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 | 49.3 | ||
Character | \(\chi\) | \(=\) | 76.49 |
Dual form | 76.8.e.a.45.3 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −22.8105 | + | 39.5090i | −0.487765 | + | 0.844834i | −0.999901 | − | 0.0140703i | \(-0.995521\pi\) |
0.512136 | + | 0.858905i | \(0.328854\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 216.474 | − | 374.944i | 0.774481 | − | 1.34144i | −0.160604 | − | 0.987019i | \(-0.551344\pi\) |
0.935086 | − | 0.354422i | \(-0.115322\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −508.391 | −0.560215 | −0.280108 | − | 0.959969i | \(-0.590370\pi\) | ||||
−0.280108 | + | 0.959969i | \(0.590370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 52.8600 | + | 91.5562i | 0.0241701 | + | 0.0418638i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1596.64 | −0.361687 | −0.180843 | − | 0.983512i | \(-0.557883\pi\) | ||||
−0.180843 | + | 0.983512i | \(0.557883\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1340.66 | + | 2322.09i | 0.169245 | + | 0.293141i | 0.938155 | − | 0.346216i | \(-0.112534\pi\) |
−0.768909 | + | 0.639358i | \(0.779200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9875.77 | + | 17105.3i | 0.755530 | + | 1.30862i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3266.04 | + | 5656.95i | −0.161232 | + | 0.279262i | −0.935311 | − | 0.353827i | \(-0.884880\pi\) |
0.774079 | + | 0.633089i | \(0.218213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17595.4 | + | 24171.7i | −0.588522 | + | 0.808482i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11596.7 | − | 20086.0i | 0.273253 | − | 0.473289i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10247.4 | − | 17749.1i | −0.175618 | − | 0.304179i | 0.764757 | − | 0.644319i | \(-0.222859\pi\) |
−0.940375 | + | 0.340140i | \(0.889526\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −54659.5 | − | 94673.1i | −0.699642 | − | 1.21182i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −104596. | −1.02269 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −98589.9 | − | 170763.i | −0.750653 | − | 1.30017i | −0.947506 | − | 0.319737i | \(-0.896406\pi\) |
0.196853 | − | 0.980433i | \(-0.436928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −256272. | −1.54502 | −0.772511 | − | 0.635002i | \(-0.780999\pi\) | ||||
−0.772511 | + | 0.635002i | \(0.780999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 36420.2 | − | 63081.6i | 0.176418 | − | 0.305565i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −110053. | + | 190618.i | −0.433876 | + | 0.751495i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 157659. | 0.511698 | 0.255849 | − | 0.966717i | \(-0.417645\pi\) | ||||
0.255849 | + | 0.966717i | \(0.417645\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −122324. | −0.330208 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −85374.6 | + | 147873.i | −0.193457 | + | 0.335078i | −0.946394 | − | 0.323015i | \(-0.895303\pi\) |
0.752936 | + | 0.658093i | \(0.228637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −473770. | + | 820594.i | −0.908716 | + | 1.57394i | −0.0928664 | + | 0.995679i | \(0.529603\pi\) |
−0.815850 | + | 0.578264i | \(0.803730\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45771.3 | 0.0748771 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −164204. | − | 284410.i | −0.230697 | − | 0.399579i | 0.727317 | − | 0.686302i | \(-0.240767\pi\) |
−0.958013 | + | 0.286724i | \(0.907434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −565082. | −0.686159 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −149000. | − | 258076.i | −0.157287 | − | 0.272428i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −558053. | − | 966577.i | −0.514885 | − | 0.891807i | −0.999851 | − | 0.0172737i | \(-0.994501\pi\) |
0.484966 | − | 0.874533i | \(-0.338832\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −345631. | + | 598651.i | −0.280120 | + | 0.485181i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −553639. | − | 1.24655e6i | −0.395972 | − | 0.891552i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 333278. | − | 577255.i | 0.211264 | − | 0.365920i | −0.740847 | − | 0.671674i | \(-0.765575\pi\) |
0.952110 | + | 0.305755i | \(0.0989088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 617751. | + | 1.06998e6i | 0.348465 | + | 0.603558i | 0.985977 | − | 0.166882i | \(-0.0533698\pi\) |
−0.637512 | + | 0.770440i | \(0.720036\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −26873.6 | − | 46546.4i | −0.0135405 | − | 0.0234528i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.16087e6 | 0.524309 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −94447.0 | − | 163587.i | −0.0383642 | − | 0.0664488i | 0.846206 | − | 0.532856i | \(-0.178881\pi\) |
−0.884570 | + | 0.466408i | \(0.845548\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 934998. | 0.342641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 677843. | − | 1.17406e6i | 0.224763 | − | 0.389301i | −0.731485 | − | 0.681857i | \(-0.761173\pi\) |
0.956248 | + | 0.292556i | \(0.0945058\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.42377e6 | + | 2.46604e6i | −0.428361 | + | 0.741942i | −0.996728 | − | 0.0808329i | \(-0.974242\pi\) |
0.568367 | + | 0.822775i | \(0.307575\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.98725e6 | 1.36504 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 811717. | 0.202622 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34677e6 | + | 4.06472e6i | −0.535519 | + | 0.927546i | 0.463619 | + | 0.886035i | \(0.346551\pi\) |
−0.999138 | + | 0.0415116i | \(0.986783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.27029e6 | − | 3.93226e6i | 0.474662 | − | 0.822138i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.12538e6 | 0.408002 | 0.204001 | − | 0.978971i | \(-0.434605\pi\) | ||||
0.204001 | + | 0.978971i | \(0.434605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41403e6 | + | 2.44917e6i | 0.249742 | + | 0.432566i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.99555e6 | 1.46457 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.16036e6 | − | 3.74186e6i | −0.324834 | − | 0.562629i | 0.656645 | − | 0.754200i | \(-0.271975\pi\) |
−0.981479 | + | 0.191571i | \(0.938642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −681579. | − | 1.18053e6i | −0.0948137 | − | 0.164222i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.84569e6 | − | 1.01250e7i | 0.753608 | − | 1.30529i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.25409e6 | + | 1.18299e7i | 0.628731 | + | 1.41562i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.40154e6 | + | 9.35575e6i | −0.600920 | + | 1.04082i | 0.391762 | + | 0.920067i | \(0.371866\pi\) |
−0.992682 | + | 0.120757i | \(0.961468\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −84398.4 | − | 146182.i | −0.00874200 | − | 0.0151416i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.81849e6 | + | 1.18100e7i | 0.658512 | + | 1.14058i | 0.981001 | + | 0.194002i | \(0.0621470\pi\) |
−0.322489 | + | 0.946573i | \(0.604520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.04217e6 | 0.635004 | 0.317502 | − | 0.948258i | \(-0.397156\pi\) | ||||
0.317502 | + | 0.948258i | \(0.397156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.02075e6 | − | 8.69620e6i | −0.423259 | − | 0.733107i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.52313e6 | −0.514770 | −0.257385 | − | 0.966309i | \(-0.582861\pi\) | ||||
−0.257385 | + | 0.966309i | \(0.582861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.68667e6 | − | 1.33137e7i | 0.568519 | − | 0.984704i | −0.428193 | − | 0.903687i | \(-0.640850\pi\) |
0.996713 | − | 0.0810173i | \(-0.0258169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.59629e6 | + | 6.22896e6i | −0.249589 | + | 0.432300i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.27249e6 | −0.278552 | −0.139276 | − | 0.990254i | \(-0.544478\pi\) | ||||
−0.139276 | + | 0.990254i | \(0.544478\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.87322e6 | −0.544050 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −141734. | + | 245491.i | −0.00818135 | + | 0.0141705i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.66043e6 | − | 2.87594e6i | 0.0903245 | − | 0.156447i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.69379e7 | −0.869183 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.89488e6 | − | 6.74613e6i | −0.188724 | − | 0.326879i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.35054e7 | −0.618476 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.41761e6 | − | 1.63118e7i | −0.407970 | − | 0.706624i | 0.586692 | − | 0.809810i | \(-0.300430\pi\) |
−0.994662 | + | 0.103186i | \(0.967096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.16139e7 | − | 3.74364e7i | −0.886480 | − | 1.53543i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59599e6 | − | 4.49639e6i | 0.100891 | − | 0.174749i | −0.811161 | − | 0.584823i | \(-0.801164\pi\) |
0.912052 | + | 0.410074i | \(0.134497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.94536e6 | − | 1.22887e7i | 0.329699 | − | 0.452924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.26424e7 | + | 3.92178e7i | −0.792052 | + | 1.37188i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −884376. | − | 1.53178e6i | −0.0293843 | − | 0.0508951i | 0.850959 | − | 0.525232i | \(-0.176021\pi\) |
−0.880344 | + | 0.474337i | \(0.842688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.85331e7 | + | 3.21003e7i | 0.585325 | + | 1.01381i | 0.994835 | + | 0.101507i | \(0.0323663\pi\) |
−0.409510 | + | 0.912306i | \(0.634300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.49823e7 | 0.450104 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.14055e6 | − | 3.70754e6i | −0.0612137 | − | 0.106025i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.53686e7 | −2.32547 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.28898e7 | − | 2.23258e7i | 0.334685 | − | 0.579691i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.95922e7 | + | 6.85756e7i | −0.980522 | + | 1.69831i | −0.320165 | + | 0.947362i | \(0.603739\pi\) |
−0.660357 | + | 0.750952i | \(0.729595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67510e7 | 1.34139 | 0.670693 | − | 0.741735i | \(-0.265997\pi\) | ||||
0.670693 | + | 0.741735i | \(0.265997\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −690572. | −0.0155880 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.54761e7 | + | 9.60875e7i | −1.19659 | + | 2.07255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.71518e7 | − | 4.70283e7i | 0.559951 | − | 0.969863i | −0.437549 | − | 0.899195i | \(-0.644153\pi\) |
0.997500 | − | 0.0706688i | \(-0.0225134\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.09179e7 | 1.00457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.20971e6 | + | 9.02348e6i | 0.0983836 | + | 0.170405i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.15429e7 | 0.208765 | 0.104383 | − | 0.994537i | \(-0.466713\pi\) | ||||
0.104383 | + | 0.994537i | \(0.466713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.57681e7 | − | 2.73111e7i | −0.273265 | − | 0.473309i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.94834e7 | − | 5.10668e7i | −0.489858 | − | 0.848459i | 0.510074 | − | 0.860131i | \(-0.329618\pi\) |
−0.999932 | + | 0.0116716i | \(0.996285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.77795e7 | − | 4.81156e7i | 0.442712 | − | 0.766800i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.14317e6 | − | 333254.i | −0.0480708 | − | 0.00509669i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.77863e7 | − | 4.81272e7i | 0.408008 | − | 0.706691i | −0.586658 | − | 0.809835i | \(-0.699557\pi\) |
0.994666 | + | 0.103144i | \(0.0328902\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.77884e7 | + | 4.81310e7i | 0.391950 | + | 0.678877i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.52045e7 | + | 2.63350e7i | 0.206094 | + | 0.356966i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.88613e7 | −0.636766 | −0.318383 | − | 0.947962i | \(-0.603140\pi\) | ||||
−0.318383 | + | 0.947962i | \(0.603140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.92377e7 | − | 1.19923e8i | −0.867896 | − | 1.50324i | −0.864142 | − | 0.503247i | \(-0.832138\pi\) |
−0.00375381 | − | 0.999993i | \(-0.501195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.63649e7 | −0.679876 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.41292e7 | − | 5.91135e7i | 0.396301 | − | 0.686413i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.21469e6 | − | 9.03211e6i | 0.0583154 | − | 0.101005i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.31758e7 | 0.572925 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.68538e8 | 1.75017 | 0.875085 | − | 0.483970i | \(-0.160806\pi\) | ||||
0.875085 | + | 0.483970i | \(0.160806\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.68747e6 | + | 8.11893e6i | −0.0469340 | + | 0.0812921i | −0.888538 | − | 0.458803i | \(-0.848278\pi\) |
0.841604 | + | 0.540095i | \(0.181612\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.64801e7 | + | 4.58648e7i | −0.255740 | + | 0.442954i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.60473e7 | 0.895062 | 0.447531 | − | 0.894268i | \(-0.352303\pi\) | ||||
0.447531 | + | 0.894268i | \(0.352303\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.88987e7 | + | 1.02015e8i | 0.529809 | + | 0.917657i | 0.999395 | + | 0.0347699i | \(0.0110698\pi\) |
−0.469586 | + | 0.882887i | \(0.655597\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.61754e6 | 0.0748510 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.01222e7 | + | 8.68142e7i | 0.420527 | + | 0.728375i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.69628e7 | + | 6.40214e7i | 0.299658 | + | 0.519023i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.08336e6 | − | 1.87643e6i | 0.00848939 | − | 0.0147041i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.80936e7 | − | 3.85935e7i | 0.212860 | − | 0.292417i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.02590e7 | + | 5.24102e7i | −0.221751 | + | 0.384085i | −0.955340 | − | 0.295509i | \(-0.904511\pi\) |
0.733589 | + | 0.679594i | \(0.237844\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.09239e7 | + | 5.35618e7i | 0.219263 | + | 0.379775i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.05118e8 | + | 3.55275e8i | 1.40757 | + | 2.43798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.30286e8 | 0.865544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.49538e7 | − | 1.12503e8i | −0.417879 | − | 0.723787i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.75146e7 | −0.109151 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.12008e8 | − | 1.94004e8i | 0.676368 | − | 1.17150i | −0.299698 | − | 0.954034i | \(-0.596886\pi\) |
0.976067 | − | 0.217471i | \(-0.0697806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.77861e6 | − | 1.00088e7i | 0.0338208 | − | 0.0585794i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.57027e8 | −0.891011 | −0.445506 | − | 0.895279i | \(-0.646976\pi\) | ||||
−0.445506 | + | 0.895279i | \(0.646976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.45255e8 | −0.799295 | −0.399648 | − | 0.916669i | \(-0.630867\pi\) | ||||
−0.399648 | + | 0.916669i | \(0.630867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.85157e7 | + | 3.20701e7i | −0.0988321 | + | 0.171182i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.48486e8 | − | 2.57185e8i | 0.769022 | − | 1.33199i | −0.169072 | − | 0.985604i | \(-0.554077\pi\) |
0.938094 | − | 0.346381i | \(-0.112590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.42184e8 | −0.714681 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.07062e8 | − | 1.85437e8i | −0.522415 | − | 0.904850i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.66836e7 | −0.458100 | −0.229050 | − | 0.973415i | \(-0.573562\pi\) | ||||
−0.229050 | + | 0.973415i | \(0.573562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.16188e7 | − | 1.06727e8i | −0.283566 | − | 0.491150i | 0.688695 | − | 0.725051i | \(-0.258184\pi\) |
−0.972260 | + | 0.233901i | \(0.924851\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.08030e7 | − | 1.87113e7i | −0.0482971 | − | 0.0836531i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.22325e8 | + | 2.11874e8i | −0.531417 | + | 0.920442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.97184e7 | − | 8.45212e6i | −0.336604 | − | 0.0356883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.84810e7 | + | 8.39715e7i | −0.199009 | + | 0.344694i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.05608e7 | − | 1.56856e8i | −0.361478 | − | 0.626098i | 0.626726 | − | 0.779240i | \(-0.284394\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.63615e7 | + | 2.83389e7i | 0.0635185 | + | 0.110017i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.29019e8 | −0.487262 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.70493e7 | + | 9.88122e7i | 0.209645 | + | 0.363115i | 0.951603 | − | 0.307331i | \(-0.0994359\pi\) |
−0.741958 | + | 0.670447i | \(0.766103\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.01526e7 | −0.286661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.04229e7 | − | 1.80530e7i | 0.0362867 | − | 0.0628505i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.80357e8 | − | 4.85593e8i | 0.950313 | − | 1.64599i | 0.205565 | − | 0.978643i | \(-0.434097\pi\) |
0.744748 | − | 0.667346i | \(-0.232570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.83216e8 | −1.59507 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.97116e8 | 0.633771 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.68775e8 | + | 4.65532e8i | −0.841891 | + | 1.45820i | 0.0464022 | + | 0.998923i | \(0.485224\pi\) |
−0.888294 | + | 0.459276i | \(0.848109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.01239e8 | − | 1.75351e8i | 0.308998 | − | 0.535200i | −0.669146 | − | 0.743131i | \(-0.733340\pi\) |
0.978143 | + | 0.207932i | \(0.0666732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.21887e7 | 0.184987 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.72716e7 | + | 1.51159e8i | 0.253051 | + | 0.438298i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.94618e8 | −1.68097 | −0.840483 | − | 0.541837i | \(-0.817729\pi\) | ||||
−0.840483 | + | 0.541837i | \(0.817729\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.35465e7 | − | 2.34633e7i | −0.0373433 | − | 0.0646805i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.19191e8 | + | 5.52855e8i | 0.858180 | + | 1.48641i | 0.873663 | + | 0.486531i | \(0.161738\pi\) |
−0.0154832 | + | 0.999880i | \(0.504929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.17486e7 | + | 5.49902e7i | −0.0832669 | + | 0.144222i | −0.904651 | − | 0.426152i | \(-0.859869\pi\) |
0.821384 | + | 0.570375i | \(0.193202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.87234e8 | − | 6.22614e7i | −1.50264 | − | 0.159317i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.34037e7 | − | 7.51774e7i | 0.108378 | − | 0.187716i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.83835e8 | + | 3.18412e8i | 0.448009 | + | 0.775974i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.46424e8 | − | 4.26819e8i | −0.586216 | − | 1.01536i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.09497e6 | −0.00486565 | −0.00243282 | − | 0.999997i | \(-0.500774\pi\) | ||||
−0.00243282 | + | 0.999997i | \(0.500774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44292e8 | − | 2.49921e8i | −0.327240 | − | 0.566796i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.67003e8 | 0.369893 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.74766e7 | − | 4.75909e7i | 0.0594449 | − | 0.102962i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.40861e8 | − | 4.17183e8i | 0.509076 | − | 0.881746i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.22133e8 | −1.28480 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.34908e8 | 1.07952 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.62337e8 | − | 4.54382e8i | 0.517459 | − | 0.896265i | −0.482335 | − | 0.875987i | \(-0.660211\pi\) |
0.999794 | − | 0.0202788i | \(-0.00645538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.60636e8 | + | 2.78229e8i | −0.309733 | + | 0.536473i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.39369e8 | −0.828262 | −0.414131 | − | 0.910217i | \(-0.635914\pi\) | ||||
−0.414131 | + | 0.910217i | \(0.635914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.84522e8 | + | 3.19602e8i | 0.340129 | + | 0.589121i | 0.984456 | − | 0.175629i | \(-0.0561960\pi\) |
−0.644328 | + | 0.764750i | \(0.722863\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.32697e7 | −0.0419473 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.22049e8 | + | 9.04216e8i | 0.920458 | + | 1.59428i | 0.798708 | + | 0.601719i | \(0.205517\pi\) |
0.121750 | + | 0.992561i | \(0.461149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.57413e8 | + | 2.72646e8i | 0.271501 | + | 0.470254i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.48796e8 | − | 2.57722e8i | 0.251087 | − | 0.434895i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.92709e7 | − | 1.78482e8i | −0.130889 | − | 0.294704i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46560e8 | − | 2.53849e8i | 0.236822 | − | 0.410188i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.50674e8 | + | 6.07385e8i | 0.554608 | + | 0.960609i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.34799e7 | + | 1.44591e8i | 0.129240 | + | 0.223850i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.40389e8 | 0.515915 | 0.257957 | − | 0.966156i | \(-0.416951\pi\) | ||||
0.257957 | + | 0.966156i | \(0.416951\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.33388e6 | + | 1.44347e7i | 0.0123678 | + | 0.0214217i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.17813e7 | −0.118849 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.65079e8 | − | 8.05540e8i | 0.661945 | − | 1.14652i | −0.318159 | − | 0.948037i | \(-0.603065\pi\) |
0.980104 | − | 0.198485i | \(-0.0636021\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.74577e7 | − | 1.68802e8i | 0.135868 | − | 0.235330i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.09173e8 | 0.558814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.05964e8 | 0.944612 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.02403e8 | − | 3.50572e8i | 0.265369 | − | 0.459632i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.71576e8 | + | 6.43589e8i | −0.477414 | + | 0.826905i | −0.999665 | − | 0.0258867i | \(-0.991759\pi\) |
0.522251 | + | 0.852792i | \(0.325092\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.17401e8 | −0.273762 | −0.136881 | − | 0.990588i | \(-0.543708\pi\) | ||||
−0.136881 | + | 0.990588i | \(0.543708\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.40228e8 | − | 2.42882e8i | −0.173085 | − | 0.299792i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.44846e8 | 0.538267 | 0.269134 | − | 0.963103i | \(-0.413263\pi\) | ||||
0.269134 | + | 0.963103i | \(0.413263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.93471e8 | − | 5.08307e8i | −0.348150 | − | 0.603013i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.57504e7 | + | 1.31204e8i | 0.0881143 | + | 0.152618i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.51367e8 | + | 9.54995e8i | −0.628941 | + | 1.08936i | 0.358824 | + | 0.933405i | \(0.383178\pi\) |
−0.987765 | + | 0.155952i | \(0.950155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.74673e8 | − | 8.50624e8i | −0.307285 | − | 0.951618i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.86363e8 | − | 6.69200e8i | 0.423957 | − | 0.734315i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.16418e8 | + | 1.06767e9i | 0.663514 | + | 1.14924i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.26617e8 | − | 9.12127e8i | −0.556113 | − | 0.963217i | −0.997816 | − | 0.0660551i | \(-0.978959\pi\) |
0.441703 | − | 0.897162i | \(-0.354375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.80516e7 | −0.0187035 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.83709e8 | + | 4.91399e8i | 0.288446 | + | 0.499604i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.77179e8 | 0.675652 | 0.337826 | − | 0.941209i | \(-0.390309\pi\) | ||||
0.337826 | + | 0.941209i | \(0.390309\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.08066e8 | − | 5.33585e8i | 0.301671 | − | 0.522510i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.64351e8 | − | 4.57869e8i | 0.254089 | − | 0.440095i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.35547e8 | −0.694022 | −0.347011 | − | 0.937861i | \(-0.612803\pi\) | ||||
−0.347011 | + | 0.937861i | \(0.612803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.59283e8 | 0.795974 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.35670e8 | + | 2.34988e8i | −0.123393 | + | 0.213722i | −0.921104 | − | 0.389318i | \(-0.872711\pi\) |
0.797711 | + | 0.603040i | \(0.206044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.75716e8 | − | 3.04349e8i | 0.156927 | − | 0.271806i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.00174e8 | −0.0878550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.60630e8 | + | 2.78220e8i | 0.138358 | + | 0.239643i | 0.926875 | − | 0.375370i | \(-0.122484\pi\) |
−0.788517 | + | 0.615012i | \(0.789151\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.33874e8 | 0.113261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.18432e8 | + | 2.05130e8i | 0.0984225 | + | 0.170473i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.01603e9 | + | 1.75981e9i | 0.829499 | + | 1.43673i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.95681e8 | + | 5.12135e8i | −0.237169 | + | 0.410788i | −0.959901 | − | 0.280340i | \(-0.909553\pi\) |
0.722732 | + | 0.691128i | \(0.242886\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.81465e8 | + | 6.33734e8i | 0.221830 | + | 0.499461i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.43066e8 | + | 1.46023e9i | −0.652915 | + | 1.13088i | 0.329498 | + | 0.944156i | \(0.393121\pi\) |
−0.982412 | + | 0.186725i | \(0.940213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.43573e8 | − | 5.95085e8i | −0.261487 | − | 0.452910i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.82918e8 | − | 1.70246e9i | −0.735233 | − | 1.27346i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.51725e8 | −0.185074 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.10054e9 | + | 1.90619e9i | 0.795380 | + | 1.37764i | 0.922598 | + | 0.385763i | \(0.126062\pi\) |
−0.127218 | + | 0.991875i | \(0.540605\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.06923e7 | 0.0573305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.69436e8 | + | 2.93471e8i | −0.118353 | + | 0.204994i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.60089e8 | − | 7.96897e8i | 0.315990 | − | 0.547311i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.69100e9 | −1.14200 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.51296e9 | −1.66892 | −0.834462 | − | 0.551065i | \(-0.814222\pi\) | ||||
−0.834462 | + | 0.551065i | \(0.814222\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.33314e9 | + | 2.30906e9i | −0.870737 | + | 1.50816i | −0.00950083 | + | 0.999955i | \(0.503024\pi\) |
−0.861236 | + | 0.508205i | \(0.830309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.73597e7 | − | 3.00678e7i | 0.0111519 | − | 0.0193157i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.14081e8 | 0.451218 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.14059e8 | − | 5.43966e8i | −0.195215 | − | 0.338123i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.95308e8 | 0.119432 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.35965e9 | − | 2.35499e9i | −0.818009 | − | 1.41683i | −0.907147 | − | 0.420813i | \(-0.861745\pi\) |
0.0891387 | − | 0.996019i | \(-0.471589\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.39158e9 | − | 2.41028e9i | −0.823759 | − | 1.42679i | −0.902864 | − | 0.429925i | \(-0.858540\pi\) |
0.0791059 | − | 0.996866i | \(-0.474793\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.94730e9 | − | 3.37283e9i | 1.13428 | − | 1.96463i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.09334e8 | + | 6.46045e7i | 0.349278 | + | 0.0370321i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.87000e8 | + | 4.97098e8i | −0.161903 | + | 0.280425i | −0.935551 | − | 0.353191i | \(-0.885097\pi\) |
0.773648 | + | 0.633616i | \(0.218430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.98702e7 | − | 5.17367e7i | −0.0165845 | − | 0.0287253i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.15965e9 | + | 2.00857e9i | 0.633742 | + | 1.09767i | 0.986780 | + | 0.162064i | \(0.0518151\pi\) |
−0.353039 | + | 0.935609i | \(0.614852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.87065e9 | −1.00631 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.80624e9 | − | 3.12849e9i | −0.956529 | − | 1.65676i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.57267e8 | −0.186265 | −0.0931325 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931325 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.36313e8 | − | 2.36100e8i | 0.0699710 | − | 0.121193i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.29452e9 | + | 2.24217e9i | −0.654282 | + | 1.13325i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.90176e8 | −0.293726 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.95976e9 | −1.45061 | −0.725303 | − | 0.688430i | \(-0.758300\pi\) | ||||
−0.725303 | + | 0.688430i | \(0.758300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.41616e8 | − | 5.91696e8i | 0.164890 | − | 0.285597i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.24003e6 | + | 7.34394e6i | −0.00201565 | + | 0.00349121i | −0.867031 | − | 0.498253i | \(-0.833975\pi\) |
0.865016 | + | 0.501745i | \(0.167308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.78532e9 | −1.30419 | −0.652096 | − | 0.758136i | \(-0.726110\pi\) | ||||
−0.652096 | + | 0.758136i | \(0.726110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.53088e9 | − | 4.38361e9i | −1.16731 | − | 2.02184i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.44386e9 | 1.56472 | 0.782359 | − | 0.622828i | \(-0.214016\pi\) | ||||
0.782359 | + | 0.622828i | \(0.214016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.80160e7 | + | 8.31662e7i | 0.0214922 | + | 0.0372256i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.23869e9 | + | 2.14548e9i | 0.546249 | + | 0.946131i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.56440e8 | − | 1.31019e9i | 0.328671 | − | 0.569274i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.25017e9 | + | 3.44599e8i | 1.39149 | + | 0.147532i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.89974e7 | − | 1.02186e8i | 0.0248896 | − | 0.0431101i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.10040e8 | + | 1.57624e9i | 0.378344 | + | 0.655310i | 0.990821 | − | 0.135177i | \(-0.0431605\pi\) |
−0.612478 | + | 0.790488i | \(0.709827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.11367e8 | + | 3.66099e8i | 0.0866025 | + | 0.150000i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.75345e8 | −0.191952 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.33859e9 | + | 4.05055e9i | 0.930803 | + | 1.61220i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.44141e9 | −0.957832 | −0.478916 | − | 0.877861i | \(-0.658970\pi\) | ||||
−0.478916 | + | 0.877861i | \(0.658970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.63299e8 | + | 4.56048e8i | −0.101828 | + | 0.176372i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.42574e9 | + | 2.46945e9i | −0.543568 | + | 0.941487i | 0.455128 | + | 0.890426i | \(0.349594\pi\) |
−0.998696 | + | 0.0510611i | \(0.983740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.28800e9 | 0.484117 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.30802e7 | −0.0270821 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.44609e8 | + | 5.96881e8i | −0.125916 | + | 0.218092i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46068e9 | + | 4.26202e9i | −0.886548 | + | 1.53555i | −0.0426198 | + | 0.999091i | \(0.513570\pi\) |
−0.843929 | + | 0.536456i | \(0.819763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.69013e9 | 0.955743 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.28043e8 | + | 9.14597e8i | 0.185004 | + | 0.320436i | 0.943578 | − | 0.331151i | \(-0.107437\pi\) |
−0.758574 | + | 0.651587i | \(0.774104\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.90410e9 | 2.04002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.26733e9 | + | 2.19508e9i | 0.431879 | + | 0.748037i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.23055e9 | − | 2.13137e9i | −0.413605 | − | 0.716384i | 0.581676 | − | 0.813420i | \(-0.302397\pi\) |
−0.995281 | + | 0.0970361i | \(0.969064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.23831e8 | − | 1.25371e9i | 0.239974 | − | 0.415647i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.84042e9 | − | 2.52827e9i | 0.601874 | − | 0.826824i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.52445e9 | − | 2.64042e9i | 0.491798 | − | 0.851820i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.62175e8 | + | 4.54100e8i | 0.0834400 | + | 0.144522i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.26764e9 | + | 2.19561e9i | 0.398024 | + | 0.689398i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.34701e8 | −0.227603 | −0.113802 | − | 0.993503i | \(-0.536303\pi\) | ||||
−0.113802 | + | 0.993503i | \(0.536303\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.36595e8 | + | 1.62223e9i | 0.286283 | + | 0.495857i | 0.972920 | − | 0.231144i | \(-0.0742468\pi\) |
−0.686636 | + | 0.727001i | \(0.740913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.53547e9 | −0.764718 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.36994e8 | − | 1.44972e9i | 0.249106 | − | 0.431465i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.49239e9 | − | 2.58490e9i | 0.438317 | − | 0.759187i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.04684e7 | 0.0204251 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.57833e8 | −0.130967 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.41209e9 | + | 2.44581e9i | −0.398680 | + | 0.690533i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.11455e9 | − | 1.93046e9i | 0.310592 | − | 0.537962i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.02232e8 | 0.248175 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.89905e9 | − | 3.28924e9i | −0.515638 | − | 0.893111i | −0.999835 | − | 0.0181523i | \(-0.994222\pi\) |
0.484197 | − | 0.874959i | \(-0.339112\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.31740e9 | 1.69332 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.32793e9 | − | 5.76414e9i | −0.880615 | − | 1.52527i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.74777e7 | + | 1.51516e8i | 0.0228529 | + | 0.0395824i | 0.877226 | − | 0.480078i | \(-0.159392\pi\) |
−0.854373 | + | 0.519661i | \(0.826058\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.53086e7 | + | 1.13118e8i | −0.0168449 | + | 0.0291761i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.86236e9 | + | 6.21556e8i | 1.49294 | + | 0.158289i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.19307e9 | − | 2.06647e9i | 0.300006 | − | 0.519625i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.55701e9 | + | 2.69682e9i | 0.386603 | + | 0.669617i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.29497e9 | − | 5.70705e9i | −0.807901 | − | 1.39932i | −0.914315 | − | 0.405003i | \(-0.867270\pi\) |
0.106415 | − | 0.994322i | \(-0.466063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.54066e9 | −0.615183 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.37900e8 | + | 4.12054e8i | 0.0568884 | + | 0.0985337i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.78616e9 | −1.13034 | −0.565169 | − | 0.824975i | \(-0.691189\pi\) | ||||
−0.565169 | + | 0.824975i | \(0.691189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.24883e8 | + | 1.60194e9i | −0.215733 | + | 0.373661i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.15420e9 | + | 1.99913e9i | −0.265913 | + | 0.460574i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.39881e9 | 1.45615 | 0.728076 | − | 0.685497i | \(-0.240415\pi\) | ||||
0.728076 | + | 0.685497i | \(0.240415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.98904e9 | −0.447113 | −0.223557 | − | 0.974691i | \(-0.571767\pi\) | ||||
−0.223557 | + | 0.974691i | \(0.571767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.84443e9 | + | 6.65875e9i | −0.853672 | + | 1.47860i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.12024e9 | + | 1.94031e9i | −0.245739 | + | 0.425632i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.46742e9 | 1.83500 | 0.917500 | − | 0.397736i | \(-0.130204\pi\) | ||||
0.917500 | + | 0.397736i | \(0.130204\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.13847e8 | − | 3.70394e8i | −0.0457856 | − | 0.0793029i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.08052e9 | −0.228569 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.91010e8 | + | 1.54327e9i | 0.186227 | + | 0.322555i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.13637e7 | + | 1.06285e8i | 0.0126726 | + | 0.0219496i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.39477e9 | − | 5.87991e9i | 0.692750 | − | 1.19988i | −0.278183 | − | 0.960528i | \(-0.589732\pi\) |
0.970933 | − | 0.239351i | \(-0.0769346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.50921e9 | − | 6.19453e9i | 0.909278 | − | 1.24912i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.19089e9 | + | 3.79473e9i | −0.436580 | + | 0.756179i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.01807e9 | + | 6.95951e9i | 0.791273 | + | 1.37053i | 0.925179 | + | 0.379531i | \(0.123915\pi\) |
−0.133906 | + | 0.990994i | \(0.542752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.18879e8 | − | 1.24513e9i | −0.139909 | − | 0.242330i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.37404e9 | −1.03369 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.84947e9 | + | 3.20338e9i | 0.351604 | + | 0.608996i | 0.986531 | − | 0.163576i | \(-0.0523030\pi\) |
−0.634927 | + | 0.772572i | \(0.718970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.34787e9 | 0.253272 | 0.126636 | − | 0.991949i | \(-0.459582\pi\) | ||||
0.126636 | + | 0.991949i | \(0.459582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.98494e6 | − | 1.72944e7i | 0.00185453 | − | 0.00321215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.66662e9 | + | 6.35077e9i | −0.673166 | + | 1.16596i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.39320e9 | −0.978783 | −0.489391 | − | 0.872064i | \(-0.662781\pi\) | ||||
−0.489391 | + | 0.872064i | \(0.662781\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.57326e9 | −0.820474 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.40283e8 | − | 7.62593e8i | 0.0780887 | − | 0.135254i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.84849e9 | + | 3.20167e9i | −0.324119 | + | 0.561391i | −0.981334 | − | 0.192313i | \(-0.938401\pi\) |
0.657214 | + | 0.753704i | \(0.271735\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.37256e9 | −0.584652 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.53667e9 | − | 7.85774e9i | −0.777569 | − | 1.34679i | −0.933339 | − | 0.358996i | \(-0.883119\pi\) |
0.155770 | − | 0.987793i | \(-0.450214\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.32148e9 | 1.41021 | 0.705104 | − | 0.709104i | \(-0.250900\pi\) | ||||
0.705104 | + | 0.709104i | \(0.250900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07184e9 | + | 1.85649e9i | 0.179602 | + | 0.311080i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.09831e9 | + | 1.90233e9i | 0.181977 | + | 0.315193i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.34670e9 | − | 2.33256e9i | 0.220644 | − | 0.382167i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.83963e8 | + | 1.99029e9i | 0.143218 | + | 0.322463i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.14922e8 | + | 8.91872e8i | −0.0825020 | + | 0.142898i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.94586e9 | − | 3.37032e9i | −0.308324 | − | 0.534034i | 0.669671 | − | 0.742657i | \(-0.266435\pi\) |
−0.977996 | + | 0.208624i | \(0.933102\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.38045e9 | − | 2.39101e9i | −0.216325 | − | 0.374686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.15468e9 | −1.26386 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.57581e8 | − | 1.31217e9i | −0.116129 | − | 0.201142i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.43323e8 | 0.0217302 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.47499e9 | − | 6.01886e9i | 0.521136 | − | 0.902633i | −0.478562 | − | 0.878054i | \(-0.658842\pi\) |
0.999698 | − | 0.0245797i | \(-0.00782475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.16974e9 | − | 7.22220e9i | 0.618544 | − | 1.07135i | −0.371208 | − | 0.928550i | \(-0.621056\pi\) |
0.989752 | − | 0.142800i | \(-0.0456105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.87154e10 | −2.74625 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.04436e9 | −0.151595 | −0.0757973 | − | 0.997123i | \(-0.524150\pi\) | ||||
−0.0757973 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.32125e8 | + | 9.21668e8i | −0.0764113 | + | 0.132348i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.97190e9 | + | 5.14747e9i | −0.422182 | + | 0.731241i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.16658e10 | −1.63952 | −0.819761 | − | 0.572706i | \(-0.805894\pi\) | ||||
−0.819761 | + | 0.572706i | \(0.805894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.12393e9 | − | 1.94670e9i | −0.156277 | − | 0.270679i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.01042e8 | −0.0414141 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.99336e9 | − | 5.18465e9i | −0.407436 | − | 0.705700i | 0.587166 | − | 0.809467i | \(-0.300244\pi\) |
−0.994602 | + | 0.103767i | \(0.966910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.92978e9 | + | 8.53862e9i | 0.663930 | + | 1.14996i | 0.979574 | + | 0.201082i | \(0.0644459\pi\) |
−0.315645 | + | 0.948877i | \(0.602221\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.99517e8 | − | 6.91984e8i | 0.0532400 | − | 0.0922143i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.67113e9 | − | 6.01419e9i | −0.352225 | − | 0.793052i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.02059e9 | + | 3.49976e9i | −0.263656 | + | 0.456665i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.10994e9 | + | 8.85067e9i | 0.659818 | + | 1.14284i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.86325e8 | − | 1.70837e9i | −0.126035 | − | 0.218299i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.87344e9 | 0.616287 | 0.308144 | − | 0.951340i | \(-0.400292\pi\) | ||||
0.308144 | + | 0.951340i | \(0.400292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.71718e9 | + | 9.90245e9i | 0.715515 | + | 1.23931i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.31850e9 | 0.287175 | 0.143587 | − | 0.989638i | \(-0.454136\pi\) | ||||
0.143587 | + | 0.989638i | \(0.454136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.74610e9 | − | 4.75638e9i | 0.336644 | − | 0.583085i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.58186e9 | − | 6.20397e9i | 0.434604 | − | 0.752757i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.49916e10 | −1.80043 | −0.900216 | − | 0.435444i | \(-0.856591\pi\) | ||||
−0.900216 | + | 0.435444i | \(0.856591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.65778e8 | −0.0910303 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.31334e9 | − | 5.73888e9i | 0.389868 | − | 0.675272i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.49632e9 | − | 2.59170e9i | 0.174284 | − | 0.301868i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.43178e10 | −1.65083 | −0.825416 | − | 0.564524i | \(-0.809060\pi\) | ||||
−0.825416 | + | 0.564524i | \(0.809060\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.29074e7 | + | 7.43178e7i | 0.00489740 | + | 0.00848255i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.60478e10 | 1.81329 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.57674e8 | − | 9.65920e8i | −0.0623830 | − | 0.108050i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.77407e9 | + | 1.17330e10i | 0.750204 | + | 1.29939i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.38902e8 | + | 1.62623e9i | −0.102945 | + | 0.178307i | −0.912897 | − | 0.408190i | \(-0.866160\pi\) |
0.809952 | + | 0.586497i | \(0.199493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.77409e9 | + | 3.81090e9i | −0.301145 | + | 0.413699i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.24329e9 | − | 5.61754e9i | 0.348597 | − | 0.603787i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.46646e9 | − | 6.00408e9i | −0.368908 | − | 0.638968i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.26084e9 | − | 5.64793e9i | −0.343611 | − | 0.595152i | 0.641489 | − | 0.767132i | \(-0.278317\pi\) |
−0.985100 | + | 0.171980i | \(0.944984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.96200e8 | −0.0517742 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.62613e9 | + | 4.54859e9i | 0.271333 | + | 0.469962i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.85349e9 | −0.189636 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.20540e9 | − | 3.81987e9i | 0.223445 | − | 0.387018i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.79683e9 | − | 1.17724e10i | 0.681954 | − | 1.18118i | −0.292430 | − | 0.956287i | \(-0.594464\pi\) |
0.974384 | − | 0.224892i | \(-0.0722029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.58018e9 | −0.355739 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.62223e9 | 0.553254 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.07778e10 | + | 1.86676e10i | −1.05038 | + | 1.81931i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.13772e9 | + | 5.43469e9i | −0.302861 | + | 0.524571i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.673922 | + | 0.738803i | \(0.264609\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.09159e10 | 1.04355 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.09471e9 | − | 5.36019e9i | −0.293028 | − | 0.507539i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.78524e8 | −0.0730143 | −0.0365072 | − | 0.999333i | \(-0.511623\pi\) | ||||
−0.0365072 | + | 0.999333i | \(0.511623\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.58062e9 | − | 9.66591e9i | −0.518414 | − | 0.897919i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.50798e8 | + | 2.61190e8i | 0.0138758 | + | 0.0240336i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.75699e8 | − | 3.04320e8i | 0.0160145 | − | 0.0277379i | −0.857907 | − | 0.513805i | \(-0.828236\pi\) |
0.873922 | + | 0.486067i | \(0.161569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.15235e9 | − | 2.95679e9i | 0.194334 | − | 0.266967i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.72945e9 | − | 6.45959e9i | 0.333567 | − | 0.577756i | −0.649641 | − | 0.760241i | \(-0.725081\pi\) |
0.983209 | + | 0.182485i | \(0.0584142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.71414e10 | + | 2.96897e10i | 1.51879 | + | 2.63062i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.12347e8 | + | 1.94591e8i | 0.00986146 | + | 0.0170805i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.31630e9 | 0.288382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.94993e8 | − | 1.72338e9i | −0.0857196 | − | 0.148471i | 0.819978 | − | 0.572395i | \(-0.193986\pi\) |
−0.905698 | + | 0.423924i | \(0.860652\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.26295e9 | 0.705266 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.22851e10 | − | 2.12784e10i | 1.03888 | − | 1.79939i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.98090e9 | − | 6.89512e9i | 0.333538 | − | 0.577705i | −0.649665 | − | 0.760221i | \(-0.725091\pi\) |
0.983203 | + | 0.182516i | \(0.0584240\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.49285e9 | −0.123929 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.78040e9 | 0.475458 | 0.237729 | − | 0.971332i | \(-0.423597\pi\) | ||||
0.237729 | + | 0.971332i | \(0.423597\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.90783e9 | + | 6.76856e9i | −0.318493 | + | 0.551646i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.49491e8 | + | 2.58926e8i | −0.0120726 | + | 0.0209103i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.78725e9 | 0.143021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.57347e9 | + | 1.31176e10i | 0.600555 | + | 1.04019i | 0.992737 | + | 0.120304i | \(0.0383870\pi\) |
−0.392182 | + | 0.919888i | \(0.628280\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.20529e9 | −0.409030 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.91740e9 | + | 1.54454e10i | 0.694400 | + | 1.20274i | 0.970382 | + | 0.241574i | \(0.0776636\pi\) |
−0.275982 | + | 0.961163i | \(0.589003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.40077e10 | + | 2.42620e10i | 1.08096 | + | 1.87228i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.82832e9 | − | 3.16675e9i | 0.139823 | − | 0.242181i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.07215e9 | − | 4.66555e9i | −0.157051 | − | 0.353607i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.08227e9 | + | 1.87455e9i | −0.0812938 | + | 0.140805i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.03121e10 | + | 1.78611e10i | 0.767684 | + | 1.32967i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.17553e10 | − | 2.03608e10i | −0.867343 | − | 1.50228i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.24456e8 | 0.0456657 | 0.0228329 | − | 0.999739i | \(-0.492731\pi\) | ||||
0.0228329 | + | 0.999739i | \(0.492731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.27902e10 | + | 2.21533e10i | 0.927059 | + | 1.60571i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.17210e9 | 0.156049 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65638e9 | + | 2.86894e9i | −0.117952 | + | 0.204299i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.10224e10 | − | 1.90914e10i | 0.778022 | − | 1.34757i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.65367e10 | −1.15703 | −0.578516 | − | 0.815671i | \(-0.696368\pi\) | ||||
−0.578516 | + | 0.815671i | \(0.696368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.14519e9 | 0.148783 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.28393e8 | − | 3.95589e8i | 0.0157025 | − | 0.0271976i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.27325e9 | − | 3.93738e9i | 0.154932 | − | 0.268351i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.51107e9 | 0.304785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.22618e10 | − | 2.12381e10i | −0.821291 | − | 1.42252i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.33903e9 | −0.553727 | −0.276863 | − | 0.960909i | \(-0.589295\pi\) | ||||
−0.276863 | + | 0.960909i | \(0.589295\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.50340e9 | + | 1.12642e10i | 0.428122 | + | 0.741529i | 0.996706 | − | 0.0810962i | \(-0.0258421\pi\) |
−0.568585 | + | 0.822625i | \(0.692509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.61863e9 | + | 7.99970e9i | 0.301437 | + | 0.522103i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.49874e9 | − | 4.32794e9i | 0.161685 | − | 0.280046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.14990e10 | − | 2.58906e10i | −0.737704 | − | 1.66098i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.20565e7 | − | 1.24806e8i | 0.00458331 | − | 0.00793853i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.08874e9 | + | 1.40101e10i | 0.510129 | + | 0.883569i | 0.999931 | + | 0.0117353i | \(0.00373556\pi\) |
−0.489802 | + | 0.871833i | \(0.662931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.06225e8 | − | 1.22322e9i | −0.0441615 | − | 0.0764899i | 0.843100 | − | 0.537757i | \(-0.180728\pi\) |
−0.887261 | + | 0.461267i | \(0.847395\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.96284e9 | −0.493718 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.49921e10 | − | 2.59671e10i | −0.921707 | − | 1.59644i | −0.796773 | − | 0.604279i | \(-0.793461\pi\) |
−0.124934 | − | 0.992165i | \(-0.539872\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.64833e9 | −0.344333 | −0.172167 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172167 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.35636e10 | − | 2.34928e10i | 0.819917 | − | 1.42014i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.84558e9 | − | 3.19664e9i | 0.110631 | − | 0.191618i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.55296e10 | −1.51754 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.68051e10 | 1.58007 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.83395e9 | + | 6.64059e9i | −0.224119 | + | 0.388186i | −0.956055 | − | 0.293188i | \(-0.905284\pi\) |
0.731936 | + | 0.681374i | \(0.238617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.08150e10 | + | 1.87321e10i | −0.626961 | + | 1.08593i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.91236e10 | −1.67436 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.20271e10 | − | 2.08315e10i | −0.685744 | − | 1.18774i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.61108e9 | 0.486929 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.44841e9 | − | 2.50871e9i | −0.0812294 | − | 0.140693i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.61561e9 | − | 2.79831e9i | −0.0898632 | − | 0.155648i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.00149e9 | + | 1.03949e10i | −0.331083 | + | 0.573453i | −0.982725 | − | 0.185074i | \(-0.940747\pi\) |
0.651641 | + | 0.758527i | \(0.274081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.05366e8 | + | 1.10637e9i | −0.0440668 | + | 0.0605368i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.27140e9 | − | 5.66624e9i | 0.177542 | − | 0.307512i | −0.763496 | − | 0.645813i | \(-0.776519\pi\) |
0.941038 | + | 0.338301i | \(0.109852\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.30042e9 | + | 1.26447e10i | 0.392981 | + | 0.680663i | 0.992841 | − | 0.119442i | \(-0.0381105\pi\) |
−0.599860 | + | 0.800105i | \(0.704777\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.98012e9 | + | 3.42967e9i | 0.105726 | + | 0.183122i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.73730e10 | −0.920102 | −0.460051 | − | 0.887893i | \(-0.652169\pi\) | ||||
−0.460051 | + | 0.887893i | \(0.652169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.20300e10 | − | 2.08366e10i | −0.631989 | − | 1.09464i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.67735e10 | −0.874092 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.74694e9 | − | 6.48989e9i | 0.193690 | − | 0.335481i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.53242e8 | − | 4.38629e8i | 0.0129859 | − | 0.0224923i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.14210e9 | −0.0580972 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.86603e9 | 0.346480 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.26637e10 | + | 2.19342e10i | −0.633962 | + | 1.09805i | 0.352772 | + | 0.935709i | \(0.385239\pi\) |
−0.986734 | + | 0.162345i | \(0.948094\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.77873e7 | − | 8.27700e7i | 0.00237329 | − | 0.00411066i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.85122e10 | 0.912099 | 0.456049 | − | 0.889955i | \(-0.349264\pi\) | ||||
0.456049 | + | 0.889955i | \(0.349264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.63509e9 | + | 9.76026e9i | 0.275447 | + | 0.477088i | 0.970248 | − | 0.242114i | \(-0.0778408\pi\) |
−0.694801 | + | 0.719202i | \(0.744507\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.31655e10 | 0.638464 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.20525e10 | − | 2.08756e10i | −0.579890 | − | 1.00440i | −0.995491 | − | 0.0948518i | \(-0.969762\pi\) |
0.415602 | − | 0.909547i | \(-0.363571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.78783e9 | + | 8.29277e9i | 0.228551 | + | 0.395862i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.62484e9 | + | 6.27840e9i | −0.171679 | + | 0.297356i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.76392e9 | + | 1.03522e9i | 0.458822 | + | 0.0486465i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.05772e10 | + | 1.83203e10i | −0.493163 | + | 0.854184i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.25351e9 | + | 2.17115e9i | 0.0579903 | + | 0.100442i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.52658e10 | + | 4.37616e10i | 1.15978 | + | 2.00879i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.29050e9 | 0.332063 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.09883e10 | + | 1.90323e10i | 0.496620 | + | 0.860170i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.99527e10 | −2.68868 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.17982e9 | − | 1.24358e10i | 0.319513 | − | 0.553412i | −0.660874 | − | 0.750497i | \(-0.729814\pi\) |
0.980386 | + | 0.197085i | \(0.0631474\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.20851e8 | + | 1.24855e9i | −0.0318326 | + | 0.0551356i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.38894e10 | −1.48508 | −0.742538 | − | 0.669803i | \(-0.766378\pi\) | ||||
−0.742538 | + | 0.669803i | \(0.766378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.39346e9 | −0.147569 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.22015e10 | + | 2.11337e10i | −0.526551 | + | 0.912013i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.31978e9 | + | 2.28592e9i | −0.0565208 | + | 0.0978969i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.15820e10 | −0.492243 | −0.246122 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246122 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19681e10 | + | 2.07294e10i | 0.504797 | + | 0.874334i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.63502e9 | 0.152160 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.61759e9 | − | 1.49261e10i | −0.358006 | − | 0.620084i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.72249e8 | + | 6.44755e8i | 0.0153481 | + | 0.0265837i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.22688e9 | − | 1.42494e10i | 0.336651 | − | 0.583097i | −0.647149 | − | 0.762363i | \(-0.724039\pi\) |
0.983801 | + | 0.179266i | \(0.0573723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.94285e9 | − | 1.36590e10i | 0.403819 | − | 0.554747i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00222e10 | − | 1.73590e10i | 0.403998 | − | 0.699744i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.25769e9 | − | 3.91044e9i | −0.0903283 | − | 0.156453i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.41425e9 | − | 5.91366e9i | −0.135584 | − | 0.234838i | 0.790237 | − | 0.612802i | \(-0.209958\pi\) |
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.68362e10 | −0.663612 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.51212e9 | − | 7.81522e9i | −0.176529 | − | 0.305758i | 0.764160 | − | 0.645027i | \(-0.223154\pi\) |
−0.940689 | + | 0.339269i | \(0.889820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.49949e9 | 0.135898 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.15112e10 | − | 1.99380e10i | 0.443720 | − | 0.768545i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.80572e9 | + | 1.52519e10i | −0.336930 | + | 0.583580i | −0.983854 | − | 0.178975i | \(-0.942722\pi\) |
0.646924 | + | 0.762555i | \(0.276055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.63515e9 | −0.289992 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.76329e10 | −1.79587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.31832e9 | + | 7.47955e9i | −0.161618 | + | 0.279930i | −0.935449 | − | 0.353462i | \(-0.885005\pi\) |
0.773831 | + | 0.633392i | \(0.218338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.64840e10 | − | 6.31922e10i | 1.35547 | − | 2.34775i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.43626e10 | −0.529716 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.49609e8 | + | 7.78746e8i | 0.0164615 | + | 0.0285122i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.81625e10 | 1.38709 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.44813e8 | − | 5.97234e8i | −0.0124420 | − | 0.0215502i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.02943e9 | + | 3.51508e9i | 0.0726990 | + | 0.125918i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.37440e10 | − | 4.11258e10i | 0.844424 | − | 1.46259i | −0.0416966 | − | 0.999130i | \(-0.513276\pi\) |
0.886121 | − | 0.463455i | \(-0.153390\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.85987e9 | + | 9.39366e8i | 0.312820 | + | 0.0331666i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.02801e10 | + | 1.78057e10i | −0.360355 | + | 0.624154i | −0.988019 | − | 0.154331i | \(-0.950678\pi\) |
0.627664 | + | 0.778485i | \(0.284011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.42208e9 | − | 1.63195e10i | −0.327908 | − | 0.567953i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.68620e9 | + | 1.15808e10i | 0.231027 | + | 0.400151i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.53009e10 | −1.21103 | −0.605514 | − | 0.795835i | \(-0.707032\pi\) | ||||
−0.605514 | + | 0.795835i | \(0.707032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.44932e9 | + | 5.97440e9i | 0.117488 | + | 0.203495i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.62527e9 | 0.0549647 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.84352e9 | − | 1.35854e10i | 0.263374 | − | 0.456178i | −0.703762 | − | 0.710436i | \(-0.748498\pi\) |
0.967136 | + | 0.254258i | \(0.0818312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.07917e10 | − | 3.60124e10i | 0.693209 | − | 1.20067i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.61688e9 | −0.252155 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.94197e10 | 0.638346 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.82705e10 | + | 3.16455e10i | −0.596339 | + | 1.03289i | 0.397018 | + | 0.917811i | \(0.370045\pi\) |
−0.993356 | + | 0.115078i | \(0.963288\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.76446e9 | + | 1.34484e10i | −0.251645 | + | 0.435863i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.10001e10 | 1.64131 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.75026e10 | − | 3.03154e10i | −0.559331 | − | 0.968790i | −0.997552 | − | 0.0699232i | \(-0.977725\pi\) |
0.438221 | − | 0.898867i | \(-0.355609\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.64906e10 | −0.523308 |
(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.49.3 | yes | 22 | |
19.7 | even | 3 | inner | 76.8.e.a.45.3 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.e.a.45.3 | ✓ | 22 | 19.7 | even | 3 | inner | |
76.8.e.a.49.3 | yes | 22 | 1.1 | even | 1 | trivial |