Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), degree \(2\), 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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.7 | ||
Character | \(\chi\) | \(=\) | 76.45 |
Dual form | 76.8.e.a.49.7 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.71048 | + | 13.3549i | 0.164876 | + | 0.285573i | 0.936611 | − | 0.350370i | \(-0.113944\pi\) |
−0.771735 | + | 0.635944i | \(0.780611\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 60.2613 | + | 104.376i | 0.215597 | + | 0.373425i | 0.953457 | − | 0.301529i | \(-0.0974969\pi\) |
−0.737860 | + | 0.674954i | \(0.764164\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1390.32 | −1.53205 | −0.766023 | − | 0.642814i | \(-0.777767\pi\) | ||||
−0.766023 | + | 0.642814i | \(0.777767\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 974.597 | − | 1688.05i | 0.445632 | − | 0.771857i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2042.99 | 0.462798 | 0.231399 | − | 0.972859i | \(-0.425670\pi\) | ||||
0.231399 | + | 0.972859i | \(0.425670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4315.46 | − | 7474.60i | 0.544786 | − | 0.943597i | −0.453835 | − | 0.891086i | \(-0.649944\pi\) |
0.998620 | − | 0.0525106i | \(-0.0167223\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −929.286 | + | 1609.57i | −0.0710935 | + | 0.123138i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −946.772 | − | 1639.86i | −0.0467384 | − | 0.0809533i | 0.841710 | − | 0.539930i | \(-0.181549\pi\) |
−0.888448 | + | 0.458977i | \(0.848216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1273.75 | + | 29870.5i | 0.0426038 | + | 0.999092i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10720.0 | − | 18567.6i | −0.252597 | − | 0.437511i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12191.9 | − | 21117.1i | 0.208942 | − | 0.361898i | −0.742440 | − | 0.669913i | \(-0.766331\pi\) |
0.951381 | + | 0.308015i | \(0.0996648\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 31799.7 | − | 55078.6i | 0.407036 | − | 0.705006i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 63784.1 | 0.623647 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 62492.6 | − | 108240.i | 0.475813 | − | 0.824132i | −0.523803 | − | 0.851839i | \(-0.675487\pi\) |
0.999616 | + | 0.0277075i | \(0.00882071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 212857. | 1.28328 | 0.641642 | − | 0.767004i | \(-0.278254\pi\) | ||||
0.641642 | + | 0.767004i | \(0.278254\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15752.4 | + | 27284.0i | 0.0763042 | + | 0.132163i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −83782.4 | − | 145115.i | −0.330305 | − | 0.572104i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 117001. | 0.379737 | 0.189869 | − | 0.981810i | \(-0.439194\pi\) | ||||
0.189869 | + | 0.981810i | \(0.439194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 133097. | 0.359288 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −88867.0 | − | 153922.i | −0.201371 | − | 0.348785i | 0.747599 | − | 0.664150i | \(-0.231206\pi\) |
−0.948970 | + | 0.315365i | \(0.897873\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −68222.9 | − | 118166.i | −0.130855 | − | 0.226648i | 0.793151 | − | 0.609025i | \(-0.208439\pi\) |
−0.924006 | + | 0.382377i | \(0.875106\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 234922. | 0.384308 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 651614. | − | 1.12863e6i | 0.915479 | − | 1.58566i | 0.109279 | − | 0.994011i | \(-0.465146\pi\) |
0.806199 | − | 0.591644i | \(-0.201521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.10945e6 | 1.34716 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14600.1 | − | 25288.2i | 0.0154121 | − | 0.0266945i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 233530. | − | 404486.i | 0.215465 | − | 0.373197i | −0.737951 | − | 0.674854i | \(-0.764207\pi\) |
0.953416 | + | 0.301658i | \(0.0975399\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 123113. | + | 213238.i | 0.0997780 | + | 0.172821i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −389098. | + | 247327.i | −0.278290 | + | 0.176893i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.20409e6 | − | 2.08555e6i | −0.763269 | − | 1.32202i | −0.941157 | − | 0.337969i | \(-0.890260\pi\) |
0.177888 | − | 0.984051i | \(-0.443073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −509201. | + | 881961.i | −0.287233 | + | 0.497502i | −0.973148 | − | 0.230179i | \(-0.926069\pi\) |
0.685915 | + | 0.727682i | \(0.259402\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.35500e6 | + | 2.34693e6i | −0.682728 | + | 1.18252i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04022e6 | 0.469817 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −992579. | + | 1.71920e6i | −0.403184 | + | 0.698335i | −0.994108 | − | 0.108392i | \(-0.965430\pi\) |
0.590924 | + | 0.806727i | \(0.298763\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 376023. | 0.137798 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.20730e6 | + | 3.82316e6i | 0.731910 | + | 1.26770i | 0.956066 | + | 0.293152i | \(0.0947041\pi\) |
−0.224156 | + | 0.974553i | \(0.571963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.07716e6 | − | 1.86569e6i | −0.324078 | − | 0.561320i | 0.657247 | − | 0.753675i | \(-0.271721\pi\) |
−0.981325 | + | 0.192355i | \(0.938387\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 980763. | 0.268441 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.84041e6 | −0.709028 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 461512. | + | 799362.i | 0.105314 | + | 0.182410i | 0.913867 | − | 0.406014i | \(-0.133082\pi\) |
−0.808552 | + | 0.588424i | \(0.799748\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.63964e6 | − | 2.83994e6i | −0.342808 | − | 0.593760i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.74443e6 | −1.48668 | −0.743338 | − | 0.668916i | \(-0.766759\pi\) | ||||
−0.743338 | + | 0.668916i | \(0.766759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 114107. | − | 197640.i | 0.0201533 | − | 0.0349066i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.92739e6 | 0.313800 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.33221e6 | + | 4.03950e6i | −0.350673 | + | 0.607383i | −0.986367 | − | 0.164558i | \(-0.947380\pi\) |
0.635695 | + | 0.771940i | \(0.280714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.99987e6 | + | 1.03921e7i | −0.834636 | + | 1.44563i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.64123e6 | + | 2.84270e6i | 0.211583 | + | 0.366472i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.04100e6 | + | 1.93299e6i | −0.363901 | + | 0.231311i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.09272e6 | − | 1.40170e7i | −0.900313 | − | 1.55939i | −0.827088 | − | 0.562072i | \(-0.810004\pi\) |
−0.0732246 | − | 0.997315i | \(-0.523329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.99109e6 | − | 3.44867e6i | 0.206238 | − | 0.357214i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.31748e6 | + | 1.44063e7i | −0.803280 | + | 1.39132i | 0.114166 | + | 0.993462i | \(0.463580\pi\) |
−0.917446 | + | 0.397860i | \(0.869753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.90128e7 | 1.71441 | 0.857206 | − | 0.514974i | \(-0.172198\pi\) | ||||
0.857206 | + | 0.514974i | \(0.172198\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.29201e6 | − | 2.23782e6i | 0.108919 | − | 0.188652i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.14505e6 | −0.248190 | −0.124095 | − | 0.992270i | \(-0.539603\pi\) | ||||
−0.124095 | + | 0.992270i | \(0.539603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −760400. | − | 1.31705e6i | −0.0562405 | − | 0.0974114i | 0.836534 | − | 0.547914i | \(-0.184578\pi\) |
−0.892775 | + | 0.450503i | \(0.851245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 902133. | + | 1.56254e6i | 0.0626095 | + | 0.108443i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.92682e7 | 1.25622 | 0.628110 | − | 0.778125i | \(-0.283829\pi\) | ||||
0.628110 | + | 0.778125i | \(0.283829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.93880e6 | 0.180189 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.41168e6 | − | 1.45694e7i | −0.485548 | − | 0.840993i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.31632e6 | + | 2.27993e6i | 0.0716054 | + | 0.124024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.53134e7 | −0.785818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.37041e6 | − | 2.37363e6i | 0.0664024 | − | 0.115012i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.70810e7 | 0.782217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.77865e6 | + | 8.27687e6i | −0.207011 | + | 0.358553i | −0.950771 | − | 0.309893i | \(-0.899707\pi\) |
0.743761 | + | 0.668446i | \(0.233040\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.05206e6 | − | 1.82223e6i | 0.0431497 | − | 0.0747374i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.30471e7 | + | 2.25982e7i | 0.507065 | + | 0.878263i | 0.999967 | + | 0.00817779i | \(0.00260310\pi\) |
−0.492901 | + | 0.870085i | \(0.664064\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.77093e6 | − | 4.15296e7i | −0.0652709 | − | 1.53065i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.84371e6 | + | 6.65750e6i | 0.134457 | + | 0.232886i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.55600e7 | − | 4.42712e7i | 0.849256 | − | 1.47095i | −0.0326178 | − | 0.999468i | \(-0.510384\pi\) |
0.881873 | − | 0.471486i | \(-0.156282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.64040e6 | − | 8.03741e6i | 0.146556 | − | 0.253843i | −0.783396 | − | 0.621522i | \(-0.786514\pi\) |
0.929952 | + | 0.367680i | \(0.119848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00970e7 | 0.603761 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.81644e6 | − | 1.52705e7i | 0.252126 | − | 0.436695i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50635e7 | 0.410335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.55436e6 | + | 1.48166e7i | 0.222114 | + | 0.384714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.51057e7 | − | 4.34844e7i | −0.621757 | − | 1.07692i | −0.989158 | − | 0.146853i | \(-0.953086\pi\) |
0.367401 | − | 0.930063i | \(-0.380248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.40690e7 | 0.568903 | 0.284451 | − | 0.958690i | \(-0.408189\pi\) | ||||
0.284451 | + | 0.958690i | \(0.408189\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.69088e6 | −0.0833125 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.28271e7 | + | 2.22171e7i | 0.276672 | + | 0.479211i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.51003e7 | − | 2.61545e7i | −0.311413 | − | 0.539384i | 0.667255 | − | 0.744829i | \(-0.267469\pi\) |
−0.978669 | + | 0.205445i | \(0.934136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.20251e6 | 0.142100 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.69507e7 | + | 2.93595e7i | −0.320108 | + | 0.554444i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.25527e7 | −0.227029 | −0.113514 | − | 0.993536i | \(-0.536211\pi\) | ||||
−0.113514 | + | 0.993536i | \(0.536211\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.89852e6 | + | 3.28834e6i | −0.0329020 | + | 0.0569879i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.56134e7 | + | 2.70432e7i | −0.259412 | + | 0.449315i | −0.966085 | − | 0.258226i | \(-0.916862\pi\) |
0.706673 | + | 0.707541i | \(0.250195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.87219e6 | − | 1.01709e7i | −0.0935830 | − | 0.162090i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.16644e7 | + | 2.69616e7i | 0.790142 | + | 0.412343i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −347200. | − | 601369.i | −0.00509822 | − | 0.00883038i | 0.863465 | − | 0.504409i | \(-0.168289\pi\) |
−0.868563 | + | 0.495578i | \(0.834956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.42117e7 | + | 7.65769e7i | −0.623597 | + | 1.08010i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.85682e7 | − | 3.21611e7i | 0.251689 | − | 0.435938i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.73363e7 | −0.877533 | −0.438767 | − | 0.898601i | \(-0.644584\pi\) | ||||
−0.438767 | + | 0.898601i | \(0.644584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −65005.9 | + | 112593.i | −0.000814850 | + | 0.00141136i | −0.866433 | − | 0.499294i | \(-0.833593\pi\) |
0.865618 | + | 0.500706i | \(0.166926\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57047e7 | −0.189431 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.05062e6 | + | 1.22120e7i | 0.0818703 | + | 0.141803i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.93424e6 | − | 3.35021e6i | −0.0216305 | − | 0.0374651i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.86803e7 | −0.955456 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.74668e7 | −0.700605 | −0.350303 | − | 0.936637i | \(-0.613921\pi\) | ||||
−0.350303 | + | 0.936637i | \(0.613921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.34728e6 | − | 5.79766e6i | −0.0335152 | − | 0.0580500i | 0.848781 | − | 0.528744i | \(-0.177337\pi\) |
−0.882296 | + | 0.470694i | \(0.844004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.02060e6 | + | 1.38921e7i | 0.0774615 | + | 0.134167i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.11025e8 | 1.03464 | 0.517318 | − | 0.855793i | \(-0.326931\pi\) | ||||
0.517318 | + | 0.855793i | \(0.326931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.52124e7 | + | 2.63487e7i | −0.136840 | + | 0.237014i | −0.926299 | − | 0.376790i | \(-0.877028\pi\) |
0.789459 | + | 0.613803i | \(0.210361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.06131e7 | −0.265901 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.68848e7 | + | 1.50489e8i | −0.728966 | + | 1.26261i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.07105e7 | − | 1.85511e7i | 0.0868301 | − | 0.150394i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.37644e7 | − | 4.11612e7i | −0.186222 | − | 0.322546i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.60227e6 | + | 6.10252e7i | 0.0197169 | + | 0.462378i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.83274e7 | + | 1.70308e8i | 0.720587 | + | 1.24809i | 0.960765 | + | 0.277364i | \(0.0894607\pi\) |
−0.240178 | + | 0.970729i | \(0.577206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.40387e7 | + | 5.89568e7i | −0.241348 | + | 0.418028i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.22239e6 | − | 1.42416e7i | 0.0564240 | − | 0.0977292i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.95940e8 | −1.96605 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.66108e7 | − | 2.87708e7i | 0.106865 | − | 0.185096i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.63430e7 | −0.101850 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.95579e7 | − | 1.55119e8i | −0.540800 | − | 0.936693i | −0.998858 | − | 0.0477711i | \(-0.984788\pi\) |
0.458058 | − | 0.888922i | \(-0.348545\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.19837e7 | − | 1.07359e8i | −0.362776 | − | 0.628347i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.13714e7 | −0.234752 | −0.117376 | − | 0.993088i | \(-0.537448\pi\) | ||||
−0.117376 | + | 0.993088i | \(0.537448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.16259e7 | 0.174028 | 0.0870140 | − | 0.996207i | \(-0.472268\pi\) | ||||
0.0870140 | + | 0.996207i | \(0.472268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.19009e7 | − | 3.79335e7i | −0.116902 | − | 0.202479i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.96025e7 | + | 1.37876e8i | 0.412269 | + | 0.714071i | 0.995138 | − | 0.0984954i | \(-0.0314030\pi\) |
−0.582868 | + | 0.812567i | \(0.698070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.57068e8 | 0.789498 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.11696e6 | + | 1.23269e7i | −0.0347276 | + | 0.0601500i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.28680e8 | 0.609702 | 0.304851 | − | 0.952400i | \(-0.401393\pi\) | ||||
0.304851 | + | 0.952400i | \(0.401393\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.10493e8 | − | 3.64584e8i | 0.968673 | − | 1.67779i | 0.269269 | − | 0.963065i | \(-0.413218\pi\) |
0.699404 | − | 0.714726i | \(-0.253449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.50327e7 | − | 1.64601e8i | 0.424865 | − | 0.735888i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.68566e7 | + | 1.15799e8i | 0.290444 | + | 0.503064i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.28767e8 | + | 1.19384e8i | 0.965950 | + | 0.504090i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.97133e7 | − | 1.03426e8i | −0.245117 | − | 0.424555i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.06004e7 | + | 8.76424e7i | −0.201974 | + | 0.349829i | −0.949164 | − | 0.314781i | \(-0.898069\pi\) |
0.747190 | + | 0.664610i | \(0.231402\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.49080e7 | − | 4.31419e7i | 0.0966978 | − | 0.167486i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.51929e6 | 0.0132912 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.08914e6 | + | 1.05467e7i | −0.0223764 | + | 0.0387570i | −0.876997 | − | 0.480496i | \(-0.840457\pi\) |
0.854620 | + | 0.519253i | \(0.173790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.62669e8 | −0.581774 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.21810e8 | − | 2.10982e8i | −0.424075 | − | 0.734519i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.46088e8 | + | 4.26238e8i | 0.834154 | + | 1.44480i | 0.894718 | + | 0.446632i | \(0.147377\pi\) |
−0.0605637 | + | 0.998164i | \(0.519290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.62912e7 | 0.185815 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.19297e7 | −0.231270 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.59482e8 | + | 2.76231e8i | 0.499550 | + | 0.865245i | 1.00000 | 0.000519964i | \(-0.000165510\pi\) | |
−0.500450 | + | 0.865765i | \(0.666832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.28060e8 | − | 3.95012e8i | −0.696077 | − | 1.20564i | −0.969816 | − | 0.243836i | \(-0.921594\pi\) |
0.273740 | − | 0.961804i | \(-0.411739\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.85048e8 | −0.550445 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.49664e7 | − | 1.12525e8i | 0.188375 | − | 0.326276i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.31963e8 | 1.22114 | 0.610572 | − | 0.791961i | \(-0.290940\pi\) | ||||
0.610572 | + | 0.791961i | \(0.290940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.07450e8 | − | 3.59314e8i | 0.571872 | − | 0.990512i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.42756e7 | + | 2.47261e7i | −0.0383816 | + | 0.0664789i | −0.884578 | − | 0.466392i | \(-0.845554\pi\) |
0.846196 | + | 0.532871i | \(0.178887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.79098e7 | − | 1.52264e8i | −0.230560 | − | 0.399342i | 0.727413 | − | 0.686200i | \(-0.240723\pi\) |
−0.957973 | + | 0.286858i | \(0.907389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.92624e7 | − | 2.57081e7i | −0.126055 | − | 0.0657829i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.23554e8 | + | 2.14001e8i | 0.308509 | + | 0.534354i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03377e8 | − | 3.52259e8i | 0.495631 | − | 0.858458i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.24798e8 | − | 2.16156e8i | 0.296880 | − | 0.514211i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.25093e8 | 0.987296 | 0.493648 | − | 0.869662i | \(-0.335663\pi\) | ||||
0.493648 | + | 0.869662i | \(0.335663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.45120e8 | − | 2.51355e8i | 0.329117 | − | 0.570048i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.30310e8 | 0.288623 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.05228e8 | − | 1.82260e8i | −0.227657 | − | 0.394313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.48516e7 | + | 1.64288e8i | 0.200476 | + | 0.347234i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.56527e8 | −0.529766 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.22740e8 | −0.247707 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.70722e8 | − | 4.68904e8i | −0.533997 | − | 0.924910i | −0.999211 | − | 0.0397119i | \(-0.987356\pi\) |
0.465214 | − | 0.885198i | \(-0.345977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.46598e8 | + | 2.53915e8i | 0.282665 | + | 0.489590i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.28809e7 | −0.0619845 | −0.0309922 | − | 0.999520i | \(-0.509867\pi\) | ||||
−0.0309922 | + | 0.999520i | \(0.509867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.15658e8 | + | 7.19940e8i | −0.766180 | + | 1.32706i | 0.173441 | + | 0.984844i | \(0.444511\pi\) |
−0.939621 | + | 0.342218i | \(0.888822\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.26616e8 | −0.588777 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.48372e8 | + | 6.03398e8i | −0.614237 | + | 1.06389i | 0.376281 | + | 0.926506i | \(0.377203\pi\) |
−0.990518 | + | 0.137384i | \(0.956131\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.27672e8 | − | 2.21134e8i | 0.220205 | − | 0.381407i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.42498e7 | − | 4.20019e7i | −0.0409205 | − | 0.0708764i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.77775e7 | − | 3.03694e7i | 0.0788886 | − | 0.0501449i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.74461e8 | − | 4.75380e8i | −0.443494 | − | 0.768155i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.17261e7 | − | 2.03102e7i | 0.0185454 | − | 0.0321216i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.05952e8 | + | 1.56916e9i | −1.40255 | + | 2.42930i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.03206e7 | 0.0914256 | 0.0457128 | − | 0.998955i | \(-0.485444\pi\) | ||||
0.0457128 | + | 0.998955i | \(0.485444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.14029e8 | − | 1.97504e8i | 0.169223 | − | 0.293103i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.39256e8 | −0.347701 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50854e8 | + | 7.80902e8i | 0.641699 | + | 1.11146i | 0.985053 | + | 0.172249i | \(0.0551035\pi\) |
−0.343354 | + | 0.939206i | \(0.611563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.48567e8 | + | 2.57325e8i | 0.207120 | + | 0.358743i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.34865e8 | 0.593901 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.97496e8 | −0.531868 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.26596e7 | + | 3.92476e7i | 0.0297088 | + | 0.0514572i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.55975e8 | − | 4.43363e8i | −0.328886 | − | 0.569647i | 0.653405 | − | 0.757008i | \(-0.273340\pi\) |
−0.982291 | + | 0.187361i | \(0.940006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.66879e8 | −1.21754 | −0.608770 | − | 0.793347i | \(-0.708337\pi\) | ||||
−0.608770 | + | 0.793347i | \(0.708337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.75258e8 | − | 4.76761e8i | 0.339754 | − | 0.588472i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.94120e8 | 0.839891 | 0.419945 | − | 0.907549i | \(-0.362049\pi\) | ||||
0.419945 | + | 0.907549i | \(0.362049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.66030e8 | + | 4.60777e8i | −0.315595 | + | 0.546627i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.02988e7 | + | 3.51586e7i | −0.0236120 | + | 0.0408972i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.15769e8 | + | 7.20133e8i | 0.474266 | + | 0.821452i | 0.999566 | − | 0.0294647i | \(-0.00938028\pi\) |
−0.525300 | + | 0.850917i | \(0.676047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.90627e8 | + | 7.60955e7i | −0.996370 | + | 0.0851302i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.18073e8 | − | 2.04509e8i | −0.129562 | − | 0.224409i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.29822e8 | − | 2.24858e8i | 0.139741 | − | 0.242038i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.72325e8 | + | 2.98476e8i | −0.181977 | + | 0.315194i | −0.942554 | − | 0.334054i | \(-0.891583\pi\) |
0.760576 | + | 0.649248i | \(0.224916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.46438e8 | −0.358949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.24681e8 | + | 5.62364e8i | −0.330102 | + | 0.571754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.50373e9 | 1.50033 | 0.750167 | − | 0.661248i | \(-0.229973\pi\) | ||||
0.750167 | + | 0.661248i | \(0.229973\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.31702e8 | + | 2.28115e8i | 0.128969 | + | 0.223380i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.39369e8 | − | 9.34215e8i | −0.518432 | − | 0.897950i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.55525e9 | −1.46745 | −0.733727 | − | 0.679445i | \(-0.762221\pi\) | ||||
−0.733727 | + | 0.679445i | \(0.762221\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.47383e8 | −0.136524 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.01073e8 | − | 3.48268e8i | −0.182876 | − | 0.316751i | 0.759983 | − | 0.649943i | \(-0.225207\pi\) |
−0.942859 | + | 0.333193i | \(0.891874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.71167e8 | − | 2.96469e8i | −0.152864 | − | 0.264769i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.65959e8 | −0.233253 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.47194e8 | + | 7.74563e8i | −0.385188 | + | 0.667165i | −0.991795 | − | 0.127837i | \(-0.959197\pi\) |
0.606607 | + | 0.795001i | \(0.292530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.61719e7 | −0.0390624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.01199e8 | + | 3.48486e8i | −0.167206 | + | 0.289609i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.56226e7 | + | 9.63411e7i | −0.0454110 | + | 0.0786542i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.01015e7 | + | 1.38740e8i | 0.0642501 | + | 0.111284i | 0.896361 | − | 0.443325i | \(-0.146201\pi\) |
−0.832111 | + | 0.554609i | \(0.812868\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.40971e8 | − | 3.43864e8i | 0.426352 | − | 0.271008i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.81408e8 | + | 3.14208e8i | 0.140492 | + | 0.243339i | 0.927682 | − | 0.373371i | \(-0.121798\pi\) |
−0.787190 | + | 0.616711i | \(0.788465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.18578e8 | − | 1.59102e9i | 0.699115 | − | 1.21090i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.97613e8 | − | 3.42276e8i | 0.147817 | − | 0.256026i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.39032e8 | 0.175742 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.24946e8 | − | 1.42885e9i | 0.596203 | − | 1.03265i | −0.397173 | − | 0.917744i | \(-0.630009\pi\) |
0.993376 | − | 0.114910i | \(-0.0366579\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.88319e8 | 0.560087 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.67407e9 | + | 2.89958e9i | 1.16936 | + | 2.02539i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.66689e8 | − | 8.08330e8i | −0.320523 | − | 0.555162i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.43119e8 | 0.0966542 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.44293e9 | 1.62242 | 0.811209 | − | 0.584756i | \(-0.198810\pi\) | ||||
0.811209 | + | 0.584756i | \(0.198810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.56978e7 | − | 6.18304e7i | −0.0233160 | − | 0.0403845i | 0.854132 | − | 0.520056i | \(-0.174089\pi\) |
−0.877448 | + | 0.479672i | \(0.840756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.27012e9 | − | 2.19992e9i | −0.815933 | − | 1.41324i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20428e8 | −0.0760968 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.07952e8 | − | 1.22621e9i | 0.440054 | − | 0.762196i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.71916e8 | 0.166278 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.03682e9 | + | 1.79582e9i | −0.623782 | + | 1.08042i | 0.364993 | + | 0.931010i | \(0.381071\pi\) |
−0.988775 | + | 0.149412i | \(0.952262\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.75885e8 | − | 1.34387e9i | 0.459293 | − | 0.795518i | −0.539631 | − | 0.841902i | \(-0.681436\pi\) |
0.998924 | + | 0.0463833i | \(0.0147696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.16147e8 | + | 2.01173e8i | 0.0676544 | + | 0.117181i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.46307e8 | + | 3.37282e8i | 0.370471 | + | 0.193334i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.87754e7 | + | 1.36443e8i | 0.0444391 | + | 0.0769707i | 0.887389 | − | 0.461021i | \(-0.152517\pi\) |
−0.842950 | + | 0.537991i | \(0.819183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.08126e9 | − | 1.87280e9i | 0.600338 | − | 1.03982i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.59312e7 | − | 1.48837e8i | 0.0469611 | − | 0.0813390i | −0.841589 | − | 0.540118i | \(-0.818380\pi\) |
0.888550 | + | 0.458779i | \(0.151713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.62167e8 | −0.302416 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.87155e8 | − | 6.70571e8i | 0.205026 | − | 0.355115i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.76795e9 | −1.44310 | −0.721548 | − | 0.692364i | \(-0.756569\pi\) | ||||
−0.721548 | + | 0.692364i | \(0.756569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.81554e8 | − | 3.14461e8i | −0.0931941 | − | 0.161417i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.85583e8 | + | 3.21440e8i | 0.0937984 | + | 0.162464i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.44624e9 | −0.719781 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.24275e9 | −0.609084 | −0.304542 | − | 0.952499i | \(-0.598503\pi\) | ||||
−0.304542 | + | 0.952499i | \(0.598503\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.03890e7 | − | 1.04597e8i | −0.0291483 | − | 0.0504863i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.96118e9 | + | 3.39687e9i | 0.932319 | + | 1.61482i | 0.779346 | + | 0.626593i | \(0.215551\pi\) |
0.152973 | + | 0.988230i | \(0.451115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.77320e9 | 0.830278 | 0.415139 | − | 0.909758i | \(-0.363733\pi\) | ||||
0.415139 | + | 0.909758i | \(0.363733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.97805e8 | + | 3.42609e8i | −0.0912332 | + | 0.158021i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.87562e9 | 1.30654 | 0.653269 | − | 0.757126i | \(-0.273397\pi\) | ||||
0.653269 | + | 0.757126i | \(0.273397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.38000e9 | − | 2.39023e9i | 0.617696 | − | 1.06988i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.32861e8 | − | 4.03328e8i | 0.102689 | − | 0.177863i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.39379e8 | − | 2.41411e8i | −0.0605595 | − | 0.104892i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.68573e9 | + | 8.79717e8i | 0.721708 | + | 0.376630i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.55195e8 | − | 7.88421e8i | −0.192036 | − | 0.332617i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.93157e8 | + | 5.07764e8i | −0.121878 | + | 0.211099i | −0.920508 | − | 0.390723i | \(-0.872225\pi\) |
0.798630 | + | 0.601822i | \(0.205558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.04913e8 | − | 8.74535e8i | 0.206875 | − | 0.358319i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.22792e8 | −0.211112 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.75355e8 | − | 1.68936e9i | 0.388210 | − | 0.672399i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.21097e9 | −1.25975 | −0.629876 | − | 0.776695i | \(-0.716894\pi\) | ||||
−0.629876 | + | 0.776695i | \(0.716894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.67875e7 | − | 1.67641e8i | −0.0374316 | − | 0.0648334i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.30136e9 | + | 2.25402e9i | 0.496149 | + | 0.859355i | 0.999990 | − | 0.00444096i | \(-0.00141361\pi\) |
−0.503841 | + | 0.863796i | \(0.668080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.36665e8 | −0.0889549 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.79942e8 | 0.177857 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.06886e9 | − | 5.31541e9i | −1.12132 | − | 1.94218i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.17591e8 | + | 3.76879e8i | 0.0783951 | + | 0.135784i | 0.902558 | − | 0.430569i | \(-0.141687\pi\) |
−0.824163 | + | 0.566353i | \(0.808354\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.81547e8 | −0.171083 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.27657e9 | + | 3.94313e9i | −0.797614 | + | 1.38151i | 0.123551 | + | 0.992338i | \(0.460572\pi\) |
−0.921166 | + | 0.389170i | \(0.872762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00489e9 | −0.692740 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.05549e7 | − | 1.56846e8i | 0.0308591 | − | 0.0534496i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.76163e8 | − | 8.24739e8i | 0.160046 | − | 0.277207i | −0.774839 | − | 0.632158i | \(-0.782169\pi\) |
0.934885 | + | 0.354951i | \(0.115503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.49759e9 | + | 2.59391e9i | 0.496502 | + | 0.859967i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.12453e7 | + | 1.90527e9i | 0.0265697 | + | 0.623081i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.14573e9 | + | 1.98447e9i | 0.369622 | + | 0.640205i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.33124e9 | − | 2.30578e9i | 0.423682 | − | 0.733838i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.35416e6 | − | 9.27368e6i | 0.00168115 | − | 0.00291183i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.55659e9 | −1.41159 | −0.705794 | − | 0.708417i | \(-0.749410\pi\) | ||||
−0.705794 | + | 0.708417i | \(0.749410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.64354e9 | + | 4.57875e9i | −0.808035 | + | 1.39956i | 0.106188 | + | 0.994346i | \(0.466136\pi\) |
−0.914223 | + | 0.405212i | \(0.867198\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.36357e9 | −0.411264 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01527e8 | − | 3.49056e8i | −0.0599787 | − | 0.103886i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.40513e9 | + | 2.43375e9i | 0.412687 | + | 0.714794i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.69402e9 | −1.36055 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.53401e9 | −0.438816 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.89524e8 | − | 3.28266e8i | −0.0535090 | − | 0.0926803i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.19195e8 | − | 8.99272e8i | −0.144684 | − | 0.250600i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.26659e9 | 0.623464 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.04906e9 | + | 3.54908e9i | −0.556372 | + | 0.963664i | 0.441424 | + | 0.897299i | \(0.354474\pi\) |
−0.997795 | + | 0.0663652i | \(0.978860\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00491e6 | −0.000537396 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.16453e7 | − | 1.58734e8i | 0.0242506 | − | 0.0420032i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.08604e8 | − | 8.80927e8i | 0.132869 | − | 0.230136i | −0.791912 | − | 0.610635i | \(-0.790914\pi\) |
0.924781 | + | 0.380499i | \(0.124248\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.92531e8 | + | 1.71911e9i | 0.256000 | + | 0.443406i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.31280e9 | + | 1.72882e9i | 0.843655 | + | 0.440269i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.41649e8 | − | 1.11137e9i | −0.161347 | − | 0.279460i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.08727e8 | + | 1.88321e8i | −0.0269969 | + | 0.0467599i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.21011e9 | − | 5.56008e9i | 0.787094 | − | 1.36329i | −0.140645 | − | 0.990060i | \(-0.544918\pi\) |
0.927740 | − | 0.373228i | \(-0.121749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.17765e9 | −0.285152 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.98279e7 | − | 5.16634e7i | 0.00713268 | − | 0.0123542i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.93235e9 | −1.63720 | −0.818599 | − | 0.574366i | \(-0.805249\pi\) | ||||
−0.818599 | + | 0.574366i | \(0.805249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.16112e9 | + | 2.01112e9i | 0.270837 | + | 0.469104i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.27962e9 | + | 3.94842e9i | 0.525197 | + | 0.909667i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.91652e9 | −1.11883 | −0.559416 | − | 0.828887i | \(-0.688974\pi\) | ||||
−0.559416 | + | 0.828887i | \(0.688974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.03802e8 | −0.203164 | −0.101582 | − | 0.994827i | \(-0.532390\pi\) | ||||
−0.101582 | + | 0.994827i | \(0.532390\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.20202e8 | − | 9.01016e8i | −0.115513 | − | 0.200074i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.75399e8 | − | 1.34303e9i | −0.170093 | − | 0.294611i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.68572e9 | −0.798742 | −0.399371 | − | 0.916789i | \(-0.630771\pi\) | ||||
−0.399371 | + | 0.916789i | \(0.630771\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.16183e7 | − | 8.94054e7i | 0.0110517 | − | 0.0191421i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.07672e10 | 2.27765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.77099e8 | − | 8.26360e8i | 0.0997169 | − | 0.172715i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.01380e9 | − | 1.75595e9i | 0.209366 | − | 0.362632i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.40741e7 | + | 1.62941e8i | 0.0191971 | + | 0.0332504i | 0.875464 | − | 0.483283i | \(-0.160556\pi\) |
−0.856267 | + | 0.516533i | \(0.827222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.71128e8 | + | 6.35817e9i | 0.0546727 | + | 1.28212i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.56053e8 | + | 1.48273e9i | 0.170586 | + | 0.295464i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.27618e8 | − | 1.43348e9i | 0.162982 | − | 0.282293i | −0.772955 | − | 0.634461i | \(-0.781222\pi\) |
0.935937 | + | 0.352168i | \(0.114556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.58646e8 | + | 2.74782e8i | −0.0308758 | + | 0.0534785i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.69181e8 | −0.0902464 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.80344e9 | + | 3.12365e9i | −0.342852 | + | 0.593838i | −0.984961 | − | 0.172776i | \(-0.944726\pi\) |
0.642109 | + | 0.766614i | \(0.278060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.35303e8 | −0.0442146 | −0.0221073 | − | 0.999756i | \(-0.507038\pi\) | ||||
−0.0221073 | + | 0.999756i | \(0.507038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.93473e9 | + | 3.35105e9i | 0.359343 | + | 0.622401i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.22803e8 | − | 1.59834e9i | −0.169420 | − | 0.293444i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.73499e9 | −0.496358 | −0.248179 | − | 0.968714i | \(-0.579832\pi\) | ||||
−0.248179 | + | 0.968714i | \(0.579832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.67969e9 | −0.480756 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.62404e9 | − | 9.74112e9i | −0.997479 | − | 1.72768i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.32909e8 | + | 4.03410e8i | 0.0408390 | + | 0.0707352i | 0.885722 | − | 0.464215i | \(-0.153664\pi\) |
−0.844883 | + | 0.534950i | \(0.820330\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.30332e8 | 0.0572647 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.09918e9 | − | 1.90383e9i | 0.188396 | − | 0.326311i | −0.756320 | − | 0.654202i | \(-0.773005\pi\) |
0.944715 | + | 0.327891i | \(0.106338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.05418e10 | 1.78647 | 0.893236 | − | 0.449587i | \(-0.148429\pi\) | ||||
0.893236 | + | 0.449587i | \(0.148429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.77651e8 | − | 1.34693e9i | 0.130306 | − | 0.225697i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.24251e9 | − | 5.61620e9i | 0.537246 | − | 0.930538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.45503e9 | − | 2.52018e9i | −0.238392 | − | 0.412907i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.94923e8 | + | 5.05287e8i | −0.128792 | + | 0.0818656i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.10773e8 | − | 1.91865e8i | −0.0177483 | − | 0.0307410i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.25684e9 | − | 9.10511e9i | 0.832955 | − | 1.44272i | −0.0627288 | − | 0.998031i | \(-0.519980\pi\) |
0.895684 | − | 0.444691i | \(-0.146686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.51630e9 | + | 2.62631e9i | −0.237615 | + | 0.411561i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.15187e9 | −0.178524 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.78777e9 | − | 8.29267e9i | 0.733915 | − | 1.27118i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.60492e9 | 1.30465 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.69373e9 | + | 2.93362e9i | 0.254004 | + | 0.439948i | 0.964624 | − | 0.263628i | \(-0.0849191\pi\) |
−0.710621 | + | 0.703575i | \(0.751586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.55153e9 | + | 2.68732e9i | 0.230155 | + | 0.398640i | 0.957854 | − | 0.287257i | \(-0.0927433\pi\) |
−0.727699 | + | 0.685897i | \(0.759410\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.53594e8 | 0.0372118 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.87239e8 | −0.0707257 | −0.0353628 | − | 0.999375i | \(-0.511259\pi\) | ||||
−0.0353628 | + | 0.999375i | \(0.511259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.45995e9 | − | 4.26075e9i | −0.353239 | − | 0.611828i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.28184e9 | − | 3.95226e9i | −0.324154 | − | 0.561451i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.15984e10 | 1.63005 | 0.815024 | − | 0.579427i | \(-0.196724\pi\) | ||||
0.815024 | + | 0.579427i | \(0.196724\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.57247e9 | + | 2.72359e9i | −0.218644 | + | 0.378702i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.19918e9 | −0.577678 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.16391e9 | + | 8.94416e9i | −0.702878 | + | 1.21742i | 0.264574 | + | 0.964365i | \(0.414769\pi\) |
−0.967452 | + | 0.253055i | \(0.918565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.26311e9 | − | 9.11597e9i | 0.708822 | − | 1.22772i | −0.256472 | − | 0.966552i | \(-0.582560\pi\) |
0.965294 | − | 0.261164i | \(-0.0841064\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.26013e8 | − | 2.18260e8i | −0.0167926 | − | 0.0290856i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.22796e9 | − | 2.68747e9i | 0.557513 | − | 0.354379i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.52381e9 | − | 2.63932e9i | −0.198834 | − | 0.344391i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.38107e9 | − | 2.39208e9i | 0.178330 | − | 0.308876i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.04029e9 | + | 1.80184e9i | −0.132931 | + | 0.230243i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.39297e9 | −0.555527 | −0.277764 | − | 0.960649i | \(-0.589593\pi\) | ||||
−0.277764 | + | 0.960649i | \(0.589593\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.02831e9 | − | 3.51314e9i | 0.253847 | − | 0.439676i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.03159e9 | −0.375500 | −0.187750 | − | 0.982217i | \(-0.560120\pi\) | ||||
−0.187750 | + | 0.982217i | \(0.560120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.12515e10 | + | 1.94881e10i | 1.37932 | + | 2.38905i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.18993e8 | − | 5.52512e8i | −0.0387049 | − | 0.0670389i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.40218e9 | −0.288492 | −0.144246 | − | 0.989542i | \(-0.546076\pi\) | ||||
−0.144246 | + | 0.989542i | \(0.546076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.16110e9 | 0.732389 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.43851e8 | + | 4.22362e8i | 0.0286930 | + | 0.0496977i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.01558e9 | − | 3.49109e9i | −0.234765 | − | 0.406624i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44559e10 | −1.66676 | −0.833378 | − | 0.552703i | \(-0.813596\pi\) | ||||
−0.833378 | + | 0.552703i | \(0.813596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.76825e9 | + | 4.79475e9i | −0.315965 | + | 0.547268i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.11855e9 | 0.126388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.68274e8 | + | 2.91458e8i | −0.0188235 | + | 0.0326033i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.22755e9 | + | 2.12617e9i | −0.135946 | + | 0.235466i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.07010e9 | + | 1.22458e10i | 0.775198 | + | 1.34268i | 0.934683 | + | 0.355482i | \(0.115683\pi\) |
−0.159485 | + | 0.987200i | \(0.550984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.49030e8 | + | 3.49488e9i | 0.0161782 | + | 0.379392i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.21107e9 | + | 2.09764e9i | 0.130169 | + | 0.225460i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.15640e10 | − | 2.00294e10i | 1.23066 | − | 2.13157i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.20648e9 | + | 1.42140e10i | −0.864759 | + | 1.49781i | 0.00252638 | + | 0.999997i | \(0.499196\pi\) |
−0.867286 | + | 0.497810i | \(0.834138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.79915e9 | 0.187726 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.59514e9 | − | 4.49492e9i | 0.268132 | − | 0.464418i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.12516e9 | 0.217430 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.92182e8 | + | 1.71851e9i | 0.100525 | + | 0.174115i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.85186e9 | − | 1.01357e10i | −0.587141 | − | 1.01696i | −0.994605 | − | 0.103737i | \(-0.966920\pi\) |
0.407463 | − | 0.913222i | \(-0.366413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.64338e10 | −2.62656 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.49200e9 | 0.638843 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.97449e9 | − | 6.88402e9i | −0.387345 | − | 0.670902i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.91258e9 | − | 8.50884e9i | −0.474176 | − | 0.821296i | 0.525387 | − | 0.850863i | \(-0.323920\pi\) |
−0.999563 | + | 0.0295671i | \(0.990587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.24078e9 | −0.405415 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.29183e8 | + | 2.23752e8i | −0.0122319 | + | 0.0211863i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.76094e9 | 0.727865 | 0.363932 | − | 0.931425i | \(-0.381434\pi\) | ||||
0.363932 | + | 0.931425i | \(0.381434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.03099e9 | + | 1.78573e9i | −0.0957745 | + | 0.165886i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.02783e9 | + | 3.51230e9i | −0.186593 | + | 0.323188i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.90874e9 | + | 1.19663e10i | 0.629714 | + | 1.09070i | 0.987609 | + | 0.156934i | \(0.0501611\pi\) |
−0.357896 | + | 0.933762i | \(0.616506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.69533e8 | + | 3.97569e9i | 0.0153070 | + | 0.358962i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.75066e9 | − | 1.34245e10i | −0.693231 | − | 1.20071i | −0.970773 | − | 0.239998i | \(-0.922853\pi\) |
0.277542 | − | 0.960713i | \(-0.410480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.02581e9 | − | 5.24085e9i | 0.268098 | − | 0.464360i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.54770e9 | + | 1.30730e10i | −0.662510 | + | 1.14750i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.37262e9 | 0.380238 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.96809e9 | − | 1.20691e10i | 0.600308 | − | 1.03976i | −0.392466 | − | 0.919766i | \(-0.628378\pi\) |
0.992774 | − | 0.119997i | \(-0.0382886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.56061e9 | −0.133203 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.45043e9 | + | 2.51221e9i | 0.122654 | + | 0.212443i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.93533e9 | + | 1.72085e10i | 0.832428 | + | 1.44181i | 0.896107 | + | 0.443837i | \(0.146383\pi\) |
−0.0636791 | + | 0.997970i | \(0.520283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.68210e8 | 0.0637726 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.10861e9 | −0.666961 | −0.333480 | − | 0.942757i | \(-0.608223\pi\) | ||||
−0.333480 | + | 0.942757i | \(0.608223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.05720e9 | + | 1.83112e9i | 0.0861630 | + | 0.149239i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.22417e8 | − | 3.85238e8i | −0.0179620 | − | 0.0311110i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.07849e10 | −1.66327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.21009e10 | + | 2.09594e10i | −0.959568 | + | 1.66202i | −0.236017 | + | 0.971749i | \(0.575842\pi\) |
−0.723551 | + | 0.690271i | \(0.757491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.87801e8 | −0.0147573 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.12978e10 | + | 1.95684e10i | −0.879763 | + | 1.52379i | −0.0281627 | + | 0.999603i | \(0.508966\pi\) |
−0.851601 | + | 0.524191i | \(0.824368\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.76879e9 | − | 1.17239e10i | 0.522342 | − | 0.904724i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.25425e9 | − | 2.17243e9i | −0.0959206 | − | 0.166139i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.48454e9 | − | 2.85056e9i | 0.339889 | − | 0.216048i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.50949e9 | + | 7.81067e9i | 0.338726 | + | 0.586691i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.98604e9 | − | 6.90402e9i | 0.296739 | − | 0.513968i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.81993e9 | − | 3.15221e9i | 0.134280 | − | 0.232579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.39366e10 | −1.01916 | −0.509582 | − | 0.860422i | \(-0.670200\pi\) | ||||
−0.509582 | + | 0.860422i | \(0.670200\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.79492e9 | + | 6.57300e9i | −0.275064 | + | 0.476424i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.67889e10 | −1.92459 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.39487e9 | + | 7.61214e9i | 0.312961 | + | 0.542064i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.34032e8 | + | 7.51766e8i | 0.0306364 | + | 0.0530637i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.99801e9 | −0.699535 | −0.349767 | − | 0.936837i | \(-0.613739\pi\) | ||||
−0.349767 | + | 0.936837i | \(0.613739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.46772e9 | −0.171152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.54592e9 | + | 7.87377e9i | 0.312542 | + | 0.541338i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.20062e9 | − | 3.81159e9i | −0.149983 | − | 0.259778i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.08588e9 | −0.276058 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.45937e9 | + | 4.25975e9i | −0.164727 | + | 0.285316i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.63818e10 | 1.08778 | 0.543892 | − | 0.839155i | \(-0.316950\pi\) | ||||
0.543892 | + | 0.839155i | \(0.316950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.38271e9 | − | 4.12697e9i | 0.156855 | − | 0.271681i | −0.776878 | − | 0.629651i | \(-0.783198\pi\) |
0.933733 | + | 0.357971i | \(0.116531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.51691e9 | − | 6.09146e9i | 0.229532 | − | 0.397562i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.56442e8 | − | 1.31020e9i | −0.0489468 | − | 0.0847783i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.44277e9 | − | 2.18837e9i | 0.220867 | − | 0.140392i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.16949e10 | + | 2.02562e10i | 0.743881 | + | 1.28844i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.12396e10 | − | 1.94676e10i | 0.708843 | − | 1.22775i | −0.256443 | − | 0.966559i | \(-0.582551\pi\) |
0.965286 | − | 0.261193i | \(-0.0841160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.56189e9 | + | 1.30976e10i | −0.472859 | + | 0.819015i | −0.999517 | − | 0.0310617i | \(-0.990111\pi\) |
0.526659 | + | 0.850077i | \(0.323444\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00369e9 | 0.124234 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.60761e10 | − | 2.78447e10i | 0.988353 | − | 1.71188i | 0.362385 | − | 0.932028i | \(-0.381962\pi\) |
0.625968 | − | 0.779849i | \(-0.284704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.77112e9 | 0.534705 | 0.267353 | − | 0.963599i | \(-0.413851\pi\) | ||||
0.267353 | + | 0.963599i | \(0.413851\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.33064e9 | + | 5.76884e9i | 0.201337 | + | 0.348726i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.05039e9 | − | 1.81933e9i | −0.0629642 | − | 0.109057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.76353e9 | −0.223714 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.35769e10 | 0.800317 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.19267e10 | − | 2.06577e10i | −0.697195 | − | 1.20758i | −0.969435 | − | 0.245347i | \(-0.921098\pi\) |
0.272241 | − | 0.962229i | \(-0.412235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.14276e8 | + | 1.41037e9i | 0.0472047 | + | 0.0817610i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.40288e8 | −0.0253128 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.07731e8 | − | 1.22583e9i | 0.0403525 | − | 0.0698925i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12905e10 | 1.20391 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.35565e9 | − | 2.34806e9i | 0.0760277 | − | 0.131684i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.42647e9 | − | 2.47071e9i | 0.0793429 | − | 0.137426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.70793e9 | + | 1.16185e10i | 0.370056 | + | 0.640955i | 0.989574 | − | 0.144027i | \(-0.0460053\pi\) |
−0.619518 | + | 0.784982i | \(0.712672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.99233e8 | + | 7.01724e9i | 0.0163730 | + | 0.383959i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.79764e9 | − | 1.35059e10i | −0.423185 | − | 0.732978i | 0.573064 | − | 0.819511i | \(-0.305755\pi\) |
−0.996249 | + | 0.0865326i | \(0.972421\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.76013e9 | − | 3.04863e9i | 0.0947475 | − | 0.164108i | −0.814756 | − | 0.579804i | \(-0.803129\pi\) |
0.909503 | + | 0.415697i | \(0.136462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.90531e9 | + | 3.30010e9i | −0.101732 | + | 0.176204i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.79917e10 | −0.952870 | −0.476435 | − | 0.879210i | \(-0.658071\pi\) | ||||
−0.476435 | + | 0.879210i | \(0.658071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.18455e7 | − | 7.24785e7i | 0.00219833 | − | 0.00380761i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.27252e9 | 0.326870 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.42864e8 | + | 1.63309e9i | 0.0487393 | + | 0.0844190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.56688e9 | + | 1.48383e10i | 0.439298 | + | 0.760886i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.15486e10 | −1.60483 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.37480e10 | −1.19839 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.47815e10 | − | 2.56023e10i | −0.739980 | − | 1.28168i | −0.952504 | − | 0.304527i | \(-0.901502\pi\) |
0.212524 | − | 0.977156i | \(-0.431832\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.27767e9 | + | 5.67710e9i | 0.162781 | + | 0.281945i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.49389e10 | 1.22874 | 0.614372 | − | 0.789016i | \(-0.289409\pi\) | ||||
0.614372 | + | 0.789016i | \(0.289409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.51697e8 | + | 1.30198e9i | −0.0367435 | + | 0.0636416i | −0.883812 | − | 0.467842i | \(-0.845032\pi\) |
0.847069 | + | 0.531483i | \(0.178365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.47578e9 | 0.217054 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.36244e10 | − | 2.35982e10i | 0.655519 | − | 1.13539i | −0.326245 | − | 0.945285i | \(-0.605783\pi\) |
0.981763 | − | 0.190107i | \(-0.0608834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.64385e9 | − | 1.15075e10i | 0.317149 | − | 0.549319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.34976e9 | − | 5.80196e9i | −0.158651 | − | 0.274791i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.45428e10 | + | 1.80265e10i | 1.62322 | + | 0.847092i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.05777e9 | − | 7.02826e9i | −0.189194 | − | 0.327693i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.62271e9 | − | 2.81062e9i | 0.0750703 | − | 0.130026i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.33020e10 | − | 2.30398e10i | 0.610603 | − | 1.05759i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.84398e8 | −0.0402820 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.46270e9 | + | 2.53348e9i | −0.0661073 | + | 0.114501i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.56693e7 | −0.000702717 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.83931e9 | − | 1.18460e10i | −0.304359 | − | 0.527166i | 0.672759 | − | 0.739862i | \(-0.265109\pi\) |
−0.977118 | + | 0.212696i | \(0.931776\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.62124e10 | + | 2.80807e10i | 0.715934 | + | 1.24003i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.39180e10 | 1.04812 | 0.524059 | − | 0.851682i | \(-0.324417\pi\) | ||||
0.524059 | + | 0.851682i | \(0.324417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.58218e10 | −0.688031 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.46386e8 | − | 1.63919e9i | −0.0408408 | − | 0.0707384i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.81396e10 | − | 3.14187e10i | −0.776847 | − | 1.34554i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.00107e10 | 1.27547 | 0.637737 | − | 0.770254i | \(-0.279871\pi\) | ||||
0.637737 | + | 0.770254i | \(0.279871\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.17479e9 | − | 7.23095e9i | 0.176086 | − | 0.304991i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.81021e10 | 1.59494 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.72059e9 | − | 6.44425e9i | 0.154567 | − | 0.267717i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.85298e10 | − | 3.20945e10i | 0.763997 | − | 1.32328i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.26478e10 | + | 2.19066e10i | 0.517559 | + | 0.896439i | 0.999792 | + | 0.0203955i | \(0.00649255\pi\) |
−0.482233 | + | 0.876043i | \(0.660174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.41316e9 | + | 3.31398e10i | 0.0573942 | + | 1.34594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.53528e8 | − | 4.39123e8i | −0.0102197 | − | 0.0177011i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.33120e8 | − | 4.03776e8i | 0.00932693 | − | 0.0161547i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.71637e9 | − | 4.70490e9i | 0.107870 | − | 0.186836i | −0.807037 | − | 0.590501i | \(-0.798930\pi\) |
0.914907 | + | 0.403664i | \(0.132264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.28197e10 | −0.505298 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.42404e10 | + | 2.46651e10i | −0.557132 | + | 0.964980i | 0.440603 | + | 0.897702i | \(0.354765\pi\) |
−0.997734 | + | 0.0672779i | \(0.978569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.33384e9 | −0.168299 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.34398e9 | − | 9.25605e9i | −0.205994 | − | 0.356791i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.86941e10 | − | 3.23791e10i | −0.715285 | − | 1.23891i | −0.962850 | − | 0.270039i | \(-0.912964\pi\) |
0.247565 | − | 0.968871i | \(-0.420370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.85938e10 | −0.706212 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.07445e10 | −0.405091 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.95647e9 | − | 1.72451e10i | −0.372632 | − | 0.645418i | 0.617338 | − | 0.786698i | \(-0.288211\pi\) |
−0.989970 | + | 0.141281i | \(0.954878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.06563e9 | − | 7.04189e9i | −0.151049 | − | 0.261624i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.93764e9 | 0.145226 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.55365e10 | + | 6.15511e10i | −1.30110 | + | 2.25357i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.77957e10 | 0.646818 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.06515e9 | + | 5.30900e9i | −0.110601 | + | 0.191567i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.03422e8 | − | 6.98748e8i | 0.0144515 | − | 0.0250308i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.79745e10 | − | 3.11328e10i | −0.639241 | − | 1.10720i | −0.985600 | − | 0.169096i | \(-0.945915\pi\) |
0.346358 | − | 0.938102i | \(-0.387418\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.73968e8 | + | 4.03903e8i | 0.0273269 | + | 0.0142608i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.09527e10 | + | 1.89706e10i | 0.383930 | + | 0.664987i | 0.991620 | − | 0.129187i | \(-0.0412369\pi\) |
−0.607690 | + | 0.794175i | \(0.707904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.45164e9 | + | 1.11746e10i | −0.224530 | + | 0.388898i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.23245e9 | − | 7.33081e9i | 0.146243 | − | 0.253300i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.41093e10 | −0.827091 | −0.413546 | − | 0.910483i | \(-0.635710\pi\) | ||||
−0.413546 | + | 0.910483i | \(0.635710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.76467e9 | + | 8.25265e9i | −0.162291 | + | 0.281096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.96433e9 | −0.100250 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.51995e10 | + | 4.36468e10i | 0.846163 | + | 1.46560i | 0.884607 | + | 0.466337i | \(0.154426\pi\) |
−0.0384442 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.69048e9 | + | 1.15883e10i | 0.223065 | + | 0.386359i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.79413e10 | −0.924989 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.32708e9 | −0.109364 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.46607e9 | + | 9.46751e9i | 0.178409 | + | 0.309014i | 0.941336 | − | 0.337471i | \(-0.109572\pi\) |
−0.762927 | + | 0.646485i | \(0.776238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.65101e8 | + | 8.05578e8i | 0.0150739 | + | 0.0261087i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.66688e9 | −0.118009 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.06226e9 | − | 1.22322e10i | 0.225689 | − | 0.390905i | −0.730837 | − | 0.682552i | \(-0.760870\pi\) |
0.956526 | + | 0.291647i | \(0.0942034\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.46279e9 | 0.236822 |
(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 | 76.8.e.a.45.7 | ✓ | 22 | |
19.11 | even | 3 | inner | 76.8.e.a.49.7 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.e.a.45.7 | ✓ | 22 | 1.1 | even | 1 | trivial | |
76.8.e.a.49.7 | yes | 22 | 19.11 | even | 3 | inner |