Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75252 | −1.94633 | −0.973164 | − | 0.230112i | \(-0.926091\pi\) | ||||
−0.973164 | + | 0.230112i | \(0.926091\pi\) | |||||||
\(3\) | −2.26942 | −1.31025 | −0.655126 | − | 0.755520i | \(-0.727384\pi\) | ||||
−0.655126 | + | 0.755520i | \(0.727384\pi\) | |||||||
\(4\) | 5.57639 | 2.78819 | ||||||||
\(5\) | 4.03697 | 1.80539 | 0.902694 | − | 0.430283i | \(-0.141586\pi\) | ||||
0.902694 | + | 0.430283i | \(0.141586\pi\) | |||||||
\(6\) | 6.24664 | 2.55018 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.84409 | −3.48041 | ||||||||
\(9\) | 2.15028 | 0.716759 | ||||||||
\(10\) | −11.1119 | −3.51388 | ||||||||
\(11\) | 5.59978 | 1.68840 | 0.844198 | − | 0.536031i | \(-0.180077\pi\) | ||||
0.844198 | + | 0.536031i | \(0.180077\pi\) | |||||||
\(12\) | −12.6552 | −3.65324 | ||||||||
\(13\) | −6.36706 | −1.76591 | −0.882953 | − | 0.469462i | \(-0.844448\pi\) | ||||
−0.882953 | + | 0.469462i | \(0.844448\pi\) | |||||||
\(14\) | −2.75252 | −0.735643 | ||||||||
\(15\) | −9.16159 | −2.36551 | ||||||||
\(16\) | 15.9433 | 3.98583 | ||||||||
\(17\) | 3.68559 | 0.893887 | 0.446943 | − | 0.894562i | \(-0.352513\pi\) | ||||
0.446943 | + | 0.894562i | \(0.352513\pi\) | |||||||
\(18\) | −5.91869 | −1.39505 | ||||||||
\(19\) | 0.306021 | 0.0702059 | 0.0351030 | − | 0.999384i | \(-0.488824\pi\) | ||||
0.0351030 | + | 0.999384i | \(0.488824\pi\) | |||||||
\(20\) | 22.5117 | 5.03377 | ||||||||
\(21\) | −2.26942 | −0.495229 | ||||||||
\(22\) | −15.4135 | −3.28617 | ||||||||
\(23\) | 4.37544 | 0.912342 | 0.456171 | − | 0.889892i | \(-0.349221\pi\) | ||||
0.456171 | + | 0.889892i | \(0.349221\pi\) | |||||||
\(24\) | 22.3404 | 4.56022 | ||||||||
\(25\) | 11.2971 | 2.25943 | ||||||||
\(26\) | 17.5255 | 3.43703 | ||||||||
\(27\) | 1.92838 | 0.371117 | ||||||||
\(28\) | 5.57639 | 1.05384 | ||||||||
\(29\) | 3.33467 | 0.619233 | 0.309617 | − | 0.950862i | \(-0.399799\pi\) | ||||
0.309617 | + | 0.950862i | \(0.399799\pi\) | |||||||
\(30\) | 25.2175 | 4.60406 | ||||||||
\(31\) | −5.49463 | −0.986864 | −0.493432 | − | 0.869784i | \(-0.664258\pi\) | ||||
−0.493432 | + | 0.869784i | \(0.664258\pi\) | |||||||
\(32\) | −24.1962 | −4.27733 | ||||||||
\(33\) | −12.7083 | −2.21222 | ||||||||
\(34\) | −10.1447 | −1.73980 | ||||||||
\(35\) | 4.03697 | 0.682373 | ||||||||
\(36\) | 11.9908 | 1.99846 | ||||||||
\(37\) | 0.873713 | 0.143638 | 0.0718188 | − | 0.997418i | \(-0.477120\pi\) | ||||
0.0718188 | + | 0.997418i | \(0.477120\pi\) | |||||||
\(38\) | −0.842329 | −0.136644 | ||||||||
\(39\) | 14.4496 | 2.31378 | ||||||||
\(40\) | −39.7403 | −6.28350 | ||||||||
\(41\) | −6.95623 | −1.08638 | −0.543190 | − | 0.839610i | \(-0.682784\pi\) | ||||
−0.543190 | + | 0.839610i | \(0.682784\pi\) | |||||||
\(42\) | 6.24664 | 0.963877 | ||||||||
\(43\) | −8.46973 | −1.29162 | −0.645811 | − | 0.763498i | \(-0.723480\pi\) | ||||
−0.645811 | + | 0.763498i | \(0.723480\pi\) | |||||||
\(44\) | 31.2265 | 4.70758 | ||||||||
\(45\) | 8.68061 | 1.29403 | ||||||||
\(46\) | −12.0435 | −1.77572 | ||||||||
\(47\) | −13.4609 | −1.96347 | −0.981737 | − | 0.190245i | \(-0.939072\pi\) | ||||
−0.981737 | + | 0.190245i | \(0.939072\pi\) | |||||||
\(48\) | −36.1821 | −5.22244 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −31.0956 | −4.39759 | ||||||||
\(51\) | −8.36416 | −1.17122 | ||||||||
\(52\) | −35.5052 | −4.92369 | ||||||||
\(53\) | 12.2196 | 1.67849 | 0.839244 | − | 0.543755i | \(-0.182998\pi\) | ||||
0.839244 | + | 0.543755i | \(0.182998\pi\) | |||||||
\(54\) | −5.30791 | −0.722315 | ||||||||
\(55\) | 22.6061 | 3.04821 | ||||||||
\(56\) | −9.84409 | −1.31547 | ||||||||
\(57\) | −0.694490 | −0.0919874 | ||||||||
\(58\) | −9.17876 | −1.20523 | ||||||||
\(59\) | 9.57366 | 1.24638 | 0.623192 | − | 0.782069i | \(-0.285835\pi\) | ||||
0.623192 | + | 0.782069i | \(0.285835\pi\) | |||||||
\(60\) | −51.0886 | −6.59551 | ||||||||
\(61\) | −7.33583 | −0.939256 | −0.469628 | − | 0.882864i | \(-0.655612\pi\) | ||||
−0.469628 | + | 0.882864i | \(0.655612\pi\) | |||||||
\(62\) | 15.1241 | 1.92076 | ||||||||
\(63\) | 2.15028 | 0.270910 | ||||||||
\(64\) | 34.7140 | 4.33925 | ||||||||
\(65\) | −25.7036 | −3.18814 | ||||||||
\(66\) | 34.9798 | 4.30571 | ||||||||
\(67\) | 12.9283 | 1.57944 | 0.789720 | − | 0.613467i | \(-0.210226\pi\) | ||||
0.789720 | + | 0.613467i | \(0.210226\pi\) | |||||||
\(68\) | 20.5523 | 2.49233 | ||||||||
\(69\) | −9.92971 | −1.19540 | ||||||||
\(70\) | −11.1119 | −1.32812 | ||||||||
\(71\) | −1.49753 | −0.177724 | −0.0888621 | − | 0.996044i | \(-0.528323\pi\) | ||||
−0.0888621 | + | 0.996044i | \(0.528323\pi\) | |||||||
\(72\) | −21.1675 | −2.49462 | ||||||||
\(73\) | 5.95771 | 0.697297 | 0.348649 | − | 0.937253i | \(-0.386641\pi\) | ||||
0.348649 | + | 0.937253i | \(0.386641\pi\) | |||||||
\(74\) | −2.40492 | −0.279566 | ||||||||
\(75\) | −25.6380 | −2.96042 | ||||||||
\(76\) | 1.70649 | 0.195748 | ||||||||
\(77\) | 5.59978 | 0.638154 | ||||||||
\(78\) | −39.7727 | −4.50338 | ||||||||
\(79\) | 5.78081 | 0.650392 | 0.325196 | − | 0.945647i | \(-0.394570\pi\) | ||||
0.325196 | + | 0.945647i | \(0.394570\pi\) | |||||||
\(80\) | 64.3628 | 7.19597 | ||||||||
\(81\) | −10.8271 | −1.20302 | ||||||||
\(82\) | 19.1472 | 2.11445 | ||||||||
\(83\) | 0.537141 | 0.0589589 | 0.0294794 | − | 0.999565i | \(-0.490615\pi\) | ||||
0.0294794 | + | 0.999565i | \(0.490615\pi\) | |||||||
\(84\) | −12.6552 | −1.38079 | ||||||||
\(85\) | 14.8786 | 1.61381 | ||||||||
\(86\) | 23.3131 | 2.51392 | ||||||||
\(87\) | −7.56778 | −0.811351 | ||||||||
\(88\) | −55.1247 | −5.87632 | ||||||||
\(89\) | 3.53672 | 0.374891 | 0.187446 | − | 0.982275i | \(-0.439979\pi\) | ||||
0.187446 | + | 0.982275i | \(0.439979\pi\) | |||||||
\(90\) | −23.8936 | −2.51861 | ||||||||
\(91\) | −6.36706 | −0.667449 | ||||||||
\(92\) | 24.3991 | 2.54379 | ||||||||
\(93\) | 12.4696 | 1.29304 | ||||||||
\(94\) | 37.0514 | 3.82156 | ||||||||
\(95\) | 1.23540 | 0.126749 | ||||||||
\(96\) | 54.9114 | 5.60437 | ||||||||
\(97\) | −9.25815 | −0.940022 | −0.470011 | − | 0.882660i | \(-0.655750\pi\) | ||||
−0.470011 | + | 0.882660i | \(0.655750\pi\) | |||||||
\(98\) | −2.75252 | −0.278047 | ||||||||
\(99\) | 12.0411 | 1.21017 | ||||||||
\(100\) | 62.9972 | 6.29972 | ||||||||
\(101\) | 6.53574 | 0.650330 | 0.325165 | − | 0.945657i | \(-0.394580\pi\) | ||||
0.325165 | + | 0.945657i | \(0.394580\pi\) | |||||||
\(102\) | 23.0225 | 2.27957 | ||||||||
\(103\) | −3.41180 | −0.336174 | −0.168087 | − | 0.985772i | \(-0.553759\pi\) | ||||
−0.168087 | + | 0.985772i | \(0.553759\pi\) | |||||||
\(104\) | 62.6780 | 6.14608 | ||||||||
\(105\) | −9.16159 | −0.894080 | ||||||||
\(106\) | −33.6347 | −3.26689 | ||||||||
\(107\) | 9.31172 | 0.900197 | 0.450099 | − | 0.892979i | \(-0.351389\pi\) | ||||
0.450099 | + | 0.892979i | \(0.351389\pi\) | |||||||
\(108\) | 10.7534 | 1.03475 | ||||||||
\(109\) | 11.3959 | 1.09153 | 0.545766 | − | 0.837938i | \(-0.316239\pi\) | ||||
0.545766 | + | 0.837938i | \(0.316239\pi\) | |||||||
\(110\) | −62.2239 | −5.93282 | ||||||||
\(111\) | −1.98282 | −0.188201 | ||||||||
\(112\) | 15.9433 | 1.50650 | ||||||||
\(113\) | −15.4706 | −1.45535 | −0.727673 | − | 0.685924i | \(-0.759398\pi\) | ||||
−0.727673 | + | 0.685924i | \(0.759398\pi\) | |||||||
\(114\) | 1.91160 | 0.179038 | ||||||||
\(115\) | 17.6635 | 1.64713 | ||||||||
\(116\) | 18.5954 | 1.72654 | ||||||||
\(117\) | −13.6910 | −1.26573 | ||||||||
\(118\) | −26.3517 | −2.42587 | ||||||||
\(119\) | 3.68559 | 0.337857 | ||||||||
\(120\) | 90.1876 | 8.23296 | ||||||||
\(121\) | 20.3575 | 1.85068 | ||||||||
\(122\) | 20.1920 | 1.82810 | ||||||||
\(123\) | 15.7866 | 1.42343 | ||||||||
\(124\) | −30.6402 | −2.75157 | ||||||||
\(125\) | 25.4213 | 2.27375 | ||||||||
\(126\) | −5.91869 | −0.527279 | ||||||||
\(127\) | 15.9098 | 1.41176 | 0.705882 | − | 0.708330i | \(-0.250551\pi\) | ||||
0.705882 | + | 0.708330i | \(0.250551\pi\) | |||||||
\(128\) | −47.1587 | −4.16828 | ||||||||
\(129\) | 19.2214 | 1.69235 | ||||||||
\(130\) | 70.7499 | 6.20518 | ||||||||
\(131\) | −2.26496 | −0.197891 | −0.0989454 | − | 0.995093i | \(-0.531547\pi\) | ||||
−0.0989454 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(132\) | −70.8662 | −6.16811 | ||||||||
\(133\) | 0.306021 | 0.0265353 | ||||||||
\(134\) | −35.5854 | −3.07411 | ||||||||
\(135\) | 7.78481 | 0.670009 | ||||||||
\(136\) | −36.2813 | −3.11110 | ||||||||
\(137\) | −0.336057 | −0.0287113 | −0.0143557 | − | 0.999897i | \(-0.504570\pi\) | ||||
−0.0143557 | + | 0.999897i | \(0.504570\pi\) | |||||||
\(138\) | 27.3318 | 2.32663 | ||||||||
\(139\) | −0.0807869 | −0.00685226 | −0.00342613 | − | 0.999994i | \(-0.501091\pi\) | ||||
−0.00342613 | + | 0.999994i | \(0.501091\pi\) | |||||||
\(140\) | 22.5117 | 1.90259 | ||||||||
\(141\) | 30.5485 | 2.57264 | ||||||||
\(142\) | 4.12199 | 0.345910 | ||||||||
\(143\) | −35.6541 | −2.98155 | ||||||||
\(144\) | 34.2826 | 2.85688 | ||||||||
\(145\) | 13.4620 | 1.11796 | ||||||||
\(146\) | −16.3987 | −1.35717 | ||||||||
\(147\) | −2.26942 | −0.187179 | ||||||||
\(148\) | 4.87216 | 0.400489 | ||||||||
\(149\) | 13.8693 | 1.13622 | 0.568109 | − | 0.822954i | \(-0.307675\pi\) | ||||
0.568109 | + | 0.822954i | \(0.307675\pi\) | |||||||
\(150\) | 70.5691 | 5.76194 | ||||||||
\(151\) | 4.05473 | 0.329969 | 0.164984 | − | 0.986296i | \(-0.447243\pi\) | ||||
0.164984 | + | 0.986296i | \(0.447243\pi\) | |||||||
\(152\) | −3.01249 | −0.244346 | ||||||||
\(153\) | 7.92504 | 0.640702 | ||||||||
\(154\) | −15.4135 | −1.24206 | ||||||||
\(155\) | −22.1817 | −1.78167 | ||||||||
\(156\) | 80.5763 | 6.45127 | ||||||||
\(157\) | −13.9466 | −1.11306 | −0.556531 | − | 0.830827i | \(-0.687868\pi\) | ||||
−0.556531 | + | 0.830827i | \(0.687868\pi\) | |||||||
\(158\) | −15.9118 | −1.26588 | ||||||||
\(159\) | −27.7314 | −2.19924 | ||||||||
\(160\) | −97.6794 | −7.72223 | ||||||||
\(161\) | 4.37544 | 0.344833 | ||||||||
\(162\) | 29.8020 | 2.34146 | ||||||||
\(163\) | 6.82129 | 0.534284 | 0.267142 | − | 0.963657i | \(-0.413921\pi\) | ||||
0.267142 | + | 0.963657i | \(0.413921\pi\) | |||||||
\(164\) | −38.7906 | −3.02904 | ||||||||
\(165\) | −51.3029 | −3.99392 | ||||||||
\(166\) | −1.47849 | −0.114753 | ||||||||
\(167\) | −10.8806 | −0.841967 | −0.420983 | − | 0.907068i | \(-0.638315\pi\) | ||||
−0.420983 | + | 0.907068i | \(0.638315\pi\) | |||||||
\(168\) | 22.3404 | 1.72360 | ||||||||
\(169\) | 27.5395 | 2.11842 | ||||||||
\(170\) | −40.9538 | −3.14101 | ||||||||
\(171\) | 0.658029 | 0.0503208 | ||||||||
\(172\) | −47.2305 | −3.60129 | ||||||||
\(173\) | 12.7630 | 0.970353 | 0.485176 | − | 0.874416i | \(-0.338755\pi\) | ||||
0.485176 | + | 0.874416i | \(0.338755\pi\) | |||||||
\(174\) | 20.8305 | 1.57916 | ||||||||
\(175\) | 11.2971 | 0.853983 | ||||||||
\(176\) | 89.2791 | 6.72966 | ||||||||
\(177\) | −21.7267 | −1.63308 | ||||||||
\(178\) | −9.73490 | −0.729662 | ||||||||
\(179\) | 8.17347 | 0.610914 | 0.305457 | − | 0.952206i | \(-0.401191\pi\) | ||||
0.305457 | + | 0.952206i | \(0.401191\pi\) | |||||||
\(180\) | 48.4064 | 3.60800 | ||||||||
\(181\) | 14.5821 | 1.08388 | 0.541940 | − | 0.840417i | \(-0.317690\pi\) | ||||
0.541940 | + | 0.840417i | \(0.317690\pi\) | |||||||
\(182\) | 17.5255 | 1.29908 | ||||||||
\(183\) | 16.6481 | 1.23066 | ||||||||
\(184\) | −43.0722 | −3.17533 | ||||||||
\(185\) | 3.52715 | 0.259322 | ||||||||
\(186\) | −34.3230 | −2.51668 | ||||||||
\(187\) | 20.6385 | 1.50923 | ||||||||
\(188\) | −75.0632 | −5.47454 | ||||||||
\(189\) | 1.92838 | 0.140269 | ||||||||
\(190\) | −3.40046 | −0.246695 | ||||||||
\(191\) | 13.9763 | 1.01129 | 0.505644 | − | 0.862742i | \(-0.331255\pi\) | ||||
0.505644 | + | 0.862742i | \(0.331255\pi\) | |||||||
\(192\) | −78.7807 | −5.68551 | ||||||||
\(193\) | −1.91960 | −0.138176 | −0.0690878 | − | 0.997611i | \(-0.522009\pi\) | ||||
−0.0690878 | + | 0.997611i | \(0.522009\pi\) | |||||||
\(194\) | 25.4833 | 1.82959 | ||||||||
\(195\) | 58.3324 | 4.17727 | ||||||||
\(196\) | 5.57639 | 0.398313 | ||||||||
\(197\) | −26.2985 | −1.87369 | −0.936846 | − | 0.349742i | \(-0.886269\pi\) | ||||
−0.936846 | + | 0.349742i | \(0.886269\pi\) | |||||||
\(198\) | −33.1433 | −2.35540 | ||||||||
\(199\) | 7.44641 | 0.527862 | 0.263931 | − | 0.964542i | \(-0.414981\pi\) | ||||
0.263931 | + | 0.964542i | \(0.414981\pi\) | |||||||
\(200\) | −111.210 | −7.86374 | ||||||||
\(201\) | −29.3397 | −2.06946 | ||||||||
\(202\) | −17.9898 | −1.26576 | ||||||||
\(203\) | 3.33467 | 0.234048 | ||||||||
\(204\) | −46.6418 | −3.26558 | ||||||||
\(205\) | −28.0821 | −1.96134 | ||||||||
\(206\) | 9.39105 | 0.654305 | ||||||||
\(207\) | 9.40840 | 0.653929 | ||||||||
\(208\) | −101.512 | −7.03860 | ||||||||
\(209\) | 1.71365 | 0.118535 | ||||||||
\(210\) | 25.2175 | 1.74017 | ||||||||
\(211\) | 22.8447 | 1.57269 | 0.786346 | − | 0.617786i | \(-0.211970\pi\) | ||||
0.786346 | + | 0.617786i | \(0.211970\pi\) | |||||||
\(212\) | 68.1411 | 4.67995 | ||||||||
\(213\) | 3.39853 | 0.232863 | ||||||||
\(214\) | −25.6307 | −1.75208 | ||||||||
\(215\) | −34.1920 | −2.33188 | ||||||||
\(216\) | −18.9831 | −1.29164 | ||||||||
\(217\) | −5.49463 | −0.373000 | ||||||||
\(218\) | −31.3676 | −2.12448 | ||||||||
\(219\) | −13.5206 | −0.913635 | ||||||||
\(220\) | 126.061 | 8.49900 | ||||||||
\(221\) | −23.4664 | −1.57852 | ||||||||
\(222\) | 5.45777 | 0.366302 | ||||||||
\(223\) | −17.9074 | −1.19916 | −0.599582 | − | 0.800313i | \(-0.704667\pi\) | ||||
−0.599582 | + | 0.800313i | \(0.704667\pi\) | |||||||
\(224\) | −24.1962 | −1.61668 | ||||||||
\(225\) | 24.2920 | 1.61947 | ||||||||
\(226\) | 42.5831 | 2.83258 | ||||||||
\(227\) | −6.64621 | −0.441124 | −0.220562 | − | 0.975373i | \(-0.570789\pi\) | ||||
−0.220562 | + | 0.975373i | \(0.570789\pi\) | |||||||
\(228\) | −3.87274 | −0.256479 | ||||||||
\(229\) | 3.04788 | 0.201409 | 0.100705 | − | 0.994916i | \(-0.467890\pi\) | ||||
0.100705 | + | 0.994916i | \(0.467890\pi\) | |||||||
\(230\) | −48.6192 | −3.20586 | ||||||||
\(231\) | −12.7083 | −0.836142 | ||||||||
\(232\) | −32.8268 | −2.15519 | ||||||||
\(233\) | −11.3683 | −0.744760 | −0.372380 | − | 0.928080i | \(-0.621458\pi\) | ||||
−0.372380 | + | 0.928080i | \(0.621458\pi\) | |||||||
\(234\) | 37.6847 | 2.46352 | ||||||||
\(235\) | −54.3412 | −3.54483 | ||||||||
\(236\) | 53.3864 | 3.47516 | ||||||||
\(237\) | −13.1191 | −0.852177 | ||||||||
\(238\) | −10.1447 | −0.657582 | ||||||||
\(239\) | −10.8856 | −0.704131 | −0.352065 | − | 0.935975i | \(-0.614521\pi\) | ||||
−0.352065 | + | 0.935975i | \(0.614521\pi\) | |||||||
\(240\) | −146.066 | −9.42854 | ||||||||
\(241\) | −3.12332 | −0.201190 | −0.100595 | − | 0.994927i | \(-0.532075\pi\) | ||||
−0.100595 | + | 0.994927i | \(0.532075\pi\) | |||||||
\(242\) | −56.0345 | −3.60203 | ||||||||
\(243\) | 18.7862 | 1.20514 | ||||||||
\(244\) | −40.9074 | −2.61883 | ||||||||
\(245\) | 4.03697 | 0.257913 | ||||||||
\(246\) | −43.4531 | −2.77047 | ||||||||
\(247\) | −1.94845 | −0.123977 | ||||||||
\(248\) | 54.0896 | 3.43470 | ||||||||
\(249\) | −1.21900 | −0.0772510 | ||||||||
\(250\) | −69.9729 | −4.42547 | ||||||||
\(251\) | 21.6662 | 1.36756 | 0.683780 | − | 0.729688i | \(-0.260335\pi\) | ||||
0.683780 | + | 0.729688i | \(0.260335\pi\) | |||||||
\(252\) | 11.9908 | 0.755348 | ||||||||
\(253\) | 24.5015 | 1.54039 | ||||||||
\(254\) | −43.7920 | −2.74776 | ||||||||
\(255\) | −33.7659 | −2.11450 | ||||||||
\(256\) | 60.3774 | 3.77358 | ||||||||
\(257\) | 0.981209 | 0.0612061 | 0.0306031 | − | 0.999532i | \(-0.490257\pi\) | ||||
0.0306031 | + | 0.999532i | \(0.490257\pi\) | |||||||
\(258\) | −52.9073 | −3.29387 | ||||||||
\(259\) | 0.873713 | 0.0542899 | ||||||||
\(260\) | −143.333 | −8.88917 | ||||||||
\(261\) | 7.17047 | 0.443841 | ||||||||
\(262\) | 6.23437 | 0.385161 | ||||||||
\(263\) | 28.4589 | 1.75485 | 0.877427 | − | 0.479711i | \(-0.159259\pi\) | ||||
0.877427 | + | 0.479711i | \(0.159259\pi\) | |||||||
\(264\) | 125.101 | 7.69945 | ||||||||
\(265\) | 49.3301 | 3.03032 | ||||||||
\(266\) | −0.842329 | −0.0516465 | ||||||||
\(267\) | −8.02631 | −0.491202 | ||||||||
\(268\) | 72.0931 | 4.40379 | ||||||||
\(269\) | 14.2842 | 0.870924 | 0.435462 | − | 0.900207i | \(-0.356585\pi\) | ||||
0.435462 | + | 0.900207i | \(0.356585\pi\) | |||||||
\(270\) | −21.4279 | −1.30406 | ||||||||
\(271\) | 5.59980 | 0.340163 | 0.170082 | − | 0.985430i | \(-0.445597\pi\) | ||||
0.170082 | + | 0.985430i | \(0.445597\pi\) | |||||||
\(272\) | 58.7606 | 3.56288 | ||||||||
\(273\) | 14.4496 | 0.874527 | ||||||||
\(274\) | 0.925006 | 0.0558816 | ||||||||
\(275\) | 63.2614 | 3.81481 | ||||||||
\(276\) | −55.3719 | −3.33300 | ||||||||
\(277\) | 14.9843 | 0.900318 | 0.450159 | − | 0.892948i | \(-0.351367\pi\) | ||||
0.450159 | + | 0.892948i | \(0.351367\pi\) | |||||||
\(278\) | 0.222368 | 0.0133367 | ||||||||
\(279\) | −11.8150 | −0.707344 | ||||||||
\(280\) | −39.7403 | −2.37494 | ||||||||
\(281\) | −10.5310 | −0.628229 | −0.314115 | − | 0.949385i | \(-0.601708\pi\) | ||||
−0.314115 | + | 0.949385i | \(0.601708\pi\) | |||||||
\(282\) | −84.0854 | −5.00721 | ||||||||
\(283\) | −20.0101 | −1.18947 | −0.594737 | − | 0.803920i | \(-0.702744\pi\) | ||||
−0.594737 | + | 0.803920i | \(0.702744\pi\) | |||||||
\(284\) | −8.35081 | −0.495530 | ||||||||
\(285\) | −2.80364 | −0.166073 | ||||||||
\(286\) | 98.1388 | 5.80307 | ||||||||
\(287\) | −6.95623 | −0.410613 | ||||||||
\(288\) | −52.0286 | −3.06581 | ||||||||
\(289\) | −3.41643 | −0.200966 | ||||||||
\(290\) | −37.0544 | −2.17591 | ||||||||
\(291\) | 21.0106 | 1.23167 | ||||||||
\(292\) | 33.2225 | 1.94420 | ||||||||
\(293\) | −15.1033 | −0.882347 | −0.441173 | − | 0.897422i | \(-0.645438\pi\) | ||||
−0.441173 | + | 0.897422i | \(0.645438\pi\) | |||||||
\(294\) | 6.24664 | 0.364311 | ||||||||
\(295\) | 38.6486 | 2.25021 | ||||||||
\(296\) | −8.60092 | −0.499918 | ||||||||
\(297\) | 10.7985 | 0.626592 | ||||||||
\(298\) | −38.1756 | −2.21145 | ||||||||
\(299\) | −27.8587 | −1.61111 | ||||||||
\(300\) | −142.967 | −8.25422 | ||||||||
\(301\) | −8.46973 | −0.488187 | ||||||||
\(302\) | −11.1607 | −0.642228 | ||||||||
\(303\) | −14.8323 | −0.852096 | ||||||||
\(304\) | 4.87899 | 0.279829 | ||||||||
\(305\) | −29.6145 | −1.69572 | ||||||||
\(306\) | −21.8139 | −1.24702 | ||||||||
\(307\) | 14.4431 | 0.824312 | 0.412156 | − | 0.911113i | \(-0.364776\pi\) | ||||
0.412156 | + | 0.911113i | \(0.364776\pi\) | |||||||
\(308\) | 31.2265 | 1.77930 | ||||||||
\(309\) | 7.74280 | 0.440473 | ||||||||
\(310\) | 61.0555 | 3.46772 | ||||||||
\(311\) | −0.259509 | −0.0147154 | −0.00735771 | − | 0.999973i | \(-0.502342\pi\) | ||||
−0.00735771 | + | 0.999973i | \(0.502342\pi\) | |||||||
\(312\) | −142.243 | −8.05291 | ||||||||
\(313\) | 21.0940 | 1.19230 | 0.596151 | − | 0.802872i | \(-0.296696\pi\) | ||||
0.596151 | + | 0.802872i | \(0.296696\pi\) | |||||||
\(314\) | 38.3884 | 2.16638 | ||||||||
\(315\) | 8.68061 | 0.489097 | ||||||||
\(316\) | 32.2360 | 1.81342 | ||||||||
\(317\) | −19.5633 | −1.09878 | −0.549392 | − | 0.835565i | \(-0.685141\pi\) | ||||
−0.549392 | + | 0.835565i | \(0.685141\pi\) | |||||||
\(318\) | 76.3313 | 4.28045 | ||||||||
\(319\) | 18.6734 | 1.04551 | ||||||||
\(320\) | 140.139 | 7.83403 | ||||||||
\(321\) | −21.1322 | −1.17949 | ||||||||
\(322\) | −12.0435 | −0.671158 | ||||||||
\(323\) | 1.12787 | 0.0627561 | ||||||||
\(324\) | −60.3763 | −3.35424 | ||||||||
\(325\) | −71.9295 | −3.98993 | ||||||||
\(326\) | −18.7758 | −1.03989 | ||||||||
\(327\) | −25.8622 | −1.43018 | ||||||||
\(328\) | 68.4778 | 3.78105 | ||||||||
\(329\) | −13.4609 | −0.742123 | ||||||||
\(330\) | 141.212 | 7.77348 | ||||||||
\(331\) | −5.71041 | −0.313872 | −0.156936 | − | 0.987609i | \(-0.550162\pi\) | ||||
−0.156936 | + | 0.987609i | \(0.550162\pi\) | |||||||
\(332\) | 2.99531 | 0.164389 | ||||||||
\(333\) | 1.87873 | 0.102954 | ||||||||
\(334\) | 29.9491 | 1.63874 | ||||||||
\(335\) | 52.1911 | 2.85150 | ||||||||
\(336\) | −36.1821 | −1.97390 | ||||||||
\(337\) | 24.0421 | 1.30965 | 0.654827 | − | 0.755779i | \(-0.272741\pi\) | ||||
0.654827 | + | 0.755779i | \(0.272741\pi\) | |||||||
\(338\) | −75.8031 | −4.12314 | ||||||||
\(339\) | 35.1092 | 1.90687 | ||||||||
\(340\) | 82.9689 | 4.49962 | ||||||||
\(341\) | −30.7687 | −1.66622 | ||||||||
\(342\) | −1.81124 | −0.0979407 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 83.3768 | 4.49537 | ||||||||
\(345\) | −40.0860 | −2.15816 | ||||||||
\(346\) | −35.1305 | −1.88862 | ||||||||
\(347\) | −0.329970 | −0.0177137 | −0.00885687 | − | 0.999961i | \(-0.502819\pi\) | ||||
−0.00885687 | + | 0.999961i | \(0.502819\pi\) | |||||||
\(348\) | −42.2009 | −2.26220 | ||||||||
\(349\) | 6.67993 | 0.357569 | 0.178784 | − | 0.983888i | \(-0.442784\pi\) | ||||
0.178784 | + | 0.983888i | \(0.442784\pi\) | |||||||
\(350\) | −31.0956 | −1.66213 | ||||||||
\(351\) | −12.2781 | −0.655357 | ||||||||
\(352\) | −135.493 | −7.22182 | ||||||||
\(353\) | −12.2971 | −0.654510 | −0.327255 | − | 0.944936i | \(-0.606124\pi\) | ||||
−0.327255 | + | 0.944936i | \(0.606124\pi\) | |||||||
\(354\) | 59.8032 | 3.17850 | ||||||||
\(355\) | −6.04549 | −0.320861 | ||||||||
\(356\) | 19.7221 | 1.04527 | ||||||||
\(357\) | −8.36416 | −0.442678 | ||||||||
\(358\) | −22.4977 | −1.18904 | ||||||||
\(359\) | −19.4540 | −1.02674 | −0.513371 | − | 0.858167i | \(-0.671604\pi\) | ||||
−0.513371 | + | 0.858167i | \(0.671604\pi\) | |||||||
\(360\) | −85.4527 | −4.50375 | ||||||||
\(361\) | −18.9064 | −0.995071 | ||||||||
\(362\) | −40.1376 | −2.10959 | ||||||||
\(363\) | −46.1998 | −2.42486 | ||||||||
\(364\) | −35.5052 | −1.86098 | ||||||||
\(365\) | 24.0511 | 1.25889 | ||||||||
\(366\) | −45.8243 | −2.39527 | ||||||||
\(367\) | 15.5108 | 0.809657 | 0.404828 | − | 0.914393i | \(-0.367331\pi\) | ||||
0.404828 | + | 0.914393i | \(0.367331\pi\) | |||||||
\(368\) | 69.7590 | 3.63644 | ||||||||
\(369\) | −14.9578 | −0.778673 | ||||||||
\(370\) | −9.70858 | −0.504725 | ||||||||
\(371\) | 12.2196 | 0.634409 | ||||||||
\(372\) | 69.5355 | 3.60525 | ||||||||
\(373\) | −7.78323 | −0.403000 | −0.201500 | − | 0.979488i | \(-0.564582\pi\) | ||||
−0.201500 | + | 0.979488i | \(0.564582\pi\) | |||||||
\(374\) | −56.8079 | −2.93747 | ||||||||
\(375\) | −57.6918 | −2.97919 | ||||||||
\(376\) | 132.510 | 6.83370 | ||||||||
\(377\) | −21.2321 | −1.09351 | ||||||||
\(378\) | −5.30791 | −0.273009 | ||||||||
\(379\) | 29.3733 | 1.50881 | 0.754404 | − | 0.656411i | \(-0.227926\pi\) | ||||
0.754404 | + | 0.656411i | \(0.227926\pi\) | |||||||
\(380\) | 6.88905 | 0.353401 | ||||||||
\(381\) | −36.1060 | −1.84977 | ||||||||
\(382\) | −38.4700 | −1.96830 | ||||||||
\(383\) | 18.0431 | 0.921960 | 0.460980 | − | 0.887410i | \(-0.347498\pi\) | ||||
0.460980 | + | 0.887410i | \(0.347498\pi\) | |||||||
\(384\) | 107.023 | 5.46149 | ||||||||
\(385\) | 22.6061 | 1.15212 | ||||||||
\(386\) | 5.28374 | 0.268935 | ||||||||
\(387\) | −18.2123 | −0.925781 | ||||||||
\(388\) | −51.6270 | −2.62097 | ||||||||
\(389\) | −16.9277 | −0.858269 | −0.429134 | − | 0.903241i | \(-0.641181\pi\) | ||||
−0.429134 | + | 0.903241i | \(0.641181\pi\) | |||||||
\(390\) | −160.561 | −8.13034 | ||||||||
\(391\) | 16.1261 | 0.815530 | ||||||||
\(392\) | −9.84409 | −0.497202 | ||||||||
\(393\) | 5.14016 | 0.259287 | ||||||||
\(394\) | 72.3873 | 3.64682 | ||||||||
\(395\) | 23.3370 | 1.17421 | ||||||||
\(396\) | 67.1457 | 3.37420 | ||||||||
\(397\) | −14.7989 | −0.742734 | −0.371367 | − | 0.928486i | \(-0.621111\pi\) | ||||
−0.371367 | + | 0.928486i | \(0.621111\pi\) | |||||||
\(398\) | −20.4964 | −1.02739 | ||||||||
\(399\) | −0.694490 | −0.0347680 | ||||||||
\(400\) | 180.114 | 9.00570 | ||||||||
\(401\) | −11.3183 | −0.565210 | −0.282605 | − | 0.959236i | \(-0.591199\pi\) | ||||
−0.282605 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(402\) | 80.7583 | 4.02786 | ||||||||
\(403\) | 34.9846 | 1.74271 | ||||||||
\(404\) | 36.4458 | 1.81325 | ||||||||
\(405\) | −43.7088 | −2.17191 | ||||||||
\(406\) | −9.17876 | −0.455534 | ||||||||
\(407\) | 4.89260 | 0.242517 | ||||||||
\(408\) | 82.3376 | 4.07632 | ||||||||
\(409\) | −30.8220 | −1.52405 | −0.762026 | − | 0.647547i | \(-0.775795\pi\) | ||||
−0.762026 | + | 0.647547i | \(0.775795\pi\) | |||||||
\(410\) | 77.2966 | 3.81741 | ||||||||
\(411\) | 0.762656 | 0.0376190 | ||||||||
\(412\) | −19.0255 | −0.937319 | ||||||||
\(413\) | 9.57366 | 0.471089 | ||||||||
\(414\) | −25.8969 | −1.27276 | ||||||||
\(415\) | 2.16842 | 0.106444 | ||||||||
\(416\) | 154.059 | 7.55335 | ||||||||
\(417\) | 0.183340 | 0.00897818 | ||||||||
\(418\) | −4.71685 | −0.230709 | ||||||||
\(419\) | 15.6141 | 0.762799 | 0.381400 | − | 0.924410i | \(-0.375442\pi\) | ||||
0.381400 | + | 0.924410i | \(0.375442\pi\) | |||||||
\(420\) | −51.0886 | −2.49287 | ||||||||
\(421\) | −38.1872 | −1.86113 | −0.930564 | − | 0.366130i | \(-0.880683\pi\) | ||||
−0.930564 | + | 0.366130i | \(0.880683\pi\) | |||||||
\(422\) | −62.8805 | −3.06098 | ||||||||
\(423\) | −28.9447 | −1.40734 | ||||||||
\(424\) | −120.291 | −5.84183 | ||||||||
\(425\) | 41.6366 | 2.01967 | ||||||||
\(426\) | −9.35453 | −0.453229 | ||||||||
\(427\) | −7.33583 | −0.355006 | ||||||||
\(428\) | 51.9257 | 2.50993 | ||||||||
\(429\) | 80.9143 | 3.90658 | ||||||||
\(430\) | 94.1144 | 4.53860 | ||||||||
\(431\) | −3.59797 | −0.173308 | −0.0866541 | − | 0.996238i | \(-0.527617\pi\) | ||||
−0.0866541 | + | 0.996238i | \(0.527617\pi\) | |||||||
\(432\) | 30.7448 | 1.47921 | ||||||||
\(433\) | 3.57470 | 0.171789 | 0.0858945 | − | 0.996304i | \(-0.472625\pi\) | ||||
0.0858945 | + | 0.996304i | \(0.472625\pi\) | |||||||
\(434\) | 15.1241 | 0.725980 | ||||||||
\(435\) | −30.5509 | −1.46480 | ||||||||
\(436\) | 63.5481 | 3.04340 | ||||||||
\(437\) | 1.33897 | 0.0640518 | ||||||||
\(438\) | 37.2157 | 1.77823 | ||||||||
\(439\) | −6.60211 | −0.315101 | −0.157551 | − | 0.987511i | \(-0.550360\pi\) | ||||
−0.157551 | + | 0.987511i | \(0.550360\pi\) | |||||||
\(440\) | −222.537 | −10.6090 | ||||||||
\(441\) | 2.15028 | 0.102394 | ||||||||
\(442\) | 64.5918 | 3.07232 | ||||||||
\(443\) | 39.2262 | 1.86369 | 0.931847 | − | 0.362852i | \(-0.118197\pi\) | ||||
0.931847 | + | 0.362852i | \(0.118197\pi\) | |||||||
\(444\) | −11.0570 | −0.524742 | ||||||||
\(445\) | 14.2776 | 0.676824 | ||||||||
\(446\) | 49.2904 | 2.33397 | ||||||||
\(447\) | −31.4753 | −1.48873 | ||||||||
\(448\) | 34.7140 | 1.64008 | ||||||||
\(449\) | 24.2865 | 1.14615 | 0.573076 | − | 0.819502i | \(-0.305750\pi\) | ||||
0.573076 | + | 0.819502i | \(0.305750\pi\) | |||||||
\(450\) | −66.8642 | −3.15201 | ||||||||
\(451\) | −38.9533 | −1.83424 | ||||||||
\(452\) | −86.2698 | −4.05779 | ||||||||
\(453\) | −9.20189 | −0.432342 | ||||||||
\(454\) | 18.2938 | 0.858573 | ||||||||
\(455\) | −25.7036 | −1.20501 | ||||||||
\(456\) | 6.83662 | 0.320154 | ||||||||
\(457\) | −16.7421 | −0.783163 | −0.391581 | − | 0.920143i | \(-0.628072\pi\) | ||||
−0.391581 | + | 0.920143i | \(0.628072\pi\) | |||||||
\(458\) | −8.38935 | −0.392009 | ||||||||
\(459\) | 7.10721 | 0.331736 | ||||||||
\(460\) | 98.4986 | 4.59252 | ||||||||
\(461\) | −18.6385 | −0.868083 | −0.434042 | − | 0.900893i | \(-0.642913\pi\) | ||||
−0.434042 | + | 0.900893i | \(0.642913\pi\) | |||||||
\(462\) | 34.9798 | 1.62741 | ||||||||
\(463\) | 0.884971 | 0.0411281 | 0.0205640 | − | 0.999789i | \(-0.493454\pi\) | ||||
0.0205640 | + | 0.999789i | \(0.493454\pi\) | |||||||
\(464\) | 53.1658 | 2.46816 | ||||||||
\(465\) | 50.3395 | 2.33444 | ||||||||
\(466\) | 31.2914 | 1.44955 | ||||||||
\(467\) | 21.5353 | 0.996534 | 0.498267 | − | 0.867024i | \(-0.333970\pi\) | ||||
0.498267 | + | 0.867024i | \(0.333970\pi\) | |||||||
\(468\) | −76.3461 | −3.52910 | ||||||||
\(469\) | 12.9283 | 0.596972 | ||||||||
\(470\) | 149.576 | 6.89941 | ||||||||
\(471\) | 31.6508 | 1.45839 | ||||||||
\(472\) | −94.2440 | −4.33793 | ||||||||
\(473\) | −47.4286 | −2.18077 | ||||||||
\(474\) | 36.1106 | 1.65862 | ||||||||
\(475\) | 3.45715 | 0.158625 | ||||||||
\(476\) | 20.5523 | 0.942012 | ||||||||
\(477\) | 26.2755 | 1.20307 | ||||||||
\(478\) | 29.9629 | 1.37047 | ||||||||
\(479\) | −41.0404 | −1.87518 | −0.937592 | − | 0.347738i | \(-0.886950\pi\) | ||||
−0.937592 | + | 0.347738i | \(0.886950\pi\) | |||||||
\(480\) | 221.676 | 10.1181 | ||||||||
\(481\) | −5.56299 | −0.253650 | ||||||||
\(482\) | 8.59700 | 0.391583 | ||||||||
\(483\) | −9.92971 | −0.451818 | ||||||||
\(484\) | 113.521 | 5.16006 | ||||||||
\(485\) | −37.3749 | −1.69711 | ||||||||
\(486\) | −51.7095 | −2.34559 | ||||||||
\(487\) | 7.54063 | 0.341699 | 0.170849 | − | 0.985297i | \(-0.445349\pi\) | ||||
0.170849 | + | 0.985297i | \(0.445349\pi\) | |||||||
\(488\) | 72.2146 | 3.26900 | ||||||||
\(489\) | −15.4804 | −0.700047 | ||||||||
\(490\) | −11.1119 | −0.501983 | ||||||||
\(491\) | −8.90635 | −0.401938 | −0.200969 | − | 0.979598i | \(-0.564409\pi\) | ||||
−0.200969 | + | 0.979598i | \(0.564409\pi\) | |||||||
\(492\) | 88.0323 | 3.96880 | ||||||||
\(493\) | 12.2902 | 0.553524 | ||||||||
\(494\) | 5.36316 | 0.241300 | ||||||||
\(495\) | 48.6095 | 2.18483 | ||||||||
\(496\) | −87.6027 | −3.93348 | ||||||||
\(497\) | −1.49753 | −0.0671734 | ||||||||
\(498\) | 3.35533 | 0.150356 | ||||||||
\(499\) | 20.9496 | 0.937835 | 0.468917 | − | 0.883242i | \(-0.344644\pi\) | ||||
0.468917 | + | 0.883242i | \(0.344644\pi\) | |||||||
\(500\) | 141.759 | 6.33967 | ||||||||
\(501\) | 24.6927 | 1.10319 | ||||||||
\(502\) | −59.6368 | −2.66172 | ||||||||
\(503\) | 5.42274 | 0.241788 | 0.120894 | − | 0.992665i | \(-0.461424\pi\) | ||||
0.120894 | + | 0.992665i | \(0.461424\pi\) | |||||||
\(504\) | −21.1675 | −0.942877 | ||||||||
\(505\) | 26.3846 | 1.17410 | ||||||||
\(506\) | −67.4409 | −2.99811 | ||||||||
\(507\) | −62.4987 | −2.77566 | ||||||||
\(508\) | 88.7191 | 3.93627 | ||||||||
\(509\) | −16.5523 | −0.733666 | −0.366833 | − | 0.930287i | \(-0.619558\pi\) | ||||
−0.366833 | + | 0.930287i | \(0.619558\pi\) | |||||||
\(510\) | 92.9414 | 4.11551 | ||||||||
\(511\) | 5.95771 | 0.263554 | ||||||||
\(512\) | −71.8728 | −3.17636 | ||||||||
\(513\) | 0.590123 | 0.0260546 | ||||||||
\(514\) | −2.70080 | −0.119127 | ||||||||
\(515\) | −13.7733 | −0.606925 | ||||||||
\(516\) | 107.186 | 4.71860 | ||||||||
\(517\) | −75.3780 | −3.31512 | ||||||||
\(518\) | −2.40492 | −0.105666 | ||||||||
\(519\) | −28.9646 | −1.27141 | ||||||||
\(520\) | 253.029 | 11.0961 | ||||||||
\(521\) | 7.19428 | 0.315187 | 0.157594 | − | 0.987504i | \(-0.449626\pi\) | ||||
0.157594 | + | 0.987504i | \(0.449626\pi\) | |||||||
\(522\) | −19.7369 | −0.863860 | ||||||||
\(523\) | 2.17422 | 0.0950720 | 0.0475360 | − | 0.998870i | \(-0.484863\pi\) | ||||
0.0475360 | + | 0.998870i | \(0.484863\pi\) | |||||||
\(524\) | −12.6303 | −0.551758 | ||||||||
\(525\) | −25.6380 | −1.11893 | ||||||||
\(526\) | −78.3339 | −3.41552 | ||||||||
\(527\) | −20.2509 | −0.882145 | ||||||||
\(528\) | −202.612 | −8.81755 | ||||||||
\(529\) | −3.85556 | −0.167633 | ||||||||
\(530\) | −135.782 | −5.89800 | ||||||||
\(531\) | 20.5860 | 0.893358 | ||||||||
\(532\) | 1.70649 | 0.0739857 | ||||||||
\(533\) | 44.2907 | 1.91844 | ||||||||
\(534\) | 22.0926 | 0.956040 | ||||||||
\(535\) | 37.5911 | 1.62521 | ||||||||
\(536\) | −127.267 | −5.49710 | ||||||||
\(537\) | −18.5491 | −0.800451 | ||||||||
\(538\) | −39.3177 | −1.69510 | ||||||||
\(539\) | 5.59978 | 0.241199 | ||||||||
\(540\) | 43.4111 | 1.86812 | ||||||||
\(541\) | −19.1835 | −0.824763 | −0.412382 | − | 0.911011i | \(-0.635303\pi\) | ||||
−0.412382 | + | 0.911011i | \(0.635303\pi\) | |||||||
\(542\) | −15.4136 | −0.662070 | ||||||||
\(543\) | −33.0930 | −1.42015 | ||||||||
\(544\) | −89.1773 | −3.82344 | ||||||||
\(545\) | 46.0050 | 1.97064 | ||||||||
\(546\) | −39.7727 | −1.70212 | ||||||||
\(547\) | −35.6979 | −1.52633 | −0.763166 | − | 0.646202i | \(-0.776356\pi\) | ||||
−0.763166 | + | 0.646202i | \(0.776356\pi\) | |||||||
\(548\) | −1.87399 | −0.0800527 | ||||||||
\(549\) | −15.7741 | −0.673221 | ||||||||
\(550\) | −174.129 | −7.42487 | ||||||||
\(551\) | 1.02048 | 0.0434738 | ||||||||
\(552\) | 97.7490 | 4.16047 | ||||||||
\(553\) | 5.78081 | 0.245825 | ||||||||
\(554\) | −41.2446 | −1.75231 | ||||||||
\(555\) | −8.00460 | −0.339777 | ||||||||
\(556\) | −0.450499 | −0.0191054 | ||||||||
\(557\) | −18.8724 | −0.799651 | −0.399826 | − | 0.916591i | \(-0.630929\pi\) | ||||
−0.399826 | + | 0.916591i | \(0.630929\pi\) | |||||||
\(558\) | 32.5210 | 1.37672 | ||||||||
\(559\) | 53.9273 | 2.28088 | ||||||||
\(560\) | 64.3628 | 2.71982 | ||||||||
\(561\) | −46.8374 | −1.97748 | ||||||||
\(562\) | 28.9870 | 1.22274 | ||||||||
\(563\) | −34.9320 | −1.47221 | −0.736105 | − | 0.676867i | \(-0.763337\pi\) | ||||
−0.736105 | + | 0.676867i | \(0.763337\pi\) | |||||||
\(564\) | 170.350 | 7.17303 | ||||||||
\(565\) | −62.4542 | −2.62747 | ||||||||
\(566\) | 55.0782 | 2.31511 | ||||||||
\(567\) | −10.8271 | −0.454697 | ||||||||
\(568\) | 14.7418 | 0.618554 | ||||||||
\(569\) | −9.90202 | −0.415114 | −0.207557 | − | 0.978223i | \(-0.566551\pi\) | ||||
−0.207557 | + | 0.978223i | \(0.566551\pi\) | |||||||
\(570\) | 7.71707 | 0.323233 | ||||||||
\(571\) | −26.8154 | −1.12219 | −0.561095 | − | 0.827752i | \(-0.689620\pi\) | ||||
−0.561095 | + | 0.827752i | \(0.689620\pi\) | |||||||
\(572\) | −198.821 | −8.31313 | ||||||||
\(573\) | −31.7181 | −1.32504 | ||||||||
\(574\) | 19.1472 | 0.799188 | ||||||||
\(575\) | 49.4299 | 2.06137 | ||||||||
\(576\) | 74.6447 | 3.11020 | ||||||||
\(577\) | 4.66582 | 0.194240 | 0.0971202 | − | 0.995273i | \(-0.469037\pi\) | ||||
0.0971202 | + | 0.995273i | \(0.469037\pi\) | |||||||
\(578\) | 9.40380 | 0.391147 | ||||||||
\(579\) | 4.35638 | 0.181045 | ||||||||
\(580\) | 75.0692 | 3.11708 | ||||||||
\(581\) | 0.537141 | 0.0222844 | ||||||||
\(582\) | −57.8323 | −2.39723 | ||||||||
\(583\) | 68.4269 | 2.83395 | ||||||||
\(584\) | −58.6483 | −2.42688 | ||||||||
\(585\) | −55.2700 | −2.28513 | ||||||||
\(586\) | 41.5723 | 1.71734 | ||||||||
\(587\) | −24.6937 | −1.01922 | −0.509608 | − | 0.860407i | \(-0.670210\pi\) | ||||
−0.509608 | + | 0.860407i | \(0.670210\pi\) | |||||||
\(588\) | −12.6552 | −0.521891 | ||||||||
\(589\) | −1.68147 | −0.0692837 | ||||||||
\(590\) | −106.381 | −4.37964 | ||||||||
\(591\) | 59.6825 | 2.45501 | ||||||||
\(592\) | 13.9299 | 0.572515 | ||||||||
\(593\) | 15.4558 | 0.634696 | 0.317348 | − | 0.948309i | \(-0.397208\pi\) | ||||
0.317348 | + | 0.948309i | \(0.397208\pi\) | |||||||
\(594\) | −29.7231 | −1.21955 | ||||||||
\(595\) | 14.8786 | 0.609964 | ||||||||
\(596\) | 77.3406 | 3.16799 | ||||||||
\(597\) | −16.8991 | −0.691632 | ||||||||
\(598\) | 76.6817 | 3.13575 | ||||||||
\(599\) | −34.4534 | −1.40773 | −0.703864 | − | 0.710335i | \(-0.748543\pi\) | ||||
−0.703864 | + | 0.710335i | \(0.748543\pi\) | |||||||
\(600\) | 252.383 | 10.3035 | ||||||||
\(601\) | 20.9532 | 0.854697 | 0.427348 | − | 0.904087i | \(-0.359448\pi\) | ||||
0.427348 | + | 0.904087i | \(0.359448\pi\) | |||||||
\(602\) | 23.3131 | 0.950172 | ||||||||
\(603\) | 27.7994 | 1.13208 | ||||||||
\(604\) | 22.6107 | 0.920017 | ||||||||
\(605\) | 82.1826 | 3.34120 | ||||||||
\(606\) | 40.8264 | 1.65846 | ||||||||
\(607\) | 35.1636 | 1.42725 | 0.713623 | − | 0.700530i | \(-0.247053\pi\) | ||||
0.713623 | + | 0.700530i | \(0.247053\pi\) | |||||||
\(608\) | −7.40454 | −0.300294 | ||||||||
\(609\) | −7.56778 | −0.306662 | ||||||||
\(610\) | 81.5147 | 3.30043 | ||||||||
\(611\) | 85.7063 | 3.46731 | ||||||||
\(612\) | 44.1931 | 1.78640 | ||||||||
\(613\) | 46.8476 | 1.89216 | 0.946079 | − | 0.323937i | \(-0.105007\pi\) | ||||
0.946079 | + | 0.323937i | \(0.105007\pi\) | |||||||
\(614\) | −39.7550 | −1.60438 | ||||||||
\(615\) | 63.7301 | 2.56985 | ||||||||
\(616\) | −55.1247 | −2.22104 | ||||||||
\(617\) | −20.3129 | −0.817768 | −0.408884 | − | 0.912586i | \(-0.634082\pi\) | ||||
−0.408884 | + | 0.912586i | \(0.634082\pi\) | |||||||
\(618\) | −21.3123 | −0.857305 | ||||||||
\(619\) | −0.422058 | −0.0169640 | −0.00848198 | − | 0.999964i | \(-0.502700\pi\) | ||||
−0.00848198 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(620\) | −123.694 | −4.96765 | ||||||||
\(621\) | 8.43750 | 0.338585 | ||||||||
\(622\) | 0.714305 | 0.0286410 | ||||||||
\(623\) | 3.53672 | 0.141696 | ||||||||
\(624\) | 230.374 | 9.22234 | ||||||||
\(625\) | 46.1396 | 1.84558 | ||||||||
\(626\) | −58.0617 | −2.32061 | ||||||||
\(627\) | −3.88899 | −0.155311 | ||||||||
\(628\) | −77.7718 | −3.10343 | ||||||||
\(629\) | 3.22015 | 0.128396 | ||||||||
\(630\) | −23.8936 | −0.951943 | ||||||||
\(631\) | 19.0673 | 0.759057 | 0.379528 | − | 0.925180i | \(-0.376086\pi\) | ||||
0.379528 | + | 0.925180i | \(0.376086\pi\) | |||||||
\(632\) | −56.9068 | −2.26363 | ||||||||
\(633\) | −51.8442 | −2.06062 | ||||||||
\(634\) | 53.8484 | 2.13859 | ||||||||
\(635\) | 64.2273 | 2.54878 | ||||||||
\(636\) | −154.641 | −6.13191 | ||||||||
\(637\) | −6.36706 | −0.252272 | ||||||||
\(638\) | −51.3990 | −2.03491 | ||||||||
\(639\) | −3.22011 | −0.127385 | ||||||||
\(640\) | −190.378 | −7.52536 | ||||||||
\(641\) | −4.16979 | −0.164697 | −0.0823484 | − | 0.996604i | \(-0.526242\pi\) | ||||
−0.0823484 | + | 0.996604i | \(0.526242\pi\) | |||||||
\(642\) | 58.1669 | 2.29567 | ||||||||
\(643\) | 17.8953 | 0.705723 | 0.352861 | − | 0.935676i | \(-0.385209\pi\) | ||||
0.352861 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(644\) | 24.3991 | 0.961460 | ||||||||
\(645\) | 77.5962 | 3.05535 | ||||||||
\(646\) | −3.10448 | −0.122144 | ||||||||
\(647\) | 30.7522 | 1.20899 | 0.604496 | − | 0.796608i | \(-0.293374\pi\) | ||||
0.604496 | + | 0.796608i | \(0.293374\pi\) | |||||||
\(648\) | 106.583 | 4.18699 | ||||||||
\(649\) | 53.6104 | 2.10439 | ||||||||
\(650\) | 197.988 | 7.76572 | ||||||||
\(651\) | 12.4696 | 0.488723 | ||||||||
\(652\) | 38.0381 | 1.48969 | ||||||||
\(653\) | 13.9743 | 0.546857 | 0.273428 | − | 0.961892i | \(-0.411842\pi\) | ||||
0.273428 | + | 0.961892i | \(0.411842\pi\) | |||||||
\(654\) | 71.1863 | 2.78360 | ||||||||
\(655\) | −9.14359 | −0.357270 | ||||||||
\(656\) | −110.905 | −4.33013 | ||||||||
\(657\) | 12.8107 | 0.499794 | ||||||||
\(658\) | 37.0514 | 1.44442 | ||||||||
\(659\) | −13.2136 | −0.514729 | −0.257365 | − | 0.966314i | \(-0.582854\pi\) | ||||
−0.257365 | + | 0.966314i | \(0.582854\pi\) | |||||||
\(660\) | −286.085 | −11.1358 | ||||||||
\(661\) | 39.8009 | 1.54807 | 0.774037 | − | 0.633140i | \(-0.218234\pi\) | ||||
0.774037 | + | 0.633140i | \(0.218234\pi\) | |||||||
\(662\) | 15.7180 | 0.610899 | ||||||||
\(663\) | 53.2551 | 2.06826 | ||||||||
\(664\) | −5.28767 | −0.205201 | ||||||||
\(665\) | 1.23540 | 0.0479066 | ||||||||
\(666\) | −5.17124 | −0.200381 | ||||||||
\(667\) | 14.5906 | 0.564952 | ||||||||
\(668\) | −60.6745 | −2.34757 | ||||||||
\(669\) | 40.6393 | 1.57121 | ||||||||
\(670\) | −143.657 | −5.54996 | ||||||||
\(671\) | −41.0790 | −1.58584 | ||||||||
\(672\) | 54.9114 | 2.11825 | ||||||||
\(673\) | 10.1016 | 0.389388 | 0.194694 | − | 0.980864i | \(-0.437629\pi\) | ||||
0.194694 | + | 0.980864i | \(0.437629\pi\) | |||||||
\(674\) | −66.1763 | −2.54902 | ||||||||
\(675\) | 21.7851 | 0.838511 | ||||||||
\(676\) | 153.571 | 5.90657 | ||||||||
\(677\) | 1.71973 | 0.0660944 | 0.0330472 | − | 0.999454i | \(-0.489479\pi\) | ||||
0.0330472 | + | 0.999454i | \(0.489479\pi\) | |||||||
\(678\) | −96.6389 | −3.71140 | ||||||||
\(679\) | −9.25815 | −0.355295 | ||||||||
\(680\) | −146.467 | −5.61673 | ||||||||
\(681\) | 15.0831 | 0.577984 | ||||||||
\(682\) | 84.6916 | 3.24301 | ||||||||
\(683\) | 7.50469 | 0.287159 | 0.143580 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143580 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(684\) | 3.66943 | 0.140304 | ||||||||
\(685\) | −1.35665 | −0.0518351 | ||||||||
\(686\) | −2.75252 | −0.105092 | ||||||||
\(687\) | −6.91692 | −0.263897 | ||||||||
\(688\) | −135.036 | −5.14818 | ||||||||
\(689\) | −77.8028 | −2.96405 | ||||||||
\(690\) | 110.338 | 4.20048 | ||||||||
\(691\) | 2.26007 | 0.0859772 | 0.0429886 | − | 0.999076i | \(-0.486312\pi\) | ||||
0.0429886 | + | 0.999076i | \(0.486312\pi\) | |||||||
\(692\) | 71.1714 | 2.70553 | ||||||||
\(693\) | 12.0411 | 0.457403 | ||||||||
\(694\) | 0.908251 | 0.0344767 | ||||||||
\(695\) | −0.326135 | −0.0123710 | ||||||||
\(696\) | 74.4979 | 2.82384 | ||||||||
\(697\) | −25.6378 | −0.971101 | ||||||||
\(698\) | −18.3867 | −0.695946 | ||||||||
\(699\) | 25.7994 | 0.975822 | ||||||||
\(700\) | 62.9972 | 2.38107 | ||||||||
\(701\) | −21.7335 | −0.820862 | −0.410431 | − | 0.911892i | \(-0.634622\pi\) | ||||
−0.410431 | + | 0.911892i | \(0.634622\pi\) | |||||||
\(702\) | 33.7958 | 1.27554 | ||||||||
\(703\) | 0.267374 | 0.0100842 | ||||||||
\(704\) | 194.391 | 7.32637 | ||||||||
\(705\) | 123.323 | 4.64462 | ||||||||
\(706\) | 33.8481 | 1.27389 | ||||||||
\(707\) | 6.53574 | 0.245802 | ||||||||
\(708\) | −121.156 | −4.55334 | ||||||||
\(709\) | 5.55232 | 0.208522 | 0.104261 | − | 0.994550i | \(-0.466752\pi\) | ||||
0.104261 | + | 0.994550i | \(0.466752\pi\) | |||||||
\(710\) | 16.6403 | 0.624501 | ||||||||
\(711\) | 12.4303 | 0.466174 | ||||||||
\(712\) | −34.8158 | −1.30478 | ||||||||
\(713\) | −24.0414 | −0.900357 | ||||||||
\(714\) | 23.0225 | 0.861597 | ||||||||
\(715\) | −143.935 | −5.38285 | ||||||||
\(716\) | 45.5784 | 1.70335 | ||||||||
\(717\) | 24.7040 | 0.922588 | ||||||||
\(718\) | 53.5476 | 1.99838 | ||||||||
\(719\) | 38.0539 | 1.41917 | 0.709585 | − | 0.704620i | \(-0.248883\pi\) | ||||
0.709585 | + | 0.704620i | \(0.248883\pi\) | |||||||
\(720\) | 138.398 | 5.15778 | ||||||||
\(721\) | −3.41180 | −0.127062 | ||||||||
\(722\) | 52.0402 | 1.93674 | ||||||||
\(723\) | 7.08812 | 0.263610 | ||||||||
\(724\) | 81.3155 | 3.02207 | ||||||||
\(725\) | 37.6722 | 1.39911 | ||||||||
\(726\) | 127.166 | 4.71957 | ||||||||
\(727\) | 43.9899 | 1.63149 | 0.815747 | − | 0.578409i | \(-0.196326\pi\) | ||||
0.815747 | + | 0.578409i | \(0.196326\pi\) | |||||||
\(728\) | 62.6780 | 2.32300 | ||||||||
\(729\) | −10.1524 | −0.376016 | ||||||||
\(730\) | −66.2013 | −2.45022 | ||||||||
\(731\) | −31.2159 | −1.15456 | ||||||||
\(732\) | 92.8362 | 3.43132 | ||||||||
\(733\) | 34.9919 | 1.29246 | 0.646228 | − | 0.763145i | \(-0.276346\pi\) | ||||
0.646228 | + | 0.763145i | \(0.276346\pi\) | |||||||
\(734\) | −42.6938 | −1.57586 | ||||||||
\(735\) | −9.16159 | −0.337930 | ||||||||
\(736\) | −105.869 | −3.90238 | ||||||||
\(737\) | 72.3954 | 2.66672 | ||||||||
\(738\) | 41.1718 | 1.51555 | ||||||||
\(739\) | −11.6467 | −0.428432 | −0.214216 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214216 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(740\) | 19.6688 | 0.723039 | ||||||||
\(741\) | 4.42186 | 0.162441 | ||||||||
\(742\) | −33.6347 | −1.23477 | ||||||||
\(743\) | 4.80862 | 0.176411 | 0.0882056 | − | 0.996102i | \(-0.471887\pi\) | ||||
0.0882056 | + | 0.996102i | \(0.471887\pi\) | |||||||
\(744\) | −122.752 | −4.50032 | ||||||||
\(745\) | 55.9899 | 2.05131 | ||||||||
\(746\) | 21.4235 | 0.784371 | ||||||||
\(747\) | 1.15500 | 0.0422593 | ||||||||
\(748\) | 115.088 | 4.20804 | ||||||||
\(749\) | 9.31172 | 0.340243 | ||||||||
\(750\) | 158.798 | 5.79848 | ||||||||
\(751\) | 43.8853 | 1.60140 | 0.800698 | − | 0.599068i | \(-0.204462\pi\) | ||||
0.800698 | + | 0.599068i | \(0.204462\pi\) | |||||||
\(752\) | −214.611 | −7.82607 | ||||||||
\(753\) | −49.1698 | −1.79185 | ||||||||
\(754\) | 58.4418 | 2.12832 | ||||||||
\(755\) | 16.3688 | 0.595722 | ||||||||
\(756\) | 10.7534 | 0.391097 | ||||||||
\(757\) | −42.6501 | −1.55014 | −0.775072 | − | 0.631872i | \(-0.782287\pi\) | ||||
−0.775072 | + | 0.631872i | \(0.782287\pi\) | |||||||
\(758\) | −80.8508 | −2.93663 | ||||||||
\(759\) | −55.6042 | −2.01830 | ||||||||
\(760\) | −12.1614 | −0.441139 | ||||||||
\(761\) | −1.24666 | −0.0451912 | −0.0225956 | − | 0.999745i | \(-0.507193\pi\) | ||||
−0.0225956 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(762\) | 99.3826 | 3.60025 | ||||||||
\(763\) | 11.3959 | 0.412560 | ||||||||
\(764\) | 77.9371 | 2.81967 | ||||||||
\(765\) | 31.9932 | 1.15672 | ||||||||
\(766\) | −49.6641 | −1.79444 | ||||||||
\(767\) | −60.9561 | −2.20100 | ||||||||
\(768\) | −137.022 | −4.94435 | ||||||||
\(769\) | −25.8256 | −0.931294 | −0.465647 | − | 0.884971i | \(-0.654178\pi\) | ||||
−0.465647 | + | 0.884971i | \(0.654178\pi\) | |||||||
\(770\) | −62.2239 | −2.24239 | ||||||||
\(771\) | −2.22678 | −0.0801954 | ||||||||
\(772\) | −10.7044 | −0.385260 | ||||||||
\(773\) | 33.0297 | 1.18799 | 0.593997 | − | 0.804467i | \(-0.297549\pi\) | ||||
0.593997 | + | 0.804467i | \(0.297549\pi\) | |||||||
\(774\) | 50.1297 | 1.80187 | ||||||||
\(775\) | −62.0736 | −2.22975 | ||||||||
\(776\) | 91.1381 | 3.27167 | ||||||||
\(777\) | −1.98282 | −0.0711334 | ||||||||
\(778\) | 46.5939 | 1.67047 | ||||||||
\(779\) | −2.12875 | −0.0762703 | ||||||||
\(780\) | 325.284 | 11.6470 | ||||||||
\(781\) | −8.38584 | −0.300069 | ||||||||
\(782\) | −44.3874 | −1.58729 | ||||||||
\(783\) | 6.43051 | 0.229808 | ||||||||
\(784\) | 15.9433 | 0.569405 | ||||||||
\(785\) | −56.3021 | −2.00951 | ||||||||
\(786\) | −14.1484 | −0.504657 | ||||||||
\(787\) | 17.3694 | 0.619152 | 0.309576 | − | 0.950875i | \(-0.399813\pi\) | ||||
0.309576 | + | 0.950875i | \(0.399813\pi\) | |||||||
\(788\) | −146.651 | −5.22422 | ||||||||
\(789\) | −64.5853 | −2.29930 | ||||||||
\(790\) | −64.2355 | −2.28540 | ||||||||
\(791\) | −15.4706 | −0.550069 | ||||||||
\(792\) | −118.533 | −4.21190 | ||||||||
\(793\) | 46.7077 | 1.65864 | ||||||||
\(794\) | 40.7343 | 1.44561 | ||||||||
\(795\) | −111.951 | −3.97049 | ||||||||
\(796\) | 41.5241 | 1.47178 | ||||||||
\(797\) | 30.5718 | 1.08291 | 0.541454 | − | 0.840730i | \(-0.317874\pi\) | ||||
0.541454 | + | 0.840730i | \(0.317874\pi\) | |||||||
\(798\) | 1.91160 | 0.0676699 | ||||||||
\(799\) | −49.6113 | −1.75512 | ||||||||
\(800\) | −273.348 | −9.66430 | ||||||||
\(801\) | 7.60493 | 0.268707 | ||||||||
\(802\) | 31.1539 | 1.10008 | ||||||||
\(803\) | 33.3619 | 1.17731 | ||||||||
\(804\) | −163.610 | −5.77007 | ||||||||
\(805\) | 17.6635 | 0.622557 | ||||||||
\(806\) | −96.2961 | −3.39188 | ||||||||
\(807\) | −32.4169 | −1.14113 | ||||||||
\(808\) | −64.3384 | −2.26342 | ||||||||
\(809\) | −36.4530 | −1.28162 | −0.640809 | − | 0.767700i | \(-0.721401\pi\) | ||||
−0.640809 | + | 0.767700i | \(0.721401\pi\) | |||||||
\(810\) | 120.310 | 4.22725 | ||||||||
\(811\) | 3.31899 | 0.116546 | 0.0582728 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582728 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(812\) | 18.5954 | 0.652571 | ||||||||
\(813\) | −12.7083 | −0.445700 | ||||||||
\(814\) | −13.4670 | −0.472018 | ||||||||
\(815\) | 27.5373 | 0.964591 | ||||||||
\(816\) | −133.353 | −4.66827 | ||||||||
\(817\) | −2.59191 | −0.0906795 | ||||||||
\(818\) | 84.8384 | 2.96630 | ||||||||
\(819\) | −13.6910 | −0.478401 | ||||||||
\(820\) | −156.597 | −5.46859 | ||||||||
\(821\) | −29.4861 | −1.02907 | −0.514536 | − | 0.857468i | \(-0.672036\pi\) | ||||
−0.514536 | + | 0.857468i | \(0.672036\pi\) | |||||||
\(822\) | −2.09923 | −0.0732190 | ||||||||
\(823\) | 25.9180 | 0.903446 | 0.451723 | − | 0.892158i | \(-0.350810\pi\) | ||||
0.451723 | + | 0.892158i | \(0.350810\pi\) | |||||||
\(824\) | 33.5860 | 1.17002 | ||||||||
\(825\) | −143.567 | −4.99836 | ||||||||
\(826\) | −26.3517 | −0.916894 | ||||||||
\(827\) | 48.0656 | 1.67140 | 0.835702 | − | 0.549183i | \(-0.185061\pi\) | ||||
0.835702 | + | 0.549183i | \(0.185061\pi\) | |||||||
\(828\) | 52.4649 | 1.82328 | ||||||||
\(829\) | −20.2709 | −0.704037 | −0.352019 | − | 0.935993i | \(-0.614505\pi\) | ||||
−0.352019 | + | 0.935993i | \(0.614505\pi\) | |||||||
\(830\) | −5.96863 | −0.207174 | ||||||||
\(831\) | −34.0056 | −1.17964 | ||||||||
\(832\) | −221.026 | −7.66270 | ||||||||
\(833\) | 3.68559 | 0.127698 | ||||||||
\(834\) | −0.504647 | −0.0174745 | ||||||||
\(835\) | −43.9247 | −1.52008 | ||||||||
\(836\) | 9.55596 | 0.330500 | ||||||||
\(837\) | −10.5957 | −0.366242 | ||||||||
\(838\) | −42.9782 | −1.48466 | ||||||||
\(839\) | 15.8256 | 0.546359 | 0.273180 | − | 0.961963i | \(-0.411925\pi\) | ||||
0.273180 | + | 0.961963i | \(0.411925\pi\) | |||||||
\(840\) | 90.1876 | 3.11177 | ||||||||
\(841\) | −17.8800 | −0.616550 | ||||||||
\(842\) | 105.111 | 3.62237 | ||||||||
\(843\) | 23.8994 | 0.823139 | ||||||||
\(844\) | 127.391 | 4.38497 | ||||||||
\(845\) | 111.176 | 3.82457 | ||||||||
\(846\) | 79.6709 | 2.73914 | ||||||||
\(847\) | 20.3575 | 0.699492 | ||||||||
\(848\) | 194.821 | 6.69017 | ||||||||
\(849\) | 45.4113 | 1.55851 | ||||||||
\(850\) | −114.606 | −3.93094 | ||||||||
\(851\) | 3.82288 | 0.131047 | ||||||||
\(852\) | 18.9515 | 0.649268 | ||||||||
\(853\) | 16.3067 | 0.558330 | 0.279165 | − | 0.960243i | \(-0.409942\pi\) | ||||
0.279165 | + | 0.960243i | \(0.409942\pi\) | |||||||
\(854\) | 20.1920 | 0.690957 | ||||||||
\(855\) | 2.65644 | 0.0908485 | ||||||||
\(856\) | −91.6654 | −3.13306 | ||||||||
\(857\) | −7.58254 | −0.259015 | −0.129507 | − | 0.991578i | \(-0.541340\pi\) | ||||
−0.129507 | + | 0.991578i | \(0.541340\pi\) | |||||||
\(858\) | −222.718 | −7.60348 | ||||||||
\(859\) | −21.6731 | −0.739477 | −0.369739 | − | 0.929136i | \(-0.620553\pi\) | ||||
−0.369739 | + | 0.929136i | \(0.620553\pi\) | |||||||
\(860\) | −190.668 | −6.50173 | ||||||||
\(861\) | 15.7866 | 0.538007 | ||||||||
\(862\) | 9.90350 | 0.337315 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −46.6594 | −1.58739 | ||||||||
\(865\) | 51.5238 | 1.75186 | ||||||||
\(866\) | −9.83944 | −0.334358 | ||||||||
\(867\) | 7.75332 | 0.263317 | ||||||||
\(868\) | −30.6402 | −1.04000 | ||||||||
\(869\) | 32.3712 | 1.09812 | ||||||||
\(870\) | 84.0921 | 2.85099 | ||||||||
\(871\) | −82.3151 | −2.78914 | ||||||||
\(872\) | −112.183 | −3.79898 | ||||||||
\(873\) | −19.9076 | −0.673770 | ||||||||
\(874\) | −3.68556 | −0.124666 | ||||||||
\(875\) | 25.4213 | 0.859398 | ||||||||
\(876\) | −75.3959 | −2.54739 | ||||||||
\(877\) | 40.3619 | 1.36293 | 0.681463 | − | 0.731853i | \(-0.261344\pi\) | ||||
0.681463 | + | 0.731853i | \(0.261344\pi\) | |||||||
\(878\) | 18.1725 | 0.613291 | ||||||||
\(879\) | 34.2759 | 1.15610 | ||||||||
\(880\) | 360.417 | 12.1497 | ||||||||
\(881\) | 38.5069 | 1.29733 | 0.648666 | − | 0.761073i | \(-0.275327\pi\) | ||||
0.648666 | + | 0.761073i | \(0.275327\pi\) | |||||||
\(882\) | −5.91869 | −0.199293 | ||||||||
\(883\) | −38.9146 | −1.30958 | −0.654791 | − | 0.755810i | \(-0.727243\pi\) | ||||
−0.654791 | + | 0.755810i | \(0.727243\pi\) | |||||||
\(884\) | −130.858 | −4.40122 | ||||||||
\(885\) | −87.7100 | −2.94834 | ||||||||
\(886\) | −107.971 | −3.62736 | ||||||||
\(887\) | −19.3811 | −0.650755 | −0.325377 | − | 0.945584i | \(-0.605491\pi\) | ||||
−0.325377 | + | 0.945584i | \(0.605491\pi\) | |||||||
\(888\) | 19.5191 | 0.655018 | ||||||||
\(889\) | 15.9098 | 0.533597 | ||||||||
\(890\) | −39.2995 | −1.31732 | ||||||||
\(891\) | −60.6296 | −2.03117 | ||||||||
\(892\) | −99.8583 | −3.34350 | ||||||||
\(893\) | −4.11931 | −0.137847 | ||||||||
\(894\) | 86.6365 | 2.89756 | ||||||||
\(895\) | 32.9961 | 1.10294 | ||||||||
\(896\) | −47.1587 | −1.57546 | ||||||||
\(897\) | 63.2231 | 2.11096 | ||||||||
\(898\) | −66.8492 | −2.23079 | ||||||||
\(899\) | −18.3228 | −0.611099 | ||||||||
\(900\) | 135.461 | 4.51538 | ||||||||
\(901\) | 45.0364 | 1.50038 | ||||||||
\(902\) | 107.220 | 3.57003 | ||||||||
\(903\) | 19.2214 | 0.639648 | ||||||||
\(904\) | 152.294 | 5.06521 | ||||||||
\(905\) | 58.8675 | 1.95682 | ||||||||
\(906\) | 25.3284 | 0.841480 | ||||||||
\(907\) | −12.1399 | −0.403098 | −0.201549 | − | 0.979478i | \(-0.564598\pi\) | ||||
−0.201549 | + | 0.979478i | \(0.564598\pi\) | |||||||
\(908\) | −37.0618 | −1.22994 | ||||||||
\(909\) | 14.0537 | 0.466130 | ||||||||
\(910\) | 70.7499 | 2.34534 | ||||||||
\(911\) | 24.1882 | 0.801392 | 0.400696 | − | 0.916211i | \(-0.368768\pi\) | ||||
0.400696 | + | 0.916211i | \(0.368768\pi\) | |||||||
\(912\) | −11.0725 | −0.366646 | ||||||||
\(913\) | 3.00787 | 0.0995459 | ||||||||
\(914\) | 46.0831 | 1.52429 | ||||||||
\(915\) | 67.2078 | 2.22182 | ||||||||
\(916\) | 16.9961 | 0.561568 | ||||||||
\(917\) | −2.26496 | −0.0747957 | ||||||||
\(918\) | −19.5628 | −0.645668 | ||||||||
\(919\) | 15.3900 | 0.507669 | 0.253835 | − | 0.967248i | \(-0.418308\pi\) | ||||
0.253835 | + | 0.967248i | \(0.418308\pi\) | |||||||
\(920\) | −173.881 | −5.73269 | ||||||||
\(921\) | −32.7775 | −1.08006 | ||||||||
\(922\) | 51.3030 | 1.68957 | ||||||||
\(923\) | 9.53487 | 0.313844 | ||||||||
\(924\) | −70.8662 | −2.33133 | ||||||||
\(925\) | 9.87046 | 0.324539 | ||||||||
\(926\) | −2.43590 | −0.0800487 | ||||||||
\(927\) | −7.33631 | −0.240956 | ||||||||
\(928\) | −80.6864 | −2.64866 | ||||||||
\(929\) | 9.34089 | 0.306465 | 0.153232 | − | 0.988190i | \(-0.451032\pi\) | ||||
0.153232 | + | 0.988190i | \(0.451032\pi\) | |||||||
\(930\) | −138.561 | −4.54359 | ||||||||
\(931\) | 0.306021 | 0.0100294 | ||||||||
\(932\) | −63.3938 | −2.07653 | ||||||||
\(933\) | 0.588936 | 0.0192809 | ||||||||
\(934\) | −59.2764 | −1.93958 | ||||||||
\(935\) | 83.3169 | 2.72475 | ||||||||
\(936\) | 134.775 | 4.40526 | ||||||||
\(937\) | −57.6677 | −1.88392 | −0.941961 | − | 0.335721i | \(-0.891020\pi\) | ||||
−0.941961 | + | 0.335721i | \(0.891020\pi\) | |||||||
\(938\) | −35.5854 | −1.16190 | ||||||||
\(939\) | −47.8712 | −1.56222 | ||||||||
\(940\) | −303.028 | −9.88368 | ||||||||
\(941\) | −30.2752 | −0.986944 | −0.493472 | − | 0.869762i | \(-0.664272\pi\) | ||||
−0.493472 | + | 0.869762i | \(0.664272\pi\) | |||||||
\(942\) | −87.1196 | −2.83851 | ||||||||
\(943\) | −30.4365 | −0.991150 | ||||||||
\(944\) | 152.636 | 4.96788 | ||||||||
\(945\) | 7.78481 | 0.253240 | ||||||||
\(946\) | 130.548 | 4.24449 | ||||||||
\(947\) | −0.954310 | −0.0310109 | −0.0155055 | − | 0.999880i | \(-0.504936\pi\) | ||||
−0.0155055 | + | 0.999880i | \(0.504936\pi\) | |||||||
\(948\) | −73.1572 | −2.37603 | ||||||||
\(949\) | −37.9331 | −1.23136 | ||||||||
\(950\) | −9.51590 | −0.308737 | ||||||||
\(951\) | 44.3974 | 1.43968 | ||||||||
\(952\) | −36.2813 | −1.17588 | ||||||||
\(953\) | 51.7656 | 1.67685 | 0.838427 | − | 0.545014i | \(-0.183476\pi\) | ||||
0.838427 | + | 0.545014i | \(0.183476\pi\) | |||||||
\(954\) | −72.3239 | −2.34157 | ||||||||
\(955\) | 56.4218 | 1.82577 | ||||||||
\(956\) | −60.7023 | −1.96325 | ||||||||
\(957\) | −42.3779 | −1.36988 | ||||||||
\(958\) | 112.965 | 3.64972 | ||||||||
\(959\) | −0.336057 | −0.0108519 | ||||||||
\(960\) | −318.035 | −10.2645 | ||||||||
\(961\) | −0.809057 | −0.0260986 | ||||||||
\(962\) | 15.3123 | 0.493687 | ||||||||
\(963\) | 20.0228 | 0.645225 | ||||||||
\(964\) | −17.4168 | −0.560958 | ||||||||
\(965\) | −7.74936 | −0.249461 | ||||||||
\(966\) | 27.3318 | 0.879385 | ||||||||
\(967\) | −9.01813 | −0.290004 | −0.145002 | − | 0.989431i | \(-0.546319\pi\) | ||||
−0.145002 | + | 0.989431i | \(0.546319\pi\) | |||||||
\(968\) | −200.401 | −6.44113 | ||||||||
\(969\) | −2.55960 | −0.0822263 | ||||||||
\(970\) | 102.875 | 3.30312 | ||||||||
\(971\) | 7.96092 | 0.255478 | 0.127739 | − | 0.991808i | \(-0.459228\pi\) | ||||
0.127739 | + | 0.991808i | \(0.459228\pi\) | |||||||
\(972\) | 104.759 | 3.36015 | ||||||||
\(973\) | −0.0807869 | −0.00258991 | ||||||||
\(974\) | −20.7558 | −0.665058 | ||||||||
\(975\) | 163.239 | 5.22782 | ||||||||
\(976\) | −116.957 | −3.74372 | ||||||||
\(977\) | 11.9982 | 0.383856 | 0.191928 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191928 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(978\) | 42.6101 | 1.36252 | ||||||||
\(979\) | 19.8048 | 0.632965 | ||||||||
\(980\) | 22.5117 | 0.719110 | ||||||||
\(981\) | 24.5044 | 0.782366 | ||||||||
\(982\) | 24.5150 | 0.782304 | ||||||||
\(983\) | 40.8538 | 1.30303 | 0.651517 | − | 0.758634i | \(-0.274133\pi\) | ||||
0.651517 | + | 0.758634i | \(0.274133\pi\) | |||||||
\(984\) | −155.405 | −4.95413 | ||||||||
\(985\) | −106.166 | −3.38274 | ||||||||
\(986\) | −33.8292 | −1.07734 | ||||||||
\(987\) | 30.5485 | 0.972368 | ||||||||
\(988\) | −10.8653 | −0.345672 | ||||||||
\(989\) | −37.0587 | −1.17840 | ||||||||
\(990\) | −133.799 | −4.25240 | ||||||||
\(991\) | 50.6979 | 1.61047 | 0.805235 | − | 0.592955i | \(-0.202039\pi\) | ||||
0.805235 | + | 0.592955i | \(0.202039\pi\) | |||||||
\(992\) | 132.949 | 4.22114 | ||||||||
\(993\) | 12.9593 | 0.411252 | ||||||||
\(994\) | 4.12199 | 0.130742 | ||||||||
\(995\) | 30.0609 | 0.952996 | ||||||||
\(996\) | −6.79761 | −0.215391 | ||||||||
\(997\) | 53.0875 | 1.68130 | 0.840650 | − | 0.541579i | \(-0.182173\pi\) | ||||
0.840650 | + | 0.541579i | \(0.182173\pi\) | |||||||
\(998\) | −57.6644 | −1.82533 | ||||||||
\(999\) | 1.68485 | 0.0533063 |
(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 | 6041.2.a.f.1.4 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.4 | ✓ | 132 | 1.1 | even | 1 | trivial |