35599 | 0.142970 | ||||||||
\(552\) | 35.8143 | 1.52436 | ||||||||
\(553\) | −54.9201 | −2.33544 | ||||||||
\(554\) | −2.89673 | −0.123070 | ||||||||
\(555\) | 1.09866 | 0.0466355 | ||||||||
\(556\) | 63.7702 | 2.70446 | ||||||||
\(557\) | 43.0859 | 1.82561 | 0.912804 | − | 0.408399i | \(-0.133913\pi\) | ||||
0.912804 | + | 0.408399i | \(0.133913\pi\) | |||||||
\(558\) | −3.70010 | −0.156638 | ||||||||
\(559\) | −0.774815 | −0.0327712 | ||||||||
\(560\) | −19.9502 | −0.843051 | ||||||||
\(561\) | 10.6987 | 0.451698 | ||||||||
\(562\) | −16.4577 | −0.694224 | ||||||||
\(563\) | 28.6212 | 1.20624 | 0.603120 | − | 0.797650i | \(-0.293924\pi\) | ||||
0.603120 | + | 0.797650i | \(0.293924\pi\) | |||||||
\(564\) | −27.8161 | −1.17127 | ||||||||
\(565\) | −4.75829 | −0.200183 | ||||||||
\(566\) | 34.3081 | 1.44208 | ||||||||
\(567\) | −19.3801 | −0.813889 | ||||||||
\(568\) | 67.3187 | 2.82463 | ||||||||
\(569\) | −4.18452 | −0.175424 | −0.0877120 | − | 0.996146i | \(-0.527956\pi\) | ||||
−0.0877120 | + | 0.996146i | \(0.527956\pi\) | |||||||
\(570\) | −21.7069 | −0.909201 | ||||||||
\(571\) | 25.5669 | 1.06994 | 0.534972 | − | 0.844870i | \(-0.320322\pi\) | ||||
0.534972 | + | 0.844870i | \(0.320322\pi\) | |||||||
\(572\) | 20.6978 | 0.865419 | ||||||||
\(573\) | 25.1691 | 1.05146 | ||||||||
\(574\) | −116.085 | −4.84530 | ||||||||
\(575\) | 17.9688 | 0.749351 | ||||||||
\(576\) | 1.30745 | 0.0544772 | ||||||||
\(577\) | 2.49787 | 0.103988 | 0.0519939 | − | 0.998647i | \(-0.483442\pi\) | ||||
0.0519939 | + | 0.998647i | \(0.483442\pi\) | |||||||
\(578\) | 26.7504 | 1.11267 | ||||||||
\(579\) | 25.3531 | 1.05364 | ||||||||
\(580\) | 1.50354 | 0.0624311 | ||||||||
\(581\) | 18.4093 | 0.763748 | ||||||||
\(582\) | −14.5714 | −0.604006 | ||||||||
\(583\) | −2.96223 | −0.122683 | ||||||||
\(584\) | 88.5930 | 3.66600 | ||||||||
\(585\) | 1.20367 | 0.0497657 | ||||||||
\(586\) | 2.00154 | 0.0826827 | ||||||||
\(587\) | −1.86412 | −0.0769407 | −0.0384703 | − | 0.999260i | \(-0.512249\pi\) | ||||
−0.0384703 | + | 0.999260i | \(0.512249\pi\) | |||||||
\(588\) | 46.3474 | 1.91134 | ||||||||
\(589\) | 11.5210 | 0.474715 | ||||||||
\(590\) | 17.0230 | 0.700825 | ||||||||
\(591\) | −0.777467 | −0.0319807 | ||||||||
\(592\) | −6.67504 | −0.274343 | ||||||||
\(593\) | −22.8207 | −0.937135 | −0.468567 | − | 0.883428i | \(-0.655230\pi\) | ||||
−0.468567 | + | 0.883428i | \(0.655230\pi\) | |||||||
\(594\) | 42.4794 | 1.74295 | ||||||||
\(595\) | −7.51103 | −0.307922 | ||||||||
\(596\) | −17.3005 | −0.708658 | ||||||||
\(597\) | 5.04098 | 0.206314 | ||||||||
\(598\) | 16.3747 | 0.669613 | ||||||||
\(599\) | −26.2578 | −1.07286 | −0.536432 | − | 0.843943i | \(-0.680228\pi\) | ||||
−0.536432 | + | 0.843943i | \(0.680228\pi\) | |||||||
\(600\) | 38.4255 | 1.56872 | ||||||||
\(601\) | 10.7505 | 0.438521 | 0.219260 | − | 0.975666i | \(-0.429636\pi\) | ||||
0.219260 | + | 0.975666i | \(0.429636\pi\) | |||||||
\(602\) | 4.71631 | 0.192223 | ||||||||
\(603\) | −3.51497 | −0.143141 | ||||||||
\(604\) | −4.42707 | −0.180135 | ||||||||
\(605\) | 1.73685 | 0.0706131 | ||||||||
\(606\) | 55.4903 | 2.25414 | ||||||||
\(607\) | 13.4646 | 0.546510 | 0.273255 | − | 0.961942i | \(-0.411900\pi\) | ||||
0.273255 | + | 0.961942i | \(0.411900\pi\) | |||||||
\(608\) | 36.9688 | 1.49928 | ||||||||
\(609\) | −2.34524 | −0.0950338 | ||||||||
\(610\) | −19.5517 | −0.791626 | ||||||||
\(611\) | −6.97235 | −0.282071 | ||||||||
\(612\) | −10.9842 | −0.444008 | ||||||||
\(613\) | −5.15806 | −0.208332 | −0.104166 | − | 0.994560i | \(-0.533217\pi\) | ||||
−0.104166 | + | 0.994560i | \(0.533217\pi\) | |||||||
\(614\) | −18.2471 | −0.736393 | ||||||||
\(615\) | −13.4141 | −0.540909 | ||||||||
\(616\) | −69.0709 | −2.78295 | ||||||||
\(617\) | −33.7739 | −1.35968 | −0.679842 | − | 0.733359i | \(-0.737952\pi\) | ||||
−0.679842 | + | 0.733359i | \(0.737952\pi\) | |||||||
\(618\) | −7.79842 | −0.313699 | ||||||||
\(619\) | 3.65876 | 0.147058 | 0.0735290 | − | 0.997293i | \(-0.476574\pi\) | ||||
0.0735290 | + | 0.997293i | \(0.476574\pi\) | |||||||
\(620\) | 5.16161 | 0.207295 | ||||||||
\(621\) | 23.1490 | 0.928936 | ||||||||
\(622\) | 43.5512 | 1.74624 | ||||||||
\(623\) | −9.14107 | −0.366229 | ||||||||
\(624\) | 15.1408 | 0.606119 | ||||||||
\(625\) | 16.2328 | 0.649310 | ||||||||
\(626\) | −1.80130 | −0.0719945 | ||||||||
\(627\) | −32.4952 | −1.29773 | ||||||||
\(628\) | 71.7094 | 2.86152 | ||||||||
\(629\) | −2.51308 | −0.100203 | ||||||||
\(630\) | −7.32676 | −0.291905 | ||||||||
\(631\) | 6.80376 | 0.270853 | 0.135427 | − | 0.990787i | \(-0.456759\pi\) | ||||
0.135427 | + | 0.990787i | \(0.456759\pi\) | |||||||
\(632\) | 89.1728 | 3.54710 | ||||||||
\(633\) | −4.33317 | −0.172228 | ||||||||
\(634\) | −18.1755 | −0.721840 | ||||||||
\(635\) | 16.0534 | 0.637061 | ||||||||
\(636\) | −6.29660 | −0.249677 | ||||||||
\(637\) | 11.6174 | 0.460298 | ||||||||
\(638\) | 3.26764 | 0.129367 | ||||||||
\(639\) | 10.6899 | 0.422887 | ||||||||
\(640\) | −10.1303 | −0.400435 | ||||||||
\(641\) | 17.7786 | 0.702211 | 0.351106 | − | 0.936336i | \(-0.385806\pi\) | ||||
0.351106 | + | 0.936336i | \(0.385806\pi\) | |||||||
\(642\) | −45.8867 | −1.81100 | ||||||||
\(643\) | −14.1207 | −0.556866 | −0.278433 | − | 0.960456i | \(-0.589815\pi\) | ||||
−0.278433 | + | 0.960456i | \(0.589815\pi\) | |||||||
\(644\) | −68.6566 | −2.70545 | ||||||||
\(645\) | 0.544989 | 0.0214589 | ||||||||
\(646\) | 49.6524 | 1.95355 | ||||||||
\(647\) | 4.75522 | 0.186947 | 0.0934734 | − | 0.995622i | \(-0.470203\pi\) | ||||
0.0934734 | + | 0.995622i | \(0.470203\pi\) | |||||||
\(648\) | 31.4672 | 1.23615 | ||||||||
\(649\) | 25.4834 | 1.00031 | ||||||||
\(650\) | 17.5686 | 0.689098 | ||||||||
\(651\) | −8.05112 | −0.315548 | ||||||||
\(652\) | −61.2048 | −2.39696 | ||||||||
\(653\) | 43.0314 | 1.68395 | 0.841974 | − | 0.539519i | \(-0.181394\pi\) | ||||
0.841974 | + | 0.539519i | \(0.181394\pi\) | |||||||
\(654\) | 7.90750 | 0.309208 | ||||||||
\(655\) | 13.0152 | 0.508548 | ||||||||
\(656\) | 81.4990 | 3.18200 | ||||||||
\(657\) | 14.0682 | 0.548853 | ||||||||
\(658\) | 42.4408 | 1.65452 | ||||||||
\(659\) | −9.02180 | −0.351440 | −0.175720 | − | 0.984440i | \(-0.556225\pi\) | ||||
−0.175720 | + | 0.984440i | \(0.556225\pi\) | |||||||
\(660\) | −14.5584 | −0.566685 | ||||||||
\(661\) | −18.3879 | −0.715206 | −0.357603 | − | 0.933874i | \(-0.616406\pi\) | ||||
−0.357603 | + | 0.933874i | \(0.616406\pi\) | |||||||
\(662\) | −46.0813 | −1.79100 | ||||||||
\(663\) | 5.70035 | 0.221383 | ||||||||
\(664\) | −29.8909 | −1.15999 | ||||||||
\(665\) | 22.8133 | 0.884663 | ||||||||
\(666\) | −2.45142 | −0.0949908 | ||||||||
\(667\) | 1.78068 | 0.0689484 | ||||||||
\(668\) | −34.6174 | −1.33939 | ||||||||
\(669\) | −8.36533 | −0.323422 | ||||||||
\(670\) | 7.11851 | 0.275012 | ||||||||
\(671\) | −29.2689 | −1.12991 | ||||||||
\(672\) | −25.8346 | −0.996590 | ||||||||
\(673\) | −23.6751 | −0.912607 | −0.456304 | − | 0.889824i | \(-0.650827\pi\) | ||||
−0.456304 | + | 0.889824i | \(0.650827\pi\) | |||||||
\(674\) | −18.9455 | −0.729754 | ||||||||
\(675\) | 24.8367 | 0.955967 | ||||||||
\(676\) | −46.5239 | −1.78938 | ||||||||
\(677\) | −27.5152 | −1.05749 | −0.528747 | − | 0.848779i | \(-0.677338\pi\) | ||||
−0.528747 | + | 0.848779i | \(0.677338\pi\) | |||||||
\(678\) | −21.9815 | −0.844195 | ||||||||
\(679\) | 15.3142 | 0.587705 | ||||||||
\(680\) | 12.1955 | 0.467677 | ||||||||
\(681\) | 14.6295 | 0.560605 | ||||||||
\(682\) | 11.2177 | 0.429548 | ||||||||
\(683\) | 39.1901 | 1.49957 | 0.749783 | − | 0.661684i | \(-0.230158\pi\) | ||||
0.749783 | + | 0.661684i | \(0.230158\pi\) | |||||||
\(684\) | 33.3623 | 1.27564 | ||||||||
\(685\) | −0.158345 | −0.00605006 | ||||||||
\(686\) | −3.46530 | −0.132306 | ||||||||
\(687\) | −0.579949 | −0.0221264 | ||||||||
\(688\) | −3.31115 | −0.126236 | ||||||||
\(689\) | −1.57830 | −0.0601285 | ||||||||
\(690\) | −11.5177 | −0.438469 | ||||||||
\(691\) | 16.3346 | 0.621397 | 0.310699 | − | 0.950508i | \(-0.399437\pi\) | ||||
0.310699 | + | 0.950508i | \(0.399437\pi\) | |||||||
\(692\) | −100.224 | −3.80995 | ||||||||
\(693\) | −10.9682 | −0.416646 | ||||||||
\(694\) | −26.9272 | −1.02214 | ||||||||
\(695\) | −11.2432 | −0.426479 | ||||||||
\(696\) | 3.80792 | 0.144339 | ||||||||
\(697\) | 30.6835 | 1.16222 | ||||||||
\(698\) | 58.5830 | 2.21740 | ||||||||
\(699\) | −25.6205 | −0.969057 | ||||||||
\(700\) | −73.6623 | −2.78417 | ||||||||
\(701\) | −13.5453 | −0.511598 | −0.255799 | − | 0.966730i | \(-0.582339\pi\) | ||||
−0.255799 | + | 0.966730i | \(0.582339\pi\) | |||||||
\(702\) | 22.6334 | 0.854243 | ||||||||
\(703\) | 7.63300 | 0.287884 | ||||||||
\(704\) | −3.96383 | −0.149393 | ||||||||
\(705\) | 4.90421 | 0.184703 | ||||||||
\(706\) | 0.792154 | 0.0298131 | ||||||||
\(707\) | −58.3188 | −2.19331 | ||||||||
\(708\) | 54.1684 | 2.03577 | ||||||||
\(709\) | 42.6654 | 1.60233 | 0.801166 | − | 0.598443i | \(-0.204214\pi\) | ||||
0.801166 | + | 0.598443i | \(0.204214\pi\) | |||||||
\(710\) | −21.6492 | −0.812481 | ||||||||
\(711\) | 14.1603 | 0.531052 | ||||||||
\(712\) | 14.8422 | 0.556235 | ||||||||
\(713\) | 6.11303 | 0.228935 | ||||||||
\(714\) | −34.6982 | −1.29855 | ||||||||
\(715\) | −3.64920 | −0.136472 | ||||||||
\(716\) | −76.7690 | −2.86899 | ||||||||
\(717\) | 37.5210 | 1.40125 | ||||||||
\(718\) | 46.0434 | 1.71832 | ||||||||
\(719\) | 19.2476 | 0.717815 | 0.358907 | − | 0.933373i | \(-0.383149\pi\) | ||||
0.358907 | + | 0.933373i | \(0.383149\pi\) | |||||||
\(720\) | 5.14385 | 0.191700 | ||||||||
\(721\) | 8.19593 | 0.305232 | ||||||||
\(722\) | −102.642 | −3.81993 | ||||||||
\(723\) | −41.8157 | −1.55514 | ||||||||
\(724\) | −47.9831 | −1.78328 | ||||||||
\(725\) | 1.91051 | 0.0709547 | ||||||||
\(726\) | 8.02360 | 0.297784 | ||||||||
\(727\) | −29.0737 | −1.07829 | −0.539143 | − | 0.842214i | \(-0.681252\pi\) | ||||
−0.539143 | + | 0.842214i | \(0.681252\pi\) | |||||||
\(728\) | −36.8016 | −1.36396 | ||||||||
\(729\) | 29.1328 | 1.07899 | ||||||||
\(730\) | −28.4909 | −1.05450 | ||||||||
\(731\) | −1.24661 | −0.0461075 | ||||||||
\(732\) | −62.2150 | −2.29953 | ||||||||
\(733\) | −1.79727 | −0.0663838 | −0.0331919 | − | 0.999449i | \(-0.510567\pi\) | ||||
−0.0331919 | + | 0.999449i | \(0.510567\pi\) | |||||||
\(734\) | 10.7333 | 0.396172 | ||||||||
\(735\) | −8.17144 | −0.301408 | ||||||||
\(736\) | 19.6156 | 0.723041 | ||||||||
\(737\) | 10.6564 | 0.392534 | ||||||||
\(738\) | 29.9307 | 1.10176 | ||||||||
\(739\) | −48.7938 | −1.79491 | −0.897455 | − | 0.441107i | \(-0.854586\pi\) | ||||
−0.897455 | + | 0.441107i | \(0.854586\pi\) | |||||||
\(740\) | 3.41971 | 0.125711 | ||||||||
\(741\) | −17.3137 | −0.636036 | ||||||||
\(742\) | 9.60715 | 0.352689 | ||||||||
\(743\) | −50.9387 | −1.86876 | −0.934380 | − | 0.356278i | \(-0.884046\pi\) | ||||
−0.934380 | + | 0.356278i | \(0.884046\pi\) | |||||||
\(744\) | 13.0725 | 0.479260 | ||||||||
\(745\) | 3.05023 | 0.111752 | ||||||||
\(746\) | 3.62342 | 0.132663 | ||||||||
\(747\) | −4.74655 | −0.173667 | ||||||||
\(748\) | 33.3010 | 1.21760 | ||||||||
\(749\) | 48.2256 | 1.76213 | ||||||||
\(750\) | −26.4294 | −0.965065 | ||||||||
\(751\) | −35.0681 | −1.27965 | −0.639827 | − | 0.768519i | \(-0.720994\pi\) | ||||
−0.639827 | + | 0.768519i | \(0.720994\pi\) | |||||||
\(752\) | −29.7961 | −1.08655 | ||||||||
\(753\) | 18.9592 | 0.690910 | ||||||||
\(754\) | 1.74103 | 0.0634044 | ||||||||
\(755\) | 0.780530 | 0.0284064 | ||||||||
\(756\) | −94.8982 | −3.45141 | ||||||||
\(757\) | 16.5499 | 0.601516 | 0.300758 | − | 0.953700i | \(-0.402760\pi\) | ||||
0.300758 | + | 0.953700i | \(0.402760\pi\) | |||||||
\(758\) | −22.7910 | −0.827808 | ||||||||
\(759\) | −17.2419 | −0.625842 | ||||||||
\(760\) | −37.0416 | −1.34364 | ||||||||
\(761\) | 29.6846 | 1.07607 | 0.538034 | − | 0.842923i | \(-0.319167\pi\) | ||||
0.538034 | + | 0.842923i | \(0.319167\pi\) | |||||||
\(762\) | 74.1608 | 2.68656 | ||||||||
\(763\) | −8.31057 | −0.300863 | ||||||||
\(764\) | 78.3421 | 2.83432 | ||||||||
\(765\) | 1.93660 | 0.0700179 | ||||||||
\(766\) | −52.8532 | −1.90966 | ||||||||
\(767\) | 13.5778 | 0.490266 | ||||||||
\(768\) | −42.9917 | −1.55133 | ||||||||
\(769\) | 20.0497 | 0.723010 | 0.361505 | − | 0.932370i | \(-0.382263\pi\) | ||||
0.361505 | + | 0.932370i | \(0.382263\pi\) | |||||||
\(770\) | 22.2127 | 0.800491 | ||||||||
\(771\) | 23.5160 | 0.846908 | ||||||||
\(772\) | 78.9146 | 2.84020 | ||||||||
\(773\) | 0.372095 | 0.0133833 | 0.00669167 | − | 0.999978i | \(-0.497870\pi\) | ||||
0.00669167 | + | 0.999978i | \(0.497870\pi\) | |||||||
\(774\) | −1.21603 | −0.0437092 | ||||||||
\(775\) | 6.55873 | 0.235597 | ||||||||
\(776\) | −24.8654 | −0.892616 | ||||||||
\(777\) | −5.33410 | −0.191360 | ||||||||
\(778\) | −68.7758 | −2.46573 | ||||||||
\(779\) | −93.1952 | −3.33907 | ||||||||
\(780\) | −7.75686 | −0.277740 | ||||||||
\(781\) | −32.4089 | −1.15968 | ||||||||
\(782\) | 26.3455 | 0.942114 | ||||||||
\(783\) | 2.46129 | 0.0879593 | ||||||||
\(784\) | 49.6466 | 1.77309 | ||||||||
\(785\) | −12.6430 | −0.451247 | ||||||||
\(786\) | 60.1256 | 2.14461 | ||||||||
\(787\) | −3.80482 | −0.135627 | −0.0678136 | − | 0.997698i | \(-0.521602\pi\) | ||||
−0.0678136 | + | 0.997698i | \(0.521602\pi\) | |||||||
\(788\) | −2.41996 | −0.0862077 | ||||||||
\(789\) | −33.6545 | −1.19813 | ||||||||
\(790\) | −28.6774 | −1.02030 | ||||||||
\(791\) | 23.1020 | 0.821411 | ||||||||
\(792\) | 17.8088 | 0.632809 | ||||||||
\(793\) | −15.5947 | −0.553786 | ||||||||
\(794\) | 84.4327 | 2.99641 | ||||||||
\(795\) | 1.11014 | 0.0393728 | ||||||||
\(796\) | 15.6907 | 0.556142 | ||||||||
\(797\) | −33.6789 | −1.19297 | −0.596484 | − | 0.802625i | \(-0.703436\pi\) | ||||
−0.596484 | + | 0.802625i | \(0.703436\pi\) | |||||||
\(798\) | 105.389 | 3.73073 | ||||||||
\(799\) | −11.2179 | −0.396861 | ||||||||
\(800\) | 21.0458 | 0.744080 | ||||||||
\(801\) | 2.35688 | 0.0832763 | ||||||||
\(802\) | 52.9760 | 1.87065 | ||||||||
\(803\) | −42.6509 | −1.50512 | ||||||||
\(804\) | 22.6516 | 0.798862 | ||||||||
\(805\) | 12.1047 | 0.426636 | ||||||||
\(806\) | 5.97689 | 0.210527 | ||||||||
\(807\) | 25.5346 | 0.898862 | ||||||||
\(808\) | 94.6913 | 3.33123 | ||||||||
\(809\) | 34.7214 | 1.22074 | 0.610370 | − | 0.792116i | \(-0.291021\pi\) | ||||
0.610370 | + | 0.792116i | \(0.291021\pi\) | |||||||
\(810\) | −10.1196 | −0.355568 | ||||||||
\(811\) | −36.1909 | −1.27083 | −0.635417 | − | 0.772169i | \(-0.719172\pi\) | ||||
−0.635417 | + | 0.772169i | \(0.719172\pi\) | |||||||
\(812\) | −7.29984 | −0.256174 | ||||||||
\(813\) | 26.1731 | 0.917931 | ||||||||
\(814\) | 7.43205 | 0.260493 | ||||||||
\(815\) | 10.7909 | 0.377989 | ||||||||
\(816\) | 24.3603 | 0.852780 | ||||||||
\(817\) | 3.78634 | 0.132467 | ||||||||
\(818\) | −84.4093 | −2.95130 | ||||||||
\(819\) | −5.84394 | −0.204204 | ||||||||
\(820\) | −41.7531 | −1.45808 | ||||||||
\(821\) | −46.1025 | −1.60899 | −0.804494 | − | 0.593961i | \(-0.797563\pi\) | ||||
−0.804494 | + | 0.593961i | \(0.797563\pi\) | |||||||
\(822\) | −0.731496 | −0.0255138 | ||||||||
\(823\) | 7.50333 | 0.261550 | 0.130775 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130775 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(824\) | −13.3076 | −0.463592 | ||||||||
\(825\) | −18.4990 | −0.644053 | ||||||||
\(826\) | −82.6483 | −2.87570 | ||||||||
\(827\) | 12.0627 | 0.419461 | 0.209731 | − | 0.977759i | \(-0.432741\pi\) | ||||
0.209731 | + | 0.977759i | \(0.432741\pi\) | |||||||
\(828\) | 17.7020 | 0.615188 | ||||||||
\(829\) | −24.4058 | −0.847647 | −0.423824 | − | 0.905745i | \(-0.639312\pi\) | ||||
−0.423824 | + | 0.905745i | \(0.639312\pi\) | |||||||
\(830\) | 9.61272 | 0.333662 | ||||||||
\(831\) | 1.62514 | 0.0563755 | ||||||||
\(832\) | −2.11197 | −0.0732193 | ||||||||
\(833\) | 18.6914 | 0.647618 | ||||||||
\(834\) | −51.9394 | −1.79852 | ||||||||
\(835\) | 6.10334 | 0.211215 | ||||||||
\(836\) | −101.145 | −3.49819 | ||||||||
\(837\) | 8.44953 | 0.292059 | ||||||||
\(838\) | −23.1775 | −0.800655 | ||||||||
\(839\) | −2.92428 | −0.100957 | −0.0504787 | − | 0.998725i | \(-0.516075\pi\) | ||||
−0.0504787 | + | 0.998725i | \(0.516075\pi\) | |||||||
\(840\) | 25.8855 | 0.893134 | ||||||||
\(841\) | −28.8107 | −0.993471 | ||||||||
\(842\) | 18.5134 | 0.638012 | ||||||||
\(843\) | 9.23318 | 0.318007 | ||||||||
\(844\) | −13.4875 | −0.464260 | ||||||||
\(845\) | 8.20256 | 0.282177 | ||||||||
\(846\) | −10.9427 | −0.376218 | ||||||||
\(847\) | −8.43259 | −0.289747 | ||||||||
\(848\) | −6.74482 | −0.231618 | ||||||||
\(849\) | −19.2477 | −0.660581 | ||||||||
\(850\) | 28.2663 | 0.969528 | ||||||||
\(851\) | 4.05006 | 0.138834 | ||||||||
\(852\) | −68.8895 | −2.36011 | ||||||||
\(853\) | −39.4593 | −1.35106 | −0.675531 | − | 0.737332i | \(-0.736085\pi\) | ||||
−0.675531 | + | 0.737332i | \(0.736085\pi\) | |||||||
\(854\) | 94.9255 | 3.24828 | ||||||||
\(855\) | −5.88206 | −0.201162 | ||||||||
\(856\) | −78.3032 | −2.67635 | ||||||||
\(857\) | −20.9968 | −0.717236 | −0.358618 | − | 0.933484i | \(-0.616752\pi\) | ||||
−0.358618 | + | 0.933484i | \(0.616752\pi\) | |||||||
\(858\) | −16.8579 | −0.575520 | ||||||||
\(859\) | −21.5884 | −0.736587 | −0.368293 | − | 0.929710i | \(-0.620058\pi\) | ||||
−0.368293 | + | 0.929710i | \(0.620058\pi\) | |||||||
\(860\) | 1.69635 | 0.0578449 | ||||||||
\(861\) | 65.1268 | 2.21952 | ||||||||
\(862\) | 32.2262 | 1.09763 | ||||||||
\(863\) | 23.1424 | 0.787777 | 0.393888 | − | 0.919158i | \(-0.371130\pi\) | ||||
0.393888 | + | 0.919158i | \(0.371130\pi\) | |||||||
\(864\) | 27.1130 | 0.922403 | ||||||||
\(865\) | 17.6704 | 0.600810 | ||||||||
\(866\) | −50.9058 | −1.72985 | ||||||||
\(867\) | −15.0077 | −0.509687 | ||||||||
\(868\) | −25.0601 | −0.850596 | ||||||||
\(869\) | −42.9301 | −1.45630 | ||||||||
\(870\) | −1.22460 | −0.0415179 | ||||||||
\(871\) | 5.67784 | 0.192386 | ||||||||
\(872\) | 13.4937 | 0.456955 | ||||||||
\(873\) | −3.94852 | −0.133637 | ||||||||
\(874\) | −80.0195 | −2.70670 | ||||||||
\(875\) | 27.7766 | 0.939020 | ||||||||
\(876\) | −90.6602 | −3.06312 | ||||||||
\(877\) | −34.9614 | −1.18056 | −0.590281 | − | 0.807198i | \(-0.700983\pi\) | ||||
−0.590281 | + | 0.807198i | \(0.700983\pi\) | |||||||
\(878\) | −8.31884 | −0.280747 | ||||||||
\(879\) | −1.12291 | −0.0378750 | ||||||||
\(880\) | −15.5947 | −0.525698 | ||||||||
\(881\) | 34.3059 | 1.15580 | 0.577898 | − | 0.816109i | \(-0.303873\pi\) | ||||
0.577898 | + | 0.816109i | \(0.303873\pi\) | |||||||
\(882\) | 18.2328 | 0.613931 | ||||||||
\(883\) | −55.0181 | −1.85151 | −0.925754 | − | 0.378127i | \(-0.876568\pi\) | ||||
−0.925754 | + | 0.378127i | \(0.876568\pi\) | |||||||
\(884\) | 17.7431 | 0.596764 | ||||||||
\(885\) | −9.55034 | −0.321031 | ||||||||
\(886\) | 69.8830 | 2.34776 | ||||||||
\(887\) | 10.6841 | 0.358737 | 0.179369 | − | 0.983782i | \(-0.442595\pi\) | ||||
0.179369 | + | 0.983782i | \(0.442595\pi\) | |||||||
\(888\) | 8.66089 | 0.290641 | ||||||||
\(889\) | −77.9410 | −2.61406 | ||||||||
\(890\) | −4.77316 | −0.159997 | ||||||||
\(891\) | −15.1491 | −0.507514 | ||||||||
\(892\) | −26.0381 | −0.871821 | ||||||||
\(893\) | 34.0723 | 1.14018 | ||||||||
\(894\) | 14.0909 | 0.471271 | ||||||||
\(895\) | 13.5350 | 0.452426 | ||||||||
\(896\) | 49.1836 | 1.64311 | ||||||||
\(897\) | −9.18666 | −0.306734 | ||||||||
\(898\) | 102.977 | 3.43637 | ||||||||
\(899\) | 0.649962 | 0.0216774 | ||||||||
\(900\) | 18.9927 | 0.633089 | ||||||||
\(901\) | −2.53935 | −0.0845979 | ||||||||
\(902\) | −90.7417 | −3.02137 | ||||||||
\(903\) | −2.64598 | −0.0880525 | ||||||||
\(904\) | −37.5103 | −1.24757 | ||||||||
\(905\) | 8.45982 | 0.281214 | ||||||||
\(906\) | 3.60576 | 0.119793 | ||||||||
\(907\) | −0.370896 | −0.0123154 | −0.00615769 | − | 0.999981i | \(-0.501960\pi\) | ||||
−0.00615769 | + | 0.999981i | \(0.501960\pi\) | |||||||
\(908\) | 45.5362 | 1.51117 | ||||||||
\(909\) | 15.0366 | 0.498732 | ||||||||
\(910\) | 11.8351 | 0.392331 | ||||||||
\(911\) | 6.15809 | 0.204027 | 0.102013 | − | 0.994783i | \(-0.467472\pi\) | ||||
0.102013 | + | 0.994783i | \(0.467472\pi\) | |||||||
\(912\) | −73.9898 | −2.45005 | ||||||||
\(913\) | 14.3902 | 0.476248 | ||||||||
\(914\) | −61.6487 | −2.03916 | ||||||||
\(915\) | 10.9690 | 0.362625 | ||||||||
\(916\) | −1.80516 | −0.0596443 | ||||||||
\(917\) | −63.1903 | −2.08673 | ||||||||
\(918\) | 36.4152 | 1.20188 | ||||||||
\(919\) | −27.7930 | −0.916805 | −0.458403 | − | 0.888745i | \(-0.651578\pi\) | ||||
−0.458403 | + | 0.888745i | \(0.651578\pi\) | |||||||
\(920\) | −19.6543 | −0.647982 | ||||||||
\(921\) | 10.2371 | 0.337324 | ||||||||
\(922\) | 32.5564 | 1.07219 | ||||||||
\(923\) | −17.2678 | −0.568376 | ||||||||
\(924\) | 70.6826 | 2.32529 | ||||||||
\(925\) | 4.34535 | 0.142874 | ||||||||
\(926\) | −54.2355 | −1.78229 | ||||||||
\(927\) | −2.11319 | −0.0694063 | ||||||||
\(928\) | 2.08561 | 0.0684634 | ||||||||
\(929\) | 45.6786 | 1.49867 | 0.749334 | − | 0.662192i | \(-0.230374\pi\) | ||||
0.749334 | + | 0.662192i | \(0.230374\pi\) | |||||||
\(930\) | −4.20402 | −0.137855 | ||||||||
\(931\) | −56.7715 | −1.86061 | ||||||||
\(932\) | −79.7471 | −2.61220 | ||||||||
\(933\) | −24.4334 | −0.799913 | ||||||||
\(934\) | −19.9422 | −0.652530 | ||||||||
\(935\) | −5.87124 | −0.192010 | ||||||||
\(936\) | 9.48871 | 0.310148 | ||||||||
\(937\) | 11.3620 | 0.371180 | 0.185590 | − | 0.982627i | \(-0.440580\pi\) | ||||
0.185590 | + | 0.982627i | \(0.440580\pi\) | |||||||
\(938\) | −34.5611 | −1.12846 | ||||||||
\(939\) | 1.01058 | 0.0329789 | ||||||||
\(940\) | 15.2650 | 0.497888 | ||||||||
\(941\) | −3.92984 | −0.128109 | −0.0640545 | − | 0.997946i | \(-0.520403\pi\) | ||||
−0.0640545 | + | 0.997946i | \(0.520403\pi\) | |||||||
\(942\) | −58.4058 | −1.90296 | ||||||||
\(943\) | −49.4493 | −1.61029 | ||||||||
\(944\) | 58.0243 | 1.88853 | ||||||||
\(945\) | 16.7314 | 0.544271 | ||||||||
\(946\) | 3.68666 | 0.119864 | ||||||||
\(947\) | −22.3293 | −0.725605 | −0.362803 | − | 0.931866i | \(-0.618180\pi\) | ||||
−0.362803 | + | 0.931866i | \(0.618180\pi\) | |||||||
\(948\) | −91.2535 | −2.96378 | ||||||||
\(949\) | −22.7248 | −0.737678 | ||||||||
\(950\) | −85.8537 | −2.78546 | ||||||||
\(951\) | 10.1969 | 0.330657 | ||||||||
\(952\) | −59.2106 | −1.91903 | ||||||||
\(953\) | 23.7675 | 0.769905 | 0.384952 | − | 0.922936i | \(-0.374218\pi\) | ||||
0.384952 | + | 0.922936i | \(0.374218\pi\) | |||||||
\(954\) | −2.47705 | −0.0801975 | ||||||||
\(955\) | −13.8124 | −0.446958 | ||||||||
\(956\) | 116.789 | 3.77722 | ||||||||
\(957\) | −1.83323 | −0.0592599 | ||||||||
\(958\) | −31.2114 | −1.00839 | ||||||||
\(959\) | 0.768782 | 0.0248253 | ||||||||
\(960\) | 1.48551 | 0.0479448 | ||||||||
\(961\) | −28.7687 | −0.928023 | ||||||||
\(962\) | 3.95986 | 0.127671 | ||||||||
\(963\) | −12.4342 | −0.400687 | ||||||||
\(964\) | −130.157 | −4.19206 | ||||||||
\(965\) | −13.9133 | −0.447885 | ||||||||
\(966\) | 55.9194 | 1.79918 | ||||||||
\(967\) | 10.0873 | 0.324387 | 0.162193 | − | 0.986759i | \(-0.448143\pi\) | ||||
0.162193 | + | 0.986759i | \(0.448143\pi\) | |||||||
\(968\) | 13.6919 | 0.440073 | ||||||||
\(969\) | −27.8563 | −0.894873 | ||||||||
\(970\) | 7.99655 | 0.256754 | ||||||||
\(971\) | −1.27634 | −0.0409598 | −0.0204799 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204799 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(972\) | 42.9248 | 1.37681 | ||||||||
\(973\) | 54.5869 | 1.74998 | ||||||||
\(974\) | 5.37708 | 0.172293 | ||||||||
\(975\) | −9.85645 | −0.315659 | ||||||||
\(976\) | −66.6437 | −2.13321 | ||||||||
\(977\) | −56.1942 | −1.79781 | −0.898906 | − | 0.438141i | \(-0.855637\pi\) | ||||
−0.898906 | + | 0.438141i | \(0.855637\pi\) | |||||||
\(978\) | 49.8500 | 1.59403 | ||||||||
\(979\) | −7.14542 | −0.228368 | ||||||||
\(980\) | −25.4346 | −0.812479 | ||||||||
\(981\) | 2.14275 | 0.0684127 | ||||||||
\(982\) | −12.7401 | −0.406554 | ||||||||
\(983\) | −11.7197 | −0.373802 | −0.186901 | − | 0.982379i | \(-0.559844\pi\) | ||||
−0.186901 | + | 0.982379i | \(0.559844\pi\) | |||||||
\(984\) | −105.745 | −3.37104 | ||||||||
\(985\) | 0.426660 | 0.0135945 | ||||||||
\(986\) | 2.80116 | 0.0892071 | ||||||||
\(987\) | −23.8104 | −0.757894 | ||||||||
\(988\) | −53.8912 | −1.71451 | ||||||||
\(989\) | 2.00903 | 0.0638834 | ||||||||
\(990\) | −5.72720 | −0.182022 | ||||||||
\(991\) | 1.12898 | 0.0358634 | 0.0179317 | − | 0.999839i | \(-0.494292\pi\) | ||||
0.0179317 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(992\) | 7.15983 | 0.227325 | ||||||||
\(993\) | 25.8528 | 0.820414 | ||||||||
\(994\) | 105.109 | 3.33386 | ||||||||
\(995\) | −2.76640 | −0.0877008 | ||||||||
\(996\) | 30.5884 | 0.969230 | ||||||||
\(997\) | 40.7124 | 1.28937 | 0.644687 | − | 0.764447i | \(-0.276988\pi\) | ||||
0.644687 | + | 0.764447i | \(0.276988\pi\) | |||||||
\(998\) | 56.0463 | 1.77411 | ||||||||
\(999\) | 5.59806 | 0.177115 |
(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 | 8003.2.a.b.1.10 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.10 | ✓ | 153 | 1.1 | even | 1 | trivial |