Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(737,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.r (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.16 | ||
Character | \(\chi\) | \(=\) | 1380.737 |
Dual form | 1380.2.r.c.1013.16 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.136960 | − | 1.72663i | −0.0790739 | − | 0.996869i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.01176 | − | 0.976134i | −0.899685 | − | 0.436540i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.818985 | − | 0.818985i | −0.309547 | − | 0.309547i | 0.535187 | − | 0.844734i | \(-0.320241\pi\) |
−0.844734 | + | 0.535187i | \(0.820241\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96248 | + | 0.472958i | −0.987495 | + | 0.157653i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.64173i | − | 1.39953i | −0.714371 | − | 0.699767i | \(-0.753287\pi\) | ||
0.714371 | − | 0.699767i | \(-0.246713\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.65679 | − | 1.65679i | 0.459511 | − | 0.459511i | −0.438984 | − | 0.898495i | \(-0.644661\pi\) |
0.898495 | + | 0.438984i | \(0.144661\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.40989 | + | 3.60724i | −0.364032 | + | 0.931387i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.49751 | − | 5.49751i | 1.33334 | − | 1.33334i | 0.430983 | − | 0.902360i | \(-0.358167\pi\) |
0.902360 | − | 0.430983i | \(-0.141833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.07783i | 0.247271i | 0.992328 | + | 0.123636i | \(0.0394554\pi\) | ||||
−0.992328 | + | 0.123636i | \(0.960545\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.30191 | + | 1.52625i | −0.284101 | + | 0.333055i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.09433 | + | 3.92749i | 0.618865 | + | 0.785497i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.22236 | + | 5.05033i | 0.235244 | + | 0.971936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.03222 | −1.49155 | −0.745773 | − | 0.666200i | \(-0.767920\pi\) | ||||
−0.745773 | + | 0.666200i | \(0.767920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.08833 | −0.554681 | −0.277341 | − | 0.960772i | \(-0.589453\pi\) | ||||
−0.277341 | + | 0.960772i | \(0.589453\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.01454 | + | 0.635731i | −1.39515 | + | 0.110667i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.848160 | + | 2.44704i | 0.143365 | + | 0.413625i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.77607 | − | 2.77607i | −0.456382 | − | 0.456382i | 0.441084 | − | 0.897466i | \(-0.354594\pi\) |
−0.897466 | + | 0.441084i | \(0.854594\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.08758 | − | 2.63375i | −0.494408 | − | 0.421737i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8391i | 1.84896i | 0.381229 | + | 0.924481i | \(0.375501\pi\) | ||||
−0.381229 | + | 0.924481i | \(0.624499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.17071 | + | 6.17071i | −0.941024 | + | 0.941024i | −0.998355 | − | 0.0573315i | \(-0.981741\pi\) |
0.0573315 | + | 0.998355i | \(0.481741\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.42147 | + | 1.94030i | 0.957256 | + | 0.289244i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.23937 | + | 5.23937i | −0.764241 | + | 0.764241i | −0.977086 | − | 0.212845i | \(-0.931727\pi\) |
0.212845 | + | 0.977086i | \(0.431727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.65853i | − | 0.808361i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.2451 | − | 8.73922i | −1.43460 | − | 1.22374i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.39767 | − | 1.39767i | −0.191984 | − | 0.191984i | 0.604569 | − | 0.796553i | \(-0.293345\pi\) |
−0.796553 | + | 0.604569i | \(0.793345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.53095 | + | 9.33803i | −0.610953 | + | 1.25914i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.86101 | − | 0.147620i | 0.246497 | − | 0.0195527i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.09918 | −0.533667 | −0.266834 | − | 0.963743i | \(-0.585977\pi\) | ||||
−0.266834 | + | 0.963743i | \(0.585977\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.47597 | 1.08524 | 0.542618 | − | 0.839979i | \(-0.317433\pi\) | ||||
0.542618 | + | 0.839979i | \(0.317433\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.81358 | + | 2.03889i | 0.354477 | + | 0.256875i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.95031 | + | 1.71581i | −0.614010 | + | 0.212820i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.89161 | + | 1.89161i | 0.231096 | + | 0.231096i | 0.813150 | − | 0.582054i | \(-0.197751\pi\) |
−0.582054 | + | 0.813150i | \(0.697751\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.12406 | + | 1.31776i | −0.135321 | + | 0.158639i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.766555i | 0.0909733i | 0.998965 | + | 0.0454867i | \(0.0144838\pi\) | ||||
−0.998965 | + | 0.0454867i | \(0.985516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.976885 | − | 0.976885i | 0.114336 | − | 0.114336i | −0.647624 | − | 0.761960i | \(-0.724237\pi\) |
0.761960 | + | 0.647624i | \(0.224237\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.35751 | − | 5.88066i | 0.734102 | − | 0.679040i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.80151 | + | 3.80151i | −0.433222 | + | 0.433222i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.42798i | − | 0.498186i | −0.968480 | − | 0.249093i | \(-0.919867\pi\) | ||
0.968480 | − | 0.249093i | \(-0.0801325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.55262 | − | 2.80226i | 0.950291 | − | 0.311362i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.24062 | + | 3.24062i | 0.355705 | + | 0.355705i | 0.862227 | − | 0.506522i | \(-0.169069\pi\) |
−0.506522 | + | 0.862227i | \(0.669069\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4260 | + | 5.69335i | −1.78165 | + | 0.617530i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.10009 | + | 13.8687i | 0.117942 | + | 1.48688i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8779 | 1.15306 | 0.576528 | − | 0.817077i | \(-0.304407\pi\) | ||||
0.576528 | + | 0.817077i | \(0.304407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.71378 | −0.284481 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.422978 | + | 5.33240i | 0.0438608 | + | 0.552944i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.05211 | − | 2.16833i | 0.107944 | − | 0.222466i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.81549 | − | 1.81549i | −0.184335 | − | 0.184335i | 0.608907 | − | 0.793242i | \(-0.291608\pi\) |
−0.793242 | + | 0.608907i | \(0.791608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.19534 | + | 13.7510i | 0.220640 | + | 1.38203i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 5.31484i | − | 0.528847i | −0.964407 | − | 0.264423i | \(-0.914818\pi\) | ||
0.964407 | − | 0.264423i | \(-0.0851816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.54157 | + | 5.54157i | −0.546027 | + | 0.546027i | −0.925289 | − | 0.379262i | \(-0.876178\pi\) |
0.379262 | + | 0.925289i | \(0.376178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.10896 | − | 1.79960i | 0.400993 | − | 0.175623i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.27792 | + | 1.27792i | −0.123541 | + | 0.123541i | −0.766174 | − | 0.642633i | \(-0.777842\pi\) |
0.642633 | + | 0.766174i | \(0.277842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.8548i | − | 1.61440i | −0.590277 | − | 0.807201i | \(-0.700982\pi\) | ||
0.590277 | − | 0.807201i | \(-0.299018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.41302 | + | 5.17344i | −0.418865 | + | 0.491041i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.3189 | + | 12.3189i | 1.15886 | + | 1.15886i | 0.984721 | + | 0.174140i | \(0.0557145\pi\) |
0.174140 | + | 0.984721i | \(0.444285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.732296 | + | 2.11276i | 0.0682869 | + | 0.197016i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.12463 | + | 5.69181i | −0.381322 | + | 0.526208i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.00477 | −0.825466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5456 | −0.958695 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.4418 | − | 1.62149i | 1.84317 | − | 0.146205i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.39128 | − | 10.9216i | −0.213882 | − | 0.976859i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.95997 | − | 3.95997i | −0.351390 | − | 0.351390i | 0.509236 | − | 0.860627i | \(-0.329928\pi\) |
−0.860627 | + | 0.509236i | \(0.829928\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.4996 | + | 9.80937i | 1.01249 | + | 0.863667i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 17.2941i | − | 1.51099i | −0.655154 | − | 0.755495i | \(-0.727396\pi\) | ||
0.655154 | − | 0.755495i | \(-0.272604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.882727 | − | 0.882727i | 0.0765421 | − | 0.0765421i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.47070 | − | 11.3532i | 0.212644 | − | 0.977130i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.34377 | + | 8.34377i | −0.712857 | + | 0.712857i | −0.967132 | − | 0.254275i | \(-0.918163\pi\) |
0.254275 | + | 0.967132i | \(0.418163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.3856i | − | 1.30499i | −0.757795 | − | 0.652493i | \(-0.773723\pi\) | ||
0.757795 | − | 0.652493i | \(-0.226277\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.76403 | + | 8.32886i | 0.822279 | + | 0.701416i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.69038 | − | 7.69038i | −0.643101 | − | 0.643101i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.1589 | + | 7.84052i | 1.34192 | + | 0.651120i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.77017 | + | 0.774992i | −0.805830 | + | 0.0639202i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9315 | −1.14132 | −0.570658 | − | 0.821188i | \(-0.693312\pi\) | ||||
−0.570658 | + | 0.821188i | \(0.693312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.88187 | −0.641417 | −0.320709 | − | 0.947178i | \(-0.603921\pi\) | ||||
−0.320709 | + | 0.947178i | \(0.603921\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.6862 | + | 18.8864i | −1.10646 | + | 1.52687i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.21297 | + | 3.01463i | 0.499038 | + | 0.242141i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9278 | + | 13.9278i | 1.11156 | + | 1.11156i | 0.992939 | + | 0.118623i | \(0.0378480\pi\) |
0.118623 | + | 0.992939i | \(0.462152\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.22182 | + | 2.60467i | −0.176202 | + | 0.206564i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.15822i | 0.0912805i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.40789 | − | 7.40789i | 0.580231 | − | 0.580231i | −0.354736 | − | 0.934967i | \(-0.615429\pi\) |
0.934967 | + | 0.354736i | \(0.115429\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.7438 | + | 6.54432i | 1.30351 | + | 0.509475i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0344 | − | 12.0344i | 0.931250 | − | 0.931250i | −0.0665339 | − | 0.997784i | \(-0.521194\pi\) |
0.997784 | + | 0.0665339i | \(0.0211941\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.51009i | 0.577699i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.509768 | − | 3.19305i | −0.0389829 | − | 0.244179i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.67284 | − | 2.67284i | −0.203212 | − | 0.203212i | 0.598163 | − | 0.801375i | \(-0.295898\pi\) |
−0.801375 | + | 0.598163i | \(0.795898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.682346 | − | 5.75076i | 0.0515805 | − | 0.434717i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.561423 | + | 7.07775i | 0.0421991 | + | 0.531996i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.6346 | −1.31807 | −0.659035 | − | 0.752112i | \(-0.729035\pi\) | ||||
−0.659035 | + | 0.752112i | \(0.729035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0816 | −1.04668 | −0.523340 | − | 0.852124i | \(-0.675314\pi\) | ||||
−0.523340 | + | 0.852124i | \(0.675314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.16087 | − | 14.6348i | −0.0858139 | − | 1.08184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.87496 | + | 8.29458i | 0.211371 | + | 0.609830i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.5180 | − | 25.5180i | −1.86606 | − | 1.86606i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.13505 | − | 5.13724i | 0.228041 | − | 0.373680i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.2736i | − | 0.743371i | −0.928359 | − | 0.371685i | \(-0.878780\pi\) | ||
0.928359 | − | 0.371685i | \(-0.121220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.94625 | − | 7.94625i | 0.571984 | − | 0.571984i | −0.360699 | − | 0.932682i | \(-0.617462\pi\) |
0.932682 | + | 0.360699i | \(0.117462\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.64056 | + | 8.31234i | 0.260706 | + | 0.595259i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.62730 | − | 5.62730i | 0.400929 | − | 0.400929i | −0.477632 | − | 0.878560i | \(-0.658505\pi\) |
0.878560 | + | 0.477632i | \(0.158505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.0362i | − | 1.56210i | −0.624466 | − | 0.781052i | \(-0.714684\pi\) | ||
0.624466 | − | 0.781052i | \(-0.285316\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00702 | − | 3.52517i | 0.212099 | − | 0.248646i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.57827 | + | 6.57827i | 0.461704 | + | 0.461704i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5566 | − | 23.8174i | 0.807146 | − | 1.66348i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.42922 | + | 1.76036i | 0.168843 | + | 0.122354i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.00299 | 0.346064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.47434 | −0.376869 | −0.188435 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188435 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.32355 | − | 0.104987i | 0.0906884 | − | 0.00719361i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.4374 | − | 6.39052i | 1.25742 | − | 0.435830i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.52930 | + | 2.52930i | 0.171700 | + | 0.171700i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.82051 | − | 1.55292i | −0.123019 | − | 0.104937i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 18.2165i | − | 1.22537i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.7499 | + | 16.7499i | −1.12166 | + | 1.12166i | −0.130167 | + | 0.991492i | \(0.541551\pi\) |
−0.991492 | + | 0.130167i | \(0.958449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.0244 | − | 10.1716i | −0.734962 | − | 0.678109i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4091 | + | 14.4091i | −0.956364 | + | 0.956364i | −0.999087 | − | 0.0427229i | \(-0.986397\pi\) |
0.0427229 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.385393i | − | 0.0254675i | −0.999919 | − | 0.0127337i | \(-0.995947\pi\) | ||
0.999919 | − | 0.0127337i | \(-0.00405338\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.08444 | + | 6.04313i | 0.466122 | + | 0.397609i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.7690 | + | 13.7690i | 0.902035 | + | 0.902035i | 0.995612 | − | 0.0935768i | \(-0.0298301\pi\) |
−0.0935768 | + | 0.995612i | \(0.529830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.6547 | − | 5.42601i | 1.02120 | − | 0.353954i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.64547 | + | 0.606456i | −0.496626 | + | 0.0393935i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.48073 | 0.613257 | 0.306629 | − | 0.951829i | \(-0.400799\pi\) | ||||
0.306629 | + | 0.951829i | \(0.400799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.18465 | 0.205141 | 0.102571 | − | 0.994726i | \(-0.467293\pi\) | ||||
0.102571 | + | 0.994726i | \(0.467293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.00983 | − | 14.3834i | −0.385530 | − | 0.922695i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.52348 | + | 11.3836i | −0.352882 | + | 0.727270i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.78574 | + | 1.78574i | 0.113624 | + | 0.113624i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.15151 | − | 6.03918i | 0.326464 | − | 0.382718i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.4714i | − | 0.787191i | −0.919284 | − | 0.393595i | \(-0.871231\pi\) | ||
0.919284 | − | 0.393595i | \(-0.128769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.28220 | + | 3.28220i | −0.206350 | + | 0.206350i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.0800 | + | 27.5818i | 0.756478 | + | 1.72724i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.24440 | + | 2.24440i | −0.140002 | + | 0.140002i | −0.773634 | − | 0.633632i | \(-0.781563\pi\) |
0.633632 | + | 0.773634i | \(0.281563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.54711i | 0.282544i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.7953 | − | 3.79890i | 1.47289 | − | 0.235146i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.03572 | + | 9.03572i | 0.557167 | + | 0.557167i | 0.928500 | − | 0.371333i | \(-0.121099\pi\) |
−0.371333 | + | 0.928500i | \(0.621099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.44745 | + | 4.17607i | 0.0889164 | + | 0.256534i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.48984 | − | 18.7821i | −0.0911767 | − | 1.14945i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.0574 | −1.77166 | −0.885829 | − | 0.464011i | \(-0.846410\pi\) | ||||
−0.885829 | + | 0.464011i | \(0.846410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0260 | −1.15575 | −0.577874 | − | 0.816126i | \(-0.696117\pi\) | ||||
−0.577874 | + | 0.816126i | \(0.696117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.371679 | + | 4.68568i | 0.0224950 | + | 0.283590i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.2303 | − | 14.3630i | 1.09933 | − | 0.866123i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.71086 | − | 5.71086i | −0.343132 | − | 0.343132i | 0.514411 | − | 0.857544i | \(-0.328011\pi\) |
−0.857544 | + | 0.514411i | \(0.828011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.14914 | − | 1.46065i | 0.547745 | − | 0.0874469i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1498i | 1.20204i | 0.799235 | + | 0.601019i | \(0.205238\pi\) | ||||
−0.799235 | + | 0.601019i | \(0.794762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.9189 | + | 11.9189i | −0.708503 | + | 0.708503i | −0.966220 | − | 0.257718i | \(-0.917030\pi\) |
0.257718 | + | 0.966220i | \(0.417030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.88800 | − | 1.51962i | −0.230305 | − | 0.0900145i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.69607 | − | 9.69607i | 0.572341 | − | 0.572341i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 43.4453i | − | 2.55561i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.88603 | + | 3.38333i | −0.169182 | + | 0.198334i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.8189 | + | 17.8189i | 1.04099 | + | 1.04099i | 0.999123 | + | 0.0418702i | \(0.0133316\pi\) |
0.0418702 | + | 0.999123i | \(0.486668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.24654 | + | 4.00134i | 0.480132 | + | 0.232967i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.4423 | − | 5.67388i | 1.36026 | − | 0.329232i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.34306 | −0.135502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1074 | 0.582583 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.17675 | + | 0.727921i | −0.527191 | + | 0.0418180i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.0516 | − | 8.27368i | −0.976371 | − | 0.473750i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.7101 | − | 18.7101i | −1.06784 | − | 1.06784i | −0.997524 | − | 0.0703199i | \(-0.977598\pi\) |
−0.0703199 | − | 0.997524i | \(-0.522402\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3272 | + | 8.80925i | 0.587493 | + | 0.501140i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.01991i | − | 0.398063i | −0.979993 | − | 0.199031i | \(-0.936220\pi\) | ||
0.979993 | − | 0.199031i | \(-0.0637795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0613853 | − | 0.0613853i | 0.00346970 | − | 0.00346970i | −0.705370 | − | 0.708840i | \(-0.749219\pi\) |
0.708840 | + | 0.705370i | \(0.249219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.67000 | − | 6.84817i | −0.206781 | − | 0.385851i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7707 | − | 10.7707i | 0.604940 | − | 0.604940i | −0.336679 | − | 0.941619i | \(-0.609304\pi\) |
0.941619 | + | 0.336679i | \(0.109304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.2834i | 2.08747i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.38151 | + | 2.03146i | 0.132923 | + | 0.113385i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.92538 | + | 5.92538i | 0.329697 | + | 0.329697i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.6337 | + | 1.38037i | 0.645320 | + | 0.0765693i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.1020 | + | 2.30844i | −1.60935 | + | 0.127657i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.58194 | 0.473137 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1511 | 0.997676 | 0.498838 | − | 0.866695i | \(-0.333760\pi\) | ||||
0.498838 | + | 0.866695i | \(0.333760\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.53701 | + | 6.91109i | 0.522625 | + | 0.378725i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.95899 | − | 5.65191i | −0.107031 | − | 0.308797i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.2826 | − | 23.2826i | −1.26829 | − | 1.26829i | −0.946973 | − | 0.321314i | \(-0.895875\pi\) |
−0.321314 | − | 0.946973i | \(-0.604125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.5829 | − | 22.9573i | 1.06360 | − | 1.24687i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.3352i | 0.776295i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.3671 | + | 10.3671i | −0.559773 | + | 0.559773i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.54765 | − | 1.55376i | 0.190999 | − | 0.0836519i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.0772 | − | 21.0772i | 1.13148 | − | 1.13148i | 0.141554 | − | 0.989930i | \(-0.454790\pi\) |
0.989930 | − | 0.141554i | \(-0.0452100\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.2313i | − | 0.761784i | −0.924619 | − | 0.380892i | \(-0.875617\pi\) | ||
0.924619 | − | 0.380892i | \(-0.124383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3925 | + | 6.34214i | 0.554713 | + | 0.338518i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.0881192 | − | 0.0881192i | −0.00469011 | − | 0.00469011i | 0.704758 | − | 0.709448i | \(-0.251056\pi\) |
−0.709448 | + | 0.704758i | \(0.751056\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.748260 | − | 1.54212i | 0.0397135 | − | 0.0818473i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.23329 | + | 15.5479i | 0.0652728 | + | 0.822881i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.59320 | 0.506310 | 0.253155 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253155 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8383 | 0.938857 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.44433 | + | 18.2084i | 0.0758077 | + | 0.955693i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.91883 | + | 1.01168i | −0.152778 | + | 0.0529540i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4758 | − | 13.4758i | −0.703432 | − | 0.703432i | 0.261714 | − | 0.965146i | \(-0.415712\pi\) |
−0.965146 | + | 0.261714i | \(0.915712\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.59941 | − | 35.0732i | −0.291494 | − | 1.82584i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.28934i | 0.118856i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.52935 | − | 7.52935i | 0.389855 | − | 0.389855i | −0.484781 | − | 0.874636i | \(-0.661101\pi\) |
0.874636 | + | 0.484781i | \(0.161101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.5301 | + | 5.62467i | −0.956888 | + | 0.290457i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.3077 | + | 13.3077i | −0.685382 | + | 0.685382i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.9050i | − | 1.02245i | −0.859446 | − | 0.511227i | \(-0.829191\pi\) | ||
0.859446 | − | 0.511227i | \(-0.170809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.29503 | + | 7.37975i | −0.322504 | + | 0.378076i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.0127 | − | 24.0127i | −1.22699 | − | 1.22699i | −0.965097 | − | 0.261894i | \(-0.915653\pi\) |
−0.261894 | − | 0.965097i | \(-0.584347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.3585 | − | 3.93693i | 0.578882 | − | 0.200644i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.3621 | − | 21.1991i | 0.780901 | − | 1.07761i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5736 | 0.941721 | 0.470860 | − | 0.882208i | \(-0.343944\pi\) | ||||
0.470860 | + | 0.882208i | \(0.343944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.77466 | −0.393181 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.8604 | + | 2.36860i | −1.50626 | + | 0.119480i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.32230 | + | 8.90801i | −0.217478 | + | 0.448211i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2110 | + | 16.2110i | 0.813606 | + | 0.813606i | 0.985172 | − | 0.171567i | \(-0.0548830\pi\) |
−0.171567 | + | 0.985172i | \(0.554883\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.64504 | − | 1.40324i | −0.0823549 | − | 0.0702500i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.9274i | 1.19488i | 0.801914 | + | 0.597440i | \(0.203815\pi\) | ||||
−0.801914 | + | 0.597440i | \(0.796185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.11672 | + | 5.11672i | −0.254882 | + | 0.254882i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.9412 | − | 2.71104i | −0.990885 | − | 0.134713i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8857 | + | 12.8857i | −0.638723 | + | 0.638723i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.9274i | − | 0.540325i | −0.962815 | − | 0.270162i | \(-0.912923\pi\) | ||
0.962815 | − | 0.270162i | \(-0.0870774\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.5493 | + | 13.2638i | 0.766993 | + | 0.654256i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.35716 | + | 3.35716i | 0.165195 | + | 0.165195i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.35606 | − | 9.68262i | −0.164743 | − | 0.475301i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.5651 | + | 2.10721i | −1.30090 | + | 0.103190i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.210640 | −0.0102904 | −0.00514522 | − | 0.999987i | \(-0.501638\pi\) | ||||
−0.00514522 | + | 0.999987i | \(0.501638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3257 | 1.33177 | 0.665886 | − | 0.746053i | \(-0.268054\pi\) | ||||
0.665886 | + | 0.746053i | \(0.268054\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.0436 | − | 17.9996i | 0.634199 | − | 0.875168i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.6025 | + | 4.58031i | 1.87250 | + | 0.222178i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.94169 | − | 6.94169i | −0.335932 | − | 0.335932i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.2251 | + | 14.3317i | −0.590235 | + | 0.691940i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.8893i | 1.05437i | 0.849750 | + | 0.527185i | \(0.176753\pi\) | ||||
−0.849750 | + | 0.527185i | \(0.823247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.84190 | − | 4.84190i | 0.232687 | − | 0.232687i | −0.581126 | − | 0.813813i | \(-0.697388\pi\) |
0.813813 | + | 0.581126i | \(0.197388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.3245 | − | 28.9742i | 0.542970 | − | 1.38921i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.762141 | − | 0.762141i | 0.0364581 | − | 0.0364581i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.8794i | 1.33061i | 0.746571 | + | 0.665306i | \(0.231699\pi\) | ||||
−0.746571 | + | 0.665306i | \(0.768301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.67624 | + | 16.7633i | 0.127440 | + | 0.798252i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9122 | + | 16.9122i | 0.803524 | + | 0.803524i | 0.983645 | − | 0.180121i | \(-0.0576489\pi\) |
−0.180121 | + | 0.983645i | \(0.557649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.8837 | − | 10.6183i | −1.03739 | − | 0.503355i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.90806 | + | 24.0546i | 0.0902483 | + | 1.13774i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.46468 | 0.305087 | 0.152544 | − | 0.988297i | \(-0.451254\pi\) | ||||
0.152544 | + | 0.988297i | \(0.451254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.9540 | 2.58768 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.07950 | + | 13.6090i | 0.0507194 | + | 0.639409i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.45945 | + | 2.64901i | 0.255943 | + | 0.124187i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.48566 | + | 3.48566i | 0.163052 | + | 0.163052i | 0.783917 | − | 0.620865i | \(-0.213219\pi\) |
−0.620865 | + | 0.783917i | \(0.713219\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.4842 | + | 21.0443i | 1.60959 | + | 0.982263i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15.5040i | − | 0.722095i | −0.932547 | − | 0.361048i | \(-0.882419\pi\) | ||
0.932547 | − | 0.361048i | \(-0.117581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6721 | − | 11.6721i | 0.542449 | − | 0.542449i | −0.381797 | − | 0.924246i | \(-0.624695\pi\) |
0.924246 | + | 0.381797i | \(0.124695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.35421 | − | 11.1404i | 0.201922 | − | 0.516623i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0317 | − | 22.0317i | 1.01951 | − | 1.01951i | 0.0197009 | − | 0.999806i | \(-0.493729\pi\) |
0.999806 | − | 0.0197009i | \(-0.00627140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.09839i | − | 0.143071i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.1406 | − | 25.9557i | 1.02019 | − | 1.19598i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.6427 | + | 28.6427i | 1.31699 | + | 1.31699i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.23316 | + | 3.33516i | −0.194231 | + | 0.153027i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.80160 | + | 3.47952i | 0.219850 | + | 0.159316i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.9596 | −1.23182 | −0.615908 | − | 0.787818i | \(-0.711211\pi\) | ||||
−0.615908 | + | 0.787818i | \(0.711211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.19872 | −0.419426 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.99981 | − | 0.158630i | 0.0909947 | − | 0.00721791i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.88016 | + | 5.42449i | 0.0853739 | + | 0.246313i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.24238 | − | 6.24238i | −0.282869 | − | 0.282869i | 0.551383 | − | 0.834252i | \(-0.314100\pi\) |
−0.834252 | + | 0.551383i | \(0.814100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8052 | − | 11.7761i | −0.624295 | − | 0.532533i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 41.1212i | − | 1.85577i | −0.372864 | − | 0.927886i | \(-0.621624\pi\) | ||
0.372864 | − | 0.927886i | \(-0.378376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.1572 | + | 44.1572i | −1.98874 | + | 1.98874i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.00637 | − | 29.8067i | 0.404806 | − | 1.33971i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.627797 | − | 0.627797i | 0.0281605 | − | 0.0281605i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.4294i | 1.63081i | 0.578894 | + | 0.815403i | \(0.303485\pi\) | ||||
−0.578894 | + | 0.815403i | \(0.696515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.4272 | − | 19.1307i | −1.00197 | − | 0.854697i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.67747 | + | 8.67747i | 0.386909 | + | 0.386909i | 0.873584 | − | 0.486674i | \(-0.161790\pi\) |
−0.486674 | + | 0.873584i | \(0.661790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.18800 | + | 10.6922i | −0.230863 | + | 0.475795i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9671 | − | 1.02858i | 0.575890 | − | 0.0456809i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0114 | −0.754016 | −0.377008 | − | 0.926210i | \(-0.623047\pi\) | ||||
−0.377008 | + | 0.926210i | \(0.623047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.60011 | −0.0707847 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.44340 | + | 1.31750i | −0.240332 | + | 0.0581690i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.5576 | − | 5.73897i | 0.729615 | − | 0.252889i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.3197 | + | 24.3197i | 1.06958 | + | 1.06958i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.24893 | + | 4.98107i | −0.186507 | + | 0.218645i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.0175i | − | 1.13985i | −0.821698 | − | 0.569923i | \(-0.806973\pi\) | ||
0.821698 | − | 0.569923i | \(-0.193027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.04305 | + | 3.04305i | −0.133063 | + | 0.133063i | −0.770501 | − | 0.637438i | \(-0.779994\pi\) |
0.637438 | + | 0.770501i | \(0.279994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.0229 | − | 0.390533i | −0.437434 | − | 0.0170443i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9782 | + | 16.9782i | −0.739580 | + | 0.739580i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.1437 | − | 1.93874i | 0.526993 | − | 0.0841340i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.6150 | + | 19.6150i | 0.849618 | + | 0.849618i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.81827 | − | 1.32344i | 0.165078 | − | 0.0572172i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.41523 | + | 30.4483i | 0.104225 | + | 1.31394i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.2653 | −1.13133 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7056 | 0.460271 | 0.230135 | − | 0.973159i | \(-0.426083\pi\) | ||||
0.230135 | + | 0.973159i | \(0.426083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.92862 | + | 24.3137i | 0.0827650 | + | 1.04340i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.4526 | + | 33.9078i | −0.704751 | + | 1.45245i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.5079 | − | 28.5079i | −1.21891 | − | 1.21891i | −0.968014 | − | 0.250895i | \(-0.919275\pi\) |
−0.250895 | − | 0.968014i | \(-0.580725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.1099 | + | 4.00878i | −1.07167 | + | 0.171090i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.65737i | − | 0.368816i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.62645 | + | 3.62645i | −0.154212 | + | 0.154212i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.9279 | − | 6.10000i | 0.591206 | − | 0.258931i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.76594 | − | 6.76594i | 0.286682 | − | 0.286682i | −0.549085 | − | 0.835767i | \(-0.685024\pi\) |
0.835767 | + | 0.549085i | \(0.185024\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.4471i | 0.864822i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −40.5651 | + | 47.5550i | −1.71266 | + | 2.00777i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0908 | + | 16.0908i | 0.678147 | + | 0.678147i | 0.959581 | − | 0.281434i | \(-0.0908101\pi\) |
−0.281434 | + | 0.959581i | \(0.590810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7577 | − | 36.8074i | −0.536720 | − | 1.54850i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.29948 | − | 4.70946i | −0.390542 | − | 0.197779i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.5344 | −1.78313 | −0.891567 | − | 0.452889i | \(-0.850393\pi\) | ||||
−0.891567 | + | 0.452889i | \(0.850393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8309 | −0.997291 | −0.498645 | − | 0.866806i | \(-0.666169\pi\) | ||||
−0.498645 | + | 0.866806i | \(0.666169\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.7387 | + | 1.40707i | −0.741043 | + | 0.0587812i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.589133 | − | 4.96517i | 0.0245686 | − | 0.207062i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.97434 | + | 7.97434i | 0.331976 | + | 0.331976i | 0.853336 | − | 0.521361i | \(-0.174575\pi\) |
−0.521361 | + | 0.853336i | \(0.674575\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.8085 | − | 12.6319i | −0.615422 | − | 0.524964i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.30805i | − | 0.220215i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.48758 | + | 6.48758i | −0.268688 | + | 0.268688i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.8537 | − | 7.42435i | 0.572780 | − | 0.306959i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.650199 | + | 0.650199i | −0.0268366 | + | 0.0268366i | −0.720398 | − | 0.693561i | \(-0.756041\pi\) |
0.693561 | + | 0.720398i | \(0.256041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.32870i | − | 0.137157i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.4870 | − | 8.94554i | −0.431376 | − | 0.367970i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.1061 | − | 21.1061i | −0.866722 | − | 0.866722i | 0.125386 | − | 0.992108i | \(-0.459983\pi\) |
−0.992108 | + | 0.125386i | \(0.959983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.1154 | + | 8.78986i | 0.742659 | + | 0.360349i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.0483 | + | 3.01808i | −1.55721 | + | 0.123522i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.58395 | −0.228154 | −0.114077 | − | 0.993472i | \(-0.536391\pi\) | ||||
−0.114077 | + | 0.993472i | \(0.536391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.1171 | −0.861383 | −0.430691 | − | 0.902499i | \(-0.641730\pi\) | ||||
−0.430691 | + | 0.902499i | \(0.641730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.49850 | − | 4.70920i | −0.264639 | − | 0.191774i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.2153 | + | 10.2940i | 0.862523 | + | 0.418509i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.0428 | − | 26.0428i | −1.05704 | − | 1.05704i | −0.998271 | − | 0.0587734i | \(-0.981281\pi\) |
−0.0587734 | − | 0.998271i | \(-0.518719\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.4573 | − | 12.2592i | 0.423750 | − | 0.496767i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3611i | 0.702354i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3672 | − | 11.3672i | 0.459119 | − | 0.459119i | −0.439247 | − | 0.898366i | \(-0.644755\pi\) |
0.898366 | + | 0.439247i | \(0.144755\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −42.7066 | − | 16.6919i | −1.72210 | − | 0.673081i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9594 | − | 11.9594i | 0.481465 | − | 0.481465i | −0.424134 | − | 0.905599i | \(-0.639421\pi\) |
0.905599 | + | 0.424134i | \(0.139421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.3866i | 0.899793i | 0.893081 | + | 0.449896i | \(0.148539\pi\) | ||||
−0.893081 | + | 0.449896i | \(0.851461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.70678 | − | 4.43546i | 0.108619 | − | 0.177989i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.90885 | − | 8.90885i | −0.356926 | − | 0.356926i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.85030 | + | 24.3058i | −0.234012 | + | 0.972234i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.685210 | − | 8.63830i | −0.0273647 | − | 0.344981i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.5229 | −1.21703 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.8795 | 0.592342 | 0.296171 | − | 0.955135i | \(-0.404290\pi\) | ||||
0.296171 | + | 0.955135i | \(0.404290\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.749766 | + | 9.45215i | 0.0298005 | + | 0.375689i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.10103 | + | 11.8319i | 0.162744 | + | 0.469537i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.37500 | − | 9.37500i | −0.371451 | − | 0.371451i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.362548 | − | 2.27091i | −0.0143422 | − | 0.0898357i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 49.1536i | − | 1.94145i | −0.240193 | − | 0.970725i | \(-0.577211\pi\) | ||
0.240193 | − | 0.970725i | \(-0.422789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.6592 | − | 24.6592i | 0.972466 | − | 0.972466i | −0.0271654 | − | 0.999631i | \(-0.508648\pi\) |
0.999631 | + | 0.0271654i | \(0.00864807\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.5592 | − | 30.9593i | −0.533894 | − | 1.21902i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.7231 | + | 16.7231i | −0.657452 | + | 0.657452i | −0.954777 | − | 0.297324i | \(-0.903906\pi\) |
0.297324 | + | 0.954777i | \(0.403906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0273i | 0.746885i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.02075 | − | 4.71357i | 0.157585 | − | 0.184739i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.7491 | − | 32.7491i | −1.28157 | − | 1.28157i | −0.939773 | − | 0.341800i | \(-0.888964\pi\) |
−0.341800 | − | 0.939773i | \(-0.611036\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.8813 | + | 34.7915i | −0.659608 | + | 1.35941i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.43198 | + | 3.35603i | −0.0948806 | + | 0.130931i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.6170 | −0.608354 | −0.304177 | − | 0.952616i | \(-0.598381\pi\) | ||||
−0.304177 | + | 0.952616i | \(0.598381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2341 | 0.787017 | 0.393508 | − | 0.919321i | \(-0.371261\pi\) | ||||
0.393508 | + | 0.919321i | \(0.371261\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.4530 | + | 2.49493i | −1.22154 | + | 0.0968949i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.63749 | + | 0.914172i | −0.102277 | + | 0.0354501i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.67964 | + | 5.67964i | 0.219916 | + | 0.219916i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.2150 | + | 26.6268i | 1.20684 | + | 1.02945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 39.3431i | − | 1.51883i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.98815 | + | 9.98815i | −0.385015 | + | 0.385015i | −0.872905 | − | 0.487890i | \(-0.837767\pi\) |
0.487890 | + | 0.872905i | \(0.337767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.0527 | + | 20.4282i | −0.617869 | + | 0.786281i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.22889 | − | 1.22889i | 0.0472302 | − | 0.0472302i | −0.683097 | − | 0.730327i | \(-0.739367\pi\) |
0.730327 | + | 0.683097i | \(0.239367\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.97372i | 0.114121i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.8526 | + | 22.9056i | 1.02899 | + | 0.877746i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.59562 | − | 3.59562i | −0.137583 | − | 0.137583i | 0.634961 | − | 0.772544i | \(-0.281016\pi\) |
−0.772544 | + | 0.634961i | \(0.781016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.9303 | − | 8.64100i | 0.952537 | − | 0.330156i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.665429 | + | 0.0527834i | −0.0253877 | + | 0.00201381i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.63128 | −0.176438 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3212 | −0.430680 | −0.215340 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215340 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.46395 | − | 13.0599i | 0.359506 | − | 0.496103i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.0184 | + | 30.9520i | −0.569679 | + | 1.17408i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 65.0858 | + | 65.0858i | 2.46530 | + | 2.46530i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.8881 | − | 25.6597i | 0.827883 | − | 0.970538i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.5830i | − | 0.550792i | −0.961331 | − | 0.275396i | \(-0.911191\pi\) | ||
0.961331 | − | 0.275396i | \(-0.0888090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.99213 | − | 2.99213i | 0.112850 | − | 0.112850i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.5128 | − | 26.2866i | −0.433596 | − | 0.990012i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.35278 | + | 4.35278i | −0.163703 | + | 0.163703i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.17171i | 0.0815602i | 0.999168 | + | 0.0407801i | \(0.0129843\pi\) | ||||
−0.999168 | + | 0.0407801i | \(0.987016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.09425 | + | 13.1178i | 0.0785404 | + | 0.491956i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.18378 | + | 2.18378i | 0.0817833 | + | 0.0817833i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.96433 | + | 22.9780i | 0.297849 | + | 0.859328i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.29848 | − | 16.3697i | −0.0484926 | − | 0.611337i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.16538 | 0.341811 | 0.170906 | − | 0.985287i | \(-0.445331\pi\) | ||||
0.170906 | + | 0.985287i | \(0.445331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.07692 | 0.338042 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.436170 | − | 5.49870i | −0.0162213 | − | 0.204499i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.8543 | − | 31.5464i | −0.923066 | − | 1.17161i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.6354 | + | 31.6354i | 1.17329 | + | 1.17329i | 0.981420 | + | 0.191872i | \(0.0614559\pi\) |
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.0117 | + | 12.3467i | −0.889321 | + | 0.457284i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 67.8471i | 2.50941i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.2496 | + | 11.2496i | −0.415515 | + | 0.415515i | −0.883655 | − | 0.468139i | \(-0.844925\pi\) |
0.468139 | + | 0.883655i | \(0.344925\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.4117 | + | 7.97789i | 0.752896 | + | 0.294269i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.78032 | − | 8.78032i | 0.323427 | − | 0.323427i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9128i | 1.39464i | 0.716758 | + | 0.697322i | \(0.245625\pi\) | ||||
−0.716758 | + | 0.697322i | \(0.754375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.83873 | − | 3.32788i | 0.104283 | − | 0.122253i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.1452 | − | 27.1452i | −0.995861 | − | 0.995861i | 0.00413027 | − | 0.999991i | \(-0.498685\pi\) |
−0.999991 | + | 0.00413027i | \(0.998685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0269 | + | 13.5990i | 1.02682 | + | 0.498231i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1330 | − | 8.06761i | −0.407334 | − | 0.295179i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.09319 | 0.0764834 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.4107 | −1.32865 | −0.664323 | − | 0.747446i | \(-0.731280\pi\) | ||||
−0.664323 | + | 0.747446i | \(0.731280\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.5335 | + | 1.70809i | −0.784726 | + | 0.0622462i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.8564 | + | 7.69376i | 0.577073 | + | 0.280004i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.48255 | − | 1.48255i | −0.0538841 | − | 0.0538841i | 0.679651 | − | 0.733535i | \(-0.262131\pi\) |
−0.733535 | + | 0.679651i | \(0.762131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.11666 | + | 5.21760i | 0.222021 | + | 0.189387i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 47.6544i | − | 1.72747i | −0.503946 | − | 0.863735i | \(-0.668119\pi\) | ||
0.503946 | − | 0.863735i | \(-0.331881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8039 | + | 13.8039i | −0.499734 | + | 0.499734i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 45.9689 | − | 24.6352i | 1.66201 | − | 0.890689i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.79148 | + | 6.79148i | −0.245226 | + | 0.245226i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.75549i | − | 0.0633044i | −0.999499 | − | 0.0316522i | \(-0.989923\pi\) | ||
0.999499 | − | 0.0316522i | \(-0.0100769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.18264 | + | 3.56785i | 0.150634 | + | 0.128493i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.0246 | − | 17.0246i | −0.612333 | − | 0.612333i | 0.331221 | − | 0.943553i | \(-0.392540\pi\) |
−0.943553 | + | 0.331221i | \(0.892540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.55631 | − | 12.1294i | −0.343273 | − | 0.435701i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.85117 | − | 0.622773i | 0.281659 | − | 0.0223419i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.7606 | −0.457195 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.55814 | 0.127320 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.81830 | − | 40.5654i | −0.350877 | − | 1.44969i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.4240 | − | 41.6148i | −0.514814 | − | 1.48530i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.190642 | − | 0.190642i | −0.00679565 | − | 0.00679565i | 0.703701 | − | 0.710496i | \(-0.251530\pi\) |
−0.710496 | + | 0.703701i | \(0.751530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.3638 | − | 16.8389i | 0.511365 | − | 0.599479i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 20.1779i | − | 0.717445i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0429 | − | 14.0429i | 0.498678 | − | 0.498678i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.01227 | − | 3.07117i | 0.248700 | − | 0.108923i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.8922 | + | 32.8922i | −1.16510 | + | 1.16510i | −0.181760 | + | 0.983343i | \(0.558179\pi\) |
−0.983343 | + | 0.181760i | \(0.941821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.6070i | 2.03799i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.2256 | + | 5.14479i | −1.13864 | + | 0.181782i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.53444 | − | 4.53444i | −0.160017 | − | 0.160017i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.13058 | − | 2.33006i | 0.0398476 | − | 0.0821237i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.97970 | + | 50.1712i | 0.140092 | + | 1.76611i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.7894 | −0.941866 | −0.470933 | − | 0.882169i | \(-0.656083\pi\) | ||||
−0.470933 | + | 0.882169i | \(0.656083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.6442 | 1.28675 | 0.643376 | − | 0.765550i | \(-0.277533\pi\) | ||||
0.643376 | + | 0.765550i | \(0.277533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.60580 | + | 32.8508i | 0.0913894 | + | 1.15213i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1340 | + | 7.67178i | −0.775319 | + | 0.268731i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.65097 | − | 6.65097i | −0.232688 | − | 0.232688i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.03952 | − | 1.28350i | 0.280923 | − | 0.0448492i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.6560i | 1.48871i | 0.667787 | + | 0.744353i | \(0.267242\pi\) | ||||
−0.667787 | + | 0.744353i | \(0.732758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.92246 | − | 5.92246i | 0.206444 | − | 0.206444i | −0.596310 | − | 0.802754i | \(-0.703367\pi\) |
0.802754 | + | 0.596310i | \(0.203367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.2964 | − | 29.5098i | −0.950339 | − | 1.02740i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7878 | − | 12.7878i | 0.444677 | − | 0.444677i | −0.448903 | − | 0.893580i | \(-0.648185\pi\) |
0.893580 | + | 0.448903i | \(0.148185\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 51.8490i | − | 1.80079i | −0.435072 | − | 0.900396i | \(-0.643277\pi\) | ||
0.435072 | − | 0.900396i | \(-0.356723\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.07837 | + | 10.6427i | −0.314925 | + | 0.369191i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.1078 | − | 31.1078i | −1.07782 | − | 1.07782i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.9575 | + | 12.4631i | −1.24436 | + | 0.431303i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.77507 | − | 15.5971i | −0.130485 | − | 0.539115i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.5279 | −1.15751 | −0.578757 | − | 0.815500i | \(-0.696462\pi\) | ||||
−0.578757 | + | 0.815500i | \(0.696462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.5166 | 1.22471 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.7912 | − | 2.75972i | 1.19827 | − | 0.0950498i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.33085 | − | 15.1085i | 0.252189 | − | 0.519747i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.63673 | + | 8.63673i | 0.296761 | + | 0.296761i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.2118 | + | 18.9470i | 0.762308 | + | 0.650260i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.92595i | 0.134580i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.7310 | + | 10.7310i | −0.367423 | + | 0.367423i | −0.866536 | − | 0.499114i | \(-0.833659\pi\) |
0.499114 | + | 0.866536i | \(0.333659\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.09132 | + | 6.92125i | −0.0715216 | + | 0.236702i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.8167 | − | 25.8167i | 0.881880 | − | 0.881880i | −0.111846 | − | 0.993726i | \(-0.535676\pi\) |
0.993726 | + | 0.111846i | \(0.0356762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 49.6389i | − | 1.69366i | −0.531865 | − | 0.846829i | \(-0.678509\pi\) | ||
0.531865 | − | 0.846829i | \(-0.321491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.0695 | − | 15.4135i | −0.615806 | − | 0.525292i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.23448 | + | 8.23448i | 0.280305 | + | 0.280305i | 0.833231 | − | 0.552926i | \(-0.186489\pi\) |
−0.552926 | + | 0.833231i | \(0.686489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.76805 | + | 7.98615i | 0.0941166 | + | 0.271537i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −75.0139 | + | 5.95027i | −2.54760 | + | 0.202082i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.5535 | −0.697229 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.26799 | 0.212383 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.23702 | + | 4.51971i | 0.211091 | + | 0.152969i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.98623 | + | 10.9031i | −0.236178 | + | 0.368591i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7536 | − | 16.7536i | −0.565729 | − | 0.565729i | 0.365200 | − | 0.930929i | \(-0.381001\pi\) |
−0.930929 | + | 0.365200i | \(0.881001\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.3262 | − | 33.2071i | 0.955418 | − | 1.12005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.3448i | 0.618050i | 0.951054 | + | 0.309025i | \(0.100003\pi\) | ||||
−0.951054 | + | 0.309025i | \(0.899997\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.92619 | + | 6.92619i | −0.233085 | + | 0.233085i | −0.813979 | − | 0.580894i | \(-0.802703\pi\) |
0.580894 | + | 0.813979i | \(0.302703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.77938 | − | 14.7867i | 0.194272 | − | 0.497050i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.1497 | + | 24.1497i | −0.810869 | + | 0.810869i | −0.984764 | − | 0.173895i | \(-0.944365\pi\) |
0.173895 | + | 0.984764i | \(0.444365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.48631i | 0.217544i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.0073 | − | 39.6989i | −0.435762 | − | 1.32996i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.64715 | − | 5.64715i | −0.188975 | − | 0.188975i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.4765 | + | 17.2137i | 1.18585 | + | 0.575391i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.320905 | + | 4.04559i | 0.0107147 | + | 0.135078i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.8062 | 0.827333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3674 | −0.511961 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.38431 | − | 17.4518i | −0.0460671 | − | 0.580759i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.3288 | + | 13.7456i | 0.941682 | + | 0.456918i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.7752 | + | 23.7752i | 0.789444 | + | 0.789444i | 0.981403 | − | 0.191959i | \(-0.0614841\pi\) |
−0.191959 | + | 0.981403i | \(0.561484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.51370 | + | 15.7451i | 0.0833740 | + | 0.522233i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.03327i | − | 0.0673653i | −0.999433 | − | 0.0336826i | \(-0.989276\pi\) | ||
0.999433 | − | 0.0336826i | \(-0.0107235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0421 | − | 15.0421i | 0.497821 | − | 0.497821i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.9502 | + | 30.5749i | −0.395061 | + | 1.01077i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.1636 | + | 14.1636i | −0.467723 | + | 0.467723i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 0.951166i | − | 0.0313761i | −0.999877 | − | 0.0156880i | \(-0.995006\pi\) | ||
0.999877 | − | 0.0156880i | \(-0.00499386\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.7429 | + | 34.8680i | −0.980062 | + | 1.14894i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.27002 | + | 1.27002i | 0.0418033 | + | 0.0418033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.31291 | − | 19.4930i | 0.0760480 | − | 0.640926i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.7959 | − | 19.0377i | 0.453116 | − | 0.625281i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.5132 | 1.19796 | 0.598979 | − | 0.800765i | \(-0.295573\pi\) | ||||
0.598979 | + | 0.800765i | \(0.295573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.09893 | 0.199884 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.1208 | + | 0.961447i | −0.396816 | + | 0.0314764i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.4270 | + | 76.2449i | 0.864255 | + | 2.49347i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.68273 | − | 4.68273i | −0.152978 | − | 0.152978i | 0.626469 | − | 0.779447i | \(-0.284500\pi\) |
−0.779447 | + | 0.626469i | \(0.784500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.114397 | − | 0.0975822i | −0.00373320 | − | 0.00318447i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.36113i | 0.305164i | 0.988291 | + | 0.152582i | \(0.0487588\pi\) | ||||
−0.988291 | + | 0.152582i | \(0.951241\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.37153 | − | 8.37153i | 0.272614 | − | 0.272614i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.3216 | + | 7.27466i | −0.368291 | + | 0.236645i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.01272 | + | 2.01272i | −0.0654046 | + | 0.0654046i | −0.739052 | − | 0.673648i | \(-0.764726\pi\) |
0.673648 | + | 0.739052i | \(0.264726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.23699i | − | 0.105077i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.0720 | − | 17.1218i | −0.650881 | − | 0.555211i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.3281 | + | 29.3281i | 0.950030 | + | 0.950030i | 0.998810 | − | 0.0487796i | \(-0.0155332\pi\) |
−0.0487796 | + | 0.998810i | \(0.515533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0284 | + | 20.6679i | −0.324511 | + | 0.668799i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 64.3745 | − | 5.10633i | 2.08093 | − | 0.165064i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.6669 | 0.441326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4622 | −0.692329 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.18140 | − | 4.39020i | 0.102519 | − | 0.141472i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.7425 | + | 8.22932i | −0.764299 | + | 0.264911i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.7275 | + | 34.7275i | 1.11676 | + | 1.11676i | 0.992214 | + | 0.124548i | \(0.0397482\pi\) |
0.124548 | + | 0.992214i | \(0.460252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.41939 | − | 11.0425i | 0.302594 | − | 0.354735i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.55288i | 0.146109i | 0.997328 | + | 0.0730544i | \(0.0232747\pi\) | ||||
−0.997328 | + | 0.0730544i | \(0.976725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6005 | + | 12.6005i | −0.403955 | + | 0.403955i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.790041 | − | 20.2761i | 0.0253016 | − | 0.649354i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.3911 | − | 38.3911i | 1.22824 | − | 1.22824i | 0.263611 | − | 0.964629i | \(-0.415086\pi\) |
0.964629 | − | 0.263611i | \(-0.0849136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 50.4923i | − | 1.61374i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.97163 | + | 49.9322i | 0.254515 | + | 1.59421i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.3476 | − | 25.3476i | −0.808463 | − | 0.808463i | 0.175938 | − | 0.984401i | \(-0.443704\pi\) |
−0.984401 | + | 0.175938i | \(0.943704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8138 | + | 5.82776i | −0.535731 | + | 0.185688i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.17538 | − | 14.8178i | −0.0374128 | − | 0.471656i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.72669 | 0.277493 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.5932 | 1.51185 | 0.755923 | − | 0.654660i | \(-0.227188\pi\) | ||||
0.755923 | + | 0.654660i | \(0.227188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.48598 | − | 31.3402i | −0.0788901 | − | 0.994552i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.5103 | + | 44.3314i | −0.681921 | + | 1.40540i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.4430 | + | 34.4430i | 1.09082 | + | 1.09082i | 0.995441 | + | 0.0953811i | \(0.0304070\pi\) |
0.0953811 | + | 0.995441i | \(0.469593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.6267 | − | 17.4134i | 0.336213 | − | 0.550936i |
(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 | 1380.2.r.c.737.16 | ✓ | 80 | |
3.2 | odd | 2 | inner | 1380.2.r.c.737.38 | yes | 80 | |
5.3 | odd | 4 | inner | 1380.2.r.c.1013.38 | yes | 80 | |
15.8 | even | 4 | inner | 1380.2.r.c.1013.16 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.r.c.737.16 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1380.2.r.c.737.38 | yes | 80 | 3.2 | odd | 2 | inner | |
1380.2.r.c.1013.16 | yes | 80 | 15.8 | even | 4 | inner | |
1380.2.r.c.1013.38 | yes | 80 | 5.3 | odd | 4 | inner |