Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.66064384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 13x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.30397\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | 0.537080 | 0.310083 | 0.155042 | − | 0.987908i | \(-0.450449\pi\) | ||||
0.155042 | + | 0.987908i | \(0.450449\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.18676 | −1.20448 | −0.602241 | − | 0.798314i | \(-0.705725\pi\) | ||||
−0.602241 | + | 0.798314i | \(0.705725\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.71155 | −0.903848 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.15544 | −1.25291 | −0.626456 | − | 0.779457i | \(-0.715495\pi\) | ||||
−0.626456 | + | 0.779457i | \(0.715495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.07086 | −0.574353 | −0.287176 | − | 0.957878i | \(-0.592717\pi\) | ||||
−0.287176 | + | 0.957878i | \(0.592717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.79470 | −1.40542 | −0.702710 | − | 0.711476i | \(-0.748027\pi\) | ||||
−0.702710 | + | 0.711476i | \(0.748027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71155 | −0.373490 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.60794 | −0.543793 | −0.271896 | − | 0.962327i | \(-0.587651\pi\) | ||||
−0.271896 | + | 0.962327i | \(0.587651\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.06756 | −0.590352 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.59933 | −0.466853 | −0.233427 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233427 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.23180 | −0.388507 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.30266 | −0.707353 | −0.353677 | − | 0.935368i | \(-0.615069\pi\) | ||||
−0.353677 | + | 0.935368i | \(0.615069\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.11222 | −0.178097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.599328 | −0.0935993 | −0.0467997 | − | 0.998904i | \(-0.514902\pi\) | ||||
−0.0467997 | + | 0.998904i | \(0.514902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.18676 | 0.485976 | 0.242988 | − | 0.970029i | \(-0.421872\pi\) | ||||
0.242988 | + | 0.970029i | \(0.421872\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7086 | 1.70787 | 0.853937 | − | 0.520376i | \(-0.174208\pi\) | ||||
0.853937 | + | 0.520376i | \(0.174208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.15544 | 0.450777 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.11222 | −0.435798 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.7503 | −1.61403 | −0.807017 | − | 0.590529i | \(-0.798919\pi\) | ||||
−0.807017 | + | 0.590529i | \(0.798919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.537080 | 0.0711380 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.71155 | 0.222824 | 0.111412 | − | 0.993774i | \(-0.464463\pi\) | ||||
0.111412 | + | 0.993774i | \(0.464463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.75476 | −1.12093 | −0.560466 | − | 0.828177i | \(-0.689378\pi\) | ||||
−0.560466 | + | 0.828177i | \(0.689378\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.64104 | 1.08867 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.76228 | 0.581805 | 0.290902 | − | 0.956753i | \(-0.406044\pi\) | ||||
0.290902 | + | 0.956753i | \(0.406044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.40067 | −0.168621 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7115 | −1.62726 | −0.813631 | − | 0.581382i | \(-0.802512\pi\) | ||||
−0.813631 | + | 0.581382i | \(0.802512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.72714 | 0.319188 | 0.159594 | − | 0.987183i | \(-0.448982\pi\) | ||||
0.159594 | + | 0.987183i | \(0.448982\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.2424 | 1.50911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.40067 | 0.157588 | 0.0787939 | − | 0.996891i | \(-0.474893\pi\) | ||||
0.0787939 | + | 0.996891i | \(0.474893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.48711 | 0.720790 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.07154 | −0.776203 | −0.388101 | − | 0.921617i | \(-0.626869\pi\) | ||||
−0.388101 | + | 0.921617i | \(0.626869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.22248 | 0.345486 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.5353 | 1.75274 | 0.876370 | − | 0.481639i | \(-0.159958\pi\) | ||||
0.876370 | + | 0.481639i | \(0.159958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59933 | 0.691798 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.39605 | −0.144763 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.07086 | −0.210264 | −0.105132 | − | 0.994458i | \(-0.533526\pi\) | ||||
−0.105132 | + | 0.994458i | \(0.533526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.2677 | 1.13244 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.71155 | −0.170305 | −0.0851525 | − | 0.996368i | \(-0.527138\pi\) | ||||
−0.0851525 | + | 0.996368i | \(0.527138\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.75296 | 0.566856 | 0.283428 | − | 0.958994i | \(-0.408528\pi\) | ||||
0.283428 | + | 0.958994i | \(0.408528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.4324 | −1.49191 | −0.745955 | − | 0.665996i | \(-0.768007\pi\) | ||||
−0.745955 | + | 0.665996i | \(0.768007\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7115 | 1.12176 | 0.560881 | − | 0.827896i | \(-0.310462\pi\) | ||||
0.560881 | + | 0.827896i | \(0.310462\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.31087 | −0.219338 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5927 | 0.996477 | 0.498239 | − | 0.867040i | \(-0.333980\pi\) | ||||
0.498239 | + | 0.867040i | \(0.333980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.61523 | 0.519128 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.4663 | 1.69280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.26765 | 0.569787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.321887 | −0.0290236 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.07484 | −0.539055 | −0.269528 | − | 0.962993i | \(-0.586868\pi\) | ||||
−0.269528 | + | 0.962993i | \(0.586868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.71155 | 0.150693 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5785 | 1.18636 | 0.593181 | − | 0.805069i | \(-0.297872\pi\) | ||||
0.593181 | + | 0.805069i | \(0.297872\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.18676 | −0.276327 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.94302 | 0.678618 | 0.339309 | − | 0.940675i | \(-0.389807\pi\) | ||||
0.339309 | + | 0.940675i | \(0.389807\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.26765 | −0.277159 | −0.138579 | − | 0.990351i | \(-0.544254\pi\) | ||||
−0.138579 | + | 0.990351i | \(0.544254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.28845 | 0.529583 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.60532 | 0.719613 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.69472 | 0.139778 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.44389 | 0.691751 | 0.345875 | − | 0.938280i | \(-0.387582\pi\) | ||||
0.345875 | + | 0.938280i | \(0.387582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.887783 | −0.0722468 | −0.0361234 | − | 0.999347i | \(-0.511501\pi\) | ||||
−0.0361234 | + | 0.999347i | \(0.511501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.7126 | 1.27029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.14172 | −0.330545 | −0.165273 | − | 0.986248i | \(-0.552850\pi\) | ||||
−0.165273 | + | 0.986248i | \(0.552850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.31087 | −0.500485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.31087 | 0.654989 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.7126 | −1.93564 | −0.967819 | − | 0.251647i | \(-0.919028\pi\) | ||||
−0.967819 | + | 0.251647i | \(0.919028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.60464 | −0.278935 | −0.139468 | − | 0.990227i | \(-0.544539\pi\) | ||||
−0.139468 | + | 0.990227i | \(0.544539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.71155 | −0.670119 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.71155 | −0.207357 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4205 | 1.70460 | 0.852300 | − | 0.523054i | \(-0.175207\pi\) | ||||
0.852300 | + | 0.523054i | \(0.175207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.919237 | 0.0690941 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.13464 | 0.383781 | 0.191890 | − | 0.981416i | \(-0.438538\pi\) | ||||
0.191890 | + | 0.981416i | \(0.438538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8462 | 1.54948 | 0.774742 | − | 0.632277i | \(-0.217880\pi\) | ||||
0.774742 | + | 0.632277i | \(0.217880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.70201 | −0.347583 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0795 | 1.76087 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.77557 | 0.711068 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.26765 | 0.381154 | 0.190577 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190577 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.07086 | −0.149064 | −0.0745318 | − | 0.997219i | \(-0.523746\pi\) | ||||
−0.0745318 | + | 0.997219i | \(0.523746\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4318 | −0.743232 | −0.371616 | − | 0.928387i | \(-0.621196\pi\) | ||||
−0.371616 | + | 0.928387i | \(0.621196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.73235 | 0.193691 | 0.0968455 | − | 0.995299i | \(-0.469125\pi\) | ||||
0.0968455 | + | 0.995299i | \(0.469125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.55773 | 0.180408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.1206 | −1.34200 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.07154 | 0.491506 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.15544 | −0.287438 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7340 | 1.08317 | 0.541585 | − | 0.840646i | \(-0.317824\pi\) | ||||
0.541585 | + | 0.840646i | \(0.317824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.36420 | −0.504586 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.28343 | 0.562316 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.46469 | 0.0989748 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8219 | 1.26041 | 0.630203 | − | 0.776430i | \(-0.282972\pi\) | ||||
0.630203 | + | 0.776430i | \(0.282972\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4418 | −0.958533 | −0.479267 | − | 0.877669i | \(-0.659097\pi\) | ||||
−0.479267 | + | 0.877669i | \(0.659097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.17785 | −0.276080 | −0.138040 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138040 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.11222 | 0.467950 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0847 | −0.791697 | −0.395849 | − | 0.918316i | \(-0.629550\pi\) | ||||
−0.395849 | + | 0.918316i | \(0.629550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.752273 | 0.0488654 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3541 | 0.734435 | 0.367218 | − | 0.930135i | \(-0.380310\pi\) | ||||
0.367218 | + | 0.930135i | \(0.380310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.40067 | −0.219057 | −0.109528 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109528 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6868 | 0.813857 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.07086 | −0.131766 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.79798 | −0.240687 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.04322 | −0.192086 | −0.0960432 | − | 0.995377i | \(-0.530619\pi\) | ||||
−0.0960432 | + | 0.995377i | \(0.530619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8371 | 0.681324 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.2881 | −1.07840 | −0.539201 | − | 0.842177i | \(-0.681274\pi\) | ||||
−0.539201 | + | 0.842177i | \(0.681274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.7115 | 0.851994 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.2693 | −1.00704 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.19336 | −0.0735859 | −0.0367930 | − | 0.999323i | \(-0.511714\pi\) | ||||
−0.0367930 | + | 0.999323i | \(0.511714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.88078 | 0.543495 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.1089 | 1.34800 | 0.674000 | − | 0.738731i | \(-0.264575\pi\) | ||||
0.674000 | + | 0.738731i | \(0.264575\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.08644 | 0.248234 | 0.124117 | − | 0.992268i | \(-0.460390\pi\) | ||||
0.124117 | + | 0.992268i | \(0.460390\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.54437 | 0.214515 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0199 | 0.602037 | 0.301019 | − | 0.953618i | \(-0.402673\pi\) | ||||
0.301019 | + | 0.953618i | \(0.402673\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.04820 | 0.421964 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.599328 | 0.0357529 | 0.0178765 | − | 0.999840i | \(-0.494309\pi\) | ||||
0.0178765 | + | 0.999840i | \(0.494309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.41856 | 0.322100 | 0.161050 | − | 0.986946i | \(-0.448512\pi\) | ||||
0.161050 | + | 0.986946i | \(0.448512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.90991 | 0.112739 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5785 | 0.975207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.11222 | −0.0651993 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.46691 | −0.202539 | −0.101269 | − | 0.994859i | \(-0.532290\pi\) | ||||
−0.101269 | + | 0.994859i | \(0.532290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.7470 | 0.739658 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.40067 | 0.312329 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1554 | −0.585350 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.919237 | −0.0528088 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5901 | −0.946846 | −0.473423 | − | 0.880835i | \(-0.656982\pi\) | ||||
−0.473423 | + | 0.880835i | \(0.656982\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.08980 | 0.175772 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.15544 | 0.235633 | 0.117817 | − | 0.993035i | \(-0.462411\pi\) | ||||
0.117817 | + | 0.993035i | \(0.462411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.919237 | 0.0519583 | 0.0259792 | − | 0.999662i | \(-0.491730\pi\) | ||||
0.0259792 | + | 0.999662i | \(0.491730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.7292 | 1.50126 | 0.750630 | − | 0.660723i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660723i | \(0.229750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.9326 | −1.39596 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.28845 | −0.462616 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.79470 | −0.322426 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.29004 | 0.347840 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.3125 | −2.05710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.6669 | 0.639340 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.5040 | −1.22587 | −0.612935 | − | 0.790133i | \(-0.710011\pi\) | ||||
−0.612935 | + | 0.790133i | \(0.710011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.68913 | 0.308991 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.8013 | 0.584926 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.2517 | 0.661530 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.4543 | −0.775946 | −0.387973 | − | 0.921671i | \(-0.626825\pi\) | ||||
−0.387973 | + | 0.921671i | \(0.626825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3541 | −0.714828 | −0.357414 | − | 0.933946i | \(-0.616342\pi\) | ||||
−0.357414 | + | 0.933946i | \(0.616342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.35248 | 0.339070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.6410 | −0.938937 | −0.469469 | − | 0.882949i | \(-0.655554\pi\) | ||||
−0.469469 | + | 0.882949i | \(0.655554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.91789 | 0.524910 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.4663 | −0.657947 | −0.328973 | − | 0.944339i | \(-0.606703\pi\) | ||||
−0.328973 | + | 0.944339i | \(0.606703\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.36623 | 0.176681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4291 | −0.857594 | −0.428797 | − | 0.903401i | \(-0.641062\pi\) | ||||
−0.428797 | + | 0.903401i | \(0.641062\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.62511 | 0.0845996 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.4455 | 1.94407 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.29334 | 0.274079 | 0.137039 | − | 0.990566i | \(-0.456241\pi\) | ||||
0.137039 | + | 0.990566i | \(0.456241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.4252 | −0.639928 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5353 | −0.746629 | −0.373314 | − | 0.927705i | \(-0.621779\pi\) | ||||
−0.373314 | + | 0.927705i | \(0.621779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.26268 | −0.167152 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.453598 | 0.0231778 | 0.0115889 | − | 0.999933i | \(-0.496311\pi\) | ||||
0.0115889 | + | 0.999933i | \(0.496311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.64104 | −0.439249 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.1554 | 0.819113 | 0.409557 | − | 0.912285i | \(-0.365683\pi\) | ||||
0.409557 | + | 0.912285i | \(0.365683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1122 | 0.764258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.29276 | 0.367871 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.7563 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.71155 | −0.0856844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0864 | 0.603568 | 0.301784 | − | 0.953376i | \(-0.402418\pi\) | ||||
0.301784 | + | 0.953376i | \(0.402418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.38284 | 0.268138 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.8794 | 0.886251 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.1346 | −0.946147 | −0.473073 | − | 0.881023i | \(-0.656855\pi\) | ||||
−0.473073 | + | 0.881023i | \(0.656855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.26604 | 0.210428 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.45428 | −0.268388 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.75499 | −0.0859423 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.04484 | −0.393016 | −0.196508 | − | 0.980502i | \(-0.562960\pi\) | ||||
−0.196508 | + | 0.980502i | \(0.562960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3591 | −1.43087 | −0.715437 | − | 0.698678i | \(-0.753772\pi\) | ||||
−0.715437 | + | 0.698678i | \(0.753772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.7484 | −1.54366 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.8993 | 1.35014 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.62175 | 0.223140 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.0448 | 1.54355 | 0.771773 | − | 0.635898i | \(-0.219370\pi\) | ||||
0.771773 | + | 0.635898i | \(0.219370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.482831 | −0.0232034 | −0.0116017 | − | 0.999933i | \(-0.503693\pi\) | ||||
−0.0116017 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.60794 | −0.124755 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3591 | 1.30578 | 0.652889 | − | 0.757454i | \(-0.273557\pi\) | ||||
0.652889 | + | 0.757454i | \(0.273557\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.55611 | −0.407434 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3815 | 1.11089 | 0.555444 | − | 0.831554i | \(-0.312548\pi\) | ||||
0.555444 | + | 0.831554i | \(0.312548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.53505 | 0.214500 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.1346 | 1.09179 | 0.545895 | − | 0.837853i | \(-0.316190\pi\) | ||||
0.545895 | + | 0.837853i | \(0.316190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.49047 | 0.117272 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.476811 | −0.0224025 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.2503 | −0.994049 | −0.497025 | − | 0.867736i | \(-0.665574\pi\) | ||||
−0.497025 | + | 0.867736i | \(0.665574\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.7756 | 0.829692 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5785 | 1.47076 | 0.735379 | − | 0.677656i | \(-0.237004\pi\) | ||||
0.735379 | + | 0.677656i | \(0.237004\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6119 | −0.725547 | −0.362774 | − | 0.931877i | \(-0.618170\pi\) | ||||
−0.362774 | + | 0.931877i | \(0.618170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.8264 | −1.38020 | −0.690101 | − | 0.723713i | \(-0.742434\pi\) | ||||
−0.690101 | + | 0.723713i | \(0.742434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.1762 | −0.700774 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.22443 | −0.102496 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.2424 | −0.608885 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.8616 | 1.45884 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.53531 | −0.207223 | −0.103612 | − | 0.994618i | \(-0.533040\pi\) | ||||
−0.103612 | + | 0.994618i | \(0.533040\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.91020 | 0.406270 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.46360 | 0.203101 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.2550 | 1.77881 | 0.889407 | − | 0.457116i | \(-0.151118\pi\) | ||||
0.889407 | + | 0.457116i | \(0.151118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.2726 | −0.600209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.8910 | −1.75513 | −0.877564 | − | 0.479460i | \(-0.840832\pi\) | ||||
−0.877564 | + | 0.479460i | \(0.840832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.7682 | −1.56588 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.6954 | 1.96001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.73235 | −0.211849 | −0.105924 | − | 0.994374i | \(-0.533780\pi\) | ||||
−0.105924 | + | 0.994374i | \(0.533780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.93598 | −0.0864931 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.85567 | 0.0827400 | 0.0413700 | − | 0.999144i | \(-0.486828\pi\) | ||||
0.0413700 | + | 0.999144i | \(0.486828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.67880 | −0.207793 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.8878 | 1.01448 | 0.507242 | − | 0.861804i | \(-0.330665\pi\) | ||||
0.507242 | + | 0.861804i | \(0.330665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.69074 | −0.384456 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.06756 | −0.135436 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −48.6543 | −2.13982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0416 | 0.528568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7340 | −1.30267 | −0.651334 | − | 0.758791i | \(-0.725790\pi\) | ||||
−0.651334 | + | 0.758791i | \(0.725790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.6497 | 1.34022 | 0.670109 | − | 0.742263i | \(-0.266248\pi\) | ||||
0.670109 | + | 0.742263i | \(0.266248\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0623 | 0.656125 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1987 | −0.704289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.64093 | −0.201399 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.24112 | 0.0537590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.75771 | 0.119004 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.1122 | −0.564783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.21946 | 0.0954220 | 0.0477110 | − | 0.998861i | \(-0.484807\pi\) | ||||
0.0477110 | + | 0.998861i | \(0.484807\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1961 | 0.480469 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.4297 | −0.616970 | −0.308485 | − | 0.951229i | \(-0.599822\pi\) | ||||
−0.308485 | + | 0.951229i | \(0.599822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.7389 | 1.01315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.46360 | −0.189812 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.4610 | −0.824588 | −0.412294 | − | 0.911051i | \(-0.635272\pi\) | ||||
−0.412294 | + | 0.911051i | \(0.635272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.59933 | −0.279122 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9326 | 0.546016 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.3649 | −0.521118 | −0.260559 | − | 0.965458i | \(-0.583907\pi\) | ||||
−0.260559 | + | 0.965458i | \(0.583907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.6729 | −0.868179 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0898 | 0.632597 | 0.316299 | − | 0.948660i | \(-0.397560\pi\) | ||||
0.316299 | + | 0.948660i | \(0.397560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1571 | −0.718000 | −0.359000 | − | 0.933337i | \(-0.616882\pi\) | ||||
−0.359000 | + | 0.933337i | \(0.616882\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.82915 | 0.118190 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5165 | 0.937374 | 0.468687 | − | 0.883364i | \(-0.344727\pi\) | ||||
0.468687 | + | 0.883364i | \(0.344727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.11222 | −0.0462222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5353 | 0.934922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.8278 | 2.02224 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.49544 | 0.309370 | 0.154685 | − | 0.987964i | \(-0.450564\pi\) | ||||
0.154685 | + | 0.987964i | \(0.450564\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.59933 | −0.107103 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.60269 | −0.230464 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.8094 | −1.14199 | −0.570997 | − | 0.820952i | \(-0.693443\pi\) | ||||
−0.570997 | + | 0.820952i | \(0.693443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.46749 | 0.0600603 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.4903 | 1.85869 | 0.929343 | − | 0.369219i | \(-0.120375\pi\) | ||||
0.929343 | + | 0.369219i | \(0.120375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5993 | −0.677101 | −0.338550 | − | 0.940948i | \(-0.609937\pi\) | ||||
−0.338550 | + | 0.940948i | \(0.609937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.9131 | −0.525863 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.08417 | −0.206360 | −0.103180 | − | 0.994663i | \(-0.532902\pi\) | ||||
−0.103180 | + | 0.994663i | \(0.532902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.2693 | −0.416132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.2469 | −0.980923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.63706 | −0.187289 | −0.0936445 | − | 0.995606i | \(-0.529852\pi\) | ||||
−0.0936445 | + | 0.995606i | \(0.529852\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.2874 | −1.62191 | −0.810955 | − | 0.585108i | \(-0.801052\pi\) | ||||
−0.810955 | + | 0.585108i | \(0.801052\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.3815 | 1.74365 | 0.871825 | − | 0.489818i | \(-0.162937\pi\) | ||||
0.871825 | + | 0.489818i | \(0.162937\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −52.6940 | −2.11114 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.23180 | −0.0891296 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.9326 | 0.994129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.53369 | −0.299911 | −0.149956 | − | 0.988693i | \(-0.547913\pi\) | ||||
−0.149956 | + | 0.988693i | \(0.547913\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.45040 | 0.335873 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.53446 | −0.258905 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 37.1795 | 1.47080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3075 | −0.920591 | −0.460296 | − | 0.887766i | \(-0.652257\pi\) | ||||
−0.460296 | + | 0.887766i | \(0.652257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.87419 | 0.0739110 | 0.0369555 | − | 0.999317i | \(-0.488234\pi\) | ||||
0.0369555 | + | 0.999317i | \(0.488234\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −47.0371 | −1.84922 | −0.924609 | − | 0.380917i | \(-0.875608\pi\) | ||||
−0.924609 | + | 0.380917i | \(0.875608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.11222 | −0.279179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44887 | 0.174365 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.1630 | −0.945571 | −0.472785 | − | 0.881178i | \(-0.656751\pi\) | ||||
−0.472785 | + | 0.881178i | \(0.656751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.39477 | −0.288497 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.2885 | −0.400781 | −0.200391 | − | 0.979716i | \(-0.564221\pi\) | ||||
−0.200391 | + | 0.979716i | \(0.564221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.93598 | 0.230883 | 0.115441 | − | 0.993314i | \(-0.463172\pi\) | ||||
0.115441 | + | 0.993314i | \(0.463172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.44496 | 0.250302 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.6476 | −0.605879 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.1089 | 0.390831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.3799 | 1.40443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.7053 | 1.56907 | 0.784537 | − | 0.620082i | \(-0.212901\pi\) | ||||
0.784537 | + | 0.620082i | \(0.212901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.8761 | −0.725469 | −0.362734 | − | 0.931893i | \(-0.618157\pi\) | ||||
−0.362734 | + | 0.931893i | \(0.618157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.59933 | 0.253259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.75638 | −0.297225 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.6576 | −0.752179 | −0.376089 | − | 0.926583i | \(-0.622731\pi\) | ||||
−0.376089 | + | 0.926583i | \(0.622731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.24384 | −0.0856079 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.3333 | 0.927025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.2451 | 1.83533 | 0.917665 | − | 0.397354i | \(-0.130072\pi\) | ||||
0.917665 | + | 0.397354i | \(0.130072\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35.9073 | −1.36401 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.47293 | 0.131546 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.49047 | −0.245492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.512889 | 0.0193715 | 0.00968577 | − | 0.999953i | \(-0.496917\pi\) | ||||
0.00968577 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.30266 | −0.162278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.45428 | 0.205129 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.84618 | −0.332225 | −0.166113 | − | 0.986107i | \(-0.553122\pi\) | ||||
−0.166113 | + | 0.986107i | \(0.553122\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.79798 | −0.142436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.77889 | 0.253871 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.09806 | 0.227736 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.84456 | −0.292553 | −0.146276 | − | 0.989244i | \(-0.546729\pi\) | ||||
−0.146276 | + | 0.989244i | \(0.546729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.3333 | −0.682767 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.82643 | −0.0679258 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.91130 | −0.107974 | −0.0539870 | − | 0.998542i | \(-0.517193\pi\) | ||||
−0.0539870 | + | 0.998542i | \(0.517193\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.6475 | −0.468427 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.4663 | −0.683001 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.7775 | 1.24760 | 0.623800 | − | 0.781584i | \(-0.285588\pi\) | ||||
0.623800 | + | 0.781584i | \(0.285588\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.7893 | −0.728950 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8030 | 1.31703 | 0.658517 | − | 0.752566i | \(-0.271184\pi\) | ||||
0.658517 | + | 0.752566i | \(0.271184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.11222 | −0.0408583 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.66948 | −0.207993 | −0.103996 | − | 0.994578i | \(-0.533163\pi\) | ||||
−0.103996 | + | 0.994578i | \(0.533163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.1748 | 0.701569 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.1795 | 1.79698 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4679 | 1.00232 | 0.501159 | − | 0.865355i | \(-0.332907\pi\) | ||||
0.501159 | + | 0.865355i | \(0.332907\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.63445 | −0.0595628 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.6370 | 1.51332 | 0.756662 | − | 0.653806i | \(-0.226829\pi\) | ||||
0.756662 | + | 0.653806i | \(0.226829\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.82040 | 0.211267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.46967 | −0.343275 | −0.171638 | − | 0.985160i | \(-0.554906\pi\) | ||||
−0.171638 | + | 0.985160i | \(0.554906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.3219 | −1.35114 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.54437 | −0.127980 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.90858 | 0.0688253 | 0.0344127 | − | 0.999408i | \(-0.489044\pi\) | ||||
0.0344127 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.28510 | −0.334395 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.4007 | 1.02150 | 0.510751 | − | 0.859729i | \(-0.329367\pi\) | ||||
0.510751 | + | 0.859729i | \(0.329367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.36420 | 0.264189 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.599328 | −0.0214732 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.9775 | 2.03881 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.4053 | −0.657753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.6708 | 0.558605 | 0.279303 | − | 0.960203i | \(-0.409897\pi\) | ||||
0.279303 | + | 0.960203i | \(0.409897\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.640931 | −0.0228178 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.7564 | −1.20024 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.1299 | 0.643811 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.9225 | 1.30786 | 0.653932 | − | 0.756554i | \(-0.273118\pi\) | ||||
0.653932 | + | 0.756554i | \(0.273118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.8478 | −2.40028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.8362 | −1.58421 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.3325 | −0.399914 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.8742 | 0.417993 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.0465 | 1.51343 | 0.756716 | − | 0.653743i | \(-0.226802\pi\) | ||||
0.756716 | + | 0.653743i | \(0.226802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.2469 | −1.13234 | −0.566170 | − | 0.824288i | \(-0.691575\pi\) | ||||
−0.566170 | + | 0.824288i | \(0.691575\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.19475 | 0.0769731 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.18676 | 0.111491 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.8944 | −0.625280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.18121 | 0.180826 | 0.0904128 | − | 0.995904i | \(-0.471181\pi\) | ||||
0.0904128 | + | 0.995904i | \(0.471181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.8517 | −0.901133 | −0.450567 | − | 0.892743i | \(-0.648778\pi\) | ||||
−0.450567 | + | 0.892743i | \(0.648778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.97816 | −0.346974 | −0.173487 | − | 0.984836i | \(-0.555504\pi\) | ||||
−0.173487 | + | 0.984836i | \(0.555504\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.9808 | 0.763425 | 0.381713 | − | 0.924281i | \(-0.375334\pi\) | ||||
0.381713 | + | 0.924281i | \(0.375334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.38149 | 0.186682 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.2848 | −0.633531 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.97359 | 0.275607 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1089 | 0.556140 | 0.278070 | − | 0.960561i | \(-0.410305\pi\) | ||||
0.278070 | + | 0.960561i | \(0.410305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.321887 | 0.0110864 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.9735 | −0.686298 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.91020 | 0.0998779 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.2211 | 0.384653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.9615 | −1.53945 | −0.769727 | − | 0.638373i | \(-0.779608\pi\) | ||||
−0.769727 | + | 0.638373i | \(0.779608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.2431 | 1.57963 | 0.789817 | − | 0.613343i | \(-0.210176\pi\) | ||||
0.789817 | + | 0.613343i | \(0.210176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7772 | 0.367713 | 0.183856 | − | 0.982953i | \(-0.441142\pi\) | ||||
0.183856 | + | 0.982953i | \(0.441142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.02578 | 0.0349584 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.7966 | 0.776007 | 0.388003 | − | 0.921658i | \(-0.373165\pi\) | ||||
0.388003 | + | 0.921658i | \(0.373165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.90400 | 0.302396 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.82040 | −0.197444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.86201 | −0.334161 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.61523 | 0.190047 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.94644 | 0.167029 | 0.0835146 | − | 0.996507i | \(-0.473385\pi\) | ||||
0.0835146 | + | 0.996507i | \(0.473385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.86201 | −0.0628039 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.53033 | 0.0852490 | 0.0426245 | − | 0.999091i | \(-0.486428\pi\) | ||||
0.0426245 | + | 0.999091i | \(0.486428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7430 | 1.00093 | 0.500465 | − | 0.865757i | \(-0.333162\pi\) | ||||
0.500465 | + | 0.865757i | \(0.333162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.5450 | 1.52925 | 0.764626 | − | 0.644474i | \(-0.222924\pi\) | ||||
0.764626 | + | 0.644474i | \(0.222924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.3591 | 0.649282 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9568 | −0.903086 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7086 | 0.391813 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.90059 | 0.0968480 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.5960 | −0.520155 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68.0897 | 2.26840 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.45428 | −0.181507 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.2034 | 1.10250 | 0.551250 | − | 0.834340i | \(-0.314151\pi\) | ||||
0.551250 | + | 0.834340i | \(0.314151\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.64093 | 0.153930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.7788 | −1.84803 | −0.924017 | − | 0.382351i | \(-0.875114\pi\) | ||||
−0.924017 | + | 0.382351i | \(0.875114\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.3853 | 0.972513 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.2715 | −1.42895 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.5769 | 0.942665 | 0.471333 | − | 0.881956i | \(-0.343773\pi\) | ||||
0.471333 | + | 0.881956i | \(0.343773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.91020 | −0.293601 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.3947 | 0.934622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.5994 | −0.512352 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.4937 | −1.78788 | −0.893940 | − | 0.448186i | \(-0.852070\pi\) | ||||
−0.893940 | + | 0.448186i | \(0.852070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.15544 | 0.103415 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.23180 | 0.0730659 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.1484 | 1.21359 | 0.606793 | − | 0.794860i | \(-0.292456\pi\) | ||||
0.606793 | + | 0.794860i | \(0.292456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.493704 | 0.0161114 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.3973 | 1.05612 | 0.528061 | − | 0.849206i | \(-0.322919\pi\) | ||||
0.528061 | + | 0.849206i | \(0.322919\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56301 | 0.0508986 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.4662 | 1.15250 | 0.576249 | − | 0.817275i | \(-0.304516\pi\) | ||||
0.576249 | + | 0.817275i | \(0.304516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.64752 | −0.183326 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.3557 | 0.465516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.3411 | 0.464553 | 0.232277 | − | 0.972650i | \(-0.425383\pi\) | ||||
0.232277 | + | 0.972650i | \(0.425383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.3908 | −0.432864 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.3125 | −0.817383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.2435 | −0.782048 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.8458 | 1.34846 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.9351 | −0.898331 | −0.449165 | − | 0.893449i | \(-0.648279\pi\) | ||||
−0.449165 | + | 0.893449i | \(0.648279\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.11222 | −0.0999788 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5993 | 1.36708 | 0.683539 | − | 0.729914i | \(-0.260440\pi\) | ||||
0.683539 | + | 0.729914i | \(0.260440\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4132 | 0.333833 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.5597 | −1.26563 | −0.632813 | − | 0.774304i | \(-0.718100\pi\) | ||||
−0.632813 | + | 0.774304i | \(0.718100\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.7114 | −2.19603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.7564 | −1.01390 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.7689 | −1.26843 | −0.634215 | − | 0.773157i | \(-0.718677\pi\) | ||||
−0.634215 | + | 0.773157i | \(0.718677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.0398 | −0.637874 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.31087 | −0.264270 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.2019 | −1.75355 | −0.876773 | − | 0.480905i | \(-0.840308\pi\) | ||||
−0.876773 | + | 0.480905i | \(0.840308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.29664 | −0.136350 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.6543 | 0.369097 | 0.184548 | − | 0.982823i | \(-0.440918\pi\) | ||||
0.184548 | + | 0.982823i | \(0.440918\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.1987 | 0.417587 |
(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 | 7600.2.a.ck.1.4 | 6 | ||
4.3 | odd | 2 | 475.2.a.j.1.6 | 6 | |||
5.2 | odd | 4 | 1520.2.d.h.609.3 | 6 | |||
5.3 | odd | 4 | 1520.2.d.h.609.4 | 6 | |||
5.4 | even | 2 | inner | 7600.2.a.ck.1.3 | 6 | ||
12.11 | even | 2 | 4275.2.a.br.1.1 | 6 | |||
20.3 | even | 4 | 95.2.b.b.39.1 | ✓ | 6 | ||
20.7 | even | 4 | 95.2.b.b.39.6 | yes | 6 | ||
20.19 | odd | 2 | 475.2.a.j.1.1 | 6 | |||
60.23 | odd | 4 | 855.2.c.d.514.6 | 6 | |||
60.47 | odd | 4 | 855.2.c.d.514.1 | 6 | |||
60.59 | even | 2 | 4275.2.a.br.1.6 | 6 | |||
76.75 | even | 2 | 9025.2.a.bx.1.1 | 6 | |||
380.227 | odd | 4 | 1805.2.b.e.1084.1 | 6 | |||
380.303 | odd | 4 | 1805.2.b.e.1084.6 | 6 | |||
380.379 | even | 2 | 9025.2.a.bx.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.1 | ✓ | 6 | 20.3 | even | 4 | ||
95.2.b.b.39.6 | yes | 6 | 20.7 | even | 4 | ||
475.2.a.j.1.1 | 6 | 20.19 | odd | 2 | |||
475.2.a.j.1.6 | 6 | 4.3 | odd | 2 | |||
855.2.c.d.514.1 | 6 | 60.47 | odd | 4 | |||
855.2.c.d.514.6 | 6 | 60.23 | odd | 4 | |||
1520.2.d.h.609.3 | 6 | 5.2 | odd | 4 | |||
1520.2.d.h.609.4 | 6 | 5.3 | odd | 4 | |||
1805.2.b.e.1084.1 | 6 | 380.227 | odd | 4 | |||
1805.2.b.e.1084.6 | 6 | 380.303 | odd | 4 | |||
4275.2.a.br.1.1 | 6 | 12.11 | even | 2 | |||
4275.2.a.br.1.6 | 6 | 60.59 | even | 2 | |||
7600.2.a.ck.1.3 | 6 | 5.4 | even | 2 | inner | ||
7600.2.a.ck.1.4 | 6 | 1.1 | even | 1 | trivial | ||
9025.2.a.bx.1.1 | 6 | 76.75 | even | 2 | |||
9025.2.a.bx.1.6 | 6 | 380.379 | even | 2 |