Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(85,756)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bo (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: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 85.4 | ||
Character | \(\chi\) | \(=\) | 756.85 |
Dual form | 756.2.bo.b.169.4 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.377044 | + | 1.69051i | −0.217687 | + | 0.976019i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.491885 | − | 2.78962i | 0.219978 | − | 1.24755i | −0.652079 | − | 0.758151i | \(-0.726103\pi\) |
0.872057 | − | 0.489404i | \(-0.162786\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.766044 | + | 0.642788i | −0.289538 | + | 0.242951i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.71568 | − | 1.27480i | −0.905225 | − | 0.424932i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.658350 | + | 3.73369i | 0.198500 | + | 1.12575i | 0.907346 | + | 0.420385i | \(0.138105\pi\) |
−0.708846 | + | 0.705363i | \(0.750784\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.581608 | + | 0.211688i | −0.161309 | + | 0.0587116i | −0.421412 | − | 0.906869i | \(-0.638466\pi\) |
0.260104 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.53043 | + | 1.88335i | 1.16975 | + | 0.486278i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.28448 | + | 5.68889i | −0.796603 | + | 1.37976i | 0.125213 | + | 0.992130i | \(0.460039\pi\) |
−0.921816 | + | 0.387628i | \(0.873295\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.623998 | + | 1.08080i | 0.143155 | + | 0.247952i | 0.928683 | − | 0.370874i | \(-0.120942\pi\) |
−0.785528 | + | 0.618826i | \(0.787609\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.797809 | − | 1.53737i | −0.174096 | − | 0.335481i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.17422 | + | 5.18079i | 1.28741 | + | 1.08027i | 0.992176 | + | 0.124846i | \(0.0398435\pi\) |
0.295238 | + | 0.955424i | \(0.404601\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.84155 | − | 1.03424i | −0.568310 | − | 0.206848i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.17899 | − | 4.11023i | 0.611797 | − | 0.791015i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.04249 | + | 2.56326i | 1.30776 | + | 0.475985i | 0.899515 | − | 0.436889i | \(-0.143920\pi\) |
0.408242 | + | 0.912874i | \(0.366142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.34513 | + | 2.80690i | 0.600803 | + | 0.504134i | 0.891704 | − | 0.452619i | \(-0.149510\pi\) |
−0.290900 | + | 0.956753i | \(0.593955\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.56008 | − | 0.294816i | −1.14196 | − | 0.0513208i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41633 | + | 2.45315i | 0.239403 | + | 0.414658i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.09143 | + | 8.81861i | −0.837026 | + | 1.44977i | 0.0553450 | + | 0.998467i | \(0.482374\pi\) |
−0.892371 | + | 0.451303i | \(0.850959\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.138569 | − | 1.06303i | −0.0221889 | − | 0.170221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.25345 | − | 1.18416i | 0.508104 | − | 0.184935i | −0.0752313 | − | 0.997166i | \(-0.523970\pi\) |
0.583335 | + | 0.812231i | \(0.301747\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.17879 | − | 6.68524i | −0.179763 | − | 1.01949i | −0.932501 | − | 0.361168i | \(-0.882378\pi\) |
0.752737 | − | 0.658321i | \(-0.228733\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.89200 | + | 6.94864i | −0.729256 | + | 1.03584i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.09562 | + | 1.75843i | −0.305677 | + | 0.256493i | −0.782703 | − | 0.622396i | \(-0.786159\pi\) |
0.477026 | + | 0.878889i | \(0.341715\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.173648 | − | 0.984808i | 0.0248069 | − | 0.140687i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.37875 | − | 7.69742i | −1.17326 | − | 1.07785i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.0845 | −1.65993 | −0.829967 | − | 0.557812i | \(-0.811641\pi\) | ||||
−0.829967 | + | 0.557812i | \(0.811641\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7394 | 1.44810 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.06237 | + | 0.647369i | −0.273168 | + | 0.0857461i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.37705 | + | 7.80964i | −0.179277 | + | 1.01673i | 0.753814 | + | 0.657088i | \(0.228212\pi\) |
−0.933091 | + | 0.359641i | \(0.882899\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.60602 | − | 4.70401i | 0.717777 | − | 0.602286i | −0.208992 | − | 0.977917i | \(-0.567018\pi\) |
0.926769 | + | 0.375631i | \(0.122574\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.89975 | − | 0.769051i | 0.365334 | − | 0.0968913i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.304444 | + | 1.72659i | 0.0377617 | + | 0.214157i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.58242 | − | 1.66787i | 0.559832 | − | 0.203762i | −0.0465774 | − | 0.998915i | \(-0.514831\pi\) |
0.606410 | + | 0.795152i | \(0.292609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.0862 | + | 8.48423i | −1.33462 | + | 1.02138i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.88875 | + | 10.1996i | −0.698866 | + | 1.21047i | 0.269994 | + | 0.962862i | \(0.412978\pi\) |
−0.968860 | + | 0.247609i | \(0.920355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.36336 | − | 11.0217i | −0.744775 | − | 1.28999i | −0.950300 | − | 0.311337i | \(-0.899223\pi\) |
0.205524 | − | 0.978652i | \(-0.434110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.81979 | − | 4.41373i | 0.325601 | − | 0.509654i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.90429 | − | 2.43699i | −0.330975 | − | 0.277721i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.33017 | − | 3.03193i | −0.937217 | − | 0.341119i | −0.172151 | − | 0.985071i | \(-0.555072\pi\) |
−0.765066 | + | 0.643951i | \(0.777294\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.74978 | + | 6.92387i | 0.638865 | + | 0.769319i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.09112 | − | 2.58096i | −0.778351 | − | 0.283297i | −0.0778664 | − | 0.996964i | \(-0.524811\pi\) |
−0.700485 | + | 0.713667i | \(0.747033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.2542 | + | 11.9607i | 1.54609 | + | 1.29732i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.98855 | + | 10.9390i | −0.749251 | + | 1.17278i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.430724 | + | 0.746036i | 0.0456567 | + | 0.0790797i | 0.887951 | − | 0.459939i | \(-0.152129\pi\) |
−0.842294 | + | 0.539018i | \(0.818795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.309467 | − | 0.536012i | 0.0324410 | − | 0.0561894i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00637 | + | 4.59667i | −0.622831 | + | 0.476652i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.32194 | − | 1.20909i | 0.340824 | − | 0.124050i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.650292 | − | 3.68799i | −0.0660272 | − | 0.374459i | −0.999860 | − | 0.0167483i | \(-0.994669\pi\) |
0.933833 | − | 0.357710i | \(-0.116442\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.97183 | − | 10.9787i | 0.298680 | − | 1.10340i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.11434 | + | 1.77414i | −0.210385 | + | 0.176534i | −0.741891 | − | 0.670521i | \(-0.766071\pi\) |
0.531506 | + | 0.847054i | \(0.321626\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.36109 | − | 13.3904i | 0.232645 | − | 1.31939i | −0.614872 | − | 0.788627i | \(-0.710792\pi\) |
0.847517 | − | 0.530768i | \(-0.178096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.68110 | + | 1.46937i | −0.456829 | + | 0.143396i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.77292 | 0.944784 | 0.472392 | − | 0.881389i | \(-0.343391\pi\) | ||||
0.472392 | + | 0.881389i | \(0.343391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4940 | 1.67562 | 0.837809 | − | 0.545964i | \(-0.183836\pi\) | ||||
0.837809 | + | 0.545964i | \(0.183836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.9883 | − | 11.9321i | −1.23279 | − | 1.13255i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.24979 | − | 7.08789i | 0.117570 | − | 0.666772i | −0.867876 | − | 0.496781i | \(-0.834515\pi\) |
0.985446 | − | 0.169991i | \(-0.0543738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.4894 | − | 14.6754i | 1.63090 | − | 1.36849i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.84932 | + | 0.166556i | 0.170969 | + | 0.0153981i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.14069 | − | 6.46916i | −0.104567 | − | 0.593027i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.17037 | + | 1.15392i | −0.288215 | + | 0.104902i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.775144 | + | 5.94649i | 0.0698923 | + | 0.536177i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.79878 | − | 4.84763i | 0.250330 | − | 0.433585i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.15801 | + | 8.93393i | 0.457699 | + | 0.792758i | 0.998839 | − | 0.0481743i | \(-0.0153403\pi\) |
−0.541140 | + | 0.840933i | \(0.682007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.7459 | + | 0.527874i | 1.03417 | + | 0.0464767i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5448 | + | 8.84812i | 0.921302 | + | 0.773064i | 0.974235 | − | 0.225534i | \(-0.0724127\pi\) |
−0.0529336 | + | 0.998598i | \(0.516857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.17273 | − | 0.426840i | −0.101689 | − | 0.0370117i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.90228 | − | 10.8899i | −0.852252 | − | 0.937256i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.457675 | + | 0.166580i | 0.0391018 | + | 0.0142319i | 0.361497 | − | 0.932373i | \(-0.382266\pi\) |
−0.322395 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.97624 | − | 7.53196i | −0.761355 | − | 0.638852i | 0.177125 | − | 0.984188i | \(-0.443320\pi\) |
−0.938479 | + | 0.345336i | \(0.887765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.18251 | − | 4.20567i | −0.183801 | − | 0.354182i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.17328 | − | 2.03218i | −0.0981144 | − | 0.169939i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.6146 | − | 18.3850i | 0.881494 | − | 1.52679i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.59936 | + | 0.664871i | 0.131913 | + | 0.0548376i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.628791 | − | 0.228861i | 0.0515126 | − | 0.0187490i | −0.316135 | − | 0.948714i | \(-0.602385\pi\) |
0.367648 | + | 0.929965i | \(0.380163\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.66174 | + | 9.42421i | 0.135231 | + | 0.766931i | 0.974699 | + | 0.223522i | \(0.0717556\pi\) |
−0.839468 | + | 0.543409i | \(0.817133\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.1718 | − | 11.2621i | 1.30741 | − | 0.910489i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.47559 | − | 7.95097i | 0.761098 | − | 0.638637i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.95408 | + | 11.0822i | −0.155953 | + | 0.884453i | 0.801957 | + | 0.597382i | \(0.203792\pi\) |
−0.957909 | + | 0.287070i | \(0.907319\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.55639 | − | 20.4290i | 0.361345 | − | 1.62013i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.05988 | −0.635207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2878 | 1.43241 | 0.716207 | − | 0.697888i | \(-0.245877\pi\) | ||||
0.716207 | + | 0.697888i | \(0.245877\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.04922 | + | 18.1551i | −0.315232 | + | 1.41337i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.486884 | + | 2.76126i | −0.0376762 | + | 0.213673i | −0.997834 | − | 0.0657871i | \(-0.979044\pi\) |
0.960157 | + | 0.279460i | \(0.0901553\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.66512 | + | 8.11000i | −0.743471 | + | 0.623846i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.316780 | − | 3.73056i | −0.0242247 | − | 0.285283i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.20550 | − | 18.1793i | −0.243710 | − | 1.38215i | −0.823471 | − | 0.567359i | \(-0.807965\pi\) |
0.579761 | − | 0.814786i | \(-0.303146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.84155 | − | 1.03424i | 0.214801 | − | 0.0781812i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6831 | − | 5.27250i | −0.953320 | − | 0.396305i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.24251 | + | 3.88414i | −0.167613 | + | 0.290314i | −0.937580 | − | 0.347769i | \(-0.886939\pi\) |
0.769967 | + | 0.638084i | \(0.220273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.49700 | − | 12.9852i | −0.557247 | − | 0.965181i | −0.997725 | − | 0.0674172i | \(-0.978524\pi\) |
0.440477 | − | 0.897764i | \(-0.354809\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.83847 | + | 11.2507i | 0.431592 | + | 0.831673i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.0962 | + | 18.5409i | 1.62454 | + | 1.36315i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.4029 | − | 8.51794i | −1.71139 | − | 0.622894i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.206757 | + | 5.19204i | 0.0150393 | + | 0.377665i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.95856 | + | 0.712858i | 0.141716 | + | 0.0515806i | 0.411905 | − | 0.911227i | \(-0.364864\pi\) |
−0.270188 | + | 0.962808i | \(0.587086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.5675 | − | 11.3845i | −0.976611 | − | 0.819474i | 0.00696374 | − | 0.999976i | \(-0.497783\pi\) |
−0.983575 | + | 0.180502i | \(0.942228\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.03361 | − | 0.136333i | −0.217241 | − | 0.00976303i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3264 | + | 21.3499i | 0.878218 | + | 1.52112i | 0.853294 | + | 0.521430i | \(0.174601\pi\) |
0.0249242 | + | 0.999689i | \(0.492066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2759 | − | 21.2624i | 0.870214 | − | 1.50725i | 0.00843836 | − | 0.999964i | \(-0.497314\pi\) |
0.861775 | − | 0.507290i | \(-0.169353\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.09177 | + | 8.37551i | 0.0770078 | + | 0.590763i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.04249 | + | 2.56326i | −0.494286 | + | 0.179905i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.70303 | − | 9.65836i | −0.118945 | − | 0.674569i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.1627 | − | 21.9402i | −0.706359 | − | 1.52495i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.62454 | + | 3.04135i | −0.250715 | + | 0.210375i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74184 | + | 9.87849i | −0.119913 | + | 0.680063i | 0.864286 | + | 0.503001i | \(0.167771\pi\) |
−0.984200 | + | 0.177063i | \(0.943340\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.0223 | − | 13.8007i | −1.02931 | − | 0.945609i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.2291 | −1.31141 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.36676 | −0.296435 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.0316 | − | 6.60170i | 1.42118 | − | 0.446101i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.706010 | − | 4.00398i | 0.0474914 | − | 0.269337i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3648 | + | 9.53621i | −0.761044 | + | 0.638592i | −0.938398 | − | 0.345555i | \(-0.887691\pi\) |
0.177354 | + | 0.984147i | \(0.443246\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.39829 | + | 6.43106i | 0.426552 | + | 0.428738i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.06478 | − | 6.03865i | −0.0706717 | − | 0.400799i | −0.999538 | − | 0.0303847i | \(-0.990327\pi\) |
0.928867 | − | 0.370415i | \(-0.120784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.05603 | + | 1.84025i | −0.334112 | + | 0.121607i | −0.503628 | − | 0.863921i | \(-0.668002\pi\) |
0.169516 | + | 0.985527i | \(0.445780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.21481 | − | 3.99089i | 0.343110 | − | 0.262581i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.667800 | + | 1.15666i | −0.0437490 | + | 0.0757756i | −0.887071 | − | 0.461633i | \(-0.847264\pi\) |
0.843322 | + | 0.537409i | \(0.180597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.87455 | + | 6.71091i | 0.252748 | + | 0.437772i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.26637 | − | 12.9391i | 0.536958 | − | 0.840484i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.45672 | + | 3.73963i | 0.288281 | + | 0.241896i | 0.775447 | − | 0.631413i | \(-0.217525\pi\) |
−0.487166 | + | 0.873310i | \(0.661969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.01473 | − | 1.46124i | −0.258611 | − | 0.0941268i | 0.209461 | − | 0.977817i | \(-0.432829\pi\) |
−0.468072 | + | 0.883690i | \(0.655051\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.8728 | + | 7.10948i | −0.889942 | + | 0.456074i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.66182 | − | 0.968824i | −0.170058 | − | 0.0618959i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.591713 | − | 0.496506i | −0.0376498 | − | 0.0315919i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.03681 | − | 11.0145i | 0.445940 | − | 0.698016i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.87016 | − | 11.8995i | −0.433641 | − | 0.751087i | 0.563543 | − | 0.826087i | \(-0.309438\pi\) |
−0.997184 | + | 0.0749992i | \(0.976105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.2786 | + | 26.4634i | −0.960560 | + | 1.66374i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.5942 | + | 19.5873i | −1.60277 | + | 1.22660i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.4442 | + | 4.89329i | −0.838626 | + | 0.305235i | −0.725394 | − | 0.688334i | \(-0.758343\pi\) |
−0.113232 | + | 0.993569i | \(0.536120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76823 | − | 10.0282i | −0.109873 | − | 0.623119i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.8575 | − | 15.9387i | −0.981553 | − | 0.986582i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3534 | + | 9.52661i | −0.700079 | + | 0.587436i | −0.921796 | − | 0.387675i | \(-0.873278\pi\) |
0.221717 | + | 0.975111i | \(0.428834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.94418 | + | 33.7111i | −0.365148 | + | 2.07086i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.42359 | + | 0.446857i | −0.0871221 | + | 0.0273472i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2959 | 1.60329 | 0.801646 | − | 0.597800i | \(-0.203958\pi\) | ||||
0.801646 | + | 0.597800i | \(0.203958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.277729 | −0.0168709 | −0.00843543 | − | 0.999964i | \(-0.502685\pi\) | ||||
−0.00843543 | + | 0.999964i | \(0.502685\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.789454 | + | 0.725259i | 0.0477799 | + | 0.0438947i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.99079 | − | 11.2904i | 0.120049 | − | 0.680834i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1572 | + | 15.2357i | −1.09096 | + | 0.915425i | −0.996784 | − | 0.0801310i | \(-0.974466\pi\) |
−0.0941762 | + | 0.995556i | \(0.530022\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.50606 | − | 11.8870i | −0.329639 | − | 0.711656i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.826871 | − | 4.68942i | −0.0493270 | − | 0.279747i | 0.950160 | − | 0.311761i | \(-0.100919\pi\) |
−0.999487 | + | 0.0320141i | \(0.989808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0955 | − | 5.13036i | 0.837893 | − | 0.304968i | 0.112799 | − | 0.993618i | \(-0.464018\pi\) |
0.725094 | + | 0.688650i | \(0.241796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.791461 | + | 6.07167i | 0.0468821 | + | 0.359655i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.73113 | + | 2.99840i | −0.102185 | + | 0.176990i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0756 | − | 22.6476i | −0.769154 | − | 1.33221i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.47979 | + | 0.291208i | 0.379852 | + | 0.0170709i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1070 | + | 8.48077i | 0.590456 | + | 0.495452i | 0.888362 | − | 0.459144i | \(-0.151844\pi\) |
−0.297906 | + | 0.954595i | \(0.596288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.1086 | + | 7.68289i | 1.22899 | + | 0.447315i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.4392 | + | 9.16339i | 1.01193 | + | 0.531714i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.68769 | − | 1.70618i | −0.271096 | − | 0.0986708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.20019 | + | 4.36348i | 0.299734 | + | 0.251507i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.20201 | − | 4.24325i | −0.126502 | − | 0.243768i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.3649 | − | 17.9525i | −0.593490 | − | 1.02796i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.20414 | − | 3.81768i | 0.125797 | − | 0.217886i | −0.796247 | − | 0.604971i | \(-0.793185\pi\) |
0.922044 | + | 0.387085i | \(0.126518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.7464 | + | 9.04022i | 1.23711 | + | 0.514280i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1789 | − | 4.43276i | 0.690602 | − | 0.251359i | 0.0272093 | − | 0.999630i | \(-0.491338\pi\) |
0.663393 | + | 0.748271i | \(0.269116\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.65545 | − | 9.38852i | −0.0935716 | − | 0.530671i | −0.995176 | − | 0.0981086i | \(-0.968721\pi\) |
0.901604 | − | 0.432562i | \(-0.142390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.719014 | − | 8.46748i | −0.0405119 | − | 0.477089i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.6555 | − | 14.8147i | 0.991629 | − | 0.832075i | 0.00582619 | − | 0.999983i | \(-0.498145\pi\) |
0.985803 | + | 0.167908i | \(0.0537010\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.93397 | + | 27.9820i | −0.276249 | + | 1.56669i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.68482 | + | 16.5213i | −0.205667 | + | 0.922127i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.19803 | −0.456151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.87160 | 0.103818 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.59600 | + | 29.5738i | −0.364760 | + | 1.63543i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.475037 | − | 2.69407i | 0.0261897 | − | 0.148529i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4673 | − | 20.5305i | 1.34485 | − | 1.12846i | 0.364493 | − | 0.931206i | \(-0.381242\pi\) |
0.980352 | − | 0.197254i | \(-0.0632023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.0686 | − | 17.4579i | 1.37375 | − | 0.956690i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.39868 | − | 13.6036i | −0.131054 | − | 0.743244i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.9642 | + | 6.53844i | −0.978573 | + | 0.356171i | −0.781285 | − | 0.624174i | \(-0.785435\pi\) |
−0.197287 | + | 0.980346i | \(0.563213\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5109 | + | 4.78523i | 0.625189 | + | 0.259898i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.27781 | + | 14.3376i | −0.448269 | + | 0.776424i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.500000 | + | 0.866025i | 0.0269975 | + | 0.0467610i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.2146 | + | 35.0994i | 0.980643 | + | 1.88969i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.2347 | + | 23.6917i | 1.51572 | + | 1.27184i | 0.851572 | + | 0.524237i | \(0.175649\pi\) |
0.664147 | + | 0.747602i | \(0.268795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.5710 | + | 10.0350i | 1.47584 | + | 0.537163i | 0.949680 | − | 0.313222i | \(-0.101408\pi\) |
0.526162 | + | 0.850384i | \(0.323631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.978840 | + | 3.06350i | −0.0522466 | + | 0.163517i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.24993 | + | 2.27479i | 0.332650 | + | 0.121075i | 0.502945 | − | 0.864318i | \(-0.332250\pi\) |
−0.170295 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.5564 | + | 21.4444i | 1.35639 | + | 1.13815i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.3663 | + | 0.510812i | 0.601568 | + | 0.0270350i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.5242 | + | 25.1567i | 0.766560 | + | 1.32772i | 0.939418 | + | 0.342774i | \(0.111367\pi\) |
−0.172857 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.72125 | − | 15.1057i | 0.459013 | − | 0.795034i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.755348 | − | 5.79463i | −0.0396455 | − | 0.304139i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.8763 | + | 12.3300i | −1.77317 | + | 0.645380i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.38025 | − | 7.82780i | −0.0720486 | − | 0.408608i | −0.999407 | − | 0.0344335i | \(-0.989037\pi\) |
0.927358 | − | 0.374174i | \(-0.122074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3449 | − | 0.931699i | −0.538533 | − | 0.0485023i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.25727 | − | 7.76777i | 0.480613 | − | 0.403282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.92757 | + | 10.9318i | −0.0998059 | + | 0.566027i | 0.893362 | + | 0.449337i | \(0.148340\pi\) |
−0.993168 | + | 0.116691i | \(0.962771\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.13972 | + | 6.55914i | 0.368693 | + | 0.338713i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.63857 | −0.238899 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.5563 | 1.46684 | 0.733418 | − | 0.679777i | \(-0.237924\pi\) | ||||
0.733418 | + | 0.679777i | \(0.237924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.0477 | + | 5.35120i | −0.873382 | + | 0.274150i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.98314 | − | 16.9182i | 0.152431 | − | 0.864480i | −0.808666 | − | 0.588268i | \(-0.799810\pi\) |
0.961097 | − | 0.276212i | \(-0.0890791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.22685 | + | 6.90315i | −0.419279 | + | 0.351817i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.32112 | + | 19.6577i | −0.270488 | + | 0.999255i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.82378 | − | 27.3570i | −0.244575 | − | 1.38706i | −0.821477 | − | 0.570242i | \(-0.806850\pi\) |
0.576902 | − | 0.816814i | \(-0.304262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −49.7520 | + | 18.1083i | −2.51607 | + | 0.915774i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.9337 | + | 14.4900i | −0.955080 | + | 0.730922i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.5554 | + | 21.7466i | −0.631732 | + | 1.09419i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.88573 | − | 4.99823i | −0.144831 | − | 0.250854i | 0.784479 | − | 0.620155i | \(-0.212930\pi\) |
−0.929310 | + | 0.369301i | \(0.879597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.16375 | − | 1.82158i | 0.0582604 | − | 0.0911932i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0845 | − | 19.3702i | −1.15278 | − | 0.967301i | −0.153003 | − | 0.988226i | \(-0.548894\pi\) |
−0.999781 | + | 0.0209252i | \(0.993339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.53974 | − | 0.924390i | −0.126513 | − | 0.0460471i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.1432 | − | 12.6340i | 1.10030 | − | 0.627786i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.2779 | − | 13.2041i | −1.79823 | − | 0.654501i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.6219 | − | 13.1083i | −0.772453 | − | 0.648165i | 0.168883 | − | 0.985636i | \(-0.445984\pi\) |
−0.941336 | + | 0.337471i | \(0.890429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.454170 | + | 0.710898i | −0.0224025 | + | 0.0350660i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.96506 | − | 6.86768i | −0.195108 | − | 0.337936i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.6879 | + | 18.5120i | −0.524648 | + | 0.908717i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.1173 | − | 12.3346i | 0.789268 | − | 0.604027i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.87119 | + | 1.40900i | −0.189120 | + | 0.0688340i | −0.434844 | − | 0.900506i | \(-0.643197\pi\) |
0.245724 | + | 0.969340i | \(0.420974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.64345 | − | 9.32049i | −0.0800971 | − | 0.454253i | −0.998307 | − | 0.0581596i | \(-0.981477\pi\) |
0.918210 | − | 0.396093i | \(-0.129634\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.93265 | − | 2.10384i | 0.385699 | − | 0.102292i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.2167 | − | 12.7683i | 0.738118 | − | 0.619355i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.27078 | + | 7.20696i | −0.0614974 | + | 0.348769i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.87780 | − | 1.21722i | 0.187222 | − | 0.0587680i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5768 | −0.846646 | −0.423323 | − | 0.905979i | \(-0.639136\pi\) | ||||
−0.423323 | + | 0.905979i | \(0.639136\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2769 | 0.493878 | 0.246939 | − | 0.969031i | \(-0.420575\pi\) | ||||
0.246939 | + | 0.969031i | \(0.420575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 27.0780 | + | 24.8761i | 1.29829 | + | 1.19272i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.74667 | + | 9.90587i | −0.0835547 | + | 0.473862i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.94284 | + | 6.66483i | −0.379091 | + | 0.318095i | −0.812345 | − | 0.583177i | \(-0.801810\pi\) |
0.433255 | + | 0.901272i | \(0.357365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.72700 | + | 2.45305i | −0.0822382 | + | 0.116812i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.09215 | + | 6.19390i | 0.0518897 | + | 0.294281i | 0.999698 | − | 0.0245584i | \(-0.00781796\pi\) |
−0.947809 | + | 0.318840i | \(0.896707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.29302 | − | 0.834592i | 0.108700 | − | 0.0395635i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.149811 | + | 1.14927i | 0.00708582 | + | 0.0543586i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.67993 | − | 16.7661i | 0.456824 | − | 0.791243i | −0.541967 | − | 0.840400i | \(-0.682320\pi\) |
0.998791 | + | 0.0491572i | \(0.0156535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.56319 | + | 11.3678i | 0.309049 | + | 0.535288i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.5583 | − | 0.744146i | −0.777977 | − | 0.0349630i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.34305 | − | 1.12695i | −0.0629630 | − | 0.0528323i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.7074 | − | 11.9045i | −1.52999 | − | 0.556870i | −0.566370 | − | 0.824151i | \(-0.691653\pi\) |
−0.963619 | + | 0.267281i | \(0.913875\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.9413 | + | 31.5849i | 0.604048 | + | 1.47426i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1205 | − | 4.41150i | −0.564508 | − | 0.205464i | 0.0439727 | − | 0.999033i | \(-0.485999\pi\) |
−0.608481 | + | 0.793569i | \(0.708221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.93530 | + | 6.65851i | 0.368785 | + | 0.309447i | 0.808281 | − | 0.588797i | \(-0.200398\pi\) |
−0.439496 | + | 0.898245i | \(0.644843\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.86850 | + | 19.0165i | 0.457641 | + | 0.881869i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.34705 | + | 2.33317i | 0.0623343 | + | 0.107966i | 0.895508 | − | 0.445045i | \(-0.146812\pi\) |
−0.833174 | + | 0.553011i | \(0.813479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43826 | + | 4.22318i | −0.112588 | + | 0.195009i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9978 | − | 7.48187i | −0.829294 | − | 0.344746i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.1845 | − | 8.80245i | 1.11201 | − | 0.404737i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.655319 | − | 3.71650i | −0.0300681 | − | 0.170525i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.8176 | + | 15.4053i | 1.50261 | + | 0.705360i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7015 | − | 14.0142i | 0.763111 | − | 0.640326i | −0.175824 | − | 0.984422i | \(-0.556259\pi\) |
0.938935 | + | 0.344095i | \(0.111814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09442 | − | 6.20676i | 0.0499013 | − | 0.283004i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.03893 | − | 13.6253i | 0.138276 | − | 0.619974i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.6080 | −0.481682 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.2996 | −0.965177 | −0.482589 | − | 0.875847i | \(-0.660303\pi\) | ||||
−0.482589 | + | 0.875847i | \(0.660303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.89532 | + | 30.9158i | −0.311817 | + | 1.39806i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.698981 | − | 3.96412i | 0.0315446 | − | 0.178898i | −0.964965 | − | 0.262379i | \(-0.915493\pi\) |
0.996509 | + | 0.0834813i | \(0.0266039\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.7130 | + | 31.6449i | −1.69851 | + | 1.42522i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.1647 | − | 13.6905i | −1.31086 | − | 0.615344i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.04514 | − | 11.5986i | −0.0917371 | − | 0.520267i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14891 | − | 0.418168i | 0.0514321 | − | 0.0187198i | −0.316176 | − | 0.948701i | \(-0.602399\pi\) |
0.367608 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.48437 | − | 1.86420i | −0.200347 | − | 0.0832864i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.273145 | − | 0.473102i | 0.0121790 | − | 0.0210946i | −0.859872 | − | 0.510510i | \(-0.829457\pi\) |
0.872051 | + | 0.489416i | \(0.162790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.90917 | + | 6.77087i | 0.173956 | + | 0.301300i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.0659 | − | 19.3969i | −0.447042 | − | 0.861445i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.17079 | + | 7.69521i | 0.406488 | + | 0.341084i | 0.822995 | − | 0.568048i | \(-0.192301\pi\) |
−0.416507 | + | 0.909133i | \(0.636746\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9592 | + | 4.35280i | 0.529044 | + | 0.192556i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.42600 | + | 0.871066i | 0.283715 | + | 0.0384585i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.1927 | − | 13.1731i | −1.59484 | − | 0.580474i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.94507 | − | 6.66671i | −0.349424 | − | 0.293202i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.9409 | + | 1.43546i | 1.40205 | + | 0.0630095i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4506 | + | 18.1010i | 0.457850 | + | 0.793020i | 0.998847 | − | 0.0480046i | \(-0.0152862\pi\) |
−0.540997 | + | 0.841025i | \(0.681953\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.9086 | + | 34.4828i | −0.870544 | + | 1.50783i | −0.00910952 | + | 0.999959i | \(0.502900\pi\) |
−0.861435 | + | 0.507868i | \(0.830434\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.677007 | + | 5.19364i | 0.0295470 | + | 0.226669i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.9551 | + | 9.81087i | −1.17418 | + | 0.427368i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.28656 | + | 41.3241i | 0.316807 | + | 1.79670i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.6953 | − | 19.4530i | 0.594327 | − | 0.844187i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.64156 | + | 1.37743i | −0.0711039 | + | 0.0596633i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.80715 | − | 27.2627i | 0.207831 | − | 1.17867i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.72067 | − | 5.25548i | −0.246865 | − | 0.226791i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.79128 | 0.163302 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.6548 | 1.36094 | 0.680472 | − | 0.732774i | \(-0.261775\pi\) | ||||
0.680472 | + | 0.732774i | \(0.261775\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.7783 | − | 7.77779i | 1.06334 | − | 0.333777i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.60501 | − | 48.8015i | 0.368598 | − | 2.09043i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8018 | + | 14.9375i | −0.761149 | + | 0.638680i | −0.938426 | − | 0.345481i | \(-0.887716\pi\) |
0.177276 | + | 0.984161i | \(0.443271\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.2208 | + | 5.62802i | −0.905681 | + | 0.240198i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.62414 | + | 9.21095i | 0.0691907 | + | 0.392400i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.33017 | − | 3.03193i | 0.354235 | − | 0.128931i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −39.6748 | + | 30.3631i | −1.68410 | + | 1.28884i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.7450 | − | 20.3430i | 0.497654 | − | 0.861961i | −0.502343 | − | 0.864669i | \(-0.667528\pi\) |
0.999996 | + | 0.00270729i | \(0.000861757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.10078 | + | 3.63865i | 0.0888534 | + | 0.153899i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.2236 | − | 36.3512i | 0.980502 | − | 1.53475i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2406 | + | 27.0531i | 1.35878 | + | 1.14015i | 0.976357 | + | 0.216164i | \(0.0693545\pi\) |
0.382422 | + | 0.923988i | \(0.375090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.1577 | − | 6.97285i | −0.805972 | − | 0.293350i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.85517 | − | 1.60810i | −0.371882 | − | 0.0675340i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6415 | + | 6.78493i | 0.781490 | + | 0.284439i | 0.701794 | − | 0.712380i | \(-0.252383\pi\) |
0.0796964 | + | 0.996819i | \(0.474605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3290 | + | 17.0581i | 0.850743 | + | 0.713858i | 0.959953 | − | 0.280160i | \(-0.0903877\pi\) |
−0.109210 | + | 0.994019i | \(0.534832\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.94356 | + | 3.04220i | −0.0811934 | + | 0.127090i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.1862 | − | 21.1071i | −0.508200 | − | 0.880227i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8913 | − | 34.4528i | 0.828086 | − | 1.43429i | −0.0714514 | − | 0.997444i | \(-0.522763\pi\) |
0.899538 | − | 0.436843i | \(-0.143904\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.3612 | − | 18.6436i | 1.01242 | − | 0.774802i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.09112 | − | 2.58096i | 0.294189 | − | 0.107076i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.95583 | − | 45.1197i | −0.329497 | − | 1.86867i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.37428 | − | 5.07696i | 0.0568195 | − | 0.209906i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.5289 | + | 22.2604i | −1.09496 | + | 0.918784i | −0.997076 | − | 0.0764130i | \(-0.975653\pi\) |
−0.0978883 | + | 0.995197i | \(0.531209\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.946330 | + | 5.36690i | −0.0389928 | + | 0.221139i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.7399 | + | 12.7881i | −1.67582 | + | 0.526030i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.39174 | 0.385672 | 0.192836 | − | 0.981231i | \(-0.438231\pi\) | ||||
0.192836 | + | 0.981231i | \(0.438231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.6076 | −0.762836 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.3159 | + | 28.7694i | 1.28167 | + | 1.17745i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.30016 | − | 7.37357i | 0.0531230 | − | 0.301276i | −0.946657 | − | 0.322243i | \(-0.895563\pi\) |
0.999780 | + | 0.0209669i | \(0.00667445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.39764 | + | 2.01186i | −0.0978020 | + | 0.0820656i | −0.690378 | − | 0.723449i | \(-0.742556\pi\) |
0.592576 | + | 0.805515i | \(0.298111\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.5706 | − | 1.31228i | −0.593359 | − | 0.0534402i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.65954 | + | 9.41171i | 0.0674698 | + | 0.382640i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.3829 | + | 7.78275i | −0.867906 | + | 0.315892i | −0.737319 | − | 0.675545i | \(-0.763908\pi\) |
−0.130587 | + | 0.991437i | \(0.541686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.67789 | − | 12.8719i | −0.0679915 | − | 0.521595i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.846588 | − | 1.46633i | 0.0342493 | − | 0.0593215i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.55596 | + | 6.15911i | 0.143624 | + | 0.248764i | 0.928859 | − | 0.370434i | \(-0.120791\pi\) |
−0.785235 | + | 0.619198i | \(0.787458\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.9697 | + | 0.762635i | 0.684285 | + | 0.0307524i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.93269 | + | 2.46082i | 0.118066 | + | 0.0990690i | 0.699909 | − | 0.714232i | \(-0.253224\pi\) |
−0.581843 | + | 0.813301i | \(0.697668\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9122 | − | 7.97540i | −0.880726 | − | 0.320558i | −0.138224 | − | 0.990401i | \(-0.544139\pi\) |
−0.742503 | + | 0.669843i | \(0.766361\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.9221 | − | 8.90780i | 1.64215 | − | 0.357458i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.809497 | − | 0.294633i | −0.0324318 | − | 0.0118042i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7286 | − | 19.9107i | −0.949145 | − | 0.796427i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.77484 | − | 7.27407i | −0.150752 | − | 0.290498i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.4454 | − | 57.9291i | −1.33355 | − | 2.30978i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.871491 | − | 1.50947i | 0.0346935 | − | 0.0600910i | −0.848157 | − | 0.529744i | \(-0.822288\pi\) |
0.882851 | + | 0.469654i | \(0.155621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0430 | − | 6.66924i | −0.637651 | − | 0.265078i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.4594 | − | 9.99441i | 1.08969 | − | 0.396616i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.107477 | + | 0.609531i | 0.00425838 | + | 0.0241505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.9944 | − | 20.1919i | 1.14700 | − | 0.798778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.2313 | − | 9.42417i | 0.443609 | − | 0.372232i | −0.393449 | − | 0.919347i | \(-0.628718\pi\) |
0.837058 | + | 0.547114i | \(0.184274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.20722 | − | 29.5316i | 0.205353 | − | 1.16461i | −0.691531 | − | 0.722347i | \(-0.743063\pi\) |
0.896884 | − | 0.442267i | \(-0.145825\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.25022 | − | 32.5070i | 0.285477 | − | 1.27996i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −47.2238 | −1.85656 | −0.928280 | − | 0.371883i | \(-0.878712\pi\) | ||||
−0.928280 | + | 0.371883i | \(0.878712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.0653 | −1.18017 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.64646 | − | 7.38207i | 0.0645299 | − | 0.289326i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.96750 | − | 33.8434i | 0.233526 | − | 1.32439i | −0.612169 | − | 0.790727i | \(-0.709703\pi\) |
0.845695 | − | 0.533666i | \(-0.179186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.8697 | − | 25.0636i | 1.16711 | − | 0.979318i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.23043 | + | 38.0433i | 0.126031 | + | 1.48421i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.77609 | − | 27.0865i | −0.186050 | − | 1.05514i | −0.924599 | − | 0.380942i | \(-0.875600\pi\) |
0.738549 | − | 0.674200i | \(-0.235511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.3524 | − | 5.95179i | 0.636035 | − | 0.231498i | −0.00382110 | − | 0.999993i | \(-0.501216\pi\) |
0.639856 | + | 0.768495i | \(0.278994\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.50259 | + | 2.70320i | 0.252540 | + | 0.104984i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.76757 | + | 3.06152i | −0.0685434 | + | 0.118721i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.2022 | + | 52.3118i | 1.16943 | + | 2.02552i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.8361 | − | 22.8079i | −0.457608 | − | 0.881806i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.2540 | + | 17.8342i | 0.820502 | + | 0.688483i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.7026 | − | 11.1748i | −1.18350 | − | 0.430759i | −0.326063 | − | 0.945348i | \(-0.605722\pi\) |
−0.857437 | + | 0.514590i | \(0.827944\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.2842 | + | 8.39160i | −0.511311 | + | 0.322993i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.7034 | + | 6.80748i | 0.718830 | + | 0.261633i | 0.675429 | − | 0.737425i | \(-0.263958\pi\) |
0.0434011 | + | 0.999058i | \(0.486181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.86875 | + | 2.40716i | 0.110092 | + | 0.0923785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.6099 | + | 0.476818i | 0.406572 | + | 0.0182717i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.29478 | − | 7.43878i | −0.164335 | − | 0.284637i | 0.772084 | − | 0.635521i | \(-0.219215\pi\) |
−0.936419 | + | 0.350884i | \(0.885881\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.689818 | − | 1.19480i | 0.0263566 | − | 0.0456510i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.20461 | − | 9.24115i | −0.0459588 | − | 0.352572i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.02844 | − | 2.55814i | 0.267762 | − | 0.0974575i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.01752 | + | 22.7845i | 0.152834 | + | 0.866763i | 0.960740 | + | 0.277451i | \(0.0894898\pi\) |
−0.807906 | + | 0.589311i | \(0.799399\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.78045 | + | 10.3205i | 0.181594 | + | 0.392042i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.4266 | + | 21.3354i | −0.964484 | + | 0.809298i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.94935 | + | 22.3979i | −0.149592 | + | 0.848380i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.70357 | − | 1.56504i | −0.0644348 | − | 0.0591952i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.0749 | −0.644911 | −0.322455 | − | 0.946585i | \(-0.604508\pi\) | ||||
−0.322455 | + | 0.946585i | \(0.604508\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.7082 | −0.479297 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.8058 | + | 4.01966i | −0.482293 | + | 0.151389i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.479282 | − | 2.71814i | 0.0180253 | − | 0.102226i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.3757 | − | 26.3273i | 1.17834 | − | 0.988744i | 0.178351 | − | 0.983967i | \(-0.442924\pi\) |
0.999989 | − | 0.00477712i | \(-0.00152061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.7569 | + | 18.8530i | 0.703440 | + | 0.707044i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.11164 | + | 34.6608i | 0.228883 | + | 1.29806i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24611 | + | 2.27340i | −0.233591 | + | 0.0850203i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.00227 | + | 6.12413i | −0.298850 | + | 0.228710i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.1060 | + | 20.9681i | −0.451476 | + | 0.781980i | −0.998478 | − | 0.0551516i | \(-0.982436\pi\) |
0.547002 | + | 0.837132i | \(0.315769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.79848 | + | 11.7753i | 0.253189 | + | 0.438536i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.98398 | − | 6.23600i | 0.148166 | − | 0.231919i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.3606 | − | 14.5672i | −0.644755 | − | 0.541014i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.8145 | + | 9.75966i | 0.994493 | + | 0.361966i | 0.787458 | − | 0.616368i | \(-0.211396\pi\) |
0.207035 | + | 0.978334i | \(0.433619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.78801 | − | 26.1328i | −0.251408 | − | 0.967881i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.9033 | + | 15.2515i | 1.54985 | + | 0.564099i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1074 | + | 17.7112i | 0.779621 | + | 0.654180i | 0.943153 | − | 0.332358i | \(-0.107844\pi\) |
−0.163532 | + | 0.986538i | \(0.552289\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.64144 | − | 4.13456i | 0.0974308 | − | 0.152505i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.24412 | + | 16.0113i | 0.340512 | + | 0.589784i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.53163 | − | 13.0452i | 0.277055 | − | 0.479874i | −0.693596 | − | 0.720364i | \(-0.743975\pi\) |
0.970652 | + | 0.240490i | \(0.0773081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.06245 | − | 0.813094i | 0.0390302 | − | 0.0298698i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.17289 | − | 1.15484i | 0.116402 | − | 0.0423669i | −0.283163 | − | 0.959072i | \(-0.591384\pi\) |
0.399564 | + | 0.916705i | \(0.369161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.329142 | − | 1.86666i | −0.0120588 | − | 0.0683891i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.9670 | + | 16.0488i | 0.584201 | + | 0.587194i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.48649 | + | 6.28191i | −0.273550 | + | 0.229536i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.38881 | − | 30.5615i | 0.196641 | − | 1.11520i | −0.713422 | − | 0.700734i | \(-0.752856\pi\) |
0.910063 | − | 0.414470i | \(-0.136033\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.7066 | − | 7.12747i | 0.827473 | − | 0.259740i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.1073 | 0.986537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.3330 | −1.46593 | −0.732963 | − | 0.680268i | \(-0.761863\pi\) | ||||
−0.732963 | + | 0.680268i | \(0.761863\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −38.9760 | − | 35.8066i | −1.41474 | − | 1.29970i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.14299 | + | 6.48224i | −0.0414335 | + | 0.234981i | −0.998491 | − | 0.0549174i | \(-0.982510\pi\) |
0.957057 | + | 0.289899i | \(0.0936216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4012 | + | 11.2449i | −0.485154 | + | 0.407093i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.4624 | − | 50.6527i | −0.848284 | − | 1.83135i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.852303 | − | 4.83365i | −0.0307749 | − | 0.174533i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0707 | − | 7.30512i | 0.723767 | − | 0.263430i | 0.0462427 | − | 0.998930i | \(-0.485275\pi\) |
0.677524 | + | 0.735501i | \(0.263053\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.20311 | − | 24.5726i | −0.115357 | − | 0.884960i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.2608 | − | 26.4324i | 0.548892 | − | 0.950708i | −0.449459 | − | 0.893301i | \(-0.648383\pi\) |
0.998351 | − | 0.0574074i | \(-0.0182834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.60236 | − | 11.4356i | −0.237164 | − | 0.410780i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.6194 | + | 0.791834i | 0.632094 | + | 0.0284069i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.30998 | + | 2.77741i | 0.118592 | + | 0.0995109i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.9590 | − | 15.2718i | −1.50141 | − | 0.546469i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.9236 | − | 20.7977i | 1.17659 | − | 0.743249i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.9538 | + | 10.9023i | 1.06910 | + | 0.389120i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.73528 | − | 3.13427i | −0.133148 | − | 0.111725i | 0.573781 | − | 0.819008i | \(-0.305476\pi\) |
−0.706930 | + | 0.707284i | \(0.749920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.8241 | − | 22.7850i | −0.420951 | − | 0.811167i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.59861 | + | 6.23298i | 0.127952 | + | 0.221619i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.26472 | + | 3.92261i | −0.0804226 | + | 0.139296i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −54.7479 | − | 22.7593i | −1.94171 | − | 0.807190i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.6052 | + | 11.8673i | −1.15494 | + | 0.420363i | −0.847286 | − | 0.531137i | \(-0.821765\pi\) |
−0.307651 | + | 0.951499i | \(0.599543\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.12050 | − | 17.6972i | −0.110395 | − | 0.626084i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.218662 | − | 2.57508i | −0.00772605 | − | 0.0909859i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.9621 | − | 31.0149i | 1.30437 | − | 1.09449i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.96453 | + | 22.4840i | −0.139731 | + | 0.792456i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.91473 | + | 44.4536i | −0.349015 | + | 1.56484i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.9270 | 0.946704 | 0.473352 | − | 0.880873i | \(-0.343044\pi\) | ||||
0.473352 | + | 0.880873i | \(0.343044\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1589 | 0.497188 | 0.248594 | − | 0.968608i | \(-0.420032\pi\) | ||||
0.248594 | + | 0.968608i | \(0.420032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.104716 | − | 0.469505i | 0.00367256 | − | 0.0164663i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.99551 | − | 51.0161i | 0.315099 | − | 1.78701i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.48982 | − | 5.44560i | 0.227050 | − | 0.190518i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52372 | + | 1.06113i | −0.0532430 | + | 0.0370788i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.24554 | + | 24.0777i | 0.148170 | + | 0.840316i | 0.964767 | + | 0.263107i | \(0.0847472\pi\) |
−0.816596 | + | 0.577209i | \(0.804142\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.9212 | + | 11.6184i | −1.11270 | + | 0.404991i | −0.831985 | − | 0.554798i | \(-0.812795\pi\) |
−0.280720 | + | 0.959790i | \(0.590573\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.3359 | + | 7.62243i | 0.638374 | + | 0.265379i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.18618 | − | 10.7148i | 0.215115 | − | 0.372590i | −0.738193 | − | 0.674589i | \(-0.764321\pi\) |
0.953308 | + | 0.302000i | \(0.0976541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.0487 | − | 17.4048i | −0.349004 | − | 0.604493i | 0.637069 | − | 0.770807i | \(-0.280147\pi\) |
−0.986073 | + | 0.166314i | \(0.946813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.9101 | − | 36.4395i | −0.655984 | − | 1.26407i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.03212 | + | 4.22245i | 0.174352 | + | 0.146299i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.46336 | + | 2.71644i | 0.258280 | + | 0.0940063i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.1712 | − | 4.82616i | 0.766347 | − | 0.166816i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.7783 | − | 13.7502i | −1.30425 | − | 0.474709i | −0.405873 | − | 0.913930i | \(-0.633032\pi\) |
−0.898379 | + | 0.439221i | \(0.855255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8111 | + | 17.4625i | 0.717622 | + | 0.602157i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.23930 | + | 0.370282i | 0.283776 | + | 0.0127532i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.8697 | + | 30.9512i | 0.614735 | + | 1.06475i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.68692 | − | 2.92183i | 0.0579632 | − | 0.100395i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.35830 | + | 25.7631i | 0.115256 | + | 0.884187i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −77.1230 | + | 28.0705i | −2.64374 | + | 0.962243i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.79903 | − | 15.8741i | −0.0958370 | − | 0.543518i | −0.994488 | − | 0.104854i | \(-0.966563\pi\) |
0.898651 | − | 0.438665i | \(-0.144548\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.5627 | − | 0.951312i | −0.361235 | − | 0.0325342i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.7401 | − | 21.5985i | 0.879264 | − | 0.737790i | −0.0867638 | − | 0.996229i | \(-0.527653\pi\) |
0.966028 | + | 0.258439i | \(0.0832081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.15581 | − | 29.2400i | 0.175914 | − | 0.997657i | −0.761170 | − | 0.648553i | \(-0.775375\pi\) |
0.937084 | − | 0.349105i | \(-0.113514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.41613 | − | 4.05702i | −0.150501 | − | 0.138263i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.2627 | 0.825913 | 0.412956 | − | 0.910751i | \(-0.364496\pi\) | ||||
0.412956 | + | 0.910751i | \(0.364496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.2900 | −1.77791 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43.2162 | − | 13.5654i | 1.46770 | − | 0.460704i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.83612 | − | 33.0983i | 0.197977 | − | 1.12278i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.31211 | + | 1.94009i | −0.0783427 | + | 0.0657373i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.93546 | + | 10.8444i | −0.0993502 | + | 0.367026i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.972005 | + | 5.51252i | 0.0328598 | + | 0.186357i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6659 | − | 10.0696i | 0.934212 | − | 0.340025i | 0.170334 | − | 0.985386i | \(-0.445515\pi\) |
0.763878 | + | 0.645361i | \(0.223293\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.1476 | + | 13.8884i | −0.612105 | + | 0.468443i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.77794 | + | 16.9359i | −0.329427 | + | 0.570584i | −0.982398 | − | 0.186798i | \(-0.940189\pi\) |
0.652971 | + | 0.757383i | \(0.273522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.47934 | + | 14.6866i | 0.285353 | + | 0.494245i | 0.972695 | − | 0.232089i | \(-0.0745560\pi\) |
−0.687342 | + | 0.726334i | \(0.741223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.9469 | + | 32.7875i | −0.704122 | + | 1.10214i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.4502 | + | 12.1251i | 0.485189 | + | 0.407122i | 0.852299 | − | 0.523056i | \(-0.175208\pi\) |
−0.367109 | + | 0.930178i | \(0.619652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.69389 | − | 3.52829i | −0.325122 | − | 0.118335i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.0662 | + | 26.0262i | −0.739245 | + | 0.871911i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.20816 | − | 1.16768i | −0.107357 | − | 0.0390748i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.73220 | + | 8.16629i | 0.325312 | + | 0.272969i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.65178 | − | 7.28129i | 0.155319 | − | 0.243115i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.3632 | + | 28.3420i | 0.545745 | + | 0.945258i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.6913 | − | 68.7474i | 1.32231 | − | 2.29031i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.33723 | + | 7.14577i | −0.310723 | + | 0.237796i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.9113 | + | 14.5265i | −1.32670 | + | 0.482879i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.75875 | + | 49.6733i | 0.290829 | + | 1.64938i | 0.683686 | + | 0.729776i | \(0.260376\pi\) |
−0.392857 | + | 0.919600i | \(0.628513\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.00353 | − | 2.12264i | 0.265460 | − | 0.0704035i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.27530 | + | 6.10470i | −0.241041 | + | 0.202258i | −0.755303 | − | 0.655375i | \(-0.772510\pi\) |
0.514262 | + | 0.857633i | \(0.328066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.96805 | − | 28.1752i | 0.164418 | − | 0.932463i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.2569 | − | 10.7531i | 1.13250 | − | 0.355486i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.7652 | −0.454568 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.2549 | −1.16295 | −0.581476 | − | 0.813564i | \(-0.697525\pi\) | ||||
−0.581476 | + | 0.813564i | \(0.697525\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.62278 | + | 5.16556i | 0.185277 | + | 0.170211i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.26581 | − | 7.17875i | 0.0416645 | − | 0.236291i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.5881 | − | 19.7928i | 0.775573 | − | 0.650783i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.4820 | + | 33.3540i | −0.771250 | + | 1.09549i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.93945 | − | 33.6843i | −0.194867 | − | 1.10515i | −0.912608 | − | 0.408836i | \(-0.865935\pi\) |
0.717741 | − | 0.696310i | \(-0.245176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.17273 | − | 0.426840i | 0.0384347 | − | 0.0139891i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.90165 | + | 22.2600i | 0.0949959 | + | 0.728758i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.2733 | + | 61.0952i | −1.15356 | + | 1.99803i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6372 | + | 37.4768i | 0.706858 | + | 1.22431i | 0.966017 | + | 0.258479i | \(0.0832212\pi\) |
−0.259159 | + | 0.965835i | \(0.583446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.4956 | + | 0.741328i | 0.538314 | + | 0.0241923i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.8639 | + | 30.9325i | 1.20173 | + | 1.00837i | 0.999579 | + | 0.0290153i | \(0.00923716\pi\) |
0.202150 | + | 0.979355i | \(0.435207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.2224 | + | 9.54419i | 0.853920 | + | 0.310802i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.5855 | + | 1.97711i | 0.474466 | + | 0.0643155i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.44280 | + | 2.70896i | 0.241859 | + | 0.0880294i | 0.460106 | − | 0.887864i | \(-0.347812\pi\) |
−0.218247 | + | 0.975894i | \(0.570034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.03413 | + | 5.06324i | 0.195876 | + | 0.164360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.3875 | + | 35.4326i | 0.596257 | + | 1.14898i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.3666 | − | 24.8838i | −0.465381 | − | 0.806064i | 0.533837 | − | 0.845587i | \(-0.320749\pi\) |
−0.999219 | + | 0.0395232i | \(0.987416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.95199 | − | 5.11299i | 0.0955240 | − | 0.165453i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.4436 | − | 18.8914i | −1.46898 | − | 0.610672i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.457675 | + | 0.166580i | −0.0147791 | + | 0.00537915i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.07187 | − | 11.7501i | −0.0668344 | − | 0.379037i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.5401 | − | 12.4585i | −0.855242 | − | 0.401469i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.4320 | + | 32.2483i | −1.23717 | + | 1.03811i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.15761 | + | 12.2364i | −0.0693840 | + | 0.393496i | 0.930262 | + | 0.366896i | \(0.119579\pi\) |
−0.999646 | + | 0.0266008i | \(0.991532\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.09102 | − | 13.8589i | 0.0992979 | − | 0.445212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.0379 | −0.418408 | −0.209204 | − | 0.977872i | \(-0.567087\pi\) | ||||
−0.209204 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7176 | 0.375650 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.705678 | + | 3.16397i | −0.0225998 | + | 0.101328i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.34500 | − | 18.9704i | 0.107016 | − | 0.606918i | −0.883380 | − | 0.468658i | \(-0.844738\pi\) |
0.990396 | − | 0.138260i | \(-0.0441511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.50190 | + | 2.09934i | −0.0799610 | + | 0.0670953i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.5079 | − | 22.3013i | −1.51681 | − | 0.712024i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.80176 | + | 27.2321i | 0.153152 | + | 0.868569i | 0.960456 | + | 0.278433i | \(0.0898150\pi\) |
−0.807303 | + | 0.590136i | \(0.799074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.6213 | − | 23.8842i | 2.09087 | − | 0.761014i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.37526 | + | 1.81884i | 0.139266 | + | 0.0578944i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.3567 | − | 47.3832i | 0.869893 | − | 1.50670i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.34138 | − | 10.9836i | −0.201441 | − | 0.348905i | 0.747552 | − | 0.664203i | \(-0.231229\pi\) |
−0.948993 | + | 0.315298i | \(0.897896\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.4819 | + | 49.1033i | 0.808643 | + | 1.55825i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.2758 | − | 44.7037i | −1.68896 | − | 1.41720i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.2768 | + | 20.4831i | 1.78231 | + | 0.648706i | 0.999656 | + | 0.0262442i | \(0.00835473\pi\) |
0.782650 | + | 0.622462i | \(0.213867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.0609 | + | 48.9612i | 0.634700 | + | 1.54907i |
(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.bo.b.85.4 | ✓ | 54 | |
27.7 | even | 9 | inner | 756.2.bo.b.169.4 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bo.b.85.4 | ✓ | 54 | 1.1 | even | 1 | trivial | |
756.2.bo.b.169.4 | yes | 54 | 27.7 | even | 9 | inner |