Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9036,2,Mod(1,9036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9036.a (trivial) |
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: | yes |
Analytic conductor: | \(72.1528232664\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 8x^{3} - 17x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.844838\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.47034 | 1.10477 | 0.552385 | − | 0.833589i | \(-0.313718\pi\) | ||||
0.552385 | + | 0.833589i | \(0.313718\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.972158 | −0.367441 | −0.183721 | − | 0.982979i | \(-0.558814\pi\) | ||||
−0.183721 | + | 0.982979i | \(0.558814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.50942 | −1.05813 | −0.529064 | − | 0.848582i | \(-0.677457\pi\) | ||||
−0.529064 | + | 0.848582i | \(0.677457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.87894 | 0.798473 | 0.399237 | − | 0.916848i | \(-0.369275\pi\) | ||||
0.399237 | + | 0.916848i | \(0.369275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.27070 | 0.550725 | 0.275362 | − | 0.961340i | \(-0.411202\pi\) | ||||
0.275362 | + | 0.961340i | \(0.411202\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.78729 | −1.55711 | −0.778556 | − | 0.627576i | \(-0.784047\pi\) | ||||
−0.778556 | + | 0.627576i | \(0.784047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.58090 | −0.746670 | −0.373335 | − | 0.927697i | \(-0.621786\pi\) | ||||
−0.373335 | + | 0.927697i | \(0.621786\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.10259 | 0.220518 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.60769 | 1.41271 | 0.706356 | − | 0.707857i | \(-0.250338\pi\) | ||||
0.706356 | + | 0.707857i | \(0.250338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.279626 | −0.0502224 | −0.0251112 | − | 0.999685i | \(-0.507994\pi\) | ||||
−0.0251112 | + | 0.999685i | \(0.507994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.40156 | −0.405938 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.37051 | −1.54050 | −0.770251 | − | 0.637741i | \(-0.779869\pi\) | ||||
−0.770251 | + | 0.637741i | \(0.779869\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4728 | 1.63558 | 0.817791 | − | 0.575516i | \(-0.195199\pi\) | ||||
0.817791 | + | 0.575516i | \(0.195199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.70457 | −0.869939 | −0.434970 | − | 0.900445i | \(-0.643241\pi\) | ||||
−0.434970 | + | 0.900445i | \(0.643241\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.12711 | 1.18546 | 0.592730 | − | 0.805401i | \(-0.298050\pi\) | ||||
0.592730 | + | 0.805401i | \(0.298050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05491 | −0.864987 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.01555 | −0.139497 | −0.0697484 | − | 0.997565i | \(-0.522220\pi\) | ||||
−0.0697484 | + | 0.997565i | \(0.522220\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.66946 | −1.16899 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.3081 | −1.60238 | −0.801188 | − | 0.598413i | \(-0.795798\pi\) | ||||
−0.801188 | + | 0.598413i | \(0.795798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.95423 | 1.27451 | 0.637255 | − | 0.770653i | \(-0.280070\pi\) | ||||
0.637255 | + | 0.770653i | \(0.280070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.11196 | 0.882130 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50345 | −0.550184 | −0.275092 | − | 0.961418i | \(-0.588708\pi\) | ||||
−0.275092 | + | 0.961418i | \(0.588708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.82624 | −1.16616 | −0.583080 | − | 0.812415i | \(-0.698153\pi\) | ||||
−0.583080 | + | 0.812415i | \(0.698153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.37302 | 0.745906 | 0.372953 | − | 0.927850i | \(-0.378345\pi\) | ||||
0.372953 | + | 0.927850i | \(0.378345\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.41171 | 0.388800 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.13734 | 0.127961 | 0.0639806 | − | 0.997951i | \(-0.479620\pi\) | ||||
0.0639806 | + | 0.997951i | \(0.479620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.53106 | 0.168055 | 0.0840277 | − | 0.996463i | \(-0.473222\pi\) | ||||
0.0840277 | + | 0.996463i | \(0.473222\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.60940 | 0.608425 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3254 | −1.62449 | −0.812243 | − | 0.583320i | \(-0.801754\pi\) | ||||
−0.812243 | + | 0.583320i | \(0.801754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.79878 | −0.293392 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.7669 | −1.72025 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.254712 | −0.0258621 | −0.0129310 | − | 0.999916i | \(-0.504116\pi\) | ||||
−0.0129310 | + | 0.999916i | \(0.504116\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7612 | −1.07078 | −0.535391 | − | 0.844604i | \(-0.679836\pi\) | ||||
−0.535391 | + | 0.844604i | \(0.679836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.73867 | −0.466915 | −0.233458 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233458 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.02191 | 0.485486 | 0.242743 | − | 0.970091i | \(-0.421953\pi\) | ||||
0.242743 | + | 0.970091i | \(0.421953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0232276 | 0.00222480 | 0.00111240 | − | 0.999999i | \(-0.499646\pi\) | ||||
0.00111240 | + | 0.999999i | \(0.499646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.83680 | −0.925369 | −0.462684 | − | 0.886523i | \(-0.653114\pi\) | ||||
−0.462684 | + | 0.886523i | \(0.653114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.84605 | −0.824899 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.20748 | −0.202359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.31600 | 0.119637 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.62794 | −0.861149 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24438 | −0.554099 | −0.277049 | − | 0.960856i | \(-0.589357\pi\) | ||||
−0.277049 | + | 0.960856i | \(0.589357\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.8403 | 1.90820 | 0.954100 | − | 0.299489i | \(-0.0968161\pi\) | ||||
0.954100 | + | 0.299489i | \(0.0968161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.59832 | 0.572147 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.61906 | 0.736376 | 0.368188 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368188 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.86187 | −0.497197 | −0.248599 | − | 0.968607i | \(-0.579970\pi\) | ||||
−0.248599 | + | 0.968607i | \(0.579970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.1034 | −0.844888 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.7936 | 1.56072 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.20332 | 0.344349 | 0.172175 | − | 0.985066i | \(-0.444921\pi\) | ||||
0.172175 | + | 0.985066i | \(0.444921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9027 | −0.968631 | −0.484316 | − | 0.874893i | \(-0.660931\pi\) | ||||
−0.484316 | + | 0.874893i | \(0.660931\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.690773 | −0.0554842 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3438 | 1.14476 | 0.572378 | − | 0.819990i | \(-0.306021\pi\) | ||||
0.572378 | + | 0.819990i | \(0.306021\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.48120 | 0.274357 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.38647 | 0.500227 | 0.250114 | − | 0.968217i | \(-0.419532\pi\) | ||||
0.250114 | + | 0.968217i | \(0.419532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.7849 | −1.60838 | −0.804191 | − | 0.594371i | \(-0.797401\pi\) | ||||
−0.804191 | + | 0.594371i | \(0.797401\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.71172 | −0.362440 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.3065 | −1.69593 | −0.847964 | − | 0.530054i | \(-0.822172\pi\) | ||||
−0.847964 | + | 0.530054i | \(0.822172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.07189 | −0.0810274 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.57389 | 0.341869 | 0.170934 | − | 0.985282i | \(-0.445321\pi\) | ||||
0.170934 | + | 0.985282i | \(0.445321\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.4328 | −1.74175 | −0.870874 | − | 0.491507i | \(-0.836446\pi\) | ||||
−0.870874 | + | 0.491507i | \(0.836446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.1484 | −1.70190 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.96882 | −0.582738 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.68497 | −0.700780 | −0.350390 | − | 0.936604i | \(-0.613951\pi\) | ||||
−0.350390 | + | 0.936604i | \(0.613951\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.2162 | −1.52718 | −0.763588 | − | 0.645703i | \(-0.776564\pi\) | ||||
−0.763588 | + | 0.645703i | \(0.776564\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.2301 | −0.728866 | −0.364433 | − | 0.931230i | \(-0.618737\pi\) | ||||
−0.364433 | + | 0.931230i | \(0.618737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.03987 | −0.144602 | −0.0723011 | − | 0.997383i | \(-0.523034\pi\) | ||||
−0.0723011 | + | 0.997383i | \(0.523034\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.39587 | −0.519088 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.8715 | 1.80694 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.8194 | 1.64762 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.1422 | −0.835901 | −0.417951 | − | 0.908470i | \(-0.637251\pi\) | ||||
−0.417951 | + | 0.908470i | \(0.637251\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0922 | −0.961083 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.271841 | 0.0184538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.53719 | 0.439739 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.5639 | −1.91278 | −0.956389 | − | 0.292096i | \(-0.905647\pi\) | ||||
−0.956389 | + | 0.292096i | \(0.905647\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.4032 | 1.88519 | 0.942593 | − | 0.333944i | \(-0.108380\pi\) | ||||
0.942593 | + | 0.333944i | \(0.108380\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.7016 | 1.30192 | 0.650958 | − | 0.759114i | \(-0.274367\pi\) | ||||
0.650958 | + | 0.759114i | \(0.274367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.3686 | 1.59644 | 0.798221 | − | 0.602365i | \(-0.205775\pi\) | ||||
0.798221 | + | 0.602365i | \(0.205775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.0767 | 1.30966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.67986 | 0.626138 | 0.313069 | − | 0.949730i | \(-0.398643\pi\) | ||||
0.313069 | + | 0.949730i | \(0.398643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.49541 | 0.482822 | 0.241411 | − | 0.970423i | \(-0.422390\pi\) | ||||
0.241411 | + | 0.970423i | \(0.422390\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.9577 | −0.955612 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.5402 | −1.24331 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.5669 | 0.790073 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.0330 | −1.37438 | −0.687189 | − | 0.726479i | \(-0.741156\pi\) | ||||
−0.687189 | + | 0.726479i | \(0.741156\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.10961 | 0.566044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.437637 | 0.0269858 | 0.0134929 | − | 0.999909i | \(-0.495705\pi\) | ||||
0.0134929 | + | 0.999909i | \(0.495705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.50876 | −0.154112 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.166462 | −0.0101494 | −0.00507468 | − | 0.999987i | \(-0.501615\pi\) | ||||
−0.00507468 | + | 0.999987i | \(0.501615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.1750 | 1.65076 | 0.825382 | − | 0.564574i | \(-0.190960\pi\) | ||||
0.825382 | + | 0.564574i | \(0.190960\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.86945 | −0.233336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0074 | 1.56263 | 0.781315 | − | 0.624137i | \(-0.214549\pi\) | ||||
0.781315 | + | 0.624137i | \(0.214549\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1033 | 0.841335 | 0.420668 | − | 0.907215i | \(-0.361796\pi\) | ||||
0.420668 | + | 0.907215i | \(0.361796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4293 | −0.857734 | −0.428867 | − | 0.903368i | \(-0.641087\pi\) | ||||
−0.428867 | + | 0.903368i | \(0.641087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.1812 | −0.600980 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8439 | −0.696702 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.0623 | −1.63942 | −0.819710 | − | 0.572779i | \(-0.805865\pi\) | ||||
−0.819710 | + | 0.572779i | \(0.805865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.4052 | −1.77026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3092 | −0.596196 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.54574 | 0.319651 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.5904 | 1.40804 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0019 | 1.25571 | 0.627857 | − | 0.778329i | \(-0.283932\pi\) | ||||
0.627857 | + | 0.778329i | \(0.283932\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.83660 | 0.387668 | 0.193834 | − | 0.981034i | \(-0.437908\pi\) | ||||
0.193834 | + | 0.981034i | \(0.437908\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.1934 | −1.25445 | −0.627223 | − | 0.778839i | \(-0.715809\pi\) | ||||
−0.627223 | + | 0.778839i | \(0.715809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.4529 | −0.811755 | −0.405878 | − | 0.913927i | \(-0.633034\pi\) | ||||
−0.405878 | + | 0.913927i | \(0.633034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.6985 | −1.49483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.4119 | −0.857540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.17429 | 0.176078 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.90083 | −0.435587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.27651 | 0.454918 | 0.227459 | − | 0.973788i | \(-0.426958\pi\) | ||||
0.227459 | + | 0.973788i | \(0.426958\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1251 | −0.607827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.45813 | 0.351797 | 0.175898 | − | 0.984408i | \(-0.443717\pi\) | ||||
0.175898 | + | 0.984408i | \(0.443717\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.981326 | 0.0531418 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6914 | 0.685273 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.2559 | −0.818979 | −0.409490 | − | 0.912315i | \(-0.634293\pi\) | ||||
−0.409490 | + | 0.912315i | \(0.634293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.41721 | 0.0758616 | 0.0379308 | − | 0.999280i | \(-0.487923\pi\) | ||||
0.0379308 | + | 0.999280i | \(0.487923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.5027 | −0.718674 | −0.359337 | − | 0.933208i | \(-0.616997\pi\) | ||||
−0.359337 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.2742 | −1.28834 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.44741 | 0.287503 | 0.143752 | − | 0.989614i | \(-0.454083\pi\) | ||||
0.143752 | + | 0.989614i | \(0.454083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.0673 | 1.42460 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7435 | 0.824055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.36536 | 0.332269 | 0.166135 | − | 0.986103i | \(-0.446871\pi\) | ||||
0.166135 | + | 0.986103i | \(0.446871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.987277 | 0.0512569 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0940 | −0.522646 | −0.261323 | − | 0.965251i | \(-0.584159\pi\) | ||||
−0.261323 | + | 0.965251i | \(0.584159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.9020 | 1.12801 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.6557 | −1.21511 | −0.607557 | − | 0.794276i | \(-0.707850\pi\) | ||||
−0.607557 | + | 0.794276i | \(0.707850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.3212 | 1.49825 | 0.749123 | − | 0.662431i | \(-0.230475\pi\) | ||||
0.749123 | + | 0.662431i | \(0.230475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.42808 | 0.429535 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.2891 | −1.23151 | −0.615753 | − | 0.787940i | \(-0.711148\pi\) | ||||
−0.615753 | + | 0.787940i | \(0.711148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.13114 | −0.411210 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.80963 | 0.141368 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.4398 | −0.523961 | −0.261980 | − | 0.965073i | \(-0.584376\pi\) | ||||
−0.261980 | + | 0.965073i | \(0.584376\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.6476 | −1.38066 | −0.690328 | − | 0.723496i | \(-0.742534\pi\) | ||||
−0.690328 | + | 0.723496i | \(0.742534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.805027 | −0.0401012 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.8850 | 1.63005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0738 | −0.992587 | −0.496294 | − | 0.868155i | \(-0.665306\pi\) | ||||
−0.496294 | + | 0.868155i | \(0.665306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.9654 | 0.588779 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.78224 | 0.185663 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.41538 | −0.264558 | −0.132279 | − | 0.991212i | \(-0.542230\pi\) | ||||
−0.132279 | + | 0.991212i | \(0.542230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.1966 | −1.13053 | −0.565266 | − | 0.824909i | \(-0.691226\pi\) | ||||
−0.565266 | + | 0.824909i | \(0.691226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.50365 | 0.121445 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.67709 | −0.468307 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.4498 | 1.51488 | 0.757441 | − | 0.652904i | \(-0.226449\pi\) | ||||
0.757441 | + | 0.652904i | \(0.226449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.30587 | −0.447211 | −0.223606 | − | 0.974680i | \(-0.571783\pi\) | ||||
−0.223606 | + | 0.974680i | \(0.571783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.3046 | 1.16265 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.9914 | −1.52687 | −0.763434 | − | 0.645886i | \(-0.776488\pi\) | ||||
−0.763434 | + | 0.645886i | \(0.776488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.46628 | 0.449757 | 0.224878 | − | 0.974387i | \(-0.427802\pi\) | ||||
0.224878 | + | 0.974387i | \(0.427802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.8589 | −1.79468 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.4021 | 0.962835 | 0.481418 | − | 0.876491i | \(-0.340122\pi\) | ||||
0.481418 | + | 0.876491i | \(0.340122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.7535 | −1.73066 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.91395 | −0.324131 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.97184 | 0.279351 | 0.139675 | − | 0.990197i | \(-0.455394\pi\) | ||||
0.139675 | + | 0.990197i | \(0.455394\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.01449 | −0.280123 | −0.140061 | − | 0.990143i | \(-0.544730\pi\) | ||||
−0.140061 | + | 0.990143i | \(0.544730\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4730 | 0.533197 | 0.266598 | − | 0.963808i | \(-0.414100\pi\) | ||||
0.266598 | + | 0.963808i | \(0.414100\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.1886 | 1.21187 | 0.605933 | − | 0.795516i | \(-0.292800\pi\) | ||||
0.605933 | + | 0.795516i | \(0.292800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.37806 | 0.202160 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0197 | 0.920508 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.48360 | −0.343371 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.68587 | 0.259794 | 0.129897 | − | 0.991527i | \(-0.458535\pi\) | ||||
0.129897 | + | 0.991527i | \(0.458535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.9771 | −1.23005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.629226 | −0.0285717 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.9258 | 0.766983 | 0.383491 | − | 0.923544i | \(-0.374722\pi\) | ||||
0.383491 | + | 0.923544i | \(0.374722\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.457098 | −0.0206285 | −0.0103143 | − | 0.999947i | \(-0.503283\pi\) | ||||
−0.0103143 | + | 0.999947i | \(0.503283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.2748 | 0.778016 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.55266 | 0.428495 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9818 | 0.939274 | 0.469637 | − | 0.882860i | \(-0.344385\pi\) | ||||
0.469637 | + | 0.882860i | \(0.344385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.22680 | −0.322227 | −0.161113 | − | 0.986936i | \(-0.551509\pi\) | ||||
−0.161113 | + | 0.986936i | \(0.551509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.5839 | −1.18297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.1215 | 1.20214 | 0.601069 | − | 0.799197i | \(-0.294742\pi\) | ||||
0.601069 | + | 0.799197i | \(0.294742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.19558 | −0.274077 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7061 | −0.515834 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.5214 | −1.25437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.03645 | −0.352083 | −0.176042 | − | 0.984383i | \(-0.556329\pi\) | ||||
−0.176042 | + | 0.984383i | \(0.556329\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.6907 | 1.56064 | 0.780322 | − | 0.625378i | \(-0.215055\pi\) | ||||
0.780322 | + | 0.625378i | \(0.215055\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.634947 | −0.0276587 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1771 | −0.442484 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.1506 | 1.30597 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.4058 | 0.536351 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.2492 | 0.915268 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.7224 | −1.01991 | −0.509953 | − | 0.860202i | \(-0.670337\pi\) | ||||
−0.509953 | + | 0.860202i | \(0.670337\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0573801 | 0.00245789 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.652965 | 0.0279188 | 0.0139594 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139594 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.6356 | −2.19975 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.10568 | −0.0470182 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.7803 | −0.456776 | −0.228388 | − | 0.973570i | \(-0.573345\pi\) | ||||
−0.228388 | + | 0.973570i | \(0.573345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.4231 | −0.694623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.4873 | 0.737000 | 0.368500 | − | 0.929628i | \(-0.379871\pi\) | ||||
0.368500 | + | 0.929628i | \(0.379871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.3003 | −1.02232 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.99957 | −0.167671 | −0.0838353 | − | 0.996480i | \(-0.526717\pi\) | ||||
−0.0838353 | + | 0.996480i | \(0.526717\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.9033 | 1.66990 | 0.834950 | − | 0.550325i | \(-0.185496\pi\) | ||||
0.834950 | + | 0.550325i | \(0.185496\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.94827 | −0.164654 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.27664 | −0.344561 | −0.172280 | − | 0.985048i | \(-0.555114\pi\) | ||||
−0.172280 | + | 0.985048i | \(0.555114\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.48843 | −0.0617505 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.56400 | 0.147606 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.2614 | −1.62049 | −0.810246 | − | 0.586090i | \(-0.800667\pi\) | ||||
−0.810246 | + | 0.586090i | \(0.800667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.89791 | 0.0782018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.9457 | −1.02440 | −0.512198 | − | 0.858868i | \(-0.671169\pi\) | ||||
−0.512198 | + | 0.858868i | \(0.671169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.45322 | −0.223560 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0175 | 0.491020 | 0.245510 | − | 0.969394i | \(-0.421045\pi\) | ||||
0.245510 | + | 0.969394i | \(0.421045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.9326 | −0.486742 | −0.243371 | − | 0.969933i | \(-0.578253\pi\) | ||||
−0.243371 | + | 0.969933i | \(0.578253\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.25098 | 0.132171 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.2623 | −1.55302 | −0.776509 | − | 0.630106i | \(-0.783011\pi\) | ||||
−0.776509 | + | 0.630106i | \(0.783011\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3974 | 0.946558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5152 | 1.31328 | 0.656639 | − | 0.754205i | \(-0.271977\pi\) | ||||
0.656639 | + | 0.754205i | \(0.271977\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0903 | 0.647770 | 0.323885 | − | 0.946096i | \(-0.395011\pi\) | ||||
0.323885 | + | 0.946096i | \(0.395011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.4841 | 1.78797 | 0.893984 | − | 0.448099i | \(-0.147899\pi\) | ||||
0.893984 | + | 0.448099i | \(0.147899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.8987 | 0.596903 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2972 | −1.17189 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.2776 | −0.848393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6044 | −1.69606 | −0.848028 | − | 0.529952i | \(-0.822210\pi\) | ||||
−0.848028 | + | 0.529952i | \(0.822210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.4257 | −0.612152 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.4317 | −0.690669 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.8680 | 1.06122 | 0.530612 | − | 0.847615i | \(-0.321962\pi\) | ||||
0.530612 | + | 0.847615i | \(0.321962\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.23302 | 0.166934 | 0.0834670 | − | 0.996511i | \(-0.473401\pi\) | ||||
0.0834670 | + | 0.996511i | \(0.473401\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.04546 | 0.237672 | 0.118836 | − | 0.992914i | \(-0.462084\pi\) | ||||
0.118836 | + | 0.992914i | \(0.462084\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.1942 | 1.69552 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.66383 | 0.0651106 | 0.0325553 | − | 0.999470i | \(-0.489635\pi\) | ||||
0.0325553 | + | 0.999470i | \(0.489635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 53.9531 | 2.10812 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.82120 | 0.304671 | 0.152335 | − | 0.988329i | \(-0.451321\pi\) | ||||
0.152335 | + | 0.988329i | \(0.451321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.4534 | 0.873336 | 0.436668 | − | 0.899623i | \(-0.356159\pi\) | ||||
0.436668 | + | 0.899623i | \(0.356159\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.3001 | 0.632091 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.2424 | −1.05483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.9336 | −1.34859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.6777 | −0.951256 | −0.475628 | − | 0.879647i | \(-0.657779\pi\) | ||||
−0.475628 | + | 0.879647i | \(0.657779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.6413 | −1.48510 | −0.742552 | − | 0.669788i | \(-0.766385\pi\) | ||||
−0.742552 | + | 0.669788i | \(0.766385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.247620 | 0.00950279 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.3316 | −0.510120 | −0.255060 | − | 0.966925i | \(-0.582095\pi\) | ||||
−0.255060 | + | 0.966925i | \(0.582095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.2920 | 0.813526 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.92371 | −0.111385 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1199 | −0.803439 | −0.401720 | − | 0.915763i | \(-0.631587\pi\) | ||||
−0.401720 | + | 0.915763i | \(0.631587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.4808 | −0.549289 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.7806 | 0.900755 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8009 | 0.785638 | 0.392819 | − | 0.919616i | \(-0.371500\pi\) | ||||
0.392819 | + | 0.919616i | \(0.371500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.6003 | 2.39873 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4616 | 0.393449 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0183 | 1.05225 | 0.526125 | − | 0.850407i | \(-0.323645\pi\) | ||||
0.526125 | + | 0.850407i | \(0.323645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00131 | 0.0374995 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.9588 | −0.933407 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5265 | 0.877391 | 0.438695 | − | 0.898636i | \(-0.355441\pi\) | ||||
0.438695 | + | 0.898636i | \(0.355441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.60674 | 0.171564 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.38816 | 0.311528 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.6375 | 0.505786 | 0.252893 | − | 0.967494i | \(-0.418618\pi\) | ||||
0.252893 | + | 0.967494i | \(0.418618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9534 | −0.479097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.2947 | −1.67300 | −0.836498 | − | 0.547970i | \(-0.815401\pi\) | ||||
−0.836498 | + | 0.547970i | \(0.815401\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.8045 | 0.582165 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.2582 | −1.40735 | −0.703676 | − | 0.710521i | \(-0.748459\pi\) | ||||
−0.703676 | + | 0.710521i | \(0.748459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5410 | 0.790264 | 0.395132 | − | 0.918624i | \(-0.370699\pi\) | ||||
0.395132 | + | 0.918624i | \(0.370699\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3836 | 0.380427 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.88209 | −0.178388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.05259 | −0.0748999 | −0.0374500 | − | 0.999299i | \(-0.511923\pi\) | ||||
−0.0374500 | + | 0.999299i | \(0.511923\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.4038 | −1.07012 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.1139 | −0.876434 | −0.438217 | − | 0.898869i | \(-0.644390\pi\) | ||||
−0.438217 | + | 0.898869i | \(0.644390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.7308 | 0.860239 | 0.430120 | − | 0.902772i | \(-0.358471\pi\) | ||||
0.430120 | + | 0.902772i | \(0.358471\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0225809 | −0.000817483 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.4342 | −1.27945 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.2832 | 1.34447 | 0.672233 | − | 0.740340i | \(-0.265335\pi\) | ||||
0.672233 | + | 0.740340i | \(0.265335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.720896 | −0.0259288 | −0.0129644 | − | 0.999916i | \(-0.504127\pi\) | ||||
−0.0129644 | + | 0.999916i | \(0.504127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.308313 | −0.0110749 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −71.0821 | −2.54678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.4844 | 1.23395 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.4340 | 1.26469 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.8920 | −1.81410 | −0.907051 | − | 0.421020i | \(-0.861672\pi\) | ||||
−0.907051 | + | 0.421020i | \(0.861672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.56293 | 0.340018 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6576 | 1.01766 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.0627 | 0.498126 | 0.249063 | − | 0.968487i | \(-0.419877\pi\) | ||||
0.249063 | + | 0.968487i | \(0.419877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.4542 | 0.652863 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.3656 | −0.789265 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.59976 | 0.303102 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.6840 | 1.57100 | 0.785502 | − | 0.618859i | \(-0.212405\pi\) | ||||
0.785502 | + | 0.618859i | \(0.212405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.73808 | 0.341950 | 0.170975 | − | 0.985275i | \(-0.445308\pi\) | ||||
0.170975 | + | 0.985275i | \(0.445308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7768 | 0.552636 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.7186 | 1.35459 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.0650 | −1.29358 | −0.646788 | − | 0.762670i | \(-0.723888\pi\) | ||||
−0.646788 | + | 0.762670i | \(0.723888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.7145 | −1.87237 | −0.936185 | − | 0.351508i | \(-0.885669\pi\) | ||||
−0.936185 | + | 0.351508i | \(0.885669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.6240 | −1.16922 | −0.584611 | − | 0.811314i | \(-0.698753\pi\) | ||||
−0.584611 | + | 0.811314i | \(0.698753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.34280 | −0.150832 | −0.0754159 | − | 0.997152i | \(-0.524028\pi\) | ||||
−0.0754159 | + | 0.997152i | \(0.524028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.7489 | −0.476370 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −51.3458 | −1.77689 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.3087 | −0.701135 | −0.350567 | − | 0.936538i | \(-0.614011\pi\) | ||||
−0.350567 | + | 0.936538i | \(0.614011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8769 | 0.995755 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6396 | −0.400413 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.27936 | −0.0439595 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.5549 | 1.15025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.46704 | 0.152948 | 0.0764742 | − | 0.997072i | \(-0.475634\pi\) | ||||
0.0764742 | + | 0.997072i | \(0.475634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.2401 | −0.964664 | −0.482332 | − | 0.875989i | \(-0.660210\pi\) | ||||
−0.482332 | + | 0.875989i | \(0.660210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.2974 | −1.51141 | −0.755703 | − | 0.654914i | \(-0.772705\pi\) | ||||
−0.755703 | + | 0.654914i | \(0.772705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.12320 | 0.276517 | 0.138259 | − | 0.990396i | \(-0.455850\pi\) | ||||
0.138259 | + | 0.990396i | \(0.455850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55.1046 | −1.87361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.99142 | −0.135399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9651 | −0.439307 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.35987 | 0.316421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.21603 | 0.311203 | 0.155602 | − | 0.987820i | \(-0.450268\pi\) | ||||
0.155602 | + | 0.987820i | \(0.450268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.3672 | 0.922025 | 0.461013 | − | 0.887394i | \(-0.347486\pi\) | ||||
0.461013 | + | 0.887394i | \(0.347486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.6386 | 0.963765 | 0.481883 | − | 0.876236i | \(-0.339953\pi\) | ||||
0.481883 | + | 0.876236i | \(0.339953\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.8728 | −1.07018 | −0.535092 | − | 0.844794i | \(-0.679723\pi\) | ||||
−0.535092 | + | 0.844794i | \(0.679723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.07052 | 0.203599 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −55.1610 | −1.84589 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2991 | 0.377687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.12731 | −0.0709498 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.30601 | −0.0768244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −57.8871 | −1.92423 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.8857 | 1.68963 | 0.844816 | − | 0.535057i | \(-0.179710\pi\) | ||||
0.844816 | + | 0.535057i | \(0.179710\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.1844 | −0.602477 | −0.301239 | − | 0.953549i | \(-0.597400\pi\) | ||||
−0.301239 | + | 0.953549i | \(0.597400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.37312 | −0.177824 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.2323 | −0.701151 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.57600 | 0.0849745 | 0.0424872 | − | 0.999097i | \(-0.486472\pi\) | ||||
0.0424872 | + | 0.999097i | \(0.486472\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.2891 | −0.931148 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.3318 | −0.339708 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.1992 | −0.761142 | −0.380571 | − | 0.924752i | \(-0.624273\pi\) | ||||
−0.380571 | + | 0.924752i | \(0.624273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.0964 | 1.34688 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.6857 | −0.643792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.9033 | −0.519539 | −0.259769 | − | 0.965671i | \(-0.583647\pi\) | ||||
−0.259769 | + | 0.965671i | \(0.583647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.26329 | 0.138979 | 0.0694896 | − | 0.997583i | \(-0.477863\pi\) | ||||
0.0694896 | + | 0.997583i | \(0.477863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.5022 | −1.22124 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.78149 | 0.252864 | 0.126432 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126432 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3475 | 0.595586 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.4808 | −0.598650 | −0.299325 | − | 0.954151i | \(-0.596762\pi\) | ||||
−0.299325 | + | 0.954151i | \(0.596762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.9252 | −0.774201 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.37908 | −0.270575 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9218 | −0.997478 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −52.4113 | −1.68718 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.95512 | −0.287977 | −0.143989 | − | 0.989579i | \(-0.545993\pi\) | ||||
−0.143989 | + | 0.989579i | \(0.545993\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.19052 | 0.0702972 | 0.0351486 | − | 0.999382i | \(-0.488810\pi\) | ||||
0.0351486 | + | 0.999382i | \(0.488810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.69866 | 0.182691 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8102 | 0.825741 | 0.412871 | − | 0.910790i | \(-0.364526\pi\) | ||||
0.412871 | + | 0.910790i | \(0.364526\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.7831 | 1.71891 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.6394 | −0.690188 | −0.345094 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345094 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.2719 | −0.805230 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.4275 | 0.649557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.4242 | −1.47471 | −0.737357 | − | 0.675503i | \(-0.763927\pi\) | ||||
−0.737357 | + | 0.675503i | \(0.763927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.03916 | −0.159752 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.29268 | 0.230961 | 0.115481 | − | 0.993310i | \(-0.463159\pi\) | ||||
0.115481 | + | 0.993310i | \(0.463159\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 9036.2.a.i.1.7 | 7 | ||
3.2 | odd | 2 | 1004.2.a.a.1.6 | ✓ | 7 | ||
12.11 | even | 2 | 4016.2.a.g.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.a.1.6 | ✓ | 7 | 3.2 | odd | 2 | ||
4016.2.a.g.1.2 | 7 | 12.11 | even | 2 | |||
9036.2.a.i.1.7 | 7 | 1.1 | even | 1 | trivial |