Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(34,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.p (of order \(4\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.1 | ||
Root | \(-0.863233 - 0.863233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.265 |
Dual form | 273.2.p.e.34.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94644 | + | 1.94644i | −1.37634 | + | 1.37634i | −0.525629 | + | 0.850714i | \(0.676170\pi\) |
−0.850714 | + | 0.525629i | \(0.823830\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | − | 5.57728i | − | 2.78864i | ||||||
\(5\) | −0.136767 | − | 0.136767i | −0.0611638 | − | 0.0611638i | 0.675863 | − | 0.737027i | \(-0.263771\pi\) |
−0.737027 | + | 0.675863i | \(0.763771\pi\) | |||||||
\(6\) | −1.94644 | − | 1.94644i | −0.794632 | − | 0.794632i | ||||
\(7\) | 1.39641 | − | 2.24723i | 0.527795 | − | 0.849372i | ||||
\(8\) | 6.96297 | + | 6.96297i | 2.46178 | + | 2.46178i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.532416 | 0.168365 | ||||||||
\(11\) | 0.555612 | + | 0.555612i | 0.167523 | + | 0.167523i | 0.785890 | − | 0.618367i | \(-0.212205\pi\) |
−0.618367 | + | 0.785890i | \(0.712205\pi\) | |||||||
\(12\) | 5.57728 | 1.61002 | ||||||||
\(13\) | 1.81044 | + | 3.11806i | 0.502126 | + | 0.864795i | ||||
\(14\) | 1.65606 | + | 7.09214i | 0.442601 | + | 1.89545i | ||||
\(15\) | 0.136767 | − | 0.136767i | 0.0353130 | − | 0.0353130i | ||||
\(16\) | −15.9515 | −3.98787 | ||||||||
\(17\) | 4.49445 | 1.09007 | 0.545033 | − | 0.838415i | \(-0.316517\pi\) | ||||
0.545033 | + | 0.838415i | \(0.316517\pi\) | |||||||
\(18\) | 1.94644 | − | 1.94644i | 0.458781 | − | 0.458781i | ||||
\(19\) | 4.15330 | + | 4.15330i | 0.952832 | + | 0.952832i | 0.998937 | − | 0.0461051i | \(-0.0146809\pi\) |
−0.0461051 | + | 0.998937i | \(0.514681\pi\) | |||||||
\(20\) | −0.762785 | + | 0.762785i | −0.170564 | + | 0.170564i | ||||
\(21\) | 2.24723 | + | 1.39641i | 0.490385 | + | 0.304722i | ||||
\(22\) | −2.16293 | −0.461139 | ||||||||
\(23\) | 0.423984i | 0.0884068i | 0.999023 | + | 0.0442034i | \(0.0140750\pi\) | ||||
−0.999023 | + | 0.0442034i | \(0.985925\pi\) | |||||||
\(24\) | −6.96297 | + | 6.96297i | −1.42131 | + | 1.42131i | ||||
\(25\) | − | 4.96259i | − | 0.992518i | ||||||
\(26\) | −9.59305 | − | 2.54521i | −1.88135 | − | 0.499157i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −12.5334 | − | 7.78819i | −2.36859 | − | 1.47183i | ||||
\(29\) | −7.01375 | −1.30242 | −0.651210 | − | 0.758897i | \(-0.725738\pi\) | ||||
−0.651210 | + | 0.758897i | \(0.725738\pi\) | |||||||
\(30\) | 0.532416i | 0.0972055i | ||||||||
\(31\) | −0.273533 | − | 0.273533i | −0.0491280 | − | 0.0491280i | 0.682116 | − | 0.731244i | \(-0.261060\pi\) |
−0.731244 | + | 0.682116i | \(0.761060\pi\) | |||||||
\(32\) | 17.1227 | − | 17.1227i | 3.02690 | − | 3.02690i | ||||
\(33\) | −0.555612 | + | 0.555612i | −0.0967196 | + | 0.0967196i | ||||
\(34\) | −8.74820 | + | 8.74820i | −1.50030 | + | 1.50030i | ||||
\(35\) | −0.498328 | + | 0.116363i | −0.0842328 | + | 0.0196689i | ||||
\(36\) | 5.57728i | 0.929547i | ||||||||
\(37\) | 5.75334 | + | 5.75334i | 0.945843 | + | 0.945843i | 0.998607 | − | 0.0527641i | \(-0.0168031\pi\) |
−0.0527641 | + | 0.998607i | \(0.516803\pi\) | |||||||
\(38\) | −16.1683 | −2.62285 | ||||||||
\(39\) | −3.11806 | + | 1.81044i | −0.499289 | + | 0.289902i | ||||
\(40\) | − | 1.90460i | − | 0.301144i | ||||||
\(41\) | 7.29133 | + | 7.29133i | 1.13871 | + | 1.13871i | 0.988681 | + | 0.150033i | \(0.0479380\pi\) |
0.150033 | + | 0.988681i | \(0.452062\pi\) | |||||||
\(42\) | −7.09214 | + | 1.65606i | −1.09434 | + | 0.255536i | ||||
\(43\) | 1.86728i | 0.284758i | 0.989812 | + | 0.142379i | \(0.0454751\pi\) | ||||
−0.989812 | + | 0.142379i | \(0.954525\pi\) | |||||||
\(44\) | 3.09880 | − | 3.09880i | 0.467162 | − | 0.467162i | ||||
\(45\) | 0.136767 | + | 0.136767i | 0.0203879 | + | 0.0203879i | ||||
\(46\) | −0.825261 | − | 0.825261i | −0.121678 | − | 0.121678i | ||||
\(47\) | 4.75098 | − | 4.75098i | 0.693002 | − | 0.693002i | −0.269890 | − | 0.962891i | \(-0.586987\pi\) |
0.962891 | + | 0.269890i | \(0.0869872\pi\) | |||||||
\(48\) | − | 15.9515i | − | 2.30240i | ||||||
\(49\) | −3.10006 | − | 6.27612i | −0.442866 | − | 0.896588i | ||||
\(50\) | 9.65940 | + | 9.65940i | 1.36605 | + | 1.36605i | ||||
\(51\) | 4.49445i | 0.629349i | ||||||||
\(52\) | 17.3903 | − | 10.0973i | 2.41160 | − | 1.40025i | ||||
\(53\) | −4.31687 | −0.592968 | −0.296484 | − | 0.955038i | \(-0.595814\pi\) | ||||
−0.296484 | + | 0.955038i | \(0.595814\pi\) | |||||||
\(54\) | 1.94644 | + | 1.94644i | 0.264877 | + | 0.264877i | ||||
\(55\) | − | 0.151978i | − | 0.0204927i | ||||||
\(56\) | 25.3706 | − | 5.92419i | 3.39029 | − | 0.791654i | ||||
\(57\) | −4.15330 | + | 4.15330i | −0.550118 | + | 0.550118i | ||||
\(58\) | 13.6519 | − | 13.6519i | 1.79258 | − | 1.79258i | ||||
\(59\) | 0.691676 | − | 0.691676i | 0.0900485 | − | 0.0900485i | −0.660648 | − | 0.750696i | \(-0.729718\pi\) |
0.750696 | + | 0.660648i | \(0.229718\pi\) | |||||||
\(60\) | −0.762785 | − | 0.762785i | −0.0984751 | − | 0.0984751i | ||||
\(61\) | 8.11937i | 1.03958i | 0.854294 | + | 0.519789i | \(0.173990\pi\) | ||||
−0.854294 | + | 0.519789i | \(0.826010\pi\) | |||||||
\(62\) | 1.06483 | 0.135234 | ||||||||
\(63\) | −1.39641 | + | 2.24723i | −0.175932 | + | 0.283124i | ||||
\(64\) | 34.7539i | 4.34423i | ||||||||
\(65\) | 0.178839 | − | 0.674054i | 0.0221822 | − | 0.0836061i | ||||
\(66\) | − | 2.16293i | − | 0.266239i | ||||||
\(67\) | 0.837691 | − | 0.837691i | 0.102340 | − | 0.102340i | −0.654083 | − | 0.756423i | \(-0.726945\pi\) |
0.756423 | + | 0.654083i | \(0.226945\pi\) | |||||||
\(68\) | − | 25.0668i | − | 3.03980i | ||||||
\(69\) | −0.423984 | −0.0510417 | ||||||||
\(70\) | 0.743473 | − | 1.19646i | 0.0888621 | − | 0.143004i | ||||
\(71\) | 1.00520 | − | 1.00520i | 0.119296 | − | 0.119296i | −0.644939 | − | 0.764234i | \(-0.723117\pi\) |
0.764234 | + | 0.644939i | \(0.223117\pi\) | |||||||
\(72\) | −6.96297 | − | 6.96297i | −0.820594 | − | 0.820594i | ||||
\(73\) | 6.81854 | − | 6.81854i | 0.798050 | − | 0.798050i | −0.184738 | − | 0.982788i | \(-0.559144\pi\) |
0.982788 | + | 0.184738i | \(0.0591436\pi\) | |||||||
\(74\) | −22.3971 | −2.60361 | ||||||||
\(75\) | 4.96259 | 0.573031 | ||||||||
\(76\) | 23.1641 | − | 23.1641i | 2.65710 | − | 2.65710i | ||||
\(77\) | 2.02445 | − | 0.472722i | 0.230708 | − | 0.0538717i | ||||
\(78\) | 2.54521 | − | 9.59305i | 0.288188 | − | 1.08620i | ||||
\(79\) | 10.9777 | 1.23509 | 0.617546 | − | 0.786535i | \(-0.288127\pi\) | ||||
0.617546 | + | 0.786535i | \(0.288127\pi\) | |||||||
\(80\) | 2.18163 | + | 2.18163i | 0.243914 | + | 0.243914i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −28.3843 | −3.13452 | ||||||||
\(83\) | −6.91260 | − | 6.91260i | −0.758756 | − | 0.758756i | 0.217340 | − | 0.976096i | \(-0.430262\pi\) |
−0.976096 | + | 0.217340i | \(0.930262\pi\) | |||||||
\(84\) | 7.78819 | − | 12.5334i | 0.849761 | − | 1.36751i | ||||
\(85\) | −0.614691 | − | 0.614691i | −0.0666726 | − | 0.0666726i | ||||
\(86\) | −3.63455 | − | 3.63455i | −0.391924 | − | 0.391924i | ||||
\(87\) | − | 7.01375i | − | 0.751953i | ||||||
\(88\) | 7.73742i | 0.824812i | ||||||||
\(89\) | −6.46820 | + | 6.46820i | −0.685628 | + | 0.685628i | −0.961262 | − | 0.275635i | \(-0.911112\pi\) |
0.275635 | + | 0.961262i | \(0.411112\pi\) | |||||||
\(90\) | −0.532416 | −0.0561216 | ||||||||
\(91\) | 9.53511 | + | 0.285633i | 0.999552 | + | 0.0299425i | ||||
\(92\) | 2.36468 | 0.246535 | ||||||||
\(93\) | 0.273533 | − | 0.273533i | 0.0283641 | − | 0.0283641i | ||||
\(94\) | 18.4950i | 1.90762i | ||||||||
\(95\) | − | 1.13606i | − | 0.116558i | ||||||
\(96\) | 17.1227 | + | 17.1227i | 1.74758 | + | 1.74758i | ||||
\(97\) | −3.19087 | − | 3.19087i | −0.323984 | − | 0.323984i | 0.526309 | − | 0.850293i | \(-0.323575\pi\) |
−0.850293 | + | 0.526309i | \(0.823575\pi\) | |||||||
\(98\) | 18.2502 | + | 6.18201i | 1.84355 | + | 0.624478i | ||||
\(99\) | −0.555612 | − | 0.555612i | −0.0558411 | − | 0.0558411i | ||||
\(100\) | −27.6778 | −2.76778 | ||||||||
\(101\) | −9.40173 | −0.935507 | −0.467753 | − | 0.883859i | \(-0.654936\pi\) | ||||
−0.467753 | + | 0.883859i | \(0.654936\pi\) | |||||||
\(102\) | −8.74820 | − | 8.74820i | −0.866201 | − | 0.866201i | ||||
\(103\) | −1.84027 | −0.181328 | −0.0906638 | − | 0.995882i | \(-0.528899\pi\) | ||||
−0.0906638 | + | 0.995882i | \(0.528899\pi\) | |||||||
\(104\) | −9.10493 | + | 34.3170i | −0.892812 | + | 3.36506i | ||||
\(105\) | −0.116363 | − | 0.498328i | −0.0113558 | − | 0.0486318i | ||||
\(106\) | 8.40254 | − | 8.40254i | 0.816127 | − | 0.816127i | ||||
\(107\) | 9.88514 | 0.955632 | 0.477816 | − | 0.878460i | \(-0.341428\pi\) | ||||
0.477816 | + | 0.878460i | \(0.341428\pi\) | |||||||
\(108\) | −5.57728 | −0.536674 | ||||||||
\(109\) | −9.76428 | + | 9.76428i | −0.935248 | + | 0.935248i | −0.998027 | − | 0.0627794i | \(-0.980004\pi\) |
0.0627794 | + | 0.998027i | \(0.480004\pi\) | |||||||
\(110\) | 0.295817 | + | 0.295817i | 0.0282050 | + | 0.0282050i | ||||
\(111\) | −5.75334 | + | 5.75334i | −0.546083 | + | 0.546083i | ||||
\(112\) | −22.2749 | + | 35.8466i | −2.10478 | + | 3.38719i | ||||
\(113\) | −9.96741 | −0.937655 | −0.468828 | − | 0.883290i | \(-0.655323\pi\) | ||||
−0.468828 | + | 0.883290i | \(0.655323\pi\) | |||||||
\(114\) | − | 16.1683i | − | 1.51430i | ||||||
\(115\) | 0.0579868 | − | 0.0579868i | 0.00540730 | − | 0.00540730i | ||||
\(116\) | 39.1176i | 3.63198i | ||||||||
\(117\) | −1.81044 | − | 3.11806i | −0.167375 | − | 0.288265i | ||||
\(118\) | 2.69261i | 0.247875i | ||||||||
\(119\) | 6.27612 | − | 10.1001i | 0.575331 | − | 0.925871i | ||||
\(120\) | 1.90460 | 0.173866 | ||||||||
\(121\) | − | 10.3826i | − | 0.943872i | ||||||
\(122\) | −15.8039 | − | 15.8039i | −1.43082 | − | 1.43082i | ||||
\(123\) | −7.29133 | + | 7.29133i | −0.657437 | + | 0.657437i | ||||
\(124\) | −1.52557 | + | 1.52557i | −0.137000 | + | 0.137000i | ||||
\(125\) | −1.36255 | + | 1.36255i | −0.121870 | + | 0.121870i | ||||
\(126\) | −1.65606 | − | 7.09214i | −0.147534 | − | 0.631818i | ||||
\(127\) | − | 2.97774i | − | 0.264232i | −0.991234 | − | 0.132116i | \(-0.957823\pi\) | ||
0.991234 | − | 0.132116i | \(-0.0421771\pi\) | |||||||
\(128\) | −33.4009 | − | 33.4009i | −2.95225 | − | 2.95225i | ||||
\(129\) | −1.86728 | −0.164405 | ||||||||
\(130\) | 0.963908 | + | 1.66011i | 0.0845403 | + | 0.145601i | ||||
\(131\) | − | 17.4307i | − | 1.52293i | −0.648206 | − | 0.761465i | \(-0.724480\pi\) | ||
0.648206 | − | 0.761465i | \(-0.275520\pi\) | |||||||
\(132\) | 3.09880 | + | 3.09880i | 0.269716 | + | 0.269716i | ||||
\(133\) | 15.1331 | − | 3.53368i | 1.31221 | − | 0.306409i | ||||
\(134\) | 3.26104i | 0.281711i | ||||||||
\(135\) | −0.136767 | + | 0.136767i | −0.0117710 | + | 0.0117710i | ||||
\(136\) | 31.2948 | + | 31.2948i | 2.68350 | + | 2.68350i | ||||
\(137\) | −7.44628 | − | 7.44628i | −0.636178 | − | 0.636178i | 0.313432 | − | 0.949611i | \(-0.398521\pi\) |
−0.949611 | + | 0.313432i | \(0.898521\pi\) | |||||||
\(138\) | 0.825261 | − | 0.825261i | 0.0702509 | − | 0.0702509i | ||||
\(139\) | − | 18.7436i | − | 1.58981i | −0.606732 | − | 0.794906i | \(-0.707520\pi\) | ||
0.606732 | − | 0.794906i | \(-0.292480\pi\) | |||||||
\(140\) | 0.648988 | + | 2.77932i | 0.0548495 | + | 0.234895i | ||||
\(141\) | 4.75098 | + | 4.75098i | 0.400105 | + | 0.400105i | ||||
\(142\) | 3.91314i | 0.328383i | ||||||||
\(143\) | −0.726530 | + | 2.73833i | −0.0607555 | + | 0.228991i | ||||
\(144\) | 15.9515 | 1.32929 | ||||||||
\(145\) | 0.959246 | + | 0.959246i | 0.0796610 | + | 0.0796610i | ||||
\(146\) | 26.5438i | 2.19678i | ||||||||
\(147\) | 6.27612 | − | 3.10006i | 0.517645 | − | 0.255689i | ||||
\(148\) | 32.0880 | − | 32.0880i | 2.63762 | − | 2.63762i | ||||
\(149\) | −7.56936 | + | 7.56936i | −0.620106 | + | 0.620106i | −0.945558 | − | 0.325452i | \(-0.894483\pi\) |
0.325452 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(150\) | −9.65940 | + | 9.65940i | −0.788687 | + | 0.788687i | ||||
\(151\) | −9.52340 | − | 9.52340i | −0.775004 | − | 0.775004i | 0.203973 | − | 0.978977i | \(-0.434615\pi\) |
−0.978977 | + | 0.203973i | \(0.934615\pi\) | |||||||
\(152\) | 57.8386i | 4.69133i | ||||||||
\(153\) | −4.49445 | −0.363355 | ||||||||
\(154\) | −3.02035 | + | 4.86060i | −0.243387 | + | 0.391679i | ||||
\(155\) | 0.0748203i | 0.00600971i | ||||||||
\(156\) | 10.0973 | + | 17.3903i | 0.808434 | + | 1.39234i | ||||
\(157\) | 18.1301i | 1.44694i | 0.690354 | + | 0.723471i | \(0.257455\pi\) | ||||
−0.690354 | + | 0.723471i | \(0.742545\pi\) | |||||||
\(158\) | −21.3676 | + | 21.3676i | −1.69991 | + | 1.69991i | ||||
\(159\) | − | 4.31687i | − | 0.342350i | ||||||
\(160\) | −4.68363 | −0.370274 | ||||||||
\(161\) | 0.952789 | + | 0.592057i | 0.0750903 | + | 0.0466607i | ||||
\(162\) | −1.94644 | + | 1.94644i | −0.152927 | + | 0.152927i | ||||
\(163\) | −0.674757 | − | 0.674757i | −0.0528510 | − | 0.0528510i | 0.680187 | − | 0.733038i | \(-0.261898\pi\) |
−0.733038 | + | 0.680187i | \(0.761898\pi\) | |||||||
\(164\) | 40.6658 | − | 40.6658i | 3.17546 | − | 3.17546i | ||||
\(165\) | 0.151978 | 0.0118315 | ||||||||
\(166\) | 26.9100 | 2.08862 | ||||||||
\(167\) | 5.13896 | − | 5.13896i | 0.397665 | − | 0.397665i | −0.479744 | − | 0.877409i | \(-0.659270\pi\) |
0.877409 | + | 0.479744i | \(0.159270\pi\) | |||||||
\(168\) | 5.92419 | + | 25.3706i | 0.457061 | + | 1.95738i | ||||
\(169\) | −6.44461 | + | 11.2901i | −0.495740 | + | 0.868471i | ||||
\(170\) | 2.39292 | 0.183529 | ||||||||
\(171\) | −4.15330 | − | 4.15330i | −0.317611 | − | 0.317611i | ||||
\(172\) | 10.4143 | 0.794086 | ||||||||
\(173\) | −0.655393 | −0.0498286 | −0.0249143 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249143 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(174\) | 13.6519 | + | 13.6519i | 1.03494 | + | 1.03494i | ||||
\(175\) | −11.1521 | − | 6.92983i | −0.843017 | − | 0.523846i | ||||
\(176\) | −8.86284 | − | 8.86284i | −0.668062 | − | 0.668062i | ||||
\(177\) | 0.691676 | + | 0.691676i | 0.0519895 | + | 0.0519895i | ||||
\(178\) | − | 25.1800i | − | 1.88732i | ||||||
\(179\) | − | 23.7340i | − | 1.77397i | −0.461802 | − | 0.886983i | \(-0.652797\pi\) | ||
0.461802 | − | 0.886983i | \(-0.347203\pi\) | |||||||
\(180\) | 0.762785 | − | 0.762785i | 0.0568547 | − | 0.0568547i | ||||
\(181\) | −7.42950 | −0.552230 | −0.276115 | − | 0.961125i | \(-0.589047\pi\) | ||||
−0.276115 | + | 0.961125i | \(0.589047\pi\) | |||||||
\(182\) | −19.1155 | + | 18.0036i | −1.41694 | + | 1.33451i | ||||
\(183\) | −8.11937 | −0.600201 | ||||||||
\(184\) | −2.95219 | + | 2.95219i | −0.217638 | + | 0.217638i | ||||
\(185\) | − | 1.57373i | − | 0.115703i | ||||||
\(186\) | 1.06483i | 0.0780773i | ||||||||
\(187\) | 2.49717 | + | 2.49717i | 0.182611 | + | 0.182611i | ||||
\(188\) | −26.4976 | − | 26.4976i | −1.93253 | − | 1.93253i | ||||
\(189\) | −2.24723 | − | 1.39641i | −0.163462 | − | 0.101574i | ||||
\(190\) | 2.21128 | + | 2.21128i | 0.160423 | + | 0.160423i | ||||
\(191\) | 19.3050 | 1.39686 | 0.698431 | − | 0.715678i | \(-0.253882\pi\) | ||||
0.698431 | + | 0.715678i | \(0.253882\pi\) | |||||||
\(192\) | −34.7539 | −2.50814 | ||||||||
\(193\) | 5.06291 | + | 5.06291i | 0.364436 | + | 0.364436i | 0.865443 | − | 0.501007i | \(-0.167037\pi\) |
−0.501007 | + | 0.865443i | \(0.667037\pi\) | |||||||
\(194\) | 12.4217 | 0.891825 | ||||||||
\(195\) | 0.674054 | + | 0.178839i | 0.0482700 | + | 0.0128069i | ||||
\(196\) | −35.0037 | + | 17.2899i | −2.50026 | + | 1.23499i | ||||
\(197\) | 11.0333 | − | 11.0333i | 0.786093 | − | 0.786093i | −0.194758 | − | 0.980851i | \(-0.562392\pi\) |
0.980851 | + | 0.194758i | \(0.0623923\pi\) | |||||||
\(198\) | 2.16293 | 0.153713 | ||||||||
\(199\) | −12.6458 | −0.896436 | −0.448218 | − | 0.893924i | \(-0.647941\pi\) | ||||
−0.448218 | + | 0.893924i | \(0.647941\pi\) | |||||||
\(200\) | 34.5544 | − | 34.5544i | 2.44336 | − | 2.44336i | ||||
\(201\) | 0.837691 | + | 0.837691i | 0.0590862 | + | 0.0590862i | ||||
\(202\) | 18.2999 | − | 18.2999i | 1.28758 | − | 1.28758i | ||||
\(203\) | −9.79409 | + | 15.7615i | −0.687410 | + | 1.10624i | ||||
\(204\) | 25.0668 | 1.75503 | ||||||||
\(205\) | − | 1.99442i | − | 0.139296i | ||||||
\(206\) | 3.58199 | − | 3.58199i | 0.249569 | − | 0.249569i | ||||
\(207\) | − | 0.423984i | − | 0.0294689i | ||||||
\(208\) | −28.8792 | − | 49.7378i | −2.00241 | − | 3.44869i | ||||
\(209\) | 4.61524i | 0.319243i | ||||||||
\(210\) | 1.19646 | + | 0.743473i | 0.0825636 | + | 0.0513045i | ||||
\(211\) | −19.1491 | −1.31828 | −0.659139 | − | 0.752021i | \(-0.729079\pi\) | ||||
−0.659139 | + | 0.752021i | \(0.729079\pi\) | |||||||
\(212\) | 24.0764i | 1.65357i | ||||||||
\(213\) | 1.00520 | + | 1.00520i | 0.0688753 | + | 0.0688753i | ||||
\(214\) | −19.2409 | + | 19.2409i | −1.31528 | + | 1.31528i | ||||
\(215\) | 0.255381 | − | 0.255381i | 0.0174169 | − | 0.0174169i | ||||
\(216\) | 6.96297 | − | 6.96297i | 0.473770 | − | 0.473770i | ||||
\(217\) | −0.996656 | + | 0.232726i | −0.0676574 | + | 0.0157984i | ||||
\(218\) | − | 38.0112i | − | 2.57444i | ||||||
\(219\) | 6.81854 | + | 6.81854i | 0.460754 | + | 0.460754i | ||||
\(220\) | −0.847625 | −0.0571469 | ||||||||
\(221\) | 8.13694 | + | 14.0140i | 0.547350 | + | 0.942683i | ||||
\(222\) | − | 22.3971i | − | 1.50319i | ||||||
\(223\) | −3.78445 | − | 3.78445i | −0.253426 | − | 0.253426i | 0.568948 | − | 0.822374i | \(-0.307351\pi\) |
−0.822374 | + | 0.568948i | \(0.807351\pi\) | |||||||
\(224\) | −14.5683 | − | 62.3891i | −0.973383 | − | 4.16855i | ||||
\(225\) | 4.96259i | 0.330839i | ||||||||
\(226\) | 19.4010 | − | 19.4010i | 1.29054 | − | 1.29054i | ||||
\(227\) | 12.8654 | + | 12.8654i | 0.853908 | + | 0.853908i | 0.990612 | − | 0.136704i | \(-0.0436508\pi\) |
−0.136704 | + | 0.990612i | \(0.543651\pi\) | |||||||
\(228\) | 23.1641 | + | 23.1641i | 1.53408 | + | 1.53408i | ||||
\(229\) | −6.95379 | + | 6.95379i | −0.459519 | + | 0.459519i | −0.898498 | − | 0.438978i | \(-0.855341\pi\) |
0.438978 | + | 0.898498i | \(0.355341\pi\) | |||||||
\(230\) | 0.225736i | 0.0148846i | ||||||||
\(231\) | 0.472722 | + | 2.02445i | 0.0311028 | + | 0.133199i | ||||
\(232\) | −48.8365 | − | 48.8365i | −3.20628 | − | 3.20628i | ||||
\(233\) | − | 19.3196i | − | 1.26567i | −0.774288 | − | 0.632833i | \(-0.781892\pi\) | ||
0.774288 | − | 0.632833i | \(-0.218108\pi\) | |||||||
\(234\) | 9.59305 | + | 2.54521i | 0.627117 | + | 0.166386i | ||||
\(235\) | −1.29955 | −0.0847733 | ||||||||
\(236\) | −3.85767 | − | 3.85767i | −0.251113 | − | 0.251113i | ||||
\(237\) | 10.9777i | 0.713081i | ||||||||
\(238\) | 7.44309 | + | 31.8753i | 0.482464 | + | 2.06617i | ||||
\(239\) | −14.4989 | + | 14.4989i | −0.937859 | + | 0.937859i | −0.998179 | − | 0.0603204i | \(-0.980788\pi\) |
0.0603204 | + | 0.998179i | \(0.480788\pi\) | |||||||
\(240\) | −2.18163 | + | 2.18163i | −0.140824 | + | 0.140824i | ||||
\(241\) | −5.11691 | + | 5.11691i | −0.329609 | + | 0.329609i | −0.852438 | − | 0.522828i | \(-0.824877\pi\) |
0.522828 | + | 0.852438i | \(0.324877\pi\) | |||||||
\(242\) | 20.2091 | + | 20.2091i | 1.29909 | + | 1.29909i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 45.2840 | 2.89901 | ||||||||
\(245\) | −0.434378 | + | 1.28235i | −0.0277514 | + | 0.0819261i | ||||
\(246\) | − | 28.3843i | − | 1.80972i | ||||||
\(247\) | −5.43094 | + | 20.4695i | −0.345562 | + | 1.30244i | ||||
\(248\) | − | 3.80921i | − | 0.241885i | ||||||
\(249\) | 6.91260 | − | 6.91260i | 0.438068 | − | 0.438068i | ||||
\(250\) | − | 5.30425i | − | 0.335470i | ||||||
\(251\) | 15.9764 | 1.00842 | 0.504211 | − | 0.863580i | \(-0.331783\pi\) | ||||
0.504211 | + | 0.863580i | \(0.331783\pi\) | |||||||
\(252\) | 12.5334 | + | 7.78819i | 0.789531 | + | 0.490610i | ||||
\(253\) | −0.235571 | + | 0.235571i | −0.0148102 | + | 0.0148102i | ||||
\(254\) | 5.79601 | + | 5.79601i | 0.363674 | + | 0.363674i | ||||
\(255\) | 0.614691 | − | 0.614691i | 0.0384934 | − | 0.0384934i | ||||
\(256\) | 60.5183 | 3.78240 | ||||||||
\(257\) | 10.3506 | 0.645652 | 0.322826 | − | 0.946458i | \(-0.395367\pi\) | ||||
0.322826 | + | 0.946458i | \(0.395367\pi\) | |||||||
\(258\) | 3.63455 | − | 3.63455i | 0.226277 | − | 0.226277i | ||||
\(259\) | 20.9631 | − | 4.89502i | 1.30258 | − | 0.304162i | ||||
\(260\) | −3.75939 | − | 0.997434i | −0.233147 | − | 0.0618582i | ||||
\(261\) | 7.01375 | 0.434140 | ||||||||
\(262\) | 33.9279 | + | 33.9279i | 2.09607 | + | 2.09607i | ||||
\(263\) | −10.9315 | −0.674064 | −0.337032 | − | 0.941493i | \(-0.609423\pi\) | ||||
−0.337032 | + | 0.941493i | \(0.609423\pi\) | |||||||
\(264\) | −7.73742 | −0.476205 | ||||||||
\(265\) | 0.590403 | + | 0.590403i | 0.0362682 | + | 0.0362682i | ||||
\(266\) | −22.5776 | + | 36.3339i | −1.38432 | + | 2.22777i | ||||
\(267\) | −6.46820 | − | 6.46820i | −0.395847 | − | 0.395847i | ||||
\(268\) | −4.67204 | − | 4.67204i | −0.285390 | − | 0.285390i | ||||
\(269\) | 0.890429i | 0.0542904i | 0.999632 | + | 0.0271452i | \(0.00864165\pi\) | ||||
−0.999632 | + | 0.0271452i | \(0.991358\pi\) | |||||||
\(270\) | − | 0.532416i | − | 0.0324018i | ||||||
\(271\) | −15.2932 | + | 15.2932i | −0.928996 | + | 0.928996i | −0.997641 | − | 0.0686449i | \(-0.978132\pi\) |
0.0686449 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(272\) | −71.6933 | −4.34704 | ||||||||
\(273\) | −0.285633 | + | 9.53511i | −0.0172873 | + | 0.577091i | ||||
\(274\) | 28.9875 | 1.75120 | ||||||||
\(275\) | 2.75727 | − | 2.75727i | 0.166270 | − | 0.166270i | ||||
\(276\) | 2.36468i | 0.142337i | ||||||||
\(277\) | − | 9.83129i | − | 0.590705i | −0.955388 | − | 0.295353i | \(-0.904563\pi\) | ||
0.955388 | − | 0.295353i | \(-0.0954371\pi\) | |||||||
\(278\) | 36.4834 | + | 36.4834i | 2.18813 | + | 2.18813i | ||||
\(279\) | 0.273533 | + | 0.273533i | 0.0163760 | + | 0.0163760i | ||||
\(280\) | −4.28008 | − | 2.65961i | −0.255783 | − | 0.158942i | ||||
\(281\) | −12.8526 | − | 12.8526i | −0.766720 | − | 0.766720i | 0.210808 | − | 0.977528i | \(-0.432391\pi\) |
−0.977528 | + | 0.210808i | \(0.932391\pi\) | |||||||
\(282\) | −18.4950 | −1.10136 | ||||||||
\(283\) | 2.25769 | 0.134206 | 0.0671029 | − | 0.997746i | \(-0.478624\pi\) | ||||
0.0671029 | + | 0.997746i | \(0.478624\pi\) | |||||||
\(284\) | −5.60629 | − | 5.60629i | −0.332672 | − | 0.332672i | ||||
\(285\) | 1.13606 | 0.0672946 | ||||||||
\(286\) | −3.91586 | − | 6.74416i | −0.231550 | − | 0.398791i | ||||
\(287\) | 26.5670 | − | 6.20356i | 1.56820 | − | 0.366185i | ||||
\(288\) | −17.1227 | + | 17.1227i | −1.00897 | + | 1.00897i | ||||
\(289\) | 3.20012 | 0.188242 | ||||||||
\(290\) | −3.73423 | −0.219282 | ||||||||
\(291\) | 3.19087 | − | 3.19087i | 0.187052 | − | 0.187052i | ||||
\(292\) | −38.0289 | − | 38.0289i | −2.22547 | − | 2.22547i | ||||
\(293\) | −3.42417 | + | 3.42417i | −0.200042 | + | 0.200042i | −0.800018 | − | 0.599976i | \(-0.795177\pi\) |
0.599976 | + | 0.800018i | \(0.295177\pi\) | |||||||
\(294\) | −6.18201 | + | 18.2502i | −0.360542 | + | 1.06437i | ||||
\(295\) | −0.189196 | −0.0110154 | ||||||||
\(296\) | 80.1207i | 4.65692i | ||||||||
\(297\) | 0.555612 | − | 0.555612i | 0.0322399 | − | 0.0322399i | ||||
\(298\) | − | 29.4667i | − | 1.70696i | ||||||
\(299\) | −1.32201 | + | 0.767598i | −0.0764538 | + | 0.0443913i | ||||
\(300\) | − | 27.6778i | − | 1.59798i | ||||||
\(301\) | 4.19620 | + | 2.60750i | 0.241865 | + | 0.150294i | ||||
\(302\) | 37.0735 | 2.13334 | ||||||||
\(303\) | − | 9.40173i | − | 0.540115i | ||||||
\(304\) | −66.2513 | − | 66.2513i | −3.79977 | − | 3.79977i | ||||
\(305\) | 1.11046 | − | 1.11046i | 0.0635846 | − | 0.0635846i | ||||
\(306\) | 8.74820 | − | 8.74820i | 0.500101 | − | 0.500101i | ||||
\(307\) | 11.2000 | − | 11.2000i | 0.639216 | − | 0.639216i | −0.311146 | − | 0.950362i | \(-0.600713\pi\) |
0.950362 | + | 0.311146i | \(0.100713\pi\) | |||||||
\(308\) | −2.63651 | − | 11.2909i | −0.150229 | − | 0.643360i | ||||
\(309\) | − | 1.84027i | − | 0.104690i | ||||||
\(310\) | −0.145633 | − | 0.145633i | −0.00827143 | − | 0.00827143i | ||||
\(311\) | −18.6012 | −1.05477 | −0.527387 | − | 0.849625i | \(-0.676828\pi\) | ||||
−0.527387 | + | 0.849625i | \(0.676828\pi\) | |||||||
\(312\) | −34.3170 | − | 9.10493i | −1.94282 | − | 0.515465i | ||||
\(313\) | 31.7181i | 1.79281i | 0.443234 | + | 0.896406i | \(0.353831\pi\) | ||||
−0.443234 | + | 0.896406i | \(0.646169\pi\) | |||||||
\(314\) | −35.2893 | − | 35.2893i | −1.99149 | − | 1.99149i | ||||
\(315\) | 0.498328 | − | 0.116363i | 0.0280776 | − | 0.00655630i | ||||
\(316\) | − | 61.2260i | − | 3.44423i | ||||||
\(317\) | −9.54944 | + | 9.54944i | −0.536350 | + | 0.536350i | −0.922455 | − | 0.386105i | \(-0.873820\pi\) |
0.386105 | + | 0.922455i | \(0.373820\pi\) | |||||||
\(318\) | 8.40254 | + | 8.40254i | 0.471191 | + | 0.471191i | ||||
\(319\) | −3.89692 | − | 3.89692i | −0.218186 | − | 0.218186i | ||||
\(320\) | 4.75316 | − | 4.75316i | 0.265710 | − | 0.265710i | ||||
\(321\) | 9.88514i | 0.551735i | ||||||||
\(322\) | −3.00696 | + | 0.702144i | −0.167571 | + | 0.0391289i | ||||
\(323\) | 18.6668 | + | 18.6668i | 1.03865 | + | 1.03865i | ||||
\(324\) | − | 5.57728i | − | 0.309849i | ||||||
\(325\) | 15.4737 | − | 8.98447i | 0.858324 | − | 0.498369i | ||||
\(326\) | 2.62675 | 0.145482 | ||||||||
\(327\) | −9.76428 | − | 9.76428i | −0.539966 | − | 0.539966i | ||||
\(328\) | 101.539i | 5.60653i | ||||||||
\(329\) | −4.04220 | − | 17.3109i | −0.222854 | − | 0.954379i | ||||
\(330\) | −0.295817 | + | 0.295817i | −0.0162842 | + | 0.0162842i | ||||
\(331\) | −12.3494 | + | 12.3494i | −0.678783 | + | 0.678783i | −0.959725 | − | 0.280942i | \(-0.909353\pi\) |
0.280942 | + | 0.959725i | \(0.409353\pi\) | |||||||
\(332\) | −38.5535 | + | 38.5535i | −2.11590 | + | 2.11590i | ||||
\(333\) | −5.75334 | − | 5.75334i | −0.315281 | − | 0.315281i | ||||
\(334\) | 20.0054i | 1.09465i | ||||||||
\(335\) | −0.229136 | −0.0125190 | ||||||||
\(336\) | −35.8466 | − | 22.2749i | −1.95559 | − | 1.21519i | ||||
\(337\) | 24.8518i | 1.35376i | 0.736091 | + | 0.676882i | \(0.236669\pi\) | ||||
−0.736091 | + | 0.676882i | \(0.763331\pi\) | |||||||
\(338\) | −9.43151 | − | 34.5197i | −0.513007 | − | 1.87762i | ||||
\(339\) | − | 9.96741i | − | 0.541356i | ||||||
\(340\) | −3.42830 | + | 3.42830i | −0.185926 | + | 0.185926i | ||||
\(341\) | − | 0.303956i | − | 0.0164602i | ||||||
\(342\) | 16.1683 | 0.874282 | ||||||||
\(343\) | −18.4328 | − | 1.79752i | −0.995279 | − | 0.0970567i | ||||
\(344\) | −13.0018 | + | 13.0018i | −0.701011 | + | 0.701011i | ||||
\(345\) | 0.0579868 | + | 0.0579868i | 0.00312191 | + | 0.00312191i | ||||
\(346\) | 1.27569 | − | 1.27569i | 0.0685813 | − | 0.0685813i | ||||
\(347\) | −15.5180 | −0.833052 | −0.416526 | − | 0.909124i | \(-0.636753\pi\) | ||||
−0.416526 | + | 0.909124i | \(0.636753\pi\) | |||||||
\(348\) | −39.1176 | −2.09693 | ||||||||
\(349\) | −8.67730 | + | 8.67730i | −0.464485 | + | 0.464485i | −0.900122 | − | 0.435637i | \(-0.856523\pi\) |
0.435637 | + | 0.900122i | \(0.356523\pi\) | |||||||
\(350\) | 35.1954 | − | 8.21835i | 1.88127 | − | 0.439289i | ||||
\(351\) | 3.11806 | − | 1.81044i | 0.166430 | − | 0.0966341i | ||||
\(352\) | 19.0272 | 1.01415 | ||||||||
\(353\) | 24.8207 | + | 24.8207i | 1.32107 | + | 1.32107i | 0.912910 | + | 0.408160i | \(0.133829\pi\) |
0.408160 | + | 0.912910i | \(0.366171\pi\) | |||||||
\(354\) | −2.69261 | −0.143111 | ||||||||
\(355\) | −0.274956 | −0.0145931 | ||||||||
\(356\) | 36.0750 | + | 36.0750i | 1.91197 | + | 1.91197i | ||||
\(357\) | 10.1001 | + | 6.27612i | 0.534552 | + | 0.332167i | ||||
\(358\) | 46.1970 | + | 46.1970i | 2.44159 | + | 2.44159i | ||||
\(359\) | −8.95183 | − | 8.95183i | −0.472459 | − | 0.472459i | 0.430250 | − | 0.902710i | \(-0.358425\pi\) |
−0.902710 | + | 0.430250i | \(0.858425\pi\) | |||||||
\(360\) | 1.90460i | 0.100381i | ||||||||
\(361\) | 15.4997i | 0.815776i | ||||||||
\(362\) | 14.4611 | − | 14.4611i | 0.760058 | − | 0.760058i | ||||
\(363\) | 10.3826 | 0.544945 | ||||||||
\(364\) | 1.59306 | − | 53.1800i | 0.0834988 | − | 2.78739i | ||||
\(365\) | −1.86510 | −0.0976236 | ||||||||
\(366\) | 15.8039 | − | 15.8039i | 0.826083 | − | 0.826083i | ||||
\(367\) | − | 21.0453i | − | 1.09855i | −0.835640 | − | 0.549277i | \(-0.814903\pi\) | ||
0.835640 | − | 0.549277i | \(-0.185097\pi\) | |||||||
\(368\) | − | 6.76318i | − | 0.352555i | ||||||
\(369\) | −7.29133 | − | 7.29133i | −0.379571 | − | 0.379571i | ||||
\(370\) | 3.06317 | + | 3.06317i | 0.159247 | + | 0.159247i | ||||
\(371\) | −6.02814 | + | 9.70099i | −0.312965 | + | 0.503650i | ||||
\(372\) | −1.52557 | − | 1.52557i | −0.0790971 | − | 0.0790971i | ||||
\(373\) | −17.6419 | −0.913462 | −0.456731 | − | 0.889605i | \(-0.650980\pi\) | ||||
−0.456731 | + | 0.889605i | \(0.650980\pi\) | |||||||
\(374\) | −9.72121 | −0.502672 | ||||||||
\(375\) | −1.36255 | − | 1.36255i | −0.0703617 | − | 0.0703617i | ||||
\(376\) | 66.1619 | 3.41204 | ||||||||
\(377\) | −12.6980 | − | 21.8693i | −0.653979 | − | 1.12633i | ||||
\(378\) | 7.09214 | − | 1.65606i | 0.364780 | − | 0.0851786i | ||||
\(379\) | −4.45288 | + | 4.45288i | −0.228729 | + | 0.228729i | −0.812162 | − | 0.583433i | \(-0.801709\pi\) |
0.583433 | + | 0.812162i | \(0.301709\pi\) | |||||||
\(380\) | −6.33615 | −0.325037 | ||||||||
\(381\) | 2.97774 | 0.152554 | ||||||||
\(382\) | −37.5761 | + | 37.5761i | −1.92256 | + | 1.92256i | ||||
\(383\) | −9.10197 | − | 9.10197i | −0.465089 | − | 0.465089i | 0.435230 | − | 0.900319i | \(-0.356667\pi\) |
−0.900319 | + | 0.435230i | \(0.856667\pi\) | |||||||
\(384\) | 33.4009 | − | 33.4009i | 1.70448 | − | 1.70448i | ||||
\(385\) | −0.341530 | − | 0.212224i | −0.0174060 | − | 0.0108160i | ||||
\(386\) | −19.7093 | −1.00318 | ||||||||
\(387\) | − | 1.86728i | − | 0.0949192i | ||||||
\(388\) | −17.7964 | + | 17.7964i | −0.903474 | + | 0.903474i | ||||
\(389\) | 5.48639i | 0.278171i | 0.990280 | + | 0.139086i | \(0.0444163\pi\) | ||||
−0.990280 | + | 0.139086i | \(0.955584\pi\) | |||||||
\(390\) | −1.66011 | + | 0.963908i | −0.0840628 | + | 0.0488094i | ||||
\(391\) | 1.90558i | 0.0963692i | ||||||||
\(392\) | 22.1148 | − | 65.2861i | 1.11697 | − | 3.29744i | ||||
\(393\) | 17.4307 | 0.879264 | ||||||||
\(394\) | 42.9515i | 2.16387i | ||||||||
\(395\) | −1.50139 | − | 1.50139i | −0.0755430 | − | 0.0755430i | ||||
\(396\) | −3.09880 | + | 3.09880i | −0.155721 | + | 0.155721i | ||||
\(397\) | 21.4027 | − | 21.4027i | 1.07417 | − | 1.07417i | 0.0771530 | − | 0.997019i | \(-0.475417\pi\) |
0.997019 | − | 0.0771530i | \(-0.0245830\pi\) | |||||||
\(398\) | 24.6143 | − | 24.6143i | 1.23380 | − | 1.23380i | ||||
\(399\) | 3.53368 | + | 15.1331i | 0.176905 | + | 0.757604i | ||||
\(400\) | 79.1607i | 3.95804i | ||||||||
\(401\) | −1.09699 | − | 1.09699i | −0.0547810 | − | 0.0547810i | 0.679186 | − | 0.733967i | \(-0.262333\pi\) |
−0.733967 | + | 0.679186i | \(0.762333\pi\) | |||||||
\(402\) | −3.26104 | −0.162646 | ||||||||
\(403\) | 0.357678 | − | 1.34811i | 0.0178172 | − | 0.0671540i | ||||
\(404\) | 52.4361i | 2.60879i | ||||||||
\(405\) | −0.136767 | − | 0.136767i | −0.00679598 | − | 0.00679598i | ||||
\(406\) | −11.6152 | − | 49.7425i | −0.576452 | − | 2.46868i | ||||
\(407\) | 6.39325i | 0.316901i | ||||||||
\(408\) | −31.2948 | + | 31.2948i | −1.54932 | + | 1.54932i | ||||
\(409\) | −9.83744 | − | 9.83744i | −0.486430 | − | 0.486430i | 0.420748 | − | 0.907178i | \(-0.361768\pi\) |
−0.907178 | + | 0.420748i | \(0.861768\pi\) | |||||||
\(410\) | 3.88202 | + | 3.88202i | 0.191719 | + | 0.191719i | ||||
\(411\) | 7.44628 | − | 7.44628i | 0.367298 | − | 0.367298i | ||||
\(412\) | 10.2637i | 0.505657i | ||||||||
\(413\) | −0.588487 | − | 2.52022i | −0.0289576 | − | 0.124012i | ||||
\(414\) | 0.825261 | + | 0.825261i | 0.0405594 | + | 0.0405594i | ||||
\(415\) | 1.89082i | 0.0928169i | ||||||||
\(416\) | 84.3894 | + | 22.3901i | 4.13753 | + | 1.09776i | ||||
\(417\) | 18.7436 | 0.917879 | ||||||||
\(418\) | −8.98331 | − | 8.98331i | −0.439388 | − | 0.439388i | ||||
\(419\) | 15.2437i | 0.744706i | 0.928091 | + | 0.372353i | \(0.121449\pi\) | ||||
−0.928091 | + | 0.372353i | \(0.878551\pi\) | |||||||
\(420\) | −2.77932 | + | 0.648988i | −0.135617 | + | 0.0316674i | ||||
\(421\) | −6.81477 | + | 6.81477i | −0.332132 | + | 0.332132i | −0.853396 | − | 0.521264i | \(-0.825461\pi\) |
0.521264 | + | 0.853396i | \(0.325461\pi\) | |||||||
\(422\) | 37.2726 | − | 37.2726i | 1.81440 | − | 1.81440i | ||||
\(423\) | −4.75098 | + | 4.75098i | −0.231001 | + | 0.231001i | ||||
\(424\) | −30.0583 | − | 30.0583i | −1.45976 | − | 1.45976i | ||||
\(425\) | − | 22.3041i | − | 1.08191i | ||||||
\(426\) | −3.91314 | −0.189592 | ||||||||
\(427\) | 18.2461 | + | 11.3380i | 0.882989 | + | 0.548684i | ||||
\(428\) | − | 55.1322i | − | 2.66492i | ||||||
\(429\) | −2.73833 | − | 0.726530i | −0.132208 | − | 0.0350772i | ||||
\(430\) | 0.994171i | 0.0479432i | ||||||||
\(431\) | 15.8122 | − | 15.8122i | 0.761646 | − | 0.761646i | −0.214974 | − | 0.976620i | \(-0.568967\pi\) |
0.976620 | + | 0.214974i | \(0.0689667\pi\) | |||||||
\(432\) | 15.9515i | 0.767467i | ||||||||
\(433\) | −13.2868 | −0.638525 | −0.319263 | − | 0.947666i | \(-0.603435\pi\) | ||||
−0.319263 | + | 0.947666i | \(0.603435\pi\) | |||||||
\(434\) | 1.48695 | − | 2.39292i | 0.0713757 | − | 0.114864i | ||||
\(435\) | −0.959246 | + | 0.959246i | −0.0459923 | + | 0.0459923i | ||||
\(436\) | 54.4581 | + | 54.4581i | 2.60807 | + | 2.60807i | ||||
\(437\) | −1.76093 | + | 1.76093i | −0.0842368 | + | 0.0842368i | ||||
\(438\) | −26.5438 | −1.26831 | ||||||||
\(439\) | 1.47611 | 0.0704508 | 0.0352254 | − | 0.999379i | \(-0.488785\pi\) | ||||
0.0352254 | + | 0.999379i | \(0.488785\pi\) | |||||||
\(440\) | 1.05822 | − | 1.05822i | 0.0504487 | − | 0.0504487i | ||||
\(441\) | 3.10006 | + | 6.27612i | 0.147622 | + | 0.298863i | ||||
\(442\) | −43.1155 | − | 11.4393i | −2.05080 | − | 0.544114i | ||||
\(443\) | 0.500905 | 0.0237987 | 0.0118994 | − | 0.999929i | \(-0.496212\pi\) | ||||
0.0118994 | + | 0.999929i | \(0.496212\pi\) | |||||||
\(444\) | 32.0880 | + | 32.0880i | 1.52283 | + | 1.52283i | ||||
\(445\) | 1.76927 | 0.0838713 | ||||||||
\(446\) | 14.7324 | 0.697602 | ||||||||
\(447\) | −7.56936 | − | 7.56936i | −0.358018 | − | 0.358018i | ||||
\(448\) | 78.0998 | + | 48.5308i | 3.68987 | + | 2.29286i | ||||
\(449\) | −1.55163 | − | 1.55163i | −0.0732259 | − | 0.0732259i | 0.669545 | − | 0.742771i | \(-0.266489\pi\) |
−0.742771 | + | 0.669545i | \(0.766489\pi\) | |||||||
\(450\) | −9.65940 | − | 9.65940i | −0.455348 | − | 0.455348i | ||||
\(451\) | 8.10230i | 0.381522i | ||||||||
\(452\) | 55.5911i | 2.61478i | ||||||||
\(453\) | 9.52340 | − | 9.52340i | 0.447449 | − | 0.447449i | ||||
\(454\) | −50.0836 | −2.35054 | ||||||||
\(455\) | −1.26502 | − | 1.34315i | −0.0593050 | − | 0.0629678i | ||||
\(456\) | −57.8386 | −2.70854 | ||||||||
\(457\) | 21.1001 | − | 21.1001i | 0.987023 | − | 0.987023i | −0.0128943 | − | 0.999917i | \(-0.504104\pi\) |
0.999917 | + | 0.0128943i | \(0.00410450\pi\) | |||||||
\(458\) | − | 27.0703i | − | 1.26491i | ||||||
\(459\) | − | 4.49445i | − | 0.209783i | ||||||
\(460\) | −0.323409 | − | 0.323409i | −0.0150790 | − | 0.0150790i | ||||
\(461\) | −0.542495 | − | 0.542495i | −0.0252665 | − | 0.0252665i | 0.694361 | − | 0.719627i | \(-0.255687\pi\) |
−0.719627 | + | 0.694361i | \(0.755687\pi\) | |||||||
\(462\) | −4.86060 | − | 3.02035i | −0.226136 | − | 0.140519i | ||||
\(463\) | −10.7562 | − | 10.7562i | −0.499882 | − | 0.499882i | 0.411519 | − | 0.911401i | \(-0.364998\pi\) |
−0.911401 | + | 0.411519i | \(0.864998\pi\) | |||||||
\(464\) | 111.880 | 5.19389 | ||||||||
\(465\) | −0.0748203 | −0.00346971 | ||||||||
\(466\) | 37.6044 | + | 37.6044i | 1.74199 | + | 1.74199i | ||||
\(467\) | 31.8438 | 1.47356 | 0.736778 | − | 0.676135i | \(-0.236346\pi\) | ||||
0.736778 | + | 0.676135i | \(0.236346\pi\) | |||||||
\(468\) | −17.3903 | + | 10.0973i | −0.803867 | + | 0.466749i | ||||
\(469\) | −0.712719 | − | 3.05225i | −0.0329103 | − | 0.140940i | ||||
\(470\) | 2.52950 | − | 2.52950i | 0.116677 | − | 0.116677i | ||||
\(471\) | −18.1301 | −0.835393 | ||||||||
\(472\) | 9.63224 | 0.443360 | ||||||||
\(473\) | −1.03748 | + | 1.03748i | −0.0477035 | + | 0.0477035i | ||||
\(474\) | −21.3676 | − | 21.3676i | −0.981444 | − | 0.981444i | ||||
\(475\) | 20.6111 | − | 20.6111i | 0.945702 | − | 0.945702i | ||||
\(476\) | −56.3309 | − | 35.0037i | −2.58192 | − | 1.60439i | ||||
\(477\) | 4.31687 | 0.197656 | ||||||||
\(478\) | − | 56.4427i | − | 2.58163i | ||||||
\(479\) | 3.51478 | − | 3.51478i | 0.160595 | − | 0.160595i | −0.622236 | − | 0.782830i | \(-0.713775\pi\) |
0.782830 | + | 0.622236i | \(0.213775\pi\) | |||||||
\(480\) | − | 4.68363i | − | 0.213778i | ||||||
\(481\) | −7.52319 | + | 28.3553i | −0.343028 | + | 1.29289i | ||||
\(482\) | − | 19.9196i | − | 0.907311i | ||||||
\(483\) | −0.592057 | + | 0.952789i | −0.0269395 | + | 0.0433534i | ||||
\(484\) | −57.9066 | −2.63212 | ||||||||
\(485\) | 0.872808i | 0.0396322i | ||||||||
\(486\) | −1.94644 | − | 1.94644i | −0.0882924 | − | 0.0882924i | ||||
\(487\) | −3.57589 | + | 3.57589i | −0.162039 | + | 0.162039i | −0.783469 | − | 0.621430i | \(-0.786552\pi\) |
0.621430 | + | 0.783469i | \(0.286552\pi\) | |||||||
\(488\) | −56.5350 | + | 56.5350i | −2.55922 | + | 2.55922i | ||||
\(489\) | 0.674757 | − | 0.674757i | 0.0305136 | − | 0.0305136i | ||||
\(490\) | −1.65052 | − | 3.34151i | −0.0745630 | − | 0.150954i | ||||
\(491\) | − | 4.24758i | − | 0.191691i | −0.995396 | − | 0.0958453i | \(-0.969445\pi\) | ||
0.995396 | − | 0.0958453i | \(-0.0305554\pi\) | |||||||
\(492\) | 40.6658 | + | 40.6658i | 1.83336 | + | 1.83336i | ||||
\(493\) | −31.5230 | −1.41972 | ||||||||
\(494\) | −29.2718 | − | 50.4138i | −1.31700 | − | 2.26822i | ||||
\(495\) | 0.151978i | 0.00683091i | ||||||||
\(496\) | 4.36326 | + | 4.36326i | 0.195916 | + | 0.195916i | ||||
\(497\) | −0.855240 | − | 3.66259i | −0.0383627 | − | 0.164290i | ||||
\(498\) | 26.9100i | 1.20586i | ||||||||
\(499\) | −3.69487 | + | 3.69487i | −0.165405 | + | 0.165405i | −0.784956 | − | 0.619551i | \(-0.787315\pi\) |
0.619551 | + | 0.784956i | \(0.287315\pi\) | |||||||
\(500\) | 7.59932 | + | 7.59932i | 0.339852 | + | 0.339852i | ||||
\(501\) | 5.13896 | + | 5.13896i | 0.229592 | + | 0.229592i | ||||
\(502\) | −31.0972 | + | 31.0972i | −1.38793 | + | 1.38793i | ||||
\(503\) | 16.9237i | 0.754591i | 0.926093 | + | 0.377296i | \(0.123146\pi\) | ||||
−0.926093 | + | 0.377296i | \(0.876854\pi\) | |||||||
\(504\) | −25.3706 | + | 5.92419i | −1.13010 | + | 0.263885i | ||||
\(505\) | 1.28584 | + | 1.28584i | 0.0572192 | + | 0.0572192i | ||||
\(506\) | − | 0.917050i | − | 0.0407679i | ||||||
\(507\) | −11.2901 | − | 6.44461i | −0.501412 | − | 0.286215i | ||||
\(508\) | −16.6077 | −0.736848 | ||||||||
\(509\) | −25.1102 | − | 25.1102i | −1.11299 | − | 1.11299i | −0.992744 | − | 0.120244i | \(-0.961632\pi\) |
−0.120244 | − | 0.992744i | \(-0.538368\pi\) | |||||||
\(510\) | 2.39292i | 0.105960i | ||||||||
\(511\) | −5.80131 | − | 24.8443i | −0.256635 | − | 1.09905i | ||||
\(512\) | −50.9936 | + | 50.9936i | −2.25362 | + | 2.25362i | ||||
\(513\) | 4.15330 | − | 4.15330i | 0.183373 | − | 0.183373i | ||||
\(514\) | −20.1468 | + | 20.1468i | −0.888638 | + | 0.888638i | ||||
\(515\) | 0.251688 | + | 0.251688i | 0.0110907 | + | 0.0110907i | ||||
\(516\) | 10.4143i | 0.458466i | ||||||||
\(517\) | 5.27940 | 0.232188 | ||||||||
\(518\) | −31.2756 | + | 50.3313i | −1.37417 | + | 2.21143i | ||||
\(519\) | − | 0.655393i | − | 0.0287686i | ||||||
\(520\) | 5.93867 | − | 3.44817i | 0.260428 | − | 0.151212i | ||||
\(521\) | − | 6.34020i | − | 0.277769i | −0.990309 | − | 0.138885i | \(-0.955648\pi\) | ||
0.990309 | − | 0.138885i | \(-0.0443517\pi\) | |||||||
\(522\) | −13.6519 | + | 13.6519i | −0.597526 | + | 0.597526i | ||||
\(523\) | 2.80026i | 0.122447i | 0.998124 | + | 0.0612234i | \(0.0195002\pi\) | ||||
−0.998124 | + | 0.0612234i | \(0.980500\pi\) | |||||||
\(524\) | −97.2161 | −4.24690 | ||||||||
\(525\) | 6.92983 | − | 11.1521i | 0.302442 | − | 0.486716i | ||||
\(526\) | 21.2775 | − | 21.2775i | 0.927743 | − | 0.927743i | ||||
\(527\) | −1.22938 | − | 1.22938i | −0.0535527 | − | 0.0535527i | ||||
\(528\) | 8.86284 | − | 8.86284i | 0.385706 | − | 0.385706i | ||||
\(529\) | 22.8202 | 0.992184 | ||||||||
\(530\) | −2.29837 | −0.0998349 | ||||||||
\(531\) | −0.691676 | + | 0.691676i | −0.0300162 | + | 0.0300162i | ||||
\(532\) | −19.7083 | − | 84.4017i | −0.854465 | − | 3.65928i | ||||
\(533\) | −9.53430 | + | 35.9353i | −0.412976 | + | 1.55653i | ||||
\(534\) | 25.1800 | 1.08964 | ||||||||
\(535\) | −1.35196 | − | 1.35196i | −0.0584501 | − | 0.0584501i | ||||
\(536\) | 11.6656 | 0.503879 | ||||||||
\(537\) | 23.7340 | 1.02420 | ||||||||
\(538\) | −1.73317 | − | 1.73317i | −0.0747223 | − | 0.0747223i | ||||
\(539\) | 1.76466 | − | 5.20952i | 0.0760091 | − | 0.224390i | ||||
\(540\) | 0.762785 | + | 0.762785i | 0.0328250 | + | 0.0328250i | ||||
\(541\) | 1.50569 | + | 1.50569i | 0.0647345 | + | 0.0647345i | 0.738733 | − | 0.673998i | \(-0.235425\pi\) |
−0.673998 | + | 0.738733i | \(0.735425\pi\) | |||||||
\(542\) | − | 59.5347i | − | 2.55723i | ||||||
\(543\) | − | 7.42950i | − | 0.318830i | ||||||
\(544\) | 76.9574 | − | 76.9574i | 3.29952 | − | 3.29952i | ||||
\(545\) | 2.67085 | 0.114407 | ||||||||
\(546\) | −18.0036 | − | 19.1155i | −0.770482 | − | 0.818069i | ||||
\(547\) | −2.65090 | −0.113344 | −0.0566722 | − | 0.998393i | \(-0.518049\pi\) | ||||
−0.0566722 | + | 0.998393i | \(0.518049\pi\) | |||||||
\(548\) | −41.5300 | + | 41.5300i | −1.77407 | + | 1.77407i | ||||
\(549\) | − | 8.11937i | − | 0.346526i | ||||||
\(550\) | 10.7338i | 0.457689i | ||||||||
\(551\) | −29.1302 | − | 29.1302i | −1.24099 | − | 1.24099i | ||||
\(552\) | −2.95219 | − | 2.95219i | −0.125654 | − | 0.125654i | ||||
\(553\) | 15.3295 | − | 24.6695i | 0.651875 | − | 1.04905i | ||||
\(554\) | 19.1361 | + | 19.1361i | 0.813013 | + | 0.813013i | ||||
\(555\) | 1.57373 | 0.0668010 | ||||||||
\(556\) | −104.538 | −4.43342 | ||||||||
\(557\) | −1.67493 | − | 1.67493i | −0.0709691 | − | 0.0709691i | 0.670731 | − | 0.741700i | \(-0.265980\pi\) |
−0.741700 | + | 0.670731i | \(0.765980\pi\) | |||||||
\(558\) | −1.06483 | −0.0450780 | ||||||||
\(559\) | −5.82229 | + | 3.38060i | −0.246257 | + | 0.142984i | ||||
\(560\) | 7.94908 | − | 1.85616i | 0.335910 | − | 0.0784371i | ||||
\(561\) | −2.49717 | + | 2.49717i | −0.105431 | + | 0.105431i | ||||
\(562\) | 50.0336 | 2.11054 | ||||||||
\(563\) | 27.1654 | 1.14489 | 0.572443 | − | 0.819945i | \(-0.305996\pi\) | ||||
0.572443 | + | 0.819945i | \(0.305996\pi\) | |||||||
\(564\) | 26.4976 | − | 26.4976i | 1.11575 | − | 1.11575i | ||||
\(565\) | 1.36321 | + | 1.36321i | 0.0573506 | + | 0.0573506i | ||||
\(566\) | −4.39447 | + | 4.39447i | −0.184713 | + | 0.184713i | ||||
\(567\) | 1.39641 | − | 2.24723i | 0.0586439 | − | 0.0943747i | ||||
\(568\) | 13.9984 | 0.587359 | ||||||||
\(569\) | 12.5703i | 0.526973i | 0.964663 | + | 0.263487i | \(0.0848725\pi\) | ||||
−0.964663 | + | 0.263487i | \(0.915127\pi\) | |||||||
\(570\) | −2.21128 | + | 2.21128i | −0.0926205 | + | 0.0926205i | ||||
\(571\) | − | 19.6741i | − | 0.823334i | −0.911334 | − | 0.411667i | \(-0.864947\pi\) | ||
0.911334 | − | 0.411667i | \(-0.135053\pi\) | |||||||
\(572\) | 15.2725 | + | 4.05206i | 0.638574 | + | 0.169425i | ||||
\(573\) | 19.3050i | 0.806478i | ||||||||
\(574\) | −39.6362 | + | 63.7860i | −1.65438 | + | 2.66238i | ||||
\(575\) | 2.10406 | 0.0877454 | ||||||||
\(576\) | − | 34.7539i | − | 1.44808i | ||||||
\(577\) | 11.0080 | + | 11.0080i | 0.458271 | + | 0.458271i | 0.898087 | − | 0.439817i | \(-0.144957\pi\) |
−0.439817 | + | 0.898087i | \(0.644957\pi\) | |||||||
\(578\) | −6.22885 | + | 6.22885i | −0.259086 | + | 0.259086i | ||||
\(579\) | −5.06291 | + | 5.06291i | −0.210407 | + | 0.210407i | ||||
\(580\) | 5.34998 | − | 5.34998i | 0.222146 | − | 0.222146i | ||||
\(581\) | −25.1870 | + | 5.88133i | −1.04493 | + | 0.243999i | ||||
\(582\) | 12.4217i | 0.514896i | ||||||||
\(583\) | −2.39851 | − | 2.39851i | −0.0993359 | − | 0.0993359i | ||||
\(584\) | 94.9546 | 3.92925 | ||||||||
\(585\) | −0.178839 | + | 0.674054i | −0.00739408 | + | 0.0278687i | ||||
\(586\) | − | 13.3299i | − | 0.550653i | ||||||
\(587\) | 21.5168 | + | 21.5168i | 0.888093 | + | 0.888093i | 0.994340 | − | 0.106247i | \(-0.0338834\pi\) |
−0.106247 | + | 0.994340i | \(0.533883\pi\) | |||||||
\(588\) | −17.2899 | − | 35.0037i | −0.713023 | − | 1.44353i | ||||
\(589\) | − | 2.27213i | − | 0.0936214i | ||||||
\(590\) | 0.368260 | − | 0.368260i | 0.0151610 | − | 0.0151610i | ||||
\(591\) | 11.0333 | + | 11.0333i | 0.453851 | + | 0.453851i | ||||
\(592\) | −91.7744 | − | 91.7744i | −3.77190 | − | 3.77190i | ||||
\(593\) | −27.5375 | + | 27.5375i | −1.13083 | + | 1.13083i | −0.140792 | + | 0.990039i | \(0.544965\pi\) |
−0.990039 | + | 0.140792i | \(0.955035\pi\) | |||||||
\(594\) | 2.16293i | 0.0887463i | ||||||||
\(595\) | −2.23971 | + | 0.522987i | −0.0918193 | + | 0.0214404i | ||||
\(596\) | 42.2164 | + | 42.2164i | 1.72925 | + | 1.72925i | ||||
\(597\) | − | 12.6458i | − | 0.517558i | ||||||
\(598\) | 1.07913 | − | 4.06730i | 0.0441289 | − | 0.166324i | ||||
\(599\) | 40.3864 | 1.65014 | 0.825072 | − | 0.565028i | \(-0.191134\pi\) | ||||
0.825072 | + | 0.565028i | \(0.191134\pi\) | |||||||
\(600\) | 34.5544 | + | 34.5544i | 1.41068 | + | 1.41068i | ||||
\(601\) | − | 44.9596i | − | 1.83394i | −0.398957 | − | 0.916969i | \(-0.630628\pi\) | ||
0.398957 | − | 0.916969i | \(-0.369372\pi\) | |||||||
\(602\) | −13.2430 | + | 3.09233i | −0.539745 | + | 0.126034i | ||||
\(603\) | −0.837691 | + | 0.837691i | −0.0341134 | + | 0.0341134i | ||||
\(604\) | −53.1147 | + | 53.1147i | −2.16121 | + | 2.16121i | ||||
\(605\) | −1.41999 | + | 1.41999i | −0.0577308 | + | 0.0577308i | ||||
\(606\) | 18.2999 | + | 18.2999i | 0.743384 | + | 0.743384i | ||||
\(607\) | 18.1530i | 0.736807i | 0.929666 | + | 0.368403i | \(0.120096\pi\) | ||||
−0.929666 | + | 0.368403i | \(0.879904\pi\) | |||||||
\(608\) | 142.232 | 5.76825 | ||||||||
\(609\) | −15.7615 | − | 9.79409i | −0.638688 | − | 0.396877i | ||||
\(610\) | 4.32289i | 0.175029i | ||||||||
\(611\) | 23.4152 | + | 6.21248i | 0.947278 | + | 0.251330i | ||||
\(612\) | 25.0668i | 1.01327i | ||||||||
\(613\) | 23.5436 | − | 23.5436i | 0.950917 | − | 0.950917i | −0.0479336 | − | 0.998851i | \(-0.515264\pi\) |
0.998851 | + | 0.0479336i | \(0.0152636\pi\) | |||||||
\(614\) | 43.6002i | 1.75956i | ||||||||
\(615\) | 1.99442 | 0.0804227 | ||||||||
\(616\) | 17.3877 | + | 10.8046i | 0.700572 | + | 0.435331i | ||||
\(617\) | −18.3137 | + | 18.3137i | −0.737283 | + | 0.737283i | −0.972051 | − | 0.234768i | \(-0.924567\pi\) |
0.234768 | + | 0.972051i | \(0.424567\pi\) | |||||||
\(618\) | 3.58199 | + | 3.58199i | 0.144089 | + | 0.144089i | ||||
\(619\) | −7.94244 | + | 7.94244i | −0.319234 | + | 0.319234i | −0.848473 | − | 0.529239i | \(-0.822477\pi\) |
0.529239 | + | 0.848473i | \(0.322477\pi\) | |||||||
\(620\) | 0.417294 | 0.0167589 | ||||||||
\(621\) | 0.423984 | 0.0170139 | ||||||||
\(622\) | 36.2061 | − | 36.2061i | 1.45173 | − | 1.45173i | ||||
\(623\) | 5.50323 | + | 23.5678i | 0.220482 | + | 0.944224i | ||||
\(624\) | 49.7378 | − | 28.8792i | 1.99110 | − | 1.15609i | ||||
\(625\) | −24.4402 | −0.977610 | ||||||||
\(626\) | −61.7374 | − | 61.7374i | −2.46752 | − | 2.46752i | ||||
\(627\) | −4.61524 | −0.184315 | ||||||||
\(628\) | 101.117 | 4.03500 | ||||||||
\(629\) | 25.8581 | + | 25.8581i | 1.03103 | + | 1.03103i | ||||
\(630\) | −0.743473 | + | 1.19646i | −0.0296207 | + | 0.0476681i | ||||
\(631\) | 4.98693 | + | 4.98693i | 0.198527 | + | 0.198527i | 0.799368 | − | 0.600842i | \(-0.205168\pi\) |
−0.600842 | + | 0.799368i | \(0.705168\pi\) | |||||||
\(632\) | 76.4377 | + | 76.4377i | 3.04053 | + | 3.04053i | ||||
\(633\) | − | 19.1491i | − | 0.761108i | ||||||
\(634\) | − | 37.1749i | − | 1.47640i | ||||||
\(635\) | −0.407256 | + | 0.407256i | −0.0161614 | + | 0.0161614i | ||||
\(636\) | −24.0764 | −0.954691 | ||||||||
\(637\) | 13.9568 | − | 21.0287i | 0.552990 | − | 0.833188i | ||||
\(638\) | 15.1703 | 0.600597 | ||||||||
\(639\) | −1.00520 | + | 1.00520i | −0.0397652 | + | 0.0397652i | ||||
\(640\) | 9.13626i | 0.361142i | ||||||||
\(641\) | − | 15.8095i | − | 0.624437i | −0.950010 | − | 0.312219i | \(-0.898928\pi\) | ||
0.950010 | − | 0.312219i | \(-0.101072\pi\) | |||||||
\(642\) | −19.2409 | − | 19.2409i | −0.759376 | − | 0.759376i | ||||
\(643\) | −16.3789 | − | 16.3789i | −0.645922 | − | 0.645922i | 0.306083 | − | 0.952005i | \(-0.400981\pi\) |
−0.952005 | + | 0.306083i | \(0.900981\pi\) | |||||||
\(644\) | 3.30207 | − | 5.31397i | 0.130120 | − | 0.209400i | ||||
\(645\) | 0.255381 | + | 0.255381i | 0.0100556 | + | 0.0100556i | ||||
\(646\) | −72.6677 | −2.85907 | ||||||||
\(647\) | 15.4382 | 0.606939 | 0.303469 | − | 0.952841i | \(-0.401855\pi\) | ||||
0.303469 | + | 0.952841i | \(0.401855\pi\) | |||||||
\(648\) | 6.96297 | + | 6.96297i | 0.273531 | + | 0.273531i | ||||
\(649\) | 0.768607 | 0.0301705 | ||||||||
\(650\) | −12.6308 | + | 47.6064i | −0.495422 | + | 1.86727i | ||||
\(651\) | −0.232726 | − | 0.996656i | −0.00912124 | − | 0.0390620i | ||||
\(652\) | −3.76331 | + | 3.76331i | −0.147383 | + | 0.147383i | ||||
\(653\) | −46.5139 | −1.82023 | −0.910114 | − | 0.414358i | \(-0.864006\pi\) | ||||
−0.910114 | + | 0.414358i | \(0.864006\pi\) | |||||||
\(654\) | 38.0112 | 1.48636 | ||||||||
\(655\) | −2.38394 | + | 2.38394i | −0.0931483 | + | 0.0931483i | ||||
\(656\) | −116.308 | − | 116.308i | −4.54105 | − | 4.54105i | ||||
\(657\) | −6.81854 | + | 6.81854i | −0.266017 | + | 0.266017i | ||||
\(658\) | 41.5625 | + | 25.8267i | 1.62028 | + | 1.00683i | ||||
\(659\) | 22.5967 | 0.880243 | 0.440121 | − | 0.897938i | \(-0.354935\pi\) | ||||
0.440121 | + | 0.897938i | \(0.354935\pi\) | |||||||
\(660\) | − | 0.847625i | − | 0.0329938i | ||||||
\(661\) | 23.1578 | − | 23.1578i | 0.900733 | − | 0.900733i | −0.0947669 | − | 0.995499i | \(-0.530211\pi\) |
0.995499 | + | 0.0947669i | \(0.0302106\pi\) | |||||||
\(662\) | − | 48.0747i | − | 1.86848i | ||||||
\(663\) | −14.0140 | + | 8.13694i | −0.544258 | + | 0.316013i | ||||
\(664\) | − | 96.2644i | − | 3.73579i | ||||||
\(665\) | −2.55299 | − | 1.58641i | −0.0990008 | − | 0.0615185i | ||||
\(666\) | 22.3971 | 0.867870 | ||||||||
\(667\) | − | 2.97372i | − | 0.115143i | ||||||
\(668\) | −28.6614 | − | 28.6614i | −1.10894 | − | 1.10894i | ||||
\(669\) | 3.78445 | − | 3.78445i | 0.146315 | − | 0.146315i | ||||
\(670\) | 0.446000 | − | 0.446000i | 0.0172305 | − | 0.0172305i | ||||
\(671\) | −4.51122 | + | 4.51122i | −0.174154 | + | 0.174154i | ||||
\(672\) | 62.3891 | − | 14.5683i | 2.40671 | − | 0.561983i | ||||
\(673\) | − | 16.3686i | − | 0.630961i | −0.948932 | − | 0.315481i | \(-0.897834\pi\) | ||
0.948932 | − | 0.315481i | \(-0.102166\pi\) | |||||||
\(674\) | −48.3726 | − | 48.3726i | −1.86324 | − | 1.86324i | ||||
\(675\) | −4.96259 | −0.191010 | ||||||||
\(676\) | 62.9682 | + | 35.9434i | 2.42185 | + | 1.38244i | ||||
\(677\) | − | 42.4344i | − | 1.63089i | −0.578836 | − | 0.815444i | \(-0.696493\pi\) | ||
0.578836 | − | 0.815444i | \(-0.303507\pi\) | |||||||
\(678\) | 19.4010 | + | 19.4010i | 0.745091 | + | 0.745091i | ||||
\(679\) | −11.6264 | + | 2.71484i | −0.446180 | + | 0.104186i | ||||
\(680\) | − | 8.56015i | − | 0.328267i | ||||||
\(681\) | −12.8654 | + | 12.8654i | −0.493004 | + | 0.493004i | ||||
\(682\) | 0.591634 | + | 0.591634i | 0.0226548 | + | 0.0226548i | ||||
\(683\) | 17.5222 | + | 17.5222i | 0.670468 | + | 0.670468i | 0.957824 | − | 0.287356i | \(-0.0927762\pi\) |
−0.287356 | + | 0.957824i | \(0.592776\pi\) | |||||||
\(684\) | −23.1641 | + | 23.1641i | −0.885701 | + | 0.885701i | ||||
\(685\) | 2.03680i | 0.0778222i | ||||||||
\(686\) | 39.3772 | − | 32.3797i | 1.50343 | − | 1.23626i | ||||
\(687\) | −6.95379 | − | 6.95379i | −0.265304 | − | 0.265304i | ||||
\(688\) | − | 29.7859i | − | 1.13558i | ||||||
\(689\) | −7.81543 | − | 13.4603i | −0.297744 | − | 0.512795i | ||||
\(690\) | −0.225736 | −0.00859363 | ||||||||
\(691\) | 23.9437 | + | 23.9437i | 0.910860 | + | 0.910860i | 0.996340 | − | 0.0854795i | \(-0.0272422\pi\) |
−0.0854795 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(692\) | 3.65531i | 0.138954i | ||||||||
\(693\) | −2.02445 | + | 0.472722i | −0.0769025 | + | 0.0179572i | ||||
\(694\) | 30.2050 | − | 30.2050i | 1.14657 | − | 1.14657i | ||||
\(695\) | −2.56350 | + | 2.56350i | −0.0972390 | + | 0.0972390i | ||||
\(696\) | 48.8365 | − | 48.8365i | 1.85114 | − | 1.85114i | ||||
\(697\) | 32.7705 | + | 32.7705i | 1.24127 | + | 1.24127i | ||||
\(698\) | − | 33.7797i | − | 1.27858i | ||||||
\(699\) | 19.3196 | 0.730733 | ||||||||
\(700\) | −38.6496 | + | 62.1982i | −1.46082 | + | 2.35087i | ||||
\(701\) | − | 11.2063i | − | 0.423255i | −0.977350 | − | 0.211628i | \(-0.932124\pi\) | ||
0.977350 | − | 0.211628i | \(-0.0678764\pi\) | |||||||
\(702\) | −2.54521 | + | 9.59305i | −0.0960628 | + | 0.362066i | ||||
\(703\) | 47.7906i | 1.80246i | ||||||||
\(704\) | −19.3097 | + | 19.3097i | −0.727760 | + | 0.727760i | ||||
\(705\) | − | 1.29955i | − | 0.0489439i | ||||||
\(706\) | −96.6240 | −3.63649 | ||||||||
\(707\) | −13.1287 | + | 21.1278i | −0.493756 | + | 0.794593i | ||||
\(708\) | 3.85767 | − | 3.85767i | 0.144980 | − | 0.144980i | ||||
\(709\) | −9.73998 | − | 9.73998i | −0.365793 | − | 0.365793i | 0.500148 | − | 0.865940i | \(-0.333279\pi\) |
−0.865940 | + | 0.500148i | \(0.833279\pi\) | |||||||
\(710\) | 0.535186 | − | 0.535186i | 0.0200852 | − | 0.0200852i | ||||
\(711\) | −10.9777 | −0.411698 | ||||||||
\(712\) | −90.0758 | −3.37573 | ||||||||
\(713\) | 0.115974 | − | 0.115974i | 0.00434325 | − | 0.00434325i | ||||
\(714\) | −31.8753 | + | 7.44309i | −1.19290 | + | 0.278551i | ||||
\(715\) | 0.473877 | − | 0.275147i | 0.0177220 | − | 0.0102899i | ||||
\(716\) | −132.371 | −4.94695 | ||||||||
\(717\) | −14.4989 | − | 14.4989i | −0.541473 | − | 0.541473i | ||||
\(718\) | 34.8485 | 1.30053 | ||||||||
\(719\) | −8.87534 | −0.330994 | −0.165497 | − | 0.986210i | \(-0.552923\pi\) | ||||
−0.165497 | + | 0.986210i | \(0.552923\pi\) | |||||||
\(720\) | −2.18163 | − | 2.18163i | −0.0813046 | − | 0.0813046i | ||||
\(721\) | −2.56978 | + | 4.13551i | −0.0957037 | + | 0.154015i | ||||
\(722\) | −30.1694 | − | 30.1694i | −1.12279 | − | 1.12279i | ||||
\(723\) | −5.11691 | − | 5.11691i | −0.190300 | − | 0.190300i | ||||
\(724\) | 41.4364i | 1.53997i | ||||||||
\(725\) | 34.8064i | 1.29268i | ||||||||
\(726\) | −20.2091 | + | 20.2091i | −0.750031 | + | 0.750031i | ||||
\(727\) | −0.610509 | −0.0226425 | −0.0113213 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113213 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(728\) | 64.4039 | + | 68.3816i | 2.38697 | + | 2.53439i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.63030 | − | 3.63030i | 0.134364 | − | 0.134364i | ||||
\(731\) | 8.39241i | 0.310404i | ||||||||
\(732\) | 45.2840i | 1.67375i | ||||||||
\(733\) | 20.8483 | + | 20.8483i | 0.770051 | + | 0.770051i | 0.978115 | − | 0.208064i | \(-0.0667164\pi\) |
−0.208064 | + | 0.978115i | \(0.566716\pi\) | |||||||
\(734\) | 40.9634 | + | 40.9634i | 1.51199 | + | 1.51199i | ||||
\(735\) | −1.28235 | − | 0.434378i | −0.0473001 | − | 0.0160223i | ||||
\(736\) | 7.25977 | + | 7.25977i | 0.267599 | + | 0.267599i | ||||
\(737\) | 0.930862 | 0.0342888 | ||||||||
\(738\) | 28.3843 | 1.04484 | ||||||||
\(739\) | −4.86809 | − | 4.86809i | −0.179076 | − | 0.179076i | 0.611877 | − | 0.790953i | \(-0.290415\pi\) |
−0.790953 | + | 0.611877i | \(0.790415\pi\) | |||||||
\(740\) | −8.77712 | −0.322653 | ||||||||
\(741\) | −20.4695 | − | 5.43094i | −0.751967 | − | 0.199511i | ||||
\(742\) | −7.14900 | − | 30.6158i | −0.262448 | − | 1.12394i | ||||
\(743\) | −1.97638 | + | 1.97638i | −0.0725063 | + | 0.0725063i | −0.742430 | − | 0.669924i | \(-0.766327\pi\) |
0.669924 | + | 0.742430i | \(0.266327\pi\) | |||||||
\(744\) | 3.80921 | 0.139652 | ||||||||
\(745\) | 2.07047 | 0.0758561 | ||||||||
\(746\) | 34.3389 | − | 34.3389i | 1.25724 | − | 1.25724i | ||||
\(747\) | 6.91260 | + | 6.91260i | 0.252919 | + | 0.252919i | ||||
\(748\) | 13.9274 | − | 13.9274i | 0.509237 | − | 0.509237i | ||||
\(749\) | 13.8037 | − | 22.2142i | 0.504378 | − | 0.811687i | ||||
\(750\) | 5.30425 | 0.193684 | ||||||||
\(751\) | − | 12.9526i | − | 0.472649i | −0.971674 | − | 0.236324i | \(-0.924057\pi\) | ||
0.971674 | − | 0.236324i | \(-0.0759428\pi\) | |||||||
\(752\) | −75.7853 | + | 75.7853i | −2.76360 | + | 2.76360i | ||||
\(753\) | 15.9764i | 0.582213i | ||||||||
\(754\) | 67.2832 | + | 17.8515i | 2.45031 | + | 0.650112i | ||||
\(755\) | 2.60497i | 0.0948044i | ||||||||
\(756\) | −7.78819 | + | 12.5334i | −0.283254 | + | 0.455836i | ||||
\(757\) | 29.8979 | 1.08666 | 0.543328 | − | 0.839520i | \(-0.317164\pi\) | ||||
0.543328 | + | 0.839520i | \(0.317164\pi\) | |||||||
\(758\) | − | 17.3346i | − | 0.629619i | ||||||
\(759\) | −0.235571 | − | 0.235571i | −0.00855068 | − | 0.00855068i | ||||
\(760\) | 7.91038 | − | 7.91038i | 0.286940 | − | 0.286940i | ||||
\(761\) | 9.08532 | − | 9.08532i | 0.329343 | − | 0.329343i | −0.522994 | − | 0.852336i | \(-0.675185\pi\) |
0.852336 | + | 0.522994i | \(0.175185\pi\) | |||||||
\(762\) | −5.79601 | + | 5.79601i | −0.209967 | + | 0.209967i | ||||
\(763\) | 8.30758 | + | 35.5775i | 0.300755 | + | 1.28799i | ||||
\(764\) | − | 107.669i | − | 3.89534i | ||||||
\(765\) | 0.614691 | + | 0.614691i | 0.0222242 | + | 0.0222242i | ||||
\(766\) | 35.4329 | 1.28024 | ||||||||
\(767\) | 3.40892 | + | 0.904450i | 0.123089 | + | 0.0326578i | ||||
\(768\) | 60.5183i | 2.18377i | ||||||||
\(769\) | 15.5692 | + | 15.5692i | 0.561441 | + | 0.561441i | 0.929717 | − | 0.368275i | \(-0.120052\pi\) |
−0.368275 | + | 0.929717i | \(0.620052\pi\) | |||||||
\(770\) | 1.07785 | − | 0.251685i | 0.0388430 | − | 0.00907010i | ||||
\(771\) | 10.3506i | 0.372767i | ||||||||
\(772\) | 28.2373 | − | 28.2373i | 1.01628 | − | 1.01628i | ||||
\(773\) | 4.63232 | + | 4.63232i | 0.166613 | + | 0.166613i | 0.785489 | − | 0.618876i | \(-0.212412\pi\) |
−0.618876 | + | 0.785489i | \(0.712412\pi\) | |||||||
\(774\) | 3.63455 | + | 3.63455i | 0.130641 | + | 0.130641i | ||||
\(775\) | −1.35743 | + | 1.35743i | −0.0487604 | + | 0.0487604i | ||||
\(776\) | − | 44.4359i | − | 1.59515i | ||||||
\(777\) | 4.89502 | + | 20.9631i | 0.175608 | + | 0.752047i | ||||
\(778\) | −10.6789 | − | 10.6789i | −0.382859 | − | 0.382859i | ||||
\(779\) | 60.5661i | 2.17001i | ||||||||
\(780\) | 0.997434 | − | 3.75939i | 0.0357139 | − | 0.134608i | ||||
\(781\) | 1.11700 | 0.0399696 | ||||||||
\(782\) | −3.70910 | − | 3.70910i | −0.132637 | − | 0.132637i | ||||
\(783\) | 7.01375i | 0.250651i | ||||||||
\(784\) | 49.4506 | + | 100.113i | 1.76609 | + | 3.57548i | ||||
\(785\) | 2.47960 | − | 2.47960i | 0.0885006 | − | 0.0885006i | ||||
\(786\) | −33.9279 | + | 33.9279i | −1.21017 | + | 1.21017i | ||||
\(787\) | 13.9297 | − | 13.9297i | 0.496539 | − | 0.496539i | −0.413820 | − | 0.910359i | \(-0.635806\pi\) |
0.910359 | + | 0.413820i | \(0.135806\pi\) | |||||||
\(788\) | −61.5360 | − | 61.5360i | −2.19213 | − | 2.19213i | ||||
\(789\) | − | 10.9315i | − | 0.389171i | ||||||
\(790\) | 5.84473 | 0.207946 | ||||||||
\(791\) | −13.9186 | + | 22.3990i | −0.494889 | + | 0.796418i | ||||
\(792\) | − | 7.73742i | − | 0.274937i | ||||||
\(793\) | −25.3167 | + | 14.6996i | −0.899022 | + | 0.521999i | ||||
\(794\) | 83.3184i | 2.95686i | ||||||||
\(795\) | −0.590403 | + | 0.590403i | −0.0209394 | + | 0.0209394i | ||||
\(796\) | 70.5291i | 2.49984i | ||||||||
\(797\) | −5.31507 | −0.188270 | −0.0941348 | − | 0.995559i | \(-0.530008\pi\) | ||||
−0.0941348 | + | 0.995559i | \(0.530008\pi\) | |||||||
\(798\) | −36.3339 | − | 22.5776i | −1.28620 | − | 0.799240i | ||||
\(799\) | 21.3531 | − | 21.3531i | 0.755417 | − | 0.755417i | ||||
\(800\) | −84.9731 | − | 84.9731i | −3.00425 | − | 3.00425i | ||||
\(801\) | 6.46820 | − | 6.46820i | 0.228543 | − | 0.228543i | ||||
\(802\) | 4.27045 | 0.150795 | ||||||||
\(803\) | 7.57693 | 0.267384 | ||||||||
\(804\) | 4.67204 | − | 4.67204i | 0.164770 | − | 0.164770i | ||||
\(805\) | −0.0493360 | − | 0.211283i | −0.00173887 | − | 0.00744676i | ||||
\(806\) | 1.92782 | + | 3.32021i | 0.0679044 | + | 0.116950i | ||||
\(807\) | −0.890429 | −0.0313446 | ||||||||
\(808\) | −65.4640 | − | 65.4640i | −2.30301 | − | 2.30301i | ||||
\(809\) | 19.9739 | 0.702243 | 0.351122 | − | 0.936330i | \(-0.385800\pi\) | ||||
0.351122 | + | 0.936330i | \(0.385800\pi\) | |||||||
\(810\) | 0.532416 | 0.0187072 | ||||||||
\(811\) | 16.2355 | + | 16.2355i | 0.570105 | + | 0.570105i | 0.932158 | − | 0.362053i | \(-0.117924\pi\) |
−0.362053 | + | 0.932158i | \(0.617924\pi\) | |||||||
\(812\) | 87.9062 | + | 54.6244i | 3.08490 | + | 1.91694i | ||||
\(813\) | −15.2932 | − | 15.2932i | −0.536356 | − | 0.536356i | ||||
\(814\) | −12.4441 | − | 12.4441i | −0.436165 | − | 0.436165i | ||||
\(815\) | 0.184568i | 0.00646514i | ||||||||
\(816\) | − | 71.6933i | − | 2.50977i | ||||||
\(817\) | −7.75537 | + | 7.75537i | −0.271326 | + | 0.271326i | ||||
\(818\) | 38.2960 | 1.33899 | ||||||||
\(819\) | −9.53511 | − | 0.285633i | −0.333184 | − | 0.00998083i | ||||
\(820\) | −11.1234 | −0.388447 | ||||||||
\(821\) | −13.7431 | + | 13.7431i | −0.479638 | + | 0.479638i | −0.905016 | − | 0.425378i | \(-0.860141\pi\) |
0.425378 | + | 0.905016i | \(0.360141\pi\) | |||||||
\(822\) | 28.9875i | 1.01106i | ||||||||
\(823\) | − | 37.8629i | − | 1.31982i | −0.751345 | − | 0.659909i | \(-0.770595\pi\) | ||
0.751345 | − | 0.659909i | \(-0.229405\pi\) | |||||||
\(824\) | −12.8138 | − | 12.8138i | −0.446389 | − | 0.446389i | ||||
\(825\) | 2.75727 | + | 2.75727i | 0.0959960 | + | 0.0959960i | ||||
\(826\) | 6.05092 | + | 3.76000i | 0.210538 | + | 0.130827i | ||||
\(827\) | −22.6682 | − | 22.6682i | −0.788252 | − | 0.788252i | 0.192956 | − | 0.981207i | \(-0.438193\pi\) |
−0.981207 | + | 0.192956i | \(0.938193\pi\) | |||||||
\(828\) | −2.36468 | −0.0821783 | ||||||||
\(829\) | −33.7537 | −1.17231 | −0.586156 | − | 0.810198i | \(-0.699360\pi\) | ||||
−0.586156 | + | 0.810198i | \(0.699360\pi\) | |||||||
\(830\) | −3.68038 | − | 3.68038i | −0.127748 | − | 0.127748i | ||||
\(831\) | 9.83129 | 0.341044 | ||||||||
\(832\) | −108.365 | + | 62.9198i | −3.75687 | + | 2.18135i | ||||
\(833\) | −13.9331 | − | 28.2077i | −0.482752 | − | 0.977339i | ||||
\(834\) | −36.4834 | + | 36.4834i | −1.26332 | + | 1.26332i | ||||
\(835\) | −1.40568 | −0.0486454 | ||||||||
\(836\) | 25.7405 | 0.890254 | ||||||||
\(837\) | −0.273533 | + | 0.273533i | −0.00945468 | + | 0.00945468i | ||||
\(838\) | −29.6711 | − | 29.6711i | −1.02497 | − | 1.02497i | ||||
\(839\) | −29.1042 | + | 29.1042i | −1.00479 | + | 1.00479i | −0.00479972 | + | 0.999988i | \(0.501528\pi\) |
−0.999988 | + | 0.00479972i | \(0.998472\pi\) | |||||||
\(840\) | 2.65961 | − | 4.28008i | 0.0917654 | − | 0.147677i | ||||
\(841\) | 20.1927 | 0.696299 | ||||||||
\(842\) | − | 26.5291i | − | 0.914254i | ||||||
\(843\) | 12.8526 | − | 12.8526i | 0.442666 | − | 0.442666i | ||||
\(844\) | 106.800i | 3.67620i | ||||||||
\(845\) | 2.42552 | − | 0.662704i | 0.0834404 | − | 0.0227977i | ||||
\(846\) | − | 18.4950i | − | 0.635872i | ||||||
\(847\) | −23.3320 | − | 14.4984i | −0.801698 | − | 0.498171i | ||||
\(848\) | 68.8605 | 2.36468 | ||||||||
\(849\) | 2.25769i | 0.0774838i | ||||||||
\(850\) | 43.4137 | + | 43.4137i | 1.48908 | + | 1.48908i | ||||
\(851\) | −2.43932 | + | 2.43932i | −0.0836190 | + | 0.0836190i | ||||
\(852\) | 5.60629 | − | 5.60629i | 0.192068 | − | 0.192068i | ||||
\(853\) | 9.97247 | − | 9.97247i | 0.341451 | − | 0.341451i | −0.515462 | − | 0.856913i | \(-0.672380\pi\) |
0.856913 | + | 0.515462i | \(0.172380\pi\) | |||||||
\(854\) | −57.5837 | + | 13.4462i | −1.97047 | + | 0.460118i | ||||
\(855\) | 1.13606i | 0.0388526i | ||||||||
\(856\) | 68.8300 | + | 68.8300i | 2.35256 | + | 2.35256i | ||||
\(857\) | −20.2894 | −0.693071 | −0.346536 | − | 0.938037i | \(-0.612642\pi\) | ||||
−0.346536 | + | 0.938037i | \(0.612642\pi\) | |||||||
\(858\) | 6.74416 | − | 3.91586i | 0.230242 | − | 0.133685i | ||||
\(859\) | − | 1.65917i | − | 0.0566102i | −0.999599 | − | 0.0283051i | \(-0.990989\pi\) | ||
0.999599 | − | 0.0283051i | \(-0.00901100\pi\) | |||||||
\(860\) | −1.42433 | − | 1.42433i | −0.0485694 | − | 0.0485694i | ||||
\(861\) | 6.20356 | + | 26.5670i | 0.211417 | + | 0.905400i | ||||
\(862\) | 61.5550i | 2.09657i | ||||||||
\(863\) | 17.5175 | − | 17.5175i | 0.596303 | − | 0.596303i | −0.343024 | − | 0.939327i | \(-0.611451\pi\) |
0.939327 | + | 0.343024i | \(0.111451\pi\) | |||||||
\(864\) | −17.1227 | − | 17.1227i | −0.582527 | − | 0.582527i | ||||
\(865\) | 0.0896359 | + | 0.0896359i | 0.00304771 | + | 0.00304771i | ||||
\(866\) | 25.8621 | − | 25.8621i | 0.878830 | − | 0.878830i | ||||
\(867\) | 3.20012i | 0.108682i | ||||||||
\(868\) | 1.29798 | + | 5.55863i | 0.0440562 | + | 0.188672i | ||||
\(869\) | 6.09937 | + | 6.09937i | 0.206907 | + | 0.206907i | ||||
\(870\) | − | 3.73423i | − | 0.126602i | ||||||
\(871\) | 4.12856 | + | 1.09538i | 0.139891 | + | 0.0371156i | ||||
\(872\) | −135.977 | −4.60475 | ||||||||
\(873\) | 3.19087 | + | 3.19087i | 0.107995 | + | 0.107995i | ||||
\(874\) | − | 6.85511i | − | 0.231878i | ||||||
\(875\) | 1.15928 | + | 4.96464i | 0.0391906 | + | 0.167835i | ||||
\(876\) | 38.0289 | − | 38.0289i | 1.28488 | − | 1.28488i | ||||
\(877\) | 18.6974 | − | 18.6974i | 0.631366 | − | 0.631366i | −0.317044 | − | 0.948411i | \(-0.602690\pi\) |
0.948411 | + | 0.317044i | \(0.102690\pi\) | |||||||
\(878\) | −2.87316 | + | 2.87316i | −0.0969645 | + | 0.0969645i | ||||
\(879\) | −3.42417 | − | 3.42417i | −0.115494 | − | 0.115494i | ||||
\(880\) | 2.42428i | 0.0817225i | ||||||||
\(881\) | 21.0446 | 0.709009 | 0.354505 | − | 0.935054i | \(-0.384650\pi\) | ||||
0.354505 | + | 0.935054i | \(0.384650\pi\) | |||||||
\(882\) | −18.2502 | − | 6.18201i | −0.614516 | − | 0.208159i | ||||
\(883\) | 54.5106i | 1.83443i | 0.398395 | + | 0.917214i | \(0.369567\pi\) | ||||
−0.398395 | + | 0.917214i | \(0.630433\pi\) | |||||||
\(884\) | 78.1599 | − | 45.3820i | 2.62880 | − | 1.52636i | ||||
\(885\) | − | 0.189196i | − | 0.00635976i | ||||||
\(886\) | −0.974984 | + | 0.974984i | −0.0327552 | + | 0.0327552i | ||||
\(887\) | 19.8555i | 0.666682i | 0.942806 | + | 0.333341i | \(0.108176\pi\) | ||||
−0.942806 | + | 0.333341i | \(0.891824\pi\) | |||||||
\(888\) | −80.1207 | −2.68867 | ||||||||
\(889\) | −6.69167 | − | 4.15816i | −0.224431 | − | 0.139460i | ||||
\(890\) | −3.44378 | + | 3.44378i | −0.115436 | + | 0.115436i | ||||
\(891\) | 0.555612 | + | 0.555612i | 0.0186137 | + | 0.0186137i | ||||
\(892\) | −21.1070 | + | 21.1070i | −0.706713 | + | 0.706713i | ||||
\(893\) | 39.4645 | 1.32063 | ||||||||
\(894\) | 29.4667 | 0.985512 | ||||||||
\(895\) | −3.24602 | + | 3.24602i | −0.108503 | + | 0.108503i | ||||
\(896\) | −121.701 | + | 28.4180i | −4.06575 | + | 0.949378i | ||||
\(897\) | −0.767598 | − | 1.32201i | −0.0256294 | − | 0.0441406i | ||||
\(898\) | 6.04031 | 0.201568 | ||||||||
\(899\) | 1.91849 | + | 1.91849i | 0.0639853 | + | 0.0639853i | ||||
\(900\) | 27.6778 | 0.922592 | ||||||||
\(901\) | −19.4020 | −0.646374 | ||||||||
\(902\) | −15.7707 | − | 15.7707i | −0.525106 | − | 0.525106i | ||||
\(903\) | −2.60750 | + | 4.19620i | −0.0867720 | + | 0.139641i | ||||
\(904\) | −69.4028 | − | 69.4028i | −2.30830 | − | 2.30830i | ||||
\(905\) | 1.01611 | + | 1.01611i | 0.0337765 | + | 0.0337765i | ||||
\(906\) | 37.0735i | 1.23169i | ||||||||
\(907\) | − | 18.8416i | − | 0.625626i | −0.949815 | − | 0.312813i | \(-0.898729\pi\) | ||
0.949815 | − | 0.312813i | \(-0.101271\pi\) | |||||||
\(908\) | 71.7541 | − | 71.7541i | 2.38124 | − | 2.38124i | ||||
\(909\) | 9.40173 | 0.311836 | ||||||||
\(910\) | 5.07665 | + | 0.152076i | 0.168289 | + | 0.00504126i | ||||
\(911\) | 0.701569 | 0.0232440 | 0.0116220 | − | 0.999932i | \(-0.496301\pi\) | ||||
0.0116220 | + | 0.999932i | \(0.496301\pi\) | |||||||
\(912\) | 66.2513 | − | 66.2513i | 2.19380 | − | 2.19380i | ||||
\(913\) | − | 7.68144i | − | 0.254219i | ||||||
\(914\) | 82.1404i | 2.71696i | ||||||||
\(915\) | 1.11046 | + | 1.11046i | 0.0367106 | + | 0.0367106i | ||||
\(916\) | 38.7832 | + | 38.7832i | 1.28143 | + | 1.28143i | ||||
\(917\) | −39.1708 | − | 24.3405i | −1.29353 | − | 0.803794i | ||||
\(918\) | 8.74820 | + | 8.74820i | 0.288734 | + | 0.288734i | ||||
\(919\) | 10.6633 | 0.351750 | 0.175875 | − | 0.984412i | \(-0.443724\pi\) | ||||
0.175875 | + | 0.984412i | \(0.443724\pi\) | |||||||
\(920\) | 0.807522 | 0.0266232 | ||||||||
\(921\) | 11.2000 | + | 11.2000i | 0.369052 | + | 0.369052i | ||||
\(922\) | 2.11187 | 0.0695508 | ||||||||
\(923\) | 4.95414 | + | 1.31442i | 0.163067 | + | 0.0432648i | ||||
\(924\) | 11.2909 | − | 2.63651i | 0.371444 | − | 0.0867346i | ||||
\(925\) | 28.5515 | − | 28.5515i | 0.938766 | − | 0.938766i | ||||
\(926\) | 41.8726 | 1.37602 | ||||||||
\(927\) | 1.84027 | 0.0604425 | ||||||||
\(928\) | −120.095 | + | 120.095i | −3.94230 | + | 3.94230i | ||||
\(929\) | 1.31466 | + | 1.31466i | 0.0431326 | + | 0.0431326i | 0.728344 | − | 0.685212i | \(-0.240290\pi\) |
−0.685212 | + | 0.728344i | \(0.740290\pi\) | |||||||
\(930\) | 0.145633 | − | 0.145633i | 0.00477551 | − | 0.00477551i | ||||
\(931\) | 13.1911 | − | 38.9420i | 0.432321 | − | 1.27627i | ||||
\(932\) | −107.751 | −3.52949 | ||||||||
\(933\) | − | 18.6012i | − | 0.608974i | ||||||
\(934\) | −61.9821 | + | 61.9821i | −2.02812 | + | 2.02812i | ||||
\(935\) | − | 0.683059i | − | 0.0223384i | ||||||
\(936\) | 9.10493 | − | 34.3170i | 0.297604 | − | 1.12169i | ||||
\(937\) | 15.3362i | 0.501012i | 0.968115 | + | 0.250506i | \(0.0805969\pi\) | ||||
−0.968115 | + | 0.250506i | \(0.919403\pi\) | |||||||
\(938\) | 7.32829 | + | 4.55375i | 0.239277 | + | 0.148685i | ||||
\(939\) | −31.7181 | −1.03508 | ||||||||
\(940\) | 7.24796i | 0.236402i | ||||||||
\(941\) | 28.8840 | + | 28.8840i | 0.941590 | + | 0.941590i | 0.998386 | − | 0.0567959i | \(-0.0180884\pi\) |
−0.0567959 | + | 0.998386i | \(0.518088\pi\) | |||||||
\(942\) | 35.2893 | − | 35.2893i | 1.14979 | − | 1.14979i | ||||
\(943\) | −3.09141 | + | 3.09141i | −0.100670 | + | 0.100670i | ||||
\(944\) | −11.0333 | + | 11.0333i | −0.359102 | + | 0.359102i | ||||
\(945\) | 0.116363 | + | 0.498328i | 0.00378528 | + | 0.0162106i | ||||
\(946\) | − | 4.03880i | − | 0.131313i | ||||||
\(947\) | −25.5186 | − | 25.5186i | −0.829243 | − | 0.829243i | 0.158169 | − | 0.987412i | \(-0.449441\pi\) |
−0.987412 | + | 0.158169i | \(0.949441\pi\) | |||||||
\(948\) | 61.2260 | 1.98853 | ||||||||
\(949\) | 33.6052 | + | 8.91607i | 1.09087 | + | 0.289428i | ||||
\(950\) | 80.2367i | 2.60322i | ||||||||
\(951\) | −9.54944 | − | 9.54944i | −0.309662 | − | 0.309662i | ||||
\(952\) | 114.027 | − | 26.6260i | 3.69563 | − | 0.862954i | ||||
\(953\) | 6.16200i | 0.199607i | 0.995007 | + | 0.0998034i | \(0.0318214\pi\) | ||||
−0.995007 | + | 0.0998034i | \(0.968179\pi\) | |||||||
\(954\) | −8.40254 | + | 8.40254i | −0.272042 | + | 0.272042i | ||||
\(955\) | −2.64028 | − | 2.64028i | −0.0854374 | − | 0.0854374i | ||||
\(956\) | 80.8647 | + | 80.8647i | 2.61535 | + | 2.61535i | ||||
\(957\) | 3.89692 | − | 3.89692i | 0.125970 | − | 0.125970i | ||||
\(958\) | 13.6827i | 0.442067i | ||||||||
\(959\) | −27.1316 | + | 6.33540i | −0.876124 | + | 0.204581i | ||||
\(960\) | 4.75316 | + | 4.75316i | 0.153408 | + | 0.153408i | ||||
\(961\) | − | 30.8504i | − | 0.995173i | ||||||
\(962\) | −40.5486 | − | 69.8355i | −1.30734 | − | 2.25159i | ||||
\(963\) | −9.88514 | −0.318544 | ||||||||
\(964\) | 28.5385 | + | 28.5385i | 0.919162 | + | 0.919162i | ||||
\(965\) | − | 1.38487i | − | 0.0445807i | ||||||
\(966\) | −0.702144 | − | 3.00696i | −0.0225911 | − | 0.0967472i | ||||
\(967\) | 4.83625 | − | 4.83625i | 0.155523 | − | 0.155523i | −0.625056 | − | 0.780580i | \(-0.714924\pi\) |
0.780580 | + | 0.625056i | \(0.214924\pi\) | |||||||
\(968\) | 72.2937 | − | 72.2937i | 2.32361 | − | 2.32361i | ||||
\(969\) | −18.6668 | + | 18.6668i | −0.599664 | + | 0.599664i | ||||
\(970\) | −1.69887 | − | 1.69887i | −0.0545475 | − | 0.0545475i | ||||
\(971\) | − | 3.33201i | − | 0.106929i | −0.998570 | − | 0.0534647i | \(-0.982974\pi\) | ||
0.998570 | − | 0.0534647i | \(-0.0170265\pi\) | |||||||
\(972\) | 5.57728 | 0.178891 | ||||||||
\(973\) | −42.1212 | − | 26.1738i | −1.35034 | − | 0.839095i | ||||
\(974\) | − | 13.9205i | − | 0.446043i | ||||||
\(975\) | 8.98447 | + | 15.4737i | 0.287733 | + | 0.495554i | ||||
\(976\) | − | 129.516i | − | 4.14571i | ||||||
\(977\) | −27.4570 | + | 27.4570i | −0.878427 | + | 0.878427i | −0.993372 | − | 0.114945i | \(-0.963331\pi\) |
0.114945 | + | 0.993372i | \(0.463331\pi\) | |||||||
\(978\) | 2.62675i | 0.0839942i | ||||||||
\(979\) | −7.18762 | −0.229717 | ||||||||
\(980\) | 7.15201 | + | 2.42265i | 0.228463 | + | 0.0773887i | ||||
\(981\) | 9.76428 | − | 9.76428i | 0.311749 | − | 0.311749i | ||||
\(982\) | 8.26767 | + | 8.26767i | 0.263832 | + | 0.263832i | ||||
\(983\) | −26.1066 | + | 26.1066i | −0.832670 | + | 0.832670i | −0.987881 | − | 0.155211i | \(-0.950394\pi\) |
0.155211 | + | 0.987881i | \(0.450394\pi\) | |||||||
\(984\) | −101.539 | −3.23693 | ||||||||
\(985\) | −3.01798 | −0.0961609 | ||||||||
\(986\) | 61.3577 | − | 61.3577i | 1.95403 | − | 1.95403i | ||||
\(987\) | 17.3109 | − | 4.04220i | 0.551011 | − | 0.128665i | ||||
\(988\) | 114.164 | + | 30.2899i | 3.63205 | + | 0.963649i | ||||
\(989\) | −0.791697 | −0.0251745 | ||||||||
\(990\) | −0.295817 | − | 0.295817i | −0.00940168 | − | 0.00940168i | ||||
\(991\) | −4.19648 | −0.133306 | −0.0666529 | − | 0.997776i | \(-0.521232\pi\) | ||||
−0.0666529 | + | 0.997776i | \(0.521232\pi\) | |||||||
\(992\) | −9.36727 | −0.297411 | ||||||||
\(993\) | −12.3494 | − | 12.3494i | −0.391896 | − | 0.391896i | ||||
\(994\) | 8.79371 | + | 5.46436i | 0.278919 | + | 0.173319i | ||||
\(995\) | 1.72952 | + | 1.72952i | 0.0548295 | + | 0.0548295i | ||||
\(996\) | −38.5535 | − | 38.5535i | −1.22161 | − | 1.22161i | ||||
\(997\) | − | 47.2495i | − | 1.49641i | −0.663470 | − | 0.748203i | \(-0.730917\pi\) | ||
0.663470 | − | 0.748203i | \(-0.269083\pi\) | |||||||
\(998\) | − | 14.3837i | − | 0.455308i | ||||||
\(999\) | 5.75334 | − | 5.75334i | 0.182028 | − | 0.182028i |
(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 | 273.2.p.e.265.1 | yes | 12 | |
3.2 | odd | 2 | 819.2.y.g.811.6 | 12 | |||
7.6 | odd | 2 | 273.2.p.f.265.1 | yes | 12 | ||
13.8 | odd | 4 | 273.2.p.f.34.1 | yes | 12 | ||
21.20 | even | 2 | 819.2.y.f.811.6 | 12 | |||
39.8 | even | 4 | 819.2.y.f.307.6 | 12 | |||
91.34 | even | 4 | inner | 273.2.p.e.34.1 | ✓ | 12 | |
273.125 | odd | 4 | 819.2.y.g.307.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.p.e.34.1 | ✓ | 12 | 91.34 | even | 4 | inner | |
273.2.p.e.265.1 | yes | 12 | 1.1 | even | 1 | trivial | |
273.2.p.f.34.1 | yes | 12 | 13.8 | odd | 4 | ||
273.2.p.f.265.1 | yes | 12 | 7.6 | odd | 2 | ||
819.2.y.f.307.6 | 12 | 39.8 | even | 4 | |||
819.2.y.f.811.6 | 12 | 21.20 | even | 2 | |||
819.2.y.g.307.6 | 12 | 273.125 | odd | 4 | |||
819.2.y.g.811.6 | 12 | 3.2 | odd | 2 |