Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.19 | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.d.1063.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.99695i | 1.34028i | 0.742236 | + | 0.670139i | \(0.233766\pi\) | ||||
−0.742236 | + | 0.670139i | \(0.766234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.713538 | − | 2.54772i | −0.269692 | − | 0.962947i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.99695 | −0.947720 | ||||||||
\(11\) | −1.70021 | −0.512631 | −0.256316 | − | 0.966593i | \(-0.582509\pi\) | ||||
−0.256316 | + | 0.966593i | \(0.582509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.66226 | −0.461029 | −0.230515 | − | 0.973069i | \(-0.574041\pi\) | ||||
−0.230515 | + | 0.973069i | \(0.574041\pi\) | |||||||
\(14\) | 2.54772 | − | 0.713538i | 0.680906 | − | 0.190701i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.46805i | 1.08366i | 0.840488 | + | 0.541830i | \(0.182269\pi\) | ||||
−0.840488 | + | 0.541830i | \(0.817731\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.13844 | − | 3.79830i | −0.490592 | − | 0.871390i | ||||
\(20\) | − | 2.99695i | − | 0.670139i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.70021i | − | 0.362485i | ||||||
\(23\) | −0.487044 | −0.101556 | −0.0507779 | − | 0.998710i | \(-0.516170\pi\) | ||||
−0.0507779 | + | 0.998710i | \(0.516170\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.98173 | −0.796345 | ||||||||
\(26\) | − | 1.66226i | − | 0.325997i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.713538 | + | 2.54772i | 0.134846 | + | 0.481473i | ||||
\(29\) | − | 1.42708i | − | 0.265001i | −0.991183 | − | 0.132501i | \(-0.957699\pi\) | ||
0.991183 | − | 0.132501i | \(-0.0423007\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.18812 | 0.572604 | 0.286302 | − | 0.958139i | \(-0.407574\pi\) | ||||
0.286302 | + | 0.958139i | \(0.407574\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.46805 | −0.766264 | ||||||||
\(35\) | 7.63539 | − | 2.13844i | 1.29062 | − | 0.361462i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.68312i | − | 1.59189i | −0.605366 | − | 0.795947i | \(-0.706973\pi\) | ||
0.605366 | − | 0.795947i | \(-0.293027\pi\) | |||||||
\(38\) | 3.79830 | − | 2.13844i | 0.616165 | − | 0.346901i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.99695 | 0.473860 | ||||||||
\(41\) | −3.63579 | −0.567814 | −0.283907 | − | 0.958852i | \(-0.591631\pi\) | ||||
−0.283907 | + | 0.958852i | \(0.591631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.40880 | −0.672336 | −0.336168 | − | 0.941802i | \(-0.609131\pi\) | ||||
−0.336168 | + | 0.941802i | \(0.609131\pi\) | |||||||
\(44\) | 1.70021 | 0.256316 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 0.487044i | − | 0.0718108i | ||||||
\(47\) | − | 2.80578i | − | 0.409266i | −0.978839 | − | 0.204633i | \(-0.934400\pi\) | ||
0.978839 | − | 0.204633i | \(-0.0656000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.98173 | + | 3.63579i | −0.854532 | + | 0.519398i | ||||
\(50\) | − | 3.98173i | − | 0.563101i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.66226 | 0.230515 | ||||||||
\(53\) | − | 8.53638i | − | 1.17256i | −0.810108 | − | 0.586281i | \(-0.800591\pi\) | ||
0.810108 | − | 0.586281i | \(-0.199409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.09543i | − | 0.687068i | ||||||
\(56\) | −2.54772 | + | 0.713538i | −0.340453 | + | 0.0953505i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.42708 | 0.187384 | ||||||||
\(59\) | 9.05625 | 1.17902 | 0.589511 | − | 0.807760i | \(-0.299320\pi\) | ||||
0.589511 | + | 0.807760i | \(0.299320\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.96081i | − | 0.507130i | −0.967318 | − | 0.253565i | \(-0.918397\pi\) | ||
0.967318 | − | 0.253565i | \(-0.0816032\pi\) | |||||||
\(62\) | 3.18812i | 0.404892i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 4.98173i | − | 0.617907i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.67429i | 0.326717i | 0.986567 | + | 0.163358i | \(0.0522327\pi\) | ||||
−0.986567 | + | 0.163358i | \(0.947767\pi\) | |||||||
\(68\) | − | 4.46805i | − | 0.541830i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.13844 | + | 7.63539i | 0.255592 | + | 0.912604i | ||||
\(71\) | − | 8.53638i | − | 1.01308i | −0.862216 | − | 0.506541i | \(-0.830924\pi\) | ||
0.862216 | − | 0.506541i | \(-0.169076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.63579i | 0.425537i | 0.977103 | + | 0.212768i | \(0.0682479\pi\) | ||||
−0.977103 | + | 0.212768i | \(0.931752\pi\) | |||||||
\(74\) | 9.68312 | 1.12564 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.13844 | + | 3.79830i | 0.245296 | + | 0.435695i | ||||
\(77\) | 1.21316 | + | 4.33164i | 0.138253 | + | 0.493636i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.7837i | − | 1.66330i | −0.555300 | − | 0.831650i | \(-0.687397\pi\) | ||
0.555300 | − | 0.831650i | \(-0.312603\pi\) | |||||||
\(80\) | 2.99695i | 0.335070i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.63579i | − | 0.401505i | ||||||
\(83\) | − | 1.60750i | − | 0.176446i | −0.996101 | − | 0.0882231i | \(-0.971881\pi\) | ||
0.996101 | − | 0.0882231i | \(-0.0281188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.3905 | −1.45241 | ||||||||
\(86\) | − | 4.40880i | − | 0.475413i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.70021i | 0.181242i | ||||||||
\(89\) | −7.27157 | −0.770785 | −0.385393 | − | 0.922753i | \(-0.625934\pi\) | ||||
−0.385393 | + | 0.922753i | \(0.625934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18609 | + | 4.23498i | 0.124336 | + | 0.443946i | ||||
\(92\) | 0.487044 | 0.0507779 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.80578 | 0.289395 | ||||||||
\(95\) | 11.3833 | − | 6.40880i | 1.16790 | − | 0.657529i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.57757 | 0.464782 | 0.232391 | − | 0.972622i | \(-0.425345\pi\) | ||||
0.232391 | + | 0.972622i | \(0.425345\pi\) | |||||||
\(98\) | −3.63579 | − | 5.98173i | −0.367270 | − | 0.604246i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.98173 | 0.398173 | ||||||||
\(101\) | 8.22618i | 0.818536i | 0.912414 | + | 0.409268i | \(0.134216\pi\) | ||||
−0.912414 | + | 0.409268i | \(0.865784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6942 | 1.25080 | 0.625400 | − | 0.780304i | \(-0.284936\pi\) | ||||
0.625400 | + | 0.780304i | \(0.284936\pi\) | |||||||
\(104\) | 1.66226i | 0.162998i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.53638 | 0.829126 | ||||||||
\(107\) | − | 9.96345i | − | 0.963203i | −0.876390 | − | 0.481602i | \(-0.840055\pi\) | ||
0.876390 | − | 0.481602i | \(-0.159945\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.21316i | − | 0.116200i | −0.998311 | − | 0.0580999i | \(-0.981496\pi\) | ||
0.998311 | − | 0.0580999i | \(-0.0185042\pi\) | |||||||
\(110\) | 5.09543 | 0.485831 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.713538 | − | 2.54772i | −0.0674230 | − | 0.240737i | ||||
\(113\) | − | 17.7993i | − | 1.67442i | −0.546881 | − | 0.837210i | \(-0.684185\pi\) | ||
0.546881 | − | 0.837210i | \(-0.315815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.45965i | − | 0.136113i | ||||||
\(116\) | 1.42708i | 0.132501i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.05625i | 0.833695i | ||||||||
\(119\) | 11.3833 | − | 3.18812i | 1.04351 | − | 0.292255i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.10930 | −0.737209 | ||||||||
\(122\) | 3.96081 | 0.358595 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.18812 | −0.286302 | ||||||||
\(125\) | 3.05172i | 0.272954i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7837i | 1.31184i | 0.754829 | + | 0.655922i | \(0.227720\pi\) | ||||
−0.754829 | + | 0.655922i | \(0.772280\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.98173 | 0.436926 | ||||||||
\(131\) | 0.764675i | 0.0668100i | 0.999442 | + | 0.0334050i | \(0.0106351\pi\) | ||||
−0.999442 | + | 0.0334050i | \(0.989365\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.15113 | + | 8.15837i | −0.706793 | + | 0.707420i | ||||
\(134\) | −2.67429 | −0.231024 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.46805 | 0.383132 | ||||||||
\(137\) | −11.8704 | −1.01415 | −0.507077 | − | 0.861901i | \(-0.669274\pi\) | ||||
−0.507077 | + | 0.861901i | \(0.669274\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.73122i | 0.740572i | 0.928918 | + | 0.370286i | \(0.120740\pi\) | ||||
−0.928918 | + | 0.370286i | \(0.879260\pi\) | |||||||
\(140\) | −7.63539 | + | 2.13844i | −0.645308 | + | 0.180731i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.53638 | 0.716357 | ||||||||
\(143\) | 2.82619 | 0.236338 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.27688 | 0.355175 | ||||||||
\(146\) | −3.63579 | −0.300900 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.68312i | 0.795947i | ||||||||
\(149\) | 8.70903 | 0.713472 | 0.356736 | − | 0.934205i | \(-0.383890\pi\) | ||||
0.356736 | + | 0.934205i | \(0.383890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.3574i | − | 1.00563i | −0.864393 | − | 0.502816i | \(-0.832297\pi\) | ||
0.864393 | − | 0.502816i | \(-0.167703\pi\) | |||||||
\(152\) | −3.79830 | + | 2.13844i | −0.308083 | + | 0.173450i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.33164 | + | 1.21316i | −0.349054 | + | 0.0977593i | ||||
\(155\) | 9.55465i | 0.767448i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.73122i | 0.696827i | 0.937341 | + | 0.348414i | \(0.113280\pi\) | ||||
−0.937341 | + | 0.348414i | \(0.886720\pi\) | |||||||
\(158\) | 14.7837 | 1.17613 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.99695 | −0.236930 | ||||||||
\(161\) | 0.347525 | + | 1.24085i | 0.0273888 | + | 0.0977928i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.96345 | 0.780398 | 0.390199 | − | 0.920731i | \(-0.372406\pi\) | ||||
0.390199 | + | 0.920731i | \(0.372406\pi\) | |||||||
\(164\) | 3.63579 | 0.283907 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.60750 | 0.124766 | ||||||||
\(167\) | 15.2863 | 1.18289 | 0.591445 | − | 0.806345i | \(-0.298558\pi\) | ||||
0.591445 | + | 0.806345i | \(0.298558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2369 | −0.787452 | ||||||||
\(170\) | − | 13.3905i | − | 1.02701i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.40880 | 0.336168 | ||||||||
\(173\) | −1.04151 | −0.0791849 | −0.0395924 | − | 0.999216i | \(-0.512606\pi\) | ||||
−0.0395924 | + | 0.999216i | \(0.512606\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.84111 | + | 10.1443i | 0.214768 | + | 0.766838i | ||||
\(176\) | −1.70021 | −0.128158 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.27157i | − | 0.545027i | ||||||
\(179\) | − | 3.26295i | − | 0.243885i | −0.992537 | − | 0.121942i | \(-0.961088\pi\) | ||
0.992537 | − | 0.121942i | \(-0.0389123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.94321 | −0.739073 | −0.369536 | − | 0.929216i | \(-0.620484\pi\) | ||||
−0.369536 | + | 0.929216i | \(0.620484\pi\) | |||||||
\(182\) | −4.23498 | + | 1.18609i | −0.313918 | + | 0.0879187i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.487044i | 0.0359054i | ||||||||
\(185\) | 29.0199 | 2.13358 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.59660i | − | 0.555518i | ||||||
\(188\) | 2.80578i | 0.204633i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.40880 | + | 11.3833i | 0.464943 | + | 0.825833i | ||||
\(191\) | 4.86154 | 0.351769 | 0.175884 | − | 0.984411i | \(-0.443721\pi\) | ||||
0.175884 | + | 0.984411i | \(0.443721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.6712i | − | 1.34398i | −0.740560 | − | 0.671991i | \(-0.765439\pi\) | ||
0.740560 | − | 0.671991i | \(-0.234561\pi\) | |||||||
\(194\) | 4.57757i | 0.328651i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.98173 | − | 3.63579i | 0.427266 | − | 0.259699i | ||||
\(197\) | 4.61357 | 0.328703 | 0.164352 | − | 0.986402i | \(-0.447447\pi\) | ||||
0.164352 | + | 0.986402i | \(0.447447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.27157i | − | 0.515468i | −0.966216 | − | 0.257734i | \(-0.917024\pi\) | ||
0.966216 | − | 0.257734i | \(-0.0829758\pi\) | |||||||
\(200\) | 3.98173i | 0.281551i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.22618 | −0.578792 | ||||||||
\(203\) | −3.63579 | + | 1.01827i | −0.255182 | + | 0.0714687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 10.8963i | − | 0.761029i | ||||||
\(206\) | 12.6942i | 0.884449i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.66226 | −0.115257 | ||||||||
\(209\) | 3.63579 | + | 6.45789i | 0.251493 | + | 0.446701i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.10062i | 0.351141i | 0.984467 | + | 0.175570i | \(0.0561770\pi\) | ||||
−0.984467 | + | 0.175570i | \(0.943823\pi\) | |||||||
\(212\) | 8.53638i | 0.586281i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.96345 | 0.681088 | ||||||||
\(215\) | − | 13.2130i | − | 0.901117i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.27485 | − | 8.12243i | −0.154427 | − | 0.551387i | ||||
\(218\) | 1.21316 | 0.0821656 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.09543i | 0.343534i | ||||||||
\(221\) | − | 7.42708i | − | 0.499599i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1181 | −1.21328 | −0.606640 | − | 0.794977i | \(-0.707483\pi\) | ||||
−0.606640 | + | 0.794977i | \(0.707483\pi\) | |||||||
\(224\) | 2.54772 | − | 0.713538i | 0.170227 | − | 0.0476753i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.7993 | 1.18399 | ||||||||
\(227\) | 4.67730 | 0.310443 | 0.155222 | − | 0.987880i | \(-0.450391\pi\) | ||||
0.155222 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.8437i | − | 1.77388i | −0.461882 | − | 0.886941i | \(-0.652826\pi\) | ||
0.461882 | − | 0.886941i | \(-0.347174\pi\) | |||||||
\(230\) | 1.45965 | 0.0962464 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.42708 | −0.0936921 | ||||||||
\(233\) | 23.7407 | 1.55531 | 0.777654 | − | 0.628693i | \(-0.216410\pi\) | ||||
0.777654 | + | 0.628693i | \(0.216410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.40880 | 0.548530 | ||||||||
\(236\) | −9.05625 | −0.589511 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.18812 | + | 11.3833i | 0.206655 | + | 0.737871i | ||||
\(239\) | −7.28786 | −0.471413 | −0.235706 | − | 0.971824i | \(-0.575740\pi\) | ||||
−0.235706 | + | 0.971824i | \(0.575740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.7327 | −1.33551 | −0.667757 | − | 0.744380i | \(-0.732745\pi\) | ||||
−0.667757 | + | 0.744380i | \(0.732745\pi\) | |||||||
\(242\) | − | 8.10930i | − | 0.521286i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.96081i | 0.253565i | ||||||||
\(245\) | −10.8963 | − | 17.9270i | −0.696138 | − | 1.14531i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.55465 | + | 6.31378i | 0.226177 | + | 0.401736i | ||||
\(248\) | − | 3.18812i | − | 0.202446i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.05172 | −0.193007 | ||||||||
\(251\) | − | 30.6247i | − | 1.93301i | −0.256643 | − | 0.966506i | \(-0.582616\pi\) | ||
0.256643 | − | 0.966506i | \(-0.417384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.828075 | 0.0520606 | ||||||||
\(254\) | −14.7837 | −0.927614 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.3841 | −1.58341 | −0.791707 | − | 0.610901i | \(-0.790807\pi\) | ||||
−0.791707 | + | 0.610901i | \(0.790807\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.6698 | + | 6.90927i | −1.53291 | + | 0.429321i | ||||
\(260\) | 4.98173i | 0.308954i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.764675 | −0.0472418 | ||||||||
\(263\) | −19.8533 | −1.22421 | −0.612103 | − | 0.790778i | \(-0.709676\pi\) | ||||
−0.612103 | + | 0.790778i | \(0.709676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.5831 | 1.57156 | ||||||||
\(266\) | −8.15837 | − | 8.15113i | −0.500222 | − | 0.499778i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.67429i | − | 0.163358i | ||||||
\(269\) | 6.46198 | 0.393994 | 0.196997 | − | 0.980404i | \(-0.436881\pi\) | ||||
0.196997 | + | 0.980404i | \(0.436881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.01473i | 0.486860i | 0.969918 | + | 0.243430i | \(0.0782727\pi\) | ||||
−0.969918 | + | 0.243430i | \(0.921727\pi\) | |||||||
\(272\) | 4.46805i | 0.270915i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 11.8704i | − | 0.717115i | ||||||
\(275\) | 6.76975 | 0.408231 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.96345 | −0.238141 | −0.119070 | − | 0.992886i | \(-0.537991\pi\) | ||||
−0.119070 | + | 0.992886i | \(0.537991\pi\) | |||||||
\(278\) | −8.73122 | −0.523664 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.13844 | − | 7.63539i | −0.127796 | − | 0.456302i | ||||
\(281\) | 23.5076i | 1.40235i | 0.712990 | + | 0.701174i | \(0.247340\pi\) | ||||
−0.712990 | + | 0.701174i | \(0.752660\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 18.9221i | − | 1.12480i | −0.826865 | − | 0.562401i | \(-0.809878\pi\) | ||
0.826865 | − | 0.562401i | \(-0.190122\pi\) | |||||||
\(284\) | 8.53638i | 0.506541i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.82619i | 0.167116i | ||||||||
\(287\) | 2.59427 | + | 9.26295i | 0.153135 | + | 0.546775i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.96345 | −0.174321 | ||||||||
\(290\) | 4.27688i | 0.251147i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 3.63579i | − | 0.212768i | ||||||
\(293\) | −18.9221 | −1.10544 | −0.552720 | − | 0.833367i | \(-0.686410\pi\) | ||||
−0.552720 | + | 0.833367i | \(0.686410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.1411i | 1.58022i | ||||||||
\(296\) | −9.68312 | −0.562820 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.70903i | 0.504501i | ||||||||
\(299\) | 0.809596 | 0.0468202 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.14585 | + | 11.2324i | 0.181324 | + | 0.647424i | ||||
\(302\) | 12.3574 | 0.711089 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.13844 | − | 3.79830i | −0.122648 | − | 0.217847i | ||||
\(305\) | 11.8704 | 0.679695 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.54969 | 0.259665 | 0.129832 | − | 0.991536i | \(-0.458556\pi\) | ||||
0.129832 | + | 0.991536i | \(0.458556\pi\) | |||||||
\(308\) | −1.21316 | − | 4.33164i | −0.0691263 | − | 0.246818i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.55465 | −0.542668 | ||||||||
\(311\) | 18.9610i | 1.07518i | 0.843207 | + | 0.537588i | \(0.180665\pi\) | ||||
−0.843207 | + | 0.537588i | \(0.819335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.5574i | − | 0.653263i | −0.945152 | − | 0.326632i | \(-0.894086\pi\) | ||
0.945152 | − | 0.326632i | \(-0.105914\pi\) | |||||||
\(314\) | −8.73122 | −0.492731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.7837i | 0.831650i | ||||||||
\(317\) | 23.8904i | 1.34182i | 0.741540 | + | 0.670908i | \(0.234096\pi\) | ||||
−0.741540 | + | 0.670908i | \(0.765904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.42632i | 0.135848i | ||||||||
\(320\) | − | 2.99695i | − | 0.167535i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.24085 | + | 0.347525i | −0.0691499 | + | 0.0193668i | ||||
\(323\) | 16.9710 | − | 9.55465i | 0.944291 | − | 0.531635i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.61868 | 0.367138 | ||||||||
\(326\) | 9.96345i | 0.551825i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.63579i | 0.200753i | ||||||||
\(329\) | −7.14834 | + | 2.00203i | −0.394101 | + | 0.110376i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.3455i | − | 1.17325i | −0.809857 | − | 0.586627i | \(-0.800456\pi\) | ||
0.809857 | − | 0.586627i | \(-0.199544\pi\) | |||||||
\(332\) | 1.60750i | 0.0882231i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.2863i | 0.836429i | ||||||||
\(335\) | −8.01473 | −0.437892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 21.0975i | − | 1.14925i | −0.818415 | − | 0.574627i | \(-0.805147\pi\) | ||
0.818415 | − | 0.574627i | \(-0.194853\pi\) | |||||||
\(338\) | − | 10.2369i | − | 0.556813i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.3905 | 0.726203 | ||||||||
\(341\) | −5.42046 | −0.293534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5311 | + | 12.6455i | 0.730613 | + | 0.682792i | ||||
\(344\) | 4.40880i | 0.237707i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 1.04151i | − | 0.0559922i | ||||||
\(347\) | −13.2915 | −0.713527 | −0.356763 | − | 0.934195i | \(-0.616120\pi\) | ||||
−0.356763 | + | 0.934195i | \(0.616120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.37895i | − | 0.234400i | −0.993108 | − | 0.117200i | \(-0.962608\pi\) | ||
0.993108 | − | 0.117200i | \(-0.0373918\pi\) | |||||||
\(350\) | −10.1443 | + | 2.84111i | −0.542236 | + | 0.151864i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 1.70021i | − | 0.0906212i | ||||||
\(353\) | 15.0116i | 0.798989i | 0.916736 | + | 0.399495i | \(0.130814\pi\) | ||||
−0.916736 | + | 0.399495i | \(0.869186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.5831 | 1.35781 | ||||||||
\(356\) | 7.27157 | 0.385393 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26295 | 0.172453 | ||||||||
\(359\) | −24.2278 | −1.27869 | −0.639347 | − | 0.768919i | \(-0.720795\pi\) | ||||
−0.639347 | + | 0.768919i | \(0.720795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.85415 | + | 16.2449i | −0.518640 | + | 0.854993i | ||||
\(362\) | − | 9.94321i | − | 0.522604i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.18609 | − | 4.23498i | −0.0621679 | − | 0.221973i | ||||
\(365\) | −10.8963 | −0.570337 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2863i | 0.797939i | 0.916964 | + | 0.398969i | \(0.130632\pi\) | ||||
−0.916964 | + | 0.398969i | \(0.869368\pi\) | |||||||
\(368\) | −0.487044 | −0.0253889 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.0199i | 1.50867i | ||||||||
\(371\) | −21.7483 | + | 6.09103i | −1.12911 | + | 0.316231i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.7029i | 1.74507i | 0.488552 | + | 0.872535i | \(0.337525\pi\) | ||||
−0.488552 | + | 0.872535i | \(0.662475\pi\) | |||||||
\(374\) | 7.59660 | 0.392811 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.80578 | −0.144697 | ||||||||
\(377\) | 2.37218i | 0.122173i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.8755i | − | 0.661371i | −0.943741 | − | 0.330686i | \(-0.892720\pi\) | ||
0.943741 | − | 0.330686i | \(-0.107280\pi\) | |||||||
\(380\) | −11.3833 | + | 6.40880i | −0.583952 | + | 0.328765i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.86154i | 0.248738i | ||||||||
\(383\) | −32.6556 | −1.66863 | −0.834313 | − | 0.551292i | \(-0.814135\pi\) | ||||
−0.834313 | + | 0.551292i | \(0.814135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.9817 | + | 3.63579i | −0.661610 | + | 0.185297i | ||||
\(386\) | 18.6712 | 0.950338 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.57757 | −0.232391 | ||||||||
\(389\) | −32.4498 | −1.64527 | −0.822634 | − | 0.568571i | \(-0.807496\pi\) | ||||
−0.822634 | + | 0.568571i | \(0.807496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.17614i | − | 0.110052i | ||||||
\(392\) | 3.63579 | + | 5.98173i | 0.183635 | + | 0.302123i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.61357i | 0.232428i | ||||||||
\(395\) | 44.3062 | 2.22928 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 31.6141i | − | 1.58667i | −0.608787 | − | 0.793334i | \(-0.708344\pi\) | ||
0.608787 | − | 0.793334i | \(-0.291656\pi\) | |||||||
\(398\) | 7.27157 | 0.364491 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.98173 | −0.199086 | ||||||||
\(401\) | 19.5442i | 0.975990i | 0.872846 | + | 0.487995i | \(0.162272\pi\) | ||||
−0.872846 | + | 0.487995i | \(0.837728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.29950 | −0.263987 | ||||||||
\(404\) | − | 8.22618i | − | 0.409268i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.01827 | − | 3.63579i | −0.0505360 | − | 0.180441i | ||||
\(407\) | 16.4633i | 0.816055i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.67287 | 0.132165 | 0.0660825 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660825 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(410\) | 10.8963 | 0.538129 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.6942 | −0.625400 | ||||||||
\(413\) | −6.46198 | − | 23.0728i | −0.317973 | − | 1.13534i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.81761 | 0.236487 | ||||||||
\(416\) | − | 1.66226i | − | 0.0814992i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.45789 | + | 3.63579i | −0.315866 | + | 0.177832i | ||||
\(419\) | 17.5994i | 0.859786i | 0.902880 | + | 0.429893i | \(0.141449\pi\) | ||||
−0.902880 | + | 0.429893i | \(0.858551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 18.1531i | − | 0.884727i | −0.896836 | − | 0.442363i | \(-0.854140\pi\) | ||
0.896836 | − | 0.442363i | \(-0.145860\pi\) | |||||||
\(422\) | −5.10062 | −0.248294 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.53638 | −0.414563 | ||||||||
\(425\) | − | 17.7905i | − | 0.862968i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0910 | + | 2.82619i | −0.488339 | + | 0.136769i | ||||
\(428\) | 9.96345i | 0.481602i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.2130 | 0.637186 | ||||||||
\(431\) | 7.10930i | 0.342443i | 0.985233 | + | 0.171222i | \(0.0547714\pi\) | ||||
−0.985233 | + | 0.171222i | \(0.945229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.02790 | 0.337739 | 0.168870 | − | 0.985638i | \(-0.445988\pi\) | ||||
0.168870 | + | 0.985638i | \(0.445988\pi\) | |||||||
\(434\) | 8.12243 | − | 2.27485i | 0.389889 | − | 0.109196i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.21316i | 0.0580999i | ||||||||
\(437\) | 1.04151 | + | 1.84994i | 0.0498224 | + | 0.0884946i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.68610 | 0.223655 | 0.111828 | − | 0.993728i | \(-0.464330\pi\) | ||||
0.111828 | + | 0.993728i | \(0.464330\pi\) | |||||||
\(440\) | −5.09543 | −0.242915 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.42708 | 0.353270 | ||||||||
\(443\) | −10.1702 | −0.483199 | −0.241600 | − | 0.970376i | \(-0.577672\pi\) | ||||
−0.241600 | + | 0.970376i | \(0.577672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 21.7926i | − | 1.03307i | ||||||
\(446\) | − | 18.1181i | − | 0.857918i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.713538 | + | 2.54772i | 0.0337115 | + | 0.120368i | ||||
\(449\) | 7.40100i | 0.349275i | 0.984633 | + | 0.174637i | \(0.0558753\pi\) | ||||
−0.984633 | + | 0.174637i | \(0.944125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.18158 | 0.291079 | ||||||||
\(452\) | 17.7993i | 0.837210i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.67730i | 0.219517i | ||||||||
\(455\) | −12.6920 | + | 3.55465i | −0.595012 | + | 0.166645i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.890697 | 0.0416651 | 0.0208325 | − | 0.999783i | \(-0.493368\pi\) | ||||
0.0208325 | + | 0.999783i | \(0.493368\pi\) | |||||||
\(458\) | 26.8437 | 1.25432 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.45965i | 0.0680565i | ||||||||
\(461\) | 12.0963i | 0.563383i | 0.959505 | + | 0.281691i | \(0.0908954\pi\) | ||||
−0.959505 | + | 0.281691i | \(0.909105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2081 | 1.49684 | 0.748420 | − | 0.663226i | \(-0.230813\pi\) | ||||
0.748420 | + | 0.663226i | \(0.230813\pi\) | |||||||
\(464\) | − | 1.42708i | − | 0.0662503i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.7407i | 1.09977i | ||||||||
\(467\) | − | 34.9016i | − | 1.61505i | −0.589832 | − | 0.807526i | \(-0.700806\pi\) | ||
0.589832 | − | 0.807526i | \(-0.299194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.81334 | − | 1.90821i | 0.314611 | − | 0.0881129i | ||||
\(470\) | 8.40880i | 0.387869i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 9.05625i | − | 0.416848i | ||||||
\(473\) | 7.49587 | 0.344660 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.51468 | + | 15.1238i | 0.390680 | + | 0.693927i | ||||
\(476\) | −11.3833 | + | 3.18812i | −0.521754 | + | 0.146127i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 7.28786i | − | 0.333339i | ||||||
\(479\) | 25.6100i | 1.17015i | 0.810979 | + | 0.585076i | \(0.198935\pi\) | ||||
−0.810979 | + | 0.585076i | \(0.801065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0959i | 0.733910i | ||||||||
\(482\) | − | 20.7327i | − | 0.944350i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.10930 | 0.368605 | ||||||||
\(485\) | 13.7188i | 0.622937i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0026i | 1.76738i | 0.468075 | + | 0.883689i | \(0.344948\pi\) | ||||
−0.468075 | + | 0.883689i | \(0.655052\pi\) | |||||||
\(488\) | −3.96081 | −0.179298 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.9270 | − | 10.8963i | 0.809857 | − | 0.492244i | ||||
\(491\) | −19.3973 | −0.875388 | −0.437694 | − | 0.899124i | \(-0.644205\pi\) | ||||
−0.437694 | + | 0.899124i | \(0.644205\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.37624 | 0.287172 | ||||||||
\(494\) | −6.31378 | + | 3.55465i | −0.284070 | + | 0.159931i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.18812 | 0.143151 | ||||||||
\(497\) | −21.7483 | + | 6.09103i | −0.975544 | + | 0.273220i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1171 | −0.811033 | −0.405517 | − | 0.914088i | \(-0.632908\pi\) | ||||
−0.405517 | + | 0.914088i | \(0.632908\pi\) | |||||||
\(500\) | − | 3.05172i | − | 0.136477i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.6247 | 1.36685 | ||||||||
\(503\) | 25.7439i | 1.14786i | 0.818903 | + | 0.573932i | \(0.194583\pi\) | ||||
−0.818903 | + | 0.573932i | \(0.805417\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.6535 | −1.09707 | ||||||||
\(506\) | 0.828075i | 0.0368124i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 14.7837i | − | 0.655922i | ||||||
\(509\) | 24.1106 | 1.06868 | 0.534342 | − | 0.845268i | \(-0.320559\pi\) | ||||
0.534342 | + | 0.845268i | \(0.320559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.26295 | − | 2.59427i | 0.409769 | − | 0.114764i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 25.3841i | − | 1.11964i | ||||||
\(515\) | 38.0440i | 1.67642i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.77041i | 0.209802i | ||||||||
\(518\) | −6.90927 | − | 24.6698i | −0.303576 | − | 1.08393i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.98173 | −0.218463 | ||||||||
\(521\) | 2.08303 | 0.0912592 | 0.0456296 | − | 0.998958i | \(-0.485471\pi\) | ||||
0.0456296 | + | 0.998958i | \(0.485471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2069 | −0.839858 | −0.419929 | − | 0.907557i | \(-0.637945\pi\) | ||||
−0.419929 | + | 0.907557i | \(0.637945\pi\) | |||||||
\(524\) | − | 0.764675i | − | 0.0334050i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 19.8533i | − | 0.865644i | ||||||
\(527\) | 14.2447i | 0.620508i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7628 | −0.989686 | ||||||||
\(530\) | 25.5831i | 1.11126i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.15113 | − | 8.15837i | 0.353397 | − | 0.353710i | ||||
\(533\) | 6.04364 | 0.261779 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.8600 | 1.29096 | ||||||||
\(536\) | 2.67429 | 0.115512 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.46198i | 0.278596i | ||||||||
\(539\) | 10.1702 | − | 6.18158i | 0.438060 | − | 0.266260i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.57292 | 0.282592 | 0.141296 | − | 0.989967i | \(-0.454873\pi\) | ||||
0.141296 | + | 0.989967i | \(0.454873\pi\) | |||||||
\(542\) | −8.01473 | −0.344262 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.46805 | −0.191566 | ||||||||
\(545\) | 3.63579 | 0.155740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.9368i | − | 1.40828i | −0.710063 | − | 0.704138i | \(-0.751334\pi\) | ||
0.710063 | − | 0.704138i | \(-0.248666\pi\) | |||||||
\(548\) | 11.8704 | 0.507077 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.76975i | 0.288663i | ||||||||
\(551\) | −5.42046 | + | 3.05172i | −0.230919 | + | 0.130007i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.6648 | + | 10.5488i | −1.60167 | + | 0.448579i | ||||
\(554\) | − | 3.96345i | − | 0.168391i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 8.73122i | − | 0.370286i | ||||||
\(557\) | −26.6852 | −1.13069 | −0.565343 | − | 0.824856i | \(-0.691256\pi\) | ||||
−0.565343 | + | 0.824856i | \(0.691256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.32859 | 0.309967 | ||||||||
\(560\) | 7.63539 | − | 2.13844i | 0.322654 | − | 0.0903656i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.5076 | −0.991610 | ||||||||
\(563\) | 11.1393 | 0.469465 | 0.234732 | − | 0.972060i | \(-0.424579\pi\) | ||||
0.234732 | + | 0.972060i | \(0.424579\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 53.3438 | 2.24419 | ||||||||
\(566\) | 18.9221 | 0.795355 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.53638 | −0.358178 | ||||||||
\(569\) | 7.92691i | 0.332313i | 0.986099 | + | 0.166157i | \(0.0531357\pi\) | ||||
−0.986099 | + | 0.166157i | \(0.946864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.99220 | −0.376312 | −0.188156 | − | 0.982139i | \(-0.560251\pi\) | ||||
−0.188156 | + | 0.982139i | \(0.560251\pi\) | |||||||
\(572\) | −2.82619 | −0.118169 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.26295 | + | 2.59427i | −0.386628 | + | 0.108283i | ||||
\(575\) | 1.93928 | 0.0808735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 13.1102i | − | 0.545783i | −0.962045 | − | 0.272892i | \(-0.912020\pi\) | ||
0.962045 | − | 0.272892i | \(-0.0879801\pi\) | |||||||
\(578\) | − | 2.96345i | − | 0.123263i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.27688 | −0.177588 | ||||||||
\(581\) | −4.09546 | + | 1.14701i | −0.169908 | + | 0.0475861i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5136i | 0.601092i | ||||||||
\(584\) | 3.63579 | 0.150450 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 18.9221i | − | 0.781664i | ||||||
\(587\) | − | 17.5212i | − | 0.723179i | −0.932337 | − | 0.361589i | \(-0.882234\pi\) | ||
0.932337 | − | 0.361589i | \(-0.117766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.81761 | − | 12.1094i | −0.280915 | − | 0.498961i | ||||
\(590\) | −27.1411 | −1.11738 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 9.68312i | − | 0.397974i | ||||||
\(593\) | 26.6485i | 1.09432i | 0.837027 | + | 0.547161i | \(0.184292\pi\) | ||||
−0.837027 | + | 0.547161i | \(0.815708\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.55465 | + | 34.1153i | 0.391703 | + | 1.39859i | ||||
\(596\) | −8.70903 | −0.356736 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.809596i | 0.0331068i | ||||||||
\(599\) | − | 24.8176i | − | 1.01402i | −0.861940 | − | 0.507010i | \(-0.830751\pi\) | ||
0.861940 | − | 0.507010i | \(-0.169249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.0015 | −0.693505 | −0.346753 | − | 0.937957i | \(-0.612716\pi\) | ||||
−0.346753 | + | 0.937957i | \(0.612716\pi\) | |||||||
\(602\) | −11.2324 | + | 3.14585i | −0.457798 | + | 0.128215i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.3574i | 0.502816i | ||||||||
\(605\) | − | 24.3032i | − | 0.988066i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.4720 | −1.56153 | −0.780766 | − | 0.624824i | \(-0.785171\pi\) | ||||
−0.780766 | + | 0.624824i | \(0.785171\pi\) | |||||||
\(608\) | 3.79830 | − | 2.13844i | 0.154041 | − | 0.0867252i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.8704i | 0.480617i | ||||||||
\(611\) | 4.66395i | 0.188683i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.67176 | −0.390639 | −0.195319 | − | 0.980740i | \(-0.562574\pi\) | ||||
−0.195319 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(614\) | 4.54969i | 0.183611i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.33164 | − | 1.21316i | 0.174527 | − | 0.0488796i | ||||
\(617\) | −14.9917 | −0.603545 | −0.301772 | − | 0.953380i | \(-0.597578\pi\) | ||||
−0.301772 | + | 0.953380i | \(0.597578\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.4624i | 0.701875i | 0.936399 | + | 0.350937i | \(0.114137\pi\) | ||||
−0.936399 | + | 0.350937i | \(0.885863\pi\) | |||||||
\(620\) | − | 9.55465i | − | 0.383724i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.9610 | −0.760265 | ||||||||
\(623\) | 5.18854 | + | 18.5259i | 0.207875 | + | 0.742225i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0545 | −1.16218 | ||||||||
\(626\) | 11.5574 | 0.461927 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 8.73122i | − | 0.348414i | ||||||
\(629\) | 43.2646 | 1.72507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0988 | 0.680694 | 0.340347 | − | 0.940300i | \(-0.389455\pi\) | ||||
0.340347 | + | 0.940300i | \(0.389455\pi\) | |||||||
\(632\) | −14.7837 | −0.588065 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.8904 | −0.948808 | ||||||||
\(635\) | −44.3062 | −1.75824 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.94321 | − | 6.04364i | 0.393964 | − | 0.239458i | ||||
\(638\) | −2.42632 | −0.0960590 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.99695 | 0.118465 | ||||||||
\(641\) | 16.7811i | 0.662812i | 0.943488 | + | 0.331406i | \(0.107523\pi\) | ||||
−0.943488 | + | 0.331406i | \(0.892477\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23.5994i | − | 0.930669i | −0.885135 | − | 0.465335i | \(-0.845934\pi\) | ||
0.885135 | − | 0.465335i | \(-0.154066\pi\) | |||||||
\(644\) | −0.347525 | − | 1.24085i | −0.0136944 | − | 0.0488964i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.55465 | + | 16.9710i | 0.375923 | + | 0.667714i | ||||
\(647\) | 21.1385i | 0.831039i | 0.909584 | + | 0.415519i | \(0.136400\pi\) | ||||
−0.909584 | + | 0.415519i | \(0.863600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.3975 | −0.604404 | ||||||||
\(650\) | 6.61868i | 0.259606i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.96345 | −0.390199 | ||||||||
\(653\) | 35.1551 | 1.37573 | 0.687863 | − | 0.725840i | \(-0.258549\pi\) | ||||
0.687863 | + | 0.725840i | \(0.258549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.29170 | −0.0895440 | ||||||||
\(656\) | −3.63579 | −0.141954 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.00203 | − | 7.14834i | −0.0780474 | − | 0.278671i | ||||
\(659\) | 8.15365i | 0.317621i | 0.987309 | + | 0.158811i | \(0.0507659\pi\) | ||||
−0.987309 | + | 0.158811i | \(0.949234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.4188 | −0.988678 | −0.494339 | − | 0.869269i | \(-0.664590\pi\) | ||||
−0.494339 | + | 0.869269i | \(0.664590\pi\) | |||||||
\(662\) | 21.3455 | 0.829616 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.60750 | −0.0623832 | ||||||||
\(665\) | −24.4503 | − | 24.4286i | −0.948140 | − | 0.947299i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.695049i | 0.0269124i | ||||||||
\(668\) | −15.2863 | −0.591445 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 8.01473i | − | 0.309636i | ||||||
\(671\) | 6.73419i | 0.259971i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.6712i | − | 0.719721i | −0.933006 | − | 0.359861i | \(-0.882824\pi\) | ||
0.933006 | − | 0.359861i | \(-0.117176\pi\) | |||||||
\(674\) | 21.0975 | 0.812646 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.2369 | 0.393726 | ||||||||
\(677\) | −42.4550 | −1.63168 | −0.815840 | − | 0.578278i | \(-0.803725\pi\) | ||||
−0.815840 | + | 0.578278i | \(0.803725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.26627 | − | 11.6624i | −0.125348 | − | 0.447560i | ||||
\(680\) | 13.3905i | 0.513503i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 5.42046i | − | 0.207560i | ||||||
\(683\) | − | 17.4816i | − | 0.668913i | −0.942411 | − | 0.334457i | \(-0.891447\pi\) | ||
0.942411 | − | 0.334457i | \(-0.108553\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 35.5749i | − | 1.35925i | ||||||
\(686\) | −12.6455 | + | 13.5311i | −0.482807 | + | 0.516621i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.40880 | −0.168084 | ||||||||
\(689\) | 14.1897i | 0.540585i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.7068i | − | 0.787722i | −0.919170 | − | 0.393861i | \(-0.871139\pi\) | ||
0.919170 | − | 0.393861i | \(-0.128861\pi\) | |||||||
\(692\) | 1.04151 | 0.0395924 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 13.2915i | − | 0.504540i | ||||||
\(695\) | −26.1671 | −0.992573 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 16.2449i | − | 0.615318i | ||||||
\(698\) | 4.37895 | 0.165746 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.84111 | − | 10.1443i | −0.107384 | − | 0.383419i | ||||
\(701\) | −10.6572 | −0.402517 | −0.201259 | − | 0.979538i | \(-0.564503\pi\) | ||||
−0.201259 | + | 0.979538i | \(0.564503\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.7794 | + | 20.7068i | −1.38716 | + | 0.780970i | ||||
\(704\) | 1.70021 | 0.0640789 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.0116 | −0.564971 | ||||||||
\(707\) | 20.9580 | − | 5.86969i | 0.788206 | − | 0.220753i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.8071 | −0.706317 | −0.353158 | − | 0.935564i | \(-0.614892\pi\) | ||||
−0.353158 | + | 0.935564i | \(0.614892\pi\) | |||||||
\(710\) | 25.5831i | 0.960118i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.27157i | 0.272514i | ||||||||
\(713\) | −1.55276 | −0.0581512 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.46996i | 0.316758i | ||||||||
\(716\) | 3.26295i | 0.121942i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 24.2278i | − | 0.904173i | ||||||
\(719\) | 16.5106i | 0.615742i | 0.951428 | + | 0.307871i | \(0.0996166\pi\) | ||||
−0.951428 | + | 0.307871i | \(0.900383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.05782 | − | 32.3413i | −0.337331 | − | 1.20445i | ||||
\(722\) | −16.2449 | − | 9.85415i | −0.604571 | − | 0.366734i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.94321 | 0.369536 | ||||||||
\(725\) | 5.68223i | 0.211033i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.743160i | 0.0275623i | 0.999905 | + | 0.0137811i | \(0.00438681\pi\) | ||||
−0.999905 | + | 0.0137811i | \(0.995613\pi\) | |||||||
\(728\) | 4.23498 | − | 1.18609i | 0.156959 | − | 0.0439594i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 10.8963i | − | 0.403289i | ||||||
\(731\) | − | 19.6987i | − | 0.728584i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.0051i | − | 0.775842i | −0.921693 | − | 0.387921i | \(-0.873193\pi\) | ||
0.921693 | − | 0.387921i | \(-0.126807\pi\) | |||||||
\(734\) | −15.2863 | −0.564228 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.487044i | − | 0.0179527i | ||||||
\(737\) | − | 4.54685i | − | 0.167485i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7083 | 0.651410 | 0.325705 | − | 0.945471i | \(-0.394398\pi\) | ||||
0.325705 | + | 0.945471i | \(0.394398\pi\) | |||||||
\(740\) | −29.0199 | −1.06679 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.09103 | − | 21.7483i | −0.223609 | − | 0.798404i | ||||
\(743\) | − | 36.7915i | − | 1.34975i | −0.737932 | − | 0.674875i | \(-0.764197\pi\) | ||
0.737932 | − | 0.674875i | \(-0.235803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.1006i | 0.956250i | ||||||||
\(746\) | −33.7029 | −1.23395 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.59660i | 0.277759i | ||||||||
\(749\) | −25.3841 | + | 7.10930i | −0.927514 | + | 0.259768i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.8014i | 1.05098i | 0.850801 | + | 0.525489i | \(0.176117\pi\) | ||||
−0.850801 | + | 0.525489i | \(0.823883\pi\) | |||||||
\(752\) | − | 2.80578i | − | 0.102316i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.37218 | −0.0863896 | ||||||||
\(755\) | 37.0346 | 1.34783 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.291697 | −0.0106019 | −0.00530095 | − | 0.999986i | \(-0.501687\pi\) | ||||
−0.00530095 | + | 0.999986i | \(0.501687\pi\) | |||||||
\(758\) | 12.8755 | 0.467660 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.40880 | − | 11.3833i | −0.232472 | − | 0.412917i | ||||
\(761\) | − | 45.9335i | − | 1.66509i | −0.553958 | − | 0.832545i | \(-0.686883\pi\) | ||
0.553958 | − | 0.832545i | \(-0.313117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.09079 | + | 0.865636i | −0.111894 | + | 0.0313381i | ||||
\(764\) | −4.86154 | −0.175884 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 32.6556i | − | 1.17990i | ||||||
\(767\) | −15.0539 | −0.543564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.9391i | − | 1.15176i | −0.817536 | − | 0.575878i | \(-0.804660\pi\) | ||
0.817536 | − | 0.575878i | \(-0.195340\pi\) | |||||||
\(770\) | −3.63579 | − | 12.9817i | −0.131025 | − | 0.467829i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.6712i | 0.671991i | ||||||||
\(773\) | 24.5745 | 0.883882 | 0.441941 | − | 0.897044i | \(-0.354290\pi\) | ||||
0.441941 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.6942 | −0.455990 | ||||||||
\(776\) | − | 4.57757i | − | 0.164325i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 32.4498i | − | 1.16338i | ||||||
\(779\) | 7.77491 | + | 13.8098i | 0.278565 | + | 0.494788i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5136i | 0.519337i | ||||||||
\(782\) | 2.17614 | 0.0778185 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.98173 | + | 3.63579i | −0.213633 | + | 0.129849i | ||||
\(785\) | −26.1671 | −0.933942 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.9716 | −1.56742 | −0.783709 | − | 0.621129i | \(-0.786674\pi\) | ||||
−0.783709 | + | 0.621129i | \(0.786674\pi\) | |||||||
\(788\) | −4.61357 | −0.164352 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 44.3062i | 1.57634i | ||||||||
\(791\) | −45.3477 | + | 12.7005i | −1.61238 | + | 0.451578i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.58392i | 0.233802i | ||||||||
\(794\) | 31.6141 | 1.12194 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.27157i | 0.257734i | ||||||||
\(797\) | −6.23006 | −0.220680 | −0.110340 | − | 0.993894i | \(-0.535194\pi\) | ||||
−0.110340 | + | 0.993894i | \(0.535194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5364 | 0.443505 | ||||||||
\(800\) | − | 3.98173i | − | 0.140775i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.5442 | −0.690129 | ||||||||
\(803\) | − | 6.18158i | − | 0.218143i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.71877 | + | 1.04151i | −0.131070 | + | 0.0367086i | ||||
\(806\) | − | 5.29950i | − | 0.186667i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.22618 | 0.289396 | ||||||||
\(809\) | 49.2127 | 1.73023 | 0.865114 | − | 0.501575i | \(-0.167246\pi\) | ||||
0.865114 | + | 0.501575i | \(0.167246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.37624 | −0.223900 | −0.111950 | − | 0.993714i | \(-0.535710\pi\) | ||||
−0.111950 | + | 0.993714i | \(0.535710\pi\) | |||||||
\(812\) | 3.63579 | − | 1.01827i | 0.127591 | − | 0.0357344i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.4633 | −0.577038 | ||||||||
\(815\) | 29.8600i | 1.04595i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.42796 | + | 16.7460i | 0.329843 | + | 0.585867i | ||||
\(818\) | 2.67287i | 0.0934547i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.8963i | 0.380515i | ||||||||
\(821\) | 30.3025 | 1.05756 | 0.528782 | − | 0.848758i | \(-0.322649\pi\) | ||||
0.528782 | + | 0.848758i | \(0.322649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 53.2548 | 1.85635 | 0.928173 | − | 0.372149i | \(-0.121379\pi\) | ||||
0.928173 | + | 0.372149i | \(0.121379\pi\) | |||||||
\(824\) | − | 12.6942i | − | 0.442225i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.0728 | − | 6.46198i | 0.802804 | − | 0.224841i | ||||
\(827\) | 16.6640i | 0.579462i | 0.957108 | + | 0.289731i | \(0.0935659\pi\) | ||||
−0.957108 | + | 0.289731i | \(0.906434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.0455 | 1.35611 | 0.678054 | − | 0.735012i | \(-0.262824\pi\) | ||||
0.678054 | + | 0.735012i | \(0.262824\pi\) | |||||||
\(830\) | 4.81761i | 0.167222i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.66226 | 0.0576286 | ||||||||
\(833\) | −16.2449 | − | 26.7266i | −0.562851 | − | 0.926023i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.8123i | 1.58540i | ||||||||
\(836\) | −3.63579 | − | 6.45789i | −0.125746 | − | 0.223351i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.5994 | −0.607961 | ||||||||
\(839\) | −13.2033 | −0.455828 | −0.227914 | − | 0.973681i | \(-0.573190\pi\) | ||||
−0.227914 | + | 0.973681i | \(0.573190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9635 | 0.929774 | ||||||||
\(842\) | 18.1531 | 0.625596 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 5.10062i | − | 0.175570i | ||||||
\(845\) | − | 30.6794i | − | 1.05540i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.78630 | + | 20.6602i | 0.198819 | + | 0.709893i | ||||
\(848\) | − | 8.53638i | − | 0.293140i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.7905 | 0.610211 | ||||||||
\(851\) | 4.71611i | 0.161666i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.8857i | − | 1.33142i | −0.746210 | − | 0.665710i | \(-0.768129\pi\) | ||
0.746210 | − | 0.665710i | \(-0.231871\pi\) | |||||||
\(854\) | −2.82619 | − | 10.0910i | −0.0967102 | − | 0.345308i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.96345 | −0.340544 | ||||||||
\(857\) | 45.1158 | 1.54112 | 0.770562 | − | 0.637365i | \(-0.219975\pi\) | ||||
0.770562 | + | 0.637365i | \(0.219975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.91930i | 0.0996051i | 0.998759 | + | 0.0498026i | \(0.0158592\pi\) | ||||
−0.998759 | + | 0.0498026i | \(0.984141\pi\) | |||||||
\(860\) | 13.2130i | 0.450559i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.10930 | −0.242144 | ||||||||
\(863\) | − | 52.6975i | − | 1.79384i | −0.442189 | − | 0.896922i | \(-0.645798\pi\) | ||
0.442189 | − | 0.896922i | \(-0.354202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 3.12137i | − | 0.106130i | ||||||
\(866\) | 7.02790i | 0.238818i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.27485 | + | 8.12243i | 0.0772133 | + | 0.275693i | ||||
\(869\) | 25.1354i | 0.852659i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.44538i | − | 0.150626i | ||||||
\(872\) | −1.21316 | −0.0410828 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.84994 | + | 1.04151i | −0.0625751 | + | 0.0352298i | ||||
\(875\) | 7.77491 | − | 2.17751i | 0.262840 | − | 0.0736134i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.29302i | − | 0.280035i | −0.990149 | − | 0.140018i | \(-0.955284\pi\) | ||
0.990149 | − | 0.140018i | \(-0.0447159\pi\) | |||||||
\(878\) | 4.68610i | 0.158148i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 5.09543i | − | 0.171767i | ||||||
\(881\) | 16.9163i | 0.569926i | 0.958538 | + | 0.284963i | \(0.0919814\pi\) | ||||
−0.958538 | + | 0.284963i | \(0.908019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.1899 | 0.376569 | 0.188284 | − | 0.982115i | \(-0.439707\pi\) | ||||
0.188284 | + | 0.982115i | \(0.439707\pi\) | |||||||
\(884\) | 7.42708i | 0.249800i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 10.1702i | − | 0.341673i | ||||||
\(887\) | −12.9240 | −0.433944 | −0.216972 | − | 0.976178i | \(-0.569618\pi\) | ||||
−0.216972 | + | 0.976178i | \(0.569618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.6648 | − | 10.5488i | 1.26324 | − | 0.353794i | ||||
\(890\) | 21.7926 | 0.730488 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.1181 | 0.606640 | ||||||||
\(893\) | −10.6572 | + | 6.00000i | −0.356630 | + | 0.200782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.77892 | 0.326873 | ||||||||
\(896\) | −2.54772 | + | 0.713538i | −0.0851133 | + | 0.0238376i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.40100 | −0.246975 | ||||||||
\(899\) | − | 4.54969i | − | 0.151741i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.1410 | 1.27066 | ||||||||
\(902\) | 6.18158i | 0.205824i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.7993 | −0.591997 | ||||||||
\(905\) | − | 29.7993i | − | 0.990563i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.8755i | 0.427525i | 0.976886 | + | 0.213762i | \(0.0685718\pi\) | ||||
−0.976886 | + | 0.213762i | \(0.931428\pi\) | |||||||
\(908\) | −4.67730 | −0.155222 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.55465 | − | 12.6920i | −0.117836 | − | 0.420737i | ||||
\(911\) | 27.0362i | 0.895750i | 0.894096 | + | 0.447875i | \(0.147819\pi\) | ||||
−0.894096 | + | 0.447875i | \(0.852181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.73308i | 0.0904518i | ||||||||
\(914\) | 0.890697i | 0.0294616i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.8437i | 0.886941i | ||||||||
\(917\) | 1.94818 | − | 0.545625i | 0.0643345 | − | 0.0180181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.5621 | 1.10711 | 0.553556 | − | 0.832812i | \(-0.313270\pi\) | ||||
0.553556 | + | 0.832812i | \(0.313270\pi\) | |||||||
\(920\) | −1.45965 | −0.0481232 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.0963 | −0.398372 | ||||||||
\(923\) | 14.1897i | 0.467060i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.5555i | 1.26770i | ||||||||
\(926\) | 32.2081i | 1.05843i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.42708 | 0.0468461 | ||||||||
\(929\) | − | 3.67898i | − | 0.120704i | −0.998177 | − | 0.0603518i | \(-0.980778\pi\) | ||
0.998177 | − | 0.0603518i | \(-0.0192222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.6014 | + | 14.9455i | 0.871825 | + | 0.489818i | ||||
\(932\) | −23.7407 | −0.777654 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.9016 | 1.14201 | ||||||||
\(935\) | 22.7666 | 0.744549 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3969i | 1.28704i | 0.765429 | + | 0.643521i | \(0.222527\pi\) | ||||
−0.765429 | + | 0.643521i | \(0.777473\pi\) | |||||||
\(938\) | 1.90821 | + | 6.81334i | 0.0623053 | + | 0.222464i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.40880 | −0.274265 | ||||||||
\(941\) | 21.0051 | 0.684747 | 0.342374 | − | 0.939564i | \(-0.388769\pi\) | ||||
0.342374 | + | 0.939564i | \(0.388769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.77079 | 0.0576648 | ||||||||
\(944\) | 9.05625 | 0.294756 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.49587i | 0.243712i | ||||||||
\(947\) | −53.0602 | −1.72423 | −0.862113 | − | 0.506716i | \(-0.830859\pi\) | ||||
−0.862113 | + | 0.506716i | \(0.830859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.04364i | − | 0.196185i | ||||||
\(950\) | −15.1238 | + | 8.51468i | −0.490681 | + | 0.276253i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.18812 | − | 11.3833i | −0.103328 | − | 0.368936i | ||||
\(953\) | − | 37.1428i | − | 1.20317i | −0.798807 | − | 0.601587i | \(-0.794535\pi\) | ||
0.798807 | − | 0.601587i | \(-0.205465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.5698i | 0.471468i | ||||||||
\(956\) | 7.28786 | 0.235706 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.6100 | −0.827422 | ||||||||
\(959\) | 8.46996 | + | 30.2423i | 0.273509 | + | 0.976576i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.8359 | −0.672125 | ||||||||
\(962\) | −16.0959 | −0.518953 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.7327 | 0.667757 | ||||||||
\(965\) | 55.9567 | 1.80131 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.4890 | 1.72009 | 0.860046 | − | 0.510217i | \(-0.170435\pi\) | ||||
0.860046 | + | 0.510217i | \(0.170435\pi\) | |||||||
\(968\) | 8.10930i | 0.260643i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.7188 | −0.440483 | ||||||||
\(971\) | 51.2794 | 1.64563 | 0.822817 | − | 0.568307i | \(-0.192401\pi\) | ||||
0.822817 | + | 0.568307i | \(0.192401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.2447 | − | 6.23006i | 0.713132 | − | 0.199726i | ||||
\(974\) | −39.0026 | −1.24972 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 3.96081i | − | 0.126783i | ||||||
\(977\) | 24.3827i | 0.780073i | 0.920799 | + | 0.390036i | \(0.127538\pi\) | ||||
−0.920799 | + | 0.390036i | \(0.872462\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3632 | 0.395128 | ||||||||
\(980\) | 10.8963 | + | 17.9270i | 0.348069 | + | 0.572656i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 19.3973i | − | 0.618993i | ||||||
\(983\) | 26.1272 | 0.833329 | 0.416665 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416665 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.8267i | 0.440554i | ||||||||
\(986\) | 6.37624i | 0.203061i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.55465 | − | 6.31378i | −0.113089 | − | 0.200868i | ||||
\(989\) | 2.14728 | 0.0682796 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.3751i | 0.837831i | 0.908025 | + | 0.418916i | \(0.137590\pi\) | ||||
−0.908025 | + | 0.418916i | \(0.862410\pi\) | |||||||
\(992\) | 3.18812i | 0.101223i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.09103 | − | 21.7483i | −0.193196 | − | 0.689814i | ||||
\(995\) | 21.7926 | 0.690871 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7359i | 0.593371i | 0.954975 | + | 0.296686i | \(0.0958813\pi\) | ||||
−0.954975 | + | 0.296686i | \(0.904119\pi\) | |||||||
\(998\) | − | 18.1171i | − | 0.573487i | ||||||
\(999\) | 0 | 0 |
(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 | 2394.2.e.d.1063.19 | yes | 24 | |
3.2 | odd | 2 | inner | 2394.2.e.d.1063.10 | yes | 24 | |
7.6 | odd | 2 | inner | 2394.2.e.d.1063.11 | yes | 24 | |
19.18 | odd | 2 | inner | 2394.2.e.d.1063.9 | ✓ | 24 | |
21.20 | even | 2 | inner | 2394.2.e.d.1063.18 | yes | 24 | |
57.56 | even | 2 | inner | 2394.2.e.d.1063.20 | yes | 24 | |
133.132 | even | 2 | inner | 2394.2.e.d.1063.17 | yes | 24 | |
399.398 | odd | 2 | inner | 2394.2.e.d.1063.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.e.d.1063.9 | ✓ | 24 | 19.18 | odd | 2 | inner | |
2394.2.e.d.1063.10 | yes | 24 | 3.2 | odd | 2 | inner | |
2394.2.e.d.1063.11 | yes | 24 | 7.6 | odd | 2 | inner | |
2394.2.e.d.1063.12 | yes | 24 | 399.398 | odd | 2 | inner | |
2394.2.e.d.1063.17 | yes | 24 | 133.132 | even | 2 | inner | |
2394.2.e.d.1063.18 | yes | 24 | 21.20 | even | 2 | inner | |
2394.2.e.d.1063.19 | yes | 24 | 1.1 | even | 1 | trivial | |
2394.2.e.d.1063.20 | yes | 24 | 57.56 | even | 2 | inner |