Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(218,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 15, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.ct (of order \(20\), degree \(8\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 368.16 | ||
Character | \(\chi\) | \(=\) | 825.368 |
Dual form | 825.2.ct.b.482.16 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.700887 | − | 1.37557i | 0.495602 | − | 0.972673i | −0.498771 | − | 0.866734i | \(-0.666215\pi\) |
0.994373 | − | 0.105939i | \(-0.0337849\pi\) | |||||||
\(3\) | −1.55912 | − | 0.754410i | −0.900160 | − | 0.435559i | ||||
\(4\) | −0.225374 | − | 0.310201i | −0.112687 | − | 0.155100i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.13051 | + | 1.61592i | −0.869777 | + | 0.659698i | ||||
\(7\) | 0.579429 | − | 3.65837i | 0.219003 | − | 1.38273i | −0.595864 | − | 0.803086i | \(-0.703190\pi\) |
0.814867 | − | 0.579648i | \(-0.196810\pi\) | |||||||
\(8\) | 2.46499 | − | 0.390417i | 0.871507 | − | 0.138033i | ||||
\(9\) | 1.86173 | + | 2.35244i | 0.620577 | + | 0.784145i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.05625 | + | 1.28815i | 0.921495 | + | 0.388391i | ||||
\(12\) | 0.117367 | + | 0.653665i | 0.0338811 | + | 0.188697i | ||||
\(13\) | −0.753699 | + | 1.47922i | −0.209038 | + | 0.410261i | −0.971591 | − | 0.236665i | \(-0.923946\pi\) |
0.762553 | + | 0.646926i | \(0.223946\pi\) | |||||||
\(14\) | −4.62622 | − | 3.36115i | −1.23641 | − | 0.898304i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.42761 | − | 4.39373i | 0.356902 | − | 1.09843i | ||||
\(17\) | 3.24281 | − | 1.65230i | 0.786497 | − | 0.400740i | −0.0141322 | − | 0.999900i | \(-0.504499\pi\) |
0.800630 | + | 0.599160i | \(0.204499\pi\) | |||||||
\(18\) | 4.54080 | − | 0.912148i | 1.07028 | − | 0.214995i | ||||
\(19\) | 2.51454 | − | 3.46096i | 0.576874 | − | 0.793999i | −0.416474 | − | 0.909147i | \(-0.636734\pi\) |
0.993348 | + | 0.115149i | \(0.0367344\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.66331 | + | 5.26672i | −0.799400 | + | 1.14929i | ||||
\(22\) | 3.91402 | − | 3.30124i | 0.834472 | − | 0.703826i | ||||
\(23\) | −4.68474 | + | 4.68474i | −0.976836 | + | 0.976836i | −0.999738 | − | 0.0229014i | \(-0.992710\pi\) |
0.0229014 | + | 0.999738i | \(0.492710\pi\) | |||||||
\(24\) | −4.13776 | − | 1.25091i | −0.844617 | − | 0.255340i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.50651 | + | 2.07353i | 0.295450 | + | 0.406652i | ||||
\(27\) | −1.12797 | − | 5.07225i | −0.217078 | − | 0.976154i | ||||
\(28\) | −1.26542 | + | 0.644762i | −0.239141 | + | 0.121849i | ||||
\(29\) | 1.41424 | − | 1.02750i | 0.262617 | − | 0.190802i | −0.448683 | − | 0.893691i | \(-0.648107\pi\) |
0.711300 | + | 0.702889i | \(0.248107\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.90176 | − | 8.93069i | −0.521171 | − | 1.60400i | −0.771765 | − | 0.635908i | \(-0.780626\pi\) |
0.250594 | − | 0.968092i | \(-0.419374\pi\) | |||||||
\(32\) | −1.51380 | − | 1.51380i | −0.267604 | − | 0.267604i | ||||
\(33\) | −3.79328 | − | 4.31405i | −0.660326 | − | 0.750979i | ||||
\(34\) | − | 5.61878i | − | 0.963613i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.310141 | − | 1.10769i | 0.0516902 | − | 0.184615i | ||||
\(37\) | −1.03578 | + | 6.53964i | −0.170281 | + | 1.07511i | 0.743450 | + | 0.668791i | \(0.233188\pi\) |
−0.913731 | + | 0.406319i | \(0.866812\pi\) | |||||||
\(38\) | −2.99838 | − | 5.88466i | −0.486402 | − | 0.954617i | ||||
\(39\) | 2.29105 | − | 1.73769i | 0.366861 | − | 0.278252i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.253449 | − | 0.348843i | 0.0395821 | − | 0.0544801i | −0.788767 | − | 0.614692i | \(-0.789280\pi\) |
0.828349 | + | 0.560212i | \(0.189280\pi\) | |||||||
\(42\) | 4.67717 | + | 8.73051i | 0.721703 | + | 1.34715i | ||||
\(43\) | −4.37451 | − | 4.37451i | −0.667107 | − | 0.667107i | 0.289938 | − | 0.957045i | \(-0.406365\pi\) |
−0.957045 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(44\) | −0.289215 | − | 1.23837i | −0.0436008 | − | 0.186691i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.16071 | + | 9.72765i | 0.466021 | + | 1.43426i | ||||
\(47\) | −0.728778 | − | 4.60133i | −0.106303 | − | 0.671172i | −0.982081 | − | 0.188458i | \(-0.939651\pi\) |
0.875778 | − | 0.482714i | \(-0.160349\pi\) | |||||||
\(48\) | −5.54049 | + | 5.77336i | −0.799701 | + | 0.833313i | ||||
\(49\) | −6.39053 | − | 2.07641i | −0.912933 | − | 0.296630i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.30245 | + | 0.129724i | −0.882520 | + | 0.0181649i | ||||
\(52\) | 0.628718 | − | 0.0995792i | 0.0871875 | − | 0.0138091i | ||||
\(53\) | −4.21809 | − | 2.14922i | −0.579399 | − | 0.295219i | 0.139624 | − | 0.990205i | \(-0.455411\pi\) |
−0.719023 | + | 0.694986i | \(0.755411\pi\) | |||||||
\(54\) | −7.76780 | − | 2.00347i | −1.05706 | − | 0.272638i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 9.24407i | − | 1.23529i | ||||||
\(57\) | −6.53145 | + | 3.49908i | −0.865112 | + | 0.463464i | ||||
\(58\) | −0.422180 | − | 2.66554i | −0.0554350 | − | 0.350003i | ||||
\(59\) | −5.28820 | + | 3.84210i | −0.688465 | + | 0.500199i | −0.876155 | − | 0.482029i | \(-0.839900\pi\) |
0.187690 | + | 0.982228i | \(0.439900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.226391 | + | 0.696760i | −0.0289864 | + | 0.0892110i | −0.964503 | − | 0.264071i | \(-0.914935\pi\) |
0.935517 | + | 0.353282i | \(0.114935\pi\) | |||||||
\(62\) | −14.3186 | − | 2.26784i | −1.81846 | − | 0.288016i | ||||
\(63\) | 9.68482 | − | 5.44783i | 1.22017 | − | 0.686363i | ||||
\(64\) | 5.64412 | − | 1.83389i | 0.705516 | − | 0.229236i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.59293 | + | 2.19426i | −1.05772 | + | 0.270094i | ||||
\(67\) | 2.93891 | − | 2.93891i | 0.359045 | − | 0.359045i | −0.504416 | − | 0.863461i | \(-0.668292\pi\) |
0.863461 | + | 0.504416i | \(0.168292\pi\) | |||||||
\(68\) | −1.24339 | − | 0.633538i | −0.150783 | − | 0.0768277i | ||||
\(69\) | 10.8383 | − | 3.76988i | 1.30478 | − | 0.453840i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.05826 | + | 0.668768i | 0.244270 | + | 0.0793681i | 0.428593 | − | 0.903498i | \(-0.359009\pi\) |
−0.184323 | + | 0.982866i | \(0.559009\pi\) | |||||||
\(72\) | 5.50759 | + | 5.07189i | 0.649075 | + | 0.597728i | ||||
\(73\) | 8.72031 | + | 1.38116i | 1.02064 | + | 0.161653i | 0.644254 | − | 0.764812i | \(-0.277168\pi\) |
0.376382 | + | 0.926465i | \(0.377168\pi\) | |||||||
\(74\) | 8.26976 | + | 6.00833i | 0.961340 | + | 0.698454i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.64030 | −0.188156 | ||||||||
\(77\) | 6.48340 | − | 10.4345i | 0.738852 | − | 1.18912i | ||||
\(78\) | −0.784540 | − | 4.36941i | −0.0888316 | − | 0.494738i | ||||
\(79\) | −0.370953 | + | 0.120530i | −0.0417355 | + | 0.0135607i | −0.329810 | − | 0.944047i | \(-0.606985\pi\) |
0.288075 | + | 0.957608i | \(0.406985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.06791 | + | 8.75921i | −0.229767 | + | 0.973246i | ||||
\(82\) | −0.302218 | − | 0.593135i | −0.0333743 | − | 0.0655008i | ||||
\(83\) | 3.72021 | + | 7.30132i | 0.408346 | + | 0.801424i | 0.999989 | − | 0.00477629i | \(-0.00152035\pi\) |
−0.591643 | + | 0.806200i | \(0.701520\pi\) | |||||||
\(84\) | 2.45935 | − | 0.0506210i | 0.268338 | − | 0.00552320i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.08348 | + | 2.95140i | −0.979497 | + | 0.318258i | ||||
\(87\) | −2.98013 | + | 0.535090i | −0.319503 | + | 0.0573677i | ||||
\(88\) | 8.03656 | + | 1.98207i | 0.856700 | + | 0.211289i | ||||
\(89\) | −7.13725 | −0.756547 | −0.378274 | − | 0.925694i | \(-0.623482\pi\) | ||||
−0.378274 | + | 0.925694i | \(0.623482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.97481 | + | 3.61441i | 0.521502 | + | 0.378893i | ||||
\(92\) | 2.50903 | + | 0.397391i | 0.261584 | + | 0.0414309i | ||||
\(93\) | −2.21320 | + | 16.1132i | −0.229498 | + | 1.67086i | ||||
\(94\) | −6.84023 | − | 2.22252i | −0.705516 | − | 0.229236i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.21817 | + | 3.50222i | 0.124329 | + | 0.357444i | ||||
\(97\) | 2.54933 | + | 1.29895i | 0.258845 | + | 0.131888i | 0.578598 | − | 0.815613i | \(-0.303600\pi\) |
−0.319753 | + | 0.947501i | \(0.603600\pi\) | |||||||
\(98\) | −7.33528 | + | 7.33528i | −0.740975 | + | 0.740975i | ||||
\(99\) | 2.65964 | + | 9.58782i | 0.267303 | + | 0.963612i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.78884 | + | 1.23107i | −0.377003 | + | 0.122496i | −0.491388 | − | 0.870941i | \(-0.663510\pi\) |
0.114385 | + | 0.993437i | \(0.463510\pi\) | |||||||
\(102\) | −4.23886 | + | 8.76037i | −0.419710 | + | 0.867406i | ||||
\(103\) | 13.2388 | + | 2.09682i | 1.30446 | + | 0.206606i | 0.769703 | − | 0.638402i | \(-0.220404\pi\) |
0.534754 | + | 0.845008i | \(0.320404\pi\) | |||||||
\(104\) | −1.28035 | + | 3.94052i | −0.125549 | + | 0.386400i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.91280 | + | 4.29590i | −0.574302 | + | 0.417255i | ||||
\(107\) | 1.39600 | + | 8.81397i | 0.134956 | + | 0.852078i | 0.958555 | + | 0.284906i | \(0.0919625\pi\) |
−0.823599 | + | 0.567172i | \(0.808037\pi\) | |||||||
\(108\) | −1.31920 | + | 1.49305i | −0.126940 | + | 0.143669i | ||||
\(109\) | 5.69249i | 0.545241i | 0.962122 | + | 0.272621i | \(0.0878904\pi\) | ||||
−0.962122 | + | 0.272621i | \(0.912110\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.54847 | − | 9.41471i | 0.621554 | − | 0.893604i | ||||
\(112\) | −15.2467 | − | 7.76857i | −1.44068 | − | 0.734061i | ||||
\(113\) | 2.37116 | − | 0.375555i | 0.223060 | − | 0.0353293i | −0.0439038 | − | 0.999036i | \(-0.513980\pi\) |
0.266964 | + | 0.963707i | \(0.413980\pi\) | |||||||
\(114\) | 0.235406 | + | 11.4369i | 0.0220478 | + | 1.07117i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.637464 | − | 0.207124i | −0.0591870 | − | 0.0192310i | ||||
\(117\) | −4.88295 | + | 0.980878i | −0.451429 | + | 0.0906822i | ||||
\(118\) | 1.57864 | + | 9.96715i | 0.145326 | + | 0.917551i | ||||
\(119\) | −4.16573 | − | 12.8208i | −0.381872 | − | 1.17528i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.68135 | + | 7.87381i | 0.698304 | + | 0.715801i | ||||
\(122\) | 0.799766 | + | 0.799766i | 0.0724074 | + | 0.0724074i | ||||
\(123\) | −0.658328 | + | 0.352684i | −0.0593595 | + | 0.0318005i | ||||
\(124\) | −2.11633 | + | 2.91287i | −0.190052 | + | 0.261584i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.705903 | − | 17.1404i | −0.0628869 | − | 1.52699i | ||||
\(127\) | 4.05650 | + | 7.96133i | 0.359956 | + | 0.706454i | 0.997978 | − | 0.0635649i | \(-0.0202470\pi\) |
−0.638022 | + | 0.770018i | \(0.720247\pi\) | |||||||
\(128\) | 2.10306 | − | 13.2782i | 0.185886 | − | 1.17364i | ||||
\(129\) | 3.52023 | + | 10.1206i | 0.309939 | + | 0.891068i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.0528i | − | 1.14043i | −0.821496 | − | 0.570214i | \(-0.806860\pi\) | ||
0.821496 | − | 0.570214i | \(-0.193140\pi\) | |||||||
\(132\) | −0.483313 | + | 2.14895i | −0.0420670 | + | 0.187042i | ||||
\(133\) | −11.2045 | − | 11.2045i | −0.971551 | − | 0.971551i | ||||
\(134\) | −1.98283 | − | 6.10251i | −0.171290 | − | 0.527177i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.34843 | − | 5.33894i | 0.630122 | − | 0.457811i | ||||
\(137\) | −11.7296 | + | 5.97653i | −1.00213 | + | 0.510610i | −0.876466 | − | 0.481463i | \(-0.840105\pi\) |
−0.125662 | + | 0.992073i | \(0.540105\pi\) | |||||||
\(138\) | 2.41071 | − | 17.5511i | 0.205213 | − | 1.49405i | ||||
\(139\) | 12.5794 | + | 17.3140i | 1.06697 | + | 1.46856i | 0.873108 | + | 0.487527i | \(0.162101\pi\) |
0.193861 | + | 0.981029i | \(0.437899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.33503 | + | 7.72383i | −0.196645 | + | 0.650464i | ||||
\(142\) | 2.36254 | − | 2.36254i | 0.198260 | − | 0.198260i | ||||
\(143\) | −4.20895 | + | 3.54999i | −0.351970 | + | 0.296865i | ||||
\(144\) | 12.9938 | − | 4.82159i | 1.08282 | − | 0.401799i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.01183 | − | 11.0273i | 0.663064 | − | 0.912629i | ||||
\(147\) | 8.39716 | + | 8.05845i | 0.692586 | + | 0.664650i | ||||
\(148\) | 2.26204 | − | 1.15257i | 0.185938 | − | 0.0947403i | ||||
\(149\) | 2.12072 | − | 6.52690i | 0.173736 | − | 0.534704i | −0.825838 | − | 0.563908i | \(-0.809297\pi\) |
0.999573 | + | 0.0292039i | \(0.00929721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7638 | − | 13.6327i | −1.52698 | − | 1.10941i | −0.957889 | − | 0.287138i | \(-0.907296\pi\) |
−0.569088 | − | 0.822276i | \(-0.692704\pi\) | |||||||
\(152\) | 4.84710 | − | 9.51296i | 0.393152 | − | 0.771603i | ||||
\(153\) | 9.92416 | + | 4.55238i | 0.802321 | + | 0.368038i | ||||
\(154\) | −9.80924 | − | 16.2318i | −0.790451 | − | 1.30799i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.05537 | − | 0.319055i | −0.0844974 | − | 0.0255448i | ||||
\(157\) | −1.23027 | + | 0.194856i | −0.0981866 | + | 0.0155512i | −0.205334 | − | 0.978692i | \(-0.565828\pi\) |
0.107148 | + | 0.994243i | \(0.465828\pi\) | |||||||
\(158\) | −0.0941991 | + | 0.594749i | −0.00749407 | + | 0.0473157i | ||||
\(159\) | 4.95513 | + | 6.53307i | 0.392967 | + | 0.518106i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.4240 | + | 19.8530i | 1.13677 | + | 1.56463i | ||||
\(162\) | 10.5995 | + | 8.98376i | 0.832777 | + | 0.705831i | ||||
\(163\) | 0.881306 | − | 1.72966i | 0.0690292 | − | 0.135477i | −0.853913 | − | 0.520415i | \(-0.825777\pi\) |
0.922942 | + | 0.384938i | \(0.125777\pi\) | |||||||
\(164\) | −0.165332 | −0.0129103 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6509 | 0.981901 | ||||||||
\(167\) | 2.51527 | − | 4.93650i | 0.194638 | − | 0.381998i | −0.772975 | − | 0.634436i | \(-0.781232\pi\) |
0.967613 | + | 0.252438i | \(0.0812324\pi\) | |||||||
\(168\) | −6.97382 | + | 14.4127i | −0.538042 | + | 1.11196i | ||||
\(169\) | 6.02119 | + | 8.28745i | 0.463168 | + | 0.637496i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.8231 | − | 0.528099i | 0.980605 | − | 0.0403848i | ||||
\(172\) | −0.371075 | + | 2.34288i | −0.0282942 | + | 0.178643i | ||||
\(173\) | 7.81885 | − | 1.23838i | 0.594456 | − | 0.0941526i | 0.148045 | − | 0.988981i | \(-0.452702\pi\) |
0.446411 | + | 0.894828i | \(0.352702\pi\) | |||||||
\(174\) | −1.35268 | + | 4.47440i | −0.102546 | + | 0.339204i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.0229 | − | 11.5894i | 0.755505 | − | 0.873582i | ||||
\(177\) | 11.1435 | − | 2.00084i | 0.837594 | − | 0.150392i | ||||
\(178\) | −5.00241 | + | 9.81778i | −0.374946 | + | 0.735874i | ||||
\(179\) | 10.6284 | + | 7.72197i | 0.794402 | + | 0.577167i | 0.909267 | − | 0.416214i | \(-0.136643\pi\) |
−0.114865 | + | 0.993381i | \(0.536643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.68205 | + | 8.25451i | −0.199355 | + | 0.613553i | 0.800543 | + | 0.599276i | \(0.204545\pi\) |
−0.999898 | + | 0.0142772i | \(0.995455\pi\) | |||||||
\(182\) | 8.45864 | − | 4.30989i | 0.626996 | − | 0.319471i | ||||
\(183\) | 0.878614 | − | 0.915543i | 0.0649490 | − | 0.0676789i | ||||
\(184\) | −9.71886 | + | 13.3769i | −0.716484 | + | 0.986155i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 20.6136 | + | 14.3379i | 1.51146 | + | 1.05131i | ||||
\(187\) | 12.0392 | − | 0.872607i | 0.880397 | − | 0.0638113i | ||||
\(188\) | −1.26309 | + | 1.26309i | −0.0921200 | + | 0.0921200i | ||||
\(189\) | −19.2097 | + | 1.18752i | −1.39730 | + | 0.0863797i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.12157 | + | 2.92009i | 0.153511 | + | 0.211290i | 0.878845 | − | 0.477107i | \(-0.158315\pi\) |
−0.725334 | + | 0.688397i | \(0.758315\pi\) | |||||||
\(192\) | −10.1834 | − | 1.39873i | −0.734923 | − | 0.100944i | ||||
\(193\) | −2.87760 | + | 1.46621i | −0.207134 | + | 0.105540i | −0.554480 | − | 0.832197i | \(-0.687083\pi\) |
0.347346 | + | 0.937737i | \(0.387083\pi\) | |||||||
\(194\) | 3.57358 | − | 2.59636i | 0.256568 | − | 0.186408i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.796155 | + | 2.45031i | 0.0568682 | + | 0.175022i | ||||
\(197\) | −0.0527933 | − | 0.0527933i | −0.00376137 | − | 0.00376137i | 0.705224 | − | 0.708985i | \(-0.250847\pi\) |
−0.708985 | + | 0.705224i | \(0.750847\pi\) | |||||||
\(198\) | 15.0528 | + | 3.06147i | 1.06976 | + | 0.217569i | ||||
\(199\) | − | 8.09606i | − | 0.573915i | −0.957943 | − | 0.286957i | \(-0.907356\pi\) | ||
0.957943 | − | 0.286957i | \(-0.0926438\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.79926 | + | 2.36498i | −0.479583 | + | 0.166813i | ||||
\(202\) | −0.962129 | + | 6.07464i | −0.0676952 | + | 0.427410i | ||||
\(203\) | −2.93953 | − | 5.76916i | −0.206315 | − | 0.404916i | ||||
\(204\) | 1.46065 | + | 1.92579i | 0.102266 | + | 0.134832i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.1632 | − | 16.7412i | 0.847452 | − | 1.16642i | ||||
\(207\) | −19.7423 | − | 2.29882i | −1.37218 | − | 0.159779i | ||||
\(208\) | 5.42329 | + | 5.42329i | 0.376038 | + | 0.376038i | ||||
\(209\) | 12.1433 | − | 7.33847i | 0.839969 | − | 0.507613i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.00822492 | + | 0.0253137i | 0.000566227 | + | 0.00174267i | 0.951339 | − | 0.308146i | \(-0.0997084\pi\) |
−0.950773 | + | 0.309888i | \(0.899708\pi\) | |||||||
\(212\) | 0.283957 | + | 1.79283i | 0.0195022 | + | 0.123132i | ||||
\(213\) | −2.70455 | − | 2.59546i | −0.185313 | − | 0.177838i | ||||
\(214\) | 13.1026 | + | 4.25731i | 0.895678 | + | 0.291024i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.76073 | − | 12.0627i | −0.323927 | − | 0.820761i | ||||
\(217\) | −34.3531 | + | 5.44100i | −2.33204 | + | 0.369359i | ||||
\(218\) | 7.83040 | + | 3.98979i | 0.530342 | + | 0.270223i | ||||
\(219\) | −12.5541 | − | 8.73209i | −0.848326 | − | 0.590060i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.04216i | 0.406439i | ||||||||
\(222\) | −8.36083 | − | 15.6065i | −0.561142 | − | 1.04744i | ||||
\(223\) | −2.42813 | − | 15.3306i | −0.162600 | − | 1.02661i | −0.925127 | − | 0.379658i | \(-0.876042\pi\) |
0.762527 | − | 0.646956i | \(-0.223958\pi\) | |||||||
\(224\) | −6.41517 | + | 4.66089i | −0.428632 | + | 0.311419i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.14531 | − | 3.52492i | 0.0761852 | − | 0.234474i | ||||
\(227\) | 29.0487 | + | 4.60086i | 1.92803 | + | 0.305370i | 0.998059 | − | 0.0622706i | \(-0.0198342\pi\) |
0.929968 | + | 0.367640i | \(0.119834\pi\) | |||||||
\(228\) | 2.55743 | + | 1.23746i | 0.169370 | + | 0.0819528i | ||||
\(229\) | −17.5192 | + | 5.69232i | −1.15770 | + | 0.376159i | −0.824038 | − | 0.566534i | \(-0.808284\pi\) |
−0.333661 | + | 0.942693i | \(0.608284\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.9803 | + | 11.3775i | −1.18302 | + | 0.748587i | ||||
\(232\) | 3.08493 | − | 3.08493i | 0.202535 | − | 0.202535i | ||||
\(233\) | −7.99977 | − | 4.07609i | −0.524082 | − | 0.267033i | 0.171872 | − | 0.985119i | \(-0.445018\pi\) |
−0.695954 | + | 0.718086i | \(0.745018\pi\) | |||||||
\(234\) | −2.07313 | + | 7.40431i | −0.135525 | + | 0.484035i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.38364 | + | 0.774493i | 0.155162 | + | 0.0504152i | ||||
\(237\) | 0.669291 | + | 0.0919296i | 0.0434751 | + | 0.00597147i | ||||
\(238\) | −20.5556 | − | 3.25568i | −1.33242 | − | 0.211034i | ||||
\(239\) | 6.08063 | + | 4.41783i | 0.393323 | + | 0.285766i | 0.766816 | − | 0.641867i | \(-0.221840\pi\) |
−0.373493 | + | 0.927633i | \(0.621840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.978249 | 0.0630146 | 0.0315073 | − | 0.999504i | \(-0.489969\pi\) | ||||
0.0315073 | + | 0.999504i | \(0.489969\pi\) | |||||||
\(242\) | 16.2147 | − | 5.04756i | 1.04232 | − | 0.324470i | ||||
\(243\) | 9.83216 | − | 12.0966i | 0.630733 | − | 0.776000i | ||||
\(244\) | 0.267158 | − | 0.0868049i | 0.0171030 | − | 0.00555711i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0237274 | + | 1.15277i | 0.00151281 | + | 0.0734978i | ||||
\(247\) | 3.22431 | + | 6.32807i | 0.205158 | + | 0.402645i | ||||
\(248\) | −10.6395 | − | 20.8812i | −0.675609 | − | 1.32596i | ||||
\(249\) | −0.292078 | − | 14.1902i | −0.0185097 | − | 0.899269i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.21468 | + | 1.04451i | −0.202909 | + | 0.0659290i | −0.408708 | − | 0.912665i | \(-0.634021\pi\) |
0.205799 | + | 0.978594i | \(0.434021\pi\) | |||||||
\(252\) | −3.87263 | − | 1.77644i | −0.243953 | − | 0.111905i | ||||
\(253\) | −20.3524 | + | 8.28311i | −1.27954 | + | 0.520755i | ||||
\(254\) | 13.7945 | 0.865543 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.18867 | − | 5.22287i | −0.449292 | − | 0.326430i | ||||
\(257\) | −12.7279 | − | 2.01590i | −0.793945 | − | 0.125748i | −0.253729 | − | 0.967275i | \(-0.581657\pi\) |
−0.540215 | + | 0.841527i | \(0.681657\pi\) | |||||||
\(258\) | 16.3888 | + | 2.25107i | 1.02032 | + | 0.140145i | ||||
\(259\) | 23.3243 | + | 7.57851i | 1.44930 | + | 0.470906i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.05006 | + | 1.41396i | 0.312591 | + | 0.0875222i | ||||
\(262\) | −17.9550 | − | 9.14853i | −1.10926 | − | 0.565198i | ||||
\(263\) | −21.9542 | + | 21.9542i | −1.35376 | + | 1.35376i | −0.472338 | + | 0.881417i | \(0.656590\pi\) |
−0.881417 | + | 0.472338i | \(0.843410\pi\) | |||||||
\(264\) | −11.0347 | − | 9.15314i | −0.679138 | − | 0.563337i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −23.2656 | + | 7.55945i | −1.42650 | + | 0.463499i | ||||
\(267\) | 11.1279 | + | 5.38441i | 0.681014 | + | 0.329521i | ||||
\(268\) | −1.57400 | − | 0.249298i | −0.0961476 | − | 0.0152283i | ||||
\(269\) | −5.77912 | + | 17.7863i | −0.352359 | + | 1.08445i | 0.605165 | + | 0.796100i | \(0.293107\pi\) |
−0.957525 | + | 0.288351i | \(0.906893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8883 | − | 10.0904i | 0.843652 | − | 0.612949i | −0.0797364 | − | 0.996816i | \(-0.525408\pi\) |
0.923388 | + | 0.383867i | \(0.125408\pi\) | |||||||
\(272\) | −2.63027 | − | 16.6069i | −0.159484 | − | 1.00694i | ||||
\(273\) | −5.02959 | − | 9.38836i | −0.304405 | − | 0.568209i | ||||
\(274\) | 20.3237i | 1.22780i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.61209 | − | 2.51242i | −0.217422 | − | 0.151230i | ||||
\(277\) | 19.0394 | + | 9.70104i | 1.14396 | + | 0.582879i | 0.920077 | − | 0.391736i | \(-0.128125\pi\) |
0.223887 | + | 0.974615i | \(0.428125\pi\) | |||||||
\(278\) | 32.6333 | − | 5.16861i | 1.95722 | − | 0.309993i | ||||
\(279\) | 15.6066 | − | 23.4528i | 0.934342 | − | 1.40408i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5791 | − | 3.43735i | −0.631094 | − | 0.205055i | −0.0240344 | − | 0.999711i | \(-0.507651\pi\) |
−0.607060 | + | 0.794656i | \(0.707651\pi\) | |||||||
\(282\) | 8.98806 | + | 8.62552i | 0.535231 | + | 0.513642i | ||||
\(283\) | 2.35054 | + | 14.8407i | 0.139725 | + | 0.882188i | 0.953584 | + | 0.301126i | \(0.0973626\pi\) |
−0.813859 | + | 0.581062i | \(0.802637\pi\) | |||||||
\(284\) | −0.256425 | − | 0.789195i | −0.0152160 | − | 0.0468301i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.93325 | + | 8.27783i | 0.114316 | + | 0.489478i | ||||
\(287\) | −1.12934 | − | 1.12934i | −0.0666628 | − | 0.0666628i | ||||
\(288\) | 0.742826 | − | 6.37940i | 0.0437715 | − | 0.375910i | ||||
\(289\) | −2.20660 | + | 3.03713i | −0.129800 | + | 0.178654i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.99478 | − | 3.94846i | −0.175557 | − | 0.231463i | ||||
\(292\) | −1.53689 | − | 3.01632i | −0.0899399 | − | 0.176517i | ||||
\(293\) | −0.210595 | + | 1.32964i | −0.0123031 | + | 0.0776785i | −0.993076 | − | 0.117474i | \(-0.962520\pi\) |
0.980773 | + | 0.195153i | \(0.0625203\pi\) | |||||||
\(294\) | 16.9704 | − | 5.90280i | 0.989734 | − | 0.344258i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16.5246i | 0.960471i | ||||||||
\(297\) | 3.08645 | − | 16.9551i | 0.179094 | − | 0.983832i | ||||
\(298\) | −7.49181 | − | 7.49181i | −0.433989 | − | 0.433989i | ||||
\(299\) | −3.39887 | − | 10.4606i | −0.196562 | − | 0.604954i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.5383 | + | 13.4689i | −1.06853 | + | 0.776333i | ||||
\(302\) | −31.9040 | + | 16.2559i | −1.83587 | + | 0.935423i | ||||
\(303\) | 6.83600 | + | 0.938949i | 0.392718 | + | 0.0539412i | ||||
\(304\) | −11.6168 | − | 15.9891i | −0.666266 | − | 0.917037i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.2178 | − | 10.4607i | 0.755612 | − | 0.597996i | ||||
\(307\) | −20.9370 | + | 20.9370i | −1.19494 | + | 1.19494i | −0.219272 | + | 0.975664i | \(0.570368\pi\) |
−0.975664 | + | 0.219272i | \(0.929632\pi\) | |||||||
\(308\) | −4.69798 | + | 0.340510i | −0.267692 | + | 0.0194024i | ||||
\(309\) | −19.0591 | − | 13.2567i | −1.08423 | − | 0.754146i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.69048 | + | 7.83228i | −0.322678 | + | 0.444128i | −0.939282 | − | 0.343145i | \(-0.888508\pi\) |
0.616605 | + | 0.787273i | \(0.288508\pi\) | |||||||
\(312\) | 4.96899 | − | 5.17785i | 0.281314 | − | 0.293138i | ||||
\(313\) | −7.70043 | + | 3.92356i | −0.435254 | + | 0.221773i | −0.657867 | − | 0.753134i | \(-0.728541\pi\) |
0.222613 | + | 0.974907i | \(0.428541\pi\) | |||||||
\(314\) | −0.594245 | + | 1.82890i | −0.0335352 | + | 0.103211i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.120992 | + | 0.0879056i | 0.00680631 | + | 0.00494508i | ||||
\(317\) | −5.15467 | + | 10.1166i | −0.289515 | + | 0.568206i | −0.989256 | − | 0.146191i | \(-0.953299\pi\) |
0.699741 | + | 0.714396i | \(0.253299\pi\) | |||||||
\(318\) | 12.4597 | − | 2.23717i | 0.698703 | − | 0.125454i | ||||
\(319\) | 5.64584 | − | 1.31856i | 0.316106 | − | 0.0738252i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.47281 | − | 14.7952i | 0.249648 | − | 0.825788i | ||||
\(322\) | 37.4188 | − | 5.92655i | 2.08527 | − | 0.330274i | ||||
\(323\) | 2.43564 | − | 15.3780i | 0.135522 | − | 0.855655i | ||||
\(324\) | 3.18316 | − | 1.33263i | 0.176842 | − | 0.0740351i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.76157 | − | 2.42459i | −0.0975643 | − | 0.134286i | ||||
\(327\) | 4.29447 | − | 8.87529i | 0.237485 | − | 0.490805i | ||||
\(328\) | 0.488556 | − | 0.958846i | 0.0269760 | − | 0.0529434i | ||||
\(329\) | −17.2556 | −0.951333 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5367 | −1.07383 | −0.536916 | − | 0.843636i | \(-0.680411\pi\) | ||||
−0.536916 | + | 0.843636i | \(0.680411\pi\) | |||||||
\(332\) | 1.42644 | − | 2.79954i | 0.0782858 | − | 0.153645i | ||||
\(333\) | −17.3124 | + | 9.73846i | −0.948715 | + | 0.533664i | ||||
\(334\) | −5.02757 | − | 6.91986i | −0.275096 | − | 0.378638i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 17.9108 | + | 23.6144i | 0.977113 | + | 1.28827i | ||||
\(337\) | −0.759730 | + | 4.79675i | −0.0413851 | + | 0.261296i | −0.999702 | − | 0.0244121i | \(-0.992229\pi\) |
0.958317 | + | 0.285708i | \(0.0922286\pi\) | |||||||
\(338\) | 15.6201 | − | 2.47398i | 0.849623 | − | 0.134567i | ||||
\(339\) | −3.98026 | − | 1.20329i | −0.216178 | − | 0.0653538i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63555 | − | 31.0323i | 0.142723 | − | 1.68050i | ||||
\(342\) | 8.26109 | − | 18.0092i | 0.446709 | − | 0.973823i | ||||
\(343\) | 0.471850 | − | 0.926057i | 0.0254775 | − | 0.0500024i | ||||
\(344\) | −12.4910 | − | 9.07527i | −0.673471 | − | 0.489306i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.77665 | − | 11.6233i | 0.203034 | − | 0.624874i | ||||
\(347\) | −13.1032 | + | 6.67642i | −0.703417 | + | 0.358409i | −0.768833 | − | 0.639449i | \(-0.779162\pi\) |
0.0654163 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(348\) | 0.837628 | + | 0.803841i | 0.0449016 | + | 0.0430904i | ||||
\(349\) | 11.7261 | − | 16.1396i | 0.627683 | − | 0.863932i | −0.370201 | − | 0.928952i | \(-0.620711\pi\) |
0.997884 | + | 0.0650201i | \(0.0207111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.35311 | + | 2.15443i | 0.445856 | + | 0.114995i | ||||
\(352\) | −2.67655 | − | 6.57655i | −0.142661 | − | 0.350531i | ||||
\(353\) | −10.9626 | + | 10.9626i | −0.583479 | + | 0.583479i | −0.935857 | − | 0.352379i | \(-0.885373\pi\) |
0.352379 | + | 0.935857i | \(0.385373\pi\) | |||||||
\(354\) | 5.05802 | − | 16.7310i | 0.268831 | − | 0.889241i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.60855 | + | 2.21398i | 0.0852530 | + | 0.117341i | ||||
\(357\) | −3.17724 | + | 23.1319i | −0.168158 | + | 1.22427i | ||||
\(358\) | 18.0714 | − | 9.20782i | 0.955102 | − | 0.486649i | ||||
\(359\) | −5.88033 | + | 4.27231i | −0.310352 | + | 0.225484i | −0.732048 | − | 0.681253i | \(-0.761435\pi\) |
0.421695 | + | 0.906738i | \(0.361435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.215960 | + | 0.664655i | 0.0113663 | + | 0.0349819i | ||||
\(362\) | 9.47483 | + | 9.47483i | 0.497986 | + | 0.497986i | ||||
\(363\) | −6.03609 | − | 18.0711i | −0.316813 | − | 0.948488i | ||||
\(364\) | − | 2.35778i | − | 0.123581i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.643583 | − | 1.85029i | −0.0336406 | − | 0.0967160i | ||||
\(367\) | −1.86113 | + | 11.7507i | −0.0971505 | + | 0.613384i | 0.890290 | + | 0.455394i | \(0.150501\pi\) |
−0.987441 | + | 0.157990i | \(0.949499\pi\) | |||||||
\(368\) | 13.8955 | + | 27.2715i | 0.724353 | + | 1.42162i | ||||
\(369\) | 1.29248 | − | 0.0532290i | 0.0672840 | − | 0.00277099i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3067 | + | 14.1860i | −0.535099 | + | 0.736500i | ||||
\(372\) | 5.49711 | − | 2.94495i | 0.285012 | − | 0.152689i | ||||
\(373\) | −9.15784 | − | 9.15784i | −0.474175 | − | 0.474175i | 0.429088 | − | 0.903263i | \(-0.358835\pi\) |
−0.903263 | + | 0.429088i | \(0.858835\pi\) | |||||||
\(374\) | 7.23782 | − | 17.1724i | 0.374259 | − | 0.887964i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.59287 | − | 11.0577i | −0.185288 | − | 0.570258i | ||||
\(377\) | 0.453992 | + | 2.86639i | 0.0233818 | + | 0.147627i | ||||
\(378\) | −11.8303 | + | 27.2566i | −0.608486 | + | 1.40193i | ||||
\(379\) | 18.6018 | + | 6.04409i | 0.955510 | + | 0.310464i | 0.744952 | − | 0.667118i | \(-0.232472\pi\) |
0.210557 | + | 0.977582i | \(0.432472\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.318480 | − | 15.4730i | −0.0163162 | − | 0.792703i | ||||
\(382\) | 5.50375 | − | 0.871709i | 0.281596 | − | 0.0446005i | ||||
\(383\) | −10.6367 | − | 5.41968i | −0.543511 | − | 0.276933i | 0.160604 | − | 0.987019i | \(-0.448656\pi\) |
−0.704115 | + | 0.710086i | \(0.748656\pi\) | |||||||
\(384\) | −13.2961 | + | 19.1158i | −0.678514 | + | 0.975497i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.98597i | 0.253779i | ||||||||
\(387\) | 2.14659 | − | 18.4349i | 0.109117 | − | 0.937101i | ||||
\(388\) | −0.171618 | − | 1.08355i | −0.00871257 | − | 0.0550090i | ||||
\(389\) | −24.7040 | + | 17.9485i | −1.25254 | + | 0.910026i | −0.998367 | − | 0.0571312i | \(-0.981805\pi\) |
−0.254177 | + | 0.967158i | \(0.581805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.45116 | + | 22.9323i | −0.376821 | + | 1.15974i | ||||
\(392\) | −16.5633 | − | 2.62337i | −0.836572 | − | 0.132500i | ||||
\(393\) | −9.84715 | + | 20.3509i | −0.496723 | + | 1.02657i | ||||
\(394\) | −0.109623 | + | 0.0356186i | −0.00552272 | + | 0.00179444i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.37474 | − | 2.98587i | 0.119335 | − | 0.150045i | ||||
\(397\) | 26.2300 | − | 26.2300i | 1.31645 | − | 1.31645i | 0.399878 | − | 0.916568i | \(-0.369053\pi\) |
0.916568 | − | 0.399878i | \(-0.130947\pi\) | |||||||
\(398\) | −11.1367 | − | 5.67442i | −0.558231 | − | 0.284433i | ||||
\(399\) | 9.01640 | + | 25.9219i | 0.451384 | + | 1.29772i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0223 | + | 7.15548i | 1.09974 | + | 0.357328i | 0.802003 | − | 0.597320i | \(-0.203768\pi\) |
0.297738 | + | 0.954648i | \(0.403768\pi\) | |||||||
\(402\) | −1.51232 | + | 11.0104i | −0.0754278 | + | 0.549150i | ||||
\(403\) | 15.3975 | + | 2.43872i | 0.767004 | + | 0.121481i | ||||
\(404\) | 1.23578 | + | 0.897849i | 0.0614825 | + | 0.0446697i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.99615 | −0.496101 | ||||||||
\(407\) | −11.5896 | + | 18.6526i | −0.574476 | + | 0.924573i | ||||
\(408\) | −15.4849 | + | 2.78035i | −0.766615 | + | 0.137648i | ||||
\(409\) | −16.5144 | + | 5.36586i | −0.816586 | + | 0.265325i | −0.687385 | − | 0.726294i | \(-0.741241\pi\) |
−0.129201 | + | 0.991618i | \(0.541241\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.7967 | − | 0.469224i | 1.12448 | − | 0.0231451i | ||||
\(412\) | −2.33325 | − | 4.57925i | −0.114951 | − | 0.225604i | ||||
\(413\) | 10.9917 | + | 21.5724i | 0.540865 | + | 1.06151i | ||||
\(414\) | −16.9993 | + | 25.5456i | −0.835470 | + | 1.25550i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.38019 | − | 1.09829i | 0.165727 | − | 0.0538480i | ||||
\(417\) | −6.55093 | − | 36.4847i | −0.320801 | − | 1.78666i | ||||
\(418\) | −1.58350 | − | 21.8473i | −0.0774515 | − | 1.06859i | ||||
\(419\) | 37.7097 | 1.84224 | 0.921120 | − | 0.389279i | \(-0.127276\pi\) | ||||
0.921120 | + | 0.389279i | \(0.127276\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0291 | + | 7.28658i | 0.488790 | + | 0.355126i | 0.804719 | − | 0.593656i | \(-0.202316\pi\) |
−0.315929 | + | 0.948783i | \(0.602316\pi\) | |||||||
\(422\) | 0.0405855 | + | 0.00642811i | 0.00197567 | + | 0.000312915i | ||||
\(423\) | 9.46753 | − | 10.2808i | 0.460327 | − | 0.499872i | ||||
\(424\) | −11.2367 | − | 3.65101i | −0.545700 | − | 0.177309i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.46581 | + | 1.90117i | −0.264819 | + | 0.0921119i | ||||
\(427\) | 2.41783 | + | 1.23194i | 0.117007 | + | 0.0596180i | ||||
\(428\) | 2.41948 | − | 2.41948i | 0.116950 | − | 0.116950i | ||||
\(429\) | 9.24041 | − | 2.35960i | 0.446131 | − | 0.113922i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.4086 | + | 10.5302i | −1.56107 | + | 0.507221i | −0.957092 | − | 0.289783i | \(-0.906417\pi\) |
−0.603974 | + | 0.797004i | \(0.706417\pi\) | |||||||
\(432\) | −23.8964 | − | 2.28519i | −1.14971 | − | 0.109946i | ||||
\(433\) | 19.3559 | + | 3.06568i | 0.930187 | + | 0.147327i | 0.603099 | − | 0.797666i | \(-0.293932\pi\) |
0.327089 | + | 0.944994i | \(0.393932\pi\) | |||||||
\(434\) | −16.5932 | + | 51.0686i | −0.796499 | + | 2.45137i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.76581 | − | 1.28294i | 0.0845671 | − | 0.0614416i | ||||
\(437\) | 4.43376 | + | 27.9937i | 0.212096 | + | 1.33912i | ||||
\(438\) | −20.8106 | + | 11.1488i | −0.994367 | + | 0.532709i | ||||
\(439\) | 0.523979i | 0.0250081i | 0.999922 | + | 0.0125041i | \(0.00398027\pi\) | ||||
−0.999922 | + | 0.0125041i | \(0.996020\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.01283 | − | 18.8990i | −0.333944 | − | 0.899953i | ||||
\(442\) | 8.31140 | + | 4.23487i | 0.395333 | + | 0.201432i | ||||
\(443\) | 26.9398 | − | 4.26685i | 1.27995 | − | 0.202724i | 0.520822 | − | 0.853665i | \(-0.325626\pi\) |
0.759128 | + | 0.650941i | \(0.225626\pi\) | |||||||
\(444\) | −4.39630 | + | 0.0904892i | −0.208639 | + | 0.00429443i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22.7901 | − | 7.40497i | −1.07914 | − | 0.350635i | ||||
\(447\) | −8.23041 | + | 8.57635i | −0.389285 | + | 0.405647i | ||||
\(448\) | −3.43867 | − | 21.7109i | −0.162462 | − | 1.02574i | ||||
\(449\) | −3.82551 | − | 11.7737i | −0.180537 | − | 0.555636i | 0.819306 | − | 0.573357i | \(-0.194359\pi\) |
−0.999843 | + | 0.0177205i | \(0.994359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.22396 | − | 0.739671i | 0.0576343 | − | 0.0348297i | ||||
\(452\) | −0.650895 | − | 0.650895i | −0.0306155 | − | 0.0306155i | ||||
\(453\) | 18.9705 | + | 35.4107i | 0.891310 | + | 1.66374i | ||||
\(454\) | 26.6886 | − | 36.7337i | 1.25256 | − | 1.72400i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.7339 | + | 11.1752i | −0.689978 | + | 0.523326i | ||||
\(457\) | −16.0603 | − | 31.5201i | −0.751268 | − | 1.47445i | −0.876028 | − | 0.482260i | \(-0.839816\pi\) |
0.124759 | − | 0.992187i | \(-0.460184\pi\) | |||||||
\(458\) | −4.44878 | + | 28.0885i | −0.207878 | + | 1.31249i | ||||
\(459\) | −12.0386 | − | 14.5846i | −0.561916 | − | 0.680751i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5799i | 0.818778i | 0.912360 | + | 0.409389i | \(0.134258\pi\) | ||||
−0.912360 | + | 0.409389i | \(0.865742\pi\) | |||||||
\(462\) | 3.04841 | + | 32.7075i | 0.141825 | + | 1.52169i | ||||
\(463\) | 27.0236 | + | 27.0236i | 1.25589 | + | 1.25589i | 0.953036 | + | 0.302858i | \(0.0979409\pi\) |
0.302858 | + | 0.953036i | \(0.402059\pi\) | |||||||
\(464\) | −2.49559 | − | 7.68064i | −0.115855 | − | 0.356565i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.2139 | + | 8.14735i | −0.519472 | + | 0.377419i | ||||
\(467\) | 16.6966 | − | 8.50733i | 0.772625 | − | 0.393672i | −0.0227875 | − | 0.999740i | \(-0.507254\pi\) |
0.795413 | + | 0.606068i | \(0.207254\pi\) | |||||||
\(468\) | 1.40476 | + | 1.29363i | 0.0649350 | + | 0.0597980i | ||||
\(469\) | −9.04872 | − | 12.4545i | −0.417831 | − | 0.575095i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.06515 | + | 0.624326i | 0.0951572 | + | 0.0287674i | ||||
\(472\) | −11.5354 | + | 11.5354i | −0.530958 | + | 0.530958i | ||||
\(473\) | −7.73459 | − | 19.0046i | −0.355637 | − | 0.873834i | ||||
\(474\) | 0.595553 | − | 0.856223i | 0.0273546 | − | 0.0393276i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.03817 | + | 4.18168i | −0.139254 | + | 0.191667i | ||||
\(477\) | −2.79704 | − | 13.9241i | −0.128068 | − | 0.637539i | ||||
\(478\) | 10.3389 | − | 5.26791i | 0.472888 | − | 0.240949i | ||||
\(479\) | −0.165337 | + | 0.508854i | −0.00755442 | + | 0.0232501i | −0.954763 | − | 0.297369i | \(-0.903891\pi\) |
0.947208 | + | 0.320619i | \(0.103891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.89289 | − | 6.46106i | −0.405481 | − | 0.294599i | ||||
\(482\) | 0.685642 | − | 1.34565i | 0.0312301 | − | 0.0612926i | ||||
\(483\) | −7.51157 | − | 41.8349i | −0.341788 | − | 1.90355i | ||||
\(484\) | 0.711285 | − | 4.15731i | 0.0323311 | − | 0.188969i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.74852 | − | 22.0032i | −0.442202 | − | 0.998084i | ||||
\(487\) | 0.862010 | − | 0.136529i | 0.0390614 | − | 0.00618671i | −0.136873 | − | 0.990589i | \(-0.543705\pi\) |
0.175935 | + | 0.984402i | \(0.443705\pi\) | |||||||
\(488\) | −0.286026 | + | 1.80590i | −0.0129478 | + | 0.0817491i | ||||
\(489\) | −2.67894 | + | 2.03189i | −0.121146 | + | 0.0918852i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.48538 | + | 7.54997i | 0.247552 | + | 0.340726i | 0.914652 | − | 0.404242i | \(-0.132465\pi\) |
−0.667100 | + | 0.744968i | \(0.732465\pi\) | |||||||
\(492\) | 0.257773 | + | 0.124728i | 0.0116213 | + | 0.00562317i | ||||
\(493\) | 2.88836 | − | 5.66873i | 0.130085 | − | 0.255307i | ||||
\(494\) | 10.9646 | 0.493319 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −43.3816 | −1.94789 | ||||||||
\(497\) | 3.63921 | − | 7.14235i | 0.163241 | − | 0.320378i | ||||
\(498\) | −19.7243 | − | 9.54397i | −0.883868 | − | 0.427675i | ||||
\(499\) | 2.53460 | + | 3.48858i | 0.113464 | + | 0.156170i | 0.861972 | − | 0.506956i | \(-0.169229\pi\) |
−0.748508 | + | 0.663126i | \(0.769229\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.64577 | + | 5.79907i | −0.341588 | + | 0.259083i | ||||
\(502\) | −0.816328 | + | 5.15409i | −0.0364345 | + | 0.230038i | ||||
\(503\) | −11.8517 | + | 1.87712i | −0.528441 | + | 0.0836968i | −0.414954 | − | 0.909843i | \(-0.636202\pi\) |
−0.113487 | + | 0.993539i | \(0.536202\pi\) | |||||||
\(504\) | 21.7461 | − | 17.2100i | 0.968648 | − | 0.766594i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.87075 | + | 33.8016i | −0.127620 | + | 1.50267i | ||||
\(507\) | −3.13564 | − | 17.4636i | −0.139259 | − | 0.775586i | ||||
\(508\) | 1.55538 | − | 3.05260i | 0.0690088 | − | 0.135437i | ||||
\(509\) | −14.3435 | − | 10.4212i | −0.635764 | − | 0.461910i | 0.222628 | − | 0.974903i | \(-0.428536\pi\) |
−0.858392 | + | 0.512994i | \(0.828536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1056 | − | 31.1018i | 0.447045 | − | 1.37586i | ||||
\(512\) | 11.7340 | − | 5.97876i | 0.518573 | − | 0.264226i | ||||
\(513\) | −20.3912 | − | 8.85048i | −0.900292 | − | 0.390758i | ||||
\(514\) | −11.6938 | + | 16.0952i | −0.515792 | + | 0.709927i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.34604 | − | 3.37289i | 0.103279 | − | 0.148483i | ||||
\(517\) | 3.69986 | − | 15.0016i | 0.162720 | − | 0.659769i | ||||
\(518\) | 26.7724 | − | 26.7724i | 1.17631 | − | 1.17631i | ||||
\(519\) | −13.1248 | − | 3.96782i | −0.576115 | − | 0.174168i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.3287 | − | 19.7218i | −0.627752 | − | 0.864026i | 0.370137 | − | 0.928977i | \(-0.379311\pi\) |
−0.997888 | + | 0.0649513i | \(0.979311\pi\) | |||||||
\(522\) | 5.48453 | − | 5.95567i | 0.240051 | − | 0.260673i | ||||
\(523\) | −25.3696 | + | 12.9265i | −1.10933 | + | 0.565234i | −0.909963 | − | 0.414690i | \(-0.863890\pi\) |
−0.199372 | + | 0.979924i | \(0.563890\pi\) | |||||||
\(524\) | −4.04898 | + | 2.94176i | −0.176881 | + | 0.128511i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.8121 | + | 45.5870i | 0.645838 | + | 1.98769i | ||||
\(527\) | −24.1660 | − | 24.1660i | −1.05269 | − | 1.05269i | ||||
\(528\) | −24.3701 | + | 10.5079i | −1.06057 | + | 0.457297i | ||||
\(529\) | − | 20.8936i | − | 0.908418i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.8835 | − | 5.28718i | −0.819474 | − | 0.229444i | ||||
\(532\) | −0.950438 | + | 6.00083i | −0.0412067 | + | 0.260169i | ||||
\(533\) | 0.324990 | + | 0.637829i | 0.0140769 | + | 0.0276274i | ||||
\(534\) | 15.2060 | − | 11.5333i | 0.658028 | − | 0.499093i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.09699 | − | 8.39179i | 0.263350 | − | 0.362470i | ||||
\(537\) | −10.7454 | − | 20.0576i | −0.463699 | − | 0.865551i | ||||
\(538\) | 20.4158 | + | 20.4158i | 0.880186 | + | 0.880186i | ||||
\(539\) | −16.8563 | − | 14.5780i | −0.726054 | − | 0.627918i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.87092 | + | 24.2242i | 0.338397 | + | 1.04148i | 0.965024 | + | 0.262160i | \(0.0844349\pi\) |
−0.626627 | + | 0.779319i | \(0.715565\pi\) | |||||||
\(542\) | −4.14595 | − | 26.1765i | −0.178084 | − | 1.12438i | ||||
\(543\) | 10.4089 | − | 10.8464i | 0.446690 | − | 0.465465i | ||||
\(544\) | −7.41020 | − | 2.40772i | −0.317710 | − | 0.103230i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.4395 | + | 0.338375i | −0.703545 | + | 0.0144811i | ||||
\(547\) | 35.3619 | − | 5.60077i | 1.51197 | − | 0.239472i | 0.655310 | − | 0.755360i | \(-0.272538\pi\) |
0.856656 | + | 0.515888i | \(0.172538\pi\) | |||||||
\(548\) | 4.49747 | + | 2.29158i | 0.192122 | + | 0.0978913i | ||||
\(549\) | −2.06056 | + | 0.764610i | −0.0879427 | + | 0.0326328i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.47831i | − | 0.318587i | ||||||
\(552\) | 25.2445 | − | 13.5242i | 1.07448 | − | 0.575627i | ||||
\(553\) | 0.226002 | + | 1.42692i | 0.00961060 | + | 0.0606789i | ||||
\(554\) | 26.6889 | − | 19.3906i | 1.13390 | − | 0.823827i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.53576 | − | 7.80426i | 0.107540 | − | 0.330974i | ||||
\(557\) | 24.8865 | + | 3.94163i | 1.05447 | + | 0.167012i | 0.659518 | − | 0.751688i | \(-0.270760\pi\) |
0.394955 | + | 0.918701i | \(0.370760\pi\) | |||||||
\(558\) | −21.3224 | − | 37.9056i | −0.902650 | − | 1.60467i | ||||
\(559\) | 9.76793 | − | 3.17379i | 0.413139 | − | 0.134237i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.4290 | − | 7.72202i | −0.820292 | − | 0.326024i | ||||
\(562\) | −12.1430 | + | 12.1430i | −0.512223 | + | 0.512223i | ||||
\(563\) | −15.5494 | − | 7.92283i | −0.655330 | − | 0.333907i | 0.0945124 | − | 0.995524i | \(-0.469871\pi\) |
−0.749843 | + | 0.661616i | \(0.769871\pi\) | |||||||
\(564\) | 2.92219 | − | 1.01642i | 0.123046 | − | 0.0427991i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.0619 | + | 7.16833i | 0.927329 | + | 0.301307i | ||||
\(567\) | 30.8462 | + | 12.6405i | 1.29542 | + | 0.530851i | ||||
\(568\) | 5.33468 | + | 0.844931i | 0.223838 | + | 0.0354525i | ||||
\(569\) | 1.65835 | + | 1.20486i | 0.0695217 | + | 0.0505104i | 0.622003 | − | 0.783015i | \(-0.286319\pi\) |
−0.552482 | + | 0.833525i | \(0.686319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6618 | 1.36685 | 0.683427 | − | 0.730019i | \(-0.260489\pi\) | ||||
0.683427 | + | 0.730019i | \(0.260489\pi\) | |||||||
\(572\) | 2.04979 | + | 0.505543i | 0.0857062 | + | 0.0211378i | ||||
\(573\) | −1.10484 | − | 6.15330i | −0.0461555 | − | 0.257058i | ||||
\(574\) | −2.34502 | + | 0.761944i | −0.0978793 | + | 0.0318029i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 14.8219 | + | 9.86323i | 0.617581 | + | 0.410968i | ||||
\(577\) | −12.4955 | − | 24.5237i | −0.520193 | − | 1.02094i | −0.990381 | − | 0.138369i | \(-0.955814\pi\) |
0.470188 | − | 0.882566i | \(-0.344186\pi\) | |||||||
\(578\) | 2.63119 | + | 5.16401i | 0.109443 | + | 0.214795i | ||||
\(579\) | 5.59265 | − | 0.115114i | 0.232423 | − | 0.00478396i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.8665 | − | 9.37930i | 1.19758 | − | 0.389119i | ||||
\(582\) | −7.53037 | + | 1.35210i | −0.312144 | + | 0.0560463i | ||||
\(583\) | −10.1230 | − | 12.0021i | −0.419253 | − | 0.497076i | ||||
\(584\) | 22.0347 | 0.911804 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.68141 | + | 1.22162i | 0.0694584 | + | 0.0504645i | ||||
\(587\) | −1.87397 | − | 0.296808i | −0.0773471 | − | 0.0122506i | 0.117641 | − | 0.993056i | \(-0.462467\pi\) |
−0.194988 | + | 0.980806i | \(0.562467\pi\) | |||||||
\(588\) | 0.607236 | − | 4.42097i | 0.0250420 | − | 0.182318i | ||||
\(589\) | −38.2054 | − | 12.4137i | −1.57422 | − | 0.511497i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0424835 | + | 0.122139i | 0.00174754 | + | 0.00502413i | ||||
\(592\) | 27.2547 | + | 13.8870i | 1.12016 | + | 0.570751i | ||||
\(593\) | −2.18360 | + | 2.18360i | −0.0896698 | + | 0.0896698i | −0.750519 | − | 0.660849i | \(-0.770196\pi\) |
0.660849 | + | 0.750519i | \(0.270196\pi\) | |||||||
\(594\) | −21.1596 | − | 16.1292i | −0.868188 | − | 0.661789i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.50260 | + | 0.813144i | −0.102511 | + | 0.0333077i | ||||
\(597\) | −6.10775 | + | 12.6228i | −0.249973 | + | 0.516615i | ||||
\(598\) | −16.7715 | − | 2.65635i | −0.685839 | − | 0.108626i | ||||
\(599\) | 11.9309 | − | 36.7195i | 0.487483 | − | 1.50032i | −0.340870 | − | 0.940110i | \(-0.610722\pi\) |
0.828353 | − | 0.560207i | \(-0.189278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.8728 | − | 9.35266i | 0.525094 | − | 0.381503i | −0.293426 | − | 0.955982i | \(-0.594795\pi\) |
0.818519 | + | 0.574479i | \(0.194795\pi\) | |||||||
\(602\) | 5.53409 | + | 34.9408i | 0.225553 | + | 1.42408i | ||||
\(603\) | 12.3851 | + | 1.44213i | 0.504358 | + | 0.0587282i | ||||
\(604\) | 8.89300i | 0.361851i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.08285 | − | 8.74528i | 0.247099 | − | 0.355253i | ||||
\(607\) | −24.0781 | − | 12.2684i | −0.977300 | − | 0.497959i | −0.109023 | − | 0.994039i | \(-0.534772\pi\) |
−0.868277 | + | 0.496080i | \(0.834772\pi\) | |||||||
\(608\) | −9.04570 | + | 1.43270i | −0.366851 | + | 0.0581036i | ||||
\(609\) | 0.230786 | + | 11.2124i | 0.00935192 | + | 0.454351i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.35564 | + | 2.38999i | 0.297577 | + | 0.0966888i | ||||
\(612\) | −0.824498 | − | 4.10447i | −0.0333284 | − | 0.165913i | ||||
\(613\) | −5.08209 | − | 32.0871i | −0.205264 | − | 1.29598i | −0.848041 | − | 0.529931i | \(-0.822218\pi\) |
0.642777 | − | 0.766053i | \(-0.277782\pi\) | |||||||
\(614\) | 14.1258 | + | 43.4746i | 0.570070 | + | 1.75449i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.9077 | − | 28.2522i | 0.479776 | − | 1.13831i | ||||
\(617\) | 30.5732 | + | 30.5732i | 1.23083 | + | 1.23083i | 0.963645 | + | 0.267187i | \(0.0860943\pi\) |
0.267187 | + | 0.963645i | \(0.413906\pi\) | |||||||
\(618\) | −31.5937 | + | 16.9256i | −1.27089 | + | 0.680848i | ||||
\(619\) | 13.3478 | − | 18.3717i | 0.536494 | − | 0.738420i | −0.451609 | − | 0.892216i | \(-0.649150\pi\) |
0.988103 | + | 0.153796i | \(0.0491498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.0464 | + | 18.4779i | 1.16559 | + | 0.741493i | ||||
\(622\) | 6.78544 | + | 13.3172i | 0.272071 | + | 0.533970i | ||||
\(623\) | −4.13553 | + | 26.1107i | −0.165687 | + | 1.04610i | ||||
\(624\) | −4.36420 | − | 12.5470i | −0.174708 | − | 0.502281i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.3424i | 0.533271i | ||||||||
\(627\) | −24.4691 | + | 2.28057i | −0.977202 | + | 0.0910774i | ||||
\(628\) | 0.337716 | + | 0.337716i | 0.0134764 | + | 0.0134764i | ||||
\(629\) | 7.44659 | + | 22.9182i | 0.296915 | + | 0.913810i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.5129 | − | 23.6220i | 1.29432 | − | 0.940377i | 0.294435 | − | 0.955671i | \(-0.404869\pi\) |
0.999883 | + | 0.0152943i | \(0.00486851\pi\) | |||||||
\(632\) | −0.867341 | + | 0.441932i | −0.0345010 | + | 0.0175791i | ||||
\(633\) | 0.00627324 | − | 0.0456722i | 0.000249339 | − | 0.00181531i | ||||
\(634\) | 10.3032 | + | 14.1812i | 0.409194 | + | 0.563208i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.909806 | − | 3.00947i | 0.0360762 | − | 0.119333i | ||||
\(637\) | 7.88799 | − | 7.88799i | 0.312534 | − | 0.312534i | ||||
\(638\) | 2.14332 | − | 8.69039i | 0.0848549 | − | 0.344056i | ||||
\(639\) | 2.25869 | + | 6.08698i | 0.0893523 | + | 0.240797i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7028 | − | 27.1186i | 0.778214 | − | 1.07112i | −0.217263 | − | 0.976113i | \(-0.569713\pi\) |
0.995477 | − | 0.0950060i | \(-0.0302870\pi\) | |||||||
\(642\) | −17.2169 | − | 16.5224i | −0.679496 | − | 0.652088i | ||||
\(643\) | −26.3578 | + | 13.4300i | −1.03945 | + | 0.529627i | −0.888482 | − | 0.458911i | \(-0.848240\pi\) |
−0.150970 | + | 0.988538i | \(0.548240\pi\) | |||||||
\(644\) | 2.90761 | − | 8.94869i | 0.114576 | − | 0.352628i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.4464 | − | 14.1286i | −0.765107 | − | 0.555883i | ||||
\(647\) | −4.73092 | + | 9.28496i | −0.185992 | + | 0.365029i | −0.965109 | − | 0.261849i | \(-0.915668\pi\) |
0.779117 | + | 0.626878i | \(0.215668\pi\) | |||||||
\(648\) | −1.67764 | + | 22.3987i | −0.0659038 | + | 0.879906i | ||||
\(649\) | −21.1113 | + | 4.93044i | −0.828689 | + | 0.193537i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 57.6655 | + | 17.4331i | 2.26009 | + | 0.683259i | ||||
\(652\) | −0.735165 | + | 0.116439i | −0.0287913 | + | 0.00456009i | ||||
\(653\) | 5.01900 | − | 31.6887i | 0.196409 | − | 1.24008i | −0.670614 | − | 0.741807i | \(-0.733969\pi\) |
0.867022 | − | 0.498269i | \(-0.166031\pi\) | |||||||
\(654\) | −9.19863 | − | 12.1279i | −0.359695 | − | 0.474239i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.17089 | − | 1.61160i | −0.0457157 | − | 0.0629223i | ||||
\(657\) | 12.9858 | + | 23.0853i | 0.506624 | + | 0.900644i | ||||
\(658\) | −12.0942 | + | 23.7363i | −0.471482 | + | 0.925336i | ||||
\(659\) | −45.4746 | −1.77144 | −0.885720 | − | 0.464219i | \(-0.846335\pi\) | ||||
−0.885720 | + | 0.464219i | \(0.846335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8275 | 0.576721 | 0.288361 | − | 0.957522i | \(-0.406890\pi\) | ||||
0.288361 | + | 0.957522i | \(0.406890\pi\) | |||||||
\(662\) | −13.6930 | + | 26.8740i | −0.532193 | + | 1.04449i | ||||
\(663\) | 4.55826 | − | 9.42047i | 0.177028 | − | 0.365861i | ||||
\(664\) | 12.0208 | + | 16.5453i | 0.466499 | + | 0.642081i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.26186 | + | 30.6400i | 0.0488961 | + | 1.18727i | ||||
\(667\) | −1.81175 | + | 11.4389i | −0.0701511 | + | 0.442917i | ||||
\(668\) | −2.09818 | + | 0.332319i | −0.0811811 | + | 0.0128578i | ||||
\(669\) | −7.77981 | + | 25.7341i | −0.300785 | + | 0.994939i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.58944 | + | 1.83785i | −0.0613596 | + | 0.0709494i | ||||
\(672\) | 13.5183 | − | 2.42724i | 0.521478 | − | 0.0936329i | ||||
\(673\) | 2.68631 | − | 5.27218i | 0.103550 | − | 0.203227i | −0.833419 | − | 0.552642i | \(-0.813620\pi\) |
0.936968 | + | 0.349415i | \(0.113620\pi\) | |||||||
\(674\) | 6.06577 | + | 4.40704i | 0.233645 | + | 0.169753i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.21375 | − | 3.73555i | 0.0466828 | − | 0.143675i | ||||
\(677\) | −25.3440 | + | 12.9134i | −0.974048 | + | 0.496302i | −0.867193 | − | 0.497972i | \(-0.834078\pi\) |
−0.106855 | + | 0.994275i | \(0.534078\pi\) | |||||||
\(678\) | −4.44492 | + | 4.63174i | −0.170706 | + | 0.177881i | ||||
\(679\) | 6.22918 | − | 8.57373i | 0.239054 | − | 0.329030i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.8195 | − | 29.0879i | −1.60253 | − | 1.11465i | ||||
\(682\) | −40.8399 | − | 25.3755i | −1.56384 | − | 0.971680i | ||||
\(683\) | 16.2674 | − | 16.2674i | 0.622456 | − | 0.622456i | −0.323703 | − | 0.946159i | \(-0.604928\pi\) |
0.946159 | + | 0.323703i | \(0.104928\pi\) | |||||||
\(684\) | −3.05380 | − | 3.85871i | −0.116765 | − | 0.147541i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.943141 | − | 1.29812i | −0.0360093 | − | 0.0495625i | ||||
\(687\) | 31.6089 | + | 4.34159i | 1.20595 | + | 0.165642i | ||||
\(688\) | −25.4655 | + | 12.9753i | −0.970864 | + | 0.494680i | ||||
\(689\) | 6.35834 | − | 4.61960i | 0.242233 | − | 0.175993i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.31586 | − | 25.5936i | −0.316350 | − | 0.973626i | −0.975195 | − | 0.221347i | \(-0.928955\pi\) |
0.658845 | − | 0.752279i | \(-0.271045\pi\) | |||||||
\(692\) | −2.14631 | − | 2.14631i | −0.0815905 | − | 0.0815905i | ||||
\(693\) | 36.6169 | − | 4.17447i | 1.39096 | − | 0.158575i | ||||
\(694\) | 22.7038i | 0.861823i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.13708 | + | 2.48248i | −0.270530 | + | 0.0940983i | ||||
\(697\) | 0.245496 | − | 1.55000i | 0.00929884 | − | 0.0587106i | ||||
\(698\) | −13.9824 | − | 27.4420i | −0.529242 | − | 1.03870i | ||||
\(699\) | 9.39759 | + | 12.3902i | 0.355450 | + | 0.468641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.2185 | + | 30.5812i | −0.839182 | + | 1.15503i | 0.146962 | + | 0.989142i | \(0.453050\pi\) |
−0.986144 | + | 0.165892i | \(0.946950\pi\) | |||||||
\(702\) | 8.81815 | − | 9.98025i | 0.332820 | − | 0.376680i | ||||
\(703\) | 20.0289 | + | 20.0289i | 0.755406 | + | 0.755406i | ||||
\(704\) | 19.6122 | + | 1.66565i | 0.739162 | + | 0.0627765i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.39624 | + | 22.7633i | 0.278361 | + | 0.856707i | ||||
\(707\) | 2.30834 | + | 14.5743i | 0.0868140 | + | 0.548122i | ||||
\(708\) | −3.13211 | − | 3.00577i | −0.117712 | − | 0.112964i | ||||
\(709\) | −4.37228 | − | 1.42064i | −0.164204 | − | 0.0533532i | 0.225761 | − | 0.974183i | \(-0.427513\pi\) |
−0.389966 | + | 0.920829i | \(0.627513\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.974155 | − | 0.648249i | −0.0365337 | − | 0.0243112i | ||||
\(712\) | −17.5933 | + | 2.78650i | −0.659336 | + | 0.104429i | ||||
\(713\) | 55.4320 | + | 28.2440i | 2.07594 | + | 1.05775i | ||||
\(714\) | 29.5925 | + | 20.5833i | 1.10747 | + | 0.770312i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 5.03726i | − | 0.188251i | ||||||
\(717\) | −6.14759 | − | 11.4752i | −0.229586 | − | 0.428550i | ||||
\(718\) | 1.75541 | + | 11.0832i | 0.0655112 | + | 0.413622i | ||||
\(719\) | −20.4061 | + | 14.8259i | −0.761021 | + | 0.552914i | −0.899223 | − | 0.437490i | \(-0.855867\pi\) |
0.138203 | + | 0.990404i | \(0.455867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3419 | − | 47.2175i | 0.571362 | − | 1.75847i | ||||
\(722\) | 1.06564 | + | 0.168781i | 0.0396591 | + | 0.00628138i | ||||
\(723\) | −1.52521 | − | 0.738001i | −0.0567232 | − | 0.0274465i | ||||
\(724\) | 3.16502 | − | 1.02838i | 0.117627 | − | 0.0382193i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −29.0887 | − | 4.36276i | −1.07958 | − | 0.161917i | ||||
\(727\) | −35.0870 | + | 35.0870i | −1.30130 | + | 1.30130i | −0.373791 | + | 0.927513i | \(0.621942\pi\) |
−0.927513 | + | 0.373791i | \(0.878058\pi\) | |||||||
\(728\) | 13.6740 | + | 6.96725i | 0.506792 | + | 0.258223i | ||||
\(729\) | −24.4554 | + | 11.4427i | −0.905754 | + | 0.423803i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.4137 | − | 6.95774i | −0.792015 | − | 0.257341i | ||||
\(732\) | −0.482019 | − | 0.0662070i | −0.0178159 | − | 0.00244708i | ||||
\(733\) | 28.3260 | + | 4.48639i | 1.04624 | + | 0.165709i | 0.655813 | − | 0.754924i | \(-0.272326\pi\) |
0.390430 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(734\) | 14.8595 | + | 10.7961i | 0.548474 | + | 0.398490i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.1835 | 0.522811 | ||||||||
\(737\) | 12.7678 | − | 5.19629i | 0.470308 | − | 0.191408i | ||||
\(738\) | 0.832665 | − | 1.81521i | 0.0306508 | − | 0.0668187i | ||||
\(739\) | −27.7671 | + | 9.02207i | −1.02143 | + | 0.331882i | −0.771396 | − | 0.636356i | \(-0.780441\pi\) |
−0.250032 | + | 0.968238i | \(0.580441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.253144 | − | 12.2987i | −0.00929949 | − | 0.451804i | ||||
\(742\) | 12.2900 | + | 24.1204i | 0.451178 | + | 0.885487i | ||||
\(743\) | −12.1167 | − | 23.7803i | −0.444517 | − | 0.872414i | −0.999186 | − | 0.0403429i | \(-0.987155\pi\) |
0.554669 | − | 0.832071i | \(-0.312845\pi\) | |||||||
\(744\) | 0.835320 | + | 40.5829i | 0.0306243 | + | 1.48784i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19.0158 | + | 6.17862i | −0.696219 | + | 0.226215i | ||||
\(747\) | −10.2499 | + | 22.3447i | −0.375023 | + | 0.817548i | ||||
\(748\) | −2.98402 | − | 3.53792i | −0.109106 | − | 0.129359i | ||||
\(749\) | 33.0536 | 1.20775 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.06481 | − | 5.13289i | −0.257799 | − | 0.187302i | 0.451377 | − | 0.892333i | \(-0.350933\pi\) |
−0.709176 | + | 0.705031i | \(0.750933\pi\) | |||||||
\(752\) | −21.2574 | − | 3.36684i | −0.775177 | − | 0.122776i | ||||
\(753\) | 5.80007 | + | 0.796661i | 0.211366 | + | 0.0290319i | ||||
\(754\) | 4.26111 | + | 1.38452i | 0.155180 | + | 0.0504212i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.69774 | + | 5.69123i | 0.170855 | + | 0.206988i | ||||
\(757\) | 21.3923 | + | 10.8999i | 0.777516 | + | 0.396164i | 0.797256 | − | 0.603641i | \(-0.206284\pi\) |
−0.0197403 | + | 0.999805i | \(0.506284\pi\) | |||||||
\(758\) | 21.3518 | − | 21.3518i | 0.775532 | − | 0.775532i | ||||
\(759\) | 37.9808 | + | 2.43965i | 1.37861 | + | 0.0885539i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.7039 | + | 15.1750i | −1.69302 | + | 0.550094i | −0.987365 | − | 0.158465i | \(-0.949345\pi\) |
−0.705651 | + | 0.708559i | \(0.749345\pi\) | |||||||
\(762\) | −21.5073 | − | 10.4067i | −0.779128 | − | 0.376995i | ||||
\(763\) | 20.8252 | + | 3.29839i | 0.753924 | + | 0.119410i | ||||
\(764\) | 0.427666 | − | 1.31622i | 0.0154724 | − | 0.0476192i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.9103 | + | 10.8329i | −0.538730 | + | 0.391410i | ||||
\(767\) | −1.69759 | − | 10.7182i | −0.0612965 | − | 0.387011i | ||||
\(768\) | 7.26784 | + | 13.5663i | 0.262255 | + | 0.489532i | ||||
\(769\) | − | 17.8644i | − | 0.644206i | −0.946705 | − | 0.322103i | \(-0.895610\pi\) | ||
0.946705 | − | 0.322103i | \(-0.104390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.3236 | + | 12.7451i | 0.659907 | + | 0.459003i | ||||
\(772\) | 1.10335 | + | 0.562187i | 0.0397106 | + | 0.0202335i | ||||
\(773\) | −31.6740 | + | 5.01667i | −1.13923 | + | 0.180437i | −0.697416 | − | 0.716667i | \(-0.745667\pi\) |
−0.441819 | + | 0.897104i | \(0.645667\pi\) | |||||||
\(774\) | −23.8540 | − | 15.8736i | −0.857414 | − | 0.570564i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.79121 | + | 2.20660i | 0.243790 | + | 0.0792122i | ||||
\(777\) | −30.6481 | − | 29.4119i | −1.09949 | − | 1.05515i | ||||
\(778\) | 7.37469 | + | 46.5620i | 0.264395 | + | 1.66933i | ||||
\(779\) | −0.570024 | − | 1.75435i | −0.0204232 | − | 0.0628563i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.42907 | + | 4.69526i | 0.194268 | + | 0.168010i | ||||
\(782\) | 26.3225 | + | 26.3225i | 0.941292 | + | 0.941292i | ||||
\(783\) | −6.80696 | − | 6.01436i | −0.243261 | − | 0.214936i | ||||
\(784\) | −18.2464 | + | 25.1139i | −0.651655 | + | 0.896927i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.0923 | + | 27.8091i | 0.752338 | + | 0.991918i | ||||
\(787\) | −24.6498 | − | 48.3779i | −0.878670 | − | 1.72449i | −0.663898 | − | 0.747823i | \(-0.731099\pi\) |
−0.214772 | − | 0.976664i | \(-0.568901\pi\) | |||||||
\(788\) | −0.00447828 | + | 0.0282748i | −0.000159532 | + | 0.00100725i | ||||
\(789\) | 50.7918 | − | 17.6669i | 1.80824 | − | 0.628957i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.89219i | − | 0.316170i | ||||||
\(792\) | 10.2992 | + | 22.5956i | 0.365967 | + | 0.802898i | ||||
\(793\) | −0.860029 | − | 0.860029i | −0.0305405 | − | 0.0305405i | ||||
\(794\) | −17.6969 | − | 54.4654i | −0.628039 | − | 1.93291i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.51140 | + | 1.82464i | −0.0890143 | + | 0.0646727i | ||||
\(797\) | 23.6919 | − | 12.0716i | 0.839209 | − | 0.427598i | 0.0191081 | − | 0.999817i | \(-0.493917\pi\) |
0.820101 | + | 0.572219i | \(0.193917\pi\) | |||||||
\(798\) | 41.9768 | + | 5.76567i | 1.48596 | + | 0.204103i | ||||
\(799\) | −9.96604 | − | 13.7171i | −0.352573 | − | 0.485275i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.2877 | − | 16.7899i | −0.469496 | − | 0.593243i | ||||
\(802\) | 25.2780 | − | 25.2780i | 0.892597 | − | 0.892597i | ||||
\(803\) | 24.8723 | + | 15.4542i | 0.877725 | + | 0.545368i | ||||
\(804\) | 2.26599 | + | 1.57613i | 0.0799155 | + | 0.0555858i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.1465 | − | 19.4710i | 0.498290 | − | 0.685838i | ||||
\(807\) | 22.4285 | − | 23.3712i | 0.789522 | − | 0.822706i | ||||
\(808\) | −8.85883 | + | 4.51380i | −0.311653 | + | 0.158795i | ||||
\(809\) | −12.6304 | + | 38.8724i | −0.444062 | + | 1.36668i | 0.439447 | + | 0.898268i | \(0.355174\pi\) |
−0.883509 | + | 0.468414i | \(0.844826\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7291 | + | 31.7710i | 1.53553 | + | 1.11563i | 0.953060 | + | 0.302783i | \(0.0979156\pi\) |
0.582475 | + | 0.812849i | \(0.302084\pi\) | |||||||
\(812\) | −1.12710 | + | 2.21206i | −0.0395535 | + | 0.0776282i | ||||
\(813\) | −29.2658 | + | 5.25476i | −1.02640 | + | 0.184293i | ||||
\(814\) | 17.5348 | + | 29.0156i | 0.614596 | + | 1.01700i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.42747 | + | 27.8765i | −0.295020 | + | 0.975871i | ||||
\(817\) | −26.1399 | + | 4.14015i | −0.914519 | + | 0.144846i | ||||
\(818\) | −4.19364 | + | 26.4776i | −0.146627 | + | 0.925767i | ||||
\(819\) | 0.759093 | + | 18.4320i | 0.0265249 | + | 0.644066i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7382 | + | 34.0493i | 0.863370 | + | 1.18833i | 0.980755 | + | 0.195241i | \(0.0625489\pi\) |
−0.117385 | + | 0.993086i | \(0.537451\pi\) | |||||||
\(822\) | 15.3324 | − | 31.6872i | 0.534780 | − | 1.10522i | ||||
\(823\) | 22.9322 | − | 45.0071i | 0.799368 | − | 1.56885i | −0.0228939 | − | 0.999738i | \(-0.507288\pi\) |
0.822262 | − | 0.569110i | \(-0.192712\pi\) | |||||||
\(824\) | 33.4522 | 1.16536 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.3782 | 1.30055 | ||||||||
\(827\) | 13.5041 | − | 26.5034i | 0.469585 | − | 0.921612i | −0.527802 | − | 0.849367i | \(-0.676984\pi\) |
0.997387 | − | 0.0722447i | \(-0.0230163\pi\) | |||||||
\(828\) | 3.73630 | + | 6.64216i | 0.129845 | + | 0.230831i | ||||
\(829\) | 30.5404 | + | 42.0353i | 1.06071 | + | 1.45995i | 0.879137 | + | 0.476569i | \(0.158120\pi\) |
0.181576 | + | 0.983377i | \(0.441880\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.3662 | − | 29.4886i | −0.775873 | − | 1.02295i | ||||
\(832\) | −1.54125 | + | 9.73109i | −0.0534333 | + | 0.337365i | ||||
\(833\) | −24.1541 | + | 3.82564i | −0.836891 | + | 0.132550i | ||||
\(834\) | −54.7786 | − | 16.5604i | −1.89683 | − | 0.573440i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.01318 | − | 2.11295i | −0.173384 | − | 0.0730780i | ||||
\(837\) | −42.0256 | + | 24.7920i | −1.45262 | + | 0.856936i | ||||
\(838\) | 26.4302 | − | 51.8723i | 0.913017 | − | 1.79190i | ||||
\(839\) | 2.72208 | + | 1.97771i | 0.0939767 | + | 0.0682780i | 0.633781 | − | 0.773512i | \(-0.281502\pi\) |
−0.539805 | + | 0.841790i | \(0.681502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.01719 | + | 24.6744i | −0.276455 | + | 0.850841i | ||||
\(842\) | 17.0525 | − | 8.68867i | 0.587667 | − | 0.299431i | ||||
\(843\) | 13.9009 | + | 13.3402i | 0.478772 | + | 0.459461i | ||||
\(844\) | 0.00599864 | − | 0.00825642i | 0.000206482 | − | 0.000284198i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.50632 | − | 20.2289i | −0.258073 | − | 0.695485i | ||||
\(847\) | 33.2561 | − | 23.5389i | 1.14269 | − | 0.808806i | ||||
\(848\) | −15.4649 | + | 15.4649i | −0.531066 | + | 0.531066i | ||||
\(849\) | 7.53119 | − | 24.9118i | 0.258470 | − | 0.854969i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7842 | − | 35.4889i | −0.883870 | − | 1.21654i | ||||
\(852\) | −0.195578 | + | 1.42390i | −0.00670039 | + | 0.0487821i | ||||
\(853\) | −19.3290 | + | 9.84864i | −0.661814 | + | 0.337211i | −0.752427 | − | 0.658675i | \(-0.771117\pi\) |
0.0906137 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(854\) | 3.38925 | − | 2.46243i | 0.115978 | − | 0.0842627i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.88224 | + | 21.1814i | 0.235230 | + | 0.723964i | ||||
\(857\) | 17.5697 | + | 17.5697i | 0.600170 | + | 0.600170i | 0.940358 | − | 0.340188i | \(-0.110491\pi\) |
−0.340188 | + | 0.940358i | \(0.610491\pi\) | |||||||
\(858\) | 3.23070 | − | 14.3646i | 0.110294 | − | 0.490400i | ||||
\(859\) | 34.1503i | 1.16519i | 0.812761 | + | 0.582597i | \(0.197963\pi\) | ||||
−0.812761 | + | 0.582597i | \(0.802037\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.908795 | + | 2.61276i | 0.0309716 | + | 0.0890427i | ||||
\(862\) | −8.22976 | + | 51.9607i | −0.280307 | + | 1.76979i | ||||
\(863\) | 13.5462 | + | 26.5858i | 0.461117 | + | 0.904993i | 0.998113 | + | 0.0614078i | \(0.0195590\pi\) |
−0.536996 | + | 0.843585i | \(0.680441\pi\) | |||||||
\(864\) | −5.97084 | + | 9.38588i | −0.203132 | + | 0.319314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.7834 | − | 24.4767i | 0.604304 | − | 0.831753i | ||||
\(867\) | 5.73160 | − | 3.07057i | 0.194655 | − | 0.104282i | ||||
\(868\) | 9.43010 | + | 9.43010i | 0.320078 | + | 0.320078i | ||||
\(869\) | −1.28899 | − | 0.109473i | −0.0437259 | − | 0.00371361i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.13223 | + | 6.56234i | 0.0722480 | + | 0.222356i | ||||
\(872\) | 2.22244 | + | 14.0319i | 0.0752614 | + | 0.475182i | ||||
\(873\) | 1.69047 | + | 8.41542i | 0.0572139 | + | 0.284819i | ||||
\(874\) | 41.6147 | + | 13.5214i | 1.40764 | + | 0.457370i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.120663 | + | 5.86227i | 0.00407683 | + | 0.198068i | ||||
\(877\) | −0.0783107 | + | 0.0124032i | −0.00264436 | + | 0.000418826i | −0.157757 | − | 0.987478i | \(-0.550426\pi\) |
0.155112 | + | 0.987897i | \(0.450426\pi\) | |||||||
\(878\) | 0.720768 | + | 0.367250i | 0.0243247 | + | 0.0123941i | ||||
\(879\) | 1.33144 | − | 1.91420i | 0.0449083 | − | 0.0645644i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.89291i | 0.265919i | 0.991121 | + | 0.132959i | \(0.0424480\pi\) | ||||
−0.991121 | + | 0.132959i | \(0.957552\pi\) | |||||||
\(882\) | −30.9121 | − | 3.59945i | −1.04086 | − | 0.121200i | ||||
\(883\) | 1.29416 | + | 8.17100i | 0.0435519 | + | 0.274976i | 0.999848 | − | 0.0174235i | \(-0.00554635\pi\) |
−0.956296 | + | 0.292399i | \(0.905546\pi\) | |||||||
\(884\) | 1.87428 | − | 1.36174i | 0.0630389 | − | 0.0458004i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0124 | − | 40.0481i | 0.437161 | − | 1.34544i | ||||
\(887\) | −28.4115 | − | 4.49994i | −0.953964 | − | 0.151093i | −0.339999 | − | 0.940426i | \(-0.610427\pi\) |
−0.613965 | + | 0.789333i | \(0.710427\pi\) | |||||||
\(888\) | 12.4663 | − | 25.7638i | 0.418341 | − | 0.864577i | ||||
\(889\) | 31.4759 | − | 10.2271i | 1.05567 | − | 0.343007i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.6032 | + | 24.1066i | −0.589730 | + | 0.807601i | ||||
\(892\) | −4.20833 | + | 4.20833i | −0.140905 | + | 0.140905i | ||||
\(893\) | −17.7575 | − | 9.04792i | −0.594234 | − | 0.302777i | ||||
\(894\) | 6.02876 | + | 17.3325i | 0.201632 | + | 0.579687i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −47.3579 | − | 15.3875i | −1.58212 | − | 0.514061i | ||||
\(897\) | −2.59235 | + | 18.8736i | −0.0865561 | + | 0.630170i | ||||
\(898\) | −18.8768 | − | 2.98979i | −0.629927 | − | 0.0997706i | ||||
\(899\) | −13.2801 | − | 9.64854i | −0.442915 | − | 0.321797i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.2296 | −0.574002 | ||||||||
\(902\) | −0.159607 | − | 2.20207i | −0.00531432 | − | 0.0733210i | ||||
\(903\) | 39.0646 | − | 7.01415i | 1.29999 | − | 0.233416i | ||||
\(904\) | 5.69828 | − | 1.85148i | 0.189522 | − | 0.0615794i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 62.0059 | − | 1.27627i | 2.06001 | − | 0.0424012i | ||||
\(907\) | 23.5265 | + | 46.1733i | 0.781184 | + | 1.53316i | 0.844737 | + | 0.535182i | \(0.179757\pi\) |
−0.0635524 | + | 0.997979i | \(0.520243\pi\) | |||||||
\(908\) | −5.11962 | − | 10.0478i | −0.169901 | − | 0.333449i | ||||
\(909\) | −9.94981 | − | 6.62108i | −0.330014 | − | 0.219607i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.84031 | + | 3.19731i | −0.326024 | + | 0.105932i | −0.467456 | − | 0.884016i | \(-0.654829\pi\) |
0.141432 | + | 0.989948i | \(0.454829\pi\) | |||||||
\(912\) | 6.04963 | + | 33.6928i | 0.200323 | + | 1.11568i | ||||
\(913\) | 1.96471 | + | 27.1069i | 0.0650224 | + | 0.897106i | ||||
\(914\) | −54.6145 | −1.80649 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.71412 | + | 4.15155i | 0.188800 | + | 0.137171i | ||||
\(917\) | −47.7519 | − | 7.56316i | −1.57691 | − | 0.249758i | ||||
\(918\) | −28.4998 | + | 6.33781i | −0.940635 | + | 0.209179i | ||||
\(919\) | −17.3422 | − | 5.63482i | −0.572066 | − | 0.185875i | 0.00867718 | − | 0.999962i | \(-0.497238\pi\) |
−0.580743 | + | 0.814087i | \(0.697238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.4384 | − | 16.8483i | 1.59610 | − | 0.555169i | ||||
\(922\) | 24.1824 | + | 12.3215i | 0.796403 | + | 0.405788i | ||||
\(923\) | −2.54056 | + | 2.54056i | −0.0836235 | + | 0.0836235i | ||||
\(924\) | 7.58161 | + | 3.01330i | 0.249417 | + | 0.0991304i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 56.1133 | − | 18.2323i | 1.84400 | − | 0.599151i | ||||
\(927\) | 19.7145 | + | 35.0471i | 0.647508 | + | 1.15110i | ||||
\(928\) | −3.69630 | − | 0.585436i | −0.121337 | − | 0.0192179i | ||||
\(929\) | −7.75215 | + | 23.8587i | −0.254340 | + | 0.782778i | 0.739619 | + | 0.673026i | \(0.235006\pi\) |
−0.993959 | + | 0.109752i | \(0.964994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.2556 | + | 16.8962i | −0.762171 | + | 0.553749i | ||||
\(932\) | 0.538535 | + | 3.40018i | 0.0176403 | + | 0.111376i | ||||
\(933\) | 14.7809 | − | 7.91853i | 0.483905 | − | 0.259241i | ||||
\(934\) | − | 28.9299i | − | 0.946617i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.6535 | + | 4.32424i | −0.380906 | + | 0.141342i | ||||
\(937\) | 25.8064 | + | 13.1490i | 0.843059 | + | 0.429560i | 0.821501 | − | 0.570207i | \(-0.193137\pi\) |
0.0215586 | + | 0.999768i | \(0.493137\pi\) | |||||||
\(938\) | −23.4741 | + | 3.71794i | −0.766458 | + | 0.121395i | ||||
\(939\) | 14.9659 | − | 0.308043i | 0.488393 | − | 0.0100526i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5051 | − | 4.38806i | −0.440253 | − | 0.143047i | 0.0804995 | − | 0.996755i | \(-0.474348\pi\) |
−0.520752 | + | 0.853708i | \(0.674348\pi\) | |||||||
\(942\) | 2.30624 | − | 2.40317i | 0.0751414 | − | 0.0782997i | ||||
\(943\) | 0.446895 | + | 2.82158i | 0.0145529 | + | 0.0918833i | ||||
\(944\) | 9.33167 | + | 28.7199i | 0.303720 | + | 0.934754i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.5632 | − | 2.68064i | −1.02621 | − | 0.0871553i | ||||
\(947\) | −34.5217 | − | 34.5217i | −1.12180 | − | 1.12180i | −0.991470 | − | 0.130335i | \(-0.958395\pi\) |
−0.130335 | − | 0.991470i | \(-0.541605\pi\) | |||||||
\(948\) | −0.122324 | − | 0.228333i | −0.00397290 | − | 0.00741591i | ||||
\(949\) | −8.61553 | + | 11.8583i | −0.279672 | + | 0.384935i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6688 | − | 11.8843i | 0.508097 | − | 0.385375i | ||||
\(952\) | −15.2739 | − | 29.9768i | −0.495031 | − | 0.971553i | ||||
\(953\) | −1.23001 | + | 7.76600i | −0.0398441 | + | 0.251566i | −0.999568 | − | 0.0293780i | \(-0.990647\pi\) |
0.959724 | + | 0.280943i | \(0.0906474\pi\) | |||||||
\(954\) | −21.1139 | − | 5.91167i | −0.683588 | − | 0.191397i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.88188i | − | 0.0932066i | ||||||
\(957\) | −9.79729 | − | 2.20347i | −0.316701 | − | 0.0712282i | ||||
\(958\) | 0.584081 | + | 0.584081i | 0.0188708 | + | 0.0188708i | ||||
\(959\) | 15.0679 | + | 46.3742i | 0.486568 | + | 1.49750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −46.2576 | + | 33.6081i | −1.49218 | + | 1.08413i | ||||
\(962\) | −15.1205 | + | 7.70430i | −0.487506 | + | 0.248397i | ||||
\(963\) | −18.1353 | + | 19.6932i | −0.584403 | + | 0.634606i | ||||
\(964\) | −0.220472 | − | 0.303453i | −0.00710092 | − | 0.00977358i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −62.8115 | − | 18.9888i | −2.02093 | − | 0.610956i | ||||
\(967\) | −3.31505 | + | 3.31505i | −0.106605 | + | 0.106605i | −0.758397 | − | 0.651793i | \(-0.774017\pi\) |
0.651793 | + | 0.758397i | \(0.274017\pi\) | |||||||
\(968\) | 22.0085 | + | 16.4100i | 0.707381 | + | 0.527436i | ||||
\(969\) | −15.3988 | + | 22.1387i | −0.494680 | + | 0.711199i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.7368 | − | 24.4126i | 0.569201 | − | 0.783438i | −0.423259 | − | 0.906009i | \(-0.639114\pi\) |
0.992460 | + | 0.122571i | \(0.0391138\pi\) | |||||||
\(972\) | −5.96830 | − | 0.323673i | −0.191433 | − | 0.0103818i | ||||
\(973\) | 70.6299 | − | 35.9878i | 2.26429 | − | 1.15371i | ||||
\(974\) | 0.416366 | − | 1.28144i | 0.0133412 | − | 0.0410601i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.73818 | + | 1.98940i | 0.0876469 | + | 0.0636792i | ||||
\(977\) | 5.18956 | − | 10.1851i | 0.166029 | − | 0.325850i | −0.792970 | − | 0.609261i | \(-0.791466\pi\) |
0.958998 | + | 0.283411i | \(0.0914662\pi\) | |||||||
\(978\) | 0.917368 | + | 5.10918i | 0.0293342 | + | 0.163374i | ||||
\(979\) | −21.8132 | − | 9.19384i | −0.697154 | − | 0.293836i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.3912 | + | 10.5979i | −0.427549 | + | 0.338365i | ||||
\(982\) | 14.2301 | − | 2.25383i | 0.454102 | − | 0.0719226i | ||||
\(983\) | 2.28158 | − | 14.4053i | 0.0727711 | − | 0.459459i | −0.924215 | − | 0.381873i | \(-0.875279\pi\) |
0.996986 | − | 0.0775852i | \(-0.0247210\pi\) | |||||||
\(984\) | −1.48508 | + | 1.12639i | −0.0473427 | + | 0.0359079i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.77331 | − | 7.94628i | −0.183860 | − | 0.253061i | ||||
\(987\) | 26.9036 | + | 13.0178i | 0.856352 | + | 0.414361i | ||||
\(988\) | 1.23629 | − | 2.42636i | 0.0393318 | − | 0.0771929i | ||||
\(989\) | 40.9869 | 1.30331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.0270 | −1.55739 | −0.778697 | − | 0.627401i | \(-0.784119\pi\) | ||||
−0.778697 | + | 0.627401i | \(0.784119\pi\) | |||||||
\(992\) | −9.12659 | + | 17.9119i | −0.289770 | + | 0.568705i | ||||
\(993\) | 30.4601 | + | 14.7386i | 0.966621 | + | 0.467717i | ||||
\(994\) | −7.27412 | − | 10.0120i | −0.230721 | − | 0.317560i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.33599 | + | 3.28871i | −0.137391 | + | 0.104207i | ||||
\(997\) | 7.37196 | − | 46.5447i | 0.233472 | − | 1.47409i | −0.540756 | − | 0.841179i | \(-0.681862\pi\) |
0.774228 | − | 0.632906i | \(-0.218138\pi\) | |||||||
\(998\) | 6.57525 | − | 1.04142i | 0.208136 | − | 0.0329655i | ||||
\(999\) | 34.3390 | − | 2.12280i | 1.08644 | − | 0.0671624i |
(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 | 825.2.ct.b.368.16 | 160 | ||
3.2 | odd | 2 | inner | 825.2.ct.b.368.5 | 160 | ||
5.2 | odd | 4 | inner | 825.2.ct.b.632.16 | 160 | ||
5.3 | odd | 4 | 165.2.v.a.137.5 | yes | 160 | ||
5.4 | even | 2 | 165.2.v.a.38.5 | ✓ | 160 | ||
11.9 | even | 5 | inner | 825.2.ct.b.218.5 | 160 | ||
15.2 | even | 4 | inner | 825.2.ct.b.632.5 | 160 | ||
15.8 | even | 4 | 165.2.v.a.137.16 | yes | 160 | ||
15.14 | odd | 2 | 165.2.v.a.38.16 | yes | 160 | ||
33.20 | odd | 10 | inner | 825.2.ct.b.218.16 | 160 | ||
55.9 | even | 10 | 165.2.v.a.53.16 | yes | 160 | ||
55.42 | odd | 20 | inner | 825.2.ct.b.482.5 | 160 | ||
55.53 | odd | 20 | 165.2.v.a.152.16 | yes | 160 | ||
165.53 | even | 20 | 165.2.v.a.152.5 | yes | 160 | ||
165.119 | odd | 10 | 165.2.v.a.53.5 | yes | 160 | ||
165.152 | even | 20 | inner | 825.2.ct.b.482.16 | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.v.a.38.5 | ✓ | 160 | 5.4 | even | 2 | ||
165.2.v.a.38.16 | yes | 160 | 15.14 | odd | 2 | ||
165.2.v.a.53.5 | yes | 160 | 165.119 | odd | 10 | ||
165.2.v.a.53.16 | yes | 160 | 55.9 | even | 10 | ||
165.2.v.a.137.5 | yes | 160 | 5.3 | odd | 4 | ||
165.2.v.a.137.16 | yes | 160 | 15.8 | even | 4 | ||
165.2.v.a.152.5 | yes | 160 | 165.53 | even | 20 | ||
165.2.v.a.152.16 | yes | 160 | 55.53 | odd | 20 | ||
825.2.ct.b.218.5 | 160 | 11.9 | even | 5 | inner | ||
825.2.ct.b.218.16 | 160 | 33.20 | odd | 10 | inner | ||
825.2.ct.b.368.5 | 160 | 3.2 | odd | 2 | inner | ||
825.2.ct.b.368.16 | 160 | 1.1 | even | 1 | trivial | ||
825.2.ct.b.482.5 | 160 | 55.42 | odd | 20 | inner | ||
825.2.ct.b.482.16 | 160 | 165.152 | even | 20 | inner | ||
825.2.ct.b.632.5 | 160 | 15.2 | even | 4 | inner | ||
825.2.ct.b.632.16 | 160 | 5.2 | odd | 4 | inner |