Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,7,Mod(19,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.f (of order \(6\), 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: | \(33.8179502921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Root | \(-7.08935 - 12.2791i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.31 |
Dual form | 147.7.f.a.19.4 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.58935 | + | 11.4131i | 0.823668 | + | 1.42664i | 0.902933 | + | 0.429782i | \(0.141409\pi\) |
−0.0792645 | + | 0.996854i | \(0.525257\pi\) | |||||||
\(3\) | −13.5000 | − | 7.79423i | −0.500000 | − | 0.288675i | ||||
\(4\) | −54.8390 | + | 94.9839i | −0.856859 | + | 1.48412i | ||||
\(5\) | 68.9069 | − | 39.7834i | 0.551255 | − | 0.318267i | −0.198373 | − | 0.980127i | \(-0.563566\pi\) |
0.749628 | + | 0.661859i | \(0.230232\pi\) | |||||||
\(6\) | − | 205.435i | − | 0.951090i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −601.976 | −1.17573 | ||||||||
\(9\) | 121.500 | + | 210.444i | 0.166667 | + | 0.288675i | ||||
\(10\) | 908.103 | + | 524.293i | 0.908103 | + | 0.524293i | ||||
\(11\) | −411.119 | + | 712.080i | −0.308880 | + | 0.534996i | −0.978118 | − | 0.208052i | \(-0.933288\pi\) |
0.669238 | + | 0.743049i | \(0.266621\pi\) | |||||||
\(12\) | 1480.65 | − | 854.855i | 0.856859 | − | 0.494708i | ||||
\(13\) | 2429.15i | 1.10567i | 0.833292 | + | 0.552833i | \(0.186453\pi\) | ||||
−0.833292 | + | 0.552833i | \(0.813547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1240.32 | −0.367503 | ||||||||
\(16\) | −456.932 | − | 791.429i | −0.111556 | − | 0.193220i | ||||
\(17\) | −6751.11 | − | 3897.76i | −1.37413 | − | 0.793355i | −0.382687 | − | 0.923878i | \(-0.625001\pi\) |
−0.991445 | + | 0.130523i | \(0.958334\pi\) | |||||||
\(18\) | −1601.21 | + | 2773.38i | −0.274556 | + | 0.475545i | ||||
\(19\) | −5786.98 | + | 3341.12i | −0.843706 | + | 0.487114i | −0.858522 | − | 0.512776i | \(-0.828617\pi\) |
0.0148160 | + | 0.999890i | \(0.495284\pi\) | |||||||
\(20\) | 8726.73i | 1.09084i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10836.0 | −1.01766 | ||||||||
\(23\) | −9416.30 | − | 16309.5i | −0.773921 | − | 1.34047i | −0.935399 | − | 0.353594i | \(-0.884959\pi\) |
0.161478 | − | 0.986876i | \(-0.448374\pi\) | |||||||
\(24\) | 8126.67 | + | 4691.94i | 0.587867 | + | 0.339405i | ||||
\(25\) | −4647.06 | + | 8048.94i | −0.297412 | + | 0.515132i | ||||
\(26\) | −27724.0 | + | 16006.5i | −1.57738 | + | 0.910701i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13888.2 | 0.569446 | 0.284723 | − | 0.958610i | \(-0.408098\pi\) | ||||
0.284723 | + | 0.958610i | \(0.408098\pi\) | |||||||
\(30\) | −8172.93 | − | 14155.9i | −0.302701 | − | 0.524293i | ||||
\(31\) | 24131.1 | + | 13932.1i | 0.810014 | + | 0.467662i | 0.846961 | − | 0.531655i | \(-0.178430\pi\) |
−0.0369467 | + | 0.999317i | \(0.511763\pi\) | |||||||
\(32\) | −13241.5 | + | 22934.9i | −0.404097 | + | 0.699917i | ||||
\(33\) | 11100.2 | − | 6408.72i | 0.308880 | − | 0.178332i | ||||
\(34\) | − | 102735.i | − | 2.61385i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −26651.7 | −0.571239 | ||||||||
\(37\) | −39837.6 | − | 69000.8i | −0.786481 | − | 1.36223i | −0.928110 | − | 0.372305i | \(-0.878567\pi\) |
0.141629 | − | 0.989920i | \(-0.454766\pi\) | |||||||
\(38\) | −76264.9 | − | 44031.5i | −1.38987 | − | 0.802441i | ||||
\(39\) | 18933.3 | − | 32793.5i | 0.319178 | − | 0.552833i | ||||
\(40\) | −41480.3 | + | 23948.6i | −0.648129 | + | 0.374198i | ||||
\(41\) | 59196.1i | 0.858898i | 0.903091 | + | 0.429449i | \(0.141292\pi\) | ||||
−0.903091 | + | 0.429449i | \(0.858708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −91825.9 | −1.15494 | −0.577471 | − | 0.816411i | \(-0.695960\pi\) | ||||
−0.577471 | + | 0.816411i | \(0.695960\pi\) | |||||||
\(44\) | −45090.7 | − | 78099.4i | −0.529333 | − | 0.916832i | ||||
\(45\) | 16744.4 | + | 9667.37i | 0.183752 | + | 0.106089i | ||||
\(46\) | 124095. | − | 214938.i | 1.27491 | − | 2.20821i | ||||
\(47\) | 4347.44 | − | 2509.99i | 0.0418735 | − | 0.0241757i | −0.478917 | − | 0.877860i | \(-0.658971\pi\) |
0.520791 | + | 0.853684i | \(0.325637\pi\) | |||||||
\(48\) | 14245.7i | 0.128813i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −122484. | −0.979875 | ||||||||
\(51\) | 60760.0 | + | 105239.i | 0.458044 | + | 0.793355i | ||||
\(52\) | −230730. | − | 133212.i | −1.64094 | − | 0.947399i | ||||
\(53\) | −93194.8 | + | 161418.i | −0.625985 | + | 1.08424i | 0.362365 | + | 0.932036i | \(0.381970\pi\) |
−0.988350 | + | 0.152201i | \(0.951364\pi\) | |||||||
\(54\) | 43232.7 | − | 24960.4i | 0.274556 | − | 0.158515i | ||||
\(55\) | 65422.9i | 0.393226i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 104166. | 0.562471 | ||||||||
\(58\) | 91514.3 | + | 158507.i | 0.469035 | + | 0.812392i | ||||
\(59\) | −195032. | − | 112602.i | −0.949618 | − | 0.548262i | −0.0566558 | − | 0.998394i | \(-0.518044\pi\) |
−0.892962 | + | 0.450132i | \(0.851377\pi\) | |||||||
\(60\) | 68018.1 | − | 117811.i | 0.314899 | − | 0.545420i | ||||
\(61\) | 125018. | − | 72179.1i | 0.550786 | − | 0.317996i | −0.198653 | − | 0.980070i | \(-0.563657\pi\) |
0.749439 | + | 0.662074i | \(0.230323\pi\) | |||||||
\(62\) | 367214.i | 1.54079i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −407497. | −1.55448 | ||||||||
\(65\) | 96639.7 | + | 167385.i | 0.351897 | + | 0.609504i | ||||
\(66\) | 146286. | + | 84458.5i | 0.508830 | + | 0.293773i | ||||
\(67\) | 117740. | − | 203932.i | 0.391471 | − | 0.678048i | −0.601173 | − | 0.799119i | \(-0.705300\pi\) |
0.992644 | + | 0.121071i | \(0.0386329\pi\) | |||||||
\(68\) | 740448. | − | 427498.i | 2.35487 | − | 1.35959i | ||||
\(69\) | 293571.i | 0.893647i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 96269.3 | 0.268975 | 0.134488 | − | 0.990915i | \(-0.457061\pi\) | ||||
0.134488 | + | 0.990915i | \(0.457061\pi\) | |||||||
\(72\) | −73140.0 | − | 126682.i | −0.195956 | − | 0.339405i | ||||
\(73\) | −238634. | − | 137775.i | −0.613428 | − | 0.354163i | 0.160878 | − | 0.986974i | \(-0.448567\pi\) |
−0.774306 | + | 0.632812i | \(0.781901\pi\) | |||||||
\(74\) | 525008. | − | 909340.i | 1.29560 | − | 2.24404i | ||||
\(75\) | 125471. | − | 72440.5i | 0.297412 | − | 0.171711i | ||||
\(76\) | − | 732893.i | − | 1.66955i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 499033. | 1.05159 | ||||||||
\(79\) | 340667. | + | 590052.i | 0.690953 | + | 1.19677i | 0.971526 | + | 0.236933i | \(0.0761423\pi\) |
−0.280573 | + | 0.959833i | \(0.590524\pi\) | |||||||
\(80\) | −62971.5 | − | 36356.6i | −0.122991 | − | 0.0710090i | ||||
\(81\) | −29524.5 | + | 51137.9i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −675610. | + | 390064.i | −1.22533 | + | 0.707447i | ||||
\(83\) | − | 128019.i | − | 0.223893i | −0.993714 | − | 0.111946i | \(-0.964291\pi\) | ||
0.993714 | − | 0.111946i | \(-0.0357085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −620264. | −1.01000 | ||||||||
\(86\) | −605073. | − | 1.04802e6i | −0.951288 | − | 1.64768i | ||||
\(87\) | −187491. | − | 108248.i | −0.284723 | − | 0.164385i | ||||
\(88\) | 247484. | − | 428655.i | 0.363161 | − | 0.629013i | ||||
\(89\) | 322756. | − | 186343.i | 0.457829 | − | 0.264328i | −0.253302 | − | 0.967387i | \(-0.581517\pi\) |
0.711131 | + | 0.703059i | \(0.248183\pi\) | |||||||
\(90\) | 254807.i | 0.349529i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.06552e6 | 2.65257 | ||||||||
\(93\) | −217180. | − | 376167.i | −0.270005 | − | 0.467662i | ||||
\(94\) | 57293.5 | + | 33078.4i | 0.0689798 | + | 0.0398255i | ||||
\(95\) | −265842. | + | 460452.i | −0.310065 | + | 0.537048i | ||||
\(96\) | 357519. | − | 206414.i | 0.404097 | − | 0.233306i | ||||
\(97\) | 620049.i | 0.679377i | 0.940538 | + | 0.339688i | \(0.110322\pi\) | ||||
−0.940538 | + | 0.339688i | \(0.889678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −199804. | −0.205920 | ||||||||
\(100\) | −509680. | − | 882792.i | −0.509680 | − | 0.882792i | ||||
\(101\) | 578698. | + | 334111.i | 0.561678 | + | 0.324285i | 0.753819 | − | 0.657082i | \(-0.228210\pi\) |
−0.192141 | + | 0.981367i | \(0.561543\pi\) | |||||||
\(102\) | −800737. | + | 1.38692e6i | −0.754553 | + | 1.30692i | ||||
\(103\) | −1.34180e6 | + | 774691.i | −1.22794 | + | 0.708952i | −0.966599 | − | 0.256294i | \(-0.917498\pi\) |
−0.261342 | + | 0.965246i | \(0.584165\pi\) | |||||||
\(104\) | − | 1.46229e6i | − | 1.29997i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.45637e6 | −2.06242 | ||||||||
\(107\) | 477948. | + | 827829.i | 0.390148 | + | 0.675755i | 0.992469 | − | 0.122498i | \(-0.0390906\pi\) |
−0.602321 | + | 0.798254i | \(0.705757\pi\) | |||||||
\(108\) | 359799. | + | 207730.i | 0.285620 | + | 0.164903i | ||||
\(109\) | −785863. | + | 1.36115e6i | −0.606830 | + | 1.05106i | 0.384929 | + | 0.922946i | \(0.374226\pi\) |
−0.991759 | + | 0.128115i | \(0.959107\pi\) | |||||||
\(110\) | −746677. | + | 431094.i | −0.560990 | + | 0.323888i | ||||
\(111\) | 1.24201e6i | 0.908150i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.47576e6 | −1.71582 | −0.857912 | − | 0.513797i | \(-0.828238\pi\) | ||||
−0.857912 | + | 0.513797i | \(0.828238\pi\) | |||||||
\(114\) | 686384. | + | 1.18885e6i | 0.463289 | + | 0.802441i | ||||
\(115\) | −1.29770e6 | − | 749225.i | −0.853256 | − | 0.492628i | ||||
\(116\) | −761615. | + | 1.31916e6i | −0.487935 | + | 0.845128i | ||||
\(117\) | −511200. | + | 295141.i | −0.319178 | + | 0.184278i | ||||
\(118\) | − | 2.96788e6i | − | 1.80634i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 746645. | 0.432086 | ||||||||
\(121\) | 547742. | + | 948717.i | 0.309186 | + | 0.535526i | ||||
\(122\) | 1.64757e6 | + | 951226.i | 0.907329 | + | 0.523847i | ||||
\(123\) | 461388. | − | 799148.i | 0.247943 | − | 0.429449i | ||||
\(124\) | −2.64665e6 | + | 1.52805e6i | −1.38814 | + | 0.801441i | ||||
\(125\) | 1.98274e6i | 1.01516i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 292592. | 0.142840 | 0.0714202 | − | 0.997446i | \(-0.477247\pi\) | ||||
0.0714202 | + | 0.997446i | \(0.477247\pi\) | |||||||
\(128\) | −1.83769e6 | − | 3.18297e6i | −0.876278 | − | 1.51776i | ||||
\(129\) | 1.23965e6 | + | 715712.i | 0.577471 | + | 0.333403i | ||||
\(130\) | −1.27359e6 | + | 2.20591e6i | −0.579693 | + | 1.00406i | ||||
\(131\) | 2.36324e6 | − | 1.36442e6i | 1.05122 | − | 0.606924i | 0.128231 | − | 0.991744i | \(-0.459070\pi\) |
0.922991 | + | 0.384820i | \(0.125737\pi\) | |||||||
\(132\) | 1.40579e6i | 0.611222i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.10332e6 | 1.28977 | ||||||||
\(135\) | −150699. | − | 261019.i | −0.0612506 | − | 0.106089i | ||||
\(136\) | 4.06400e6 | + | 2.34635e6i | 1.61561 | + | 0.932775i | ||||
\(137\) | 453922. | − | 786216.i | 0.176530 | − | 0.305760i | −0.764159 | − | 0.645027i | \(-0.776846\pi\) |
0.940690 | + | 0.339268i | \(0.110179\pi\) | |||||||
\(138\) | −3.35055e6 | + | 1.93444e6i | −1.27491 | + | 0.736069i | ||||
\(139\) | − | 4640.07i | − | 0.00172775i | −1.00000 | 0.000863874i | \(-0.999725\pi\) | |||
1.00000 | 0.000863874i | \(-0.000274980\pi\) | ||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −78253.8 | −0.0279157 | ||||||||
\(142\) | 634352. | + | 1.09873e6i | 0.221547 | + | 0.383730i | ||||
\(143\) | −1.72975e6 | − | 998669.i | −0.591526 | − | 0.341518i | ||||
\(144\) | 111034. | − | 192317.i | 0.0371852 | − | 0.0644066i | ||||
\(145\) | 956994. | − | 552521.i | 0.313910 | − | 0.181236i | ||||
\(146\) | − | 3.63140e6i | − | 1.16685i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.73862e6 | 2.69561 | ||||||||
\(149\) | 823601. | + | 1.42652e6i | 0.248976 | + | 0.431240i | 0.963242 | − | 0.268635i | \(-0.0865725\pi\) |
−0.714266 | + | 0.699875i | \(0.753239\pi\) | |||||||
\(150\) | 1.65354e6 | + | 954671.i | 0.489937 | + | 0.282865i | ||||
\(151\) | 1.22295e6 | − | 2.11820e6i | 0.355203 | − | 0.615229i | −0.631950 | − | 0.775009i | \(-0.717745\pi\) |
0.987153 | + | 0.159780i | \(0.0510785\pi\) | |||||||
\(152\) | 3.48362e6 | − | 2.01127e6i | 0.991974 | − | 0.572716i | ||||
\(153\) | − | 1.89431e6i | − | 0.528904i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.21707e6 | 0.595366 | ||||||||
\(156\) | 2.07657e6 | + | 3.59672e6i | 0.546981 | + | 0.947399i | ||||
\(157\) | 2.43822e6 | + | 1.40771e6i | 0.630049 | + | 0.363759i | 0.780771 | − | 0.624817i | \(-0.214826\pi\) |
−0.150722 | + | 0.988576i | \(0.548160\pi\) | |||||||
\(158\) | −4.48954e6 | + | 7.77612e6i | −1.13823 | + | 1.97148i | ||||
\(159\) | 2.51626e6 | − | 1.45276e6i | 0.625985 | − | 0.361413i | ||||
\(160\) | 2.10716e6i | 0.514444i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −778189. | −0.183037 | ||||||||
\(163\) | 781407. | + | 1.35344e6i | 0.180432 | + | 0.312518i | 0.942028 | − | 0.335535i | \(-0.108917\pi\) |
−0.761596 | + | 0.648053i | \(0.775584\pi\) | |||||||
\(164\) | −5.62268e6 | − | 3.24625e6i | −1.27471 | − | 0.735955i | ||||
\(165\) | 509921. | − | 883210.i | 0.113515 | − | 0.196613i | ||||
\(166\) | 1.46109e6 | − | 843562.i | 0.319414 | − | 0.184414i | ||||
\(167\) | 1.15538e6i | 0.248070i | 0.992278 | + | 0.124035i | \(0.0395835\pi\) | ||||
−0.992278 | + | 0.124035i | \(0.960416\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07394e6 | −0.222495 | ||||||||
\(170\) | −4.08713e6 | − | 7.07913e6i | −0.831902 | − | 1.44090i | ||||
\(171\) | −1.40624e6 | − | 811891.i | −0.281235 | − | 0.162371i | ||||
\(172\) | 5.03564e6 | − | 8.72198e6i | 0.989622 | − | 1.71408i | ||||
\(173\) | 4.98920e6 | − | 2.88052e6i | 0.963591 | − | 0.556330i | 0.0663149 | − | 0.997799i | \(-0.478876\pi\) |
0.897277 | + | 0.441469i | \(0.145542\pi\) | |||||||
\(174\) | − | 2.85313e6i | − | 0.541594i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 751414. | 0.137829 | ||||||||
\(177\) | 1.75528e6 | + | 3.04024e6i | 0.316539 | + | 0.548262i | ||||
\(178\) | 4.25350e6 | + | 2.45576e6i | 0.754199 | + | 0.435437i | ||||
\(179\) | 597801. | − | 1.03542e6i | 0.104231 | − | 0.180534i | −0.809193 | − | 0.587543i | \(-0.800095\pi\) |
0.913424 | + | 0.407010i | \(0.133429\pi\) | |||||||
\(180\) | −1.83649e6 | + | 1.06030e6i | −0.314899 | + | 0.181807i | ||||
\(181\) | 1.00030e7i | 1.68692i | 0.537191 | + | 0.843461i | \(0.319486\pi\) | ||||
−0.537191 | + | 0.843461i | \(0.680514\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.25032e6 | −0.367190 | ||||||||
\(184\) | 5.66838e6 | + | 9.81793e6i | 0.909925 | + | 1.57604i | ||||
\(185\) | −5.49017e6 | − | 3.16975e6i | −0.867104 | − | 0.500622i | ||||
\(186\) | 2.86215e6 | − | 4.95739e6i | 0.444789 | − | 0.770397i | ||||
\(187\) | 5.55102e6 | − | 3.20489e6i | 0.848884 | − | 0.490103i | ||||
\(188\) | 550582.i | 0.0828606i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.00690e6 | −1.02156 | ||||||||
\(191\) | 3.79135e6 | + | 6.56682e6i | 0.544120 | + | 0.942443i | 0.998662 | + | 0.0517175i | \(0.0164695\pi\) |
−0.454542 | + | 0.890725i | \(0.650197\pi\) | |||||||
\(192\) | 5.50122e6 | + | 3.17613e6i | 0.777240 | + | 0.448740i | ||||
\(193\) | −3.54806e6 | + | 6.14542e6i | −0.493537 | + | 0.854830i | −0.999972 | − | 0.00744730i | \(-0.997629\pi\) |
0.506436 | + | 0.862278i | \(0.330963\pi\) | |||||||
\(194\) | −7.07667e6 | + | 4.08572e6i | −0.969223 | + | 0.559581i | ||||
\(195\) | − | 3.01293e6i | − | 0.406336i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00096e6 | 0.261722 | 0.130861 | − | 0.991401i | \(-0.458226\pi\) | ||||
0.130861 | + | 0.991401i | \(0.458226\pi\) | |||||||
\(198\) | −1.31658e6 | − | 2.28038e6i | −0.169610 | − | 0.293773i | ||||
\(199\) | 3.76381e6 | + | 2.17304e6i | 0.477605 | + | 0.275745i | 0.719418 | − | 0.694578i | \(-0.244409\pi\) |
−0.241813 | + | 0.970323i | \(0.577742\pi\) | |||||||
\(200\) | 2.79742e6 | − | 4.84527e6i | 0.349677 | − | 0.605658i | ||||
\(201\) | −3.17898e6 | + | 1.83539e6i | −0.391471 | + | 0.226016i | ||||
\(202\) | 8.80630e6i | 1.06841i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.33281e7 | −1.56992 | ||||||||
\(205\) | 2.35502e6 | + | 4.07902e6i | 0.273359 | + | 0.473472i | ||||
\(206\) | −1.76832e7 | − | 1.02094e7i | −2.02283 | − | 1.16788i | ||||
\(207\) | 2.28816e6 | − | 3.96321e6i | 0.257974 | − | 0.446824i | ||||
\(208\) | 1.92250e6 | − | 1.10995e6i | 0.213637 | − | 0.123343i | ||||
\(209\) | − | 5.49439e6i | − | 0.601839i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03642e7 | 1.10328 | 0.551641 | − | 0.834082i | \(-0.314002\pi\) | ||||
0.551641 | + | 0.834082i | \(0.314002\pi\) | |||||||
\(212\) | −1.02214e7 | − | 1.77040e7i | −1.07276 | − | 1.85808i | ||||
\(213\) | −1.29964e6 | − | 750345.i | −0.134488 | − | 0.0776465i | ||||
\(214\) | −6.29872e6 | + | 1.09097e7i | −0.642704 | + | 1.11320i | ||||
\(215\) | −6.32744e6 | + | 3.65315e6i | −0.636667 | + | 0.367580i | ||||
\(216\) | 2.28028e6i | 0.226270i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.07133e7 | −1.99931 | ||||||||
\(219\) | 2.14770e6 | + | 3.71993e6i | 0.204476 | + | 0.354163i | ||||
\(220\) | −6.21413e6 | − | 3.58773e6i | −0.583596 | − | 0.336939i | ||||
\(221\) | 9.46822e6 | − | 1.63994e7i | 0.877185 | − | 1.51933i | ||||
\(222\) | −1.41752e7 | + | 8.18406e6i | −1.29560 | + | 0.748014i | ||||
\(223\) | − | 4.84791e6i | − | 0.437159i | −0.975819 | − | 0.218580i | \(-0.929858\pi\) | ||
0.975819 | − | 0.218580i | \(-0.0701424\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.25847e6 | −0.198275 | ||||||||
\(226\) | −1.63136e7 | − | 2.82560e7i | −1.41327 | − | 2.44785i | ||||
\(227\) | 1.30838e7 | + | 7.55396e6i | 1.11856 | + | 0.645798i | 0.941032 | − | 0.338318i | \(-0.109858\pi\) |
0.177524 | + | 0.984117i | \(0.443191\pi\) | |||||||
\(228\) | −5.71234e6 | + | 9.89406e6i | −0.481958 | + | 0.834776i | ||||
\(229\) | 3.68382e6 | − | 2.12685e6i | 0.306755 | − | 0.177105i | −0.338718 | − | 0.940888i | \(-0.609993\pi\) |
0.645474 | + | 0.763783i | \(0.276660\pi\) | |||||||
\(230\) | − | 1.97476e7i | − | 1.62305i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.36037e6 | −0.669517 | ||||||||
\(233\) | −6.29087e6 | − | 1.08961e7i | −0.497328 | − | 0.861397i | 0.502667 | − | 0.864480i | \(-0.332352\pi\) |
−0.999995 | + | 0.00308269i | \(0.999019\pi\) | |||||||
\(234\) | −6.73694e6 | − | 3.88958e6i | −0.525794 | − | 0.303567i | ||||
\(235\) | 199712. | − | 345912.i | 0.0153887 | − | 0.0266540i | ||||
\(236\) | 2.13907e7 | − | 1.23499e7i | 1.62738 | − | 0.939567i | ||||
\(237\) | − | 1.06209e7i | − | 0.797844i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.54342e6 | 0.552554 | 0.276277 | − | 0.961078i | \(-0.410899\pi\) | ||||
0.276277 | + | 0.961078i | \(0.410899\pi\) | |||||||
\(240\) | 566743. | + | 981628.i | 0.0409971 | + | 0.0710090i | ||||
\(241\) | −1.69553e7 | − | 9.78914e6i | −1.21131 | − | 0.699348i | −0.248262 | − | 0.968693i | \(-0.579860\pi\) |
−0.963044 | + | 0.269345i | \(0.913193\pi\) | |||||||
\(242\) | −7.21853e6 | + | 1.25029e7i | −0.509334 | + | 0.882192i | ||||
\(243\) | 797162. | − | 460241.i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 1.58329e7i | 1.08991i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.21610e7 | 0.816890 | ||||||||
\(247\) | −8.11606e6 | − | 1.40574e7i | −0.538585 | − | 0.932857i | ||||
\(248\) | −1.45264e7 | − | 8.38679e6i | −0.952361 | − | 0.549846i | ||||
\(249\) | −997810. | + | 1.72826e6i | −0.0646323 | + | 0.111946i | ||||
\(250\) | −2.26291e7 | + | 1.30649e7i | −1.44826 | + | 0.836156i | ||||
\(251\) | − | 1.39590e7i | − | 0.882743i | −0.897324 | − | 0.441372i | \(-0.854492\pi\) | ||
0.897324 | − | 0.441372i | \(-0.145508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.54849e7 | 0.956195 | ||||||||
\(254\) | 1.92799e6 | + | 3.33938e6i | 0.117653 | + | 0.203781i | ||||
\(255\) | 8.37356e6 | + | 4.83448e6i | 0.504998 | + | 0.291561i | ||||
\(256\) | 1.11784e7 | − | 1.93616e7i | 0.666285 | − | 1.15404i | ||||
\(257\) | 567649. | − | 327732.i | 0.0334411 | − | 0.0193072i | −0.483186 | − | 0.875518i | \(-0.660521\pi\) |
0.516627 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(258\) | 1.88643e7i | 1.09845i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.11985e7 | −1.20610 | ||||||||
\(261\) | 1.68742e6 | + | 2.92269e6i | 0.0949076 | + | 0.164385i | ||||
\(262\) | 3.11445e7 | + | 1.79813e7i | 1.73172 | + | 0.999808i | ||||
\(263\) | 7.46998e6 | − | 1.29384e7i | 0.410632 | − | 0.711235i | −0.584327 | − | 0.811518i | \(-0.698642\pi\) |
0.994959 | + | 0.100283i | \(0.0319749\pi\) | |||||||
\(264\) | −6.68206e6 | + | 3.85789e6i | −0.363161 | + | 0.209671i | ||||
\(265\) | 1.48304e7i | 0.796922i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.80960e6 | −0.305220 | ||||||||
\(268\) | 1.29135e7 | + | 2.23668e7i | 0.670871 | + | 1.16198i | ||||
\(269\) | 2.72017e7 | + | 1.57049e7i | 1.39746 | + | 0.806825i | 0.994126 | − | 0.108227i | \(-0.0345174\pi\) |
0.403335 | + | 0.915052i | \(0.367851\pi\) | |||||||
\(270\) | 1.98602e6 | − | 3.43989e6i | 0.100900 | − | 0.174764i | ||||
\(271\) | 1.29500e6 | − | 747670.i | 0.0650673 | − | 0.0375666i | −0.467113 | − | 0.884197i | \(-0.654706\pi\) |
0.532181 | + | 0.846631i | \(0.321373\pi\) | |||||||
\(272\) | 7.12403e6i | 0.354013i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.19642e7 | 0.581610 | ||||||||
\(275\) | −3.82099e6 | − | 6.61815e6i | −0.183729 | − | 0.318228i | ||||
\(276\) | −2.78845e7 | − | 1.60991e7i | −1.32628 | − | 0.765730i | ||||
\(277\) | 991747. | − | 1.71776e6i | 0.0466618 | − | 0.0808207i | −0.841751 | − | 0.539866i | \(-0.818475\pi\) |
0.888413 | + | 0.459045i | \(0.151808\pi\) | |||||||
\(278\) | 52957.5 | − | 30575.1i | 0.00246487 | − | 0.00142309i | ||||
\(279\) | 6.77101e6i | 0.311775i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.50353e6 | −0.157902 | −0.0789508 | − | 0.996879i | \(-0.525157\pi\) | ||||
−0.0789508 | + | 0.996879i | \(0.525157\pi\) | |||||||
\(282\) | −515642. | − | 893117.i | −0.0229933 | − | 0.0398255i | ||||
\(283\) | −2.82715e7 | − | 1.63226e7i | −1.24736 | − | 0.720161i | −0.276774 | − | 0.960935i | \(-0.589265\pi\) |
−0.970581 | + | 0.240774i | \(0.922599\pi\) | |||||||
\(284\) | −5.27931e6 | + | 9.14403e6i | −0.230474 | + | 0.399193i | ||||
\(285\) | 7.17773e6 | − | 4.14407e6i | 0.310065 | − | 0.179016i | ||||
\(286\) | − | 2.63223e7i | − | 1.12519i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.43535e6 | −0.269398 | ||||||||
\(289\) | 1.83162e7 | + | 3.17246e7i | 0.758826 | + | 1.31432i | ||||
\(290\) | 1.26119e7 | + | 7.28150e6i | 0.517115 | + | 0.298557i | ||||
\(291\) | 4.83280e6 | − | 8.37066e6i | 0.196119 | − | 0.339688i | ||||
\(292\) | 2.61729e7 | − | 1.51109e7i | 1.05124 | − | 0.606935i | ||||
\(293\) | 2.57653e7i | 1.02431i | 0.858892 | + | 0.512156i | \(0.171153\pi\) | ||||
−0.858892 | + | 0.512156i | \(0.828847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.79187e7 | −0.697976 | ||||||||
\(296\) | 2.39813e7 | + | 4.15368e7i | 0.924692 | + | 1.60161i | ||||
\(297\) | 2.69735e6 | + | 1.55732e6i | 0.102960 | + | 0.0594440i | ||||
\(298\) | −1.08540e7 | + | 1.87996e7i | −0.410148 | + | 0.710397i | ||||
\(299\) | 3.96182e7 | − | 2.28736e7i | 1.48211 | − | 0.855698i | ||||
\(300\) | 1.58902e7i | 0.588528i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.22336e7 | 1.17028 | ||||||||
\(303\) | −5.20828e6 | − | 9.02100e6i | −0.187226 | − | 0.324285i | ||||
\(304\) | 5.28851e6 | + | 3.05332e6i | 0.188240 | + | 0.108681i | ||||
\(305\) | 5.74306e6 | − | 9.94727e6i | 0.202416 | − | 0.350594i | ||||
\(306\) | 2.16199e7 | − | 1.24823e7i | 0.754553 | − | 0.435641i | ||||
\(307\) | − | 1.89894e7i | − | 0.656289i | −0.944628 | − | 0.328145i | \(-0.893577\pi\) | ||
0.944628 | − | 0.328145i | \(-0.106423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.41525e7 | 0.818627 | ||||||||
\(310\) | 1.46090e7 | + | 2.53036e7i | 0.490384 | + | 0.849370i | ||||
\(311\) | −2.80365e7 | − | 1.61869e7i | −0.932057 | − | 0.538124i | −0.0445958 | − | 0.999005i | \(-0.514200\pi\) |
−0.887462 | + | 0.460881i | \(0.847533\pi\) | |||||||
\(312\) | −1.13974e7 | + | 1.97409e7i | −0.375268 | + | 0.649984i | ||||
\(313\) | −2.81397e7 | + | 1.62465e7i | −0.917671 | + | 0.529818i | −0.882891 | − | 0.469577i | \(-0.844406\pi\) |
−0.0347798 | + | 0.999395i | \(0.511073\pi\) | |||||||
\(314\) | 3.71035e7i | 1.19847i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.47273e7 | −2.36820 | ||||||||
\(317\) | 8.17142e6 | + | 1.41533e7i | 0.256519 | + | 0.444304i | 0.965307 | − | 0.261118i | \(-0.0840910\pi\) |
−0.708788 | + | 0.705422i | \(0.750758\pi\) | |||||||
\(318\) | 3.31610e7 | + | 1.91455e7i | 1.03121 | + | 0.595368i | ||||
\(319\) | −5.70972e6 | + | 9.88952e6i | −0.175891 | + | 0.304651i | ||||
\(320\) | −2.80794e7 | + | 1.62116e7i | −0.856915 | + | 0.494740i | ||||
\(321\) | − | 1.49009e7i | − | 0.450504i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.20914e7 | 1.54582 | ||||||||
\(324\) | −3.23819e6 | − | 5.60870e6i | −0.0952065 | − | 0.164903i | ||||
\(325\) | −1.95521e7 | − | 1.12884e7i | −0.569564 | − | 0.328838i | ||||
\(326\) | −1.02979e7 | + | 1.78365e7i | −0.297233 | + | 0.514822i | ||||
\(327\) | 2.12183e7 | − | 1.22504e7i | 0.606830 | − | 0.350354i | ||||
\(328\) | − | 3.56346e7i | − | 1.00984i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.34402e7 | 0.373993 | ||||||||
\(331\) | −2.58785e7 | − | 4.48229e7i | −0.713601 | − | 1.23599i | −0.963497 | − | 0.267720i | \(-0.913730\pi\) |
0.249896 | − | 0.968273i | \(-0.419604\pi\) | |||||||
\(332\) | 1.21598e7 | + | 7.02044e6i | 0.332285 | + | 0.191845i | ||||
\(333\) | 9.68054e6 | − | 1.67672e7i | 0.262160 | − | 0.454075i | ||||
\(334\) | −1.31864e7 | + | 7.61318e6i | −0.353905 | + | 0.204327i | ||||
\(335\) | − | 1.87364e7i | − | 0.498370i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.13986e7 | 1.60424 | 0.802119 | − | 0.597164i | \(-0.203706\pi\) | ||||
0.802119 | + | 0.597164i | \(0.203706\pi\) | |||||||
\(338\) | −7.07658e6 | − | 1.22570e7i | −0.183262 | − | 0.317420i | ||||
\(339\) | 3.34227e7 | + | 1.92966e7i | 0.857912 | + | 0.495316i | ||||
\(340\) | 3.40146e7 | − | 5.89151e7i | 0.865424 | − | 1.49896i | ||||
\(341\) | −1.98416e7 | + | 1.14555e7i | −0.500395 | + | 0.288903i | ||||
\(342\) | − | 2.13993e7i | − | 0.534961i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.52770e7 | 1.35790 | ||||||||
\(345\) | 1.16793e7 | + | 2.02291e7i | 0.284419 | + | 0.492628i | ||||
\(346\) | 6.57512e7 | + | 3.79615e7i | 1.58736 | + | 0.916462i | ||||
\(347\) | −1.77833e7 | + | 3.08017e7i | −0.425623 | + | 0.737200i | −0.996478 | − | 0.0838501i | \(-0.973278\pi\) |
0.570855 | + | 0.821051i | \(0.306612\pi\) | |||||||
\(348\) | 2.05636e7 | − | 1.18724e7i | 0.487935 | − | 0.281709i | ||||
\(349\) | − | 5.17156e7i | − | 1.21659i | −0.793710 | − | 0.608297i | \(-0.791853\pi\) | ||
0.793710 | − | 0.608297i | \(-0.208147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.20159e6 | 0.212785 | ||||||||
\(352\) | −1.08876e7 | − | 1.88579e7i | −0.249635 | − | 0.432381i | ||||
\(353\) | 669058. | + | 386281.i | 0.0152104 | + | 0.00878171i | 0.507586 | − | 0.861601i | \(-0.330538\pi\) |
−0.492376 | + | 0.870383i | \(0.663871\pi\) | |||||||
\(354\) | −2.31324e7 | + | 4.00664e7i | −0.521447 | + | 0.903172i | ||||
\(355\) | 6.63362e6 | − | 3.82992e6i | 0.148274 | − | 0.0856061i | ||||
\(356\) | 4.08754e7i | 0.905967i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.57565e7 | 0.343407 | ||||||||
\(359\) | 2.08340e7 | + | 3.60856e7i | 0.450287 | + | 0.779920i | 0.998404 | − | 0.0564819i | \(-0.0179883\pi\) |
−0.548117 | + | 0.836402i | \(0.684655\pi\) | |||||||
\(360\) | −1.00797e7 | − | 5.81952e6i | −0.216043 | − | 0.124733i | ||||
\(361\) | −1.19684e6 | + | 2.07298e6i | −0.0254398 | + | 0.0440630i | ||||
\(362\) | −1.14165e8 | + | 6.59133e7i | −2.40662 | + | 1.38946i | ||||
\(363\) | − | 1.70769e7i | − | 0.357017i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.19247e7 | −0.450874 | ||||||||
\(366\) | −1.48281e7 | − | 2.56831e7i | −0.302443 | − | 0.523847i | ||||
\(367\) | −5.71734e6 | − | 3.30091e6i | −0.115663 | − | 0.0667783i | 0.441052 | − | 0.897481i | \(-0.354605\pi\) |
−0.556716 | + | 0.830703i | \(0.687939\pi\) | |||||||
\(368\) | −8.60521e6 | + | 1.49047e7i | −0.172670 | + | 0.299074i | ||||
\(369\) | −1.24575e7 | + | 7.19233e6i | −0.247943 | + | 0.143150i | ||||
\(370\) | − | 8.35464e7i | − | 1.64939i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.76398e7 | 0.925424 | ||||||||
\(373\) | 2.47581e6 | + | 4.28823e6i | 0.0477080 | + | 0.0826326i | 0.888893 | − | 0.458114i | \(-0.151475\pi\) |
−0.841185 | + | 0.540747i | \(0.818142\pi\) | |||||||
\(374\) | 7.31553e7 | + | 4.22362e7i | 1.39840 | + | 0.807365i | ||||
\(375\) | 1.54539e7 | − | 2.67669e7i | 0.293052 | − | 0.507580i | ||||
\(376\) | −2.61705e6 | + | 1.51095e6i | −0.0492321 | + | 0.0284242i | ||||
\(377\) | 3.37365e7i | 0.629616i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.05876e8 | −1.94482 | −0.972409 | − | 0.233282i | \(-0.925053\pi\) | ||||
−0.972409 | + | 0.233282i | \(0.925053\pi\) | |||||||
\(380\) | −2.91570e7 | − | 5.05014e7i | −0.531364 | − | 0.920349i | ||||
\(381\) | −3.94999e6 | − | 2.28053e6i | −0.0714202 | − | 0.0412345i | ||||
\(382\) | −4.99651e7 | + | 8.65421e7i | −0.896348 | + | 1.55252i | ||||
\(383\) | 4.26092e7 | − | 2.46004e7i | 0.758414 | − | 0.437871i | −0.0703117 | − | 0.997525i | \(-0.522399\pi\) |
0.828726 | + | 0.559654i | \(0.189066\pi\) | |||||||
\(384\) | 5.72935e7i | 1.01184i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.35177e7 | −1.62604 | ||||||||
\(387\) | −1.11568e7 | − | 1.93242e7i | −0.192490 | − | 0.333403i | ||||
\(388\) | −5.88947e7 | − | 3.40028e7i | −1.00828 | − | 0.582130i | ||||
\(389\) | −3.33099e7 | + | 5.76945e7i | −0.565880 | + | 0.980134i | 0.431087 | + | 0.902310i | \(0.358130\pi\) |
−0.996967 | + | 0.0778231i | \(0.975203\pi\) | |||||||
\(390\) | 3.43868e7 | − | 1.98532e7i | 0.579693 | − | 0.334686i | ||||
\(391\) | 1.46810e8i | 2.45598i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.25384e7 | −0.700815 | ||||||||
\(394\) | 1.31850e7 | + | 2.28372e7i | 0.215572 | + | 0.373382i | ||||
\(395\) | 4.69486e7 | + | 2.71058e7i | 0.761783 | + | 0.439816i | ||||
\(396\) | 1.09570e7 | − | 1.89782e7i | 0.176444 | − | 0.305611i | ||||
\(397\) | −4.16040e7 | + | 2.40201e7i | −0.664911 | + | 0.383887i | −0.794146 | − | 0.607727i | \(-0.792081\pi\) |
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(398\) | 5.72756e7i | 0.908491i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.49355e6 | 0.132712 | ||||||||
\(401\) | −6.97156e6 | − | 1.20751e7i | −0.108118 | − | 0.187265i | 0.806890 | − | 0.590702i | \(-0.201149\pi\) |
−0.915008 | + | 0.403436i | \(0.867816\pi\) | |||||||
\(402\) | −4.18948e7 | − | 2.41880e7i | −0.644885 | − | 0.372324i | ||||
\(403\) | −3.38431e7 | + | 5.86180e7i | −0.517077 | + | 0.895604i | ||||
\(404\) | −6.34704e7 | + | 3.66446e7i | −0.962558 | + | 0.555733i | ||||
\(405\) | 4.69834e6i | 0.0707261i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.55121e7 | 0.971713 | ||||||||
\(408\) | −3.65760e7 | − | 6.33515e7i | −0.538538 | − | 0.932775i | ||||
\(409\) | −1.93849e7 | − | 1.11919e7i | −0.283331 | − | 0.163581i | 0.351599 | − | 0.936151i | \(-0.385638\pi\) |
−0.634931 | + | 0.772569i | \(0.718971\pi\) | |||||||
\(410\) | −3.10361e7 | + | 5.37562e7i | −0.450315 | + | 0.779968i | ||||
\(411\) | −1.22559e7 | + | 7.07594e6i | −0.176530 | + | 0.101920i | ||||
\(412\) | − | 1.69933e8i | − | 2.42989i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.03099e7 | 0.849939 | ||||||||
\(415\) | −5.09304e6 | − | 8.82140e6i | −0.0712578 | − | 0.123422i | ||||
\(416\) | −5.57122e7 | − | 3.21654e7i | −0.773874 | − | 0.446796i | ||||
\(417\) | −36165.8 | + | 62641.0i | −0.000498758 | + | 0.000863874i | ||||
\(418\) | 6.27079e7 | − | 3.62044e7i | 0.858605 | − | 0.495716i | ||||
\(419\) | − | 5.41233e7i | − | 0.735770i | −0.929871 | − | 0.367885i | \(-0.880082\pi\) | ||
0.929871 | − | 0.367885i | \(-0.119918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.30034e8 | −1.74265 | −0.871323 | − | 0.490709i | \(-0.836738\pi\) | ||||
−0.871323 | + | 0.490709i | \(0.836738\pi\) | |||||||
\(422\) | 6.82930e7 | + | 1.18287e8i | 0.908738 | + | 1.57398i | ||||
\(423\) | 1.05643e6 | + | 609928.i | 0.0139578 | + | 0.00805856i | ||||
\(424\) | 5.61010e7 | − | 9.71697e7i | 0.735992 | − | 1.27477i | ||||
\(425\) | 6.27456e7 | − | 3.62262e7i | 0.817366 | − | 0.471907i | ||||
\(426\) | − | 1.97771e7i | − | 0.255820i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.04841e8 | −1.33721 | ||||||||
\(429\) | 1.55677e7 | + | 2.69641e7i | 0.197175 | + | 0.341518i | ||||
\(430\) | −8.33874e7 | − | 4.81437e7i | −1.04881 | − | 0.605528i | ||||
\(431\) | 5.99710e7 | − | 1.03873e8i | 0.749047 | − | 1.29739i | −0.199233 | − | 0.979952i | \(-0.563845\pi\) |
0.948280 | − | 0.317436i | \(-0.102822\pi\) | |||||||
\(432\) | −2.99793e6 | + | 1.73085e6i | −0.0371852 | + | 0.0214689i | ||||
\(433\) | 1.11549e8i | 1.37404i | 0.726636 | + | 0.687022i | \(0.241083\pi\) | ||||
−0.726636 | + | 0.687022i | \(0.758917\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.72259e7 | −0.209273 | ||||||||
\(436\) | −8.61918e7 | − | 1.49289e8i | −1.03994 | − | 1.80122i | ||||
\(437\) | 1.08984e8 | + | 6.29219e7i | 1.30592 | + | 0.753976i | ||||
\(438\) | −2.83039e7 | + | 4.90239e7i | −0.336841 | + | 0.583425i | ||||
\(439\) | −1.06743e8 | + | 6.16284e7i | −1.26168 | + | 0.728429i | −0.973399 | − | 0.229118i | \(-0.926416\pi\) |
−0.288277 | + | 0.957547i | \(0.593082\pi\) | |||||||
\(440\) | − | 3.93830e7i | − | 0.462329i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.49557e8 | 2.89004 | ||||||||
\(443\) | 3.55708e7 | + | 6.16104e7i | 0.409150 | + | 0.708669i | 0.994795 | − | 0.101899i | \(-0.0324919\pi\) |
−0.585645 | + | 0.810568i | \(0.699159\pi\) | |||||||
\(444\) | −1.17971e8 | − | 6.81108e7i | −1.34781 | − | 0.778157i | ||||
\(445\) | 1.48267e7 | − | 2.56806e7i | 0.168254 | − | 0.291424i | ||||
\(446\) | 5.53296e7 | − | 3.19445e7i | 0.623667 | − | 0.360074i | ||||
\(447\) | − | 2.56773e7i | − | 0.287493i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.07566e8 | −1.18833 | −0.594165 | − | 0.804343i | \(-0.702517\pi\) | ||||
−0.594165 | + | 0.804343i | \(0.702517\pi\) | |||||||
\(450\) | −1.48818e7 | − | 2.57761e7i | −0.163312 | − | 0.282865i | ||||
\(451\) | −4.21524e7 | − | 2.43367e7i | −0.459507 | − | 0.265297i | ||||
\(452\) | 1.35768e8 | − | 2.35157e8i | 1.47022 | − | 2.54649i | ||||
\(453\) | −3.30195e7 | + | 1.90638e7i | −0.355203 | + | 0.205076i | ||||
\(454\) | 1.99103e8i | 2.12769i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.27052e7 | −0.661316 | ||||||||
\(457\) | −6.43381e6 | − | 1.11437e7i | −0.0674093 | − | 0.116756i | 0.830351 | − | 0.557241i | \(-0.188140\pi\) |
−0.897760 | + | 0.440485i | \(0.854807\pi\) | |||||||
\(458\) | 4.85479e7 | + | 2.80292e7i | 0.505329 | + | 0.291752i | ||||
\(459\) | −1.47647e7 | + | 2.55732e7i | −0.152681 | + | 0.264452i | ||||
\(460\) | 1.42329e8 | − | 8.21735e7i | 1.46224 | − | 0.844225i | ||||
\(461\) | − | 7.08717e6i | − | 0.0723386i | −0.999346 | − | 0.0361693i | \(-0.988484\pi\) | ||
0.999346 | − | 0.0361693i | \(-0.0115156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.44698e8 | 1.45788 | 0.728938 | − | 0.684580i | \(-0.240014\pi\) | ||||
0.728938 | + | 0.684580i | \(0.240014\pi\) | |||||||
\(464\) | −6.34596e6 | − | 1.09915e7i | −0.0635249 | − | 0.110028i | ||||
\(465\) | −2.99304e7 | − | 1.72803e7i | −0.297683 | − | 0.171867i | ||||
\(466\) | 8.29054e7 | − | 1.43596e8i | 0.819267 | − | 1.41901i | ||||
\(467\) | −7.34759e7 | + | 4.24214e7i | −0.721431 | + | 0.416518i | −0.815279 | − | 0.579068i | \(-0.803416\pi\) |
0.0938485 | + | 0.995586i | \(0.470083\pi\) | |||||||
\(468\) | − | 6.47410e7i | − | 0.631599i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.26389e6 | 0.0507006 | ||||||||
\(471\) | −2.19440e7 | − | 3.80082e7i | −0.210016 | − | 0.363759i | ||||
\(472\) | 1.17404e8 | + | 6.77834e7i | 1.11650 | + | 0.644610i | ||||
\(473\) | 3.77514e7 | − | 6.53874e7i | 0.356738 | − | 0.617889i | ||||
\(474\) | 1.21218e8 | − | 6.99851e7i | 1.13823 | − | 0.657159i | ||||
\(475\) | − | 6.21054e7i | − | 0.579494i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.52927e7 | −0.417323 | ||||||||
\(478\) | 4.97062e7 | + | 8.60937e7i | 0.455121 | + | 0.788293i | ||||
\(479\) | −1.38250e8 | − | 7.98185e7i | −1.25793 | − | 0.726268i | −0.285261 | − | 0.958450i | \(-0.592080\pi\) |
−0.972672 | + | 0.232182i | \(0.925414\pi\) | |||||||
\(480\) | 1.64237e7 | − | 2.84467e7i | 0.148507 | − | 0.257222i | ||||
\(481\) | 1.67613e8 | − | 9.67714e7i | 1.50616 | − | 0.869585i | ||||
\(482\) | − | 2.58016e8i | − | 2.30412i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.20150e8 | −1.05972 | ||||||||
\(485\) | 2.46677e7 | + | 4.27256e7i | 0.216223 | + | 0.374510i | ||||
\(486\) | 1.05055e7 | + | 6.06538e6i | 0.0915187 | + | 0.0528383i | ||||
\(487\) | −6.90017e7 | + | 1.19515e8i | −0.597411 | + | 1.03475i | 0.395791 | + | 0.918341i | \(0.370471\pi\) |
−0.993202 | + | 0.116405i | \(0.962863\pi\) | |||||||
\(488\) | −7.52577e7 | + | 4.34501e7i | −0.647577 | + | 0.373879i | ||||
\(489\) | − | 2.43619e7i | − | 0.208345i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.91824e7 | −0.331014 | −0.165507 | − | 0.986209i | \(-0.552926\pi\) | ||||
−0.165507 | + | 0.986209i | \(0.552926\pi\) | |||||||
\(492\) | 5.06041e7 | + | 8.76489e7i | 0.424904 | + | 0.735955i | ||||
\(493\) | −9.37609e7 | − | 5.41329e7i | −0.782494 | − | 0.451773i | ||||
\(494\) | 1.06959e8 | − | 1.85258e8i | 0.887231 | − | 1.53673i | ||||
\(495\) | −1.37679e7 | + | 7.94889e6i | −0.113515 | + | 0.0655376i | ||||
\(496\) | − | 2.54641e7i | − | 0.208681i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.62997e7 | −0.212942 | ||||||||
\(499\) | −1.14482e7 | − | 1.98288e7i | −0.0921370 | − | 0.159586i | 0.816273 | − | 0.577666i | \(-0.196036\pi\) |
−0.908410 | + | 0.418080i | \(0.862703\pi\) | |||||||
\(500\) | −1.88328e8 | − | 1.08731e8i | −1.50662 | − | 0.869849i | ||||
\(501\) | 9.00527e6 | − | 1.55976e7i | 0.0716116 | − | 0.124035i | ||||
\(502\) | 1.59316e8 | − | 9.19810e7i | 1.25935 | − | 0.727088i | ||||
\(503\) | 1.38751e8i | 1.09027i | 0.838349 | + | 0.545133i | \(0.183521\pi\) | ||||
−0.838349 | + | 0.545133i | \(0.816479\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.31683e7 | 0.412837 | ||||||||
\(506\) | 1.02035e8 | + | 1.76730e8i | 0.787588 | + | 1.36414i | ||||
\(507\) | 1.44982e7 | + | 8.37055e6i | 0.111248 | + | 0.0642289i | ||||
\(508\) | −1.60454e7 | + | 2.77915e7i | −0.122394 | + | 0.211993i | ||||
\(509\) | 5.07588e7 | − | 2.93056e7i | 0.384909 | − | 0.222227i | −0.295043 | − | 0.955484i | \(-0.595334\pi\) |
0.679952 | + | 0.733257i | \(0.262001\pi\) | |||||||
\(510\) | 1.27424e8i | 0.960598i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.94097e7 | 0.442636 | ||||||||
\(513\) | 1.26561e7 | + | 2.19211e7i | 0.0937451 | + | 0.162371i | ||||
\(514\) | 7.48087e6 | + | 4.31908e6i | 0.0550888 | + | 0.0318055i | ||||
\(515\) | −6.16397e7 | + | 1.06763e8i | −0.451272 | + | 0.781627i | ||||
\(516\) | −1.35962e8 | + | 7.84978e7i | −0.989622 | + | 0.571358i | ||||
\(517\) | 4.12763e6i | 0.0298696i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.98057e7 | −0.642394 | ||||||||
\(520\) | −5.81748e7 | − | 1.00762e8i | −0.413737 | − | 0.716614i | ||||
\(521\) | 1.88084e8 | + | 1.08590e8i | 1.32996 | + | 0.767853i | 0.985293 | − | 0.170872i | \(-0.0546583\pi\) |
0.344668 | + | 0.938725i | \(0.387992\pi\) | |||||||
\(522\) | −2.22380e7 | + | 3.85173e7i | −0.156345 | + | 0.270797i | ||||
\(523\) | −1.64929e7 | + | 9.52217e6i | −0.115290 | + | 0.0665627i | −0.556536 | − | 0.830823i | \(-0.687870\pi\) |
0.441246 | + | 0.897386i | \(0.354537\pi\) | |||||||
\(524\) | 2.99294e8i | 2.08019i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.96889e8 | 1.35290 | ||||||||
\(527\) | −1.08608e8 | − | 1.88114e8i | −0.742044 | − | 1.28526i | ||||
\(528\) | −1.01441e7 | − | 5.85669e6i | −0.0689146 | − | 0.0397879i | ||||
\(529\) | −1.03315e8 | + | 1.78948e8i | −0.697908 | + | 1.20881i | ||||
\(530\) | −1.69261e8 | + | 9.77228e7i | −1.13692 | + | 0.656400i | ||||
\(531\) | − | 5.47244e7i | − | 0.365508i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.43796e8 | −0.949654 | ||||||||
\(534\) | −3.82815e7 | − | 6.63054e7i | −0.251400 | − | 0.435437i | ||||
\(535\) | 6.58678e7 | + | 3.80288e7i | 0.430142 | + | 0.248342i | ||||
\(536\) | −7.08766e7 | + | 1.22762e8i | −0.460266 | + | 0.797204i | ||||
\(537\) | −1.61406e7 | + | 9.31879e6i | −0.104231 | + | 0.0601778i | ||||
\(538\) | 4.13941e8i | 2.65822i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.30568e7 | 0.209932 | ||||||||
\(541\) | 5.05360e7 | + | 8.75310e7i | 0.319161 | + | 0.552803i | 0.980313 | − | 0.197449i | \(-0.0632657\pi\) |
−0.661152 | + | 0.750252i | \(0.729932\pi\) | |||||||
\(542\) | 1.70664e7 | + | 9.85332e6i | 0.107188 | + | 0.0618849i | ||||
\(543\) | 7.79657e7 | − | 1.35041e8i | 0.486972 | − | 0.843461i | ||||
\(544\) | 1.78789e8 | − | 1.03224e8i | 1.11057 | − | 0.641185i | ||||
\(545\) | 1.25057e8i | 0.772537i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.29198e7 | −0.140039 | −0.0700196 | − | 0.997546i | \(-0.522306\pi\) | ||||
−0.0700196 | + | 0.997546i | \(0.522306\pi\) | |||||||
\(548\) | 4.97852e7 | + | 8.62305e7i | 0.302523 | + | 0.523986i | ||||
\(549\) | 3.03793e7 | + | 1.75395e7i | 0.183595 | + | 0.105999i | ||||
\(550\) | 5.03557e7 | − | 8.72186e7i | 0.302664 | − | 0.524229i | ||||
\(551\) | −8.03708e7 | + | 4.64021e7i | −0.480445 | + | 0.277385i | ||||
\(552\) | − | 1.76723e8i | − | 1.05069i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.61399e7 | 0.153735 | ||||||||
\(555\) | 4.94116e7 | + | 8.55834e7i | 0.289035 | + | 0.500622i | ||||
\(556\) | 440732. | + | 254457.i | 0.00256419 | + | 0.00148044i | ||||
\(557\) | −6.91655e7 | + | 1.19798e8i | −0.400243 | + | 0.693242i | −0.993755 | − | 0.111584i | \(-0.964408\pi\) |
0.593512 | + | 0.804825i | \(0.297741\pi\) | |||||||
\(558\) | −7.72781e7 | + | 4.46165e7i | −0.444789 | + | 0.256799i | ||||
\(559\) | − | 2.23059e8i | − | 1.27698i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.99184e7 | −0.565923 | ||||||||
\(562\) | −2.30859e7 | − | 3.99860e7i | −0.130059 | − | 0.225268i | ||||
\(563\) | −1.95097e8 | − | 1.12639e8i | −1.09326 | − | 0.631195i | −0.158819 | − | 0.987308i | \(-0.550769\pi\) |
−0.934443 | + | 0.356112i | \(0.884102\pi\) | |||||||
\(564\) | 4.29136e6 | − | 7.43285e6i | 0.0239198 | − | 0.0414303i | ||||
\(565\) | −1.70597e8 | + | 9.84941e7i | −0.945857 | + | 0.546091i | ||||
\(566\) | − | 4.30221e8i | − | 2.37270i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.79518e7 | −0.316244 | ||||||||
\(569\) | −1.10276e8 | − | 1.91003e8i | −0.598609 | − | 1.03682i | −0.993027 | − | 0.117890i | \(-0.962387\pi\) |
0.394417 | − | 0.918931i | \(-0.370946\pi\) | |||||||
\(570\) | 9.45931e7 | + | 5.46134e7i | 0.510781 | + | 0.294900i | ||||
\(571\) | 3.36594e7 | − | 5.82999e7i | 0.180800 | − | 0.313155i | −0.761353 | − | 0.648337i | \(-0.775465\pi\) |
0.942153 | + | 0.335182i | \(0.108798\pi\) | |||||||
\(572\) | 1.89715e8 | − | 1.09532e8i | 1.01371 | − | 0.585265i | ||||
\(573\) | − | 1.18203e8i | − | 0.628295i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.75032e8 | 0.920693 | ||||||||
\(576\) | −4.95109e7 | − | 8.57555e7i | −0.259080 | − | 0.448740i | ||||
\(577\) | 9.29650e6 | + | 5.36734e6i | 0.0483941 | + | 0.0279403i | 0.524002 | − | 0.851717i | \(-0.324438\pi\) |
−0.475608 | + | 0.879657i | \(0.657772\pi\) | |||||||
\(578\) | −2.41384e8 | + | 4.18089e8i | −1.25004 | + | 2.16513i | ||||
\(579\) | 9.57977e7 | − | 5.53088e7i | 0.493537 | − | 0.284943i | ||||
\(580\) | 1.21199e8i | 0.621175i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.27380e8 | 0.646149 | ||||||||
\(583\) | −7.66284e7 | − | 1.32724e8i | −0.386709 | − | 0.669799i | ||||
\(584\) | 1.43652e8 | + | 8.29374e7i | 0.721228 | + | 0.416401i | ||||
\(585\) | −2.34835e7 | + | 4.06745e7i | −0.117299 | + | 0.203168i | ||||
\(586\) | −2.94062e8 | + | 1.69777e8i | −1.46132 | + | 0.843694i | ||||
\(587\) | − | 2.34143e8i | − | 1.15762i | −0.815461 | − | 0.578812i | \(-0.803516\pi\) | ||
0.815461 | − | 0.578812i | \(-0.196484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.86195e8 | −0.911219 | ||||||||
\(590\) | −1.18073e8 | − | 2.04508e8i | −0.574901 | − | 0.995757i | ||||
\(591\) | −2.70130e7 | − | 1.55960e7i | −0.130861 | − | 0.0755527i | ||||
\(592\) | −3.64061e7 | + | 6.30573e7i | −0.175473 | + | 0.303928i | ||||
\(593\) | −1.45328e8 | + | 8.39054e7i | −0.696926 | + | 0.402370i | −0.806202 | − | 0.591641i | \(-0.798480\pi\) |
0.109275 | + | 0.994012i | \(0.465147\pi\) | |||||||
\(594\) | 4.10468e7i | 0.195849i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.80662e8 | −0.853350 | ||||||||
\(597\) | −3.38743e7 | − | 5.86720e7i | −0.159202 | − | 0.275745i | ||||
\(598\) | 5.22116e8 | + | 3.01444e8i | 2.44154 | + | 1.40962i | ||||
\(599\) | −2.72137e7 | + | 4.71356e7i | −0.126622 | + | 0.219315i | −0.922366 | − | 0.386318i | \(-0.873747\pi\) |
0.795744 | + | 0.605633i | \(0.207080\pi\) | |||||||
\(600\) | −7.55302e7 | + | 4.36074e7i | −0.349677 | + | 0.201886i | ||||
\(601\) | − | 1.02729e7i | − | 0.0473226i | −0.999720 | − | 0.0236613i | \(-0.992468\pi\) | ||
0.999720 | − | 0.0236613i | \(-0.00753233\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.72217e7 | 0.260981 | ||||||||
\(604\) | 1.34130e8 | + | 2.32320e8i | 0.608717 | + | 1.05433i | ||||
\(605\) | 7.54864e7 | + | 4.35821e7i | 0.340881 | + | 0.196808i | ||||
\(606\) | 6.86383e7 | − | 1.18885e8i | 0.308424 | − | 0.534207i | ||||
\(607\) | −3.20092e8 | + | 1.84805e8i | −1.43123 | + | 0.826319i | −0.997214 | − | 0.0745880i | \(-0.976236\pi\) |
−0.434012 | + | 0.900907i | \(0.642902\pi\) | |||||||
\(608\) | − | 1.76965e8i | − | 0.787366i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.51372e8 | 0.666893 | ||||||||
\(611\) | 6.09714e6 | + | 1.05606e7i | 0.0267302 | + | 0.0462981i | ||||
\(612\) | 1.79929e8 | + | 1.03882e8i | 0.784958 | + | 0.453196i | ||||
\(613\) | −2.33412e7 | + | 4.04282e7i | −0.101331 | + | 0.175510i | −0.912233 | − | 0.409671i | \(-0.865643\pi\) |
0.810902 | + | 0.585182i | \(0.198977\pi\) | |||||||
\(614\) | 2.16727e8 | − | 1.25127e8i | 0.936285 | − | 0.540565i | ||||
\(615\) | − | 7.34224e7i | − | 0.315648i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.39158e8 | 1.86967 | 0.934836 | − | 0.355080i | \(-0.115546\pi\) | ||||
0.934836 | + | 0.355080i | \(0.115546\pi\) | |||||||
\(618\) | 1.59149e8 | + | 2.75654e8i | 0.674277 | + | 1.16788i | ||||
\(619\) | 1.84752e8 | + | 1.06666e8i | 0.778962 | + | 0.449734i | 0.836062 | − | 0.548635i | \(-0.184852\pi\) |
−0.0571005 | + | 0.998368i | \(0.518186\pi\) | |||||||
\(620\) | −1.21582e8 | + | 2.10586e8i | −0.510145 | + | 0.883596i | ||||
\(621\) | −6.17803e7 | + | 3.56689e7i | −0.257974 | + | 0.148941i | ||||
\(622\) | − | 4.26644e8i | − | 1.77294i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.46049e7 | −0.142424 | ||||||||
\(625\) | 6.26968e6 | + | 1.08594e7i | 0.0256806 | + | 0.0444801i | ||||
\(626\) | −3.70845e8 | − | 2.14107e8i | −1.51171 | − | 0.872788i | ||||
\(627\) | −4.28245e7 | + | 7.41743e7i | −0.173736 | + | 0.300920i | ||||
\(628\) | −2.67419e8 | + | 1.54395e8i | −1.07973 | + | 0.623381i | ||||
\(629\) | 6.21109e8i | 2.49584i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.58817e8 | 1.03016 | 0.515080 | − | 0.857142i | \(-0.327762\pi\) | ||||
0.515080 | + | 0.857142i | \(0.327762\pi\) | |||||||
\(632\) | −2.05073e8 | − | 3.55197e8i | −0.812377 | − | 1.40708i | ||||
\(633\) | −1.39916e8 | − | 8.07806e7i | −0.551641 | − | 0.318490i | ||||
\(634\) | −1.07689e8 | + | 1.86522e8i | −0.422573 | + | 0.731918i | ||||
\(635\) | 2.01616e7 | − | 1.16403e7i | 0.0787415 | − | 0.0454614i | ||||
\(636\) | 3.18672e8i | 1.23872i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.50493e8 | −0.579502 | ||||||||
\(639\) | 1.16967e7 | + | 2.02593e7i | 0.0448292 | + | 0.0776465i | ||||
\(640\) | −2.53259e8 | − | 1.46219e8i | −0.966106 | − | 0.557781i | ||||
\(641\) | −6.64356e7 | + | 1.15070e8i | −0.252247 | + | 0.436905i | −0.964144 | − | 0.265379i | \(-0.914503\pi\) |
0.711897 | + | 0.702284i | \(0.247836\pi\) | |||||||
\(642\) | 1.70066e8 | − | 9.81874e7i | 0.642704 | − | 0.371066i | ||||
\(643\) | − | 1.84168e8i | − | 0.692757i | −0.938095 | − | 0.346378i | \(-0.887411\pi\) | ||
0.938095 | − | 0.346378i | \(-0.112589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.13894e8 | 0.424445 | ||||||||
\(646\) | 3.43248e8 | + | 5.94523e8i | 1.27324 | + | 2.20532i | ||||
\(647\) | 2.88189e8 | + | 1.66386e8i | 1.06405 | + | 0.614332i | 0.926551 | − | 0.376169i | \(-0.122759\pi\) |
0.137504 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(648\) | 1.77730e7 | − | 3.07838e7i | 0.0653185 | − | 0.113135i | ||||
\(649\) | 1.60363e8 | − | 9.25854e7i | 0.586636 | − | 0.338695i | ||||
\(650\) | − | 2.97532e8i | − | 1.08341i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.71406e8 | −0.618420 | ||||||||
\(653\) | −1.28291e8 | − | 2.22206e8i | −0.460741 | − | 0.798026i | 0.538257 | − | 0.842780i | \(-0.319083\pi\) |
−0.998998 | + | 0.0447544i | \(0.985749\pi\) | |||||||
\(654\) | 2.79629e8 | + | 1.61444e8i | 0.999654 | + | 0.577150i | ||||
\(655\) | 1.08563e8 | − | 1.88036e8i | 0.386328 | − | 0.669140i | ||||
\(656\) | 4.68495e7 | − | 2.70486e7i | 0.165956 | − | 0.0958149i | ||||
\(657\) | − | 6.69588e7i | − | 0.236108i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.84717e8 | 0.645431 | 0.322715 | − | 0.946496i | \(-0.395404\pi\) | ||||
0.322715 | + | 0.946496i | \(0.395404\pi\) | |||||||
\(660\) | 5.59271e7 | + | 9.68686e7i | 0.194532 | + | 0.336939i | ||||
\(661\) | −1.74480e8 | − | 1.00736e8i | −0.604144 | − | 0.348803i | 0.166526 | − | 0.986037i | \(-0.446745\pi\) |
−0.770670 | + | 0.637234i | \(0.780078\pi\) | |||||||
\(662\) | 3.41045e8 | − | 5.90707e8i | 1.17554 | − | 2.03610i | ||||
\(663\) | −2.55642e8 | + | 1.47595e8i | −0.877185 | + | 0.506443i | ||||
\(664\) | 7.70644e7i | 0.263239i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.55154e8 | 0.863733 | ||||||||
\(667\) | −1.30776e8 | − | 2.26510e8i | −0.440706 | − | 0.763326i | ||||
\(668\) | −1.09742e8 | − | 6.33597e7i | −0.368166 | − | 0.212561i | ||||
\(669\) | −3.77857e7 | + | 6.54468e7i | −0.126197 | + | 0.218580i | ||||
\(670\) | 2.13840e8 | − | 1.23461e8i | 0.710992 | − | 0.410492i | ||||
\(671\) | 1.18697e8i | 0.392891i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.93893e8 | −1.62027 | −0.810135 | − | 0.586243i | \(-0.800606\pi\) | ||||
−0.810135 | + | 0.586243i | \(0.800606\pi\) | |||||||
\(674\) | 4.04577e8 | + | 7.00747e8i | 1.32136 | + | 2.28866i | ||||
\(675\) | 3.04894e7 | + | 1.76030e7i | 0.0991373 | + | 0.0572369i | ||||
\(676\) | 5.88939e7 | − | 1.02007e8i | 0.190647 | − | 0.330211i | ||||
\(677\) | 2.71512e8 | − | 1.56758e8i | 0.875030 | − | 0.505199i | 0.00601364 | − | 0.999982i | \(-0.498086\pi\) |
0.869017 | + | 0.494783i | \(0.164752\pi\) | |||||||
\(678\) | 5.08608e8i | 1.63190i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.73384e8 | 1.18749 | ||||||||
\(681\) | −1.17755e8 | − | 2.03957e8i | −0.372852 | − | 0.645798i | ||||
\(682\) | −2.61486e8 | − | 1.50969e8i | −0.824318 | − | 0.475920i | ||||
\(683\) | 7.42502e7 | − | 1.28605e8i | 0.233043 | − | 0.403642i | −0.725659 | − | 0.688054i | \(-0.758465\pi\) |
0.958702 | + | 0.284412i | \(0.0917984\pi\) | |||||||
\(684\) | 1.54233e8 | − | 8.90465e7i | 0.481958 | − | 0.278259i | ||||
\(685\) | − | 7.22343e7i | − | 0.224735i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.63087e7 | −0.204503 | ||||||||
\(688\) | 4.19582e7 | + | 7.26737e7i | 0.128840 | + | 0.223158i | ||||
\(689\) | −3.92108e8 | − | 2.26384e8i | −1.19880 | − | 0.692130i | ||||
\(690\) | −1.53917e8 | + | 2.66593e8i | −0.468533 | + | 0.811524i | ||||
\(691\) | 3.35862e8 | − | 1.93910e8i | 1.01795 | − | 0.587714i | 0.104441 | − | 0.994531i | \(-0.466695\pi\) |
0.913510 | + | 0.406817i | \(0.133361\pi\) | |||||||
\(692\) | 6.31859e8i | 1.90678i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.68722e8 | −1.40229 | ||||||||
\(695\) | −184598. | − | 319733.i | −0.000549886 | − | 0.000952430i | ||||
\(696\) | 1.12865e8 | + | 6.51626e7i | 0.334758 | + | 0.193273i | ||||
\(697\) | 2.30732e8 | − | 3.99640e8i | 0.681412 | − | 1.18024i | ||||
\(698\) | 5.90235e8 | − | 3.40772e8i | 1.73564 | − | 1.00207i | ||||
\(699\) | 1.96130e8i | 0.574265i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.86782e7 | 0.141312 | 0.0706562 | − | 0.997501i | \(-0.477491\pi\) | ||||
0.0706562 | + | 0.997501i | \(0.477491\pi\) | |||||||
\(702\) | 6.06325e7 | + | 1.05019e8i | 0.175265 | + | 0.303567i | ||||
\(703\) | 4.61079e8 | + | 2.66204e8i | 1.32712 | + | 0.766212i | ||||
\(704\) | 1.67530e8 | − | 2.90171e8i | 0.480148 | − | 0.831640i | ||||
\(705\) | −5.39223e6 | + | 3.11320e6i | −0.0153887 | + | 0.00888465i | ||||
\(706\) | 1.01814e7i | 0.0289329i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.85032e8 | −1.08492 | ||||||||
\(709\) | 1.58977e8 | + | 2.75357e8i | 0.446064 | + | 0.772605i | 0.998126 | − | 0.0611981i | \(-0.0194921\pi\) |
−0.552062 | + | 0.833803i | \(0.686159\pi\) | |||||||
\(710\) | 8.74224e7 | + | 5.04734e7i | 0.244257 | + | 0.141022i | ||||
\(711\) | −8.27820e7 | + | 1.43383e8i | −0.230318 | + | 0.398922i | ||||
\(712\) | −1.94291e8 | + | 1.12174e8i | −0.538285 | + | 0.310779i | ||||
\(713\) | − | 5.24756e8i | − | 1.44773i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.58922e8 | −0.434776 | ||||||||
\(716\) | 6.55655e7 | + | 1.13563e8i | 0.178623 | + | 0.309384i | ||||
\(717\) | −1.01836e8 | − | 5.87951e7i | −0.276277 | − | 0.159509i | ||||
\(718\) | −2.74565e8 | + | 4.75561e8i | −0.741774 | + | 1.28479i | ||||
\(719\) | 1.50536e8 | − | 8.69119e7i | 0.404998 | − | 0.233826i | −0.283640 | − | 0.958931i | \(-0.591542\pi\) |
0.688638 | + | 0.725105i | \(0.258209\pi\) | |||||||
\(720\) | − | 1.76693e7i | − | 0.0473393i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.15455e7 | −0.0838157 | ||||||||
\(723\) | 1.52598e8 | + | 2.64307e8i | 0.403769 | + | 0.699348i | ||||
\(724\) | −9.50125e8 | − | 5.48555e8i | −2.50360 | − | 1.44545i | ||||
\(725\) | −6.45394e7 | + | 1.11785e8i | −0.169360 | + | 0.293340i | ||||
\(726\) | 1.94900e8 | − | 1.12526e8i | 0.509334 | − | 0.294064i | ||||
\(727\) | − | 4.58803e8i | − | 1.19405i | −0.802222 | − | 0.597026i | \(-0.796349\pi\) | ||
0.802222 | − | 0.597026i | \(-0.203651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −1.44469e8 | − | 2.50228e8i | −0.371370 | − | 0.643232i | ||||
\(731\) | 6.19927e8 | + | 3.57915e8i | 1.58704 | + | 0.916279i | ||||
\(732\) | 1.23405e8 | − | 2.13744e8i | 0.314630 | − | 0.544956i | ||||
\(733\) | −5.55746e8 | + | 3.20860e8i | −1.41112 | + | 0.814711i | −0.995494 | − | 0.0948235i | \(-0.969771\pi\) |
−0.415627 | + | 0.909535i | \(0.636438\pi\) | |||||||
\(734\) | − | 8.70033e7i | − | 0.220013i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.98742e8 | 1.25096 | ||||||||
\(737\) | 9.68105e7 | + | 1.67681e8i | 0.241835 | + | 0.418871i | ||||
\(738\) | −1.64173e8 | − | 9.47855e7i | −0.408445 | − | 0.235816i | ||||
\(739\) | 1.70001e8 | − | 2.94450e8i | 0.421229 | − | 0.729590i | −0.574831 | − | 0.818272i | \(-0.694932\pi\) |
0.996060 | + | 0.0886823i | \(0.0282656\pi\) | |||||||
\(740\) | 6.02151e8 | − | 3.47652e8i | 1.48597 | − | 0.857926i | ||||
\(741\) | 2.53034e8i | 0.621904i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.08554e8 | 1.48365 | 0.741827 | − | 0.670591i | \(-0.233960\pi\) | ||||
0.741827 | + | 0.670591i | \(0.233960\pi\) | |||||||
\(744\) | 1.30737e8 | + | 2.26443e8i | 0.317454 | + | 0.549846i | ||||
\(745\) | 1.13504e8 | + | 6.55313e7i | 0.274499 | + | 0.158482i | ||||
\(746\) | −3.26280e7 | + | 5.65133e7i | −0.0785911 | + | 0.136124i | ||||
\(747\) | 2.69409e7 | − | 1.55543e7i | 0.0646323 | − | 0.0373155i | ||||
\(748\) | 7.03011e8i | 1.67980i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.07324e8 | 0.965509 | ||||||||
\(751\) | −8.06132e7 | − | 1.39626e8i | −0.190321 | − | 0.329645i | 0.755036 | − | 0.655684i | \(-0.227619\pi\) |
−0.945357 | + | 0.326038i | \(0.894286\pi\) | |||||||
\(752\) | −3.97296e6 | − | 2.29379e6i | −0.00934245 | − | 0.00539387i | ||||
\(753\) | −1.08800e8 | + | 1.88447e8i | −0.254826 | + | 0.441372i | ||||
\(754\) | −3.85038e8 | + | 2.22302e8i | −0.898233 | + | 0.518595i | ||||
\(755\) | − | 1.94612e8i | − | 0.452198i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.60953e8 | 0.371031 | 0.185516 | − | 0.982641i | \(-0.440604\pi\) | ||||
0.185516 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(758\) | −6.97652e8 | − | 1.20837e9i | −1.60189 | − | 2.77455i | ||||
\(759\) | −2.09046e8 | − | 1.20693e8i | −0.478098 | − | 0.276030i | ||||
\(760\) | 1.60030e8 | − | 2.77181e8i | 0.364554 | − | 0.631426i | ||||
\(761\) | 3.75605e8 | − | 2.16856e8i | 0.852271 | − | 0.492059i | −0.00914540 | − | 0.999958i | \(-0.502911\pi\) |
0.861416 | + | 0.507899i | \(0.169578\pi\) | |||||||
\(762\) | − | 6.01088e7i | − | 0.135854i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.31656e8 | −1.86493 | ||||||||
\(765\) | −7.53621e7 | − | 1.30531e8i | −0.168333 | − | 0.291561i | ||||
\(766\) | 5.61533e8 | + | 3.24201e8i | 1.24936 | + | 0.721321i | ||||
\(767\) | 2.73526e8 | − | 4.73760e8i | 0.606194 | − | 1.04996i | ||||
\(768\) | −3.01817e8 | + | 1.74254e8i | −0.666285 | + | 0.384680i | ||||
\(769\) | − | 3.73405e8i | − | 0.821110i | −0.911836 | − | 0.410555i | \(-0.865335\pi\) | ||
0.911836 | − | 0.410555i | \(-0.134665\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.02177e7 | −0.0222941 | ||||||||
\(772\) | −3.89144e8 | − | 6.74018e8i | −0.845782 | − | 1.46494i | ||||
\(773\) | −5.92885e8 | − | 3.42302e8i | −1.28361 | − | 0.741090i | −0.306100 | − | 0.951999i | \(-0.599024\pi\) |
−0.977506 | + | 0.210909i | \(0.932358\pi\) | |||||||
\(774\) | 1.47033e8 | − | 2.54668e8i | 0.317096 | − | 0.549227i | ||||
\(775\) | −2.24278e8 | + | 1.29487e8i | −0.481816 | + | 0.278176i | ||||
\(776\) | − | 3.73254e8i | − | 0.798766i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.77962e8 | −1.86439 | ||||||||
\(779\) | −1.97781e8 | − | 3.42567e8i | −0.418381 | − | 0.724658i | ||||
\(780\) | 2.86180e8 | + | 1.65226e8i | 0.603052 | + | 0.348172i | ||||
\(781\) | −3.95782e7 | + | 6.85514e7i | −0.0830812 | + | 0.143901i | ||||
\(782\) | −1.67555e9 | + | 9.67380e8i | −3.50379 | + | 2.02291i | ||||
\(783\) | − | 5.26085e7i | − | 0.109590i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.24014e8 | 0.463091 | ||||||||
\(786\) | −2.80300e8 | − | 4.85494e8i | −0.577239 | − | 0.999808i | ||||
\(787\) | −6.27494e8 | − | 3.62284e8i | −1.28732 | − | 0.743233i | −0.309142 | − | 0.951016i | \(-0.600042\pi\) |
−0.978175 | + | 0.207783i | \(0.933375\pi\) | |||||||
\(788\) | −1.09731e8 | + | 1.90059e8i | −0.224259 | + | 0.388428i | ||||
\(789\) | −2.01690e8 | + | 1.16446e8i | −0.410632 | + | 0.237078i | ||||
\(790\) | 7.14438e8i | 1.44905i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.20277e8 | 0.242107 | ||||||||
\(793\) | 1.75334e8 | + | 3.03687e8i | 0.351597 | + | 0.608984i | ||||
\(794\) | −5.48287e8 | − | 3.16553e8i | −1.09533 | − | 0.632391i | ||||
\(795\) | 1.15592e8 | − | 2.00211e8i | 0.230052 | − | 0.398461i | ||||
\(796\) | −4.12807e8 | + | 2.38334e8i | −0.818480 | + | 0.472550i | ||||
\(797\) | 5.85510e7i | 0.115654i | 0.998327 | + | 0.0578268i | \(0.0184171\pi\) | ||||
−0.998327 | + | 0.0578268i | \(0.981583\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.91334e7 | −0.0767197 | ||||||||
\(800\) | −1.23068e8 | − | 2.13159e8i | −0.240367 | − | 0.416327i | ||||
\(801\) | 7.84296e7 | + | 4.52813e7i | 0.152610 | + | 0.0881093i | ||||
\(802\) | 9.18761e7 | − | 1.59134e8i | 0.178106 | − | 0.308489i | ||||
\(803\) | 1.96214e8 | − | 1.13284e8i | 0.378951 | − | 0.218788i | ||||
\(804\) | − | 4.02603e8i | − | 0.774655i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.92017e8 | −1.70360 | ||||||||
\(807\) | −2.44816e8 | − | 4.24033e8i | −0.465821 | − | 0.806825i | ||||
\(808\) | −3.48362e8 | − | 2.01127e8i | −0.660384 | − | 0.381273i | ||||
\(809\) | −2.55763e8 | + | 4.42994e8i | −0.483049 | + | 0.836666i | −0.999811 | − | 0.0194637i | \(-0.993804\pi\) |
0.516761 | + | 0.856129i | \(0.327137\pi\) | |||||||
\(810\) | −5.36226e7 | + | 3.09590e7i | −0.100900 | + | 0.0582548i | ||||
\(811\) | − | 7.81509e8i | − | 1.46511i | −0.680706 | − | 0.732557i | \(-0.738327\pi\) | ||
0.680706 | − | 0.732557i | \(-0.261673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.33101e7 | −0.0433782 | ||||||||
\(814\) | 4.31682e8 | + | 7.47695e8i | 0.800370 | + | 1.38628i | ||||
\(815\) | 1.07689e8 | + | 6.21741e7i | 0.198929 | + | 0.114851i | ||||
\(816\) | 5.55263e7 | − | 9.61744e7i | 0.102195 | − | 0.177006i | ||||
\(817\) | 5.31395e8 | − | 3.06801e8i | 0.974431 | − | 0.562588i | ||||
\(818\) | − | 2.94989e8i | − | 0.538947i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.16588e8 | −0.936921 | ||||||||
\(821\) | 2.75815e8 | + | 4.77726e8i | 0.498412 | + | 0.863275i | 0.999998 | − | 0.00183255i | \(-0.000583318\pi\) |
−0.501586 | + | 0.865108i | \(0.667250\pi\) | |||||||
\(822\) | −1.61517e8 | − | 9.32517e7i | −0.290805 | − | 0.167896i | ||||
\(823\) | 1.78646e8 | − | 3.09423e8i | 0.320474 | − | 0.555077i | −0.660112 | − | 0.751167i | \(-0.729491\pi\) |
0.980586 | + | 0.196090i | \(0.0628245\pi\) | |||||||
\(824\) | 8.07733e8 | − | 4.66345e8i | 1.44373 | − | 0.833539i | ||||
\(825\) | 1.19127e8i | 0.212152i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.42420e8 | −0.782201 | −0.391101 | − | 0.920348i | \(-0.627906\pi\) | ||||
−0.391101 | + | 0.920348i | \(0.627906\pi\) | |||||||
\(828\) | 2.50961e8 | + | 4.34677e8i | 0.442094 | + | 0.765730i | ||||
\(829\) | 1.02602e8 | + | 5.92376e7i | 0.180092 | + | 0.103976i | 0.587336 | − | 0.809343i | \(-0.300177\pi\) |
−0.407244 | + | 0.913319i | \(0.633510\pi\) | |||||||
\(830\) | 6.71196e7 | − | 1.16255e8i | 0.117386 | − | 0.203318i | ||||
\(831\) | −2.67772e7 | + | 1.54598e7i | −0.0466618 | + | 0.0269402i | ||||
\(832\) | − | 9.89871e8i | − | 1.71873i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −953236. | −0.00164324 | ||||||||
\(835\) | 4.59648e7 | + | 7.96134e7i | 0.0789526 | + | 0.136750i | ||||
\(836\) | 5.21878e8 | + | 3.01307e8i | 0.893204 | + | 0.515691i | ||||
\(837\) | 5.27748e7 | − | 9.14086e7i | 0.0900016 | − | 0.155887i | ||||
\(838\) | 6.17714e8 | − | 3.56637e8i | 1.04968 | − | 0.606031i | ||||
\(839\) | 1.02452e9i | 1.73474i | 0.497660 | + | 0.867372i | \(0.334193\pi\) | ||||
−0.497660 | + | 0.867372i | \(0.665807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.01941e8 | −0.675731 | ||||||||
\(842\) | −8.56837e8 | − | 1.48408e9i | −1.43536 | − | 2.48612i | ||||
\(843\) | 4.72976e7 | + | 2.73073e7i | 0.0789508 | + | 0.0455823i | ||||
\(844\) | −5.68359e8 | + | 9.84427e8i | −0.945357 | + | 1.63741i | ||||
\(845\) | −7.40021e7 | + | 4.27251e7i | −0.122652 | + | 0.0708130i | ||||
\(846\) | 1.60761e7i | 0.0265503i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.70335e8 | 0.279328 | ||||||||
\(849\) | 2.54444e8 | + | 4.40710e8i | 0.415785 | + | 0.720161i | ||||
\(850\) | 8.26905e8 | + | 4.77414e8i | 1.34648 | + | 0.777389i | ||||
\(851\) | −7.50246e8 | + | 1.29946e9i | −1.21735 | + | 2.10851i | ||||
\(852\) | 1.42541e8 | − | 8.22963e7i | 0.230474 | − | 0.133064i | ||||
\(853\) | 1.03709e9i | 1.67097i | 0.549517 | + | 0.835483i | \(0.314812\pi\) | ||||
−0.549517 | + | 0.835483i | \(0.685188\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.29199e8 | −0.206710 | ||||||||
\(856\) | −2.87713e8 | − | 4.98333e8i | −0.458710 | − | 0.794508i | ||||
\(857\) | −4.76107e8 | − | 2.74881e8i | −0.756419 | − | 0.436719i | 0.0715895 | − | 0.997434i | \(-0.477193\pi\) |
−0.828009 | + | 0.560715i | \(0.810526\pi\) | |||||||
\(858\) | −2.05162e8 | + | 3.55351e8i | −0.324814 | + | 0.562595i | ||||
\(859\) | −1.23390e8 | + | 7.12392e7i | −0.194671 | + | 0.112393i | −0.594167 | − | 0.804342i | \(-0.702518\pi\) |
0.399497 | + | 0.916735i | \(0.369185\pi\) | |||||||
\(860\) | − | 8.01340e8i | − | 1.25986i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.58068e9 | 2.46787 | ||||||||
\(863\) | 2.00417e8 | + | 3.47132e8i | 0.311818 | + | 0.540085i | 0.978756 | − | 0.205028i | \(-0.0657287\pi\) |
−0.666938 | + | 0.745113i | \(0.732395\pi\) | |||||||
\(864\) | 8.68772e7 | + | 5.01586e7i | 0.134699 | + | 0.0777685i | ||||
\(865\) | 2.29194e8 | − | 3.96975e8i | 0.354123 | − | 0.613359i | ||||
\(866\) | −1.27311e9 | + | 7.35033e8i | −1.96026 | + | 1.13176i | ||||
\(867\) | − | 5.71043e8i | − | 0.876216i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.60219e8 | −0.853687 | ||||||||
\(870\) | −1.13507e8 | − | 1.96601e8i | −0.172372 | − | 0.298557i | ||||
\(871\) | 4.95380e8 | + | 2.86008e8i | 0.749694 | + | 0.432836i | ||||
\(872\) | 4.73070e8 | − | 8.19382e8i | 0.713471 | − | 1.23577i | ||||
\(873\) | −1.30486e8 | + | 7.53359e7i | −0.196119 | + | 0.113229i | ||||
\(874\) | 1.65846e9i | 2.48410i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.71112e8 | −0.700828 | ||||||||
\(877\) | 1.80269e8 | + | 3.12235e8i | 0.267252 | + | 0.462895i | 0.968151 | − | 0.250366i | \(-0.0805509\pi\) |
−0.700899 | + | 0.713261i | \(0.747218\pi\) | |||||||
\(878\) | −1.40674e9 | − | 8.12181e8i | −2.07840 | − | 1.19997i | ||||
\(879\) | 2.00821e8 | − | 3.47832e8i | 0.295694 | − | 0.512156i | ||||
\(880\) | 5.17776e7 | − | 2.98938e7i | 0.0759791 | − | 0.0438665i | ||||
\(881\) | 1.27541e9i | 1.86519i | 0.360924 | + | 0.932595i | \(0.382461\pi\) | ||||
−0.360924 | + | 0.932595i | \(0.617539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.92638e8 | −0.425058 | −0.212529 | − | 0.977155i | \(-0.568170\pi\) | ||||
−0.212529 | + | 0.977155i | \(0.568170\pi\) | |||||||
\(884\) | 1.03845e9 | + | 1.79866e9i | 1.50325 | + | 2.60370i | ||||
\(885\) | 2.41902e8 | + | 1.39662e8i | 0.348988 | + | 0.201488i | ||||
\(886\) | −4.68777e8 | + | 8.11945e8i | −0.674008 | + | 1.16742i | ||||
\(887\) | 7.14682e8 | − | 4.12622e8i | 1.02410 | − | 0.591264i | 0.108811 | − | 0.994062i | \(-0.465296\pi\) |
0.915289 | + | 0.402798i | \(0.131962\pi\) | |||||||
\(888\) | − | 7.47662e8i | − | 1.06774i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.90794e8 | 0.554342 | ||||||||
\(891\) | −2.42762e7 | − | 4.20476e7i | −0.0343200 | − | 0.0594440i | ||||
\(892\) | 4.60473e8 | + | 2.65854e8i | 0.648798 | + | 0.374584i | ||||
\(893\) | −1.67724e7 | + | 2.90506e7i | −0.0235526 | + | 0.0407944i | ||||
\(894\) | 2.93058e8 | − | 1.69197e8i | 0.410148 | − | 0.236799i | ||||
\(895\) | − | 9.51302e7i | − | 0.132693i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.13127e8 | −0.988075 | ||||||||
\(898\) | −7.08792e8 | − | 1.22766e9i | −0.978790 | − | 1.69531i | ||||
\(899\) | 3.35138e8 | + | 1.93492e8i | 0.461259 | + | 0.266308i | ||||
\(900\) | 1.23852e8 | − | 2.14518e8i | 0.169893 | − | 0.294264i | ||||
\(901\) | 1.25834e9 | − | 7.26501e8i | 1.72037 | − | 0.993257i | ||||
\(902\) | − | 6.41451e8i | − | 0.874065i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.49035e9 | 2.01735 | ||||||||
\(905\) | 3.97954e8 | + | 6.89276e8i | 0.536892 | + | 0.929924i | ||||
\(906\) | −4.35154e8 | − | 2.51236e8i | −0.585138 | − | 0.337830i | ||||
\(907\) | 4.80348e8 | − | 8.31987e8i | 0.643775 | − | 1.11505i | −0.340808 | − | 0.940133i | \(-0.610700\pi\) |
0.984583 | − | 0.174918i | \(-0.0559662\pi\) | |||||||
\(908\) | −1.43501e9 | + | 8.28502e8i | −1.91689 | + | 1.10672i | ||||
\(909\) | 1.62378e8i | 0.216190i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.01677e9 | 1.34483 | 0.672413 | − | 0.740176i | \(-0.265258\pi\) | ||||
0.672413 | + | 0.740176i | \(0.265258\pi\) | |||||||
\(912\) | −4.75966e7 | − | 8.24397e7i | −0.0627468 | − | 0.108681i | ||||
\(913\) | 9.11598e7 | + | 5.26311e7i | 0.119782 | + | 0.0691561i | ||||
\(914\) | 8.47892e7 | − | 1.46859e8i | 0.111046 | − | 0.192337i | ||||
\(915\) | −1.55063e8 | + | 8.95255e7i | −0.202416 | + | 0.116865i | ||||
\(916\) | 4.66538e8i | 0.607017i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.89158e8 | −0.503035 | ||||||||
\(919\) | 2.43093e8 | + | 4.21050e8i | 0.313203 | + | 0.542484i | 0.979054 | − | 0.203601i | \(-0.0652646\pi\) |
−0.665851 | + | 0.746085i | \(0.731931\pi\) | |||||||
\(920\) | 7.81181e8 | + | 4.51015e8i | 1.00320 | + | 0.579199i | ||||
\(921\) | −1.48007e8 | + | 2.56356e8i | −0.189454 | + | 0.328145i | ||||
\(922\) | 8.08865e7 | − | 4.66998e7i | 0.103201 | − | 0.0595830i | ||||
\(923\) | 2.33852e8i | 0.297397i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.40511e8 | 0.935635 | ||||||||
\(926\) | 9.53467e8 | + | 1.65145e9i | 1.20081 | + | 2.07986i | ||||
\(927\) | −3.26058e8 | − | 1.88250e8i | −0.409314 | − | 0.236317i | ||||
\(928\) | −1.83900e8 | + | 3.18525e8i | −0.230112 | + | 0.398565i | ||||
\(929\) | −7.80354e8 | + | 4.50538e8i | −0.973295 | + | 0.561932i | −0.900239 | − | 0.435395i | \(-0.856609\pi\) |
−0.0730561 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(930\) | − | 4.55465e8i | − | 0.566247i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.37994e9 | 1.70456 | ||||||||
\(933\) | 2.52329e8 | + | 4.37046e8i | 0.310686 | + | 0.538124i | ||||
\(934\) | −9.68317e8 | − | 5.59058e8i | −1.18844 | − | 0.686146i | ||||
\(935\) | 2.55003e8 | − | 4.41677e8i | 0.311968 | − | 0.540344i | ||||
\(936\) | 3.07730e8 | − | 1.77668e8i | 0.375268 | − | 0.216661i | ||||
\(937\) | 6.19442e8i | 0.752977i | 0.926421 | + | 0.376489i | \(0.122869\pi\) | ||||
−0.926421 | + | 0.376489i | \(0.877131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.06515e8 | 0.611781 | ||||||||
\(940\) | 2.19040e7 | + | 3.79389e7i | 0.0263718 | + | 0.0456774i | ||||
\(941\) | 4.29312e8 | + | 2.47863e8i | 0.515234 | + | 0.297470i | 0.734982 | − | 0.678086i | \(-0.237190\pi\) |
−0.219749 | + | 0.975557i | \(0.570524\pi\) | |||||||
\(942\) | 2.89193e8 | − | 5.00898e8i | 0.345968 | − | 0.599234i | ||||
\(943\) | 9.65460e8 | − | 5.57408e8i | 1.15133 | − | 0.664720i | ||||
\(944\) | 2.05805e8i | 0.244647i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.95029e8 | 1.17534 | ||||||||
\(947\) | −5.84700e8 | − | 1.01273e9i | −0.688467 | − | 1.19246i | −0.972334 | − | 0.233597i | \(-0.924950\pi\) |
0.283866 | − | 0.958864i | \(-0.408383\pi\) | |||||||
\(948\) | 1.00882e9 | + | 5.82442e8i | 1.18410 | + | 0.683640i | ||||
\(949\) | 3.34676e8 | − | 5.79677e8i | 0.391585 | − | 0.678246i | ||||
\(950\) | 7.08815e8 | − | 4.09234e8i | 0.826726 | − | 0.477311i | ||||
\(951\) | − | 2.54760e8i | − | 0.296203i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.23017e8 | −0.257667 | −0.128834 | − | 0.991666i | \(-0.541123\pi\) | ||||
−0.128834 | + | 0.991666i | \(0.541123\pi\) | |||||||
\(954\) | −2.98449e8 | − | 5.16929e8i | −0.343736 | − | 0.595368i | ||||
\(955\) | 5.22501e8 | + | 3.01666e8i | 0.599897 | + | 0.346351i | ||||
\(956\) | −4.13673e8 | + | 7.16503e8i | −0.473461 | + | 0.820058i | ||||
\(957\) | 1.54162e8 | − | 8.90057e7i | 0.175891 | − | 0.101550i | ||||
\(958\) | − | 2.10381e9i | − | 2.39282i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.05429e8 | 0.571277 | ||||||||
\(961\) | −5.55442e7 | − | 9.62054e7i | −0.0625847 | − | 0.108400i | ||||
\(962\) | 2.20892e9 | + | 1.27532e9i | 2.48116 | + | 1.43250i | ||||
\(963\) | −1.16141e8 | + | 2.01163e8i | −0.130049 | + | 0.225252i | ||||
\(964\) | 1.85962e9 | − | 1.07365e9i | 2.07584 | − | 1.19849i | ||||
\(965\) | 5.64616e8i | 0.628306i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.77842e8 | 0.528451 | 0.264226 | − | 0.964461i | \(-0.414884\pi\) | ||||
0.264226 | + | 0.964461i | \(0.414884\pi\) | |||||||
\(968\) | −3.29727e8 | − | 5.71105e8i | −0.363521 | − | 0.629636i | ||||
\(969\) | −7.03234e8 | − | 4.06012e8i | −0.772909 | − | 0.446239i | ||||
\(970\) | −3.25088e8 | + | 5.63068e8i | −0.356193 | + | 0.616944i | ||||
\(971\) | −8.66630e8 | + | 5.00349e8i | −0.946621 | + | 0.546532i | −0.892030 | − | 0.451977i | \(-0.850719\pi\) |
−0.0545914 | + | 0.998509i | \(0.517386\pi\) | |||||||
\(972\) | 1.00957e8i | 0.109935i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.81871e9 | −1.96827 | ||||||||
\(975\) | 1.75969e8 | + | 3.04786e8i | 0.189855 | + | 0.328838i | ||||
\(976\) | −1.14249e8 | − | 6.59618e7i | −0.122886 | − | 0.0709485i | ||||
\(977\) | 2.65667e8 | − | 4.60149e8i | 0.284875 | − | 0.493417i | −0.687704 | − | 0.725991i | \(-0.741381\pi\) |
0.972579 | + | 0.232574i | \(0.0747147\pi\) | |||||||
\(978\) | 2.78044e8 | − | 1.60529e8i | 0.297233 | − | 0.171607i | ||||
\(979\) | 3.06437e8i | 0.326583i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.81929e8 | −0.404554 | ||||||||
\(982\) | −2.58186e8 | − | 4.47192e8i | −0.272646 | − | 0.472236i | ||||
\(983\) | −6.03725e8 | − | 3.48561e8i | −0.635592 | − | 0.366959i | 0.147322 | − | 0.989089i | \(-0.452935\pi\) |
−0.782915 | + | 0.622129i | \(0.786268\pi\) | |||||||
\(984\) | −2.77744e8 | + | 4.81067e8i | −0.291514 | + | 0.504918i | ||||
\(985\) | 1.37880e8 | − | 7.96052e7i | 0.144276 | − | 0.0832976i | ||||
\(986\) | − | 1.42680e9i | − | 1.48844i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.78031e9 | 1.84597 | ||||||||
\(989\) | 8.64660e8 | + | 1.49764e9i | 0.893833 | + | 1.54816i | ||||
\(990\) | −1.81443e8 | − | 1.04756e8i | −0.186997 | − | 0.107963i | ||||
\(991\) | −3.67589e8 | + | 6.36684e8i | −0.377696 | + | 0.654188i | −0.990727 | − | 0.135871i | \(-0.956617\pi\) |
0.613031 | + | 0.790059i | \(0.289950\pi\) | |||||||
\(992\) | −6.39063e8 | + | 3.68963e8i | −0.654649 | + | 0.377962i | ||||
\(993\) | 8.06812e8i | 0.823995i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.45803e8 | 0.351043 | ||||||||
\(996\) | −1.09438e8 | − | 1.89552e8i | −0.110762 | − | 0.191845i | ||||
\(997\) | 4.85470e8 | + | 2.80286e8i | 0.489866 | + | 0.282824i | 0.724519 | − | 0.689255i | \(-0.242062\pi\) |
−0.234653 | + | 0.972079i | \(0.575395\pi\) | |||||||
\(998\) | 1.50872e8 | − | 2.61318e8i | 0.151781 | − | 0.262892i | ||||
\(999\) | −2.61375e8 | + | 1.50905e8i | −0.262160 | + | 0.151358i |
(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 | 147.7.f.a.31.4 | 8 | ||
7.2 | even | 3 | 21.7.f.b.19.4 | yes | 8 | ||
7.3 | odd | 6 | 147.7.d.a.97.1 | 8 | |||
7.4 | even | 3 | 147.7.d.a.97.2 | 8 | |||
7.5 | odd | 6 | inner | 147.7.f.a.19.4 | 8 | ||
7.6 | odd | 2 | 21.7.f.b.10.4 | ✓ | 8 | ||
21.2 | odd | 6 | 63.7.m.c.19.1 | 8 | |||
21.11 | odd | 6 | 441.7.d.d.244.7 | 8 | |||
21.17 | even | 6 | 441.7.d.d.244.8 | 8 | |||
21.20 | even | 2 | 63.7.m.c.10.1 | 8 | |||
28.23 | odd | 6 | 336.7.bh.b.145.2 | 8 | |||
28.27 | even | 2 | 336.7.bh.b.241.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.f.b.10.4 | ✓ | 8 | 7.6 | odd | 2 | ||
21.7.f.b.19.4 | yes | 8 | 7.2 | even | 3 | ||
63.7.m.c.10.1 | 8 | 21.20 | even | 2 | |||
63.7.m.c.19.1 | 8 | 21.2 | odd | 6 | |||
147.7.d.a.97.1 | 8 | 7.3 | odd | 6 | |||
147.7.d.a.97.2 | 8 | 7.4 | even | 3 | |||
147.7.f.a.19.4 | 8 | 7.5 | odd | 6 | inner | ||
147.7.f.a.31.4 | 8 | 1.1 | even | 1 | trivial | ||
336.7.bh.b.145.2 | 8 | 28.23 | odd | 6 | |||
336.7.bh.b.241.2 | 8 | 28.27 | even | 2 | |||
441.7.d.d.244.7 | 8 | 21.11 | odd | 6 | |||
441.7.d.d.244.8 | 8 | 21.17 | even | 6 |