Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(881,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.q (of order \(3\), degree \(2\), not 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.4601315889.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(1.07988 - 1.87040i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.961 |
Dual form | 1520.2.q.o.881.1 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.579878 | + | 1.00438i | −0.334793 | + | 0.579878i | −0.983445 | − | 0.181207i | \(-0.942000\pi\) |
0.648652 | + | 0.761085i | \(0.275333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43525 | 0.920440 | 0.460220 | − | 0.887805i | \(-0.347771\pi\) | ||||
0.460220 | + | 0.887805i | \(0.347771\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.827483 | + | 1.43324i | 0.275828 | + | 0.477748i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.75477 | 1.73513 | 0.867564 | − | 0.497326i | \(-0.165685\pi\) | ||||
0.867564 | + | 0.497326i | \(0.165685\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.797505 | + | 1.38132i | 0.221188 | + | 0.383109i | 0.955169 | − | 0.296061i | \(-0.0956732\pi\) |
−0.733981 | + | 0.679170i | \(0.762340\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.579878 | − | 1.00438i | −0.149724 | − | 0.259329i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.99203 | − | 5.18234i | 0.725673 | − | 1.25690i | −0.233023 | − | 0.972471i | \(-0.574862\pi\) |
0.958696 | − | 0.284432i | \(-0.0918050\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.149412 | − | 4.35634i | −0.0342775 | − | 0.999412i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41215 | + | 2.44592i | −0.308156 | + | 0.533743i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.470022 | − | 0.814102i | −0.0980064 | − | 0.169752i | 0.812853 | − | 0.582469i | \(-0.197913\pi\) |
−0.910859 | + | 0.412717i | \(0.864580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.39862 | −1.03897 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.30917 | − | 2.26755i | −0.243106 | − | 0.421073i | 0.718491 | − | 0.695536i | \(-0.244833\pi\) |
−0.961598 | + | 0.274463i | \(0.911500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.26913 | 0.946364 | 0.473182 | − | 0.880965i | \(-0.343105\pi\) | ||||
0.473182 | + | 0.880965i | \(0.343105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.33706 | + | 5.77996i | −0.580908 | + | 1.00616i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.21763 | + | 2.10899i | −0.205817 | + | 0.356485i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.89384 | −0.475744 | −0.237872 | − | 0.971297i | \(-0.576450\pi\) | ||||
−0.237872 | + | 0.971297i | \(0.576450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.84982 | −0.296209 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.15767 | − | 5.46925i | 0.493145 | − | 0.854153i | −0.506823 | − | 0.862050i | \(-0.669180\pi\) |
0.999969 | + | 0.00789701i | \(0.00251372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.26961 | − | 3.93108i | 0.346113 | − | 0.599485i | −0.639443 | − | 0.768839i | \(-0.720835\pi\) |
0.985555 | + | 0.169354i | \(0.0541682\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.65497 | −0.246708 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.47718 | + | 7.75471i | 0.653064 | + | 1.13114i | 0.982375 | + | 0.186919i | \(0.0598502\pi\) |
−0.329311 | + | 0.944221i | \(0.606816\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.06953 | −0.152791 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.47002 | + | 6.01025i | 0.485900 | + | 0.841604i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.09819 | + | 1.90213i | 0.150848 | + | 0.261277i | 0.931540 | − | 0.363640i | \(-0.118466\pi\) |
−0.780691 | + | 0.624917i | \(0.785133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87738 | + | 4.98377i | −0.387986 | + | 0.672012i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.46205 | + | 2.37608i | 0.591013 | + | 0.314719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.39939 | + | 9.35202i | −0.702941 | + | 1.21753i | 0.264489 | + | 0.964389i | \(0.414797\pi\) |
−0.967430 | + | 0.253140i | \(0.918537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26434 | + | 9.11811i | 0.674030 | + | 1.16745i | 0.976751 | + | 0.214375i | \(0.0687716\pi\) |
−0.302721 | + | 0.953079i | \(0.597895\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.01513 | + | 3.49031i | 0.253883 | + | 0.439738i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.59501 | −0.197837 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.504789 | + | 0.874320i | 0.0616698 | + | 0.106815i | 0.895212 | − | 0.445641i | \(-0.147024\pi\) |
−0.833542 | + | 0.552456i | \(0.813691\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.09022 | 0.131247 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41694 | − | 7.65036i | 0.524194 | − | 0.907931i | −0.475409 | − | 0.879765i | \(-0.657700\pi\) |
0.999603 | − | 0.0281662i | \(-0.00896677\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.12499 | − | 8.87674i | 0.599835 | − | 1.03894i | −0.393011 | − | 0.919534i | \(-0.628566\pi\) |
0.992845 | − | 0.119410i | \(-0.0381003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.15976 | 0.133917 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.0143 | 1.59708 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.80229 | − | 6.58577i | 0.427792 | − | 0.740957i | −0.568885 | − | 0.822417i | \(-0.692625\pi\) |
0.996677 | + | 0.0814604i | \(0.0259584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.648093 | − | 1.12253i | 0.0720103 | − | 0.124726i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.11355 | −0.341756 | −0.170878 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170878 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.99203 | + | 5.18234i | 0.324531 | + | 0.562104i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.03663 | 0.325561 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.55706 | + | 9.62511i | 0.589047 | + | 1.02026i | 0.994358 | + | 0.106081i | \(0.0338302\pi\) |
−0.405310 | + | 0.914179i | \(0.632837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.94213 | + | 3.36387i | 0.203590 | + | 0.352629i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.05545 | + | 5.29220i | −0.316836 | + | 0.548776i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.84741 | + | 2.04877i | 0.394735 | + | 0.210200i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.02888 | + | 3.51412i | −0.206002 | + | 0.356805i | −0.950451 | − | 0.310873i | \(-0.899379\pi\) |
0.744450 | + | 0.667678i | \(0.232712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.76197 | + | 8.24798i | 0.478596 | + | 0.828953i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56503 | + | 9.63892i | 0.553741 | + | 0.959108i | 0.998000 | + | 0.0632098i | \(0.0201337\pi\) |
−0.444259 | + | 0.895898i | \(0.646533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5791 | −1.14092 | −0.570460 | − | 0.821326i | \(-0.693235\pi\) | ||||
−0.570460 | + | 0.821326i | \(0.693235\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41215 | − | 2.44592i | −0.137812 | − | 0.238697i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.9177 | −1.73217 | −0.866086 | − | 0.499894i | \(-0.833372\pi\) | ||||
−0.866086 | + | 0.499894i | \(0.833372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.81235 | + | 4.87113i | −0.269374 | + | 0.466570i | −0.968700 | − | 0.248233i | \(-0.920150\pi\) |
0.699326 | + | 0.714803i | \(0.253484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.67807 | − | 2.90650i | 0.159275 | − | 0.275873i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6789 | −1.47494 | −0.737472 | − | 0.675378i | \(-0.763981\pi\) | ||||
−0.737472 | + | 0.675378i | \(0.763981\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.940044 | 0.0876595 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.31984 | + | 2.28604i | −0.122020 | + | 0.211344i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.28635 | − | 12.6203i | 0.667939 | − | 1.15690i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.1173 | 2.01067 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.66213 | + | 6.34299i | 0.330203 | + | 0.571928i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.05996 | + | 5.30000i | 0.271527 | + | 0.470299i | 0.969253 | − | 0.246066i | \(-0.0791380\pi\) |
−0.697726 | + | 0.716365i | \(0.745805\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.63220 | + | 4.55910i | 0.231752 | + | 0.401406i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.44055 | + | 12.8874i | −0.650084 | + | 1.12598i | 0.333018 | + | 0.942920i | \(0.391933\pi\) |
−0.983102 | + | 0.183058i | \(0.941400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.363857 | − | 10.6088i | −0.0315504 | − | 0.919899i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.69931 | − | 4.67535i | 0.232320 | − | 0.402390i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.67518 | − | 15.0258i | −0.741170 | − | 1.28374i | −0.951963 | − | 0.306214i | \(-0.900938\pi\) |
0.210793 | − | 0.977531i | \(-0.432396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.35267 | − | 5.80700i | −0.284370 | − | 0.492543i | 0.688086 | − | 0.725629i | \(-0.258451\pi\) |
−0.972456 | + | 0.233086i | \(0.925118\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3849 | −0.874564 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.58946 | + | 7.94917i | 0.383790 | + | 0.664743i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.61834 | 0.217441 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.620199 | − | 1.07422i | 0.0511532 | − | 0.0885999i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.19642 | + | 12.4646i | −0.589553 | + | 1.02114i | 0.404737 | + | 0.914433i | \(0.367363\pi\) |
−0.994291 | + | 0.106704i | \(0.965970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7219 | −1.03529 | −0.517645 | − | 0.855595i | \(-0.673191\pi\) | ||||
−0.517645 | + | 0.855595i | \(0.673191\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.90341 | 0.800644 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.63457 | + | 4.56320i | −0.211614 | + | 0.366525i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.68765 | − | 2.92309i | 0.134689 | − | 0.233288i | −0.790790 | − | 0.612088i | \(-0.790330\pi\) |
0.925479 | + | 0.378800i | \(0.123663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.54727 | −0.202012 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.14462 | − | 1.98255i | −0.0902089 | − | 0.156246i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.307960 | −0.0241213 | −0.0120607 | − | 0.999927i | \(-0.503839\pi\) | ||||
−0.0120607 | + | 0.999927i | \(0.503839\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.33706 | − | 5.77996i | −0.259790 | − | 0.449969i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.13215 | + | 12.3532i | 0.551902 | + | 0.955923i | 0.998137 | + | 0.0610070i | \(0.0194312\pi\) |
−0.446235 | + | 0.894916i | \(0.647235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.22797 | − | 9.05511i | 0.402152 | − | 0.696547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.12005 | − | 3.81894i | 0.468012 | − | 0.292042i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.67357 | + | 11.5590i | −0.507382 | + | 0.878811i | 0.492581 | + | 0.870266i | \(0.336053\pi\) |
−0.999963 | + | 0.00854514i | \(0.997280\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.21763 | − | 2.10899i | −0.0920440 | − | 0.159425i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.26197 | − | 10.8461i | −0.470679 | − | 0.815239i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2207 | 1.06291 | 0.531454 | − | 0.847087i | \(-0.321646\pi\) | ||||
0.531454 | + | 0.847087i | \(0.321646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.94132 | − | 8.55861i | −0.367285 | − | 0.636157i | 0.621855 | − | 0.783133i | \(-0.286379\pi\) |
−0.989140 | + | 0.146976i | \(0.953046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2107 | −0.902641 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.44692 | − | 2.50613i | 0.106379 | − | 0.184255i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.2184 | − | 29.8232i | 1.25914 | − | 2.18089i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.1470 | −0.956305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9942 | 0.940228 | 0.470114 | − | 0.882606i | \(-0.344213\pi\) | ||||
0.470114 | + | 0.882606i | \(0.344213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.25795 | + | 12.5711i | −0.522439 | + | 0.904890i | 0.477221 | + | 0.878784i | \(0.341644\pi\) |
−0.999659 | + | 0.0261066i | \(0.991689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.924911 | − | 1.60199i | 0.0662343 | − | 0.114721i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.0010 | −1.78125 | −0.890624 | − | 0.454740i | \(-0.849732\pi\) | ||||
−0.890624 | + | 0.454740i | \(0.849732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.12769 | − | 1.95322i | −0.0799401 | − | 0.138460i | 0.823284 | − | 0.567630i | \(-0.192140\pi\) |
−0.903224 | + | 0.429170i | \(0.858806\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.17086 | −0.0825864 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.18816 | − | 5.52205i | −0.223765 | − | 0.387572i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.15767 | + | 5.46925i | 0.220541 | + | 0.381989i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.777871 | − | 1.34731i | 0.0540657 | − | 0.0936446i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.859833 | − | 25.0697i | −0.0594759 | − | 1.73411i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1081 | − | 19.2397i | 0.764710 | − | 1.32452i | −0.175689 | − | 0.984446i | \(-0.556215\pi\) |
0.940400 | − | 0.340071i | \(-0.110451\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.12257 | + | 8.87255i | 0.350993 | + | 0.607937i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.26961 | + | 3.93108i | 0.154786 | + | 0.268098i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.8317 | 0.871071 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.94373 | + | 10.2949i | 0.401640 | + | 0.695662i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.54463 | 0.642041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.10799 | − | 8.84730i | 0.342056 | − | 0.592459i | −0.642758 | − | 0.766069i | \(-0.722210\pi\) |
0.984814 | + | 0.173610i | \(0.0555432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.827483 | − | 1.43324i | 0.0551656 | − | 0.0955495i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.15180 | −0.275565 | −0.137782 | − | 0.990463i | \(-0.543997\pi\) | ||||
−0.137782 | + | 0.990463i | \(0.543997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.53286 | 0.431703 | 0.215852 | − | 0.976426i | \(-0.430747\pi\) | ||||
0.215852 | + | 0.976426i | \(0.430747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.12660 | + | 14.0757i | −0.534691 | + | 0.926111i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.57410 | + | 4.45848i | −0.168635 | + | 0.292084i | −0.937940 | − | 0.346797i | \(-0.887269\pi\) |
0.769305 | + | 0.638882i | \(0.220603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.95437 | −0.584118 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.40973 | + | 7.63788i | 0.286443 | + | 0.496134i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.9962 | −0.905338 | −0.452669 | − | 0.891679i | \(-0.649528\pi\) | ||||
−0.452669 | + | 0.891679i | \(0.649528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.61285 | − | 13.1858i | −0.490387 | − | 0.849375i | 0.509552 | − | 0.860440i | \(-0.329811\pi\) |
−0.999939 | + | 0.0110652i | \(0.996478\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.34631 | − | 12.7242i | −0.471266 | − | 0.816256i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.534767 | − | 0.926244i | 0.0341650 | − | 0.0591756i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.89834 | − | 3.68059i | 0.375302 | − | 0.234190i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.80548 | − | 3.12718i | 0.114417 | − | 0.198177i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.05630 | − | 5.29366i | −0.192912 | − | 0.334133i | 0.753302 | − | 0.657674i | \(-0.228460\pi\) |
−0.946214 | + | 0.323542i | \(0.895126\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.70487 | − | 4.68497i | −0.170053 | − | 0.294541i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.94004 | −0.434602 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0613414 | − | 0.106246i | −0.00382637 | − | 0.00662747i | 0.864106 | − | 0.503310i | \(-0.167885\pi\) |
−0.867932 | + | 0.496683i | \(0.834551\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.04723 | −0.437893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.16663 | − | 3.75271i | 0.134111 | − | 0.232287i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.03027 | + | 8.71267i | −0.310179 | + | 0.537247i | −0.978401 | − | 0.206716i | \(-0.933722\pi\) |
0.668222 | + | 0.743962i | \(0.267056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.19639 | −0.134923 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.8897 | −0.788835 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.85614 | + | 4.94698i | −0.174142 | + | 0.301623i | −0.939864 | − | 0.341549i | \(-0.889049\pi\) |
0.765722 | + | 0.643172i | \(0.222382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.35560 | + | 11.0082i | −0.386075 | + | 0.668702i | −0.991918 | − | 0.126883i | \(-0.959503\pi\) |
0.605843 | + | 0.795585i | \(0.292836\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.50479 | −0.272642 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.87738 | − | 4.98377i | −0.173513 | − | 0.300533i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6019 | 1.05760 | 0.528799 | − | 0.848747i | \(-0.322642\pi\) | ||||
0.528799 | + | 0.848747i | \(0.322642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.36012 | + | 7.55195i | 0.261034 | + | 0.452123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2502 | + | 17.7539i | 0.611476 | + | 1.05911i | 0.990992 | + | 0.133922i | \(0.0427571\pi\) |
−0.379516 | + | 0.925185i | \(0.623910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.92805 | + | 10.2677i | −0.352386 | + | 0.610350i | −0.986667 | − | 0.162752i | \(-0.947963\pi\) |
0.634281 | + | 0.773103i | \(0.281296\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.28877 | + | 2.67621i | −0.254045 | + | 0.158525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.68973 | − | 13.3190i | 0.453911 | − | 0.786196i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.40447 | − | 16.2890i | −0.553204 | − | 0.958177i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.35301 | − | 4.07552i | −0.137936 | − | 0.238911i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.9814 | −1.45943 | −0.729715 | − | 0.683751i | \(-0.760347\pi\) | ||||
−0.729715 | + | 0.683751i | \(0.760347\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.39939 | − | 9.35202i | −0.314365 | − | 0.544495i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −31.0678 | −1.80274 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.749690 | − | 1.29850i | 0.0433557 | − | 0.0750943i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.52708 | − | 9.57319i | 0.318576 | − | 0.551789i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9082 | −0.741554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.5287 | −0.602871 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.45997 | − | 14.6531i | 0.482836 | − | 0.836296i | −0.516970 | − | 0.856003i | \(-0.672940\pi\) |
0.999806 | + | 0.0197074i | \(0.00627348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.71444 | − | 11.6298i | 0.381971 | − | 0.661594i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2133 | 0.862670 | 0.431335 | − | 0.902192i | \(-0.358043\pi\) | ||||
0.431335 | + | 0.902192i | \(0.358043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.4637 | − | 21.5877i | −0.704488 | − | 1.22021i | −0.966876 | − | 0.255246i | \(-0.917844\pi\) |
0.262389 | − | 0.964962i | \(-0.415490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.03027 | −0.227080 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.6152 | + | 21.8502i | 0.708541 | + | 1.22723i | 0.965398 | + | 0.260780i | \(0.0839798\pi\) |
−0.256857 | + | 0.966449i | \(0.582687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.53396 | − | 13.0492i | −0.421821 | − | 0.730615i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3901 | − | 17.9962i | 0.579919 | − | 1.00445i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.0231 | − | 12.2600i | −1.28104 | − | 0.682163i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.797505 | − | 1.38132i | 0.0442376 | − | 0.0766218i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.26164 | − | 5.64933i | −0.180369 | − | 0.312408i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.9031 | + | 18.8847i | 0.601106 | + | 1.04115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.2063 | 1.11064 | 0.555320 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555320 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.39460 | − | 4.14757i | −0.131223 | − | 0.227285i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00958 | −0.0551592 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9123 | − | 27.5610i | 0.866800 | − | 1.50134i | 0.00155051 | − | 0.999999i | \(-0.499506\pi\) |
0.865249 | − | 0.501342i | \(-0.167160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.09183 | − | 15.7475i | 0.493800 | − | 0.855287i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.3226 | 1.64206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6514 | −1.06107 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.545111 | + | 0.944159i | −0.0293478 | + | 0.0508318i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.65128 | + | 2.86009i | −0.0886451 | + | 0.153538i | −0.906939 | − | 0.421263i | \(-0.861587\pi\) |
0.818294 | + | 0.574801i | \(0.194920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8486 | 0.955416 | 0.477708 | − | 0.878519i | \(-0.341468\pi\) | ||||
0.477708 | + | 0.878519i | \(0.341468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.30543 | − | 7.45723i | −0.229807 | − | 0.398037i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.29523 | −0.441511 | −0.220755 | − | 0.975329i | \(-0.570852\pi\) | ||||
−0.220755 | + | 0.975329i | \(0.570852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.41694 | + | 7.65036i | 0.234427 | + | 0.406039i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.45039 | + | 14.6365i | 0.447242 | + | 0.774646i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.17511 | − | 7.23150i | 0.220354 | − | 0.381664i | −0.734562 | − | 0.678542i | \(-0.762612\pi\) |
0.954915 | + | 0.296878i | \(0.0959455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9554 | + | 1.30178i | −0.997650 | + | 0.0685148i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.8254 | + | 22.2142i | −0.673156 | + | 1.16594i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.12499 | + | 8.87674i | 0.268254 | + | 0.464630i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.20988 | + | 12.4879i | 0.376353 | + | 0.651862i | 0.990528 | − | 0.137307i | \(-0.0438448\pi\) |
−0.614176 | + | 0.789169i | \(0.710511\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.4517 | 0.544093 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.67438 | + | 4.63216i | 0.138847 | + | 0.240490i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.1157 | −1.24866 | −0.624332 | − | 0.781159i | \(-0.714629\pi\) | ||||
−0.624332 | + | 0.781159i | \(0.714629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.579878 | + | 1.00438i | −0.0299448 | + | 0.0518659i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.08814 | − | 3.61676i | 0.107545 | − | 0.186273i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.6757 | −0.856571 | −0.428285 | − | 0.903644i | \(-0.640882\pi\) | ||||
−0.428285 | + | 0.903644i | \(0.640882\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.09760 | −0.363621 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.43895 | + | 9.42053i | −0.277917 | + | 0.481367i | −0.970867 | − | 0.239619i | \(-0.922977\pi\) |
0.692950 | + | 0.720986i | \(0.256311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.00716 | + | 12.1368i | −0.357118 | + | 0.618546i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.51226 | 0.381870 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.2272 | − | 31.5704i | −0.924154 | − | 1.60068i | −0.792917 | − | 0.609330i | \(-0.791438\pi\) |
−0.131237 | − | 0.991351i | \(-0.541895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.62528 | −0.284482 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.62922 | − | 14.9463i | −0.435287 | − | 0.753939i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.80229 | + | 6.58577i | 0.191314 | + | 0.331366i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.29191 | + | 7.43380i | −0.215405 | + | 0.373092i | −0.953398 | − | 0.301717i | \(-0.902440\pi\) |
0.737993 | + | 0.674808i | \(0.235774\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.8662 | + | 5.78635i | 0.543992 | + | 0.289680i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.52785 | − | 14.7707i | 0.425860 | − | 0.737612i | −0.570640 | − | 0.821200i | \(-0.693305\pi\) |
0.996500 | + | 0.0835885i | \(0.0266381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.20216 | + | 7.27836i | 0.209325 | + | 0.362561i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.648093 | + | 1.12253i | 0.0322040 | + | 0.0557790i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.6533 | −0.825476 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.89702 | + | 10.2139i | 0.291589 | + | 0.505047i | 0.974186 | − | 0.225749i | \(-0.0724828\pi\) |
−0.682597 | + | 0.730795i | \(0.739149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.1222 | 0.992553 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.1489 | + | 22.7745i | −0.647015 | + | 1.12066i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.55677 | − | 2.69641i | 0.0764190 | − | 0.132362i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.77656 | 0.380820 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.14280 | −0.0558292 | −0.0279146 | − | 0.999610i | \(-0.508887\pi\) | ||||
−0.0279146 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.75944 | + | 16.9039i | −0.475646 | + | 0.823843i | −0.999611 | − | 0.0278967i | \(-0.991119\pi\) |
0.523965 | + | 0.851740i | \(0.324452\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.40959 | + | 12.8338i | −0.360266 | + | 0.624000i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.98406 | −0.290269 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.8200 | + | 22.2049i | 0.620404 | + | 1.07457i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.6453 | −0.513960 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.4392 | − | 31.9377i | −0.888187 | − | 1.53838i | −0.842017 | − | 0.539451i | \(-0.818632\pi\) |
−0.0461694 | − | 0.998934i | \(-0.514701\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.184467 | − | 0.319506i | −0.00886490 | − | 0.0153545i | 0.861559 | − | 0.507658i | \(-0.169488\pi\) |
−0.870424 | + | 0.492303i | \(0.836155\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.51832 | + | 2.62980i | −0.0727976 | + | 0.126089i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.47628 | + | 2.16921i | −0.166293 | + | 0.103767i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.13220 | + | 1.96102i | −0.0540367 | + | 0.0935944i | −0.891778 | − | 0.452472i | \(-0.850542\pi\) |
0.837742 | + | 0.546067i | \(0.183875\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.885022 | − | 1.53290i | −0.0421439 | − | 0.0729954i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.23137 | − | 14.2572i | −0.391084 | − | 0.677378i | 0.601508 | − | 0.798866i | \(-0.294567\pi\) |
−0.992593 | + | 0.121488i | \(0.961233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.1141 | −0.526860 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.34609 | − | 14.4558i | −0.394756 | − | 0.683738i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1613 | 0.668315 | 0.334158 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334158 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.1717 | − | 31.4742i | 0.855670 | − | 1.48206i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.37713 | − | 12.7776i | 0.346608 | − | 0.600342i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.88426 | −0.182097 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.22073 | 0.0571033 | 0.0285516 | − | 0.999592i | \(-0.490910\pi\) | ||||
0.0285516 | + | 0.999592i | \(0.490910\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.1528 | + | 27.9775i | −0.753950 | + | 1.30588i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.34580 | − | 7.52714i | 0.202404 | − | 0.350574i | −0.746898 | − | 0.664938i | \(-0.768458\pi\) |
0.949303 | + | 0.314364i | \(0.101791\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.7149 | 0.916229 | 0.458114 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458114 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.05545 | − | 5.29220i | −0.141693 | − | 0.245420i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4795 | 0.531207 | 0.265604 | − | 0.964082i | \(-0.414429\pi\) | ||||
0.265604 | + | 0.964082i | \(0.414429\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.22929 | + | 2.12919i | 0.0567633 | + | 0.0983170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.95726 | + | 3.39008i | 0.0901858 | + | 0.156206i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.0611 | − | 22.6225i | 0.600549 | − | 1.04018i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.69799 | + | 2.30756i | −0.169676 | + | 0.105878i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.81747 | + | 3.14796i | −0.0832164 | + | 0.144135i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6316 | + | 34.0029i | 0.896989 | + | 1.55363i | 0.831324 | + | 0.555789i | \(0.187584\pi\) |
0.0656652 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.30785 | − | 3.99731i | −0.105229 | − | 0.182262i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.65497 | 0.120805 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.02888 | − | 3.51412i | −0.0921267 | − | 0.159568i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.5943 | −1.43168 | −0.715838 | − | 0.698266i | \(-0.753955\pi\) | ||||
−0.715838 | + | 0.698266i | \(0.753955\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.178579 | − | 0.309309i | 0.00807564 | − | 0.0139874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.53187 | + | 9.58148i | −0.249650 | + | 0.432406i | −0.963429 | − | 0.267965i | \(-0.913649\pi\) |
0.713779 | + | 0.700371i | \(0.246982\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.6683 | −0.705663 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.52395 | −0.428070 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.7564 | − | 18.6306i | 0.482489 | − | 0.835696i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1868 | + | 17.6440i | −0.456023 | + | 0.789854i | −0.998746 | − | 0.0500570i | \(-0.984060\pi\) |
0.542724 | + | 0.839911i | \(0.317393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.5431 | −0.739091 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.83622 | − | 11.8407i | −0.304812 | − | 0.527950i | 0.672407 | − | 0.740181i | \(-0.265260\pi\) |
−0.977219 | + | 0.212231i | \(0.931927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1301 | −0.495281 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.06317 | + | 10.5017i | 0.269275 | + | 0.466398i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.86196 | + | 6.68912i | 0.171179 | + | 0.296490i | 0.938832 | − | 0.344375i | \(-0.111909\pi\) |
−0.767654 | + | 0.640865i | \(0.778576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4807 | − | 21.6171i | 0.552112 | − | 0.956285i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.806621 | + | 23.5182i | 0.0356132 | + | 1.03836i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.78953 | − | 10.0278i | 0.255117 | − | 0.441876i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.7651 | + | 44.6265i | 1.13315 | + | 1.96267i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.73971 | − | 13.4056i | −0.339736 | − | 0.588439i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.16876 | −0.0950151 | −0.0475075 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475075 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9466 | − | 20.6921i | −0.522389 | − | 0.904804i | −0.999661 | − | 0.0260485i | \(-0.991708\pi\) |
0.477272 | − | 0.878756i | \(-0.341626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82430 | 0.123263 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.7654 | − | 27.3065i | 0.686751 | − | 1.18949i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0582 | − | 19.1533i | 0.480790 | − | 0.832752i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.8716 | −0.775562 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0730 | 0.436312 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.95887 | − | 15.5172i | 0.387326 | − | 0.670868i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.24629 | + | 14.2830i | −0.355854 | + | 0.616356i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.15492 | −0.265111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.2275 | − | 36.7671i | −0.912641 | − | 1.58074i | −0.810319 | − | 0.585990i | \(-0.800706\pi\) |
−0.102323 | − | 0.994751i | \(-0.532627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.4614 | 0.491858 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.81235 | − | 4.87113i | −0.120468 | − | 0.208656i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.01535 | + | 10.4189i | 0.257198 | + | 0.445480i | 0.965490 | − | 0.260439i | \(-0.0838674\pi\) |
−0.708292 | + | 0.705919i | \(0.750534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.71231 | + | 15.0902i | −0.371833 | + | 0.644033i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.68259 | + | 6.04198i | −0.412492 | + | 0.257397i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.25956 | − | 16.0380i | 0.393756 | − | 0.682006i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.67807 | + | 2.90650i | 0.0712301 | + | 0.123374i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.37635 | + | 7.58006i | 0.185432 | + | 0.321178i | 0.943722 | − | 0.330740i | \(-0.107298\pi\) |
−0.758290 | + | 0.651917i | \(0.773965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.24011 | 0.306224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.9692 | + | 34.5876i | 0.843099 | + | 1.46029i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.9707 | 1.51598 | 0.757991 | − | 0.652265i | \(-0.226181\pi\) | ||||
0.757991 | + | 0.652265i | \(0.226181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.83943 | − | 13.5783i | 0.329807 | − | 0.571243i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.57827 | − | 2.73365i | 0.0662812 | − | 0.114802i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.3125 | −0.851543 | −0.425772 | − | 0.904831i | \(-0.639997\pi\) | ||||
−0.425772 | + | 0.904831i | \(0.639997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.1773 | −0.425906 | −0.212953 | − | 0.977062i | \(-0.568308\pi\) | ||||
−0.212953 | + | 0.977062i | \(0.568308\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.53505 | + | 13.0511i | −0.314781 | + | 0.545217i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.470022 | + | 0.814102i | −0.0196013 | + | 0.0339504i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.7441 | −1.36316 | −0.681578 | − | 0.731745i | \(-0.738706\pi\) | ||||
−0.681578 | + | 0.731745i | \(0.738706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.41745 | − | 14.5794i | −0.349817 | − | 0.605901i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.58228 | −0.314566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.31984 | + | 10.9463i | 0.261741 | + | 0.453349i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.31984 | − | 2.28604i | −0.0545689 | − | 0.0945160i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.38663 | − | 7.59786i | 0.181056 | − | 0.313597i | −0.761185 | − | 0.648535i | \(-0.775382\pi\) |
0.942240 | + | 0.334938i | \(0.108715\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.787274 | − | 22.9541i | −0.0324390 | − | 0.945808i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.4975 | − | 25.1105i | 0.596349 | − | 1.03291i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.1603 | + | 27.9905i | 0.663625 | + | 1.14943i | 0.979656 | + | 0.200684i | \(0.0643163\pi\) |
−0.316031 | + | 0.948749i | \(0.602350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.28635 | + | 12.6203i | 0.298711 | + | 0.517383i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.61570 | 0.107053 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.77520 | − | 16.9311i | −0.399404 | − | 0.691787i | 0.594249 | − | 0.804281i | \(-0.297449\pi\) |
−0.993652 | + | 0.112494i | \(0.964116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.401837 | −0.0163913 | −0.00819564 | − | 0.999966i | \(-0.502609\pi\) | ||||
−0.00819564 | + | 0.999966i | \(0.502609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.835409 | + | 1.44697i | −0.0340205 | + | 0.0589252i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0587 | + | 19.1542i | −0.449599 | + | 0.778728i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.4453 | −0.545727 | −0.272863 | − | 0.962053i | \(-0.587971\pi\) | ||||
−0.272863 | + | 0.962053i | \(0.587971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.39497 | 0.299659 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.14115 | + | 12.3688i | −0.288900 | + | 0.500390i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3527 | − | 17.9313i | 0.418140 | − | 0.724239i | −0.577613 | − | 0.816311i | \(-0.696016\pi\) |
0.995752 | + | 0.0920716i | \(0.0293489\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.32425 | −0.295342 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.63936 | + | 8.03560i | 0.186773 | + | 0.323501i | 0.944173 | − | 0.329451i | \(-0.106864\pi\) |
−0.757399 | + | 0.652952i | \(0.773530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.89129 | 0.116211 | 0.0581053 | − | 0.998310i | \(-0.481494\pi\) | ||||
0.0581053 | + | 0.998310i | \(0.481494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.53747 | + | 4.39503i | 0.101825 | + | 0.176366i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.5329 | + | 23.4396i | 0.542183 | + | 0.939088i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.6781 | + | 13.6738i | 1.02548 | + | 0.546078i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.65844 | + | 14.9969i | −0.345234 | + | 0.597964i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2270 | + | 26.3740i | 0.606178 | + | 1.04993i | 0.991864 | + | 0.127301i | \(0.0406314\pi\) |
−0.385686 | + | 0.922630i | \(0.626035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.8826 | + | 22.3134i | 0.512039 | + | 0.886877i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.11991 | −0.242861 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.852959 | − | 1.47737i | −0.0337955 | − | 0.0585355i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.6198 | 0.578349 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0369 | − | 17.3845i | 0.396434 | − | 0.686645i | −0.596849 | − | 0.802354i | \(-0.703581\pi\) |
0.993283 | + | 0.115709i | \(0.0369141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.04457 | + | 1.80924i | −0.0411937 | + | 0.0713496i | −0.885887 | − | 0.463901i | \(-0.846449\pi\) |
0.844693 | + | 0.535250i | \(0.179783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.26439 | −0.207285 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.10623 | 0.0828043 | 0.0414021 | − | 0.999143i | \(-0.486818\pi\) | ||||
0.0414021 | + | 0.999143i | \(0.486818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.0722 | + | 53.8187i | −1.21969 | + | 2.11257i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.44081 | + | 12.8879i | −0.291628 | + | 0.505115i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.83067 | 0.0716395 | 0.0358197 | − | 0.999358i | \(-0.488596\pi\) | ||||
0.0358197 | + | 0.999358i | \(0.488596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.44055 | − | 12.8874i | −0.290726 | − | 0.503553i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.9634 | 0.661804 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0268 | + | 20.8310i | 0.468497 | + | 0.811460i | 0.999352 | − | 0.0360024i | \(-0.0114624\pi\) |
−0.530855 | + | 0.847463i | \(0.678129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.72110 | + | 15.1054i | 0.339211 | + | 0.587531i | 0.984285 | − | 0.176589i | \(-0.0565065\pi\) |
−0.645073 | + | 0.764121i | \(0.723173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.53472 | + | 9.58642i | −0.214951 | + | 0.372306i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.36941 | + | 4.98929i | 0.363330 | + | 0.193476i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.23068 | + | 2.13159i | −0.0476519 | + | 0.0825356i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.92402 | + | 10.2607i | 0.229036 | + | 0.396702i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.2951 | + | 52.4726i | 1.16953 | + | 2.02568i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.5187 | 1.83171 | 0.915856 | − | 0.401506i | \(-0.131513\pi\) | ||||
0.915856 | + | 0.401506i | \(0.131513\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.69931 | + | 4.67535i | 0.103897 | + | 0.179954i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.5531 | 0.559321 | 0.279661 | − | 0.960099i | \(-0.409778\pi\) | ||||
0.279661 | + | 0.960099i | \(0.409778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.94084 | + | 8.55778i | −0.189612 | + | 0.328418i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.40754 | − | 4.16998i | 0.0922570 | − | 0.159794i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.33714 | −0.127692 | −0.0638460 | − | 0.997960i | \(-0.520337\pi\) | ||||
−0.0638460 | + | 0.997960i | \(0.520337\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3504 | 0.662923 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.78826 | + | 6.56146i | −0.144531 | + | 0.250335i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.75163 | + | 3.03391i | −0.0667318 | + | 0.115583i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3318 | 0.735415 | 0.367708 | − | 0.929941i | \(-0.380143\pi\) | ||||
0.367708 | + | 0.929941i | \(0.380143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.5966 | + | 20.0859i | 0.440519 | + | 0.763001i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.70534 | 0.254348 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.8957 | − | 32.7283i | −0.715725 | − | 1.23967i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.98533 | − | 5.17074i | −0.112916 | − | 0.195575i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.96892 | + | 8.60643i | −0.187674 | + | 0.325060i | −0.944474 | − | 0.328586i | \(-0.893428\pi\) |
0.756801 | + | 0.653646i | \(0.226761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.432375 | + | 12.6065i | 0.0163073 | + | 0.475464i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.19244 | − | 8.99357i | 0.195559 | − | 0.338717i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.5523 | + | 23.4732i | 0.509686 | + | 0.882801i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6059 | − | 32.2264i | −0.698760 | − | 1.21029i | −0.968897 | − | 0.247466i | \(-0.920402\pi\) |
0.270136 | − | 0.962822i | \(-0.412931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5853 | 0.471987 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.47661 | − | 4.28961i | −0.0927497 | − | 0.160647i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.17891 | −0.343272 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.11608 | − | 14.0575i | 0.303100 | − | 0.524985i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.32109 | + | 2.28819i | −0.0492683 | + | 0.0853351i | −0.889608 | − | 0.456725i | \(-0.849022\pi\) |
0.840340 | + | 0.542060i | \(0.182356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.1980 | −1.05015 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6581 | 0.656711 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.30917 | + | 2.26755i | −0.0486213 | + | 0.0842145i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.08653 | + | 8.81013i | −0.188649 | + | 0.326750i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654397i | \(0.227077\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.9284 | 0.775126 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5815 | − | 23.5238i | −0.502329 | − | 0.870060i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8222 | 0.547472 | 0.273736 | − | 0.961805i | \(-0.411741\pi\) | ||||
0.273736 | + | 0.961805i | \(0.411741\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.620199 | + | 1.07422i | 0.0228764 | + | 0.0396231i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.90494 | + | 5.03151i | 0.107005 | + | 0.185338i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7433 | − | 30.7323i | 0.652697 | − | 1.13050i | −0.329769 | − | 0.944062i | \(-0.606971\pi\) |
0.982466 | − | 0.186443i | \(-0.0596959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.276386 | + | 8.05845i | 0.0101533 | + | 0.296035i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.36941 | + | 7.56804i | −0.160298 | + | 0.277645i | −0.934976 | − | 0.354712i | \(-0.884579\pi\) |
0.774677 | + | 0.632357i | \(0.217912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.19642 | − | 12.4646i | −0.263656 | − | 0.456666i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.57641 | − | 4.46247i | −0.0942658 | − | 0.163273i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.6342 | −1.59436 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.54957 | + | 11.3442i | 0.238997 | + | 0.413955i | 0.960427 | − | 0.278533i | \(-0.0898480\pi\) |
−0.721430 | + | 0.692488i | \(0.756515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.08911 | 0.258342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.36093 | − | 11.0175i | 0.231498 | − | 0.400966i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.21901 | − | 14.2357i | 0.298725 | − | 0.517407i | −0.677119 | − | 0.735873i | \(-0.736772\pi\) |
0.975845 | + | 0.218466i | \(0.0701053\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.27397 | 0.227731 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3918 | 0.594203 | 0.297101 | − | 0.954846i | \(-0.403980\pi\) | ||||
0.297101 | + | 0.954846i | \(0.403980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.84879 | + | 11.8625i | −0.247943 | + | 0.429450i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.95171 | + | 8.57661i | −0.179029 | + | 0.310088i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.2242 | −0.621929 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0210 | + | 43.3377i | 0.902282 | + | 1.56280i | 0.824525 | + | 0.565825i | \(0.191442\pi\) |
0.0777564 | + | 0.996972i | \(0.475224\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.142282 | 0.00512416 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.3436 | − | 42.1644i | −0.875580 | − | 1.51655i | −0.856144 | − | 0.516737i | \(-0.827146\pi\) |
−0.0194356 | − | 0.999811i | \(-0.506187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.63457 | − | 4.56320i | −0.0946364 | − | 0.163915i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.08653 | − | 7.07808i | 0.146603 | − | 0.253925i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.2977 | − | 12.9387i | −0.870555 | − | 0.463577i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4185 | − | 44.0261i | 0.909544 | − | 1.57538i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.06771 | + | 12.2416i | 0.252579 | + | 0.437480i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.68765 | + | 2.92309i | 0.0602348 | + | 0.104330i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.51678 | −0.232298 | −0.116149 | − | 0.993232i | \(-0.537055\pi\) | ||||
−0.116149 | + | 0.993232i | \(0.537055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.83388 | − | 10.1046i | −0.207692 | − | 0.359732i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.1820 | −1.35760 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.39668 | + | 14.5435i | −0.298175 | + | 0.516454i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.27364 | − | 2.20600i | 0.0451712 | − | 0.0782388i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.3796 | 1.35947 | 0.679737 | − | 0.733456i | \(-0.262094\pi\) | ||||
0.679737 | + | 0.733456i | \(0.262094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.5834 | 1.89565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.19675 | + | 15.9292i | −0.324951 | + | 0.562832i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.4931 | − | 51.0836i | 1.04079 | − | 1.80270i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.28925 | 0.0806853 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.31243 | − | 5.73729i | −0.116603 | − | 0.201962i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.1409 | 0.883906 | 0.441953 | − | 0.897038i | \(-0.354286\pi\) | ||||
0.441953 | + | 0.897038i | \(0.354286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5053 | − | 40.7124i | −0.825383 | − | 1.42961i | −0.901626 | − | 0.432517i | \(-0.857626\pi\) |
0.0762426 | − | 0.997089i | \(-0.475708\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.37094 | − | 12.7668i | −0.258510 | − | 0.447753i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.153980 | − | 0.266702i | 0.00539369 | − | 0.00934215i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.4642 | − | 9.29984i | −0.610996 | − | 0.325360i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.21416 | + | 5.56708i | −0.112312 | + | 0.194530i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.91021 | + | 17.1650i | 0.345869 | + | 0.599062i | 0.985511 | − | 0.169610i | \(-0.0542509\pi\) |
−0.639642 | + | 0.768673i | \(0.720918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.6084 | − | 33.9627i | −0.683505 | − | 1.18387i | −0.973904 | − | 0.226960i | \(-0.927121\pi\) |
0.290399 | − | 0.956906i | \(-0.406212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.67412 | 0.232363 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.92176 | − | 10.2568i | −0.205920 | − | 0.356663i | 0.744506 | − | 0.667616i | \(-0.232685\pi\) |
−0.950425 | + | 0.310953i | \(0.899352\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.9321 | 1.63002 | 0.815010 | − | 0.579447i | \(-0.196731\pi\) | ||||
0.815010 | + | 0.579447i | \(0.196731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.2070 | + | 17.6790i | −0.354076 | + | 0.613278i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.20008 | + | 5.54270i | −0.110876 | + | 0.192043i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.2643 | −0.493636 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.4461 | −0.983240 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.5669 | + | 46.0153i | −0.917192 | + | 1.58862i | −0.113532 | + | 0.993534i | \(0.536217\pi\) |
−0.803660 | + | 0.595089i | \(0.797117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0722 | − | 19.1775i | 0.381799 | − | 0.661294i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.7755 | −0.818870 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.22797 | + | 9.05511i | 0.179848 | + | 0.311505i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53.8613 | 1.85070 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.87509 | − | 11.9080i | −0.235952 | − | 0.408682i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.36017 | + | 2.35588i | 0.0466259 | + | 0.0807584i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1499 | + | 36.6327i | −0.724159 | + | 1.25428i | 0.235160 | + | 0.971957i | \(0.424438\pi\) |
−0.959319 | + | 0.282324i | \(0.908895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.247272 | + | 7.20959i | 0.00845654 | + | 0.246563i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.7692 | + | 20.3849i | −0.402028 | + | 0.696333i | −0.993971 | − | 0.109647i | \(-0.965028\pi\) |
0.591942 | + | 0.805980i | \(0.298361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.74062 | + | 8.21099i | 0.161748 | + | 0.280156i | 0.935496 | − | 0.353338i | \(-0.114954\pi\) |
−0.773748 | + | 0.633494i | \(0.781620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.91821 | + | 15.4468i | 0.303932 | + | 0.526425i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.8204 | −0.776816 | −0.388408 | − | 0.921487i | \(-0.626975\pi\) | ||||
−0.388408 | + | 0.921487i | \(0.626975\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.67357 | − | 11.5590i | −0.226908 | − | 0.393016i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.8138 | 0.740834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.8813 | − | 37.8996i | 0.742273 | − | 1.28565i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.805144 | + | 1.39455i | −0.0272813 | + | 0.0472525i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.71546 | −0.227284 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.43525 | 0.0823266 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6471 | − | 21.9054i | 0.427062 | − | 0.739693i | −0.569549 | − | 0.821958i | \(-0.692882\pi\) |
0.996611 | + | 0.0822647i | \(0.0262153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.4862 | − | 25.0908i | 0.488606 | − | 0.846291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.2871 | −1.12147 | −0.560736 | − | 0.827995i | \(-0.689482\pi\) | ||||
−0.560736 | + | 0.827995i | \(0.689482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.65544 | − | 13.2596i | −0.257626 | − | 0.446222i | 0.707979 | − | 0.706233i | \(-0.249607\pi\) |
−0.965606 | + | 0.260011i | \(0.916274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.5239 | 0.420988 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.6027 | + | 37.4171i | 0.725349 | + | 1.25634i | 0.958830 | + | 0.283980i | \(0.0916550\pi\) |
−0.233481 | + | 0.972361i | \(0.575012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.45177 | + | 12.9068i | 0.249924 | + | 0.432882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.72962 | − | 6.45990i | 0.124947 | − | 0.216415i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.1132 | − | 20.6628i | 1.10809 | − | 0.691453i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.11036 | + | 12.3155i | −0.237673 | + | 0.411662i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.869457 | + | 1.50594i | 0.0290303 | + | 0.0502820i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.89818 | − | 11.9480i | −0.230067 | − | 0.398488i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1433 | 0.437867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.41007 | + | 11.1026i | 0.213314 | + | 0.369470i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.88263 | 0.328510 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.16392 | − | 12.4083i | 0.237874 | − | 0.412010i | −0.722230 | − | 0.691653i | \(-0.756883\pi\) |
0.960104 | + | 0.279643i | \(0.0902161\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.20994 | + | 15.9521i | −0.305475 | + | 0.529097i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.61162 | 0.152790 | 0.0763949 | − | 0.997078i | \(-0.475659\pi\) | ||||
0.0763949 | + | 0.997078i | \(0.475659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.9177 | −0.592990 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.10535 | − | 10.5748i | 0.201837 | − | 0.349592i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.1196 | + | 31.3841i | −0.598363 | + | 1.03640i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4921 | −0.873892 | −0.436946 | − | 0.899488i | \(-0.643940\pi\) | ||||
−0.436946 | + | 0.899488i | \(0.643940\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.81149 | + | 16.9940i | 0.323300 | + | 0.559972i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0901 | 0.463782 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.44692 | + | 2.50613i | 0.0475744 | + | 0.0824012i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.58148 | − | 16.5956i | −0.314697 | − | 0.545072i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.37863 | − | 4.11990i | 0.0780402 | − | 0.135170i | −0.824364 | − | 0.566060i | \(-0.808467\pi\) |
0.902404 | + | 0.430890i | \(0.141800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.159802 | + | 4.65925i | 0.00523729 | + | 0.152701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.82188 | + | 15.2799i | −0.288815 | + | 0.500243i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.2184 | + | 29.8232i | 0.563103 | + | 0.975322i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.96833 | + | 10.3375i | 0.194977 | + | 0.337710i | 0.946893 | − | 0.321549i | \(-0.104203\pi\) |
−0.751916 | + | 0.659259i | \(0.770870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.9096 | 0.943429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.99715 | + | 15.5835i | 0.293299 | + | 0.508008i | 0.974588 | − | 0.224006i | \(-0.0719136\pi\) |
−0.681289 | + | 0.732015i | \(0.738580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.93670 | −0.193326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.57351 | − | 11.3857i | 0.213836 | − | 0.370375i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6096 | + | 21.8404i | −0.409755 | + | 0.709717i | −0.994862 | − | 0.101239i | \(-0.967719\pi\) |
0.585107 | + | 0.810956i | \(0.301053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.3488 | 0.530705 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.2611 | −0.948858 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.1589 | + | 36.6484i | −0.685405 | + | 1.18716i | 0.287904 | + | 0.957659i | \(0.407042\pi\) |
−0.973309 | + | 0.229498i | \(0.926292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.49710 | + | 11.2533i | −0.210241 | + | 0.364149i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.4751 | 0.564890 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.1263 | − | 36.5918i | −0.682203 | − | 1.18161i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.23623 | −0.104395 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.8266 | − | 25.6805i | −0.477781 | − | 0.827542i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.25795 | − | 12.5711i | −0.233642 | − | 0.404679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.84820 | + | 11.8614i | −0.220223 | + | 0.381438i | −0.954876 | − | 0.297006i | \(-0.904012\pi\) |
0.734652 | + | 0.678444i | \(0.237345\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.6642 | − | 16.0146i | 0.824454 | − | 0.514463i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2906 | + | 33.4123i | −0.619065 | + | 1.07225i | 0.370591 | + | 0.928796i | \(0.379155\pi\) |
−0.989657 | + | 0.143457i | \(0.954178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.16461 | − | 14.1415i | −0.261745 | − | 0.453356i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.924911 | + | 1.60199i | 0.0296209 | + | 0.0513048i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.4592 | −0.558568 | −0.279284 | − | 0.960209i | \(-0.590097\pi\) | ||||
−0.279284 | + | 0.960209i | \(0.590097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.9796 | + | 55.3903i | 1.02207 | + | 1.77028i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.30869 | −0.297204 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.9581 | − | 38.0325i | 0.700353 | − | 1.21305i | −0.267989 | − | 0.963422i | \(-0.586359\pi\) |
0.968342 | − | 0.249625i | \(-0.0803075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.5005 | − | 21.6515i | 0.398299 | − | 0.689875i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.2898 | −0.804984 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.26707 | −0.135685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.1731 | − | 40.1370i | 0.736118 | − | 1.27499i | −0.218112 | − | 0.975924i | \(-0.569990\pi\) |
0.954231 | − | 0.299071i | \(-0.0966767\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.7172 | + | 20.2948i | −0.371834 | + | 0.644035i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.25539 | 0.0715006 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.86857 | − | 10.1647i | −0.185859 | − | 0.321918i | 0.758006 | − | 0.652247i | \(-0.226174\pi\) |
−0.943866 | + | 0.330329i | \(0.892840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.6227 | 0.494281 |
(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 | 1520.2.q.o.961.1 | 8 | ||
4.3 | odd | 2 | 95.2.e.c.11.4 | ✓ | 8 | ||
12.11 | even | 2 | 855.2.k.h.676.1 | 8 | |||
19.7 | even | 3 | inner | 1520.2.q.o.881.1 | 8 | ||
20.3 | even | 4 | 475.2.j.c.49.2 | 16 | |||
20.7 | even | 4 | 475.2.j.c.49.7 | 16 | |||
20.19 | odd | 2 | 475.2.e.e.201.1 | 8 | |||
76.7 | odd | 6 | 95.2.e.c.26.4 | yes | 8 | ||
76.11 | odd | 6 | 1805.2.a.o.1.1 | 4 | |||
76.27 | even | 6 | 1805.2.a.i.1.4 | 4 | |||
228.83 | even | 6 | 855.2.k.h.406.1 | 8 | |||
380.7 | even | 12 | 475.2.j.c.349.2 | 16 | |||
380.83 | even | 12 | 475.2.j.c.349.7 | 16 | |||
380.159 | odd | 6 | 475.2.e.e.26.1 | 8 | |||
380.179 | even | 6 | 9025.2.a.bp.1.1 | 4 | |||
380.239 | odd | 6 | 9025.2.a.bg.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.c.11.4 | ✓ | 8 | 4.3 | odd | 2 | ||
95.2.e.c.26.4 | yes | 8 | 76.7 | odd | 6 | ||
475.2.e.e.26.1 | 8 | 380.159 | odd | 6 | |||
475.2.e.e.201.1 | 8 | 20.19 | odd | 2 | |||
475.2.j.c.49.2 | 16 | 20.3 | even | 4 | |||
475.2.j.c.49.7 | 16 | 20.7 | even | 4 | |||
475.2.j.c.349.2 | 16 | 380.7 | even | 12 | |||
475.2.j.c.349.7 | 16 | 380.83 | even | 12 | |||
855.2.k.h.406.1 | 8 | 228.83 | even | 6 | |||
855.2.k.h.676.1 | 8 | 12.11 | even | 2 | |||
1520.2.q.o.881.1 | 8 | 19.7 | even | 3 | inner | ||
1520.2.q.o.961.1 | 8 | 1.1 | even | 1 | trivial | ||
1805.2.a.i.1.4 | 4 | 76.27 | even | 6 | |||
1805.2.a.o.1.1 | 4 | 76.11 | odd | 6 | |||
9025.2.a.bg.1.4 | 4 | 380.239 | odd | 6 | |||
9025.2.a.bp.1.1 | 4 | 380.179 | even | 6 |