Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,6,Mod(145,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.145");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.i (of order \(3\), degree \(2\), not 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: | \(69.2858101592\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{16} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.5 | ||
Root | \(1.11227i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.289 |
Dual form | 432.6.i.d.145.5 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 55.1996 | + | 95.6086i | 0.987441 | + | 1.71030i | 0.630542 | + | 0.776155i | \(0.282833\pi\) |
0.356899 | + | 0.934143i | \(0.383834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 50.8724 | − | 88.1135i | 0.392407 | − | 0.679669i | −0.600359 | − | 0.799730i | \(-0.704976\pi\) |
0.992766 | + | 0.120061i | \(0.0383092\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 75.1560 | − | 130.174i | 0.187276 | − | 0.324371i | −0.757065 | − | 0.653339i | \(-0.773367\pi\) |
0.944341 | + | 0.328968i | \(0.106701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −317.712 | − | 550.293i | −0.521405 | − | 0.903100i | −0.999690 | − | 0.0248953i | \(-0.992075\pi\) |
0.478285 | − | 0.878205i | \(-0.341259\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1498.54 | −1.25761 | −0.628806 | − | 0.777562i | \(-0.716456\pi\) | ||||
−0.628806 | + | 0.777562i | \(0.716456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1437.69 | −0.913651 | −0.456825 | − | 0.889556i | \(-0.651014\pi\) | ||||
−0.456825 | + | 0.889556i | \(0.651014\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 632.053 | + | 1094.75i | 0.249134 | + | 0.431513i | 0.963286 | − | 0.268478i | \(-0.0865206\pi\) |
−0.714151 | + | 0.699991i | \(0.753187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4531.50 | + | 7848.79i | −1.45008 | + | 2.51161i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1388.75 | + | 2405.38i | −0.306640 | + | 0.531116i | −0.977625 | − | 0.210355i | \(-0.932538\pi\) |
0.670985 | + | 0.741471i | \(0.265871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3484.34 | − | 6035.05i | −0.651203 | − | 1.12792i | −0.982831 | − | 0.184506i | \(-0.940931\pi\) |
0.331628 | − | 0.943410i | \(-0.392402\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11232.5 | 1.54992 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7950.71 | −0.954776 | −0.477388 | − | 0.878693i | \(-0.658416\pi\) | ||||
−0.477388 | + | 0.878693i | \(0.658416\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1013.77 | − | 1755.90i | −0.0941843 | − | 0.163132i | 0.815084 | − | 0.579343i | \(-0.196691\pi\) |
−0.909268 | + | 0.416211i | \(0.863358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6261.65 | + | 10845.5i | −0.516438 | + | 0.894496i | 0.483380 | + | 0.875410i | \(0.339409\pi\) |
−0.999818 | + | 0.0190856i | \(0.993924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3241.17 | − | 5613.87i | 0.214021 | − | 0.370696i | −0.738948 | − | 0.673763i | \(-0.764677\pi\) |
0.952969 | + | 0.303066i | \(0.0980104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3227.51 | + | 5590.21i | 0.192034 | + | 0.332612i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9827.54 | −0.480568 | −0.240284 | − | 0.970703i | \(-0.577241\pi\) | ||||
−0.240284 | + | 0.970703i | \(0.577241\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16594.3 | 0.739696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23544.0 | − | 40779.3i | −0.880541 | − | 1.52514i | −0.850741 | − | 0.525586i | \(-0.823846\pi\) |
−0.0298005 | − | 0.999556i | \(-0.509487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4168.92 | + | 7220.78i | −0.143450 | + | 0.248462i | −0.928793 | − | 0.370598i | \(-0.879153\pi\) |
0.785344 | + | 0.619060i | \(0.212486\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 35075.2 | − | 60752.0i | 1.02971 | − | 1.78352i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3630.45 | − | 6288.12i | −0.0988036 | − | 0.171133i | 0.812386 | − | 0.583120i | \(-0.198168\pi\) |
−0.911190 | + | 0.411987i | \(0.864835\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3582.33 | 0.0843372 | 0.0421686 | − | 0.999111i | \(-0.486573\pi\) | ||||
0.0421686 | + | 0.999111i | \(0.486573\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58077.5 | 1.27556 | 0.637780 | − | 0.770218i | \(-0.279853\pi\) | ||||
0.637780 | + | 0.770218i | \(0.279853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7646.73 | − | 13244.5i | −0.146977 | − | 0.254571i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31871.4 | + | 55202.9i | −0.574558 | + | 0.995163i | 0.421532 | + | 0.906814i | \(0.361493\pi\) |
−0.996090 | + | 0.0883495i | \(0.971841\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −41423.3 | + | 71747.2i | −0.660008 | + | 1.14317i | 0.320605 | + | 0.947213i | \(0.396114\pi\) |
−0.980613 | + | 0.195954i | \(0.937220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −82718.9 | − | 143273.i | −1.24182 | − | 2.15089i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3861.51 | 0.0516752 | 0.0258376 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258376 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −64651.0 | −0.818412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −79359.8 | − | 137455.i | −0.902176 | − | 1.56262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −34638.6 | + | 59995.8i | −0.373793 | + | 0.647428i | −0.990146 | − | 0.140042i | \(-0.955276\pi\) |
0.616353 | + | 0.787470i | \(0.288610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12722.8 | + | 22036.6i | −0.124103 | + | 0.214952i | −0.921382 | − | 0.388659i | \(-0.872939\pi\) |
0.797279 | + | 0.603611i | \(0.206272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −31693.9 | − | 54895.4i | −0.294363 | − | 0.509851i | 0.680474 | − | 0.732772i | \(-0.261774\pi\) |
−0.974836 | + | 0.222922i | \(0.928441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −61158.9 | −0.516417 | −0.258208 | − | 0.966089i | \(-0.583132\pi\) | ||||
−0.258208 | + | 0.966089i | \(0.583132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −124036. | −0.999957 | −0.499979 | − | 0.866038i | \(-0.666659\pi\) | ||||
−0.499979 | + | 0.866038i | \(0.666659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58718.5 | + | 101703.i | 0.432592 | + | 0.749272i | 0.997096 | − | 0.0761589i | \(-0.0242656\pi\) |
−0.564503 | + | 0.825431i | \(0.690932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −69778.2 | + | 120859.i | −0.492011 | + | 0.852188i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −76234.3 | + | 132042.i | −0.493495 | + | 0.854759i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69228.6 | + | 119908.i | 0.429855 | + | 0.744531i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −655551. | −3.75259 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 29838.6 | 0.164161 | 0.0820803 | − | 0.996626i | \(-0.473844\pi\) | ||||
0.0820803 | + | 0.996626i | \(0.473844\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 86028.8 | + | 149006.i | 0.437992 | + | 0.758624i | 0.997535 | − | 0.0701777i | \(-0.0223566\pi\) |
−0.559543 | + | 0.828801i | \(0.689023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73138.5 | + | 126680.i | −0.358523 | + | 0.620980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 95180.7 | − | 164858.i | 0.433259 | − | 0.750426i | −0.563893 | − | 0.825848i | \(-0.690697\pi\) |
0.997152 | + | 0.0754216i | \(0.0240303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −168532. | − | 291905.i | −0.739852 | − | 1.28146i | −0.952562 | − | 0.304345i | \(-0.901562\pi\) |
0.212710 | − | 0.977115i | \(-0.431771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −95511.9 | −0.390586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −306634. | −1.21115 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −27549.4 | − | 47716.9i | −0.101659 | − | 0.176079i | 0.810709 | − | 0.585449i | \(-0.199082\pi\) |
−0.912368 | + | 0.409370i | \(0.865748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 167032. | − | 289308.i | 0.596152 | − | 1.03257i | −0.397231 | − | 0.917719i | \(-0.630029\pi\) |
0.993383 | − | 0.114847i | \(-0.0366378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 384669. | − | 666266.i | 1.28605 | − | 2.22750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60053.4 | + | 104015.i | 0.194441 | + | 0.336782i | 0.946717 | − | 0.322066i | \(-0.104377\pi\) |
−0.752276 | + | 0.658848i | \(0.771044\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 128616. | 0.391048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −367083. | −1.08217 | −0.541085 | − | 0.840968i | \(-0.681986\pi\) | ||||
−0.541085 | + | 0.840968i | \(0.681986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −294724. | − | 510477.i | −0.817758 | − | 1.41640i | −0.907331 | − | 0.420418i | \(-0.861884\pi\) |
0.0895730 | − | 0.995980i | \(-0.471450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16235.3 | + | 28120.4i | −0.0437264 | + | 0.0757363i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 218229. | − | 377983.i | 0.554366 | − | 0.960190i | −0.443587 | − | 0.896231i | \(-0.646294\pi\) |
0.997953 | − | 0.0639583i | \(-0.0203725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 461056. | + | 798572.i | 1.13804 | + | 1.97115i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 241064. | 0.562341 | 0.281171 | − | 0.959658i | \(-0.409277\pi\) | ||||
0.281171 | + | 0.959658i | \(0.409277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27128.8 | 0.0615510 | 0.0307755 | − | 0.999526i | \(-0.490202\pi\) | ||||
0.0307755 | + | 0.999526i | \(0.490202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −438876. | − | 760156.i | −0.942785 | − | 1.63295i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −112624. | + | 195071.i | −0.235520 | + | 0.407933i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 28036.3 | − | 48560.2i | 0.0556079 | − | 0.0963157i | −0.836881 | − | 0.547384i | \(-0.815624\pi\) |
0.892489 | + | 0.451068i | \(0.148957\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −177242. | − | 306992.i | −0.342510 | − | 0.593244i | 0.642388 | − | 0.766379i | \(-0.277944\pi\) |
−0.984898 | + | 0.173135i | \(0.944610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 816895. | 1.49969 | 0.749844 | − | 0.661615i | \(-0.230129\pi\) | ||||
0.749844 | + | 0.661615i | \(0.230129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −860396. | −1.54016 | −0.770079 | − | 0.637948i | \(-0.779783\pi\) | ||||
−0.770079 | + | 0.637948i | \(0.779783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 141298. | + | 244735.i | 0.240655 | + | 0.416827i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 111919. | − | 193850.i | 0.186003 | − | 0.322166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −108051. | + | 187149.i | −0.171105 | + | 0.296362i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −193586. | − | 335300.i | −0.299341 | − | 0.518475i | 0.676644 | − | 0.736310i | \(-0.263434\pi\) |
−0.975985 | + | 0.217836i | \(0.930100\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.38256e6 | −2.03981 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −709026. | −1.02215 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 476105. | + | 824637.i | 0.655725 | + | 1.13575i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −147497. | + | 255472.i | −0.198619 | + | 0.344018i | −0.948081 | − | 0.318029i | \(-0.896979\pi\) |
0.749462 | + | 0.662047i | \(0.230312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −343990. | + | 595808.i | −0.443079 | + | 0.767435i | −0.997916 | − | 0.0645238i | \(-0.979447\pi\) |
0.554837 | + | 0.831959i | \(0.312780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 543233. | + | 940908.i | 0.684538 | + | 1.18565i | 0.973582 | + | 0.228339i | \(0.0733294\pi\) |
−0.289044 | + | 0.957316i | \(0.593337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −168058. | −0.202801 | −0.101400 | − | 0.994846i | \(-0.532332\pi\) | ||||
−0.101400 | + | 0.994846i | \(0.532332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 715646. | 0.845334 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 773138. | + | 1.33911e6i | 0.875512 | + | 1.51643i | 0.856217 | + | 0.516617i | \(0.172809\pi\) |
0.0192952 | + | 0.999814i | \(0.493858\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 576865. | − | 999160.i | 0.639782 | − | 1.10813i | −0.345699 | − | 0.938346i | \(-0.612358\pi\) |
0.985480 | − | 0.169789i | \(-0.0543086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −356314. | + | 617155.i | −0.379244 | + | 0.656869i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 456770. | + | 791149.i | 0.476382 | + | 0.825118i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −586711. | −0.587814 | −0.293907 | − | 0.955834i | \(-0.594956\pi\) | ||||
−0.293907 | + | 0.955834i | \(0.594956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 190010. | 0.186628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 54171.0 | + | 93826.9i | 0.0511604 | + | 0.0886124i | 0.890471 | − | 0.455039i | \(-0.150375\pi\) |
−0.839311 | + | 0.543651i | \(0.817041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −404471. | + | 700565.i | −0.374661 | + | 0.648931i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 868353. | − | 1.50403e6i | 0.774117 | − | 1.34081i | −0.161172 | − | 0.986926i | \(-0.551527\pi\) |
0.935289 | − | 0.353884i | \(-0.115139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −542476. | − | 939597.i | −0.474533 | − | 0.821915i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18297.3 | −0.0154172 | −0.00770860 | − | 0.999970i | \(-0.502454\pi\) | ||||
−0.00770860 | + | 0.999970i | \(0.502454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7105.09 | −0.00587688 | −0.00293844 | − | 0.999996i | \(-0.500935\pi\) | ||||
−0.00293844 | + | 0.999996i | \(0.500935\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 681139. | + | 1.17977e6i | 0.543130 | + | 0.940729i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −355202. | + | 615227.i | −0.278148 | + | 0.481766i | −0.970924 | − | 0.239386i | \(-0.923054\pi\) |
0.692777 | + | 0.721152i | \(0.256387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −514224. | + | 890661.i | −0.388496 | + | 0.672894i | −0.992247 | − | 0.124278i | \(-0.960338\pi\) |
0.603752 | + | 0.797172i | \(0.293672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −922317. | − | 1.59750e6i | −0.684564 | − | 1.18570i | −0.973574 | − | 0.228374i | \(-0.926659\pi\) |
0.289010 | − | 0.957326i | \(-0.406674\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −206291. | −0.147834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 825769. | 0.581586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 470486. | + | 814906.i | 0.320168 | + | 0.554547i | 0.980522 | − | 0.196407i | \(-0.0629274\pi\) |
−0.660355 | + | 0.750954i | \(0.729594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.59924e6 | − | 4.50201e6i | 1.73896 | − | 3.01198i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 401621. | − | 695629.i | 0.259800 | − | 0.449987i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 637090. | + | 1.10347e6i | 0.405307 | + | 0.702013i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −920492. | −0.566592 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.93094e6 | 1.77485 | 0.887425 | − | 0.460952i | \(-0.152492\pi\) | ||||
0.887425 | + | 0.460952i | \(0.152492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.14126e6 | + | 1.97671e6i | 0.669086 | + | 1.15889i | 0.978160 | + | 0.207853i | \(0.0666477\pi\) |
−0.309074 | + | 0.951038i | \(0.600019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −401324. | + | 695114.i | −0.231544 | + | 0.401047i | −0.958263 | − | 0.285889i | \(-0.907711\pi\) |
0.726718 | + | 0.686936i | \(0.241045\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 555982. | − | 962990.i | 0.310751 | − | 0.538237i | −0.667774 | − | 0.744364i | \(-0.732753\pi\) |
0.978525 | + | 0.206127i | \(0.0660861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 208746. | + | 361558.i | 0.114853 | + | 0.198930i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.15443e6 | 1.14902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.75885e6 | 3.02432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −329772. | − | 571182.i | −0.167967 | − | 0.290927i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −613290. | + | 1.06225e6i | −0.307678 | + | 0.532913i | −0.977854 | − | 0.209289i | \(-0.932885\pi\) |
0.670176 | + | 0.742202i | \(0.266218\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 400799. | − | 694203.i | 0.195126 | − | 0.337967i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.15064e6 | − | 1.99297e6i | −0.551907 | − | 0.955930i | −0.998137 | − | 0.0610122i | \(-0.980567\pi\) |
0.446230 | − | 0.894918i | \(-0.352766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.04748e6 | −0.487818 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.36679e6 | 1.08624 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −809651. | − | 1.40236e6i | −0.360973 | − | 0.625223i | 0.627149 | − | 0.778900i | \(-0.284222\pi\) |
−0.988121 | + | 0.153677i | \(0.950889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 139307. | − | 241287.i | 0.0612223 | − | 0.106040i | −0.833790 | − | 0.552082i | \(-0.813833\pi\) |
0.895012 | + | 0.446042i | \(0.147167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.68496e6 | − | 2.91844e6i | 0.719704 | − | 1.24656i | −0.241413 | − | 0.970422i | \(-0.577611\pi\) |
0.961117 | − | 0.276142i | \(-0.0890559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 197743. | + | 342501.i | 0.0832781 | + | 0.144242i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 272571. | 0.111621 | 0.0558103 | − | 0.998441i | \(-0.482226\pi\) | ||||
0.0558103 | + | 0.998441i | \(0.482226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −409156. | −0.165242 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.20586e6 | + | 5.55271e6i | 1.25954 | + | 2.18159i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.97882e6 | + | 3.42743e6i | −0.766906 | + | 1.32832i | 0.172327 | + | 0.985040i | \(0.444871\pi\) |
−0.939233 | + | 0.343281i | \(0.888462\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −499950. | + | 865939.i | −0.188578 | + | 0.326627i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 961939. | + | 1.66613e6i | 0.357994 | + | 0.620063i | 0.987626 | − | 0.156830i | \(-0.0501276\pi\) |
−0.629632 | + | 0.776894i | \(0.716794\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.76489e6 | 0.639534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.11015e6 | 1.11220 | 0.556101 | − | 0.831115i | \(-0.312297\pi\) | ||||
0.556101 | + | 0.831115i | \(0.312297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.41711e6 | + | 2.45450e6i | 0.493634 | + | 0.855000i | 0.999973 | − | 0.00733479i | \(-0.00233476\pi\) |
−0.506339 | + | 0.862335i | \(0.669001\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 844193. | − | 1.46218e6i | 0.290262 | − | 0.502748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.02692e6 | + | 1.77867e6i | −0.344081 | + | 0.595966i | −0.985186 | − | 0.171487i | \(-0.945143\pi\) |
0.641105 | + | 0.767453i | \(0.278476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −947157. | − | 1.64052e6i | −0.313314 | − | 0.542676i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.03716e6 | −2.26937 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.82167e6 | −1.21696 | −0.608480 | − | 0.793569i | \(-0.708220\pi\) | ||||
−0.608480 | + | 0.793569i | \(0.708220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.65864e6 | + | 4.60491e6i | 0.825656 | + | 1.43008i | 0.901417 | + | 0.432953i | \(0.142528\pi\) |
−0.0757604 | + | 0.997126i | \(0.524138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.21403e6 | + | 3.83482e6i | −0.679081 | + | 1.17620i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −597543. | + | 1.03498e6i | −0.178807 | + | 0.309702i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.57922e6 | − | 2.73528e6i | −0.466803 | − | 0.808526i | 0.532478 | − | 0.846444i | \(-0.321261\pi\) |
−0.999281 | + | 0.0379179i | \(0.987927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.79095e6 | −1.38212 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.14620e6 | −2.60688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.80782e6 | + | 3.13124e6i | 0.503060 | + | 0.871326i | 0.999994 | + | 0.00353739i | \(0.00112599\pi\) |
−0.496933 | + | 0.867789i | \(0.665541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −514445. | + | 891044.i | −0.141460 | + | 0.245016i | −0.928047 | − | 0.372464i | \(-0.878513\pi\) |
0.786587 | + | 0.617480i | \(0.211846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.79064e6 | − | 1.17617e7i | 1.82364 | − | 3.15863i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 424166. | + | 734677.i | 0.112581 | + | 0.194996i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.21668e6 | 1.61200 | 0.806001 | − | 0.591914i | \(-0.201628\pi\) | ||||
0.806001 | + | 0.591914i | \(0.201628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −598070. | −0.153297 | −0.0766483 | − | 0.997058i | \(-0.524422\pi\) | ||||
−0.0766483 | + | 0.997058i | \(0.524422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −908694. | − | 1.57390e6i | −0.227622 | − | 0.394253i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −246548. | + | 427034.i | −0.0610577 | + | 0.105755i | −0.894938 | − | 0.446190i | \(-0.852781\pi\) |
0.833881 | + | 0.551945i | \(0.186114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 97755.8 | − | 169318.i | 0.0236665 | − | 0.0409915i | −0.853950 | − | 0.520356i | \(-0.825799\pi\) |
0.877616 | + | 0.479364i | \(0.159133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 213154. | + | 369194.i | 0.0510263 | + | 0.0883801i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.51225e6 | 0.354004 | 0.177002 | − | 0.984210i | \(-0.443360\pi\) | ||||
0.177002 | + | 0.984210i | \(0.443360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −304763. | −0.0705538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.56871e6 | − | 6.18119e6i | −0.808133 | − | 1.39973i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28236e6 | + | 2.22111e6i | −0.287223 | + | 0.497484i | −0.973146 | − | 0.230190i | \(-0.926065\pi\) |
0.685923 | + | 0.727674i | \(0.259399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.68336e6 | + | 4.64772e6i | −0.588067 | + | 1.01856i | 0.406418 | + | 0.913687i | \(0.366778\pi\) |
−0.994485 | + | 0.104875i | \(0.966556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.75107e6 | + | 4.76500e6i | 0.596417 | + | 1.03302i | 0.993345 | + | 0.115175i | \(0.0367428\pi\) |
−0.396928 | + | 0.917850i | \(0.629924\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 964114. | 0.204567 | 0.102284 | − | 0.994755i | \(-0.467385\pi\) | ||||
0.102284 | + | 0.994755i | \(0.467385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −738757. | −0.155085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 941202. | + | 1.63021e6i | 0.193433 | + | 0.335035i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.51488e6 | − | 1.12841e7i | 1.32487 | − | 2.29474i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 281267. | − | 487168.i | 0.0560118 | − | 0.0970153i | −0.836660 | − | 0.547723i | \(-0.815495\pi\) |
0.892672 | + | 0.450707i | \(0.148828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.52603e6 | + | 4.37522e6i | 0.497825 | + | 0.862258i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.64815e6 | −1.47639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.14185e6 | −0.600292 | −0.300146 | − | 0.953893i | \(-0.597035\pi\) | ||||
−0.300146 | + | 0.953893i | \(0.597035\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.86681e6 | − | 4.96545e6i | −0.536654 | − | 0.929512i | −0.999081 | − | 0.0428549i | \(-0.986355\pi\) |
0.462427 | − | 0.886657i | \(-0.346979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.08110e6 | − | 3.60457e6i | 0.385634 | − | 0.667937i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 182241. | − | 315651.i | 0.0330945 | − | 0.0573214i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 857810. | + | 1.48577e6i | 0.154220 | + | 0.267116i | 0.932775 | − | 0.360460i | \(-0.117380\pi\) |
−0.778555 | + | 0.627576i | \(0.784047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.15229e6 | −0.907989 | −0.453995 | − | 0.891004i | \(-0.650001\pi\) | ||||
−0.453995 | + | 0.891004i | \(0.650001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.80919e6 | −0.490176 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −521280. | − | 902884.i | −0.0891819 | − | 0.154468i | 0.817984 | − | 0.575242i | \(-0.195092\pi\) |
−0.907166 | + | 0.420774i | \(0.861759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.95454e6 | − | 5.11742e6i | 0.500539 | − | 0.866959i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.49898e6 | − | 6.06041e6i | 0.581331 | − | 1.00690i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −487187. | − | 843833.i | −0.0801621 | − | 0.138845i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.52239e6 | −1.53692 | −0.768461 | − | 0.639897i | \(-0.778977\pi\) | ||||
−0.768461 | + | 0.639897i | \(0.778977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.97573e6 | 0.475706 | 0.237853 | − | 0.971301i | \(-0.423556\pi\) | ||||
0.237853 | + | 0.971301i | \(0.423556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.22143e6 | + | 9.04378e6i | 0.818960 | + | 1.41848i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.41919e6 | − | 4.19016e6i | 0.375864 | − | 0.651016i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −644172. | + | 1.11574e6i | −0.0982163 | + | 0.170116i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.37595e6 | − | 5.84731e6i | −0.509931 | − | 0.883226i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 970266. | 0.143853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.80579e6 | 0.265261 | 0.132631 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132631 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.84674e6 | − | 1.18589e7i | −0.987399 | − | 1.71023i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.68486e6 | + | 8.11442e6i | −0.669466 | + | 1.15955i | 0.308587 | + | 0.951196i | \(0.400144\pi\) |
−0.978054 | + | 0.208353i | \(0.933190\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.99658e6 | − | 3.45819e6i | 0.280162 | − | 0.485254i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.24275e6 | + | 5.61660e6i | 0.450921 | + | 0.781018i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.53733e6 | −0.483101 | −0.241550 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241550 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.95761e6 | 1.07709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.39030e6 | − | 2.40807e6i | −0.184858 | − | 0.320183i | 0.758671 | − | 0.651474i | \(-0.225849\pi\) |
−0.943529 | + | 0.331291i | \(0.892516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.48248e6 | + | 1.12280e7i | −0.854319 | + | 1.47972i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.67647e6 | − | 6.36782e6i | 0.476047 | − | 0.824537i | −0.523576 | − | 0.851979i | \(-0.675403\pi\) |
0.999623 | + | 0.0274412i | \(0.00873590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.87585e6 | − | 4.98112e6i | −0.369128 | − | 0.639348i | 0.620302 | − | 0.784363i | \(-0.287010\pi\) |
−0.989429 | + | 0.145016i | \(0.953677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.14566e7 | −1.44506 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.30488e7 | −1.63167 | −0.815835 | − | 0.578285i | \(-0.803722\pi\) | ||||
−0.815835 | + | 0.578285i | \(0.803722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.21460e6 | + | 7.29990e6i | 0.517983 | + | 0.897173i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −738598. | + | 1.27929e6i | −0.0899989 | + | 0.155883i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −623618. | + | 1.08014e6i | −0.0747005 | + | 0.129385i | −0.900956 | − | 0.433910i | \(-0.857133\pi\) |
0.826255 | + | 0.563296i | \(0.190467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00939e6 | + | 8.67652e6i | 0.594972 | + | 1.03052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.32769e7 | 1.55045 | 0.775226 | − | 0.631684i | \(-0.217636\pi\) | ||||
0.775226 | + | 0.631684i | \(0.217636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.68324e7 | −1.94919 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.02457e6 | − | 3.50666e6i | −0.230551 | − | 0.399325i | 0.727420 | − | 0.686193i | \(-0.240719\pi\) |
−0.957970 | + | 0.286868i | \(0.907386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.41857e6 | − | 5.92113e6i | 0.386063 | − | 0.668681i | −0.605853 | − | 0.795577i | \(-0.707168\pi\) |
0.991916 | + | 0.126896i | \(0.0405014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.64279e6 | + | 1.32377e7i | −0.848914 | + | 1.47036i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 348100. | + | 602927.i | 0.0383471 | + | 0.0664191i | 0.884562 | − | 0.466423i | \(-0.154457\pi\) |
−0.846215 | + | 0.532842i | \(0.821124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.11904e6 | −0.446367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.42785e6 | −0.153473 | −0.0767363 | − | 0.997051i | \(-0.524450\pi\) | ||||
−0.0767363 | + | 0.997051i | \(0.524450\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.51675e6 | − | 1.30194e7i | −0.794908 | − | 1.37682i | −0.922897 | − | 0.385046i | \(-0.874186\pi\) |
0.127989 | − | 0.991776i | \(-0.459148\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.58151e6 | + | 6.20336e6i | −0.375699 | + | 0.650730i | −0.990431 | − | 0.138006i | \(-0.955931\pi\) |
0.614732 | + | 0.788736i | \(0.289264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 196444. | − | 340251.i | 0.0202777 | − | 0.0351221i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.20252e7 | − | 3.81488e7i | −2.25538 | − | 3.90644i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.19145e7 | 1.20074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.38021e7 | −1.37998 | −0.689989 | − | 0.723820i | \(-0.742385\pi\) | ||||
−0.689989 | + | 0.723820i | \(0.742385\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.64708e6 | + | 2.85283e6i | 0.162099 | + | 0.280764i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.05084e6 | − | 3.55215e6i | 0.200254 | − | 0.346851i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.02329e6 | + | 3.50445e6i | −0.194497 | + | 0.336879i | −0.946736 | − | 0.322012i | \(-0.895641\pi\) |
0.752238 | + | 0.658891i | \(0.228974\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.44381e6 | + | 9.42896e6i | 0.519249 | + | 0.899366i | 0.999750 | + | 0.0223713i | \(0.00712159\pi\) |
−0.480501 | + | 0.876994i | \(0.659545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.45797e6 | −0.794339 | −0.397169 | − | 0.917745i | \(-0.630007\pi\) | ||||
−0.397169 | + | 0.917745i | \(0.630007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.07788e6 | −0.659617 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.47774e6 | + | 4.29157e6i | 0.227391 | + | 0.393853i | 0.957034 | − | 0.289975i | \(-0.0936472\pi\) |
−0.729643 | + | 0.683828i | \(0.760314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.49752e6 | + | 1.64502e7i | −0.864982 | + | 1.49819i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.37152e6 | + | 1.44999e7i | −0.750915 | + | 1.30062i | 0.196464 | + | 0.980511i | \(0.437054\pi\) |
−0.947380 | + | 0.320113i | \(0.896279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.53992e6 | + | 1.30595e7i | 0.671217 | + | 1.16258i | 0.977559 | + | 0.210661i | \(0.0675617\pi\) |
−0.306342 | + | 0.951922i | \(0.599105\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.61489e7 | −1.41608 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.51105e6 | −0.305578 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 626639. | + | 1.08537e6i | 0.0537293 | + | 0.0930619i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.07096e6 | + | 1.22473e7i | −0.601784 | + | 1.04232i | 0.390767 | + | 0.920490i | \(0.372210\pi\) |
−0.992551 | + | 0.121831i | \(0.961123\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.29397e6 | − | 1.26335e7i | 0.611635 | − | 1.05938i | −0.379330 | − | 0.925262i | \(-0.623845\pi\) |
0.990965 | − | 0.134122i | \(-0.0428213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52429e6 | + | 6.10425e6i | 0.293358 | + | 0.508110i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.10096e7 | −0.903065 | −0.451532 | − | 0.892255i | \(-0.649122\pi\) | ||||
−0.451532 | + | 0.892255i | \(0.649122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.10158e7 | 1.71127 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.12233e6 | + | 5.40803e6i | 0.250571 | + | 0.434001i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.51793e6 | − | 9.55733e6i | 0.439623 | − | 0.761450i | −0.558037 | − | 0.829816i | \(-0.688445\pi\) |
0.997660 | + | 0.0683661i | \(0.0217786\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.86058e7 | − | 3.22261e7i | 1.46112 | − | 2.53073i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.51917e6 | + | 2.63128e6i | 0.118447 | + | 0.205157i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.51294e7 | 1.93146 | 0.965732 | − | 0.259542i | \(-0.0835717\pi\) | ||||
0.965732 | + | 0.259542i | \(0.0835717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.14306e7 | 0.872332 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.29448e6 | + | 2.24211e6i | 0.0973974 | + | 0.168697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.26506e6 | + | 1.08514e7i | −0.468068 | + | 0.810718i | −0.999334 | − | 0.0364869i | \(-0.988383\pi\) |
0.531266 | + | 0.847205i | \(0.321717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.40457e6 | − | 7.62894e6i | 0.324474 | − | 0.562006i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.27222e6 | − | 9.13175e6i | −0.385681 | − | 0.668019i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.72246e6 | −0.124258 | −0.0621292 | − | 0.998068i | \(-0.519789\pi\) | ||||
−0.0621292 | + | 0.998068i | \(0.519789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.44937e6 | −0.462040 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.25862e7 | − | 2.18000e7i | −0.889304 | − | 1.54032i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.49425e6 | − | 6.05221e6i | 0.245198 | − | 0.424696i | −0.716989 | − | 0.697084i | \(-0.754480\pi\) |
0.962187 | + | 0.272389i | \(0.0878136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.38335e6 | − | 1.62524e7i | 0.649478 | − | 1.12493i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.96305e6 | + | 5.13214e6i | 0.203694 | + | 0.352808i | 0.949716 | − | 0.313113i | \(-0.101372\pi\) |
−0.746022 | + | 0.665922i | \(0.768039\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.09140e6 | −0.0740142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.06632e7 | 0.718254 | 0.359127 | − | 0.933289i | \(-0.383075\pi\) | ||||
0.359127 | + | 0.933289i | \(0.383075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.24932e6 | + | 1.60203e7i | 0.614664 | + | 1.06463i | 0.990443 | + | 0.137920i | \(0.0440417\pi\) |
−0.375779 | + | 0.926709i | \(0.622625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.04143e6 | − | 5.26791e6i | 0.200765 | − | 0.347734i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.11130e6 | + | 5.38892e6i | −0.202645 | + | 0.350992i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.30624e7 | − | 2.26247e7i | −0.845127 | − | 1.46380i | −0.885511 | − | 0.464618i | \(-0.846192\pi\) |
0.0403845 | − | 0.999184i | \(-0.487142\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.68804e7 | 2.35466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.49174e7 | 1.58039 | 0.790193 | − | 0.612858i | \(-0.209980\pi\) | ||||
0.790193 | + | 0.612858i | \(0.209980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.62194e6 | + | 9.73748e6i | 0.351904 | + | 0.609516i | 0.986583 | − | 0.163260i | \(-0.0522010\pi\) |
−0.634679 | + | 0.772776i | \(0.718868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.31000e6 | + | 1.09292e7i | −0.392390 | + | 0.679640i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.49604e7 | + | 2.59122e7i | −0.918237 | + | 1.59043i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.33731e6 | − | 7.51244e6i | −0.264487 | − | 0.458105i | 0.702942 | − | 0.711247i | \(-0.251869\pi\) |
−0.967429 | + | 0.253142i | \(0.918536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.17066e7 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.31571e7 | 3.77718 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.45748e6 | + | 2.52443e6i | 0.0860516 | + | 0.149046i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 269233. | − | 466326.i | 0.0157943 | − | 0.0273566i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.62985e6 | + | 1.14832e7i | −0.383998 | + | 0.665105i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.93215e6 | + | 6.81068e6i | 0.226304 | + | 0.391971i | 0.956710 | − | 0.291043i | \(-0.0940023\pi\) |
−0.730406 | + | 0.683014i | \(0.760669\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.19486e7 | 0.679009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.29807e6 | 0.299181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.48089e6 | + | 1.64214e7i | 0.528693 | + | 0.915723i | 0.999440 | + | 0.0334547i | \(0.0106509\pi\) |
−0.470747 | + | 0.882268i | \(0.656016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.85703e6 | + | 8.41262e6i | −0.269156 | + | 0.466192i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.36488e6 | − | 7.56019e6i | 0.238882 | − | 0.413755i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.09956e6 | + | 1.22968e7i | 0.386137 | + | 0.668809i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.09408e7 | 1.12492 | 0.562459 | − | 0.826825i | \(-0.309855\pi\) | ||||
0.562459 | + | 0.826825i | \(0.309855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.21466e7 | −1.71626 | −0.858130 | − | 0.513432i | \(-0.828374\pi\) | ||||
−0.858130 | + | 0.513432i | \(0.828374\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.02629e7 | − | 3.50963e7i | −1.06858 | − | 1.85083i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.00229e6 | − | 1.55924e7i | 0.471844 | − | 0.817257i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.48802e7 | + | 2.57733e7i | −0.770463 | + | 1.33448i | 0.166846 | + | 0.985983i | \(0.446642\pi\) |
−0.937309 | + | 0.348498i | \(0.886692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.26102e6 | − | 1.43085e7i | −0.425142 | − | 0.736368i | 0.571291 | − | 0.820747i | \(-0.306443\pi\) |
−0.996434 | + | 0.0843793i | \(0.973109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.49588e7 | 1.26900 | 0.634498 | − | 0.772925i | \(-0.281207\pi\) | ||||
0.634498 | + | 0.772925i | \(0.281207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.92909e7 | −1.48029 | −0.740145 | − | 0.672447i | \(-0.765243\pi\) | ||||
−0.740145 | + | 0.672447i | \(0.765243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.83655e6 | − | 8.37716e6i | −0.241504 | − | 0.418296i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.25373e7 | − | 5.63563e7i | 1.61498 | − | 2.79722i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.87417e7 | + | 3.24616e7i | −0.919189 | + | 1.59208i | −0.118539 | + | 0.992949i | \(0.537821\pi\) |
−0.800650 | + | 0.599133i | \(0.795512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.39833e6 | + | 1.10822e7i | 0.311944 | + | 0.540303i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.58473e6 | −0.172709 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.40873e7 | 0.674713 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.02527e6 | − | 8.70402e6i | −0.237868 | − | 0.411999i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.41357e6 | + | 1.28407e7i | −0.348863 | + | 0.604248i | −0.986048 | − | 0.166463i | \(-0.946765\pi\) |
0.637185 | + | 0.770711i | \(0.280099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.66185e6 | − | 4.61046e6i | 0.123803 | − | 0.214433i | −0.797461 | − | 0.603370i | \(-0.793824\pi\) |
0.921264 | + | 0.388937i | \(0.127158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.34434e7 | + | 2.32846e7i | 0.621621 | + | 1.07668i | 0.989184 | + | 0.146680i | \(0.0468589\pi\) |
−0.367563 | + | 0.929999i | \(0.619808\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.21441e6 | −0.101212 | −0.0506060 | − | 0.998719i | \(-0.516115\pi\) | ||||
−0.0506060 | + | 0.998719i | \(0.516115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.81846e7 | 2.18961 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.79066e6 | + | 8.29766e6i | 0.215202 | + | 0.372740i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.30687e6 | + | 3.99562e6i | −0.103033 | + | 0.178459i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.33494e7 | + | 5.77629e7i | −1.47254 | + | 2.55052i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.62323e7 | − | 2.81151e7i | −0.712657 | − | 1.23436i | −0.963856 | − | 0.266423i | \(-0.914158\pi\) |
0.251199 | − | 0.967935i | \(-0.419175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.78418e6 | −0.337888 | −0.168944 | − | 0.985626i | \(-0.554036\pi\) | ||||
−0.168944 | + | 0.985626i | \(0.554036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.71890e7 | −0.741906 | −0.370953 | − | 0.928652i | \(-0.620969\pi\) | ||||
−0.370953 | + | 0.928652i | \(0.620969\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.81716e7 | + | 3.14742e7i | 0.775506 | + | 1.34322i | 0.934510 | + | 0.355938i | \(0.115838\pi\) |
−0.159004 | + | 0.987278i | \(0.550828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51796e6 | − | 2.62918e6i | 0.0644178 | − | 0.111575i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.65979e6 | + | 8.07099e6i | −0.195541 | + | 0.338687i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.33067e7 | + | 2.30478e7i | 0.555279 | + | 0.961771i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.93555e7 | 0.798739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.47270e7 | 0.604368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.49750e6 | + | 2.59375e6i | 0.0607779 | + | 0.105270i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.39209e6 | + | 7.60732e6i | −0.177277 | + | 0.307053i | −0.940947 | − | 0.338554i | \(-0.890062\pi\) |
0.763670 | + | 0.645607i | \(0.223396\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.83503e6 | − | 3.17836e6i | 0.0732566 | − | 0.126884i | −0.827070 | − | 0.562099i | \(-0.809994\pi\) |
0.900327 | + | 0.435214i | \(0.143327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.22641e6 | + | 1.07845e7i | 0.247207 | + | 0.428175i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.75060e7 | 0.687484 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.38118e7 | −1.32063 | −0.660313 | − | 0.750990i | \(-0.729576\pi\) | ||||
−0.660313 | + | 0.750990i | \(0.729576\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.13815e6 | − | 1.97133e6i | −0.0439739 | − | 0.0761650i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.60286e7 | − | 6.24034e7i | 1.38450 | − | 2.39803i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.89173e6 | + | 1.02048e7i | −0.223977 | + | 0.387939i | −0.956012 | − | 0.293327i | \(-0.905237\pi\) |
0.732035 | + | 0.681267i | \(0.238571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.64014e6 | − | 8.03697e6i | −0.175452 | − | 0.303891i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.48673e7 | −0.930250 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.78550e7 | −1.40856 | −0.704278 | − | 0.709924i | \(-0.748729\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.28136e7 | + | 3.95143e7i | 0.839884 | + | 1.45472i | 0.889991 | + | 0.455978i | \(0.150710\pi\) |
−0.0501075 | + | 0.998744i | \(0.515956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.28151e6 | − | 2.21964e6i | 0.0469291 | − | 0.0812836i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.07942e7 | + | 3.60166e7i | −0.753472 | + | 1.30505i | 0.192659 | + | 0.981266i | \(0.438289\pi\) |
−0.946130 | + | 0.323786i | \(0.895044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.84519e7 | − | 3.19597e7i | −0.665084 | − | 1.15196i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.40042e7 | 1.92617 | 0.963087 | − | 0.269190i | \(-0.0867560\pi\) | ||||
0.963087 | + | 0.269190i | \(0.0867560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.19036e6 | 0.219638 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.68413e6 | − | 1.67734e7i | −0.340028 | − | 0.588945i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.96668e6 | + | 1.72628e7i | −0.348130 | + | 0.602979i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.95674e7 | − | 3.38917e7i | 0.676416 | − | 1.17159i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.64673e6 | + | 1.49766e7i | 0.297362 | + | 0.515046i | 0.975532 | − | 0.219859i | \(-0.0705598\pi\) |
−0.678169 | + | 0.734906i | \(0.737226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.55169e7 | 1.54926 | 0.774630 | − | 0.632415i | \(-0.217936\pi\) | ||||
0.774630 | + | 0.632415i | \(0.217936\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.42944e7 | −1.16129 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.29826e6 | + | 5.71275e6i | 0.110547 | + | 0.191474i | 0.915991 | − | 0.401199i | \(-0.131406\pi\) |
−0.805444 | + | 0.592672i | \(0.798073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 290216. | − | 502669.i | 0.00967753 | − | 0.0167620i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.84729e7 | − | 3.19959e7i | 0.609748 | − | 1.05611i | −0.381534 | − | 0.924355i | \(-0.624604\pi\) |
0.991282 | − | 0.131760i | \(-0.0420627\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.50923e7 | + | 7.81022e7i | 1.48085 | + | 2.56491i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.58308e7 | −0.514649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.56015e6 | 0.244538 | 0.122269 | − | 0.992497i | \(-0.460983\pi\) | ||||
0.122269 | + | 0.992497i | \(0.460983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.74935e7 | − | 8.22612e7i | −1.52082 | − | 2.63413i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.80763e6 | − | 1.35232e7i | 0.248761 | − | 0.430866i | −0.714422 | − | 0.699715i | \(-0.753310\pi\) |
0.963182 | + | 0.268850i | \(0.0866434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 432.6.i.d.289.5 | 10 | ||
3.2 | odd | 2 | 144.6.i.d.97.1 | 10 | |||
4.3 | odd | 2 | 108.6.e.a.73.5 | 10 | |||
9.4 | even | 3 | inner | 432.6.i.d.145.5 | 10 | ||
9.5 | odd | 6 | 144.6.i.d.49.1 | 10 | |||
12.11 | even | 2 | 36.6.e.a.25.5 | yes | 10 | ||
36.7 | odd | 6 | 324.6.a.d.1.1 | 5 | |||
36.11 | even | 6 | 324.6.a.e.1.5 | 5 | |||
36.23 | even | 6 | 36.6.e.a.13.5 | ✓ | 10 | ||
36.31 | odd | 6 | 108.6.e.a.37.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.5 | ✓ | 10 | 36.23 | even | 6 | ||
36.6.e.a.25.5 | yes | 10 | 12.11 | even | 2 | ||
108.6.e.a.37.5 | 10 | 36.31 | odd | 6 | |||
108.6.e.a.73.5 | 10 | 4.3 | odd | 2 | |||
144.6.i.d.49.1 | 10 | 9.5 | odd | 6 | |||
144.6.i.d.97.1 | 10 | 3.2 | odd | 2 | |||
324.6.a.d.1.1 | 5 | 36.7 | odd | 6 | |||
324.6.a.e.1.5 | 5 | 36.11 | even | 6 | |||
432.6.i.d.145.5 | 10 | 9.4 | even | 3 | inner | ||
432.6.i.d.289.5 | 10 | 1.1 | even | 1 | trivial |