Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Character | \(\chi\) | \(=\) | 1148.113 |
Dual form | 1148.2.ba.a.701.18 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.47691i | − | 1.43004i | −0.699102 | − | 0.715022i | \(-0.746417\pi\) | ||
0.699102 | − | 0.715022i | \(-0.253583\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.848862 | + | 2.61253i | 0.379622 | + | 1.16836i | 0.940307 | + | 0.340328i | \(0.110538\pi\) |
−0.560684 | + | 0.828030i | \(0.689462\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | − | 0.809017i | −0.222162 | − | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.13508 | −1.04503 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.155866 | + | 0.0506441i | 0.0469955 | + | 0.0152698i | 0.332420 | − | 0.943131i | \(-0.392135\pi\) |
−0.285425 | + | 0.958401i | \(0.592135\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.900389 | − | 1.23928i | 0.249723 | − | 0.343714i | −0.665691 | − | 0.746227i | \(-0.731863\pi\) |
0.915414 | + | 0.402513i | \(0.131863\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.47099 | − | 2.10255i | 1.67080 | − | 0.542877i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.74636 | + | 1.54219i | 1.15116 | + | 0.374035i | 0.821581 | − | 0.570092i | \(-0.193092\pi\) |
0.329581 | + | 0.944127i | \(0.393092\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.52565 | − | 2.09988i | −0.350009 | − | 0.481746i | 0.597322 | − | 0.802001i | \(-0.296231\pi\) |
−0.947331 | + | 0.320255i | \(0.896231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00386 | + | 1.45589i | −0.437279 | + | 0.317701i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.99142 | − | 2.89994i | −0.832269 | − | 0.604678i | 0.0879317 | − | 0.996127i | \(-0.471974\pi\) |
−0.920200 | + | 0.391448i | \(0.871974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.05965 | + | 1.49642i | −0.411929 | + | 0.299284i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.334588i | 0.0643916i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.83715 | − | 2.54645i | 1.45532 | − | 0.472863i | 0.528685 | − | 0.848818i | \(-0.322685\pi\) |
0.926638 | + | 0.375955i | \(0.122685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.93261 | − | 9.02563i | 0.526712 | − | 1.62105i | −0.234195 | − | 0.972190i | \(-0.575245\pi\) |
0.760906 | − | 0.648862i | \(-0.224755\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.125441 | − | 0.386067i | 0.0218364 | − | 0.0672057i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61463 | − | 2.22235i | 0.272922 | − | 0.375645i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.271365 | − | 0.835175i | −0.0446121 | − | 0.137302i | 0.926269 | − | 0.376862i | \(-0.122997\pi\) |
−0.970882 | + | 0.239560i | \(0.922997\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.06958 | − | 2.23018i | −0.491527 | − | 0.357115i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.38925 | − | 0.421255i | 0.997834 | − | 0.0657889i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.34171 | + | 1.70135i | 0.357108 | + | 0.259454i | 0.751845 | − | 0.659340i | \(-0.229164\pi\) |
−0.394737 | + | 0.918794i | \(0.629164\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.66125 | − | 8.19049i | −0.396716 | − | 1.22097i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.824651 | − | 1.13504i | 0.120288 | − | 0.165562i | −0.744627 | − | 0.667481i | \(-0.767373\pi\) |
0.864915 | + | 0.501919i | \(0.167373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | + | 0.951057i | −0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.81986 | − | 11.7563i | 0.534887 | − | 1.64621i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.299152 | − | 0.0972005i | 0.0410917 | − | 0.0133515i | −0.288399 | − | 0.957510i | \(-0.593123\pi\) |
0.329491 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.450195i | 0.0607043i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.20122 | + | 3.77891i | −0.688918 | + | 0.500528i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.07298 | + | 1.50611i | 0.269878 | + | 0.196078i | 0.714491 | − | 0.699645i | \(-0.246658\pi\) |
−0.444612 | + | 0.895723i | \(0.646658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.09102 | + | 4.42538i | −0.779875 | + | 0.566612i | −0.904942 | − | 0.425536i | \(-0.860086\pi\) |
0.125066 | + | 0.992148i | \(0.460086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.84276 | + | 2.53634i | 0.232165 | + | 0.319548i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00196 | + | 1.30031i | 0.496382 | + | 0.161284i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85065 | − | 1.25115i | 0.470432 | − | 0.152853i | −0.0642008 | − | 0.997937i | \(-0.520450\pi\) |
0.534633 | + | 0.845084i | \(0.320450\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.18288 | + | 9.88639i | −0.864717 | + | 1.19018i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.81283 | − | 0.913945i | −0.333822 | − | 0.108465i | 0.137310 | − | 0.990528i | \(-0.456154\pi\) |
−0.471132 | + | 0.882063i | \(0.656154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.41632 | −1.10210 | −0.551048 | − | 0.834473i | \(-0.685772\pi\) | ||||
−0.551048 | + | 0.834473i | \(0.685772\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.70650 | + | 5.10156i | 0.427990 | + | 0.589077i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0506441 | − | 0.155866i | −0.00577143 | − | 0.0177626i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.527193i | 0.0593138i | 0.999560 | + | 0.0296569i | \(0.00944147\pi\) | ||||
−0.999560 | + | 0.0296569i | \(0.990559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.57650 | −0.952945 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.32300 | −0.803804 | −0.401902 | − | 0.915683i | \(-0.631651\pi\) | ||||
−0.401902 | + | 0.915683i | \(0.631651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.7091i | 1.48696i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.30732 | − | 19.4119i | −0.676215 | − | 2.08118i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.01496 | + | 5.52611i | 0.425584 | + | 0.585767i | 0.966933 | − | 0.255032i | \(-0.0820859\pi\) |
−0.541348 | + | 0.840799i | \(0.682086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.53183 | −0.160580 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.3557 | − | 7.26380i | −2.31818 | − | 0.753221i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.19093 | − | 5.76832i | 0.429980 | − | 0.591817i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1577 | − | 3.62537i | 1.13290 | − | 0.368101i | 0.318221 | − | 0.948017i | \(-0.396915\pi\) |
0.814676 | + | 0.579916i | \(0.196915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.488654 | − | 0.158773i | −0.0491116 | − | 0.0159573i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.98319 | − | 2.72962i | −0.197335 | − | 0.271608i | 0.698870 | − | 0.715249i | \(-0.253687\pi\) |
−0.896205 | + | 0.443641i | \(0.853687\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.36426 | + | 0.991196i | −0.134425 | + | 0.0976655i | −0.652966 | − | 0.757387i | \(-0.726475\pi\) |
0.518541 | + | 0.855053i | \(0.326475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.50456 | − | 3.99929i | −0.537190 | − | 0.390291i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1729 | − | 10.2972i | 1.37014 | − | 0.995468i | 0.372418 | − | 0.928065i | \(-0.378529\pi\) |
0.997726 | − | 0.0674026i | \(-0.0214712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.48403i | − | 0.812623i | −0.913735 | − | 0.406312i | \(-0.866815\pi\) | ||
0.913735 | − | 0.406312i | \(-0.133185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.06865 | + | 0.672146i | −0.196348 | + | 0.0637973i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.81543 | − | 5.58731i | 0.170781 | − | 0.525610i | −0.828635 | − | 0.559790i | \(-0.810882\pi\) |
0.999416 | + | 0.0341796i | \(0.0108818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.18800 | − | 12.8893i | 0.390533 | − | 1.20194i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.82280 | + | 3.88524i | −0.260968 | + | 0.359191i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.54219 | − | 4.74636i | −0.141372 | − | 0.435098i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.87746 | − | 6.44985i | −0.807042 | − | 0.586350i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.04341 | − | 15.8256i | −0.0940811 | − | 1.42695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.45395 | + | 3.96252i | 0.487816 | + | 0.354419i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.72960 | + | 5.32315i | 0.153477 | + | 0.472353i | 0.998003 | − | 0.0631604i | \(-0.0201180\pi\) |
−0.844526 | + | 0.535514i | \(0.820118\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.21410 | − | 5.80022i | 0.371031 | − | 0.510680i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.76665 | + | 14.6702i | −0.416464 | + | 1.28174i | 0.494471 | + | 0.869194i | \(0.335362\pi\) |
−0.910935 | + | 0.412550i | \(0.864638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.802084 | + | 2.46856i | −0.0695495 | + | 0.214051i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.874121 | + | 0.284019i | −0.0752324 | + | 0.0244445i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.49271i | − | 0.554709i | −0.960768 | − | 0.277355i | \(-0.910542\pi\) | ||
0.960768 | − | 0.277355i | \(-0.0894577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3649 | + | 9.71018i | −1.13360 | + | 0.823607i | −0.986214 | − | 0.165473i | \(-0.947085\pi\) |
−0.147383 | + | 0.989079i | \(0.547085\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.81138 | − | 2.04259i | −0.236761 | − | 0.172017i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.203103 | − | 0.147563i | 0.0169843 | − | 0.0123398i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.3053 | + | 18.3132i | 1.10495 | + | 1.52083i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.35568 | + | 0.765407i | 0.194293 | + | 0.0631297i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.1266 | + | 6.53952i | −1.64883 | + | 0.535738i | −0.978487 | − | 0.206311i | \(-0.933854\pi\) |
−0.670346 | + | 0.742049i | \(0.733854\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.5667 | + | 17.2965i | −1.02266 | + | 1.40757i | −0.112341 | + | 0.993670i | \(0.535835\pi\) |
−0.910321 | + | 0.413903i | \(0.864165\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.8802 | − | 4.83488i | −1.20300 | − | 0.390877i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.0691 | 2.09392 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.35909 | + | 5.99977i | 0.347893 | + | 0.478834i | 0.946726 | − | 0.322040i | \(-0.104369\pi\) |
−0.598833 | + | 0.800874i | \(0.704369\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.240757 | − | 0.740973i | −0.0190933 | − | 0.0587630i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.93367i | 0.388827i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8114 | 1.16011 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.11509 | 0.0868098 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.7365i | 1.75940i | 0.475528 | + | 0.879701i | \(0.342257\pi\) | ||||
−0.475528 | + | 0.879701i | \(0.657743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.29211 | + | 10.1321i | 0.253239 | + | 0.779390i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.78305 | + | 6.58330i | 0.365769 | + | 0.503438i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.02308 | 0.381897 | 0.190949 | − | 0.981600i | \(-0.438844\pi\) | ||||
0.190949 | + | 0.981600i | \(0.438844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.42126 | + | 0.786715i | 0.183030 | + | 0.0594701i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.73049 | − | 5.13457i | 0.280401 | − | 0.385938i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.27510 | − | 1.71398i | 0.394279 | − | 0.128109i | −0.105166 | − | 0.994455i | \(-0.533537\pi\) |
0.499445 | + | 0.866346i | \(0.333537\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.75954 | − | 0.896629i | −0.205115 | − | 0.0666459i | 0.204658 | − | 0.978834i | \(-0.434392\pi\) |
−0.409772 | + | 0.912188i | \(0.634392\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.9613 | + | 15.0869i | 0.810281 | + | 1.11526i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.95157 | − | 1.41790i | 0.143482 | − | 0.104246i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.661696 | + | 0.480750i | 0.0483880 | + | 0.0351559i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.270688 | − | 0.196666i | 0.0196896 | − | 0.0143054i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.55967i | 0.257569i | 0.991673 | + | 0.128784i | \(0.0411075\pi\) | ||||
−0.991673 | + | 0.128784i | \(0.958892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1027 | − | 5.55699i | 1.23108 | − | 0.400001i | 0.379972 | − | 0.924998i | \(-0.375934\pi\) |
0.851104 | + | 0.524997i | \(0.175934\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.22076 | − | 9.91249i | 0.230644 | − | 0.709848i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.25992 | − | 16.1884i | 0.374754 | − | 1.15337i | −0.568891 | − | 0.822413i | \(-0.692627\pi\) |
0.943645 | − | 0.330961i | \(-0.107373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4383 | + | 19.8727i | −1.02351 | + | 1.40874i | −0.113790 | + | 0.993505i | \(0.536299\pi\) |
−0.909716 | + | 0.415231i | \(0.863701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.09899 | − | 9.53772i | −0.218586 | − | 0.672739i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.66668 | − | 4.84363i | −0.467909 | − | 0.339956i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.52413 | + | 16.3345i | 0.455665 | + | 1.14085i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.5134 | + | 9.09154i | 0.869744 | + | 0.631906i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.131452 | − | 0.404566i | −0.00909270 | − | 0.0279844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8499 | − | 16.3100i | 0.815783 | − | 1.12283i | −0.174622 | − | 0.984636i | \(-0.555870\pi\) |
0.990405 | − | 0.138194i | \(-0.0441297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.26376 | + | 6.96713i | −0.155110 | + | 0.477380i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.45704 | + | 7.56201i | −0.167569 | + | 0.515725i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.02563 | + | 2.93261i | −0.612700 | + | 0.199078i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.3234i | 1.57605i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.18478 | − | 4.49350i | 0.416033 | − | 0.302266i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.687250 | − | 0.499316i | −0.0460216 | − | 0.0334367i | 0.564537 | − | 0.825408i | \(-0.309055\pi\) |
−0.610558 | + | 0.791971i | \(0.709055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.45716 | − | 4.69140i | 0.430478 | − | 0.312760i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.61213 | + | 9.10082i | 0.438863 | + | 0.604043i | 0.969959 | − | 0.243269i | \(-0.0782197\pi\) |
−0.531096 | + | 0.847312i | \(0.678220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8320 | + | 5.46903i | 1.11229 | + | 0.361404i | 0.806819 | − | 0.590799i | \(-0.201187\pi\) |
0.305468 | + | 0.952202i | \(0.401187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.386067 | + | 0.125441i | −0.0254013 | + | 0.00825340i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.39424 | − | 4.67177i | 0.222364 | − | 0.306058i | −0.683230 | − | 0.730203i | \(-0.739425\pi\) |
0.905594 | + | 0.424145i | \(0.139425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.66533 | + | 1.19094i | 0.239099 | + | 0.0776881i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.30581 | 0.0848214 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.38345 | − | 4.65692i | −0.218857 | − | 0.301231i | 0.685445 | − | 0.728125i | \(-0.259608\pi\) |
−0.904302 | + | 0.426894i | \(0.859608\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.200267 | − | 0.616359i | −0.0129003 | − | 0.0397032i | 0.944399 | − | 0.328801i | \(-0.106645\pi\) |
−0.957299 | + | 0.289098i | \(0.906645\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2470i | 1.42715i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.74697 | −0.175498 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.97602 | −0.252988 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.1384i | 1.14948i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.724737 | + | 2.23051i | 0.0457450 | + | 0.140789i | 0.971320 | − | 0.237775i | \(-0.0764181\pi\) |
−0.925575 | + | 0.378564i | \(0.876418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.475264 | − | 0.654144i | −0.0298796 | − | 0.0411257i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 33.9562 | 2.12642 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.91677 | − | 2.57231i | −0.493835 | − | 0.160457i | 0.0515034 | − | 0.998673i | \(-0.483599\pi\) |
−0.545338 | + | 0.838216i | \(0.683599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.516166 | + | 0.710442i | −0.0320730 | + | 0.0441447i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.5701 | + | 7.98332i | −1.52085 | + | 0.494155i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.36148 | + | 2.39189i | 0.453928 | + | 0.147490i | 0.527053 | − | 0.849833i | \(-0.323297\pi\) |
−0.0731245 | + | 0.997323i | \(0.523297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.507878 | + | 0.699034i | 0.0311987 | + | 0.0429413i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.6877 | − | 9.94468i | 0.837673 | − | 0.608605i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.98183 | + | 2.89297i | 0.242776 | + | 0.176387i | 0.702519 | − | 0.711665i | \(-0.252058\pi\) |
−0.459743 | + | 0.888052i | \(0.652058\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1834 | + | 7.39865i | −0.618596 | + | 0.449436i | −0.852431 | − | 0.522840i | \(-0.824872\pi\) |
0.233835 | + | 0.972276i | \(0.424872\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.79421i | 0.229636i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.396815 | + | 0.128933i | −0.0239288 | + | 0.00777495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00393 | − | 3.08977i | 0.0603201 | − | 0.185646i | −0.916356 | − | 0.400365i | \(-0.868883\pi\) |
0.976676 | + | 0.214719i | \(0.0688834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.19396 | + | 28.2961i | −0.550428 | + | 1.69404i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.44508 | − | 11.6237i | 0.503791 | − | 0.693409i | −0.479066 | − | 0.877779i | \(-0.659024\pi\) |
0.982857 | + | 0.184370i | \(0.0590245\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.11438 | + | 6.50738i | 0.125687 | + | 0.386823i | 0.994026 | − | 0.109148i | \(-0.0348121\pi\) |
−0.868339 | + | 0.495971i | \(0.834812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.2876 | − | 10.3806i | −0.846325 | − | 0.614891i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.09631 | − | 4.92141i | −0.241798 | − | 0.290501i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.39634 | + | 4.64721i | 0.376255 | + | 0.273366i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.97972 | − | 27.6367i | −0.526400 | − | 1.62009i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.24497 | + | 8.59546i | −0.364835 | + | 0.502152i | −0.951488 | − | 0.307686i | \(-0.900445\pi\) |
0.586653 | + | 0.809838i | \(0.300445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.17507 | + | 6.69418i | −0.126638 | + | 0.389750i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0169449 | + | 0.0521511i | −0.000983244 | + | 0.00302611i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.18766 | + | 2.33541i | −0.415673 | + | 0.135060i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.89452i | − | 0.166837i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.76103 | + | 4.91218i | −0.388411 | + | 0.282197i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.7319 | − | 12.1564i | −0.958064 | − | 0.696074i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.847494 | − | 0.615740i | 0.0483690 | − | 0.0351422i | −0.563338 | − | 0.826227i | \(-0.690483\pi\) |
0.611707 | + | 0.791084i | \(0.290483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.45510 | + | 3.37916i | 0.139666 | + | 0.192234i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.73717 | + | 0.564442i | 0.0985061 | + | 0.0320066i | 0.357855 | − | 0.933777i | \(-0.383508\pi\) |
−0.259349 | + | 0.965784i | \(0.583508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5739 | + | 4.41044i | −0.767244 | + | 0.249293i | −0.666385 | − | 0.745608i | \(-0.732159\pi\) |
−0.100859 | + | 0.994901i | \(0.532159\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.06200 | + | 6.96725i | −0.285211 | + | 0.392560i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.74945 | − | 1.54319i | −0.266756 | − | 0.0866742i | 0.172585 | − | 0.984995i | \(-0.444788\pi\) |
−0.439341 | + | 0.898320i | \(0.644788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.35051 | 0.0756141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.5052 | − | 35.1049i | −1.42356 | − | 1.95937i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00290 | − | 12.3196i | −0.222727 | − | 0.685484i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.89984i | 0.216324i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.0142 | −1.16209 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.40298 | −0.0773488 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0992i | 1.43454i | 0.696794 | + | 0.717271i | \(0.254609\pi\) | ||||
−0.696794 | + | 0.717271i | \(0.745391\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.850751 | + | 2.61834i | 0.0466209 | + | 0.143484i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.53735 | + | 8.99788i | 0.357173 | + | 0.491607i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2879 | 0.669364 | 0.334682 | − | 0.942331i | \(-0.391371\pi\) | ||||
0.334682 | + | 0.942331i | \(0.391371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.8393 | − | 4.49665i | −0.751646 | − | 0.244225i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.914190 | − | 1.25827i | 0.0495061 | − | 0.0681394i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | − | 0.309017i | 0.0513522 | − | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.9257 | − | 10.3733i | −1.71882 | − | 0.558480i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.408068 | − | 0.561658i | −0.0219063 | − | 0.0301514i | 0.797923 | − | 0.602759i | \(-0.205932\pi\) |
−0.819830 | + | 0.572608i | \(0.805932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1142 | + | 12.4342i | −0.916102 | + | 0.665587i | −0.942551 | − | 0.334063i | \(-0.891580\pi\) |
0.0264488 | + | 0.999650i | \(0.491580\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.414649 | + | 0.301260i | 0.0221323 | + | 0.0160801i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.5437 | + | 17.8320i | −1.30633 | + | 0.949103i | −0.999996 | − | 0.00282206i | \(-0.999102\pi\) |
−0.306332 | + | 0.951925i | \(0.599102\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 8.12442i | − | 0.431199i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.7563 | + | 3.81986i | −0.622210 | + | 0.202168i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.14939 | − | 15.8482i | 0.271774 | − | 0.836436i | −0.718280 | − | 0.695754i | \(-0.755070\pi\) |
0.990055 | − | 0.140682i | \(-0.0449295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.78944 | − | 11.6627i | 0.199444 | − | 0.613826i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.9757 | + | 21.9887i | −0.838507 | + | 1.15411i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.99315 | − | 24.6004i | −0.418381 | − | 1.28764i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0582 | + | 15.2997i | 1.09923 | + | 0.798637i | 0.980934 | − | 0.194341i | \(-0.0622569\pi\) |
0.118296 | + | 0.992978i | \(0.462257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.0308 | + | 1.32067i | −1.04276 | + | 0.0687513i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.254474 | − | 0.184886i | −0.0132116 | − | 0.00959882i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3720 | + | 31.9217i | 0.537041 | + | 1.65284i | 0.739197 | + | 0.673489i | \(0.235205\pi\) |
−0.202156 | + | 0.979353i | \(0.564795\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.81481 | − | 13.5089i | 0.506835 | − | 0.697598i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.90073 | − | 12.0052i | 0.200898 | − | 0.618300i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.74548 | − | 5.37205i | 0.0896595 | − | 0.275944i | −0.896166 | − | 0.443720i | \(-0.853659\pi\) |
0.985825 | + | 0.167776i | \(0.0536586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.1850 | − | 4.28406i | 0.675486 | − | 0.219479i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 32.9177i | − | 1.68202i | −0.541022 | − | 0.841008i | \(-0.681962\pi\) | ||
0.541022 | − | 0.841008i | \(-0.318038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.364215 | − | 0.264618i | 0.0185621 | − | 0.0134862i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.34147 | − | 5.33389i | −0.373188 | − | 0.271137i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.2319 | + | 13.9728i | −0.975098 | + | 0.708450i | −0.956608 | − | 0.291379i | \(-0.905886\pi\) |
−0.0184904 | + | 0.999829i | \(0.505886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.4725 | − | 19.9197i | −0.731905 | − | 1.00738i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.3369 | + | 11.8066i | 1.83295 | + | 0.595562i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.37731 | + | 0.447514i | −0.0692998 | + | 0.0225169i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.7349 | + | 14.7753i | −0.538770 | + | 0.741553i | −0.988435 | − | 0.151644i | \(-0.951543\pi\) |
0.449665 | + | 0.893197i | \(0.351543\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.11440 | + | 1.98669i | 0.306103 | + | 0.0994588i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.65854 | 0.332512 | 0.166256 | − | 0.986083i | \(-0.446832\pi\) | ||||
0.166256 | + | 0.986083i | \(0.446832\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.54480 | − | 11.7609i | −0.425647 | − | 0.585852i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.28026 | − | 22.4063i | −0.361759 | − | 1.11338i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.143919i | − | 0.00713378i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0934 | 1.14189 | 0.570947 | − | 0.820987i | \(-0.306576\pi\) | ||||
0.570947 | + | 0.820987i | \(0.306576\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.0818 | −0.793259 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.56234i | − | 0.126084i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.21621 | − | 19.1315i | −0.305142 | − | 0.939130i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.0512 | + | 33.1037i | 1.17779 | + | 1.62110i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.3711 | 1.58143 | 0.790716 | − | 0.612183i | \(-0.209708\pi\) | ||||
0.790716 | + | 0.612183i | \(0.209708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.3641 | − | 5.96684i | −0.895009 | − | 0.290806i | −0.174834 | − | 0.984598i | \(-0.555939\pi\) |
−0.720176 | + | 0.693792i | \(0.755939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.58535 | + | 3.55843i | −0.125704 | + | 0.173017i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0836 | + | 3.92620i | −0.586140 | + | 0.190449i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.16042 | + | 2.32656i | 0.346517 | + | 0.112590i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.365499 | − | 0.503067i | −0.0176465 | − | 0.0242883i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.6933 | + | 14.3080i | −0.948591 | + | 0.689192i | −0.950473 | − | 0.310807i | \(-0.899401\pi\) |
0.00188235 | + | 0.999998i | \(0.499401\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.37243 | − | 3.90330i | −0.258183 | − | 0.187581i | 0.451163 | − | 0.892442i | \(-0.351009\pi\) |
−0.709346 | + | 0.704861i | \(0.751009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 45.3601 | − | 32.9561i | 2.17485 | − | 1.58012i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.8058i | 0.612585i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.2402 | + | 10.8004i | −1.58647 | + | 0.515474i | −0.963712 | − | 0.266944i | \(-0.913986\pi\) |
−0.622754 | + | 0.782418i | \(0.713986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.968794 | − | 2.98164i | 0.0461330 | − | 0.141983i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.410449 | + | 1.26323i | −0.0195010 | + | 0.0600179i | −0.960333 | − | 0.278854i | \(-0.910045\pi\) |
0.940832 | + | 0.338872i | \(0.110045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0290 | + | 15.1801i | −0.522824 | + | 0.719605i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.1978 | + | 49.8517i | 0.766129 | + | 2.35790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.9213 | − | 23.9187i | −1.55365 | − | 1.12880i | −0.940981 | − | 0.338459i | \(-0.890094\pi\) |
−0.612673 | − | 0.790337i | \(-0.709906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.01720 | + | 0.257918i | 0.0478983 | + | 0.0121449i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 42.8420 | + | 31.1265i | 2.01289 | + | 1.46245i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.30031 | − | 4.00196i | −0.0609597 | − | 0.187615i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5892 | + | 17.3275i | −0.588897 | + | 0.810548i | −0.994636 | − | 0.103442i | \(-0.967015\pi\) |
0.405738 | + | 0.913989i | \(0.367015\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.515998 | + | 1.58808i | −0.0240847 | + | 0.0741251i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.30162 | − | 16.3167i | 0.246921 | − | 0.759945i | −0.748393 | − | 0.663255i | \(-0.769174\pi\) |
0.995315 | − | 0.0966901i | \(-0.0308256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.2718 | + | 9.18607i | −1.31390 | + | 0.426913i | −0.880397 | − | 0.474238i | \(-0.842724\pi\) |
−0.433506 | + | 0.901151i | \(0.642724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 64.5708i | − | 2.99440i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3039 | − | 14.7516i | 0.939551 | − | 0.682624i | −0.00876181 | − | 0.999962i | \(-0.502789\pi\) |
0.948312 | + | 0.317338i | \(0.102789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.27556 | − | 2.37984i | −0.151251 | − | 0.109891i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.8609 | − | 10.7971i | 0.684754 | − | 0.497503i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.278831 | + | 0.383778i | 0.0128207 | + | 0.0176461i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.28462 | + | 2.04200i | 0.288358 | + | 0.0936932i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.937867 | + | 0.304732i | −0.0429420 | + | 0.0139527i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.57051 | + | 6.29077i | −0.208832 | + | 0.287433i | −0.900566 | − | 0.434720i | \(-0.856847\pi\) |
0.691734 | + | 0.722153i | \(0.256847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27935 | − | 0.415686i | −0.0583333 | − | 0.0189536i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.2202 | 0.556040 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.9428 | + | 26.0725i | 0.860146 | + | 1.18389i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.43355 | − | 16.7227i | −0.246218 | − | 0.757780i | −0.995434 | − | 0.0954544i | \(-0.969570\pi\) |
0.749216 | − | 0.662326i | \(-0.230430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.6864i | − | 1.65902i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0345 | 0.904144 | 0.452072 | − | 0.891982i | \(-0.350685\pi\) | ||||
0.452072 | + | 0.891982i | \(0.350685\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.1251 | 1.85218 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 1.41140i | − | 0.0634377i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.913945 | + | 2.81283i | 0.0409960 | + | 0.126173i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.2086 | + | 20.9328i | 0.680830 | + | 0.937082i | 0.999943 | − | 0.0106342i | \(-0.00338503\pi\) |
−0.319113 | + | 0.947717i | \(0.603385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.3162 | 2.51602 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.5368 | − | 11.5466i | −1.58451 | − | 0.514838i | −0.621295 | − | 0.783577i | \(-0.713393\pi\) |
−0.963213 | + | 0.268739i | \(0.913393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.44777 | − | 7.49821i | 0.242422 | − | 0.333666i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.0962 | − | 8.15426i | 1.11456 | − | 0.362143i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.6203 | − | 7.02485i | −0.958301 | − | 0.311371i | −0.212217 | − | 0.977223i | \(-0.568068\pi\) |
−0.746084 | + | 0.665852i | \(0.768068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.53477 | + | 7.61796i | 0.244844 | + | 0.336999i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.702596 | − | 0.510466i | 0.0310204 | − | 0.0225376i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.74760 | − | 2.72279i | −0.165139 | − | 0.119980i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.186018 | − | 0.135150i | 0.00818107 | − | 0.00594390i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.4417i | − | 0.546130i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.3511 | + | 13.7607i | −1.85544 | + | 0.602868i | −0.859681 | + | 0.510831i | \(0.829338\pi\) |
−0.995756 | + | 0.0920373i | \(0.970662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.49661 | − | 13.8391i | 0.196623 | − | 0.605143i | −0.803331 | − | 0.595533i | \(-0.796941\pi\) |
0.999954 | − | 0.00961007i | \(-0.00305903\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.94862 | − | 5.99724i | 0.0850449 | − | 0.261741i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.8384 | − | 38.3163i | 1.21266 | − | 1.66908i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.414410 | + | 1.27542i | 0.0180178 | + | 0.0554532i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.49895 | − | 4.72176i | −0.282030 | − | 0.204907i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.23076 | − | 8.29736i | 0.226569 | − | 0.359399i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.9325 | + | 28.2861i | 1.68320 | + | 1.22292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.24538 | − | 13.0659i | −0.183202 | − | 0.563837i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0963307 | + | 0.132588i | −0.00414926 | + | 0.00571096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.17414 | + | 25.1574i | −0.351434 | + | 1.08160i | 0.606615 | + | 0.794996i | \(0.292527\pi\) |
−0.958049 | + | 0.286606i | \(0.907473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.22087 | + | 6.83513i | −0.0953066 | + | 0.293323i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.1648 | − | 7.20177i | 0.949434 | − | 0.308490i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15.3456i | − | 0.656129i | −0.944655 | − | 0.328064i | \(-0.893604\pi\) | ||
0.944655 | − | 0.328064i | \(-0.106396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.0959 | − | 13.8739i | 0.814991 | − | 0.592126i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.3040 | − | 12.5721i | −0.737176 | − | 0.535590i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.426508 | − | 0.309876i | 0.0181370 | − | 0.0131773i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.51200 | − | 4.83385i | −0.149076 | − | 0.205186i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.6337 | + | 8.32889i | 1.08613 | + | 0.352906i | 0.796751 | − | 0.604307i | \(-0.206550\pi\) |
0.289382 | + | 0.957214i | \(0.406550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.21691 | − | 1.37016i | 0.178356 | − | 0.0579515i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.19078 | − | 1.63896i | 0.0502746 | − | 0.0691970i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.1374 | + | 7.19289i | 0.932981 | + | 0.303144i | 0.735781 | − | 0.677219i | \(-0.236815\pi\) |
0.197200 | + | 0.980363i | \(0.436815\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.1381 | 0.678933 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.04114 | + | 6.93854i | 0.211708 | + | 0.291391i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.46306 | − | 29.1243i | −0.396712 | − | 1.22095i | −0.927620 | − | 0.373525i | \(-0.878149\pi\) |
0.530908 | − | 0.847430i | \(-0.321851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.87036i | 0.287516i | 0.989613 | + | 0.143758i | \(0.0459186\pi\) | ||||
−0.989613 | + | 0.143758i | \(0.954081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.81699 | 0.368335 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.5604 | 0.523807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6288i | 0.484115i | 0.970262 | + | 0.242058i | \(0.0778223\pi\) | ||||
−0.970262 | + | 0.242058i | \(0.922178\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.7642 | − | 42.3617i | −0.572019 | − | 1.76049i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.30435 | + | 5.92443i | 0.178575 | + | 0.245787i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0515504 | 0.00213500 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.5465 | − | 4.07659i | −0.518733 | − | 0.168546i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.24716 | + | 12.7276i | −0.381671 | + | 0.525325i | −0.956026 | − | 0.293281i | \(-0.905253\pi\) |
0.574355 | + | 0.818606i | \(0.305253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4269 | + | 7.61186i | −0.965289 | + | 0.313641i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.0971 | − | 13.0284i | −1.64938 | − | 0.535915i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.7060 | − | 20.2410i | −0.603901 | − | 0.831199i | 0.392157 | − | 0.919898i | \(-0.371729\pi\) |
−0.996058 | + | 0.0886993i | \(0.971729\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0909 | − | 8.05801i | 0.454683 | − | 0.330346i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 49.2228 | + | 35.7625i | 2.01456 | + | 1.46366i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5101 | + | 7.63607i | −0.429433 | + | 0.312001i | −0.781422 | − | 0.624003i | \(-0.785505\pi\) |
0.351989 | + | 0.936004i | \(0.385505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.5825i | − | 1.69618i | −0.529849 | − | 0.848092i | \(-0.677751\pi\) | ||
0.529849 | − | 0.848092i | \(-0.322249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0721 | + | 3.92247i | −0.491615 | + | 0.159735i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.31468 | − | 28.6676i | 0.378695 | − | 1.16550i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.59912 | − | 14.1546i | 0.186672 | − | 0.574519i | −0.813301 | − | 0.581844i | \(-0.802332\pi\) |
0.999973 | + | 0.00732491i | \(0.00233161\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.9972 | + | 16.5128i | −0.486152 | + | 0.669131i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.664119 | − | 2.04395i | −0.0268674 | − | 0.0826892i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.1568 | + | 13.9182i | 0.773735 | + | 0.562151i | 0.903092 | − | 0.429447i | \(-0.141291\pi\) |
−0.129358 | + | 0.991598i | \(0.541291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 40.4591 | − | 16.1597i | 1.63147 | − | 0.651621i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5918 | − | 8.42190i | −0.466666 | − | 0.339053i | 0.329474 | − | 0.944165i | \(-0.393128\pi\) |
−0.796141 | + | 0.605112i | \(0.793128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0788 | + | 31.0193i | 0.405101 | + | 1.24677i | 0.920811 | + | 0.390009i | \(0.127528\pi\) |
−0.515710 | + | 0.856763i | \(0.672472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.970285 | − | 1.33548i | 0.0389362 | − | 0.0535911i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.11079 | − | 6.49634i | 0.0845669 | − | 0.260270i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.65613 | + | 29.7185i | −0.386245 | + | 1.18874i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.00207 | + | 0.325594i | −0.0400190 | + | 0.0130030i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.38254i | − | 0.174743i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3712 | − | 10.4413i | 0.572109 | − | 0.415661i | −0.263762 | − | 0.964588i | \(-0.584963\pi\) |
0.835871 | + | 0.548926i | \(0.184963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −40.3985 | − | 29.3512i | −1.60570 | − | 1.16661i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.4387 | + | 9.03724i | −0.493614 | + | 0.358632i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.900389 | + | 1.23928i | 0.0356747 | + | 0.0491020i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.81847 | + | 2.86529i | 0.348853 | + | 0.113349i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.55926 | − | 2.13123i | 0.259075 | − | 0.0841786i | −0.176600 | − | 0.984283i | \(-0.556510\pi\) |
0.435675 | + | 0.900104i | \(0.356510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.1918 | + | 37.4263i | −1.07234 | + | 1.47595i | −0.204657 | + | 0.978834i | \(0.565608\pi\) |
−0.867684 | + | 0.497116i | \(0.834392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.7304 | + | 6.08588i | 0.737509 | + | 0.239631i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.87973 | −0.0738996 | −0.0369498 | − | 0.999317i | \(-0.511764\pi\) | ||||
−0.0369498 | + | 0.999317i | \(0.511764\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.246832 | + | 0.339735i | 0.00968900 | + | 0.0133358i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.26380 | + | 22.3557i | 0.284691 | + | 0.876188i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.9076i | 1.32691i | 0.748217 | + | 0.663454i | \(0.230910\pi\) | ||||
−0.748217 | + | 0.663454i | \(0.769090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.3726 | −1.65563 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.5209 | 1.15172 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.71100i | − | 0.261424i | −0.991420 | − | 0.130712i | \(-0.958274\pi\) | ||
0.991420 | − | 0.130712i | \(-0.0417263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.55752 | + | 4.79356i | 0.0605806 | + | 0.186448i | 0.976767 | − | 0.214305i | \(-0.0687486\pi\) |
−0.916186 | + | 0.400753i | \(0.868749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.1300 | − | 15.3191i | −0.432253 | − | 0.594946i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.13004 | −0.276491 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.6659 | − | 12.5633i | −1.49715 | − | 0.486453i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.23676 | + | 1.70226i | −0.0478159 | + | 0.0658130i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.17350 | + | 0.381295i | −0.0453027 | + | 0.0147197i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.03487 | − | 0.336250i | −0.0398914 | − | 0.0129615i | 0.289003 | − | 0.957328i | \(-0.406676\pi\) |
−0.328895 | + | 0.944367i | \(0.606676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500685 | − | 0.689134i | −0.0192714 | − | 0.0265248i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.1924 | − | 11.0379i | 0.583892 | − | 0.424222i | −0.256233 | − | 0.966615i | \(-0.582482\pi\) |
0.840125 | + | 0.542393i | \(0.182482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.49134 | − | 6.89587i | −0.364244 | − | 0.264639i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.5419 | − | 16.3777i | 0.863808 | − | 0.627593i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.8963i | − | 0.761309i | −0.924717 | − | 0.380655i | \(-0.875699\pi\) | ||
0.924717 | − | 0.380655i | \(-0.124301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.9624 | − | 5.51141i | 0.648099 | − | 0.210580i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.5463 | − | 41.6912i | 0.516824 | − | 1.59062i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.148895 | − | 0.458252i | 0.00567245 | − | 0.0174580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0448 | − | 19.3310i | 0.534288 | − | 0.735385i | −0.453488 | − | 0.891262i | \(-0.649821\pi\) |
0.987776 | + | 0.155878i | \(0.0498206\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.158773 | + | 0.488654i | 0.00603130 | + | 0.0185624i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.7131 | − | 26.6736i | −1.39261 | − | 1.01179i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.9754 | + | 7.85399i | 1.17328 | + | 0.297491i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5716 | − | 8.40723i | −0.437676 | − | 0.317990i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.76115 | + | 11.5756i | 0.142057 | + | 0.437206i | 0.996621 | − | 0.0821402i | \(-0.0261755\pi\) |
−0.854564 | + | 0.519346i | \(0.826176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.33976 | + | 1.84402i | −0.0505300 | + | 0.0695486i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.94984 | − | 9.07868i | 0.111097 | − | 0.341923i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.04262 | + | 3.20887i | −0.0392119 | + | 0.120682i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8955 | + | 6.46443i | −0.747190 | + | 0.242777i | −0.657772 | − | 0.753217i | \(-0.728501\pi\) |
−0.0894185 | + | 0.995994i | \(0.528501\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.65279i | − | 0.0619846i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.8790 | + | 27.5207i | −1.41858 | + | 1.03066i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.557918 | + | 0.405351i | 0.0208649 | + | 0.0151593i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.5348 | + | 8.38050i | −0.430774 | + | 0.312975i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.7061 | − | 24.3703i | −0.660325 | − | 0.908859i | 0.339167 | − | 0.940726i | \(-0.389855\pi\) |
−0.999492 | + | 0.0318667i | \(0.989855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.60379 | + | 0.521103i | 0.0597282 | + | 0.0194069i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.52667 | + | 0.496044i | −0.0567773 | + | 0.0184481i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.3312 | + | 16.9725i | −0.457970 | + | 0.630341i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.3722 | − | 7.91900i | −0.903914 | − | 0.293700i | −0.180063 | − | 0.983655i | \(-0.557630\pi\) |
−0.723852 | + | 0.689956i | \(0.757630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.3743 | 1.08794 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.49082 | + | 11.6866i | 0.314044 | + | 0.432245i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.19680 | − | 3.68338i | −0.0442049 | − | 0.136049i | 0.926518 | − | 0.376250i | \(-0.122787\pi\) |
−0.970723 | + | 0.240201i | \(0.922787\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.80401i | 0.250970i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.663551 | 0.0244422 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.6299 | 0.685313 | 0.342657 | − | 0.939461i | \(-0.388673\pi\) | ||||
0.342657 | + | 0.939461i | \(0.388673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.84825i | 0.361785i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.46240 | − | 13.7339i | −0.163710 | − | 0.503846i | 0.835229 | − | 0.549902i | \(-0.185335\pi\) |
−0.998939 | + | 0.0460556i | \(0.985335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.1693 | − | 47.0301i | −1.25187 | − | 1.72305i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.9582 | 0.839997 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.6612 | − | 5.41356i | −0.608788 | − | 0.197807i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.81761 | − | 5.25449i | 0.139307 | − | 0.191739i | −0.733663 | − | 0.679513i | \(-0.762191\pi\) |
0.872970 | + | 0.487774i | \(0.162191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.52478 | − | 1.79511i | 0.201334 | − | 0.0654174i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55.8551 | − | 18.1484i | −2.03277 | − | 0.660488i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.2623 | − | 19.6304i | −0.518372 | − | 0.713478i | 0.466931 | − | 0.884294i | \(-0.345360\pi\) |
−0.985303 | + | 0.170816i | \(0.945360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.62026 | + | 1.17719i | −0.0588116 | + | 0.0427291i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.4652 | − | 18.5015i | −0.923112 | − | 0.670680i | 0.0211847 | − | 0.999776i | \(-0.493256\pi\) |
−0.944297 | + | 0.329096i | \(0.893256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.86373 | + | 4.98679i | −0.248484 | + | 0.180534i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 42.9792i | − | 1.55392i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.73297 | − | 1.21292i | 0.134790 | − | 0.0437958i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.8712 | + | 39.6134i | −0.464147 | + | 1.42850i | 0.395905 | + | 0.918291i | \(0.370431\pi\) |
−0.860052 | + | 0.510206i | \(0.829569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.37139 | + | 19.6091i | −0.229460 | + | 0.706205i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.8514 | − | 35.5814i | 0.929811 | − | 1.27977i | −0.0301226 | − | 0.999546i | \(-0.509590\pi\) |
0.959933 | − | 0.280228i | \(-0.0904102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.46601 | + | 22.9780i | 0.268187 | + | 0.825395i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.75970 | + | 1.27850i | 0.0631289 | + | 0.0458658i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.6324 | − | 12.7740i | −0.380944 | − | 0.457676i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.392140 | − | 0.284907i | −0.0140319 | − | 0.0101948i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.852011 | + | 2.62222i | 0.0304484 | + | 0.0937105i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.9743 | + | 16.4812i | −0.427381 | + | 0.588240i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.650560 | + | 2.00222i | −0.0231899 | + | 0.0713713i | −0.961982 | − | 0.273114i | \(-0.911946\pi\) |
0.938792 | + | 0.344485i | \(0.111946\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.92449 | − | 18.2337i | 0.210918 | − | 0.649137i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.58731 | + | 1.81543i | −0.198662 | + | 0.0645492i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.5330i | 0.409550i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.73144 | − | 1.25797i | 0.0614080 | − | 0.0446155i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.38745 | − | 3.18767i | −0.155411 | − | 0.112913i | 0.507362 | − | 0.861733i | \(-0.330621\pi\) |
−0.662773 | + | 0.748820i | \(0.730621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.66453 | − | 4.11552i | 0.200397 | − | 0.145597i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.5872 | − | 17.3248i | −0.444748 | − | 0.612143i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.46769 | − | 0.476881i | −0.0517936 | − | 0.0168287i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.8893 | + | 4.18800i | −0.454289 | + | 0.147608i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.16562 | − | 9.86263i | 0.252242 | − | 0.347181i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.4866 | + | 14.1297i | 1.52891 | + | 0.496772i | 0.948290 | − | 0.317404i | \(-0.102811\pi\) |
0.580618 | + | 0.814176i | \(0.302811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.6675 | −1.81429 | −0.907145 | − | 0.420819i | \(-0.861743\pi\) | ||||
−0.907145 | + | 0.420819i | \(0.861743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.3258 | + | 25.2233i | 0.642713 | + | 0.884619i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5728 | + | 38.6951i | 0.440406 | + | 1.35543i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.51300i | − | 0.262847i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.80243 | 0.167810 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.6961 | 1.83911 | 0.919554 | − | 0.392963i | \(-0.128550\pi\) | ||||
0.919554 | + | 0.392963i | \(0.128550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.5820i | − | 0.647729i | −0.946103 | − | 0.323865i | \(-0.895018\pi\) | ||
0.946103 | − | 0.323865i | \(-0.104982\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.319355 | + | 0.982874i | 0.0111185 | + | 0.0342193i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.0555 | + | 44.1207i | 1.11468 | + | 1.53423i | 0.814335 | + | 0.580395i | \(0.197102\pi\) |
0.300345 | + | 0.953831i | \(0.402898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.22489 | −0.0772737 | −0.0386369 | − | 0.999253i | \(-0.512302\pi\) | ||||
−0.0386369 | + | 0.999253i | \(0.512302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.65308 | − | 2.48664i | −0.265482 | − | 0.0862605i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.93341 | + | 4.03750i | −0.101637 | + | 0.139891i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −59.3997 | + | 19.3001i | −2.05561 | + | 0.667908i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.01987 | + | 0.981216i | 0.104382 | + | 0.0339158i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.1941 | + | 31.9239i | 0.800748 | + | 1.10214i | 0.992686 | + | 0.120728i | \(0.0385229\pi\) |
−0.191938 | + | 0.981407i | \(0.561477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.4751 | − | 22.8680i | 1.08535 | − | 0.788551i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.7907 | − | 20.9177i | −0.991606 | − | 0.720444i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.6758 | + | 17.2014i | −0.814471 | + | 0.591748i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9731i | 0.377042i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.1182 | − | 5.23712i | 0.553175 | − | 0.179737i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.33882 | + | 4.12047i | −0.0458942 | + | 0.141248i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.54879 | − | 17.0774i | 0.189987 | − | 0.584720i | −0.810012 | − | 0.586414i | \(-0.800539\pi\) |
0.999999 | + | 0.00169423i | \(0.000539291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.1389 | + | 18.0842i | −0.449341 | + | 0.618465i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.7202 | + | 39.1486i | 0.434512 | + | 1.33729i | 0.893585 | + | 0.448893i | \(0.148182\pi\) |
−0.459073 | + | 0.888399i | \(0.651818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0638 | + | 7.31181i | 0.343374 | + | 0.249476i | 0.746084 | − | 0.665852i | \(-0.231932\pi\) |
−0.402710 | + | 0.915328i | \(0.631932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.1899 | + | 10.1462i | −0.415430 | + | 0.345781i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.23984 | + | 3.08043i | 0.144326 | + | 0.104859i | 0.657605 | − | 0.753363i | \(-0.271570\pi\) |
−0.513279 | + | 0.858222i | \(0.671570\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.26390 | + | 13.1229i | 0.144977 | + | 0.446193i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.5107 | − | 15.8432i | 0.390925 | − | 0.538062i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0266992 | + | 0.0821717i | −0.000905708 | + | 0.00278748i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.91656 | − | 5.89856i | 0.0649401 | − | 0.199865i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.9805 | + | 11.3658i | −1.18391 | + | 0.384675i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 6.74145i | − | 0.227903i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.19594 | − | 0.868900i | 0.0403840 | − | 0.0293407i | −0.567410 | − | 0.823435i | \(-0.692055\pi\) |
0.607794 | + | 0.794095i | \(0.292055\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.2902 | + | 15.4682i | 0.718100 | + | 0.521730i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.2737 | − | 12.5501i | 0.581966 | − | 0.422823i | −0.257467 | − | 0.966287i | \(-0.582888\pi\) |
0.839432 | + | 0.543464i | \(0.182888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.47138 | + | 10.2835i | 0.251432 | + | 0.346067i | 0.916012 | − | 0.401150i | \(-0.131390\pi\) |
−0.664580 | + | 0.747217i | \(0.731390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.5809 | + | 5.38746i | 0.557360 | + | 0.181097i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.8791 | − | 4.83450i | 0.499590 | − | 0.162327i | −0.0483729 | − | 0.998829i | \(-0.515404\pi\) |
0.547963 | + | 0.836503i | \(0.315404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.28989 | − | 4.52814i | 0.110339 | − | 0.151869i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.33679 | − | 0.434349i | −0.0447841 | − | 0.0145512i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.64157 | −0.121861 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.95566 | + | 12.3264i | 0.299355 | + | 0.412026i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.78461 | + | 17.8032i | 0.193142 | + | 0.594431i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 78.2030i | − | 2.60822i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56979 | 0.0522972 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.16946 | −0.238585 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.97048i | − | 0.264948i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.40927 | − | 25.8811i | −0.279225 | − | 0.859367i | −0.988070 | − | 0.154003i | \(-0.950783\pi\) |
0.708845 | − | 0.705364i | \(-0.249217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.21746 | + | 8.55760i | 0.206220 | + | 0.283838i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.4160 | −1.90228 | −0.951139 | − | 0.308763i | \(-0.900085\pi\) | ||||
−0.951139 | + | 0.308763i | \(0.900085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.14141 | − | 0.370866i | −0.0377751 | − | 0.0122739i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.1103 | + | 41.4433i | −0.995417 | + | 1.37007i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.6702 | − | 4.76665i | 0.484454 | − | 0.157409i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.4961 | − | 10.8836i | −1.10494 | − | 0.359015i | −0.300935 | − | 0.953645i | \(-0.597299\pi\) |
−0.804000 | + | 0.594629i | \(0.797299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.52513 | − | 2.09917i | −0.0502548 | − | 0.0691699i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.66528 | + | 2.66298i | −0.120644 | + | 0.0876531i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.80869 | + | 1.31409i | 0.0594693 | + | 0.0432070i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.27708 | − | 3.10748i | 0.140478 | − | 0.102063i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.5999i | 1.56170i | 0.624717 | + | 0.780851i | \(0.285214\pi\) | ||||
−0.624717 | + | 0.780851i | \(0.714786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.46856 | − | 0.802084i | 0.0809038 | − | 0.0262872i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.39807 | − | 4.30282i | 0.0457708 | − | 0.140868i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.694285 | + | 2.13679i | −0.0227055 | + | 0.0698805i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.5971 | + | 44.8660i | −1.06490 | + | 1.46571i | −0.189766 | + | 0.981829i | \(0.560773\pi\) |
−0.875134 | + | 0.483880i | \(0.839227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.9243 | + | 33.6214i | 0.356500 | + | 1.09719i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.3821 | + | 24.2535i | 1.08823 | + | 0.790642i | 0.979099 | − | 0.203385i | \(-0.0651944\pi\) |
0.109127 | + | 0.994028i | \(0.465194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.7238 | − | 16.8470i | −0.870247 | − | 0.548614i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.743572 | + | 0.540237i | 0.0241884 | + | 0.0175739i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.0090 | + | 40.0377i | 0.422737 | + | 1.30105i | 0.905144 | + | 0.425104i | \(0.139763\pi\) |
−0.482407 | + | 0.875947i | \(0.660237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.47835 | + | 11.6694i | −0.275219 | + | 0.378806i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.82235 | + | 11.7640i | −0.123948 | + | 0.381473i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.66963 | − | 14.3716i | 0.151264 | − | 0.465543i | −0.846499 | − | 0.532390i | \(-0.821294\pi\) |
0.997763 | + | 0.0668470i | \(0.0212940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.29975 | + | 3.02167i | −0.300933 | + | 0.0977790i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.34510i | − | 0.108132i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.25271 | + | 3.81632i | −0.169619 | + | 0.123235i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −47.7823 | − | 34.7159i | −1.54137 | − | 1.11987i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.4331 | + | 32.2826i | −1.43184 | + | 1.04029i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.0356 | + | 39.9640i | 0.934688 | + | 1.28649i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.9758 | + | 12.3391i | 1.22122 | + | 0.396798i | 0.847526 | − | 0.530754i | \(-0.178091\pi\) |
0.373694 | + | 0.927552i | \(0.378091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.5147 | + | 9.91481i | −0.980272 | + | 0.318510i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.08032 | + | 6.99246i | −0.163035 | + | 0.224399i | −0.882717 | − | 0.469906i | \(-0.844288\pi\) |
0.719681 | + | 0.694305i | \(0.244288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.7114 | + | 5.10494i | 0.503684 | + | 0.163657i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.65955 | 0.309353 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.2621 | + | 15.5010i | 0.360308 | + | 0.495921i | 0.950235 | − | 0.311536i | \(-0.100843\pi\) |
−0.589926 | + | 0.807457i | \(0.700843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.345932 | + | 1.06467i | 0.0110560 | + | 0.0340270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.5982i | 0.849214i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.18153 | −0.0695799 | −0.0347899 | − | 0.999395i | \(-0.511076\pi\) | ||||
−0.0347899 | + | 0.999395i | \(0.511076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.7575 | 1.48982 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.47506i | 0.110612i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.41294 | − | 13.5816i | −0.140323 | − | 0.431871i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.21471 | + | 4.42467i | 0.102119 | + | 0.140554i | 0.857018 | − | 0.515286i | \(-0.172314\pi\) |
−0.754900 | + | 0.655840i | \(0.772314\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.6454 | 2.05146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −64.1740 | − | 20.8514i | −2.03445 | − | 0.661034i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.23638 | + | 3.07811i | −0.0708268 | + | 0.0974847i | −0.842961 | − | 0.537975i | \(-0.819189\pi\) |
0.772134 | + | 0.635460i | \(0.219189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.279440 | − | 0.0907955i | 0.00884108 | − | 0.00287264i |
(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 | 1148.2.ba.a.113.3 | ✓ | 80 | |
41.4 | even | 10 | inner | 1148.2.ba.a.701.18 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.3 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1148.2.ba.a.701.18 | yes | 80 | 41.4 | even | 10 | inner |