Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,6,Mod(13,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("36.13");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.77381751327\) |
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: | \( 2^{8}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 13.5 | ||
Root | \(1.11227i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.13 |
Dual form | 36.6.e.a.25.5 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 13.7082 | + | 7.42194i | 0.879381 | + | 0.476118i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −55.1996 | + | 95.6086i | −0.987441 | + | 1.71030i | −0.356899 | + | 0.934143i | \(0.616166\pi\) |
−0.630542 | + | 0.776155i | \(0.717167\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −50.8724 | − | 88.1135i | −0.392407 | − | 0.679669i | 0.600359 | − | 0.799730i | \(-0.295024\pi\) |
−0.992766 | + | 0.120061i | \(0.961691\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 132.829 | + | 203.483i | 0.546623 | + | 0.837379i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 75.1560 | + | 130.174i | 0.187276 | + | 0.324371i | 0.944341 | − | 0.328968i | \(-0.106701\pi\) |
−0.757065 | + | 0.653339i | \(0.773367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −317.712 | + | 550.293i | −0.521405 | + | 0.903100i | 0.478285 | + | 0.878205i | \(0.341259\pi\) |
−0.999690 | + | 0.0248953i | \(0.992075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1466.29 | + | 900.933i | −1.68264 | + | 1.03387i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1498.54 | 1.25761 | 0.628806 | − | 0.777562i | \(-0.283544\pi\) | ||||
0.628806 | + | 0.777562i | \(0.283544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1437.69 | 0.913651 | 0.456825 | − | 0.889556i | \(-0.348986\pi\) | ||||
0.456825 | + | 0.889556i | \(0.348986\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −43.3949 | − | 1585.45i | −0.0214729 | − | 0.784520i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 632.053 | − | 1094.75i | 0.249134 | − | 0.431513i | −0.714151 | − | 0.699991i | \(-0.753187\pi\) |
0.963286 | + | 0.268478i | \(0.0865206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4531.50 | − | 7848.79i | −1.45008 | − | 2.51161i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 310.614 | + | 3775.24i | 0.0819995 | + | 0.996632i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1388.75 | + | 2405.38i | 0.306640 | + | 0.531116i | 0.977625 | − | 0.210355i | \(-0.0674620\pi\) |
−0.670985 | + | 0.741471i | \(0.734129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3484.34 | − | 6035.05i | 0.651203 | − | 1.12792i | −0.331628 | − | 0.943410i | \(-0.607598\pi\) |
0.982831 | − | 0.184506i | \(-0.0590686\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 64.1092 | + | 2342.26i | 0.0102479 | + | 0.374412i | ||||
\(34\) | 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 | ||||||||
\(39\) | −8439.51 | + | 5185.49i | −0.888496 | + | 0.545919i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1013.77 | − | 1755.90i | 0.0941843 | − | 0.163132i | −0.815084 | − | 0.579343i | \(-0.803309\pi\) |
0.909268 | + | 0.416211i | \(0.136642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6261.65 | + | 10845.5i | 0.516438 | + | 0.894496i | 0.999818 | + | 0.0190856i | \(0.00607551\pi\) |
−0.483380 | + | 0.875410i | \(0.660591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −26786.9 | + | 1467.45i | −1.97193 | + | 0.108027i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3241.17 | + | 5613.87i | 0.214021 | + | 0.370696i | 0.952969 | − | 0.303066i | \(-0.0980104\pi\) |
−0.738948 | + | 0.673763i | \(0.764677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3227.51 | − | 5590.21i | 0.192034 | − | 0.332612i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20542.3 | + | 11122.1i | 1.10592 | + | 0.598771i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9827.54 | 0.480568 | 0.240284 | − | 0.970703i | \(-0.422759\pi\) | ||||
0.240284 | + | 0.970703i | \(0.422759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16594.3 | −0.739696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19708.1 | + | 10670.4i | 0.803448 | + | 0.435006i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23544.0 | + | 40779.3i | −0.880541 | + | 1.52514i | −0.0298005 | + | 0.999556i | \(0.509487\pi\) |
−0.850741 | + | 0.525586i | \(0.823846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4168.92 | − | 7220.78i | −0.143450 | − | 0.248462i | 0.785344 | − | 0.619060i | \(-0.212486\pi\) |
−0.928793 | + | 0.370598i | \(0.879153\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11172.3 | − | 22055.7i | 0.354641 | − | 0.700116i | ||||
\(64\) | 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 | \(-0.801832\pi\) |
0.911190 | + | 0.411987i | \(0.135165\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16789.5 | − | 10316.0i | 0.424535 | − | 0.260848i | ||||
\(70\) | 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 | ||||||||
\(75\) | −3865.44 | − | 141225.i | −0.0793497 | − | 2.89907i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7646.73 | − | 13244.5i | 0.146977 | − | 0.254571i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31871.4 | + | 55202.9i | 0.574558 | + | 0.995163i | 0.996090 | + | 0.0883495i | \(0.0281592\pi\) |
−0.421532 | + | 0.906814i | \(0.638507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −23761.7 | + | 54057.1i | −0.402406 | + | 0.915461i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −41423.3 | − | 71747.2i | −0.660008 | − | 1.14317i | −0.980613 | − | 0.195954i | \(-0.937220\pi\) |
0.320605 | − | 0.947213i | \(-0.396114\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −82718.9 | + | 143273.i | −1.24182 | + | 2.15089i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1184.62 | + | 43280.7i | 0.0167796 | + | 0.613050i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3861.51 | −0.0516752 | −0.0258376 | − | 0.999666i | \(-0.508225\pi\) | ||||
−0.0258376 | + | 0.999666i | \(0.508225\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 64651.0 | 0.818412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 92555.9 | − | 56869.1i | 1.10968 | − | 0.681819i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −79359.8 | + | 137455.i | −0.902176 | + | 1.56262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −34638.6 | − | 59995.8i | −0.373793 | − | 0.647428i | 0.616353 | − | 0.787470i | \(-0.288610\pi\) |
−0.990146 | + | 0.140042i | \(0.955276\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16505.3 | + | 32583.9i | −0.169252 | + | 0.334130i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12722.8 | + | 22036.6i | 0.124103 | + | 0.214952i | 0.921382 | − | 0.388659i | \(-0.127061\pi\) |
−0.797279 | + | 0.603611i | \(0.793728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 31693.9 | − | 54895.4i | 0.294363 | − | 0.509851i | −0.680474 | − | 0.732772i | \(-0.738226\pi\) |
0.974836 | + | 0.222922i | \(0.0715594\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 153978. | + | 83367.3i | 1.36297 | + | 0.737942i | ||||
\(106\) | 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 | ||||||||
\(111\) | −108990. | − | 59009.7i | −0.839612 | − | 0.454586i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −58718.5 | + | 101703.i | −0.432592 | + | 0.749272i | −0.997096 | − | 0.0761589i | \(-0.975734\pi\) |
0.564503 | + | 0.825431i | \(0.309068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 69778.2 | + | 120859.i | 0.492011 | + | 0.852188i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −154177. | + | 8446.19i | −1.04125 | + | 0.0570422i | ||||
\(118\) | 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 | ||||||||
\(123\) | 26929.1 | − | 16546.0i | 0.160494 | − | 0.0986124i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 655551. | 3.75259 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29838.6 | −0.164161 | −0.0820803 | − | 0.996626i | \(-0.526156\pi\) | ||||
−0.0820803 | + | 0.996626i | \(0.526156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5341.28 | + | 195146.i | 0.0282599 | + | 1.03249i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 86028.8 | − | 149006.i | 0.437992 | − | 0.758624i | −0.559543 | − | 0.828801i | \(-0.689023\pi\) |
0.997535 | + | 0.0701777i | \(0.0223566\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73138.5 | − | 126680.i | −0.358523 | − | 0.620980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −378091. | − | 178694.i | −1.78551 | − | 0.843872i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −95180.7 | − | 164858.i | −0.433259 | − | 0.750426i | 0.563893 | − | 0.825848i | \(-0.309303\pi\) |
−0.997152 | + | 0.0754216i | \(0.975970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 168532. | − | 291905.i | 0.739852 | − | 1.28146i | −0.212710 | − | 0.977115i | \(-0.568229\pi\) |
0.952562 | − | 0.304345i | \(-0.0984376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2764.77 | + | 101012.i | 0.0117115 | + | 0.427883i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −95511.9 | −0.390586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −306634. | −1.21115 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 85733.5 | − | 52677.3i | 0.327233 | − | 0.201062i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27549.4 | − | 47716.9i | 0.101659 | − | 0.176079i | −0.810709 | − | 0.585449i | \(-0.800918\pi\) |
0.912368 | + | 0.409370i | \(0.134252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −167032. | − | 289308.i | −0.596152 | − | 1.03257i | −0.993383 | − | 0.114847i | \(-0.963362\pi\) |
0.397231 | − | 0.917719i | \(-0.369971\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 199050. | + | 304928.i | 0.687440 | + | 1.05310i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 384669. | + | 666266.i | 1.28605 | + | 2.22750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60053.4 | − | 104015.i | 0.194441 | − | 0.336782i | −0.752276 | − | 0.658848i | \(-0.771044\pi\) |
0.946717 | + | 0.322066i | \(0.104377\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 134718. | + | 72939.4i | 0.422603 | + | 0.228807i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −128616. | −0.391048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 367083. | 1.08217 | 0.541085 | − | 0.840968i | \(-0.318014\pi\) | ||||
0.541085 | + | 0.840968i | \(0.318014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −227478. | − | 123162.i | −0.650475 | − | 0.352182i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −294724. | + | 510477.i | −0.817758 | + | 1.41640i | 0.0895730 | + | 0.995980i | \(0.471450\pi\) |
−0.907331 | + | 0.420418i | \(0.861884\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16235.3 | − | 28120.4i | −0.0437264 | − | 0.0757363i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 190967. | + | 292545.i | 0.499423 | + | 0.765072i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −218229. | − | 377983.i | −0.554366 | − | 0.960190i | −0.997953 | − | 0.0639583i | \(-0.979628\pi\) |
0.443587 | − | 0.896231i | \(-0.353706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −461056. | + | 798572.i | −1.13804 | + | 1.97115i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −625407. | + | 384269.i | −1.50048 | + | 0.921940i | ||||
\(178\) | 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 | ||||||||
\(183\) | −3556.15 | − | 129925.i | −0.00784969 | − | 0.286792i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 438876. | − | 760156.i | 0.942785 | − | 1.63295i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 112624. | + | 195071.i | 0.235520 | + | 0.407933i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 316848. | − | 219425.i | 0.645203 | − | 0.446818i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 28036.3 | + | 48560.2i | 0.0556079 | + | 0.0963157i | 0.892489 | − | 0.451068i | \(-0.148957\pi\) |
−0.836881 | + | 0.547384i | \(0.815624\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −177242. | + | 306992.i | −0.342510 | + | 0.593244i | −0.984898 | − | 0.173135i | \(-0.944610\pi\) |
0.642388 | + | 0.766379i | \(0.277944\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29919.6 | − | 1.09313e6i | −0.0563469 | − | 2.05866i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −816895. | −1.49969 | −0.749844 | − | 0.661615i | \(-0.769871\pi\) | ||||
−0.749844 | + | 0.661615i | \(0.769871\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 860396. | 1.54016 | 0.770079 | − | 0.637948i | \(-0.220217\pi\) | ||||
0.770079 | + | 0.637948i | \(0.220217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 96436.9 | − | 59253.8i | 0.168366 | − | 0.103449i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 141298. | − | 244735.i | 0.240655 | − | 0.416827i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 111919. | + | 193850.i | 0.186003 | + | 0.322166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 306718. | − | 16802.8i | 0.497523 | − | 0.0272555i | ||||
\(208\) | 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 | \(-0.736566\pi\) |
0.975985 | + | 0.217836i | \(0.0698997\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 49107.3 | + | 26587.8i | 0.0741646 | + | 0.0401545i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.38256e6 | −2.03981 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −709026. | −1.02215 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 796138. | + | 431048.i | 1.12170 | + | 0.607317i | ||||
\(220\) | 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 | \(-0.103021\pi\) |
−0.749462 | + | 0.662047i | \(0.769688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 995178. | − | 1.96463e6i | 1.31052 | − | 2.58717i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −343990. | − | 595808.i | −0.443079 | − | 0.767435i | 0.554837 | − | 0.831959i | \(-0.312780\pi\) |
−0.997916 | + | 0.0645238i | \(0.979447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 543233. | − | 940908.i | 0.684538 | − | 1.18565i | −0.289044 | − | 0.957316i | \(-0.593337\pi\) |
0.973582 | − | 0.228339i | \(-0.0733294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 203123. | − | 124805.i | 0.250455 | − | 0.153887i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 168058. | 0.202801 | 0.101400 | − | 0.994846i | \(-0.467668\pi\) | ||||
0.101400 | + | 0.994846i | \(0.467668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −715646. | −0.845334 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27186.8 | + | 993280.i | 0.0314403 | + | 1.14869i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 773138. | − | 1.33911e6i | 0.875512 | − | 1.51643i | 0.0192952 | − | 0.999814i | \(-0.493858\pi\) |
0.856217 | − | 0.516617i | \(-0.172809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 576865. | + | 999160.i | 0.639782 | + | 1.10813i | 0.985480 | + | 0.169789i | \(0.0543086\pi\) |
−0.345699 | + | 0.938346i | \(0.612358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −726938. | + | 564668.i | −0.789736 | + | 0.613447i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 356314. | + | 617155.i | 0.379244 | + | 0.656869i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −456770. | + | 791149.i | −0.476382 | + | 0.825118i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35334.7 | − | 1.29097e6i | −0.0361162 | − | 1.31952i | ||||
\(250\) | 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 | ||||||||
\(255\) | −2.19729e6 | + | 1.35009e6i | −2.11611 | + | 1.30020i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −54171.0 | + | 93826.9i | −0.0511604 | + | 0.0886124i | −0.890471 | − | 0.455039i | \(-0.849625\pi\) |
0.839311 | + | 0.543651i | \(0.182959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 404471. | + | 700565.i | 0.374661 | + | 0.648931i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −304988. | + | 602092.i | −0.277128 | + | 0.547094i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 868353. | + | 1.50403e6i | 0.774117 | + | 1.34081i | 0.935289 | + | 0.353884i | \(0.115139\pi\) |
−0.161172 | + | 0.986926i | \(0.551527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −542476. | + | 939597.i | −0.474533 | + | 0.821915i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −52934.4 | − | 28659.9i | −0.0454423 | − | 0.0246035i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18297.3 | 0.0154172 | 0.00770860 | − | 0.999970i | \(-0.497546\pi\) | ||||
0.00770860 | + | 0.999970i | \(0.497546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7105.09 | 0.00587688 | 0.00293844 | − | 0.999996i | \(-0.499065\pi\) | ||||
0.00293844 | + | 0.999996i | \(0.499065\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 886249. | + | 479836.i | 0.719696 | + | 0.389661i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 681139. | − | 1.17977e6i | 0.543130 | − | 0.940729i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −355202. | − | 615227.i | −0.278148 | − | 0.481766i | 0.692777 | − | 0.721152i | \(-0.256387\pi\) |
−0.970924 | + | 0.239386i | \(0.923054\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.69085e6 | − | 92629.2i | 1.30046 | − | 0.0712422i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 514224. | + | 890661.i | 0.388496 | + | 0.672894i | 0.992247 | − | 0.124278i | \(-0.0396615\pi\) |
−0.603752 | + | 0.797172i | \(0.706328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 922317. | − | 1.59750e6i | 0.684564 | − | 1.18570i | −0.289010 | − | 0.957326i | \(-0.593326\pi\) |
0.973574 | − | 0.228374i | \(-0.0733407\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.10806e6 | + | 1.29526e6i | −1.53735 | + | 0.944593i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −206291. | −0.147834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 825769. | 0.581586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29547.2 | − | 1.07952e6i | −0.0204543 | − | 0.747306i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −470486. | + | 814906.i | −0.320168 | + | 0.554547i | −0.980522 | − | 0.196407i | \(-0.937073\pi\) |
0.660355 | + | 0.750954i | \(0.270406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.59924e6 | − | 4.50201e6i | −1.73896 | − | 3.01198i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −468093. | + | 324166.i | −0.307923 | + | 0.213244i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 401621. | + | 695629.i | 0.259800 | + | 0.449987i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 637090. | − | 1.10347e6i | 0.405307 | − | 0.702013i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10852.8 | + | 396511.i | 0.00679101 | + | 0.248112i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 920492. | 0.566592 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.93094e6 | −1.77485 | −0.887425 | − | 0.460952i | \(-0.847508\pi\) | ||||
−0.887425 | + | 0.460952i | \(0.847508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 841897. | − | 517287.i | 0.501606 | − | 0.308202i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.14126e6 | − | 1.97671e6i | 0.669086 | − | 1.15889i | −0.309074 | − | 0.951038i | \(-0.600019\pi\) |
0.978160 | − | 0.207853i | \(-0.0666477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −401324. | − | 695114.i | −0.231544 | − | 0.401047i | 0.726718 | − | 0.686936i | \(-0.241045\pi\) |
−0.958263 | + | 0.285889i | \(0.907711\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.49201e6 | + | 2.28563e6i | 0.847220 | + | 1.29787i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −555982. | − | 962990.i | −0.310751 | − | 0.538237i | 0.667774 | − | 0.744364i | \(-0.267247\pi\) |
−0.978525 | + | 0.206127i | \(0.933914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −208746. | + | 361558.i | −0.114853 | + | 0.198930i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −838378. | − | 453918.i | −0.454127 | − | 0.245875i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.15443e6 | 1.14902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.75885e6 | 3.02432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.70031e6 | − | 920588.i | −0.879344 | − | 0.476098i | ||||
\(328\) | 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 | \(-0.0671149\pi\) |
−0.670176 | + | 0.742202i | \(0.733782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.05609e6 | − | 1.61783e6i | −0.521903 | − | 0.799509i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 400799. | + | 694203.i | 0.195126 | + | 0.337967i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.15064e6 | + | 1.99297e6i | −0.551907 | + | 0.955930i | 0.446230 | + | 0.894918i | \(0.352766\pi\) |
−0.998137 | + | 0.0610122i | \(0.980567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.55976e6 | + | 958365.i | −0.737155 | + | 0.452931i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.04748e6 | 0.487818 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.36679e6 | −1.08624 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 59521.8 | + | 2.17465e6i | 0.0269233 | + | 0.983654i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −809651. | + | 1.40236e6i | −0.360973 | + | 0.625223i | −0.988121 | − | 0.153677i | \(-0.950889\pi\) |
0.627149 | + | 0.778900i | \(0.284222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 139307. | + | 241287.i | 0.0612223 | + | 0.106040i | 0.895012 | − | 0.446042i | \(-0.147167\pi\) |
−0.833790 | + | 0.552082i | \(0.813833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.17617e6 | − | 1.02851e6i | −0.942814 | − | 0.445595i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.68496e6 | − | 2.91844e6i | −0.719704 | − | 1.24656i | −0.961117 | − | 0.276142i | \(-0.910944\pi\) |
0.241413 | − | 0.970422i | \(-0.422389\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −197743. | + | 342501.i | −0.0832781 | + | 0.144242i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −65029.0 | − | 2.37586e6i | −0.0270045 | − | 0.986621i | ||||
\(358\) | 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 | ||||||||
\(363\) | 1.83895e6 | − | 1.12991e6i | 0.732492 | − | 0.450065i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.20586e6 | + | 5.55271e6i | −1.25954 | + | 2.18159i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.97882e6 | + | 3.42743e6i | 0.766906 | + | 1.32832i | 0.939233 | + | 0.343281i | \(0.111538\pi\) |
−0.172327 | + | 0.985040i | \(0.555129\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 491953. | − | 26950.4i | 0.188087 | − | 0.0103038i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −499950. | − | 865939.i | −0.188578 | − | 0.326627i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 961939. | − | 1.66613e6i | 0.357994 | − | 0.620063i | −0.629632 | − | 0.776894i | \(-0.716794\pi\) |
0.987626 | + | 0.156830i | \(0.0501276\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.98642e6 | + | 4.86546e6i | 3.29996 | + | 1.78668i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.76489e6 | −0.639534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.11015e6 | −1.11220 | −0.556101 | − | 0.831115i | \(-0.687703\pi\) | ||||
−0.556101 | + | 0.831115i | \(0.687703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −409033. | − | 221460.i | −0.144360 | − | 0.0781598i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.41711e6 | − | 2.45450e6i | 0.493634 | − | 0.855000i | −0.506339 | − | 0.862335i | \(-0.669001\pi\) |
0.999973 | + | 0.00733479i | \(0.00233476\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 844193. | + | 1.46218e6i | 0.290262 | + | 0.502748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.37514e6 | + | 2.71474e6i | −0.466735 | + | 0.921406i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.02692e6 | + | 1.77867e6i | 0.344081 | + | 0.595966i | 0.985186 | − | 0.171487i | \(-0.0548571\pi\) |
−0.641105 | + | 0.767453i | \(0.721524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 947157. | − | 1.64052e6i | 0.313314 | − | 0.542676i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.28522e6 | − | 1.40411e6i | 0.746356 | − | 0.458584i | ||||
\(394\) | 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 | ||||||||
\(399\) | −62388.2 | − | 2.27938e6i | −0.0196187 | − | 0.716778i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.65864e6 | + | 4.60491e6i | −0.825656 | + | 1.43008i | 0.0757604 | + | 0.997126i | \(0.475862\pi\) |
−0.901417 | + | 0.432953i | \(0.857472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.21403e6 | + | 3.83482e6i | 0.679081 | + | 1.17620i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.85669e6 | − | 5.25575e6i | −1.16836 | − | 1.59220i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −597543. | − | 1.03498e6i | −0.178807 | − | 0.309702i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.57922e6 | + | 2.73528e6i | −0.466803 | + | 0.808526i | −0.999281 | − | 0.0379179i | \(-0.987927\pi\) |
0.532478 | + | 0.846444i | \(0.321261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −81190.6 | − | 2.96633e6i | −0.0237083 | − | 0.866193i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.79095e6 | 1.38212 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.14620e6 | 2.60688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.47677e6 | − | 2.75067e6i | 1.26074 | − | 0.774636i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.80782e6 | − | 3.13124e6i | 0.503060 | − | 0.871326i | −0.496933 | − | 0.867789i | \(-0.665541\pi\) |
0.999994 | − | 0.00353739i | \(-0.00112599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −514445. | − | 891044.i | −0.141460 | − | 0.245016i | 0.786587 | − | 0.617480i | \(-0.211846\pi\) |
−0.928047 | + | 0.372464i | \(0.878513\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −711805. | + | 1.40521e6i | −0.193424 | + | 0.381848i | ||||
\(424\) | 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 | ||||||||
\(429\) | −1.30930e6 | − | 708884.i | −0.343474 | − | 0.185965i | ||||
\(430\) | 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 | ||||||||
\(435\) | −4.20339e6 | − | 2.27582e6i | −1.06507 | − | 0.576653i | ||||
\(436\) | 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 | \(-0.147219\pi\) |
−0.833881 | + | 0.551945i | \(0.813886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.56622e6 | − | 85801.4i | 0.383492 | − | 0.0210086i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 97755.8 | + | 169318.i | 0.0236665 | + | 0.0409915i | 0.877616 | − | 0.479364i | \(-0.159133\pi\) |
−0.853950 | + | 0.520356i | \(0.825799\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 213154. | − | 369194.i | 0.0510263 | − | 0.0883801i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 731804. | − | 449643.i | 0.173231 | − | 0.106439i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.51225e6 | −0.354004 | −0.177002 | − | 0.984210i | \(-0.556640\pi\) | ||||
−0.177002 | + | 0.984210i | \(0.556640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 304763. | 0.0705538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −142481. | − | 5.20559e6i | −0.0326220 | − | 1.19186i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.56871e6 | + | 6.18119e6i | −0.808133 | + | 1.39973i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28236e6 | − | 2.22111e6i | −0.287223 | − | 0.497484i | 0.685923 | − | 0.727674i | \(-0.259399\pi\) |
−0.973146 | + | 0.230190i | \(0.926065\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 465467. | + | 5.65735e6i | 0.103123 | + | 1.25338i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.68336e6 | + | 4.64772e6i | 0.588067 | + | 1.01856i | 0.994485 | + | 0.104875i | \(0.0334443\pi\) |
−0.406418 | + | 0.913687i | \(0.633222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.75107e6 | + | 4.76500e6i | −0.596417 | + | 1.03302i | 0.396928 | + | 0.917850i | \(0.370076\pi\) |
−0.993345 | + | 0.115175i | \(0.963257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 328128. | + | 1.19883e7i | 0.0703738 | + | 2.57113i | ||||
\(466\) | 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 | ||||||||
\(471\) | 1.59522e6 | − | 980152.i | 0.331336 | − | 0.203583i | ||||
\(472\) | 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 | ||||||||
\(477\) | 1.30539e6 | + | 1.99974e6i | 0.262690 | + | 0.402417i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 281267. | + | 487168.i | 0.0560118 | + | 0.0970153i | 0.892672 | − | 0.450707i | \(-0.148828\pi\) |
−0.836660 | + | 0.547723i | \(0.815495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.52603e6 | − | 4.37522e6i | 0.497825 | − | 0.862258i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.76309e6 | − | 954581.i | −0.343881 | − | 0.186185i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.64815e6 | 1.47639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.14185e6 | 0.600292 | 0.300146 | − | 0.953893i | \(-0.402965\pi\) | ||||
0.300146 | + | 0.953893i | \(0.402965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.03205e6 | + | 2.72447e6i | 0.951641 | + | 0.515241i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.86681e6 | + | 4.96545e6i | −0.536654 | + | 0.929512i | 0.462427 | + | 0.886657i | \(0.346979\pi\) |
−0.999081 | + | 0.0428549i | \(0.986355\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.08110e6 | + | 3.60457e6i | 0.385634 | + | 0.667937i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.20422e6 | − | 3.37667e6i | −0.404335 | − | 0.619405i | ||||
\(496\) | 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 | \(-0.882620\pi\) |
0.778555 | + | 0.627576i | \(0.215953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.82887e6 | + | 4.81030e6i | −1.39349 | + | 0.856205i | ||||
\(502\) | 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 | ||||||||
\(507\) | −13849.0 | − | 505977.i | −0.00239275 | − | 0.0874200i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 521280. | − | 902884.i | 0.0891819 | − | 0.154468i | −0.817984 | − | 0.575242i | \(-0.804908\pi\) |
0.907166 | + | 0.420774i | \(0.138241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.95454e6 | − | 5.11742e6i | −0.500539 | − | 0.866959i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 446565. | + | 5.42761e6i | 0.0749189 | + | 0.910574i | ||||
\(514\) | 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 | ||||||||
\(519\) | −186152. | − | 6.80115e6i | −0.0303354 | − | 1.10832i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.52239e6 | 1.53692 | 0.768461 | − | 0.639897i | \(-0.221023\pi\) | ||||
0.768461 | + | 0.639897i | \(0.221023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.97573e6 | −0.475706 | −0.237853 | − | 0.971301i | \(-0.576444\pi\) | ||||
−0.237853 | + | 0.971301i | \(0.576444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.22472e7 | + | 7.52506e6i | −1.93927 | + | 1.19155i | ||||
\(526\) | 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 | ||||||||
\(531\) | −1.14252e7 | + | 625903.i | −1.75845 | + | 0.0963320i | ||||
\(532\) | 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 | ||||||||
\(537\) | 3.30456e6 | + | 1.78916e6i | 0.494513 | + | 0.267741i | ||||
\(538\) | 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 | ||||||||
\(543\) | 371888. | + | 201349.i | 0.0541268 | + | 0.0293055i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.84674e6 | − | 1.18589e7i | 0.987399 | − | 1.71023i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.68486e6 | + | 8.11442e6i | 0.669466 | + | 1.15955i | 0.978054 | + | 0.208353i | \(0.0668104\pi\) |
−0.308587 | + | 0.951196i | \(0.599856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 915551. | − | 1.80744e6i | 0.129644 | − | 0.255937i | ||||
\(550\) | 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 | ||||||||
\(555\) | 1.16580e7 | − | 7.16305e6i | 1.60655 | − | 0.987110i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.53733e6 | 0.483101 | 0.241550 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241550 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.95761e6 | −1.07709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 96070.3 | + | 3.50997e6i | 0.0128879 | + | 0.470864i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.39030e6 | + | 2.40807e6i | −0.184858 | + | 0.320183i | −0.943529 | − | 0.331291i | \(-0.892516\pi\) |
0.758671 | + | 0.651474i | \(0.225849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.48248e6 | − | 1.12280e7i | −0.854319 | − | 1.47972i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.97197e6 | − | 656288.i | 0.780117 | − | 0.0857308i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.67647e6 | − | 6.36782e6i | −0.476047 | − | 0.824537i | 0.523576 | − | 0.851979i | \(-0.324597\pi\) |
−0.999623 | + | 0.0274412i | \(0.991264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.87585e6 | − | 4.98112e6i | 0.369128 | − | 0.639348i | −0.620302 | − | 0.784363i | \(-0.712990\pi\) |
0.989429 | + | 0.145016i | \(0.0463232\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23915.3 | + | 873757.i | 0.00304292 | + | 0.111174i | ||||
\(574\) | 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 | ||||||||
\(579\) | −4.70814e6 | + | 2.89283e6i | −0.583651 | + | 0.358613i | ||||
\(580\) | 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 | ||||||||
\(585\) | 7.70298e6 | − | 1.52069e7i | 0.930613 | − | 1.83717i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −623618. | − | 1.08014e6i | −0.0747005 | − | 0.129385i | 0.826255 | − | 0.563296i | \(-0.190467\pi\) |
−0.900956 | + | 0.433910i | \(0.857133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00939e6 | − | 8.67652e6i | 0.594972 | − | 1.03052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.11982e7 | − | 6.06295e6i | −1.31880 | − | 0.714028i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.32769e7 | −1.55045 | −0.775226 | − | 0.631684i | \(-0.782364\pi\) | ||||
−0.775226 | + | 0.631684i | \(0.782364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.68324e7 | 1.94919 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.17945e7 | + | 6.38581e6i | 1.35439 | + | 0.733297i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.02457e6 | + | 3.50666e6i | −0.230551 | + | 0.399325i | −0.957970 | − | 0.286868i | \(-0.907386\pi\) |
0.727420 | + | 0.686193i | \(0.240719\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.41857e6 | + | 5.92113e6i | 0.386063 | + | 0.668681i | 0.991916 | − | 0.126896i | \(-0.0405014\pi\) |
−0.605853 | + | 0.795577i | \(0.707168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.76175e6 | − | 96513.3i | 0.197311 | − | 0.0108092i | ||||
\(604\) | 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 | \(-0.845543\pi\) |
0.846215 | + | 0.532842i | \(0.178876\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.75335e6 | − | 2.30617e6i | 0.410087 | − | 0.251970i | ||||
\(610\) | 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 | ||||||||
\(615\) | 95468.7 | + | 3.48799e6i | 0.0101783 | + | 0.371866i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.51675e6 | − | 1.30194e7i | 0.794908 | − | 1.37682i | −0.127989 | − | 0.991776i | \(-0.540852\pi\) |
0.922897 | − | 0.385046i | \(-0.125814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.58151e6 | + | 6.20336e6i | 0.375699 | + | 0.650730i | 0.990431 | − | 0.138006i | \(-0.0440693\pi\) |
−0.614732 | + | 0.788736i | \(0.710736\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.32926e6 | + | 2.04611e6i | 0.450489 | + | 0.212912i | ||||
\(622\) | 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 | ||||||||
\(627\) | 92169.0 | + | 3.36743e6i | 0.00936302 | + | 0.342082i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.19145e7 | −1.20074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.38021e7 | 1.37998 | 0.689989 | − | 0.723820i | \(-0.257615\pi\) | ||||
0.689989 | + | 0.723820i | \(0.257615\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.14229e6 | − | 3.15958e6i | 0.510090 | − | 0.313415i | ||||
\(634\) | 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 | ||||||||
\(639\) | 475839. | + | 728943.i | 0.0461007 | + | 0.0706222i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.02329e6 | + | 3.50445e6i | 0.194497 | + | 0.336879i | 0.946736 | − | 0.322012i | \(-0.104359\pi\) |
−0.752238 | + | 0.658891i | \(0.771026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.44381e6 | + | 9.42896e6i | −0.519249 | + | 0.899366i | 0.480501 | + | 0.876994i | \(0.340455\pi\) |
−0.999750 | + | 0.0223713i | \(0.992878\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.89525e7 | − | 1.02613e7i | −1.79377 | − | 0.971189i | ||||
\(646\) | 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 | ||||||||
\(651\) | −9.71947e6 | − | 5.26235e6i | −0.898856 | − | 0.486662i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.47774e6 | + | 4.29157e6i | −0.227391 | + | 0.393853i | −0.957034 | − | 0.289975i | \(-0.906353\pi\) |
0.729643 | + | 0.683828i | \(0.239686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.49752e6 | + | 1.64502e7i | 0.864982 | + | 1.49819i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.71441e6 | + | 1.18178e7i | 0.697251 | + | 1.06813i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.37152e6 | − | 1.44999e7i | −0.750915 | − | 1.30062i | −0.947380 | − | 0.320113i | \(-0.896279\pi\) |
0.196464 | − | 0.980511i | \(-0.437054\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.53992e6 | − | 1.30595e7i | 0.671217 | − | 1.16258i | −0.306342 | − | 0.951922i | \(-0.599105\pi\) |
0.977559 | − | 0.210661i | \(-0.0675617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.26469e7 | + | 7.77067e6i | −1.11738 | + | 0.686554i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.61489e7 | 1.41608 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.51105e6 | 0.305578 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 125817. | + | 4.59677e6i | 0.0108686 | + | 0.397089i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 626639. | − | 1.08537e6i | 0.0537293 | − | 0.0930619i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.07096e6 | − | 1.22473e7i | −0.601784 | − | 1.04232i | −0.992551 | − | 0.121831i | \(-0.961123\pi\) |
0.390767 | − | 0.920490i | \(-0.372210\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82235e7 | − | 1.95454e7i | 2.38425 | − | 1.65115i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.29397e6 | − | 1.26335e7i | −0.611635 | − | 1.05938i | −0.990965 | − | 0.134122i | \(-0.957179\pi\) |
0.379330 | − | 0.925262i | \(-0.376155\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.52429e6 | + | 6.10425e6i | −0.293358 | + | 0.508110i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −293428. | − | 1.07205e7i | −0.0242457 | − | 0.885826i | ||||
\(682\) | 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 | ||||||||
\(687\) | 1.44301e7 | − | 8.86630e6i | 1.16648 | − | 0.716722i | ||||
\(688\) | 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 | \(-0.311555\pi\) |
−0.997660 | + | 0.0683661i | \(0.978221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.71074e6 | − | 203284.i | 0.293513 | − | 0.0160794i | ||||
\(694\) | 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 | ||||||||
\(699\) | 2.30377e6 | + | 1.24732e6i | 0.178339 | + | 0.0965570i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.51294e7 | −1.93146 | −0.965732 | − | 0.259542i | \(-0.916428\pi\) | ||||
−0.965732 | + | 0.259542i | \(0.916428\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.14306e7 | −0.872332 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.81022e6 | − | 5.31148e6i | −0.743371 | − | 0.402479i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.29448e6 | − | 2.24211e6i | 0.0973974 | − | 0.168697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.26506e6 | − | 1.08514e7i | −0.468068 | − | 0.810718i | 0.531266 | − | 0.847205i | \(-0.321717\pi\) |
−0.999334 | + | 0.0364869i | \(0.988383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.99939e6 | + | 1.38179e7i | −0.519262 | + | 1.02510i | ||||
\(712\) | 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 | ||||||||
\(717\) | 2.05371e7 | − | 1.26187e7i | 1.49191 | − | 0.916674i | ||||
\(718\) | 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 | ||||||||
\(723\) | 492075. | + | 1.79781e7i | 0.0350095 | + | 1.27908i | ||||
\(724\) | 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 | \(-0.245520\pi\) |
−0.962187 | + | 0.272389i | \(0.912186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.41559e7 | + | 2.34528e6i | −0.986552 | + | 0.163447i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.38335e6 | + | 1.62524e7i | 0.649478 | + | 1.12493i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.96305e6 | − | 5.13214e6i | 0.203694 | − | 0.352808i | −0.746022 | − | 0.665922i | \(-0.768039\pi\) |
0.949716 | + | 0.313113i | \(0.101372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 303942. | + | 1.11046e7i | 0.0207526 | + | 0.758203i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.09140e6 | 0.0740142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.06632e7 | −0.718254 | −0.359127 | − | 0.933289i | \(-0.616925\pi\) | ||||
−0.359127 | + | 0.933289i | \(0.616925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.21334e7 | + | 7.45511e6i | −0.811775 | + | 0.498779i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.24932e6 | − | 1.60203e7i | 0.614664 | − | 1.06463i | −0.375779 | − | 0.926709i | \(-0.622625\pi\) |
0.990443 | − | 0.137920i | \(-0.0440417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.04143e6 | + | 5.26791e6i | 0.200765 | + | 0.347734i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.09710e6 | − | 1.79591e7i | 0.596488 | − | 1.17756i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.11130e6 | + | 5.38892e6i | 0.202645 | + | 0.350992i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.30624e7 | − | 2.26247e7i | 0.845127 | − | 1.46380i | −0.0403845 | − | 0.999184i | \(-0.512858\pi\) |
0.885511 | − | 0.464618i | \(-0.153808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.04275e6 | − | 4.35454e6i | −0.516913 | − | 0.279869i | ||||
\(754\) | 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 | ||||||||
\(759\) | 2.60470e6 | + | 1.41025e6i | 0.164117 | + | 0.0888567i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.62194e6 | + | 9.73748e6i | −0.351904 | + | 0.609516i | −0.986583 | − | 0.163260i | \(-0.947799\pi\) |
0.634679 | + | 0.772776i | \(0.281132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.31000e6 | + | 1.09292e7i | 0.392390 | + | 0.679640i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.01412e7 | + | 2.19903e6i | −2.47992 | + | 0.135856i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.49604e7 | − | 2.59122e7i | −0.918237 | − | 1.59043i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.33731e6 | + | 7.51244e6i | −0.264487 | + | 0.458105i | −0.967429 | − | 0.253142i | \(-0.918536\pi\) |
0.702942 | + | 0.711247i | \(0.251869\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.43896e6 | + | 884144.i | −0.0871794 | + | 0.0535657i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.17066e7 | 1.30660 | 0.653300 | − | 0.757099i | \(-0.273384\pi\) | ||||
0.653300 | + | 0.757099i | \(0.273384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.31571e7 | −3.77718 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 345020. | + | 1.26054e7i | 0.0205018 | + | 0.749041i | ||||
\(778\) | 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 | ||||||||
\(783\) | −8.64953e6 | + | 5.99000e6i | −0.504183 | + | 0.349158i | ||||
\(784\) | 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 | \(-0.905998\pi\) |
0.730406 | + | 0.683014i | \(0.239331\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 740718. | + | 2.70624e7i | 0.0423604 | + | 1.54766i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.19486e7 | 0.679009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.29807e6 | 0.299181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.44100e7 | + | 8.85395e6i | −0.808624 | + | 0.496843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.48089e6 | + | 1.64214e7i | −0.528693 | + | 0.915723i | 0.470747 | + | 0.882268i | \(0.343984\pi\) |
−0.999440 | + | 0.0334547i | \(0.989349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.85703e6 | + | 8.41262e6i | 0.269156 | + | 0.466192i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −512923. | − | 785752.i | −0.0282469 | − | 0.0432717i | ||||
\(802\) | 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 | ||||||||
\(807\) | 250822. | + | 135801.i | 0.0135576 | + | 0.00734040i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.09408e7 | −1.12492 | −0.562459 | − | 0.826825i | \(-0.690145\pi\) | ||||
−0.562459 | + | 0.826825i | \(0.690145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.21466e7 | 1.71626 | 0.858130 | − | 0.513432i | \(-0.171626\pi\) | ||||
0.858130 | + | 0.513432i | \(0.171626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 97398.1 | + | 52733.6i | 0.00516802 | + | 0.00279809i | ||||
\(814\) | 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 | ||||||||
\(819\) | 8.58756e6 | + | 1.31554e7i | 0.447363 | + | 0.685321i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.48802e7 | + | 2.57733e7i | 0.770463 | + | 1.33448i | 0.937309 | + | 0.348498i | \(0.113308\pi\) |
−0.166846 | + | 0.985983i | \(0.553358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.26102e6 | − | 1.43085e7i | 0.425142 | − | 0.736368i | −0.571291 | − | 0.820747i | \(-0.693557\pi\) |
0.996434 | + | 0.0843793i | \(0.0268907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.80933e7 | − | 1.11171e7i | 0.925516 | − | 0.568665i | ||||
\(826\) | 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 | ||||||||
\(831\) | −302992. | − | 1.10699e7i | −0.0152205 | − | 0.556087i | ||||
\(832\) | 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 | ||||||||
\(837\) | 2.38661e7 | + | 1.12796e7i | 1.17752 | + | 0.556521i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.87417e7 | − | 3.24616e7i | −0.919189 | − | 1.59208i | −0.800650 | − | 0.599133i | \(-0.795512\pi\) |
−0.118539 | − | 0.992949i | \(-0.537821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.39833e6 | − | 1.10822e7i | 0.311944 | − | 0.540303i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 438640. | + | 1.60259e7i | 0.0212588 | + | 0.776700i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.58473e6 | 0.172709 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40873e7 | −0.674713 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.44999e7 | − | 1.50535e7i | 1.16653 | − | 0.716749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.02527e6 | + | 8.70402e6i | −0.237868 | + | 0.411999i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.41357e6 | − | 1.28407e7i | −0.348863 | − | 0.604248i | 0.637185 | − | 0.770711i | \(-0.280099\pi\) |
−0.986048 | + | 0.166463i | \(0.946765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.85111e7 | + | 2.10973e6i | −1.80165 | + | 0.0986989i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.66185e6 | − | 4.61046e6i | −0.123803 | − | 0.214433i | 0.797461 | − | 0.603370i | \(-0.206176\pi\) |
−0.921264 | + | 0.388937i | \(0.872842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.34434e7 | + | 2.32846e7i | −0.621621 | + | 1.07668i | 0.367563 | + | 0.929999i | \(0.380192\pi\) |
−0.989184 | + | 0.146680i | \(0.953141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.82788e6 | − | 1.53108e6i | −0.130003 | − | 0.0703866i | ||||
\(862\) | 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 | ||||||||
\(867\) | 1.13198e7 | + | 6.12881e6i | 0.511436 | + | 0.276904i | ||||
\(868\) | 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 | ||||||||
\(873\) | 7.60710e6 | − | 1.50176e7i | 0.337818 | − | 0.666905i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.33494e7 | − | 5.77629e7i | −1.47254 | − | 2.55052i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.62323e7 | + | 2.81151e7i | −0.712657 | + | 1.23436i | 0.251199 | + | 0.967935i | \(0.419175\pi\) |
−0.963856 | + | 0.266423i | \(0.914158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.24977e7 | + | 7.67897e6i | −0.545579 | + | 0.335221i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.78418e6 | 0.337888 | 0.168944 | − | 0.985626i | \(-0.445964\pi\) | ||||
0.168944 | + | 0.985626i | \(0.445964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.71890e7 | 0.741906 | 0.370953 | − | 0.928652i | \(-0.379031\pi\) | ||||
0.370953 | + | 0.928652i | \(0.379031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.21719e6 | − | 8.10058e7i | −0.0951578 | − | 3.47663i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.81716e7 | − | 3.14742e7i | 0.775506 | − | 1.34322i | −0.159004 | − | 0.987278i | \(-0.550828\pi\) |
0.934510 | − | 0.355938i | \(-0.115838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51796e6 | + | 2.62918e6i | 0.0644178 | + | 0.111575i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.82266e6 | + | 969564.i | −0.372310 | + | 0.0409150i | ||||
\(892\) | 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 | ||||||||
\(897\) | 342589. | + | 1.25166e7i | 0.0142165 | + | 0.519405i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.93555e7 | 0.798739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.47270e7 | 0.604368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.69233e7 | − | 1.03982e7i | 0.690661 | − | 0.424363i | ||||
\(904\) | 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 | \(-0.109938\pi\) |
−0.763670 | + | 0.645607i | \(0.776604\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.79411e6 | + | 5.51600e6i | −0.112159 | + | 0.221419i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.83503e6 | + | 3.17836e6i | 0.0732566 | + | 0.126884i | 0.900327 | − | 0.435214i | \(-0.143327\pi\) |
−0.827070 | + | 0.562099i | \(0.809994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.22641e6 | − | 1.07845e7i | 0.247207 | − | 0.428175i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.26183e7 | + | 6.83184e6i | 0.498250 | + | 0.269765i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.75060e7 | −0.687484 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.38118e7 | 1.32063 | 0.660313 | − | 0.750990i | \(-0.270424\pi\) | ||||
0.660313 | + | 0.750990i | \(0.270424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.01780e7 | − | 2.17533e7i | −1.56077 | − | 0.845038i | ||||
\(922\) | 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 | ||||||||
\(927\) | 1.53802e7 | − | 842564.i | 0.587844 | − | 0.0322035i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.89173e6 | + | 1.02048e7i | 0.223977 | + | 0.387939i | 0.956012 | − | 0.293327i | \(-0.0947626\pi\) |
−0.732035 | + | 0.681267i | \(0.761429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.64014e6 | − | 8.03697e6i | 0.175452 | − | 0.303891i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.03156e7 | − | 1.86268e7i | 1.14015 | − | 0.700544i | ||||
\(934\) | 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 | ||||||||
\(939\) | −342335. | − | 1.25074e7i | −0.0126703 | − | 0.462915i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.28136e7 | + | 3.95143e7i | −0.839884 | + | 1.45472i | 0.0501075 | + | 0.998744i | \(0.484044\pi\) |
−0.889991 | + | 0.455978i | \(0.849290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.28151e6 | − | 2.21964e6i | −0.0469291 | − | 0.0812836i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.48898e6 | + | 4.24055e7i | 0.127092 | + | 1.54470i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.07942e7 | − | 3.60166e7i | −0.753472 | − | 1.30505i | −0.946130 | − | 0.323786i | \(-0.895044\pi\) |
0.192659 | − | 0.981266i | \(-0.438289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.84519e7 | + | 3.19597e7i | −0.665084 | + | 1.15196i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −474261. | − | 1.73273e7i | −0.0170046 | − | 0.621270i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.40042e7 | −1.92617 | −0.963087 | − | 0.269190i | \(-0.913244\pi\) | ||||
−0.963087 | + | 0.269190i | \(0.913244\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.19036e6 | −0.219638 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.54499e6 | + | 3.40701e6i | −0.195713 | + | 0.120252i | ||||
\(958\) | 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 | ||||||||
\(963\) | −8.12370e6 | − | 1.24448e7i | −0.282285 | − | 0.432436i | ||||
\(964\) | 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 | \(-0.929440\pi\) |
0.678169 | + | 0.734906i | \(0.262774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.95334e7 | + | 1.59901e7i | 1.01042 | + | 0.547068i | ||||
\(970\) | 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 | ||||||||
\(975\) | 7.89434e7 | + | 4.27418e7i | 2.65953 | + | 1.43993i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.29826e6 | + | 5.71275e6i | −0.110547 | + | 0.191474i | −0.915991 | − | 0.401199i | \(-0.868594\pi\) |
0.805444 | + | 0.592672i | \(0.201927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −290216. | − | 502669.i | −0.00967753 | − | 0.0167620i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.64756e7 | − | 2.52392e7i | −0.546600 | − | 0.837343i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.84729e7 | + | 3.19959e7i | 0.609748 | + | 1.05611i | 0.991282 | + | 0.131760i | \(0.0420627\pi\) |
−0.381534 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.50923e7 | − | 7.81022e7i | 1.48085 | − | 2.56491i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.75986e6 | − | 5.38233e6i | 0.286223 | − | 0.175864i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.58308e7 | 0.514649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.56015e6 | −0.244538 | −0.122269 | − | 0.992497i | \(-0.539017\pi\) | ||||
−0.122269 | + | 0.992497i | \(0.539017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 523145. | + | 1.91133e7i | 0.0168364 | + | 0.615125i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.74935e7 | + | 8.22612e7i | −1.52082 | + | 2.63413i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.80763e6 | + | 1.35232e7i | 0.248761 | + | 0.430866i | 0.963182 | − | 0.268850i | \(-0.0866434\pi\) |
−0.714422 | + | 0.699715i | \(0.753310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.46960e6 | − | 3.00158e7i | −0.0782911 | − | 0.951561i |
(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 | 36.6.e.a.13.5 | ✓ | 10 | |
3.2 | odd | 2 | 108.6.e.a.37.5 | 10 | |||
4.3 | odd | 2 | 144.6.i.d.49.1 | 10 | |||
9.2 | odd | 6 | 108.6.e.a.73.5 | 10 | |||
9.4 | even | 3 | 324.6.a.e.1.5 | 5 | |||
9.5 | odd | 6 | 324.6.a.d.1.1 | 5 | |||
9.7 | even | 3 | inner | 36.6.e.a.25.5 | yes | 10 | |
12.11 | even | 2 | 432.6.i.d.145.5 | 10 | |||
36.7 | odd | 6 | 144.6.i.d.97.1 | 10 | |||
36.11 | even | 6 | 432.6.i.d.289.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
36.6.e.a.25.5 | yes | 10 | 9.7 | even | 3 | inner | |
108.6.e.a.37.5 | 10 | 3.2 | odd | 2 | |||
108.6.e.a.73.5 | 10 | 9.2 | odd | 6 | |||
144.6.i.d.49.1 | 10 | 4.3 | odd | 2 | |||
144.6.i.d.97.1 | 10 | 36.7 | odd | 6 | |||
324.6.a.d.1.1 | 5 | 9.5 | odd | 6 | |||
324.6.a.e.1.5 | 5 | 9.4 | even | 3 | |||
432.6.i.d.145.5 | 10 | 12.11 | even | 2 | |||
432.6.i.d.289.5 | 10 | 36.11 | even | 6 |