Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(193,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 2, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bp (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 193.19 | ||
Character | \(\chi\) | \(=\) | 756.193 |
Dual form | 756.2.bp.a.709.19 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.17989 | + | 1.26802i | 0.681209 | + | 0.732089i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.75808 | − | 1.36783i | 1.68066 | − | 0.611712i | 0.687264 | − | 0.726408i | \(-0.258812\pi\) |
0.993401 | + | 0.114696i | \(0.0365895\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59104 | − | 0.535278i | 0.979320 | − | 0.202316i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.215726 | + | 2.99223i | −0.0719088 | + | 0.997411i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.974227 | − | 0.354590i | −0.293741 | − | 0.106913i | 0.190947 | − | 0.981600i | \(-0.438844\pi\) |
−0.484687 | + | 0.874688i | \(0.661067\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.95754 | + | 0.712485i | −0.542923 | + | 0.197608i | −0.598899 | − | 0.800824i | \(-0.704395\pi\) |
0.0559763 | + | 0.998432i | \(0.482173\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.16854 | + | 3.15142i | 1.59271 | + | 0.813692i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.153243 | − | 0.265426i | −0.0371670 | − | 0.0643751i | 0.846844 | − | 0.531842i | \(-0.178500\pi\) |
−0.884011 | + | 0.467467i | \(0.845167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.388297 | − | 0.672550i | 0.0890814 | − | 0.154294i | −0.818042 | − | 0.575159i | \(-0.804940\pi\) |
0.907123 | + | 0.420865i | \(0.138274\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.73588 | + | 2.65391i | 0.815235 | + | 0.579130i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.439761 | − | 2.49401i | 0.0916965 | − | 0.520037i | −0.904013 | − | 0.427505i | \(-0.859393\pi\) |
0.995710 | − | 0.0925322i | \(-0.0294961\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.42198 | − | 7.06688i | 1.68440 | − | 1.41338i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.04873 | + | 3.25696i | −0.779179 | + | 0.626802i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.90667 | − | 3.24176i | −1.65393 | − | 0.601980i | −0.664536 | − | 0.747257i | \(-0.731371\pi\) |
−0.989391 | + | 0.145276i | \(0.953593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.70422 | + | 1.34823i | −0.665298 | + | 0.242149i | −0.652522 | − | 0.757770i | \(-0.726289\pi\) |
−0.0127760 | + | 0.999918i | \(0.504067\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.699854 | − | 1.65371i | −0.121829 | − | 0.287874i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.00516 | − | 5.55571i | 1.52215 | − | 0.939087i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.1327 | −1.83020 | −0.915102 | − | 0.403223i | \(-0.867890\pi\) | ||||
−0.915102 | + | 0.403223i | \(0.867890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.21312 | − | 1.64153i | −0.514511 | − | 0.262856i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.30886 | + | 1.56830i | −0.672931 | + | 0.244927i | −0.655809 | − | 0.754927i | \(-0.727672\pi\) |
−0.0171215 | + | 0.999853i | \(0.505450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.781068 | + | 4.42966i | 0.119112 | + | 0.675517i | 0.984632 | + | 0.174642i | \(0.0558769\pi\) |
−0.865520 | + | 0.500874i | \(0.833012\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.28215 | + | 11.5401i | 0.489274 | + | 1.72030i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.60578 | + | 2.76828i | 1.10942 | + | 0.403795i | 0.830780 | − | 0.556602i | \(-0.187895\pi\) |
0.278637 | + | 0.960396i | \(0.410117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.42695 | − | 2.77385i | 0.918136 | − | 0.396265i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.155753 | − | 0.507488i | 0.0218098 | − | 0.0710625i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.78182 | − | 8.28236i | 0.656834 | − | 1.13767i | −0.324597 | − | 0.945853i | \(-0.605229\pi\) |
0.981431 | − | 0.191817i | \(-0.0614381\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.14624 | −0.559079 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.31095 | − | 0.301167i | 0.173640 | − | 0.0398906i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3022 | + | 8.64456i | 1.34123 | + | 1.12543i | 0.981308 | + | 0.192443i | \(0.0616409\pi\) |
0.359921 | + | 0.932983i | \(0.382804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.68941 | − | 2.79872i | −0.984528 | − | 0.358339i | −0.200929 | − | 0.979606i | \(-0.564396\pi\) |
−0.783599 | + | 0.621267i | \(0.786618\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.04272 | + | 7.86846i | 0.131371 | + | 0.991333i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.38202 | + | 5.35515i | −0.791592 | + | 0.664225i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.81338 | + | 10.2842i | −0.221540 | + | 1.25641i | 0.647651 | + | 0.761937i | \(0.275752\pi\) |
−0.869191 | + | 0.494477i | \(0.835360\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.68131 | − | 2.38503i | 0.443178 | − | 0.287124i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.987174 | − | 1.70984i | 0.117156 | − | 0.202920i | −0.801484 | − | 0.598017i | \(-0.795956\pi\) |
0.918640 | + | 0.395097i | \(0.129289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.18187 | 0.372410 | 0.186205 | − | 0.982511i | \(-0.440381\pi\) | ||||
0.186205 | + | 0.982511i | \(0.440381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18.8979 | + | 2.34107i | 2.18214 | + | 0.270324i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.71406 | − | 0.397273i | −0.309296 | − | 0.0452734i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.931268 | + | 5.28148i | 0.104776 | + | 0.594213i | 0.991310 | + | 0.131549i | \(0.0419952\pi\) |
−0.886534 | + | 0.462664i | \(0.846894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.90692 | − | 1.29101i | −0.989658 | − | 0.143445i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.70366 | + | 2.43993i | 0.735823 | + | 0.267818i | 0.682627 | − | 0.730767i | \(-0.260837\pi\) |
0.0531953 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.938958 | − | 0.787879i | −0.101844 | − | 0.0854575i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.39827 | − | 15.1187i | −0.685967 | − | 1.62090i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.30794 | + | 2.26541i | −0.138641 | + | 0.240133i | −0.926982 | − | 0.375105i | \(-0.877607\pi\) |
0.788342 | + | 0.615238i | \(0.210940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.69068 | + | 2.89390i | −0.491716 | + | 0.303363i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.08014 | − | 3.10625i | −0.630481 | − | 0.322104i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.539317 | − | 3.05862i | 0.0553328 | − | 0.313808i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31999 | + | 7.48602i | 0.134024 | + | 0.760090i | 0.975534 | + | 0.219848i | \(0.0705562\pi\) |
−0.841510 | + | 0.540242i | \(0.818333\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.27118 | − | 2.83862i | 0.127759 | − | 0.285292i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.102391 | + | 0.580686i | 0.0101882 | + | 0.0577804i | 0.989478 | − | 0.144683i | \(-0.0462163\pi\) |
−0.979290 | + | 0.202464i | \(0.935105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4888 | + | 4.90952i | −1.32909 | + | 0.483749i | −0.906360 | − | 0.422507i | \(-0.861150\pi\) |
−0.422730 | + | 0.906256i | \(0.638928\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.6698 | + | 4.86356i | 1.72440 | + | 0.474634i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.45480 | + | 4.25184i | 0.237314 | + | 0.411040i | 0.959943 | − | 0.280196i | \(-0.0903995\pi\) |
−0.722628 | + | 0.691237i | \(0.757066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.25895 | + | 5.64467i | −0.312151 | + | 0.540661i | −0.978828 | − | 0.204686i | \(-0.934383\pi\) |
0.666677 | + | 0.745347i | \(0.267716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.1353 | − | 14.1164i | −1.24675 | − | 1.33987i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.164509 | + | 0.932979i | −0.0154757 | + | 0.0877673i | −0.991567 | − | 0.129592i | \(-0.958633\pi\) |
0.976092 | + | 0.217359i | \(0.0697443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.75872 | − | 9.97420i | −0.164002 | − | 0.930099i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.70963 | − | 6.01111i | −0.158055 | − | 0.555727i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.539136 | − | 0.605700i | −0.0494225 | − | 0.0555244i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.60310 | − | 6.37976i | −0.691191 | − | 0.579978i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.07260 | − | 3.61328i | −0.637715 | − | 0.325799i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9860 | − | 20.7604i | 1.07206 | − | 1.85687i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.90354 | − | 15.4214i | −0.790061 | − | 1.36843i | −0.925929 | − | 0.377699i | \(-0.876715\pi\) |
0.135868 | − | 0.990727i | \(-0.456618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.69530 | + | 6.21691i | −0.413398 | + | 0.547368i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.55592 | − | 20.1666i | 0.310682 | − | 1.76197i | −0.284788 | − | 0.958591i | \(-0.591923\pi\) |
0.595470 | − | 0.803377i | \(-0.296966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.646091 | − | 1.95045i | 0.0560232 | − | 0.169125i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.7605 | + | 17.7779i | −0.926116 | + | 1.53008i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.3866 | − | 12.9109i | 1.31457 | − | 1.10305i | 0.327140 | − | 0.944976i | \(-0.393915\pi\) |
0.987427 | − | 0.158076i | \(-0.0505292\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3937 | − | 9.56042i | −0.966398 | − | 0.810904i | 0.0155838 | − | 0.999879i | \(-0.495039\pi\) |
−0.981982 | + | 0.188974i | \(0.939484\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.46375 | + | 12.9105i | 0.460131 | + | 1.08726i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.15973 | 0.180605 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −37.9061 | −3.14793 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.1004 | + | 4.87664i | 0.915544 | + | 0.402219i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.32756 | + | 7.82675i | 0.764143 | + | 0.641192i | 0.939202 | − | 0.343366i | \(-0.111567\pi\) |
−0.175059 | + | 0.984558i | \(0.556011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5900 | + | 4.58237i | 1.02456 | + | 0.372908i | 0.799006 | − | 0.601323i | \(-0.205360\pi\) |
0.225551 | + | 0.974231i | \(0.427582\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.827274 | − | 0.401281i | 0.0668811 | − | 0.0324416i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0766 | + | 10.1335i | −0.970017 | + | 0.813941i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.19728 | − | 4.36103i | −0.414788 | − | 0.348048i | 0.411388 | − | 0.911460i | \(-0.365044\pi\) |
−0.826176 | + | 0.563412i | \(0.809488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.1442 | − | 3.70884i | 1.28032 | − | 0.294130i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.195551 | − | 6.69747i | −0.0154116 | − | 0.527834i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.65586 | + | 14.9924i | 0.677980 | + | 1.17430i | 0.975588 | + | 0.219607i | \(0.0704776\pi\) |
−0.297609 | + | 0.954688i | \(0.596189\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.89210 | − | 5.25750i | −0.380850 | − | 0.409296i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.61900 | − | 9.18182i | 0.125282 | − | 0.710511i | −0.855858 | − | 0.517212i | \(-0.826970\pi\) |
0.981140 | − | 0.193299i | \(-0.0619188\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.63426 | + | 5.56681i | −0.510328 | + | 0.428216i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.92866 | + | 1.30696i | 0.147488 | + | 0.0999459i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.41074 | − | 3.70105i | 0.335342 | − | 0.281385i | −0.459530 | − | 0.888162i | \(-0.651982\pi\) |
0.794872 | + | 0.606777i | \(0.207538\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.0389 | − | 22.8187i | 1.36361 | − | 1.72493i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.19399 | + | 23.2629i | 0.0897460 | + | 1.74855i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.84363 | − | 6.65737i | −0.287287 | − | 0.497595i | 0.685874 | − | 0.727720i | \(-0.259420\pi\) |
−0.973161 | + | 0.230125i | \(0.926087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.31512 | − | 12.6702i | −0.543729 | − | 0.941766i | −0.998686 | − | 0.0512523i | \(-0.983679\pi\) |
0.454957 | − | 0.890513i | \(-0.349655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.52383 | − | 13.0525i | −0.408333 | − | 0.964866i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −41.8375 | + | 15.2276i | −3.07596 | + | 1.11956i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0551768 | + | 0.312923i | 0.00403493 | + | 0.0228832i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.74704 | + | 10.6061i | −0.636253 | + | 0.771480i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.87096 | + | 10.6107i | 0.135378 | + | 0.767764i | 0.974596 | + | 0.223970i | \(0.0719018\pi\) |
−0.839218 | + | 0.543794i | \(0.816987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.67419 | − | 3.15715i | 0.624382 | − | 0.227256i | −0.0104023 | − | 0.999946i | \(-0.503311\pi\) |
0.634784 | + | 0.772689i | \(0.281089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.3205 | − | 1.77402i | −1.02551 | − | 0.127040i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8434 | − | 18.7813i | −0.772559 | − | 1.33811i | −0.936156 | − | 0.351584i | \(-0.885643\pi\) |
0.163597 | − | 0.986527i | \(-0.447690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.42032 | + | 9.38827i | 0.384236 | + | 0.665517i | 0.991663 | − | 0.128859i | \(-0.0411314\pi\) |
−0.607427 | + | 0.794376i | \(0.707798\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.1801 | + | 9.83481i | −1.07072 | + | 0.693694i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.8128 | − | 3.63198i | −1.74151 | − | 0.254915i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.0479 | + | 11.7876i | −0.981146 | + | 0.823279i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.36779 | + | 1.85389i | 0.512097 | + | 0.128854i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.616769 | + | 0.517530i | −0.0426628 | + | 0.0357983i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.30865 | − | 13.0930i | 0.158934 | − | 0.901358i | −0.796167 | − | 0.605077i | \(-0.793142\pi\) |
0.955101 | − | 0.296281i | \(-0.0957465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.33285 | − | 0.765663i | 0.228363 | − | 0.0524624i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.99433 | + | 15.5786i | 0.613408 | + | 1.06245i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.87611 | + | 5.47610i | −0.602549 | + | 0.371742i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.75426 | + | 4.03467i | 0.253689 | + | 0.272637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.489092 | + | 0.410397i | 0.0328999 | + | 0.0276063i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6778 | − | 8.95976i | 0.715040 | − | 0.599990i | −0.210968 | − | 0.977493i | \(-0.567662\pi\) |
0.926008 | + | 0.377503i | \(0.123217\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.3289 | + | 26.7251i | 1.28859 | + | 1.78167i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.17399 | + | 0.791269i | 0.144293 | + | 0.0525184i | 0.413157 | − | 0.910660i | \(-0.364426\pi\) |
−0.268864 | + | 0.963178i | \(0.586648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2314 | + | 11.1025i | 0.874355 | + | 0.733671i | 0.965011 | − | 0.262211i | \(-0.0844516\pi\) |
−0.0906551 | + | 0.995882i | \(0.528896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.69854 | − | 3.91021i | −0.177551 | − | 0.257273i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0313 | 0.984733 | 0.492367 | − | 0.870388i | \(-0.336132\pi\) | ||||
0.492367 | + | 0.870388i | \(0.336132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.3697 | 2.11156 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.59821 | + | 7.41242i | −0.363643 | + | 0.481488i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.8507 | − | 9.94390i | −0.766557 | − | 0.643217i | 0.173268 | − | 0.984875i | \(-0.444567\pi\) |
−0.939825 | + | 0.341657i | \(0.889012\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6617 | + | 15.6590i | −1.20210 | + | 1.00869i | −0.202537 | + | 0.979275i | \(0.564919\pi\) |
−0.999567 | + | 0.0294111i | \(0.990637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.87216 | − | 12.8174i | −0.569149 | − | 0.822234i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.3589 | − | 19.2153i | 1.30068 | − | 1.22762i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.280924 | + | 1.59320i | −0.0178747 | + | 0.101373i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.81570 | + | 11.3792i | 0.305183 | + | 0.721128i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.32366 | + | 2.29265i | 0.0835487 | + | 0.144711i | 0.904772 | − | 0.425897i | \(-0.140041\pi\) |
−0.821223 | + | 0.570607i | \(0.806708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31278 | + | 2.27380i | −0.0825336 | + | 0.142952i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.108823 | − | 2.12022i | −0.00681473 | − | 0.132774i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.4866 | − | 17.1903i | −1.27792 | − | 1.07230i | −0.993527 | − | 0.113596i | \(-0.963763\pi\) |
−0.284394 | − | 0.958707i | \(-0.591792\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.8452 | + | 5.95909i | −1.79236 | + | 0.370280i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.6215 | − | 25.9515i | 0.719354 | − | 1.60636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.20945 | + | 29.5442i | 0.321228 | + | 1.82178i | 0.534953 | + | 0.844882i | \(0.320329\pi\) |
−0.213725 | + | 0.976894i | \(0.568560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.64162 | − | 37.6665i | 0.407991 | − | 2.31383i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.41579 | + | 1.01445i | −0.270242 | + | 0.0620833i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.18287 | + | 2.04879i | −0.0721210 | + | 0.124917i | −0.899831 | − | 0.436239i | \(-0.856310\pi\) |
0.827710 | + | 0.561157i | \(0.189643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.935621 | − | 1.62054i | −0.0568349 | − | 0.0984409i | 0.836208 | − | 0.548412i | \(-0.184768\pi\) |
−0.893043 | + | 0.449971i | \(0.851434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.20399 | − | 2.53337i | −0.557051 | − | 0.153326i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.7108 | + | 3.89840i | −0.645884 | + | 0.235082i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.94888 | + | 16.7240i | 0.177181 | + | 1.00484i | 0.935596 | + | 0.353073i | \(0.114863\pi\) |
−0.758415 | + | 0.651772i | \(0.774026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.23511 | − | 11.3747i | −0.193681 | − | 0.680988i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.85516 | + | 21.8637i | 0.229980 | + | 1.30428i | 0.852933 | + | 0.522021i | \(0.174822\pi\) |
−0.622953 | + | 0.782259i | \(0.714067\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.21874 | − | 29.5969i | 0.310222 | − | 1.75936i | −0.287623 | − | 0.957744i | \(-0.592865\pi\) |
0.597845 | − | 0.801612i | \(-0.296024\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.51471 | − | 2.92497i | 0.267428 | − | 0.173260i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3249 | + | 6.36995i | −0.609462 | + | 0.376006i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.45303 | − | 14.6411i | 0.497237 | − | 0.861240i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.93495 | + | 10.5064i | −0.465155 | + | 0.615898i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.74653 | − | 2.30461i | −0.160454 | − | 0.134637i | 0.559026 | − | 0.829150i | \(-0.311175\pi\) |
−0.719480 | + | 0.694513i | \(0.755620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 50.5407 | + | 18.3953i | 2.94259 | + | 1.07102i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.09927 | − | 1.73738i | 0.295889 | − | 0.100813i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.916096 | + | 5.19544i | 0.0529792 | + | 0.300460i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.39488 | + | 11.0593i | 0.253316 | + | 0.637449i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.615509 | + | 0.814977i | −0.0353601 | + | 0.0468192i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.7256 | −1.87386 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.22311 | + | 15.9749i | −0.526390 | + | 0.911735i | 0.473137 | + | 0.880989i | \(0.343122\pi\) |
−0.999527 | + | 0.0307460i | \(0.990212\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.1406 | − | 11.3113i | −1.25953 | − | 0.643478i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.63504 | − | 26.2866i | 0.262829 | − | 1.49058i | −0.512318 | − | 0.858796i | \(-0.671213\pi\) |
0.775147 | − | 0.631781i | \(-0.217676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.3119 | − | 19.5610i | 1.31767 | − | 1.10566i | 0.330875 | − | 0.943675i | \(-0.392656\pi\) |
0.986794 | − | 0.161981i | \(-0.0517883\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.6813 | + | 28.1440i | 0.827200 | + | 1.58574i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.6415 | − | 4.23717i | −0.653853 | − | 0.237983i | −0.00627266 | − | 0.999980i | \(-0.501997\pi\) |
−0.647580 | + | 0.761997i | \(0.724219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.52762 | + | 6.31642i | 0.421466 | + | 0.353652i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.49500 | + | 8.12941i | −0.139258 | + | 0.453740i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.238016 | −0.0132436 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4513 | + | 19.8342i | −0.635204 | + | 1.10020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.0027 | + | 2.52768i | −0.608452 | + | 0.139781i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.1887 | + | 3.10150i | 1.16817 | + | 0.170991i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.9295 | + | 6.52579i | 0.985492 | + | 0.358690i | 0.783973 | − | 0.620795i | \(-0.213190\pi\) |
0.201519 | + | 0.979485i | \(0.435412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.40162 | − | 33.3116i | 0.131608 | − | 1.82547i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.25219 | + | 41.1292i | 0.396230 | + | 2.24713i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.8212 | + | 6.12241i | −0.916308 | + | 0.333509i | −0.756769 | − | 0.653683i | \(-0.773223\pi\) |
−0.159539 | + | 0.987192i | \(0.551001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.37713 | + | 0.892211i | −0.0747957 | + | 0.0484582i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.08682 | 0.221314 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1677 | − | 10.6274i | 0.818979 | − | 0.573824i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5723 | − | 13.9985i | 0.569196 | − | 0.753656i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3108 | + | 5.20872i | −0.768246 | + | 0.279619i | −0.696263 | − | 0.717787i | \(-0.745155\pi\) |
−0.0719834 | + | 0.997406i | \(0.522933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.61713 | − | 2.40844i | −0.354207 | − | 0.128921i | 0.158787 | − | 0.987313i | \(-0.449242\pi\) |
−0.512994 | + | 0.858392i | \(0.671464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.60501 | − | 9.26028i | 0.299173 | − | 0.494277i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.61321 | + | 2.19274i | −0.139087 | + | 0.116708i | −0.709677 | − | 0.704527i | \(-0.751159\pi\) |
0.570590 | + | 0.821235i | \(0.306715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.37112 | − | 7.77598i | 0.0727713 | − | 0.412706i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.131916 | − | 1.39829i | 0.00698174 | − | 0.0740054i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.98322 | + | 6.89914i | −0.210226 | + | 0.364122i | −0.951785 | − | 0.306765i | \(-0.900753\pi\) |
0.741559 | + | 0.670888i | \(0.234087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.19845 | + | 15.9322i | 0.484129 | + | 0.838536i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.881178 | − | 17.1683i | −0.0462499 | − | 0.901100i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9577 | − | 4.35226i | 0.625897 | − | 0.227808i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.11912 | + | 2.22718i | 0.319416 | + | 0.116258i | 0.496752 | − | 0.867892i | \(-0.334526\pi\) |
−0.177336 | + | 0.984150i | \(0.556748\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.76317 | − | 13.2314i | −0.195903 | − | 0.688801i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.95652 | − | 24.0195i | 0.413082 | − | 1.24703i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.62680 | − | 3.13990i | 0.446679 | − | 0.162578i | −0.108880 | − | 0.994055i | \(-0.534727\pi\) |
0.555559 | + | 0.831477i | \(0.312504\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 40.4667 | − | 9.29650i | 2.08969 | − | 0.480069i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7448 | 1.01691 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.49943 | −0.385220 | −0.192610 | − | 0.981275i | \(-0.561695\pi\) | ||||
−0.192610 | + | 0.981275i | \(0.561695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.04936 | − | 29.4853i | 0.463613 | − | 1.51058i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.65983 | − | 2.78795i | 0.391399 | − | 0.142458i | −0.138821 | − | 0.990317i | \(-0.544331\pi\) |
0.530220 | + | 0.847860i | \(0.322109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.7431 | + | 2.21939i | −0.547517 | + | 0.113111i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.4231 | + | 1.38154i | −0.682333 | + | 0.0702278i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.7047 | + | 10.0837i | 1.40468 | + | 0.511263i | 0.929565 | − | 0.368658i | \(-0.120183\pi\) |
0.475119 | + | 0.879922i | \(0.342405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.729364 | + | 0.265467i | −0.0368855 | + | 0.0134252i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.7672 | − | 19.2854i | 1.50156 | − | 0.972821i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.7239 | + | 18.5744i | 0.539580 | + | 0.934580i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2950 | + | 26.4917i | −0.767633 | + | 1.32958i | 0.171210 | + | 0.985235i | \(0.445232\pi\) |
−0.938843 | + | 0.344345i | \(0.888101\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.23551 | − | 1.48206i | 0.161978 | − | 0.0741958i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.83088 | + | 27.3973i | −0.241243 | + | 1.36815i | 0.587817 | + | 0.808994i | \(0.299988\pi\) |
−0.829059 | + | 0.559160i | \(0.811124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.29056 | − | 5.27841i | 0.313355 | − | 0.262936i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35.2388 | + | 7.33144i | −1.75103 | + | 0.364302i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8458 | + | 3.94754i | 0.537605 | + | 0.195672i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.96999 | − | 3.26481i | 0.443537 | − | 0.161434i | −0.110590 | − | 0.993866i | \(-0.535274\pi\) |
0.554128 | + | 0.832432i | \(0.313052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.5257 | + | 4.27704i | 1.70303 | + | 0.210971i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.3206 | + | 16.8838i | 1.54118 | + | 0.830799i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.5303 | 1.40050 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.32049 | − | 25.7276i | −0.0646648 | − | 1.25988i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.88681 | − | 2.14262i | 0.287589 | − | 0.104674i | −0.194197 | − | 0.980962i | \(-0.562210\pi\) |
0.481787 | + | 0.876289i | \(0.339988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.967375 | + | 5.48626i | 0.0471470 | + | 0.267384i | 0.999264 | − | 0.0383488i | \(-0.0122098\pi\) |
−0.952117 | + | 0.305733i | \(0.901099\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.92410 | + | 22.1611i | −0.482526 | + | 1.07751i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.16634 | − | 1.15246i | −0.153590 | − | 0.0559023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.4216 | − | 3.13561i | −1.03667 | − | 0.151743i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.54824 | + | 2.73857i | 0.123030 | + | 0.132219i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.87104 | − | 8.43690i | 0.234630 | − | 0.406391i | −0.724535 | − | 0.689238i | \(-0.757946\pi\) |
0.959165 | + | 0.282847i | \(0.0912788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.60092 | −0.413334 | −0.206667 | − | 0.978411i | \(-0.566262\pi\) | ||||
−0.206667 | + | 0.978411i | \(0.566262\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −44.7250 | − | 48.0656i | −2.14440 | − | 2.30457i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.50659 | − | 1.26418i | −0.0720699 | − | 0.0604738i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6860 | + | 5.34525i | 0.700922 | + | 0.255115i | 0.667805 | − | 0.744337i | \(-0.267234\pi\) |
0.0331178 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.91355 | + | 19.8293i | 0.329217 | + | 0.944254i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.47957 | + | 5.43701i | −0.307854 | + | 0.258320i | −0.783604 | − | 0.621260i | \(-0.786621\pi\) |
0.475750 | + | 0.879580i | \(0.342177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.81663 | + | 10.3026i | −0.0861166 | + | 0.488391i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.08104 | + | 21.0622i | 0.0511313 | + | 0.996207i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.8251 | − | 22.2137i | 0.605253 | − | 1.04833i | −0.386758 | − | 0.922181i | \(-0.626405\pi\) |
0.992011 | − | 0.126148i | \(-0.0402615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.75391 | 0.223853 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.04423 | + | 21.3709i | 0.424935 | + | 1.00409i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.6696 | + | 17.2916i | −0.640839 | + | 0.810641i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.44825 | − | 8.21344i | −0.0677463 | − | 0.384209i | −0.999763 | − | 0.0217919i | \(-0.993063\pi\) |
0.932016 | − | 0.362417i | \(-0.118048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48492 | + | 0.575529i | 0.0693102 | + | 0.0268634i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.40759 | + | 0.512321i | 0.0655580 | + | 0.0238612i | 0.374591 | − | 0.927190i | \(-0.377783\pi\) |
−0.309033 | + | 0.951051i | \(0.600005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8247 | − | 16.6349i | −0.921333 | − | 0.773090i | 0.0529082 | − | 0.998599i | \(-0.483151\pi\) |
−0.974241 | + | 0.225509i | \(0.927595\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.0985 | − | 3.35696i | −1.25666 | − | 0.155675i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.3477 | + | 19.6548i | −0.525109 | + | 0.909515i | 0.474463 | + | 0.880275i | \(0.342642\pi\) |
−0.999572 | + | 0.0292403i | \(0.990691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.806366 | + | 27.6174i | 0.0372345 | + | 1.27525i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.602350 | − | 11.7358i | −0.0277548 | − | 0.540755i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.809773 | − | 4.59245i | 0.0372334 | − | 0.211161i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.48260 | − | 8.40825i | −0.0680264 | − | 0.385797i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.7512 | + | 16.0951i | 1.08749 | + | 0.736942i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.17236 | − | 29.3339i | −0.236331 | − | 1.34030i | −0.839792 | − | 0.542908i | \(-0.817323\pi\) |
0.603461 | − | 0.797392i | \(-0.293788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.7927 | − | 7.93188i | 0.993660 | − | 0.361663i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.26176 | − | 8.15022i | 0.375923 | − | 0.370848i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.2002 | + | 26.3275i | 0.690206 | + | 1.19547i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1802 | − | 21.0968i | 0.551938 | − | 0.955985i | −0.446196 | − | 0.894935i | \(-0.647222\pi\) |
0.998135 | − | 0.0610500i | \(-0.0194449\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.79764 | + | 28.6651i | −0.397843 | + | 1.29628i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.89390 | + | 39.0972i | −0.311117 | + | 1.76443i | 0.282094 | + | 0.959387i | \(0.408971\pi\) |
−0.593211 | + | 0.805047i | \(0.702140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.504443 | + | 2.86084i | 0.0227190 | + | 0.128846i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.894454 | − | 12.4065i | 0.0402027 | − | 0.557632i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.64257 | − | 4.95866i | 0.0736792 | − | 0.222426i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3279 | + | 21.2526i | 1.13383 | + | 0.951399i | 0.999220 | − | 0.0394997i | \(-0.0125764\pi\) |
0.134613 | + | 0.990898i | \(0.457021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.5529 | − | 8.78061i | 0.605501 | − | 0.392289i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.61071 | + | 14.9142i | −0.383933 | + | 0.664991i | −0.991620 | − | 0.129185i | \(-0.958764\pi\) |
0.607688 | + | 0.794176i | \(0.292097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.17907 | + | 2.04221i | 0.0524679 | + | 0.0908771i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.8865 | − | 1.84414i | −0.661132 | − | 0.0819009i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.58159 | − | 37.3261i | 0.291724 | − | 1.65445i | −0.388503 | − | 0.921448i | \(-0.627008\pi\) |
0.680227 | − | 0.733002i | \(-0.261881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.24436 | − | 1.70319i | 0.364709 | − | 0.0753446i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.618357 | + | 3.98764i | 0.0273011 | + | 0.176059i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −43.9765 | + | 36.9007i | −1.93784 | + | 1.62604i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.42815 | − | 5.39386i | −0.282710 | − | 0.237222i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.89716 | + | 1.22606i | 0.434437 | + | 0.0538180i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7559 | 0.515037 | 0.257518 | − | 0.966273i | \(-0.417095\pi\) | ||||
0.257518 | + | 0.966273i | \(0.417095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.47076 | −0.151766 | −0.0758829 | − | 0.997117i | \(-0.524178\pi\) | ||||
−0.0758829 | + | 0.997117i | \(0.524178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 50.2183 | − | 4.04984i | 2.19171 | − | 0.176749i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.925502 | + | 0.776588i | 0.0403155 | + | 0.0338287i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.5862 | + | 5.67293i | 0.677663 | + | 0.246649i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.0890 | + | 28.9617i | −1.21896 | + | 1.25683i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.31736 | − | 6.14000i | 0.316950 | − | 0.265953i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0411 | + | 12.6210i | 0.650284 | + | 0.545653i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.90659 | − | 12.7287i | 0.168582 | − | 0.549286i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.24489 | + | 0.423430i | −0.312060 | + | 0.0182384i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.28017 | − | 7.41347i | −0.184019 | − | 0.318730i | 0.759227 | − | 0.650826i | \(-0.225577\pi\) |
−0.943245 | + | 0.332096i | \(0.892244\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.43493 | − | 24.2251i | 0.319064 | − | 1.03960i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.52646 | + | 25.6708i | −0.193892 | + | 1.09962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.1571 | + | 23.6266i | −1.20391 | + | 1.01020i | −0.204401 | + | 0.978887i | \(0.565525\pi\) |
−0.999510 | + | 0.0313134i | \(0.990031\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0332 | − | 22.4048i | 0.428207 | − | 0.956212i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.63868 | + | 4.73141i | −0.240216 | + | 0.201565i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.24001 | + | 13.1860i | 0.222828 | + | 0.560727i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −68.6725 | − | 35.0838i | −2.91499 | − | 1.48922i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.9154 | − | 24.1022i | −0.589614 | − | 1.02124i | −0.994283 | − | 0.106778i | \(-0.965947\pi\) |
0.404669 | − | 0.914463i | \(-0.367387\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.68504 | − | 8.11472i | −0.198156 | − | 0.343216i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.331689 | + | 0.439180i | −0.0140039 | + | 0.0185422i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.1878 | + | 7.34777i | −0.850816 | + | 0.309672i | −0.730373 | − | 0.683049i | \(-0.760654\pi\) |
−0.120443 | + | 0.992720i | \(0.538431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.657917 | + | 3.73123i | 0.0276788 | + | 0.156974i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.7692 | + | 1.42263i | −0.998214 | + | 0.0597449i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.49844 | + | 19.8406i | 0.146662 | + | 0.831762i | 0.966018 | + | 0.258476i | \(0.0832204\pi\) |
−0.819355 | + | 0.573286i | \(0.805668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.8816 | + | 13.4238i | −1.54345 | + | 0.561769i | −0.966869 | − | 0.255272i | \(-0.917835\pi\) |
−0.576579 | + | 0.817041i | \(0.695613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.2470 | + | 14.8919i | −0.469852 | + | 0.622116i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9212 | − | 24.1122i | −0.580555 | − | 1.00555i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.63475 | + | 2.83148i | 0.0680557 | + | 0.117876i | 0.898045 | − | 0.439903i | \(-0.144987\pi\) |
−0.829990 | + | 0.557779i | \(0.811654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.2379 | + | 7.27393i | 0.591706 | + | 0.302294i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.6755 | + | 2.73364i | 0.774790 | + | 0.113410i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.59542 | + | 6.37331i | −0.314570 | + | 0.263956i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.6471 | − | 20.2518i | −0.605583 | − | 0.837307i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9958 | + | 12.5830i | −0.618944 | + | 0.519356i | −0.897471 | − | 0.441073i | \(-0.854598\pi\) |
0.278527 | + | 0.960428i | \(0.410154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.531588 | + | 3.01479i | −0.0219037 | + | 0.124222i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0210 | − | 35.9094i | 0.453343 | − | 1.47712i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.8803 | − | 36.1658i | −0.857452 | − | 1.48515i | −0.874351 | − | 0.485293i | \(-0.838713\pi\) |
0.0168995 | − | 0.999857i | \(-0.494620\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.85461 | − | 1.53882i | −0.117028 | − | 0.0630855i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.50910 | + | 17.9502i | −0.225472 | + | 0.734651i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.16302 | + | 6.01049i | 0.292673 | + | 0.245582i | 0.777287 | − | 0.629146i | \(-0.216595\pi\) |
−0.484614 | + | 0.874728i | \(0.661040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.3323 | − | 31.3256i | 1.52282 | − | 1.27780i | 0.690803 | − | 0.723043i | \(-0.257257\pi\) |
0.832015 | − | 0.554753i | \(-0.187187\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.3815 | − | 7.64463i | −1.23723 | − | 0.311314i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.2995 | − | 13.5759i | −1.51644 | − | 0.551939i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2934 | + | 14.5109i | 0.701919 | + | 0.588980i | 0.922319 | − | 0.386430i | \(-0.126292\pi\) |
−0.220400 | + | 0.975410i | \(0.570736\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.6709 | − | 35.7483i | −0.999714 | − | 1.44859i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8610 | −0.682121 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7396 | −0.797275 | −0.398637 | − | 0.917109i | \(-0.630517\pi\) | ||||
−0.398637 | + | 0.917109i | \(0.630517\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −31.5217 | − | 3.90491i | −1.27108 | − | 0.157461i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.35270 | + | 7.84784i | 0.376525 | + | 0.315942i | 0.811337 | − | 0.584579i | \(-0.198740\pi\) |
−0.434811 | + | 0.900522i | \(0.643185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.06747 | + | 5.09121i | −0.243872 | + | 0.204633i | −0.756528 | − | 0.653961i | \(-0.773106\pi\) |
0.512656 | + | 0.858594i | \(0.328662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.34241 | + | 11.5299i | 0.254512 | + | 0.462677i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.17629 | + | 6.56987i | −0.0871910 | + | 0.263216i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.10221 | − | 40.2787i | 0.284089 | − | 1.61115i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.38395 | − | 0.171444i | −0.0552698 | − | 0.00684682i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.70601 | + | 2.95490i | 0.0680232 | + | 0.117820i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.64257 | − | 16.7014i | 0.383865 | − | 0.664873i | −0.607746 | − | 0.794131i | \(-0.707926\pi\) |
0.991611 | + | 0.129258i | \(0.0412596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3260 | − | 12.5209i | 0.768141 | − | 0.497659i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −54.5540 | − | 45.7762i | −2.16491 | − | 1.81657i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6047 | + | 10.0090i | −0.420173 | + | 0.396572i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.90327 | + | 3.32271i | 0.193970 | + | 0.131444i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.22997 | + | 23.9893i | 0.167074 | + | 0.947522i | 0.946901 | + | 0.321527i | \(0.104196\pi\) |
−0.779827 | + | 0.625995i | \(0.784693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.329571 | − | 1.86909i | 0.0129970 | − | 0.0737096i | −0.977619 | − | 0.210381i | \(-0.932529\pi\) |
0.990616 | + | 0.136672i | \(0.0436405\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.14165 | + | 29.7860i | −0.359952 | + | 1.17282i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.204404 | − | 0.354039i | 0.00803596 | − | 0.0139187i | −0.861979 | − | 0.506943i | \(-0.830775\pi\) |
0.870015 | + | 0.493025i | \(0.164109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.97139 | − | 12.0748i | −0.273651 | − | 0.473978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4166 | − | 4.79386i | −0.682610 | − | 0.187886i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.6196 | − | 7.50491i | 0.806906 | − | 0.293690i | 0.0945609 | − | 0.995519i | \(-0.469855\pi\) |
0.712345 | + | 0.701829i | \(0.247633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2211 | − | 80.6517i | −0.555663 | − | 3.15132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.686415 | + | 9.52091i | −0.0267796 | + | 0.371446i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.66416 | − | 26.4518i | −0.181690 | − | 1.03041i | −0.930135 | − | 0.367218i | \(-0.880310\pi\) |
0.748445 | − | 0.663197i | \(-0.230801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.57555 | − | 14.6066i | 0.100177 | − | 0.568133i | −0.892860 | − | 0.450334i | \(-0.851305\pi\) |
0.993037 | − | 0.117799i | \(-0.0375839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0566843 | + | 1.10440i | 0.00220144 | + | 0.0428913i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.239821 | − | 8.21368i | −0.00929986 | − | 0.318513i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0018 | + | 20.7877i | −0.464711 | + | 0.804903i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.9598 | + | 2.96813i | 0.926338 | + | 0.114755i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.49883 | + | 5.45317i | 0.250885 | + | 0.210517i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.9536 | + | 15.6338i | 1.65574 | + | 0.602640i | 0.989685 | − | 0.143262i | \(-0.0457593\pi\) |
0.666055 | + | 0.745902i | \(0.267982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.0818 | + | 56.0419i | −0.426539 | + | 2.15706i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.09570 | + | 11.8853i | 0.0805443 | + | 0.456789i | 0.998229 | + | 0.0594810i | \(0.0189446\pi\) |
−0.917685 | + | 0.397308i | \(0.869944\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.42724 | + | 18.6900i | 0.285031 | + | 0.717256i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.56173 | + | 3.69027i | 0.0598456 | + | 0.141411i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.29677 | 0.279203 | 0.139602 | − | 0.990208i | \(-0.455418\pi\) | ||||
0.139602 | + | 0.990208i | \(0.455418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.1642 | − | 69.5664i | 1.53459 | − | 2.65800i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.53348 | + | 29.8773i | 0.0585060 | + | 1.13989i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.45954 | + | 19.6200i | −0.131798 | + | 0.747463i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5445 | − | 15.5607i | 0.705466 | − | 0.591956i | −0.217857 | − | 0.975981i | \(-0.569907\pi\) |
0.923323 | + | 0.384024i | \(0.125462\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.77423 | − | 8.03541i | 0.0673974 | − | 0.305240i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −55.8953 | − | 20.3442i | −2.12023 | − | 0.771701i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.07657 | + | 0.903350i | 0.0407780 | + | 0.0342168i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.7353 | + | 19.0599i | 0.670809 | + | 0.720912i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.97538 | −0.338995 | −0.169498 | − | 0.985531i | \(-0.554215\pi\) | ||||
−0.169498 | + | 0.985531i | \(0.554215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.32279 | + | 7.48729i | −0.163037 | + | 0.282389i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38.1926 | + | 41.0452i | 1.43842 | + | 1.54585i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.576126 | + | 1.44977i | 0.0216674 | + | 0.0545242i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.0831 | + | 15.6810i | 1.61802 | + | 0.588911i | 0.983004 | − | 0.183587i | \(-0.0587708\pi\) |
0.635017 | + | 0.772498i | \(0.280993\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.0043 | + | 1.64721i | −0.600209 | + | 0.0617754i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.73352 | + | 9.83126i | 0.0649207 | + | 0.368184i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.11642 | − | 2.95414i | 0.303537 | − | 0.110478i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.37346 | − | 26.7595i | −0.0512928 | − | 0.999353i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.97194 | 0.371891 | 0.185945 | − | 0.982560i | \(-0.440465\pi\) | ||||
0.185945 | + | 0.982560i | \(0.440465\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.3220 | + | 19.9410i | −1.20373 | + | 0.742641i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41.8746 | − | 5.18742i | −1.55733 | − | 0.192922i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −97.9210 | + | 35.6403i | −3.63669 | + | 1.32365i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.15330 | − | 2.96756i | −0.302389 | − | 0.110061i | 0.186369 | − | 0.982480i | \(-0.440328\pi\) |
−0.488759 | + | 0.872419i | \(0.662550\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.78446 | − | 26.3731i | 0.214239 | − | 0.976781i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.05605 | − | 0.886132i | 0.0390594 | − | 0.0327748i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.01962 | + | 34.1390i | −0.222340 | + | 1.26095i | 0.645366 | + | 0.763873i | \(0.276705\pi\) |
−0.867706 | + | 0.497078i | \(0.834406\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 48.3865 | + | 3.14339i | 1.78476 | + | 0.115946i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.41331 | − | 9.37614i | 0.199402 | − | 0.345374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.94358 | − | 12.0266i | −0.255424 | − | 0.442407i | 0.709587 | − | 0.704618i | \(-0.248882\pi\) |
−0.965011 | + | 0.262211i | \(0.915548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.35166 | + | 1.52358i | −0.0863903 | + | 0.0559701i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.2416 | − | 16.8306i | 1.69644 | − | 0.617454i | 0.701029 | − | 0.713133i | \(-0.252724\pi\) |
0.995412 | + | 0.0956791i | \(0.0305023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.7594 | + | 16.6550i | 1.67649 | + | 0.610194i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.74701 | + | 19.5326i | −0.320036 | + | 0.714659i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.63639 | + | 9.70267i | 0.315567 | + | 0.354528i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.7227 | − | 4.99464i | 0.500747 | − | 0.182257i | −0.0792829 | − | 0.996852i | \(-0.525263\pi\) |
0.580030 | + | 0.814595i | \(0.303041\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.34534 | + | 4.38349i | −0.0490269 | + | 0.159743i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.5820 | 1.95005 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.9195 | −0.614948 | −0.307474 | − | 0.951556i | \(-0.599484\pi\) | ||||
−0.307474 | + | 0.951556i | \(0.599484\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.43214 | + | 1.01820i | −0.160876 | + | 0.0369585i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.2651 | − | 14.6553i | 1.45961 | − | 0.531254i | 0.514351 | − | 0.857580i | \(-0.328033\pi\) |
0.945257 | + | 0.326326i | \(0.105811\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.42260 | + | 16.3700i | −0.196311 | + | 0.592634i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.56008 | − | 2.63962i | 0.0925598 | − | 0.0954355i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.3260 | − | 9.58189i | −0.950577 | − | 0.345982i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4562 | + | 6.35354i | −0.629487 | + | 0.229114i | −0.637008 | − | 0.770857i | \(-0.719828\pi\) |
0.00752124 | + | 0.999972i | \(0.497606\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.37434 | − | 46.2600i | −0.0855098 | − | 1.66601i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.1688 | − | 45.3256i | −0.941225 | − | 1.63025i | −0.763139 | − | 0.646235i | \(-0.776343\pi\) |
−0.178086 | − | 0.984015i | \(-0.556991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.6691 | + | 37.5320i | −0.778378 | + | 1.34819i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −41.5904 | − | 29.5451i | −1.49205 | − | 1.05993i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.618359 | + | 3.50689i | −0.0221550 | + | 0.125647i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.56802 | + | 1.31573i | −0.0561082 | + | 0.0470804i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 46.6190 | − | 15.8836i | 1.66603 | − | 0.567634i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.4969 | − | 9.28013i | −0.910025 | − | 0.331222i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.430912 | − | 0.156839i | 0.0153604 | − | 0.00559072i | −0.334329 | − | 0.942457i | \(-0.608510\pi\) |
0.349689 | + | 0.936866i | \(0.386287\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.3160 | + | 41.4646i | −1.11488 | + | 1.47618i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0731532 | + | 2.50544i | 0.00260103 | + | 0.0890833i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0463 | 0.605334 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 55.5981 | − | 36.0206i | 1.97186 | − | 1.27752i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.21846 | − | 1.89936i | 0.184847 | − | 0.0672789i | −0.247938 | − | 0.968776i | \(-0.579753\pi\) |
0.432785 | + | 0.901497i | \(0.357531\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.430765 | − | 2.44299i | −0.0152394 | − | 0.0864267i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.49648 | − | 4.40236i | −0.229542 | − | 0.155550i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.09987 | − | 1.12826i | −0.109392 | − | 0.0398154i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.89588 | − | 24.9021i | −0.348784 | − | 0.877685i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.99356 | + | 0.917449i | −0.140580 | + | 0.0322957i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.1897 | + | 28.0413i | −0.569198 | + | 0.985880i | 0.427447 | + | 0.904040i | \(0.359413\pi\) |
−0.996645 | + | 0.0818400i | \(0.973920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.3335 | 0.678890 | 0.339445 | − | 0.940626i | \(-0.389761\pi\) | ||||
0.339445 | + | 0.940626i | \(0.389761\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.950945 | − | 3.09844i | 0.0333511 | − | 0.108667i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.0365 | + | 44.5029i | 1.85779 | + | 1.55887i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.28245 | + | 1.19472i | 0.114838 | + | 0.0417978i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.64733 | − | 14.6599i | −0.267219 | − | 0.512258i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.76489 | − | 5.67642i | 0.236096 | − | 0.198108i | −0.517061 | − | 0.855948i | \(-0.672974\pi\) |
0.753158 | + | 0.657840i | \(0.228530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.41473 | + | 53.3936i | −0.328177 | + | 1.86118i | 0.158163 | + | 0.987413i | \(0.449443\pi\) |
−0.486339 | + | 0.873770i | \(0.661668\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.5807 | − | 8.98174i | −0.612083 | − | 0.312704i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.3137 | + | 19.5959i | −0.393415 | + | 0.681415i | −0.992898 | − | 0.118973i | \(-0.962040\pi\) |
0.599482 | + | 0.800388i | \(0.295373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.64577 | −0.335012 | −0.167506 | − | 0.985871i | \(-0.553571\pi\) | ||||
−0.167506 | + | 0.985871i | \(0.553571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.7269 | + | 23.4716i | −0.614939 | + | 0.814222i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.72114 | − | 1.28080i | −0.0596340 | − | 0.0443772i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.47482 | − | 36.7205i | −0.224070 | − | 1.27077i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.6063 | − | 17.5231i | 0.366607 | − | 0.605687i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6127 | + | 10.7781i | 1.02234 | + | 0.372103i | 0.798161 | − | 0.602444i | \(-0.205806\pi\) |
0.224183 | + | 0.974547i | \(0.428029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.6044 | + | 39.1058i | 1.60705 | + | 1.34847i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.1749 | + | 30.6851i | −0.798185 | + | 1.05685i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.3176 | + | 29.9950i | −0.595745 | + | 1.03186i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.1149 | − | 12.4604i | −0.794237 | − | 0.428145i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.6869 | − | 28.3036i | 1.49933 | − | 0.971379i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.89573 | + | 27.7650i | −0.167823 | + | 0.951773i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.51141 | − | 19.9142i | −0.120228 | − | 0.681849i | −0.984028 | − | 0.178014i | \(-0.943033\pi\) |
0.863800 | − | 0.503835i | \(-0.168078\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.03576 | + | 2.27359i | 0.309016 | + | 0.0777551i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.44257 | − | 19.5238i | −0.117596 | − | 0.666919i | −0.985432 | − | 0.170069i | \(-0.945601\pi\) |
0.867836 | − | 0.496850i | \(-0.165510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.44898 | + | 2.34724i | −0.220036 | + | 0.0800867i | −0.449686 | − | 0.893187i | \(-0.648464\pi\) |
0.229650 | + | 0.973273i | \(0.426242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.2595 | − | 5.57635i | −0.690441 | − | 0.190042i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.76289 | − | 16.9098i | −0.332333 | − | 0.575617i | 0.650636 | − | 0.759390i | \(-0.274502\pi\) |
−0.982969 | + | 0.183773i | \(0.941169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5135 | − | 19.9420i | 0.391471 | − | 0.678047i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5388 | − | 6.55627i | 0.969227 | − | 0.222663i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.965492 | − | 5.47558i | 0.0327521 | − | 0.185746i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.77758 | − | 21.4237i | −0.127998 | − | 0.725915i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.6847 | + | 2.33478i | −0.767760 | + | 0.0790202i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.9437 | − | 60.2069i | 0.674219 | − | 2.03536i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.4492 | − | 28.0672i | −1.12950 | − | 0.947763i | −0.130455 | − | 0.991454i | \(-0.541644\pi\) |
−0.999045 | + | 0.0436912i | \(0.986088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.318314 | − | 6.20182i | −0.0107365 | − | 0.209182i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.828121 | − | 1.43435i | 0.0279001 | − | 0.0483244i | −0.851738 | − | 0.523968i | \(-0.824451\pi\) |
0.879638 | + | 0.475643i | \(0.157785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.42828 | + | 4.20591i | 0.0817183 | + | 0.141540i | 0.903988 | − | 0.427558i | \(-0.140626\pi\) |
−0.822270 | + | 0.569098i | \(0.807293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.3068 | + | 85.7908i | 1.22044 | + | 2.88383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.108152 | + | 0.613359i | −0.00363138 | + | 0.0205946i | −0.986570 | − | 0.163341i | \(-0.947773\pi\) |
0.982938 | + | 0.183936i | \(0.0588839\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.3241 | − | 35.1915i | −1.05058 | − | 1.18029i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.21959 | + | 4.41604i | 0.275367 | + | 0.147943i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.81511 | − | 4.04035i | 0.161131 | − | 0.135205i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.5508 | − | 19.7615i | −0.787217 | − | 0.660554i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.50701 | + | 7.29166i | −0.183874 | + | 0.243462i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.3629 | 1.24612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.93113 | −0.0976502 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.83793 | + | 18.6215i | −0.294108 | + | 0.619686i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.8214 | − | 37.6096i | −1.48991 | − | 1.25019i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.42149 | + | 1.24532i | 0.113609 | + | 0.0413501i | 0.398199 | − | 0.917299i | \(-0.369635\pi\) |
−0.284590 | + | 0.958649i | \(0.591858\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.75964 | + | 0.181107i | −0.0583634 | + | 0.00600694i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5558 | + | 13.0528i | −0.515386 | + | 0.432460i | −0.863020 | − | 0.505170i | \(-0.831430\pi\) |
0.347634 | + | 0.937630i | \(0.386985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.66572 | − | 4.75410i | −0.187508 | − | 0.157338i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −38.6125 | − | 41.4965i | −1.27649 | − | 1.37183i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.58123 | − | 54.1559i | −0.0522168 | − | 1.78839i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.8975 | − | 44.8558i | −0.854280 | − | 1.47966i | −0.877312 | − | 0.479921i | \(-0.840665\pi\) |
0.0230323 | − | 0.999735i | \(-0.492668\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.1386 | + | 7.15354i | −1.02605 | + | 0.235717i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.714197 | + | 4.05041i | −0.0235081 | + | 0.133321i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −93.7593 | + | 78.6734i | −3.08279 | + | 2.58677i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.7805 | − | 41.4207i | −0.386923 | − | 1.36043i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.73144 | + | 3.97015i | −0.155234 | + | 0.130257i | −0.717096 | − | 0.696974i | \(-0.754529\pi\) |
0.561863 | + | 0.827230i | \(0.310085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.630013 | − | 5.39953i | 0.0206478 | − | 0.176962i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.8007 | − | 25.1380i | 1.27028 | − | 0.822980i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.635384 | + | 1.10052i | 0.0207793 | + | 0.0359908i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.05305 | − | 3.55599i | −0.0670703 | − | 0.116169i | 0.830540 | − | 0.556959i | \(-0.188032\pi\) |
−0.897610 | + | 0.440790i | \(0.854698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.3092 | + | 6.48006i | 1.70705 | + | 0.211469i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.2167 | − | 12.0899i | 1.08283 | − | 0.394119i | 0.261871 | − | 0.965103i | \(-0.415660\pi\) |
0.820961 | + | 0.570984i | \(0.193438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.01648 | + | 11.4360i | 0.0656655 | + | 0.372408i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.3647 | + | 51.8230i | −0.597405 | + | 1.68580i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.05842 | + | 23.0164i | 0.131881 | + | 0.747934i | 0.976981 | + | 0.213326i | \(0.0684296\pi\) |
−0.845100 | + | 0.534608i | \(0.820459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.22864 | + | 2.26704i | −0.202190 | + | 0.0735912i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.36290 | − | 19.7610i | −0.271186 | − | 0.640795i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.05136 | − | 5.28512i | −0.0988433 | − | 0.171202i | 0.812363 | − | 0.583152i | \(-0.198181\pi\) |
−0.911206 | + | 0.411951i | \(0.864848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.5448 | + | 37.3168i | 0.697175 | + | 1.20754i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.872430 | + | 16.9978i | 0.0282017 | + | 0.549461i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.9564 | − | 41.6887i | 1.06422 | − | 1.34620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.8438 | + | 9.93815i | −0.382059 | + | 0.320585i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.2520 | + | 6.42810i | −0.427041 | + | 0.207143i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.2799 | − | 23.7296i | 0.910361 | − | 0.763883i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.59228 | + | 48.7293i | −0.276309 | + | 1.56703i | 0.458463 | + | 0.888713i | \(0.348400\pi\) |
−0.734772 | + | 0.678314i | \(0.762711\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.280832 | − | 0.301808i | −0.00902163 | − | 0.00969546i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0633848 | + | 0.109786i | 0.00203412 | + | 0.00352319i | 0.867041 | − | 0.498237i | \(-0.166019\pi\) |
−0.865007 | + | 0.501761i | \(0.832686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.6389 | − | 18.6726i | −1.11047 | − | 0.598617i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.6614 | + | 8.88175i | −1.23815 | + | 0.284444i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.6429 | + | 23.1951i | 0.884374 | + | 0.742078i | 0.967074 | − | 0.254497i | \(-0.0819098\pi\) |
−0.0826996 | + | 0.996575i | \(0.526354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.07752 | − | 1.74324i | 0.0663977 | − | 0.0557143i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.1871 | − | 10.9693i | −0.516815 | − | 0.350221i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.0491 | + | 16.0326i | 1.40495 | + | 0.511360i | 0.929643 | − | 0.368461i | \(-0.120115\pi\) |
0.475306 | + | 0.879821i | \(0.342337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66.4399 | − | 55.7497i | −2.11695 | − | 1.77633i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.0675 | + | 30.5270i | 0.670586 | + | 0.971685i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3911 | 0.362216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2243 | 0.642447 | 0.321223 | − | 0.947003i | \(-0.395906\pi\) | ||||
0.321223 | + | 0.947003i | \(0.395906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.8800 | + | 30.4345i | 0.408733 | + | 0.965811i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.2115 | + | 27.8678i | 1.05288 | + | 0.883469i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.3227 | + | 22.9265i | −0.865318 | + | 0.726088i | −0.963107 | − | 0.269119i | \(-0.913268\pi\) |
0.0977887 | + | 0.995207i | \(0.468823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.0733 | − | 36.2587i | 1.42606 | − | 1.14717i |
(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 | 756.2.bp.a.193.19 | ✓ | 144 | |
7.2 | even | 3 | 756.2.bq.a.625.3 | yes | 144 | ||
27.7 | even | 9 | 756.2.bq.a.277.3 | yes | 144 | ||
189.142 | even | 9 | inner | 756.2.bp.a.709.19 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bp.a.193.19 | ✓ | 144 | 1.1 | even | 1 | trivial | |
756.2.bp.a.709.19 | yes | 144 | 189.142 | even | 9 | inner | |
756.2.bq.a.277.3 | yes | 144 | 27.7 | even | 9 | ||
756.2.bq.a.625.3 | yes | 144 | 7.2 | even | 3 |