Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.17 | ||
Character | \(\chi\) | \(=\) | 684.353 |
Dual form | 684.3.m.a.653.17 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.06149 | + | 2.80593i | −0.353829 | + | 0.935310i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.84834i | − | 0.369668i | −0.982770 | − | 0.184834i | \(-0.940825\pi\) | ||
0.982770 | − | 0.184834i | \(-0.0591748\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46982 | − | 4.27785i | 0.352831 | − | 0.611121i | −0.633913 | − | 0.773404i | \(-0.718552\pi\) |
0.986744 | + | 0.162283i | \(0.0518858\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.74649 | − | 5.95692i | −0.749610 | − | 0.661880i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.4350 | − | 6.02464i | −0.948635 | − | 0.547694i | −0.0559781 | − | 0.998432i | \(-0.517828\pi\) |
−0.892657 | + | 0.450738i | \(0.851161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.11176 | + | 8.85383i | −0.393212 | + | 0.681064i | −0.992871 | − | 0.119192i | \(-0.961970\pi\) |
0.599659 | + | 0.800256i | \(0.295303\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.18632 | + | 1.96199i | 0.345755 | + | 0.130799i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.2730 | + | 9.39522i | 0.957235 | + | 0.552660i | 0.895321 | − | 0.445422i | \(-0.146946\pi\) |
0.0619139 | + | 0.998081i | \(0.480280\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.26716 | + | 17.1071i | 0.435114 | + | 0.900375i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.38166 | + | 11.4710i | 0.446746 | + | 0.546239i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.3016 | + | 9.41172i | 0.708764 | + | 0.409205i | 0.810603 | − | 0.585596i | \(-0.199139\pi\) |
−0.101839 | + | 0.994801i | \(0.532473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.5836 | 0.863345 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 23.8760 | − | 12.6070i | 0.884296 | − | 0.466926i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.70293i | − | 0.162170i | −0.996707 | − | 0.0810850i | \(-0.974161\pi\) | ||
0.996707 | − | 0.0810850i | \(-0.0258385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.2830 | + | 24.7388i | 0.460740 | + | 0.798026i | 0.998998 | − | 0.0447545i | \(-0.0142506\pi\) |
−0.538258 | + | 0.842780i | \(0.680917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 27.9813 | − | 22.8848i | 0.847919 | − | 0.693477i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.90692 | − | 4.56506i | −0.225912 | − | 0.130430i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −52.8630 | −1.42873 | −0.714365 | − | 0.699773i | \(-0.753285\pi\) | ||||
−0.714365 | + | 0.699773i | \(0.753285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.4172 | − | 23.7415i | −0.497876 | − | 0.608755i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.43066i | 0.181236i | 0.995886 | + | 0.0906178i | \(0.0288842\pi\) | ||||
−0.995886 | + | 0.0906178i | \(0.971116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.6996 | + | 35.8527i | 0.481385 | + | 0.833784i | 0.999772 | − | 0.0213626i | \(-0.00680046\pi\) |
−0.518386 | + | 0.855146i | \(0.673467\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.0104 | + | 12.4698i | −0.244676 | + | 0.277107i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.31930i | 0.0919000i | 0.998944 | + | 0.0459500i | \(0.0146315\pi\) | ||||
−0.998944 | + | 0.0459500i | \(0.985369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.3000 | + | 21.3043i | 0.251021 | + | 0.434781i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −43.6359 | + | 35.6880i | −0.855606 | + | 0.699764i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 41.4703 | − | 23.9429i | 0.782459 | − | 0.451753i | −0.0548421 | − | 0.998495i | \(-0.517466\pi\) |
0.837301 | + | 0.546742i | \(0.184132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1356 | + | 19.2874i | −0.202465 | + | 0.350680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −56.7769 | + | 5.03809i | −0.996086 | + | 0.0883876i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50.8643i | 0.862107i | 0.902326 | + | 0.431053i | \(0.141858\pi\) | ||||
−0.902326 | + | 0.431053i | \(0.858142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.0213 | 0.377399 | 0.188699 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188699 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −42.1454 | + | 14.1480i | −0.668974 | + | 0.224571i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.3649 | + | 9.44828i | 0.251768 | + | 0.145358i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −19.3966 | + | 33.5959i | −0.289502 | + | 0.501432i | −0.973691 | − | 0.227873i | \(-0.926823\pi\) |
0.684189 | + | 0.729305i | \(0.260156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −43.7125 | + | 35.7507i | −0.633515 | + | 0.518126i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 95.0990 | + | 54.9054i | 1.33942 | + | 0.773316i | 0.986722 | − | 0.162420i | \(-0.0519301\pi\) |
0.352701 | + | 0.935736i | \(0.385263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5505 | − | 20.0061i | 0.158226 | − | 0.274056i | −0.776003 | − | 0.630730i | \(-0.782756\pi\) |
0.934229 | + | 0.356673i | \(0.116089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −22.9107 | + | 60.5622i | −0.305477 | + | 0.807496i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −51.5450 | + | 29.7595i | −0.669415 | + | 0.386487i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.5143 | + | 129.062i | 0.943218 | + | 1.63370i | 0.759280 | + | 0.650764i | \(0.225551\pi\) |
0.183939 | + | 0.982938i | \(0.441115\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.0303 | + | 80.3766i | 0.123831 | + | 0.992303i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −64.2549 | − | 37.0976i | −0.774156 | − | 0.446959i | 0.0601995 | − | 0.998186i | \(-0.480826\pi\) |
−0.834355 | + | 0.551227i | \(0.814160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3656 | − | 30.0781i | 0.204301 | − | 0.353859i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.1961 | + | 4.99210i | 0.151679 | + | 0.0573805i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.22299 | + | 5.32490i | −0.103629 | + | 0.0598303i | −0.550919 | − | 0.834559i | \(-0.685723\pi\) |
0.447290 | + | 0.894389i | \(0.352389\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.2502 | + | 43.7346i | 0.277475 | + | 0.480601i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −84.5765 | + | 13.8171i | −0.909425 | + | 0.148571i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 31.6198 | − | 15.2805i | 0.332840 | − | 0.160848i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −50.3430 | − | 87.1966i | −0.519000 | − | 0.898934i | −0.999756 | − | 0.0220799i | \(-0.992971\pi\) |
0.480756 | − | 0.876854i | \(-0.340362\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 34.5112 | + | 102.805i | 0.348598 | + | 1.03844i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 147.156i | − | 1.45699i | −0.685052 | − | 0.728495i | \(-0.740220\pi\) | ||
0.685052 | − | 0.728495i | \(-0.259780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −28.4113 | − | 49.2098i | −0.275838 | − | 0.477765i | 0.694509 | − | 0.719484i | \(-0.255622\pi\) |
−0.970346 | + | 0.241720i | \(0.922289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.2023 | − | 17.3405i | 0.201927 | − | 0.165148i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 62.5758i | 0.584821i | 0.956293 | + | 0.292410i | \(0.0944573\pi\) | ||||
−0.956293 | + | 0.292410i | \(0.905543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −32.2512 | + | 55.8606i | −0.295882 | + | 0.512483i | −0.975190 | − | 0.221371i | \(-0.928947\pi\) |
0.679308 | + | 0.733854i | \(0.262280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 56.1134 | − | 148.330i | 0.505526 | − | 1.33631i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −110.388 | + | 63.7326i | −0.976885 | + | 0.564005i | −0.901328 | − | 0.433137i | \(-0.857407\pi\) |
−0.0755570 | + | 0.997141i | \(0.524073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.3961 | − | 30.1309i | 0.151270 | − | 0.262008i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 87.2280 | − | 29.2819i | 0.745538 | − | 0.250273i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 80.3826 | − | 46.4089i | 0.675484 | − | 0.389991i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.0925 | + | 20.9449i | 0.0999384 | + | 0.173098i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.8499 | − | 7.88754i | −0.169511 | − | 0.0641264i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 86.1025i | − | 0.688820i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118.378 | + | 205.036i | 0.932109 | + | 1.61446i | 0.779710 | + | 0.626141i | \(0.215367\pi\) |
0.152399 | + | 0.988319i | \(0.451300\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −122.573 | + | 20.0244i | −0.950175 | + | 0.155228i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 251.709i | − | 1.92144i | −0.277521 | − | 0.960720i | \(-0.589513\pi\) | ||
0.277521 | − | 0.960720i | \(-0.410487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 93.6001 | + | 6.88581i | 0.703760 | + | 0.0517730i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.3020 | − | 44.1310i | −0.172608 | − | 0.326896i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.26681i | 0.0384439i | 0.999815 | + | 0.0192219i | \(0.00611891\pi\) | ||||
−0.999815 | + | 0.0192219i | \(0.993881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −81.3395 | + | 140.884i | −0.585176 | + | 1.01355i | 0.409677 | + | 0.912230i | \(0.365641\pi\) |
−0.994853 | + | 0.101324i | \(0.967692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1197 | − | 4.58488i | −0.0859550 | − | 0.0325169i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 106.682 | − | 61.5930i | 0.746030 | − | 0.430720i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.69263 | −0.0599492 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −72.8346 | + | 11.8988i | −0.495473 | + | 0.0809443i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 71.4060i | − | 0.479235i | −0.970867 | − | 0.239617i | \(-0.922978\pi\) | ||
0.970867 | − | 0.239617i | \(-0.0770220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.78566 | − | 13.4852i | 0.0515607 | − | 0.0893057i | −0.839093 | − | 0.543988i | \(-0.816914\pi\) |
0.890654 | + | 0.454682i | \(0.150247\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −53.8191 | − | 160.322i | −0.351759 | − | 1.04785i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 45.7258 | − | 26.3998i | 0.295005 | − | 0.170321i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −149.220 | −0.950445 | −0.475223 | − | 0.879866i | \(-0.657633\pi\) | ||||
−0.475223 | + | 0.879866i | \(0.657633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.1619 | + | 141.778i | 0.145672 | + | 0.891685i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 80.5238 | − | 46.4904i | 0.500148 | − | 0.288760i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 157.638 | 0.967101 | 0.483551 | − | 0.875316i | \(-0.339347\pi\) | ||||
0.483551 | + | 0.875316i | \(0.339347\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −42.2989 | − | 51.7190i | −0.256357 | − | 0.313449i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 213.793 | + | 123.433i | 1.28020 | + | 0.739123i | 0.976884 | − | 0.213768i | \(-0.0685738\pi\) |
0.303313 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.2398 | + | 55.8410i | 0.190768 | + | 0.330420i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.1314 | − | 164.660i | 0.269774 | − | 0.962924i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 90.5755 | − | 52.2938i | 0.523558 | − | 0.302276i | −0.214831 | − | 0.976651i | \(-0.568920\pi\) |
0.738389 | + | 0.674375i | \(0.235587\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53.3076 | − | 92.3315i | 0.304615 | − | 0.527608i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −142.722 | − | 53.9918i | −0.806337 | − | 0.305038i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 238.780i | − | 1.33397i | −0.745072 | − | 0.666985i | \(-0.767585\pi\) | ||
0.745072 | − | 0.666985i | \(-0.232415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 108.062 | + | 187.169i | 0.597029 | + | 1.03408i | 0.993257 | + | 0.115933i | \(0.0369857\pi\) |
−0.396228 | + | 0.918152i | \(0.629681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.4368 | + | 64.5963i | −0.133535 | + | 0.352985i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 97.7090i | 0.528157i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −113.206 | − | 196.078i | −0.605377 | − | 1.04854i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.03853 | − | 133.275i | 0.0266589 | − | 0.705158i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 150.835 | + | 87.0849i | 0.789714 | + | 0.455942i | 0.839862 | − | 0.542800i | \(-0.182636\pi\) |
−0.0501477 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −43.1000 | −0.223316 | −0.111658 | − | 0.993747i | \(-0.535616\pi\) | ||||
−0.111658 | + | 0.993747i | \(0.535616\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −43.8823 | + | 35.8895i | −0.225038 | + | 0.184049i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 229.707i | − | 1.16603i | −0.812463 | − | 0.583013i | \(-0.801874\pi\) | ||
0.812463 | − | 0.583013i | \(-0.198126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −32.8318 | − | 56.8663i | −0.164984 | − | 0.285760i | 0.771666 | − | 0.636028i | \(-0.219424\pi\) |
−0.936650 | + | 0.350268i | \(0.886090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −73.6786 | − | 90.0872i | −0.366560 | − | 0.448195i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.1184 | − | 11.6154i | −0.0991055 | − | 0.0572186i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7344 | 0.0669970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −53.9136 | − | 160.603i | −0.260452 | − | 0.775861i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.7966 | − | 228.319i | 0.0803666 | − | 1.09244i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −154.549 | −0.732460 | −0.366230 | − | 0.930524i | \(-0.619352\pi\) | ||||
−0.366230 | + | 0.930524i | \(0.619352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −255.007 | + | 208.560i | −1.19722 | + | 0.979154i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 66.2681 | − | 38.2599i | 0.308224 | − | 0.177953i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 141.105 | 0.650254 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 43.8750 | + | 53.6462i | 0.200342 | + | 0.244960i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −166.367 | + | 96.0522i | −0.752793 | + | 0.434625i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −65.4369 | − | 113.340i | −0.293439 | − | 0.508251i | 0.681182 | − | 0.732115i | \(-0.261466\pi\) |
−0.974621 | + | 0.223863i | \(0.928133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −145.614 | − | 128.572i | −0.647172 | − | 0.571431i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 140.131 | + | 80.9047i | 0.617318 | + | 0.356409i | 0.775824 | − | 0.630949i | \(-0.217334\pi\) |
−0.158506 | + | 0.987358i | \(0.550668\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 168.547 | + | 291.933i | 0.736015 | + | 1.27482i | 0.954277 | + | 0.298925i | \(0.0966280\pi\) |
−0.218262 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.7888 | − | 176.221i | −0.124627 | − | 0.762861i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.44103 | − | 4.29608i | −0.0319357 | − | 0.0184381i | 0.483947 | − | 0.875097i | \(-0.339203\pi\) |
−0.515883 | + | 0.856659i | \(0.672536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.98355 | 0.0339725 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −441.236 | + | 72.0837i | −1.86176 | + | 0.304151i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −216.237 | + | 124.844i | −0.904756 | + | 0.522361i | −0.878740 | − | 0.477300i | \(-0.841615\pi\) |
−0.0260161 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 277.831 | 1.15283 | 0.576414 | − | 0.817158i | \(-0.304452\pi\) | ||||
0.576414 | + | 0.817158i | \(0.304452\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −236.178 | − | 57.1743i | −0.971926 | − | 0.235285i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39.3776 | − | 22.7346i | 0.160725 | − | 0.0927945i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −193.723 | − | 14.2515i | −0.784305 | − | 0.0576984i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 172.299 | − | 140.916i | 0.691964 | − | 0.565929i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 413.219 | − | 238.572i | 1.64629 | − | 0.950486i | 0.667761 | − | 0.744376i | \(-0.267253\pi\) |
0.978529 | − | 0.206110i | \(-0.0660805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −113.404 | − | 196.422i | −0.448239 | − | 0.776372i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 65.9636 | + | 80.6540i | 0.258681 | + | 0.316290i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −152.662 | − | 88.1392i | −0.594014 | − | 0.342954i | 0.172669 | − | 0.984980i | \(-0.444761\pi\) |
−0.766683 | + | 0.642026i | \(0.778094\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −130.562 | + | 226.140i | −0.504100 | + | 0.873127i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.0150 | + | 31.7283i | −0.107337 | + | 0.121564i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 163.347 | − | 94.3087i | 0.621093 | − | 0.358588i | −0.156201 | − | 0.987725i | \(-0.549925\pi\) |
0.777294 | + | 0.629137i | \(0.216592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −44.2547 | − | 76.6513i | −0.166999 | − | 0.289250i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.15121 | − | 31.5314i | −0.0192929 | − | 0.118095i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −356.589 | − | 205.877i | −1.32561 | − | 0.765340i | −0.340991 | − | 0.940067i | \(-0.610763\pi\) |
−0.984617 | + | 0.174726i | \(0.944096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3004 | − | 42.0896i | 0.0896695 | − | 0.155312i | −0.817702 | − | 0.575642i | \(-0.804752\pi\) |
0.907371 | + | 0.420330i | \(0.138086\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −149.519 | + | 24.4266i | −0.547689 | + | 0.0894747i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −225.225 | − | 130.034i | −0.818999 | − | 0.472849i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −76.9499 | + | 133.281i | −0.277798 | + | 0.481159i | −0.970837 | − | 0.239740i | \(-0.922938\pi\) |
0.693040 | + | 0.720900i | \(0.256271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 51.0071 | − | 251.983i | 0.182821 | − | 0.903163i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 134.415i | 0.478346i | 0.970977 | + | 0.239173i | \(0.0768763\pi\) | ||||
−0.970977 | + | 0.239173i | \(0.923124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −63.6634 | −0.224959 | −0.112480 | − | 0.993654i | \(-0.535879\pi\) | ||||
−0.112480 | + | 0.993654i | \(0.535879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.31211 | + | 104.943i | 0.0326741 | + | 0.368222i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.7872 | + | 18.3524i | 0.110757 | + | 0.0639455i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0401 | + | 55.4951i | 0.110866 | + | 0.192025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 298.106 | − | 48.7009i | 1.02442 | − | 0.167357i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 186.208 | − | 107.507i | 0.635523 | − | 0.366919i | −0.147365 | − | 0.989082i | \(-0.547079\pi\) |
0.782888 | + | 0.622163i | \(0.213746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 94.0146 | 0.318694 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −325.098 | − | 12.2905i | −1.09461 | − | 0.0413822i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −166.659 | + | 96.2209i | −0.557390 | + | 0.321809i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 204.496 | 0.679390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 412.909 | + | 156.204i | 1.36274 | + | 0.515525i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 42.5513i | − | 0.139512i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −137.106 | + | 237.474i | −0.446599 | + | 0.773532i | −0.998162 | − | 0.0606011i | \(-0.980698\pi\) |
0.551563 | + | 0.834133i | \(0.314032\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 168.237 | − | 27.4845i | 0.544457 | − | 0.0889467i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −395.495 | + | 228.339i | −1.27169 | + | 0.734209i | −0.975305 | − | 0.220861i | \(-0.929113\pi\) |
−0.296382 | + | 0.955070i | \(0.595780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99.5291 | 0.317984 | 0.158992 | − | 0.987280i | \(-0.449176\pi\) | ||||
0.158992 | + | 0.987280i | \(0.449176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.1503 | + | 77.8990i | 0.0830168 | + | 0.247299i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 123.813i | 0.390577i | 0.980746 | + | 0.195289i | \(0.0625644\pi\) | ||||
−0.980746 | + | 0.195289i | \(0.937436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.3335 | + | 49.0750i | −0.0888197 | + | 0.153840i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −175.583 | − | 66.4234i | −0.546989 | − | 0.206926i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.1937 | + | 356.056i | −0.0810951 | + | 1.10234i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −110.330 | + | 191.098i | −0.339478 | + | 0.587993i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −122.507 | − | 149.790i | −0.374639 | − | 0.458073i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.4773 | + | 10.6679i | 0.0561620 | + | 0.0324252i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 284.794 | − | 493.278i | 0.860406 | − | 1.49027i | −0.0111320 | − | 0.999938i | \(-0.503544\pi\) |
0.871538 | − | 0.490328i | \(-0.163123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 356.640 | + | 314.901i | 1.07099 | + | 0.945648i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 62.0968 | + | 35.8516i | 0.185364 | + | 0.107020i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −177.343 | −0.526241 | −0.263120 | − | 0.964763i | \(-0.584752\pi\) | ||||
−0.263120 | + | 0.964763i | \(0.584752\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −61.6537 | − | 377.392i | −0.181869 | − | 1.11325i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 344.199i | − | 1.00938i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 363.557 | 1.05993 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 66.0795 | + | 80.7957i | 0.191535 | + | 0.234190i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 388.316i | − | 1.11907i | −0.828808 | − | 0.559533i | \(-0.810980\pi\) | ||
0.828808 | − | 0.559533i | \(-0.189020\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −165.385 | + | 286.456i | −0.473884 | + | 0.820791i | −0.999553 | − | 0.0298982i | \(-0.990482\pi\) |
0.525669 | + | 0.850689i | \(0.323815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.4282 | + | 275.838i | −0.0297100 | + | 0.785863i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −152.631 | − | 88.1216i | −0.432383 | − | 0.249636i | 0.267979 | − | 0.963425i | \(-0.413644\pi\) |
−0.700361 | + | 0.713789i | \(0.746978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 101.484 | − | 175.775i | 0.285870 | − | 0.495142i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44.8951 | + | 274.810i | 0.125757 | + | 0.769777i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −208.764 | − | 120.530i | −0.581515 | − | 0.335738i | 0.180220 | − | 0.983626i | \(-0.442319\pi\) |
−0.761735 | + | 0.647888i | \(0.775652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −224.308 | + | 282.855i | −0.621352 | + | 0.783532i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −71.6060 | + | 11.6981i | −0.197262 | + | 0.0322262i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.9781 | − | 21.3493i | −0.101310 | − | 0.0584913i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 190.391 | 0.518775 | 0.259388 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259388 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 44.2638 | − | 50.1309i | 0.119956 | − | 0.135856i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 236.538i | − | 0.637569i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 143.800 | + | 249.069i | 0.385523 | + | 0.667745i | 0.991842 | − | 0.127477i | \(-0.0406878\pi\) |
−0.606319 | + | 0.795222i | \(0.707354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 241.598 | + | 91.3966i | 0.644260 | + | 0.243724i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.6390 | + | 24.0403i | 0.110448 | + | 0.0637673i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 127.708 | 0.336961 | 0.168481 | − | 0.985705i | \(-0.446114\pi\) | ||||
0.168481 | + | 0.985705i | \(0.446114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −700.975 | + | 114.517i | −1.83983 | + | 0.300568i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 387.164i | 1.01087i | 0.862864 | + | 0.505436i | \(0.168668\pi\) | ||||
−0.862864 | + | 0.505436i | \(0.831332\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 55.0057 | + | 95.2727i | 0.142872 | + | 0.247462i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 73.9221 | − | 365.186i | 0.191013 | − | 0.943632i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 18.9972i | − | 0.0488361i | −0.999702 | − | 0.0244180i | \(-0.992227\pi\) | ||
0.999702 | − | 0.0244180i | \(-0.00777327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 176.850 | + | 306.314i | 0.452302 | + | 0.783411i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 706.277 | + | 267.185i | 1.79714 | + | 0.679861i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 238.552 | − | 137.728i | 0.603928 | − | 0.348678i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 112.212 | − | 194.357i | 0.282650 | − | 0.489564i | −0.689387 | − | 0.724394i | \(-0.742120\pi\) |
0.972037 | + | 0.234829i | \(0.0754531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −118.676 | + | 255.326i | −0.297434 | + | 0.639915i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 175.758i | − | 0.438300i | −0.975691 | − | 0.219150i | \(-0.929672\pi\) | ||
0.975691 | − | 0.219150i | \(-0.0703284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −292.044 | −0.724675 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 148.563 | − | 18.5394i | 0.366823 | − | 0.0457764i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 551.625 | + | 318.481i | 1.35534 | + | 0.782508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 317.177 | − | 549.367i | 0.775494 | − | 1.34320i | −0.159022 | − | 0.987275i | \(-0.550834\pi\) |
0.934516 | − | 0.355921i | \(-0.115833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7783 | − | 5.59065i | −0.0359569 | − | 0.0136026i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 217.590 | + | 125.625i | 0.526852 | + | 0.304178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −68.5690 | + | 118.765i | −0.165227 | + | 0.286181i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −308.970 | − | 377.779i | −0.740936 | − | 0.905946i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −329.899 | + | 190.467i | −0.787348 | + | 0.454575i | −0.839028 | − | 0.544088i | \(-0.816876\pi\) |
0.0516803 | + | 0.998664i | \(0.483542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −134.754 | − | 233.400i | −0.320080 | − | 0.554395i | 0.660424 | − | 0.750893i | \(-0.270377\pi\) |
−0.980504 | + | 0.196498i | \(0.937043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.7297 | − | 29.1401i | 0.0608268 | − | 0.0688892i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 351.230 | + | 202.783i | 0.826424 | + | 0.477136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 56.8585 | − | 98.4817i | 0.133158 | − | 0.230636i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 59.5839 | + | 364.723i | 0.138890 | + | 0.850170i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 601.019 | − | 346.999i | 1.39448 | − | 0.805101i | 0.400669 | − | 0.916223i | \(-0.368778\pi\) |
0.993807 | + | 0.111122i | \(0.0354443\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −324.494 | − | 562.041i | −0.749409 | − | 1.29802i | −0.948106 | − | 0.317954i | \(-0.897004\pi\) |
0.198697 | − | 0.980061i | \(-0.436329\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.22711 | − | 24.3909i | 0.0212117 | − | 0.0560711i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.2397 | + | 356.681i | −0.0600452 | + | 0.816205i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −163.442 | − | 283.090i | −0.372306 | − | 0.644852i | 0.617614 | − | 0.786481i | \(-0.288099\pi\) |
−0.989920 | + | 0.141629i | \(0.954766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.9257 | − | 216.999i | 0.0996048 | − | 0.492062i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 804.929i | 1.81699i | 0.417891 | + | 0.908497i | \(0.362770\pi\) | ||||
−0.417891 | + | 0.908497i | \(0.637230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.84223 | + | 17.0472i | 0.0221174 | + | 0.0383084i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 200.360 | + | 75.7965i | 0.448233 | + | 0.169567i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 201.130i | 0.447951i | 0.974595 | + | 0.223975i | \(0.0719035\pi\) | ||||
−0.974595 | + | 0.223975i | \(0.928096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.7670 | − | 77.5388i | 0.0992617 | − | 0.171926i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.5741 | + | 36.1604i | 0.0652849 | + | 0.0798242i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 80.8366 | − | 46.6710i | 0.177663 | − | 0.102574i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −211.138 | + | 365.702i | −0.462010 | + | 0.800224i | −0.999061 | − | 0.0433255i | \(-0.986205\pi\) |
0.537051 | + | 0.843549i | \(0.319538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 506.979 | + | 19.1666i | 1.10453 | + | 0.0417574i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −315.862 | + | 182.363i | −0.685167 | + | 0.395582i | −0.801799 | − | 0.597594i | \(-0.796124\pi\) |
0.116632 | + | 0.993175i | \(0.462790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 168.041 | + | 291.055i | 0.362939 | + | 0.628629i | 0.988443 | − | 0.151592i | \(-0.0484400\pi\) |
−0.625504 | + | 0.780221i | \(0.715107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.5387 | + | 156.326i | 0.0549219 | + | 0.336186i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.3762i | 0.0714693i | 0.999361 | + | 0.0357347i | \(0.0113771\pi\) | ||||
−0.999361 | + | 0.0357347i | \(0.988623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 95.8122 | + | 165.952i | 0.204290 | + | 0.353841i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 158.395 | − | 418.701i | 0.336295 | − | 0.888961i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 498.830i | − | 1.05461i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 178.435 | + | 369.234i | 0.375654 | + | 0.777335i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −422.405 | − | 85.5046i | −0.885545 | − | 0.179255i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 481.973i | 1.00621i | 0.864226 | + | 0.503104i | \(0.167809\pi\) | ||||
−0.864226 | + | 0.503104i | \(0.832191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 270.223 | − | 468.040i | 0.561795 | − | 0.973057i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 44.9740 | + | 275.293i | 0.0931138 | + | 0.569965i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −161.169 | + | 93.0510i | −0.332308 | + | 0.191858i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −887.516 | −1.82241 | −0.911207 | − | 0.411948i | \(-0.864849\pi\) | ||||
−0.911207 | + | 0.411948i | \(0.864849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −167.330 | + | 442.320i | −0.342188 | + | 0.904540i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 930.811i | 1.89575i | 0.318649 | + | 0.947873i | \(0.396771\pi\) | ||||
−0.318649 | + | 0.947873i | \(0.603229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.1851 | − | 76.5308i | 0.0896249 | − | 0.155235i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 190.020 | − | 63.7886i | 0.383878 | − | 0.128866i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 469.754 | − | 271.213i | 0.945179 | − | 0.545699i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −652.342 | −1.30730 | −0.653649 | − | 0.756798i | \(-0.726763\pi\) | ||||
−0.653649 | + | 0.756798i | \(0.726763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −573.284 | + | 468.865i | −1.14428 | + | 0.935859i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −264.025 | + | 152.435i | −0.524901 | + | 0.303052i | −0.738937 | − | 0.673774i | \(-0.764672\pi\) |
0.214037 | + | 0.976826i | \(0.431339\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −271.994 | −0.538603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −190.908 | + | 31.1882i | −0.376545 | + | 0.0615152i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.7282 | − | 25.8238i | −0.0878746 | − | 0.0507344i | 0.455419 | − | 0.890277i | \(-0.349490\pi\) |
−0.543293 | + | 0.839543i | \(0.682823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −57.0554 | − | 98.8228i | −0.111654 | − | 0.193391i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 413.056 | + | 304.226i | 0.805178 | + | 0.593033i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −90.9565 | + | 52.5137i | −0.176614 | + | 0.101968i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.0222 | − | 45.0718i | 0.0503331 | − | 0.0871795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50.5880 | + | 309.658i | 0.0974722 | + | 0.596643i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 733.507i | − | 1.40788i | −0.710258 | − | 0.703941i | \(-0.751422\pi\) | ||
0.710258 | − | 0.703941i | \(-0.248578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 376.499 | + | 652.115i | 0.719883 | + | 1.24687i | 0.961046 | + | 0.276389i | \(0.0891378\pi\) |
−0.241163 | + | 0.970485i | \(0.577529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 202.490 | + | 247.586i | 0.385696 | + | 0.471592i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 536.766i | 1.01853i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −87.3391 | − | 151.276i | −0.165102 | − | 0.285965i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 302.994 | − | 343.156i | 0.570611 | − | 0.646244i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −65.7897 | − | 37.9837i | −0.123433 | − | 0.0712640i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 115.661 | 0.216190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 670.001 | + | 253.462i | 1.24767 | + | 0.471997i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 296.413i | − | 0.549931i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −161.332 | − | 279.436i | −0.298211 | − | 0.516517i | 0.677516 | − | 0.735508i | \(-0.263057\pi\) |
−0.975727 | + | 0.218992i | \(0.929723\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −639.891 | + | 104.537i | −1.17844 | + | 0.192518i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 103.250 | + | 59.6112i | 0.189449 | + | 0.109378i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 108.112 | 0.197645 | 0.0988223 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988223 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −155.313 | − | 137.136i | −0.282902 | − | 0.249793i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 80.4537 | − | 38.8799i | 0.146014 | − | 0.0705625i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 736.146 | 1.33119 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −274.165 | − | 103.717i | −0.493990 | − | 0.186877i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −605.693 | + | 349.697i | −1.08742 | + | 0.627822i | −0.932888 | − | 0.360165i | \(-0.882720\pi\) |
−0.154532 | + | 0.987988i | \(0.549387\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −423.245 | −0.757146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 670.347 | − | 109.513i | 1.19491 | − | 0.195210i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −973.582 | + | 562.098i | −1.72928 | + | 0.998398i | −0.836348 | + | 0.548199i | \(0.815314\pi\) |
−0.892928 | + | 0.450199i | \(0.851353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 117.800 | + | 204.035i | 0.208495 | + | 0.361124i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 368.612 | + | 155.607i | 0.650109 | + | 0.274440i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 76.7723 | + | 44.3245i | 0.134925 | + | 0.0778989i | 0.565943 | − | 0.824444i | \(-0.308512\pi\) |
−0.431018 | + | 0.902343i | \(0.641846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −387.994 | − | 672.025i | −0.679499 | − | 1.17693i | −0.975132 | − | 0.221625i | \(-0.928864\pi\) |
0.295633 | − | 0.955302i | \(-0.404469\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −404.464 | + | 330.794i | −0.705871 | + | 0.577302i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 351.847 | + | 203.139i | 0.611908 | + | 0.353285i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 749.821 | 1.29952 | 0.649758 | − | 0.760141i | \(-0.274870\pi\) | ||||
0.649758 | + | 0.760141i | \(0.274870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 45.7500 | − | 120.935i | 0.0790156 | − | 0.208870i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −317.396 | + | 183.248i | −0.546292 | + | 0.315402i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −576.989 | −0.989690 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −54.1231 | − | 161.227i | −0.0925180 | − | 0.275602i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −90.3895 | + | 52.1864i | −0.153986 | + | 0.0889036i | −0.575013 | − | 0.818144i | \(-0.695003\pi\) |
0.421027 | + | 0.907048i | \(0.361670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −305.130 | + | 448.860i | −0.518048 | + | 0.762072i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 644.542 | + | 243.831i | 1.09060 | + | 0.412574i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −785.885 | + | 453.731i | −1.32527 | + | 0.765145i | −0.984564 | − | 0.175025i | \(-0.944000\pi\) |
−0.340706 | + | 0.940170i | \(0.610666\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −85.7795 | − | 148.574i | −0.144167 | − | 0.249705i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 194.413 | − | 31.7608i | 0.325650 | − | 0.0532007i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 84.5937 | + | 48.8402i | 0.141225 | + | 0.0815362i | 0.568948 | − | 0.822374i | \(-0.307351\pi\) |
−0.427723 | + | 0.903910i | \(0.640684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −456.977 | + | 791.508i | −0.760361 | + | 1.31698i | 0.182303 | + | 0.983242i | \(0.441645\pi\) |
−0.942664 | + | 0.333742i | \(0.891689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 330.987 | − | 111.111i | 0.548901 | − | 0.184263i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 38.7133 | − | 22.3512i | 0.0639890 | − | 0.0369441i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 107.749 | + | 186.627i | 0.177511 | + | 0.307457i | 0.941027 | − | 0.338331i | \(-0.109862\pi\) |
−0.763517 | + | 0.645788i | \(0.776529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 53.9474 | − | 44.1213i | 0.0885836 | − | 0.0724488i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.2424 | − | 22.0792i | −0.0625898 | − | 0.0361362i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 401.592 | − | 695.578i | 0.655126 | − | 1.13471i | −0.326736 | − | 0.945116i | \(-0.605949\pi\) |
0.981862 | − | 0.189596i | \(-0.0607178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.5789 | + | 38.5378i | −0.0237055 | + | 0.0626630i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −332.782 | − | 192.132i | −0.539355 | − | 0.311397i | 0.205462 | − | 0.978665i | \(-0.434130\pi\) |
−0.744818 | + | 0.667268i | \(0.767464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −55.6379 | + | 96.3677i | −0.0898835 | + | 0.155683i | −0.907462 | − | 0.420135i | \(-0.861983\pi\) |
0.817578 | + | 0.575818i | \(0.195316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 507.870 | + | 19.2003i | 0.817826 | + | 0.0309184i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 52.6061i | 0.0844399i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 380.444 | 0.608710 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 622.819 | + | 289.488i | 0.993331 | + | 0.461703i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −860.240 | − | 496.660i | −1.36763 | − | 0.789602i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −396.481 | − | 686.725i | −0.628337 | − | 1.08831i | −0.987885 | − | 0.155186i | \(-0.950402\pi\) |
0.359548 | − | 0.933127i | \(-0.382931\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 164.052 | − | 433.654i | 0.259166 | − | 0.685078i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 378.977 | − | 218.803i | 0.596815 | − | 0.344571i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −251.499 | −0.394818 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −314.517 | − | 936.916i | −0.492203 | − | 1.46622i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 465.052 | − | 268.498i | 0.725510 | − | 0.418873i | −0.0912673 | − | 0.995826i | \(-0.529092\pi\) |
0.816777 | + | 0.576953i | \(0.195758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −502.827 | −0.782001 | −0.391001 | − | 0.920390i | \(-0.627871\pi\) | ||||
−0.391001 | + | 0.920390i | \(0.627871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.0119 | + | 226.556i | 0.0573828 | + | 0.351249i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 42.7301i | − | 0.0660435i | −0.999455 | − | 0.0330217i | \(-0.989487\pi\) | ||
0.999455 | − | 0.0330217i | \(-0.0105131\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 306.439 | − | 530.768i | 0.472171 | − | 0.817824i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −149.781 | + | 395.931i | −0.230079 | + | 0.608189i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 539.034 | − | 311.211i | 0.825473 | − | 0.476587i | −0.0268270 | − | 0.999640i | \(-0.508540\pi\) |
0.852300 | + | 0.523053i | \(0.175207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −465.243 | −0.710295 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −197.100 | + | 66.1655i | −0.300000 | + | 0.100708i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 921.084i | 1.39770i | 0.715269 | + | 0.698850i | \(0.246304\pi\) | ||||
−0.715269 | + | 0.698850i | \(0.753696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 55.6683 | − | 96.4203i | 0.0842183 | − | 0.145870i | −0.820840 | − | 0.571159i | \(-0.806494\pi\) |
0.905058 | + | 0.425288i | \(0.139827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −92.9191 | − | 568.773i | −0.140149 | − | 0.857878i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7273 | − | 173.005i | 0.0191389 | − | 0.260158i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.2627 | − | 76.6652i | 0.0663608 | − | 0.114940i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 387.485 | − | 63.3024i | 0.579200 | − | 0.0946225i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −240.227 | − | 138.695i | −0.358014 | − | 0.206699i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 223.538 | − | 387.179i | 0.332152 | − | 0.575304i | −0.650782 | − | 0.759265i | \(-0.725559\pi\) |
0.982934 | + | 0.183961i | \(0.0588921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 515.331 | − | 272.105i | 0.763453 | − | 0.403118i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 202.443 | + | 116.881i | 0.299030 | + | 0.172645i | 0.642007 | − | 0.766699i | \(-0.278102\pi\) |
−0.342977 | + | 0.939344i | \(0.611435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −497.352 | −0.732477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −375.760 | + | 307.319i | −0.551777 | + | 0.451276i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 496.474i | 0.726902i | 0.931613 | + | 0.363451i | \(0.118402\pi\) | ||||
−0.931613 | + | 0.363451i | \(0.881598\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.73487 | 0.0142115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −998.054 | + | 163.050i | −1.45277 | + | 0.237336i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 489.561i | 0.710539i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 237.938 | − | 412.120i | 0.344338 | − | 0.596411i | −0.640895 | − | 0.767628i | \(-0.721437\pi\) |
0.985233 | + | 0.171217i | \(0.0547701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 525.022 | + | 106.277i | 0.757608 | + | 0.153358i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 260.402 | + | 150.343i | 0.374679 | + | 0.216321i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −69.8126 | + | 120.919i | −0.100162 | + | 0.173485i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.9530 | − | 16.3188i | 0.0285451 | − | 0.0233459i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −484.715 | − | 279.850i | −0.691462 | − | 0.399216i | 0.112697 | − | 0.993629i | \(-0.464051\pi\) |
−0.804160 | + | 0.594413i | \(0.797384\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −437.027 | − | 904.335i | −0.621661 | − | 1.28639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.47443 | + | 22.4013i | −0.0120205 | + | 0.0317749i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −629.510 | − | 363.448i | −0.890397 | − | 0.514071i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 690.685 | 0.974168 | 0.487084 | − | 0.873355i | \(-0.338061\pi\) | ||||
0.487084 | + | 0.873355i | \(0.338061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 266.105 | − | 1314.59i | 0.374268 | − | 1.84894i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 537.709i | 0.754150i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −113.845 | − | 197.185i | −0.159224 | − | 0.275784i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −120.772 | − | 739.266i | −0.168441 | − | 1.03105i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −673.685 | − | 388.952i | −0.936975 | − | 0.540963i | −0.0479641 | − | 0.998849i | \(-0.515273\pi\) |
−0.889011 | + | 0.457886i | \(0.848607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −280.682 | −0.389296 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −294.914 | + | 779.576i | −0.407904 | + | 1.07825i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 101.506i | − | 0.140009i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 210.717 | + | 364.972i | 0.289844 | + | 0.502025i | 0.973772 | − | 0.227525i | \(-0.0730632\pi\) |
−0.683928 | + | 0.729549i | \(0.739730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 411.127 | − | 602.010i | 0.563960 | − | 0.825802i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 777.908i | 1.06417i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 216.673 | + | 375.289i | 0.295598 | + | 0.511990i | 0.975124 | − | 0.221661i | \(-0.0711479\pi\) |
−0.679526 | + | 0.733651i | \(0.737815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.9931 | + | 134.623i | 0.0299225 | + | 0.183161i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 404.807 | − | 233.715i | 0.549263 | − | 0.317117i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 354.109 | − | 613.335i | 0.479174 | − | 0.829953i | −0.520541 | − | 0.853837i | \(-0.674270\pi\) |
0.999715 | + | 0.0238836i | \(0.00760311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 245.624 | − | 528.446i | 0.331476 | − | 0.713153i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 815.843i | − | 1.09804i | −0.835810 | − | 0.549019i | \(-0.815001\pi\) | ||
0.835810 | − | 0.549019i | \(-0.184999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −131.983 | −0.177158 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 212.508 | + | 633.040i | 0.284482 | + | 0.847443i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 267.690 | + | 154.551i | 0.357396 | + | 0.206343i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 541.246 | − | 937.465i | 0.720700 | − | 1.24829i | −0.240019 | − | 0.970768i | \(-0.577154\pi\) |
0.960720 | − | 0.277521i | \(-0.0895129\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 230.790 | + | 1412.70i | 0.306494 | + | 1.87610i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.9252 | − | 14.3906i | −0.0330135 | − | 0.0190604i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 160.866 | − | 278.628i | 0.212505 | − | 0.368069i | −0.739993 | − | 0.672614i | \(-0.765171\pi\) |
0.952498 | + | 0.304546i | \(0.0985046\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 671.524 | − | 109.705i | 0.884749 | − | 0.144539i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 958.373 | − | 553.317i | 1.25936 | − | 0.727092i | 0.286410 | − | 0.958107i | \(-0.407538\pi\) |
0.972950 | + | 0.231015i | \(0.0742048\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 159.309 | + | 275.931i | 0.208793 | + | 0.361640i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −296.329 | + | 99.4761i | −0.387358 | + | 0.130034i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −450.344 | − | 260.006i | −0.587150 | − | 0.338991i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 420.271 | − | 727.930i | 0.546516 | − | 0.946593i | −0.451994 | − | 0.892021i | \(-0.649287\pi\) |
0.998510 | − | 0.0545721i | \(-0.0173795\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 409.361 | − | 334.799i | 0.530948 | − | 0.434240i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −676.445 | + | 390.545i | −0.875090 | + | 0.505233i | −0.869036 | − | 0.494748i | \(-0.835260\pi\) |
−0.00605359 | + | 0.999982i | \(0.501927\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 308.278 | + | 533.953i | 0.397778 | + | 0.688972i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −495.943 | − | 606.392i | −0.638280 | − | 0.780428i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −127.117 | + | 61.4304i | −0.163180 | + | 0.0788581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −661.571 | − | 1145.87i | −0.847081 | − | 1.46719i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −59.2899 | − | 112.287i | −0.0757214 | − | 0.143406i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 275.809i | 0.351350i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −383.786 | − | 664.737i | −0.487657 | − | 0.844647i | 0.512242 | − | 0.858841i | \(-0.328815\pi\) |
−0.999899 | + | 0.0141942i | \(0.995482\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 91.2325 | + | 558.449i | 0.115631 | + | 0.707794i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 629.631i | 0.795993i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −117.680 | + | 203.827i | −0.148398 | + | 0.257033i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 262.054 | − | 42.8111i | 0.329628 | − | 0.0538505i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −796.725 | + | 459.990i | −0.999655 | + | 0.577151i | −0.908146 | − | 0.418653i | \(-0.862502\pi\) |
−0.0915091 | + | 0.995804i | \(0.529169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.5808 | + | 70.2880i | −0.0507894 | + | 0.0879699i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 93.9428 | + | 19.0162i | 0.117282 | + | 0.0237406i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −241.059 | + | 139.176i | −0.300198 | + | 0.173319i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −85.9302 | − | 148.835i | −0.106746 | − | 0.184889i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 956.189 | − | 782.028i | 1.18487 | − | 0.969055i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1141.94i | − | 1.41155i | −0.708438 | − | 0.705773i | \(-0.750600\pi\) | ||
0.708438 | − | 0.705773i | \(-0.249400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −618.024 | − | 1070.45i | −0.762052 | − | 1.31991i | −0.941791 | − | 0.336198i | \(-0.890859\pi\) |
0.179739 | − | 0.983714i | \(-0.442475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 92.3058 | + | 112.863i | 0.113537 | + | 0.138823i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 291.368i | − | 0.357507i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −442.210 | + | 650.510i | −0.541261 | + | 0.796218i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 90.1733 | − | 445.469i | 0.110102 | − | 0.543918i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1225.85i | 1.49311i | 0.665321 | + | 0.746557i | \(0.268295\pi\) | ||||
−0.665321 | + | 0.746557i | \(0.731705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −133.180 | + | 230.675i | −0.161823 | + | 0.280286i | −0.935522 | − | 0.353267i | \(-0.885071\pi\) |
0.773700 | + | 0.633553i | \(0.218404\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 603.938 | − | 493.936i | 0.732046 | − | 0.598710i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 725.041 | − | 418.603i | 0.876712 | − | 0.506170i | 0.00713916 | − | 0.999975i | \(-0.497728\pi\) |
0.869573 | + | 0.493805i | \(0.164394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −425.019 | −0.512689 | −0.256344 | − | 0.966586i | \(-0.582518\pi\) | ||||
−0.256344 | + | 0.966586i | \(0.582518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −292.296 | − | 357.392i | −0.351740 | − | 0.430075i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 462.245i | 0.554916i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 228.147 | − | 395.163i | 0.273230 | − | 0.473249i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 652.902 | + | 410.599i | 0.780050 | + | 0.490560i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −209.917 | + | 121.195i | −0.250199 | + | 0.144452i | −0.619855 | − | 0.784716i | \(-0.712809\pi\) |
0.369657 | + | 0.929168i | \(0.379475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 818.882 | 0.973701 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −377.160 | − | 142.680i | −0.447402 | − | 0.169253i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 103.213 | − | 59.5902i | 0.122146 | − | 0.0705210i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 119.465 | 0.141045 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 67.5779 | − | 178.635i | 0.0795970 | − | 0.210407i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −861.751 | − | 497.532i | −1.01263 | − | 0.584644i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −716.594 | − | 1241.18i | −0.840087 | − | 1.45507i | −0.889820 | − | 0.456311i | \(-0.849170\pi\) |
0.0497333 | − | 0.998763i | \(-0.484163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −304.348 | − | 85.2666i | −0.355962 | − | 0.0997270i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1159.74 | + | 669.577i | −1.35326 | + | 0.781303i | −0.988704 | − | 0.149880i | \(-0.952111\pi\) |
−0.364552 | + | 0.931183i | \(0.618778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −177.580 | + | 307.577i | −0.206728 | + | 0.358064i | −0.950682 | − | 0.310167i | \(-0.899615\pi\) |
0.743954 | + | 0.668231i | \(0.232948\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −85.2371 | + | 69.7119i | −0.0989978 | + | 0.0809662i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 71.3787i | − | 0.0827100i | −0.999145 | − | 0.0413550i | \(-0.986833\pi\) | ||
0.999145 | − | 0.0413550i | \(-0.0131675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −96.6568 | − | 167.415i | −0.111742 | − | 0.193543i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −189.726 | + | 30.9950i | −0.218830 | + | 0.0357498i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1795.69i | − | 2.06638i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −198.302 | − | 343.469i | −0.227671 | − | 0.394338i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −179.784 | + | 888.160i | −0.205939 | + | 1.01737i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −368.333 | − | 212.657i | −0.420952 | − | 0.243037i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 726.017 | 0.827841 | 0.413920 | − | 0.910313i | \(-0.364159\pi\) | ||||
0.413920 | + | 0.910313i | \(0.364159\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 104.001 | + | 636.605i | 0.118317 | + | 0.724238i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 738.131i | − | 0.837833i | −0.908025 | − | 0.418916i | \(-0.862410\pi\) | ||
0.908025 | − | 0.418916i | \(-0.137590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 172.011 | + | 297.931i | 0.194803 | + | 0.337408i | 0.946836 | − | 0.321717i | \(-0.104260\pi\) |
−0.752033 | + | 0.659125i | \(0.770927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −99.7953 | + | 263.799i | −0.112763 | + | 0.298077i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 596.382 | + | 344.321i | 0.672359 | + | 0.388186i | 0.796970 | − | 0.604019i | \(-0.206435\pi\) |
−0.124611 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1169.49 | 1.31551 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 379.574 | − | 899.157i | 0.426009 | − | 1.00915i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −73.8909 | + | 35.7084i | −0.0827445 | + | 0.0399870i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −441.348 | −0.493126 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −93.0823 | − | 569.772i | −0.103771 | − | 0.635197i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 116.345 | − | 67.1718i | 0.129416 | − | 0.0747183i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 899.795 | 0.998663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −217.070 | + | 573.803i | −0.240388 | + | 0.635441i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 345.953 | − | 199.736i | 0.382268 | − | 0.220703i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −279.863 | − | 484.737i | −0.308559 | − | 0.534440i | 0.669488 | − | 0.742823i | \(-0.266513\pi\) |
−0.978047 | + | 0.208382i | \(0.933180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −876.595 | + | 992.786i | −0.964351 | + | 1.09217i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.3919 | + | 14.0827i | 0.0267749 | + | 0.0154585i | 0.513328 | − | 0.858193i | \(-0.328413\pi\) |
−0.486553 | + | 0.873651i | \(0.661746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 446.999 | + | 774.225i | 0.489594 | + | 0.848001i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 119.396 | + | 45.1676i | 0.130487 | + | 0.0493635i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1076.77 | − | 621.674i | −1.17423 | − | 0.677943i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 212.578 | 0.231314 | 0.115657 | − | 0.993289i | \(-0.463103\pi\) | ||||
0.115657 | + | 0.993289i | \(0.463103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −520.800 | − | 636.785i | −0.565473 | − | 0.691407i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −972.246 | + | 561.327i | −1.05335 | + | 0.608155i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1140.98 | −1.23349 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −101.462 | + | 501.237i | −0.109452 | + | 0.540709i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1138.90 | − | 657.544i | 1.22594 | − | 0.707797i | 0.259762 | − | 0.965673i | \(-0.416356\pi\) |
0.966178 | + | 0.257875i | \(0.0830224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −262.769 | + | 386.544i | −0.282243 | + | 0.415192i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −220.891 | − | 1352.11i | −0.236753 | − | 1.44921i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −362.419 | + | 209.243i | −0.387614 | + | 0.223789i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −201.216 | − | 348.516i | −0.214745 | − | 0.371948i | 0.738449 | − | 0.674309i | \(-0.235559\pi\) |
−0.953194 | + | 0.302361i | \(0.902225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −105.649 | + | 279.272i | −0.112512 | + | 0.297414i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 784.539 | + | 452.954i | 0.833729 | + | 0.481353i | 0.855128 | − | 0.518418i | \(-0.173479\pi\) |
−0.0213991 | + | 0.999771i | \(0.506812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −69.9353 | + | 121.131i | −0.0741625 | + | 0.128453i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −246.337 | − | 9.31292i | −0.260675 | − | 0.00985494i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1287.51 | − | 743.345i | 1.35957 | − | 0.784947i | 0.370003 | − | 0.929031i | \(-0.379357\pi\) |
0.989566 | + | 0.144083i | \(0.0460234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 118.087 | + | 204.533i | 0.124433 | + | 0.215525i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −347.411 | − | 131.426i | −0.365311 | − | 0.138198i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 910.211 | + | 525.511i | 0.955101 | + | 0.551428i | 0.894662 | − | 0.446744i | \(-0.147417\pi\) |
0.0604392 | + | 0.998172i | \(0.480750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 160.963 | − | 278.795i | 0.168547 | − | 0.291932i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −107.625 | − | 131.594i | −0.112461 | − | 0.137507i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.5306 | + | 13.0081i | 0.0234939 | + | 0.0135642i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.4944 | − | 125.564i | 0.0754364 | − | 0.130660i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 372.759 | − | 422.167i | 0.387081 | − | 0.438387i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 79.6635i | 0.0825528i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1156.99 | −1.19647 | −0.598237 | − | 0.801319i | \(-0.704132\pi\) | ||||
−0.598237 | + | 0.801319i | \(0.704132\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −971.264 | − | 451.447i | −1.00234 | − | 0.465889i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 453.947 | + | 262.086i | 0.467504 | + | 0.269914i | 0.715194 | − | 0.698926i | \(-0.246338\pi\) |
−0.247690 | + | 0.968839i | \(0.579671\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 401.787 | + | 695.916i | 0.412936 | + | 0.715227i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −419.093 | − | 512.427i | −0.429839 | − | 0.525566i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −379.565 | + | 219.142i | −0.388501 | + | 0.224301i | −0.681510 | − | 0.731809i | \(-0.738677\pi\) |
0.293010 | + | 0.956109i | \(0.405343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 128.322 | 0.131075 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 550.339 | − | 184.746i | 0.560998 | − | 0.188324i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 695.110 | − | 401.322i | 0.707131 | − | 0.408262i | −0.102867 | − | 0.994695i | \(-0.532802\pi\) |
0.809998 | + | 0.586433i | \(0.199468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −424.577 | −0.431043 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.5467 | + | 40.5222i | −0.0501993 | + | 0.0410560i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 779.274i | 0.787942i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −767.110 | + | 1328.67i | −0.774077 | + | 1.34074i | 0.161236 | + | 0.986916i | \(0.448452\pi\) |
−0.935312 | + | 0.353824i | \(0.884881\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1081.80 | + | 1322.72i | 1.08942 | + | 1.33205i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −105.108 | + | 60.6843i | −0.105637 | + | 0.0609893i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 928.495 | 0.931289 | 0.465644 | − | 0.884972i | \(-0.345823\pi\) | ||||
0.465644 | + | 0.884972i | \(0.345823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1262.16 | + | 666.444i | −1.26342 | + | 0.667111i |
(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 | 684.3.m.a.353.17 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.m.a.1493.25 | 80 | |||
9.4 | even | 3 | 2052.3.be.a.125.16 | 80 | |||
9.5 | odd | 6 | 684.3.be.a.581.11 | yes | 80 | ||
19.7 | even | 3 | 684.3.be.a.425.11 | yes | 80 | ||
57.26 | odd | 6 | 2052.3.be.a.197.16 | 80 | |||
171.121 | even | 3 | 2052.3.m.a.881.16 | 80 | |||
171.140 | odd | 6 | inner | 684.3.m.a.653.17 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.17 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.m.a.653.17 | yes | 80 | 171.140 | odd | 6 | inner | |
684.3.be.a.425.11 | yes | 80 | 19.7 | even | 3 | ||
684.3.be.a.581.11 | yes | 80 | 9.5 | odd | 6 | ||
2052.3.m.a.881.16 | 80 | 171.121 | even | 3 | |||
2052.3.m.a.1493.25 | 80 | 3.2 | odd | 2 | |||
2052.3.be.a.125.16 | 80 | 9.4 | even | 3 | |||
2052.3.be.a.197.16 | 80 | 57.26 | odd | 6 |