Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(161,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.l (of order \(4\), 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: | \(5.11042572936\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.4 | ||
Root | \(-0.966675 + 1.03225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.161 |
Dual form | 640.2.l.b.481.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.209571 | − | 0.209571i | −0.120996 | − | 0.120996i | 0.644016 | − | 0.765012i | \(-0.277267\pi\) |
−0.765012 | + | 0.644016i | \(0.777267\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73696i | 0.656511i | 0.944589 | + | 0.328255i | \(0.106461\pi\) | ||||
−0.944589 | + | 0.328255i | \(0.893539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.91216i | − | 0.970720i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.505430 | + | 0.505430i | −0.152393 | + | 0.152393i | −0.779186 | − | 0.626793i | \(-0.784367\pi\) |
0.626793 | + | 0.779186i | \(0.284367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.88750 | + | 1.88750i | 0.523498 | + | 0.523498i | 0.918626 | − | 0.395128i | \(-0.129300\pi\) |
−0.395128 | + | 0.918626i | \(0.629300\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.296378 | 0.0765246 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.53524 | 1.09996 | 0.549979 | − | 0.835178i | \(-0.314636\pi\) | ||||
0.549979 | + | 0.835178i | \(0.314636\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.22022 | + | 3.22022i | 0.738768 | + | 0.738768i | 0.972340 | − | 0.233571i | \(-0.0750413\pi\) |
−0.233571 | + | 0.972340i | \(0.575041\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.364018 | − | 0.364018i | 0.0794352 | − | 0.0794352i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.85045i | 1.84545i | 0.385463 | + | 0.922723i | \(0.374042\pi\) | ||||
−0.385463 | + | 0.922723i | \(0.625958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.23902 | + | 1.23902i | −0.238449 | + | 0.238449i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44059 | + | 2.44059i | 0.453205 | + | 0.453205i | 0.896417 | − | 0.443212i | \(-0.146161\pi\) |
−0.443212 | + | 0.896417i | \(0.646161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.70401 | −1.02447 | −0.512235 | − | 0.858845i | \(-0.671182\pi\) | ||||
−0.512235 | + | 0.858845i | \(0.671182\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.211847 | 0.0368779 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.22822 | − | 1.22822i | −0.207607 | − | 0.207607i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.35670 | − | 5.35670i | 0.880636 | − | 0.880636i | −0.112963 | − | 0.993599i | \(-0.536034\pi\) |
0.993599 | + | 0.112963i | \(0.0360342\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.791130i | − | 0.126682i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0343i | 1.56709i | 0.621335 | + | 0.783545i | \(0.286591\pi\) | ||||
−0.621335 | + | 0.783545i | \(0.713409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.10564 | − | 2.10564i | 0.321107 | − | 0.321107i | −0.528085 | − | 0.849192i | \(-0.677090\pi\) |
0.849192 | + | 0.528085i | \(0.177090\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.05921 | + | 2.05921i | 0.306969 | + | 0.306969i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.32303 | 0.630578 | 0.315289 | − | 0.948996i | \(-0.397899\pi\) | ||||
0.315289 | + | 0.948996i | \(0.397899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.98295 | 0.568993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.950456 | − | 0.950456i | −0.133091 | − | 0.133091i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37458 | − | 1.37458i | 0.188814 | − | 0.188814i | −0.606369 | − | 0.795183i | \(-0.707375\pi\) |
0.795183 | + | 0.606369i | \(0.207375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.714786i | − | 0.0963817i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.34973i | − | 0.178776i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.64140 | + | 6.64140i | −0.864637 | + | 0.864637i | −0.991872 | − | 0.127236i | \(-0.959389\pi\) |
0.127236 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.26208 | − | 5.26208i | −0.673741 | − | 0.673741i | 0.284836 | − | 0.958576i | \(-0.408061\pi\) |
−0.958576 | + | 0.284836i | \(0.908061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.05832 | 0.637288 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.66933 | −0.331089 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5578 | + | 10.5578i | 1.28984 | + | 1.28984i | 0.934884 | + | 0.354954i | \(0.115503\pi\) |
0.354954 | + | 0.934884i | \(0.384497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.85480 | − | 1.85480i | 0.223292 | − | 0.223292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.0437i | − | 1.66668i | −0.552764 | − | 0.833338i | \(-0.686427\pi\) | ||
0.552764 | − | 0.833338i | \(-0.313573\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.63830i | − | 0.776954i | −0.921458 | − | 0.388477i | \(-0.873001\pi\) | ||
0.921458 | − | 0.388477i | \(-0.126999\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.209571 | + | 0.209571i | −0.0241992 | + | 0.0241992i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.877914 | − | 0.877914i | −0.100048 | − | 0.100048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.27297 | 0.480746 | 0.240373 | − | 0.970681i | \(-0.422730\pi\) | ||||
0.240373 | + | 0.970681i | \(0.422730\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.21715 | −0.913017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.15483 | − | 9.15483i | −1.00487 | − | 1.00487i | −0.999988 | − | 0.00488547i | \(-0.998445\pi\) |
−0.00488547 | − | 0.999988i | \(-0.501555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20690 | + | 3.20690i | −0.347837 | + | 0.347837i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.02295i | − | 0.109672i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.23826i | 0.343255i | 0.985162 | + | 0.171627i | \(0.0549025\pi\) | ||||
−0.985162 | + | 0.171627i | \(0.945097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.27852 | + | 3.27852i | −0.343682 | + | 0.343682i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.19540 | + | 1.19540i | 0.123957 | + | 0.123957i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.55407 | −0.467238 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.94129 | 0.197108 | 0.0985541 | − | 0.995132i | \(-0.468578\pi\) | ||||
0.0985541 | + | 0.995132i | \(0.468578\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.47189 | + | 1.47189i | 0.147931 | + | 0.147931i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3395 | + | 10.3395i | −1.02882 | + | 1.02882i | −0.0292464 | + | 0.999572i | \(0.509311\pi\) |
−0.999572 | + | 0.0292464i | \(0.990689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.96401i | − | 0.489118i | −0.969634 | − | 0.244559i | \(-0.921357\pi\) | ||
0.969634 | − | 0.244559i | \(-0.0786433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.514799i | 0.0502392i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.74631 | − | 2.74631i | 0.265496 | − | 0.265496i | −0.561787 | − | 0.827282i | \(-0.689886\pi\) |
0.827282 | + | 0.561787i | \(0.189886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.99959 | − | 6.99959i | −0.670439 | − | 0.670439i | 0.287378 | − | 0.957817i | \(-0.407216\pi\) |
−0.957817 | + | 0.287378i | \(0.907216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.24522 | −0.213107 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.53194 | −0.614474 | −0.307237 | − | 0.951633i | \(-0.599404\pi\) | ||||
−0.307237 | + | 0.951633i | \(0.599404\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.25821 | − | 6.25821i | −0.583582 | − | 0.583582i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.49670 | − | 5.49670i | 0.508170 | − | 0.508170i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.87756i | 0.722134i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4891i | 0.953553i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.10289 | − | 2.10289i | 0.189612 | − | 0.189612i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.50861 | −0.222603 | −0.111302 | − | 0.993787i | \(-0.535502\pi\) | ||||
−0.111302 | + | 0.993787i | \(0.535502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.882562 | −0.0777053 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.55783 | − | 8.55783i | −0.747701 | − | 0.747701i | 0.226346 | − | 0.974047i | \(-0.427322\pi\) |
−0.974047 | + | 0.226346i | \(0.927322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.59340 | + | 5.59340i | −0.485009 | + | 0.485009i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.75224i | − | 0.150809i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.47131i | − | 0.552881i | −0.961031 | − | 0.276440i | \(-0.910845\pi\) | ||
0.961031 | − | 0.276440i | \(-0.0891549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4430 | − | 16.4430i | 1.39468 | − | 1.39468i | 0.580223 | − | 0.814458i | \(-0.302965\pi\) |
0.814458 | − | 0.580223i | \(-0.197035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.905982 | − | 0.905982i | −0.0762974 | − | 0.0762974i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.90800 | −0.159555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.45151 | −0.286632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.834712 | − | 0.834712i | −0.0688459 | − | 0.0688459i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.72803 | − | 2.72803i | 0.223489 | − | 0.223489i | −0.586477 | − | 0.809966i | \(-0.699486\pi\) |
0.809966 | + | 0.586477i | \(0.199486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.5196i | − | 0.937453i | −0.883343 | − | 0.468726i | \(-0.844713\pi\) | ||
0.883343 | − | 0.468726i | \(-0.155287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 13.2074i | − | 1.06775i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.03334 | − | 4.03334i | 0.323966 | − | 0.323966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.28013 | − | 3.28013i | −0.261783 | − | 0.261783i | 0.563995 | − | 0.825778i | \(-0.309264\pi\) |
−0.825778 | + | 0.563995i | \(0.809264\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.576147 | −0.0456914 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.3729 | −1.21156 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.27367 | + | 9.27367i | 0.726370 | + | 0.726370i | 0.969895 | − | 0.243525i | \(-0.0783037\pi\) |
−0.243525 | + | 0.969895i | \(0.578304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.149799 | + | 0.149799i | −0.0116618 | + | 0.0116618i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.08065i | 0.547917i | 0.961742 | + | 0.273958i | \(0.0883331\pi\) | ||||
−0.961742 | + | 0.273958i | \(0.911667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.87470i | − | 0.451900i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.37778 | − | 9.37778i | 0.717137 | − | 0.717137i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.21471 | + | 5.21471i | 0.396467 | + | 0.396467i | 0.876985 | − | 0.480518i | \(-0.159551\pi\) |
−0.480518 | + | 0.876985i | \(0.659551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73696 | 0.131302 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.78369 | 0.209235 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.32196 | − | 6.32196i | −0.472525 | − | 0.472525i | 0.430206 | − | 0.902731i | \(-0.358441\pi\) |
−0.902731 | + | 0.430206i | \(0.858441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0695 | + | 13.0695i | −0.971448 | + | 0.971448i | −0.999604 | − | 0.0281553i | \(-0.991037\pi\) |
0.0281553 | + | 0.999604i | \(0.491037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.20556i | 0.163040i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.57552i | 0.556963i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.29225 | + | 2.29225i | −0.167626 | + | 0.167626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.15213 | − | 2.15213i | −0.156545 | − | 0.156545i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1722 | −1.60433 | −0.802164 | − | 0.597104i | \(-0.796318\pi\) | ||||
−0.802164 | + | 0.597104i | \(0.796318\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.97695 | 0.574193 | 0.287097 | − | 0.957902i | \(-0.407310\pi\) | ||||
0.287097 | + | 0.957902i | \(0.407310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.559414 | + | 0.559414i | 0.0400604 | + | 0.0400604i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.76327 | + | 5.76327i | −0.410616 | + | 0.410616i | −0.881953 | − | 0.471337i | \(-0.843772\pi\) |
0.471337 | + | 0.881953i | \(0.343772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.38869i | − | 0.381994i | −0.981591 | − | 0.190997i | \(-0.938828\pi\) | ||
0.981591 | − | 0.190997i | \(-0.0611721\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.42521i | − | 0.312130i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.23921 | + | 4.23921i | −0.297534 | + | 0.297534i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.09530 | − | 7.09530i | −0.495557 | − | 0.495557i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.7739 | 1.79141 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.25519 | −0.225166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7547 | − | 10.7547i | −0.740384 | − | 0.740384i | 0.232268 | − | 0.972652i | \(-0.425385\pi\) |
−0.972652 | + | 0.232268i | \(0.925385\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.94315 | + | 2.94315i | −0.201661 | + | 0.201661i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.97782i | 0.203086i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.90766i | − | 0.672576i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.39120 | + | 1.39120i | −0.0940084 | + | 0.0940084i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.56026 | + | 8.56026i | 0.575826 | + | 0.575826i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.98714 | −0.266998 | −0.133499 | − | 0.991049i | \(-0.542621\pi\) | ||||
−0.133499 | + | 0.991049i | \(0.542621\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.91216 | −0.194144 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.82103 | + | 3.82103i | 0.253611 | + | 0.253611i | 0.822449 | − | 0.568839i | \(-0.192607\pi\) |
−0.568839 | + | 0.822449i | \(0.692607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.80687 | − | 8.80687i | 0.581974 | − | 0.581974i | −0.353471 | − | 0.935445i | \(-0.614999\pi\) |
0.935445 | + | 0.353471i | \(0.114999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.367971i | 0.0242107i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6042i | 1.08778i | 0.839157 | + | 0.543889i | \(0.183049\pi\) | ||||
−0.839157 | + | 0.543889i | \(0.816951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.05684 | + | 3.05684i | −0.199406 | + | 0.199406i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.895491 | − | 0.895491i | −0.0581684 | − | 0.0581684i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.81234 | 0.246600 | 0.123300 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123300 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.54985 | 0.615160 | 0.307580 | − | 0.951522i | \(-0.400481\pi\) | ||||
0.307580 | + | 0.951522i | \(0.400481\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.43913 | + | 5.43913i | 0.348921 | + | 0.348921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.81637 | + | 2.81637i | −0.179932 | + | 0.179932i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1563i | 0.773487i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.83718i | 0.243171i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9933 | + | 11.9933i | −0.757010 | + | 0.757010i | −0.975777 | − | 0.218767i | \(-0.929797\pi\) |
0.218767 | + | 0.975777i | \(0.429797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.47328 | − | 4.47328i | −0.281233 | − | 0.281233i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.34415 | 0.0841738 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.8752 | 1.17740 | 0.588702 | − | 0.808350i | \(-0.299639\pi\) | ||||
0.588702 | + | 0.808350i | \(0.299639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.30440 | + | 9.30440i | 0.578147 | + | 0.578147i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.10738 | − | 7.10738i | 0.439936 | − | 0.439936i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 23.1398i | − | 1.42686i | −0.700727 | − | 0.713429i | \(-0.747141\pi\) | ||
0.700727 | − | 0.713429i | \(-0.252859\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.94396i | 0.119416i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.678646 | − | 0.678646i | 0.0415325 | − | 0.0415325i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.6368 | + | 10.6368i | 0.648539 | + | 0.648539i | 0.952640 | − | 0.304101i | \(-0.0983560\pi\) |
−0.304101 | + | 0.952640i | \(0.598356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.9763 | 1.21348 | 0.606738 | − | 0.794902i | \(-0.292478\pi\) | ||||
0.606738 | + | 0.794902i | \(0.292478\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.37417 | 0.0831683 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.505430 | + | 0.505430i | 0.0304786 | + | 0.0304786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.1534 | − | 16.1534i | 0.970563 | − | 0.970563i | −0.0290160 | − | 0.999579i | \(-0.509237\pi\) |
0.999579 | + | 0.0290160i | \(0.00923738\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.6110i | 0.994474i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.43520i | − | 0.562857i | −0.959582 | − | 0.281429i | \(-0.909192\pi\) | ||
0.959582 | − | 0.281429i | \(-0.0908082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.71287 | + | 8.71287i | −0.517926 | + | 0.517926i | −0.916943 | − | 0.399017i | \(-0.869351\pi\) |
0.399017 | + | 0.916943i | \(0.369351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.954403 | + | 0.954403i | 0.0565339 | + | 0.0565339i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4292 | −1.02881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.56843 | 0.209908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.406838 | − | 0.406838i | −0.0238493 | − | 0.0238493i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1045 | − | 11.1045i | 0.648729 | − | 0.648729i | −0.303957 | − | 0.952686i | \(-0.598308\pi\) |
0.952686 | + | 0.303957i | \(0.0983079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.39236i | − | 0.546844i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.25247i | − | 0.0726759i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.7052 | + | 16.7052i | −0.966087 | + | 0.966087i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.65742 | + | 3.65742i | 0.210810 | + | 0.210810i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.33372 | 0.248966 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.44171 | 0.426111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.99854 | + | 2.99854i | 0.171136 | + | 0.171136i | 0.787478 | − | 0.616343i | \(-0.211386\pi\) |
−0.616343 | + | 0.787478i | \(0.711386\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.04031 | + | 1.04031i | −0.0591814 | + | 0.0591814i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.06099i | 0.513802i | 0.966438 | + | 0.256901i | \(0.0827014\pi\) | ||||
−0.966438 | + | 0.256901i | \(0.917299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5699i | 1.10616i | 0.833129 | + | 0.553078i | \(0.186547\pi\) | ||||
−0.833129 | + | 0.553078i | \(0.813453\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.57677 | + | 3.57677i | −0.201528 | + | 0.201528i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.1019 | + | 11.1019i | 0.623546 | + | 0.623546i | 0.946436 | − | 0.322890i | \(-0.104654\pi\) |
−0.322890 | + | 0.946436i | \(0.604654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.46709 | −0.138131 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.15109 | −0.0642478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6045 | + | 14.6045i | 0.812614 | + | 0.812614i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.88750 | − | 1.88750i | 0.104700 | − | 0.104700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.93382i | 0.162241i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.50894i | 0.413981i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.14718 | − | 8.14718i | 0.447810 | − | 0.447810i | −0.446816 | − | 0.894626i | \(-0.647442\pi\) |
0.894626 | + | 0.446816i | \(0.147442\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.5996 | − | 15.5996i | −0.854851 | − | 0.854851i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.9309 | −0.815765 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.1380 | −1.36935 | −0.684677 | − | 0.728847i | \(-0.740057\pi\) | ||||
−0.684677 | + | 0.728847i | \(0.740057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.36891 | + | 1.36891i | 0.0743488 | + | 0.0743488i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.88298 | − | 2.88298i | 0.156122 | − | 0.156122i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0770i | 1.03006i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.62308i | 0.141222i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.36719 | + | 7.36719i | −0.395491 | + | 0.395491i | −0.876639 | − | 0.481148i | \(-0.840220\pi\) |
0.481148 | + | 0.876639i | \(0.340220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.25982 | + | 3.25982i | 0.174494 | + | 0.174494i | 0.788951 | − | 0.614457i | \(-0.210625\pi\) |
−0.614457 | + | 0.788951i | \(0.710625\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.67729 | −0.249655 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.502832 | 0.0267630 | 0.0133815 | − | 0.999910i | \(-0.495740\pi\) | ||||
0.0133815 | + | 0.999910i | \(0.495740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.93037 | + | 9.93037i | 0.527049 | + | 0.527049i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.65091 | − | 1.65091i | 0.0873754 | − | 0.0873754i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.95161i | − | 0.314114i | −0.987590 | − | 0.157057i | \(-0.949799\pi\) | ||
0.987590 | − | 0.157057i | \(-0.0502007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.73958i | 0.0915571i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.19821 | − | 2.19821i | 0.115376 | − | 0.115376i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.69399 | + | 4.69399i | 0.245695 | + | 0.245695i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.95365 | 0.101980 | 0.0509898 | − | 0.998699i | \(-0.483762\pi\) | ||||
0.0509898 | + | 0.998699i | \(0.483762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.2214 | 1.52121 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.38760 | + | 2.38760i | 0.123958 | + | 0.123958i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6509 | − | 18.6509i | 0.965708 | − | 0.965708i | −0.0337233 | − | 0.999431i | \(-0.510736\pi\) |
0.999431 | + | 0.0337233i | \(0.0107365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 0.296378i | − | 0.0153049i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.21320i | 0.474504i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.85143 | − | 3.85143i | 0.197835 | − | 0.197835i | −0.601236 | − | 0.799071i | \(-0.705325\pi\) |
0.799071 | + | 0.601236i | \(0.205325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.525732 | + | 0.525732i | 0.0269341 | + | 0.0269341i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.29258 | 0.117145 | 0.0585726 | − | 0.998283i | \(-0.481345\pi\) | ||||
0.0585726 | + | 0.998283i | \(0.481345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.24156 | 0.0632757 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.13195 | − | 6.13195i | −0.311705 | − | 0.311705i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.90500 | + | 4.90500i | −0.248693 | + | 0.248693i | −0.820434 | − | 0.571741i | \(-0.806268\pi\) |
0.571741 | + | 0.820434i | \(0.306268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.1389i | 2.02991i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.58695i | 0.180938i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.02144 | + | 3.02144i | −0.152025 | + | 0.152025i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8616 | + | 10.8616i | 0.545126 | + | 0.545126i | 0.925027 | − | 0.379901i | \(-0.124042\pi\) |
−0.379901 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.34443 | 0.117368 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.10783 | −0.354948 | −0.177474 | − | 0.984125i | \(-0.556793\pi\) | ||||
−0.177474 | + | 0.984125i | \(0.556793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.7663 | − | 10.7663i | −0.536308 | − | 0.536308i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.81041 | − | 5.81041i | 0.288721 | − | 0.288721i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.41487i | 0.268405i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.1697i | − | 1.44235i | −0.692752 | − | 0.721176i | \(-0.743602\pi\) | ||
0.692752 | − | 0.721176i | \(-0.256398\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.35620 | + | 1.35620i | −0.0668964 | + | 0.0668964i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5359 | − | 11.5359i | −0.567643 | − | 0.567643i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9469 | 0.635538 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.89198 | −0.337502 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.06616 | − | 3.06616i | −0.149792 | − | 0.149792i | 0.628233 | − | 0.778025i | \(-0.283778\pi\) |
−0.778025 | + | 0.628233i | \(0.783778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.532242 | − | 0.532242i | 0.0259399 | − | 0.0259399i | −0.694018 | − | 0.719958i | \(-0.744161\pi\) |
0.719958 | + | 0.694018i | \(0.244161\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 12.5893i | − | 0.612115i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.53524i | − | 0.219992i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.14005 | − | 9.14005i | 0.442318 | − | 0.442318i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.399861 | + | 0.399861i | 0.0193055 | + | 0.0193055i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7237 | 0.805555 | 0.402777 | − | 0.915298i | \(-0.368045\pi\) | ||||
0.402777 | + | 0.915298i | \(0.368045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.3675 | 1.36326 | 0.681628 | − | 0.731699i | \(-0.261272\pi\) | ||||
0.681628 | + | 0.731699i | \(0.261272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.723337 | + | 0.723337i | 0.0346814 | + | 0.0346814i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.5004 | + | 28.5004i | −1.36336 | + | 1.36336i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.5018i | − | 0.644405i | −0.946671 | − | 0.322203i | \(-0.895577\pi\) | ||
0.946671 | − | 0.322203i | \(-0.104423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 11.5990i | − | 0.552333i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.55246 | − | 9.55246i | 0.453851 | − | 0.453851i | −0.442780 | − | 0.896630i | \(-0.646008\pi\) |
0.896630 | + | 0.442780i | \(0.146008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.28980 | − | 2.28980i | −0.108547 | − | 0.108547i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.14343 | −0.0540824 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.35573 | −0.441524 | −0.220762 | − | 0.975328i | \(-0.570854\pi\) | ||||
−0.220762 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.07162 | − | 5.07162i | −0.238813 | − | 0.238813i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.41418 | + | 2.41418i | −0.113428 | + | 0.113428i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.63652i | − | 0.217364i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.84779i | − | 0.320326i | −0.987091 | − | 0.160163i | \(-0.948798\pi\) | ||
0.987091 | − | 0.160163i | \(-0.0512020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.61925 | + | 5.61925i | −0.262284 | + | 0.262284i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7403 | + | 11.7403i | 0.546801 | + | 0.546801i | 0.925514 | − | 0.378713i | \(-0.123633\pi\) |
−0.378713 | + | 0.925514i | \(0.623633\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6096 | −1.23665 | −0.618326 | − | 0.785922i | \(-0.712189\pi\) | ||||
−0.618326 | + | 0.785922i | \(0.712189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.69055 | −0.0783972 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.47583 | − | 1.47583i | −0.0682933 | − | 0.0682933i | 0.672135 | − | 0.740428i | \(-0.265377\pi\) |
−0.740428 | + | 0.672135i | \(0.765377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.3385 | + | 18.3385i | −0.846792 | + | 0.846792i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.37484i | 0.0633494i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.12851i | 0.0978688i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.22022 | − | 3.22022i | 0.147754 | − | 0.147754i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.00301 | − | 4.00301i | −0.183285 | − | 0.183285i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.78600 | −0.127296 | −0.0636479 | − | 0.997972i | \(-0.520273\pi\) | ||||
−0.0636479 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2215 | 0.922022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.22172 | + | 3.22172i | 0.146593 | + | 0.146593i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.37270 | + | 1.37270i | −0.0623311 | + | 0.0623311i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.9499i | − | 0.768073i | −0.923318 | − | 0.384036i | \(-0.874534\pi\) | ||
0.923318 | − | 0.384036i | \(-0.125466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.88699i | − | 0.175776i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.8390 | − | 22.8390i | 1.03071 | − | 1.03071i | 0.0311972 | − | 0.999513i | \(-0.490068\pi\) |
0.999513 | − | 0.0311972i | \(-0.00993197\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0687 | + | 11.0687i | 0.498507 | + | 0.498507i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.08157 | −0.0935597 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.3933 | 1.09419 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.33906 | − | 2.33906i | −0.104711 | − | 0.104711i | 0.652811 | − | 0.757521i | \(-0.273590\pi\) |
−0.757521 | + | 0.652811i | \(0.773590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.48390 | − | 1.48390i | 0.0662958 | − | 0.0662958i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.58801i | 0.0708057i | 0.999373 | + | 0.0354029i | \(0.0112714\pi\) | ||||
−0.999373 | + | 0.0354029i | \(0.988729\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 14.6223i | − | 0.650682i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.23117 | + | 1.23117i | −0.0546781 | + | 0.0546781i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.61613 | + | 3.61613i | 0.160282 | + | 0.160282i | 0.782692 | − | 0.622410i | \(-0.213846\pi\) |
−0.622410 | + | 0.782692i | \(0.713846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.5305 | 0.510079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.97981 | −0.352317 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.51009 | + | 3.51009i | 0.154673 | + | 0.154673i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.18499 | + | 2.18499i | −0.0960956 | + | 0.0960956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.18571i | − | 0.0959419i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.93031i | − | 0.391244i | −0.980679 | − | 0.195622i | \(-0.937327\pi\) | ||
0.980679 | − | 0.195622i | \(-0.0626725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0355 | + | 15.0355i | −0.657455 | + | 0.657455i | −0.954777 | − | 0.297323i | \(-0.903906\pi\) |
0.297323 | + | 0.954777i | \(0.403906\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.364018 | − | 0.364018i | −0.0158870 | − | 0.0158870i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.8691 | −1.12687 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.3305 | −2.40567 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.3408 | + | 19.3408i | 0.839320 | + | 0.839320i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.9397 | + | 18.9397i | −0.820368 | + | 0.820368i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.88387i | 0.167914i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.64980i | 0.114347i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.01310 | + | 2.01310i | −0.0867106 | + | 0.0867106i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.57591 | − | 5.57591i | −0.239727 | − | 0.239727i | 0.577010 | − | 0.816737i | \(-0.304219\pi\) |
−0.816737 | + | 0.577010i | \(0.804219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.47798 | 0.235083 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.89891 | 0.424023 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.8366 | − | 32.8366i | −1.40399 | − | 1.40399i | −0.786856 | − | 0.617136i | \(-0.788293\pi\) |
−0.617136 | − | 0.786856i | \(-0.711707\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.3240 | + | 15.3240i | −0.654013 | + | 0.654013i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.7184i | 0.669628i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.42199i | 0.315615i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.58761 | − | 1.58761i | 0.0673903 | − | 0.0673903i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2077 | − | 24.2077i | −1.02571 | − | 1.02571i | −0.999661 | − | 0.0260537i | \(-0.991706\pi\) |
−0.0260537 | − | 0.999661i | \(-0.508294\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.94877 | 0.336197 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.960778 | 0.0405641 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.3407 | − | 22.3407i | −0.941547 | − | 0.941547i | 0.0568365 | − | 0.998384i | \(-0.481899\pi\) |
−0.998384 | + | 0.0568365i | \(0.981899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.61878 | − | 4.61878i | 0.194314 | − | 0.194314i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 14.2729i | − | 0.599406i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3339i | 1.22974i | 0.788629 | + | 0.614870i | \(0.210791\pi\) | ||||
−0.788629 | + | 0.614870i | \(0.789209\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9934 | + | 23.9934i | −1.00409 | + | 1.00409i | −0.00410070 | + | 0.999992i | \(0.501305\pi\) |
−0.999992 | + | 0.00410070i | \(0.998695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.64666 | + | 4.64666i | 0.194117 | + | 0.194117i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.85045 | 0.369089 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.9232 | −1.32898 | −0.664490 | − | 0.747297i | \(-0.731351\pi\) | ||||
−0.664490 | + | 0.747297i | \(0.731351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.67174 | − | 1.67174i | −0.0694751 | − | 0.0694751i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.9016 | − | 15.9016i | 0.659710 | − | 0.659710i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.38951i | 0.0575477i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.77350i | 0.321395i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.2847 | − | 26.2847i | 1.08488 | − | 1.08488i | 0.0888379 | − | 0.996046i | \(-0.471685\pi\) |
0.996046 | − | 0.0888379i | \(-0.0283153\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3681 | − | 18.3681i | −0.756846 | − | 0.756846i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.41563 | 0.0993658 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.2085 | −1.56904 | −0.784518 | − | 0.620106i | \(-0.787090\pi\) | ||||
−0.784518 | + | 0.620106i | \(0.787090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.57027 | − | 5.57027i | −0.228359 | − | 0.228359i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.12931 | + | 1.12931i | −0.0462197 | + | 0.0462197i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.1150i | − | 1.02617i | −0.858337 | − | 0.513086i | \(-0.828502\pi\) | ||
0.858337 | − | 0.513086i | \(-0.171498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.2022i | − | 0.905647i | −0.891600 | − | 0.452823i | \(-0.850417\pi\) | ||
0.891600 | − | 0.452823i | \(-0.149583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.7459 | − | 30.7459i | 1.25207 | − | 1.25207i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.41690 | − | 7.41690i | −0.301540 | − | 0.301540i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9648 | 0.526226 | 0.263113 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.77683 | 0.0720009 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.15970 | + | 8.15970i | 0.330106 | + | 0.330106i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.42804 | + | 7.42804i | −0.300016 | + | 0.300016i | −0.841020 | − | 0.541004i | \(-0.818044\pi\) |
0.541004 | + | 0.841020i | \(0.318044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.97394i | 0.119921i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2743i | 0.936989i | 0.883467 | + | 0.468494i | \(0.155203\pi\) | ||||
−0.883467 | + | 0.468494i | \(0.844797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.6213 | − | 31.6213i | 1.27097 | − | 1.27097i | 0.325386 | − | 0.945581i | \(-0.394506\pi\) |
0.945581 | − | 0.325386i | \(-0.105494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.9659 | − | 10.9659i | −0.440045 | − | 0.440045i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.62474 | −0.225351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.682194 | + | 0.682194i | 0.0272442 | + | 0.0272442i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.2939 | − | 24.2939i | 0.968663 | − | 0.968663i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 29.9258i | − | 1.19133i | −0.803234 | − | 0.595663i | \(-0.796889\pi\) | ||
0.803234 | − | 0.595663i | \(-0.203111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.50775i | 0.179167i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.77386 | − | 1.77386i | 0.0703933 | − | 0.0703933i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.51782 | + | 7.51782i | 0.297867 | + | 0.297867i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.8974 | −1.61788 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2240 | 0.403825 | 0.201912 | − | 0.979404i | \(-0.435284\pi\) | ||||
0.201912 | + | 0.979404i | \(0.435284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7202 | + | 13.7202i | 0.541074 | + | 0.541074i | 0.923844 | − | 0.382770i | \(-0.125030\pi\) |
−0.382770 | + | 0.923844i | \(0.625030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.624066 | − | 0.624066i | 0.0245726 | − | 0.0245726i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 18.6767i | − | 0.734255i | −0.930171 | − | 0.367128i | \(-0.880341\pi\) | ||
0.930171 | − | 0.367128i | \(-0.119659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.71353i | − | 0.263529i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.07636 | + | 2.07636i | −0.0813790 | + | 0.0813790i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7935 | − | 12.7935i | −0.500647 | − | 0.500647i | 0.410992 | − | 0.911639i | \(-0.365183\pi\) |
−0.911639 | + | 0.410992i | \(0.865183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.1026 | 0.472888 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.3318 | −0.754205 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3193 | − | 12.3193i | −0.479893 | − | 0.479893i | 0.425204 | − | 0.905097i | \(-0.360202\pi\) |
−0.905097 | + | 0.425204i | \(0.860202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0352 | − | 24.0352i | 0.934862 | − | 0.934862i | −0.0631421 | − | 0.998005i | \(-0.520112\pi\) |
0.998005 | + | 0.0631421i | \(0.0201121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.58797i | − | 0.139345i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 7.91026i | − | 0.306747i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.6003 | + | 21.6003i | −0.836367 | + | 0.836367i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.835589 | + | 0.835589i | 0.0323057 | + | 0.0323057i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.31923 | 0.205347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.5360 | −0.830150 | −0.415075 | − | 0.909787i | \(-0.636245\pi\) | ||||
−0.415075 | + | 0.909787i | \(0.636245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.23902 | + | 1.23902i | 0.0476898 | + | 0.0476898i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1852 | + | 13.1852i | −0.506750 | + | 0.506750i | −0.913527 | − | 0.406778i | \(-0.866652\pi\) |
0.406778 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.37195i | 0.129404i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.60156i | − | 0.0613717i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.6011 | + | 30.6011i | −1.17092 | + | 1.17092i | −0.188926 | + | 0.981991i | \(0.560501\pi\) |
−0.981991 | + | 0.188926i | \(0.939499\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.57590 | + | 4.57590i | 0.174836 | + | 0.174836i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.69133 | −0.140833 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.18905 | 0.197687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2675 | + | 25.2675i | 0.961220 | + | 0.961220i | 0.999276 | − | 0.0380558i | \(-0.0121165\pi\) |
−0.0380558 | + | 0.999276i | \(0.512116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.55663 | + | 2.55663i | −0.0971182 | + | 0.0971182i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.2540i | 0.882074i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.5079i | 1.72373i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.47976 | − | 3.47976i | 0.131617 | − | 0.131617i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5583 | − | 18.5583i | −0.700937 | − | 0.700937i | 0.263675 | − | 0.964612i | \(-0.415065\pi\) |
−0.964612 | + | 0.263675i | \(0.915065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4995 | 1.30117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.28125 | 0.0482547 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.9593 | − | 17.9593i | −0.675431 | − | 0.675431i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.38093 | + | 4.38093i | −0.164529 | + | 0.164529i | −0.784570 | − | 0.620040i | \(-0.787116\pi\) |
0.620040 | + | 0.784570i | \(0.287116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 12.4436i | − | 0.466670i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 50.4831i | − | 1.89061i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.34916 | − | 1.34916i | 0.0504556 | − | 0.0504556i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.798957 | − | 0.798957i | −0.0298376 | − | 0.0298376i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.61691 | 0.0603007 | 0.0301503 | − | 0.999545i | \(-0.490401\pi\) | ||||
0.0301503 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.62231 | 0.321112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00137 | − | 2.00137i | −0.0744319 | − | 0.0744319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44059 | − | 2.44059i | 0.0906411 | − | 0.0906411i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.3600i | − | 1.45978i | −0.683563 | − | 0.729891i | \(-0.739571\pi\) | ||
0.683563 | − | 0.729891i | \(-0.260429\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3717i | 0.828581i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.54958 | − | 9.54958i | 0.353204 | − | 0.353204i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0787 | + | 34.0787i | 1.25873 | + | 1.25873i | 0.951701 | + | 0.307026i | \(0.0993339\pi\) |
0.307026 | + | 0.951701i | \(0.400666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.18046 | 0.0435420 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.6724 | −0.393124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4278 | − | 15.4278i | −0.567520 | − | 0.567520i | 0.363913 | − | 0.931433i | \(-0.381441\pi\) |
−0.931433 | + | 0.363913i | \(0.881441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.54761 | − | 2.54761i | 0.0935888 | − | 0.0935888i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.5004i | − | 0.862147i | −0.902317 | − | 0.431074i | \(-0.858135\pi\) | ||
0.902317 | − | 0.431074i | \(-0.141865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.85801i | 0.141347i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.6603 | + | 26.6603i | −0.975451 | + | 0.975451i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.77024 | + | 4.77024i | 0.174301 | + | 0.174301i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8586 | 0.396236 | 0.198118 | − | 0.980178i | \(-0.436517\pi\) | ||||
0.198118 | + | 0.980178i | \(0.436517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.02690 | 0.183190 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.14560 | + | 8.14560i | 0.296449 | + | 0.296449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.8434 | + | 18.8434i | −0.684874 | + | 0.684874i | −0.961094 | − | 0.276220i | \(-0.910918\pi\) |
0.276220 | + | 0.961094i | \(0.410918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.87494i | 0.0680561i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2837i | 0.807783i | 0.914807 | + | 0.403891i | \(0.132343\pi\) | ||||
−0.914807 | + | 0.403891i | \(0.867657\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1580 | − | 12.1580i | 0.440151 | − | 0.440151i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.33901 | + | 9.33901i | 0.337653 | + | 0.337653i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.0713 | −0.905271 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.5399 | 0.380077 | 0.190039 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190039 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.95571 | − | 3.95571i | −0.142461 | − | 0.142461i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.07768 | + | 4.07768i | −0.146664 | + | 0.146664i | −0.776626 | − | 0.629962i | \(-0.783070\pi\) |
0.629962 | + | 0.776626i | \(0.283070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.70401i | 0.204894i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 3.89987i | − | 0.139907i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.3125 | + | 32.3125i | −1.15772 | + | 1.15772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.09809 | + | 7.09809i | 0.253990 | + | 0.253990i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.04786 | −0.216133 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.63881 | 0.165566 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.16669 | + | 8.16669i | 0.291111 | + | 0.291111i | 0.837519 | − | 0.546408i | \(-0.184005\pi\) |
−0.546408 | + | 0.837519i | \(0.684005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.84943 | + | 4.84943i | −0.172644 | + | 0.172644i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.3458i | − | 0.403409i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 19.8643i | − | 0.705403i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.407397 | − | 0.407397i | 0.0144489 | − | 0.0144489i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.9971 | − | 17.9971i | −0.637491 | − | 0.637491i | 0.312445 | − | 0.949936i | \(-0.398852\pi\) |
−0.949936 | + | 0.312445i | \(0.898852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.6060 | 0.693609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.43033 | 0.333204 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.35520 | + | 3.35520i | 0.118402 | + | 0.118402i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.8703 | − | 10.8703i | 0.383128 | − | 0.383128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.45835i | − | 0.156941i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.0296i | 1.47768i | 0.673879 | + | 0.738841i | \(0.264627\pi\) | ||||
−0.673879 | + | 0.738841i | \(0.735373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7601 | + | 18.7601i | −0.658757 | + | 0.658757i | −0.955086 | − | 0.296329i | \(-0.904238\pi\) |
0.296329 | + | 0.955086i | \(0.404238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.18646 | − | 4.18646i | −0.146826 | − | 0.146826i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.1149 | −0.459397 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5612 | 0.474447 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.54757 | + | 9.54757i | 0.333619 | + | 0.333619i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.4050 | − | 21.4050i | 0.747038 | − | 0.747038i | −0.226884 | − | 0.973922i | \(-0.572854\pi\) |
0.973922 | + | 0.226884i | \(0.0728538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.7323i | 1.52441i | 0.647334 | + | 0.762206i | \(0.275884\pi\) | ||||
−0.647334 | + | 0.762206i | \(0.724116\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.211847i | − | 0.00737557i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.9621 | − | 19.9621i | 0.694149 | − | 0.694149i | −0.268993 | − | 0.963142i | \(-0.586691\pi\) |
0.963142 | + | 0.268993i | \(0.0866908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.3869 | − | 31.3869i | −1.09011 | − | 1.09011i | −0.995516 | − | 0.0945964i | \(-0.969844\pi\) |
−0.0945964 | − | 0.995516i | \(-0.530156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.77057 | −0.234868 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0637 | 0.625869 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.00677 | − | 5.00677i | −0.173267 | − | 0.173267i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.06737 | − | 7.06737i | 0.244284 | − | 0.244284i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.5335i | 1.88271i | 0.337423 | + | 0.941353i | \(0.390445\pi\) | ||||
−0.337423 | + | 0.941353i | \(0.609555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 17.0871i | − | 0.589210i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.97735 | + | 1.97735i | −0.0681035 | + | 0.0681035i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.15404 | + | 4.15404i | 0.142903 | + | 0.142903i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.2192 | −0.626018 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.65193 | 0.125334 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.4092 | + | 47.4092i | 1.62517 | + | 1.62517i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.5932 | + | 21.5932i | −0.739336 | + | 0.739336i | −0.972449 | − | 0.233114i | \(-0.925109\pi\) |
0.233114 | + | 0.972449i | \(0.425109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.2622i | 0.453557i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 41.3609i | − | 1.41286i | −0.707782 | − | 0.706431i | \(-0.750304\pi\) | ||
0.707782 | − | 0.706431i | \(-0.249696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.700596 | − | 0.700596i | 0.0239040 | − | 0.0239040i | −0.695054 | − | 0.718958i | \(-0.744619\pi\) |
0.718958 | + | 0.695054i | \(0.244619\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.65265 | + | 3.65265i | 0.124482 | + | 0.124482i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.0780 | 1.87488 | 0.937439 | − | 0.348150i | \(-0.113190\pi\) | ||||
0.937439 | + | 0.348150i | \(0.113190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.37471 | −0.250748 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.747840 | − | 0.747840i | −0.0253980 | − | 0.0253980i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.15969 | + | 2.15969i | −0.0732623 | + | 0.0732623i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.8556i | 1.35045i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.65335i | − | 0.191337i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.22822 | + | 1.22822i | −0.0415214 | + | 0.0415214i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.5100 | + | 36.5100i | 1.23285 | + | 1.23285i | 0.962863 | + | 0.269992i | \(0.0870211\pi\) |
0.269992 | + | 0.962863i | \(0.412979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.65435 | −0.156987 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.3503 | 1.83111 | 0.915554 | − | 0.402196i | \(-0.131753\pi\) | ||||
0.915554 | + | 0.402196i | \(0.131753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.5476 | − | 35.5476i | −1.19627 | − | 1.19627i | −0.975274 | − | 0.220999i | \(-0.929068\pi\) |
−0.220999 | − | 0.975274i | \(-0.570932\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.96837 | + | 1.96837i | −0.0661660 | + | 0.0661660i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.817003i | − | 0.0274323i | −0.999906 | − | 0.0137161i | \(-0.995634\pi\) | ||
0.999906 | − | 0.0137161i | \(-0.00436612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.35737i | − | 0.146141i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.15320 | − | 4.15320i | 0.139137 | − | 0.139137i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.9211 | + | 13.9211i | 0.465851 | + | 0.465851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.94060 | 0.298851 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.00186 | 0.233785 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.9211 | − | 13.9211i | −0.464296 | − | 0.464296i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.23407 | − | 6.23407i | 0.207687 | − | 0.207687i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.53298i | − | 0.0510144i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.4831i | − | 0.614398i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.36159 | − | 3.36159i | 0.111620 | − | 0.111620i | −0.649091 | − | 0.760711i | \(-0.724851\pi\) |
0.760711 | + | 0.649091i | \(0.224851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.1103 | + | 30.1103i | 0.998695 | + | 0.998695i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6568 | 1.14823 | 0.574116 | − | 0.818774i | \(-0.305346\pi\) | ||||
0.574116 | + | 0.818774i | \(0.305346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.25426 | 0.306271 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.55957 | − | 1.55957i | −0.0515577 | − | 0.0515577i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.8646 | − | 14.8646i | 0.490874 | − | 0.490874i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24.3452i | − | 0.803074i | −0.915843 | − | 0.401537i | \(-0.868476\pi\) | ||
0.915843 | − | 0.401537i | \(-0.131524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.25681i | − | 0.0414135i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.5074 | − | 26.5074i | 0.872501 | − | 0.872501i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.35670 | − | 5.35670i | −0.176127 | − | 0.176127i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.4560 | −0.474797 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.16600 | 0.103873 | 0.0519366 | − | 0.998650i | \(-0.483461\pi\) | ||||
0.0519366 | + | 0.998650i | \(0.483461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.8260 | + | 12.8260i | 0.420354 | + | 0.420354i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.89892 | − | 1.89892i | 0.0621680 | − | 0.0621680i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.24173i | − | 0.106016i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4847i | 0.767211i | 0.923497 | + | 0.383606i | \(0.125318\pi\) | ||||
−0.923497 | + | 0.383606i | \(0.874682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.10129 | − | 4.10129i | 0.133840 | − | 0.133840i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.7583 | − | 27.7583i | −0.904896 | − | 0.904896i | 0.0909585 | − | 0.995855i | \(-0.471007\pi\) |
−0.995855 | + | 0.0909585i | \(0.971007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −88.8078 | −2.89198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.04357 | 0.0990074 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.2916 | + | 27.2916i | 0.886857 | + | 0.886857i | 0.994220 | − | 0.107363i | \(-0.0342407\pi\) |
−0.107363 | + | 0.994220i | \(0.534241\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.5298 | − | 12.5298i | 0.406734 | − | 0.406734i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.65329i | − | 0.150893i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.1516i | − | 0.393630i | −0.980441 | − | 0.196815i | \(-0.936940\pi\) | ||
0.980441 | − | 0.196815i | \(-0.0630598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.6781 | − | 15.6781i | 0.507333 | − | 0.507333i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.517031 | + | 0.517031i | 0.0167132 | + | 0.0167132i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2404 | 0.362972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.53571 | 0.0495392 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.99769 | − | 7.99769i | −0.257722 | − | 0.257722i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.64056 | + | 5.64056i | −0.181576 | + | 0.181576i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2694i | 1.55224i | 0.630585 | + | 0.776120i | \(0.282815\pi\) | ||||
−0.630585 | + | 0.776120i | \(0.717185\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.12135i | − | 0.196646i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.92047 | + | 5.92047i | −0.189997 | + | 0.189997i | −0.795695 | − | 0.605698i | \(-0.792894\pi\) |
0.605698 | + | 0.795695i | \(0.292894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.5610 | + | 28.5610i | 0.915623 | + | 0.915623i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.791130 | −0.0253365 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.7522 | −0.887872 | −0.443936 | − | 0.896059i | \(-0.646418\pi\) | ||||
−0.443936 | + | 0.896059i | \(0.646418\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.63671 | − | 1.63671i | −0.0523096 | − | 0.0523096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.3839 | + | 20.3839i | −0.650808 | + | 0.650808i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.3604i | 0.904556i | 0.891877 | + | 0.452278i | \(0.149389\pi\) | ||||
−0.891877 | + | 0.452278i | \(0.850611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.15050i | − | 0.259697i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.57366 | − | 1.57366i | 0.0500901 | − | 0.0500901i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.6358 | + | 18.6358i | 0.592585 | + | 0.592585i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7506 | −1.38979 | −0.694893 | − | 0.719114i | \(-0.744548\pi\) | ||||
−0.694893 | + | 0.719114i | \(0.744548\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.41483 | −0.108366 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.81038 | + | 3.81038i | 0.120797 | + | 0.120797i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.5572 | + | 10.5572i | −0.334349 | + | 0.334349i | −0.854235 | − | 0.519887i | \(-0.825974\pi\) |
0.519887 | + | 0.854235i | \(0.325974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.2741i | 0.419974i |
(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 | 640.2.l.b.161.4 | 16 | ||
4.3 | odd | 2 | 640.2.l.a.161.5 | 16 | |||
8.3 | odd | 2 | 320.2.l.a.81.4 | 16 | |||
8.5 | even | 2 | 80.2.l.a.61.6 | yes | 16 | ||
16.3 | odd | 4 | 320.2.l.a.241.4 | 16 | |||
16.5 | even | 4 | inner | 640.2.l.b.481.4 | 16 | ||
16.11 | odd | 4 | 640.2.l.a.481.5 | 16 | |||
16.13 | even | 4 | 80.2.l.a.21.6 | ✓ | 16 | ||
24.5 | odd | 2 | 720.2.t.c.541.3 | 16 | |||
24.11 | even | 2 | 2880.2.t.c.721.1 | 16 | |||
32.5 | even | 8 | 5120.2.a.s.1.6 | 8 | |||
32.11 | odd | 8 | 5120.2.a.t.1.6 | 8 | |||
32.21 | even | 8 | 5120.2.a.v.1.3 | 8 | |||
32.27 | odd | 8 | 5120.2.a.u.1.3 | 8 | |||
40.3 | even | 4 | 1600.2.q.h.849.5 | 16 | |||
40.13 | odd | 4 | 400.2.q.g.349.7 | 16 | |||
40.19 | odd | 2 | 1600.2.l.i.401.5 | 16 | |||
40.27 | even | 4 | 1600.2.q.g.849.4 | 16 | |||
40.29 | even | 2 | 400.2.l.h.301.3 | 16 | |||
40.37 | odd | 4 | 400.2.q.h.349.2 | 16 | |||
48.29 | odd | 4 | 720.2.t.c.181.3 | 16 | |||
48.35 | even | 4 | 2880.2.t.c.2161.4 | 16 | |||
80.3 | even | 4 | 1600.2.q.g.49.4 | 16 | |||
80.13 | odd | 4 | 400.2.q.h.149.2 | 16 | |||
80.19 | odd | 4 | 1600.2.l.i.1201.5 | 16 | |||
80.29 | even | 4 | 400.2.l.h.101.3 | 16 | |||
80.67 | even | 4 | 1600.2.q.h.49.5 | 16 | |||
80.77 | odd | 4 | 400.2.q.g.149.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.6 | ✓ | 16 | 16.13 | even | 4 | ||
80.2.l.a.61.6 | yes | 16 | 8.5 | even | 2 | ||
320.2.l.a.81.4 | 16 | 8.3 | odd | 2 | |||
320.2.l.a.241.4 | 16 | 16.3 | odd | 4 | |||
400.2.l.h.101.3 | 16 | 80.29 | even | 4 | |||
400.2.l.h.301.3 | 16 | 40.29 | even | 2 | |||
400.2.q.g.149.7 | 16 | 80.77 | odd | 4 | |||
400.2.q.g.349.7 | 16 | 40.13 | odd | 4 | |||
400.2.q.h.149.2 | 16 | 80.13 | odd | 4 | |||
400.2.q.h.349.2 | 16 | 40.37 | odd | 4 | |||
640.2.l.a.161.5 | 16 | 4.3 | odd | 2 | |||
640.2.l.a.481.5 | 16 | 16.11 | odd | 4 | |||
640.2.l.b.161.4 | 16 | 1.1 | even | 1 | trivial | ||
640.2.l.b.481.4 | 16 | 16.5 | even | 4 | inner | ||
720.2.t.c.181.3 | 16 | 48.29 | odd | 4 | |||
720.2.t.c.541.3 | 16 | 24.5 | odd | 2 | |||
1600.2.l.i.401.5 | 16 | 40.19 | odd | 2 | |||
1600.2.l.i.1201.5 | 16 | 80.19 | odd | 4 | |||
1600.2.q.g.49.4 | 16 | 80.3 | even | 4 | |||
1600.2.q.g.849.4 | 16 | 40.27 | even | 4 | |||
1600.2.q.h.49.5 | 16 | 80.67 | even | 4 | |||
1600.2.q.h.849.5 | 16 | 40.3 | even | 4 | |||
2880.2.t.c.721.1 | 16 | 24.11 | even | 2 | |||
2880.2.t.c.2161.4 | 16 | 48.35 | even | 4 | |||
5120.2.a.s.1.6 | 8 | 32.5 | even | 8 | |||
5120.2.a.t.1.6 | 8 | 32.11 | odd | 8 | |||
5120.2.a.u.1.3 | 8 | 32.27 | odd | 8 | |||
5120.2.a.v.1.3 | 8 | 32.21 | even | 8 |