Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.4 | ||
Root | \(1.53767i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.301 |
Dual form | 375.2.g.d.76.4 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24400 | − | 0.903822i | 0.879644 | − | 0.639099i | −0.0535136 | − | 0.998567i | \(-0.517042\pi\) |
0.933157 | + | 0.359469i | \(0.117042\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 0.112618 | − | 0.346603i | 0.0563090 | − | 0.173301i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.475167 | + | 1.46241i | 0.193986 | + | 0.597028i | ||||
\(7\) | 1.68601 | 0.637251 | 0.318625 | − | 0.947881i | \(-0.396779\pi\) | ||||
0.318625 | + | 0.947881i | \(0.396779\pi\) | |||||||
\(8\) | 0.777165 | + | 2.39187i | 0.274769 | + | 0.845653i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.40891 | − | 1.75017i | 0.726312 | − | 0.527697i | −0.162082 | − | 0.986777i | \(-0.551821\pi\) |
0.888395 | + | 0.459080i | \(0.151821\pi\) | |||||||
\(12\) | 0.294838 | + | 0.214212i | 0.0851123 | + | 0.0618377i | ||||
\(13\) | −0.188414 | − | 0.136890i | −0.0522565 | − | 0.0379666i | 0.561350 | − | 0.827578i | \(-0.310282\pi\) |
−0.613607 | + | 0.789612i | \(0.710282\pi\) | |||||||
\(14\) | 2.09740 | − | 1.52385i | 0.560554 | − | 0.407266i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.71829 | + | 2.70150i | 0.929573 | + | 0.675375i | ||||
\(17\) | 2.30496 | + | 7.09394i | 0.559035 | + | 1.72053i | 0.685041 | + | 0.728505i | \(0.259784\pi\) |
−0.126005 | + | 0.992030i | \(0.540216\pi\) | |||||||
\(18\) | −1.53767 | −0.362433 | ||||||||
\(19\) | 0.232853 | + | 0.716646i | 0.0534200 | + | 0.164410i | 0.974207 | − | 0.225656i | \(-0.0724524\pi\) |
−0.920787 | + | 0.390065i | \(0.872452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.521005 | + | 1.60349i | −0.113693 | + | 0.349910i | ||||
\(22\) | 1.41484 | − | 4.35444i | 0.301646 | − | 0.928370i | ||||
\(23\) | −0.706046 | + | 0.512972i | −0.147221 | + | 0.106962i | −0.658958 | − | 0.752180i | \(-0.729002\pi\) |
0.511737 | + | 0.859142i | \(0.329002\pi\) | |||||||
\(24\) | −2.51496 | −0.513364 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.358112 | −0.0702315 | ||||||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 0.189875 | − | 0.584375i | 0.0358830 | − | 0.110436i | ||||
\(29\) | 2.12444 | − | 6.53835i | 0.394498 | − | 1.21414i | −0.534854 | − | 0.844945i | \(-0.679633\pi\) |
0.929352 | − | 0.369195i | \(-0.120367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.03433 | − | 9.33870i | −0.544981 | − | 1.67728i | −0.721035 | − | 0.692899i | \(-0.756333\pi\) |
0.176054 | − | 0.984381i | \(-0.443667\pi\) | |||||||
\(32\) | 2.03733 | 0.360152 | ||||||||
\(33\) | 0.920120 | + | 2.83184i | 0.160172 | + | 0.492960i | ||||
\(34\) | 9.27904 | + | 6.74162i | 1.59134 | + | 1.15618i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.294838 | + | 0.214212i | −0.0491396 | + | 0.0357020i | ||||
\(37\) | −8.19304 | − | 5.95259i | −1.34693 | − | 0.978600i | −0.999158 | − | 0.0410198i | \(-0.986939\pi\) |
−0.347769 | − | 0.937580i | \(-0.613061\pi\) | |||||||
\(38\) | 0.937390 | + | 0.681054i | 0.152065 | + | 0.110482i | ||||
\(39\) | 0.188414 | − | 0.136890i | 0.0301703 | − | 0.0219200i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.07210 | − | 2.23201i | −0.479781 | − | 0.348581i | 0.321460 | − | 0.946923i | \(-0.395826\pi\) |
−0.801241 | + | 0.598342i | \(0.795826\pi\) | |||||||
\(42\) | 0.801135 | + | 2.46564i | 0.123618 | + | 0.380457i | ||||
\(43\) | −5.27322 | −0.804159 | −0.402079 | − | 0.915605i | \(-0.631712\pi\) | ||||
−0.402079 | + | 0.915605i | \(0.631712\pi\) | |||||||
\(44\) | −0.335328 | − | 1.03203i | −0.0505526 | − | 0.155585i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.414688 | + | 1.27628i | −0.0611425 | + | 0.188177i | ||||
\(47\) | −2.64749 | + | 8.14814i | −0.386176 | + | 1.18853i | 0.549447 | + | 0.835529i | \(0.314839\pi\) |
−0.935623 | + | 0.353000i | \(0.885161\pi\) | |||||||
\(48\) | −3.71829 | + | 2.70150i | −0.536689 | + | 0.389928i | ||||
\(49\) | −4.15738 | −0.593911 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.45901 | −1.04447 | ||||||||
\(52\) | −0.0686654 | + | 0.0498883i | −0.00952217 | + | 0.00691826i | ||||
\(53\) | 1.84754 | − | 5.68614i | 0.253779 | − | 0.781051i | −0.740289 | − | 0.672289i | \(-0.765311\pi\) |
0.994068 | − | 0.108762i | \(-0.0346887\pi\) | |||||||
\(54\) | 0.475167 | − | 1.46241i | 0.0646621 | − | 0.199009i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.31031 | + | 4.03270i | 0.175097 | + | 0.538893i | ||||
\(57\) | −0.753527 | −0.0998070 | ||||||||
\(58\) | −3.26669 | − | 10.0538i | −0.428937 | − | 1.32013i | ||||
\(59\) | 3.11564 | + | 2.26365i | 0.405622 | + | 0.294702i | 0.771827 | − | 0.635833i | \(-0.219343\pi\) |
−0.366205 | + | 0.930534i | \(0.619343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.55679 | − | 2.58416i | 0.455400 | − | 0.330867i | −0.336324 | − | 0.941746i | \(-0.609184\pi\) |
0.791724 | + | 0.610879i | \(0.209184\pi\) | |||||||
\(62\) | −12.2152 | − | 8.87488i | −1.55134 | − | 1.12711i | ||||
\(63\) | −1.36401 | − | 0.991010i | −0.171849 | − | 0.124856i | ||||
\(64\) | −4.90214 | + | 3.56161i | −0.612768 | + | 0.445202i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.70411 | + | 2.69119i | 0.455944 | + | 0.331263i | ||||
\(67\) | 0.554013 | + | 1.70508i | 0.0676835 | + | 0.208308i | 0.979178 | − | 0.203004i | \(-0.0650705\pi\) |
−0.911494 | + | 0.411312i | \(0.865070\pi\) | |||||||
\(68\) | 2.71836 | 0.329650 | ||||||||
\(69\) | −0.269686 | − | 0.830007i | −0.0324663 | − | 0.0999211i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.35179 | + | 4.16039i | −0.160428 | + | 0.493748i | −0.998670 | − | 0.0515506i | \(-0.983584\pi\) |
0.838242 | + | 0.545298i | \(0.183584\pi\) | |||||||
\(72\) | 0.777165 | − | 2.39187i | 0.0915897 | − | 0.281884i | ||||
\(73\) | 12.1780 | − | 8.84783i | 1.42533 | − | 1.03556i | 0.434463 | − | 0.900690i | \(-0.356938\pi\) |
0.990863 | − | 0.134870i | \(-0.0430617\pi\) | |||||||
\(74\) | −15.5723 | −1.81024 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.274615 | 0.0315005 | ||||||||
\(77\) | 4.06143 | − | 2.95080i | 0.462843 | − | 0.336275i | ||||
\(78\) | 0.110663 | − | 0.340585i | 0.0125301 | − | 0.0385636i | ||||
\(79\) | 2.27926 | − | 7.01484i | 0.256437 | − | 0.789232i | −0.737106 | − | 0.675777i | \(-0.763808\pi\) |
0.993543 | − | 0.113455i | \(-0.0361917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −5.83904 | −0.644814 | ||||||||
\(83\) | 1.34253 | + | 4.13188i | 0.147362 | + | 0.453532i | 0.997307 | − | 0.0733383i | \(-0.0233653\pi\) |
−0.849946 | + | 0.526871i | \(0.823365\pi\) | |||||||
\(84\) | 0.497099 | + | 0.361163i | 0.0542379 | + | 0.0394061i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.55991 | + | 4.76605i | −0.707373 | + | 0.513937i | ||||
\(87\) | 5.56185 | + | 4.04092i | 0.596293 | + | 0.433232i | ||||
\(88\) | 6.05830 | + | 4.40161i | 0.645817 | + | 0.469213i | ||||
\(89\) | −9.79170 | + | 7.11409i | −1.03792 | + | 0.754092i | −0.969878 | − | 0.243591i | \(-0.921675\pi\) |
−0.0680399 | + | 0.997683i | \(0.521675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.317667 | − | 0.230798i | −0.0333005 | − | 0.0241942i | ||||
\(92\) | 0.0982841 | + | 0.302487i | 0.0102468 | + | 0.0315365i | ||||
\(93\) | 9.81929 | 1.01821 | ||||||||
\(94\) | 4.07098 | + | 12.5292i | 0.419889 | + | 1.29229i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.629569 | + | 1.93761i | −0.0642551 | + | 0.197757i | ||||
\(97\) | 2.92771 | − | 9.01055i | 0.297264 | − | 0.914883i | −0.685188 | − | 0.728366i | \(-0.740280\pi\) |
0.982452 | − | 0.186517i | \(-0.0597199\pi\) | |||||||
\(98\) | −5.17180 | + | 3.75753i | −0.522430 | + | 0.379568i | ||||
\(99\) | −2.97757 | −0.299257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.54468 | −0.651220 | −0.325610 | − | 0.945504i | \(-0.605570\pi\) | ||||
−0.325610 | + | 0.945504i | \(0.605570\pi\) | |||||||
\(102\) | −9.27904 | + | 6.74162i | −0.918762 | + | 0.667520i | ||||
\(103\) | −0.216560 | + | 0.666504i | −0.0213383 | + | 0.0656726i | −0.961159 | − | 0.275996i | \(-0.910992\pi\) |
0.939820 | + | 0.341669i | \(0.110992\pi\) | |||||||
\(104\) | 0.180995 | − | 0.557047i | 0.0177481 | − | 0.0546229i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.84091 | − | 8.74342i | −0.275934 | − | 0.849236i | ||||
\(107\) | 12.5288 | 1.21120 | 0.605602 | − | 0.795768i | \(-0.292933\pi\) | ||||
0.605602 | + | 0.795768i | \(0.292933\pi\) | |||||||
\(108\) | −0.112618 | − | 0.346603i | −0.0108367 | − | 0.0333519i | ||||
\(109\) | −3.46541 | − | 2.51776i | −0.331926 | − | 0.241158i | 0.409322 | − | 0.912390i | \(-0.365765\pi\) |
−0.741247 | + | 0.671232i | \(0.765765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.19304 | − | 5.95259i | 0.777649 | − | 0.564995i | ||||
\(112\) | 6.26907 | + | 4.55474i | 0.592371 | + | 0.430383i | ||||
\(113\) | −6.65628 | − | 4.83607i | −0.626170 | − | 0.454939i | 0.228901 | − | 0.973450i | \(-0.426487\pi\) |
−0.855071 | + | 0.518511i | \(0.826487\pi\) | |||||||
\(114\) | −0.937390 | + | 0.681054i | −0.0877946 | + | 0.0637865i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.02696 | − | 1.47267i | −0.188198 | − | 0.136734i | ||||
\(117\) | 0.0719676 | + | 0.221493i | 0.00665340 | + | 0.0204771i | ||||
\(118\) | 5.92180 | 0.545146 | ||||||||
\(119\) | 3.88618 | + | 11.9604i | 0.356246 | + | 1.09641i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.659464 | + | 2.02962i | −0.0599512 | + | 0.184511i | ||||
\(122\) | 2.08904 | − | 6.42940i | 0.189133 | − | 0.582091i | ||||
\(123\) | 3.07210 | − | 2.23201i | 0.277002 | − | 0.201253i | ||||
\(124\) | −3.57854 | −0.321362 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.59253 | −0.230961 | ||||||||
\(127\) | −9.66627 | + | 7.02296i | −0.857743 | + | 0.623187i | −0.927270 | − | 0.374393i | \(-0.877851\pi\) |
0.0695269 | + | 0.997580i | \(0.477851\pi\) | |||||||
\(128\) | −4.13836 | + | 12.7366i | −0.365783 | + | 1.12576i | ||||
\(129\) | 1.62951 | − | 5.01513i | 0.143471 | − | 0.441558i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.63068 | + | 20.4071i | 0.579326 | + | 1.78298i | 0.620953 | + | 0.783848i | \(0.286746\pi\) |
−0.0416276 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(132\) | 1.08514 | 0.0944497 | ||||||||
\(133\) | 0.392591 | + | 1.20827i | 0.0340420 | + | 0.104770i | ||||
\(134\) | 2.23028 | + | 1.62039i | 0.192667 | + | 0.139981i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.1764 | + | 11.0263i | −1.30137 | + | 0.945500i | ||||
\(137\) | −8.10570 | − | 5.88914i | −0.692517 | − | 0.503143i | 0.184970 | − | 0.982744i | \(-0.440781\pi\) |
−0.877487 | + | 0.479601i | \(0.840781\pi\) | |||||||
\(138\) | −1.08567 | − | 0.788784i | −0.0924182 | − | 0.0671458i | ||||
\(139\) | 5.31902 | − | 3.86450i | 0.451154 | − | 0.327782i | −0.338897 | − | 0.940823i | \(-0.610054\pi\) |
0.790051 | + | 0.613041i | \(0.210054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.93123 | − | 5.03583i | −0.583714 | − | 0.424093i | ||||
\(142\) | 2.07862 | + | 6.39733i | 0.174434 | + | 0.536852i | ||||
\(143\) | −0.693452 | −0.0579894 | ||||||||
\(144\) | −1.42026 | − | 4.37112i | −0.118355 | − | 0.364260i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.15261 | − | 22.0135i | 0.591954 | − | 1.82185i | ||||
\(147\) | 1.28470 | − | 3.95390i | 0.105960 | − | 0.326112i | ||||
\(148\) | −2.98587 | + | 2.16936i | −0.245437 | + | 0.178320i | ||||
\(149\) | 10.9143 | 0.894132 | 0.447066 | − | 0.894501i | \(-0.352469\pi\) | ||||
0.447066 | + | 0.894501i | \(0.352469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4128 | 1.66117 | 0.830584 | − | 0.556894i | \(-0.188007\pi\) | ||||
0.830584 | + | 0.556894i | \(0.188007\pi\) | |||||||
\(152\) | −1.53316 | + | 1.11390i | −0.124356 | + | 0.0903496i | ||||
\(153\) | 2.30496 | − | 7.09394i | 0.186345 | − | 0.573511i | ||||
\(154\) | 2.38544 | − | 7.34162i | 0.192224 | − | 0.591605i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0262278 | − | 0.0807210i | −0.00209991 | − | 0.00646285i | ||||
\(157\) | 3.49944 | 0.279286 | 0.139643 | − | 0.990202i | \(-0.455405\pi\) | ||||
0.139643 | + | 0.990202i | \(0.455405\pi\) | |||||||
\(158\) | −3.50476 | − | 10.7865i | −0.278824 | − | 0.858131i | ||||
\(159\) | 4.83692 | + | 3.51423i | 0.383592 | + | 0.278696i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.19040 | + | 0.864875i | −0.0938165 | + | 0.0681617i | ||||
\(162\) | 1.24400 | + | 0.903822i | 0.0977382 | + | 0.0710109i | ||||
\(163\) | −4.83272 | − | 3.51118i | −0.378528 | − | 0.275017i | 0.382210 | − | 0.924075i | \(-0.375163\pi\) |
−0.760738 | + | 0.649059i | \(0.775163\pi\) | |||||||
\(164\) | −1.11959 | + | 0.813432i | −0.0874256 | + | 0.0635184i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.40459 | + | 3.92666i | 0.419477 | + | 0.304768i | ||||
\(167\) | −0.722381 | − | 2.22326i | −0.0558995 | − | 0.172041i | 0.919209 | − | 0.393771i | \(-0.128830\pi\) |
−0.975108 | + | 0.221730i | \(0.928830\pi\) | |||||||
\(168\) | −4.24024 | −0.327141 | ||||||||
\(169\) | −4.00046 | − | 12.3122i | −0.307728 | − | 0.947089i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.232853 | − | 0.716646i | 0.0178067 | − | 0.0548033i | ||||
\(172\) | −0.593860 | + | 1.82771i | −0.0452814 | + | 0.139362i | ||||
\(173\) | −4.91154 | + | 3.56844i | −0.373417 | + | 0.271303i | −0.758626 | − | 0.651526i | \(-0.774129\pi\) |
0.385209 | + | 0.922829i | \(0.374129\pi\) | |||||||
\(174\) | 10.5712 | 0.801403 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.6851 | 1.03155 | ||||||||
\(177\) | −3.11564 | + | 2.26365i | −0.234186 | + | 0.170146i | ||||
\(178\) | −5.75105 | + | 17.6999i | −0.431059 | + | 1.32666i | ||||
\(179\) | 3.53007 | − | 10.8644i | 0.263850 | − | 0.812045i | −0.728107 | − | 0.685464i | \(-0.759599\pi\) |
0.991956 | − | 0.126581i | \(-0.0404005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.42581 | − | 7.46586i | −0.180309 | − | 0.554933i | 0.819527 | − | 0.573040i | \(-0.194236\pi\) |
−0.999836 | + | 0.0181070i | \(0.994236\pi\) | |||||||
\(182\) | −0.603779 | −0.0447551 | ||||||||
\(183\) | 1.35857 | + | 4.18125i | 0.100428 | + | 0.309087i | ||||
\(184\) | −1.77568 | − | 1.29010i | −0.130905 | − | 0.0951077i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.2152 | − | 8.87488i | 0.895664 | − | 0.650738i | ||||
\(187\) | 17.9681 | + | 13.0546i | 1.31395 | + | 0.954644i | ||||
\(188\) | 2.52601 | + | 1.83526i | 0.184228 | + | 0.133850i | ||||
\(189\) | 1.36401 | − | 0.991010i | 0.0992170 | − | 0.0720854i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1646 | − | 7.38502i | −0.735485 | − | 0.534361i | 0.155809 | − | 0.987787i | \(-0.450202\pi\) |
−0.891294 | + | 0.453426i | \(0.850202\pi\) | |||||||
\(192\) | −1.87245 | − | 5.76281i | −0.135133 | − | 0.415895i | ||||
\(193\) | −10.1437 | −0.730161 | −0.365081 | − | 0.930976i | \(-0.618959\pi\) | ||||
−0.365081 | + | 0.930976i | \(0.618959\pi\) | |||||||
\(194\) | −4.50186 | − | 13.8553i | −0.323214 | − | 0.994752i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.468196 | + | 1.44096i | −0.0334426 | + | 0.102926i | ||||
\(197\) | −0.632566 | + | 1.94684i | −0.0450685 | + | 0.138706i | −0.971059 | − | 0.238841i | \(-0.923233\pi\) |
0.925990 | + | 0.377547i | \(0.123233\pi\) | |||||||
\(198\) | −3.70411 | + | 2.69119i | −0.263240 | + | 0.191255i | ||||
\(199\) | 3.57125 | 0.253159 | 0.126580 | − | 0.991956i | \(-0.459600\pi\) | ||||
0.126580 | + | 0.991956i | \(0.459600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.79282 | −0.126456 | ||||||||
\(202\) | −8.14161 | + | 5.91522i | −0.572842 | + | 0.416194i | ||||
\(203\) | 3.58182 | − | 11.0237i | 0.251394 | − | 0.773712i | ||||
\(204\) | −0.840020 | + | 2.58531i | −0.0588131 | + | 0.181008i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.332999 | + | 1.02487i | 0.0232011 | + | 0.0714058i | ||||
\(207\) | 0.872721 | 0.0606583 | ||||||||
\(208\) | −0.330767 | − | 1.01800i | −0.0229346 | − | 0.0705854i | ||||
\(209\) | 1.81517 | + | 1.31880i | 0.125558 | + | 0.0912234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.01474 | + | 2.19034i | −0.207543 | + | 0.150789i | −0.686701 | − | 0.726940i | \(-0.740942\pi\) |
0.479158 | + | 0.877729i | \(0.340942\pi\) | |||||||
\(212\) | −1.76276 | − | 1.28072i | −0.121067 | − | 0.0879604i | ||||
\(213\) | −3.53904 | − | 2.57126i | −0.242491 | − | 0.176180i | ||||
\(214\) | 15.5859 | − | 11.3238i | 1.06543 | − | 0.774078i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.03464 | + | 1.47826i | 0.138440 | + | 0.100583i | ||||
\(217\) | −5.11590 | − | 15.7451i | −0.347290 | − | 1.06885i | ||||
\(218\) | −6.58659 | −0.446100 | ||||||||
\(219\) | 4.65158 | + | 14.3161i | 0.314325 | + | 0.967391i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.536807 | − | 1.65212i | 0.0361096 | − | 0.111134i | ||||
\(222\) | 4.81209 | − | 14.8101i | 0.322966 | − | 0.993988i | ||||
\(223\) | −21.2357 | + | 15.4287i | −1.42205 | + | 1.03318i | −0.430622 | + | 0.902533i | \(0.641706\pi\) |
−0.991429 | + | 0.130647i | \(0.958294\pi\) | |||||||
\(224\) | 3.43495 | 0.229507 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.6514 | −0.841557 | ||||||||
\(227\) | 3.63338 | − | 2.63981i | 0.241156 | − | 0.175210i | −0.460642 | − | 0.887586i | \(-0.652381\pi\) |
0.701798 | + | 0.712376i | \(0.252381\pi\) | |||||||
\(228\) | −0.0848607 | + | 0.261174i | −0.00562004 | + | 0.0172967i | ||||
\(229\) | −2.32979 | + | 7.17035i | −0.153957 | + | 0.473830i | −0.998054 | − | 0.0623605i | \(-0.980137\pi\) |
0.844097 | + | 0.536191i | \(0.180137\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.55133 | + | 4.77450i | 0.102070 | + | 0.314139i | ||||
\(232\) | 17.2899 | 1.13514 | ||||||||
\(233\) | 3.20266 | + | 9.85679i | 0.209814 | + | 0.645740i | 0.999481 | + | 0.0322049i | \(0.0102529\pi\) |
−0.789668 | + | 0.613535i | \(0.789747\pi\) | |||||||
\(234\) | 0.289719 | + | 0.210493i | 0.0189395 | + | 0.0137603i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.13546 | − | 0.824962i | 0.0739124 | − | 0.0537005i | ||||
\(237\) | 5.96718 | + | 4.33541i | 0.387610 | + | 0.281615i | ||||
\(238\) | 15.6445 | + | 11.3664i | 1.01408 | + | 0.736775i | ||||
\(239\) | 15.0265 | − | 10.9174i | 0.971985 | − | 0.706188i | 0.0160815 | − | 0.999871i | \(-0.494881\pi\) |
0.955903 | + | 0.293683i | \(0.0948809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.39735 | + | 3.19486i | 0.283258 | + | 0.205799i | 0.720337 | − | 0.693624i | \(-0.243987\pi\) |
−0.437079 | + | 0.899423i | \(0.643987\pi\) | |||||||
\(242\) | 1.01404 | + | 3.12089i | 0.0651849 | + | 0.200619i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.495117 | − | 1.52381i | −0.0316966 | − | 0.0975522i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.80436 | − | 5.55325i | 0.115042 | − | 0.354063i | ||||
\(247\) | 0.0542295 | − | 0.166901i | 0.00345054 | − | 0.0106197i | ||||
\(248\) | 19.9787 | − | 14.5154i | 1.26865 | − | 0.921729i | ||||
\(249\) | −4.34451 | −0.275322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.3577 | 1.47432 | 0.737162 | − | 0.675716i | \(-0.236166\pi\) | ||||
0.737162 | + | 0.675716i | \(0.236166\pi\) | |||||||
\(252\) | −0.497099 | + | 0.361163i | −0.0313143 | + | 0.0227511i | ||||
\(253\) | −0.803008 | + | 2.47140i | −0.0504847 | + | 0.155376i | ||||
\(254\) | −5.67738 | + | 17.4732i | −0.356230 | + | 1.09636i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.61854 | + | 8.05903i | 0.163659 | + | 0.503690i | ||||
\(257\) | 4.48380 | 0.279692 | 0.139846 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139846 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(258\) | −2.50566 | − | 7.71163i | −0.155996 | − | 0.480105i | ||||
\(259\) | −13.8135 | − | 10.0361i | −0.858330 | − | 0.623614i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.56185 | + | 4.04092i | −0.344270 | + | 0.250127i | ||||
\(262\) | 26.6930 | + | 19.3936i | 1.64910 | + | 1.19814i | ||||
\(263\) | 6.25006 | + | 4.54093i | 0.385395 | + | 0.280006i | 0.763566 | − | 0.645730i | \(-0.223447\pi\) |
−0.378171 | + | 0.925736i | \(0.623447\pi\) | |||||||
\(264\) | −6.05830 | + | 4.40161i | −0.372862 | + | 0.270900i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.58045 | + | 1.14826i | 0.0969034 | + | 0.0704044i | ||||
\(267\) | −3.74010 | − | 11.5108i | −0.228890 | − | 0.704451i | ||||
\(268\) | 0.653376 | 0.0399113 | ||||||||
\(269\) | 3.31865 | + | 10.2138i | 0.202342 | + | 0.622743i | 0.999812 | + | 0.0193855i | \(0.00617097\pi\) |
−0.797470 | + | 0.603358i | \(0.793829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.94563 | + | 24.4541i | −0.482662 | + | 1.48548i | 0.352676 | + | 0.935746i | \(0.385272\pi\) |
−0.835338 | + | 0.549737i | \(0.814728\pi\) | |||||||
\(272\) | −10.5938 | + | 32.6042i | −0.642341 | + | 1.97692i | ||||
\(273\) | 0.317667 | − | 0.230798i | 0.0192261 | − | 0.0139685i | ||||
\(274\) | −15.4063 | −0.930726 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.318054 | −0.0191446 | ||||||||
\(277\) | −7.78635 | + | 5.65712i | −0.467837 | + | 0.339903i | −0.796598 | − | 0.604510i | \(-0.793369\pi\) |
0.328761 | + | 0.944413i | \(0.393369\pi\) | |||||||
\(278\) | 3.12407 | − | 9.61490i | 0.187369 | − | 0.576663i | ||||
\(279\) | −3.03433 | + | 9.33870i | −0.181660 | + | 0.559093i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.875368 | − | 2.69411i | −0.0522201 | − | 0.160717i | 0.921545 | − | 0.388270i | \(-0.126927\pi\) |
−0.973766 | + | 0.227553i | \(0.926927\pi\) | |||||||
\(282\) | −13.1740 | −0.784498 | ||||||||
\(283\) | 7.31238 | + | 22.5052i | 0.434676 | + | 1.33780i | 0.893418 | + | 0.449226i | \(0.148300\pi\) |
−0.458742 | + | 0.888569i | \(0.651700\pi\) | |||||||
\(284\) | 1.28977 | + | 0.937071i | 0.0765336 | + | 0.0556049i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.862658 | + | 0.626757i | −0.0510100 | + | 0.0370609i | ||||
\(287\) | −5.17958 | − | 3.76318i | −0.305741 | − | 0.222134i | ||||
\(288\) | −1.64823 | − | 1.19751i | −0.0971231 | − | 0.0705640i | ||||
\(289\) | −31.2579 | + | 22.7102i | −1.83870 | + | 1.33589i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.66483 | + | 5.56883i | 0.449321 | + | 0.326450i | ||||
\(292\) | −1.69522 | − | 5.21735i | −0.0992052 | − | 0.305322i | ||||
\(293\) | 23.2376 | 1.35755 | 0.678777 | − | 0.734345i | \(-0.262510\pi\) | ||||
0.678777 | + | 0.734345i | \(0.262510\pi\) | |||||||
\(294\) | −1.97545 | − | 6.07981i | −0.115211 | − | 0.354582i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.87047 | − | 24.2228i | 0.457462 | − | 1.40792i | ||||
\(297\) | 0.920120 | − | 2.83184i | 0.0533908 | − | 0.164320i | ||||
\(298\) | 13.5774 | − | 9.86455i | 0.786517 | − | 0.571438i | ||||
\(299\) | 0.203250 | 0.0117542 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.89069 | −0.512451 | ||||||||
\(302\) | 25.3936 | − | 18.4495i | 1.46124 | − | 1.06165i | ||||
\(303\) | 2.02242 | − | 6.22436i | 0.116185 | − | 0.357580i | ||||
\(304\) | −1.07020 | + | 3.29375i | −0.0613805 | + | 0.188910i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.54428 | − | 10.9082i | −0.202613 | − | 0.623579i | ||||
\(307\) | −21.8131 | −1.24494 | −0.622470 | − | 0.782643i | \(-0.713871\pi\) | ||||
−0.622470 | + | 0.782643i | \(0.713871\pi\) | |||||||
\(308\) | −0.565366 | − | 1.74002i | −0.0322147 | − | 0.0991467i | ||||
\(309\) | −0.566962 | − | 0.411922i | −0.0322533 | − | 0.0234334i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.12364 | + | 5.90217i | −0.460649 | + | 0.334681i | −0.793786 | − | 0.608197i | \(-0.791893\pi\) |
0.333137 | + | 0.942879i | \(0.391893\pi\) | |||||||
\(312\) | 0.473852 | + | 0.344274i | 0.0268266 | + | 0.0194907i | ||||
\(313\) | −4.89752 | − | 3.55825i | −0.276824 | − | 0.201124i | 0.440707 | − | 0.897651i | \(-0.354728\pi\) |
−0.717531 | + | 0.696527i | \(0.754728\pi\) | |||||||
\(314\) | 4.35332 | − | 3.16287i | 0.245672 | − | 0.178491i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.17468 | − | 1.58000i | −0.122335 | − | 0.0888817i | ||||
\(317\) | −2.62636 | − | 8.08309i | −0.147511 | − | 0.453992i | 0.849814 | − | 0.527082i | \(-0.176714\pi\) |
−0.997325 | + | 0.0730902i | \(0.976714\pi\) | |||||||
\(318\) | 9.19338 | 0.515539 | ||||||||
\(319\) | −6.32566 | − | 19.4684i | −0.354169 | − | 1.09002i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.87161 | + | 11.9156i | −0.216092 | + | 0.665063i | ||||
\(322\) | −0.699167 | + | 2.15182i | −0.0389631 | + | 0.119916i | ||||
\(323\) | −4.54713 | + | 3.30369i | −0.253009 | + | 0.183822i | ||||
\(324\) | 0.364440 | 0.0202466 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.18540 | −0.508733 | ||||||||
\(327\) | 3.46541 | − | 2.51776i | 0.191637 | − | 0.139233i | ||||
\(328\) | 2.95114 | − | 9.08268i | 0.162950 | − | 0.501507i | ||||
\(329\) | −4.46369 | + | 13.7378i | −0.246091 | + | 0.757391i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.03526 | + | 15.4969i | 0.276763 | + | 0.851789i | 0.988748 | + | 0.149594i | \(0.0477966\pi\) |
−0.711984 | + | 0.702195i | \(0.752203\pi\) | |||||||
\(332\) | 1.58331 | 0.0868955 | ||||||||
\(333\) | 3.12946 | + | 9.63150i | 0.171493 | + | 0.527803i | ||||
\(334\) | −2.90808 | − | 2.11284i | −0.159123 | − | 0.115610i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.26907 | + | 4.55474i | −0.342006 | + | 0.248482i | ||||
\(337\) | −19.9796 | − | 14.5161i | −1.08836 | − | 0.790740i | −0.109239 | − | 0.994015i | \(-0.534841\pi\) |
−0.979122 | + | 0.203275i | \(0.934841\pi\) | |||||||
\(338\) | −16.1046 | − | 11.7007i | −0.875974 | − | 0.636432i | ||||
\(339\) | 6.65628 | − | 4.83607i | 0.361519 | − | 0.262659i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.6537 | − | 17.1854i | −1.28092 | − | 0.930644i | ||||
\(342\) | −0.358051 | − | 1.10197i | −0.0193612 | − | 0.0595876i | ||||
\(343\) | −18.8114 | −1.01572 | ||||||||
\(344\) | −4.09816 | − | 12.6128i | −0.220958 | − | 0.680039i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.88474 | + | 8.87831i | −0.155084 | + | 0.477301i | ||||
\(347\) | −4.30975 | + | 13.2640i | −0.231359 | + | 0.712051i | 0.766224 | + | 0.642573i | \(0.222133\pi\) |
−0.997584 | + | 0.0694775i | \(0.977867\pi\) | |||||||
\(348\) | 2.02696 | − | 1.47267i | 0.108656 | − | 0.0789435i | ||||
\(349\) | 18.4966 | 0.990099 | 0.495049 | − | 0.868865i | \(-0.335150\pi\) | ||||
0.495049 | + | 0.868865i | \(0.335150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.232892 | −0.0124309 | ||||||||
\(352\) | 4.90773 | − | 3.56568i | 0.261583 | − | 0.190051i | ||||
\(353\) | −0.136503 | + | 0.420113i | −0.00726532 | + | 0.0223604i | −0.954623 | − | 0.297815i | \(-0.903742\pi\) |
0.947358 | + | 0.320176i | \(0.103742\pi\) | |||||||
\(354\) | −1.82994 | + | 5.63197i | −0.0972601 | + | 0.299336i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.36304 | + | 4.19500i | 0.0722409 | + | 0.222335i | ||||
\(357\) | −12.5760 | −0.665590 | ||||||||
\(358\) | −5.42809 | − | 16.7059i | −0.286883 | − | 0.882936i | ||||
\(359\) | −3.73869 | − | 2.71631i | −0.197320 | − | 0.143362i | 0.484738 | − | 0.874659i | \(-0.338915\pi\) |
−0.682058 | + | 0.731298i | \(0.738915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9120 | − | 10.8342i | 0.784840 | − | 0.570220i | ||||
\(362\) | −9.76552 | − | 7.09506i | −0.513264 | − | 0.372908i | ||||
\(363\) | −1.72650 | − | 1.25437i | −0.0906176 | − | 0.0658376i | ||||
\(364\) | −0.115770 | + | 0.0841120i | −0.00606801 | + | 0.00440867i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.46917 | + | 3.97359i | 0.285878 | + | 0.207703i | ||||
\(367\) | 2.71223 | + | 8.34738i | 0.141577 | + | 0.435730i | 0.996555 | − | 0.0829348i | \(-0.0264293\pi\) |
−0.854978 | + | 0.518665i | \(0.826429\pi\) | |||||||
\(368\) | −4.01108 | −0.209092 | ||||||||
\(369\) | 1.17344 | + | 3.61147i | 0.0610867 | + | 0.188005i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.11496 | − | 9.58687i | 0.161721 | − | 0.497725i | ||||
\(372\) | 1.10583 | − | 3.40339i | 0.0573345 | − | 0.176458i | ||||
\(373\) | 12.5361 | − | 9.10804i | 0.649097 | − | 0.471596i | −0.213867 | − | 0.976863i | \(-0.568606\pi\) |
0.862963 | + | 0.505266i | \(0.168606\pi\) | |||||||
\(374\) | 34.1513 | 1.76592 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.5468 | −1.11119 | ||||||||
\(377\) | −1.29531 | + | 0.941098i | −0.0667118 | + | 0.0484690i | ||||
\(378\) | 0.801135 | − | 2.46564i | 0.0412060 | − | 0.126819i | ||||
\(379\) | −8.43404 | + | 25.9573i | −0.433227 | + | 1.33334i | 0.461665 | + | 0.887054i | \(0.347252\pi\) |
−0.894892 | + | 0.446282i | \(0.852748\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.69219 | − | 11.3634i | −0.189157 | − | 0.582164i | ||||
\(382\) | −19.3196 | −0.988474 | ||||||||
\(383\) | −4.04941 | − | 12.4628i | −0.206915 | − | 0.636820i | −0.999629 | − | 0.0272261i | \(-0.991333\pi\) |
0.792714 | − | 0.609594i | \(-0.208667\pi\) | |||||||
\(384\) | −10.8344 | − | 7.87162i | −0.552889 | − | 0.401697i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.6188 | + | 9.16812i | −0.642282 | + | 0.466645i | ||||
\(387\) | 4.26612 | + | 3.09952i | 0.216859 | + | 0.157558i | ||||
\(388\) | −2.79337 | − | 2.02950i | −0.141812 | − | 0.103032i | ||||
\(389\) | −13.6769 | + | 9.93685i | −0.693447 | + | 0.503818i | −0.877791 | − | 0.479043i | \(-0.840984\pi\) |
0.184345 | + | 0.982862i | \(0.440984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.26641 | − | 3.82627i | −0.266334 | − | 0.193503i | ||||
\(392\) | −3.23097 | − | 9.94390i | −0.163189 | − | 0.502243i | ||||
\(393\) | −21.4573 | −1.08238 | ||||||||
\(394\) | 0.972680 | + | 2.99360i | 0.0490029 | + | 0.150815i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.335328 | + | 1.03203i | −0.0168509 | + | 0.0518617i | ||||
\(397\) | 3.21619 | − | 9.89842i | 0.161416 | − | 0.496787i | −0.837338 | − | 0.546685i | \(-0.815890\pi\) |
0.998754 | + | 0.0498977i | \(0.0158895\pi\) | |||||||
\(398\) | 4.44265 | − | 3.22778i | 0.222690 | − | 0.161794i | ||||
\(399\) | −1.27045 | −0.0636021 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.694800 | −0.0346967 | −0.0173483 | − | 0.999850i | \(-0.505522\pi\) | ||||
−0.0173483 | + | 0.999850i | \(0.505522\pi\) | |||||||
\(402\) | −2.23028 | + | 1.62039i | −0.111236 | + | 0.0808179i | ||||
\(403\) | −0.706670 | + | 2.17491i | −0.0352017 | + | 0.108340i | ||||
\(404\) | −0.737049 | + | 2.26840i | −0.0366696 | + | 0.112857i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.50766 | − | 16.9508i | −0.273341 | − | 0.841256i | ||||
\(407\) | −30.1543 | −1.49469 | ||||||||
\(408\) | −5.79688 | − | 17.8410i | −0.286988 | − | 0.883260i | ||||
\(409\) | 0.962002 | + | 0.698936i | 0.0475680 | + | 0.0345601i | 0.611315 | − | 0.791387i | \(-0.290641\pi\) |
−0.563747 | + | 0.825947i | \(0.690641\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.10570 | − | 5.88914i | 0.399825 | − | 0.290490i | ||||
\(412\) | 0.206623 | + | 0.150121i | 0.0101796 | + | 0.00739592i | ||||
\(413\) | 5.25299 | + | 3.81652i | 0.258483 | + | 0.187799i | ||||
\(414\) | 1.08567 | − | 0.788784i | 0.0533577 | − | 0.0387666i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.383860 | − | 0.278891i | −0.0188203 | − | 0.0136737i | ||||
\(417\) | 2.03169 | + | 6.25289i | 0.0994921 | + | 0.306205i | ||||
\(418\) | 3.45005 | 0.168747 | ||||||||
\(419\) | 0.611361 | + | 1.88158i | 0.0298670 | + | 0.0919210i | 0.964879 | − | 0.262695i | \(-0.0846114\pi\) |
−0.935012 | + | 0.354616i | \(0.884611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.42467 | − | 10.5400i | 0.166908 | − | 0.513690i | −0.832264 | − | 0.554380i | \(-0.812955\pi\) |
0.999172 | + | 0.0406895i | \(0.0129554\pi\) | |||||||
\(422\) | −1.77068 | + | 5.44958i | −0.0861951 | + | 0.265281i | ||||
\(423\) | 6.93123 | − | 5.03583i | 0.337008 | − | 0.244850i | ||||
\(424\) | 15.0363 | 0.730229 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.72655 | −0.325902 | ||||||||
\(427\) | 5.99677 | − | 4.35690i | 0.290204 | − | 0.210845i | ||||
\(428\) | 1.41097 | − | 4.34251i | 0.0682017 | − | 0.209903i | ||||
\(429\) | 0.214289 | − | 0.659512i | 0.0103460 | − | 0.0318416i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.21800 | − | 9.90398i | −0.155005 | − | 0.477058i | 0.843156 | − | 0.537669i | \(-0.180695\pi\) |
−0.998161 | + | 0.0606112i | \(0.980695\pi\) | |||||||
\(432\) | 4.59606 | 0.221128 | ||||||||
\(433\) | 3.17185 | + | 9.76195i | 0.152429 | + | 0.469129i | 0.997891 | − | 0.0649063i | \(-0.0206749\pi\) |
−0.845462 | + | 0.534035i | \(0.820675\pi\) | |||||||
\(434\) | −20.5950 | − | 14.9631i | −0.988590 | − | 0.718253i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.26293 | + | 0.917573i | −0.0604834 | + | 0.0439438i | ||||
\(437\) | −0.532024 | − | 0.386538i | −0.0254502 | − | 0.0184906i | ||||
\(438\) | 18.7258 | + | 13.6051i | 0.894752 | + | 0.650075i | ||||
\(439\) | 19.9920 | − | 14.5251i | 0.954168 | − | 0.693244i | 0.00237925 | − | 0.999997i | \(-0.499243\pi\) |
0.951789 | + | 0.306753i | \(0.0992427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.36339 | + | 2.44365i | 0.160161 | + | 0.116364i | ||||
\(442\) | −0.825434 | − | 2.54043i | −0.0392619 | − | 0.120836i | ||||
\(443\) | −7.52935 | −0.357730 | −0.178865 | − | 0.983874i | \(-0.557243\pi\) | ||||
−0.178865 | + | 0.983874i | \(0.557243\pi\) | |||||||
\(444\) | −1.14050 | − | 3.51010i | −0.0541257 | − | 0.166582i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.4726 | + | 38.3867i | −0.590594 | + | 1.81766i | ||||
\(447\) | −3.37269 | + | 10.3801i | −0.159523 | + | 0.490961i | ||||
\(448\) | −8.26505 | + | 6.00491i | −0.390487 | + | 0.283705i | ||||
\(449\) | −31.6627 | −1.49426 | −0.747128 | − | 0.664681i | \(-0.768568\pi\) | ||||
−0.747128 | + | 0.664681i | \(0.768568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3068 | −0.532416 | ||||||||
\(452\) | −2.42581 | + | 1.76245i | −0.114101 | + | 0.0828989i | ||||
\(453\) | −6.30789 | + | 19.4137i | −0.296371 | + | 0.912135i | ||||
\(454\) | 2.13403 | − | 6.56786i | 0.100155 | − | 0.308245i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.585614 | − | 1.80234i | −0.0274239 | − | 0.0844021i | ||||
\(457\) | −2.95742 | −0.138342 | −0.0691712 | − | 0.997605i | \(-0.522035\pi\) | ||||
−0.0691712 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(458\) | 3.58245 | + | 11.0257i | 0.167397 | + | 0.515195i | ||||
\(459\) | 6.03447 | + | 4.38430i | 0.281665 | + | 0.204642i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.2396 | − | 10.3457i | 0.663204 | − | 0.481846i | −0.204539 | − | 0.978858i | \(-0.565570\pi\) |
0.867743 | + | 0.497012i | \(0.165570\pi\) | |||||||
\(462\) | 6.24516 | + | 4.53737i | 0.290551 | + | 0.211098i | ||||
\(463\) | −21.3112 | − | 15.4835i | −0.990414 | − | 0.719578i | −0.0304024 | − | 0.999538i | \(-0.509679\pi\) |
−0.960012 | + | 0.279960i | \(0.909679\pi\) | |||||||
\(464\) | 25.5626 | − | 18.5723i | 1.18671 | − | 0.862198i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.8929 | + | 9.36724i | 0.597252 | + | 0.433929i | ||||
\(467\) | 2.27408 | + | 6.99888i | 0.105232 | + | 0.323870i | 0.989785 | − | 0.142570i | \(-0.0455365\pi\) |
−0.884553 | + | 0.466439i | \(0.845537\pi\) | |||||||
\(468\) | 0.0848751 | 0.00392335 | ||||||||
\(469\) | 0.934070 | + | 2.87477i | 0.0431313 | + | 0.132745i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.08139 | + | 3.32816i | −0.0498276 | + | 0.153354i | ||||
\(472\) | −2.99297 | + | 9.21143i | −0.137763 | + | 0.423990i | ||||
\(473\) | −12.7027 | + | 9.22905i | −0.584070 | + | 0.424352i | ||||
\(474\) | 11.3416 | 0.520939 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.58317 | 0.210069 | ||||||||
\(477\) | −4.83692 | + | 3.51423i | −0.221467 | + | 0.160905i | ||||
\(478\) | 8.82566 | − | 27.1626i | 0.403676 | − | 1.24239i | ||||
\(479\) | −8.79679 | + | 27.0737i | −0.401936 | + | 1.23703i | 0.521491 | + | 0.853257i | \(0.325376\pi\) |
−0.923427 | + | 0.383774i | \(0.874624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.728827 | + | 2.24310i | 0.0332316 | + | 0.102276i | ||||
\(482\) | 8.35791 | 0.380692 | ||||||||
\(483\) | −0.454692 | − | 1.39940i | −0.0206892 | − | 0.0636748i | ||||
\(484\) | 0.629204 | + | 0.457144i | 0.0286002 | + | 0.0207793i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.24400 | + | 0.903822i | −0.0564292 | + | 0.0409982i | ||||
\(487\) | −1.92875 | − | 1.40132i | −0.0873999 | − | 0.0634998i | 0.543227 | − | 0.839586i | \(-0.317202\pi\) |
−0.630627 | + | 0.776086i | \(0.717202\pi\) | |||||||
\(488\) | 8.94516 | + | 6.49904i | 0.404929 | + | 0.294198i | ||||
\(489\) | 4.83272 | − | 3.51118i | 0.218543 | − | 0.158781i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8105 | + | 15.1197i | 0.939163 | + | 0.682342i | 0.948219 | − | 0.317617i | \(-0.102883\pi\) |
−0.00905626 | + | 0.999959i | \(0.502883\pi\) | |||||||
\(492\) | −0.427647 | − | 1.31616i | −0.0192798 | − | 0.0593371i | ||||
\(493\) | 51.2794 | 2.30951 | ||||||||
\(494\) | −0.0833872 | − | 0.256640i | −0.00375177 | − | 0.0115468i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.9460 | − | 42.9212i | 0.626192 | − | 1.92722i | ||||
\(497\) | −2.27913 | + | 7.01445i | −0.102233 | + | 0.314641i | ||||
\(498\) | −5.40459 | + | 3.92666i | −0.242185 | + | 0.175958i | ||||
\(499\) | 29.9989 | 1.34293 | 0.671467 | − | 0.741035i | \(-0.265665\pi\) | ||||
0.671467 | + | 0.741035i | \(0.265665\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.33767 | 0.104440 | ||||||||
\(502\) | 29.0570 | − | 21.1112i | 1.29688 | − | 0.942238i | ||||
\(503\) | −4.27216 | + | 13.1483i | −0.190486 | + | 0.586256i | −1.00000 | 0.000845408i | \(-0.999731\pi\) | |
0.809514 | + | 0.587101i | \(0.199731\pi\) | |||||||
\(504\) | 1.31031 | − | 4.03270i | 0.0583656 | − | 0.179631i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.23476 | + | 3.80021i | 0.0548920 | + | 0.168940i | ||||
\(507\) | 12.9458 | 0.574941 | ||||||||
\(508\) | 1.34558 | + | 4.14127i | 0.0597004 | + | 0.183739i | ||||
\(509\) | −25.8511 | − | 18.7819i | −1.14583 | − | 0.832493i | −0.157908 | − | 0.987454i | \(-0.550475\pi\) |
−0.987921 | + | 0.154960i | \(0.950475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.5322 | − | 14.9175i | 0.908290 | − | 0.659911i | ||||
\(512\) | −11.1273 | − | 8.08447i | −0.491763 | − | 0.357286i | ||||
\(513\) | 0.609616 | + | 0.442912i | 0.0269152 | + | 0.0195550i | ||||
\(514\) | 5.57787 | − | 4.05256i | 0.246029 | − | 0.178751i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.55474 | − | 1.12959i | −0.0684438 | − | 0.0497273i | ||||
\(517\) | 7.88310 | + | 24.2617i | 0.346698 | + | 1.06703i | ||||
\(518\) | −26.2549 | −1.15358 | ||||||||
\(519\) | −1.87604 | − | 5.77386i | −0.0823490 | − | 0.253444i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9889 | + | 36.8979i | −0.525242 | + | 1.61653i | 0.238595 | + | 0.971119i | \(0.423313\pi\) |
−0.763837 | + | 0.645409i | \(0.776687\pi\) | |||||||
\(522\) | −3.26669 | + | 10.0538i | −0.142979 | + | 0.440045i | ||||
\(523\) | −19.1853 | + | 13.9389i | −0.838914 | + | 0.609507i | −0.922067 | − | 0.387030i | \(-0.873501\pi\) |
0.0831532 | + | 0.996537i | \(0.473501\pi\) | |||||||
\(524\) | 7.81991 | 0.341614 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8793 | 0.517962 | ||||||||
\(527\) | 59.2542 | − | 43.0507i | 2.58115 | − | 1.87532i | ||||
\(528\) | −4.22893 | + | 13.0153i | −0.184041 | + | 0.566419i | ||||
\(529\) | −6.87203 | + | 21.1499i | −0.298784 | + | 0.919562i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.19007 | − | 3.66266i | −0.0516446 | − | 0.158946i | ||||
\(532\) | 0.463003 | 0.0200737 | ||||||||
\(533\) | 0.273284 | + | 0.841081i | 0.0118372 | + | 0.0364313i | ||||
\(534\) | −15.0564 | − | 10.9391i | −0.651556 | − | 0.473383i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.64776 | + | 2.65025i | −0.157559 | + | 0.114473i | ||||
\(537\) | 9.24183 | + | 6.71458i | 0.398815 | + | 0.289756i | ||||
\(538\) | 13.3598 | + | 9.70648i | 0.575983 | + | 0.418476i | ||||
\(539\) | −10.0147 | + | 7.27613i | −0.431365 | + | 0.313405i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.27953 | − | 1.65618i | −0.0980046 | − | 0.0712045i | 0.537704 | − | 0.843134i | \(-0.319292\pi\) |
−0.635708 | + | 0.771929i | \(0.719292\pi\) | |||||||
\(542\) | 12.2178 | + | 37.6025i | 0.524799 | + | 1.61516i | ||||
\(543\) | 7.85007 | 0.336879 | ||||||||
\(544\) | 4.69597 | + | 14.4527i | 0.201338 | + | 0.619654i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.186578 | − | 0.574228i | 0.00798480 | − | 0.0245747i | ||||
\(547\) | −1.36703 | + | 4.20728i | −0.0584499 | + | 0.179890i | −0.976019 | − | 0.217687i | \(-0.930149\pi\) |
0.917569 | + | 0.397577i | \(0.130149\pi\) | |||||||
\(548\) | −2.95404 | + | 2.14623i | −0.126190 | + | 0.0916826i | ||||
\(549\) | −4.39643 | −0.187635 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.18036 | 0.220691 | ||||||||
\(552\) | 1.77568 | − | 1.29010i | 0.0755778 | − | 0.0549105i | ||||
\(553\) | 3.84285 | − | 11.8271i | 0.163415 | − | 0.502938i | ||||
\(554\) | −4.57323 | + | 14.0749i | −0.194298 | + | 0.597987i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.740427 | − | 2.27880i | −0.0314011 | − | 0.0966426i | ||||
\(557\) | 7.20182 | 0.305151 | 0.152575 | − | 0.988292i | \(-0.451243\pi\) | ||||
0.152575 | + | 0.988292i | \(0.451243\pi\) | |||||||
\(558\) | 4.66580 | + | 14.3599i | 0.197519 | + | 0.607902i | ||||
\(559\) | 0.993546 | + | 0.721854i | 0.0420225 | + | 0.0305312i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.9681 | + | 13.0546i | −0.758612 | + | 0.551164i | ||||
\(562\) | −3.52395 | − | 2.56030i | −0.148649 | − | 0.108000i | ||||
\(563\) | 18.8103 | + | 13.6665i | 0.792761 | + | 0.575975i | 0.908782 | − | 0.417272i | \(-0.137014\pi\) |
−0.116020 | + | 0.993247i | \(0.537014\pi\) | |||||||
\(564\) | −2.52601 | + | 1.83526i | −0.106364 | + | 0.0772782i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.4373 | + | 21.3875i | 1.23734 | + | 0.898982i | ||||
\(567\) | 0.521005 | + | 1.60349i | 0.0218801 | + | 0.0673402i | ||||
\(568\) | −11.0017 | −0.461620 | ||||||||
\(569\) | −6.37307 | − | 19.6143i | −0.267173 | − | 0.822273i | −0.991185 | − | 0.132486i | \(-0.957704\pi\) |
0.724012 | − | 0.689787i | \(-0.242296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.557381 | − | 1.71544i | 0.0233257 | − | 0.0717890i | −0.938716 | − | 0.344691i | \(-0.887984\pi\) |
0.962042 | + | 0.272902i | \(0.0879836\pi\) | |||||||
\(572\) | −0.0780952 | + | 0.240352i | −0.00326533 | + | 0.0100496i | ||||
\(573\) | 10.1646 | − | 7.38502i | 0.424633 | − | 0.308514i | ||||
\(574\) | −9.84466 | −0.410908 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.05938 | 0.252474 | ||||||||
\(577\) | 13.3377 | − | 9.69043i | 0.555257 | − | 0.403418i | −0.274463 | − | 0.961598i | \(-0.588500\pi\) |
0.829720 | + | 0.558180i | \(0.188500\pi\) | |||||||
\(578\) | −18.3590 | + | 56.5032i | −0.763633 | + | 2.35022i | ||||
\(579\) | 3.13458 | − | 9.64725i | 0.130269 | − | 0.400926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.26351 | + | 6.96637i | 0.0939063 | + | 0.289014i | ||||
\(582\) | 14.5683 | 0.603876 | ||||||||
\(583\) | −5.50118 | − | 16.9309i | −0.227835 | − | 0.701205i | ||||
\(584\) | 30.6271 | + | 22.2519i | 1.26736 | + | 0.920791i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.9076 | − | 21.0026i | 1.19416 | − | 0.867610i | ||||
\(587\) | 5.88286 | + | 4.27415i | 0.242811 | + | 0.176413i | 0.702535 | − | 0.711649i | \(-0.252051\pi\) |
−0.459723 | + | 0.888062i | \(0.652051\pi\) | |||||||
\(588\) | −1.22575 | − | 0.890562i | −0.0505492 | − | 0.0367261i | ||||
\(589\) | 5.98599 | − | 4.34908i | 0.246649 | − | 0.179201i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.65608 | − | 1.20321i | −0.0681220 | − | 0.0494935i | ||||
\(592\) | −14.3832 | − | 44.2670i | −0.591146 | − | 1.81936i | ||||
\(593\) | 2.47898 | 0.101800 | 0.0508998 | − | 0.998704i | \(-0.483791\pi\) | ||||
0.0508998 | + | 0.998704i | \(0.483791\pi\) | |||||||
\(594\) | −1.41484 | − | 4.35444i | −0.0580518 | − | 0.178665i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.22914 | − | 3.78291i | 0.0503477 | − | 0.154954i | ||||
\(597\) | −1.10358 | + | 3.39646i | −0.0451664 | + | 0.139008i | ||||
\(598\) | 0.252843 | − | 0.183701i | 0.0103395 | − | 0.00751211i | ||||
\(599\) | 30.2951 | 1.23782 | 0.618912 | − | 0.785460i | \(-0.287574\pi\) | ||||
0.618912 | + | 0.785460i | \(0.287574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.46130 | 0.181980 | 0.0909900 | − | 0.995852i | \(-0.470997\pi\) | ||||
0.0909900 | + | 0.995852i | \(0.470997\pi\) | |||||||
\(602\) | −11.0600 | + | 8.03560i | −0.450774 | + | 0.327506i | ||||
\(603\) | 0.554013 | − | 1.70508i | 0.0225612 | − | 0.0694361i | ||||
\(604\) | 2.29885 | − | 7.07512i | 0.0935387 | − | 0.287882i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.10982 | − | 9.57103i | −0.126328 | − | 0.388797i | ||||
\(607\) | 17.2931 | 0.701906 | 0.350953 | − | 0.936393i | \(-0.385858\pi\) | ||||
0.350953 | + | 0.936393i | \(0.385858\pi\) | |||||||
\(608\) | 0.474397 | + | 1.46004i | 0.0192393 | + | 0.0592126i | ||||
\(609\) | 9.37732 | + | 6.81302i | 0.379988 | + | 0.276077i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.61423 | − | 1.17280i | 0.0653046 | − | 0.0474466i | ||||
\(612\) | −2.19920 | − | 1.59781i | −0.0888974 | − | 0.0645877i | ||||
\(613\) | −11.5794 | − | 8.41293i | −0.467688 | − | 0.339795i | 0.328852 | − | 0.944382i | \(-0.393338\pi\) |
−0.796539 | + | 0.604587i | \(0.793338\pi\) | |||||||
\(614\) | −27.1356 | + | 19.7152i | −1.09510 | + | 0.795640i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.2143 | + | 7.42115i | 0.411547 | + | 0.299006i | ||||
\(617\) | −8.14472 | − | 25.0669i | −0.327894 | − | 1.00915i | −0.970117 | − | 0.242637i | \(-0.921988\pi\) |
0.642223 | − | 0.766518i | \(-0.278012\pi\) | |||||||
\(618\) | −1.07761 | −0.0433477 | ||||||||
\(619\) | −0.864708 | − | 2.66130i | −0.0347555 | − | 0.106967i | 0.932174 | − | 0.362011i | \(-0.117910\pi\) |
−0.966929 | + | 0.255045i | \(0.917910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.269686 | + | 0.830007i | −0.0108221 | + | 0.0333070i | ||||
\(622\) | −4.77133 | + | 14.6846i | −0.191313 | + | 0.588800i | ||||
\(623\) | −16.5089 | + | 11.9944i | −0.661414 | + | 0.480545i | ||||
\(624\) | 1.07039 | 0.0428497 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.30856 | −0.372045 | ||||||||
\(627\) | −1.81517 | + | 1.31880i | −0.0724911 | + | 0.0526679i | ||||
\(628\) | 0.394100 | − | 1.21291i | 0.0157263 | − | 0.0484006i | ||||
\(629\) | 23.3427 | − | 71.8415i | 0.930735 | − | 2.86451i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9403 | + | 33.6707i | 0.435526 | + | 1.34041i | 0.892547 | + | 0.450955i | \(0.148916\pi\) |
−0.457021 | + | 0.889456i | \(0.651084\pi\) | |||||||
\(632\) | 18.5499 | 0.737877 | ||||||||
\(633\) | −1.15153 | − | 3.54404i | −0.0457692 | − | 0.140863i | ||||
\(634\) | −10.5729 | − | 7.68164i | −0.419902 | − | 0.305077i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.76276 | − | 1.28072i | 0.0698981 | − | 0.0507840i | ||||
\(637\) | 0.783307 | + | 0.569106i | 0.0310357 | + | 0.0225488i | ||||
\(638\) | −25.4651 | − | 18.5015i | −1.00817 | − | 0.732481i | ||||
\(639\) | 3.53904 | − | 2.57126i | 0.140002 | − | 0.101718i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.6994 | − | 9.95321i | −0.541094 | − | 0.393128i | 0.283397 | − | 0.959003i | \(-0.408539\pi\) |
−0.824491 | + | 0.565875i | \(0.808539\pi\) | |||||||
\(642\) | 5.95327 | + | 18.3223i | 0.234957 | + | 0.723122i | ||||
\(643\) | 25.9118 | 1.02186 | 0.510931 | − | 0.859622i | \(-0.329301\pi\) | ||||
0.510931 | + | 0.859622i | \(0.329301\pi\) | |||||||
\(644\) | 0.165708 | + | 0.509996i | 0.00652980 | + | 0.0200966i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.67071 | + | 8.21960i | −0.105078 | + | 0.323396i | ||||
\(647\) | 3.37629 | − | 10.3911i | 0.132736 | − | 0.408518i | −0.862495 | − | 0.506065i | \(-0.831100\pi\) |
0.995231 | + | 0.0975468i | \(0.0310996\pi\) | |||||||
\(648\) | −2.03464 | + | 1.47826i | −0.0799283 | + | 0.0580713i | ||||
\(649\) | 11.4671 | 0.450121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.5554 | 0.648857 | ||||||||
\(652\) | −1.76124 | + | 1.27961i | −0.0689753 | + | 0.0501135i | ||||
\(653\) | 4.40596 | − | 13.5602i | 0.172419 | − | 0.530650i | −0.827088 | − | 0.562073i | \(-0.810004\pi\) |
0.999506 | + | 0.0314233i | \(0.0100040\pi\) | |||||||
\(654\) | 2.03537 | − | 6.26422i | 0.0795892 | − | 0.244950i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.39319 | − | 16.5985i | −0.210569 | − | 0.648063i | ||||
\(657\) | −15.0528 | −0.587267 | ||||||||
\(658\) | 6.86370 | + | 21.1243i | 0.267575 | + | 0.823511i | ||||
\(659\) | −18.5179 | − | 13.4540i | −0.721355 | − | 0.524095i | 0.165462 | − | 0.986216i | \(-0.447088\pi\) |
−0.886817 | + | 0.462121i | \(0.847088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.2838 | − | 23.4556i | 1.25570 | − | 0.912316i | 0.257158 | − | 0.966369i | \(-0.417214\pi\) |
0.998538 | + | 0.0540529i | \(0.0172140\pi\) | |||||||
\(662\) | 20.2704 | + | 14.7273i | 0.787830 | + | 0.572392i | ||||
\(663\) | 1.40538 | + | 1.02107i | 0.0545804 | + | 0.0396550i | ||||
\(664\) | −8.83953 | + | 6.42230i | −0.343040 | + | 0.249233i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.5982 | + | 9.15314i | 0.488171 | + | 0.354677i | ||||
\(667\) | 1.85404 | + | 5.70615i | 0.0717887 | + | 0.220943i | ||||
\(668\) | −0.851941 | −0.0329626 | ||||||||
\(669\) | −8.11133 | − | 24.9641i | −0.313602 | − | 0.965168i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.04524 | − | 12.4500i | 0.156165 | − | 0.480626i | ||||
\(672\) | −1.06146 | + | 3.26683i | −0.0409466 | + | 0.126021i | ||||
\(673\) | 1.74624 | − | 1.26872i | 0.0673126 | − | 0.0489054i | −0.553620 | − | 0.832769i | \(-0.686754\pi\) |
0.620933 | + | 0.783864i | \(0.286754\pi\) | |||||||
\(674\) | −37.9747 | −1.46273 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.71795 | −0.181460 | ||||||||
\(677\) | −33.9577 | + | 24.6717i | −1.30510 | + | 0.948210i | −0.999992 | − | 0.00410738i | \(-0.998693\pi\) |
−0.305108 | + | 0.952318i | \(0.598693\pi\) | |||||||
\(678\) | 3.90949 | − | 12.0322i | 0.150143 | − | 0.462093i | ||||
\(679\) | 4.93613 | − | 15.1919i | 0.189431 | − | 0.583010i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.38783 | + | 4.27129i | 0.0531817 | + | 0.163676i | ||||
\(682\) | −44.9579 | −1.72153 | ||||||||
\(683\) | −9.02521 | − | 27.7767i | −0.345340 | − | 1.06285i | −0.961401 | − | 0.275149i | \(-0.911273\pi\) |
0.616061 | − | 0.787698i | \(-0.288727\pi\) | |||||||
\(684\) | −0.222168 | − | 0.161415i | −0.00849481 | − | 0.00617184i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −23.4015 | + | 17.0022i | −0.893473 | + | 0.649146i | ||||
\(687\) | −6.09946 | − | 4.43152i | −0.232709 | − | 0.169073i | ||||
\(688\) | −19.6074 | − | 14.2456i | −0.747524 | − | 0.543108i | ||||
\(689\) | −1.12648 | + | 0.818435i | −0.0429154 | + | 0.0311799i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0221 | − | 26.1716i | −1.37034 | − | 0.995614i | −0.997710 | − | 0.0676353i | \(-0.978455\pi\) |
−0.372634 | − | 0.927978i | \(-0.621545\pi\) | |||||||
\(692\) | 0.683703 | + | 2.10422i | 0.0259905 | + | 0.0799905i | ||||
\(693\) | −5.02021 | −0.190702 | ||||||||
\(694\) | 6.62698 | + | 20.3958i | 0.251557 | + | 0.774212i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.34287 | + | 16.4437i | −0.202521 | + | 0.623295i | ||||
\(697\) | 8.75268 | − | 26.9380i | 0.331531 | − | 1.02035i | ||||
\(698\) | 23.0098 | − | 16.7176i | 0.870934 | − | 0.632771i | ||||
\(699\) | −10.3640 | −0.392004 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.50567 | −0.170177 | −0.0850884 | − | 0.996373i | \(-0.527117\pi\) | ||||
−0.0850884 | + | 0.996373i | \(0.527117\pi\) | |||||||
\(702\) | −0.289719 | + | 0.210493i | −0.0109347 | + | 0.00794454i | ||||
\(703\) | 2.35813 | − | 7.25759i | 0.0889387 | − | 0.273725i | ||||
\(704\) | −5.57536 | + | 17.1592i | −0.210129 | + | 0.646711i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.209897 | + | 0.645997i | 0.00789958 | + | 0.0243124i | ||||
\(707\) | −11.0344 | −0.414990 | ||||||||
\(708\) | 0.433708 | + | 1.33482i | 0.0162998 | + | 0.0501655i | ||||
\(709\) | 41.4788 | + | 30.1361i | 1.55777 | + | 1.13178i | 0.937809 | + | 0.347151i | \(0.112851\pi\) |
0.619959 | + | 0.784634i | \(0.287149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.96718 | + | 4.33541i | −0.223787 | + | 0.162591i | ||||
\(712\) | −24.6257 | − | 17.8916i | −0.922887 | − | 0.670517i | ||||
\(713\) | 6.93287 | + | 5.03702i | 0.259638 | + | 0.188638i | ||||
\(714\) | −15.6445 | + | 11.3664i | −0.585482 | + | 0.425378i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.36809 | − | 2.44706i | −0.125871 | − | 0.0914509i | ||||
\(717\) | 5.73962 | + | 17.6647i | 0.214350 | + | 0.659701i | ||||
\(718\) | −7.10600 | −0.265194 | ||||||||
\(719\) | 10.8976 | + | 33.5393i | 0.406411 | + | 1.25080i | 0.919712 | + | 0.392595i | \(0.128422\pi\) |
−0.513301 | + | 0.858209i | \(0.671578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.365122 | + | 1.12373i | −0.0135979 | + | 0.0418499i | ||||
\(722\) | 8.75838 | − | 26.9555i | 0.325953 | − | 1.00318i | ||||
\(723\) | −4.39735 | + | 3.19486i | −0.163539 | + | 0.118818i | ||||
\(724\) | −2.86088 | −0.106324 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.28150 | −0.121788 | ||||||||
\(727\) | −35.5998 | + | 25.8648i | −1.32032 | + | 0.959271i | −0.320396 | + | 0.947284i | \(0.603816\pi\) |
−0.999928 | + | 0.0119876i | \(0.996184\pi\) | |||||||
\(728\) | 0.305160 | − | 0.939184i | 0.0113100 | − | 0.0348085i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.1546 | − | 37.4079i | −0.449553 | − | 1.38358i | ||||
\(732\) | 1.60223 | 0.0592202 | ||||||||
\(733\) | −8.61356 | − | 26.5098i | −0.318149 | − | 0.979162i | −0.974439 | − | 0.224653i | \(-0.927875\pi\) |
0.656290 | − | 0.754509i | \(-0.272125\pi\) | |||||||
\(734\) | 10.9186 | + | 7.93281i | 0.403012 | + | 0.292805i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.43845 | + | 1.04509i | −0.0530219 | + | 0.0385226i | ||||
\(737\) | 4.31874 | + | 3.13775i | 0.159083 | + | 0.115581i | ||||
\(738\) | 4.72388 | + | 3.43210i | 0.173888 | + | 0.126337i | ||||
\(739\) | 26.2456 | − | 19.0685i | 0.965459 | − | 0.701447i | 0.0110469 | − | 0.999939i | \(-0.496484\pi\) |
0.954412 | + | 0.298492i | \(0.0964836\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.141975 | + | 0.103151i | 0.00521557 | + | 0.00378933i | ||||
\(742\) | −4.78979 | − | 14.7415i | −0.175839 | − | 0.541176i | ||||
\(743\) | 9.09256 | 0.333574 | 0.166787 | − | 0.985993i | \(-0.446661\pi\) | ||||
0.166787 | + | 0.985993i | \(0.446661\pi\) | |||||||
\(744\) | 7.63120 | + | 23.4864i | 0.279773 | + | 0.861054i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.36297 | − | 22.6609i | 0.269577 | − | 0.829674i | ||||
\(747\) | 1.34253 | − | 4.13188i | 0.0491205 | − | 0.151177i | ||||
\(748\) | 6.54827 | − | 4.75760i | 0.239429 | − | 0.173955i | ||||
\(749\) | 21.1236 | 0.771840 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.8861 | −1.82037 | −0.910185 | − | 0.414202i | \(-0.864061\pi\) | ||||
−0.910185 | + | 0.414202i | \(0.864061\pi\) | |||||||
\(752\) | −31.8563 | + | 23.1450i | −1.16168 | + | 0.844011i | ||||
\(753\) | −7.21792 | + | 22.2145i | −0.263036 | + | 0.809540i | ||||
\(754\) | −0.760786 | + | 2.34146i | −0.0277062 | + | 0.0852709i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.189875 | − | 0.584375i | −0.00690568 | − | 0.0212535i | ||||
\(757\) | 31.1239 | 1.13122 | 0.565608 | − | 0.824674i | \(-0.308642\pi\) | ||||
0.565608 | + | 0.824674i | \(0.308642\pi\) | |||||||
\(758\) | 12.9688 | + | 39.9138i | 0.471048 | + | 1.44974i | ||||
\(759\) | −2.10230 | − | 1.52741i | −0.0763087 | − | 0.0554415i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.6544 | + | 22.9982i | −1.14747 | + | 0.833686i | −0.988142 | − | 0.153540i | \(-0.950933\pi\) |
−0.159327 | + | 0.987226i | \(0.550933\pi\) | |||||||
\(762\) | −14.8636 | − | 10.7990i | −0.538450 | − | 0.391207i | ||||
\(763\) | −5.84270 | − | 4.24497i | −0.211520 | − | 0.153678i | ||||
\(764\) | −3.70438 | + | 2.69139i | −0.134020 | + | 0.0973712i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.3016 | − | 11.8438i | −0.589002 | − | 0.427935i | ||||
\(767\) | −0.277158 | − | 0.853003i | −0.0100076 | − | 0.0308002i | ||||
\(768\) | −8.47377 | −0.305771 | ||||||||
\(769\) | 4.43076 | + | 13.6365i | 0.159777 | + | 0.491744i | 0.998614 | − | 0.0526398i | \(-0.0167635\pi\) |
−0.838836 | + | 0.544384i | \(0.816764\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.38557 | + | 4.26435i | −0.0499001 | + | 0.153577i | ||||
\(772\) | −1.14237 | + | 3.51584i | −0.0411146 | + | 0.126538i | ||||
\(773\) | 3.43830 | − | 2.49807i | 0.123667 | − | 0.0898493i | −0.524232 | − | 0.851575i | \(-0.675648\pi\) |
0.647899 | + | 0.761726i | \(0.275648\pi\) | |||||||
\(774\) | 8.10849 | 0.291454 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23.8274 | 0.855352 | ||||||||
\(777\) | 13.8135 | − | 10.0361i | 0.495557 | − | 0.360043i | ||||
\(778\) | −8.03298 | + | 24.7230i | −0.287996 | + | 0.886361i | ||||
\(779\) | 0.884215 | − | 2.72134i | 0.0316803 | − | 0.0975020i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.02506 | + | 12.3879i | 0.144028 | + | 0.443273i | ||||
\(782\) | −10.0097 | −0.357946 | ||||||||
\(783\) | −2.12444 | − | 6.53835i | −0.0759212 | − | 0.233661i | ||||
\(784\) | −15.4584 | − | 11.2312i | −0.552084 | − | 0.401113i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −26.6930 | + | 19.3936i | −0.952109 | + | 0.691747i | ||||
\(787\) | 21.9483 | + | 15.9464i | 0.782374 | + | 0.568428i | 0.905690 | − | 0.423940i | \(-0.139353\pi\) |
−0.123317 | + | 0.992367i | \(0.539353\pi\) | |||||||
\(788\) | 0.603541 | + | 0.438498i | 0.0215002 | + | 0.0156208i | ||||
\(789\) | −6.25006 | + | 4.54093i | −0.222508 | + | 0.161662i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2225 | − | 8.15364i | −0.399027 | − | 0.289910i | ||||
\(792\) | −2.31406 | − | 7.12195i | −0.0822267 | − | 0.253068i | ||||
\(793\) | −1.02389 | −0.0363595 | ||||||||
\(794\) | −4.94545 | − | 15.2205i | −0.175507 | − | 0.540156i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.402187 | − | 1.23781i | 0.0142552 | − | 0.0438729i | ||||
\(797\) | −3.89902 | + | 12.0000i | −0.138111 | + | 0.425060i | −0.996061 | − | 0.0886722i | \(-0.971738\pi\) |
0.857950 | + | 0.513733i | \(0.171738\pi\) | |||||||
\(798\) | −1.58045 | + | 1.14826i | −0.0559472 | + | 0.0406480i | ||||
\(799\) | −63.9049 | −2.26079 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.1032 | 0.427646 | ||||||||
\(802\) | −0.864334 | + | 0.627976i | −0.0305207 | + | 0.0221746i | ||||
\(803\) | 13.8504 | − | 42.6272i | 0.488770 | − | 1.50428i | ||||
\(804\) | −0.201904 | + | 0.621398i | −0.00712062 | + | 0.0219150i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.08663 | + | 3.34430i | 0.0382748 | + | 0.117798i | ||||
\(807\) | −10.7394 | −0.378044 | ||||||||
\(808\) | −5.08629 | − | 15.6540i | −0.178935 | − | 0.550706i | ||||
\(809\) | 30.2684 | + | 21.9913i | 1.06418 | + | 0.773172i | 0.974857 | − | 0.222831i | \(-0.0715297\pi\) |
0.0893229 | + | 0.996003i | \(0.471530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.0948 | + | 21.8651i | −1.05677 | + | 0.767789i | −0.973488 | − | 0.228737i | \(-0.926540\pi\) |
−0.0832825 | + | 0.996526i | \(0.526540\pi\) | |||||||
\(812\) | −3.41747 | − | 2.48293i | −0.119930 | − | 0.0871339i | ||||
\(813\) | −20.8019 | − | 15.1135i | −0.729555 | − | 0.530053i | ||||
\(814\) | −37.5121 | + | 27.2541i | −1.31480 | + | 0.955257i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −27.7348 | − | 20.1505i | −0.970912 | − | 0.705409i | ||||
\(817\) | −1.22788 | − | 3.77903i | −0.0429582 | − | 0.132212i | ||||
\(818\) | 1.82845 | 0.0639302 | ||||||||
\(819\) | 0.121338 | + | 0.373439i | 0.00423989 | + | 0.0130490i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.48994 | − | 26.1294i | 0.296301 | − | 0.911921i | −0.686480 | − | 0.727148i | \(-0.740845\pi\) |
0.982781 | − | 0.184772i | \(-0.0591548\pi\) | |||||||
\(822\) | 4.76080 | − | 14.6522i | 0.166052 | − | 0.511055i | ||||
\(823\) | 18.9526 | − | 13.7698i | 0.660645 | − | 0.479987i | −0.206236 | − | 0.978502i | \(-0.566121\pi\) |
0.866881 | + | 0.498516i | \(0.166121\pi\) | |||||||
\(824\) | −1.76249 | −0.0613993 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.98420 | 0.347395 | ||||||||
\(827\) | −26.2583 | + | 19.0778i | −0.913090 | + | 0.663399i | −0.941794 | − | 0.336189i | \(-0.890862\pi\) |
0.0287047 | + | 0.999588i | \(0.490862\pi\) | |||||||
\(828\) | 0.0982841 | − | 0.302487i | 0.00341561 | − | 0.0105122i | ||||
\(829\) | −0.0476213 | + | 0.146563i | −0.00165395 | + | 0.00509035i | −0.951880 | − | 0.306471i | \(-0.900852\pi\) |
0.950226 | + | 0.311561i | \(0.100852\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.97412 | − | 9.15340i | −0.103171 | − | 0.317528i | ||||
\(832\) | 1.41118 | 0.0489239 | ||||||||
\(833\) | −9.58260 | − | 29.4922i | −0.332018 | − | 1.02185i | ||||
\(834\) | 8.17892 | + | 5.94233i | 0.283213 | + | 0.205766i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.661522 | − | 0.480624i | 0.0228792 | − | 0.0166227i | ||||
\(837\) | −7.94397 | − | 5.77163i | −0.274584 | − | 0.199497i | ||||
\(838\) | 2.46115 | + | 1.78813i | 0.0850189 | + | 0.0617698i | ||||
\(839\) | 28.6568 | − | 20.8204i | 0.989342 | − | 0.718799i | 0.0295652 | − | 0.999563i | \(-0.490588\pi\) |
0.959777 | + | 0.280764i | \(0.0905877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7752 | − | 10.7348i | −0.509491 | − | 0.370167i | ||||
\(842\) | −5.26602 | − | 16.2072i | −0.181479 | − | 0.558535i | ||||
\(843\) | 2.83275 | 0.0975651 | ||||||||
\(844\) | 0.419663 | + | 1.29159i | 0.0144454 | + | 0.0444583i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.07098 | − | 12.5292i | 0.139963 | − | 0.430762i | ||||
\(847\) | −1.11186 | + | 3.42195i | −0.0382040 | + | 0.117580i | ||||
\(848\) | 22.2308 | − | 16.1516i | 0.763408 | − | 0.554648i | ||||
\(849\) | −23.6634 | −0.812125 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.83818 | 0.302969 | ||||||||
\(852\) | −1.28977 | + | 0.937071i | −0.0441867 | + | 0.0321035i | ||||
\(853\) | 11.3121 | − | 34.8150i | 0.387318 | − | 1.19204i | −0.547467 | − | 0.836828i | \(-0.684408\pi\) |
0.934785 | − | 0.355215i | \(-0.115592\pi\) | |||||||
\(854\) | 3.52213 | − | 10.8400i | 0.120525 | − | 0.370938i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.73693 | + | 29.9672i | 0.332801 | + | 1.02426i | ||||
\(857\) | 2.04867 | 0.0699813 | 0.0349907 | − | 0.999388i | \(-0.488860\pi\) | ||||
0.0349907 | + | 0.999388i | \(0.488860\pi\) | |||||||
\(858\) | −0.329506 | − | 1.01411i | −0.0112491 | − | 0.0346213i | ||||
\(859\) | −11.4736 | − | 8.33605i | −0.391474 | − | 0.284422i | 0.374585 | − | 0.927192i | \(-0.377785\pi\) |
−0.766059 | + | 0.642770i | \(0.777785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.17958 | − | 3.76318i | 0.176519 | − | 0.128249i | ||||
\(862\) | −12.9546 | − | 9.41209i | −0.441237 | − | 0.320577i | ||||
\(863\) | 34.8976 | + | 25.3546i | 1.18793 | + | 0.863081i | 0.993044 | − | 0.117745i | \(-0.0375667\pi\) |
0.194885 | + | 0.980826i | \(0.437567\pi\) | |||||||
\(864\) | 1.64823 | − | 1.19751i | 0.0560740 | − | 0.0407402i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.7689 | + | 9.27711i | 0.433903 | + | 0.315249i | ||||
\(867\) | −11.9395 | − | 36.7459i | −0.405485 | − | 1.24796i | ||||
\(868\) | −6.03344 | −0.204788 | ||||||||
\(869\) | −6.78666 | − | 20.8872i | −0.230222 | − | 0.708550i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.129025 | − | 0.397099i | 0.00437185 | − | 0.0134552i | ||||
\(872\) | 3.32897 | − | 10.2455i | 0.112733 | − | 0.346957i | ||||
\(873\) | −7.66483 | + | 5.56883i | −0.259415 | + | 0.188476i | ||||
\(874\) | −1.01120 | −0.0342044 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.48584 | 0.185350 | ||||||||
\(877\) | −5.45827 | + | 3.96567i | −0.184313 | + | 0.133911i | −0.676116 | − | 0.736795i | \(-0.736338\pi\) |
0.491803 | + | 0.870707i | \(0.336338\pi\) | |||||||
\(878\) | 11.7421 | − | 36.1385i | 0.396277 | − | 1.21962i | ||||
\(879\) | −7.18080 | + | 22.1002i | −0.242202 | + | 0.745423i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.30839 | + | 16.3375i | 0.178844 | + | 0.550426i | 0.999788 | − | 0.0205829i | \(-0.00655221\pi\) |
−0.820944 | + | 0.571009i | \(0.806552\pi\) | |||||||
\(882\) | 6.39269 | 0.215253 | ||||||||
\(883\) | 17.5712 | + | 54.0787i | 0.591319 | + | 1.81989i | 0.572257 | + | 0.820075i | \(0.306068\pi\) |
0.0190624 | + | 0.999818i | \(0.493932\pi\) | |||||||
\(884\) | −0.512176 | − | 0.372118i | −0.0172263 | − | 0.0125157i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.36654 | + | 6.80519i | −0.314675 | + | 0.228625i | ||||
\(887\) | 29.8768 | + | 21.7067i | 1.00316 | + | 0.728841i | 0.962764 | − | 0.270342i | \(-0.0871369\pi\) |
0.0403995 | + | 0.999184i | \(0.487137\pi\) | |||||||
\(888\) | 20.6051 | + | 14.9705i | 0.691463 | + | 0.502378i | ||||
\(889\) | −16.2974 | + | 11.8408i | −0.546597 | + | 0.397126i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.40891 | + | 1.75017i | 0.0807014 | + | 0.0586330i | ||||
\(892\) | 2.95609 | + | 9.09791i | 0.0989772 | + | 0.304621i | ||||
\(893\) | −6.45581 | −0.216036 | ||||||||
\(894\) | 5.18610 | + | 15.9612i | 0.173449 | + | 0.533822i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.97730 | + | 21.4739i | −0.233095 | + | 0.717393i | ||||
\(897\) | −0.0628076 | + | 0.193302i | −0.00209708 | + | 0.00645416i | ||||
\(898\) | −39.3885 | + | 28.6174i | −1.31441 | + | 0.954976i | ||||
\(899\) | −67.5058 | −2.25145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.5956 | 1.48570 | ||||||||
\(902\) | −14.0657 | + | 10.2193i | −0.468336 | + | 0.340266i | ||||
\(903\) | 2.74737 | − | 8.45555i | 0.0914269 | − | 0.281383i | ||||
\(904\) | 6.39421 | − | 19.6793i | 0.212668 | − | 0.654525i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.69948 | + | 29.8519i | 0.322244 | + | 0.991764i | ||||
\(907\) | 25.7833 | 0.856120 | 0.428060 | − | 0.903750i | \(-0.359197\pi\) | ||||
0.428060 | + | 0.903750i | \(0.359197\pi\) | |||||||
\(908\) | −0.505779 | − | 1.55663i | −0.0167849 | − | 0.0516585i | ||||
\(909\) | 5.29476 | + | 3.84687i | 0.175616 | + | 0.127593i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.8488 | − | 15.8741i | 0.723882 | − | 0.525931i | −0.163740 | − | 0.986504i | \(-0.552356\pi\) |
0.887622 | + | 0.460572i | \(0.152356\pi\) | |||||||
\(912\) | −2.80183 | − | 2.03565i | −0.0927780 | − | 0.0674071i | ||||
\(913\) | 10.4655 | + | 7.60364i | 0.346358 | + | 0.251644i | ||||
\(914\) | −3.67905 | + | 2.67298i | −0.121692 | + | 0.0884145i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.22289 | + | 1.61502i | 0.0734462 | + | 0.0533618i | ||||
\(917\) | 11.1794 | + | 34.4066i | 0.369176 | + | 1.13621i | ||||
\(918\) | 11.4695 | 0.378551 | ||||||||
\(919\) | −8.01412 | − | 24.6649i | −0.264362 | − | 0.813621i | −0.991840 | − | 0.127490i | \(-0.959308\pi\) |
0.727478 | − | 0.686131i | \(-0.240692\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.74062 | − | 20.7455i | 0.222111 | − | 0.683588i | ||||
\(922\) | 8.36347 | − | 25.7401i | 0.275436 | − | 0.847705i | ||||
\(923\) | 0.824214 | − | 0.598827i | 0.0271293 | − | 0.0197106i | ||||
\(924\) | 1.82956 | 0.0601882 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −40.5055 | −1.33109 | ||||||||
\(927\) | 0.566962 | − | 0.411922i | 0.0186215 | − | 0.0135293i | ||||
\(928\) | 4.32818 | − | 13.3208i | 0.142079 | − | 0.437275i | ||||
\(929\) | 4.66201 | − | 14.3482i | 0.152955 | − | 0.470749i | −0.844993 | − | 0.534778i | \(-0.820395\pi\) |
0.997948 | + | 0.0640296i | \(0.0203952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.968057 | − | 2.97937i | −0.0317268 | − | 0.0976450i | ||||
\(932\) | 3.77707 | 0.123722 | ||||||||
\(933\) | −3.10295 | − | 9.54991i | −0.101586 | − | 0.312650i | ||||
\(934\) | 9.15470 | + | 6.65128i | 0.299551 | + | 0.217637i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.473852 | + | 0.344274i | −0.0154883 | + | 0.0112529i | ||||
\(937\) | 0.530361 | + | 0.385330i | 0.0173262 | + | 0.0125882i | 0.596415 | − | 0.802677i | \(-0.296591\pi\) |
−0.579088 | + | 0.815265i | \(0.696591\pi\) | |||||||
\(938\) | 3.76027 | + | 2.73199i | 0.122777 | + | 0.0892028i | ||||
\(939\) | 4.89752 | − | 3.55825i | 0.159824 | − | 0.116119i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.4596 | + | 21.4036i | 0.960354 | + | 0.697738i | 0.953233 | − | 0.302237i | \(-0.0977333\pi\) |
0.00712112 | + | 0.999975i | \(0.497733\pi\) | |||||||
\(942\) | 1.66282 | + | 5.11763i | 0.0541776 | + | 0.166741i | ||||
\(943\) | 3.31400 | 0.107919 | ||||||||
\(944\) | 5.46963 | + | 16.8338i | 0.178021 | + | 0.547893i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.46079 | + | 22.9619i | −0.242571 | + | 0.746557i | ||||
\(947\) | 14.0333 | − | 43.1901i | 0.456021 | − | 1.40349i | −0.413911 | − | 0.910317i | \(-0.635838\pi\) |
0.869932 | − | 0.493171i | \(-0.164162\pi\) | |||||||
\(948\) | 2.17468 | − | 1.58000i | 0.0706302 | − | 0.0513159i | ||||
\(949\) | −3.50568 | −0.113799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.49907 | 0.275601 | ||||||||
\(952\) | −25.5876 | + | 18.5905i | −0.829298 | + | 0.602520i | ||||
\(953\) | −14.2932 | + | 43.9898i | −0.463001 | + | 1.42497i | 0.398478 | + | 0.917178i | \(0.369538\pi\) |
−0.861479 | + | 0.507793i | \(0.830462\pi\) | |||||||
\(954\) | −2.84091 | + | 8.74342i | −0.0919779 | + | 0.283079i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.09174 | − | 6.43773i | −0.0676518 | − | 0.208211i | ||||
\(957\) | 20.4703 | 0.661710 | ||||||||
\(958\) | 13.5266 | + | 41.6306i | 0.437024 | + | 1.34502i | ||||
\(959\) | −13.6663 | − | 9.92913i | −0.441307 | − | 0.320628i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −52.9246 | + | 38.4520i | −1.70724 | + | 1.24039i | ||||
\(962\) | 2.93402 | + | 2.13169i | 0.0945967 | + | 0.0687285i | ||||
\(963\) | −10.1360 | − | 7.36423i | −0.326628 | − | 0.237309i | ||||
\(964\) | 1.60257 | − | 1.16433i | 0.0516153 | − | 0.0375007i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.83044 | − | 1.32990i | −0.0588936 | − | 0.0427887i | ||||
\(967\) | −0.901526 | − | 2.77461i | −0.0289911 | − | 0.0892255i | 0.935514 | − | 0.353290i | \(-0.114937\pi\) |
−0.964505 | + | 0.264064i | \(0.914937\pi\) | |||||||
\(968\) | −5.36709 | −0.172505 | ||||||||
\(969\) | −1.73685 | − | 5.34548i | −0.0557957 | − | 0.171721i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.376445 | + | 1.15858i | −0.0120807 | + | 0.0371806i | −0.956915 | − | 0.290368i | \(-0.906222\pi\) |
0.944834 | + | 0.327548i | \(0.106222\pi\) | |||||||
\(972\) | −0.112618 | + | 0.346603i | −0.00361222 | + | 0.0111173i | ||||
\(973\) | 8.96791 | − | 6.51557i | 0.287498 | − | 0.208879i | ||||
\(974\) | −3.66591 | −0.117463 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.2063 | 0.646787 | ||||||||
\(977\) | −36.1404 | + | 26.2575i | −1.15623 | + | 0.840053i | −0.989297 | − | 0.145915i | \(-0.953387\pi\) |
−0.166936 | + | 0.985968i | \(0.553387\pi\) | |||||||
\(978\) | 2.83845 | − | 8.73584i | 0.0907635 | − | 0.279341i | ||||
\(979\) | −11.1364 | + | 34.2743i | −0.355921 | + | 1.09541i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.32367 | + | 4.07383i | 0.0422614 | + | 0.130067i | ||||
\(982\) | 39.5538 | 1.26221 | ||||||||
\(983\) | −11.1651 | − | 34.3627i | −0.356112 | − | 1.09600i | −0.955362 | − | 0.295437i | \(-0.904535\pi\) |
0.599251 | − | 0.800561i | \(-0.295465\pi\) | |||||||
\(984\) | 7.72619 | + | 5.61341i | 0.246302 | + | 0.178949i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 63.7918 | − | 46.3474i | 2.03154 | − | 1.47600i | ||||
\(987\) | −11.6861 | − | 8.49044i | −0.371972 | − | 0.270254i | ||||
\(988\) | −0.0517412 | − | 0.0375922i | −0.00164611 | − | 0.00119597i | ||||
\(989\) | 3.72314 | − | 2.70502i | 0.118389 | − | 0.0860145i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.3765 | + | 23.5229i | 1.02847 | + | 0.747229i | 0.968002 | − | 0.250941i | \(-0.0807399\pi\) |
0.0604705 | + | 0.998170i | \(0.480740\pi\) | |||||||
\(992\) | −6.18192 | − | 19.0260i | −0.196276 | − | 0.604076i | ||||
\(993\) | −16.2945 | −0.517089 | ||||||||
\(994\) | 3.50456 | + | 10.7859i | 0.111158 | + | 0.342109i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.489270 | + | 1.50582i | −0.0155031 | + | 0.0477137i | ||||
\(997\) | 1.00226 | − | 3.08464i | 0.0317419 | − | 0.0976915i | −0.933930 | − | 0.357455i | \(-0.883645\pi\) |
0.965672 | + | 0.259763i | \(0.0836446\pi\) | |||||||
\(998\) | 37.3187 | − | 27.1136i | 1.18130 | − | 0.858267i | ||||
\(999\) | −10.1272 | −0.320409 |
(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 | 375.2.g.d.301.4 | 16 | ||
5.2 | odd | 4 | 375.2.i.c.199.4 | 16 | |||
5.3 | odd | 4 | 75.2.i.a.64.1 | yes | 16 | ||
5.4 | even | 2 | 375.2.g.e.301.1 | 16 | |||
15.8 | even | 4 | 225.2.m.b.64.4 | 16 | |||
25.3 | odd | 20 | 1875.2.b.h.1249.14 | 16 | |||
25.4 | even | 10 | 1875.2.a.m.1.8 | 8 | |||
25.9 | even | 10 | 375.2.g.e.76.1 | 16 | |||
25.12 | odd | 20 | 75.2.i.a.34.1 | ✓ | 16 | ||
25.13 | odd | 20 | 375.2.i.c.49.4 | 16 | |||
25.16 | even | 5 | inner | 375.2.g.d.76.4 | 16 | ||
25.21 | even | 5 | 1875.2.a.p.1.1 | 8 | |||
25.22 | odd | 20 | 1875.2.b.h.1249.3 | 16 | |||
75.29 | odd | 10 | 5625.2.a.bd.1.1 | 8 | |||
75.62 | even | 20 | 225.2.m.b.109.4 | 16 | |||
75.71 | odd | 10 | 5625.2.a.t.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.1 | ✓ | 16 | 25.12 | odd | 20 | ||
75.2.i.a.64.1 | yes | 16 | 5.3 | odd | 4 | ||
225.2.m.b.64.4 | 16 | 15.8 | even | 4 | |||
225.2.m.b.109.4 | 16 | 75.62 | even | 20 | |||
375.2.g.d.76.4 | 16 | 25.16 | even | 5 | inner | ||
375.2.g.d.301.4 | 16 | 1.1 | even | 1 | trivial | ||
375.2.g.e.76.1 | 16 | 25.9 | even | 10 | |||
375.2.g.e.301.1 | 16 | 5.4 | even | 2 | |||
375.2.i.c.49.4 | 16 | 25.13 | odd | 20 | |||
375.2.i.c.199.4 | 16 | 5.2 | odd | 4 | |||
1875.2.a.m.1.8 | 8 | 25.4 | even | 10 | |||
1875.2.a.p.1.1 | 8 | 25.21 | even | 5 | |||
1875.2.b.h.1249.3 | 16 | 25.22 | odd | 20 | |||
1875.2.b.h.1249.14 | 16 | 25.3 | odd | 20 | |||
5625.2.a.t.1.8 | 8 | 75.71 | odd | 10 | |||
5625.2.a.bd.1.1 | 8 | 75.29 | odd | 10 |