Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63308 | −1.86187 | −0.930936 | − | 0.365183i | \(-0.881006\pi\) | ||||
−0.930936 | + | 0.365183i | \(0.881006\pi\) | |||||||
\(3\) | 2.70578 | 1.56219 | 0.781093 | − | 0.624415i | \(-0.214663\pi\) | ||||
0.781093 | + | 0.624415i | \(0.214663\pi\) | |||||||
\(4\) | 4.93313 | 2.46656 | ||||||||
\(5\) | 2.79051 | 1.24796 | 0.623978 | − | 0.781442i | \(-0.285516\pi\) | ||||
0.623978 | + | 0.781442i | \(0.285516\pi\) | |||||||
\(6\) | −7.12456 | −2.90859 | ||||||||
\(7\) | −5.09743 | −1.92665 | −0.963324 | − | 0.268342i | \(-0.913524\pi\) | ||||
−0.963324 | + | 0.268342i | \(0.913524\pi\) | |||||||
\(8\) | −7.72317 | −2.73055 | ||||||||
\(9\) | 4.32127 | 1.44042 | ||||||||
\(10\) | −7.34766 | −2.32353 | ||||||||
\(11\) | −0.629200 | −0.189711 | −0.0948555 | − | 0.995491i | \(-0.530239\pi\) | ||||
−0.0948555 | + | 0.995491i | \(0.530239\pi\) | |||||||
\(12\) | 13.3480 | 3.85323 | ||||||||
\(13\) | −1.20129 | −0.333178 | −0.166589 | − | 0.986026i | \(-0.553275\pi\) | ||||
−0.166589 | + | 0.986026i | \(0.553275\pi\) | |||||||
\(14\) | 13.4220 | 3.58717 | ||||||||
\(15\) | 7.55053 | 1.94954 | ||||||||
\(16\) | 10.4695 | 2.61738 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −11.3783 | −2.68188 | ||||||||
\(19\) | −4.74739 | −1.08913 | −0.544563 | − | 0.838720i | \(-0.683305\pi\) | ||||
−0.544563 | + | 0.838720i | \(0.683305\pi\) | |||||||
\(20\) | 13.7660 | 3.07816 | ||||||||
\(21\) | −13.7925 | −3.00978 | ||||||||
\(22\) | 1.65674 | 0.353217 | ||||||||
\(23\) | −1.58864 | −0.331255 | −0.165627 | − | 0.986188i | \(-0.552965\pi\) | ||||
−0.165627 | + | 0.986188i | \(0.552965\pi\) | |||||||
\(24\) | −20.8972 | −4.26563 | ||||||||
\(25\) | 2.78697 | 0.557394 | ||||||||
\(26\) | 3.16309 | 0.620334 | ||||||||
\(27\) | 3.57506 | 0.688022 | ||||||||
\(28\) | −25.1463 | −4.75220 | ||||||||
\(29\) | −6.31747 | −1.17312 | −0.586562 | − | 0.809904i | \(-0.699519\pi\) | ||||
−0.586562 | + | 0.809904i | \(0.699519\pi\) | |||||||
\(30\) | −19.8812 | −3.62979 | ||||||||
\(31\) | 9.25295 | 1.66188 | 0.830939 | − | 0.556363i | \(-0.187804\pi\) | ||||
0.830939 | + | 0.556363i | \(0.187804\pi\) | |||||||
\(32\) | −12.1207 | −2.14266 | ||||||||
\(33\) | −1.70248 | −0.296364 | ||||||||
\(34\) | −2.63308 | −0.451570 | ||||||||
\(35\) | −14.2245 | −2.40437 | ||||||||
\(36\) | 21.3174 | 3.55290 | ||||||||
\(37\) | 3.59230 | 0.590571 | 0.295286 | − | 0.955409i | \(-0.404585\pi\) | ||||
0.295286 | + | 0.955409i | \(0.404585\pi\) | |||||||
\(38\) | 12.5003 | 2.02781 | ||||||||
\(39\) | −3.25043 | −0.520485 | ||||||||
\(40\) | −21.5516 | −3.40761 | ||||||||
\(41\) | 5.58238 | 0.871822 | 0.435911 | − | 0.899990i | \(-0.356426\pi\) | ||||
0.435911 | + | 0.899990i | \(0.356426\pi\) | |||||||
\(42\) | 36.3169 | 5.60382 | ||||||||
\(43\) | 8.15637 | 1.24384 | 0.621918 | − | 0.783083i | \(-0.286354\pi\) | ||||
0.621918 | + | 0.783083i | \(0.286354\pi\) | |||||||
\(44\) | −3.10393 | −0.467934 | ||||||||
\(45\) | 12.0586 | 1.79758 | ||||||||
\(46\) | 4.18303 | 0.616754 | ||||||||
\(47\) | 2.64958 | 0.386481 | 0.193241 | − | 0.981151i | \(-0.438100\pi\) | ||||
0.193241 | + | 0.981151i | \(0.438100\pi\) | |||||||
\(48\) | 28.3282 | 4.08883 | ||||||||
\(49\) | 18.9838 | 2.71197 | ||||||||
\(50\) | −7.33832 | −1.03780 | ||||||||
\(51\) | 2.70578 | 0.378886 | ||||||||
\(52\) | −5.92611 | −0.821804 | ||||||||
\(53\) | −10.7493 | −1.47653 | −0.738267 | − | 0.674508i | \(-0.764356\pi\) | ||||
−0.738267 | + | 0.674508i | \(0.764356\pi\) | |||||||
\(54\) | −9.41344 | −1.28101 | ||||||||
\(55\) | −1.75579 | −0.236751 | ||||||||
\(56\) | 39.3683 | 5.26082 | ||||||||
\(57\) | −12.8454 | −1.70142 | ||||||||
\(58\) | 16.6344 | 2.18421 | ||||||||
\(59\) | 5.28430 | 0.687958 | 0.343979 | − | 0.938977i | \(-0.388225\pi\) | ||||
0.343979 | + | 0.938977i | \(0.388225\pi\) | |||||||
\(60\) | 37.2477 | 4.80866 | ||||||||
\(61\) | 9.37335 | 1.20013 | 0.600067 | − | 0.799950i | \(-0.295141\pi\) | ||||
0.600067 | + | 0.799950i | \(0.295141\pi\) | |||||||
\(62\) | −24.3638 | −3.09420 | ||||||||
\(63\) | −22.0274 | −2.77519 | ||||||||
\(64\) | 10.9759 | 1.37199 | ||||||||
\(65\) | −3.35221 | −0.415791 | ||||||||
\(66\) | 4.48277 | 0.551791 | ||||||||
\(67\) | −0.944014 | −0.115330 | −0.0576648 | − | 0.998336i | \(-0.518365\pi\) | ||||
−0.0576648 | + | 0.998336i | \(0.518365\pi\) | |||||||
\(68\) | 4.93313 | 0.598230 | ||||||||
\(69\) | −4.29852 | −0.517481 | ||||||||
\(70\) | 37.4542 | 4.47663 | ||||||||
\(71\) | 13.8769 | 1.64688 | 0.823440 | − | 0.567403i | \(-0.192052\pi\) | ||||
0.823440 | + | 0.567403i | \(0.192052\pi\) | |||||||
\(72\) | −33.3739 | −3.93315 | ||||||||
\(73\) | −5.11346 | −0.598485 | −0.299242 | − | 0.954177i | \(-0.596734\pi\) | ||||
−0.299242 | + | 0.954177i | \(0.596734\pi\) | |||||||
\(74\) | −9.45884 | −1.09957 | ||||||||
\(75\) | 7.54094 | 0.870752 | ||||||||
\(76\) | −23.4195 | −2.68640 | ||||||||
\(77\) | 3.20730 | 0.365506 | ||||||||
\(78\) | 8.55865 | 0.969076 | ||||||||
\(79\) | 12.7727 | 1.43704 | 0.718518 | − | 0.695508i | \(-0.244821\pi\) | ||||
0.718518 | + | 0.695508i | \(0.244821\pi\) | |||||||
\(80\) | 29.2153 | 3.26637 | ||||||||
\(81\) | −3.29045 | −0.365605 | ||||||||
\(82\) | −14.6989 | −1.62322 | ||||||||
\(83\) | 14.5151 | 1.59324 | 0.796620 | − | 0.604480i | \(-0.206619\pi\) | ||||
0.796620 | + | 0.604480i | \(0.206619\pi\) | |||||||
\(84\) | −68.0404 | −7.42382 | ||||||||
\(85\) | 2.79051 | 0.302674 | ||||||||
\(86\) | −21.4764 | −2.31586 | ||||||||
\(87\) | −17.0937 | −1.83264 | ||||||||
\(88\) | 4.85942 | 0.518016 | ||||||||
\(89\) | 10.3474 | 1.09682 | 0.548411 | − | 0.836209i | \(-0.315233\pi\) | ||||
0.548411 | + | 0.836209i | \(0.315233\pi\) | |||||||
\(90\) | −31.7512 | −3.34687 | ||||||||
\(91\) | 6.12349 | 0.641916 | ||||||||
\(92\) | −7.83698 | −0.817062 | ||||||||
\(93\) | 25.0365 | 2.59616 | ||||||||
\(94\) | −6.97657 | −0.719578 | ||||||||
\(95\) | −13.2477 | −1.35918 | ||||||||
\(96\) | −32.7961 | −3.34724 | ||||||||
\(97\) | −6.69361 | −0.679633 | −0.339816 | − | 0.940492i | \(-0.610365\pi\) | ||||
−0.339816 | + | 0.940492i | \(0.610365\pi\) | |||||||
\(98\) | −49.9859 | −5.04934 | ||||||||
\(99\) | −2.71894 | −0.273264 | ||||||||
\(100\) | 13.7485 | 1.37485 | ||||||||
\(101\) | 2.61584 | 0.260286 | 0.130143 | − | 0.991495i | \(-0.458456\pi\) | ||||
0.130143 | + | 0.991495i | \(0.458456\pi\) | |||||||
\(102\) | −7.12456 | −0.705436 | ||||||||
\(103\) | −12.3409 | −1.21598 | −0.607992 | − | 0.793943i | \(-0.708025\pi\) | ||||
−0.607992 | + | 0.793943i | \(0.708025\pi\) | |||||||
\(104\) | 9.27776 | 0.909759 | ||||||||
\(105\) | −38.4883 | −3.75607 | ||||||||
\(106\) | 28.3039 | 2.74912 | ||||||||
\(107\) | 1.23460 | 0.119354 | 0.0596768 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596768 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(108\) | 17.6363 | 1.69705 | ||||||||
\(109\) | 16.5492 | 1.58513 | 0.792563 | − | 0.609791i | \(-0.208746\pi\) | ||||
0.792563 | + | 0.609791i | \(0.208746\pi\) | |||||||
\(110\) | 4.62315 | 0.440800 | ||||||||
\(111\) | 9.72000 | 0.922581 | ||||||||
\(112\) | −53.3676 | −5.04276 | ||||||||
\(113\) | −14.9594 | −1.40726 | −0.703632 | − | 0.710565i | \(-0.748440\pi\) | ||||
−0.703632 | + | 0.710565i | \(0.748440\pi\) | |||||||
\(114\) | 33.8231 | 3.16782 | ||||||||
\(115\) | −4.43313 | −0.413391 | ||||||||
\(116\) | −31.1649 | −2.89359 | ||||||||
\(117\) | −5.19109 | −0.479916 | ||||||||
\(118\) | −13.9140 | −1.28089 | ||||||||
\(119\) | −5.09743 | −0.467281 | ||||||||
\(120\) | −58.3140 | −5.32332 | ||||||||
\(121\) | −10.6041 | −0.964010 | ||||||||
\(122\) | −24.6808 | −2.23450 | ||||||||
\(123\) | 15.1047 | 1.36195 | ||||||||
\(124\) | 45.6460 | 4.09913 | ||||||||
\(125\) | −6.17549 | −0.552353 | ||||||||
\(126\) | 57.9999 | 5.16704 | ||||||||
\(127\) | −7.77864 | −0.690242 | −0.345121 | − | 0.938558i | \(-0.612162\pi\) | ||||
−0.345121 | + | 0.938558i | \(0.612162\pi\) | |||||||
\(128\) | −4.65898 | −0.411799 | ||||||||
\(129\) | 22.0694 | 1.94310 | ||||||||
\(130\) | 8.82666 | 0.774149 | ||||||||
\(131\) | −7.38141 | −0.644917 | −0.322458 | − | 0.946584i | \(-0.604509\pi\) | ||||
−0.322458 | + | 0.946584i | \(0.604509\pi\) | |||||||
\(132\) | −8.39855 | −0.731000 | ||||||||
\(133\) | 24.1995 | 2.09836 | ||||||||
\(134\) | 2.48567 | 0.214729 | ||||||||
\(135\) | 9.97627 | 0.858621 | ||||||||
\(136\) | −7.72317 | −0.662257 | ||||||||
\(137\) | 7.11938 | 0.608250 | 0.304125 | − | 0.952632i | \(-0.401636\pi\) | ||||
0.304125 | + | 0.952632i | \(0.401636\pi\) | |||||||
\(138\) | 11.3184 | 0.963484 | ||||||||
\(139\) | 4.08365 | 0.346370 | 0.173185 | − | 0.984889i | \(-0.444594\pi\) | ||||
0.173185 | + | 0.984889i | \(0.444594\pi\) | |||||||
\(140\) | −70.1711 | −5.93054 | ||||||||
\(141\) | 7.16919 | 0.603755 | ||||||||
\(142\) | −36.5389 | −3.06628 | ||||||||
\(143\) | 0.755851 | 0.0632074 | ||||||||
\(144\) | 45.2415 | 3.77013 | ||||||||
\(145\) | −17.6290 | −1.46401 | ||||||||
\(146\) | 13.4642 | 1.11430 | ||||||||
\(147\) | 51.3661 | 4.23660 | ||||||||
\(148\) | 17.7213 | 1.45668 | ||||||||
\(149\) | 15.6416 | 1.28141 | 0.640706 | − | 0.767786i | \(-0.278642\pi\) | ||||
0.640706 | + | 0.767786i | \(0.278642\pi\) | |||||||
\(150\) | −19.8559 | −1.62123 | ||||||||
\(151\) | 13.5726 | 1.10452 | 0.552261 | − | 0.833671i | \(-0.313765\pi\) | ||||
0.552261 | + | 0.833671i | \(0.313765\pi\) | |||||||
\(152\) | 36.6650 | 2.97392 | ||||||||
\(153\) | 4.32127 | 0.349354 | ||||||||
\(154\) | −8.44510 | −0.680525 | ||||||||
\(155\) | 25.8205 | 2.07395 | ||||||||
\(156\) | −16.0348 | −1.28381 | ||||||||
\(157\) | 17.4093 | 1.38941 | 0.694706 | − | 0.719293i | \(-0.255534\pi\) | ||||
0.694706 | + | 0.719293i | \(0.255534\pi\) | |||||||
\(158\) | −33.6315 | −2.67558 | ||||||||
\(159\) | −29.0854 | −2.30662 | ||||||||
\(160\) | −33.8231 | −2.67395 | ||||||||
\(161\) | 8.09800 | 0.638211 | ||||||||
\(162\) | 8.66403 | 0.680710 | ||||||||
\(163\) | 20.6814 | 1.61989 | 0.809944 | − | 0.586507i | \(-0.199497\pi\) | ||||
0.809944 | + | 0.586507i | \(0.199497\pi\) | |||||||
\(164\) | 27.5386 | 2.15040 | ||||||||
\(165\) | −4.75079 | −0.369849 | ||||||||
\(166\) | −38.2195 | −2.96641 | ||||||||
\(167\) | 18.1352 | 1.40335 | 0.701673 | − | 0.712500i | \(-0.252437\pi\) | ||||
0.701673 | + | 0.712500i | \(0.252437\pi\) | |||||||
\(168\) | 106.522 | 8.21837 | ||||||||
\(169\) | −11.5569 | −0.888993 | ||||||||
\(170\) | −7.34766 | −0.563540 | ||||||||
\(171\) | −20.5148 | −1.56880 | ||||||||
\(172\) | 40.2364 | 3.06800 | ||||||||
\(173\) | 17.3581 | 1.31971 | 0.659855 | − | 0.751393i | \(-0.270618\pi\) | ||||
0.659855 | + | 0.751393i | \(0.270618\pi\) | |||||||
\(174\) | 45.0092 | 3.41214 | ||||||||
\(175\) | −14.2064 | −1.07390 | ||||||||
\(176\) | −6.58741 | −0.496545 | ||||||||
\(177\) | 14.2982 | 1.07472 | ||||||||
\(178\) | −27.2455 | −2.04214 | ||||||||
\(179\) | 4.46749 | 0.333916 | 0.166958 | − | 0.985964i | \(-0.446606\pi\) | ||||
0.166958 | + | 0.985964i | \(0.446606\pi\) | |||||||
\(180\) | 59.4864 | 4.43386 | ||||||||
\(181\) | −12.2531 | −0.910766 | −0.455383 | − | 0.890296i | \(-0.650498\pi\) | ||||
−0.455383 | + | 0.890296i | \(0.650498\pi\) | |||||||
\(182\) | −16.1236 | −1.19516 | ||||||||
\(183\) | 25.3623 | 1.87483 | ||||||||
\(184\) | 12.2694 | 0.904510 | ||||||||
\(185\) | 10.0244 | 0.737007 | ||||||||
\(186\) | −65.9231 | −4.83372 | ||||||||
\(187\) | −0.629200 | −0.0460117 | ||||||||
\(188\) | 13.0707 | 0.953280 | ||||||||
\(189\) | −18.2236 | −1.32558 | ||||||||
\(190\) | 34.8822 | 2.53062 | ||||||||
\(191\) | −7.99654 | −0.578609 | −0.289305 | − | 0.957237i | \(-0.593424\pi\) | ||||
−0.289305 | + | 0.957237i | \(0.593424\pi\) | |||||||
\(192\) | 29.6984 | 2.14330 | ||||||||
\(193\) | 14.7125 | 1.05903 | 0.529516 | − | 0.848300i | \(-0.322374\pi\) | ||||
0.529516 | + | 0.848300i | \(0.322374\pi\) | |||||||
\(194\) | 17.6248 | 1.26539 | ||||||||
\(195\) | −9.07036 | −0.649542 | ||||||||
\(196\) | 93.6495 | 6.68925 | ||||||||
\(197\) | −18.2213 | −1.29822 | −0.649108 | − | 0.760696i | \(-0.724858\pi\) | ||||
−0.649108 | + | 0.760696i | \(0.724858\pi\) | |||||||
\(198\) | 7.15920 | 0.508782 | ||||||||
\(199\) | 18.2708 | 1.29518 | 0.647590 | − | 0.761989i | \(-0.275777\pi\) | ||||
0.647590 | + | 0.761989i | \(0.275777\pi\) | |||||||
\(200\) | −21.5242 | −1.52199 | ||||||||
\(201\) | −2.55430 | −0.180166 | ||||||||
\(202\) | −6.88773 | −0.484619 | ||||||||
\(203\) | 32.2029 | 2.26020 | ||||||||
\(204\) | 13.3480 | 0.934546 | ||||||||
\(205\) | 15.5777 | 1.08800 | ||||||||
\(206\) | 32.4946 | 2.26400 | ||||||||
\(207\) | −6.86495 | −0.477147 | ||||||||
\(208\) | −12.5769 | −0.872051 | ||||||||
\(209\) | 2.98706 | 0.206619 | ||||||||
\(210\) | 101.343 | 6.99332 | ||||||||
\(211\) | −17.2474 | −1.18736 | −0.593681 | − | 0.804700i | \(-0.702326\pi\) | ||||
−0.593681 | + | 0.804700i | \(0.702326\pi\) | |||||||
\(212\) | −53.0279 | −3.64197 | ||||||||
\(213\) | 37.5478 | 2.57273 | ||||||||
\(214\) | −3.25081 | −0.222221 | ||||||||
\(215\) | 22.7605 | 1.55225 | ||||||||
\(216\) | −27.6108 | −1.87868 | ||||||||
\(217\) | −47.1662 | −3.20185 | ||||||||
\(218\) | −43.5754 | −2.95130 | ||||||||
\(219\) | −13.8359 | −0.934944 | ||||||||
\(220\) | −8.66155 | −0.583961 | ||||||||
\(221\) | −1.20129 | −0.0808074 | ||||||||
\(222\) | −25.5936 | −1.71773 | ||||||||
\(223\) | 1.93787 | 0.129769 | 0.0648847 | − | 0.997893i | \(-0.479332\pi\) | ||||
0.0648847 | + | 0.997893i | \(0.479332\pi\) | |||||||
\(224\) | 61.7846 | 4.12816 | ||||||||
\(225\) | 12.0432 | 0.802883 | ||||||||
\(226\) | 39.3894 | 2.62014 | ||||||||
\(227\) | 21.0477 | 1.39698 | 0.698492 | − | 0.715618i | \(-0.253855\pi\) | ||||
0.698492 | + | 0.715618i | \(0.253855\pi\) | |||||||
\(228\) | −63.3681 | −4.19666 | ||||||||
\(229\) | −1.28845 | −0.0851431 | −0.0425715 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425715 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(230\) | 11.6728 | 0.769682 | ||||||||
\(231\) | 8.67827 | 0.570988 | ||||||||
\(232\) | 48.7909 | 3.20328 | ||||||||
\(233\) | −7.00149 | −0.458683 | −0.229341 | − | 0.973346i | \(-0.573657\pi\) | ||||
−0.229341 | + | 0.973346i | \(0.573657\pi\) | |||||||
\(234\) | 13.6686 | 0.893543 | ||||||||
\(235\) | 7.39369 | 0.482311 | ||||||||
\(236\) | 26.0681 | 1.69689 | ||||||||
\(237\) | 34.5601 | 2.24492 | ||||||||
\(238\) | 13.4220 | 0.870016 | ||||||||
\(239\) | −10.0232 | −0.648344 | −0.324172 | − | 0.945998i | \(-0.605086\pi\) | ||||
−0.324172 | + | 0.945998i | \(0.605086\pi\) | |||||||
\(240\) | 79.0503 | 5.10267 | ||||||||
\(241\) | −23.6446 | −1.52308 | −0.761541 | − | 0.648117i | \(-0.775557\pi\) | ||||
−0.761541 | + | 0.648117i | \(0.775557\pi\) | |||||||
\(242\) | 27.9215 | 1.79486 | ||||||||
\(243\) | −19.6284 | −1.25916 | ||||||||
\(244\) | 46.2399 | 2.96021 | ||||||||
\(245\) | 52.9746 | 3.38442 | ||||||||
\(246\) | −39.7720 | −2.53577 | ||||||||
\(247\) | 5.70299 | 0.362873 | ||||||||
\(248\) | −71.4621 | −4.53785 | ||||||||
\(249\) | 39.2748 | 2.48894 | ||||||||
\(250\) | 16.2606 | 1.02841 | ||||||||
\(251\) | 11.9889 | 0.756733 | 0.378366 | − | 0.925656i | \(-0.376486\pi\) | ||||
0.378366 | + | 0.925656i | \(0.376486\pi\) | |||||||
\(252\) | −108.664 | −6.84518 | ||||||||
\(253\) | 0.999574 | 0.0628427 | ||||||||
\(254\) | 20.4818 | 1.28514 | ||||||||
\(255\) | 7.55053 | 0.472832 | ||||||||
\(256\) | −9.68431 | −0.605269 | ||||||||
\(257\) | 28.2659 | 1.76318 | 0.881589 | − | 0.472017i | \(-0.156474\pi\) | ||||
0.881589 | + | 0.472017i | \(0.156474\pi\) | |||||||
\(258\) | −58.1105 | −3.61780 | ||||||||
\(259\) | −18.3115 | −1.13782 | ||||||||
\(260\) | −16.5369 | −1.02557 | ||||||||
\(261\) | −27.2995 | −1.68980 | ||||||||
\(262\) | 19.4359 | 1.20075 | ||||||||
\(263\) | −7.93940 | −0.489565 | −0.244782 | − | 0.969578i | \(-0.578716\pi\) | ||||
−0.244782 | + | 0.969578i | \(0.578716\pi\) | |||||||
\(264\) | 13.1485 | 0.809237 | ||||||||
\(265\) | −29.9962 | −1.84265 | ||||||||
\(266\) | −63.7193 | −3.90688 | ||||||||
\(267\) | 27.9978 | 1.71344 | ||||||||
\(268\) | −4.65694 | −0.284468 | ||||||||
\(269\) | 23.2796 | 1.41938 | 0.709690 | − | 0.704514i | \(-0.248835\pi\) | ||||
0.709690 | + | 0.704514i | \(0.248835\pi\) | |||||||
\(270\) | −26.2684 | −1.59864 | ||||||||
\(271\) | −6.93319 | −0.421162 | −0.210581 | − | 0.977576i | \(-0.567536\pi\) | ||||
−0.210581 | + | 0.977576i | \(0.567536\pi\) | |||||||
\(272\) | 10.4695 | 0.634807 | ||||||||
\(273\) | 16.5688 | 1.00279 | ||||||||
\(274\) | −18.7459 | −1.13248 | ||||||||
\(275\) | −1.75356 | −0.105744 | ||||||||
\(276\) | −21.2052 | −1.27640 | ||||||||
\(277\) | 4.55603 | 0.273745 | 0.136873 | − | 0.990589i | \(-0.456295\pi\) | ||||
0.136873 | + | 0.990589i | \(0.456295\pi\) | |||||||
\(278\) | −10.7526 | −0.644897 | ||||||||
\(279\) | 39.9845 | 2.39381 | ||||||||
\(280\) | 109.858 | 6.56527 | ||||||||
\(281\) | −12.9068 | −0.769956 | −0.384978 | − | 0.922926i | \(-0.625791\pi\) | ||||
−0.384978 | + | 0.922926i | \(0.625791\pi\) | |||||||
\(282\) | −18.8771 | −1.12411 | ||||||||
\(283\) | 12.4555 | 0.740404 | 0.370202 | − | 0.928951i | \(-0.379288\pi\) | ||||
0.370202 | + | 0.928951i | \(0.379288\pi\) | |||||||
\(284\) | 68.4564 | 4.06214 | ||||||||
\(285\) | −35.8453 | −2.12329 | ||||||||
\(286\) | −1.99022 | −0.117684 | ||||||||
\(287\) | −28.4558 | −1.67969 | ||||||||
\(288\) | −52.3769 | −3.08634 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 46.4186 | 2.72579 | ||||||||
\(291\) | −18.1115 | −1.06171 | ||||||||
\(292\) | −25.2253 | −1.47620 | ||||||||
\(293\) | −14.0921 | −0.823267 | −0.411633 | − | 0.911350i | \(-0.635042\pi\) | ||||
−0.411633 | + | 0.911350i | \(0.635042\pi\) | |||||||
\(294\) | −135.251 | −7.88801 | ||||||||
\(295\) | 14.7459 | 0.858541 | ||||||||
\(296\) | −27.7440 | −1.61259 | ||||||||
\(297\) | −2.24943 | −0.130525 | ||||||||
\(298\) | −41.1857 | −2.38582 | ||||||||
\(299\) | 1.90842 | 0.110367 | ||||||||
\(300\) | 37.2004 | 2.14777 | ||||||||
\(301\) | −41.5765 | −2.39643 | ||||||||
\(302\) | −35.7378 | −2.05648 | ||||||||
\(303\) | 7.07791 | 0.406615 | ||||||||
\(304\) | −49.7029 | −2.85065 | ||||||||
\(305\) | 26.1565 | 1.49771 | ||||||||
\(306\) | −11.3783 | −0.650452 | ||||||||
\(307\) | −8.67457 | −0.495084 | −0.247542 | − | 0.968877i | \(-0.579623\pi\) | ||||
−0.247542 | + | 0.968877i | \(0.579623\pi\) | |||||||
\(308\) | 15.8220 | 0.901545 | ||||||||
\(309\) | −33.3918 | −1.89959 | ||||||||
\(310\) | −67.9875 | −3.86143 | ||||||||
\(311\) | −6.16714 | −0.349707 | −0.174853 | − | 0.984594i | \(-0.555945\pi\) | ||||
−0.174853 | + | 0.984594i | \(0.555945\pi\) | |||||||
\(312\) | 25.1036 | 1.42121 | ||||||||
\(313\) | 3.33188 | 0.188329 | 0.0941645 | − | 0.995557i | \(-0.469982\pi\) | ||||
0.0941645 | + | 0.995557i | \(0.469982\pi\) | |||||||
\(314\) | −45.8401 | −2.58691 | ||||||||
\(315\) | −61.4677 | −3.46331 | ||||||||
\(316\) | 63.0092 | 3.54454 | ||||||||
\(317\) | 19.2978 | 1.08387 | 0.541936 | − | 0.840420i | \(-0.317692\pi\) | ||||
0.541936 | + | 0.840420i | \(0.317692\pi\) | |||||||
\(318\) | 76.5842 | 4.29463 | ||||||||
\(319\) | 3.97495 | 0.222555 | ||||||||
\(320\) | 30.6284 | 1.71218 | ||||||||
\(321\) | 3.34057 | 0.186452 | ||||||||
\(322\) | −21.3227 | −1.18827 | ||||||||
\(323\) | −4.74739 | −0.264152 | ||||||||
\(324\) | −16.2322 | −0.901789 | ||||||||
\(325\) | −3.34795 | −0.185711 | ||||||||
\(326\) | −54.4557 | −3.01602 | ||||||||
\(327\) | 44.7785 | 2.47626 | ||||||||
\(328\) | −43.1137 | −2.38056 | ||||||||
\(329\) | −13.5061 | −0.744613 | ||||||||
\(330\) | 12.5092 | 0.688611 | ||||||||
\(331\) | −17.0096 | −0.934930 | −0.467465 | − | 0.884012i | \(-0.654833\pi\) | ||||
−0.467465 | + | 0.884012i | \(0.654833\pi\) | |||||||
\(332\) | 71.6049 | 3.92983 | ||||||||
\(333\) | 15.5233 | 0.850672 | ||||||||
\(334\) | −47.7515 | −2.61285 | ||||||||
\(335\) | −2.63428 | −0.143926 | ||||||||
\(336\) | −144.401 | −7.87773 | ||||||||
\(337\) | −11.5670 | −0.630093 | −0.315046 | − | 0.949076i | \(-0.602020\pi\) | ||||
−0.315046 | + | 0.949076i | \(0.602020\pi\) | |||||||
\(338\) | 30.4303 | 1.65519 | ||||||||
\(339\) | −40.4770 | −2.19841 | ||||||||
\(340\) | 13.7660 | 0.746564 | ||||||||
\(341\) | −5.82195 | −0.315277 | ||||||||
\(342\) | 54.0171 | 2.92091 | ||||||||
\(343\) | −61.0866 | −3.29836 | ||||||||
\(344\) | −62.9931 | −3.39636 | ||||||||
\(345\) | −11.9951 | −0.645794 | ||||||||
\(346\) | −45.7053 | −2.45713 | ||||||||
\(347\) | −6.69435 | −0.359372 | −0.179686 | − | 0.983724i | \(-0.557508\pi\) | ||||
−0.179686 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(348\) | −84.3255 | −4.52032 | ||||||||
\(349\) | 29.5670 | 1.58268 | 0.791341 | − | 0.611374i | \(-0.209383\pi\) | ||||
0.791341 | + | 0.611374i | \(0.209383\pi\) | |||||||
\(350\) | 37.4066 | 1.99947 | ||||||||
\(351\) | −4.29469 | −0.229233 | ||||||||
\(352\) | 7.62637 | 0.406487 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | −37.6483 | −2.00098 | ||||||||
\(355\) | 38.7236 | 2.05523 | ||||||||
\(356\) | 51.0450 | 2.70538 | ||||||||
\(357\) | −13.7925 | −0.729979 | ||||||||
\(358\) | −11.7633 | −0.621709 | ||||||||
\(359\) | 20.6343 | 1.08904 | 0.544518 | − | 0.838749i | \(-0.316713\pi\) | ||||
0.544518 | + | 0.838749i | \(0.316713\pi\) | |||||||
\(360\) | −93.1303 | −4.90840 | ||||||||
\(361\) | 3.53775 | 0.186197 | ||||||||
\(362\) | 32.2635 | 1.69573 | ||||||||
\(363\) | −28.6924 | −1.50596 | ||||||||
\(364\) | 30.2079 | 1.58333 | ||||||||
\(365\) | −14.2692 | −0.746883 | ||||||||
\(366\) | −66.7809 | −3.49070 | ||||||||
\(367\) | −21.1046 | −1.10165 | −0.550825 | − | 0.834621i | \(-0.685687\pi\) | ||||
−0.550825 | + | 0.834621i | \(0.685687\pi\) | |||||||
\(368\) | −16.6323 | −0.867019 | ||||||||
\(369\) | 24.1230 | 1.25579 | ||||||||
\(370\) | −26.3950 | −1.37221 | ||||||||
\(371\) | 54.7940 | 2.84476 | ||||||||
\(372\) | 123.508 | 6.40360 | ||||||||
\(373\) | 3.49642 | 0.181038 | 0.0905189 | − | 0.995895i | \(-0.471147\pi\) | ||||
0.0905189 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(374\) | 1.65674 | 0.0856678 | ||||||||
\(375\) | −16.7096 | −0.862878 | ||||||||
\(376\) | −20.4632 | −1.05531 | ||||||||
\(377\) | 7.58911 | 0.390859 | ||||||||
\(378\) | 47.9844 | 2.46805 | ||||||||
\(379\) | −19.8239 | −1.01828 | −0.509142 | − | 0.860683i | \(-0.670037\pi\) | ||||
−0.509142 | + | 0.860683i | \(0.670037\pi\) | |||||||
\(380\) | −65.3525 | −3.35251 | ||||||||
\(381\) | −21.0473 | −1.07829 | ||||||||
\(382\) | 21.0556 | 1.07730 | ||||||||
\(383\) | −2.69266 | −0.137589 | −0.0687943 | − | 0.997631i | \(-0.521915\pi\) | ||||
−0.0687943 | + | 0.997631i | \(0.521915\pi\) | |||||||
\(384\) | −12.6062 | −0.643307 | ||||||||
\(385\) | 8.95003 | 0.456136 | ||||||||
\(386\) | −38.7394 | −1.97178 | ||||||||
\(387\) | 35.2459 | 1.79165 | ||||||||
\(388\) | −33.0204 | −1.67636 | ||||||||
\(389\) | 14.2518 | 0.722594 | 0.361297 | − | 0.932451i | \(-0.382334\pi\) | ||||
0.361297 | + | 0.932451i | \(0.382334\pi\) | |||||||
\(390\) | 23.8830 | 1.20936 | ||||||||
\(391\) | −1.58864 | −0.0803411 | ||||||||
\(392\) | −146.615 | −7.40518 | ||||||||
\(393\) | −19.9725 | −1.00748 | ||||||||
\(394\) | 47.9783 | 2.41711 | ||||||||
\(395\) | 35.6423 | 1.79336 | ||||||||
\(396\) | −13.4129 | −0.674023 | ||||||||
\(397\) | −15.7945 | −0.792703 | −0.396351 | − | 0.918099i | \(-0.629724\pi\) | ||||
−0.396351 | + | 0.918099i | \(0.629724\pi\) | |||||||
\(398\) | −48.1085 | −2.41146 | ||||||||
\(399\) | 65.4787 | 3.27803 | ||||||||
\(400\) | 29.1782 | 1.45891 | ||||||||
\(401\) | −0.423162 | −0.0211317 | −0.0105658 | − | 0.999944i | \(-0.503363\pi\) | ||||
−0.0105658 | + | 0.999944i | \(0.503363\pi\) | |||||||
\(402\) | 6.72568 | 0.335446 | ||||||||
\(403\) | −11.1155 | −0.553700 | ||||||||
\(404\) | 12.9043 | 0.642012 | ||||||||
\(405\) | −9.18204 | −0.456259 | ||||||||
\(406\) | −84.7928 | −4.20820 | ||||||||
\(407\) | −2.26028 | −0.112038 | ||||||||
\(408\) | −20.8972 | −1.03457 | ||||||||
\(409\) | −18.8010 | −0.929648 | −0.464824 | − | 0.885403i | \(-0.653882\pi\) | ||||
−0.464824 | + | 0.885403i | \(0.653882\pi\) | |||||||
\(410\) | −41.0174 | −2.02571 | ||||||||
\(411\) | 19.2635 | 0.950199 | ||||||||
\(412\) | −60.8792 | −2.99930 | ||||||||
\(413\) | −26.9364 | −1.32545 | ||||||||
\(414\) | 18.0760 | 0.888386 | ||||||||
\(415\) | 40.5046 | 1.98829 | ||||||||
\(416\) | 14.5605 | 0.713887 | ||||||||
\(417\) | 11.0495 | 0.541095 | ||||||||
\(418\) | −7.86518 | −0.384699 | ||||||||
\(419\) | −3.04013 | −0.148520 | −0.0742599 | − | 0.997239i | \(-0.523659\pi\) | ||||
−0.0742599 | + | 0.997239i | \(0.523659\pi\) | |||||||
\(420\) | −189.868 | −9.26460 | ||||||||
\(421\) | 19.1728 | 0.934423 | 0.467211 | − | 0.884146i | \(-0.345259\pi\) | ||||
0.467211 | + | 0.884146i | \(0.345259\pi\) | |||||||
\(422\) | 45.4139 | 2.21072 | ||||||||
\(423\) | 11.4495 | 0.556696 | ||||||||
\(424\) | 83.0190 | 4.03176 | ||||||||
\(425\) | 2.78697 | 0.135188 | ||||||||
\(426\) | −98.8665 | −4.79010 | ||||||||
\(427\) | −47.7800 | −2.31224 | ||||||||
\(428\) | 6.09046 | 0.294393 | ||||||||
\(429\) | 2.04517 | 0.0987417 | ||||||||
\(430\) | −59.9302 | −2.89009 | ||||||||
\(431\) | 11.9769 | 0.576906 | 0.288453 | − | 0.957494i | \(-0.406859\pi\) | ||||
0.288453 | + | 0.957494i | \(0.406859\pi\) | |||||||
\(432\) | 37.4292 | 1.80081 | ||||||||
\(433\) | 14.5934 | 0.701313 | 0.350657 | − | 0.936504i | \(-0.385958\pi\) | ||||
0.350657 | + | 0.936504i | \(0.385958\pi\) | |||||||
\(434\) | 124.193 | 5.96144 | ||||||||
\(435\) | −47.7002 | −2.28705 | ||||||||
\(436\) | 81.6393 | 3.90981 | ||||||||
\(437\) | 7.54191 | 0.360779 | ||||||||
\(438\) | 36.4311 | 1.74075 | ||||||||
\(439\) | 7.81298 | 0.372893 | 0.186447 | − | 0.982465i | \(-0.440303\pi\) | ||||
0.186447 | + | 0.982465i | \(0.440303\pi\) | |||||||
\(440\) | 13.5603 | 0.646461 | ||||||||
\(441\) | 82.0341 | 3.90638 | ||||||||
\(442\) | 3.16309 | 0.150453 | ||||||||
\(443\) | 21.1567 | 1.00518 | 0.502591 | − | 0.864524i | \(-0.332380\pi\) | ||||
0.502591 | + | 0.864524i | \(0.332380\pi\) | |||||||
\(444\) | 47.9500 | 2.27561 | ||||||||
\(445\) | 28.8745 | 1.36878 | ||||||||
\(446\) | −5.10257 | −0.241614 | ||||||||
\(447\) | 42.3229 | 2.00180 | ||||||||
\(448\) | −55.9489 | −2.64333 | ||||||||
\(449\) | −17.9303 | −0.846185 | −0.423093 | − | 0.906086i | \(-0.639055\pi\) | ||||
−0.423093 | + | 0.906086i | \(0.639055\pi\) | |||||||
\(450\) | −31.7109 | −1.49486 | ||||||||
\(451\) | −3.51244 | −0.165394 | ||||||||
\(452\) | −73.7967 | −3.47111 | ||||||||
\(453\) | 36.7245 | 1.72547 | ||||||||
\(454\) | −55.4203 | −2.60100 | ||||||||
\(455\) | 17.0877 | 0.801082 | ||||||||
\(456\) | 99.2074 | 4.64581 | ||||||||
\(457\) | 7.42332 | 0.347248 | 0.173624 | − | 0.984812i | \(-0.444452\pi\) | ||||
0.173624 | + | 0.984812i | \(0.444452\pi\) | |||||||
\(458\) | 3.39259 | 0.158525 | ||||||||
\(459\) | 3.57506 | 0.166870 | ||||||||
\(460\) | −21.8692 | −1.01966 | ||||||||
\(461\) | 9.33948 | 0.434983 | 0.217492 | − | 0.976062i | \(-0.430213\pi\) | ||||
0.217492 | + | 0.976062i | \(0.430213\pi\) | |||||||
\(462\) | −22.8506 | −1.06311 | ||||||||
\(463\) | 16.4791 | 0.765850 | 0.382925 | − | 0.923779i | \(-0.374917\pi\) | ||||
0.382925 | + | 0.923779i | \(0.374917\pi\) | |||||||
\(464\) | −66.1408 | −3.07051 | ||||||||
\(465\) | 69.8646 | 3.23989 | ||||||||
\(466\) | 18.4355 | 0.854008 | ||||||||
\(467\) | −7.02063 | −0.324876 | −0.162438 | − | 0.986719i | \(-0.551936\pi\) | ||||
−0.162438 | + | 0.986719i | \(0.551936\pi\) | |||||||
\(468\) | −25.6083 | −1.18374 | ||||||||
\(469\) | 4.81204 | 0.222200 | ||||||||
\(470\) | −19.4682 | −0.898001 | ||||||||
\(471\) | 47.1058 | 2.17052 | ||||||||
\(472\) | −40.8116 | −1.87851 | ||||||||
\(473\) | −5.13199 | −0.235969 | ||||||||
\(474\) | −90.9995 | −4.17975 | ||||||||
\(475\) | −13.2308 | −0.607073 | ||||||||
\(476\) | −25.1463 | −1.15258 | ||||||||
\(477\) | −46.4508 | −2.12683 | ||||||||
\(478\) | 26.3918 | 1.20713 | ||||||||
\(479\) | 11.3866 | 0.520268 | 0.260134 | − | 0.965572i | \(-0.416233\pi\) | ||||
0.260134 | + | 0.965572i | \(0.416233\pi\) | |||||||
\(480\) | −91.5179 | −4.17720 | ||||||||
\(481\) | −4.31539 | −0.196765 | ||||||||
\(482\) | 62.2582 | 2.83578 | ||||||||
\(483\) | 21.9114 | 0.997004 | ||||||||
\(484\) | −52.3114 | −2.37779 | ||||||||
\(485\) | −18.6786 | −0.848152 | ||||||||
\(486\) | 51.6833 | 2.34440 | ||||||||
\(487\) | −31.7884 | −1.44047 | −0.720235 | − | 0.693730i | \(-0.755966\pi\) | ||||
−0.720235 | + | 0.693730i | \(0.755966\pi\) | |||||||
\(488\) | −72.3920 | −3.27703 | ||||||||
\(489\) | 55.9593 | 2.53057 | ||||||||
\(490\) | −139.486 | −6.30135 | ||||||||
\(491\) | 14.9969 | 0.676799 | 0.338400 | − | 0.941002i | \(-0.390114\pi\) | ||||
0.338400 | + | 0.941002i | \(0.390114\pi\) | |||||||
\(492\) | 74.5136 | 3.35933 | ||||||||
\(493\) | −6.31747 | −0.284525 | ||||||||
\(494\) | −15.0165 | −0.675622 | ||||||||
\(495\) | −7.58725 | −0.341021 | ||||||||
\(496\) | 96.8738 | 4.34976 | ||||||||
\(497\) | −70.7363 | −3.17296 | ||||||||
\(498\) | −103.414 | −4.63408 | ||||||||
\(499\) | −17.2507 | −0.772248 | −0.386124 | − | 0.922447i | \(-0.626186\pi\) | ||||
−0.386124 | + | 0.922447i | \(0.626186\pi\) | |||||||
\(500\) | −30.4645 | −1.36241 | ||||||||
\(501\) | 49.0700 | 2.19228 | ||||||||
\(502\) | −31.5678 | −1.40894 | ||||||||
\(503\) | −34.6405 | −1.54454 | −0.772271 | − | 0.635293i | \(-0.780879\pi\) | ||||
−0.772271 | + | 0.635293i | \(0.780879\pi\) | |||||||
\(504\) | 170.121 | 7.57780 | ||||||||
\(505\) | 7.29955 | 0.324826 | ||||||||
\(506\) | −2.63196 | −0.117005 | ||||||||
\(507\) | −31.2705 | −1.38877 | ||||||||
\(508\) | −38.3730 | −1.70253 | ||||||||
\(509\) | 4.86172 | 0.215492 | 0.107746 | − | 0.994178i | \(-0.465637\pi\) | ||||
0.107746 | + | 0.994178i | \(0.465637\pi\) | |||||||
\(510\) | −19.8812 | −0.880353 | ||||||||
\(511\) | 26.0655 | 1.15307 | ||||||||
\(512\) | 34.8175 | 1.53873 | ||||||||
\(513\) | −16.9722 | −0.749343 | ||||||||
\(514\) | −74.4265 | −3.28281 | ||||||||
\(515\) | −34.4374 | −1.51749 | ||||||||
\(516\) | 108.871 | 4.79278 | ||||||||
\(517\) | −1.66712 | −0.0733197 | ||||||||
\(518\) | 48.2158 | 2.11848 | ||||||||
\(519\) | 46.9672 | 2.06163 | ||||||||
\(520\) | 25.8897 | 1.13534 | ||||||||
\(521\) | −32.1808 | −1.40987 | −0.704934 | − | 0.709273i | \(-0.749023\pi\) | ||||
−0.704934 | + | 0.709273i | \(0.749023\pi\) | |||||||
\(522\) | 71.8818 | 3.14618 | ||||||||
\(523\) | 7.36268 | 0.321948 | 0.160974 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160974 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(524\) | −36.4135 | −1.59073 | ||||||||
\(525\) | −38.4394 | −1.67763 | ||||||||
\(526\) | 20.9051 | 0.911506 | ||||||||
\(527\) | 9.25295 | 0.403065 | ||||||||
\(528\) | −17.8241 | −0.775695 | ||||||||
\(529\) | −20.4762 | −0.890270 | ||||||||
\(530\) | 78.9824 | 3.43078 | ||||||||
\(531\) | 22.8349 | 0.990950 | ||||||||
\(532\) | 119.379 | 5.17575 | ||||||||
\(533\) | −6.70605 | −0.290471 | ||||||||
\(534\) | −73.7206 | −3.19020 | ||||||||
\(535\) | 3.44518 | 0.148948 | ||||||||
\(536\) | 7.29078 | 0.314914 | ||||||||
\(537\) | 12.0881 | 0.521639 | ||||||||
\(538\) | −61.2970 | −2.64270 | ||||||||
\(539\) | −11.9446 | −0.514491 | ||||||||
\(540\) | 49.2142 | 2.11784 | ||||||||
\(541\) | −21.2582 | −0.913962 | −0.456981 | − | 0.889477i | \(-0.651069\pi\) | ||||
−0.456981 | + | 0.889477i | \(0.651069\pi\) | |||||||
\(542\) | 18.2557 | 0.784149 | ||||||||
\(543\) | −33.1543 | −1.42279 | ||||||||
\(544\) | −12.1207 | −0.519672 | ||||||||
\(545\) | 46.1808 | 1.97817 | ||||||||
\(546\) | −43.6271 | −1.86707 | ||||||||
\(547\) | −32.8677 | −1.40532 | −0.702661 | − | 0.711525i | \(-0.748005\pi\) | ||||
−0.702661 | + | 0.711525i | \(0.748005\pi\) | |||||||
\(548\) | 35.1208 | 1.50029 | ||||||||
\(549\) | 40.5047 | 1.72870 | ||||||||
\(550\) | 4.61727 | 0.196881 | ||||||||
\(551\) | 29.9915 | 1.27768 | ||||||||
\(552\) | 33.1983 | 1.41301 | ||||||||
\(553\) | −65.1077 | −2.76866 | ||||||||
\(554\) | −11.9964 | −0.509678 | ||||||||
\(555\) | 27.1238 | 1.15134 | ||||||||
\(556\) | 20.1452 | 0.854345 | ||||||||
\(557\) | 39.3424 | 1.66699 | 0.833496 | − | 0.552525i | \(-0.186336\pi\) | ||||
0.833496 | + | 0.552525i | \(0.186336\pi\) | |||||||
\(558\) | −105.282 | −4.45696 | ||||||||
\(559\) | −9.79816 | −0.414418 | ||||||||
\(560\) | −148.923 | −6.29314 | ||||||||
\(561\) | −1.70248 | −0.0718787 | ||||||||
\(562\) | 33.9847 | 1.43356 | ||||||||
\(563\) | −27.6562 | −1.16557 | −0.582785 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582785 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(564\) | 35.3666 | 1.48920 | ||||||||
\(565\) | −41.7445 | −1.75620 | ||||||||
\(566\) | −32.7964 | −1.37854 | ||||||||
\(567\) | 16.7728 | 0.704393 | ||||||||
\(568\) | −107.173 | −4.49690 | ||||||||
\(569\) | −32.2565 | −1.35226 | −0.676132 | − | 0.736780i | \(-0.736345\pi\) | ||||
−0.676132 | + | 0.736780i | \(0.736345\pi\) | |||||||
\(570\) | 94.3838 | 3.95330 | ||||||||
\(571\) | 20.0863 | 0.840585 | 0.420292 | − | 0.907389i | \(-0.361927\pi\) | ||||
0.420292 | + | 0.907389i | \(0.361927\pi\) | |||||||
\(572\) | 3.72871 | 0.155905 | ||||||||
\(573\) | −21.6369 | −0.903895 | ||||||||
\(574\) | 74.9265 | 3.12737 | ||||||||
\(575\) | −4.42750 | −0.184639 | ||||||||
\(576\) | 47.4298 | 1.97624 | ||||||||
\(577\) | 12.7216 | 0.529609 | 0.264804 | − | 0.964302i | \(-0.414693\pi\) | ||||
0.264804 | + | 0.964302i | \(0.414693\pi\) | |||||||
\(578\) | −2.63308 | −0.109522 | ||||||||
\(579\) | 39.8090 | 1.65440 | ||||||||
\(580\) | −86.9661 | −3.61107 | ||||||||
\(581\) | −73.9898 | −3.06961 | ||||||||
\(582\) | 47.6890 | 1.97677 | ||||||||
\(583\) | 6.76348 | 0.280115 | ||||||||
\(584\) | 39.4921 | 1.63420 | ||||||||
\(585\) | −14.4858 | −0.598915 | ||||||||
\(586\) | 37.1056 | 1.53282 | ||||||||
\(587\) | 30.8908 | 1.27500 | 0.637499 | − | 0.770451i | \(-0.279969\pi\) | ||||
0.637499 | + | 0.770451i | \(0.279969\pi\) | |||||||
\(588\) | 253.395 | 10.4498 | ||||||||
\(589\) | −43.9274 | −1.81000 | ||||||||
\(590\) | −38.8272 | −1.59849 | ||||||||
\(591\) | −49.3030 | −2.02805 | ||||||||
\(592\) | 37.6096 | 1.54575 | ||||||||
\(593\) | 18.4540 | 0.757815 | 0.378908 | − | 0.925435i | \(-0.376300\pi\) | ||||
0.378908 | + | 0.925435i | \(0.376300\pi\) | |||||||
\(594\) | 5.92294 | 0.243021 | ||||||||
\(595\) | −14.2245 | −0.583146 | ||||||||
\(596\) | 77.1622 | 3.16069 | ||||||||
\(597\) | 49.4368 | 2.02331 | ||||||||
\(598\) | −5.02503 | −0.205489 | ||||||||
\(599\) | 47.3061 | 1.93287 | 0.966437 | − | 0.256902i | \(-0.0827019\pi\) | ||||
0.966437 | + | 0.256902i | \(0.0827019\pi\) | |||||||
\(600\) | −58.2400 | −2.37764 | ||||||||
\(601\) | −39.6256 | −1.61636 | −0.808181 | − | 0.588934i | \(-0.799548\pi\) | ||||
−0.808181 | + | 0.588934i | \(0.799548\pi\) | |||||||
\(602\) | 109.475 | 4.46185 | ||||||||
\(603\) | −4.07933 | −0.166123 | ||||||||
\(604\) | 66.9554 | 2.72438 | ||||||||
\(605\) | −29.5909 | −1.20304 | ||||||||
\(606\) | −18.6367 | −0.757065 | ||||||||
\(607\) | 38.9455 | 1.58075 | 0.790374 | − | 0.612625i | \(-0.209886\pi\) | ||||
0.790374 | + | 0.612625i | \(0.209886\pi\) | |||||||
\(608\) | 57.5419 | 2.33363 | ||||||||
\(609\) | 87.1340 | 3.53085 | ||||||||
\(610\) | −68.8721 | −2.78855 | ||||||||
\(611\) | −3.18291 | −0.128767 | ||||||||
\(612\) | 21.3174 | 0.861704 | ||||||||
\(613\) | −23.7534 | −0.959391 | −0.479695 | − | 0.877435i | \(-0.659253\pi\) | ||||
−0.479695 | + | 0.877435i | \(0.659253\pi\) | |||||||
\(614\) | 22.8409 | 0.921782 | ||||||||
\(615\) | 42.1499 | 1.69965 | ||||||||
\(616\) | −24.7706 | −0.998034 | ||||||||
\(617\) | −1.45981 | −0.0587697 | −0.0293848 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293848 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(618\) | 87.9233 | 3.53679 | ||||||||
\(619\) | −33.9880 | −1.36609 | −0.683046 | − | 0.730376i | \(-0.739345\pi\) | ||||
−0.683046 | + | 0.730376i | \(0.739345\pi\) | |||||||
\(620\) | 127.376 | 5.11553 | ||||||||
\(621\) | −5.67950 | −0.227911 | ||||||||
\(622\) | 16.2386 | 0.651109 | ||||||||
\(623\) | −52.7451 | −2.11319 | ||||||||
\(624\) | −34.0304 | −1.36231 | ||||||||
\(625\) | −31.1676 | −1.24671 | ||||||||
\(626\) | −8.77312 | −0.350644 | ||||||||
\(627\) | 8.08234 | 0.322778 | ||||||||
\(628\) | 85.8823 | 3.42708 | ||||||||
\(629\) | 3.59230 | 0.143235 | ||||||||
\(630\) | 161.849 | 6.44824 | ||||||||
\(631\) | −8.84464 | −0.352100 | −0.176050 | − | 0.984381i | \(-0.556332\pi\) | ||||
−0.176050 | + | 0.984381i | \(0.556332\pi\) | |||||||
\(632\) | −98.6455 | −3.92391 | ||||||||
\(633\) | −46.6678 | −1.85488 | ||||||||
\(634\) | −50.8127 | −2.01803 | ||||||||
\(635\) | −21.7064 | −0.861392 | ||||||||
\(636\) | −143.482 | −5.68943 | ||||||||
\(637\) | −22.8050 | −0.903568 | ||||||||
\(638\) | −10.4664 | −0.414368 | ||||||||
\(639\) | 59.9656 | 2.37220 | ||||||||
\(640\) | −13.0009 | −0.513908 | ||||||||
\(641\) | 3.82470 | 0.151067 | 0.0755334 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755334 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(642\) | −8.79600 | −0.347150 | ||||||||
\(643\) | −11.4785 | −0.452669 | −0.226335 | − | 0.974050i | \(-0.572674\pi\) | ||||
−0.226335 | + | 0.974050i | \(0.572674\pi\) | |||||||
\(644\) | 39.9485 | 1.57419 | ||||||||
\(645\) | 61.5849 | 2.42490 | ||||||||
\(646\) | 12.5003 | 0.491817 | ||||||||
\(647\) | −18.4076 | −0.723678 | −0.361839 | − | 0.932241i | \(-0.617851\pi\) | ||||
−0.361839 | + | 0.932241i | \(0.617851\pi\) | |||||||
\(648\) | 25.4127 | 0.998306 | ||||||||
\(649\) | −3.32488 | −0.130513 | ||||||||
\(650\) | 8.81544 | 0.345770 | ||||||||
\(651\) | −127.622 | −5.00189 | ||||||||
\(652\) | 102.024 | 3.99556 | ||||||||
\(653\) | −14.4054 | −0.563726 | −0.281863 | − | 0.959455i | \(-0.590952\pi\) | ||||
−0.281863 | + | 0.959455i | \(0.590952\pi\) | |||||||
\(654\) | −117.906 | −4.61048 | ||||||||
\(655\) | −20.5979 | −0.804828 | ||||||||
\(656\) | 58.4448 | 2.28189 | ||||||||
\(657\) | −22.0966 | −0.862071 | ||||||||
\(658\) | 35.5626 | 1.38637 | ||||||||
\(659\) | 24.5298 | 0.955546 | 0.477773 | − | 0.878483i | \(-0.341444\pi\) | ||||
0.477773 | + | 0.878483i | \(0.341444\pi\) | |||||||
\(660\) | −23.4363 | −0.912256 | ||||||||
\(661\) | −31.9769 | −1.24376 | −0.621878 | − | 0.783114i | \(-0.713630\pi\) | ||||
−0.621878 | + | 0.783114i | \(0.713630\pi\) | |||||||
\(662\) | 44.7876 | 1.74072 | ||||||||
\(663\) | −3.25043 | −0.126236 | ||||||||
\(664\) | −112.103 | −4.35043 | ||||||||
\(665\) | 67.5291 | 2.61867 | ||||||||
\(666\) | −40.8742 | −1.58384 | ||||||||
\(667\) | 10.0362 | 0.388603 | ||||||||
\(668\) | 89.4634 | 3.46144 | ||||||||
\(669\) | 5.24346 | 0.202724 | ||||||||
\(670\) | 6.93629 | 0.267972 | ||||||||
\(671\) | −5.89771 | −0.227679 | ||||||||
\(672\) | 167.176 | 6.44895 | ||||||||
\(673\) | 3.84789 | 0.148325 | 0.0741626 | − | 0.997246i | \(-0.476372\pi\) | ||||
0.0741626 | + | 0.997246i | \(0.476372\pi\) | |||||||
\(674\) | 30.4568 | 1.17315 | ||||||||
\(675\) | 9.96359 | 0.383499 | ||||||||
\(676\) | −57.0117 | −2.19276 | ||||||||
\(677\) | −27.5568 | −1.05910 | −0.529548 | − | 0.848280i | \(-0.677638\pi\) | ||||
−0.529548 | + | 0.848280i | \(0.677638\pi\) | |||||||
\(678\) | 106.579 | 4.09315 | ||||||||
\(679\) | 34.1202 | 1.30941 | ||||||||
\(680\) | −21.5516 | −0.826467 | ||||||||
\(681\) | 56.9505 | 2.18235 | ||||||||
\(682\) | 15.3297 | 0.587004 | ||||||||
\(683\) | 34.6126 | 1.32441 | 0.662207 | − | 0.749321i | \(-0.269620\pi\) | ||||
0.662207 | + | 0.749321i | \(0.269620\pi\) | |||||||
\(684\) | −101.202 | −3.86955 | ||||||||
\(685\) | 19.8667 | 0.759069 | ||||||||
\(686\) | 160.846 | 6.14113 | ||||||||
\(687\) | −3.48626 | −0.133009 | ||||||||
\(688\) | 85.3932 | 3.25559 | ||||||||
\(689\) | 12.9131 | 0.491948 | ||||||||
\(690\) | 31.5841 | 1.20239 | ||||||||
\(691\) | −8.73729 | −0.332382 | −0.166191 | − | 0.986094i | \(-0.553147\pi\) | ||||
−0.166191 | + | 0.986094i | \(0.553147\pi\) | |||||||
\(692\) | 85.6297 | 3.25515 | ||||||||
\(693\) | 13.8596 | 0.526483 | ||||||||
\(694\) | 17.6268 | 0.669104 | ||||||||
\(695\) | 11.3955 | 0.432255 | ||||||||
\(696\) | 132.018 | 5.00412 | ||||||||
\(697\) | 5.58238 | 0.211448 | ||||||||
\(698\) | −77.8523 | −2.94675 | ||||||||
\(699\) | −18.9445 | −0.716547 | ||||||||
\(700\) | −70.0819 | −2.64885 | ||||||||
\(701\) | 16.9615 | 0.640629 | 0.320314 | − | 0.947311i | \(-0.396211\pi\) | ||||
0.320314 | + | 0.947311i | \(0.396211\pi\) | |||||||
\(702\) | 11.3083 | 0.426803 | ||||||||
\(703\) | −17.0541 | −0.643207 | ||||||||
\(704\) | −6.90603 | −0.260281 | ||||||||
\(705\) | 20.0057 | 0.753460 | ||||||||
\(706\) | 2.63308 | 0.0990974 | ||||||||
\(707\) | −13.3341 | −0.501480 | ||||||||
\(708\) | 70.5348 | 2.65086 | ||||||||
\(709\) | −7.22766 | −0.271441 | −0.135720 | − | 0.990747i | \(-0.543335\pi\) | ||||
−0.135720 | + | 0.990747i | \(0.543335\pi\) | |||||||
\(710\) | −101.962 | −3.82658 | ||||||||
\(711\) | 55.1941 | 2.06994 | ||||||||
\(712\) | −79.9147 | −2.99493 | ||||||||
\(713\) | −14.6996 | −0.550505 | ||||||||
\(714\) | 36.3169 | 1.35913 | ||||||||
\(715\) | 2.10921 | 0.0788801 | ||||||||
\(716\) | 22.0387 | 0.823625 | ||||||||
\(717\) | −27.1205 | −1.01283 | ||||||||
\(718\) | −54.3318 | −2.02764 | ||||||||
\(719\) | 32.2279 | 1.20190 | 0.600948 | − | 0.799288i | \(-0.294790\pi\) | ||||
0.600948 | + | 0.799288i | \(0.294790\pi\) | |||||||
\(720\) | 126.247 | 4.70495 | ||||||||
\(721\) | 62.9068 | 2.34277 | ||||||||
\(722\) | −9.31519 | −0.346676 | ||||||||
\(723\) | −63.9771 | −2.37934 | ||||||||
\(724\) | −60.4462 | −2.24646 | ||||||||
\(725\) | −17.6066 | −0.653892 | ||||||||
\(726\) | 75.5496 | 2.80391 | ||||||||
\(727\) | −22.4636 | −0.833130 | −0.416565 | − | 0.909106i | \(-0.636766\pi\) | ||||
−0.416565 | + | 0.909106i | \(0.636766\pi\) | |||||||
\(728\) | −47.2927 | −1.75279 | ||||||||
\(729\) | −43.2390 | −1.60144 | ||||||||
\(730\) | 37.5719 | 1.39060 | ||||||||
\(731\) | 8.15637 | 0.301674 | ||||||||
\(732\) | 125.115 | 4.62439 | ||||||||
\(733\) | −39.6452 | −1.46433 | −0.732165 | − | 0.681128i | \(-0.761490\pi\) | ||||
−0.732165 | + | 0.681128i | \(0.761490\pi\) | |||||||
\(734\) | 55.5701 | 2.05113 | ||||||||
\(735\) | 143.338 | 5.28709 | ||||||||
\(736\) | 19.2555 | 0.709768 | ||||||||
\(737\) | 0.593973 | 0.0218793 | ||||||||
\(738\) | −63.5178 | −2.33812 | ||||||||
\(739\) | 31.3222 | 1.15221 | 0.576103 | − | 0.817377i | \(-0.304573\pi\) | ||||
0.576103 | + | 0.817377i | \(0.304573\pi\) | |||||||
\(740\) | 49.4515 | 1.81787 | ||||||||
\(741\) | 15.4311 | 0.566874 | ||||||||
\(742\) | −144.277 | −5.29658 | ||||||||
\(743\) | 33.5752 | 1.23176 | 0.615878 | − | 0.787842i | \(-0.288802\pi\) | ||||
0.615878 | + | 0.787842i | \(0.288802\pi\) | |||||||
\(744\) | −193.361 | −7.08896 | ||||||||
\(745\) | 43.6482 | 1.59915 | ||||||||
\(746\) | −9.20637 | −0.337069 | ||||||||
\(747\) | 62.7237 | 2.29494 | ||||||||
\(748\) | −3.10393 | −0.113491 | ||||||||
\(749\) | −6.29330 | −0.229952 | ||||||||
\(750\) | 43.9977 | 1.60657 | ||||||||
\(751\) | −20.7154 | −0.755915 | −0.377957 | − | 0.925823i | \(-0.623373\pi\) | ||||
−0.377957 | + | 0.925823i | \(0.623373\pi\) | |||||||
\(752\) | 27.7398 | 1.01157 | ||||||||
\(753\) | 32.4394 | 1.18216 | ||||||||
\(754\) | −19.9828 | −0.727729 | ||||||||
\(755\) | 37.8745 | 1.37840 | ||||||||
\(756\) | −89.8996 | −3.26962 | ||||||||
\(757\) | −24.4176 | −0.887474 | −0.443737 | − | 0.896157i | \(-0.646348\pi\) | ||||
−0.443737 | + | 0.896157i | \(0.646348\pi\) | |||||||
\(758\) | 52.1979 | 1.89591 | ||||||||
\(759\) | 2.70463 | 0.0981719 | ||||||||
\(760\) | 102.314 | 3.71132 | ||||||||
\(761\) | −8.06229 | −0.292258 | −0.146129 | − | 0.989266i | \(-0.546681\pi\) | ||||
−0.146129 | + | 0.989266i | \(0.546681\pi\) | |||||||
\(762\) | 55.4193 | 2.00763 | ||||||||
\(763\) | −84.3584 | −3.05398 | ||||||||
\(764\) | −39.4480 | −1.42718 | ||||||||
\(765\) | 12.0586 | 0.435978 | ||||||||
\(766\) | 7.09001 | 0.256172 | ||||||||
\(767\) | −6.34797 | −0.229212 | ||||||||
\(768\) | −26.2036 | −0.945542 | ||||||||
\(769\) | 10.4938 | 0.378417 | 0.189208 | − | 0.981937i | \(-0.439408\pi\) | ||||
0.189208 | + | 0.981937i | \(0.439408\pi\) | |||||||
\(770\) | −23.5662 | −0.849266 | ||||||||
\(771\) | 76.4814 | 2.75441 | ||||||||
\(772\) | 72.5789 | 2.61217 | ||||||||
\(773\) | −10.4408 | −0.375529 | −0.187765 | − | 0.982214i | \(-0.560124\pi\) | ||||
−0.187765 | + | 0.982214i | \(0.560124\pi\) | |||||||
\(774\) | −92.8053 | −3.33582 | ||||||||
\(775\) | 25.7877 | 0.926321 | ||||||||
\(776\) | 51.6959 | 1.85577 | ||||||||
\(777\) | −49.5470 | −1.77749 | ||||||||
\(778\) | −37.5261 | −1.34538 | ||||||||
\(779\) | −26.5018 | −0.949525 | ||||||||
\(780\) | −44.7453 | −1.60214 | ||||||||
\(781\) | −8.73132 | −0.312431 | ||||||||
\(782\) | 4.18303 | 0.149585 | ||||||||
\(783\) | −22.5854 | −0.807135 | ||||||||
\(784\) | 198.751 | 7.09825 | ||||||||
\(785\) | 48.5809 | 1.73393 | ||||||||
\(786\) | 52.5893 | 1.87580 | ||||||||
\(787\) | −11.9673 | −0.426588 | −0.213294 | − | 0.976988i | \(-0.568419\pi\) | ||||
−0.213294 | + | 0.976988i | \(0.568419\pi\) | |||||||
\(788\) | −89.8882 | −3.20213 | ||||||||
\(789\) | −21.4823 | −0.764790 | ||||||||
\(790\) | −93.8491 | −3.33900 | ||||||||
\(791\) | 76.2546 | 2.71130 | ||||||||
\(792\) | 20.9989 | 0.746162 | ||||||||
\(793\) | −11.2601 | −0.399858 | ||||||||
\(794\) | 41.5882 | 1.47591 | ||||||||
\(795\) | −81.1632 | −2.87856 | ||||||||
\(796\) | 90.1321 | 3.19465 | ||||||||
\(797\) | −21.4467 | −0.759683 | −0.379841 | − | 0.925052i | \(-0.624021\pi\) | ||||
−0.379841 | + | 0.925052i | \(0.624021\pi\) | |||||||
\(798\) | −172.411 | −6.10327 | ||||||||
\(799\) | 2.64958 | 0.0937354 | ||||||||
\(800\) | −33.7801 | −1.19431 | ||||||||
\(801\) | 44.7138 | 1.57989 | ||||||||
\(802\) | 1.11422 | 0.0393445 | ||||||||
\(803\) | 3.21739 | 0.113539 | ||||||||
\(804\) | −12.6007 | −0.444392 | ||||||||
\(805\) | 22.5976 | 0.796460 | ||||||||
\(806\) | 29.2679 | 1.03092 | ||||||||
\(807\) | 62.9895 | 2.21733 | ||||||||
\(808\) | −20.2026 | −0.710725 | ||||||||
\(809\) | 24.9347 | 0.876657 | 0.438328 | − | 0.898815i | \(-0.355571\pi\) | ||||
0.438328 | + | 0.898815i | \(0.355571\pi\) | |||||||
\(810\) | 24.1771 | 0.849496 | ||||||||
\(811\) | 13.6818 | 0.480435 | 0.240217 | − | 0.970719i | \(-0.422781\pi\) | ||||
0.240217 | + | 0.970719i | \(0.422781\pi\) | |||||||
\(812\) | 158.861 | 5.57493 | ||||||||
\(813\) | −18.7597 | −0.657932 | ||||||||
\(814\) | 5.95150 | 0.208600 | ||||||||
\(815\) | 57.7116 | 2.02155 | ||||||||
\(816\) | 28.3282 | 0.991686 | ||||||||
\(817\) | −38.7215 | −1.35469 | ||||||||
\(818\) | 49.5045 | 1.73088 | ||||||||
\(819\) | 26.4612 | 0.924630 | ||||||||
\(820\) | 76.8469 | 2.68361 | ||||||||
\(821\) | 13.1310 | 0.458274 | 0.229137 | − | 0.973394i | \(-0.426410\pi\) | ||||
0.229137 | + | 0.973394i | \(0.426410\pi\) | |||||||
\(822\) | −50.7224 | −1.76915 | ||||||||
\(823\) | 13.9871 | 0.487559 | 0.243779 | − | 0.969831i | \(-0.421613\pi\) | ||||
0.243779 | + | 0.969831i | \(0.421613\pi\) | |||||||
\(824\) | 95.3108 | 3.32031 | ||||||||
\(825\) | −4.74476 | −0.165191 | ||||||||
\(826\) | 70.9257 | 2.46782 | ||||||||
\(827\) | 2.39687 | 0.0833472 | 0.0416736 | − | 0.999131i | \(-0.486731\pi\) | ||||
0.0416736 | + | 0.999131i | \(0.486731\pi\) | |||||||
\(828\) | −33.8657 | −1.17691 | ||||||||
\(829\) | 23.3984 | 0.812660 | 0.406330 | − | 0.913727i | \(-0.366808\pi\) | ||||
0.406330 | + | 0.913727i | \(0.366808\pi\) | |||||||
\(830\) | −106.652 | −3.70195 | ||||||||
\(831\) | 12.3276 | 0.427641 | ||||||||
\(832\) | −13.1852 | −0.457115 | ||||||||
\(833\) | 18.9838 | 0.657750 | ||||||||
\(834\) | −29.0942 | −1.00745 | ||||||||
\(835\) | 50.6066 | 1.75131 | ||||||||
\(836\) | 14.7356 | 0.509640 | ||||||||
\(837\) | 33.0799 | 1.14341 | ||||||||
\(838\) | 8.00491 | 0.276525 | ||||||||
\(839\) | −18.7964 | −0.648924 | −0.324462 | − | 0.945899i | \(-0.605183\pi\) | ||||
−0.324462 | + | 0.945899i | \(0.605183\pi\) | |||||||
\(840\) | 297.252 | 10.2562 | ||||||||
\(841\) | 10.9104 | 0.376222 | ||||||||
\(842\) | −50.4835 | −1.73977 | ||||||||
\(843\) | −34.9231 | −1.20281 | ||||||||
\(844\) | −85.0838 | −2.92871 | ||||||||
\(845\) | −32.2497 | −1.10942 | ||||||||
\(846\) | −30.1476 | −1.03650 | ||||||||
\(847\) | 54.0537 | 1.85731 | ||||||||
\(848\) | −112.540 | −3.86465 | ||||||||
\(849\) | 33.7020 | 1.15665 | ||||||||
\(850\) | −7.33832 | −0.251702 | ||||||||
\(851\) | −5.70689 | −0.195630 | ||||||||
\(852\) | 185.228 | 6.34581 | ||||||||
\(853\) | 40.8049 | 1.39713 | 0.698566 | − | 0.715545i | \(-0.253822\pi\) | ||||
0.698566 | + | 0.715545i | \(0.253822\pi\) | |||||||
\(854\) | 125.809 | 4.30509 | ||||||||
\(855\) | −57.2467 | −1.95780 | ||||||||
\(856\) | −9.53505 | −0.325901 | ||||||||
\(857\) | −52.1108 | −1.78007 | −0.890035 | − | 0.455893i | \(-0.849320\pi\) | ||||
−0.890035 | + | 0.455893i | \(0.849320\pi\) | |||||||
\(858\) | −5.38510 | −0.183844 | ||||||||
\(859\) | 37.2242 | 1.27007 | 0.635037 | − | 0.772482i | \(-0.280985\pi\) | ||||
0.635037 | + | 0.772482i | \(0.280985\pi\) | |||||||
\(860\) | 112.280 | 3.82873 | ||||||||
\(861\) | −76.9953 | −2.62399 | ||||||||
\(862\) | −31.5361 | −1.07412 | ||||||||
\(863\) | 23.5426 | 0.801400 | 0.400700 | − | 0.916209i | \(-0.368767\pi\) | ||||
0.400700 | + | 0.916209i | \(0.368767\pi\) | |||||||
\(864\) | −43.3324 | −1.47420 | ||||||||
\(865\) | 48.4380 | 1.64694 | ||||||||
\(866\) | −38.4256 | −1.30575 | ||||||||
\(867\) | 2.70578 | 0.0918932 | ||||||||
\(868\) | −232.677 | −7.89758 | ||||||||
\(869\) | −8.03656 | −0.272622 | ||||||||
\(870\) | 125.599 | 4.25820 | ||||||||
\(871\) | 1.13403 | 0.0384252 | ||||||||
\(872\) | −127.812 | −4.32827 | ||||||||
\(873\) | −28.9249 | −0.978959 | ||||||||
\(874\) | −19.8585 | −0.671723 | ||||||||
\(875\) | 31.4792 | 1.06419 | ||||||||
\(876\) | −68.2543 | −2.30610 | ||||||||
\(877\) | −2.93054 | −0.0989573 | −0.0494786 | − | 0.998775i | \(-0.515756\pi\) | ||||
−0.0494786 | + | 0.998775i | \(0.515756\pi\) | |||||||
\(878\) | −20.5722 | −0.694279 | ||||||||
\(879\) | −38.1301 | −1.28609 | ||||||||
\(880\) | −18.3823 | −0.619666 | ||||||||
\(881\) | −17.9111 | −0.603440 | −0.301720 | − | 0.953397i | \(-0.597561\pi\) | ||||
−0.301720 | + | 0.953397i | \(0.597561\pi\) | |||||||
\(882\) | −216.003 | −7.27318 | ||||||||
\(883\) | −53.4075 | −1.79731 | −0.898653 | − | 0.438661i | \(-0.855453\pi\) | ||||
−0.898653 | + | 0.438661i | \(0.855453\pi\) | |||||||
\(884\) | −5.92611 | −0.199317 | ||||||||
\(885\) | 39.8993 | 1.34120 | ||||||||
\(886\) | −55.7072 | −1.87152 | ||||||||
\(887\) | −3.12584 | −0.104955 | −0.0524777 | − | 0.998622i | \(-0.516712\pi\) | ||||
−0.0524777 | + | 0.998622i | \(0.516712\pi\) | |||||||
\(888\) | −75.0692 | −2.51916 | ||||||||
\(889\) | 39.6511 | 1.32985 | ||||||||
\(890\) | −76.0291 | −2.54850 | ||||||||
\(891\) | 2.07035 | 0.0693594 | ||||||||
\(892\) | 9.55976 | 0.320084 | ||||||||
\(893\) | −12.5786 | −0.420927 | ||||||||
\(894\) | −111.440 | −3.72710 | ||||||||
\(895\) | 12.4666 | 0.416712 | ||||||||
\(896\) | 23.7488 | 0.793392 | ||||||||
\(897\) | 5.16377 | 0.172413 | ||||||||
\(898\) | 47.2121 | 1.57549 | ||||||||
\(899\) | −58.4552 | −1.94959 | ||||||||
\(900\) | 59.4108 | 1.98036 | ||||||||
\(901\) | −10.7493 | −0.358112 | ||||||||
\(902\) | 9.24854 | 0.307943 | ||||||||
\(903\) | −112.497 | −3.74367 | ||||||||
\(904\) | 115.534 | 3.84261 | ||||||||
\(905\) | −34.1925 | −1.13660 | ||||||||
\(906\) | −96.6988 | −3.21260 | ||||||||
\(907\) | 9.83541 | 0.326579 | 0.163290 | − | 0.986578i | \(-0.447789\pi\) | ||||
0.163290 | + | 0.986578i | \(0.447789\pi\) | |||||||
\(908\) | 103.831 | 3.44575 | ||||||||
\(909\) | 11.3038 | 0.374922 | ||||||||
\(910\) | −44.9933 | −1.49151 | ||||||||
\(911\) | 27.9397 | 0.925683 | 0.462842 | − | 0.886441i | \(-0.346830\pi\) | ||||
0.462842 | + | 0.886441i | \(0.346830\pi\) | |||||||
\(912\) | −134.485 | −4.45325 | ||||||||
\(913\) | −9.13291 | −0.302255 | ||||||||
\(914\) | −19.5462 | −0.646532 | ||||||||
\(915\) | 70.7737 | 2.33971 | ||||||||
\(916\) | −6.35608 | −0.210011 | ||||||||
\(917\) | 37.6262 | 1.24253 | ||||||||
\(918\) | −9.41344 | −0.310690 | ||||||||
\(919\) | −23.2793 | −0.767913 | −0.383957 | − | 0.923351i | \(-0.625439\pi\) | ||||
−0.383957 | + | 0.923351i | \(0.625439\pi\) | |||||||
\(920\) | 34.2378 | 1.12879 | ||||||||
\(921\) | −23.4715 | −0.773412 | ||||||||
\(922\) | −24.5916 | −0.809883 | ||||||||
\(923\) | −16.6701 | −0.548704 | ||||||||
\(924\) | 42.8110 | 1.40838 | ||||||||
\(925\) | 10.0116 | 0.329181 | ||||||||
\(926\) | −43.3909 | −1.42591 | ||||||||
\(927\) | −53.3283 | −1.75153 | ||||||||
\(928\) | 76.5724 | 2.51361 | ||||||||
\(929\) | −11.1442 | −0.365629 | −0.182815 | − | 0.983147i | \(-0.558521\pi\) | ||||
−0.182815 | + | 0.983147i | \(0.558521\pi\) | |||||||
\(930\) | −183.959 | −6.03227 | ||||||||
\(931\) | −90.1236 | −2.95368 | ||||||||
\(932\) | −34.5392 | −1.13137 | ||||||||
\(933\) | −16.6870 | −0.546306 | ||||||||
\(934\) | 18.4859 | 0.604877 | ||||||||
\(935\) | −1.75579 | −0.0574205 | ||||||||
\(936\) | 40.0917 | 1.31044 | ||||||||
\(937\) | 12.2398 | 0.399855 | 0.199928 | − | 0.979811i | \(-0.435929\pi\) | ||||
0.199928 | + | 0.979811i | \(0.435929\pi\) | |||||||
\(938\) | −12.6705 | −0.413707 | ||||||||
\(939\) | 9.01535 | 0.294205 | ||||||||
\(940\) | 36.4740 | 1.18965 | ||||||||
\(941\) | −30.0195 | −0.978608 | −0.489304 | − | 0.872113i | \(-0.662749\pi\) | ||||
−0.489304 | + | 0.872113i | \(0.662749\pi\) | |||||||
\(942\) | −124.033 | −4.04123 | ||||||||
\(943\) | −8.86841 | −0.288795 | ||||||||
\(944\) | 55.3240 | 1.80064 | ||||||||
\(945\) | −50.8533 | −1.65426 | ||||||||
\(946\) | 13.5130 | 0.439344 | ||||||||
\(947\) | 11.4160 | 0.370971 | 0.185486 | − | 0.982647i | \(-0.440614\pi\) | ||||
0.185486 | + | 0.982647i | \(0.440614\pi\) | |||||||
\(948\) | 170.489 | 5.53723 | ||||||||
\(949\) | 6.14274 | 0.199402 | ||||||||
\(950\) | 34.8379 | 1.13029 | ||||||||
\(951\) | 52.2156 | 1.69321 | ||||||||
\(952\) | 39.3683 | 1.27594 | ||||||||
\(953\) | −24.3550 | −0.788935 | −0.394468 | − | 0.918910i | \(-0.629071\pi\) | ||||
−0.394468 | + | 0.918910i | \(0.629071\pi\) | |||||||
\(954\) | 122.309 | 3.95989 | ||||||||
\(955\) | −22.3145 | −0.722079 | ||||||||
\(956\) | −49.4455 | −1.59918 | ||||||||
\(957\) | 10.7554 | 0.347672 | ||||||||
\(958\) | −29.9819 | −0.968672 | ||||||||
\(959\) | −36.2905 | −1.17188 | ||||||||
\(960\) | 82.8738 | 2.67474 | ||||||||
\(961\) | 54.6170 | 1.76184 | ||||||||
\(962\) | 11.3628 | 0.366351 | ||||||||
\(963\) | 5.33505 | 0.171920 | ||||||||
\(964\) | −116.642 | −3.75678 | ||||||||
\(965\) | 41.0556 | 1.32163 | ||||||||
\(966\) | −57.6946 | −1.85629 | ||||||||
\(967\) | −28.0613 | −0.902392 | −0.451196 | − | 0.892425i | \(-0.649002\pi\) | ||||
−0.451196 | + | 0.892425i | \(0.649002\pi\) | |||||||
\(968\) | 81.8974 | 2.63228 | ||||||||
\(969\) | −12.8454 | −0.412654 | ||||||||
\(970\) | 49.1823 | 1.57915 | ||||||||
\(971\) | 44.1080 | 1.41549 | 0.707746 | − | 0.706467i | \(-0.249712\pi\) | ||||
0.707746 | + | 0.706467i | \(0.249712\pi\) | |||||||
\(972\) | −96.8296 | −3.10581 | ||||||||
\(973\) | −20.8161 | −0.667334 | ||||||||
\(974\) | 83.7015 | 2.68197 | ||||||||
\(975\) | −9.05884 | −0.290115 | ||||||||
\(976\) | 98.1343 | 3.14120 | ||||||||
\(977\) | −2.74982 | −0.0879747 | −0.0439873 | − | 0.999032i | \(-0.514006\pi\) | ||||
−0.0439873 | + | 0.999032i | \(0.514006\pi\) | |||||||
\(978\) | −147.345 | −4.71159 | ||||||||
\(979\) | −6.51058 | −0.208079 | ||||||||
\(980\) | 261.330 | 8.34789 | ||||||||
\(981\) | 71.5135 | 2.28325 | ||||||||
\(982\) | −39.4880 | −1.26011 | ||||||||
\(983\) | −27.7878 | −0.886294 | −0.443147 | − | 0.896449i | \(-0.646138\pi\) | ||||
−0.443147 | + | 0.896449i | \(0.646138\pi\) | |||||||
\(984\) | −116.656 | −3.71887 | ||||||||
\(985\) | −50.8469 | −1.62012 | ||||||||
\(986\) | 16.6344 | 0.529748 | ||||||||
\(987\) | −36.5445 | −1.16322 | ||||||||
\(988\) | 28.1336 | 0.895049 | ||||||||
\(989\) | −12.9576 | −0.412027 | ||||||||
\(990\) | 19.9779 | 0.634938 | ||||||||
\(991\) | 53.8238 | 1.70977 | 0.854885 | − | 0.518818i | \(-0.173628\pi\) | ||||
0.854885 | + | 0.518818i | \(0.173628\pi\) | |||||||
\(992\) | −112.152 | −3.56085 | ||||||||
\(993\) | −46.0242 | −1.46053 | ||||||||
\(994\) | 186.255 | 5.90764 | ||||||||
\(995\) | 50.9848 | 1.61633 | ||||||||
\(996\) | 193.747 | 6.13912 | ||||||||
\(997\) | −40.7736 | −1.29131 | −0.645656 | − | 0.763628i | \(-0.723416\pi\) | ||||
−0.645656 | + | 0.763628i | \(0.723416\pi\) | |||||||
\(998\) | 45.4226 | 1.43783 | ||||||||
\(999\) | 12.8427 | 0.406326 |
(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 | 6001.2.a.d.1.5 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.d.1.5 | ✓ | 121 | 1.1 | even | 1 | trivial |