Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(343,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.6 | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.d.343.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58671 | + | 1.21751i | −0.793356 | + | 0.608757i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.03532 | − | 3.86369i | 0.258829 | − | 0.965923i | ||||
\(5\) | 1.46825 | 0.293650 | 0.146825 | − | 0.989162i | \(-0.453095\pi\) | ||||
0.146825 | + | 0.989162i | \(0.453095\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.38949i | − | 0.912784i | −0.889779 | − | 0.456392i | \(-0.849142\pi\) | ||
0.889779 | − | 0.456392i | \(-0.150858\pi\) | |||||||
\(8\) | 3.06136 | + | 7.39108i | 0.382669 | + | 0.923885i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.32969 | + | 1.78762i | −0.232969 | + | 0.178762i | ||||
\(11\) | − | 9.33972i | − | 0.849065i | −0.905413 | − | 0.424533i | \(-0.860438\pi\) | ||
0.905413 | − | 0.424533i | \(-0.139562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.7114 | −1.74703 | −0.873514 | − | 0.486800i | \(-0.838164\pi\) | ||||
−0.873514 | + | 0.486800i | \(0.838164\pi\) | |||||||
\(14\) | 7.77929 | + | 10.1383i | 0.555664 | + | 0.724163i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.8562 | − | 8.00028i | −0.866015 | − | 0.500018i | ||||
\(17\) | −5.17560 | −0.304447 | −0.152223 | − | 0.988346i | \(-0.548643\pi\) | ||||
−0.152223 | + | 0.988346i | \(0.548643\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.35890i | − | 0.229416i | ||||||
\(20\) | 1.52010 | − | 5.67287i | 0.0760051 | − | 0.283643i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.3712 | + | 14.8194i | 0.516875 | + | 0.673611i | ||||
\(23\) | 37.0351i | 1.61022i | 0.593123 | + | 0.805112i | \(0.297895\pi\) | ||||
−0.593123 | + | 0.805112i | \(0.702105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22.8442 | −0.913770 | ||||||||
\(26\) | 36.0364 | − | 27.6514i | 1.38602 | − | 1.06352i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −24.6870 | − | 6.61513i | −0.881679 | − | 0.236255i | ||||
\(29\) | 23.0104 | 0.793461 | 0.396731 | − | 0.917935i | \(-0.370145\pi\) | ||||
0.396731 | + | 0.917935i | \(0.370145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.9233i | 0.642688i | 0.946962 | + | 0.321344i | \(0.104135\pi\) | ||||
−0.946962 | + | 0.321344i | \(0.895865\pi\) | |||||||
\(32\) | 31.7263 | − | 4.17604i | 0.991448 | − | 0.130501i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.21218 | − | 6.30136i | 0.241535 | − | 0.185334i | ||||
\(35\) | − | 9.38136i | − | 0.268039i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.3546 | 0.658232 | 0.329116 | − | 0.944290i | \(-0.393249\pi\) | ||||
0.329116 | + | 0.944290i | \(0.393249\pi\) | |||||||
\(38\) | 5.30702 | + | 6.91632i | 0.139659 | + | 0.182008i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.49483 | + | 10.8520i | 0.112371 | + | 0.271299i | ||||
\(41\) | −57.3392 | −1.39852 | −0.699259 | − | 0.714868i | \(-0.746487\pi\) | ||||
−0.699259 | + | 0.714868i | \(0.746487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 78.8346i | 1.83336i | 0.399618 | + | 0.916682i | \(0.369143\pi\) | ||||
−0.399618 | + | 0.916682i | \(0.630857\pi\) | |||||||
\(44\) | −36.0858 | − | 9.66955i | −0.820132 | − | 0.219763i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −45.0908 | − | 58.7641i | −0.980236 | − | 1.27748i | ||||
\(47\) | 50.2690i | 1.06955i | 0.844994 | + | 0.534776i | \(0.179604\pi\) | ||||
−0.844994 | + | 0.534776i | \(0.820396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.17447 | 0.166826 | ||||||||
\(50\) | 36.2473 | − | 27.8132i | 0.724945 | − | 0.556264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −23.5134 | + | 87.7497i | −0.452181 | + | 1.68749i | ||||
\(53\) | 82.4964 | 1.55654 | 0.778268 | − | 0.627932i | \(-0.216098\pi\) | ||||
0.778268 | + | 0.627932i | \(0.216098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13.7130i | − | 0.249328i | ||||||
\(56\) | 47.2252 | − | 19.5605i | 0.843307 | − | 0.349294i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −36.5109 | + | 28.0155i | −0.629498 | + | 0.483025i | ||||
\(59\) | 86.4304i | 1.46492i | 0.680809 | + | 0.732461i | \(0.261628\pi\) | ||||
−0.680809 | + | 0.732461i | \(0.738372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −114.416 | −1.87567 | −0.937836 | − | 0.347080i | \(-0.887173\pi\) | ||||
−0.937836 | + | 0.347080i | \(0.887173\pi\) | |||||||
\(62\) | −24.2570 | − | 31.6126i | −0.391241 | − | 0.509881i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −45.2562 | + | 45.2535i | −0.707128 | + | 0.707085i | ||||
\(65\) | −33.3459 | −0.513015 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 64.7258i | − | 0.966057i | −0.875605 | − | 0.483029i | \(-0.839537\pi\) | ||
0.875605 | − | 0.483029i | \(-0.160463\pi\) | |||||||
\(68\) | −5.35837 | + | 19.9969i | −0.0787996 | + | 0.294072i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.4219 | + | 14.8855i | 0.163171 | + | 0.212650i | ||||
\(71\) | − | 25.1687i | − | 0.354489i | −0.984167 | − | 0.177245i | \(-0.943282\pi\) | ||
0.984167 | − | 0.177245i | \(-0.0567184\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −58.1281 | −0.796275 | −0.398137 | − | 0.917326i | \(-0.630343\pi\) | ||||
−0.398137 | + | 0.917326i | \(0.630343\pi\) | |||||||
\(74\) | −38.6437 | + | 29.6520i | −0.522212 | + | 0.400703i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.8414 | − | 4.51283i | −0.221598 | − | 0.0593794i | ||||
\(77\) | −59.6760 | −0.775013 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 47.6673i | − | 0.603383i | −0.953406 | − | 0.301692i | \(-0.902449\pi\) | ||
0.953406 | − | 0.301692i | \(-0.0975513\pi\) | |||||||
\(80\) | −20.3444 | − | 11.7464i | −0.254305 | − | 0.146830i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 90.9809 | − | 69.8114i | 1.10952 | − | 0.851358i | ||||
\(83\) | 51.5116i | 0.620622i | 0.950635 | + | 0.310311i | \(0.100433\pi\) | ||||
−0.950635 | + | 0.310311i | \(0.899567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.59907 | −0.0894008 | ||||||||
\(86\) | −95.9823 | − | 125.088i | −1.11607 | − | 1.45451i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 69.0306 | − | 28.5922i | 0.784439 | − | 0.324911i | ||||
\(89\) | 4.37527 | 0.0491603 | 0.0245801 | − | 0.999698i | \(-0.492175\pi\) | ||||
0.0245801 | + | 0.999698i | \(0.492175\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 145.114i | 1.59466i | ||||||||
\(92\) | 143.092 | + | 38.3430i | 1.55535 | + | 0.416772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −61.2032 | − | 79.7624i | −0.651098 | − | 0.848536i | ||||
\(95\) | − | 6.39995i | − | 0.0673679i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.1637 | 0.166636 | 0.0833178 | − | 0.996523i | \(-0.473448\pi\) | ||||
0.0833178 | + | 0.996523i | \(0.473448\pi\) | |||||||
\(98\) | −12.9705 | + | 9.95254i | −0.132352 | + | 0.101556i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −23.6510 | + | 88.2631i | −0.236510 | + | 0.882631i | ||||
\(101\) | −188.996 | −1.87124 | −0.935621 | − | 0.353005i | \(-0.885160\pi\) | ||||
−0.935621 | + | 0.353005i | \(0.885160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 124.907i | − | 1.21268i | −0.795204 | − | 0.606342i | \(-0.792636\pi\) | ||
0.795204 | − | 0.606342i | \(-0.207364\pi\) | |||||||
\(104\) | −69.5275 | − | 167.862i | −0.668534 | − | 1.61405i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −130.898 | + | 100.441i | −1.23489 | + | 0.947553i | ||||
\(107\) | 36.4119i | 0.340298i | 0.985418 | + | 0.170149i | \(0.0544250\pi\) | ||||
−0.985418 | + | 0.170149i | \(0.945575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.16177 | −0.0565300 | −0.0282650 | − | 0.999600i | \(-0.508998\pi\) | ||||
−0.0282650 | + | 0.999600i | \(0.508998\pi\) | |||||||
\(110\) | 16.6958 | + | 21.7587i | 0.151780 | + | 0.197806i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −51.1177 | + | 88.5343i | −0.456408 | + | 0.790485i | ||||
\(113\) | −132.916 | −1.17625 | −0.588123 | − | 0.808772i | \(-0.700133\pi\) | ||||
−0.588123 | + | 0.808772i | \(0.700133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 54.3768i | 0.472842i | ||||||||
\(116\) | 23.8230 | − | 88.9050i | 0.205371 | − | 0.766423i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −105.230 | − | 137.140i | −0.891782 | − | 1.16221i | ||||
\(119\) | 33.0694i | 0.277894i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 33.7697 | 0.279088 | ||||||||
\(122\) | 181.545 | − | 139.303i | 1.48808 | − | 1.14183i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 76.9777 | + | 20.6269i | 0.620788 | + | 0.166346i | ||||
\(125\) | −70.2473 | −0.561978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 79.3189i | − | 0.624558i | −0.949990 | − | 0.312279i | \(-0.898908\pi\) | ||
0.949990 | − | 0.312279i | \(-0.101092\pi\) | |||||||
\(128\) | 16.7118 | − | 126.904i | 0.130561 | − | 0.991440i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 52.9104 | − | 40.5992i | 0.407003 | − | 0.312301i | ||||
\(131\) | − | 20.4646i | − | 0.156218i | −0.996945 | − | 0.0781091i | \(-0.975112\pi\) | ||
0.996945 | − | 0.0781091i | \(-0.0248882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.8511 | −0.209407 | ||||||||
\(134\) | 78.8046 | + | 102.701i | 0.588094 | + | 0.766428i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.8443 | − | 38.2533i | −0.116502 | − | 0.281274i | ||||
\(137\) | −241.403 | −1.76206 | −0.881032 | − | 0.473057i | \(-0.843151\pi\) | ||||
−0.881032 | + | 0.473057i | \(0.843151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 108.101i | 0.777703i | 0.921300 | + | 0.388852i | \(0.127128\pi\) | ||||
−0.921300 | + | 0.388852i | \(0.872872\pi\) | |||||||
\(140\) | −36.2467 | − | 9.71267i | −0.258905 | − | 0.0693762i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 30.6433 | + | 39.9355i | 0.215798 | + | 0.281236i | ||||
\(143\) | 212.118i | 1.48334i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.7850 | 0.233000 | ||||||||
\(146\) | 92.2325 | − | 70.7718i | 0.631730 | − | 0.484738i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 25.2147 | − | 94.0986i | 0.170369 | − | 0.635801i | ||||
\(149\) | −211.062 | −1.41652 | −0.708262 | − | 0.705950i | \(-0.750520\pi\) | ||||
−0.708262 | + | 0.705950i | \(0.750520\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 122.207i | − | 0.809318i | −0.914468 | − | 0.404659i | \(-0.867390\pi\) | ||
0.914468 | − | 0.404659i | \(-0.132610\pi\) | |||||||
\(152\) | 32.2170 | − | 13.3441i | 0.211954 | − | 0.0877904i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 94.6887 | − | 72.6564i | 0.614861 | − | 0.471795i | ||||
\(155\) | 29.2524i | 0.188725i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −163.540 | −1.04165 | −0.520827 | − | 0.853662i | \(-0.674376\pi\) | ||||
−0.520827 | + | 0.853662i | \(0.674376\pi\) | |||||||
\(158\) | 58.0356 | + | 75.6343i | 0.367314 | + | 0.478698i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 46.5822 | − | 6.13146i | 0.291139 | − | 0.0383216i | ||||
\(161\) | 236.636 | 1.46979 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 79.0594i | − | 0.485027i | −0.970148 | − | 0.242514i | \(-0.922028\pi\) | ||
0.970148 | − | 0.242514i | \(-0.0779719\pi\) | |||||||
\(164\) | −59.3642 | + | 221.541i | −0.361977 | + | 1.35086i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −62.7162 | − | 81.7342i | −0.377808 | − | 0.492374i | ||||
\(167\) | 266.850i | 1.59790i | 0.601395 | + | 0.798952i | \(0.294612\pi\) | ||||
−0.601395 | + | 0.798952i | \(0.705388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 346.806 | 2.05210 | ||||||||
\(170\) | 12.0575 | − | 9.25198i | 0.0709267 | − | 0.0544234i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 304.593 | + | 81.6187i | 1.77089 | + | 0.474527i | ||||
\(173\) | 231.160 | 1.33618 | 0.668092 | − | 0.744079i | \(-0.267111\pi\) | ||||
0.668092 | + | 0.744079i | \(0.267111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 145.963i | 0.834074i | ||||||||
\(176\) | −74.7203 | + | 129.413i | −0.424547 | + | 0.735303i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.94229 | + | 5.32695i | −0.0390016 | + | 0.0299267i | ||||
\(179\) | − | 25.6269i | − | 0.143167i | −0.997435 | − | 0.0715834i | \(-0.977195\pi\) | ||
0.997435 | − | 0.0715834i | \(-0.0228052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 140.431 | 0.775859 | 0.387930 | − | 0.921689i | \(-0.373190\pi\) | ||||
0.387930 | + | 0.921689i | \(0.373190\pi\) | |||||||
\(182\) | −176.678 | − | 230.254i | −0.970760 | − | 1.26513i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −273.730 | + | 113.378i | −1.48766 | + | 0.616183i | ||||
\(185\) | 35.7586 | 0.193290 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 48.3386i | 0.258495i | ||||||||
\(188\) | 194.224 | + | 52.0442i | 1.03311 | + | 0.276831i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.79204 | + | 10.1549i | 0.0410107 | + | 0.0534468i | ||||
\(191\) | − | 342.544i | − | 1.79342i | −0.442615 | − | 0.896712i | \(-0.645949\pi\) | ||
0.442615 | − | 0.896712i | \(-0.354051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 148.829 | 0.771134 | 0.385567 | − | 0.922680i | \(-0.374006\pi\) | ||||
0.385567 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(194\) | −25.6471 | + | 19.6795i | −0.132201 | + | 0.101441i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.46315 | − | 31.5836i | 0.0431793 | − | 0.161141i | ||||
\(197\) | −16.3370 | −0.0829288 | −0.0414644 | − | 0.999140i | \(-0.513202\pi\) | ||||
−0.0414644 | + | 0.999140i | \(0.513202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.7453i | 0.119323i | 0.998219 | + | 0.0596616i | \(0.0190022\pi\) | ||||
−0.998219 | + | 0.0596616i | \(0.980998\pi\) | |||||||
\(200\) | −69.9343 | − | 168.844i | −0.349672 | − | 0.844218i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 299.882 | − | 230.105i | 1.48456 | − | 1.13913i | ||||
\(203\) | − | 147.024i | − | 0.724259i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −84.1883 | −0.410675 | ||||||||
\(206\) | 152.076 | + | 198.191i | 0.738231 | + | 0.962091i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 314.694 | + | 181.697i | 1.51295 | + | 0.873544i | ||||
\(209\) | −40.7109 | −0.194789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 210.424i | − | 0.997270i | −0.866812 | − | 0.498635i | \(-0.833835\pi\) | ||
0.866812 | − | 0.498635i | \(-0.166165\pi\) | |||||||
\(212\) | 85.4098 | − | 318.741i | 0.402876 | − | 1.50349i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −44.3321 | − | 57.7753i | −0.207159 | − | 0.269978i | ||||
\(215\) | 115.749i | 0.538367i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 127.300 | 0.586636 | ||||||||
\(218\) | 9.77695 | − | 7.50204i | 0.0448484 | − | 0.0344130i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −52.9830 | − | 14.1973i | −0.240832 | − | 0.0645333i | ||||
\(221\) | 117.545 | 0.531877 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 217.878i | 0.977031i | 0.872555 | + | 0.488515i | \(0.162461\pi\) | ||||
−0.872555 | + | 0.488515i | \(0.837539\pi\) | |||||||
\(224\) | −26.6827 | − | 202.715i | −0.119119 | − | 0.904978i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 210.899 | − | 161.827i | 0.933182 | − | 0.716048i | ||||
\(227\) | 219.138i | 0.965364i | 0.875796 | + | 0.482682i | \(0.160337\pi\) | ||||
−0.875796 | + | 0.482682i | \(0.839663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.20028 | 0.0227087 | 0.0113543 | − | 0.999936i | \(-0.496386\pi\) | ||||
0.0113543 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(230\) | −66.2046 | − | 86.2804i | −0.287846 | − | 0.375132i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 70.4429 | + | 170.072i | 0.303633 | + | 0.733067i | ||||
\(233\) | 254.277 | 1.09132 | 0.545660 | − | 0.838007i | \(-0.316279\pi\) | ||||
0.545660 | + | 0.838007i | \(0.316279\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 73.8074i | 0.314074i | ||||||||
\(236\) | 333.941 | + | 89.4827i | 1.41500 | + | 0.379164i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −40.2625 | − | 52.4716i | −0.169170 | − | 0.220469i | ||||
\(239\) | 56.1364i | 0.234880i | 0.993080 | + | 0.117440i | \(0.0374688\pi\) | ||||
−0.993080 | + | 0.117440i | \(0.962531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −162.609 | −0.674726 | −0.337363 | − | 0.941375i | \(-0.609535\pi\) | ||||
−0.337363 | + | 0.941375i | \(0.609535\pi\) | |||||||
\(242\) | −53.5828 | + | 41.1151i | −0.221417 | + | 0.169897i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −118.457 | + | 442.068i | −0.485478 | + | 1.81175i | ||||
\(245\) | 12.0022 | 0.0489884 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 98.9965i | 0.400796i | ||||||||
\(248\) | −147.255 | + | 60.9924i | −0.593770 | + | 0.245937i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 111.462 | − | 85.5271i | 0.445849 | − | 0.342109i | ||||
\(251\) | 364.538i | 1.45234i | 0.687515 | + | 0.726171i | \(0.258702\pi\) | ||||
−0.687515 | + | 0.726171i | \(0.741298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 345.898 | 1.36718 | ||||||||
\(254\) | 96.5719 | + | 125.856i | 0.380204 | + | 0.495497i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 127.991 | + | 221.708i | 0.499965 | + | 0.866046i | ||||
\(257\) | −21.3907 | −0.0832321 | −0.0416161 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416161 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 155.613i | − | 0.600823i | ||||||
\(260\) | −34.5236 | + | 128.838i | −0.132783 | + | 0.495533i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.9159 | + | 32.4714i | 0.0950989 | + | 0.123937i | ||||
\(263\) | 80.6177i | 0.306531i | 0.988185 | + | 0.153266i | \(0.0489790\pi\) | ||||
−0.988185 | + | 0.153266i | \(0.951021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 121.125 | 0.457077 | ||||||||
\(266\) | 44.1917 | − | 33.9092i | 0.166134 | − | 0.127478i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −250.081 | − | 67.0116i | −0.933137 | − | 0.250043i | ||||
\(269\) | 156.970 | 0.583533 | 0.291766 | − | 0.956490i | \(-0.405757\pi\) | ||||
0.291766 | + | 0.956490i | \(0.405757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 190.237i | − | 0.701980i | −0.936379 | − | 0.350990i | \(-0.885845\pi\) | ||
0.936379 | − | 0.350990i | \(-0.114155\pi\) | |||||||
\(272\) | 71.7143 | + | 41.4062i | 0.263656 | + | 0.152229i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 383.037 | − | 293.911i | 1.39794 | − | 1.07267i | ||||
\(275\) | 213.359i | 0.775850i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −128.837 | −0.465116 | −0.232558 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232558 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(278\) | −131.614 | − | 171.525i | −0.473432 | − | 0.616996i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 69.3384 | − | 28.7197i | 0.247637 | − | 0.102570i | ||||
\(281\) | 67.8107 | 0.241319 | 0.120660 | − | 0.992694i | \(-0.461499\pi\) | ||||
0.120660 | + | 0.992694i | \(0.461499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 446.393i | − | 1.57736i | −0.614803 | − | 0.788680i | \(-0.710765\pi\) | ||
0.614803 | − | 0.788680i | \(-0.289235\pi\) | |||||||
\(284\) | −97.2442 | − | 26.0576i | −0.342409 | − | 0.0917520i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −258.256 | − | 336.570i | −0.902994 | − | 1.17682i | ||||
\(287\) | 366.368i | 1.27654i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −262.213 | −0.907312 | ||||||||
\(290\) | −53.6071 | + | 41.1337i | −0.184852 | + | 0.141840i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −60.1809 | + | 224.589i | −0.206099 | + | 0.769140i | ||||
\(293\) | −428.704 | −1.46315 | −0.731577 | − | 0.681759i | \(-0.761215\pi\) | ||||
−0.731577 | + | 0.681759i | \(0.761215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 126.901i | 0.430174i | ||||||||
\(296\) | 74.5580 | + | 180.007i | 0.251885 | + | 0.608131i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 334.895 | − | 256.971i | 1.12381 | − | 0.862319i | ||||
\(299\) | − | 841.118i | − | 2.81310i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 503.713 | 1.67346 | ||||||||
\(302\) | 148.789 | + | 193.908i | 0.492678 | + | 0.642078i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −34.8724 | + | 60.3980i | −0.114712 | + | 0.198678i | ||||
\(305\) | −167.991 | −0.550791 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 150.905i | 0.491548i | 0.969327 | + | 0.245774i | \(0.0790422\pi\) | ||||
−0.969327 | + | 0.245774i | \(0.920958\pi\) | |||||||
\(308\) | −61.7835 | + | 230.570i | −0.200596 | + | 0.748603i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −35.6153 | − | 46.4152i | −0.114888 | − | 0.149727i | ||||
\(311\) | − | 446.649i | − | 1.43617i | −0.695955 | − | 0.718086i | \(-0.745019\pi\) | ||
0.695955 | − | 0.718086i | \(-0.254981\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −116.567 | −0.372420 | −0.186210 | − | 0.982510i | \(-0.559620\pi\) | ||||
−0.186210 | + | 0.982510i | \(0.559620\pi\) | |||||||
\(314\) | 259.491 | − | 199.112i | 0.826403 | − | 0.634115i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −184.172 | − | 49.3507i | −0.582822 | − | 0.156173i | ||||
\(317\) | 216.378 | 0.682580 | 0.341290 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341290 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 214.910i | − | 0.673700i | ||||||
\(320\) | −66.4474 | + | 66.4434i | −0.207648 | + | 0.207636i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −375.473 | + | 288.107i | −1.16606 | + | 0.894743i | ||||
\(323\) | 22.5599i | 0.0698449i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 518.824 | 1.59638 | ||||||||
\(326\) | 96.2560 | + | 125.445i | 0.295264 | + | 0.384799i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −175.536 | − | 423.799i | −0.535170 | − | 1.29207i | ||||
\(329\) | 321.193 | 0.976270 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 267.016i | 0.806696i | 0.915047 | + | 0.403348i | \(0.132154\pi\) | ||||
−0.915047 | + | 0.403348i | \(0.867846\pi\) | |||||||
\(332\) | 199.025 | + | 53.3308i | 0.599473 | + | 0.160635i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −324.894 | − | 423.414i | −0.972735 | − | 1.26771i | ||||
\(335\) | − | 95.0337i | − | 0.283683i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −91.5477 | −0.271655 | −0.135827 | − | 0.990733i | \(-0.543369\pi\) | ||||
−0.135827 | + | 0.990733i | \(0.543369\pi\) | |||||||
\(338\) | −550.281 | + | 422.241i | −1.62805 | + | 1.24923i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.86743 | + | 29.3605i | −0.0231395 | + | 0.0863543i | ||||
\(341\) | 186.078 | 0.545684 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 365.315i | − | 1.06506i | ||||||
\(344\) | −582.673 | + | 241.341i | −1.69382 | + | 0.701572i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −366.784 | + | 281.441i | −1.06007 | + | 0.813412i | ||||
\(347\) | − | 221.079i | − | 0.637116i | −0.947903 | − | 0.318558i | \(-0.896802\pi\) | ||
0.947903 | − | 0.318558i | \(-0.103198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −649.433 | −1.86084 | −0.930420 | − | 0.366496i | \(-0.880557\pi\) | ||||
−0.930420 | + | 0.366496i | \(0.880557\pi\) | |||||||
\(350\) | −177.712 | − | 231.601i | −0.507749 | − | 0.661718i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −39.0030 | − | 296.315i | −0.110804 | − | 0.841804i | ||||
\(353\) | 473.760 | 1.34210 | 0.671048 | − | 0.741414i | \(-0.265845\pi\) | ||||
0.671048 | + | 0.741414i | \(0.265845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 36.9540i | − | 0.104096i | ||||||
\(356\) | 4.52978 | − | 16.9047i | 0.0127241 | − | 0.0474851i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 31.2011 | + | 40.6625i | 0.0871539 | + | 0.113582i | ||||
\(359\) | − | 617.624i | − | 1.72040i | −0.509957 | − | 0.860200i | \(-0.670339\pi\) | ||
0.509957 | − | 0.860200i | \(-0.329661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −222.823 | + | 170.976i | −0.615533 | + | 0.472310i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 560.675 | + | 150.239i | 1.54032 | + | 0.412743i | ||||
\(365\) | −85.3465 | −0.233826 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 101.299i | 0.276019i | 0.990431 | + | 0.138010i | \(0.0440705\pi\) | ||||
−0.990431 | + | 0.138010i | \(0.955929\pi\) | |||||||
\(368\) | 296.292 | − | 513.168i | 0.805140 | − | 1.39448i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −56.7386 | + | 43.5366i | −0.153348 | + | 0.117667i | ||||
\(371\) | − | 527.110i | − | 1.42078i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −181.952 | −0.487807 | −0.243904 | − | 0.969799i | \(-0.578428\pi\) | ||||
−0.243904 | + | 0.969799i | \(0.578428\pi\) | |||||||
\(374\) | −58.8530 | − | 76.6995i | −0.157361 | − | 0.205079i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −371.542 | + | 153.891i | −0.988144 | + | 0.409285i | ||||
\(377\) | −522.597 | −1.38620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 631.319i | 1.66575i | 0.553461 | + | 0.832875i | \(0.313307\pi\) | ||||
−0.553461 | + | 0.832875i | \(0.686693\pi\) | |||||||
\(380\) | −24.7275 | − | 6.62597i | −0.0650722 | − | 0.0174368i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 417.052 | + | 543.519i | 1.09176 | + | 1.42282i | ||||
\(383\) | − | 212.170i | − | 0.553970i | −0.960874 | − | 0.276985i | \(-0.910665\pi\) | ||
0.960874 | − | 0.276985i | \(-0.0893352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −87.6193 | −0.227582 | ||||||||
\(386\) | −236.149 | + | 181.201i | −0.611784 | + | 0.469433i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.7345 | − | 62.4514i | 0.0431301 | − | 0.160957i | ||||
\(389\) | −347.500 | −0.893316 | −0.446658 | − | 0.894705i | \(-0.647386\pi\) | ||||
−0.446658 | + | 0.894705i | \(0.647386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 191.679i | − | 0.490227i | ||||||
\(392\) | 25.0250 | + | 60.4182i | 0.0638392 | + | 0.154128i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.9221 | − | 19.8905i | 0.0657921 | − | 0.0504835i | ||||
\(395\) | − | 69.9875i | − | 0.177183i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −313.220 | −0.788967 | −0.394484 | − | 0.918903i | \(-0.629077\pi\) | ||||
−0.394484 | + | 0.918903i | \(0.629077\pi\) | |||||||
\(398\) | −28.9103 | − | 37.6770i | −0.0726389 | − | 0.0946658i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 316.535 | + | 182.760i | 0.791339 | + | 0.456901i | ||||
\(401\) | −484.232 | −1.20756 | −0.603780 | − | 0.797151i | \(-0.706340\pi\) | ||||
−0.603780 | + | 0.797151i | \(0.706340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 452.486i | − | 1.12279i | ||||||
\(404\) | −195.670 | + | 730.221i | −0.484332 | + | 1.80748i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 179.005 | + | 233.286i | 0.440898 | + | 0.574595i | ||||
\(407\) | − | 227.465i | − | 0.558881i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −216.439 | −0.529191 | −0.264596 | − | 0.964359i | \(-0.585238\pi\) | ||||
−0.264596 | + | 0.964359i | \(0.585238\pi\) | |||||||
\(410\) | 133.583 | − | 102.501i | 0.325811 | − | 0.250001i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −482.600 | − | 129.318i | −1.17136 | − | 0.313878i | ||||
\(413\) | 552.246 | 1.33716 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 75.6319i | 0.182246i | ||||||||
\(416\) | −720.548 | + | 94.8434i | −1.73209 | + | 0.227989i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 64.5965 | − | 49.5661i | 0.154537 | − | 0.118579i | ||||
\(419\) | 63.6377i | 0.151880i | 0.997112 | + | 0.0759400i | \(0.0241958\pi\) | ||||
−0.997112 | + | 0.0759400i | \(0.975804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −85.5706 | −0.203256 | −0.101628 | − | 0.994822i | \(-0.532405\pi\) | ||||
−0.101628 | + | 0.994822i | \(0.532405\pi\) | |||||||
\(422\) | 256.194 | + | 333.882i | 0.607095 | + | 0.791190i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 252.551 | + | 609.738i | 0.595639 | + | 1.43806i | ||||
\(425\) | 118.233 | 0.278194 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 731.059i | 1.71208i | ||||||||
\(428\) | 140.685 | + | 37.6978i | 0.328702 | + | 0.0880790i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −140.926 | − | 183.660i | −0.327735 | − | 0.427117i | ||||
\(431\) | 116.175i | 0.269547i | 0.990876 | + | 0.134773i | \(0.0430306\pi\) | ||||
−0.990876 | + | 0.134773i | \(0.956969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 223.452 | 0.516055 | 0.258028 | − | 0.966138i | \(-0.416927\pi\) | ||||
0.258028 | + | 0.966138i | \(0.416927\pi\) | |||||||
\(434\) | −201.988 | + | 154.990i | −0.465411 | + | 0.357119i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.37937 | + | 23.8072i | −0.0146316 | + | 0.0546036i | ||||
\(437\) | 161.432 | 0.369411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 194.178i | − | 0.442319i | −0.975238 | − | 0.221159i | \(-0.929016\pi\) | ||
0.975238 | − | 0.221159i | \(-0.0709841\pi\) | |||||||
\(440\) | 101.354 | − | 41.9805i | 0.230350 | − | 0.0954102i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −186.510 | + | 143.113i | −0.421968 | + | 0.323784i | ||||
\(443\) | 329.812i | 0.744498i | 0.928133 | + | 0.372249i | \(0.121413\pi\) | ||||
−0.928133 | + | 0.372249i | \(0.878587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.42398 | 0.0144359 | ||||||||
\(446\) | −265.269 | − | 345.710i | −0.594775 | − | 0.775133i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 289.146 | + | 289.164i | 0.645416 | + | 0.645455i | ||||
\(449\) | 28.5707 | 0.0636318 | 0.0318159 | − | 0.999494i | \(-0.489871\pi\) | ||||
0.0318159 | + | 0.999494i | \(0.489871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 535.532i | 1.18743i | ||||||||
\(452\) | −137.610 | + | 513.546i | −0.304446 | + | 1.13616i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −266.803 | − | 347.709i | −0.587673 | − | 0.765878i | ||||
\(455\) | 213.063i | 0.468271i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 242.317 | 0.530235 | 0.265117 | − | 0.964216i | \(-0.414589\pi\) | ||||
0.265117 | + | 0.964216i | \(0.414589\pi\) | |||||||
\(458\) | −8.25136 | + | 6.33142i | −0.0180161 | + | 0.0138241i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 210.095 | + | 56.2972i | 0.456729 | + | 0.122385i | ||||
\(461\) | −54.2147 | −0.117602 | −0.0588012 | − | 0.998270i | \(-0.518728\pi\) | ||||
−0.0588012 | + | 0.998270i | \(0.518728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 363.355i | 0.784784i | 0.919798 | + | 0.392392i | \(0.128352\pi\) | ||||
−0.919798 | + | 0.392392i | \(0.871648\pi\) | |||||||
\(464\) | −318.837 | − | 184.089i | −0.687150 | − | 0.396745i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −403.465 | + | 309.587i | −0.865805 | + | 0.664349i | ||||
\(467\) | − | 683.263i | − | 1.46309i | −0.681793 | − | 0.731545i | \(-0.738800\pi\) | ||
0.681793 | − | 0.731545i | \(-0.261200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −413.565 | −0.881801 | ||||||||
\(470\) | −89.8616 | − | 117.111i | −0.191195 | − | 0.249173i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −638.814 | + | 264.594i | −1.35342 | + | 0.560581i | ||||
\(473\) | 736.293 | 1.55664 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 99.5757i | 0.209633i | ||||||||
\(476\) | 127.770 | + | 34.2373i | 0.268424 | + | 0.0719270i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −68.3469 | − | 89.0723i | −0.142985 | − | 0.186344i | ||||
\(479\) | 432.689i | 0.903317i | 0.892191 | + | 0.451659i | \(0.149167\pi\) | ||||
−0.892191 | + | 0.451659i | \(0.850833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −553.125 | −1.14995 | ||||||||
\(482\) | 258.014 | − | 197.979i | 0.535298 | − | 0.410744i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 34.9623 | − | 130.476i | 0.0722361 | − | 0.269578i | ||||
\(485\) | 23.7323 | 0.0489325 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 809.853i | − | 1.66294i | −0.555568 | − | 0.831471i | \(-0.687499\pi\) | ||
0.555568 | − | 0.831471i | \(-0.312501\pi\) | |||||||
\(488\) | −350.268 | − | 845.658i | −0.717762 | − | 1.73291i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19.0440 | + | 14.6128i | −0.0388653 | + | 0.0298221i | ||||
\(491\) | 296.648i | 0.604171i | 0.953281 | + | 0.302085i | \(0.0976827\pi\) | ||||
−0.953281 | + | 0.302085i | \(0.902317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −119.092 | −0.241567 | ||||||||
\(494\) | −120.530 | − | 157.079i | −0.243987 | − | 0.317974i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 159.392 | − | 276.063i | 0.321355 | − | 0.556578i | ||||
\(497\) | −160.815 | −0.323572 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 30.5867i | − | 0.0612960i | −0.999530 | − | 0.0306480i | \(-0.990243\pi\) | ||
0.999530 | − | 0.0306480i | \(-0.00975708\pi\) | |||||||
\(500\) | −72.7281 | + | 271.414i | −0.145456 | + | 0.542828i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −443.830 | − | 578.417i | −0.884123 | − | 1.15222i | ||||
\(503\) | − | 544.773i | − | 1.08305i | −0.840685 | − | 0.541524i | \(-0.817847\pi\) | ||
0.840685 | − | 0.541524i | \(-0.182153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −277.493 | −0.549490 | ||||||||
\(506\) | −548.840 | + | 421.136i | −1.08466 | + | 0.832284i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −306.464 | − | 82.1200i | −0.603275 | − | 0.161654i | ||||
\(509\) | −750.280 | −1.47403 | −0.737014 | − | 0.675877i | \(-0.763765\pi\) | ||||
−0.737014 | + | 0.675877i | \(0.763765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 371.408i | 0.726827i | ||||||||
\(512\) | −473.017 | − | 195.955i | −0.923862 | − | 0.382725i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33.9408 | − | 26.0434i | 0.0660327 | − | 0.0506682i | ||||
\(515\) | − | 183.394i | − | 0.356105i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 469.498 | 0.908120 | ||||||||
\(518\) | 189.461 | + | 246.913i | 0.365756 | + | 0.476667i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −102.084 | − | 246.463i | −0.196315 | − | 0.473967i | ||||
\(521\) | 449.862 | 0.863460 | 0.431730 | − | 0.902003i | \(-0.357903\pi\) | ||||
0.431730 | + | 0.902003i | \(0.357903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 147.673i | 0.282358i | 0.989984 | + | 0.141179i | \(0.0450894\pi\) | ||||
−0.989984 | + | 0.141179i | \(0.954911\pi\) | |||||||
\(524\) | −79.0688 | − | 21.1873i | −0.150895 | − | 0.0404338i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −98.1532 | − | 127.917i | −0.186603 | − | 0.243188i | ||||
\(527\) | − | 103.115i | − | 0.195664i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −842.602 | −1.59282 | ||||||||
\(530\) | −192.191 | + | 147.472i | −0.362625 | + | 0.278249i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −28.8347 | + | 107.608i | −0.0542006 | + | 0.202271i | ||||
\(533\) | 1302.25 | 2.44325 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.4618i | 0.0999286i | ||||||||
\(536\) | 478.394 | − | 198.149i | 0.892526 | − | 0.369680i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −249.067 | + | 191.114i | −0.462949 | + | 0.355230i | ||||
\(539\) | − | 76.3472i | − | 0.141646i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 267.803 | 0.495014 | 0.247507 | − | 0.968886i | \(-0.420389\pi\) | ||||
0.247507 | + | 0.968886i | \(0.420389\pi\) | |||||||
\(542\) | 231.616 | + | 301.851i | 0.427336 | + | 0.556920i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −164.203 | + | 21.6135i | −0.301843 | + | 0.0397306i | ||||
\(545\) | −9.04701 | −0.0166000 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 931.607i | 1.70312i | 0.524257 | + | 0.851560i | \(0.324343\pi\) | ||||
−0.524257 | + | 0.851560i | \(0.675657\pi\) | |||||||
\(548\) | −249.928 | + | 932.706i | −0.456073 | + | 1.70202i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −259.767 | − | 338.539i | −0.472304 | − | 0.615526i | ||||
\(551\) | − | 100.300i | − | 0.182033i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −304.569 | −0.550758 | ||||||||
\(554\) | 204.428 | − | 156.861i | 0.369003 | − | 0.283143i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 417.668 | + | 111.918i | 0.751201 | + | 0.201292i | ||||
\(557\) | −96.1417 | −0.172606 | −0.0863031 | − | 0.996269i | \(-0.527505\pi\) | ||||
−0.0863031 | + | 0.996269i | \(0.527505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1790.44i | − | 3.20294i | ||||||
\(560\) | −75.0535 | + | 129.990i | −0.134024 | + | 0.232126i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −107.596 | + | 82.5606i | −0.191452 | + | 0.146905i | ||||
\(563\) | 205.785i | 0.365515i | 0.983158 | + | 0.182758i | \(0.0585024\pi\) | ||||
−0.983158 | + | 0.182758i | \(0.941498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −195.154 | −0.345404 | ||||||||
\(566\) | 543.490 | + | 708.298i | 0.960230 | + | 1.25141i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 186.024 | − | 77.0504i | 0.327507 | − | 0.135652i | ||||
\(569\) | 497.783 | 0.874838 | 0.437419 | − | 0.899258i | \(-0.355893\pi\) | ||||
0.437419 | + | 0.899258i | \(0.355893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 902.458i | 1.58049i | 0.612792 | + | 0.790244i | \(0.290046\pi\) | ||||
−0.612792 | + | 0.790244i | \(0.709954\pi\) | |||||||
\(572\) | 819.557 | + | 219.609i | 1.43279 | + | 0.383931i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −446.059 | − | 581.321i | −0.777106 | − | 1.01275i | ||||
\(575\) | − | 846.040i | − | 1.47137i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.74046 | 0.0168812 | 0.00844061 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844061 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(578\) | 416.057 | − | 319.248i | 0.719822 | − | 0.552333i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34.9781 | − | 130.535i | 0.0603071 | − | 0.225060i | ||||
\(581\) | 329.133 | 0.566494 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 770.493i | − | 1.32160i | ||||||
\(584\) | −177.951 | − | 429.629i | −0.304710 | − | 0.735667i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 680.230 | − | 521.954i | 1.16080 | − | 0.890706i | ||||
\(587\) | 674.185i | 1.14853i | 0.818671 | + | 0.574263i | \(0.194711\pi\) | ||||
−0.818671 | + | 0.574263i | \(0.805289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 86.8438 | 0.147443 | ||||||||
\(590\) | −154.504 | − | 201.356i | −0.261872 | − | 0.341282i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −337.463 | − | 194.843i | −0.570039 | − | 0.329127i | ||||
\(593\) | 496.880 | 0.837908 | 0.418954 | − | 0.908007i | \(-0.362397\pi\) | ||||
0.418954 | + | 0.908007i | \(0.362397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.5541i | 0.0816036i | ||||||||
\(596\) | −218.516 | + | 815.479i | −0.366637 | + | 1.36825i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1024.07 | + | 1334.61i | 1.71250 | + | 2.23179i | ||||
\(599\) | − | 77.0314i | − | 0.128600i | −0.997931 | − | 0.0643000i | \(-0.979519\pi\) | ||
0.997931 | − | 0.0643000i | \(-0.0204814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −686.862 | −1.14287 | −0.571433 | − | 0.820649i | \(-0.693612\pi\) | ||||
−0.571433 | + | 0.820649i | \(0.693612\pi\) | |||||||
\(602\) | −799.248 | + | 613.278i | −1.32765 | + | 1.01873i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −472.171 | − | 126.523i | −0.781739 | − | 0.209475i | ||||
\(605\) | 49.5824 | 0.0819543 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 301.232i | − | 0.496263i | −0.968726 | − | 0.248132i | \(-0.920183\pi\) | ||
0.968726 | − | 0.248132i | \(-0.0798166\pi\) | |||||||
\(608\) | −18.2029 | − | 138.292i | −0.0299390 | − | 0.227454i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 266.554 | − | 204.532i | 0.436973 | − | 0.335298i | ||||
\(611\) | − | 1141.68i | − | 1.86854i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 823.267 | 1.34301 | 0.671507 | − | 0.740999i | \(-0.265647\pi\) | ||||
0.671507 | + | 0.740999i | \(0.265647\pi\) | |||||||
\(614\) | −183.730 | − | 239.444i | −0.299234 | − | 0.389973i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −182.689 | − | 441.070i | −0.296574 | − | 0.716023i | ||||
\(617\) | 366.129 | 0.593402 | 0.296701 | − | 0.954970i | \(-0.404114\pi\) | ||||
0.296701 | + | 0.954970i | \(0.404114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 419.279i | − | 0.677349i | −0.940904 | − | 0.338674i | \(-0.890021\pi\) | ||
0.940904 | − | 0.338674i | \(-0.109979\pi\) | |||||||
\(620\) | 113.022 | + | 30.2855i | 0.182294 | + | 0.0488476i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 543.802 | + | 708.704i | 0.874280 | + | 1.13940i | ||||
\(623\) | − | 27.9557i | − | 0.0448727i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 467.965 | 0.748745 | ||||||||
\(626\) | 184.959 | − | 141.922i | 0.295462 | − | 0.226713i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −169.315 | + | 631.867i | −0.269610 | + | 1.00616i | ||||
\(629\) | −126.049 | −0.200396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 535.084i | − | 0.847993i | −0.905664 | − | 0.423996i | \(-0.860627\pi\) | ||
0.905664 | − | 0.423996i | \(-0.139373\pi\) | |||||||
\(632\) | 352.313 | − | 145.926i | 0.557457 | − | 0.230896i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −343.329 | + | 263.443i | −0.541529 | + | 0.415525i | ||||
\(635\) | − | 116.460i | − | 0.183401i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −185.653 | −0.291449 | ||||||||
\(638\) | 261.657 | + | 341.001i | 0.410120 | + | 0.534484i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.5372 | − | 186.327i | 0.0383393 | − | 0.291136i | ||||
\(641\) | 647.399 | 1.00998 | 0.504992 | − | 0.863124i | \(-0.331496\pi\) | ||||
0.504992 | + | 0.863124i | \(0.331496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 724.071i | 1.12608i | 0.826429 | + | 0.563041i | \(0.190369\pi\) | ||||
−0.826429 | + | 0.563041i | \(0.809631\pi\) | |||||||
\(644\) | 244.992 | − | 914.287i | 0.380423 | − | 1.41970i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.4670 | − | 35.7961i | −0.0425186 | − | 0.0554119i | ||||
\(647\) | − | 281.255i | − | 0.434707i | −0.976093 | − | 0.217353i | \(-0.930258\pi\) | ||
0.976093 | − | 0.217353i | \(-0.0697424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 807.236 | 1.24381 | ||||||||
\(650\) | −823.224 | + | 631.676i | −1.26650 | + | 0.971809i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −305.461 | − | 81.8514i | −0.468499 | − | 0.125539i | ||||
\(653\) | −927.635 | −1.42057 | −0.710287 | − | 0.703912i | \(-0.751435\pi\) | ||||
−0.710287 | + | 0.703912i | \(0.751435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 30.0471i | − | 0.0458734i | ||||||
\(656\) | 794.506 | + | 458.730i | 1.21114 | + | 0.699283i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −509.641 | + | 391.057i | −0.774530 | + | 0.594312i | ||||
\(659\) | − | 333.439i | − | 0.505977i | −0.967469 | − | 0.252989i | \(-0.918586\pi\) | ||
0.967469 | − | 0.252989i | \(-0.0814136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 264.400 | 0.400000 | 0.200000 | − | 0.979796i | \(-0.435906\pi\) | ||||
0.200000 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(662\) | −325.096 | − | 423.678i | −0.491082 | − | 0.639997i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −380.727 | + | 157.695i | −0.573384 | + | 0.237493i | ||||
\(665\) | −40.8924 | −0.0614923 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 852.193i | 1.27765i | ||||||||
\(668\) | 1031.03 | + | 276.274i | 1.54345 | + | 0.413583i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 115.705 | + | 150.791i | 0.172694 | + | 0.225061i | ||||
\(671\) | 1068.61i | 1.59257i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −190.774 | −0.283467 | −0.141734 | − | 0.989905i | \(-0.545268\pi\) | ||||
−0.141734 | + | 0.989905i | \(0.545268\pi\) | |||||||
\(674\) | 145.260 | − | 111.461i | 0.215519 | − | 0.165372i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 359.053 | − | 1339.95i | 0.531144 | − | 1.98218i | ||||
\(677\) | 518.388 | 0.765713 | 0.382856 | − | 0.923808i | \(-0.374940\pi\) | ||||
0.382856 | + | 0.923808i | \(0.374940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 103.277i | − | 0.152102i | ||||||
\(680\) | −23.2634 | − | 56.1653i | −0.0342109 | − | 0.0825961i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −295.253 | + | 226.553i | −0.432922 | + | 0.332189i | ||||
\(683\) | 1024.21i | 1.49957i | 0.661679 | + | 0.749787i | \(0.269844\pi\) | ||||
−0.661679 | + | 0.749787i | \(0.730156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −354.440 | −0.517430 | ||||||||
\(686\) | 444.777 | + | 579.651i | 0.648363 | + | 0.844972i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 630.699 | − | 1092.35i | 0.916714 | − | 1.58772i | ||||
\(689\) | −1873.61 | −2.71931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 405.284i | − | 0.586518i | −0.956033 | − | 0.293259i | \(-0.905260\pi\) | ||
0.956033 | − | 0.293259i | \(-0.0947399\pi\) | |||||||
\(692\) | 239.323 | − | 893.131i | 0.345843 | − | 1.29065i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 269.167 | + | 350.789i | 0.387849 | + | 0.505460i | ||||
\(695\) | 158.719i | 0.228372i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 296.765 | 0.425774 | ||||||||
\(698\) | 1030.46 | − | 790.694i | 1.47631 | − | 1.13280i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 563.956 | + | 151.118i | 0.805652 | + | 0.215882i | ||||
\(701\) | 93.5411 | 0.133440 | 0.0667198 | − | 0.997772i | \(-0.478747\pi\) | ||||
0.0667198 | + | 0.997772i | \(0.478747\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 106.159i | − | 0.151009i | ||||||
\(704\) | 422.654 | + | 422.680i | 0.600361 | + | 0.600398i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −751.721 | + | 576.810i | −1.06476 | + | 0.817011i | ||||
\(707\) | 1207.58i | 1.70804i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 597.864 | 0.843249 | 0.421625 | − | 0.906771i | \(-0.361460\pi\) | ||||
0.421625 | + | 0.906771i | \(0.361460\pi\) | |||||||
\(710\) | 44.9920 | + | 58.6354i | 0.0633690 | + | 0.0825850i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.3942 | + | 32.3380i | 0.0188121 | + | 0.0454185i | ||||
\(713\) | −737.864 | −1.03487 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 311.442i | 0.435583i | ||||||||
\(716\) | −99.0144 | − | 26.5319i | −0.138288 | − | 0.0370557i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 751.966 | + | 979.991i | 1.04731 | + | 1.36489i | ||||
\(719\) | 1190.68i | 1.65602i | 0.560714 | + | 0.828010i | \(0.310527\pi\) | ||||
−0.560714 | + | 0.828010i | \(0.689473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −798.088 | −1.10692 | ||||||||
\(722\) | 30.1475 | − | 23.1328i | 0.0417556 | − | 0.0320399i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 145.390 | − | 542.580i | 0.200815 | − | 0.749420i | ||||
\(725\) | −525.655 | −0.725041 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 198.257i | 0.272705i | 0.990660 | + | 0.136353i | \(0.0435381\pi\) | ||||
−0.990660 | + | 0.136353i | \(0.956462\pi\) | |||||||
\(728\) | −1072.55 | + | 444.245i | −1.47328 | + | 0.610227i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 135.420 | − | 103.911i | 0.185507 | − | 0.142343i | ||||
\(731\) | − | 408.016i | − | 0.558162i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 125.026 | 0.170568 | 0.0852841 | − | 0.996357i | \(-0.472820\pi\) | ||||
0.0852841 | + | 0.996357i | \(0.472820\pi\) | |||||||
\(734\) | −123.333 | − | 160.733i | −0.168029 | − | 0.218982i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 154.660 | + | 1174.99i | 0.210136 | + | 1.59645i | ||||
\(737\) | −604.521 | −0.820245 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1209.59i | 1.63679i | 0.574657 | + | 0.818395i | \(0.305136\pi\) | ||||
−0.574657 | + | 0.818395i | \(0.694864\pi\) | |||||||
\(740\) | 37.0214 | − | 138.160i | 0.0500289 | − | 0.186703i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 641.764 | + | 836.372i | 0.864911 | + | 1.12719i | ||||
\(743\) | 253.947i | 0.341786i | 0.985290 | + | 0.170893i | \(0.0546652\pi\) | ||||
−0.985290 | + | 0.170893i | \(0.945335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −309.892 | −0.415962 | ||||||||
\(746\) | 288.706 | − | 221.529i | 0.387005 | − | 0.296956i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 186.765 | + | 50.0457i | 0.249686 | + | 0.0669060i | ||||
\(749\) | 232.654 | 0.310619 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 996.217i | − | 1.32652i | −0.748388 | − | 0.663261i | \(-0.769172\pi\) | ||
0.748388 | − | 0.663261i | \(-0.230828\pi\) | |||||||
\(752\) | 402.166 | − | 696.539i | 0.534795 | − | 0.926249i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 829.211 | − | 636.269i | 1.09975 | − | 0.843859i | ||||
\(755\) | − | 179.430i | − | 0.237656i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 512.909 | 0.677555 | 0.338778 | − | 0.940866i | \(-0.389987\pi\) | ||||
0.338778 | + | 0.940866i | \(0.389987\pi\) | |||||||
\(758\) | −768.640 | − | 1001.72i | −1.01404 | − | 1.32153i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 47.3026 | − | 19.5925i | 0.0622402 | − | 0.0257796i | ||||
\(761\) | 140.112 | 0.184115 | 0.0920576 | − | 0.995754i | \(-0.470656\pi\) | ||||
0.0920576 | + | 0.995754i | \(0.470656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.3705i | 0.0515996i | ||||||||
\(764\) | −1323.48 | − | 354.641i | −1.73231 | − | 0.464190i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 258.321 | + | 336.653i | 0.337233 | + | 0.439495i | ||||
\(767\) | − | 1962.95i | − | 2.55926i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 914.743 | 1.18952 | 0.594761 | − | 0.803902i | \(-0.297247\pi\) | ||||
0.594761 | + | 0.803902i | \(0.297247\pi\) | |||||||
\(770\) | 139.027 | − | 106.678i | 0.180554 | − | 0.138543i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 154.085 | − | 575.029i | 0.199592 | − | 0.744856i | ||||
\(773\) | 352.461 | 0.455965 | 0.227982 | − | 0.973665i | \(-0.426787\pi\) | ||||
0.227982 | + | 0.973665i | \(0.426787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 455.134i | − | 0.587269i | ||||||
\(776\) | 49.4827 | + | 119.467i | 0.0637664 | + | 0.153952i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 551.382 | − | 423.086i | 0.708718 | − | 0.543812i | ||||
\(779\) | 249.936i | 0.320842i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −235.069 | −0.300984 | ||||||||
\(782\) | 233.372 | + | 304.139i | 0.298430 | + | 0.388925i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −113.267 | − | 65.3980i | −0.144474 | − | 0.0834159i | ||||
\(785\) | −240.117 | −0.305882 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 971.341i | − | 1.23423i | −0.786872 | − | 0.617116i | \(-0.788301\pi\) | ||
0.786872 | − | 0.617116i | \(-0.211699\pi\) | |||||||
\(788\) | −16.9139 | + | 63.1210i | −0.0214644 | + | 0.0801028i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 85.2108 | + | 111.050i | 0.107862 | + | 0.140570i | ||||
\(791\) | 849.263i | 1.07366i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2598.54 | 3.27685 | ||||||||
\(794\) | 496.990 | − | 381.350i | 0.625932 | − | 0.480290i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 91.7446 | + | 24.5839i | 0.115257 | + | 0.0308843i | ||||
\(797\) | 774.703 | 0.972024 | 0.486012 | − | 0.873952i | \(-0.338451\pi\) | ||||
0.486012 | + | 0.873952i | \(0.338451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 260.172i | − | 0.325622i | ||||||
\(800\) | −724.764 | + | 95.3984i | −0.905955 | + | 0.119248i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 768.337 | − | 589.560i | 0.958026 | − | 0.735112i | ||||
\(803\) | 542.900i | 0.676089i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 347.440 | 0.431603 | ||||||||
\(806\) | 550.909 | + | 717.966i | 0.683509 | + | 0.890776i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −578.582 | − | 1396.88i | −0.716067 | − | 1.72881i | ||||
\(809\) | −1067.09 | −1.31902 | −0.659511 | − | 0.751695i | \(-0.729236\pi\) | ||||
−0.659511 | + | 0.751695i | \(0.729236\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1348.15i | − | 1.66233i | −0.556024 | − | 0.831166i | \(-0.687674\pi\) | ||
0.556024 | − | 0.831166i | \(-0.312326\pi\) | |||||||
\(812\) | −568.057 | − | 152.217i | −0.699578 | − | 0.187459i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 276.942 | + | 360.921i | 0.340223 | + | 0.443392i | ||||
\(815\) | − | 116.079i | − | 0.142428i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 343.632 | 0.420602 | ||||||||
\(818\) | 343.427 | − | 263.518i | 0.419837 | − | 0.322149i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −87.1615 | + | 325.278i | −0.106294 | + | 0.396680i | ||||
\(821\) | −464.614 | −0.565913 | −0.282956 | − | 0.959133i | \(-0.591315\pi\) | ||||
−0.282956 | + | 0.959133i | \(0.591315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1030.57i | 1.25221i | 0.779738 | + | 0.626106i | \(0.215352\pi\) | ||||
−0.779738 | + | 0.626106i | \(0.784648\pi\) | |||||||
\(824\) | 923.194 | − | 382.383i | 1.12038 | − | 0.464057i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −876.256 | + | 672.368i | −1.06084 | + | 0.814004i | ||||
\(827\) | − | 805.473i | − | 0.973969i | −0.873411 | − | 0.486985i | \(-0.838097\pi\) | ||
0.873411 | − | 0.486985i | \(-0.161903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 755.129 | 0.910892 | 0.455446 | − | 0.890263i | \(-0.349480\pi\) | ||||
0.455446 | + | 0.890263i | \(0.349480\pi\) | |||||||
\(830\) | −92.0830 | − | 120.006i | −0.110943 | − | 0.144586i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1027.83 | − | 1027.77i | 1.23537 | − | 1.23530i | ||||
\(833\) | −42.3077 | −0.0507896 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 391.802i | 0.469224i | ||||||||
\(836\) | −42.1486 | + | 157.294i | −0.0504170 | + | 0.188151i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −77.4799 | − | 100.975i | −0.0924581 | − | 0.120495i | ||||
\(839\) | − | 386.315i | − | 0.460447i | −0.973138 | − | 0.230223i | \(-0.926054\pi\) | ||
0.973138 | − | 0.230223i | \(-0.0739457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −311.522 | −0.370419 | ||||||||
\(842\) | 135.776 | − | 104.184i | 0.161254 | − | 0.123733i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −813.013 | − | 217.855i | −0.963286 | − | 0.258122i | ||||
\(845\) | 509.197 | 0.602600 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 215.771i | − | 0.254747i | ||||||
\(848\) | −1143.09 | − | 659.995i | −1.34798 | − | 0.778295i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −187.601 | + | 143.950i | −0.220707 | + | 0.169353i | ||||
\(851\) | 901.975i | 1.05990i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −621.728 | −0.728872 | −0.364436 | − | 0.931228i | \(-0.618738\pi\) | ||||
−0.364436 | + | 0.931228i | \(0.618738\pi\) | |||||||
\(854\) | −890.075 | − | 1159.98i | −1.04224 | − | 1.35829i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −269.124 | + | 111.470i | −0.314397 | + | 0.130222i | ||||
\(857\) | −341.259 | −0.398202 | −0.199101 | − | 0.979979i | \(-0.563802\pi\) | ||||
−0.199101 | + | 0.979979i | \(0.563802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 86.1874i | − | 0.100335i | −0.998741 | − | 0.0501673i | \(-0.984025\pi\) | ||
0.998741 | − | 0.0501673i | \(-0.0159754\pi\) | |||||||
\(860\) | 447.218 | + | 119.837i | 0.520021 | + | 0.139345i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −141.444 | − | 184.336i | −0.164089 | − | 0.213847i | ||||
\(863\) | − | 720.200i | − | 0.834531i | −0.908785 | − | 0.417266i | \(-0.862988\pi\) | ||
0.908785 | − | 0.417266i | \(-0.137012\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 339.400 | 0.392370 | ||||||||
\(866\) | −354.554 | + | 272.056i | −0.409416 | + | 0.314152i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 131.796 | − | 491.848i | 0.151838 | − | 0.566645i | ||||
\(869\) | −445.199 | −0.512312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1470.01i | 1.68773i | ||||||||
\(872\) | −18.8634 | − | 45.5421i | −0.0216323 | − | 0.0522272i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −256.147 | + | 196.546i | −0.293074 | + | 0.224881i | ||||
\(875\) | 448.844i | 0.512965i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1224.25 | −1.39596 | −0.697978 | − | 0.716119i | \(-0.745917\pi\) | ||||
−0.697978 | + | 0.716119i | \(0.745917\pi\) | |||||||
\(878\) | 236.415 | + | 308.105i | 0.269265 | + | 0.350917i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −109.708 | + | 190.011i | −0.124668 | + | 0.215922i | ||||
\(881\) | −301.507 | −0.342233 | −0.171116 | − | 0.985251i | \(-0.554737\pi\) | ||||
−0.171116 | + | 0.985251i | \(0.554737\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 885.527i | 1.00286i | 0.865198 | + | 0.501431i | \(0.167193\pi\) | ||||
−0.865198 | + | 0.501431i | \(0.832807\pi\) | |||||||
\(884\) | 121.696 | − | 454.157i | 0.137665 | − | 0.513752i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −401.552 | − | 523.318i | −0.453219 | − | 0.590652i | ||||
\(887\) | 1647.19i | 1.85703i | 0.371291 | + | 0.928516i | \(0.378915\pi\) | ||||
−0.371291 | + | 0.928516i | \(0.621085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −506.807 | −0.570086 | ||||||||
\(890\) | −10.1930 | + | 7.82130i | −0.0114528 | + | 0.00878797i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 841.813 | + | 225.572i | 0.943737 | + | 0.252884i | ||||
\(893\) | 219.117 | 0.245372 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 37.6267i | − | 0.0420410i | ||||||
\(896\) | −810.854 | − | 106.780i | −0.904971 | − | 0.119174i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −45.3335 | + | 34.7852i | −0.0504827 | + | 0.0387363i | ||||
\(899\) | 458.444i | 0.509948i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −426.968 | −0.473883 | ||||||||
\(902\) | −652.018 | − | 849.736i | −0.722858 | − | 0.942057i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −406.902 | − | 982.391i | −0.450113 | − | 1.08672i | ||||
\(905\) | 206.187 | 0.227831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 720.605i | 0.794493i | 0.917712 | + | 0.397246i | \(0.130034\pi\) | ||||
−0.917712 | + | 0.397246i | \(0.869966\pi\) | |||||||
\(908\) | 846.681 | + | 226.877i | 0.932468 | + | 0.249864i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −259.408 | − | 338.070i | −0.285064 | − | 0.371506i | ||||
\(911\) | − | 616.939i | − | 0.677211i | −0.940928 | − | 0.338605i | \(-0.890045\pi\) | ||
0.940928 | − | 0.338605i | \(-0.109955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 481.104 | 0.526948 | ||||||||
\(914\) | −384.488 | + | 295.025i | −0.420665 | + | 0.322784i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.38393 | − | 20.0923i | 0.00587766 | − | 0.0219348i | ||||
\(917\) | −130.758 | −0.142593 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0960i | 0.0142503i | 0.999975 | + | 0.00712513i | \(0.00226802\pi\) | ||||
−0.999975 | + | 0.00712513i | \(0.997732\pi\) | |||||||
\(920\) | −401.904 | + | 166.467i | −0.436852 | + | 0.180942i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 86.0232 | − | 66.0072i | 0.0933007 | − | 0.0715914i | ||||
\(923\) | 571.616i | 0.619302i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −556.362 | −0.601472 | ||||||||
\(926\) | −442.390 | − | 576.540i | −0.477743 | − | 0.622613i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 730.035 | − | 96.0922i | 0.786676 | − | 0.103548i | ||||
\(929\) | −429.548 | −0.462377 | −0.231188 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231188 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 35.6317i | − | 0.0382725i | ||||||
\(932\) | 263.257 | − | 982.450i | 0.282465 | − | 1.05413i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 831.883 | + | 1084.14i | 0.890667 | + | 1.16075i | ||||
\(935\) | 70.9731i | 0.0759071i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.9330 | −0.0148698 | −0.00743489 | − | 0.999972i | \(-0.502367\pi\) | ||||
−0.00743489 | + | 0.999972i | \(0.502367\pi\) | |||||||
\(938\) | 656.208 | − | 503.521i | 0.699583 | − | 0.536803i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 285.169 | + | 76.4139i | 0.303371 | + | 0.0812914i | ||||
\(941\) | −560.573 | −0.595721 | −0.297860 | − | 0.954609i | \(-0.596273\pi\) | ||||
−0.297860 | + | 0.954609i | \(0.596273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2123.57i | − | 2.25193i | ||||||
\(944\) | 691.468 | − | 1197.60i | 0.732487 | − | 1.26865i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1168.29 | + | 896.448i | −1.23497 | + | 0.947619i | ||||
\(947\) | − | 1022.02i | − | 1.07922i | −0.841916 | − | 0.539608i | \(-0.818572\pi\) | ||
0.841916 | − | 0.539608i | \(-0.181428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1320.17 | 1.39111 | ||||||||
\(950\) | −121.235 | − | 157.998i | −0.127616 | − | 0.166314i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −244.419 | + | 101.237i | −0.256742 | + | 0.106342i | ||||
\(953\) | −1648.92 | −1.73024 | −0.865120 | − | 0.501565i | \(-0.832758\pi\) | ||||
−0.865120 | + | 0.501565i | \(0.832758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 502.940i | − | 0.526639i | ||||||
\(956\) | 216.894 | + | 58.1189i | 0.226876 | + | 0.0607938i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −526.805 | − | 686.553i | −0.549901 | − | 0.716652i | ||||
\(959\) | 1542.44i | 1.60838i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 564.060 | 0.586952 | ||||||||
\(962\) | 877.651 | − | 673.438i | 0.912319 | − | 0.700040i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −168.351 | + | 628.271i | −0.174638 | + | 0.651733i | ||||
\(965\) | 218.518 | 0.226443 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1235.61i | − | 1.27778i | −0.769299 | − | 0.638889i | \(-0.779394\pi\) | ||
0.769299 | − | 0.638889i | \(-0.220606\pi\) | |||||||
\(968\) | 103.381 | + | 249.595i | 0.106799 | + | 0.257846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −37.6563 | + | 28.8944i | −0.0388209 | + | 0.0297880i | ||||
\(971\) | 1012.04i | 1.04226i | 0.853476 | + | 0.521131i | \(0.174490\pi\) | ||||
−0.853476 | + | 0.521131i | \(0.825510\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 690.708 | 0.709875 | ||||||||
\(974\) | 986.008 | + | 1285.00i | 1.01233 | + | 1.31931i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1585.38 | + | 915.360i | 1.62436 | + | 0.937869i | ||||
\(977\) | −303.876 | −0.311030 | −0.155515 | − | 0.987834i | \(-0.549704\pi\) | ||||
−0.155515 | + | 0.987834i | \(0.549704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 40.8637i | − | 0.0417403i | ||||||
\(980\) | 12.4260 | − | 46.3727i | 0.0126796 | − | 0.0473190i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −361.173 | − | 470.695i | −0.367793 | − | 0.479323i | ||||
\(983\) | 1429.58i | 1.45431i | 0.686474 | + | 0.727154i | \(0.259157\pi\) | ||||
−0.686474 | + | 0.727154i | \(0.740843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.9867 | −0.0243520 | ||||||||
\(986\) | 188.965 | − | 144.997i | 0.191649 | − | 0.147056i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 382.492 | + | 102.493i | 0.387138 | + | 0.103737i | ||||
\(989\) | −2919.65 | −2.95213 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 190.067i | 0.191793i | 0.995391 | + | 0.0958966i | \(0.0305718\pi\) | ||||
−0.995391 | + | 0.0958966i | \(0.969428\pi\) | |||||||
\(992\) | 83.2006 | + | 632.095i | 0.0838716 | + | 0.637192i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 255.168 | − | 195.795i | 0.256708 | − | 0.196977i | ||||
\(995\) | 34.8640i | 0.0350392i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −841.121 | −0.843652 | −0.421826 | − | 0.906677i | \(-0.638611\pi\) | ||||
−0.421826 | + | 0.906677i | \(0.638611\pi\) | |||||||
\(998\) | 37.2397 | + | 48.5323i | 0.0373144 | + | 0.0486295i | ||||
\(999\) | 0 | 0 |
(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.g.d.343.6 | yes | 36 | |
3.2 | odd | 2 | inner | 684.3.g.d.343.31 | yes | 36 | |
4.3 | odd | 2 | inner | 684.3.g.d.343.5 | ✓ | 36 | |
12.11 | even | 2 | inner | 684.3.g.d.343.32 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.g.d.343.5 | ✓ | 36 | 4.3 | odd | 2 | inner | |
684.3.g.d.343.6 | yes | 36 | 1.1 | even | 1 | trivial | |
684.3.g.d.343.31 | yes | 36 | 3.2 | odd | 2 | inner | |
684.3.g.d.343.32 | yes | 36 | 12.11 | even | 2 | inner |