Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(197,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.g (of order \(2\), degree \(1\), 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: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.6 | ||
Character | \(\chi\) | \(=\) | 231.197 |
Dual form | 231.2.g.a.197.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92194 | −1.35901 | −0.679507 | − | 0.733669i | \(-0.737806\pi\) | ||||
−0.679507 | + | 0.733669i | \(0.737806\pi\) | |||||||
\(3\) | 1.23500 | + | 1.21441i | 0.713025 | + | 0.701139i | ||||
\(4\) | 1.69384 | 0.846921 | ||||||||
\(5\) | − | 0.413489i | − | 0.184918i | −0.995717 | − | 0.0924588i | \(-0.970527\pi\) | ||
0.995717 | − | 0.0924588i | \(-0.0294727\pi\) | |||||||
\(6\) | −2.37358 | − | 2.33402i | −0.969012 | − | 0.952858i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0.588415 | 0.208036 | ||||||||
\(9\) | 0.0504282 | + | 2.99958i | 0.0168094 | + | 0.999859i | ||||
\(10\) | 0.794699i | 0.251306i | ||||||||
\(11\) | 3.07734 | − | 1.23694i | 0.927851 | − | 0.372950i | ||||
\(12\) | 2.09189 | + | 2.05702i | 0.603876 | + | 0.593809i | ||||
\(13\) | 1.35904i | 0.376929i | 0.982080 | + | 0.188464i | \(0.0603510\pi\) | ||||
−0.982080 | + | 0.188464i | \(0.939649\pi\) | |||||||
\(14\) | − | 1.92194i | − | 0.513659i | ||||||
\(15\) | 0.502144 | − | 0.510656i | 0.129653 | − | 0.131851i | ||||
\(16\) | −4.51858 | −1.12965 | ||||||||
\(17\) | −1.64016 | −0.397797 | −0.198899 | − | 0.980020i | \(-0.563736\pi\) | ||||
−0.198899 | + | 0.980020i | \(0.563736\pi\) | |||||||
\(18\) | −0.0969199 | − | 5.76500i | −0.0228442 | − | 1.35882i | ||||
\(19\) | 4.21243i | 0.966397i | 0.875511 | + | 0.483198i | \(0.160525\pi\) | ||||
−0.875511 | + | 0.483198i | \(0.839475\pi\) | |||||||
\(20\) | − | 0.700384i | − | 0.156611i | ||||||
\(21\) | −1.21441 | + | 1.23500i | −0.265005 | + | 0.269498i | ||||
\(22\) | −5.91444 | + | 2.37731i | −1.26096 | + | 0.506845i | ||||
\(23\) | 6.16223i | 1.28491i | 0.766322 | + | 0.642457i | \(0.222085\pi\) | ||||
−0.766322 | + | 0.642457i | \(0.777915\pi\) | |||||||
\(24\) | 0.726690 | + | 0.714576i | 0.148335 | + | 0.145862i | ||||
\(25\) | 4.82903 | 0.965805 | ||||||||
\(26\) | − | 2.61198i | − | 0.512252i | ||||||
\(27\) | −3.58043 | + | 3.76570i | −0.689054 | + | 0.724710i | ||||
\(28\) | 1.69384i | 0.320106i | ||||||||
\(29\) | 2.73184 | 0.507290 | 0.253645 | − | 0.967297i | \(-0.418370\pi\) | ||||
0.253645 | + | 0.967297i | \(0.418370\pi\) | |||||||
\(30\) | −0.965088 | + | 0.981450i | −0.176200 | + | 0.179187i | ||||
\(31\) | 4.56717 | 0.820289 | 0.410144 | − | 0.912021i | \(-0.365478\pi\) | ||||
0.410144 | + | 0.912021i | \(0.365478\pi\) | |||||||
\(32\) | 7.50760 | 1.32717 | ||||||||
\(33\) | 5.30264 | + | 2.20953i | 0.923071 | + | 0.384630i | ||||
\(34\) | 3.15228 | 0.540612 | ||||||||
\(35\) | 0.413489 | 0.0698923 | ||||||||
\(36\) | 0.0854175 | + | 5.08081i | 0.0142362 | + | 0.846802i | ||||
\(37\) | −6.41046 | −1.05387 | −0.526937 | − | 0.849904i | \(-0.676660\pi\) | ||||
−0.526937 | + | 0.849904i | \(0.676660\pi\) | |||||||
\(38\) | − | 8.09602i | − | 1.31335i | ||||||
\(39\) | −1.65042 | + | 1.67840i | −0.264279 | + | 0.268760i | ||||
\(40\) | − | 0.243303i | − | 0.0384696i | ||||||
\(41\) | −3.57034 | −0.557593 | −0.278796 | − | 0.960350i | \(-0.589935\pi\) | ||||
−0.278796 | + | 0.960350i | \(0.589935\pi\) | |||||||
\(42\) | 2.33402 | − | 2.37358i | 0.360146 | − | 0.366252i | ||||
\(43\) | − | 1.20233i | − | 0.183353i | −0.995789 | − | 0.0916765i | \(-0.970777\pi\) | ||
0.995789 | − | 0.0916765i | \(-0.0292226\pi\) | |||||||
\(44\) | 5.21252 | − | 2.09517i | 0.785817 | − | 0.315859i | ||||
\(45\) | 1.24029 | − | 0.0208515i | 0.184892 | − | 0.00310836i | ||||
\(46\) | − | 11.8434i | − | 1.74622i | ||||||
\(47\) | − | 8.33307i | − | 1.21550i | −0.794127 | − | 0.607752i | \(-0.792072\pi\) | ||
0.794127 | − | 0.607752i | \(-0.207928\pi\) | |||||||
\(48\) | −5.58043 | − | 5.48740i | −0.805466 | − | 0.792038i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −9.28109 | −1.31254 | ||||||||
\(51\) | −2.02559 | − | 1.99182i | −0.283639 | − | 0.278911i | ||||
\(52\) | 2.30199i | 0.319229i | ||||||||
\(53\) | 5.91727i | 0.812799i | 0.913696 | + | 0.406399i | \(0.133216\pi\) | ||||
−0.913696 | + | 0.406399i | \(0.866784\pi\) | |||||||
\(54\) | 6.88136 | − | 7.23745i | 0.936435 | − | 0.984892i | ||||
\(55\) | −0.511459 | − | 1.27244i | −0.0689651 | − | 0.171576i | ||||
\(56\) | 0.588415i | 0.0786303i | ||||||||
\(57\) | −5.11560 | + | 5.20233i | −0.677578 | + | 0.689065i | ||||
\(58\) | −5.25043 | −0.689415 | ||||||||
\(59\) | − | 10.3712i | − | 1.35021i | −0.737722 | − | 0.675105i | \(-0.764098\pi\) | ||
0.737722 | − | 0.675105i | \(-0.235902\pi\) | |||||||
\(60\) | 0.850552 | − | 0.864972i | 0.109806 | − | 0.111667i | ||||
\(61\) | − | 15.5857i | − | 1.99555i | −0.0667043 | − | 0.997773i | \(-0.521248\pi\) | ||
0.0667043 | − | 0.997773i | \(-0.478752\pi\) | |||||||
\(62\) | −8.77782 | −1.11478 | ||||||||
\(63\) | −2.99958 | + | 0.0504282i | −0.377911 | + | 0.00635336i | ||||
\(64\) | −5.39197 | −0.673997 | ||||||||
\(65\) | 0.561946 | 0.0697008 | ||||||||
\(66\) | −10.1913 | − | 4.24658i | −1.25447 | − | 0.522718i | ||||
\(67\) | 6.12792 | 0.748645 | 0.374322 | − | 0.927299i | \(-0.377875\pi\) | ||||
0.374322 | + | 0.927299i | \(0.377875\pi\) | |||||||
\(68\) | −2.77817 | −0.336903 | ||||||||
\(69\) | −7.48346 | + | 7.61032i | −0.900902 | + | 0.916175i | ||||
\(70\) | −0.794699 | −0.0949847 | ||||||||
\(71\) | − | 8.31333i | − | 0.986611i | −0.869856 | − | 0.493305i | \(-0.835789\pi\) | ||
0.869856 | − | 0.493305i | \(-0.164211\pi\) | |||||||
\(72\) | 0.0296727 | + | 1.76500i | 0.00349697 | + | 0.208007i | ||||
\(73\) | − | 0.290444i | − | 0.0339939i | −0.999856 | − | 0.0169969i | \(-0.994589\pi\) | ||
0.999856 | − | 0.0169969i | \(-0.00541056\pi\) | |||||||
\(74\) | 12.3205 | 1.43223 | ||||||||
\(75\) | 5.96383 | + | 5.86441i | 0.688643 | + | 0.677163i | ||||
\(76\) | 7.13518i | 0.818462i | ||||||||
\(77\) | 1.23694 | + | 3.07734i | 0.140962 | + | 0.350695i | ||||
\(78\) | 3.17201 | − | 3.22579i | 0.359159 | − | 0.365248i | ||||
\(79\) | − | 16.6717i | − | 1.87571i | −0.347025 | − | 0.937856i | \(-0.612808\pi\) | ||
0.347025 | − | 0.937856i | \(-0.387192\pi\) | |||||||
\(80\) | 1.86838i | 0.208891i | ||||||||
\(81\) | −8.99491 | + | 0.302527i | −0.999435 | + | 0.0336141i | ||||
\(82\) | 6.86196 | 0.757777 | ||||||||
\(83\) | 3.53351 | 0.387853 | 0.193926 | − | 0.981016i | \(-0.437878\pi\) | ||||
0.193926 | + | 0.981016i | \(0.437878\pi\) | |||||||
\(84\) | −2.05702 | + | 2.09189i | −0.224439 | + | 0.228244i | ||||
\(85\) | 0.678187i | 0.0735597i | ||||||||
\(86\) | 2.31080i | 0.249180i | ||||||||
\(87\) | 3.37381 | + | 3.31757i | 0.361711 | + | 0.355681i | ||||
\(88\) | 1.81075 | − | 0.727832i | 0.193027 | − | 0.0775871i | ||||
\(89\) | 9.17912i | 0.972985i | 0.873685 | + | 0.486493i | \(0.161724\pi\) | ||||
−0.873685 | + | 0.486493i | \(0.838276\pi\) | |||||||
\(90\) | −2.38376 | + | 0.0400752i | −0.251270 | + | 0.00422430i | ||||
\(91\) | −1.35904 | −0.142466 | ||||||||
\(92\) | 10.4378i | 1.08822i | ||||||||
\(93\) | 5.64044 | + | 5.54641i | 0.584886 | + | 0.575136i | ||||
\(94\) | 16.0156i | 1.65189i | ||||||||
\(95\) | 1.74179 | 0.178704 | ||||||||
\(96\) | 9.27185 | + | 9.11729i | 0.946305 | + | 0.930529i | ||||
\(97\) | 12.9612 | 1.31601 | 0.658007 | − | 0.753012i | \(-0.271400\pi\) | ||||
0.658007 | + | 0.753012i | \(0.271400\pi\) | |||||||
\(98\) | 1.92194 | 0.194145 | ||||||||
\(99\) | 3.86547 | + | 9.16832i | 0.388494 | + | 0.921451i | ||||
\(100\) | 8.17961 | 0.817961 | ||||||||
\(101\) | −12.6217 | −1.25591 | −0.627953 | − | 0.778251i | \(-0.716107\pi\) | ||||
−0.627953 | + | 0.778251i | \(0.716107\pi\) | |||||||
\(102\) | 3.89306 | + | 3.82816i | 0.385470 | + | 0.379044i | ||||
\(103\) | −12.8103 | −1.26224 | −0.631120 | − | 0.775685i | \(-0.717405\pi\) | ||||
−0.631120 | + | 0.775685i | \(0.717405\pi\) | |||||||
\(104\) | 0.799678i | 0.0784149i | ||||||||
\(105\) | 0.510656 | + | 0.502144i | 0.0498350 | + | 0.0490042i | ||||
\(106\) | − | 11.3726i | − | 1.10461i | ||||||
\(107\) | 5.35301 | 0.517495 | 0.258747 | − | 0.965945i | \(-0.416690\pi\) | ||||
0.258747 | + | 0.965945i | \(0.416690\pi\) | |||||||
\(108\) | −6.06468 | + | 6.37851i | −0.583574 | + | 0.613772i | ||||
\(109\) | 11.9771i | 1.14720i | 0.819135 | + | 0.573601i | \(0.194454\pi\) | ||||
−0.819135 | + | 0.573601i | \(0.805546\pi\) | |||||||
\(110\) | 0.982991 | + | 2.44555i | 0.0937245 | + | 0.233175i | ||||
\(111\) | −7.91690 | − | 7.78492i | −0.751438 | − | 0.738912i | ||||
\(112\) | − | 4.51858i | − | 0.426966i | ||||||
\(113\) | − | 4.67841i | − | 0.440108i | −0.975488 | − | 0.220054i | \(-0.929377\pi\) | ||
0.975488 | − | 0.220054i | \(-0.0706233\pi\) | |||||||
\(114\) | 9.83186 | − | 9.99854i | 0.920838 | − | 0.936449i | ||||
\(115\) | 2.54801 | 0.237603 | ||||||||
\(116\) | 4.62731 | 0.429635 | ||||||||
\(117\) | −4.07653 | + | 0.0685338i | −0.376876 | + | 0.00633595i | ||||
\(118\) | 19.9327i | 1.83495i | ||||||||
\(119\) | − | 1.64016i | − | 0.150353i | ||||||
\(120\) | 0.295469 | − | 0.300478i | 0.0269725 | − | 0.0274298i | ||||
\(121\) | 7.93998 | − | 7.61293i | 0.721817 | − | 0.692084i | ||||
\(122\) | 29.9548i | 2.71198i | ||||||||
\(123\) | −4.40935 | − | 4.33584i | −0.397578 | − | 0.390950i | ||||
\(124\) | 7.73607 | 0.694720 | ||||||||
\(125\) | − | 4.06419i | − | 0.363512i | ||||||
\(126\) | 5.76500 | − | 0.0969199i | 0.513587 | − | 0.00863431i | ||||
\(127\) | 7.00839i | 0.621894i | 0.950427 | + | 0.310947i | \(0.100646\pi\) | ||||
−0.950427 | + | 0.310947i | \(0.899354\pi\) | |||||||
\(128\) | −4.65217 | −0.411198 | ||||||||
\(129\) | 1.46011 | − | 1.48487i | 0.128556 | − | 0.130735i | ||||
\(130\) | −1.08002 | −0.0947244 | ||||||||
\(131\) | −7.89101 | −0.689441 | −0.344720 | − | 0.938705i | \(-0.612026\pi\) | ||||
−0.344720 | + | 0.938705i | \(0.612026\pi\) | |||||||
\(132\) | 8.98184 | + | 3.74260i | 0.781768 | + | 0.325751i | ||||
\(133\) | −4.21243 | −0.365264 | ||||||||
\(134\) | −11.7775 | −1.01742 | ||||||||
\(135\) | 1.55708 | + | 1.48047i | 0.134012 | + | 0.127418i | ||||
\(136\) | −0.965096 | −0.0827563 | ||||||||
\(137\) | 4.27223i | 0.365002i | 0.983206 | + | 0.182501i | \(0.0584192\pi\) | ||||
−0.983206 | + | 0.182501i | \(0.941581\pi\) | |||||||
\(138\) | 14.3827 | − | 14.6266i | 1.22434 | − | 1.24510i | ||||
\(139\) | 9.33606i | 0.791874i | 0.918278 | + | 0.395937i | \(0.129580\pi\) | ||||
−0.918278 | + | 0.395937i | \(0.870420\pi\) | |||||||
\(140\) | 0.700384 | 0.0591933 | ||||||||
\(141\) | 10.1197 | − | 10.2913i | 0.852236 | − | 0.866684i | ||||
\(142\) | 15.9777i | 1.34082i | ||||||||
\(143\) | 1.68104 | + | 4.18221i | 0.140576 | + | 0.349734i | ||||
\(144\) | −0.227864 | − | 13.5538i | −0.0189887 | − | 1.12949i | ||||
\(145\) | − | 1.12958i | − | 0.0938069i | ||||||
\(146\) | 0.558215i | 0.0461982i | ||||||||
\(147\) | −1.23500 | − | 1.21441i | −0.101861 | − | 0.100163i | ||||
\(148\) | −10.8583 | −0.892548 | ||||||||
\(149\) | 14.6400 | 1.19936 | 0.599679 | − | 0.800240i | \(-0.295295\pi\) | ||||
0.599679 | + | 0.800240i | \(0.295295\pi\) | |||||||
\(150\) | −11.4621 | − | 11.2710i | −0.935877 | − | 0.920275i | ||||
\(151\) | − | 17.6272i | − | 1.43448i | −0.696827 | − | 0.717240i | \(-0.745405\pi\) | ||
0.696827 | − | 0.717240i | \(-0.254595\pi\) | |||||||
\(152\) | 2.47866i | 0.201046i | ||||||||
\(153\) | −0.0827103 | − | 4.91978i | −0.00668673 | − | 0.397741i | ||||
\(154\) | −2.37731 | − | 5.91444i | −0.191569 | − | 0.476600i | ||||
\(155\) | − | 1.88847i | − | 0.151686i | ||||||
\(156\) | −2.79556 | + | 2.84295i | −0.223824 | + | 0.227618i | ||||
\(157\) | −4.42328 | −0.353016 | −0.176508 | − | 0.984299i | \(-0.556480\pi\) | ||||
−0.176508 | + | 0.984299i | \(0.556480\pi\) | |||||||
\(158\) | 32.0419i | 2.54912i | ||||||||
\(159\) | −7.18597 | + | 7.30780i | −0.569885 | + | 0.579546i | ||||
\(160\) | − | 3.10431i | − | 0.245417i | ||||||
\(161\) | −6.16223 | −0.485652 | ||||||||
\(162\) | 17.2877 | − | 0.581437i | 1.35825 | − | 0.0456820i | ||||
\(163\) | −3.64734 | −0.285682 | −0.142841 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142841 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(164\) | −6.04759 | −0.472237 | ||||||||
\(165\) | 0.913615 | − | 2.19258i | 0.0711248 | − | 0.170692i | ||||
\(166\) | −6.79118 | −0.527097 | ||||||||
\(167\) | −6.34851 | −0.491262 | −0.245631 | − | 0.969363i | \(-0.578995\pi\) | ||||
−0.245631 | + | 0.969363i | \(0.578995\pi\) | |||||||
\(168\) | −0.714576 | + | 0.726690i | −0.0551308 | + | 0.0560654i | ||||
\(169\) | 11.1530 | 0.857925 | ||||||||
\(170\) | − | 1.30343i | − | 0.0999688i | ||||||
\(171\) | −12.6355 | + | 0.212425i | −0.966260 | + | 0.0162446i | ||||
\(172\) | − | 2.03655i | − | 0.155286i | ||||||
\(173\) | −14.2027 | −1.07981 | −0.539905 | − | 0.841726i | \(-0.681540\pi\) | ||||
−0.539905 | + | 0.841726i | \(0.681540\pi\) | |||||||
\(174\) | −6.48425 | − | 6.37616i | −0.491570 | − | 0.483375i | ||||
\(175\) | 4.82903i | 0.365040i | ||||||||
\(176\) | −13.9052 | + | 5.58919i | −1.04814 | + | 0.421301i | ||||
\(177\) | 12.5948 | − | 12.8083i | 0.946684 | − | 0.962733i | ||||
\(178\) | − | 17.6417i | − | 1.32230i | ||||||
\(179\) | − | 25.1186i | − | 1.87746i | −0.344660 | − | 0.938728i | \(-0.612006\pi\) | ||
0.344660 | − | 0.938728i | \(-0.387994\pi\) | |||||||
\(180\) | 2.10086 | − | 0.0353191i | 0.156589 | − | 0.00263253i | ||||
\(181\) | 6.77948 | 0.503914 | 0.251957 | − | 0.967738i | \(-0.418926\pi\) | ||||
0.251957 | + | 0.967738i | \(0.418926\pi\) | |||||||
\(182\) | 2.61198 | 0.193613 | ||||||||
\(183\) | 18.9274 | − | 19.2483i | 1.39915 | − | 1.42287i | ||||
\(184\) | 3.62595i | 0.267309i | ||||||||
\(185\) | 2.65065i | 0.194880i | ||||||||
\(186\) | −10.8406 | − | 10.6599i | −0.794869 | − | 0.781618i | ||||
\(187\) | −5.04732 | + | 2.02877i | −0.369097 | + | 0.148358i | ||||
\(188\) | − | 14.1149i | − | 1.02944i | ||||||
\(189\) | −3.76570 | − | 3.58043i | −0.273915 | − | 0.260438i | ||||
\(190\) | −3.34761 | −0.242861 | ||||||||
\(191\) | − | 11.1330i | − | 0.805556i | −0.915298 | − | 0.402778i | \(-0.868045\pi\) | ||
0.915298 | − | 0.402778i | \(-0.131955\pi\) | |||||||
\(192\) | −6.65906 | − | 6.54805i | −0.480576 | − | 0.472565i | ||||
\(193\) | 21.6435i | 1.55794i | 0.627064 | + | 0.778968i | \(0.284256\pi\) | ||||
−0.627064 | + | 0.778968i | \(0.715744\pi\) | |||||||
\(194\) | −24.9107 | −1.78848 | ||||||||
\(195\) | 0.694001 | + | 0.682431i | 0.0496984 | + | 0.0488699i | ||||
\(196\) | −1.69384 | −0.120989 | ||||||||
\(197\) | 10.0414 | 0.715421 | 0.357710 | − | 0.933833i | \(-0.383557\pi\) | ||||
0.357710 | + | 0.933833i | \(0.383557\pi\) | |||||||
\(198\) | −7.42918 | − | 17.6209i | −0.527969 | − | 1.25227i | ||||
\(199\) | −19.8549 | −1.40747 | −0.703737 | − | 0.710461i | \(-0.748486\pi\) | ||||
−0.703737 | + | 0.710461i | \(0.748486\pi\) | |||||||
\(200\) | 2.84147 | 0.200923 | ||||||||
\(201\) | 7.56796 | + | 7.44180i | 0.533803 | + | 0.524904i | ||||
\(202\) | 24.2581 | 1.70679 | ||||||||
\(203\) | 2.73184i | 0.191738i | ||||||||
\(204\) | −3.43103 | − | 3.37383i | −0.240220 | − | 0.236216i | ||||
\(205\) | 1.47629i | 0.103109i | ||||||||
\(206\) | 24.6207 | 1.71540 | ||||||||
\(207\) | −18.4841 | + | 0.310750i | −1.28473 | + | 0.0215986i | ||||
\(208\) | − | 6.14092i | − | 0.425796i | ||||||
\(209\) | 5.21050 | + | 12.9630i | 0.360418 | + | 0.896672i | ||||
\(210\) | −0.981450 | − | 0.965088i | −0.0677265 | − | 0.0665974i | ||||
\(211\) | 1.16287i | 0.0800555i | 0.999199 | + | 0.0400278i | \(0.0127446\pi\) | ||||
−0.999199 | + | 0.0400278i | \(0.987255\pi\) | |||||||
\(212\) | 10.0229i | 0.688377i | ||||||||
\(213\) | 10.0958 | − | 10.2669i | 0.691751 | − | 0.703478i | ||||
\(214\) | −10.2881 | −0.703283 | ||||||||
\(215\) | −0.497148 | −0.0339052 | ||||||||
\(216\) | −2.10678 | + | 2.21580i | −0.143348 | + | 0.150766i | ||||
\(217\) | 4.56717i | 0.310040i | ||||||||
\(218\) | − | 23.0193i | − | 1.55907i | ||||||
\(219\) | 0.352717 | − | 0.358697i | 0.0238344 | − | 0.0242385i | ||||
\(220\) | −0.866330 | − | 2.15532i | −0.0584080 | − | 0.145311i | ||||
\(221\) | − | 2.22904i | − | 0.149941i | ||||||
\(222\) | 15.2158 | + | 14.9621i | 1.02122 | + | 1.00419i | ||||
\(223\) | −12.4329 | −0.832568 | −0.416284 | − | 0.909235i | \(-0.636668\pi\) | ||||
−0.416284 | + | 0.909235i | \(0.636668\pi\) | |||||||
\(224\) | 7.50760i | 0.501623i | ||||||||
\(225\) | 0.243519 | + | 14.4850i | 0.0162346 | + | 0.965669i | ||||
\(226\) | 8.99161i | 0.598113i | ||||||||
\(227\) | 27.4133 | 1.81948 | 0.909742 | − | 0.415174i | \(-0.136279\pi\) | ||||
0.909742 | + | 0.415174i | \(0.136279\pi\) | |||||||
\(228\) | −8.66502 | + | 8.81192i | −0.573855 | + | 0.583584i | ||||
\(229\) | −27.2215 | −1.79885 | −0.899423 | − | 0.437080i | \(-0.856013\pi\) | ||||
−0.899423 | + | 0.437080i | \(0.856013\pi\) | |||||||
\(230\) | −4.89712 | −0.322906 | ||||||||
\(231\) | −2.20953 | + | 5.30264i | −0.145376 | + | 0.348888i | ||||
\(232\) | 1.60746 | 0.105535 | ||||||||
\(233\) | 10.8221 | 0.708982 | 0.354491 | − | 0.935059i | \(-0.384654\pi\) | ||||
0.354491 | + | 0.935059i | \(0.384654\pi\) | |||||||
\(234\) | 7.83484 | − | 0.131718i | 0.512179 | − | 0.00861065i | ||||
\(235\) | −3.44563 | −0.224768 | ||||||||
\(236\) | − | 17.5671i | − | 1.14352i | ||||||
\(237\) | 20.2462 | − | 20.5895i | 1.31513 | − | 1.33743i | ||||
\(238\) | 3.15228i | 0.204332i | ||||||||
\(239\) | 19.9099 | 1.28786 | 0.643931 | − | 0.765083i | \(-0.277302\pi\) | ||||
0.643931 | + | 0.765083i | \(0.277302\pi\) | |||||||
\(240\) | −2.26898 | + | 2.30744i | −0.146462 | + | 0.148945i | ||||
\(241\) | 7.69265i | 0.495527i | 0.968821 | + | 0.247764i | \(0.0796956\pi\) | ||||
−0.968821 | + | 0.247764i | \(0.920304\pi\) | |||||||
\(242\) | −15.2601 | + | 14.6316i | −0.980959 | + | 0.940553i | ||||
\(243\) | −11.4761 | − | 10.5499i | −0.736190 | − | 0.676775i | ||||
\(244\) | − | 26.3997i | − | 1.69007i | ||||||
\(245\) | 0.413489i | 0.0264168i | ||||||||
\(246\) | 8.47449 | + | 8.33322i | 0.540314 | + | 0.531307i | ||||
\(247\) | −5.72484 | −0.364263 | ||||||||
\(248\) | 2.68740 | 0.170650 | ||||||||
\(249\) | 4.36386 | + | 4.29112i | 0.276549 | + | 0.271938i | ||||
\(250\) | 7.81112i | 0.494018i | ||||||||
\(251\) | − | 9.61917i | − | 0.607157i | −0.952806 | − | 0.303578i | \(-0.901819\pi\) | ||
0.952806 | − | 0.303578i | \(-0.0981814\pi\) | |||||||
\(252\) | −5.08081 | + | 0.0854175i | −0.320061 | + | 0.00538079i | ||||
\(253\) | 7.62228 | + | 18.9632i | 0.479208 | + | 1.19221i | ||||
\(254\) | − | 13.4697i | − | 0.845164i | ||||||
\(255\) | −0.823596 | + | 0.837558i | −0.0515756 | + | 0.0524499i | ||||
\(256\) | 19.7251 | 1.23282 | ||||||||
\(257\) | 12.9172i | 0.805751i | 0.915255 | + | 0.402875i | \(0.131989\pi\) | ||||
−0.915255 | + | 0.402875i | \(0.868011\pi\) | |||||||
\(258\) | −2.80625 | + | 2.85382i | −0.174709 | + | 0.177671i | ||||
\(259\) | − | 6.41046i | − | 0.398327i | ||||||
\(260\) | 0.951848 | 0.0590311 | ||||||||
\(261\) | 0.137762 | + | 8.19437i | 0.00852725 | + | 0.507218i | ||||
\(262\) | 15.1660 | 0.936960 | ||||||||
\(263\) | 1.86943 | 0.115274 | 0.0576369 | − | 0.998338i | \(-0.481643\pi\) | ||||
0.0576369 | + | 0.998338i | \(0.481643\pi\) | |||||||
\(264\) | 3.12015 | + | 1.30012i | 0.192032 | + | 0.0800169i | ||||
\(265\) | 2.44672 | 0.150301 | ||||||||
\(266\) | 8.09602 | 0.496399 | ||||||||
\(267\) | −11.1472 | + | 11.3362i | −0.682197 | + | 0.693763i | ||||
\(268\) | 10.3797 | 0.634043 | ||||||||
\(269\) | − | 12.9253i | − | 0.788071i | −0.919095 | − | 0.394036i | \(-0.871079\pi\) | ||
0.919095 | − | 0.394036i | \(-0.128921\pi\) | |||||||
\(270\) | −2.99260 | − | 2.84536i | −0.182124 | − | 0.173163i | ||||
\(271\) | 20.2282i | 1.22878i | 0.789003 | + | 0.614389i | \(0.210597\pi\) | ||||
−0.789003 | + | 0.614389i | \(0.789403\pi\) | |||||||
\(272\) | 7.41120 | 0.449370 | ||||||||
\(273\) | −1.67840 | − | 1.65042i | −0.101582 | − | 0.0998882i | ||||
\(274\) | − | 8.21097i | − | 0.496043i | ||||||
\(275\) | 14.8605 | − | 5.97319i | 0.896124 | − | 0.360197i | ||||
\(276\) | −12.6758 | + | 12.8907i | −0.762993 | + | 0.775928i | ||||
\(277\) | 7.26198i | 0.436330i | 0.975912 | + | 0.218165i | \(0.0700071\pi\) | ||||
−0.975912 | + | 0.218165i | \(0.929993\pi\) | |||||||
\(278\) | − | 17.9433i | − | 1.07617i | ||||||
\(279\) | 0.230314 | + | 13.6996i | 0.0137886 | + | 0.820173i | ||||
\(280\) | 0.243303 | 0.0145401 | ||||||||
\(281\) | −25.5479 | −1.52406 | −0.762030 | − | 0.647541i | \(-0.775797\pi\) | ||||
−0.762030 | + | 0.647541i | \(0.775797\pi\) | |||||||
\(282\) | −19.4495 | + | 19.7792i | −1.15820 | + | 1.17784i | ||||
\(283\) | − | 19.3170i | − | 1.14828i | −0.818758 | − | 0.574139i | \(-0.805337\pi\) | ||
0.818758 | − | 0.574139i | \(-0.194663\pi\) | |||||||
\(284\) | − | 14.0815i | − | 0.835582i | ||||||
\(285\) | 2.15110 | + | 2.11524i | 0.127420 | + | 0.125296i | ||||
\(286\) | −3.23085 | − | 8.03794i | −0.191044 | − | 0.475294i | ||||
\(287\) | − | 3.57034i | − | 0.210750i | ||||||
\(288\) | 0.378595 | + | 22.5196i | 0.0223089 | + | 1.32698i | ||||
\(289\) | −14.3099 | −0.841757 | ||||||||
\(290\) | 2.17099i | 0.127485i | ||||||||
\(291\) | 16.0071 | + | 15.7402i | 0.938351 | + | 0.922708i | ||||
\(292\) | − | 0.491966i | − | 0.0287902i | ||||||
\(293\) | −19.4631 | −1.13705 | −0.568523 | − | 0.822667i | \(-0.692485\pi\) | ||||
−0.568523 | + | 0.822667i | \(0.692485\pi\) | |||||||
\(294\) | 2.37358 | + | 2.33402i | 0.138430 | + | 0.136123i | ||||
\(295\) | −4.28835 | −0.249678 | ||||||||
\(296\) | −3.77202 | −0.219244 | ||||||||
\(297\) | −6.36025 | + | 16.0171i | −0.369059 | + | 0.929406i | ||||
\(298\) | −28.1372 | −1.62995 | ||||||||
\(299\) | −8.37469 | −0.484321 | ||||||||
\(300\) | 10.1018 | + | 9.93338i | 0.583227 | + | 0.573504i | ||||
\(301\) | 1.20233 | 0.0693009 | ||||||||
\(302\) | 33.8783i | 1.94948i | ||||||||
\(303\) | −15.5877 | − | 15.3279i | −0.895492 | − | 0.880564i | ||||
\(304\) | − | 19.0342i | − | 1.09169i | ||||||
\(305\) | −6.44451 | −0.369012 | ||||||||
\(306\) | 0.158964 | + | 9.45552i | 0.00908737 | + | 0.540536i | ||||
\(307\) | − | 8.73827i | − | 0.498719i | −0.968411 | − | 0.249360i | \(-0.919780\pi\) | ||
0.968411 | − | 0.249360i | \(-0.0802201\pi\) | |||||||
\(308\) | 2.09517 | + | 5.21252i | 0.119384 | + | 0.297011i | ||||
\(309\) | −15.8207 | − | 15.5570i | −0.900009 | − | 0.885005i | ||||
\(310\) | 3.62953i | 0.206143i | ||||||||
\(311\) | − | 10.6726i | − | 0.605185i | −0.953120 | − | 0.302593i | \(-0.902148\pi\) | ||
0.953120 | − | 0.302593i | \(-0.0978522\pi\) | |||||||
\(312\) | −0.971135 | + | 0.987599i | −0.0549797 | + | 0.0559118i | ||||
\(313\) | 26.7253 | 1.51060 | 0.755302 | − | 0.655377i | \(-0.227490\pi\) | ||||
0.755302 | + | 0.655377i | \(0.227490\pi\) | |||||||
\(314\) | 8.50127 | 0.479754 | ||||||||
\(315\) | 0.0208515 | + | 1.24029i | 0.00117485 | + | 0.0698824i | ||||
\(316\) | − | 28.2392i | − | 1.58858i | ||||||
\(317\) | 16.7346i | 0.939907i | 0.882691 | + | 0.469953i | \(0.155729\pi\) | ||||
−0.882691 | + | 0.469953i | \(0.844271\pi\) | |||||||
\(318\) | 13.8110 | − | 14.0451i | 0.774482 | − | 0.787612i | ||||
\(319\) | 8.40679 | − | 3.37911i | 0.470690 | − | 0.189194i | ||||
\(320\) | 2.22952i | 0.124634i | ||||||||
\(321\) | 6.61094 | + | 6.50073i | 0.368987 | + | 0.362835i | ||||
\(322\) | 11.8434 | 0.660008 | ||||||||
\(323\) | − | 6.90905i | − | 0.384430i | ||||||
\(324\) | −15.2360 | + | 0.512432i | −0.846443 | + | 0.0284685i | ||||
\(325\) | 6.56282i | 0.364040i | ||||||||
\(326\) | 7.00996 | 0.388246 | ||||||||
\(327\) | −14.5451 | + | 14.7917i | −0.804348 | + | 0.817984i | ||||
\(328\) | −2.10084 | −0.116000 | ||||||||
\(329\) | 8.33307 | 0.459417 | ||||||||
\(330\) | −1.75591 | + | 4.21400i | −0.0966597 | + | 0.231973i | ||||
\(331\) | −0.0281857 | −0.00154923 | −0.000774613 | − | 1.00000i | \(-0.500247\pi\) | ||||
−0.000774613 | 1.00000i | \(0.500247\pi\) | ||||||||
\(332\) | 5.98520 | 0.328481 | ||||||||
\(333\) | −0.323268 | − | 19.2287i | −0.0177150 | − | 1.05372i | ||||
\(334\) | 12.2014 | 0.667633 | ||||||||
\(335\) | − | 2.53383i | − | 0.138438i | ||||||
\(336\) | 5.48740 | − | 5.58043i | 0.299362 | − | 0.304437i | ||||
\(337\) | − | 28.5132i | − | 1.55321i | −0.629987 | − | 0.776606i | \(-0.716940\pi\) | ||
0.629987 | − | 0.776606i | \(-0.283060\pi\) | |||||||
\(338\) | −21.4354 | −1.16593 | ||||||||
\(339\) | 5.68149 | − | 5.77781i | 0.308576 | − | 0.313808i | ||||
\(340\) | 1.14874i | 0.0622993i | ||||||||
\(341\) | 14.0547 | − | 5.64930i | 0.761106 | − | 0.305927i | ||||
\(342\) | 24.2846 | − | 0.408268i | 1.31316 | − | 0.0220766i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 0.707467i | − | 0.0381441i | ||||||
\(345\) | 3.14678 | + | 3.09432i | 0.169417 | + | 0.166593i | ||||
\(346\) | 27.2967 | 1.46748 | ||||||||
\(347\) | −32.0737 | −1.72181 | −0.860903 | − | 0.508769i | \(-0.830101\pi\) | ||||
−0.860903 | + | 0.508769i | \(0.830101\pi\) | |||||||
\(348\) | 5.71471 | + | 5.61944i | 0.306340 | + | 0.301234i | ||||
\(349\) | − | 24.5954i | − | 1.31656i | −0.752773 | − | 0.658280i | \(-0.771284\pi\) | ||
0.752773 | − | 0.658280i | \(-0.228716\pi\) | |||||||
\(350\) | − | 9.28109i | − | 0.496095i | ||||||
\(351\) | −5.11773 | − | 4.86593i | −0.273164 | − | 0.259724i | ||||
\(352\) | 23.1034 | − | 9.28642i | 1.23142 | − | 0.494968i | ||||
\(353\) | 21.2100i | 1.12889i | 0.825470 | + | 0.564446i | \(0.190910\pi\) | ||||
−0.825470 | + | 0.564446i | \(0.809090\pi\) | |||||||
\(354\) | −24.2064 | + | 24.6168i | −1.28656 | + | 1.30837i | ||||
\(355\) | −3.43747 | −0.182442 | ||||||||
\(356\) | 15.5480i | 0.824042i | ||||||||
\(357\) | 1.99182 | − | 2.02559i | 0.105418 | − | 0.107206i | ||||
\(358\) | 48.2764i | 2.55149i | ||||||||
\(359\) | 12.0531 | 0.636141 | 0.318070 | − | 0.948067i | \(-0.396965\pi\) | ||||
0.318070 | + | 0.948067i | \(0.396965\pi\) | |||||||
\(360\) | 0.729806 | − | 0.0122693i | 0.0384642 | − | 0.000646651i | ||||
\(361\) | 1.25547 | 0.0660776 | ||||||||
\(362\) | −13.0297 | −0.684827 | ||||||||
\(363\) | 19.0510 | + | 0.240442i | 0.999920 | + | 0.0126199i | ||||
\(364\) | −2.30199 | −0.120657 | ||||||||
\(365\) | −0.120095 | −0.00628607 | ||||||||
\(366\) | −36.3773 | + | 36.9940i | −1.90147 | + | 1.93371i | ||||
\(367\) | −13.3568 | −0.697219 | −0.348609 | − | 0.937268i | \(-0.613346\pi\) | ||||
−0.348609 | + | 0.937268i | \(0.613346\pi\) | |||||||
\(368\) | − | 27.8445i | − | 1.45150i | ||||||
\(369\) | −0.180046 | − | 10.7095i | −0.00937281 | − | 0.557514i | ||||
\(370\) | − | 5.09439i | − | 0.264845i | ||||||
\(371\) | −5.91727 | −0.307209 | ||||||||
\(372\) | 9.55402 | + | 9.39475i | 0.495353 | + | 0.487095i | ||||
\(373\) | 1.91862i | 0.0993425i | 0.998766 | + | 0.0496713i | \(0.0158174\pi\) | ||||
−0.998766 | + | 0.0496713i | \(0.984183\pi\) | |||||||
\(374\) | 9.70064 | − | 3.89917i | 0.501608 | − | 0.201621i | ||||
\(375\) | 4.93558 | − | 5.01926i | 0.254872 | − | 0.259193i | ||||
\(376\) | − | 4.90331i | − | 0.252869i | ||||||
\(377\) | 3.71267i | 0.191212i | ||||||||
\(378\) | 7.23745 | + | 6.88136i | 0.372254 | + | 0.353939i | ||||
\(379\) | 23.5384 | 1.20909 | 0.604544 | − | 0.796572i | \(-0.293355\pi\) | ||||
0.604544 | + | 0.796572i | \(0.293355\pi\) | |||||||
\(380\) | 2.95032 | 0.151348 | ||||||||
\(381\) | −8.51105 | + | 8.65533i | −0.436034 | + | 0.443426i | ||||
\(382\) | 21.3969i | 1.09476i | ||||||||
\(383\) | − | 10.1166i | − | 0.516932i | −0.966020 | − | 0.258466i | \(-0.916783\pi\) | ||
0.966020 | − | 0.258466i | \(-0.0832170\pi\) | |||||||
\(384\) | −5.74541 | − | 5.64963i | −0.293194 | − | 0.288307i | ||||
\(385\) | 1.27244 | − | 0.511459i | 0.0648497 | − | 0.0260663i | ||||
\(386\) | − | 41.5975i | − | 2.11726i | ||||||
\(387\) | 3.60647 | − | 0.0606312i | 0.183327 | − | 0.00308206i | ||||
\(388\) | 21.9543 | 1.11456 | ||||||||
\(389\) | − | 5.43831i | − | 0.275733i | −0.990451 | − | 0.137867i | \(-0.955975\pi\) | ||
0.990451 | − | 0.137867i | \(-0.0440246\pi\) | |||||||
\(390\) | −1.33383 | − | 1.31159i | −0.0675409 | − | 0.0664149i | ||||
\(391\) | − | 10.1070i | − | 0.511135i | ||||||
\(392\) | −0.588415 | −0.0297195 | ||||||||
\(393\) | −9.74536 | − | 9.58290i | −0.491588 | − | 0.483393i | ||||
\(394\) | −19.2990 | −0.972268 | ||||||||
\(395\) | −6.89355 | −0.346852 | ||||||||
\(396\) | 6.54749 | + | 15.5297i | 0.329024 | + | 0.780397i | ||||
\(397\) | 25.7021 | 1.28995 | 0.644975 | − | 0.764204i | \(-0.276868\pi\) | ||||
0.644975 | + | 0.764204i | \(0.276868\pi\) | |||||||
\(398\) | 38.1598 | 1.91278 | ||||||||
\(399\) | −5.20233 | − | 5.11560i | −0.260442 | − | 0.256100i | ||||
\(400\) | −21.8204 | −1.09102 | ||||||||
\(401\) | 35.2490i | 1.76025i | 0.474741 | + | 0.880125i | \(0.342542\pi\) | ||||
−0.474741 | + | 0.880125i | \(0.657458\pi\) | |||||||
\(402\) | −14.5451 | − | 14.3027i | −0.725446 | − | 0.713352i | ||||
\(403\) | 6.20695i | 0.309190i | ||||||||
\(404\) | −21.3792 | −1.06365 | ||||||||
\(405\) | 0.125091 | + | 3.71929i | 0.00621583 | + | 0.184813i | ||||
\(406\) | − | 5.25043i | − | 0.260574i | ||||||
\(407\) | −19.7271 | + | 7.92933i | −0.977838 | + | 0.393042i | ||||
\(408\) | −1.19189 | − | 1.17202i | −0.0590073 | − | 0.0580236i | ||||
\(409\) | 29.2925i | 1.44842i | 0.689579 | + | 0.724210i | \(0.257795\pi\) | ||||
−0.689579 | + | 0.724210i | \(0.742205\pi\) | |||||||
\(410\) | − | 2.83734i | − | 0.140126i | ||||||
\(411\) | −5.18823 | + | 5.27619i | −0.255917 | + | 0.260255i | ||||
\(412\) | −21.6987 | −1.06902 | ||||||||
\(413\) | 10.3712 | 0.510331 | ||||||||
\(414\) | 35.5252 | − | 0.597242i | 1.74597 | − | 0.0293529i | ||||
\(415\) | − | 1.46106i | − | 0.0717208i | ||||||
\(416\) | 10.2031i | 0.500248i | ||||||||
\(417\) | −11.3378 | + | 11.5300i | −0.555214 | + | 0.564626i | ||||
\(418\) | −10.0142 | − | 24.9142i | −0.489813 | − | 1.21859i | ||||
\(419\) | 7.55837i | 0.369250i | 0.982809 | + | 0.184625i | \(0.0591071\pi\) | ||||
−0.982809 | + | 0.184625i | \(0.940893\pi\) | |||||||
\(420\) | 0.864972 | + | 0.850552i | 0.0422063 | + | 0.0415027i | ||||
\(421\) | −2.30918 | −0.112542 | −0.0562712 | − | 0.998416i | \(-0.517921\pi\) | ||||
−0.0562712 | + | 0.998416i | \(0.517921\pi\) | |||||||
\(422\) | − | 2.23497i | − | 0.108797i | ||||||
\(423\) | 24.9957 | − | 0.420222i | 1.21533 | − | 0.0204319i | ||||
\(424\) | 3.48181i | 0.169092i | ||||||||
\(425\) | −7.92038 | −0.384195 | ||||||||
\(426\) | −19.4034 | + | 19.7324i | −0.940100 | + | 0.956037i | ||||
\(427\) | 15.5857 | 0.754245 | ||||||||
\(428\) | 9.06715 | 0.438277 | ||||||||
\(429\) | −3.00283 | + | 7.20648i | −0.144978 | + | 0.347932i | ||||
\(430\) | 0.955488 | 0.0460777 | ||||||||
\(431\) | 16.2294 | 0.781745 | 0.390872 | − | 0.920445i | \(-0.372173\pi\) | ||||
0.390872 | + | 0.920445i | \(0.372173\pi\) | |||||||
\(432\) | 16.1785 | − | 17.0156i | 0.778387 | − | 0.818666i | ||||
\(433\) | 1.66823 | 0.0801698 | 0.0400849 | − | 0.999196i | \(-0.487237\pi\) | ||||
0.0400849 | + | 0.999196i | \(0.487237\pi\) | |||||||
\(434\) | − | 8.77782i | − | 0.421349i | ||||||
\(435\) | 1.37178 | − | 1.39503i | 0.0657717 | − | 0.0668867i | ||||
\(436\) | 20.2874i | 0.971590i | ||||||||
\(437\) | −25.9579 | −1.24174 | ||||||||
\(438\) | −0.677901 | + | 0.689393i | −0.0323913 | + | 0.0329405i | ||||
\(439\) | 34.5341i | 1.64822i | 0.566426 | + | 0.824112i | \(0.308326\pi\) | ||||
−0.566426 | + | 0.824112i | \(0.691674\pi\) | |||||||
\(440\) | −0.300950 | − | 0.748725i | −0.0143472 | − | 0.0356941i | ||||
\(441\) | −0.0504282 | − | 2.99958i | −0.00240134 | − | 0.142837i | ||||
\(442\) | 4.28407i | 0.203772i | ||||||||
\(443\) | 23.1357i | 1.09921i | 0.835424 | + | 0.549606i | \(0.185222\pi\) | ||||
−0.835424 | + | 0.549606i | \(0.814778\pi\) | |||||||
\(444\) | −13.4100 | − | 13.1864i | −0.636409 | − | 0.625800i | ||||
\(445\) | 3.79546 | 0.179922 | ||||||||
\(446\) | 23.8952 | 1.13147 | ||||||||
\(447\) | 18.0804 | + | 17.7790i | 0.855173 | + | 0.840916i | ||||
\(448\) | − | 5.39197i | − | 0.254747i | ||||||
\(449\) | 14.1968i | 0.669989i | 0.942220 | + | 0.334995i | \(0.108734\pi\) | ||||
−0.942220 | + | 0.334995i | \(0.891266\pi\) | |||||||
\(450\) | −0.468029 | − | 27.8393i | −0.0220631 | − | 1.31236i | ||||
\(451\) | −10.9871 | + | 4.41628i | −0.517363 | + | 0.207954i | ||||
\(452\) | − | 7.92449i | − | 0.372737i | ||||||
\(453\) | 21.4066 | − | 21.7695i | 1.00577 | − | 1.02282i | ||||
\(454\) | −52.6866 | −2.47271 | ||||||||
\(455\) | 0.561946i | 0.0263444i | ||||||||
\(456\) | −3.01010 | + | 3.06113i | −0.140961 | + | 0.143351i | ||||
\(457\) | − | 15.8942i | − | 0.743500i | −0.928333 | − | 0.371750i | \(-0.878758\pi\) | ||
0.928333 | − | 0.371750i | \(-0.121242\pi\) | |||||||
\(458\) | 52.3180 | 2.44466 | ||||||||
\(459\) | 5.87248 | − | 6.17636i | 0.274104 | − | 0.288288i | ||||
\(460\) | 4.31593 | 0.201231 | ||||||||
\(461\) | 25.5065 | 1.18795 | 0.593977 | − | 0.804482i | \(-0.297557\pi\) | ||||
0.593977 | + | 0.804482i | \(0.297557\pi\) | |||||||
\(462\) | 4.24658 | − | 10.1913i | 0.197569 | − | 0.474144i | ||||
\(463\) | 13.2452 | 0.615558 | 0.307779 | − | 0.951458i | \(-0.400414\pi\) | ||||
0.307779 | + | 0.951458i | \(0.400414\pi\) | |||||||
\(464\) | −12.3440 | −0.573058 | ||||||||
\(465\) | 2.29338 | − | 2.33226i | 0.106353 | − | 0.108156i | ||||
\(466\) | −20.7995 | −0.963517 | ||||||||
\(467\) | − | 28.3407i | − | 1.31145i | −0.754999 | − | 0.655726i | \(-0.772363\pi\) | ||
0.754999 | − | 0.655726i | \(-0.227637\pi\) | |||||||
\(468\) | −6.90500 | + | 0.116085i | −0.319184 | + | 0.00536605i | ||||
\(469\) | 6.12792i | 0.282961i | ||||||||
\(470\) | 6.62228 | 0.305463 | ||||||||
\(471\) | −5.46273 | − | 5.37167i | −0.251710 | − | 0.247513i | ||||
\(472\) | − | 6.10255i | − | 0.280892i | ||||||
\(473\) | −1.48720 | − | 3.69996i | −0.0683815 | − | 0.170124i | ||||
\(474\) | −38.9120 | + | 39.5717i | −1.78729 | + | 1.81759i | ||||
\(475\) | 20.3419i | 0.933351i | ||||||||
\(476\) | − | 2.77817i | − | 0.127337i | ||||||
\(477\) | −17.7493 | + | 0.298397i | −0.812684 | + | 0.0136627i | ||||
\(478\) | −38.2655 | −1.75022 | ||||||||
\(479\) | 1.53713 | 0.0702331 | 0.0351165 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351165 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(480\) | 3.76989 | − | 3.83381i | 0.172071 | − | 0.174988i | ||||
\(481\) | − | 8.71205i | − | 0.397235i | ||||||
\(482\) | − | 14.7848i | − | 0.673429i | ||||||
\(483\) | −7.61032 | − | 7.48346i | −0.346282 | − | 0.340509i | ||||
\(484\) | 13.4491 | − | 12.8951i | 0.611322 | − | 0.586141i | ||||
\(485\) | − | 5.35932i | − | 0.243354i | ||||||
\(486\) | 22.0563 | + | 20.2762i | 1.00049 | + | 0.919747i | ||||
\(487\) | −7.17846 | −0.325287 | −0.162643 | − | 0.986685i | \(-0.552002\pi\) | ||||
−0.162643 | + | 0.986685i | \(0.552002\pi\) | |||||||
\(488\) | − | 9.17087i | − | 0.415146i | ||||||
\(489\) | −4.50445 | − | 4.42936i | −0.203698 | − | 0.200303i | ||||
\(490\) | − | 0.794699i | − | 0.0359008i | ||||||
\(491\) | 37.4970 | 1.69221 | 0.846107 | − | 0.533013i | \(-0.178940\pi\) | ||||
0.846107 | + | 0.533013i | \(0.178940\pi\) | |||||||
\(492\) | −7.46875 | − | 7.34424i | −0.336717 | − | 0.331104i | ||||
\(493\) | −4.48066 | −0.201799 | ||||||||
\(494\) | 11.0028 | 0.495038 | ||||||||
\(495\) | 3.79100 | − | 1.59833i | 0.170393 | − | 0.0718394i | ||||
\(496\) | −20.6372 | −0.926635 | ||||||||
\(497\) | 8.31333 | 0.372904 | ||||||||
\(498\) | −8.38707 | − | 8.24726i | −0.375834 | − | 0.369568i | ||||
\(499\) | 13.2712 | 0.594100 | 0.297050 | − | 0.954862i | \(-0.403997\pi\) | ||||
0.297050 | + | 0.954862i | \(0.403997\pi\) | |||||||
\(500\) | − | 6.88410i | − | 0.307866i | ||||||
\(501\) | −7.84038 | − | 7.70968i | −0.350282 | − | 0.344443i | ||||
\(502\) | 18.4874i | 0.825135i | ||||||||
\(503\) | −39.4829 | −1.76046 | −0.880228 | − | 0.474551i | \(-0.842610\pi\) | ||||
−0.880228 | + | 0.474551i | \(0.842610\pi\) | |||||||
\(504\) | −1.76500 | + | 0.0296727i | −0.0786192 | + | 0.00132173i | ||||
\(505\) | 5.21893i | 0.232239i | ||||||||
\(506\) | −14.6495 | − | 36.4462i | −0.651251 | − | 1.62023i | ||||
\(507\) | 13.7739 | + | 13.5443i | 0.611722 | + | 0.601524i | ||||
\(508\) | 11.8711i | 0.526696i | ||||||||
\(509\) | − | 0.384496i | − | 0.0170425i | −0.999964 | − | 0.00852125i | \(-0.997288\pi\) | ||
0.999964 | − | 0.00852125i | \(-0.00271243\pi\) | |||||||
\(510\) | 1.58290 | − | 1.60973i | 0.0700920 | − | 0.0712802i | ||||
\(511\) | 0.290444 | 0.0128485 | ||||||||
\(512\) | −28.6061 | −1.26422 | ||||||||
\(513\) | −15.8627 | − | 15.0823i | −0.700357 | − | 0.665899i | ||||
\(514\) | − | 24.8260i | − | 1.09503i | ||||||
\(515\) | 5.29693i | 0.233411i | ||||||||
\(516\) | 2.47320 | − | 2.51513i | 0.108877 | − | 0.110723i | ||||
\(517\) | −10.3075 | − | 25.6437i | −0.453322 | − | 1.12781i | ||||
\(518\) | 12.3205i | 0.541332i | ||||||||
\(519\) | −17.5403 | − | 17.2478i | −0.769932 | − | 0.757097i | ||||
\(520\) | 0.330658 | 0.0145003 | ||||||||
\(521\) | − | 21.4053i | − | 0.937783i | −0.883256 | − | 0.468892i | \(-0.844653\pi\) | ||
0.883256 | − | 0.468892i | \(-0.155347\pi\) | |||||||
\(522\) | −0.264770 | − | 15.7491i | −0.0115887 | − | 0.689317i | ||||
\(523\) | 38.1637i | 1.66878i | 0.551174 | + | 0.834390i | \(0.314180\pi\) | ||||
−0.551174 | + | 0.834390i | \(0.685820\pi\) | |||||||
\(524\) | −13.3661 | −0.583902 | ||||||||
\(525\) | −5.86441 | + | 5.96383i | −0.255944 | + | 0.260283i | ||||
\(526\) | −3.59292 | −0.156659 | ||||||||
\(527\) | −7.49090 | −0.326309 | ||||||||
\(528\) | −23.9604 | − | 9.98394i | −1.04274 | − | 0.434495i | ||||
\(529\) | −14.9730 | −0.651002 | ||||||||
\(530\) | −4.70244 | −0.204261 | ||||||||
\(531\) | 31.1091 | − | 0.522999i | 1.35002 | − | 0.0226962i | ||||
\(532\) | −7.13518 | −0.309349 | ||||||||
\(533\) | − | 4.85222i | − | 0.210173i | ||||||
\(534\) | 21.4242 | − | 21.7874i | 0.927116 | − | 0.942834i | ||||
\(535\) | − | 2.21341i | − | 0.0956939i | ||||||
\(536\) | 3.60576 | 0.155745 | ||||||||
\(537\) | 30.5043 | − | 31.0214i | 1.31636 | − | 1.33867i | ||||
\(538\) | 24.8417i | 1.07100i | ||||||||
\(539\) | −3.07734 | + | 1.23694i | −0.132550 | + | 0.0532786i | ||||
\(540\) | 2.63744 | + | 2.50768i | 0.113497 | + | 0.107913i | ||||
\(541\) | − | 9.20566i | − | 0.395782i | −0.980224 | − | 0.197891i | \(-0.936591\pi\) | ||
0.980224 | − | 0.197891i | \(-0.0634092\pi\) | |||||||
\(542\) | − | 38.8774i | − | 1.66993i | ||||||
\(543\) | 8.37262 | + | 8.23305i | 0.359304 | + | 0.353314i | ||||
\(544\) | −12.3137 | −0.527944 | ||||||||
\(545\) | 4.95241 | 0.212138 | ||||||||
\(546\) | 3.22579 | + | 3.17201i | 0.138051 | + | 0.135750i | ||||
\(547\) | − | 38.8699i | − | 1.66196i | −0.556305 | − | 0.830978i | \(-0.687781\pi\) | ||
0.556305 | − | 0.830978i | \(-0.312219\pi\) | |||||||
\(548\) | 7.23649i | 0.309128i | ||||||||
\(549\) | 46.7505 | − | 0.785959i | 1.99526 | − | 0.0335439i | ||||
\(550\) | −28.5610 | + | 11.4801i | −1.21785 | + | 0.489513i | ||||
\(551\) | 11.5077i | 0.490243i | ||||||||
\(552\) | −4.40338 | + | 4.47803i | −0.187420 | + | 0.190598i | ||||
\(553\) | 16.6717 | 0.708952 | ||||||||
\(554\) | − | 13.9571i | − | 0.592979i | ||||||
\(555\) | −3.21897 | + | 3.27355i | −0.136638 | + | 0.138954i | ||||
\(556\) | 15.8138i | 0.670655i | ||||||||
\(557\) | −29.6798 | −1.25757 | −0.628787 | − | 0.777578i | \(-0.716448\pi\) | ||||
−0.628787 | + | 0.777578i | \(0.716448\pi\) | |||||||
\(558\) | −0.442650 | − | 26.3297i | −0.0187389 | − | 1.11463i | ||||
\(559\) | 1.63400 | 0.0691110 | ||||||||
\(560\) | −1.86838 | −0.0789535 | ||||||||
\(561\) | −8.69718 | − | 3.62398i | −0.367195 | − | 0.153005i | ||||
\(562\) | 49.1015 | 2.07122 | ||||||||
\(563\) | −22.9672 | −0.967954 | −0.483977 | − | 0.875081i | \(-0.660808\pi\) | ||||
−0.483977 | + | 0.875081i | \(0.660808\pi\) | |||||||
\(564\) | 17.1413 | − | 17.4319i | 0.721777 | − | 0.734013i | ||||
\(565\) | −1.93447 | −0.0813837 | ||||||||
\(566\) | 37.1261i | 1.56053i | ||||||||
\(567\) | −0.302527 | − | 8.99491i | −0.0127049 | − | 0.377751i | ||||
\(568\) | − | 4.89169i | − | 0.205251i | ||||||
\(569\) | −18.5180 | −0.776314 | −0.388157 | − | 0.921593i | \(-0.626888\pi\) | ||||
−0.388157 | + | 0.921593i | \(0.626888\pi\) | |||||||
\(570\) | −4.13428 | − | 4.06536i | −0.173166 | − | 0.170279i | ||||
\(571\) | − | 9.78122i | − | 0.409332i | −0.978832 | − | 0.204666i | \(-0.934389\pi\) | ||
0.978832 | − | 0.204666i | \(-0.0656107\pi\) | |||||||
\(572\) | 2.84742 | + | 7.08400i | 0.119056 | + | 0.296197i | ||||
\(573\) | 13.5200 | − | 13.7492i | 0.564806 | − | 0.574382i | ||||
\(574\) | 6.86196i | 0.286413i | ||||||||
\(575\) | 29.7576i | 1.24098i | ||||||||
\(576\) | −0.271908 | − | 16.1736i | −0.0113295 | − | 0.673901i | ||||
\(577\) | −32.9536 | −1.37188 | −0.685938 | − | 0.727660i | \(-0.740608\pi\) | ||||
−0.685938 | + | 0.727660i | \(0.740608\pi\) | |||||||
\(578\) | 27.5027 | 1.14396 | ||||||||
\(579\) | −26.2841 | + | 26.7297i | −1.09233 | + | 1.11085i | ||||
\(580\) | − | 1.91334i | − | 0.0794471i | ||||||
\(581\) | 3.53351i | 0.146595i | ||||||||
\(582\) | −30.7646 | − | 30.2517i | −1.27523 | − | 1.25397i | ||||
\(583\) | 7.31927 | + | 18.2094i | 0.303133 | + | 0.754157i | ||||
\(584\) | − | 0.170902i | − | 0.00707196i | ||||||
\(585\) | 0.0283379 | + | 1.68560i | 0.00117163 | + | 0.0696910i | ||||
\(586\) | 37.4069 | 1.54526 | ||||||||
\(587\) | − | 12.3669i | − | 0.510438i | −0.966883 | − | 0.255219i | \(-0.917852\pi\) | ||
0.966883 | − | 0.255219i | \(-0.0821476\pi\) | |||||||
\(588\) | −2.09189 | − | 2.05702i | −0.0862680 | − | 0.0848299i | ||||
\(589\) | 19.2389i | 0.792724i | ||||||||
\(590\) | 8.24194 | 0.339315 | ||||||||
\(591\) | 12.4011 | + | 12.1944i | 0.510113 | + | 0.501609i | ||||
\(592\) | 28.9662 | 1.19050 | ||||||||
\(593\) | −0.769454 | −0.0315977 | −0.0157988 | − | 0.999875i | \(-0.505029\pi\) | ||||
−0.0157988 | + | 0.999875i | \(0.505029\pi\) | |||||||
\(594\) | 12.2240 | − | 30.7838i | 0.501557 | − | 1.26308i | ||||
\(595\) | −0.678187 | −0.0278030 | ||||||||
\(596\) | 24.7979 | 1.01576 | ||||||||
\(597\) | −24.5207 | − | 24.1119i | −1.00356 | − | 0.986834i | ||||
\(598\) | 16.0956 | 0.658199 | ||||||||
\(599\) | 23.1559i | 0.946123i | 0.881029 | + | 0.473062i | \(0.156851\pi\) | ||||
−0.881029 | + | 0.473062i | \(0.843149\pi\) | |||||||
\(600\) | 3.50921 | + | 3.45071i | 0.143263 | + | 0.140875i | ||||
\(601\) | 37.3517i | 1.52361i | 0.647809 | + | 0.761803i | \(0.275686\pi\) | ||||
−0.647809 | + | 0.761803i | \(0.724314\pi\) | |||||||
\(602\) | −2.31080 | −0.0941810 | ||||||||
\(603\) | 0.309020 | + | 18.3812i | 0.0125843 | + | 0.748539i | ||||
\(604\) | − | 29.8577i | − | 1.21489i | ||||||
\(605\) | −3.14786 | − | 3.28309i | −0.127979 | − | 0.133477i | ||||
\(606\) | 29.9587 | + | 29.4592i | 1.21699 | + | 1.19670i | ||||
\(607\) | − | 34.6424i | − | 1.40609i | −0.711144 | − | 0.703046i | \(-0.751823\pi\) | ||
0.711144 | − | 0.703046i | \(-0.248177\pi\) | |||||||
\(608\) | 31.6252i | 1.28257i | ||||||||
\(609\) | −3.31757 | + | 3.37381i | −0.134435 | + | 0.136714i | ||||
\(610\) | 12.3859 | 0.501492 | ||||||||
\(611\) | 11.3249 | 0.458158 | ||||||||
\(612\) | −0.140098 | − | 8.33334i | −0.00566314 | − | 0.336855i | ||||
\(613\) | − | 21.0615i | − | 0.850668i | −0.905037 | − | 0.425334i | \(-0.860157\pi\) | ||
0.905037 | − | 0.425334i | \(-0.139843\pi\) | |||||||
\(614\) | 16.7944i | 0.677767i | ||||||||
\(615\) | −1.79282 | + | 1.82322i | −0.0722936 | + | 0.0735192i | ||||
\(616\) | 0.727832 | + | 1.81075i | 0.0293252 | + | 0.0729573i | ||||
\(617\) | 38.2694i | 1.54067i | 0.637640 | + | 0.770334i | \(0.279911\pi\) | ||||
−0.637640 | + | 0.770334i | \(0.720089\pi\) | |||||||
\(618\) | 30.4064 | + | 29.8995i | 1.22313 | + | 1.20274i | ||||
\(619\) | 14.3645 | 0.577357 | 0.288679 | − | 0.957426i | \(-0.406784\pi\) | ||||
0.288679 | + | 0.957426i | \(0.406784\pi\) | |||||||
\(620\) | − | 3.19878i | − | 0.128466i | ||||||
\(621\) | −23.2051 | − | 22.0634i | −0.931189 | − | 0.885375i | ||||
\(622\) | 20.5120i | 0.822456i | ||||||||
\(623\) | −9.17912 | −0.367754 | ||||||||
\(624\) | 7.45758 | − | 7.58400i | 0.298542 | − | 0.303603i | ||||
\(625\) | 22.4646 | 0.898586 | ||||||||
\(626\) | −51.3644 | −2.05293 | ||||||||
\(627\) | −9.30748 | + | 22.3370i | −0.371705 | + | 0.892053i | ||||
\(628\) | −7.49234 | −0.298977 | ||||||||
\(629\) | 10.5142 | 0.419228 | ||||||||
\(630\) | −0.0400752 | − | 2.38376i | −0.00159664 | − | 0.0949713i | ||||
\(631\) | 12.9501 | 0.515536 | 0.257768 | − | 0.966207i | \(-0.417013\pi\) | ||||
0.257768 | + | 0.966207i | \(0.417013\pi\) | |||||||
\(632\) | − | 9.80988i | − | 0.390216i | ||||||
\(633\) | −1.41220 | + | 1.43614i | −0.0561300 | + | 0.0570816i | ||||
\(634\) | − | 32.1628i | − | 1.27735i | ||||||
\(635\) | 2.89789 | 0.114999 | ||||||||
\(636\) | −12.1719 | + | 12.3783i | −0.482647 | + | 0.490830i | ||||
\(637\) | − | 1.35904i | − | 0.0538470i | ||||||
\(638\) | −16.1573 | + | 6.49444i | −0.639675 | + | 0.257117i | ||||
\(639\) | 24.9365 | − | 0.419226i | 0.986471 | − | 0.0165843i | ||||
\(640\) | 1.92362i | 0.0760377i | ||||||||
\(641\) | 34.7902i | 1.37413i | 0.726596 | + | 0.687065i | \(0.241101\pi\) | ||||
−0.726596 | + | 0.687065i | \(0.758899\pi\) | |||||||
\(642\) | −12.7058 | − | 12.4940i | −0.501458 | − | 0.493099i | ||||
\(643\) | −19.3039 | −0.761273 | −0.380637 | − | 0.924725i | \(-0.624295\pi\) | ||||
−0.380637 | + | 0.924725i | \(0.624295\pi\) | |||||||
\(644\) | −10.4378 | −0.411309 | ||||||||
\(645\) | −0.613976 | − | 0.603741i | −0.0241753 | − | 0.0237723i | ||||
\(646\) | 13.2788i | 0.522446i | ||||||||
\(647\) | 44.4284i | 1.74666i | 0.487128 | + | 0.873331i | \(0.338044\pi\) | ||||
−0.487128 | + | 0.873331i | \(0.661956\pi\) | |||||||
\(648\) | −5.29275 | + | 0.178011i | −0.207919 | + | 0.00699294i | ||||
\(649\) | −12.8284 | − | 31.9155i | −0.503561 | − | 1.25279i | ||||
\(650\) | − | 12.6133i | − | 0.494736i | ||||||
\(651\) | −5.54641 | + | 5.64044i | −0.217381 | + | 0.221066i | ||||
\(652\) | −6.17802 | −0.241950 | ||||||||
\(653\) | − | 25.8911i | − | 1.01320i | −0.862182 | − | 0.506599i | \(-0.830902\pi\) | ||
0.862182 | − | 0.506599i | \(-0.169098\pi\) | |||||||
\(654\) | 27.9548 | − | 28.4288i | 1.09312 | − | 1.11165i | ||||
\(655\) | 3.26284i | 0.127490i | ||||||||
\(656\) | 16.1329 | 0.629882 | ||||||||
\(657\) | 0.871209 | − | 0.0146466i | 0.0339891 | − | 0.000571417i | ||||
\(658\) | −16.0156 | −0.624355 | ||||||||
\(659\) | 36.4163 | 1.41858 | 0.709289 | − | 0.704917i | \(-0.249016\pi\) | ||||
0.709289 | + | 0.704917i | \(0.249016\pi\) | |||||||
\(660\) | 1.54752 | − | 3.71389i | 0.0602371 | − | 0.144563i | ||||
\(661\) | −31.8343 | −1.23821 | −0.619105 | − | 0.785308i | \(-0.712505\pi\) | ||||
−0.619105 | + | 0.785308i | \(0.712505\pi\) | |||||||
\(662\) | 0.0541711 | 0.00210542 | ||||||||
\(663\) | 2.70696 | − | 2.75285i | 0.105130 | − | 0.106912i | ||||
\(664\) | 2.07917 | 0.0806874 | ||||||||
\(665\) | 1.74179i | 0.0675437i | ||||||||
\(666\) | 0.621301 | + | 36.9563i | 0.0240749 | + | 1.43203i | ||||
\(667\) | 16.8342i | 0.651824i | ||||||||
\(668\) | −10.7534 | −0.416061 | ||||||||
\(669\) | −15.3546 | − | 15.0986i | −0.593642 | − | 0.583745i | ||||
\(670\) | 4.86985i | 0.188139i | ||||||||
\(671\) | −19.2785 | − | 47.9624i | −0.744239 | − | 1.85157i | ||||
\(672\) | −9.11729 | + | 9.27185i | −0.351707 | + | 0.357670i | ||||
\(673\) | 12.2118i | 0.470732i | 0.971907 | + | 0.235366i | \(0.0756289\pi\) | ||||
−0.971907 | + | 0.235366i | \(0.924371\pi\) | |||||||
\(674\) | 54.8005i | 2.11084i | ||||||||
\(675\) | −17.2900 | + | 18.1847i | −0.665492 | + | 0.699929i | ||||
\(676\) | 18.8915 | 0.726595 | ||||||||
\(677\) | −1.16457 | −0.0447582 | −0.0223791 | − | 0.999750i | \(-0.507124\pi\) | ||||
−0.0223791 | + | 0.999750i | \(0.507124\pi\) | |||||||
\(678\) | −10.9195 | + | 11.1046i | −0.419360 | + | 0.426469i | ||||
\(679\) | 12.9612i | 0.497407i | ||||||||
\(680\) | 0.399056i | 0.0153031i | ||||||||
\(681\) | 33.8553 | + | 33.2909i | 1.29734 | + | 1.27571i | ||||
\(682\) | −27.0123 | + | 10.8576i | −1.03435 | + | 0.415759i | ||||
\(683\) | 17.1511i | 0.656269i | 0.944631 | + | 0.328135i | \(0.106420\pi\) | ||||
−0.944631 | + | 0.328135i | \(0.893580\pi\) | |||||||
\(684\) | −21.4025 | + | 0.359815i | −0.818346 | + | 0.0137579i | ||||
\(685\) | 1.76652 | 0.0674952 | ||||||||
\(686\) | 1.92194i | 0.0733799i | ||||||||
\(687\) | −33.6184 | − | 33.0580i | −1.28262 | − | 1.26124i | ||||
\(688\) | 5.43281i | 0.207124i | ||||||||
\(689\) | −8.04178 | −0.306367 | ||||||||
\(690\) | −6.04792 | − | 5.94709i | −0.230240 | − | 0.226402i | ||||
\(691\) | 3.24097 | 0.123292 | 0.0616461 | − | 0.998098i | \(-0.480365\pi\) | ||||
0.0616461 | + | 0.998098i | \(0.480365\pi\) | |||||||
\(692\) | −24.0571 | −0.914514 | ||||||||
\(693\) | −9.16832 | + | 3.86547i | −0.348276 | + | 0.146837i | ||||
\(694\) | 61.6436 | 2.33996 | ||||||||
\(695\) | 3.86035 | 0.146432 | ||||||||
\(696\) | 1.98520 | + | 1.95211i | 0.0752489 | + | 0.0739945i | ||||
\(697\) | 5.85592 | 0.221809 | ||||||||
\(698\) | 47.2708i | 1.78922i | ||||||||
\(699\) | 13.3653 | + | 13.1425i | 0.505522 | + | 0.497095i | ||||
\(700\) | 8.17961i | 0.309160i | ||||||||
\(701\) | 1.96664 | 0.0742788 | 0.0371394 | − | 0.999310i | \(-0.488175\pi\) | ||||
0.0371394 | + | 0.999310i | \(0.488175\pi\) | |||||||
\(702\) | 9.83595 | + | 9.35202i | 0.371234 | + | 0.352969i | ||||
\(703\) | − | 27.0036i | − | 1.01846i | ||||||
\(704\) | −16.5929 | + | 6.66952i | −0.625369 | + | 0.251367i | ||||
\(705\) | −4.25534 | − | 4.18440i | −0.160265 | − | 0.157594i | ||||
\(706\) | − | 40.7642i | − | 1.53418i | ||||||
\(707\) | − | 12.6217i | − | 0.474688i | ||||||
\(708\) | 21.3336 | − | 21.6953i | 0.801767 | − | 0.815359i | ||||
\(709\) | −25.8765 | −0.971812 | −0.485906 | − | 0.874011i | \(-0.661510\pi\) | ||||
−0.485906 | + | 0.874011i | \(0.661510\pi\) | |||||||
\(710\) | 6.60659 | 0.247941 | ||||||||
\(711\) | 50.0080 | − | 0.840724i | 1.87545 | − | 0.0315296i | ||||
\(712\) | 5.40114i | 0.202416i | ||||||||
\(713\) | 28.1440i | 1.05400i | ||||||||
\(714\) | −3.82816 | + | 3.89306i | −0.143265 | + | 0.145694i | ||||
\(715\) | 1.72930 | − | 0.695091i | 0.0646720 | − | 0.0259949i | ||||
\(716\) | − | 42.5470i | − | 1.59006i | ||||||
\(717\) | 24.5886 | + | 24.1787i | 0.918279 | + | 0.902970i | ||||
\(718\) | −23.1654 | −0.864524 | ||||||||
\(719\) | 25.2880i | 0.943085i | 0.881843 | + | 0.471542i | \(0.156303\pi\) | ||||
−0.881843 | + | 0.471542i | \(0.843697\pi\) | |||||||
\(720\) | −5.60435 | + | 0.0942192i | −0.208862 | + | 0.00351134i | ||||
\(721\) | − | 12.8103i | − | 0.477082i | ||||||
\(722\) | −2.41294 | −0.0898005 | ||||||||
\(723\) | −9.34202 | + | 9.50039i | −0.347433 | + | 0.353323i | ||||
\(724\) | 11.4834 | 0.426776 | ||||||||
\(725\) | 13.1921 | 0.489944 | ||||||||
\(726\) | −36.6149 | − | 0.462115i | −1.35891 | − | 0.0171507i | ||||
\(727\) | 44.7443 | 1.65948 | 0.829738 | − | 0.558154i | \(-0.188490\pi\) | ||||
0.829738 | + | 0.558154i | \(0.188490\pi\) | |||||||
\(728\) | −0.799678 | −0.0296380 | ||||||||
\(729\) | −1.36105 | − | 26.9657i | −0.0504092 | − | 0.998729i | ||||
\(730\) | 0.230816 | 0.00854287 | ||||||||
\(731\) | 1.97201i | 0.0729373i | ||||||||
\(732\) | 32.0600 | − | 32.6036i | 1.18497 | − | 1.20506i | ||||
\(733\) | − | 7.08238i | − | 0.261594i | −0.991409 | − | 0.130797i | \(-0.958246\pi\) | ||
0.991409 | − | 0.130797i | \(-0.0417536\pi\) | |||||||
\(734\) | 25.6709 | 0.947531 | ||||||||
\(735\) | −0.502144 | + | 0.510656i | −0.0185218 | + | 0.0188358i | ||||
\(736\) | 46.2635i | 1.70530i | ||||||||
\(737\) | 18.8577 | − | 7.57984i | 0.694631 | − | 0.279207i | ||||
\(738\) | 0.346037 | + | 20.5830i | 0.0127378 | + | 0.757670i | ||||
\(739\) | 4.71652i | 0.173500i | 0.996230 | + | 0.0867499i | \(0.0276481\pi\) | ||||
−0.996230 | + | 0.0867499i | \(0.972352\pi\) | |||||||
\(740\) | 4.48979i | 0.165048i | ||||||||
\(741\) | −7.07015 | − | 6.95229i | −0.259728 | − | 0.255399i | ||||
\(742\) | 11.3726 | 0.417502 | ||||||||
\(743\) | −6.91850 | −0.253815 | −0.126908 | − | 0.991915i | \(-0.540505\pi\) | ||||
−0.126908 | + | 0.991915i | \(0.540505\pi\) | |||||||
\(744\) | 3.31892 | + | 3.26359i | 0.121678 | + | 0.119649i | ||||
\(745\) | − | 6.05349i | − | 0.221783i | ||||||
\(746\) | − | 3.68747i | − | 0.135008i | ||||||
\(747\) | 0.178188 | + | 10.5990i | 0.00651957 | + | 0.387798i | ||||
\(748\) | −8.54937 | + | 3.43642i | −0.312596 | + | 0.125648i | ||||
\(749\) | 5.35301i | 0.195595i | ||||||||
\(750\) | −9.48588 | + | 9.64670i | −0.346375 | + | 0.352248i | ||||
\(751\) | 27.8696 | 1.01698 | 0.508488 | − | 0.861069i | \(-0.330204\pi\) | ||||
0.508488 | + | 0.861069i | \(0.330204\pi\) | |||||||
\(752\) | 37.6537i | 1.37309i | ||||||||
\(753\) | 11.6816 | − | 11.8796i | 0.425701 | − | 0.432918i | ||||
\(754\) | − | 7.13552i | − | 0.259860i | ||||||
\(755\) | −7.28864 | −0.265261 | ||||||||
\(756\) | −6.37851 | − | 6.06468i | −0.231984 | − | 0.220570i | ||||
\(757\) | −29.8479 | −1.08484 | −0.542420 | − | 0.840107i | \(-0.682492\pi\) | ||||
−0.542420 | + | 0.840107i | \(0.682492\pi\) | |||||||
\(758\) | −45.2394 | −1.64317 | ||||||||
\(759\) | −13.6156 | + | 32.6761i | −0.494216 | + | 1.18607i | ||||
\(760\) | 1.02490 | 0.0371769 | ||||||||
\(761\) | 41.1535 | 1.49181 | 0.745906 | − | 0.666051i | \(-0.232017\pi\) | ||||
0.745906 | + | 0.666051i | \(0.232017\pi\) | |||||||
\(762\) | 16.3577 | − | 16.6350i | 0.592577 | − | 0.602623i | ||||
\(763\) | −11.9771 | −0.433602 | ||||||||
\(764\) | − | 18.8576i | − | 0.682243i | ||||||
\(765\) | −2.03427 | + | 0.0341998i | −0.0735494 | + | 0.00123650i | ||||
\(766\) | 19.4434i | 0.702519i | ||||||||
\(767\) | 14.0948 | 0.508933 | ||||||||
\(768\) | 24.3604 | + | 23.9543i | 0.879032 | + | 0.864378i | ||||
\(769\) | − | 7.21978i | − | 0.260352i | −0.991491 | − | 0.130176i | \(-0.958446\pi\) | ||
0.991491 | − | 0.130176i | \(-0.0415543\pi\) | |||||||
\(770\) | −2.44555 | + | 0.982991i | −0.0881317 | + | 0.0354245i | ||||
\(771\) | −15.6867 | + | 15.9526i | −0.564943 | + | 0.574520i | ||||
\(772\) | 36.6607i | 1.31945i | ||||||||
\(773\) | 8.26163i | 0.297150i | 0.988901 | + | 0.148575i | \(0.0474687\pi\) | ||||
−0.988901 | + | 0.148575i | \(0.952531\pi\) | |||||||
\(774\) | −6.93141 | + | 0.116529i | −0.249144 | + | 0.00418856i | ||||
\(775\) | 22.0550 | 0.792239 | ||||||||
\(776\) | 7.62659 | 0.273779 | ||||||||
\(777\) | 7.78492 | − | 7.91690i | 0.279282 | − | 0.284017i | ||||
\(778\) | 10.4521i | 0.374726i | ||||||||
\(779\) | − | 15.0398i | − | 0.538856i | ||||||
\(780\) | 1.17553 | + | 1.15593i | 0.0420906 | + | 0.0413890i | ||||
\(781\) | −10.2830 | − | 25.5829i | −0.367956 | − | 0.915428i | ||||
\(782\) | 19.4251i | 0.694640i | ||||||||
\(783\) | −9.78116 | + | 10.2873i | −0.349550 | + | 0.367638i | ||||
\(784\) | 4.51858 | 0.161378 | ||||||||
\(785\) | 1.82898i | 0.0652790i | ||||||||
\(786\) | 18.7300 | + | 18.4177i | 0.668076 | + | 0.656939i | ||||
\(787\) | − | 27.8702i | − | 0.993465i | −0.867904 | − | 0.496733i | \(-0.834533\pi\) | ||
0.867904 | − | 0.496733i | \(-0.165467\pi\) | |||||||
\(788\) | 17.0086 | 0.605905 | ||||||||
\(789\) | 2.30873 | + | 2.27025i | 0.0821931 | + | 0.0808229i | ||||
\(790\) | 13.2490 | 0.471377 | ||||||||
\(791\) | 4.67841 | 0.166345 | ||||||||
\(792\) | 2.27450 | + | 5.39478i | 0.0808208 | + | 0.191695i | ||||
\(793\) | 21.1815 | 0.752179 | ||||||||
\(794\) | −49.3977 | −1.75306 | ||||||||
\(795\) | 3.02169 | + | 2.97132i | 0.107168 | + | 0.105382i | ||||
\(796\) | −33.6310 | −1.19202 | ||||||||
\(797\) | − | 1.97594i | − | 0.0699914i | −0.999387 | − | 0.0349957i | \(-0.988858\pi\) | ||
0.999387 | − | 0.0349957i | \(-0.0111418\pi\) | |||||||
\(798\) | 9.99854 | + | 9.83186i | 0.353945 | + | 0.348044i | ||||
\(799\) | 13.6676i | 0.483524i | ||||||||
\(800\) | 36.2544 | 1.28179 | ||||||||
\(801\) | −27.5335 | + | 0.462887i | −0.972848 | + | 0.0163553i | ||||
\(802\) | − | 67.7464i | − | 2.39221i | ||||||
\(803\) | −0.359260 | − | 0.893793i | −0.0126780 | − | 0.0315413i | ||||
\(804\) | 12.8189 | + | 12.6052i | 0.452089 | + | 0.444552i | ||||
\(805\) | 2.54801i | 0.0898056i | ||||||||
\(806\) | − | 11.9294i | − | 0.420194i | ||||||
\(807\) | 15.6966 | − | 15.9627i | 0.552547 | − | 0.561915i | ||||
\(808\) | −7.42680 | −0.261274 | ||||||||
\(809\) | −26.8892 | −0.945373 | −0.472687 | − | 0.881231i | \(-0.656716\pi\) | ||||
−0.472687 | + | 0.881231i | \(0.656716\pi\) | |||||||
\(810\) | −0.240418 | − | 7.14825i | −0.00844741 | − | 0.251164i | ||||
\(811\) | − | 6.63605i | − | 0.233023i | −0.993189 | − | 0.116512i | \(-0.962829\pi\) | ||
0.993189 | − | 0.116512i | \(-0.0371712\pi\) | |||||||
\(812\) | 4.62731i | 0.162387i | ||||||||
\(813\) | −24.5653 | + | 24.9818i | −0.861543 | + | 0.876149i | ||||
\(814\) | 37.9143 | − | 15.2397i | 1.32890 | − | 0.534150i | ||||
\(815\) | 1.50813i | 0.0528276i | ||||||||
\(816\) | 9.15280 | + | 9.00022i | 0.320412 | + | 0.315071i | ||||
\(817\) | 5.06471 | 0.177192 | ||||||||
\(818\) | − | 56.2983i | − | 1.96842i | ||||||
\(819\) | −0.0685338 | − | 4.07653i | −0.00239476 | − | 0.142446i | ||||
\(820\) | 2.50061i | 0.0873250i | ||||||||
\(821\) | −0.765204 | −0.0267058 | −0.0133529 | − | 0.999911i | \(-0.504250\pi\) | ||||
−0.0133529 | + | 0.999911i | \(0.504250\pi\) | |||||||
\(822\) | 9.97146 | − | 10.1405i | 0.347795 | − | 0.353691i | ||||
\(823\) | 46.9375 | 1.63614 | 0.818069 | − | 0.575120i | \(-0.195045\pi\) | ||||
0.818069 | + | 0.575120i | \(0.195045\pi\) | |||||||
\(824\) | −7.53780 | −0.262592 | ||||||||
\(825\) | 25.6066 | + | 10.6699i | 0.891507 | + | 0.371477i | ||||
\(826\) | −19.9327 | −0.693548 | ||||||||
\(827\) | −2.55853 | −0.0889688 | −0.0444844 | − | 0.999010i | \(-0.514164\pi\) | ||||
−0.0444844 | + | 0.999010i | \(0.514164\pi\) | |||||||
\(828\) | −31.3091 | + | 0.526362i | −1.08807 | + | 0.0182923i | ||||
\(829\) | −21.0300 | −0.730402 | −0.365201 | − | 0.930929i | \(-0.619000\pi\) | ||||
−0.365201 | + | 0.930929i | \(0.619000\pi\) | |||||||
\(830\) | 2.80807i | 0.0974696i | ||||||||
\(831\) | −8.81900 | + | 8.96851i | −0.305928 | + | 0.311114i | ||||
\(832\) | − | 7.32788i | − | 0.254049i | ||||||
\(833\) | 1.64016 | 0.0568282 | ||||||||
\(834\) | 21.7905 | − | 22.1599i | 0.754544 | − | 0.767335i | ||||
\(835\) | 2.62504i | 0.0908431i | ||||||||
\(836\) | 8.82576 | + | 21.9574i | 0.305245 | + | 0.759411i | ||||
\(837\) | −16.3524 | + | 17.1986i | −0.565223 | + | 0.594471i | ||||
\(838\) | − | 14.5267i | − | 0.501817i | ||||||
\(839\) | 16.4101i | 0.566538i | 0.959040 | + | 0.283269i | \(0.0914190\pi\) | ||||
−0.959040 | + | 0.283269i | \(0.908581\pi\) | |||||||
\(840\) | 0.300478 | + | 0.295469i | 0.0103675 | + | 0.0101947i | ||||
\(841\) | −21.5370 | −0.742657 | ||||||||
\(842\) | 4.43809 | 0.152947 | ||||||||
\(843\) | −31.5516 | − | 31.0256i | −1.08669 | − | 1.06858i | ||||
\(844\) | 1.96973i | 0.0678007i | ||||||||
\(845\) | − | 4.61165i | − | 0.158645i | ||||||
\(846\) | −48.0401 | + | 0.807640i | −1.65165 | + | 0.0277672i | ||||
\(847\) | 7.61293 | + | 7.93998i | 0.261583 | + | 0.272821i | ||||
\(848\) | − | 26.7377i | − | 0.918175i | ||||||
\(849\) | 23.4587 | − | 23.8564i | 0.805102 | − | 0.818751i | ||||
\(850\) | 15.2225 | 0.522126 | ||||||||
\(851\) | − | 39.5027i | − | 1.35414i | ||||||
\(852\) | 17.1006 | − | 17.3906i | 0.585858 | − | 0.595791i | ||||
\(853\) | − | 37.0834i | − | 1.26971i | −0.772630 | − | 0.634856i | \(-0.781059\pi\) | ||
0.772630 | − | 0.634856i | \(-0.218941\pi\) | |||||||
\(854\) | −29.9548 | −1.02503 | ||||||||
\(855\) | 0.0878353 | + | 5.22463i | 0.00300390 | + | 0.178679i | ||||
\(856\) | 3.14979 | 0.107658 | ||||||||
\(857\) | −51.6425 | −1.76407 | −0.882037 | − | 0.471180i | \(-0.843828\pi\) | ||||
−0.882037 | + | 0.471180i | \(0.843828\pi\) | |||||||
\(858\) | 5.77125 | − | 13.8504i | 0.197027 | − | 0.472845i | ||||
\(859\) | −20.1363 | −0.687043 | −0.343522 | − | 0.939145i | \(-0.611620\pi\) | ||||
−0.343522 | + | 0.939145i | \(0.611620\pi\) | |||||||
\(860\) | −0.842091 | −0.0287151 | ||||||||
\(861\) | 4.33584 | − | 4.40935i | 0.147765 | − | 0.150270i | ||||
\(862\) | −31.1920 | −1.06240 | ||||||||
\(863\) | − | 1.50058i | − | 0.0510803i | −0.999674 | − | 0.0255402i | \(-0.991869\pi\) | ||
0.999674 | − | 0.0255402i | \(-0.00813057\pi\) | |||||||
\(864\) | −26.8804 | + | 28.2714i | −0.914491 | + | 0.961813i | ||||
\(865\) | 5.87265i | 0.199676i | ||||||||
\(866\) | −3.20623 | −0.108952 | ||||||||
\(867\) | −17.6726 | − | 17.3780i | −0.600194 | − | 0.590189i | ||||
\(868\) | 7.73607i | 0.262579i | ||||||||
\(869\) | −20.6218 | − | 51.3044i | −0.699547 | − | 1.74038i | ||||
\(870\) | −2.63647 | + | 2.68116i | −0.0893846 | + | 0.0909000i | ||||
\(871\) | 8.32807i | 0.282186i | ||||||||
\(872\) | 7.04754i | 0.238660i | ||||||||
\(873\) | 0.653612 | + | 38.8782i | 0.0221214 | + | 1.31583i | ||||
\(874\) | 49.8895 | 1.68754 | ||||||||
\(875\) | 4.06419 | 0.137395 | ||||||||
\(876\) | 0.597448 | − | 0.607576i | 0.0201859 | − | 0.0205281i | ||||
\(877\) | − | 10.2813i | − | 0.347176i | −0.984818 | − | 0.173588i | \(-0.944464\pi\) | ||
0.984818 | − | 0.173588i | \(-0.0555360\pi\) | |||||||
\(878\) | − | 66.3725i | − | 2.23996i | ||||||
\(879\) | −24.0369 | − | 23.6361i | −0.810743 | − | 0.797227i | ||||
\(880\) | 2.31107 | + | 5.74964i | 0.0779061 | + | 0.193820i | ||||
\(881\) | − | 58.2128i | − | 1.96124i | −0.195920 | − | 0.980620i | \(-0.562769\pi\) | ||
0.195920 | − | 0.980620i | \(-0.437231\pi\) | |||||||
\(882\) | 0.0969199 | + | 5.76500i | 0.00326346 | + | 0.194118i | ||||
\(883\) | −4.96966 | −0.167243 | −0.0836213 | − | 0.996498i | \(-0.526649\pi\) | ||||
−0.0836213 | + | 0.996498i | \(0.526649\pi\) | |||||||
\(884\) | − | 3.77564i | − | 0.126988i | ||||||
\(885\) | −5.29610 | − | 5.20781i | −0.178026 | − | 0.175059i | ||||
\(886\) | − | 44.4654i | − | 1.49384i | ||||||
\(887\) | 39.5512 | 1.32800 | 0.664000 | − | 0.747733i | \(-0.268858\pi\) | ||||
0.664000 | + | 0.747733i | \(0.268858\pi\) | |||||||
\(888\) | −4.65842 | − | 4.58077i | −0.156326 | − | 0.153720i | ||||
\(889\) | −7.00839 | −0.235054 | ||||||||
\(890\) | −7.29464 | −0.244517 | ||||||||
\(891\) | −27.3062 | + | 12.0571i | −0.914791 | + | 0.403928i | ||||
\(892\) | −21.0594 | −0.705119 | ||||||||
\(893\) | 35.1024 | 1.17466 | ||||||||
\(894\) | −34.7494 | − | 34.1701i | −1.16219 | − | 1.14282i | ||||
\(895\) | −10.3863 | −0.347175 | ||||||||
\(896\) | − | 4.65217i | − | 0.155418i | ||||||
\(897\) | −10.3427 | − | 10.1703i | −0.345333 | − | 0.339576i | ||||
\(898\) | − | 27.2854i | − | 0.910525i | ||||||
\(899\) | 12.4768 | 0.416124 | ||||||||
\(900\) | 0.412483 | + | 24.5354i | 0.0137494 | + | 0.817846i | ||||
\(901\) | − | 9.70526i | − | 0.323329i | ||||||
\(902\) | 21.1166 | − | 8.48780i | 0.703105 | − | 0.282613i | ||||
\(903\) | 1.48487 | + | 1.46011i | 0.0494133 | + | 0.0485896i | ||||
\(904\) | − | 2.75285i | − | 0.0915583i | ||||||
\(905\) | − | 2.80324i | − | 0.0931827i | ||||||
\(906\) | −41.1421 | + | 41.8396i | −1.36685 | + | 1.39003i | ||||
\(907\) | −17.3361 | −0.575634 | −0.287817 | − | 0.957685i | \(-0.592930\pi\) | ||||
−0.287817 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(908\) | 46.4338 | 1.54096 | ||||||||
\(909\) | −0.636490 | − | 37.8597i | −0.0211110 | − | 1.25573i | ||||
\(910\) | − | 1.08002i | − | 0.0358025i | ||||||
\(911\) | 24.3870i | 0.807976i | 0.914764 | + | 0.403988i | \(0.132376\pi\) | ||||
−0.914764 | + | 0.403988i | \(0.867624\pi\) | |||||||
\(912\) | 23.1153 | − | 23.5071i | 0.765423 | − | 0.778399i | ||||
\(913\) | 10.8738 | − | 4.37072i | 0.359870 | − | 0.144650i | ||||
\(914\) | 30.5477i | 1.01043i | ||||||||
\(915\) | −7.95894 | − | 7.82626i | −0.263115 | − | 0.258728i | ||||
\(916\) | −46.1089 | −1.52348 | ||||||||
\(917\) | − | 7.89101i | − | 0.260584i | ||||||
\(918\) | −11.2865 | + | 11.8706i | −0.372511 | + | 0.391787i | ||||
\(919\) | − | 5.37606i | − | 0.177340i | −0.996061 | − | 0.0886700i | \(-0.971738\pi\) | ||
0.996061 | − | 0.0886700i | \(-0.0282616\pi\) | |||||||
\(920\) | 1.49929 | 0.0494301 | ||||||||
\(921\) | 10.6118 | − | 10.7917i | 0.349671 | − | 0.355599i | ||||
\(922\) | −49.0218 | −1.61445 | ||||||||
\(923\) | 11.2981 | 0.371882 | ||||||||
\(924\) | −3.74260 | + | 8.98184i | −0.123122 | + | 0.295481i | ||||
\(925\) | −30.9563 | −1.01784 | ||||||||
\(926\) | −25.4565 | −0.836553 | ||||||||
\(927\) | −0.646003 | − | 38.4256i | −0.0212175 | − | 1.26206i | ||||
\(928\) | 20.5096 | 0.673260 | ||||||||
\(929\) | − | 23.9905i | − | 0.787101i | −0.919303 | − | 0.393551i | \(-0.871247\pi\) | ||
0.919303 | − | 0.393551i | \(-0.128753\pi\) | |||||||
\(930\) | −4.40773 | + | 4.48245i | −0.144535 | + | 0.146985i | ||||
\(931\) | − | 4.21243i | − | 0.138057i | ||||||
\(932\) | 18.3310 | 0.600452 | ||||||||
\(933\) | 12.9608 | − | 13.1806i | 0.424319 | − | 0.431512i | ||||
\(934\) | 54.4691i | 1.78228i | ||||||||
\(935\) | 0.838874 | + | 2.08701i | 0.0274341 | + | 0.0682525i | ||||
\(936\) | −2.39869 | + | 0.0403263i | −0.0784038 | + | 0.00131811i | ||||
\(937\) | 25.8520i | 0.844546i | 0.906469 | + | 0.422273i | \(0.138768\pi\) | ||||
−0.906469 | + | 0.422273i | \(0.861232\pi\) | |||||||
\(938\) | − | 11.7775i | − | 0.384548i | ||||||
\(939\) | 33.0056 | + | 32.4554i | 1.07710 | + | 1.05914i | ||||
\(940\) | −5.83635 | −0.190361 | ||||||||
\(941\) | 21.1934 | 0.690884 | 0.345442 | − | 0.938440i | \(-0.387729\pi\) | ||||
0.345442 | + | 0.938440i | \(0.387729\pi\) | |||||||
\(942\) | 10.4990 | + | 10.3240i | 0.342077 | + | 0.336374i | ||||
\(943\) | − | 22.0012i | − | 0.716459i | ||||||
\(944\) | 46.8629i | 1.52526i | ||||||||
\(945\) | −1.48047 | + | 1.55708i | −0.0481596 | + | 0.0506517i | ||||
\(946\) | 2.85830 | + | 7.11109i | 0.0929315 | + | 0.231202i | ||||
\(947\) | − | 44.9355i | − | 1.46021i | −0.683336 | − | 0.730104i | \(-0.739472\pi\) | ||
0.683336 | − | 0.730104i | \(-0.260528\pi\) | |||||||
\(948\) | 34.2939 | − | 34.8753i | 1.11381 | − | 1.13270i | ||||
\(949\) | 0.394724 | 0.0128133 | ||||||||
\(950\) | − | 39.0959i | − | 1.26844i | ||||||
\(951\) | −20.3226 | + | 20.6671i | −0.659005 | + | 0.670177i | ||||
\(952\) | − | 0.965096i | − | 0.0312789i | ||||||
\(953\) | −43.7243 | −1.41637 | −0.708184 | − | 0.706028i | \(-0.750485\pi\) | ||||
−0.708184 | + | 0.706028i | \(0.750485\pi\) | |||||||
\(954\) | 34.1130 | − | 0.573501i | 1.10445 | − | 0.0185678i | ||||
\(955\) | −4.60337 | −0.148962 | ||||||||
\(956\) | 33.7242 | 1.09072 | ||||||||
\(957\) | 14.4860 | + | 6.03608i | 0.468265 | + | 0.195119i | ||||
\(958\) | −2.95426 | −0.0954478 | ||||||||
\(959\) | −4.27223 | −0.137958 | ||||||||
\(960\) | −2.70754 | + | 2.75345i | −0.0873856 | + | 0.0888671i | ||||
\(961\) | −10.1409 | −0.327127 | ||||||||
\(962\) | 16.7440i | 0.539849i | ||||||||
\(963\) | 0.269943 | + | 16.0567i | 0.00869878 | + | 0.517422i | ||||
\(964\) | 13.0301i | 0.419673i | ||||||||
\(965\) | 8.94935 | 0.288090 | ||||||||
\(966\) | 14.6266 | + | 14.3827i | 0.470602 | + | 0.462757i | ||||
\(967\) | − | 17.8707i | − | 0.574682i | −0.957828 | − | 0.287341i | \(-0.907229\pi\) | ||
0.957828 | − | 0.287341i | \(-0.0927714\pi\) | |||||||
\(968\) | 4.67201 | − | 4.47956i | 0.150164 | − | 0.143979i | ||||
\(969\) | 8.39040 | − | 8.53265i | 0.269539 | − | 0.274108i | ||||
\(970\) | 10.3003i | 0.330722i | ||||||||
\(971\) | 25.6948i | 0.824586i | 0.911051 | + | 0.412293i | \(0.135272\pi\) | ||||
−0.911051 | + | 0.412293i | \(0.864728\pi\) | |||||||
\(972\) | −19.4387 | − | 17.8698i | −0.623495 | − | 0.573175i | ||||
\(973\) | −9.33606 | −0.299300 | ||||||||
\(974\) | 13.7965 | 0.442070 | ||||||||
\(975\) | −7.96994 | + | 8.10506i | −0.255242 | + | 0.259570i | ||||
\(976\) | 70.4253i | 2.25426i | ||||||||
\(977\) | − | 30.5104i | − | 0.976114i | −0.872812 | − | 0.488057i | \(-0.837706\pi\) | ||
0.872812 | − | 0.488057i | \(-0.162294\pi\) | |||||||
\(978\) | 8.65727 | + | 8.51295i | 0.276829 | + | 0.272214i | ||||
\(979\) | 11.3540 | + | 28.2472i | 0.362875 | + | 0.902786i | ||||
\(980\) | 0.700384i | 0.0223730i | ||||||||
\(981\) | −35.9264 | + | 0.603986i | −1.14704 | + | 0.0192838i | ||||
\(982\) | −72.0668 | −2.29974 | ||||||||
\(983\) | 7.50598i | 0.239404i | 0.992810 | + | 0.119702i | \(0.0381938\pi\) | ||||
−0.992810 | + | 0.119702i | \(0.961806\pi\) | |||||||
\(984\) | −2.59453 | − | 2.55128i | −0.0827106 | − | 0.0813318i | ||||
\(985\) | − | 4.15201i | − | 0.132294i | ||||||
\(986\) | 8.61154 | 0.274247 | ||||||||
\(987\) | 10.2913 | + | 10.1197i | 0.327576 | + | 0.322115i | ||||
\(988\) | −9.69697 | −0.308502 | ||||||||
\(989\) | 7.40901 | 0.235593 | ||||||||
\(990\) | −7.28606 | + | 3.07188i | −0.231566 | + | 0.0976308i | ||||
\(991\) | −39.5227 | −1.25548 | −0.627740 | − | 0.778423i | \(-0.716020\pi\) | ||||
−0.627740 | + | 0.778423i | \(0.716020\pi\) | |||||||
\(992\) | 34.2885 | 1.08866 | ||||||||
\(993\) | −0.0348092 | − | 0.0342289i | −0.00110464 | − | 0.00108622i | ||||
\(994\) | −15.9777 | −0.506782 | ||||||||
\(995\) | 8.20975i | 0.260267i | ||||||||
\(996\) | 7.39170 | + | 7.26847i | 0.234215 | + | 0.230310i | ||||
\(997\) | − | 16.1240i | − | 0.510652i | −0.966855 | − | 0.255326i | \(-0.917817\pi\) | ||
0.966855 | − | 0.255326i | \(-0.0821828\pi\) | |||||||
\(998\) | −25.5064 | −0.807391 | ||||||||
\(999\) | 22.9522 | − | 24.1399i | 0.726176 | − | 0.763753i |
(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 | 231.2.g.a.197.6 | yes | 24 | |
3.2 | odd | 2 | inner | 231.2.g.a.197.19 | yes | 24 | |
11.10 | odd | 2 | inner | 231.2.g.a.197.20 | yes | 24 | |
33.32 | even | 2 | inner | 231.2.g.a.197.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.g.a.197.5 | ✓ | 24 | 33.32 | even | 2 | inner | |
231.2.g.a.197.6 | yes | 24 | 1.1 | even | 1 | trivial | |
231.2.g.a.197.19 | yes | 24 | 3.2 | odd | 2 | inner | |
231.2.g.a.197.20 | yes | 24 | 11.10 | odd | 2 | inner |