Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2671,2,Mod(1,2671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2671, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2671.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: | \(21.3280423799\) |
Analytic rank: | \(0\) |
Dimension: | \(122\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.39 | ||
Character | \(\chi\) | \(=\) | 2671.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.01100 | −0.714882 | −0.357441 | − | 0.933936i | \(-0.616351\pi\) | ||||
−0.357441 | + | 0.933936i | \(0.616351\pi\) | |||||||
\(3\) | −0.165355 | −0.0954675 | −0.0477338 | − | 0.998860i | \(-0.515200\pi\) | ||||
−0.0477338 | + | 0.998860i | \(0.515200\pi\) | |||||||
\(4\) | −0.977888 | −0.488944 | ||||||||
\(5\) | −2.31604 | −1.03577 | −0.517883 | − | 0.855452i | \(-0.673280\pi\) | ||||
−0.517883 | + | 0.855452i | \(0.673280\pi\) | |||||||
\(6\) | 0.167173 | 0.0682480 | ||||||||
\(7\) | −1.01194 | −0.382479 | −0.191239 | − | 0.981543i | \(-0.561251\pi\) | ||||
−0.191239 | + | 0.981543i | \(0.561251\pi\) | |||||||
\(8\) | 3.01063 | 1.06442 | ||||||||
\(9\) | −2.97266 | −0.990886 | ||||||||
\(10\) | 2.34151 | 0.740450 | ||||||||
\(11\) | −0.218595 | −0.0659089 | −0.0329545 | − | 0.999457i | \(-0.510492\pi\) | ||||
−0.0329545 | + | 0.999457i | \(0.510492\pi\) | |||||||
\(12\) | 0.161698 | 0.0466783 | ||||||||
\(13\) | 0.505652 | 0.140243 | 0.0701213 | − | 0.997538i | \(-0.477661\pi\) | ||||
0.0701213 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(14\) | 1.02307 | 0.273427 | ||||||||
\(15\) | 0.382968 | 0.0988820 | ||||||||
\(16\) | −1.08796 | −0.271990 | ||||||||
\(17\) | −5.73669 | −1.39135 | −0.695675 | − | 0.718356i | \(-0.744895\pi\) | ||||
−0.695675 | + | 0.718356i | \(0.744895\pi\) | |||||||
\(18\) | 3.00534 | 0.708366 | ||||||||
\(19\) | −7.05039 | −1.61747 | −0.808735 | − | 0.588173i | \(-0.799847\pi\) | ||||
−0.808735 | + | 0.588173i | \(0.799847\pi\) | |||||||
\(20\) | 2.26483 | 0.506431 | ||||||||
\(21\) | 0.167330 | 0.0365143 | ||||||||
\(22\) | 0.220999 | 0.0471171 | ||||||||
\(23\) | 0.146062 | 0.0304561 | 0.0152281 | − | 0.999884i | \(-0.495153\pi\) | ||||
0.0152281 | + | 0.999884i | \(0.495153\pi\) | |||||||
\(24\) | −0.497822 | −0.101617 | ||||||||
\(25\) | 0.364049 | 0.0728098 | ||||||||
\(26\) | −0.511212 | −0.100257 | ||||||||
\(27\) | 0.987607 | 0.190065 | ||||||||
\(28\) | 0.989568 | 0.187011 | ||||||||
\(29\) | −6.06175 | −1.12564 | −0.562820 | − | 0.826580i | \(-0.690283\pi\) | ||||
−0.562820 | + | 0.826580i | \(0.690283\pi\) | |||||||
\(30\) | −0.387179 | −0.0706889 | ||||||||
\(31\) | 7.28560 | 1.30853 | 0.654266 | − | 0.756264i | \(-0.272978\pi\) | ||||
0.654266 | + | 0.756264i | \(0.272978\pi\) | |||||||
\(32\) | −4.92134 | −0.869978 | ||||||||
\(33\) | 0.0361457 | 0.00629216 | ||||||||
\(34\) | 5.79977 | 0.994652 | ||||||||
\(35\) | 2.34370 | 0.396158 | ||||||||
\(36\) | 2.90693 | 0.484488 | ||||||||
\(37\) | −6.84193 | −1.12481 | −0.562404 | − | 0.826863i | \(-0.690123\pi\) | ||||
−0.562404 | + | 0.826863i | \(0.690123\pi\) | |||||||
\(38\) | 7.12791 | 1.15630 | ||||||||
\(39\) | −0.0836119 | −0.0133886 | ||||||||
\(40\) | −6.97275 | −1.10249 | ||||||||
\(41\) | −4.17529 | −0.652071 | −0.326035 | − | 0.945358i | \(-0.605713\pi\) | ||||
−0.326035 | + | 0.945358i | \(0.605713\pi\) | |||||||
\(42\) | −0.169170 | −0.0261034 | ||||||||
\(43\) | −1.89201 | −0.288528 | −0.144264 | − | 0.989539i | \(-0.546081\pi\) | ||||
−0.144264 | + | 0.989539i | \(0.546081\pi\) | |||||||
\(44\) | 0.213762 | 0.0322258 | ||||||||
\(45\) | 6.88480 | 1.02633 | ||||||||
\(46\) | −0.147668 | −0.0217725 | ||||||||
\(47\) | 8.78285 | 1.28111 | 0.640555 | − | 0.767912i | \(-0.278704\pi\) | ||||
0.640555 | + | 0.767912i | \(0.278704\pi\) | |||||||
\(48\) | 0.179899 | 0.0259662 | ||||||||
\(49\) | −5.97597 | −0.853710 | ||||||||
\(50\) | −0.368052 | −0.0520504 | ||||||||
\(51\) | 0.948588 | 0.132829 | ||||||||
\(52\) | −0.494471 | −0.0685708 | ||||||||
\(53\) | 2.46364 | 0.338406 | 0.169203 | − | 0.985581i | \(-0.445881\pi\) | ||||
0.169203 | + | 0.985581i | \(0.445881\pi\) | |||||||
\(54\) | −0.998466 | −0.135874 | ||||||||
\(55\) | 0.506276 | 0.0682662 | ||||||||
\(56\) | −3.04659 | −0.407118 | ||||||||
\(57\) | 1.16581 | 0.154416 | ||||||||
\(58\) | 6.12841 | 0.804699 | ||||||||
\(59\) | −13.6770 | −1.78059 | −0.890296 | − | 0.455383i | \(-0.849502\pi\) | ||||
−0.890296 | + | 0.455383i | \(0.849502\pi\) | |||||||
\(60\) | −0.374500 | −0.0483477 | ||||||||
\(61\) | −2.55026 | −0.326528 | −0.163264 | − | 0.986582i | \(-0.552202\pi\) | ||||
−0.163264 | + | 0.986582i | \(0.552202\pi\) | |||||||
\(62\) | −7.36571 | −0.935446 | ||||||||
\(63\) | 3.00816 | 0.378993 | ||||||||
\(64\) | 7.15137 | 0.893922 | ||||||||
\(65\) | −1.17111 | −0.145258 | ||||||||
\(66\) | −0.0365432 | −0.00449815 | ||||||||
\(67\) | −12.7317 | −1.55543 | −0.777714 | − | 0.628619i | \(-0.783621\pi\) | ||||
−0.777714 | + | 0.628619i | \(0.783621\pi\) | |||||||
\(68\) | 5.60984 | 0.680293 | ||||||||
\(69\) | −0.0241521 | −0.00290757 | ||||||||
\(70\) | −2.36948 | −0.283206 | ||||||||
\(71\) | 9.24961 | 1.09773 | 0.548863 | − | 0.835912i | \(-0.315061\pi\) | ||||
0.548863 | + | 0.835912i | \(0.315061\pi\) | |||||||
\(72\) | −8.94958 | −1.05472 | ||||||||
\(73\) | −13.7175 | −1.60551 | −0.802757 | − | 0.596307i | \(-0.796634\pi\) | ||||
−0.802757 | + | 0.596307i | \(0.796634\pi\) | |||||||
\(74\) | 6.91717 | 0.804104 | ||||||||
\(75\) | −0.0601972 | −0.00695097 | ||||||||
\(76\) | 6.89449 | 0.790852 | ||||||||
\(77\) | 0.221206 | 0.0252088 | ||||||||
\(78\) | 0.0845313 | 0.00957128 | ||||||||
\(79\) | −4.72867 | −0.532017 | −0.266008 | − | 0.963971i | \(-0.585705\pi\) | ||||
−0.266008 | + | 0.963971i | \(0.585705\pi\) | |||||||
\(80\) | 2.51976 | 0.281718 | ||||||||
\(81\) | 8.75467 | 0.972741 | ||||||||
\(82\) | 4.22120 | 0.466153 | ||||||||
\(83\) | 2.10913 | 0.231507 | 0.115754 | − | 0.993278i | \(-0.463072\pi\) | ||||
0.115754 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(84\) | −0.163630 | −0.0178535 | ||||||||
\(85\) | 13.2864 | 1.44111 | ||||||||
\(86\) | 1.91281 | 0.206264 | ||||||||
\(87\) | 1.00234 | 0.107462 | ||||||||
\(88\) | −0.658110 | −0.0701547 | ||||||||
\(89\) | 3.30801 | 0.350648 | 0.175324 | − | 0.984511i | \(-0.443903\pi\) | ||||
0.175324 | + | 0.984511i | \(0.443903\pi\) | |||||||
\(90\) | −6.96050 | −0.733701 | ||||||||
\(91\) | −0.511692 | −0.0536398 | ||||||||
\(92\) | −0.142833 | −0.0148913 | ||||||||
\(93\) | −1.20471 | −0.124922 | ||||||||
\(94\) | −8.87942 | −0.915842 | ||||||||
\(95\) | 16.3290 | 1.67532 | ||||||||
\(96\) | 0.813766 | 0.0830547 | ||||||||
\(97\) | −9.74610 | −0.989567 | −0.494783 | − | 0.869016i | \(-0.664753\pi\) | ||||
−0.494783 | + | 0.869016i | \(0.664753\pi\) | |||||||
\(98\) | 6.04168 | 0.610302 | ||||||||
\(99\) | 0.649809 | 0.0653082 | ||||||||
\(100\) | −0.355999 | −0.0355999 | ||||||||
\(101\) | 1.32007 | 0.131352 | 0.0656758 | − | 0.997841i | \(-0.479080\pi\) | ||||
0.0656758 | + | 0.997841i | \(0.479080\pi\) | |||||||
\(102\) | −0.959018 | −0.0949569 | ||||||||
\(103\) | 17.8613 | 1.75993 | 0.879964 | − | 0.475040i | \(-0.157566\pi\) | ||||
0.879964 | + | 0.475040i | \(0.157566\pi\) | |||||||
\(104\) | 1.52233 | 0.149277 | ||||||||
\(105\) | −0.387542 | −0.0378203 | ||||||||
\(106\) | −2.49073 | −0.241921 | ||||||||
\(107\) | −0.378696 | −0.0366099 | −0.0183050 | − | 0.999832i | \(-0.505827\pi\) | ||||
−0.0183050 | + | 0.999832i | \(0.505827\pi\) | |||||||
\(108\) | −0.965768 | −0.0929311 | ||||||||
\(109\) | 6.23618 | 0.597317 | 0.298659 | − | 0.954360i | \(-0.403461\pi\) | ||||
0.298659 | + | 0.954360i | \(0.403461\pi\) | |||||||
\(110\) | −0.511842 | −0.0488023 | ||||||||
\(111\) | 1.13135 | 0.107383 | ||||||||
\(112\) | 1.10095 | 0.104030 | ||||||||
\(113\) | −0.527570 | −0.0496296 | −0.0248148 | − | 0.999692i | \(-0.507900\pi\) | ||||
−0.0248148 | + | 0.999692i | \(0.507900\pi\) | |||||||
\(114\) | −1.17863 | −0.110389 | ||||||||
\(115\) | −0.338287 | −0.0315454 | ||||||||
\(116\) | 5.92771 | 0.550375 | ||||||||
\(117\) | −1.50313 | −0.138964 | ||||||||
\(118\) | 13.8274 | 1.27291 | ||||||||
\(119\) | 5.80521 | 0.532162 | ||||||||
\(120\) | 1.15298 | 0.105252 | ||||||||
\(121\) | −10.9522 | −0.995656 | ||||||||
\(122\) | 2.57831 | 0.233429 | ||||||||
\(123\) | 0.690403 | 0.0622516 | ||||||||
\(124\) | −7.12450 | −0.639799 | ||||||||
\(125\) | 10.7371 | 0.960351 | ||||||||
\(126\) | −3.04124 | −0.270935 | ||||||||
\(127\) | 18.9217 | 1.67903 | 0.839513 | − | 0.543340i | \(-0.182841\pi\) | ||||
0.839513 | + | 0.543340i | \(0.182841\pi\) | |||||||
\(128\) | 2.61267 | 0.230930 | ||||||||
\(129\) | 0.312852 | 0.0275451 | ||||||||
\(130\) | 1.18399 | 0.103843 | ||||||||
\(131\) | −18.1298 | −1.58401 | −0.792003 | − | 0.610517i | \(-0.790962\pi\) | ||||
−0.792003 | + | 0.610517i | \(0.790962\pi\) | |||||||
\(132\) | −0.0353465 | −0.00307651 | ||||||||
\(133\) | 7.13460 | 0.618648 | ||||||||
\(134\) | 12.8717 | 1.11195 | ||||||||
\(135\) | −2.28734 | −0.196863 | ||||||||
\(136\) | −17.2711 | −1.48098 | ||||||||
\(137\) | 4.08860 | 0.349313 | 0.174656 | − | 0.984629i | \(-0.444119\pi\) | ||||
0.174656 | + | 0.984629i | \(0.444119\pi\) | |||||||
\(138\) | 0.0244177 | 0.00207857 | ||||||||
\(139\) | 17.9300 | 1.52080 | 0.760402 | − | 0.649453i | \(-0.225002\pi\) | ||||
0.760402 | + | 0.649453i | \(0.225002\pi\) | |||||||
\(140\) | −2.29188 | −0.193699 | ||||||||
\(141\) | −1.45228 | −0.122304 | ||||||||
\(142\) | −9.35131 | −0.784745 | ||||||||
\(143\) | −0.110533 | −0.00924324 | ||||||||
\(144\) | 3.23413 | 0.269511 | ||||||||
\(145\) | 14.0393 | 1.16590 | ||||||||
\(146\) | 13.8683 | 1.14775 | ||||||||
\(147\) | 0.988154 | 0.0815016 | ||||||||
\(148\) | 6.69064 | 0.549968 | ||||||||
\(149\) | −0.219919 | −0.0180164 | −0.00900821 | − | 0.999959i | \(-0.502867\pi\) | ||||
−0.00900821 | + | 0.999959i | \(0.502867\pi\) | |||||||
\(150\) | 0.0608591 | 0.00496912 | ||||||||
\(151\) | 6.00917 | 0.489019 | 0.244510 | − | 0.969647i | \(-0.421373\pi\) | ||||
0.244510 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(152\) | −21.2261 | −1.72167 | ||||||||
\(153\) | 17.0532 | 1.37867 | ||||||||
\(154\) | −0.223638 | −0.0180213 | ||||||||
\(155\) | −16.8737 | −1.35533 | ||||||||
\(156\) | 0.0817630 | 0.00654628 | ||||||||
\(157\) | 19.1751 | 1.53034 | 0.765171 | − | 0.643827i | \(-0.222654\pi\) | ||||
0.765171 | + | 0.643827i | \(0.222654\pi\) | |||||||
\(158\) | 4.78066 | 0.380329 | ||||||||
\(159\) | −0.407374 | −0.0323068 | ||||||||
\(160\) | 11.3980 | 0.901093 | ||||||||
\(161\) | −0.147807 | −0.0116488 | ||||||||
\(162\) | −8.85093 | −0.695395 | ||||||||
\(163\) | 20.2337 | 1.58483 | 0.792413 | − | 0.609985i | \(-0.208825\pi\) | ||||
0.792413 | + | 0.609985i | \(0.208825\pi\) | |||||||
\(164\) | 4.08296 | 0.318826 | ||||||||
\(165\) | −0.0837150 | −0.00651720 | ||||||||
\(166\) | −2.13232 | −0.165500 | ||||||||
\(167\) | 6.88392 | 0.532694 | 0.266347 | − | 0.963877i | \(-0.414183\pi\) | ||||
0.266347 | + | 0.963877i | \(0.414183\pi\) | |||||||
\(168\) | 0.503768 | 0.0388665 | ||||||||
\(169\) | −12.7443 | −0.980332 | ||||||||
\(170\) | −13.4325 | −1.03023 | ||||||||
\(171\) | 20.9584 | 1.60273 | ||||||||
\(172\) | 1.85017 | 0.141074 | ||||||||
\(173\) | 9.99045 | 0.759560 | 0.379780 | − | 0.925077i | \(-0.376000\pi\) | ||||
0.379780 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(174\) | −1.01336 | −0.0768226 | ||||||||
\(175\) | −0.368397 | −0.0278482 | ||||||||
\(176\) | 0.237823 | 0.0179266 | ||||||||
\(177\) | 2.26155 | 0.169989 | ||||||||
\(178\) | −3.34438 | −0.250672 | ||||||||
\(179\) | −19.3231 | −1.44428 | −0.722139 | − | 0.691748i | \(-0.756841\pi\) | ||||
−0.722139 | + | 0.691748i | \(0.756841\pi\) | |||||||
\(180\) | −6.73256 | −0.501816 | ||||||||
\(181\) | 6.13660 | 0.456130 | 0.228065 | − | 0.973646i | \(-0.426760\pi\) | ||||
0.228065 | + | 0.973646i | \(0.426760\pi\) | |||||||
\(182\) | 0.517318 | 0.0383462 | ||||||||
\(183\) | 0.421698 | 0.0311728 | ||||||||
\(184\) | 0.439740 | 0.0324181 | ||||||||
\(185\) | 15.8462 | 1.16504 | ||||||||
\(186\) | 1.21795 | 0.0893047 | ||||||||
\(187\) | 1.25401 | 0.0917024 | ||||||||
\(188\) | −8.58864 | −0.626391 | ||||||||
\(189\) | −0.999403 | −0.0726959 | ||||||||
\(190\) | −16.5085 | −1.19766 | ||||||||
\(191\) | 16.5464 | 1.19725 | 0.598627 | − | 0.801028i | \(-0.295713\pi\) | ||||
0.598627 | + | 0.801028i | \(0.295713\pi\) | |||||||
\(192\) | −1.18251 | −0.0853405 | ||||||||
\(193\) | −6.28569 | −0.452454 | −0.226227 | − | 0.974075i | \(-0.572639\pi\) | ||||
−0.226227 | + | 0.974075i | \(0.572639\pi\) | |||||||
\(194\) | 9.85327 | 0.707423 | ||||||||
\(195\) | 0.193649 | 0.0138675 | ||||||||
\(196\) | 5.84383 | 0.417416 | ||||||||
\(197\) | −11.6303 | −0.828621 | −0.414311 | − | 0.910136i | \(-0.635977\pi\) | ||||
−0.414311 | + | 0.910136i | \(0.635977\pi\) | |||||||
\(198\) | −0.656954 | −0.0466877 | ||||||||
\(199\) | −12.9014 | −0.914556 | −0.457278 | − | 0.889324i | \(-0.651176\pi\) | ||||
−0.457278 | + | 0.889324i | \(0.651176\pi\) | |||||||
\(200\) | 1.09602 | 0.0775001 | ||||||||
\(201\) | 2.10525 | 0.148493 | ||||||||
\(202\) | −1.33458 | −0.0939008 | ||||||||
\(203\) | 6.13416 | 0.430533 | ||||||||
\(204\) | −0.927612 | −0.0649459 | ||||||||
\(205\) | 9.67014 | 0.675392 | ||||||||
\(206\) | −18.0577 | −1.25814 | ||||||||
\(207\) | −0.434193 | −0.0301785 | ||||||||
\(208\) | −0.550129 | −0.0381446 | ||||||||
\(209\) | 1.54118 | 0.106606 | ||||||||
\(210\) | 0.391804 | 0.0270370 | ||||||||
\(211\) | −13.7094 | −0.943797 | −0.471898 | − | 0.881653i | \(-0.656431\pi\) | ||||
−0.471898 | + | 0.881653i | \(0.656431\pi\) | |||||||
\(212\) | −2.40916 | −0.165462 | ||||||||
\(213\) | −1.52947 | −0.104797 | ||||||||
\(214\) | 0.382860 | 0.0261718 | ||||||||
\(215\) | 4.38197 | 0.298848 | ||||||||
\(216\) | 2.97332 | 0.202309 | ||||||||
\(217\) | −7.37262 | −0.500486 | ||||||||
\(218\) | −6.30475 | −0.427011 | ||||||||
\(219\) | 2.26825 | 0.153274 | ||||||||
\(220\) | −0.495081 | −0.0333783 | ||||||||
\(221\) | −2.90077 | −0.195127 | ||||||||
\(222\) | −1.14379 | −0.0767658 | ||||||||
\(223\) | −0.0515454 | −0.00345174 | −0.00172587 | − | 0.999999i | \(-0.500549\pi\) | ||||
−0.00172587 | + | 0.999999i | \(0.500549\pi\) | |||||||
\(224\) | 4.98012 | 0.332748 | ||||||||
\(225\) | −1.08219 | −0.0721462 | ||||||||
\(226\) | 0.533371 | 0.0354793 | ||||||||
\(227\) | 17.4384 | 1.15743 | 0.578714 | − | 0.815530i | \(-0.303555\pi\) | ||||
0.578714 | + | 0.815530i | \(0.303555\pi\) | |||||||
\(228\) | −1.14004 | −0.0755007 | ||||||||
\(229\) | −21.0706 | −1.39238 | −0.696192 | − | 0.717856i | \(-0.745124\pi\) | ||||
−0.696192 | + | 0.717856i | \(0.745124\pi\) | |||||||
\(230\) | 0.342006 | 0.0225512 | ||||||||
\(231\) | −0.0365775 | −0.00240662 | ||||||||
\(232\) | −18.2497 | −1.19815 | ||||||||
\(233\) | −0.718155 | −0.0470479 | −0.0235239 | − | 0.999723i | \(-0.507489\pi\) | ||||
−0.0235239 | + | 0.999723i | \(0.507489\pi\) | |||||||
\(234\) | 1.51966 | 0.0993432 | ||||||||
\(235\) | −20.3414 | −1.32693 | ||||||||
\(236\) | 13.3746 | 0.870609 | ||||||||
\(237\) | 0.781907 | 0.0507903 | ||||||||
\(238\) | −5.86904 | −0.380433 | ||||||||
\(239\) | 23.2198 | 1.50197 | 0.750984 | − | 0.660321i | \(-0.229580\pi\) | ||||
0.750984 | + | 0.660321i | \(0.229580\pi\) | |||||||
\(240\) | −0.416654 | −0.0268949 | ||||||||
\(241\) | 19.1893 | 1.23609 | 0.618046 | − | 0.786142i | \(-0.287925\pi\) | ||||
0.618046 | + | 0.786142i | \(0.287925\pi\) | |||||||
\(242\) | 11.0726 | 0.711776 | ||||||||
\(243\) | −4.41044 | −0.282930 | ||||||||
\(244\) | 2.49387 | 0.159654 | ||||||||
\(245\) | 13.8406 | 0.884243 | ||||||||
\(246\) | −0.697995 | −0.0445025 | ||||||||
\(247\) | −3.56504 | −0.226838 | ||||||||
\(248\) | 21.9343 | 1.39283 | ||||||||
\(249\) | −0.348754 | −0.0221014 | ||||||||
\(250\) | −10.8551 | −0.686538 | ||||||||
\(251\) | 19.3018 | 1.21832 | 0.609159 | − | 0.793048i | \(-0.291507\pi\) | ||||
0.609159 | + | 0.793048i | \(0.291507\pi\) | |||||||
\(252\) | −2.94165 | −0.185306 | ||||||||
\(253\) | −0.0319285 | −0.00200733 | ||||||||
\(254\) | −19.1297 | −1.20030 | ||||||||
\(255\) | −2.19697 | −0.137580 | ||||||||
\(256\) | −16.9441 | −1.05901 | ||||||||
\(257\) | −2.01807 | −0.125884 | −0.0629418 | − | 0.998017i | \(-0.520048\pi\) | ||||
−0.0629418 | + | 0.998017i | \(0.520048\pi\) | |||||||
\(258\) | −0.316292 | −0.0196915 | ||||||||
\(259\) | 6.92366 | 0.430215 | ||||||||
\(260\) | 1.14522 | 0.0710232 | ||||||||
\(261\) | 18.0195 | 1.11538 | ||||||||
\(262\) | 18.3291 | 1.13238 | ||||||||
\(263\) | −12.8064 | −0.789677 | −0.394838 | − | 0.918751i | \(-0.629199\pi\) | ||||
−0.394838 | + | 0.918751i | \(0.629199\pi\) | |||||||
\(264\) | 0.108821 | 0.00669750 | ||||||||
\(265\) | −5.70588 | −0.350510 | ||||||||
\(266\) | −7.21305 | −0.442260 | ||||||||
\(267\) | −0.546994 | −0.0334755 | ||||||||
\(268\) | 12.4502 | 0.760517 | ||||||||
\(269\) | −25.0242 | −1.52575 | −0.762876 | − | 0.646544i | \(-0.776214\pi\) | ||||
−0.762876 | + | 0.646544i | \(0.776214\pi\) | |||||||
\(270\) | 2.31249 | 0.140734 | ||||||||
\(271\) | −16.7333 | −1.01647 | −0.508237 | − | 0.861217i | \(-0.669703\pi\) | ||||
−0.508237 | + | 0.861217i | \(0.669703\pi\) | |||||||
\(272\) | 6.24128 | 0.378433 | ||||||||
\(273\) | 0.0846106 | 0.00512086 | ||||||||
\(274\) | −4.13356 | −0.249717 | ||||||||
\(275\) | −0.0795793 | −0.00479881 | ||||||||
\(276\) | 0.0236180 | 0.00142164 | ||||||||
\(277\) | −18.9063 | −1.13597 | −0.567984 | − | 0.823040i | \(-0.692276\pi\) | ||||
−0.567984 | + | 0.823040i | \(0.692276\pi\) | |||||||
\(278\) | −18.1272 | −1.08719 | ||||||||
\(279\) | −21.6576 | −1.29661 | ||||||||
\(280\) | 7.05603 | 0.421679 | ||||||||
\(281\) | 31.9292 | 1.90474 | 0.952368 | − | 0.304950i | \(-0.0986396\pi\) | ||||
0.952368 | + | 0.304950i | \(0.0986396\pi\) | |||||||
\(282\) | 1.46825 | 0.0874332 | ||||||||
\(283\) | −12.5918 | −0.748504 | −0.374252 | − | 0.927327i | \(-0.622101\pi\) | ||||
−0.374252 | + | 0.927327i | \(0.622101\pi\) | |||||||
\(284\) | −9.04508 | −0.536727 | ||||||||
\(285\) | −2.70007 | −0.159939 | ||||||||
\(286\) | 0.111748 | 0.00660782 | ||||||||
\(287\) | 4.22516 | 0.249403 | ||||||||
\(288\) | 14.6295 | 0.862049 | ||||||||
\(289\) | 15.9096 | 0.935858 | ||||||||
\(290\) | −14.1936 | −0.833479 | ||||||||
\(291\) | 1.61156 | 0.0944715 | ||||||||
\(292\) | 13.4142 | 0.785006 | ||||||||
\(293\) | 9.60465 | 0.561110 | 0.280555 | − | 0.959838i | \(-0.409482\pi\) | ||||
0.280555 | + | 0.959838i | \(0.409482\pi\) | |||||||
\(294\) | −0.999020 | −0.0582640 | ||||||||
\(295\) | 31.6765 | 1.84427 | ||||||||
\(296\) | −20.5985 | −1.19727 | ||||||||
\(297\) | −0.215886 | −0.0125270 | ||||||||
\(298\) | 0.222337 | 0.0128796 | ||||||||
\(299\) | 0.0738567 | 0.00427124 | ||||||||
\(300\) | 0.0588661 | 0.00339863 | ||||||||
\(301\) | 1.91461 | 0.110356 | ||||||||
\(302\) | −6.07524 | −0.349591 | ||||||||
\(303\) | −0.218279 | −0.0125398 | ||||||||
\(304\) | 7.67054 | 0.439936 | ||||||||
\(305\) | 5.90652 | 0.338206 | ||||||||
\(306\) | −17.2407 | −0.985586 | ||||||||
\(307\) | −0.309692 | −0.0176751 | −0.00883753 | − | 0.999961i | \(-0.502813\pi\) | ||||
−0.00883753 | + | 0.999961i | \(0.502813\pi\) | |||||||
\(308\) | −0.216315 | −0.0123257 | ||||||||
\(309\) | −2.95345 | −0.168016 | ||||||||
\(310\) | 17.0593 | 0.968902 | ||||||||
\(311\) | −26.7336 | −1.51592 | −0.757962 | − | 0.652299i | \(-0.773805\pi\) | ||||
−0.757962 | + | 0.652299i | \(0.773805\pi\) | |||||||
\(312\) | −0.251725 | −0.0142511 | ||||||||
\(313\) | −24.9391 | −1.40964 | −0.704821 | − | 0.709385i | \(-0.748973\pi\) | ||||
−0.704821 | + | 0.709385i | \(0.748973\pi\) | |||||||
\(314\) | −19.3860 | −1.09401 | ||||||||
\(315\) | −6.96703 | −0.392548 | ||||||||
\(316\) | 4.62411 | 0.260126 | ||||||||
\(317\) | 30.1627 | 1.69411 | 0.847054 | − | 0.531507i | \(-0.178374\pi\) | ||||
0.847054 | + | 0.531507i | \(0.178374\pi\) | |||||||
\(318\) | 0.411853 | 0.0230956 | ||||||||
\(319\) | 1.32507 | 0.0741897 | ||||||||
\(320\) | −16.5629 | −0.925893 | ||||||||
\(321\) | 0.0626191 | 0.00349506 | ||||||||
\(322\) | 0.149432 | 0.00832753 | ||||||||
\(323\) | 40.4459 | 2.25047 | ||||||||
\(324\) | −8.56108 | −0.475616 | ||||||||
\(325\) | 0.184082 | 0.0102110 | ||||||||
\(326\) | −20.4562 | −1.13296 | ||||||||
\(327\) | −1.03118 | −0.0570244 | ||||||||
\(328\) | −12.5703 | −0.694076 | ||||||||
\(329\) | −8.88775 | −0.489998 | ||||||||
\(330\) | 0.0846355 | 0.00465903 | ||||||||
\(331\) | −13.1988 | −0.725470 | −0.362735 | − | 0.931892i | \(-0.618157\pi\) | ||||
−0.362735 | + | 0.931892i | \(0.618157\pi\) | |||||||
\(332\) | −2.06249 | −0.113194 | ||||||||
\(333\) | 20.3387 | 1.11456 | ||||||||
\(334\) | −6.95962 | −0.380813 | ||||||||
\(335\) | 29.4872 | 1.61106 | ||||||||
\(336\) | −0.182048 | −0.00993153 | ||||||||
\(337\) | 14.5417 | 0.792138 | 0.396069 | − | 0.918221i | \(-0.370374\pi\) | ||||
0.396069 | + | 0.918221i | \(0.370374\pi\) | |||||||
\(338\) | 12.8844 | 0.700822 | ||||||||
\(339\) | 0.0872362 | 0.00473802 | ||||||||
\(340\) | −12.9926 | −0.704623 | ||||||||
\(341\) | −1.59260 | −0.0862439 | ||||||||
\(342\) | −21.1888 | −1.14576 | ||||||||
\(343\) | 13.1310 | 0.709005 | ||||||||
\(344\) | −5.69613 | −0.307115 | ||||||||
\(345\) | 0.0559372 | 0.00301156 | ||||||||
\(346\) | −10.1003 | −0.542996 | ||||||||
\(347\) | 8.12988 | 0.436435 | 0.218217 | − | 0.975900i | \(-0.429976\pi\) | ||||
0.218217 | + | 0.975900i | \(0.429976\pi\) | |||||||
\(348\) | −0.980175 | −0.0525429 | ||||||||
\(349\) | −2.82897 | −0.151431 | −0.0757157 | − | 0.997129i | \(-0.524124\pi\) | ||||
−0.0757157 | + | 0.997129i | \(0.524124\pi\) | |||||||
\(350\) | 0.372448 | 0.0199082 | ||||||||
\(351\) | 0.499385 | 0.0266552 | ||||||||
\(352\) | 1.07578 | 0.0573393 | ||||||||
\(353\) | −11.0300 | −0.587069 | −0.293535 | − | 0.955948i | \(-0.594832\pi\) | ||||
−0.293535 | + | 0.955948i | \(0.594832\pi\) | |||||||
\(354\) | −2.28642 | −0.121522 | ||||||||
\(355\) | −21.4225 | −1.13699 | ||||||||
\(356\) | −3.23486 | −0.171447 | ||||||||
\(357\) | −0.959918 | −0.0508042 | ||||||||
\(358\) | 19.5356 | 1.03249 | ||||||||
\(359\) | 4.24418 | 0.223999 | 0.112000 | − | 0.993708i | \(-0.464274\pi\) | ||||
0.112000 | + | 0.993708i | \(0.464274\pi\) | |||||||
\(360\) | 20.7276 | 1.09244 | ||||||||
\(361\) | 30.7080 | 1.61621 | ||||||||
\(362\) | −6.20408 | −0.326079 | ||||||||
\(363\) | 1.81100 | 0.0950528 | ||||||||
\(364\) | 0.500377 | 0.0262269 | ||||||||
\(365\) | 31.7703 | 1.66294 | ||||||||
\(366\) | −0.426335 | −0.0222849 | ||||||||
\(367\) | −11.3734 | −0.593686 | −0.296843 | − | 0.954926i | \(-0.595934\pi\) | ||||
−0.296843 | + | 0.954926i | \(0.595934\pi\) | |||||||
\(368\) | −0.158910 | −0.00828376 | ||||||||
\(369\) | 12.4117 | 0.646128 | ||||||||
\(370\) | −16.0204 | −0.832863 | ||||||||
\(371\) | −2.49306 | −0.129433 | ||||||||
\(372\) | 1.17807 | 0.0610800 | ||||||||
\(373\) | −24.4613 | −1.26656 | −0.633278 | − | 0.773924i | \(-0.718291\pi\) | ||||
−0.633278 | + | 0.773924i | \(0.718291\pi\) | |||||||
\(374\) | −1.26780 | −0.0655564 | ||||||||
\(375\) | −1.77542 | −0.0916824 | ||||||||
\(376\) | 26.4419 | 1.36364 | ||||||||
\(377\) | −3.06514 | −0.157863 | ||||||||
\(378\) | 1.01039 | 0.0519690 | ||||||||
\(379\) | −17.4839 | −0.898085 | −0.449043 | − | 0.893510i | \(-0.648235\pi\) | ||||
−0.449043 | + | 0.893510i | \(0.648235\pi\) | |||||||
\(380\) | −15.9679 | −0.819137 | ||||||||
\(381\) | −3.12878 | −0.160292 | ||||||||
\(382\) | −16.7283 | −0.855894 | ||||||||
\(383\) | −32.2317 | −1.64697 | −0.823483 | − | 0.567342i | \(-0.807972\pi\) | ||||
−0.823483 | + | 0.567342i | \(0.807972\pi\) | |||||||
\(384\) | −0.432018 | −0.0220463 | ||||||||
\(385\) | −0.512323 | −0.0261104 | ||||||||
\(386\) | 6.35480 | 0.323451 | ||||||||
\(387\) | 5.62429 | 0.285899 | ||||||||
\(388\) | 9.53059 | 0.483843 | ||||||||
\(389\) | 9.76934 | 0.495325 | 0.247663 | − | 0.968846i | \(-0.420338\pi\) | ||||
0.247663 | + | 0.968846i | \(0.420338\pi\) | |||||||
\(390\) | −0.195778 | −0.00991360 | ||||||||
\(391\) | −0.837914 | −0.0423751 | ||||||||
\(392\) | −17.9914 | −0.908705 | ||||||||
\(393\) | 2.99784 | 0.151221 | ||||||||
\(394\) | 11.7581 | 0.592366 | ||||||||
\(395\) | 10.9518 | 0.551045 | ||||||||
\(396\) | −0.635440 | −0.0319321 | ||||||||
\(397\) | −29.0332 | −1.45714 | −0.728568 | − | 0.684974i | \(-0.759814\pi\) | ||||
−0.728568 | + | 0.684974i | \(0.759814\pi\) | |||||||
\(398\) | 13.0433 | 0.653800 | ||||||||
\(399\) | −1.17974 | −0.0590608 | ||||||||
\(400\) | −0.396071 | −0.0198035 | ||||||||
\(401\) | 28.8923 | 1.44281 | 0.721407 | − | 0.692511i | \(-0.243496\pi\) | ||||
0.721407 | + | 0.692511i | \(0.243496\pi\) | |||||||
\(402\) | −2.12840 | −0.106155 | ||||||||
\(403\) | 3.68398 | 0.183512 | ||||||||
\(404\) | −1.29088 | −0.0642235 | ||||||||
\(405\) | −20.2762 | −1.00753 | ||||||||
\(406\) | −6.20161 | −0.307781 | ||||||||
\(407\) | 1.49561 | 0.0741348 | ||||||||
\(408\) | 2.85585 | 0.141386 | ||||||||
\(409\) | 35.7645 | 1.76844 | 0.884219 | − | 0.467072i | \(-0.154691\pi\) | ||||
0.884219 | + | 0.467072i | \(0.154691\pi\) | |||||||
\(410\) | −9.77647 | −0.482826 | ||||||||
\(411\) | −0.676069 | −0.0333480 | ||||||||
\(412\) | −17.4664 | −0.860507 | ||||||||
\(413\) | 13.8403 | 0.681039 | ||||||||
\(414\) | 0.438968 | 0.0215741 | ||||||||
\(415\) | −4.88483 | −0.239787 | ||||||||
\(416\) | −2.48849 | −0.122008 | ||||||||
\(417\) | −2.96481 | −0.145187 | ||||||||
\(418\) | −1.55813 | −0.0762105 | ||||||||
\(419\) | 35.0002 | 1.70987 | 0.854936 | − | 0.518734i | \(-0.173596\pi\) | ||||
0.854936 | + | 0.518734i | \(0.173596\pi\) | |||||||
\(420\) | 0.378973 | 0.0184920 | ||||||||
\(421\) | −35.1477 | −1.71300 | −0.856498 | − | 0.516151i | \(-0.827364\pi\) | ||||
−0.856498 | + | 0.516151i | \(0.827364\pi\) | |||||||
\(422\) | 13.8602 | 0.674703 | ||||||||
\(423\) | −26.1084 | −1.26943 | ||||||||
\(424\) | 7.41710 | 0.360206 | ||||||||
\(425\) | −2.08843 | −0.101304 | ||||||||
\(426\) | 1.54628 | 0.0749177 | ||||||||
\(427\) | 2.58073 | 0.124890 | ||||||||
\(428\) | 0.370322 | 0.0179002 | ||||||||
\(429\) | 0.0182772 | 0.000882429 0 | ||||||||
\(430\) | −4.43015 | −0.213641 | ||||||||
\(431\) | −2.20728 | −0.106321 | −0.0531604 | − | 0.998586i | \(-0.516929\pi\) | ||||
−0.0531604 | + | 0.998586i | \(0.516929\pi\) | |||||||
\(432\) | −1.07448 | −0.0516958 | ||||||||
\(433\) | −21.5181 | −1.03409 | −0.517047 | − | 0.855957i | \(-0.672969\pi\) | ||||
−0.517047 | + | 0.855957i | \(0.672969\pi\) | |||||||
\(434\) | 7.45369 | 0.357788 | ||||||||
\(435\) | −2.32146 | −0.111305 | ||||||||
\(436\) | −6.09828 | −0.292055 | ||||||||
\(437\) | −1.02980 | −0.0492618 | ||||||||
\(438\) | −2.29320 | −0.109573 | ||||||||
\(439\) | 15.8230 | 0.755188 | 0.377594 | − | 0.925971i | \(-0.376751\pi\) | ||||
0.377594 | + | 0.925971i | \(0.376751\pi\) | |||||||
\(440\) | 1.52421 | 0.0726638 | ||||||||
\(441\) | 17.7645 | 0.845929 | ||||||||
\(442\) | 2.93266 | 0.139493 | ||||||||
\(443\) | −22.0597 | −1.04809 | −0.524044 | − | 0.851691i | \(-0.675577\pi\) | ||||
−0.524044 | + | 0.851691i | \(0.675577\pi\) | |||||||
\(444\) | −1.10633 | −0.0525040 | ||||||||
\(445\) | −7.66148 | −0.363189 | ||||||||
\(446\) | 0.0521122 | 0.00246758 | ||||||||
\(447\) | 0.0363645 | 0.00171998 | ||||||||
\(448\) | −7.23679 | −0.341906 | ||||||||
\(449\) | −9.46744 | −0.446796 | −0.223398 | − | 0.974727i | \(-0.571715\pi\) | ||||
−0.223398 | + | 0.974727i | \(0.571715\pi\) | |||||||
\(450\) | 1.09409 | 0.0515760 | ||||||||
\(451\) | 0.912698 | 0.0429773 | ||||||||
\(452\) | 0.515905 | 0.0242661 | ||||||||
\(453\) | −0.993644 | −0.0466855 | ||||||||
\(454\) | −17.6302 | −0.827425 | ||||||||
\(455\) | 1.18510 | 0.0555583 | ||||||||
\(456\) | 3.50984 | 0.164363 | ||||||||
\(457\) | −21.9256 | −1.02564 | −0.512819 | − | 0.858497i | \(-0.671399\pi\) | ||||
−0.512819 | + | 0.858497i | \(0.671399\pi\) | |||||||
\(458\) | 21.3023 | 0.995390 | ||||||||
\(459\) | −5.66559 | −0.264447 | ||||||||
\(460\) | 0.330806 | 0.0154239 | ||||||||
\(461\) | 12.4927 | 0.581841 | 0.290921 | − | 0.956747i | \(-0.406038\pi\) | ||||
0.290921 | + | 0.956747i | \(0.406038\pi\) | |||||||
\(462\) | 0.0369797 | 0.00172045 | ||||||||
\(463\) | −1.81679 | −0.0844333 | −0.0422166 | − | 0.999108i | \(-0.513442\pi\) | ||||
−0.0422166 | + | 0.999108i | \(0.513442\pi\) | |||||||
\(464\) | 6.59494 | 0.306163 | ||||||||
\(465\) | 2.79015 | 0.129390 | ||||||||
\(466\) | 0.726051 | 0.0336337 | ||||||||
\(467\) | −6.90171 | −0.319373 | −0.159687 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159687 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(468\) | 1.46989 | 0.0679458 | ||||||||
\(469\) | 12.8838 | 0.594918 | ||||||||
\(470\) | 20.5651 | 0.948598 | ||||||||
\(471\) | −3.17070 | −0.146098 | ||||||||
\(472\) | −41.1764 | −1.89530 | ||||||||
\(473\) | 0.413584 | 0.0190166 | ||||||||
\(474\) | −0.790505 | −0.0363091 | ||||||||
\(475\) | −2.56669 | −0.117768 | ||||||||
\(476\) | −5.67684 | −0.260198 | ||||||||
\(477\) | −7.32355 | −0.335322 | ||||||||
\(478\) | −23.4752 | −1.07373 | ||||||||
\(479\) | −27.0104 | −1.23414 | −0.617068 | − | 0.786910i | \(-0.711680\pi\) | ||||
−0.617068 | + | 0.786910i | \(0.711680\pi\) | |||||||
\(480\) | −1.88472 | −0.0860252 | ||||||||
\(481\) | −3.45964 | −0.157746 | ||||||||
\(482\) | −19.4003 | −0.883660 | ||||||||
\(483\) | 0.0244406 | 0.00111208 | ||||||||
\(484\) | 10.7100 | 0.486820 | ||||||||
\(485\) | 22.5724 | 1.02496 | ||||||||
\(486\) | 4.45894 | 0.202262 | ||||||||
\(487\) | −8.59437 | −0.389448 | −0.194724 | − | 0.980858i | \(-0.562381\pi\) | ||||
−0.194724 | + | 0.980858i | \(0.562381\pi\) | |||||||
\(488\) | −7.67791 | −0.347563 | ||||||||
\(489\) | −3.34574 | −0.151299 | ||||||||
\(490\) | −13.9928 | −0.632129 | ||||||||
\(491\) | 11.5260 | 0.520161 | 0.260080 | − | 0.965587i | \(-0.416251\pi\) | ||||
0.260080 | + | 0.965587i | \(0.416251\pi\) | |||||||
\(492\) | −0.675137 | −0.0304375 | ||||||||
\(493\) | 34.7744 | 1.56616 | ||||||||
\(494\) | 3.60424 | 0.162163 | ||||||||
\(495\) | −1.50498 | −0.0676440 | ||||||||
\(496\) | −7.92644 | −0.355908 | ||||||||
\(497\) | −9.36009 | −0.419857 | ||||||||
\(498\) | 0.352589 | 0.0157999 | ||||||||
\(499\) | −3.95509 | −0.177054 | −0.0885270 | − | 0.996074i | \(-0.528216\pi\) | ||||
−0.0885270 | + | 0.996074i | \(0.528216\pi\) | |||||||
\(500\) | −10.4996 | −0.469558 | ||||||||
\(501\) | −1.13829 | −0.0508550 | ||||||||
\(502\) | −19.5140 | −0.870954 | ||||||||
\(503\) | 26.3194 | 1.17352 | 0.586761 | − | 0.809760i | \(-0.300403\pi\) | ||||
0.586761 | + | 0.809760i | \(0.300403\pi\) | |||||||
\(504\) | 9.05647 | 0.403407 | ||||||||
\(505\) | −3.05733 | −0.136049 | ||||||||
\(506\) | 0.0322796 | 0.00143500 | ||||||||
\(507\) | 2.10733 | 0.0935899 | ||||||||
\(508\) | −18.5033 | −0.820949 | ||||||||
\(509\) | −4.11736 | −0.182499 | −0.0912493 | − | 0.995828i | \(-0.529086\pi\) | ||||
−0.0912493 | + | 0.995828i | \(0.529086\pi\) | |||||||
\(510\) | 2.22113 | 0.0983531 | ||||||||
\(511\) | 13.8814 | 0.614075 | ||||||||
\(512\) | 11.9051 | 0.526137 | ||||||||
\(513\) | −6.96301 | −0.307424 | ||||||||
\(514\) | 2.04026 | 0.0899920 | ||||||||
\(515\) | −41.3676 | −1.82287 | ||||||||
\(516\) | −0.305934 | −0.0134680 | ||||||||
\(517\) | −1.91989 | −0.0844366 | ||||||||
\(518\) | −6.99979 | −0.307553 | ||||||||
\(519\) | −1.65197 | −0.0725133 | ||||||||
\(520\) | −3.52578 | −0.154616 | ||||||||
\(521\) | −9.91059 | −0.434191 | −0.217095 | − | 0.976150i | \(-0.569658\pi\) | ||||
−0.217095 | + | 0.976150i | \(0.569658\pi\) | |||||||
\(522\) | −18.2177 | −0.797365 | ||||||||
\(523\) | −6.25084 | −0.273330 | −0.136665 | − | 0.990617i | \(-0.543638\pi\) | ||||
−0.136665 | + | 0.990617i | \(0.543638\pi\) | |||||||
\(524\) | 17.7289 | 0.774491 | ||||||||
\(525\) | 0.0609162 | 0.00265860 | ||||||||
\(526\) | 12.9472 | 0.564525 | ||||||||
\(527\) | −41.7952 | −1.82063 | ||||||||
\(528\) | −0.0393251 | −0.00171141 | ||||||||
\(529\) | −22.9787 | −0.999072 | ||||||||
\(530\) | 5.76862 | 0.250573 | ||||||||
\(531\) | 40.6570 | 1.76436 | ||||||||
\(532\) | −6.97684 | −0.302484 | ||||||||
\(533\) | −2.11124 | −0.0914481 | ||||||||
\(534\) | 0.553009 | 0.0239310 | ||||||||
\(535\) | 0.877076 | 0.0379193 | ||||||||
\(536\) | −38.3305 | −1.65563 | ||||||||
\(537\) | 3.19517 | 0.137882 | ||||||||
\(538\) | 25.2994 | 1.09073 | ||||||||
\(539\) | 1.30632 | 0.0562671 | ||||||||
\(540\) | 2.23676 | 0.0962548 | ||||||||
\(541\) | −45.8569 | −1.97154 | −0.985770 | − | 0.168098i | \(-0.946237\pi\) | ||||
−0.985770 | + | 0.168098i | \(0.946237\pi\) | |||||||
\(542\) | 16.9173 | 0.726659 | ||||||||
\(543\) | −1.01472 | −0.0435456 | ||||||||
\(544\) | 28.2322 | 1.21045 | ||||||||
\(545\) | −14.4432 | −0.618681 | ||||||||
\(546\) | −0.0855409 | −0.00366081 | ||||||||
\(547\) | 39.9554 | 1.70837 | 0.854185 | − | 0.519969i | \(-0.174056\pi\) | ||||
0.854185 | + | 0.519969i | \(0.174056\pi\) | |||||||
\(548\) | −3.99819 | −0.170794 | ||||||||
\(549\) | 7.58106 | 0.323552 | ||||||||
\(550\) | 0.0804544 | 0.00343059 | ||||||||
\(551\) | 42.7377 | 1.82069 | ||||||||
\(552\) | −0.0727130 | −0.00309487 | ||||||||
\(553\) | 4.78515 | 0.203485 | ||||||||
\(554\) | 19.1141 | 0.812082 | ||||||||
\(555\) | −2.62024 | −0.111223 | ||||||||
\(556\) | −17.5335 | −0.743588 | ||||||||
\(557\) | 25.9730 | 1.10051 | 0.550256 | − | 0.834996i | \(-0.314530\pi\) | ||||
0.550256 | + | 0.834996i | \(0.314530\pi\) | |||||||
\(558\) | 21.8957 | 0.926920 | ||||||||
\(559\) | −0.956697 | −0.0404640 | ||||||||
\(560\) | −2.54986 | −0.107751 | ||||||||
\(561\) | −0.207357 | −0.00875461 | ||||||||
\(562\) | −32.2803 | −1.36166 | ||||||||
\(563\) | 16.2957 | 0.686783 | 0.343392 | − | 0.939192i | \(-0.388424\pi\) | ||||
0.343392 | + | 0.939192i | \(0.388424\pi\) | |||||||
\(564\) | 1.42017 | 0.0598000 | ||||||||
\(565\) | 1.22187 | 0.0514047 | ||||||||
\(566\) | 12.7302 | 0.535092 | ||||||||
\(567\) | −8.85924 | −0.372053 | ||||||||
\(568\) | 27.8472 | 1.16844 | ||||||||
\(569\) | 15.4272 | 0.646744 | 0.323372 | − | 0.946272i | \(-0.395184\pi\) | ||||
0.323372 | + | 0.946272i | \(0.395184\pi\) | |||||||
\(570\) | 2.72976 | 0.114337 | ||||||||
\(571\) | 36.6907 | 1.53546 | 0.767729 | − | 0.640775i | \(-0.221387\pi\) | ||||
0.767729 | + | 0.640775i | \(0.221387\pi\) | |||||||
\(572\) | 0.108089 | 0.00451943 | ||||||||
\(573\) | −2.73602 | −0.114299 | ||||||||
\(574\) | −4.27162 | −0.178294 | ||||||||
\(575\) | 0.0531738 | 0.00221750 | ||||||||
\(576\) | −21.2586 | −0.885774 | ||||||||
\(577\) | 19.2897 | 0.803041 | 0.401520 | − | 0.915850i | \(-0.368482\pi\) | ||||
0.401520 | + | 0.915850i | \(0.368482\pi\) | |||||||
\(578\) | −16.0845 | −0.669028 | ||||||||
\(579\) | 1.03937 | 0.0431947 | ||||||||
\(580\) | −13.7288 | −0.570059 | ||||||||
\(581\) | −2.13432 | −0.0885466 | ||||||||
\(582\) | −1.62928 | −0.0675360 | ||||||||
\(583\) | −0.538539 | −0.0223040 | ||||||||
\(584\) | −41.2984 | −1.70894 | ||||||||
\(585\) | 3.48131 | 0.143935 | ||||||||
\(586\) | −9.71026 | −0.401127 | ||||||||
\(587\) | 43.5333 | 1.79681 | 0.898405 | − | 0.439168i | \(-0.144727\pi\) | ||||
0.898405 | + | 0.439168i | \(0.144727\pi\) | |||||||
\(588\) | −0.966304 | −0.0398497 | ||||||||
\(589\) | −51.3663 | −2.11651 | ||||||||
\(590\) | −32.0248 | −1.31844 | ||||||||
\(591\) | 1.92312 | 0.0791064 | ||||||||
\(592\) | 7.44375 | 0.305936 | ||||||||
\(593\) | 2.94911 | 0.121105 | 0.0605527 | − | 0.998165i | \(-0.480714\pi\) | ||||
0.0605527 | + | 0.998165i | \(0.480714\pi\) | |||||||
\(594\) | 0.218260 | 0.00895531 | ||||||||
\(595\) | −13.4451 | −0.551195 | ||||||||
\(596\) | 0.215056 | 0.00880902 | ||||||||
\(597\) | 2.13331 | 0.0873104 | ||||||||
\(598\) | −0.0746688 | −0.00305344 | ||||||||
\(599\) | 40.0061 | 1.63461 | 0.817303 | − | 0.576208i | \(-0.195468\pi\) | ||||
0.817303 | + | 0.576208i | \(0.195468\pi\) | |||||||
\(600\) | −0.181232 | −0.00739875 | ||||||||
\(601\) | 4.70362 | 0.191864 | 0.0959322 | − | 0.995388i | \(-0.469417\pi\) | ||||
0.0959322 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(602\) | −1.93566 | −0.0788915 | ||||||||
\(603\) | 37.8470 | 1.54125 | ||||||||
\(604\) | −5.87629 | −0.239103 | ||||||||
\(605\) | 25.3658 | 1.03127 | ||||||||
\(606\) | 0.220679 | 0.00896448 | ||||||||
\(607\) | 25.6662 | 1.04176 | 0.520879 | − | 0.853631i | \(-0.325604\pi\) | ||||
0.520879 | + | 0.853631i | \(0.325604\pi\) | |||||||
\(608\) | 34.6974 | 1.40716 | ||||||||
\(609\) | −1.01431 | −0.0411020 | ||||||||
\(610\) | −5.97147 | −0.241778 | ||||||||
\(611\) | 4.44106 | 0.179666 | ||||||||
\(612\) | −16.6761 | −0.674092 | ||||||||
\(613\) | −27.6866 | −1.11825 | −0.559126 | − | 0.829082i | \(-0.688863\pi\) | ||||
−0.559126 | + | 0.829082i | \(0.688863\pi\) | |||||||
\(614\) | 0.313097 | 0.0126356 | ||||||||
\(615\) | −1.59900 | −0.0644780 | ||||||||
\(616\) | 0.665970 | 0.0268327 | ||||||||
\(617\) | −23.7340 | −0.955493 | −0.477747 | − | 0.878498i | \(-0.658546\pi\) | ||||
−0.477747 | + | 0.878498i | \(0.658546\pi\) | |||||||
\(618\) | 2.98593 | 0.120112 | ||||||||
\(619\) | 10.1068 | 0.406228 | 0.203114 | − | 0.979155i | \(-0.434894\pi\) | ||||
0.203114 | + | 0.979155i | \(0.434894\pi\) | |||||||
\(620\) | 16.5006 | 0.662681 | ||||||||
\(621\) | 0.144252 | 0.00578864 | ||||||||
\(622\) | 27.0276 | 1.08371 | ||||||||
\(623\) | −3.34752 | −0.134115 | ||||||||
\(624\) | 0.0909664 | 0.00364157 | ||||||||
\(625\) | −26.6877 | −1.06751 | ||||||||
\(626\) | 25.2133 | 1.00773 | ||||||||
\(627\) | −0.254841 | −0.0101774 | ||||||||
\(628\) | −18.7511 | −0.748251 | ||||||||
\(629\) | 39.2500 | 1.56500 | ||||||||
\(630\) | 7.04364 | 0.280625 | ||||||||
\(631\) | −28.8533 | −1.14863 | −0.574316 | − | 0.818634i | \(-0.694732\pi\) | ||||
−0.574316 | + | 0.818634i | \(0.694732\pi\) | |||||||
\(632\) | −14.2363 | −0.566289 | ||||||||
\(633\) | 2.26692 | 0.0901020 | ||||||||
\(634\) | −30.4944 | −1.21109 | ||||||||
\(635\) | −43.8233 | −1.73908 | ||||||||
\(636\) | 0.398366 | 0.0157962 | ||||||||
\(637\) | −3.02176 | −0.119726 | ||||||||
\(638\) | −1.33964 | −0.0530369 | ||||||||
\(639\) | −27.4959 | −1.08772 | ||||||||
\(640\) | −6.05106 | −0.239189 | ||||||||
\(641\) | 15.2099 | 0.600756 | 0.300378 | − | 0.953820i | \(-0.402887\pi\) | ||||
0.300378 | + | 0.953820i | \(0.402887\pi\) | |||||||
\(642\) | −0.0633077 | −0.00249855 | ||||||||
\(643\) | 1.63211 | 0.0643640 | 0.0321820 | − | 0.999482i | \(-0.489754\pi\) | ||||
0.0321820 | + | 0.999482i | \(0.489754\pi\) | |||||||
\(644\) | 0.144539 | 0.00569562 | ||||||||
\(645\) | −0.724578 | −0.0285302 | ||||||||
\(646\) | −40.8906 | −1.60882 | ||||||||
\(647\) | −42.1264 | −1.65616 | −0.828080 | − | 0.560610i | \(-0.810567\pi\) | ||||
−0.828080 | + | 0.560610i | \(0.810567\pi\) | |||||||
\(648\) | 26.3571 | 1.03540 | ||||||||
\(649\) | 2.98972 | 0.117357 | ||||||||
\(650\) | −0.186106 | −0.00729968 | ||||||||
\(651\) | 1.21910 | 0.0477802 | ||||||||
\(652\) | −19.7863 | −0.774891 | ||||||||
\(653\) | −28.1328 | −1.10092 | −0.550460 | − | 0.834862i | \(-0.685548\pi\) | ||||
−0.550460 | + | 0.834862i | \(0.685548\pi\) | |||||||
\(654\) | 1.04252 | 0.0407657 | ||||||||
\(655\) | 41.9893 | 1.64066 | ||||||||
\(656\) | 4.54255 | 0.177357 | ||||||||
\(657\) | 40.7775 | 1.59088 | ||||||||
\(658\) | 8.98548 | 0.350290 | ||||||||
\(659\) | −48.1661 | −1.87629 | −0.938143 | − | 0.346248i | \(-0.887455\pi\) | ||||
−0.938143 | + | 0.346248i | \(0.887455\pi\) | |||||||
\(660\) | 0.0818639 | 0.00318655 | ||||||||
\(661\) | −25.2043 | −0.980335 | −0.490168 | − | 0.871628i | \(-0.663064\pi\) | ||||
−0.490168 | + | 0.871628i | \(0.663064\pi\) | |||||||
\(662\) | 13.3439 | 0.518625 | ||||||||
\(663\) | 0.479655 | 0.0186283 | ||||||||
\(664\) | 6.34981 | 0.246420 | ||||||||
\(665\) | −16.5240 | −0.640774 | ||||||||
\(666\) | −20.5624 | −0.796776 | ||||||||
\(667\) | −0.885394 | −0.0342826 | ||||||||
\(668\) | −6.73170 | −0.260457 | ||||||||
\(669\) | 0.00852328 | 0.000329529 0 | ||||||||
\(670\) | −29.8114 | −1.15172 | ||||||||
\(671\) | 0.557476 | 0.0215211 | ||||||||
\(672\) | −0.823486 | −0.0317667 | ||||||||
\(673\) | −32.2595 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(674\) | −14.7016 | −0.566285 | ||||||||
\(675\) | 0.359537 | 0.0138386 | ||||||||
\(676\) | 12.4625 | 0.479327 | ||||||||
\(677\) | −6.15792 | −0.236668 | −0.118334 | − | 0.992974i | \(-0.537755\pi\) | ||||
−0.118334 | + | 0.992974i | \(0.537755\pi\) | |||||||
\(678\) | −0.0881954 | −0.00338712 | ||||||||
\(679\) | 9.86251 | 0.378488 | ||||||||
\(680\) | 40.0005 | 1.53395 | ||||||||
\(681\) | −2.88352 | −0.110497 | ||||||||
\(682\) | 1.61011 | 0.0616542 | ||||||||
\(683\) | −32.7408 | −1.25279 | −0.626396 | − | 0.779505i | \(-0.715471\pi\) | ||||
−0.626396 | + | 0.779505i | \(0.715471\pi\) | |||||||
\(684\) | −20.4950 | −0.783644 | ||||||||
\(685\) | −9.46937 | −0.361806 | ||||||||
\(686\) | −13.2753 | −0.506855 | ||||||||
\(687\) | 3.48412 | 0.132927 | ||||||||
\(688\) | 2.05843 | 0.0784768 | ||||||||
\(689\) | 1.24574 | 0.0474590 | ||||||||
\(690\) | −0.0565523 | −0.00215291 | ||||||||
\(691\) | −50.9047 | −1.93651 | −0.968253 | − | 0.249974i | \(-0.919578\pi\) | ||||
−0.968253 | + | 0.249974i | \(0.919578\pi\) | |||||||
\(692\) | −9.76954 | −0.371382 | ||||||||
\(693\) | −0.657570 | −0.0249790 | ||||||||
\(694\) | −8.21927 | −0.311999 | ||||||||
\(695\) | −41.5267 | −1.57520 | ||||||||
\(696\) | 3.01767 | 0.114385 | ||||||||
\(697\) | 23.9523 | 0.907259 | ||||||||
\(698\) | 2.86008 | 0.108256 | ||||||||
\(699\) | 0.118750 | 0.00449154 | ||||||||
\(700\) | 0.360251 | 0.0136162 | ||||||||
\(701\) | 37.8577 | 1.42987 | 0.714933 | − | 0.699193i | \(-0.246457\pi\) | ||||
0.714933 | + | 0.699193i | \(0.246457\pi\) | |||||||
\(702\) | −0.504876 | −0.0190553 | ||||||||
\(703\) | 48.2383 | 1.81934 | ||||||||
\(704\) | −1.56326 | −0.0589174 | ||||||||
\(705\) | 3.36355 | 0.126679 | ||||||||
\(706\) | 11.1513 | 0.419685 | ||||||||
\(707\) | −1.33583 | −0.0502392 | ||||||||
\(708\) | −2.21154 | −0.0831149 | ||||||||
\(709\) | −37.9785 | −1.42631 | −0.713156 | − | 0.701005i | \(-0.752735\pi\) | ||||
−0.713156 | + | 0.701005i | \(0.752735\pi\) | |||||||
\(710\) | 21.6580 | 0.812811 | ||||||||
\(711\) | 14.0567 | 0.527168 | ||||||||
\(712\) | 9.95919 | 0.373236 | ||||||||
\(713\) | 1.06415 | 0.0398528 | ||||||||
\(714\) | 0.970473 | 0.0363190 | ||||||||
\(715\) | 0.255999 | 0.00957383 | ||||||||
\(716\) | 18.8958 | 0.706171 | ||||||||
\(717\) | −3.83951 | −0.143389 | ||||||||
\(718\) | −4.29085 | −0.160133 | ||||||||
\(719\) | 7.41758 | 0.276629 | 0.138315 | − | 0.990388i | \(-0.455832\pi\) | ||||
0.138315 | + | 0.990388i | \(0.455832\pi\) | |||||||
\(720\) | −7.49038 | −0.279150 | ||||||||
\(721\) | −18.0747 | −0.673136 | ||||||||
\(722\) | −31.0456 | −1.15540 | ||||||||
\(723\) | −3.17304 | −0.118007 | ||||||||
\(724\) | −6.00091 | −0.223022 | ||||||||
\(725\) | −2.20677 | −0.0819576 | ||||||||
\(726\) | −1.83091 | −0.0679515 | ||||||||
\(727\) | −9.45230 | −0.350566 | −0.175283 | − | 0.984518i | \(-0.556084\pi\) | ||||
−0.175283 | + | 0.984518i | \(0.556084\pi\) | |||||||
\(728\) | −1.54051 | −0.0570953 | ||||||||
\(729\) | −25.5347 | −0.945730 | ||||||||
\(730\) | −32.1197 | −1.18880 | ||||||||
\(731\) | 10.8538 | 0.401444 | ||||||||
\(732\) | −0.412373 | −0.0152418 | ||||||||
\(733\) | −7.51009 | −0.277391 | −0.138696 | − | 0.990335i | \(-0.544291\pi\) | ||||
−0.138696 | + | 0.990335i | \(0.544291\pi\) | |||||||
\(734\) | 11.4984 | 0.424415 | ||||||||
\(735\) | −2.28861 | −0.0844165 | ||||||||
\(736\) | −0.718823 | −0.0264962 | ||||||||
\(737\) | 2.78309 | 0.102517 | ||||||||
\(738\) | −12.5482 | −0.461905 | ||||||||
\(739\) | 25.4681 | 0.936859 | 0.468430 | − | 0.883501i | \(-0.344820\pi\) | ||||
0.468430 | + | 0.883501i | \(0.344820\pi\) | |||||||
\(740\) | −15.4958 | −0.569637 | ||||||||
\(741\) | 0.589496 | 0.0216557 | ||||||||
\(742\) | 2.52047 | 0.0925295 | ||||||||
\(743\) | −34.4841 | −1.26510 | −0.632550 | − | 0.774519i | \(-0.717992\pi\) | ||||
−0.632550 | + | 0.774519i | \(0.717992\pi\) | |||||||
\(744\) | −3.62693 | −0.132970 | ||||||||
\(745\) | 0.509340 | 0.0186608 | ||||||||
\(746\) | 24.7302 | 0.905438 | ||||||||
\(747\) | −6.26972 | −0.229397 | ||||||||
\(748\) | −1.22628 | −0.0448374 | ||||||||
\(749\) | 0.383219 | 0.0140025 | ||||||||
\(750\) | 1.79494 | 0.0655421 | ||||||||
\(751\) | −14.7004 | −0.536426 | −0.268213 | − | 0.963360i | \(-0.586433\pi\) | ||||
−0.268213 | + | 0.963360i | \(0.586433\pi\) | |||||||
\(752\) | −9.55539 | −0.348449 | ||||||||
\(753\) | −3.19164 | −0.116310 | ||||||||
\(754\) | 3.09884 | 0.112853 | ||||||||
\(755\) | −13.9175 | −0.506509 | ||||||||
\(756\) | 0.977304 | 0.0355442 | ||||||||
\(757\) | 44.5642 | 1.61971 | 0.809856 | − | 0.586628i | \(-0.199545\pi\) | ||||
0.809856 | + | 0.586628i | \(0.199545\pi\) | |||||||
\(758\) | 17.6761 | 0.642025 | ||||||||
\(759\) | 0.00527953 | 0.000191635 0 | ||||||||
\(760\) | 49.1606 | 1.78324 | ||||||||
\(761\) | −31.1285 | −1.12841 | −0.564203 | − | 0.825636i | \(-0.690817\pi\) | ||||
−0.564203 | + | 0.825636i | \(0.690817\pi\) | |||||||
\(762\) | 3.16319 | 0.114590 | ||||||||
\(763\) | −6.31066 | −0.228461 | ||||||||
\(764\) | −16.1805 | −0.585390 | ||||||||
\(765\) | −39.4959 | −1.42798 | ||||||||
\(766\) | 32.5862 | 1.17739 | ||||||||
\(767\) | −6.91579 | −0.249715 | ||||||||
\(768\) | 2.80179 | 0.101101 | ||||||||
\(769\) | 16.6611 | 0.600813 | 0.300406 | − | 0.953811i | \(-0.402878\pi\) | ||||
0.300406 | + | 0.953811i | \(0.402878\pi\) | |||||||
\(770\) | 0.517956 | 0.0186658 | ||||||||
\(771\) | 0.333697 | 0.0120178 | ||||||||
\(772\) | 6.14670 | 0.221225 | ||||||||
\(773\) | −47.4838 | −1.70787 | −0.853937 | − | 0.520376i | \(-0.825792\pi\) | ||||
−0.853937 | + | 0.520376i | \(0.825792\pi\) | |||||||
\(774\) | −5.68613 | −0.204384 | ||||||||
\(775\) | 2.65231 | 0.0952739 | ||||||||
\(776\) | −29.3419 | −1.05331 | ||||||||
\(777\) | −1.14486 | −0.0410716 | ||||||||
\(778\) | −9.87676 | −0.354099 | ||||||||
\(779\) | 29.4374 | 1.05470 | ||||||||
\(780\) | −0.189367 | −0.00678041 | ||||||||
\(781\) | −2.02192 | −0.0723500 | ||||||||
\(782\) | 0.847128 | 0.0302932 | ||||||||
\(783\) | −5.98663 | −0.213945 | ||||||||
\(784\) | 6.50161 | 0.232200 | ||||||||
\(785\) | −44.4104 | −1.58507 | ||||||||
\(786\) | −3.03081 | −0.108105 | ||||||||
\(787\) | −7.35369 | −0.262131 | −0.131065 | − | 0.991374i | \(-0.541840\pi\) | ||||
−0.131065 | + | 0.991374i | \(0.541840\pi\) | |||||||
\(788\) | 11.3731 | 0.405149 | ||||||||
\(789\) | 2.11760 | 0.0753885 | ||||||||
\(790\) | −11.0722 | −0.393932 | ||||||||
\(791\) | 0.533872 | 0.0189823 | ||||||||
\(792\) | 1.95633 | 0.0695153 | ||||||||
\(793\) | −1.28955 | −0.0457931 | ||||||||
\(794\) | 29.3525 | 1.04168 | ||||||||
\(795\) | 0.943494 | 0.0334623 | ||||||||
\(796\) | 12.6161 | 0.447167 | ||||||||
\(797\) | 13.2563 | 0.469563 | 0.234782 | − | 0.972048i | \(-0.424563\pi\) | ||||
0.234782 | + | 0.972048i | \(0.424563\pi\) | |||||||
\(798\) | 1.19271 | 0.0422215 | ||||||||
\(799\) | −50.3845 | −1.78247 | ||||||||
\(800\) | −1.79161 | −0.0633429 | ||||||||
\(801\) | −9.83357 | −0.347452 | ||||||||
\(802\) | −29.2100 | −1.03144 | ||||||||
\(803\) | 2.99858 | 0.105818 | ||||||||
\(804\) | −2.05870 | −0.0726046 | ||||||||
\(805\) | 0.342327 | 0.0120654 | ||||||||
\(806\) | −3.72448 | −0.131189 | ||||||||
\(807\) | 4.13787 | 0.145660 | ||||||||
\(808\) | 3.97423 | 0.139813 | ||||||||
\(809\) | −17.1489 | −0.602923 | −0.301461 | − | 0.953478i | \(-0.597474\pi\) | ||||
−0.301461 | + | 0.953478i | \(0.597474\pi\) | |||||||
\(810\) | 20.4991 | 0.720266 | ||||||||
\(811\) | −53.2000 | −1.86810 | −0.934052 | − | 0.357136i | \(-0.883753\pi\) | ||||
−0.934052 | + | 0.357136i | \(0.883753\pi\) | |||||||
\(812\) | −5.99852 | −0.210507 | ||||||||
\(813\) | 2.76692 | 0.0970403 | ||||||||
\(814\) | −1.51206 | −0.0529976 | ||||||||
\(815\) | −46.8621 | −1.64151 | ||||||||
\(816\) | −1.03203 | −0.0361281 | ||||||||
\(817\) | 13.3394 | 0.466686 | ||||||||
\(818\) | −36.1577 | −1.26422 | ||||||||
\(819\) | 1.52108 | 0.0531510 | ||||||||
\(820\) | −9.45632 | −0.330229 | ||||||||
\(821\) | 42.7850 | 1.49321 | 0.746604 | − | 0.665269i | \(-0.231683\pi\) | ||||
0.746604 | + | 0.665269i | \(0.231683\pi\) | |||||||
\(822\) | 0.683503 | 0.0238399 | ||||||||
\(823\) | 41.9401 | 1.46194 | 0.730969 | − | 0.682411i | \(-0.239068\pi\) | ||||
0.730969 | + | 0.682411i | \(0.239068\pi\) | |||||||
\(824\) | 53.7739 | 1.87330 | ||||||||
\(825\) | 0.0131588 | 0.000458131 0 | ||||||||
\(826\) | −13.9925 | −0.486862 | ||||||||
\(827\) | −17.6450 | −0.613578 | −0.306789 | − | 0.951778i | \(-0.599255\pi\) | ||||
−0.306789 | + | 0.951778i | \(0.599255\pi\) | |||||||
\(828\) | 0.424592 | 0.0147556 | ||||||||
\(829\) | 6.52471 | 0.226613 | 0.113306 | − | 0.993560i | \(-0.463856\pi\) | ||||
0.113306 | + | 0.993560i | \(0.463856\pi\) | |||||||
\(830\) | 4.93854 | 0.171419 | ||||||||
\(831\) | 3.12624 | 0.108448 | ||||||||
\(832\) | 3.61611 | 0.125366 | ||||||||
\(833\) | 34.2823 | 1.18781 | ||||||||
\(834\) | 2.99741 | 0.103792 | ||||||||
\(835\) | −15.9435 | −0.551746 | ||||||||
\(836\) | −1.50710 | −0.0521242 | ||||||||
\(837\) | 7.19531 | 0.248706 | ||||||||
\(838\) | −35.3851 | −1.22236 | ||||||||
\(839\) | 18.7574 | 0.647578 | 0.323789 | − | 0.946129i | \(-0.395043\pi\) | ||||
0.323789 | + | 0.946129i | \(0.395043\pi\) | |||||||
\(840\) | −1.16675 | −0.0402566 | ||||||||
\(841\) | 7.74485 | 0.267064 | ||||||||
\(842\) | 35.5342 | 1.22459 | ||||||||
\(843\) | −5.27964 | −0.181841 | ||||||||
\(844\) | 13.4063 | 0.461464 | ||||||||
\(845\) | 29.5164 | 1.01539 | ||||||||
\(846\) | 26.3955 | 0.907495 | ||||||||
\(847\) | 11.0830 | 0.380817 | ||||||||
\(848\) | −2.68034 | −0.0920431 | ||||||||
\(849\) | 2.08211 | 0.0714579 | ||||||||
\(850\) | 2.11140 | 0.0724204 | ||||||||
\(851\) | −0.999349 | −0.0342572 | ||||||||
\(852\) | 1.49565 | 0.0512400 | ||||||||
\(853\) | 3.72327 | 0.127482 | 0.0637411 | − | 0.997966i | \(-0.479697\pi\) | ||||
0.0637411 | + | 0.997966i | \(0.479697\pi\) | |||||||
\(854\) | −2.60910 | −0.0892817 | ||||||||
\(855\) | −48.5405 | −1.66005 | ||||||||
\(856\) | −1.14011 | −0.0389683 | ||||||||
\(857\) | 5.36052 | 0.183112 | 0.0915559 | − | 0.995800i | \(-0.470816\pi\) | ||||
0.0915559 | + | 0.995800i | \(0.470816\pi\) | |||||||
\(858\) | −0.0184781 | −0.000630833 0 | ||||||||
\(859\) | 5.70168 | 0.194539 | 0.0972695 | − | 0.995258i | \(-0.468989\pi\) | ||||
0.0972695 | + | 0.995258i | \(0.468989\pi\) | |||||||
\(860\) | −4.28507 | −0.146120 | ||||||||
\(861\) | −0.698650 | −0.0238099 | ||||||||
\(862\) | 2.23155 | 0.0760068 | ||||||||
\(863\) | −23.3086 | −0.793434 | −0.396717 | − | 0.917941i | \(-0.629851\pi\) | ||||
−0.396717 | + | 0.917941i | \(0.629851\pi\) | |||||||
\(864\) | −4.86035 | −0.165352 | ||||||||
\(865\) | −23.1383 | −0.786726 | ||||||||
\(866\) | 21.7547 | 0.739255 | ||||||||
\(867\) | −2.63072 | −0.0893440 | ||||||||
\(868\) | 7.20959 | 0.244710 | ||||||||
\(869\) | 1.03366 | 0.0350647 | ||||||||
\(870\) | 2.34698 | 0.0795702 | ||||||||
\(871\) | −6.43782 | −0.218137 | ||||||||
\(872\) | 18.7748 | 0.635796 | ||||||||
\(873\) | 28.9718 | 0.980548 | ||||||||
\(874\) | 1.04112 | 0.0352164 | ||||||||
\(875\) | −10.8653 | −0.367314 | ||||||||
\(876\) | −2.21810 | −0.0749426 | ||||||||
\(877\) | 25.2049 | 0.851109 | 0.425555 | − | 0.904933i | \(-0.360079\pi\) | ||||
0.425555 | + | 0.904933i | \(0.360079\pi\) | |||||||
\(878\) | −15.9969 | −0.539870 | ||||||||
\(879\) | −1.58817 | −0.0535677 | ||||||||
\(880\) | −0.550807 | −0.0185677 | ||||||||
\(881\) | 26.8752 | 0.905450 | 0.452725 | − | 0.891650i | \(-0.350452\pi\) | ||||
0.452725 | + | 0.891650i | \(0.350452\pi\) | |||||||
\(882\) | −17.9598 | −0.604739 | ||||||||
\(883\) | −19.4627 | −0.654973 | −0.327487 | − | 0.944856i | \(-0.606202\pi\) | ||||
−0.327487 | + | 0.944856i | \(0.606202\pi\) | |||||||
\(884\) | 2.83662 | 0.0954060 | ||||||||
\(885\) | −5.23785 | −0.176068 | ||||||||
\(886\) | 22.3023 | 0.749259 | ||||||||
\(887\) | 3.16833 | 0.106382 | 0.0531910 | − | 0.998584i | \(-0.483061\pi\) | ||||
0.0531910 | + | 0.998584i | \(0.483061\pi\) | |||||||
\(888\) | 3.40606 | 0.114300 | ||||||||
\(889\) | −19.1477 | −0.642192 | ||||||||
\(890\) | 7.74572 | 0.259637 | ||||||||
\(891\) | −1.91373 | −0.0641123 | ||||||||
\(892\) | 0.0504057 | 0.00168771 | ||||||||
\(893\) | −61.9225 | −2.07216 | ||||||||
\(894\) | −0.0367644 | −0.00122959 | ||||||||
\(895\) | 44.7532 | 1.49593 | ||||||||
\(896\) | −2.64388 | −0.0883258 | ||||||||
\(897\) | −0.0122126 | −0.000407765 0 | ||||||||
\(898\) | 9.57154 | 0.319407 | ||||||||
\(899\) | −44.1635 | −1.47294 | ||||||||
\(900\) | 1.05826 | 0.0352754 | ||||||||
\(901\) | −14.1331 | −0.470842 | ||||||||
\(902\) | −0.922734 | −0.0307237 | ||||||||
\(903\) | −0.316589 | −0.0105354 | ||||||||
\(904\) | −1.58832 | −0.0528267 | ||||||||
\(905\) | −14.2126 | −0.472444 | ||||||||
\(906\) | 1.00457 | 0.0333746 | ||||||||
\(907\) | −12.2670 | −0.407320 | −0.203660 | − | 0.979042i | \(-0.565284\pi\) | ||||
−0.203660 | + | 0.979042i | \(0.565284\pi\) | |||||||
\(908\) | −17.0528 | −0.565918 | ||||||||
\(909\) | −3.92411 | −0.130154 | ||||||||
\(910\) | −1.19813 | −0.0397176 | ||||||||
\(911\) | −48.4249 | −1.60439 | −0.802193 | − | 0.597064i | \(-0.796334\pi\) | ||||
−0.802193 | + | 0.597064i | \(0.796334\pi\) | |||||||
\(912\) | −1.26836 | −0.0419996 | ||||||||
\(913\) | −0.461046 | −0.0152584 | ||||||||
\(914\) | 22.1667 | 0.733210 | ||||||||
\(915\) | −0.976670 | −0.0322877 | ||||||||
\(916\) | 20.6047 | 0.680798 | ||||||||
\(917\) | 18.3463 | 0.605849 | ||||||||
\(918\) | 5.72789 | 0.189048 | ||||||||
\(919\) | −22.8781 | −0.754678 | −0.377339 | − | 0.926075i | \(-0.623161\pi\) | ||||
−0.377339 | + | 0.926075i | \(0.623161\pi\) | |||||||
\(920\) | −1.01846 | −0.0335775 | ||||||||
\(921\) | 0.0512090 | 0.00168739 | ||||||||
\(922\) | −12.6300 | −0.415948 | ||||||||
\(923\) | 4.67708 | 0.153948 | ||||||||
\(924\) | 0.0357687 | 0.00117670 | ||||||||
\(925\) | −2.49080 | −0.0818970 | ||||||||
\(926\) | 1.83676 | 0.0603598 | ||||||||
\(927\) | −53.0956 | −1.74389 | ||||||||
\(928\) | 29.8320 | 0.979282 | ||||||||
\(929\) | 45.1914 | 1.48268 | 0.741341 | − | 0.671128i | \(-0.234190\pi\) | ||||
0.741341 | + | 0.671128i | \(0.234190\pi\) | |||||||
\(930\) | −2.82083 | −0.0924987 | ||||||||
\(931\) | 42.1329 | 1.38085 | ||||||||
\(932\) | 0.702275 | 0.0230038 | ||||||||
\(933\) | 4.42053 | 0.144721 | ||||||||
\(934\) | 6.97760 | 0.228314 | ||||||||
\(935\) | −2.90434 | −0.0949822 | ||||||||
\(936\) | −4.52537 | −0.147916 | ||||||||
\(937\) | −5.19362 | −0.169668 | −0.0848341 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848341 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(938\) | −13.0255 | −0.425296 | ||||||||
\(939\) | 4.12380 | 0.134575 | ||||||||
\(940\) | 19.8917 | 0.648794 | ||||||||
\(941\) | 49.6383 | 1.61816 | 0.809081 | − | 0.587697i | \(-0.199965\pi\) | ||||
0.809081 | + | 0.587697i | \(0.199965\pi\) | |||||||
\(942\) | 3.20556 | 0.104443 | ||||||||
\(943\) | −0.609853 | −0.0198595 | ||||||||
\(944\) | 14.8800 | 0.484303 | ||||||||
\(945\) | 2.31466 | 0.0752958 | ||||||||
\(946\) | −0.418131 | −0.0135946 | ||||||||
\(947\) | −28.6531 | −0.931099 | −0.465550 | − | 0.885022i | \(-0.654143\pi\) | ||||
−0.465550 | + | 0.885022i | \(0.654143\pi\) | |||||||
\(948\) | −0.764618 | −0.0248336 | ||||||||
\(949\) | −6.93629 | −0.225161 | ||||||||
\(950\) | 2.59491 | 0.0841899 | ||||||||
\(951\) | −4.98755 | −0.161732 | ||||||||
\(952\) | 17.4773 | 0.566444 | ||||||||
\(953\) | 15.2516 | 0.494048 | 0.247024 | − | 0.969009i | \(-0.420547\pi\) | ||||
0.247024 | + | 0.969009i | \(0.420547\pi\) | |||||||
\(954\) | 7.40407 | 0.239716 | ||||||||
\(955\) | −38.3221 | −1.24007 | ||||||||
\(956\) | −22.7064 | −0.734378 | ||||||||
\(957\) | −0.219106 | −0.00708271 | ||||||||
\(958\) | 27.3074 | 0.882262 | ||||||||
\(959\) | −4.13744 | −0.133605 | ||||||||
\(960\) | 2.73875 | 0.0883927 | ||||||||
\(961\) | 22.0799 | 0.712256 | ||||||||
\(962\) | 3.49768 | 0.112770 | ||||||||
\(963\) | 1.12573 | 0.0362763 | ||||||||
\(964\) | −18.7650 | −0.604380 | ||||||||
\(965\) | 14.5579 | 0.468636 | ||||||||
\(966\) | −0.0247093 | −0.000795009 0 | ||||||||
\(967\) | −18.3538 | −0.590220 | −0.295110 | − | 0.955463i | \(-0.595356\pi\) | ||||
−0.295110 | + | 0.955463i | \(0.595356\pi\) | |||||||
\(968\) | −32.9731 | −1.05980 | ||||||||
\(969\) | −6.68791 | −0.214847 | ||||||||
\(970\) | −22.8206 | −0.732725 | ||||||||
\(971\) | 3.48125 | 0.111719 | 0.0558593 | − | 0.998439i | \(-0.482210\pi\) | ||||
0.0558593 | + | 0.998439i | \(0.482210\pi\) | |||||||
\(972\) | 4.31292 | 0.138337 | ||||||||
\(973\) | −18.1442 | −0.581675 | ||||||||
\(974\) | 8.68887 | 0.278409 | ||||||||
\(975\) | −0.0304388 | −0.000974822 0 | ||||||||
\(976\) | 2.77459 | 0.0888123 | ||||||||
\(977\) | −18.6386 | −0.596302 | −0.298151 | − | 0.954519i | \(-0.596370\pi\) | ||||
−0.298151 | + | 0.954519i | \(0.596370\pi\) | |||||||
\(978\) | 3.38252 | 0.108161 | ||||||||
\(979\) | −0.723114 | −0.0231108 | ||||||||
\(980\) | −13.5345 | −0.432345 | ||||||||
\(981\) | −18.5380 | −0.591873 | ||||||||
\(982\) | −11.6527 | −0.371853 | ||||||||
\(983\) | 45.3085 | 1.44512 | 0.722559 | − | 0.691310i | \(-0.242966\pi\) | ||||
0.722559 | + | 0.691310i | \(0.242966\pi\) | |||||||
\(984\) | 2.07855 | 0.0662618 | ||||||||
\(985\) | 26.9362 | 0.858257 | ||||||||
\(986\) | −35.1567 | −1.11962 | ||||||||
\(987\) | 1.46963 | 0.0467789 | ||||||||
\(988\) | 3.48621 | 0.110911 | ||||||||
\(989\) | −0.276351 | −0.00878745 | ||||||||
\(990\) | 1.52153 | 0.0483575 | ||||||||
\(991\) | 6.74006 | 0.214105 | 0.107053 | − | 0.994253i | \(-0.465859\pi\) | ||||
0.107053 | + | 0.994253i | \(0.465859\pi\) | |||||||
\(992\) | −35.8549 | −1.13839 | ||||||||
\(993\) | 2.18248 | 0.0692588 | ||||||||
\(994\) | 9.46301 | 0.300148 | ||||||||
\(995\) | 29.8802 | 0.947266 | ||||||||
\(996\) | 0.341043 | 0.0108063 | ||||||||
\(997\) | 25.0811 | 0.794327 | 0.397164 | − | 0.917748i | \(-0.369995\pi\) | ||||
0.397164 | + | 0.917748i | \(0.369995\pi\) | |||||||
\(998\) | 3.99857 | 0.126573 | ||||||||
\(999\) | −6.75714 | −0.213786 |
(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 | 2671.2.a.b.1.39 | ✓ | 122 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2671.2.a.b.1.39 | ✓ | 122 | 1.1 | even | 1 | trivial |