Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{42} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(8.15670i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.161 |
Dual form | 162.7.b.c.161.11 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.65685i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | − 110.679i | − 0.885428i | −0.896663 | − | 0.442714i | \(-0.854016\pi\) | ||||
0.896663 | − | 0.442714i | \(-0.145984\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 326.338 | 0.951423 | 0.475711 | − | 0.879601i | \(-0.342191\pi\) | ||||
0.475711 | + | 0.879601i | \(0.342191\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −626.092 | −0.626092 | ||||||||
\(11\) | − 625.637i | − 0.470050i | −0.971989 | − | 0.235025i | \(-0.924483\pi\) | ||||
0.971989 | − | 0.235025i | \(-0.0755172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2028.01 | −0.923082 | −0.461541 | − | 0.887119i | \(-0.652703\pi\) | ||||
−0.461541 | + | 0.887119i | \(0.652703\pi\) | |||||||
\(14\) | − 1846.05i | − 0.672758i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | − 4126.55i | − 0.839924i | −0.907542 | − | 0.419962i | \(-0.862043\pi\) | ||||
0.907542 | − | 0.419962i | \(-0.137957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12194.5 | 1.77788 | 0.888942 | − | 0.458020i | \(-0.151441\pi\) | ||||
0.888942 | + | 0.458020i | \(0.151441\pi\) | |||||||
\(20\) | 3541.71i | 0.442714i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3539.14 | −0.332376 | ||||||||
\(23\) | − 21450.5i | − 1.76300i | −0.472182 | − | 0.881501i | \(-0.656533\pi\) | ||||
0.472182 | − | 0.881501i | \(-0.343467\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3375.26 | 0.216017 | ||||||||
\(26\) | 11472.2i | 0.652717i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10442.8 | −0.475711 | ||||||||
\(29\) | 24751.4i | 1.01486i | 0.861693 | + | 0.507429i | \(0.169404\pi\) | ||||
−0.861693 | + | 0.507429i | \(0.830596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40531.8 | −1.36054 | −0.680269 | − | 0.732963i | \(-0.738137\pi\) | ||||
−0.680269 | + | 0.732963i | \(0.738137\pi\) | |||||||
\(32\) | − 5792.62i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −23343.3 | −0.593916 | ||||||||
\(35\) | − 36118.6i | − 0.842417i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30093.7 | −0.594115 | −0.297058 | − | 0.954860i | \(-0.596005\pi\) | ||||
−0.297058 | + | 0.954860i | \(0.596005\pi\) | |||||||
\(38\) | − 68982.5i | − 1.25715i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 20035.0 | 0.313046 | ||||||||
\(41\) | 59229.9i | 0.859388i | 0.902975 | + | 0.429694i | \(0.141379\pi\) | ||||
−0.902975 | + | 0.429694i | \(0.858621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −87935.7 | −1.10601 | −0.553006 | − | 0.833177i | \(-0.686519\pi\) | ||||
−0.553006 | + | 0.833177i | \(0.686519\pi\) | |||||||
\(44\) | 20020.4i | 0.235025i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −121342. | −1.24663 | ||||||||
\(47\) | − 129770.i | − 1.24992i | −0.780658 | − | 0.624958i | \(-0.785116\pi\) | ||||
0.780658 | − | 0.624958i | \(-0.214884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11152.5 | −0.0947946 | ||||||||
\(50\) | − 19093.4i | − 0.152747i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 64896.3 | 0.461541 | ||||||||
\(53\) | − 165599.i | − 1.11232i | −0.831074 | − | 0.556161i | \(-0.812274\pi\) | ||||
0.831074 | − | 0.556161i | \(-0.187726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −69244.6 | −0.416196 | ||||||||
\(56\) | 59073.5i | 0.336379i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 140015. | 0.717613 | ||||||||
\(59\) | 53250.1i | 0.259277i | 0.991561 | + | 0.129639i | \(0.0413818\pi\) | ||||
−0.991561 | + | 0.129639i | \(0.958618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −266982. | −1.17623 | −0.588115 | − | 0.808778i | \(-0.700130\pi\) | ||||
−0.588115 | + | 0.808778i | \(0.700130\pi\) | |||||||
\(62\) | 229282.i | 0.962046i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 224457.i | 0.817323i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −407280. | −1.35416 | −0.677079 | − | 0.735911i | \(-0.736754\pi\) | ||||
−0.677079 | + | 0.735911i | \(0.736754\pi\) | |||||||
\(68\) | 132049.i | 0.419962i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −204318. | −0.595679 | ||||||||
\(71\) | 186563.i | 0.521254i | 0.965440 | + | 0.260627i | \(0.0839293\pi\) | ||||
−0.965440 | + | 0.260627i | \(0.916071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −242102. | −0.622344 | −0.311172 | − | 0.950354i | \(-0.600721\pi\) | ||||
−0.311172 | + | 0.950354i | \(0.600721\pi\) | |||||||
\(74\) | 170236.i | 0.420103i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −390224. | −0.888942 | ||||||||
\(77\) | − 204169.i | − 0.447217i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −126373. | −0.256314 | −0.128157 | − | 0.991754i | \(-0.540906\pi\) | ||||
−0.128157 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(80\) | − 113335.i | − 0.221357i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 335055. | 0.607679 | ||||||||
\(83\) | 68971.7i | 0.120625i | 0.998180 | + | 0.0603124i | \(0.0192097\pi\) | ||||
−0.998180 | + | 0.0603124i | \(0.980790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −456720. | −0.743693 | ||||||||
\(86\) | 497439.i | 0.782069i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 113252. | 0.166188 | ||||||||
\(89\) | 413126.i | 0.586020i | 0.956109 | + | 0.293010i | \(0.0946569\pi\) | ||||
−0.956109 | + | 0.293010i | \(0.905343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −661817. | −0.878241 | ||||||||
\(92\) | 686414.i | 0.881501i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −734091. | −0.883825 | ||||||||
\(95\) | − 1.34967e6i | − 1.57419i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 978443. | 1.07206 | 0.536031 | − | 0.844198i | \(-0.319923\pi\) | ||||
0.536031 | + | 0.844198i | \(0.319923\pi\) | |||||||
\(98\) | 63088.0i | 0.0670299i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −108008. | −0.108008 | ||||||||
\(101\) | − 1.12624e6i | − 1.09312i | −0.837420 | − | 0.546560i | \(-0.815937\pi\) | ||||
0.837420 | − | 0.546560i | \(-0.184063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.05758e6 | 0.967839 | 0.483919 | − | 0.875113i | \(-0.339213\pi\) | ||||
0.483919 | + | 0.875113i | \(0.339213\pi\) | |||||||
\(104\) | − 367109.i | − 0.326359i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −936771. | −0.786531 | ||||||||
\(107\) | − 607244.i | − 0.495692i | −0.968799 | − | 0.247846i | \(-0.920277\pi\) | ||||
0.968799 | − | 0.247846i | \(-0.0797227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 961305. | 0.742303 | 0.371152 | − | 0.928572i | \(-0.378963\pi\) | ||||
0.371152 | + | 0.928572i | \(0.378963\pi\) | |||||||
\(110\) | 391707.i | 0.294295i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 334170. | 0.237856 | ||||||||
\(113\) | 1.33878e6i | 0.927839i | 0.885877 | + | 0.463919i | \(0.153557\pi\) | ||||
−0.885877 | + | 0.463919i | \(0.846443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.37410e6 | −1.56101 | ||||||||
\(116\) | − 792044.i | − 0.507429i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 301228. | 0.183337 | ||||||||
\(119\) | − 1.34665e6i | − 0.799123i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.38014e6 | 0.779053 | ||||||||
\(122\) | 1.51028e6i | 0.831720i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.29702e6 | 0.680269 | ||||||||
\(125\) | − 2.10292e6i | − 1.07670i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.62823e6 | −0.794885 | −0.397443 | − | 0.917627i | \(-0.630102\pi\) | ||||
−0.397443 | + | 0.917627i | \(0.630102\pi\) | |||||||
\(128\) | 185364.i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.26972e6 | 0.577934 | ||||||||
\(131\) | − 1.38103e6i | − 0.614313i | −0.951659 | − | 0.307156i | \(-0.900623\pi\) | ||||
0.951659 | − | 0.307156i | \(-0.0993774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.97953e6 | 1.69152 | ||||||||
\(134\) | 2.30393e6i | 0.957534i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 746985. | 0.296958 | ||||||||
\(137\) | − 3.54766e6i | − 1.37968i | −0.723960 | − | 0.689842i | \(-0.757680\pi\) | ||||
0.723960 | − | 0.689842i | \(-0.242320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.22032e6 | 1.19910 | 0.599548 | − | 0.800339i | \(-0.295347\pi\) | ||||
0.599548 | + | 0.800339i | \(0.295347\pi\) | |||||||
\(140\) | 1.15580e6i | 0.421208i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.05536e6 | 0.368582 | ||||||||
\(143\) | 1.26880e6i | 0.433895i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.73945e6 | 0.898585 | ||||||||
\(146\) | 1.36954e6i | 0.440063i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 962999. | 0.297058 | ||||||||
\(149\) | − 913857.i | − 0.276261i | −0.990414 | − | 0.138130i | \(-0.955891\pi\) | ||||
0.990414 | − | 0.138130i | \(-0.0441093\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.59890e6 | 0.464398 | 0.232199 | − | 0.972668i | \(-0.425408\pi\) | ||||
0.232199 | + | 0.972668i | \(0.425408\pi\) | |||||||
\(152\) | 2.20744e6i | 0.628577i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.15495e6 | −0.316230 | ||||||||
\(155\) | 4.48600e6i | 1.20466i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.67074e6 | −1.46535 | −0.732673 | − | 0.680580i | \(-0.761728\pi\) | ||||
−0.732673 | + | 0.680580i | \(0.761728\pi\) | |||||||
\(158\) | 714872.i | 0.181241i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −641119. | −0.156523 | ||||||||
\(161\) | − 7.00010e6i | − 1.67736i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.58510e6 | 1.28964 | 0.644820 | − | 0.764335i | \(-0.276932\pi\) | ||||
0.644820 | + | 0.764335i | \(0.276932\pi\) | |||||||
\(164\) | − 1.89536e6i | − 0.429694i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 390163. | 0.0852946 | ||||||||
\(167\) | − 5.92882e6i | − 1.27297i | −0.771288 | − | 0.636486i | \(-0.780387\pi\) | ||||
0.771288 | − | 0.636486i | \(-0.219613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −713983. | −0.147920 | ||||||||
\(170\) | 2.58360e6i | 0.525870i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.81394e6 | 0.553006 | ||||||||
\(173\) | 2.24430e6i | 0.433453i | 0.976232 | + | 0.216727i | \(0.0695380\pi\) | ||||
−0.976232 | + | 0.216727i | \(0.930462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.10148e6 | 0.205523 | ||||||||
\(176\) | − 640652.i | − 0.117513i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.33699e6 | 0.414379 | ||||||||
\(179\) | 777450.i | 0.135554i | 0.997700 | + | 0.0677772i | \(0.0215907\pi\) | ||||
−0.997700 | + | 0.0677772i | \(0.978409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.10696e6 | 0.692604 | 0.346302 | − | 0.938123i | \(-0.387437\pi\) | ||||
0.346302 | + | 0.938123i | \(0.387437\pi\) | |||||||
\(182\) | 3.74380e6i | 0.621010i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.88295e6 | 0.623316 | ||||||||
\(185\) | 3.33073e6i | 0.526047i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.58172e6 | −0.394807 | ||||||||
\(188\) | 4.15264e6i | 0.624958i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.63489e6 | −1.11312 | ||||||||
\(191\) | 4.26795e6i | 0.612518i | 0.951948 | + | 0.306259i | \(0.0990773\pi\) | ||||
−0.951948 | + | 0.306259i | \(0.900923\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.10012e6 | −1.12673 | −0.563365 | − | 0.826208i | \(-0.690493\pi\) | ||||
−0.563365 | + | 0.826208i | \(0.690493\pi\) | |||||||
\(194\) | − 5.53491e6i | − 0.758063i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 356880. | 0.0473973 | ||||||||
\(197\) | 4.08228e6i | 0.533955i | 0.963703 | + | 0.266977i | \(0.0860249\pi\) | ||||
−0.963703 | + | 0.266977i | \(0.913975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.02814e6 | 0.130464 | 0.0652322 | − | 0.997870i | \(-0.479221\pi\) | ||||
0.0652322 | + | 0.997870i | \(0.479221\pi\) | |||||||
\(200\) | 610987.i | 0.0763734i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.37098e6 | −0.772952 | ||||||||
\(203\) | 8.07732e6i | 0.965560i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.55548e6 | 0.760927 | ||||||||
\(206\) | − 5.98260e6i | − 0.684365i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.07668e6 | −0.230770 | ||||||||
\(209\) | − 7.62933e6i | − 0.835695i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.54504e7 | 1.64472 | 0.822359 | − | 0.568969i | \(-0.192657\pi\) | ||||
0.822359 | + | 0.568969i | \(0.192657\pi\) | |||||||
\(212\) | 5.29918e6i | 0.556161i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.43509e6 | −0.350507 | ||||||||
\(215\) | 9.73259e6i | 0.979294i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.32271e7 | −1.29445 | ||||||||
\(218\) | − 5.43796e6i | − 0.524888i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.21583e6 | 0.208098 | ||||||||
\(221\) | 8.36868e6i | 0.775318i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.81129e6 | −0.253508 | −0.126754 | − | 0.991934i | \(-0.540456\pi\) | ||||
−0.126754 | + | 0.991934i | \(0.540456\pi\) | |||||||
\(224\) | − 1.89035e6i | − 0.168189i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.57326e6 | 0.656081 | ||||||||
\(227\) | − 7.45718e6i | − 0.637525i | −0.947835 | − | 0.318762i | \(-0.896733\pi\) | ||||
0.947835 | − | 0.318762i | \(-0.103267\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.26246e7 | 1.05127 | 0.525633 | − | 0.850712i | \(-0.323829\pi\) | ||||
0.525633 | + | 0.850712i | \(0.323829\pi\) | |||||||
\(230\) | 1.34300e7i | 1.10380i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.48048e6 | −0.358807 | ||||||||
\(233\) | − 1.64283e7i | − 1.29875i | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
0.760469 | − | 0.649374i | \(-0.224969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.43628e7 | −1.10671 | ||||||||
\(236\) | − 1.70400e6i | − 0.129639i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.61780e6 | −0.565065 | ||||||||
\(239\) | − 9.75791e6i | − 0.714765i | −0.933958 | − | 0.357382i | \(-0.883669\pi\) | ||||
0.933958 | − | 0.357382i | \(-0.116331\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.47403e7 | −1.05307 | −0.526534 | − | 0.850154i | \(-0.676509\pi\) | ||||
−0.526534 | + | 0.850154i | \(0.676509\pi\) | |||||||
\(242\) | − 7.80725e6i | − 0.550873i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.54341e6 | 0.588115 | ||||||||
\(245\) | 1.23434e6i | 0.0839338i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.47306e7 | −1.64113 | ||||||||
\(248\) | − 7.33704e6i | − 0.481023i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.18959e7 | −0.761339 | ||||||||
\(251\) | 1.31485e7i | 0.831486i | 0.909482 | + | 0.415743i | \(0.136478\pi\) | ||||
−0.909482 | + | 0.415743i | \(0.863522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.34202e7 | −0.828700 | ||||||||
\(254\) | 9.21065e6i | 0.562069i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − 2.15267e7i | − 1.26817i | −0.773262 | − | 0.634087i | \(-0.781376\pi\) | ||||
0.773262 | − | 0.634087i | \(-0.218624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.82073e6 | −0.565255 | ||||||||
\(260\) | − 7.18263e6i | − 0.408661i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.81229e6 | −0.434385 | ||||||||
\(263\) | − 8.49122e6i | − 0.466770i | −0.972384 | − | 0.233385i | \(-0.925020\pi\) | ||||
0.972384 | − | 0.233385i | \(-0.0749803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.83283e7 | −0.984882 | ||||||||
\(266\) | − 2.25116e7i | − 1.19608i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.30330e7 | 0.677079 | ||||||||
\(269\) | 883900.i | 0.0454094i | 0.999742 | + | 0.0227047i | \(0.00722776\pi\) | ||||
−0.999742 | + | 0.0227047i | \(0.992772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.17663e6 | −0.310345 | −0.155172 | − | 0.987887i | \(-0.549593\pi\) | ||||
−0.155172 | + | 0.987887i | \(0.549593\pi\) | |||||||
\(272\) | − 4.22558e6i | − 0.209981i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00686e7 | −0.975584 | ||||||||
\(275\) | − 2.11169e6i | − 0.101539i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.80573e6 | −0.273160 | −0.136580 | − | 0.990629i | \(-0.543611\pi\) | ||||
−0.136580 | + | 0.990629i | \(0.543611\pi\) | |||||||
\(278\) | − 1.82169e7i | − 0.847889i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.53817e6 | 0.297839 | ||||||||
\(281\) | 1.35800e7i | 0.612039i | 0.952025 | + | 0.306020i | \(0.0989973\pi\) | ||||
−0.952025 | + | 0.306020i | \(0.901003\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.06204e6 | 0.223340 | 0.111670 | − | 0.993745i | \(-0.464380\pi\) | ||||
0.111670 | + | 0.993745i | \(0.464380\pi\) | |||||||
\(284\) | − 5.97000e6i | − 0.260627i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.17741e6 | 0.306810 | ||||||||
\(287\) | 1.93290e7i | 0.817642i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.10918e6 | 0.294528 | ||||||||
\(290\) | − 1.54967e7i | − 0.635395i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.74727e6 | 0.311172 | ||||||||
\(293\) | 3.76667e7i | 1.49746i | 0.662875 | + | 0.748730i | \(0.269336\pi\) | ||||
−0.662875 | + | 0.748730i | \(0.730664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.89365e6 | 0.229572 | ||||||||
\(296\) | − 5.44755e6i | − 0.210051i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.16956e6 | −0.195346 | ||||||||
\(299\) | 4.35017e7i | 1.62740i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.86968e7 | −1.05229 | ||||||||
\(302\) | − 9.04475e6i | − 0.328379i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.24872e7 | 0.444471 | ||||||||
\(305\) | 2.95491e7i | 1.04147i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.60441e7 | 1.59132 | 0.795662 | − | 0.605740i | \(-0.207123\pi\) | ||||
0.795662 | + | 0.605740i | \(0.207123\pi\) | |||||||
\(308\) | 6.53341e6i | 0.223608i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.53766e7 | 0.851823 | ||||||||
\(311\) | 2.85310e7i | 0.948498i | 0.880391 | + | 0.474249i | \(0.157280\pi\) | ||||
−0.880391 | + | 0.474249i | \(0.842720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.20513e7 | 0.719120 | 0.359560 | − | 0.933122i | \(-0.382927\pi\) | ||||
0.359560 | + | 0.933122i | \(0.382927\pi\) | |||||||
\(314\) | 3.20785e7i | 1.03616i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.04392e6 | 0.128157 | ||||||||
\(317\) | − 1.73192e7i | − 0.543689i | −0.962341 | − | 0.271844i | \(-0.912366\pi\) | ||||
0.962341 | − | 0.271844i | \(-0.0876336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.54854e7 | 0.477035 | ||||||||
\(320\) | 3.62671e6i | 0.110679i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.95985e7 | −1.18607 | ||||||||
\(323\) | − 5.03212e7i | − 1.49329i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.84506e6 | −0.199401 | ||||||||
\(326\) | − 3.15941e7i | − 0.911913i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.07218e7 | −0.303840 | ||||||||
\(329\) | − 4.23489e7i | − 1.18920i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41600e7 | 0.390461 | 0.195231 | − | 0.980757i | \(-0.437454\pi\) | ||||
0.195231 | + | 0.980757i | \(0.437454\pi\) | |||||||
\(332\) | − 2.20709e6i | − 0.0603124i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.35385e7 | −0.900127 | ||||||||
\(335\) | 4.50772e7i | 1.19901i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.81393e7 | 1.25780 | 0.628898 | − | 0.777488i | \(-0.283506\pi\) | ||||
0.628898 | + | 0.777488i | \(0.283506\pi\) | |||||||
\(338\) | 4.03890e6i | 0.104595i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.46150e7 | 0.371846 | ||||||||
\(341\) | 2.53582e7i | 0.639521i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.20328e7 | −1.04161 | ||||||||
\(344\) | − 1.59181e7i | − 0.391034i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.26957e7 | 0.306498 | ||||||||
\(347\) | 5.48516e7i | 1.31281i | 0.754410 | + | 0.656404i | \(0.227923\pi\) | ||||
−0.754410 | + | 0.656404i | \(0.772077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.71985e7 | −0.404589 | −0.202295 | − | 0.979325i | \(-0.564840\pi\) | ||||
−0.202295 | + | 0.979325i | \(0.564840\pi\) | |||||||
\(350\) | − 6.23089e6i | − 0.145327i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.62408e6 | −0.0830939 | ||||||||
\(353\) | 7.22010e6i | 0.164142i | 0.996626 | + | 0.0820709i | \(0.0261534\pi\) | ||||
−0.996626 | + | 0.0820709i | \(0.973847\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.06485e7 | 0.461533 | ||||||||
\(356\) | − 1.32200e7i | − 0.293010i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.39792e6 | 0.0958514 | ||||||||
\(359\) | 1.62223e6i | 0.0350614i | 0.999846 | + | 0.0175307i | \(0.00558048\pi\) | ||||
−0.999846 | + | 0.0175307i | \(0.994420\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.01660e8 | 2.16087 | ||||||||
\(362\) | − 2.32325e7i | − 0.489745i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.11781e7 | 0.439120 | ||||||||
\(365\) | 2.67955e7i | 0.551041i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.17291e7 | 0.439586 | 0.219793 | − | 0.975547i | \(-0.429462\pi\) | ||||
0.219793 | + | 0.975547i | \(0.429462\pi\) | |||||||
\(368\) | − 2.19653e7i | − 0.440751i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.88415e7 | 0.371971 | ||||||||
\(371\) | − 5.40413e7i | − 1.05829i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.07342e7 | 1.17033 | 0.585163 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585163 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(374\) | 1.46044e7i | 0.279170i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.34909e7 | 0.441912 | ||||||||
\(377\) | − 5.01961e7i | − 0.936797i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.01121e7 | 0.369437 | 0.184719 | − | 0.982791i | \(-0.440863\pi\) | ||||
0.184719 | + | 0.982791i | \(0.440863\pi\) | |||||||
\(380\) | 4.31894e7i | 0.787094i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.41431e7 | 0.433116 | ||||||||
\(383\) | 4.72489e7i | 0.840998i | 0.907293 | + | 0.420499i | \(0.138145\pi\) | ||||
−0.907293 | + | 0.420499i | \(0.861855\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.25971e7 | −0.395978 | ||||||||
\(386\) | 4.58212e7i | 0.796718i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.13102e7 | −0.536031 | ||||||||
\(389\) | − 1.93628e7i | − 0.328942i | −0.986382 | − | 0.164471i | \(-0.947408\pi\) | ||||
0.986382 | − | 0.164471i | \(-0.0525917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.85163e7 | −1.48079 | ||||||||
\(392\) | − 2.01882e6i | − 0.0335149i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.30929e7 | 0.377563 | ||||||||
\(395\) | 1.39867e7i | 0.226947i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.66656e7 | −0.585986 | −0.292993 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292993 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(398\) | − 5.81602e6i | − 0.0922522i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.45627e6 | 0.0540042 | ||||||||
\(401\) | − 1.21073e8i | − 1.87765i | −0.344391 | − | 0.938826i | \(-0.611915\pi\) | ||||
0.344391 | − | 0.938826i | \(-0.388085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.21989e7 | 1.25589 | ||||||||
\(404\) | 3.60397e7i | 0.546560i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.56922e7 | 0.682754 | ||||||||
\(407\) | 1.88277e7i | 0.279264i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.98285e7 | 0.582135 | 0.291067 | − | 0.956703i | \(-0.405990\pi\) | ||||
0.291067 | + | 0.956703i | \(0.405990\pi\) | |||||||
\(410\) | − 3.70834e7i | − 0.538056i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.38427e7 | −0.483919 | ||||||||
\(413\) | 1.73775e7i | 0.246683i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.63369e6 | 0.106805 | ||||||||
\(416\) | 1.17475e7i | 0.163179i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.31580e7 | −0.590925 | ||||||||
\(419\) | 5.41631e7i | 0.736311i | 0.929764 | + | 0.368155i | \(0.120011\pi\) | ||||
−0.929764 | + | 0.368155i | \(0.879989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.41272e7 | 0.725386 | 0.362693 | − | 0.931909i | \(-0.381857\pi\) | ||||
0.362693 | + | 0.931909i | \(0.381857\pi\) | |||||||
\(422\) | − 8.74005e7i | − 1.16299i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.99767e7 | 0.393265 | ||||||||
\(425\) | − 1.39282e7i | − 0.181438i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.71263e7 | −1.11909 | ||||||||
\(428\) | 1.94318e7i | 0.247846i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.50559e7 | 0.692466 | ||||||||
\(431\) | 8.08186e7i | 1.00944i | 0.863284 | + | 0.504719i | \(0.168404\pi\) | ||||
−0.863284 | + | 0.504719i | \(0.831596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.33718e7 | −0.164713 | −0.0823563 | − | 0.996603i | \(-0.526245\pi\) | ||||
−0.0823563 | + | 0.996603i | \(0.526245\pi\) | |||||||
\(434\) | 7.48236e7i | 0.915312i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.07617e7 | −0.371152 | ||||||||
\(437\) | − 2.61578e8i | − 3.13441i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.63606e7 | −0.902560 | −0.451280 | − | 0.892382i | \(-0.649032\pi\) | ||||
−0.451280 | + | 0.892382i | \(0.649032\pi\) | |||||||
\(440\) | − 1.25346e7i | − 0.147147i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.73404e7 | 0.548233 | ||||||||
\(443\) | 1.11204e8i | 1.27911i | 0.768743 | + | 0.639557i | \(0.220882\pi\) | ||||
−0.768743 | + | 0.639557i | \(0.779118\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57242e7 | 0.518879 | ||||||||
\(446\) | 1.59031e7i | 0.179257i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.06934e7 | −0.118928 | ||||||||
\(449\) | − 1.36515e8i | − 1.50814i | −0.656793 | − | 0.754071i | \(-0.728087\pi\) | ||||
0.656793 | − | 0.754071i | \(-0.271913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.70564e7 | 0.403956 | ||||||||
\(452\) | − 4.28408e7i | − 0.463919i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.21842e7 | −0.450798 | ||||||||
\(455\) | 7.32489e7i | 0.777619i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08409e8 | −1.13584 | −0.567920 | − | 0.823084i | \(-0.692252\pi\) | ||||
−0.567920 | + | 0.823084i | \(0.692252\pi\) | |||||||
\(458\) | − 7.14157e7i | − 0.743357i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.59713e7 | 0.780506 | ||||||||
\(461\) | − 1.64142e8i | − 1.67540i | −0.546132 | − | 0.837699i | \(-0.683900\pi\) | ||||
0.546132 | − | 0.837699i | \(-0.316100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.73969e7 | 0.376784 | 0.188392 | − | 0.982094i | \(-0.439672\pi\) | ||||
0.188392 | + | 0.982094i | \(0.439672\pi\) | |||||||
\(464\) | 2.53454e7i | 0.253715i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.29326e7 | −0.918354 | ||||||||
\(467\) | 1.45951e8i | 1.43304i | 0.697569 | + | 0.716518i | \(0.254265\pi\) | ||||
−0.697569 | + | 0.716518i | \(0.745735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.32911e8 | −1.28838 | ||||||||
\(470\) | 8.12481e7i | 0.782564i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.63931e6 | −0.0916684 | ||||||||
\(473\) | 5.50158e7i | 0.519881i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.11596e7 | 0.384053 | ||||||||
\(476\) | 4.30928e7i | 0.399561i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.51991e7 | −0.505415 | ||||||||
\(479\) | − 1.32972e8i | − 1.20991i | −0.796258 | − | 0.604957i | \(-0.793190\pi\) | ||||
0.796258 | − | 0.604957i | \(-0.206810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.10304e7 | 0.548417 | ||||||||
\(482\) | 8.33840e7i | 0.744632i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.41645e7 | −0.389526 | ||||||||
\(485\) | − 1.08293e8i | − 0.949235i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.62190e7 | −0.400160 | −0.200080 | − | 0.979780i | \(-0.564120\pi\) | ||||
−0.200080 | + | 0.979780i | \(0.564120\pi\) | |||||||
\(488\) | − 4.83288e7i | − 0.415860i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.98249e6 | 0.0593502 | ||||||||
\(491\) | − 9.15791e7i | − 0.773663i | −0.922150 | − | 0.386832i | \(-0.873569\pi\) | ||||
0.922150 | − | 0.386832i | \(-0.126431\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.02138e8 | 0.852404 | ||||||||
\(494\) | 1.39897e8i | 1.16046i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.15046e7 | −0.340135 | ||||||||
\(497\) | 6.08824e7i | 0.495933i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.71899e7 | −0.460275 | −0.230138 | − | 0.973158i | \(-0.573918\pi\) | ||||
−0.230138 | + | 0.973158i | \(0.573918\pi\) | |||||||
\(500\) | 6.72935e7i | 0.538348i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.43791e7 | 0.587949 | ||||||||
\(503\) | − 1.85206e8i | − 1.45530i | −0.685950 | − | 0.727649i | \(-0.740613\pi\) | ||||
0.685950 | − | 0.727649i | \(-0.259387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.24651e8 | −0.967879 | ||||||||
\(506\) | 7.59161e7i | 0.585979i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.21033e7 | 0.397443 | ||||||||
\(509\) | 1.25335e8i | 0.950430i | 0.879870 | + | 0.475215i | \(0.157630\pi\) | ||||
−0.879870 | + | 0.475215i | \(0.842370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.90072e7 | −0.592112 | ||||||||
\(512\) | − 5.93164e6i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.21774e8 | −0.896734 | ||||||||
\(515\) | − 1.17052e8i | − 0.856952i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.11890e7 | −0.587524 | ||||||||
\(518\) | 5.55544e7i | 0.399696i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.06311e7 | −0.288967 | ||||||||
\(521\) | 1.64203e8i | 1.16109i | 0.814227 | + | 0.580546i | \(0.197161\pi\) | ||||
−0.814227 | + | 0.580546i | \(0.802839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.39702e8 | −0.976559 | −0.488280 | − | 0.872687i | \(-0.662375\pi\) | ||||
−0.488280 | + | 0.872687i | \(0.662375\pi\) | |||||||
\(524\) | 4.41930e7i | 0.307156i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.80336e7 | −0.330056 | ||||||||
\(527\) | 1.67256e8i | 1.14275i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.12086e8 | −2.10818 | ||||||||
\(530\) | 1.03680e8i | 0.696417i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.27345e8 | −0.845760 | ||||||||
\(533\) | − 1.20119e8i | − 0.793285i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.72089e7 | −0.438900 | ||||||||
\(536\) | − 7.37256e7i | − 0.478767i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.00009e6 | 0.0321093 | ||||||||
\(539\) | 6.97741e6i | 0.0445582i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.45535e8 | 0.919130 | 0.459565 | − | 0.888144i | \(-0.348005\pi\) | ||||
0.459565 | + | 0.888144i | \(0.348005\pi\) | |||||||
\(542\) | 3.49403e7i | 0.219447i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.39035e7 | −0.148479 | ||||||||
\(545\) | − 1.06396e8i | − 0.657257i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.57155e6 | −0.0523718 | −0.0261859 | − | 0.999657i | \(-0.508336\pi\) | ||||
−0.0261859 | + | 0.999657i | \(0.508336\pi\) | |||||||
\(548\) | 1.13525e8i | 0.689842i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.19455e7 | −0.0717987 | ||||||||
\(551\) | 3.01831e8i | 1.80430i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.12402e7 | −0.243863 | ||||||||
\(554\) | 3.28422e7i | 0.193153i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.03050e8 | −0.599548 | ||||||||
\(557\) | − 8.68427e7i | − 0.502536i | −0.967918 | − | 0.251268i | \(-0.919152\pi\) | ||||
0.967918 | − | 0.251268i | \(-0.0808476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.78335e8 | 1.02094 | ||||||||
\(560\) | − 3.69855e7i | − 0.210604i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.68198e7 | 0.432777 | ||||||||
\(563\) | − 6.07412e6i | − 0.0340375i | −0.999855 | − | 0.0170188i | \(-0.994582\pi\) | ||||
0.999855 | − | 0.0170188i | \(-0.00541750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.48174e8 | 0.821535 | ||||||||
\(566\) | − 2.86352e7i | − 0.157925i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.37714e7 | −0.184291 | ||||||||
\(569\) | 1.56056e8i | 0.847116i | 0.905869 | + | 0.423558i | \(0.139219\pi\) | ||||
−0.905869 | + | 0.423558i | \(0.860781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.02008e8 | 0.547933 | 0.273967 | − | 0.961739i | \(-0.411664\pi\) | ||||
0.273967 | + | 0.961739i | \(0.411664\pi\) | |||||||
\(572\) | − 4.06015e7i | − 0.216947i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.09341e8 | 0.578160 | ||||||||
\(575\) | − 7.24009e7i | − 0.380838i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.90791e8 | 1.51375 | 0.756874 | − | 0.653561i | \(-0.226726\pi\) | ||||
0.756874 | + | 0.653561i | \(0.226726\pi\) | |||||||
\(578\) | − 4.02156e7i | − 0.208262i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.76623e7 | −0.449292 | ||||||||
\(581\) | 2.25081e7i | 0.114765i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.03605e8 | −0.522848 | ||||||||
\(584\) | − 4.38252e7i | − 0.220032i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.13075e8 | 1.05886 | ||||||||
\(587\) | 1.08186e8i | 0.534880i | 0.963574 | + | 0.267440i | \(0.0861778\pi\) | ||||
−0.963574 | + | 0.267440i | \(0.913822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.94265e8 | −2.41888 | ||||||||
\(590\) | − 3.33395e7i | − 0.162332i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.08160e7 | −0.148529 | ||||||||
\(593\) | − 2.75079e8i | − 1.31915i | −0.751641 | − | 0.659573i | \(-0.770737\pi\) | ||||
0.751641 | − | 0.659573i | \(-0.229263\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.49045e8 | −0.707566 | ||||||||
\(596\) | 2.92434e7i | 0.138130i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.46083e8 | 1.15074 | ||||||||
\(599\) | − 3.39727e8i | − 1.58070i | −0.612654 | − | 0.790351i | \(-0.709898\pi\) | ||||
0.612654 | − | 0.790351i | \(-0.290102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.61656e8 | 0.744679 | 0.372340 | − | 0.928097i | \(-0.378556\pi\) | ||||
0.372340 | + | 0.928097i | \(0.378556\pi\) | |||||||
\(602\) | 1.62333e8i | 0.744078i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.11648e7 | −0.232199 | ||||||||
\(605\) | − 1.52752e8i | − 0.689795i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.27189e8 | 1.01583 | 0.507916 | − | 0.861406i | \(-0.330416\pi\) | ||||
0.507916 | + | 0.861406i | \(0.330416\pi\) | |||||||
\(608\) | − 7.06381e7i | − 0.314288i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.67155e8 | 0.736428 | ||||||||
\(611\) | 2.63175e8i | 1.15378i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.32276e8 | −0.574247 | −0.287124 | − | 0.957894i | \(-0.592699\pi\) | ||||
−0.287124 | + | 0.957894i | \(0.592699\pi\) | |||||||
\(614\) | − 2.60465e8i | − 1.12524i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.69586e7 | 0.158115 | ||||||||
\(617\) | − 3.56815e8i | − 1.51910i | −0.650447 | − | 0.759551i | \(-0.725419\pi\) | ||||
0.650447 | − | 0.759551i | \(-0.274581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.12067e8 | 1.31576 | 0.657880 | − | 0.753123i | \(-0.271453\pi\) | ||||
0.657880 | + | 0.753123i | \(0.271453\pi\) | |||||||
\(620\) | − 1.43552e8i | − 0.602329i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.61396e8 | 0.670689 | ||||||||
\(623\) | 1.34819e8i | 0.557553i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.80010e8 | −0.737320 | ||||||||
\(626\) | − 1.24741e8i | − 0.508495i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.81464e8 | 0.732673 | ||||||||
\(629\) | 1.24183e8i | 0.499012i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.95005e7 | 0.0776172 | 0.0388086 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388086 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(632\) | − 2.28759e7i | − 0.0906206i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.79723e7 | −0.384446 | ||||||||
\(635\) | 1.80210e8i | 0.703814i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.26174e7 | 0.0875031 | ||||||||
\(638\) | − 8.75985e7i | − 0.337314i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.05158e7 | 0.0782615 | ||||||||
\(641\) | − 4.28268e8i | − 1.62608i | −0.582208 | − | 0.813040i | \(-0.697811\pi\) | ||||
0.582208 | − | 0.813040i | \(-0.302189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.22005e8 | 1.21124 | 0.605619 | − | 0.795755i | \(-0.292926\pi\) | ||||
0.605619 | + | 0.795755i | \(0.292926\pi\) | |||||||
\(644\) | 2.24003e8i | 0.838680i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.84660e8 | −1.05591 | ||||||||
\(647\) | − 8.47366e7i | − 0.312866i | −0.987689 | − | 0.156433i | \(-0.950001\pi\) | ||||
0.987689 | − | 0.156433i | \(-0.0499995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.33153e7 | 0.121873 | ||||||||
\(650\) | 3.87215e7i | 0.140998i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.78723e8 | −0.644820 | ||||||||
\(653\) | 4.37807e8i | 1.57233i | 0.618019 | + | 0.786163i | \(0.287935\pi\) | ||||
−0.618019 | + | 0.786163i | \(0.712065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.52850e8 | −0.543930 | ||||||||
\(656\) | 6.06514e7i | 0.214847i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.39562e8 | −0.840891 | ||||||||
\(659\) | 2.72708e8i | 0.952888i | 0.879205 | + | 0.476444i | \(0.158074\pi\) | ||||
−0.879205 | + | 0.476444i | \(0.841926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.94289e8 | 1.01899 | 0.509495 | − | 0.860474i | \(-0.329832\pi\) | ||||
0.509495 | + | 0.860474i | \(0.329832\pi\) | |||||||
\(662\) | − 8.01008e7i | − 0.276098i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.24852e7 | −0.0426473 | ||||||||
\(665\) | − 4.40449e8i | − 1.49772i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.30928e8 | 1.78920 | ||||||||
\(668\) | 1.89722e8i | 0.636486i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.54995e8 | 0.847828 | ||||||||
\(671\) | 1.67034e8i | 0.552887i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.97051e7 | 0.0974508 | 0.0487254 | − | 0.998812i | \(-0.484484\pi\) | ||||
0.0487254 | + | 0.998812i | \(0.484484\pi\) | |||||||
\(674\) | − 2.72317e8i | − 0.889396i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.28475e7 | 0.0739601 | ||||||||
\(677\) | − 5.39379e8i | − 1.73831i | −0.494536 | − | 0.869157i | \(-0.664662\pi\) | ||||
0.494536 | − | 0.869157i | \(-0.335338\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.19303e8 | 1.01998 | ||||||||
\(680\) | − 8.26752e7i | − 0.262935i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.43448e8 | 0.452210 | ||||||||
\(683\) | 5.86183e8i | 1.83980i | 0.392152 | + | 0.919901i | \(0.371731\pi\) | ||||
−0.392152 | + | 0.919901i | \(0.628269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.92649e8 | −1.22161 | ||||||||
\(686\) | 2.37774e8i | 0.736531i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.00462e7 | −0.276503 | ||||||||
\(689\) | 3.35837e8i | 1.02676i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.69056e8 | −1.42164 | −0.710822 | − | 0.703372i | \(-0.751677\pi\) | ||||
−0.710822 | + | 0.703372i | \(0.751677\pi\) | |||||||
\(692\) | − 7.18176e7i | − 0.216727i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.10288e8 | 0.928295 | ||||||||
\(695\) | − 3.56420e8i | − 1.06171i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.44415e8 | 0.721821 | ||||||||
\(698\) | 9.72895e7i | 0.286088i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.52472e7 | −0.102762 | ||||||||
\(701\) | − 5.94604e7i | − 0.172613i | −0.996269 | − | 0.0863065i | \(-0.972494\pi\) | ||||
0.996269 | − | 0.0863065i | \(-0.0275064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.66978e8 | −1.05627 | ||||||||
\(704\) | 2.05009e7i | 0.0587563i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.08431e7 | 0.116066 | ||||||||
\(707\) | − 3.67535e8i | − 1.04002i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.68042e8 | 1.87441 | 0.937206 | − | 0.348777i | \(-0.113403\pi\) | ||||
0.937206 | + | 0.348777i | \(0.113403\pi\) | |||||||
\(710\) | − 1.16805e8i | − 0.326353i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.47838e7 | −0.207189 | ||||||||
\(713\) | 8.69425e8i | 2.39863i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.40429e8 | 0.384183 | ||||||||
\(716\) | − 2.48784e7i | − 0.0677772i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.17673e6 | 0.0247922 | ||||||||
\(719\) | 6.40752e8i | 1.72387i | 0.507022 | + | 0.861933i | \(0.330746\pi\) | ||||
−0.507022 | + | 0.861933i | \(0.669254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.45130e8 | 0.920824 | ||||||||
\(722\) | − 5.75076e8i | − 1.52797i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.31423e8 | −0.346302 | ||||||||
\(725\) | 8.35424e7i | 0.219226i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.29279e8 | 0.856960 | 0.428480 | − | 0.903551i | \(-0.359049\pi\) | ||||
0.428480 | + | 0.903551i | \(0.359049\pi\) | |||||||
\(728\) | − 1.19802e8i | − 0.310505i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.51578e8 | 0.389645 | ||||||||
\(731\) | 3.62871e8i | 0.928966i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.62595e8 | 0.920683 | 0.460342 | − | 0.887742i | \(-0.347727\pi\) | ||||
0.460342 | + | 0.887742i | \(0.347727\pi\) | |||||||
\(734\) | − 1.22918e8i | − 0.310834i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.24254e8 | −0.311658 | ||||||||
\(737\) | 2.54810e8i | 0.636522i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.76953e7 | 0.0438454 | 0.0219227 | − | 0.999760i | \(-0.493021\pi\) | ||||
0.0219227 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(740\) | − 1.06583e8i | − 0.263023i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.05704e8 | −0.748324 | ||||||||
\(743\) | 1.28993e8i | 0.314486i | 0.987560 | + | 0.157243i | \(0.0502605\pi\) | ||||
−0.987560 | + | 0.157243i | \(0.949739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.01144e8 | −0.244609 | ||||||||
\(746\) | − 3.43565e8i | − 0.827546i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.26150e7 | 0.197403 | ||||||||
\(749\) | − 1.98167e8i | − 0.471613i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.37629e8 | −0.797114 | −0.398557 | − | 0.917144i | \(-0.630489\pi\) | ||||
−0.398557 | + | 0.917144i | \(0.630489\pi\) | |||||||
\(752\) | − 1.32885e8i | − 0.312479i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.83952e8 | −0.662416 | ||||||||
\(755\) | − 1.76964e8i | − 0.411192i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.58119e7 | −0.220868 | −0.110434 | − | 0.993883i | \(-0.535224\pi\) | ||||
−0.110434 | + | 0.993883i | \(0.535224\pi\) | |||||||
\(758\) | − 1.13771e8i | − 0.261232i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.44316e8 | 0.556560 | ||||||||
\(761\) | − 3.34633e8i | − 0.759303i | −0.925130 | − | 0.379651i | \(-0.876044\pi\) | ||||
0.925130 | − | 0.379651i | \(-0.123956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.13710e8 | 0.706244 | ||||||||
\(764\) | − 1.36574e8i | − 0.306259i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.67280e8 | 0.594676 | ||||||||
\(767\) | − 1.07992e8i | − 0.239334i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.42574e8 | −0.533415 | −0.266708 | − | 0.963778i | \(-0.585936\pi\) | ||||
−0.266708 | + | 0.963778i | \(0.585936\pi\) | |||||||
\(770\) | 1.27829e8i | 0.279999i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.59204e8 | 0.563365 | ||||||||
\(773\) | − 2.36476e8i | − 0.511974i | −0.966680 | − | 0.255987i | \(-0.917599\pi\) | ||||
0.966680 | − | 0.255987i | \(-0.0824005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.36805e8 | −0.293899 | ||||||||
\(776\) | 1.77117e8i | 0.379031i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.09533e8 | −0.232597 | ||||||||
\(779\) | 7.22279e8i | 1.52789i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.16720e8 | 0.245016 | ||||||||
\(782\) | 5.00724e8i | 1.04708i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.14201e7 | −0.0236986 | ||||||||
\(785\) | 6.27629e8i | 1.29746i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.96838e8 | −1.01927 | −0.509636 | − | 0.860390i | \(-0.670220\pi\) | ||||
−0.509636 | + | 0.860390i | \(0.670220\pi\) | |||||||
\(788\) | − 1.30633e8i | − 0.266977i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.91210e7 | 0.160476 | ||||||||
\(791\) | 4.36893e8i | 0.882767i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.41442e8 | 1.08576 | ||||||||
\(794\) | 2.07412e8i | 0.414355i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.29004e7 | −0.0652322 | ||||||||
\(797\) | − 1.06050e8i | − 0.209476i | −0.994500 | − | 0.104738i | \(-0.966600\pi\) | ||||
0.994500 | − | 0.104738i | \(-0.0334004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.35503e8 | −1.04984 | ||||||||
\(800\) | − 1.95516e7i | − 0.0381867i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.84894e8 | −1.32770 | ||||||||
\(803\) | 1.51468e8i | 0.292533i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.74761e8 | −1.48518 | ||||||||
\(806\) | − 4.64987e8i | − 0.888047i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.03872e8 | 0.386476 | ||||||||
\(809\) | 2.99505e8i | 0.565664i | 0.959169 | + | 0.282832i | \(0.0912739\pi\) | ||||
−0.959169 | + | 0.282832i | \(0.908726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.31983e8 | −0.809848 | −0.404924 | − | 0.914350i | \(-0.632702\pi\) | ||||
−0.404924 | + | 0.914350i | \(0.632702\pi\) | |||||||
\(812\) | − 2.58474e8i | − 0.482780i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.06506e8 | 0.197470 | ||||||||
\(815\) | − 6.18151e8i | − 1.14188i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07233e9 | −1.96636 | ||||||||
\(818\) | − 2.25304e8i | − 0.411632i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.09775e8 | −0.380463 | ||||||||
\(821\) | − 2.64725e8i | − 0.478371i | −0.970974 | − | 0.239186i | \(-0.923120\pi\) | ||||
0.970974 | − | 0.239186i | \(-0.0768804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.66538e8 | −0.657537 | −0.328768 | − | 0.944411i | \(-0.606634\pi\) | ||||
−0.328768 | + | 0.944411i | \(0.606634\pi\) | |||||||
\(824\) | 1.91443e8i | 0.342183i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.83023e7 | 0.174431 | ||||||||
\(827\) | − 5.77816e8i | − 1.02158i | −0.859705 | − | 0.510791i | \(-0.829353\pi\) | ||||
0.859705 | − | 0.510791i | \(-0.170647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.22169e8 | −0.565484 | −0.282742 | − | 0.959196i | \(-0.591244\pi\) | ||||
−0.282742 | + | 0.959196i | \(0.591244\pi\) | |||||||
\(830\) | − 4.31827e7i | − 0.0755223i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.64538e7 | 0.115385 | ||||||||
\(833\) | 4.60213e7i | 0.0796203i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.56193e8 | −1.12713 | ||||||||
\(836\) | 2.44139e8i | 0.417847i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.06393e8 | 0.520650 | ||||||||
\(839\) | 8.83088e8i | 1.49526i | 0.664113 | + | 0.747632i | \(0.268809\pi\) | ||||
−0.664113 | + | 0.747632i | \(0.731191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78078e7 | −0.0299380 | ||||||||
\(842\) | − 3.06190e8i | − 0.512925i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.94412e8 | −0.822359 | ||||||||
\(845\) | 7.90226e7i | 0.130973i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.50392e8 | 0.741209 | ||||||||
\(848\) | − 1.69574e8i | − 0.278081i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.87896e7 | −0.128296 | ||||||||
\(851\) | 6.45524e8i | 1.04743i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.61854e8 | 0.744145 | 0.372073 | − | 0.928204i | \(-0.378647\pi\) | ||||
0.372073 | + | 0.928204i | \(0.378647\pi\) | |||||||
\(854\) | 4.92861e8i | 0.791317i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.09923e8 | 0.175254 | ||||||||
\(857\) | 4.26122e8i | 0.677004i | 0.940966 | + | 0.338502i | \(0.109920\pi\) | ||||
−0.940966 | + | 0.338502i | \(0.890080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.09587e8 | −0.488431 | −0.244216 | − | 0.969721i | \(-0.578531\pi\) | ||||
−0.244216 | + | 0.969721i | \(0.578531\pi\) | |||||||
\(860\) | − 3.11443e8i | − 0.489647i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.57179e8 | 0.713781 | ||||||||
\(863\) | − 3.39614e8i | − 0.528388i | −0.964470 | − | 0.264194i | \(-0.914894\pi\) | ||||
0.964470 | − | 0.264194i | \(-0.0851059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.48396e8 | 0.383792 | ||||||||
\(866\) | 7.56424e7i | 0.116469i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.23266e8 | 0.647223 | ||||||||
\(869\) | 7.90634e7i | 0.120480i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.25969e8 | 1.25000 | ||||||||
\(872\) | 1.74015e8i | 0.262444i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.47971e9 | −2.21636 | ||||||||
\(875\) | − 6.86263e8i | − 1.02439i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.82927e8 | 0.864203 | 0.432101 | − | 0.901825i | \(-0.357772\pi\) | ||||
0.432101 | + | 0.901825i | \(0.357772\pi\) | |||||||
\(878\) | 4.31961e8i | 0.638206i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.09065e7 | −0.104049 | ||||||||
\(881\) | − 5.04493e8i | − 0.737781i | −0.929473 | − | 0.368890i | \(-0.879738\pi\) | ||||
0.929473 | − | 0.368890i | \(-0.120262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.92257e8 | −0.860256 | −0.430128 | − | 0.902768i | \(-0.641532\pi\) | ||||
−0.430128 | + | 0.902768i | \(0.641532\pi\) | |||||||
\(884\) | − 2.67798e8i | − 0.387659i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.29065e8 | 0.904471 | ||||||||
\(887\) | 3.81132e8i | 0.546141i | 0.961994 | + | 0.273071i | \(0.0880393\pi\) | ||||
−0.961994 | + | 0.273071i | \(0.911961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.31353e8 | −0.756272 | ||||||||
\(890\) | − 2.58655e8i | − 0.366903i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.99614e7 | 0.126754 | ||||||||
\(893\) | − 1.58248e9i | − 2.22221i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.60470e7 | 0.120024 | ||||||||
\(896\) | 6.04913e7i | 0.0840947i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.72247e8 | −1.06642 | ||||||||
\(899\) | − 1.00322e9i | − 1.38075i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.83353e8 | −0.934267 | ||||||||
\(902\) | − 2.09623e8i | − 0.285640i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.42344e8 | −0.328041 | ||||||||
\(905\) | − 4.54552e8i | − 0.613251i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.32768e9 | −1.77939 | −0.889695 | − | 0.456556i | \(-0.849083\pi\) | ||||
−0.889695 | + | 0.456556i | \(0.849083\pi\) | |||||||
\(908\) | 2.38630e8i | 0.318762i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.14359e8 | 0.549860 | ||||||||
\(911\) | − 1.12864e9i | − 1.49279i | −0.665503 | − | 0.746396i | \(-0.731783\pi\) | ||||
0.665503 | − | 0.746396i | \(-0.268217\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.31512e7 | 0.0566997 | ||||||||
\(914\) | 6.13255e8i | 0.803161i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.03988e8 | −0.525633 | ||||||||
\(917\) | − 4.50683e8i | − 0.584471i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.60932e8 | −0.207347 | −0.103673 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103673 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(920\) | − 4.29759e8i | − 0.551901i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.28530e8 | −1.18469 | ||||||||
\(923\) | − 3.78351e8i | − 0.481160i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01574e8 | −0.128339 | ||||||||
\(926\) | − 2.11549e8i | − 0.266427i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.43375e8 | 0.179403 | ||||||||
\(929\) | 2.29903e8i | 0.286747i | 0.989669 | + | 0.143373i | \(0.0457949\pi\) | ||||
−0.989669 | + | 0.143373i | \(0.954205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.35999e8 | −0.168534 | ||||||||
\(932\) | 5.25706e8i | 0.649374i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.25624e8 | 1.01331 | ||||||||
\(935\) | 2.85741e8i | 0.349573i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.89016e8 | −0.959107 | −0.479553 | − | 0.877513i | \(-0.659201\pi\) | ||||
−0.479553 | + | 0.877513i | \(0.659201\pi\) | |||||||
\(938\) | 7.51859e8i | 0.911019i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.59609e8 | 0.553356 | ||||||||
\(941\) | 2.44392e8i | 0.293304i | 0.989188 | + | 0.146652i | \(0.0468498\pi\) | ||||
−0.989188 | + | 0.146652i | \(0.953150\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.27051e9 | 1.51510 | ||||||||
\(944\) | 5.45282e7i | 0.0648194i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.11216e8 | 0.367612 | ||||||||
\(947\) | 4.77586e8i | 0.562343i | 0.959657 | + | 0.281172i | \(0.0907230\pi\) | ||||
−0.959657 | + | 0.281172i | \(0.909277\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.90986e8 | 0.574474 | ||||||||
\(950\) | − 2.32834e8i | − 0.271566i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.43770e8 | 0.282533 | ||||||||
\(953\) | 1.14002e9i | 1.31715i | 0.752517 | + | 0.658573i | \(0.228840\pi\) | ||||
−0.752517 | + | 0.658573i | \(0.771160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.72370e8 | 0.542341 | ||||||||
\(956\) | 3.12253e8i | 0.357382i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.52204e8 | −0.855538 | ||||||||
\(959\) | − 1.15773e9i | − 1.31266i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.55322e8 | 0.851064 | ||||||||
\(962\) | − 3.45240e8i | − 0.387789i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.71691e8 | 0.526534 | ||||||||
\(965\) | 8.96510e8i | 0.997638i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.02793e8 | 0.334863 | 0.167431 | − | 0.985884i | \(-0.446453\pi\) | ||||
0.167431 | + | 0.985884i | \(0.446453\pi\) | |||||||
\(968\) | 2.49832e8i | 0.275437i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.12595e8 | −0.671210 | ||||||||
\(971\) | 2.05629e8i | 0.224608i | 0.993674 | + | 0.112304i | \(0.0358231\pi\) | ||||
−0.993674 | + | 0.112304i | \(0.964177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.05091e9 | 1.14085 | ||||||||
\(974\) | 2.61454e8i | 0.282956i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.73389e8 | −0.294057 | ||||||||
\(977\) | − 5.87684e7i | − 0.0630173i | −0.999503 | − | 0.0315087i | \(-0.989969\pi\) | ||||
0.999503 | − | 0.0315087i | \(-0.0100312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.58467e8 | 0.275459 | ||||||||
\(980\) | − 3.94989e7i | − 0.0419669i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.18050e8 | −0.547063 | ||||||||
\(983\) | − 8.12264e7i | − 0.0855138i | −0.999086 | − | 0.0427569i | \(-0.986386\pi\) | ||||
0.999086 | − | 0.0427569i | \(-0.0136141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.51821e8 | 0.472779 | ||||||||
\(986\) | − 5.77778e8i | − 0.602741i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.91379e8 | 0.820566 | ||||||||
\(989\) | 1.88626e9i | 1.94990i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.17703e8 | 0.223688 | 0.111844 | − | 0.993726i | \(-0.464324\pi\) | ||||
0.111844 | + | 0.993726i | \(0.464324\pi\) | |||||||
\(992\) | 2.34785e8i | 0.240511i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.44403e8 | 0.350678 | ||||||||
\(995\) | − 1.13793e8i | − 0.115517i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.19903e8 | 0.221894 | 0.110947 | − | 0.993826i | \(-0.464612\pi\) | ||||
0.110947 | + | 0.993826i | \(0.464612\pi\) | |||||||
\(998\) | 3.23515e8i | 0.325464i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.7.b.c.161.2 | 12 | ||
3.2 | odd | 2 | inner | 162.7.b.c.161.11 | 12 | ||
9.2 | odd | 6 | 18.7.d.a.5.4 | ✓ | 12 | ||
9.4 | even | 3 | 18.7.d.a.11.4 | yes | 12 | ||
9.5 | odd | 6 | 54.7.d.a.35.3 | 12 | |||
9.7 | even | 3 | 54.7.d.a.17.3 | 12 | |||
36.7 | odd | 6 | 432.7.q.b.17.6 | 12 | |||
36.11 | even | 6 | 144.7.q.c.113.6 | 12 | |||
36.23 | even | 6 | 432.7.q.b.305.6 | 12 | |||
36.31 | odd | 6 | 144.7.q.c.65.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.7.d.a.5.4 | ✓ | 12 | 9.2 | odd | 6 | ||
18.7.d.a.11.4 | yes | 12 | 9.4 | even | 3 | ||
54.7.d.a.17.3 | 12 | 9.7 | even | 3 | |||
54.7.d.a.35.3 | 12 | 9.5 | odd | 6 | |||
144.7.q.c.65.6 | 12 | 36.31 | odd | 6 | |||
144.7.q.c.113.6 | 12 | 36.11 | even | 6 | |||
162.7.b.c.161.2 | 12 | 1.1 | even | 1 | trivial | ||
162.7.b.c.161.11 | 12 | 3.2 | odd | 2 | inner | ||
432.7.q.b.17.6 | 12 | 36.7 | odd | 6 | |||
432.7.q.b.305.6 | 12 | 36.23 | even | 6 |