Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(68,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.30 | ||
Character | \(\chi\) | \(=\) | 273.269 |
Dual form | 273.2.r.b.68.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39671i | 1.69473i | 0.531013 | + | 0.847364i | \(0.321812\pi\) | ||||
−0.531013 | + | 0.847364i | \(0.678188\pi\) | |||||||
\(3\) | 1.60287 | − | 0.656371i | 0.925415 | − | 0.378956i | ||||
\(4\) | −3.74420 | −1.87210 | ||||||||
\(5\) | 1.10064 | + | 1.90637i | 0.492223 | + | 0.852555i | 0.999960 | − | 0.00895706i | \(-0.00285116\pi\) |
−0.507737 | + | 0.861512i | \(0.669518\pi\) | |||||||
\(6\) | 1.57313 | + | 3.84160i | 0.642228 | + | 1.56833i | ||||
\(7\) | −1.62460 | + | 2.08822i | −0.614042 | + | 0.789273i | ||||
\(8\) | − | 4.18035i | − | 1.47798i | ||||||
\(9\) | 2.13835 | − | 2.10415i | 0.712784 | − | 0.701383i | ||||
\(10\) | −4.56901 | + | 2.63792i | −1.44485 | + | 0.834184i | ||||
\(11\) | 1.30172 | − | 0.751546i | 0.392482 | − | 0.226600i | −0.290753 | − | 0.956798i | \(-0.593906\pi\) |
0.683235 | + | 0.730199i | \(0.260572\pi\) | |||||||
\(12\) | −6.00145 | + | 2.45759i | −1.73247 | + | 0.709445i | ||||
\(13\) | 3.47069 | − | 0.976871i | 0.962598 | − | 0.270935i | ||||
\(14\) | −5.00485 | − | 3.89370i | −1.33760 | − | 1.04063i | ||||
\(15\) | 3.01547 | + | 2.33322i | 0.778591 | + | 0.602436i | ||||
\(16\) | 2.53065 | 0.632664 | ||||||||
\(17\) | −4.90720 | −1.19017 | −0.595085 | − | 0.803662i | \(-0.702882\pi\) | ||||
−0.595085 | + | 0.803662i | \(0.702882\pi\) | |||||||
\(18\) | 5.04303 | + | 5.12501i | 1.18865 | + | 1.20798i | ||||
\(19\) | −2.77060 | − | 1.59960i | −0.635618 | − | 0.366974i | 0.147306 | − | 0.989091i | \(-0.452940\pi\) |
−0.782925 | + | 0.622117i | \(0.786273\pi\) | |||||||
\(20\) | −4.12104 | − | 7.13784i | −0.921491 | − | 1.59607i | ||||
\(21\) | −1.23337 | + | 4.41348i | −0.269144 | + | 0.963100i | ||||
\(22\) | 1.80123 | + | 3.11983i | 0.384025 | + | 0.665150i | ||||
\(23\) | 4.94443i | 1.03099i | 0.856894 | + | 0.515493i | \(0.172391\pi\) | ||||
−0.856894 | + | 0.515493i | \(0.827609\pi\) | |||||||
\(24\) | −2.74386 | − | 6.70053i | −0.560088 | − | 1.36774i | ||||
\(25\) | 0.0771661 | − | 0.133656i | 0.0154332 | − | 0.0267311i | ||||
\(26\) | 2.34127 | + | 8.31824i | 0.459161 | + | 1.63134i | ||||
\(27\) | 2.04639 | − | 4.77622i | 0.393827 | − | 0.919184i | ||||
\(28\) | 6.08284 | − | 7.81872i | 1.14955 | − | 1.47760i | ||||
\(29\) | −0.775914 | − | 0.447974i | −0.144084 | − | 0.0831867i | 0.426225 | − | 0.904617i | \(-0.359843\pi\) |
−0.570309 | + | 0.821430i | \(0.693176\pi\) | |||||||
\(30\) | −5.59206 | + | 7.22720i | −1.02096 | + | 1.31950i | ||||
\(31\) | 2.33226 | + | 1.34653i | 0.418886 | + | 0.241844i | 0.694601 | − | 0.719395i | \(-0.255581\pi\) |
−0.275714 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(32\) | − | 2.29545i | − | 0.405783i | ||||||
\(33\) | 1.59318 | − | 2.05904i | 0.277337 | − | 0.358432i | ||||
\(34\) | − | 11.7611i | − | 2.01702i | ||||||
\(35\) | −5.76903 | − | 0.798709i | −0.975145 | − | 0.135006i | ||||
\(36\) | −8.00643 | + | 7.87837i | −1.33440 | + | 1.31306i | ||||
\(37\) | 10.0463 | 1.65160 | 0.825800 | − | 0.563964i | \(-0.190724\pi\) | ||||
0.825800 | + | 0.563964i | \(0.190724\pi\) | |||||||
\(38\) | 3.83378 | − | 6.64031i | 0.621922 | − | 1.07720i | ||||
\(39\) | 4.92187 | − | 3.84386i | 0.788129 | − | 0.615510i | ||||
\(40\) | 7.96929 | − | 4.60107i | 1.26006 | − | 0.727493i | ||||
\(41\) | 4.98596 | − | 8.63593i | 0.778676 | − | 1.34871i | −0.154030 | − | 0.988066i | \(-0.549225\pi\) |
0.932705 | − | 0.360639i | \(-0.117441\pi\) | |||||||
\(42\) | −10.5778 | − | 2.95603i | −1.63219 | − | 0.456125i | ||||
\(43\) | −0.820714 | − | 1.42152i | −0.125158 | − | 0.216780i | 0.796637 | − | 0.604458i | \(-0.206610\pi\) |
−0.921795 | + | 0.387679i | \(0.873277\pi\) | |||||||
\(44\) | −4.87389 | + | 2.81394i | −0.734766 | + | 0.424217i | ||||
\(45\) | 6.36486 | + | 1.76057i | 0.948817 | + | 0.262451i | ||||
\(46\) | −11.8504 | −1.74724 | ||||||||
\(47\) | −0.165217 | − | 0.286164i | −0.0240993 | − | 0.0417413i | 0.853724 | − | 0.520725i | \(-0.174338\pi\) |
−0.877824 | + | 0.478984i | \(0.841005\pi\) | |||||||
\(48\) | 4.05630 | − | 1.66105i | 0.585476 | − | 0.239752i | ||||
\(49\) | −1.72133 | − | 6.78506i | −0.245904 | − | 0.969294i | ||||
\(50\) | 0.320334 | + | 0.184945i | 0.0453020 | + | 0.0261551i | ||||
\(51\) | −7.86558 | + | 3.22095i | −1.10140 | + | 0.451023i | ||||
\(52\) | −12.9950 | + | 3.65760i | −1.80208 | + | 0.507218i | ||||
\(53\) | −5.36111 | − | 3.09524i | −0.736404 | − | 0.425163i | 0.0843561 | − | 0.996436i | \(-0.473117\pi\) |
−0.820761 | + | 0.571272i | \(0.806450\pi\) | |||||||
\(54\) | 11.4472 | + | 4.90459i | 1.55777 | + | 0.667430i | ||||
\(55\) | 2.86545 | + | 1.65437i | 0.386377 | + | 0.223075i | ||||
\(56\) | 8.72948 | + | 6.79140i | 1.16653 | + | 0.907539i | ||||
\(57\) | −5.49083 | − | 0.745410i | −0.727278 | − | 0.0987319i | ||||
\(58\) | 1.07366 | − | 1.85964i | 0.140979 | − | 0.244182i | ||||
\(59\) | 13.8477 | 1.80282 | 0.901410 | − | 0.432966i | \(-0.142533\pi\) | ||||
0.901410 | + | 0.432966i | \(0.142533\pi\) | |||||||
\(60\) | −11.2905 | − | 8.73607i | −1.45760 | − | 1.12782i | ||||
\(61\) | 2.44902 | + | 1.41394i | 0.313565 | + | 0.181037i | 0.648521 | − | 0.761197i | \(-0.275388\pi\) |
−0.334956 | + | 0.942234i | \(0.608721\pi\) | |||||||
\(62\) | −3.22724 | + | 5.58975i | −0.409860 | + | 0.709899i | ||||
\(63\) | 0.919954 | + | 7.88376i | 0.115903 | + | 0.993260i | ||||
\(64\) | 10.5628 | 1.32035 | ||||||||
\(65\) | 5.68228 | + | 5.54125i | 0.704800 | + | 0.687307i | ||||
\(66\) | 4.93490 | + | 3.81839i | 0.607445 | + | 0.470011i | ||||
\(67\) | 3.46728 | + | 6.00551i | 0.423596 | + | 0.733690i | 0.996288 | − | 0.0860807i | \(-0.0274343\pi\) |
−0.572692 | + | 0.819771i | \(0.694101\pi\) | |||||||
\(68\) | 18.3736 | 2.22812 | ||||||||
\(69\) | 3.24539 | + | 7.92526i | 0.390698 | + | 0.954089i | ||||
\(70\) | 1.91427 | − | 13.8267i | 0.228799 | − | 1.65260i | ||||
\(71\) | −13.9370 | + | 8.04655i | −1.65402 | + | 0.954950i | −0.678628 | + | 0.734482i | \(0.737425\pi\) |
−0.975394 | + | 0.220469i | \(0.929241\pi\) | |||||||
\(72\) | −8.79607 | − | 8.93905i | −1.03663 | − | 1.05348i | ||||
\(73\) | −2.87045 | − | 1.65726i | −0.335961 | − | 0.193967i | 0.322524 | − | 0.946561i | \(-0.395469\pi\) |
−0.658485 | + | 0.752594i | \(0.728802\pi\) | |||||||
\(74\) | 24.0780i | 2.79901i | ||||||||
\(75\) | 0.0359591 | − | 0.264882i | 0.00415220 | − | 0.0305859i | ||||
\(76\) | 10.3737 | + | 5.98924i | 1.18994 | + | 0.687014i | ||||
\(77\) | −0.545377 | + | 3.93923i | −0.0621515 | + | 0.448917i | ||||
\(78\) | 9.21260 | + | 11.7963i | 1.04312 | + | 1.33566i | ||||
\(79\) | −3.02508 | − | 5.23959i | −0.340348 | − | 0.589500i | 0.644149 | − | 0.764900i | \(-0.277211\pi\) |
−0.984497 | + | 0.175400i | \(0.943878\pi\) | |||||||
\(80\) | 2.78535 | + | 4.82437i | 0.311412 | + | 0.539381i | ||||
\(81\) | 0.145107 | − | 8.99883i | 0.0161230 | − | 0.999870i | ||||
\(82\) | 20.6978 | + | 11.9499i | 2.28569 | + | 1.31964i | ||||
\(83\) | 2.74309 | 0.301094 | 0.150547 | − | 0.988603i | \(-0.451897\pi\) | ||||
0.150547 | + | 0.988603i | \(0.451897\pi\) | |||||||
\(84\) | 4.61799 | − | 16.5250i | 0.503864 | − | 1.80302i | ||||
\(85\) | −5.40108 | − | 9.35495i | −0.585829 | − | 1.01469i | ||||
\(86\) | 3.40696 | − | 1.96701i | 0.367382 | − | 0.212108i | ||||
\(87\) | −1.53772 | − | 0.208754i | −0.164861 | − | 0.0223808i | ||||
\(88\) | −3.14172 | − | 5.44162i | −0.334909 | − | 0.580079i | ||||
\(89\) | −12.6297 | −1.33874 | −0.669372 | − | 0.742928i | \(-0.733437\pi\) | ||||
−0.669372 | + | 0.742928i | \(0.733437\pi\) | |||||||
\(90\) | −4.21958 | + | 15.2547i | −0.444783 | + | 1.60799i | ||||
\(91\) | −3.59858 | + | 8.83460i | −0.377234 | + | 0.926118i | ||||
\(92\) | − | 18.5130i | − | 1.93011i | ||||||
\(93\) | 4.62213 | + | 0.627479i | 0.479292 | + | 0.0650665i | ||||
\(94\) | 0.685851 | − | 0.395976i | 0.0707401 | − | 0.0408418i | ||||
\(95\) | − | 7.04238i | − | 0.722533i | ||||||
\(96\) | −1.50667 | − | 3.67930i | −0.153774 | − | 0.375517i | ||||
\(97\) | −11.5690 | + | 6.67939i | −1.17466 | + | 0.678190i | −0.954773 | − | 0.297336i | \(-0.903902\pi\) |
−0.219886 | + | 0.975526i | \(0.570568\pi\) | |||||||
\(98\) | 16.2618 | − | 4.12552i | 1.64269 | − | 0.416741i | ||||
\(99\) | 1.20216 | − | 4.34607i | 0.120822 | − | 0.436797i | ||||
\(100\) | −0.288926 | + | 0.500434i | −0.0288926 | + | 0.0500434i | ||||
\(101\) | −8.75688 | − | 15.1674i | −0.871342 | − | 1.50921i | −0.860609 | − | 0.509267i | \(-0.829917\pi\) |
−0.0107340 | − | 0.999942i | \(-0.503417\pi\) | |||||||
\(102\) | −7.71966 | − | 18.8515i | −0.764361 | − | 1.86658i | ||||
\(103\) | 2.76437 | − | 1.59601i | 0.272381 | − | 0.157259i | −0.357588 | − | 0.933879i | \(-0.616401\pi\) |
0.629969 | + | 0.776620i | \(0.283067\pi\) | |||||||
\(104\) | −4.08366 | − | 14.5087i | −0.400436 | − | 1.42270i | ||||
\(105\) | −9.77123 | + | 2.50641i | −0.953574 | + | 0.244600i | ||||
\(106\) | 7.41837 | − | 12.8490i | 0.720536 | − | 1.24801i | ||||
\(107\) | − | 2.05885i | − | 0.199036i | −0.995036 | − | 0.0995181i | \(-0.968270\pi\) | ||
0.995036 | − | 0.0995181i | \(-0.0317301\pi\) | |||||||
\(108\) | −7.66209 | + | 17.8831i | −0.737285 | + | 1.72081i | ||||
\(109\) | 2.54162 | − | 4.40221i | 0.243443 | − | 0.421656i | −0.718250 | − | 0.695785i | \(-0.755056\pi\) |
0.961693 | + | 0.274130i | \(0.0883898\pi\) | |||||||
\(110\) | −3.96504 | + | 6.86764i | −0.378051 | + | 0.654804i | ||||
\(111\) | 16.1028 | − | 6.59410i | 1.52841 | − | 0.625884i | ||||
\(112\) | −4.11131 | + | 5.28457i | −0.388482 | + | 0.499345i | ||||
\(113\) | −3.72227 | + | 2.14905i | −0.350161 | + | 0.202166i | −0.664756 | − | 0.747060i | \(-0.731465\pi\) |
0.314595 | + | 0.949226i | \(0.398131\pi\) | |||||||
\(114\) | 1.78653 | − | 13.1599i | 0.167324 | − | 1.23254i | ||||
\(115\) | −9.42593 | + | 5.44206i | −0.878972 | + | 0.507475i | ||||
\(116\) | 2.90518 | + | 1.67731i | 0.269739 | + | 0.155734i | ||||
\(117\) | 5.36609 | − | 9.39176i | 0.496095 | − | 0.868268i | ||||
\(118\) | 33.1889i | 3.05529i | ||||||||
\(119\) | 7.97225 | − | 10.2473i | 0.730815 | − | 0.939370i | ||||
\(120\) | 9.75368 | − | 12.6057i | 0.890385 | − | 1.15074i | ||||
\(121\) | −4.37036 | + | 7.56968i | −0.397305 | + | 0.688153i | ||||
\(122\) | −3.38881 | + | 5.86959i | −0.306808 | + | 0.531408i | ||||
\(123\) | 2.32344 | − | 17.1149i | 0.209497 | − | 1.54320i | ||||
\(124\) | −8.73246 | − | 5.04169i | −0.784198 | − | 0.452757i | ||||
\(125\) | 11.3462 | 1.01483 | ||||||||
\(126\) | −18.8951 | + | 2.20486i | −1.68331 | + | 0.196425i | ||||
\(127\) | −8.84285 | + | 15.3163i | −0.784676 | + | 1.35910i | 0.144516 | + | 0.989502i | \(0.453837\pi\) |
−0.929192 | + | 0.369596i | \(0.879496\pi\) | |||||||
\(128\) | 20.7251i | 1.83186i | ||||||||
\(129\) | −2.24854 | − | 1.73981i | −0.197973 | − | 0.153182i | ||||
\(130\) | −13.2807 | + | 13.6188i | −1.16480 | + | 1.19444i | ||||
\(131\) | −6.22200 | − | 10.7768i | −0.543619 | − | 0.941576i | −0.998692 | − | 0.0511218i | \(-0.983720\pi\) |
0.455073 | − | 0.890454i | \(-0.349613\pi\) | |||||||
\(132\) | −5.96519 | + | 7.70945i | −0.519204 | + | 0.671021i | ||||
\(133\) | 7.84145 | − | 3.18689i | 0.679940 | − | 0.276339i | ||||
\(134\) | −14.3934 | + | 8.31006i | −1.24340 | + | 0.717880i | ||||
\(135\) | 11.3576 | − | 1.35575i | 0.977506 | − | 0.116684i | ||||
\(136\) | 20.5138i | 1.75904i | ||||||||
\(137\) | 9.44464i | 0.806910i | 0.914999 | + | 0.403455i | \(0.132191\pi\) | ||||
−0.914999 | + | 0.403455i | \(0.867809\pi\) | |||||||
\(138\) | −18.9945 | + | 7.77824i | −1.61692 | + | 0.662128i | ||||
\(139\) | −3.90386 | + | 2.25389i | −0.331121 | + | 0.191173i | −0.656339 | − | 0.754466i | \(-0.727896\pi\) |
0.325218 | + | 0.945639i | \(0.394562\pi\) | |||||||
\(140\) | 21.6004 | + | 2.99053i | 1.82557 | + | 0.252746i | ||||
\(141\) | −0.452650 | − | 0.350238i | −0.0381200 | − | 0.0294954i | ||||
\(142\) | −19.2852 | − | 33.4030i | −1.61838 | − | 2.80312i | ||||
\(143\) | 3.78369 | − | 3.87999i | 0.316408 | − | 0.324461i | ||||
\(144\) | 5.41143 | − | 5.32488i | 0.450953 | − | 0.443740i | ||||
\(145\) | − | 1.97224i | − | 0.163786i | ||||||
\(146\) | 3.97196 | − | 6.87963i | 0.328722 | − | 0.569362i | ||||
\(147\) | −7.21258 | − | 9.74570i | −0.594884 | − | 0.803812i | ||||
\(148\) | −37.6153 | −3.09196 | ||||||||
\(149\) | −16.3166 | − | 9.42041i | −1.33671 | − | 0.771750i | −0.350392 | − | 0.936603i | \(-0.613952\pi\) |
−0.986318 | + | 0.164853i | \(0.947285\pi\) | |||||||
\(150\) | 0.634844 | + | 0.0861835i | 0.0518348 | + | 0.00703686i | ||||
\(151\) | −4.12058 | + | 7.13706i | −0.335328 | + | 0.580805i | −0.983548 | − | 0.180648i | \(-0.942181\pi\) |
0.648220 | + | 0.761453i | \(0.275514\pi\) | |||||||
\(152\) | −6.68690 | + | 11.5820i | −0.542379 | + | 0.939428i | ||||
\(153\) | −10.4933 | + | 10.3255i | −0.848335 | + | 0.834766i | ||||
\(154\) | −9.44119 | − | 1.30711i | −0.760792 | − | 0.105330i | ||||
\(155\) | 5.92821i | 0.476165i | ||||||||
\(156\) | −18.4285 | + | 14.3922i | −1.47546 | + | 1.15230i | ||||
\(157\) | 12.0751 | + | 6.97157i | 0.963699 | + | 0.556392i | 0.897310 | − | 0.441402i | \(-0.145519\pi\) |
0.0663895 | + | 0.997794i | \(0.478852\pi\) | |||||||
\(158\) | 12.5578 | − | 7.25023i | 0.999042 | − | 0.576797i | ||||
\(159\) | −10.6248 | − | 1.44237i | −0.842598 | − | 0.114387i | ||||
\(160\) | 4.37599 | − | 2.52648i | 0.345952 | − | 0.199735i | ||||
\(161\) | −10.3251 | − | 8.03274i | −0.813729 | − | 0.633069i | ||||
\(162\) | 21.5676 | + | 0.347780i | 1.69451 | + | 0.0273242i | ||||
\(163\) | −5.61643 | + | 9.72795i | −0.439913 | + | 0.761952i | −0.997682 | − | 0.0680444i | \(-0.978324\pi\) |
0.557769 | + | 0.829996i | \(0.311657\pi\) | |||||||
\(164\) | −18.6684 | + | 32.3347i | −1.45776 | + | 2.52491i | ||||
\(165\) | 5.67881 | + | 0.770930i | 0.442095 | + | 0.0600168i | ||||
\(166\) | 6.57439i | 0.510272i | ||||||||
\(167\) | −2.80640 | + | 4.86082i | −0.217165 | + | 0.376142i | −0.953940 | − | 0.299997i | \(-0.903014\pi\) |
0.736775 | + | 0.676138i | \(0.236348\pi\) | |||||||
\(168\) | 18.4499 | + | 5.15592i | 1.42344 | + | 0.397788i | ||||
\(169\) | 11.0914 | − | 6.78084i | 0.853188 | − | 0.521603i | ||||
\(170\) | 22.4211 | − | 12.9448i | 1.71962 | − | 0.992821i | ||||
\(171\) | −9.29032 | + | 2.40923i | −0.710449 | + | 0.184238i | ||||
\(172\) | 3.07292 | + | 5.32246i | 0.234308 | + | 0.405834i | ||||
\(173\) | 11.9534 | − | 20.7038i | 0.908797 | − | 1.57408i | 0.0930589 | − | 0.995661i | \(-0.470336\pi\) |
0.815738 | − | 0.578422i | \(-0.196331\pi\) | |||||||
\(174\) | 0.500323 | − | 3.68547i | 0.0379294 | − | 0.279395i | ||||
\(175\) | 0.153738 | + | 0.378277i | 0.0116215 | + | 0.0285951i | ||||
\(176\) | 3.29419 | − | 1.90190i | 0.248309 | − | 0.143361i | ||||
\(177\) | 22.1960 | − | 9.08925i | 1.66836 | − | 0.683190i | ||||
\(178\) | − | 30.2696i | − | 2.26881i | ||||||
\(179\) | −16.9456 | + | 9.78353i | −1.26657 | + | 0.731255i | −0.974338 | − | 0.225092i | \(-0.927732\pi\) |
−0.292233 | + | 0.956347i | \(0.594398\pi\) | |||||||
\(180\) | −23.8313 | − | 6.59195i | −1.77628 | − | 0.491335i | ||||
\(181\) | 1.52824i | 0.113593i | 0.998386 | + | 0.0567967i | \(0.0180887\pi\) | ||||
−0.998386 | + | 0.0567967i | \(0.981911\pi\) | |||||||
\(182\) | −21.1740 | − | 8.62474i | −1.56952 | − | 0.639308i | ||||
\(183\) | 4.85352 | + | 0.658893i | 0.358783 | + | 0.0487067i | ||||
\(184\) | 20.6694 | 1.52377 | ||||||||
\(185\) | 11.0574 | + | 19.1519i | 0.812955 | + | 1.40808i | ||||
\(186\) | −1.50388 | + | 11.0779i | −0.110270 | + | 0.812270i | ||||
\(187\) | −6.38778 | + | 3.68799i | −0.467121 | + | 0.269692i | ||||
\(188\) | 0.618605 | + | 1.07146i | 0.0451164 | + | 0.0781439i | ||||
\(189\) | 6.64924 | + | 12.0328i | 0.483661 | + | 0.875255i | ||||
\(190\) | 16.8785 | 1.22450 | ||||||||
\(191\) | 5.34689 | + | 3.08703i | 0.386887 | + | 0.223370i | 0.680811 | − | 0.732459i | \(-0.261628\pi\) |
−0.293923 | + | 0.955829i | \(0.594961\pi\) | |||||||
\(192\) | 16.9308 | − | 6.93315i | 1.22188 | − | 0.500357i | ||||
\(193\) | −5.22852 | − | 9.05607i | −0.376357 | − | 0.651870i | 0.614172 | − | 0.789172i | \(-0.289490\pi\) |
−0.990529 | + | 0.137302i | \(0.956157\pi\) | |||||||
\(194\) | −16.0085 | − | 27.7276i | −1.14935 | − | 1.99073i | ||||
\(195\) | 12.7450 | + | 5.15218i | 0.912691 | + | 0.368956i | ||||
\(196\) | 6.44501 | + | 25.4046i | 0.460358 | + | 1.81462i | ||||
\(197\) | 4.00557 | + | 2.31262i | 0.285385 | + | 0.164767i | 0.635859 | − | 0.771805i | \(-0.280646\pi\) |
−0.350474 | + | 0.936573i | \(0.613979\pi\) | |||||||
\(198\) | 10.4163 | + | 2.88123i | 0.740252 | + | 0.204760i | ||||
\(199\) | − | 8.76573i | − | 0.621386i | −0.950510 | − | 0.310693i | \(-0.899439\pi\) | ||
0.950510 | − | 0.310693i | \(-0.100561\pi\) | |||||||
\(200\) | −0.558727 | − | 0.322581i | −0.0395080 | − | 0.0228099i | ||||
\(201\) | 9.49943 | + | 7.35020i | 0.670038 | + | 0.518443i | ||||
\(202\) | 36.3517 | − | 20.9877i | 2.55770 | − | 1.47669i | ||||
\(203\) | 2.19602 | − | 0.892499i | 0.154130 | − | 0.0626412i | ||||
\(204\) | 29.4503 | − | 12.0599i | 2.06194 | − | 0.844360i | ||||
\(205\) | 21.9510 | 1.53313 | ||||||||
\(206\) | 3.82517 | + | 6.62538i | 0.266512 | + | 0.461612i | ||||
\(207\) | 10.4038 | + | 10.5729i | 0.723116 | + | 0.734871i | ||||
\(208\) | 8.78313 | − | 2.47212i | 0.609001 | − | 0.171411i | ||||
\(209\) | −4.80870 | −0.332625 | ||||||||
\(210\) | −6.00712 | − | 23.4188i | −0.414531 | − | 1.61605i | ||||
\(211\) | 0.494306 | − | 0.856163i | 0.0340294 | − | 0.0589407i | −0.848509 | − | 0.529181i | \(-0.822499\pi\) |
0.882539 | + | 0.470240i | \(0.155833\pi\) | |||||||
\(212\) | 20.0731 | + | 11.5892i | 1.37862 | + | 0.795949i | ||||
\(213\) | −17.0577 | + | 22.0454i | −1.16877 | + | 1.51053i | ||||
\(214\) | 4.93445 | 0.337312 | ||||||||
\(215\) | 1.80663 | − | 3.12917i | 0.123211 | − | 0.213408i | ||||
\(216\) | −19.9663 | − | 8.55461i | −1.35853 | − | 0.582067i | ||||
\(217\) | −6.60085 | + | 2.68270i | −0.448095 | + | 0.182113i | ||||
\(218\) | 10.5508 | + | 6.09152i | 0.714591 | + | 0.412570i | ||||
\(219\) | −5.68872 | − | 0.772275i | −0.384408 | − | 0.0521855i | ||||
\(220\) | −10.7288 | − | 6.19429i | −0.723338 | − | 0.417619i | ||||
\(221\) | −17.0314 | + | 4.79370i | −1.14566 | + | 0.322459i | ||||
\(222\) | 15.8041 | + | 38.5938i | 1.06070 | + | 2.59025i | ||||
\(223\) | −18.4022 | − | 10.6245i | −1.23230 | − | 0.711471i | −0.264795 | − | 0.964305i | \(-0.585304\pi\) |
−0.967510 | + | 0.252833i | \(0.918638\pi\) | |||||||
\(224\) | 4.79341 | + | 3.72920i | 0.320273 | + | 0.249168i | ||||
\(225\) | −0.116223 | − | 0.448172i | −0.00774821 | − | 0.0298781i | ||||
\(226\) | −5.15065 | − | 8.92118i | −0.342616 | − | 0.593428i | ||||
\(227\) | 3.98583 | 0.264549 | 0.132274 | − | 0.991213i | \(-0.457772\pi\) | ||||
0.132274 | + | 0.991213i | \(0.457772\pi\) | |||||||
\(228\) | 20.5588 | + | 2.79097i | 1.36154 | + | 0.184836i | ||||
\(229\) | 1.31206 | − | 0.757520i | 0.0867036 | − | 0.0500583i | −0.456021 | − | 0.889969i | \(-0.650726\pi\) |
0.542725 | + | 0.839910i | \(0.317393\pi\) | |||||||
\(230\) | −13.0430 | − | 22.5912i | −0.860032 | − | 1.48962i | ||||
\(231\) | 1.71143 | + | 6.67203i | 0.112604 | + | 0.438987i | ||||
\(232\) | −1.87269 | + | 3.24359i | −0.122948 | + | 0.212952i | ||||
\(233\) | 5.86812 | − | 3.38796i | 0.384433 | − | 0.221953i | −0.295312 | − | 0.955401i | \(-0.595424\pi\) |
0.679745 | + | 0.733448i | \(0.262090\pi\) | |||||||
\(234\) | 22.5093 | + | 12.8609i | 1.47148 | + | 0.840746i | ||||
\(235\) | 0.363690 | − | 0.629929i | 0.0237245 | − | 0.0410920i | ||||
\(236\) | −51.8487 | −3.37506 | ||||||||
\(237\) | −8.28791 | − | 6.41278i | −0.538357 | − | 0.416555i | ||||
\(238\) | 24.5598 | + | 19.1072i | 1.59198 | + | 1.23853i | ||||
\(239\) | 15.4434i | 0.998954i | 0.866327 | + | 0.499477i | \(0.166474\pi\) | ||||
−0.866327 | + | 0.499477i | \(0.833526\pi\) | |||||||
\(240\) | 7.63112 | + | 5.90459i | 0.492586 | + | 0.381139i | ||||
\(241\) | 7.03908i | 0.453427i | 0.973962 | + | 0.226713i | \(0.0727981\pi\) | ||||
−0.973962 | + | 0.226713i | \(0.927202\pi\) | |||||||
\(242\) | −18.1423 | − | 10.4745i | −1.16623 | − | 0.673324i | ||||
\(243\) | −5.67399 | − | 14.5192i | −0.363986 | − | 0.931404i | ||||
\(244\) | −9.16964 | − | 5.29409i | −0.587026 | − | 0.338920i | ||||
\(245\) | 11.0403 | − | 10.7494i | 0.705337 | − | 0.686756i | ||||
\(246\) | 41.0193 | + | 5.56860i | 2.61530 | + | 0.355041i | ||||
\(247\) | −11.1785 | − | 2.84522i | −0.711271 | − | 0.181037i | ||||
\(248\) | 5.62897 | − | 9.74966i | 0.357440 | − | 0.619104i | ||||
\(249\) | 4.39681 | − | 1.80049i | 0.278637 | − | 0.114101i | ||||
\(250\) | 27.1934i | 1.71986i | ||||||||
\(251\) | −1.69284 | − | 2.93209i | −0.106851 | − | 0.185072i | 0.807642 | − | 0.589673i | \(-0.200744\pi\) |
−0.914493 | + | 0.404602i | \(0.867410\pi\) | |||||||
\(252\) | −3.44450 | − | 29.5184i | −0.216983 | − | 1.85948i | ||||
\(253\) | 3.71597 | + | 6.43625i | 0.233621 | + | 0.404643i | ||||
\(254\) | −36.7086 | − | 21.1937i | −2.30330 | − | 1.32981i | ||||
\(255\) | −14.7975 | − | 11.4496i | −0.926657 | − | 0.717002i | ||||
\(256\) | −28.5464 | −1.78415 | ||||||||
\(257\) | 20.6197 | 1.28622 | 0.643112 | − | 0.765772i | \(-0.277643\pi\) | ||||
0.643112 | + | 0.765772i | \(0.277643\pi\) | |||||||
\(258\) | 4.16981 | − | 5.38909i | 0.259601 | − | 0.335510i | ||||
\(259\) | −16.3212 | + | 20.9789i | −1.01415 | + | 1.30356i | ||||
\(260\) | −21.2756 | − | 20.7476i | −1.31946 | − | 1.28671i | ||||
\(261\) | −2.60178 | + | 0.674712i | −0.161046 | + | 0.0417636i | ||||
\(262\) | 25.8289 | − | 14.9123i | 1.59571 | − | 0.921286i | ||||
\(263\) | −4.80598 | + | 2.77473i | −0.296349 | + | 0.171097i | −0.640802 | − | 0.767706i | \(-0.721398\pi\) |
0.344452 | + | 0.938804i | \(0.388065\pi\) | |||||||
\(264\) | −8.60748 | − | 6.66005i | −0.529754 | − | 0.409898i | ||||
\(265\) | − | 13.6270i | − | 0.837100i | ||||||
\(266\) | 7.63805 | + | 18.7936i | 0.468319 | + | 1.15231i | ||||
\(267\) | −20.2437 | + | 8.28976i | −1.23889 | + | 0.507325i | ||||
\(268\) | −12.9822 | − | 22.4859i | −0.793015 | − | 1.37354i | ||||
\(269\) | 9.16772 | 0.558966 | 0.279483 | − | 0.960151i | \(-0.409837\pi\) | ||||
0.279483 | + | 0.960151i | \(0.409837\pi\) | |||||||
\(270\) | 3.24932 | + | 27.2208i | 0.197748 | + | 1.65661i | ||||
\(271\) | − | 6.82441i | − | 0.414553i | −0.978282 | − | 0.207277i | \(-0.933540\pi\) | ||
0.978282 | − | 0.207277i | \(-0.0664600\pi\) | |||||||
\(272\) | −12.4184 | −0.752978 | ||||||||
\(273\) | 0.0307453 | + | 16.5227i | 0.00186079 | + | 0.999998i | ||||
\(274\) | −22.6360 | −1.36749 | ||||||||
\(275\) | − | 0.231976i | − | 0.0139887i | ||||||
\(276\) | −12.1514 | − | 29.6738i | −0.731427 | − | 1.78615i | ||||
\(277\) | −2.96712 | −0.178277 | −0.0891385 | − | 0.996019i | \(-0.528411\pi\) | ||||
−0.0891385 | + | 0.996019i | \(0.528411\pi\) | |||||||
\(278\) | −5.40192 | − | 9.35640i | −0.323986 | − | 0.561160i | ||||
\(279\) | 7.82050 | − | 2.02807i | 0.468201 | − | 0.121417i | ||||
\(280\) | −3.33888 | + | 24.1165i | −0.199536 | + | 1.44124i | ||||
\(281\) | 25.9693i | 1.54920i | 0.632454 | + | 0.774598i | \(0.282048\pi\) | ||||
−0.632454 | + | 0.774598i | \(0.717952\pi\) | |||||||
\(282\) | 0.839419 | − | 1.08487i | 0.0499867 | − | 0.0646030i | ||||
\(283\) | −9.43593 | + | 5.44784i | −0.560908 | + | 0.323840i | −0.753510 | − | 0.657437i | \(-0.771641\pi\) |
0.192602 | + | 0.981277i | \(0.438307\pi\) | |||||||
\(284\) | 52.1831 | − | 30.1279i | 3.09650 | − | 1.78776i | ||||
\(285\) | −4.62242 | − | 11.2880i | −0.273808 | − | 0.668642i | ||||
\(286\) | 9.29921 | + | 9.06840i | 0.549874 | + | 0.536226i | ||||
\(287\) | 9.93353 | + | 24.4417i | 0.586358 | + | 1.44275i | ||||
\(288\) | −4.82998 | − | 4.90849i | −0.284609 | − | 0.289235i | ||||
\(289\) | 7.08062 | 0.416507 | ||||||||
\(290\) | 4.72688 | 0.277572 | ||||||||
\(291\) | −14.1595 | + | 18.2998i | −0.830042 | + | 1.07275i | ||||
\(292\) | 10.7476 | + | 6.20511i | 0.628953 | + | 0.363126i | ||||
\(293\) | 5.70408 | + | 9.87975i | 0.333236 | + | 0.577181i | 0.983144 | − | 0.182831i | \(-0.0585262\pi\) |
−0.649909 | + | 0.760012i | \(0.725193\pi\) | |||||||
\(294\) | 23.3576 | − | 17.2864i | 1.36224 | − | 1.00817i | ||||
\(295\) | 15.2414 | + | 26.3989i | 0.887390 | + | 1.53700i | ||||
\(296\) | − | 41.9969i | − | 2.44102i | ||||||
\(297\) | −0.925735 | − | 7.75524i | −0.0537166 | − | 0.450004i | ||||
\(298\) | 22.5780 | − | 39.1062i | 1.30791 | − | 2.26536i | ||||
\(299\) | 4.83007 | + | 17.1606i | 0.279330 | + | 0.992424i | ||||
\(300\) | −0.134638 | + | 0.991771i | −0.00777335 | + | 0.0572599i | ||||
\(301\) | 4.30178 | + | 0.595571i | 0.247951 | + | 0.0343282i | ||||
\(302\) | −17.1054 | − | 9.87583i | −0.984307 | − | 0.568290i | ||||
\(303\) | −23.9915 | − | 18.5635i | −1.37828 | − | 1.06644i | ||||
\(304\) | −7.01142 | − | 4.04805i | −0.402133 | − | 0.232171i | ||||
\(305\) | 6.22499i | 0.356442i | ||||||||
\(306\) | −24.7472 | − | 25.1494i | −1.41470 | − | 1.43770i | ||||
\(307\) | − | 1.16158i | − | 0.0662951i | −0.999450 | − | 0.0331476i | \(-0.989447\pi\) | ||
0.999450 | − | 0.0331476i | \(-0.0105531\pi\) | |||||||
\(308\) | 2.04200 | − | 14.7493i | 0.116354 | − | 0.840419i | ||||
\(309\) | 3.38334 | − | 4.37264i | 0.192471 | − | 0.248751i | ||||
\(310\) | −14.2082 | −0.806970 | ||||||||
\(311\) | 3.49022 | − | 6.04524i | 0.197912 | − | 0.342794i | −0.749939 | − | 0.661507i | \(-0.769917\pi\) |
0.947851 | + | 0.318713i | \(0.103251\pi\) | |||||||
\(312\) | −16.0687 | − | 20.5751i | −0.909708 | − | 1.16484i | ||||
\(313\) | 17.1288 | − | 9.88930i | 0.968175 | − | 0.558976i | 0.0694956 | − | 0.997582i | \(-0.477861\pi\) |
0.898679 | + | 0.438606i | \(0.144528\pi\) | |||||||
\(314\) | −16.7088 | + | 28.9405i | −0.942933 | + | 1.63321i | ||||
\(315\) | −14.0168 | + | 10.4310i | −0.789759 | + | 0.587720i | ||||
\(316\) | 11.3265 | + | 19.6181i | 0.637166 | + | 1.10360i | ||||
\(317\) | 6.37868 | − | 3.68273i | 0.358262 | − | 0.206843i | −0.310056 | − | 0.950718i | \(-0.600348\pi\) |
0.668318 | + | 0.743875i | \(0.267014\pi\) | |||||||
\(318\) | 3.45693 | − | 25.4644i | 0.193855 | − | 1.42797i | ||||
\(319\) | −1.34669 | −0.0754003 | ||||||||
\(320\) | 11.6259 | + | 20.1367i | 0.649909 | + | 1.12568i | ||||
\(321\) | −1.35137 | − | 3.30005i | −0.0754260 | − | 0.184191i | ||||
\(322\) | 19.2521 | − | 24.7462i | 1.07288 | − | 1.37905i | ||||
\(323\) | 13.5959 | + | 7.84958i | 0.756494 | + | 0.436762i | ||||
\(324\) | −0.543311 | + | 33.6935i | −0.0301840 | + | 1.87186i | ||||
\(325\) | 0.137256 | − | 0.539259i | 0.00761358 | − | 0.0299127i | ||||
\(326\) | −23.3150 | − | 13.4609i | −1.29130 | − | 0.745533i | ||||
\(327\) | 1.18439 | − | 8.72440i | 0.0654967 | − | 0.482461i | ||||
\(328\) | −36.1012 | − | 20.8430i | −1.99335 | − | 1.15086i | ||||
\(329\) | 0.865985 | + | 0.119894i | 0.0477433 | + | 0.00660995i | ||||
\(330\) | −1.84769 | + | 13.6104i | −0.101712 | + | 0.749230i | ||||
\(331\) | −1.15274 | + | 1.99660i | −0.0633601 | + | 0.109743i | −0.895965 | − | 0.444124i | \(-0.853515\pi\) |
0.832605 | + | 0.553867i | \(0.186848\pi\) | |||||||
\(332\) | −10.2707 | −0.563678 | ||||||||
\(333\) | 21.4825 | − | 21.1389i | 1.17723 | − | 1.15840i | ||||
\(334\) | −11.6500 | − | 6.72611i | −0.637458 | − | 0.368036i | ||||
\(335\) | −7.63249 | + | 13.2199i | −0.417007 | + | 0.722278i | ||||
\(336\) | −3.12124 | + | 11.1690i | −0.170277 | + | 0.609318i | ||||
\(337\) | −9.99425 | −0.544421 | −0.272211 | − | 0.962238i | \(-0.587755\pi\) | ||||
−0.272211 | + | 0.962238i | \(0.587755\pi\) | |||||||
\(338\) | 16.2517 | + | 26.5829i | 0.883975 | + | 1.44592i | ||||
\(339\) | −4.55571 | + | 5.88783i | −0.247432 | + | 0.319783i | ||||
\(340\) | 20.2227 | + | 35.0268i | 1.09673 | + | 1.89960i | ||||
\(341\) | 4.04792 | 0.219207 | ||||||||
\(342\) | −5.77422 | − | 22.2662i | −0.312234 | − | 1.20402i | ||||
\(343\) | 16.9652 | + | 7.42851i | 0.916034 | + | 0.401102i | ||||
\(344\) | −5.94244 | + | 3.43087i | −0.320395 | + | 0.184980i | ||||
\(345\) | −11.5365 | + | 14.9098i | −0.621103 | + | 0.802717i | ||||
\(346\) | 49.6210 | + | 28.6487i | 2.66764 | + | 1.54016i | ||||
\(347\) | − | 30.3026i | − | 1.62673i | −0.581754 | − | 0.813365i | \(-0.697633\pi\) | ||
0.581754 | − | 0.813365i | \(-0.302367\pi\) | |||||||
\(348\) | 5.75755 | + | 0.781619i | 0.308637 | + | 0.0418992i | ||||
\(349\) | 18.7898 | + | 10.8483i | 1.00580 | + | 0.580696i | 0.909958 | − | 0.414701i | \(-0.136114\pi\) |
0.0958377 | + | 0.995397i | \(0.469447\pi\) | |||||||
\(350\) | −0.906620 | + | 0.368465i | −0.0484609 | + | 0.0196953i | ||||
\(351\) | 2.43663 | − | 18.5759i | 0.130058 | − | 0.991506i | ||||
\(352\) | −1.72514 | − | 2.98803i | −0.0919502 | − | 0.159262i | ||||
\(353\) | −7.88107 | − | 13.6504i | −0.419467 | − | 0.726538i | 0.576419 | − | 0.817154i | \(-0.304450\pi\) |
−0.995886 | + | 0.0906163i | \(0.971116\pi\) | |||||||
\(354\) | 21.7843 | + | 53.1974i | 1.15782 | + | 2.82741i | ||||
\(355\) | −30.6794 | − | 17.7128i | −1.62830 | − | 0.940097i | ||||
\(356\) | 47.2881 | 2.50626 | ||||||||
\(357\) | 6.05240 | − | 21.6578i | 0.320327 | − | 1.14625i | ||||
\(358\) | −23.4482 | − | 40.6136i | −1.23928 | − | 2.14649i | ||||
\(359\) | 5.88803 | − | 3.39946i | 0.310759 | − | 0.179417i | −0.336507 | − | 0.941681i | \(-0.609246\pi\) |
0.647266 | + | 0.762264i | \(0.275912\pi\) | |||||||
\(360\) | 7.35981 | − | 26.6073i | 0.387896 | − | 1.40233i | ||||
\(361\) | −4.38253 | − | 7.59077i | −0.230660 | − | 0.399514i | ||||
\(362\) | −3.66275 | −0.192510 | ||||||||
\(363\) | −2.03657 | + | 15.0018i | −0.106892 | + | 0.787388i | ||||
\(364\) | 13.4738 | − | 33.0786i | 0.706220 | − | 1.73379i | ||||
\(365\) | − | 7.29620i | − | 0.381900i | ||||||
\(366\) | −1.57917 | + | 11.6325i | −0.0825447 | + | 0.608039i | ||||
\(367\) | −14.0718 | + | 8.12438i | −0.734544 | + | 0.424089i | −0.820082 | − | 0.572246i | \(-0.806072\pi\) |
0.0855383 | + | 0.996335i | \(0.472739\pi\) | |||||||
\(368\) | 12.5127i | 0.652267i | ||||||||
\(369\) | −7.50955 | − | 28.9579i | −0.390932 | − | 1.50749i | ||||
\(370\) | −45.9016 | + | 26.5013i | −2.38631 | + | 1.37774i | ||||
\(371\) | 15.1732 | − | 6.16664i | 0.787753 | − | 0.320156i | ||||
\(372\) | −17.3062 | − | 2.34941i | −0.897284 | − | 0.121811i | ||||
\(373\) | 6.67655 | − | 11.5641i | 0.345699 | − | 0.598767i | −0.639782 | − | 0.768557i | \(-0.720975\pi\) |
0.985480 | + | 0.169789i | \(0.0543086\pi\) | |||||||
\(374\) | −8.83902 | − | 15.3096i | −0.457055 | − | 0.791642i | ||||
\(375\) | 18.1864 | − | 7.44730i | 0.939140 | − | 0.384577i | ||||
\(376\) | −1.19626 | + | 0.690663i | −0.0616926 | + | 0.0356182i | ||||
\(377\) | −3.13057 | − | 0.796814i | −0.161233 | − | 0.0410380i | ||||
\(378\) | −28.8390 | + | 15.9363i | −1.48332 | + | 0.819674i | ||||
\(379\) | −11.9437 | + | 20.6870i | −0.613504 | + | 1.06262i | 0.377141 | + | 0.926156i | \(0.376907\pi\) |
−0.990645 | + | 0.136464i | \(0.956426\pi\) | |||||||
\(380\) | 26.3681i | 1.35266i | ||||||||
\(381\) | −4.12074 | + | 30.3541i | −0.211112 | + | 1.55509i | ||||
\(382\) | −7.39870 | + | 12.8149i | −0.378551 | + | 0.655669i | ||||
\(383\) | 0.798871 | − | 1.38369i | 0.0408204 | − | 0.0707030i | −0.844893 | − | 0.534935i | \(-0.820336\pi\) |
0.885714 | + | 0.464232i | \(0.153670\pi\) | |||||||
\(384\) | 13.6034 | + | 33.2196i | 0.694194 | + | 1.69523i | ||||
\(385\) | −8.10991 | + | 3.29600i | −0.413319 | + | 0.167980i | ||||
\(386\) | 21.7047 | − | 12.5312i | 1.10474 | − | 0.637823i | ||||
\(387\) | −4.74607 | − | 1.31280i | −0.241256 | − | 0.0667336i | ||||
\(388\) | 43.3169 | − | 25.0090i | 2.19908 | − | 1.26964i | ||||
\(389\) | 19.3984 | + | 11.1997i | 0.983539 | + | 0.567846i | 0.903337 | − | 0.428932i | \(-0.141110\pi\) |
0.0802022 | + | 0.996779i | \(0.474443\pi\) | |||||||
\(390\) | −12.3483 | + | 30.5461i | −0.625279 | + | 1.54676i | ||||
\(391\) | − | 24.2633i | − | 1.22705i | ||||||
\(392\) | −28.3639 | + | 7.19576i | −1.43259 | + | 0.363441i | ||||
\(393\) | −17.0466 | − | 13.1899i | −0.859889 | − | 0.665340i | ||||
\(394\) | −5.54266 | + | 9.60017i | −0.279235 | + | 0.483650i | ||||
\(395\) | 6.65907 | − | 11.5338i | 0.335054 | − | 0.580331i | ||||
\(396\) | −4.50114 | + | 16.2726i | −0.226191 | + | 0.817728i | ||||
\(397\) | 17.6893 | + | 10.2130i | 0.887803 | + | 0.512573i | 0.873223 | − | 0.487320i | \(-0.162026\pi\) |
0.0145798 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(398\) | 21.0089 | 1.05308 | ||||||||
\(399\) | 10.4770 | − | 10.2551i | 0.524506 | − | 0.513395i | ||||
\(400\) | 0.195281 | − | 0.338236i | 0.00976404 | − | 0.0169118i | ||||
\(401\) | 32.5300i | 1.62447i | 0.583330 | + | 0.812235i | \(0.301749\pi\) | ||||
−0.583330 | + | 0.812235i | \(0.698251\pi\) | |||||||
\(402\) | −17.6163 | + | 22.7674i | −0.878620 | + | 1.13553i | ||||
\(403\) | 9.40996 | + | 2.39508i | 0.468743 | + | 0.119308i | ||||
\(404\) | 32.7876 | + | 56.7897i | 1.63124 | + | 2.82539i | ||||
\(405\) | 17.3148 | − | 9.62788i | 0.860380 | − | 0.478413i | ||||
\(406\) | 2.13906 | + | 5.26322i | 0.106160 | + | 0.261209i | ||||
\(407\) | 13.0774 | − | 7.55024i | 0.648223 | − | 0.374252i | ||||
\(408\) | 13.4647 | + | 32.8808i | 0.666600 | + | 1.62784i | ||||
\(409\) | − | 26.4267i | − | 1.30672i | −0.757049 | − | 0.653358i | \(-0.773360\pi\) | ||
0.757049 | − | 0.653358i | \(-0.226640\pi\) | |||||||
\(410\) | 52.6102i | 2.59823i | ||||||||
\(411\) | 6.19919 | + | 15.1385i | 0.305784 | + | 0.746727i | ||||
\(412\) | −10.3504 | + | 5.97578i | −0.509926 | + | 0.294406i | ||||
\(413\) | −22.4971 | + | 28.9171i | −1.10701 | + | 1.42292i | ||||
\(414\) | −25.3403 | + | 24.9349i | −1.24541 | + | 1.22549i | ||||
\(415\) | 3.01917 | + | 5.22936i | 0.148205 | + | 0.256699i | ||||
\(416\) | −2.24236 | − | 7.96682i | −0.109941 | − | 0.390605i | ||||
\(417\) | −4.77797 | + | 6.17507i | −0.233978 | + | 0.302394i | ||||
\(418\) | − | 11.5251i | − | 0.563709i | ||||||
\(419\) | −7.22669 | + | 12.5170i | −0.353047 | + | 0.611495i | −0.986782 | − | 0.162055i | \(-0.948188\pi\) |
0.633735 | + | 0.773550i | \(0.281521\pi\) | |||||||
\(420\) | 36.5855 | − | 9.38449i | 1.78519 | − | 0.457916i | ||||
\(421\) | −29.6577 | −1.44543 | −0.722713 | − | 0.691148i | \(-0.757105\pi\) | ||||
−0.722713 | + | 0.691148i | \(0.757105\pi\) | |||||||
\(422\) | 2.05197 | + | 1.18471i | 0.0998884 | + | 0.0576706i | ||||
\(423\) | −0.955423 | − | 0.264278i | −0.0464543 | − | 0.0128497i | ||||
\(424\) | −12.9392 | + | 22.4113i | −0.628381 | + | 1.08839i | ||||
\(425\) | −0.378670 | + | 0.655875i | −0.0183682 | + | 0.0318146i | ||||
\(426\) | −52.8364 | − | 40.8822i | −2.55993 | − | 1.98075i | ||||
\(427\) | −6.93132 | + | 2.81700i | −0.335430 | + | 0.136324i | ||||
\(428\) | 7.70874i | 0.372616i | ||||||||
\(429\) | 3.51803 | − | 8.70262i | 0.169852 | − | 0.420166i | ||||
\(430\) | 7.49971 | + | 4.32996i | 0.361668 | + | 0.208809i | ||||
\(431\) | −10.4396 | + | 6.02731i | −0.502858 | + | 0.290325i | −0.729893 | − | 0.683561i | \(-0.760430\pi\) |
0.227035 | + | 0.973887i | \(0.427097\pi\) | |||||||
\(432\) | 5.17870 | − | 12.0870i | 0.249160 | − | 0.581535i | ||||
\(433\) | −23.4870 | + | 13.5603i | −1.12872 | + | 0.651664i | −0.943612 | − | 0.331055i | \(-0.892595\pi\) |
−0.185104 | + | 0.982719i | \(0.559262\pi\) | |||||||
\(434\) | −6.42964 | − | 15.8203i | −0.308632 | − | 0.759399i | ||||
\(435\) | −1.29452 | − | 3.16123i | −0.0620676 | − | 0.151570i | ||||
\(436\) | −9.51634 | + | 16.4828i | −0.455750 | + | 0.789382i | ||||
\(437\) | 7.90914 | − | 13.6990i | 0.378345 | − | 0.655313i | ||||
\(438\) | 1.85092 | − | 13.6342i | 0.0884403 | − | 0.651467i | ||||
\(439\) | 4.20603i | 0.200743i | 0.994950 | + | 0.100371i | \(0.0320031\pi\) | ||||
−0.994950 | + | 0.100371i | \(0.967997\pi\) | |||||||
\(440\) | 6.91583 | − | 11.9786i | 0.329699 | − | 0.571056i | ||||
\(441\) | −17.9576 | − | 10.8869i | −0.855123 | − | 0.518424i | ||||
\(442\) | −11.4891 | − | 40.8193i | −0.546481 | − | 1.94157i | ||||
\(443\) | 10.9258 | − | 6.30802i | 0.519101 | − | 0.299703i | −0.217466 | − | 0.976068i | \(-0.569779\pi\) |
0.736567 | + | 0.676365i | \(0.236446\pi\) | |||||||
\(444\) | −60.2923 | + | 24.6896i | −2.86135 | + | 1.17172i | ||||
\(445\) | −13.9008 | − | 24.0769i | −0.658960 | − | 1.14135i | ||||
\(446\) | 25.4639 | − | 44.1048i | 1.20575 | − | 2.08842i | ||||
\(447\) | −32.3366 | − | 4.38988i | −1.52947 | − | 0.207634i | ||||
\(448\) | −17.1604 | + | 22.0575i | −0.810753 | + | 1.04212i | ||||
\(449\) | 5.18515 | − | 2.99365i | 0.244702 | − | 0.141279i | −0.372634 | − | 0.927979i | \(-0.621545\pi\) |
0.617336 | + | 0.786699i | \(0.288212\pi\) | |||||||
\(450\) | 1.07414 | − | 0.278553i | 0.0506353 | − | 0.0131311i | ||||
\(451\) | − | 14.9887i | − | 0.705790i | ||||||
\(452\) | 13.9369 | − | 8.04649i | 0.655538 | − | 0.378475i | ||||
\(453\) | −1.92018 | + | 14.1444i | −0.0902177 | + | 0.664560i | ||||
\(454\) | 9.55287i | 0.448338i | ||||||||
\(455\) | −20.8028 | + | 2.86353i | −0.975250 | + | 0.134244i | ||||
\(456\) | −3.11607 | + | 22.9536i | −0.145923 | + | 1.07490i | ||||
\(457\) | 37.7688 | 1.76675 | 0.883374 | − | 0.468669i | \(-0.155266\pi\) | ||||
0.883374 | + | 0.468669i | \(0.155266\pi\) | |||||||
\(458\) | 1.81555 | + | 3.14463i | 0.0848353 | + | 0.146939i | ||||
\(459\) | −10.0420 | + | 23.4379i | −0.468722 | + | 1.09399i | ||||
\(460\) | 35.2926 | − | 20.3762i | 1.64553 | − | 0.950045i | ||||
\(461\) | 7.86795 | + | 13.6277i | 0.366447 | + | 0.634705i | 0.989007 | − | 0.147867i | \(-0.0472408\pi\) |
−0.622560 | + | 0.782572i | \(0.713907\pi\) | |||||||
\(462\) | −15.9909 | + | 4.10180i | −0.743964 | + | 0.190833i | ||||
\(463\) | −23.9163 | −1.11148 | −0.555742 | − | 0.831355i | \(-0.687566\pi\) | ||||
−0.555742 | + | 0.831355i | \(0.687566\pi\) | |||||||
\(464\) | −1.96357 | − | 1.13367i | −0.0911565 | − | 0.0526292i | ||||
\(465\) | 3.89111 | + | 9.50212i | 0.180446 | + | 0.440650i | ||||
\(466\) | 8.11995 | + | 14.0642i | 0.376149 | + | 0.651510i | ||||
\(467\) | 11.4121 | + | 19.7663i | 0.528087 | + | 0.914674i | 0.999464 | + | 0.0327419i | \(0.0104239\pi\) |
−0.471377 | + | 0.881932i | \(0.656243\pi\) | |||||||
\(468\) | −20.0917 | + | 35.1647i | −0.928740 | + | 1.62549i | ||||
\(469\) | −18.1738 | − | 2.51612i | −0.839188 | − | 0.116184i | ||||
\(470\) | 1.50975 | + | 0.871657i | 0.0696398 | + | 0.0402066i | ||||
\(471\) | 23.9307 | + | 3.24873i | 1.10267 | + | 0.149693i | ||||
\(472\) | − | 57.8883i | − | 2.66452i | ||||||
\(473\) | −2.13667 | − | 1.23361i | −0.0982443 | − | 0.0567214i | ||||
\(474\) | 15.3696 | − | 19.8637i | 0.705947 | − | 0.912369i | ||||
\(475\) | −0.427592 | + | 0.246871i | −0.0196193 | + | 0.0113272i | ||||
\(476\) | −29.8497 | + | 38.3680i | −1.36816 | + | 1.75860i | ||||
\(477\) | −17.9768 | + | 4.66186i | −0.823100 | + | 0.213452i | ||||
\(478\) | −37.0134 | −1.69295 | ||||||||
\(479\) | −1.19588 | − | 2.07132i | −0.0546411 | − | 0.0946412i | 0.837411 | − | 0.546574i | \(-0.184068\pi\) |
−0.892052 | + | 0.451932i | \(0.850735\pi\) | |||||||
\(480\) | 5.35581 | − | 6.92187i | 0.244458 | − | 0.315939i | ||||
\(481\) | 34.8676 | − | 9.81393i | 1.58983 | − | 0.447476i | ||||
\(482\) | −16.8706 | −0.768435 | ||||||||
\(483\) | −21.8222 | − | 6.09832i | −0.992942 | − | 0.277483i | ||||
\(484\) | 16.3635 | − | 28.3424i | 0.743796 | − | 1.28829i | ||||
\(485\) | −25.4668 | − | 14.7033i | −1.15639 | − | 0.667641i | ||||
\(486\) | 34.7982 | − | 13.5989i | 1.57848 | − | 0.616858i | ||||
\(487\) | 40.0884 | 1.81658 | 0.908290 | − | 0.418340i | \(-0.137388\pi\) | ||||
0.908290 | + | 0.418340i | \(0.137388\pi\) | |||||||
\(488\) | 5.91077 | − | 10.2378i | 0.267568 | − | 0.463442i | ||||
\(489\) | −2.61724 | + | 19.2791i | −0.118356 | + | 0.871829i | ||||
\(490\) | 25.7632 | + | 26.4603i | 1.16386 | + | 1.19535i | ||||
\(491\) | 3.37799 | + | 1.95028i | 0.152447 | + | 0.0880151i | 0.574283 | − | 0.818657i | \(-0.305281\pi\) |
−0.421836 | + | 0.906672i | \(0.638614\pi\) | |||||||
\(492\) | −8.69942 | + | 64.0816i | −0.392200 | + | 2.88902i | ||||
\(493\) | 3.80756 | + | 2.19830i | 0.171484 | + | 0.0990064i | ||||
\(494\) | 6.81917 | − | 26.7916i | 0.306809 | − | 1.20541i | ||||
\(495\) | 9.60838 | − | 2.49171i | 0.431865 | − | 0.111994i | ||||
\(496\) | 5.90215 | + | 3.40761i | 0.265014 | + | 0.153006i | ||||
\(497\) | 5.83918 | − | 42.1761i | 0.261923 | − | 1.89186i | ||||
\(498\) | 4.31524 | + | 10.5379i | 0.193371 | + | 0.472213i | ||||
\(499\) | 16.3007 | + | 28.2336i | 0.729718 | + | 1.26391i | 0.957002 | + | 0.290081i | \(0.0936822\pi\) |
−0.227284 | + | 0.973829i | \(0.572984\pi\) | |||||||
\(500\) | −42.4824 | −1.89987 | ||||||||
\(501\) | −1.30777 | + | 9.63328i | −0.0584269 | + | 0.430383i | ||||
\(502\) | 7.02736 | − | 4.05725i | 0.313646 | − | 0.181084i | ||||
\(503\) | −6.79105 | − | 11.7625i | −0.302798 | − | 0.524462i | 0.673971 | − | 0.738758i | \(-0.264587\pi\) |
−0.976769 | + | 0.214296i | \(0.931254\pi\) | |||||||
\(504\) | 32.9568 | − | 3.84573i | 1.46801 | − | 0.171302i | ||||
\(505\) | 19.2764 | − | 33.3877i | 0.857789 | − | 1.48573i | ||||
\(506\) | −15.4258 | + | 8.90609i | −0.685760 | + | 0.395924i | ||||
\(507\) | 13.3273 | − | 18.1489i | 0.591888 | − | 0.806020i | ||||
\(508\) | 33.1094 | − | 57.3472i | 1.46899 | − | 2.54437i | ||||
\(509\) | −15.4269 | −0.683787 | −0.341894 | − | 0.939739i | \(-0.611068\pi\) | ||||
−0.341894 | + | 0.939739i | \(0.611068\pi\) | |||||||
\(510\) | 27.4413 | − | 35.4653i | 1.21512 | − | 1.57043i | ||||
\(511\) | 8.12406 | − | 3.30175i | 0.359387 | − | 0.146061i | ||||
\(512\) | − | 26.9670i | − | 1.19179i | ||||||
\(513\) | −13.3098 | + | 9.95957i | −0.587641 | + | 0.439726i | ||||
\(514\) | 49.4195i | 2.17980i | ||||||||
\(515\) | 6.08517 | + | 3.51327i | 0.268145 | + | 0.154813i | ||||
\(516\) | 8.41899 | + | 6.51420i | 0.370625 | + | 0.286772i | ||||
\(517\) | −0.430130 | − | 0.248336i | −0.0189171 | − | 0.0109218i | ||||
\(518\) | −50.2802 | − | 39.1172i | −2.20918 | − | 1.71871i | ||||
\(519\) | 5.57022 | − | 41.0313i | 0.244506 | − | 1.80107i | ||||
\(520\) | 23.1643 | − | 23.7539i | 1.01582 | − | 1.04168i | ||||
\(521\) | 8.81691 | − | 15.2713i | 0.386276 | − | 0.669050i | −0.605669 | − | 0.795716i | \(-0.707095\pi\) |
0.991945 | + | 0.126667i | \(0.0404279\pi\) | |||||||
\(522\) | −1.61709 | − | 6.23571i | −0.0707780 | − | 0.272930i | ||||
\(523\) | − | 16.0990i | − | 0.703958i | −0.936008 | − | 0.351979i | \(-0.885509\pi\) | ||
0.936008 | − | 0.351979i | \(-0.114491\pi\) | |||||||
\(524\) | 23.2964 | + | 40.3506i | 1.01771 | + | 1.76273i | ||||
\(525\) | 0.494712 | + | 0.505418i | 0.0215910 | + | 0.0220583i | ||||
\(526\) | −6.65022 | − | 11.5185i | −0.289964 | − | 0.502232i | ||||
\(527\) | −11.4449 | − | 6.60770i | −0.498547 | − | 0.287836i | ||||
\(528\) | 4.03179 | − | 5.21071i | 0.175461 | − | 0.226767i | ||||
\(529\) | −1.44743 | −0.0629317 | ||||||||
\(530\) | 32.6599 | 1.41866 | ||||||||
\(531\) | 29.6113 | − | 29.1377i | 1.28502 | − | 1.26447i | ||||
\(532\) | −29.3600 | + | 11.9324i | −1.27292 | + | 0.517334i | ||||
\(533\) | 8.86854 | − | 34.8433i | 0.384139 | − | 1.50923i | ||||
\(534\) | −19.8681 | − | 48.5181i | −0.859778 | − | 2.09959i | ||||
\(535\) | 3.92493 | − | 2.26606i | 0.169689 | − | 0.0979702i | ||||
\(536\) | 25.1051 | − | 14.4944i | 1.08438 | − | 0.626064i | ||||
\(537\) | −20.7398 | + | 26.8043i | −0.894990 | + | 1.15669i | ||||
\(538\) | 21.9723i | 0.947294i | ||||||||
\(539\) | −7.33996 | − | 7.53856i | −0.316155 | − | 0.324709i | ||||
\(540\) | −42.5252 | + | 5.07619i | −1.82999 | + | 0.218444i | ||||
\(541\) | −11.6387 | − | 20.1589i | −0.500388 | − | 0.866697i | −1.00000 | 0.000447572i | \(-0.999858\pi\) | |
0.499612 | − | 0.866249i | \(-0.333476\pi\) | |||||||
\(542\) | 16.3561 | 0.702555 | ||||||||
\(543\) | 1.00310 | + | 2.44957i | 0.0430470 | + | 0.105121i | ||||
\(544\) | 11.2642i | 0.482951i | ||||||||
\(545\) | 11.1897 | 0.479313 | ||||||||
\(546\) | −39.6000 | + | 0.0736874i | −1.69472 | + | 0.00315353i | ||||
\(547\) | 32.4180 | 1.38609 | 0.693046 | − | 0.720893i | \(-0.256268\pi\) | ||||
0.693046 | + | 0.720893i | \(0.256268\pi\) | |||||||
\(548\) | − | 35.3627i | − | 1.51062i | ||||||
\(549\) | 8.21202 | − | 2.12960i | 0.350481 | − | 0.0908891i | ||||
\(550\) | 0.555977 | 0.0237070 | ||||||||
\(551\) | 1.43316 | + | 2.48231i | 0.0610548 | + | 0.105750i | ||||
\(552\) | 33.1303 | − | 13.5668i | 1.41012 | − | 0.577443i | ||||
\(553\) | 15.8560 | + | 2.19522i | 0.674264 | + | 0.0933503i | ||||
\(554\) | − | 7.11132i | − | 0.302131i | ||||||
\(555\) | 30.2943 | + | 23.4402i | 1.28592 | + | 0.994983i | ||||
\(556\) | 14.6168 | − | 8.43904i | 0.619892 | − | 0.357895i | ||||
\(557\) | −7.16449 | + | 4.13642i | −0.303569 | + | 0.175266i | −0.644045 | − | 0.764987i | \(-0.722745\pi\) |
0.340476 | + | 0.940253i | \(0.389412\pi\) | |||||||
\(558\) | 4.86068 | + | 18.7435i | 0.205769 | + | 0.793474i | ||||
\(559\) | −4.23709 | − | 4.13193i | −0.179210 | − | 0.174762i | ||||
\(560\) | −14.5994 | − | 2.02126i | −0.616939 | − | 0.0854137i | ||||
\(561\) | −7.81806 | + | 10.1041i | −0.330079 | + | 0.426595i | ||||
\(562\) | −62.2407 | −2.62547 | ||||||||
\(563\) | −41.4857 | −1.74841 | −0.874206 | − | 0.485555i | \(-0.838617\pi\) | ||||
−0.874206 | + | 0.485555i | \(0.838617\pi\) | |||||||
\(564\) | 1.69481 | + | 1.31136i | 0.0713645 | + | 0.0552184i | ||||
\(565\) | −8.19378 | − | 4.73068i | −0.344715 | − | 0.199021i | ||||
\(566\) | −13.0569 | − | 22.6152i | −0.548821 | − | 0.950586i | ||||
\(567\) | 18.5558 | + | 14.9225i | 0.779270 | + | 0.626688i | ||||
\(568\) | 33.6374 | + | 58.2616i | 1.41139 | + | 2.44460i | ||||
\(569\) | 15.4494i | 0.647673i | 0.946113 | + | 0.323837i | \(0.104973\pi\) | ||||
−0.946113 | + | 0.323837i | \(0.895027\pi\) | |||||||
\(570\) | 27.0540 | − | 11.0786i | 1.13317 | − | 0.464031i | ||||
\(571\) | −16.0896 | + | 27.8680i | −0.673329 | + | 1.16624i | 0.303625 | + | 0.952792i | \(0.401803\pi\) |
−0.976954 | + | 0.213449i | \(0.931530\pi\) | |||||||
\(572\) | −14.1669 | + | 14.5275i | −0.592349 | + | 0.607425i | ||||
\(573\) | 10.5966 | + | 1.43854i | 0.442679 | + | 0.0600961i | ||||
\(574\) | −58.5797 | + | 23.8078i | −2.44507 | + | 0.993716i | ||||
\(575\) | 0.660852 | + | 0.381543i | 0.0275594 | + | 0.0159114i | ||||
\(576\) | 22.5871 | − | 22.2258i | 0.941128 | − | 0.926075i | ||||
\(577\) | −19.3075 | − | 11.1472i | −0.803783 | − | 0.464064i | 0.0410092 | − | 0.999159i | \(-0.486943\pi\) |
−0.844792 | + | 0.535094i | \(0.820276\pi\) | |||||||
\(578\) | 16.9702i | 0.705866i | ||||||||
\(579\) | −14.3248 | − | 11.0838i | −0.595317 | − | 0.460627i | ||||
\(580\) | 7.38447i | 0.306623i | ||||||||
\(581\) | −4.45644 | + | 5.72819i | −0.184884 | + | 0.237645i | ||||
\(582\) | −43.8592 | − | 33.9361i | −1.81802 | − | 1.40670i | ||||
\(583\) | −9.30484 | −0.385367 | ||||||||
\(584\) | −6.92790 | + | 11.9995i | −0.286679 | + | 0.496542i | ||||
\(585\) | 23.8103 | − | 0.107225i | 0.984436 | − | 0.00443319i | ||||
\(586\) | −23.6789 | + | 13.6710i | −0.978165 | + | 0.564744i | ||||
\(587\) | 19.0213 | − | 32.9459i | 0.785094 | − | 1.35982i | −0.143849 | − | 0.989600i | \(-0.545948\pi\) |
0.928943 | − | 0.370223i | \(-0.120719\pi\) | |||||||
\(588\) | 27.0054 | + | 36.4899i | 1.11368 | + | 1.50482i | ||||
\(589\) | −4.30784 | − | 7.46139i | −0.177501 | − | 0.307441i | ||||
\(590\) | −63.2704 | + | 36.5292i | −2.60480 | + | 1.50388i | ||||
\(591\) | 7.93832 | + | 1.07767i | 0.326539 | + | 0.0443294i | ||||
\(592\) | 25.4237 | 1.04491 | ||||||||
\(593\) | −0.484442 | − | 0.839079i | −0.0198937 | − | 0.0344568i | 0.855907 | − | 0.517129i | \(-0.172999\pi\) |
−0.875801 | + | 0.482673i | \(0.839666\pi\) | |||||||
\(594\) | 18.5870 | − | 2.21872i | 0.762635 | − | 0.0910350i | ||||
\(595\) | 28.3098 | + | 3.91942i | 1.16059 | + | 0.160681i | ||||
\(596\) | 61.0928 | + | 35.2719i | 2.50246 | + | 1.44479i | ||||
\(597\) | −5.75358 | − | 14.0503i | −0.235478 | − | 0.575040i | ||||
\(598\) | −41.1290 | + | 11.5763i | −1.68189 | + | 0.473389i | ||||
\(599\) | −32.1172 | − | 18.5429i | −1.31228 | − | 0.757642i | −0.329803 | − | 0.944050i | \(-0.606982\pi\) |
−0.982472 | + | 0.186408i | \(0.940315\pi\) | |||||||
\(600\) | −1.10730 | − | 0.150322i | −0.0452052 | − | 0.00613686i | ||||
\(601\) | −9.42183 | − | 5.43970i | −0.384324 | − | 0.221890i | 0.295374 | − | 0.955382i | \(-0.404556\pi\) |
−0.679698 | + | 0.733492i | \(0.737889\pi\) | |||||||
\(602\) | −1.42741 | + | 10.3101i | −0.0581769 | + | 0.420209i | ||||
\(603\) | 20.0508 | + | 5.54622i | 0.816530 | + | 0.225859i | ||||
\(604\) | 15.4283 | − | 26.7226i | 0.627768 | − | 1.08733i | ||||
\(605\) | −19.2408 | −0.782251 | ||||||||
\(606\) | 44.4912 | − | 57.5007i | 1.80733 | − | 2.33580i | ||||
\(607\) | 14.0368 | + | 8.10415i | 0.569736 | + | 0.328937i | 0.757044 | − | 0.653364i | \(-0.226643\pi\) |
−0.187308 | + | 0.982301i | \(0.559976\pi\) | |||||||
\(608\) | −3.67182 | + | 6.35977i | −0.148912 | + | 0.257923i | ||||
\(609\) | 2.93411 | − | 2.87196i | 0.118896 | − | 0.116378i | ||||
\(610\) | −14.9195 | −0.604072 | ||||||||
\(611\) | −0.852962 | − | 0.831792i | −0.0345072 | − | 0.0336507i | ||||
\(612\) | 39.2892 | − | 38.6607i | 1.58817 | − | 1.56277i | ||||
\(613\) | 16.3691 | + | 28.3521i | 0.661142 | + | 1.14513i | 0.980316 | + | 0.197435i | \(0.0632611\pi\) |
−0.319174 | + | 0.947696i | \(0.603406\pi\) | |||||||
\(614\) | 2.78398 | 0.112352 | ||||||||
\(615\) | 35.1846 | − | 14.4080i | 1.41878 | − | 0.580988i | ||||
\(616\) | 16.4674 | + | 2.27987i | 0.663489 | + | 0.0918584i | ||||
\(617\) | 33.8949 | − | 19.5692i | 1.36456 | − | 0.787828i | 0.374331 | − | 0.927295i | \(-0.377872\pi\) |
0.990227 | + | 0.139467i | \(0.0445389\pi\) | |||||||
\(618\) | 10.4799 | + | 8.10886i | 0.421565 | + | 0.326186i | ||||
\(619\) | −4.41436 | − | 2.54863i | −0.177428 | − | 0.102438i | 0.408656 | − | 0.912689i | \(-0.365998\pi\) |
−0.586084 | + | 0.810250i | \(0.699331\pi\) | |||||||
\(620\) | − | 22.1964i | − | 0.891430i | ||||||
\(621\) | 23.6157 | + | 10.1182i | 0.947666 | + | 0.406031i | ||||
\(622\) | 14.4887 | + | 8.36504i | 0.580943 | + | 0.335407i | ||||
\(623\) | 20.5182 | − | 26.3736i | 0.822045 | − | 1.05663i | ||||
\(624\) | 12.4555 | − | 9.72748i | 0.498621 | − | 0.389411i | ||||
\(625\) | 12.1023 | + | 20.9617i | 0.484090 | + | 0.838469i | ||||
\(626\) | 23.7017 | + | 41.0526i | 0.947312 | + | 1.64079i | ||||
\(627\) | −7.70770 | + | 3.15630i | −0.307816 | + | 0.126050i | ||||
\(628\) | −45.2117 | − | 26.1030i | −1.80414 | − | 1.04162i | ||||
\(629\) | −49.2991 | −1.96569 | ||||||||
\(630\) | −25.0000 | − | 33.5942i | −0.996025 | − | 1.33843i | ||||
\(631\) | 24.5250 | + | 42.4785i | 0.976324 | + | 1.69104i | 0.675496 | + | 0.737364i | \(0.263930\pi\) |
0.300828 | + | 0.953678i | \(0.402737\pi\) | |||||||
\(632\) | −21.9033 | + | 12.6459i | −0.871266 | + | 0.503026i | ||||
\(633\) | 0.230345 | − | 1.69676i | 0.00915538 | − | 0.0674402i | ||||
\(634\) | 8.82643 | + | 15.2878i | 0.350542 | + | 0.607157i | ||||
\(635\) | −38.9313 | −1.54494 | ||||||||
\(636\) | 39.7812 | + | 5.40052i | 1.57743 | + | 0.214145i | ||||
\(637\) | −12.6023 | − | 21.8674i | −0.499323 | − | 0.866416i | ||||
\(638\) | − | 3.22763i | − | 0.127783i | ||||||
\(639\) | −12.8712 | + | 46.5320i | −0.509175 | + | 1.84078i | ||||
\(640\) | −39.5098 | + | 22.8110i | −1.56176 | + | 0.901683i | ||||
\(641\) | − | 25.8865i | − | 1.02246i | −0.859445 | − | 0.511228i | \(-0.829191\pi\) | ||
0.859445 | − | 0.511228i | \(-0.170809\pi\) | |||||||
\(642\) | 7.90926 | − | 3.23883i | 0.312154 | − | 0.127827i | ||||
\(643\) | 19.3103 | − | 11.1488i | 0.761526 | − | 0.439667i | −0.0683177 | − | 0.997664i | \(-0.521763\pi\) |
0.829843 | + | 0.557997i | \(0.188430\pi\) | |||||||
\(644\) | 38.6592 | + | 30.0762i | 1.52338 | + | 1.18517i | ||||
\(645\) | 0.841882 | − | 6.20146i | 0.0331491 | − | 0.244182i | ||||
\(646\) | −18.8131 | + | 32.5853i | −0.740193 | + | 1.28205i | ||||
\(647\) | 9.84729 | + | 17.0560i | 0.387137 | + | 0.670541i | 0.992063 | − | 0.125741i | \(-0.0401307\pi\) |
−0.604926 | + | 0.796282i | \(0.706797\pi\) | |||||||
\(648\) | −37.6182 | − | 0.606599i | −1.47778 | − | 0.0238295i | ||||
\(649\) | 18.0258 | − | 10.4072i | 0.707575 | − | 0.408518i | ||||
\(650\) | 1.29245 | + | 0.328962i | 0.0506939 | + | 0.0129029i | ||||
\(651\) | −8.81943 | + | 8.63261i | −0.345661 | + | 0.338339i | ||||
\(652\) | 21.0291 | − | 36.4234i | 0.823562 | − | 1.42645i | ||||
\(653\) | 9.34844i | 0.365833i | 0.983128 | + | 0.182916i | \(0.0585538\pi\) | ||||
−0.983128 | + | 0.182916i | \(0.941446\pi\) | |||||||
\(654\) | 20.9098 | + | 2.83862i | 0.817639 | + | 0.110999i | ||||
\(655\) | 13.6964 | − | 23.7229i | 0.535163 | − | 0.926930i | ||||
\(656\) | 12.6177 | − | 21.8546i | 0.492640 | − | 0.853277i | ||||
\(657\) | −9.62516 | + | 2.49606i | −0.375513 | + | 0.0973807i | ||||
\(658\) | −0.287350 | + | 2.07551i | −0.0112021 | + | 0.0809119i | ||||
\(659\) | −12.6857 | + | 7.32409i | −0.494165 | + | 0.285306i | −0.726301 | − | 0.687377i | \(-0.758762\pi\) |
0.232136 | + | 0.972683i | \(0.425429\pi\) | |||||||
\(660\) | −21.2626 | − | 2.88652i | −0.827646 | − | 0.112358i | ||||
\(661\) | −1.74192 | + | 1.00570i | −0.0677529 | + | 0.0391172i | −0.533494 | − | 0.845804i | \(-0.679121\pi\) |
0.465741 | + | 0.884921i | \(0.345788\pi\) | |||||||
\(662\) | −4.78526 | − | 2.76277i | −0.185984 | − | 0.107378i | ||||
\(663\) | −24.1526 | + | 18.8626i | −0.938009 | + | 0.732562i | ||||
\(664\) | − | 11.4671i | − | 0.445009i | ||||||
\(665\) | 14.7060 | + | 11.4411i | 0.570276 | + | 0.443666i | ||||
\(666\) | 50.6637 | + | 51.4873i | 1.96318 | + | 1.99509i | ||||
\(667\) | 2.21498 | − | 3.83646i | 0.0857643 | − | 0.148548i | ||||
\(668\) | 10.5077 | − | 18.1999i | 0.406556 | − | 0.704176i | ||||
\(669\) | −36.4699 | − | 4.95099i | −1.41001 | − | 0.191417i | ||||
\(670\) | −31.6841 | − | 18.2928i | −1.22406 | − | 0.706714i | ||||
\(671\) | 4.25057 | 0.164092 | ||||||||
\(672\) | 10.1309 | + | 2.83114i | 0.390809 | + | 0.109214i | ||||
\(673\) | −3.60802 | + | 6.24928i | −0.139079 | + | 0.240892i | −0.927148 | − | 0.374695i | \(-0.877748\pi\) |
0.788069 | + | 0.615587i | \(0.211081\pi\) | |||||||
\(674\) | − | 23.9533i | − | 0.922646i | ||||||
\(675\) | −0.480457 | − | 0.642074i | −0.0184928 | − | 0.0247134i | ||||
\(676\) | −41.5286 | + | 25.3889i | −1.59726 | + | 0.976494i | ||||
\(677\) | 12.2214 | + | 21.1681i | 0.469706 | + | 0.813554i | 0.999400 | − | 0.0346344i | \(-0.0110267\pi\) |
−0.529694 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(678\) | −14.1114 | − | 10.9187i | −0.541945 | − | 0.419331i | ||||
\(679\) | 4.84706 | − | 35.0101i | 0.186013 | − | 1.34356i | ||||
\(680\) | −39.1069 | + | 22.5784i | −1.49968 | + | 0.865841i | ||||
\(681\) | 6.38875 | − | 2.61619i | 0.244817 | − | 0.100252i | ||||
\(682\) | 9.70168i | 0.371496i | ||||||||
\(683\) | 6.35051i | 0.242995i | 0.992592 | + | 0.121498i | \(0.0387697\pi\) | ||||
−0.992592 | + | 0.121498i | \(0.961230\pi\) | |||||||
\(684\) | 34.7849 | − | 9.02065i | 1.33003 | − | 0.344913i | ||||
\(685\) | −18.0050 | + | 10.3952i | −0.687935 | + | 0.397180i | ||||
\(686\) | −17.8040 | + | 40.6606i | −0.679758 | + | 1.55243i | ||||
\(687\) | 1.60585 | − | 2.07540i | 0.0612669 | − | 0.0791816i | ||||
\(688\) | −2.07694 | − | 3.59737i | −0.0791828 | − | 0.137149i | ||||
\(689\) | −21.6304 | − | 5.50551i | −0.824053 | − | 0.209743i | ||||
\(690\) | −35.7344 | − | 27.6495i | −1.36039 | − | 1.05260i | ||||
\(691\) | − | 5.74331i | − | 0.218486i | −0.994015 | − | 0.109243i | \(-0.965157\pi\) | ||
0.994015 | − | 0.109243i | \(-0.0348427\pi\) | |||||||
\(692\) | −44.7558 | + | 77.5193i | −1.70136 | + | 2.94684i | ||||
\(693\) | 7.12253 | + | 9.57103i | 0.270562 | + | 0.363573i | ||||
\(694\) | 72.6265 | 2.75686 | ||||||||
\(695\) | −8.59352 | − | 4.96147i | −0.325971 | − | 0.188199i | ||||
\(696\) | −0.872665 | + | 6.42821i | −0.0330783 | + | 0.243661i | ||||
\(697\) | −24.4671 | + | 42.3782i | −0.926757 | + | 1.60519i | ||||
\(698\) | −26.0002 | + | 45.0337i | −0.984122 | + | 1.70455i | ||||
\(699\) | 7.18204 | − | 9.28211i | 0.271650 | − | 0.351082i | ||||
\(700\) | −0.575627 | − | 1.41635i | −0.0217567 | − | 0.0535329i | ||||
\(701\) | 14.7876i | 0.558520i | 0.960216 | + | 0.279260i | \(0.0900891\pi\) | ||||
−0.960216 | + | 0.279260i | \(0.909911\pi\) | |||||||
\(702\) | 44.5209 | + | 5.83990i | 1.68033 | + | 0.220413i | ||||
\(703\) | −27.8342 | − | 16.0701i | −1.04979 | − | 0.606095i | ||||
\(704\) | 13.7498 | − | 7.93846i | 0.518215 | − | 0.299192i | ||||
\(705\) | 0.169478 | − | 1.24841i | 0.00638291 | − | 0.0470177i | ||||
\(706\) | 32.7160 | − | 18.8886i | 1.23128 | − | 0.710882i | ||||
\(707\) | 45.8993 | + | 6.35464i | 1.72622 | + | 0.238991i | ||||
\(708\) | −83.1065 | + | 34.0320i | −3.12333 | + | 1.27900i | ||||
\(709\) | 24.3473 | − | 42.1707i | 0.914381 | − | 1.58375i | 0.106576 | − | 0.994305i | \(-0.466011\pi\) |
0.807805 | − | 0.589450i | \(-0.200655\pi\) | |||||||
\(710\) | 42.4523 | − | 73.5296i | 1.59321 | − | 2.75952i | ||||
\(711\) | −17.4936 | − | 4.83887i | −0.656060 | − | 0.181472i | ||||
\(712\) | 52.7964i | 1.97863i | ||||||||
\(713\) | −6.65784 | + | 11.5317i | −0.249338 | + | 0.431866i | ||||
\(714\) | 51.9075 | + | 14.5058i | 1.94259 | + | 0.542867i | ||||
\(715\) | 11.5612 | + | 2.94263i | 0.432365 | + | 0.110048i | ||||
\(716\) | 63.4476 | − | 36.6315i | 2.37115 | − | 1.36898i | ||||
\(717\) | 10.1366 | + | 24.7538i | 0.378560 | + | 0.924446i | ||||
\(718\) | 8.14751 | + | 14.1119i | 0.304062 | + | 0.526651i | ||||
\(719\) | 14.8764 | − | 25.7667i | 0.554796 | − | 0.960935i | −0.443123 | − | 0.896461i | \(-0.646130\pi\) |
0.997919 | − | 0.0644743i | \(-0.0205371\pi\) | |||||||
\(720\) | 16.1073 | + | 4.45541i | 0.600282 | + | 0.166043i | ||||
\(721\) | −1.15818 | + | 8.36549i | −0.0431330 | + | 0.311547i | ||||
\(722\) | 18.1928 | − | 10.5036i | 0.677068 | − | 0.390905i | ||||
\(723\) | 4.62025 | + | 11.2827i | 0.171829 | + | 0.419608i | ||||
\(724\) | − | 5.72206i | − | 0.212659i | ||||||
\(725\) | −0.119749 | + | 0.0691369i | −0.00444735 | + | 0.00256768i | ||||
\(726\) | −35.9548 | − | 4.88106i | −1.33441 | − | 0.181153i | ||||
\(727\) | − | 40.6361i | − | 1.50711i | −0.657385 | − | 0.753555i | \(-0.728337\pi\) | ||
0.657385 | − | 0.753555i | \(-0.271663\pi\) | |||||||
\(728\) | 36.9317 | + | 15.0433i | 1.36878 | + | 0.557542i | ||||
\(729\) | −18.6246 | − | 19.5480i | −0.689800 | − | 0.724000i | ||||
\(730\) | 17.4868 | 0.647217 | ||||||||
\(731\) | 4.02741 | + | 6.97568i | 0.148959 | + | 0.258005i | ||||
\(732\) | −18.1726 | − | 2.46703i | −0.671678 | − | 0.0911840i | ||||
\(733\) | −24.6541 | + | 14.2340i | −0.910619 | + | 0.525746i | −0.880630 | − | 0.473804i | \(-0.842880\pi\) |
−0.0299887 | + | 0.999550i | \(0.509547\pi\) | |||||||
\(734\) | −19.4718 | − | 33.7261i | −0.718716 | − | 1.24485i | ||||
\(735\) | 10.6404 | − | 24.4764i | 0.392479 | − | 0.902826i | ||||
\(736\) | 11.3497 | 0.418356 | ||||||||
\(737\) | 9.02683 | + | 5.21164i | 0.332508 | + | 0.191973i | ||||
\(738\) | 69.4035 | − | 17.9982i | 2.55478 | − | 0.662523i | ||||
\(739\) | −15.6689 | − | 27.1393i | −0.576389 | − | 0.998335i | −0.995889 | − | 0.0905800i | \(-0.971128\pi\) |
0.419500 | − | 0.907755i | \(-0.362205\pi\) | |||||||
\(740\) | −41.4011 | − | 71.7088i | −1.52193 | − | 2.63607i | ||||
\(741\) | −19.7852 | + | 2.77674i | −0.726826 | + | 0.102006i | ||||
\(742\) | 14.7796 | + | 36.3657i | 0.542577 | + | 1.33503i | ||||
\(743\) | 11.8552 | + | 6.84459i | 0.434924 | + | 0.251104i | 0.701442 | − | 0.712726i | \(-0.252540\pi\) |
−0.266518 | + | 0.963830i | \(0.585873\pi\) | |||||||
\(744\) | 2.62308 | − | 19.3221i | 0.0961667 | − | 0.708382i | ||||
\(745\) | − | 41.4741i | − | 1.51949i | ||||||
\(746\) | 27.7158 | + | 16.0017i | 1.01475 | + | 0.585865i | ||||
\(747\) | 5.86570 | − | 5.77188i | 0.214615 | − | 0.211182i | ||||
\(748\) | 23.9171 | − | 13.8086i | 0.874497 | − | 0.504891i | ||||
\(749\) | 4.29933 | + | 3.34481i | 0.157094 | + | 0.122217i | ||||
\(750\) | 17.8490 | + | 43.5874i | 0.651753 | + | 1.59159i | ||||
\(751\) | 38.3433 | 1.39917 | 0.699583 | − | 0.714551i | \(-0.253369\pi\) | ||||
0.699583 | + | 0.714551i | \(0.253369\pi\) | |||||||
\(752\) | −0.418107 | − | 0.724182i | −0.0152468 | − | 0.0264082i | ||||
\(753\) | −4.63794 | − | 3.58861i | −0.169016 | − | 0.130776i | ||||
\(754\) | 1.90973 | − | 7.50307i | 0.0695482 | − | 0.273246i | ||||
\(755\) | −18.1412 | −0.660225 | ||||||||
\(756\) | −24.8961 | − | 45.0532i | −0.905463 | − | 1.63857i | ||||
\(757\) | −3.23204 | + | 5.59806i | −0.117471 | + | 0.203465i | −0.918765 | − | 0.394806i | \(-0.870812\pi\) |
0.801294 | + | 0.598271i | \(0.204145\pi\) | |||||||
\(758\) | −49.5807 | − | 28.6254i | −1.80085 | − | 1.03972i | ||||
\(759\) | 10.1808 | + | 7.87738i | 0.369538 | + | 0.285931i | ||||
\(760\) | −29.4396 | −1.06789 | ||||||||
\(761\) | −6.91097 | + | 11.9702i | −0.250523 | + | 0.433918i | −0.963670 | − | 0.267096i | \(-0.913936\pi\) |
0.713147 | + | 0.701014i | \(0.247269\pi\) | |||||||
\(762\) | −72.7499 | − | 9.87620i | −2.63545 | − | 0.357777i | ||||
\(763\) | 5.06367 | + | 12.4593i | 0.183317 | + | 0.451057i | ||||
\(764\) | −20.0199 | − | 11.5585i | −0.724293 | − | 0.418171i | ||||
\(765\) | −31.2336 | − | 8.63949i | −1.12925 | − | 0.312362i | ||||
\(766\) | 3.31629 | + | 1.91466i | 0.119822 | + | 0.0691795i | ||||
\(767\) | 48.0612 | − | 13.5274i | 1.73539 | − | 0.488448i | ||||
\(768\) | −45.7560 | + | 18.7370i | −1.65108 | + | 0.676114i | ||||
\(769\) | 1.89305 | + | 1.09295i | 0.0682650 | + | 0.0394128i | 0.533744 | − | 0.845646i | \(-0.320785\pi\) |
−0.465479 | + | 0.885059i | \(0.654118\pi\) | |||||||
\(770\) | −7.89955 | − | 19.4371i | −0.284680 | − | 0.700463i | ||||
\(771\) | 33.0507 | − | 13.5342i | 1.19029 | − | 0.487423i | ||||
\(772\) | 19.5767 | + | 33.9078i | 0.704579 | + | 1.22037i | ||||
\(773\) | −8.34018 | −0.299975 | −0.149988 | − | 0.988688i | \(-0.547923\pi\) | ||||
−0.149988 | + | 0.988688i | \(0.547923\pi\) | |||||||
\(774\) | 3.14641 | − | 11.3749i | 0.113095 | − | 0.408863i | ||||
\(775\) | 0.359943 | − | 0.207813i | 0.0129295 | − | 0.00746487i | ||||
\(776\) | 27.9222 | + | 48.3626i | 1.00235 | + | 1.73612i | ||||
\(777\) | −12.3908 | + | 44.3391i | −0.444517 | + | 1.59066i | ||||
\(778\) | −26.8424 | + | 46.4923i | −0.962345 | + | 1.66683i | ||||
\(779\) | −27.6281 | + | 15.9511i | −0.989881 | + | 0.571508i | ||||
\(780\) | −47.7200 | − | 19.2908i | −1.70865 | − | 0.690722i | ||||
\(781\) | −12.0947 | + | 20.9486i | −0.432783 | + | 0.749602i | ||||
\(782\) | 58.1521 | 2.07951 | ||||||||
\(783\) | −3.72744 | + | 2.78921i | −0.133208 | + | 0.0996782i | ||||
\(784\) | −4.35609 | − | 17.1706i | −0.155575 | − | 0.613237i | ||||
\(785\) | 30.6929i | 1.09548i | ||||||||
\(786\) | 31.6122 | − | 40.8558i | 1.12757 | − | 1.45728i | ||||
\(787\) | − | 5.94642i | − | 0.211967i | −0.994368 | − | 0.105983i | \(-0.966201\pi\) | ||
0.994368 | − | 0.105983i | \(-0.0337991\pi\) | |||||||
\(788\) | −14.9977 | − | 8.65890i | −0.534270 | − | 0.308461i | ||||
\(789\) | −5.88208 | + | 7.60203i | −0.209408 | + | 0.270640i | ||||
\(790\) | 27.6432 | + | 15.9598i | 0.983502 | + | 0.567825i | ||||
\(791\) | 1.55951 | − | 11.2643i | 0.0554498 | − | 0.400511i | ||||
\(792\) | −18.1681 | − | 5.02545i | −0.645575 | − | 0.178572i | ||||
\(793\) | 9.88105 | + | 2.51499i | 0.350886 | + | 0.0893099i | ||||
\(794\) | −24.4774 | + | 42.3962i | −0.868672 | + | 1.50458i | ||||
\(795\) | −8.94438 | − | 21.8423i | −0.317224 | − | 0.774665i | ||||
\(796\) | 32.8207i | 1.16330i | ||||||||
\(797\) | 12.4919 | + | 21.6366i | 0.442486 | + | 0.766409i | 0.997873 | − | 0.0651832i | \(-0.0207632\pi\) |
−0.555387 | + | 0.831592i | \(0.687430\pi\) | |||||||
\(798\) | 24.5784 | + | 25.1103i | 0.870065 | + | 0.888894i | ||||
\(799\) | 0.810752 | + | 1.40426i | 0.0286823 | + | 0.0496793i | ||||
\(800\) | −0.306800 | − | 0.177131i | −0.0108470 | − | 0.00626254i | ||||
\(801\) | −27.0067 | + | 26.5747i | −0.954235 | + | 0.938972i | ||||
\(802\) | −77.9648 | −2.75303 | ||||||||
\(803\) | −4.98202 | −0.175812 | ||||||||
\(804\) | −35.5678 | − | 27.5206i | −1.25438 | − | 0.970578i | ||||
\(805\) | 3.94916 | − | 28.5246i | 0.139190 | − | 1.00536i | ||||
\(806\) | −5.74031 | + | 22.5529i | −0.202194 | + | 0.794392i | ||||
\(807\) | 14.6946 | − | 6.01743i | 0.517275 | − | 0.211823i | ||||
\(808\) | −63.4048 | + | 36.6068i | −2.23057 | + | 1.28782i | ||||
\(809\) | −19.3679 | + | 11.1821i | −0.680939 | + | 0.393140i | −0.800209 | − | 0.599722i | \(-0.795278\pi\) |
0.119270 | + | 0.992862i | \(0.461945\pi\) | |||||||
\(810\) | 23.0752 | + | 41.4986i | 0.810780 | + | 1.45811i | ||||
\(811\) | 27.6233i | 0.969986i | 0.874518 | + | 0.484993i | \(0.161178\pi\) | ||||
−0.874518 | + | 0.484993i | \(0.838822\pi\) | |||||||
\(812\) | −8.22235 | + | 3.34170i | −0.288548 | + | 0.117271i | ||||
\(813\) | −4.47935 | − | 10.9386i | −0.157098 | − | 0.383634i | ||||
\(814\) | 18.0957 | + | 31.3427i | 0.634255 | + | 1.09856i | ||||
\(815\) | −24.7268 | −0.866141 | ||||||||
\(816\) | −19.9051 | + | 8.15110i | −0.696817 | + | 0.285346i | ||||
\(817\) | 5.25127i | 0.183719i | ||||||||
\(818\) | 63.3370 | 2.21453 | ||||||||
\(819\) | 10.8943 | + | 26.4635i | 0.380678 | + | 0.924708i | ||||
\(820\) | −82.1892 | −2.87017 | ||||||||
\(821\) | − | 13.4264i | − | 0.468586i | −0.972166 | − | 0.234293i | \(-0.924723\pi\) | ||
0.972166 | − | 0.234293i | \(-0.0752775\pi\) | |||||||
\(822\) | −36.2825 | + | 14.8577i | −1.26550 | + | 0.518220i | ||||
\(823\) | 6.11903 | 0.213296 | 0.106648 | − | 0.994297i | \(-0.465988\pi\) | ||||
0.106648 | + | 0.994297i | \(0.465988\pi\) | |||||||
\(824\) | −6.67187 | − | 11.5560i | −0.232426 | − | 0.402573i | ||||
\(825\) | −0.152262 | − | 0.371826i | −0.00530109 | − | 0.0129453i | ||||
\(826\) | −69.3058 | − | 53.9189i | −2.41146 | − | 1.87608i | ||||
\(827\) | − | 32.0820i | − | 1.11560i | −0.829975 | − | 0.557801i | \(-0.811645\pi\) | ||
0.829975 | − | 0.557801i | \(-0.188355\pi\) | |||||||
\(828\) | −38.9541 | − | 39.5873i | −1.35375 | − | 1.37575i | ||||
\(829\) | −33.3697 | + | 19.2660i | −1.15898 | + | 0.669136i | −0.951059 | − | 0.309010i | \(-0.900002\pi\) |
−0.207919 | + | 0.978146i | \(0.566669\pi\) | |||||||
\(830\) | −12.5332 | + | 7.23606i | −0.435035 | + | 0.251167i | ||||
\(831\) | −4.75589 | + | 1.94753i | −0.164980 | + | 0.0675592i | ||||
\(832\) | 36.6604 | − | 10.3185i | 1.27097 | − | 0.357731i | ||||
\(833\) | 8.44691 | + | 33.2956i | 0.292668 | + | 1.15363i | ||||
\(834\) | −14.7998 | − | 11.4514i | −0.512476 | − | 0.396529i | ||||
\(835\) | −12.3554 | −0.427575 | ||||||||
\(836\) | 18.0048 | 0.622708 | ||||||||
\(837\) | 11.2040 | − | 8.38387i | 0.387268 | − | 0.289789i | ||||
\(838\) | −29.9996 | − | 17.3203i | −1.03632 | − | 0.598319i | ||||
\(839\) | −20.9048 | − | 36.2081i | −0.721713 | − | 1.25004i | −0.960313 | − | 0.278926i | \(-0.910022\pi\) |
0.238599 | − | 0.971118i | \(-0.423312\pi\) | |||||||
\(840\) | 10.4776 | + | 40.8471i | 0.361513 | + | 1.40936i | ||||
\(841\) | −14.0986 | − | 24.4196i | −0.486160 | − | 0.842054i | ||||
\(842\) | − | 71.0807i | − | 2.44960i | ||||||
\(843\) | 17.0455 | + | 41.6252i | 0.587078 | + | 1.43365i | ||||
\(844\) | −1.85078 | + | 3.20565i | −0.0637065 | + | 0.110343i | ||||
\(845\) | 25.1345 | + | 13.6811i | 0.864654 | + | 0.470645i | ||||
\(846\) | 0.633398 | − | 2.28987i | 0.0217767 | − | 0.0787273i | ||||
\(847\) | −8.70707 | − | 21.4240i | −0.299178 | − | 0.736137i | ||||
\(848\) | −13.5671 | − | 7.83297i | −0.465896 | − | 0.268985i | ||||
\(849\) | −11.5487 | + | 14.9256i | −0.396351 | + | 0.512246i | ||||
\(850\) | −1.57194 | − | 0.907560i | −0.0539171 | − | 0.0311291i | ||||
\(851\) | 49.6732i | 1.70278i | ||||||||
\(852\) | 63.8674 | − | 82.5425i | 2.18806 | − | 2.82786i | ||||
\(853\) | 22.5503i | 0.772109i | 0.922476 | + | 0.386054i | \(0.126162\pi\) | ||||
−0.922476 | + | 0.386054i | \(0.873838\pi\) | |||||||
\(854\) | −6.75153 | − | 16.6123i | −0.231033 | − | 0.568462i | ||||
\(855\) | −14.8182 | − | 15.0591i | −0.506772 | − | 0.515010i | ||||
\(856\) | −8.60669 | −0.294171 | ||||||||
\(857\) | −7.35349 | + | 12.7366i | −0.251191 | + | 0.435075i | −0.963854 | − | 0.266431i | \(-0.914155\pi\) |
0.712663 | + | 0.701506i | \(0.247489\pi\) | |||||||
\(858\) | 20.8576 | + | 8.43169i | 0.712067 | + | 0.287853i | ||||
\(859\) | −13.1023 | + | 7.56462i | −0.447045 | + | 0.258101i | −0.706581 | − | 0.707632i | \(-0.749764\pi\) |
0.259537 | + | 0.965733i | \(0.416430\pi\) | |||||||
\(860\) | −6.76439 | + | 11.7163i | −0.230664 | + | 0.399521i | ||||
\(861\) | 31.9650 | + | 32.6567i | 1.08936 | + | 1.11294i | ||||
\(862\) | −14.4457 | − | 25.0207i | −0.492023 | − | 0.852208i | ||||
\(863\) | 29.5253 | − | 17.0464i | 1.00505 | − | 0.580267i | 0.0953128 | − | 0.995447i | \(-0.469615\pi\) |
0.909739 | + | 0.415180i | \(0.136282\pi\) | |||||||
\(864\) | −10.9636 | − | 4.69739i | −0.372989 | − | 0.159808i | ||||
\(865\) | 52.6256 | 1.78932 | ||||||||
\(866\) | −32.4999 | − | 56.2916i | −1.10439 | − | 1.91287i | ||||
\(867\) | 11.3493 | − | 4.64752i | 0.385442 | − | 0.157838i | ||||
\(868\) | 24.7149 | − | 10.0446i | 0.838880 | − | 0.340935i | ||||
\(869\) | −7.87558 | − | 4.54697i | −0.267161 | − | 0.154245i | ||||
\(870\) | 7.57655 | − | 3.10259i | 0.256869 | − | 0.105188i | ||||
\(871\) | 17.9005 | + | 17.4562i | 0.606535 | + | 0.591481i | ||||
\(872\) | −18.4028 | − | 10.6248i | −0.623197 | − | 0.359803i | ||||
\(873\) | −10.6843 | + | 38.6259i | −0.361608 | + | 1.30729i | ||||
\(874\) | 32.8326 | + | 18.9559i | 1.11058 | + | 0.641192i | ||||
\(875\) | −18.4330 | + | 23.6933i | −0.623150 | + | 0.800980i | ||||
\(876\) | 21.2997 | + | 2.89156i | 0.719651 | + | 0.0976966i | ||||
\(877\) | −19.5195 | + | 33.8088i | −0.659128 | + | 1.14164i | 0.321714 | + | 0.946837i | \(0.395741\pi\) |
−0.980842 | + | 0.194806i | \(0.937592\pi\) | |||||||
\(878\) | −10.0806 | −0.340205 | ||||||||
\(879\) | 15.6277 | + | 12.0919i | 0.527108 | + | 0.407850i | ||||
\(880\) | 7.25147 | + | 4.18664i | 0.244447 | + | 0.141131i | ||||
\(881\) | 12.3427 | − | 21.3781i | 0.415835 | − | 0.720248i | −0.579680 | − | 0.814844i | \(-0.696823\pi\) |
0.995516 | + | 0.0945959i | \(0.0301559\pi\) | |||||||
\(882\) | 26.0927 | − | 43.0391i | 0.878588 | − | 1.44920i | ||||
\(883\) | 17.3258 | 0.583059 | 0.291529 | − | 0.956562i | \(-0.405836\pi\) | ||||
0.291529 | + | 0.956562i | \(0.405836\pi\) | |||||||
\(884\) | 63.7690 | − | 17.9486i | 2.14478 | − | 0.603677i | ||||
\(885\) | 41.7574 | + | 32.3099i | 1.40366 | + | 1.08608i | ||||
\(886\) | 15.1185 | + | 26.1860i | 0.507915 | + | 0.879735i | ||||
\(887\) | −20.6414 | −0.693070 | −0.346535 | − | 0.938037i | \(-0.612642\pi\) | ||||
−0.346535 | + | 0.938037i | \(0.612642\pi\) | |||||||
\(888\) | −27.5656 | − | 67.3154i | −0.925041 | − | 2.25896i | ||||
\(889\) | −17.6176 | − | 43.3487i | −0.590876 | − | 1.45387i | ||||
\(890\) | 57.7052 | − | 33.3161i | 1.93428 | − | 1.11676i | ||||
\(891\) | −6.57414 | − | 11.8230i | −0.220242 | − | 0.396084i | ||||
\(892\) | 68.9017 | + | 39.7804i | 2.30700 | + | 1.33195i | ||||
\(893\) | 1.05713i | 0.0353754i | ||||||||
\(894\) | 10.5212 | − | 77.5015i | 0.351883 | − | 2.59204i | ||||
\(895\) | −37.3021 | − | 21.5364i | −1.24687 | − | 0.719881i | ||||
\(896\) | −43.2786 | − | 33.6701i | −1.44584 | − | 1.12484i | ||||
\(897\) | 19.0057 | + | 24.3358i | 0.634582 | + | 0.812550i | ||||
\(898\) | 7.17490 | + | 12.4273i | 0.239429 | + | 0.414704i | ||||
\(899\) | −1.20642 | − | 2.08959i | −0.0402364 | − | 0.0696916i | ||||
\(900\) | 0.435163 | + | 1.67805i | 0.0145054 | + | 0.0559349i | ||||
\(901\) | 26.3080 | + | 15.1889i | 0.876447 | + | 0.506017i | ||||
\(902\) | 35.9235 | 1.19612 | ||||||||
\(903\) | 7.28609 | − | 1.86895i | 0.242466 | − | 0.0621946i | ||||
\(904\) | 8.98378 | + | 15.5604i | 0.298796 | + | 0.517530i | ||||
\(905\) | −2.91340 | + | 1.68205i | −0.0968447 | + | 0.0559133i | ||||
\(906\) | −33.8999 | − | 4.60210i | −1.12625 | − | 0.152894i | ||||
\(907\) | −21.6610 | − | 37.5179i | −0.719242 | − | 1.24576i | −0.961301 | − | 0.275501i | \(-0.911156\pi\) |
0.242059 | − | 0.970262i | \(-0.422177\pi\) | |||||||
\(908\) | −14.9238 | −0.495263 | ||||||||
\(909\) | −50.6397 | − | 14.0074i | −1.67961 | − | 0.464596i | ||||
\(910\) | −6.86303 | − | 49.8582i | −0.227507 | − | 1.65278i | ||||
\(911\) | − | 13.2577i | − | 0.439246i | −0.975585 | − | 0.219623i | \(-0.929517\pi\) | ||
0.975585 | − | 0.219623i | \(-0.0704827\pi\) | |||||||
\(912\) | −13.8954 | − | 1.88638i | −0.460122 | − | 0.0624641i | ||||
\(913\) | 3.57073 | − | 2.06156i | 0.118174 | − | 0.0682277i | ||||
\(914\) | 90.5206i | 2.99416i | ||||||||
\(915\) | 4.08591 | + | 9.97783i | 0.135076 | + | 0.329857i | ||||
\(916\) | −4.91263 | + | 2.83631i | −0.162318 | + | 0.0937143i | ||||
\(917\) | 32.6127 | + | 4.51515i | 1.07697 | + | 0.149103i | ||||
\(918\) | −56.1737 | − | 24.0678i | −1.85401 | − | 0.794356i | ||||
\(919\) | 5.47411 | − | 9.48144i | 0.180574 | − | 0.312764i | −0.761502 | − | 0.648163i | \(-0.775538\pi\) |
0.942076 | + | 0.335399i | \(0.108871\pi\) | |||||||
\(920\) | 22.7497 | + | 39.4036i | 0.750035 | + | 1.29910i | ||||
\(921\) | −0.762431 | − | 1.86186i | −0.0251230 | − | 0.0613505i | ||||
\(922\) | −32.6616 | + | 18.8572i | −1.07565 | + | 0.621028i | ||||
\(923\) | −40.5108 | + | 41.5418i | −1.33343 | + | 1.36737i | ||||
\(924\) | −6.40796 | − | 24.9814i | −0.210806 | − | 0.821829i | ||||
\(925\) | 0.775233 | − | 1.34274i | 0.0254895 | − | 0.0441491i | ||||
\(926\) | − | 57.3203i | − | 1.88366i | ||||||
\(927\) | 2.55295 | − | 9.22948i | 0.0838500 | − | 0.303136i | ||||
\(928\) | −1.02830 | + | 1.78107i | −0.0337557 | + | 0.0584666i | ||||
\(929\) | −8.02130 | + | 13.8933i | −0.263170 | + | 0.455824i | −0.967083 | − | 0.254463i | \(-0.918101\pi\) |
0.703912 | + | 0.710287i | \(0.251435\pi\) | |||||||
\(930\) | −22.7738 | + | 9.32584i | −0.746782 | + | 0.305806i | ||||
\(931\) | −6.08430 | + | 21.5521i | −0.199405 | + | 0.706342i | ||||
\(932\) | −21.9714 | + | 12.6852i | −0.719698 | + | 0.415518i | ||||
\(933\) | 1.62643 | − | 11.9806i | 0.0532469 | − | 0.392227i | ||||
\(934\) | −47.3740 | + | 27.3514i | −1.55012 | + | 0.894964i | ||||
\(935\) | −14.0613 | − | 8.11832i | −0.459855 | − | 0.265497i | ||||
\(936\) | −39.2608 | − | 22.4321i | −1.28328 | − | 0.733216i | ||||
\(937\) | 22.6768i | 0.740820i | 0.928868 | + | 0.370410i | \(0.120783\pi\) | ||||
−0.928868 | + | 0.370410i | \(0.879217\pi\) | |||||||
\(938\) | 6.03040 | − | 43.5572i | 0.196899 | − | 1.42219i | ||||
\(939\) | 20.9640 | − | 27.0940i | 0.684136 | − | 0.884181i | ||||
\(940\) | −1.36173 | + | 2.35858i | −0.0444147 | + | 0.0769285i | ||||
\(941\) | 8.19499 | − | 14.1941i | 0.267149 | − | 0.462716i | −0.700975 | − | 0.713185i | \(-0.747252\pi\) |
0.968124 | + | 0.250470i | \(0.0805851\pi\) | |||||||
\(942\) | −7.78625 | + | 57.3549i | −0.253690 | + | 1.86872i | ||||
\(943\) | 42.6998 | + | 24.6527i | 1.39050 | + | 0.802803i | ||||
\(944\) | 35.0438 | 1.14058 | ||||||||
\(945\) | −15.6205 | + | 25.9197i | −0.508135 | + | 0.843168i | ||||
\(946\) | 2.95660 | − | 5.12098i | 0.0961273 | − | 0.166497i | ||||
\(947\) | 16.4860i | 0.535723i | 0.963457 | + | 0.267861i | \(0.0863169\pi\) | ||||
−0.963457 | + | 0.267861i | \(0.913683\pi\) | |||||||
\(948\) | 31.0316 | + | 24.0108i | 1.00786 | + | 0.779833i | ||||
\(949\) | −11.5814 | − | 2.94777i | −0.375948 | − | 0.0956886i | ||||
\(950\) | −0.591676 | − | 1.02481i | −0.0191965 | − | 0.0332493i | ||||
\(951\) | 7.80692 | − | 10.0897i | 0.253157 | − | 0.327181i | ||||
\(952\) | −42.8373 | − | 33.3268i | −1.38837 | − | 1.08013i | ||||
\(953\) | 2.87033 | − | 1.65718i | 0.0929790 | − | 0.0536815i | −0.452790 | − | 0.891617i | \(-0.649571\pi\) |
0.545769 | + | 0.837936i | \(0.316238\pi\) | |||||||
\(954\) | −11.1731 | − | 43.0851i | −0.361743 | − | 1.39493i | ||||
\(955\) | 13.5909i | 0.439791i | ||||||||
\(956\) | − | 57.8234i | − | 1.87014i | ||||||
\(957\) | −2.15857 | + | 0.883930i | −0.0697765 | + | 0.0285734i | ||||
\(958\) | 4.96436 | − | 2.86617i | 0.160391 | − | 0.0926018i | ||||
\(959\) | −19.7225 | − | 15.3438i | −0.636873 | − | 0.495477i | ||||
\(960\) | 31.8519 | + | 24.6455i | 1.02802 | + | 0.795429i | ||||
\(961\) | −11.8737 | − | 20.5659i | −0.383023 | − | 0.663415i | ||||
\(962\) | 23.5211 | + | 83.5674i | 0.758351 | + | 2.69432i | ||||
\(963\) | −4.33212 | − | 4.40254i | −0.139601 | − | 0.141870i | ||||
\(964\) | − | 26.3557i | − | 0.848861i | ||||||
\(965\) | 11.5095 | − | 19.9350i | 0.370503 | − | 0.641731i | ||||
\(966\) | 14.6159 | − | 52.3013i | 0.470259 | − | 1.68277i | ||||
\(967\) | 18.2322 | 0.586308 | 0.293154 | − | 0.956065i | \(-0.405295\pi\) | ||||
0.293154 | + | 0.956065i | \(0.405295\pi\) | |||||||
\(968\) | 31.6439 | + | 18.2696i | 1.01707 | + | 0.587207i | ||||
\(969\) | 26.9446 | + | 3.65788i | 0.865585 | + | 0.117508i | ||||
\(970\) | 35.2394 | − | 61.0365i | 1.13147 | − | 1.95976i | ||||
\(971\) | −6.65694 | + | 11.5302i | −0.213631 | + | 0.370020i | −0.952848 | − | 0.303447i | \(-0.901862\pi\) |
0.739217 | + | 0.673467i | \(0.235196\pi\) | |||||||
\(972\) | 21.2446 | + | 54.3627i | 0.681420 | + | 1.74368i | ||||
\(973\) | 1.63559 | − | 11.8138i | 0.0524347 | − | 0.378733i | ||||
\(974\) | 96.0803i | 3.07861i | ||||||||
\(975\) | −0.133952 | − | 0.954451i | −0.00428990 | − | 0.0305669i | ||||
\(976\) | 6.19763 | + | 3.57820i | 0.198381 | + | 0.114536i | ||||
\(977\) | 27.7242 | − | 16.0066i | 0.886977 | − | 0.512096i | 0.0140243 | − | 0.999902i | \(-0.495536\pi\) |
0.872952 | + | 0.487805i | \(0.162202\pi\) | |||||||
\(978\) | −46.2062 | − | 6.27275i | −1.47751 | − | 0.200580i | ||||
\(979\) | −16.4402 | + | 9.49178i | −0.525433 | + | 0.303359i | ||||
\(980\) | −41.3370 | + | 40.2481i | −1.32046 | + | 1.28568i | ||||
\(981\) | −3.82804 | − | 14.7614i | −0.122220 | − | 0.471296i | ||||
\(982\) | −4.67426 | + | 8.09605i | −0.149162 | + | 0.258355i | ||||
\(983\) | 6.83560 | − | 11.8396i | 0.218022 | − | 0.377625i | −0.736181 | − | 0.676784i | \(-0.763373\pi\) |
0.954203 | + | 0.299159i | \(0.0967062\pi\) | |||||||
\(984\) | −71.5461 | − | 9.71277i | −2.28081 | − | 0.309632i | ||||
\(985\) | 10.1815i | 0.324408i | ||||||||
\(986\) | −5.26868 | + | 9.12562i | −0.167789 | + | 0.290619i | ||||
\(987\) | 1.46675 | − | 0.376235i | 0.0466872 | − | 0.0119757i | ||||
\(988\) | 41.8546 | + | 10.6531i | 1.33157 | + | 0.338920i | ||||
\(989\) | 7.02861 | − | 4.05797i | 0.223497 | − | 0.129036i | ||||
\(990\) | 5.97190 | + | 23.0285i | 0.189800 | + | 0.731893i | ||||
\(991\) | 7.32083 | + | 12.6801i | 0.232554 | + | 0.402795i | 0.958559 | − | 0.284894i | \(-0.0919585\pi\) |
−0.726005 | + | 0.687689i | \(0.758625\pi\) | |||||||
\(992\) | 3.09090 | − | 5.35360i | 0.0981362 | − | 0.169977i | ||||
\(993\) | −0.537171 | + | 3.95690i | −0.0170466 | + | 0.125568i | ||||
\(994\) | 101.084 | + | 13.9948i | 3.20618 | + | 0.443888i | ||||
\(995\) | 16.7107 | − | 9.64795i | 0.529766 | − | 0.305861i | ||||
\(996\) | −16.4626 | + | 6.74140i | −0.521636 | + | 0.213609i | ||||
\(997\) | 46.0995i | 1.45999i | 0.683454 | + | 0.729994i | \(0.260477\pi\) | ||||
−0.683454 | + | 0.729994i | \(0.739523\pi\) | |||||||
\(998\) | −67.6677 | + | 39.0679i | −2.14198 | + | 1.23667i | ||||
\(999\) | 20.5586 | − | 47.9833i | 0.650445 | − | 1.51812i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 273.2.r.b.269.30 | yes | 64 | |
3.2 | odd | 2 | inner | 273.2.r.b.269.3 | yes | 64 | |
7.5 | odd | 6 | 273.2.bf.b.152.30 | yes | 64 | ||
13.3 | even | 3 | 273.2.bf.b.185.3 | yes | 64 | ||
21.5 | even | 6 | 273.2.bf.b.152.3 | yes | 64 | ||
39.29 | odd | 6 | 273.2.bf.b.185.30 | yes | 64 | ||
91.68 | odd | 6 | inner | 273.2.r.b.68.30 | yes | 64 | |
273.68 | even | 6 | inner | 273.2.r.b.68.3 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.r.b.68.3 | ✓ | 64 | 273.68 | even | 6 | inner | |
273.2.r.b.68.30 | yes | 64 | 91.68 | odd | 6 | inner | |
273.2.r.b.269.3 | yes | 64 | 3.2 | odd | 2 | inner | |
273.2.r.b.269.30 | yes | 64 | 1.1 | even | 1 | trivial | |
273.2.bf.b.152.3 | yes | 64 | 21.5 | even | 6 | ||
273.2.bf.b.152.30 | yes | 64 | 7.5 | odd | 6 | ||
273.2.bf.b.185.3 | yes | 64 | 13.3 | even | 3 | ||
273.2.bf.b.185.30 | yes | 64 | 39.29 | odd | 6 |