Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
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: | \( x^{7} - 3x^{6} - 7x^{5} + 24x^{4} + x^{3} - 35x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.58319\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −1.58319 | −0.914057 | −0.457029 | − | 0.889452i | \(-0.651086\pi\) | ||||
−0.457029 | + | 0.889452i | \(0.651086\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.84620 | −1.07576 | −0.537881 | − | 0.843020i | \(-0.680775\pi\) | ||||
−0.537881 | + | 0.843020i | \(0.680775\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.493499 | −0.164500 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.98637 | −0.598913 | −0.299457 | − | 0.954110i | \(-0.596805\pi\) | ||||
−0.299457 | + | 0.954110i | \(0.596805\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.69204 | −1.30134 | −0.650668 | − | 0.759362i | \(-0.725511\pi\) | ||||
−0.650668 | + | 0.759362i | \(0.725511\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16675 | −0.768050 | −0.384025 | − | 0.923323i | \(-0.625462\pi\) | ||||
−0.384025 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.16110 | 1.41345 | 0.706727 | − | 0.707486i | \(-0.250171\pi\) | ||||
0.706727 | + | 0.707486i | \(0.250171\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.50609 | 0.983309 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.53088 | 1.06442 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.61816 | −1.22896 | −0.614481 | − | 0.788932i | \(-0.710635\pi\) | ||||
−0.614481 | + | 0.788932i | \(0.710635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.29732 | 1.49024 | 0.745121 | − | 0.666929i | \(-0.232392\pi\) | ||||
0.745121 | + | 0.666929i | \(0.232392\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.14481 | 0.547441 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.71181 | 0.281420 | 0.140710 | − | 0.990051i | \(-0.455061\pi\) | ||||
0.140710 | + | 0.990051i | \(0.455061\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.42840 | 1.18950 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.72440 | 1.05018 | 0.525088 | − | 0.851048i | \(-0.324033\pi\) | ||||
0.525088 | + | 0.851048i | \(0.324033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.177968 | −0.0271399 | −0.0135700 | − | 0.999908i | \(-0.504320\pi\) | ||||
−0.0135700 | + | 0.999908i | \(0.504320\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4749 | 1.67378 | 0.836891 | − | 0.547369i | \(-0.184371\pi\) | ||||
0.836891 | + | 0.547369i | \(0.184371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.10086 | 0.157266 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.01358 | 0.702042 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.18762 | −0.849934 | −0.424967 | − | 0.905209i | \(-0.639714\pi\) | ||||
−0.424967 | + | 0.905209i | \(0.639714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.75422 | −1.29198 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.61559 | 0.991465 | 0.495733 | − | 0.868475i | \(-0.334900\pi\) | ||||
0.495733 | + | 0.868475i | \(0.334900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8577 | 1.51822 | 0.759109 | − | 0.650964i | \(-0.225635\pi\) | ||||
0.759109 | + | 0.650964i | \(0.225635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.40460 | 0.176963 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.07554 | 0.375737 | 0.187868 | − | 0.982194i | \(-0.439842\pi\) | ||||
0.187868 | + | 0.982194i | \(0.439842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.58319 | −0.190594 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.96195 | 0.232840 | 0.116420 | − | 0.993200i | \(-0.462858\pi\) | ||||
0.116420 | + | 0.993200i | \(0.462858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.94732 | −0.579041 | −0.289520 | − | 0.957172i | \(-0.593496\pi\) | ||||
−0.289520 | + | 0.957172i | \(0.593496\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65361 | 0.644289 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.53182 | −0.959905 | −0.479952 | − | 0.877295i | \(-0.659346\pi\) | ||||
−0.479952 | + | 0.877295i | \(0.659346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.27596 | −0.808440 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.49429 | 0.383548 | 0.191774 | − | 0.981439i | \(-0.438576\pi\) | ||||
0.191774 | + | 0.981439i | \(0.438576\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.4778 | 1.12334 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.07506 | 0.749954 | 0.374977 | − | 0.927034i | \(-0.377651\pi\) | ||||
0.374977 | + | 0.927034i | \(0.377651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3545 | 1.39993 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.1363 | −1.36217 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00705 | 0.711458 | 0.355729 | − | 0.934589i | \(-0.384233\pi\) | ||||
0.355729 | + | 0.934589i | \(0.384233\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.980272 | 0.0985210 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.22362 | 0.718777 | 0.359389 | − | 0.933188i | \(-0.382985\pi\) | ||||
0.359389 | + | 0.933188i | \(0.382985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8178 | −1.26297 | −0.631487 | − | 0.775386i | \(-0.717555\pi\) | ||||
−0.631487 | + | 0.775386i | \(0.717555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6841 | −1.12954 | −0.564772 | − | 0.825247i | \(-0.691036\pi\) | ||||
−0.564772 | + | 0.825247i | \(0.691036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.6019 | −1.30283 | −0.651413 | − | 0.758723i | \(-0.725824\pi\) | ||||
−0.651413 | + | 0.758723i | \(0.725824\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.71013 | −0.257234 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.44526 | −0.135959 | −0.0679795 | − | 0.997687i | \(-0.521655\pi\) | ||||
−0.0679795 | + | 0.997687i | \(0.521655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.31552 | 0.214069 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.01322 | 0.826240 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.05433 | −0.641303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.6460 | −0.959920 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.12328 | −0.809561 | −0.404780 | − | 0.914414i | \(-0.632652\pi\) | ||||
−0.404780 | + | 0.914414i | \(0.632652\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.281758 | 0.0248074 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.33180 | −0.815323 | −0.407661 | − | 0.913133i | \(-0.633656\pi\) | ||||
−0.407661 | + | 0.913133i | \(0.633656\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5357 | −1.52054 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.0013 | 1.79426 | 0.897129 | − | 0.441768i | \(-0.145649\pi\) | ||||
0.897129 | + | 0.441768i | \(0.145649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1299 | 1.36812 | 0.684061 | − | 0.729425i | \(-0.260212\pi\) | ||||
0.684061 | + | 0.729425i | \(0.260212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1669 | −1.52993 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.32012 | 0.779388 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.74288 | −0.143750 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.57227 | −0.784191 | −0.392096 | − | 0.919925i | \(-0.628250\pi\) | ||||
−0.392096 | + | 0.919925i | \(0.628250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.04120 | −0.247489 | −0.123745 | − | 0.992314i | \(-0.539490\pi\) | ||||
−0.123745 | + | 0.992314i | \(0.539490\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.56279 | 0.126344 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4786 | 0.995900 | 0.497950 | − | 0.867206i | \(-0.334086\pi\) | ||||
0.497950 | + | 0.867206i | \(0.334086\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.79619 | 0.776889 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.84620 | −0.224312 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3939 | −1.28407 | −0.642034 | − | 0.766676i | \(-0.721909\pi\) | ||||
−0.642034 | + | 0.766676i | \(0.721909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.13265 | −0.629323 | −0.314662 | − | 0.949204i | \(-0.601891\pi\) | ||||
−0.314662 | + | 0.949204i | \(0.601891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.01521 | 0.693477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.04050 | −0.232513 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5256 | 0.800250 | 0.400125 | − | 0.916461i | \(-0.368967\pi\) | ||||
0.400125 | + | 0.916461i | \(0.368967\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0570 | −0.906256 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.5421 | −1.53539 | −0.767695 | − | 0.640816i | \(-0.778596\pi\) | ||||
−0.767695 | + | 0.640816i | \(0.778596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0754 | −1.64085 | −0.820424 | − | 0.571756i | \(-0.806263\pi\) | ||||
−0.820424 | + | 0.571756i | \(0.806263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.7730 | −1.38774 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.29034 | 0.459995 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.7420 | −1.14506 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.50910 | 0.326267 | 0.163133 | − | 0.986604i | \(-0.447840\pi\) | ||||
0.163133 | + | 0.986604i | \(0.447840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1534 | −1.52266 | −0.761329 | − | 0.648366i | \(-0.775453\pi\) | ||||
−0.761329 | + | 0.648366i | \(0.775453\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1475 | −0.722980 | −0.361490 | − | 0.932376i | \(-0.617732\pi\) | ||||
−0.361490 | + | 0.932376i | \(0.617732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.57598 | −0.466159 | −0.233079 | − | 0.972458i | \(-0.574880\pi\) | ||||
−0.233079 | + | 0.972458i | \(0.574880\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.86917 | −0.343445 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.8366 | 1.32207 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.493499 | −0.0343005 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.2382 | −0.846536 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.5357 | 1.82680 | 0.913398 | − | 0.407069i | \(-0.133449\pi\) | ||||
0.913398 | + | 0.407069i | \(0.133449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.10614 | −0.212829 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.6158 | −1.60315 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.83257 | 0.529276 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.8585 | 0.999492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9231 | −1.40111 | −0.700557 | − | 0.713597i | \(-0.747065\pi\) | ||||
−0.700557 | + | 0.713597i | \(0.747065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.32581 | −0.618975 | −0.309488 | − | 0.950903i | \(-0.600158\pi\) | ||||
−0.309488 | + | 0.950903i | \(0.600158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.5189 | 1.95066 | 0.975332 | − | 0.220742i | \(-0.0708479\pi\) | ||||
0.975332 | + | 0.220742i | \(0.0708479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.95076 | −0.588917 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.9849 | 1.89886 | 0.949431 | − | 0.313974i | \(-0.101661\pi\) | ||||
0.949431 | + | 0.313974i | \(0.101661\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5075 | 0.877408 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.62209 | 0.622401 | 0.311201 | − | 0.950344i | \(-0.399269\pi\) | ||||
0.311201 | + | 0.950344i | \(0.399269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5745 | 1.00324 | 0.501621 | − | 0.865088i | \(-0.332737\pi\) | ||||
0.501621 | + | 0.865088i | \(0.332737\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.07340 | −0.325459 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.9081 | −1.83938 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.53214 | −0.350585 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.8066 | 1.43954 | 0.719770 | − | 0.694213i | \(-0.244247\pi\) | ||||
0.719770 | + | 0.694213i | \(0.244247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.98637 | −0.124882 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5591 | −0.721038 | −0.360519 | − | 0.932752i | \(-0.617400\pi\) | ||||
−0.360519 | + | 0.932752i | \(0.617400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.87216 | −0.302742 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.26606 | 0.202164 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.57534 | 0.405453 | 0.202726 | − | 0.979235i | \(-0.435020\pi\) | ||||
0.202726 | + | 0.979235i | \(0.435020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.2012 | −0.685501 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.6536 | −1.01539 | −0.507694 | − | 0.861537i | \(-0.669502\pi\) | ||||
−0.507694 | + | 0.861537i | \(0.669502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8675 | 1.44985 | 0.724925 | − | 0.688828i | \(-0.241874\pi\) | ||||
0.724925 | + | 0.688828i | \(0.241874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.1427 | −1.27962 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.65369 | −0.339697 | −0.169849 | − | 0.985470i | \(-0.554328\pi\) | ||||
−0.169849 | + | 0.985470i | \(0.554328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.09472 | −0.245144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.7408 | −1.89350 | −0.946750 | − | 0.321971i | \(-0.895655\pi\) | ||||
−0.946750 | + | 0.321971i | \(0.895655\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.998092 | −0.0593304 | −0.0296652 | − | 0.999560i | \(-0.509444\pi\) | ||||
−0.0296652 | + | 0.999560i | \(0.509444\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.1390 | −1.12974 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.97168 | −0.410099 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0935 | −0.650314 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.8947 | −0.811739 | −0.405869 | − | 0.913931i | \(-0.633031\pi\) | ||||
−0.405869 | + | 0.913931i | \(0.633031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9864 | −0.637495 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.69204 | −0.271347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.506534 | 0.0291961 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.4364 | −0.657003 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.66633 | 0.209249 | 0.104624 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104624 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.2930 | 1.15443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4210 | 0.817741 | 0.408870 | − | 0.912593i | \(-0.365923\pi\) | ||||
0.408870 | + | 0.912593i | \(0.365923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5046 | 0.593754 | 0.296877 | − | 0.954916i | \(-0.404055\pi\) | ||||
0.296877 | + | 0.954916i | \(0.404055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.0818 | −1.80189 | −0.900946 | − | 0.433931i | \(-0.857126\pi\) | ||||
−0.900946 | + | 0.433931i | \(0.857126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.1461 | 0.736042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.4982 | 1.03247 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5107 | −1.08560 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.5344 | 1.19086 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32.6598 | −1.80059 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.71307 | −0.533879 | −0.266939 | − | 0.963713i | \(-0.586012\pi\) | ||||
−0.266939 | + | 0.963713i | \(0.586012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.844778 | −0.0462935 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.131832 | −0.00718136 | −0.00359068 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359068 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.28813 | 0.124274 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4815 | −0.892526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7901 | 0.906582 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.1981 | 0.708512 | 0.354256 | − | 0.935148i | \(-0.384734\pi\) | ||||
0.354256 | + | 0.935148i | \(0.384734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0451 | −1.82239 | −0.911197 | − | 0.411971i | \(-0.864841\pi\) | ||||
−0.911197 | + | 0.411971i | \(0.864841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.9511 | −1.38517 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.8593 | 0.577984 | 0.288992 | − | 0.957331i | \(-0.406680\pi\) | ||||
0.288992 | + | 0.957331i | \(0.406680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.2697 | −0.755231 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3091 | 1.07188 | 0.535938 | − | 0.844257i | \(-0.319958\pi\) | ||||
0.535938 | + | 0.844257i | \(0.319958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9592 | 0.997853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.1684 | 0.586188 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.6731 | 0.974727 | 0.487364 | − | 0.873199i | \(-0.337959\pi\) | ||||
0.487364 | + | 0.873199i | \(0.337959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.31848 | −0.172753 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.6112 | 0.914328 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.51979 | 0.492916 | 0.246458 | − | 0.969153i | \(-0.420733\pi\) | ||||
0.246458 | + | 0.969153i | \(0.420733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.0527 | 1.59929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8304 | −0.967251 | −0.483625 | − | 0.875275i | \(-0.660680\pi\) | ||||
−0.483625 | + | 0.875275i | \(0.660680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4439 | 0.739985 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9401 | 0.559015 | 0.279507 | − | 0.960144i | \(-0.409829\pi\) | ||||
0.279507 | + | 0.960144i | \(0.409829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0878272 | 0.00446451 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.2830 | 1.12979 | 0.564896 | − | 0.825162i | \(-0.308916\pi\) | ||||
0.564896 | + | 0.825162i | \(0.308916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.16675 | −0.160150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7740 | 0.745252 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8388 | −0.543983 | −0.271991 | − | 0.962300i | \(-0.587682\pi\) | ||||
−0.271991 | + | 0.962300i | \(0.587682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.7625 | 1.38986 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.71329 | −0.135495 | −0.0677476 | − | 0.997702i | \(-0.521581\pi\) | ||||
−0.0677476 | + | 0.997702i | \(0.521581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.9313 | −1.93931 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.40029 | −0.168546 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6271 | 1.06939 | 0.534696 | − | 0.845044i | \(-0.320426\pi\) | ||||
0.534696 | + | 0.845044i | \(0.320426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.2490 | −1.64005 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.6755 | −1.06658 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.5368 | −1.25054 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.00587 | −0.195700 | −0.0978498 | − | 0.995201i | \(-0.531196\pi\) | ||||
−0.0978498 | + | 0.995201i | \(0.531196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4251 | 1.23914 | 0.619572 | − | 0.784940i | \(-0.287306\pi\) | ||||
0.619572 | + | 0.784940i | \(0.287306\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.66284 | −0.275337 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.7493 | −1.63324 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.7556 | −0.712405 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.07679 | −0.0518673 | −0.0259336 | − | 0.999664i | \(-0.508256\pi\) | ||||
−0.0259336 | + | 0.999664i | \(0.508256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.93871 | −0.189283 | −0.0946413 | − | 0.995511i | \(-0.530170\pi\) | ||||
−0.0946413 | + | 0.995511i | \(0.530170\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.16110 | 0.294726 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.1539 | −0.627802 | −0.313901 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313901 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.543274 | −0.0258702 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.95394 | 0.425415 | 0.212707 | − | 0.977116i | \(-0.431772\pi\) | ||||
0.212707 | + | 0.977116i | \(0.431772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.1548 | 0.716795 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.23267 | 0.388524 | 0.194262 | − | 0.980950i | \(-0.437769\pi\) | ||||
0.194262 | + | 0.980950i | \(0.437769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.3571 | −0.628964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.81480 | 0.226219 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.3473 | 1.70026 | 0.850128 | − | 0.526576i | \(-0.176524\pi\) | ||||
0.850128 | + | 0.526576i | \(0.176524\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.5149 | −0.817527 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2421 | −0.709894 | −0.354947 | − | 0.934886i | \(-0.615501\pi\) | ||||
−0.354947 | + | 0.934886i | \(0.615501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.57424 | 0.259057 | 0.129528 | − | 0.991576i | \(-0.458654\pi\) | ||||
0.129528 | + | 0.991576i | \(0.458654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.21488 | 0.287590 | 0.143795 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143795 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.75360 | −0.404204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.7560 | −0.910309 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.353511 | 0.0162545 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.05358 | 0.139814 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.4168 | 1.57254 | 0.786272 | − | 0.617880i | \(-0.212008\pi\) | ||||
0.786272 | + | 0.617880i | \(0.212008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.03189 | −0.366223 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.50609 | 0.205034 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.7752 | −1.03204 | −0.516021 | − | 0.856576i | \(-0.672587\pi\) | ||||
−0.516021 | + | 0.856576i | \(0.672587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.9547 | 1.17371 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.16911 | −0.143020 | −0.0715099 | − | 0.997440i | \(-0.522782\pi\) | ||||
−0.0715099 | + | 0.997440i | \(0.522782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.9581 | 0.943905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.58410 | −0.250481 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0809 | 0.630346 | 0.315173 | − | 0.949034i | \(-0.397937\pi\) | ||||
0.315173 | + | 0.949034i | \(0.397937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.8756 | 0.575237 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.4946 | −0.958399 | −0.479199 | − | 0.877706i | \(-0.659073\pi\) | ||||
−0.479199 | + | 0.877706i | \(0.659073\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.2728 | −0.633878 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.0952 | −1.51124 | −0.755622 | − | 0.655008i | \(-0.772665\pi\) | ||||
−0.755622 | + | 0.655008i | \(0.772665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0811 | 0.622910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.0764 | 1.50451 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.7933 | −1.00245 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6641 | −0.731474 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.1367 | −0.619339 | −0.309669 | − | 0.950844i | \(-0.600218\pi\) | ||||
−0.309669 | + | 0.950844i | \(0.600218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2020 | 0.489828 | 0.244914 | − | 0.969545i | \(-0.421240\pi\) | ||||
0.244914 | + | 0.969545i | \(0.421240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.2756 | −1.14458 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.75829 | −0.163096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.5511 | −1.36663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.5221 | 1.40343 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.18672 | −0.0941887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.6704 | −1.44760 | −0.723802 | − | 0.690008i | \(-0.757607\pi\) | ||||
−0.723802 | + | 0.690008i | \(0.757607\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.9496 | 1.49983 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.1062 | −0.987949 | −0.493975 | − | 0.869476i | \(-0.664456\pi\) | ||||
−0.493975 | + | 0.869476i | \(0.664456\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.85174 | −0.249746 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.7752 | −1.73708 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.2833 | 1.03263 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.48937 | −0.147849 | −0.0739246 | − | 0.997264i | \(-0.523552\pi\) | ||||
−0.0739246 | + | 0.997264i | \(0.523552\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.835034 | 0.0353182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.95883 | −0.420462 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.8593 | −1.63772 | −0.818862 | − | 0.573991i | \(-0.805394\pi\) | ||||
−0.818862 | + | 0.573991i | \(0.805394\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.7089 | 0.869690 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.2055 | −0.972823 | −0.486412 | − | 0.873730i | \(-0.661694\pi\) | ||||
−0.486412 | + | 0.873730i | \(0.661694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.39836 | 0.225914 | 0.112957 | − | 0.993600i | \(-0.463968\pi\) | ||||
0.112957 | + | 0.993600i | \(0.463968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.13877 | −0.298226 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.1082 | 0.545701 | 0.272850 | − | 0.962056i | \(-0.412034\pi\) | ||||
0.272850 | + | 0.962056i | \(0.412034\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.4900 | 1.39180 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.94546 | −0.412607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.2909 | 0.509037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.9646 | 0.535108 | 0.267554 | − | 0.963543i | \(-0.413785\pi\) | ||||
0.267554 | + | 0.963543i | \(0.413785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.1206 | 2.10639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.0655 | 0.660845 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.0225 | 0.699030 | 0.349515 | − | 0.936931i | \(-0.386346\pi\) | ||||
0.349515 | + | 0.936931i | \(0.386346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.4110 | 0.426096 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.98111 | 0.244381 | 0.122191 | − | 0.992507i | \(-0.461008\pi\) | ||||
0.122191 | + | 0.992507i | \(0.461008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3680 | −0.871617 | −0.435809 | − | 0.900039i | \(-0.643538\pi\) | ||||
−0.435809 | + | 0.900039i | \(0.643538\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.51778 | −0.0618086 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.5464 | 0.712186 | 0.356093 | − | 0.934450i | \(-0.384109\pi\) | ||||
0.356093 | + | 0.934450i | \(0.384109\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.8220 | −1.20845 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.8405 | −2.17815 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.4601 | −1.83612 | −0.918059 | − | 0.396444i | \(-0.870244\pi\) | ||||
−0.918059 | + | 0.396444i | \(0.870244\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.8720 | −1.04157 | −0.520785 | − | 0.853688i | \(-0.674360\pi\) | ||||
−0.520785 | + | 0.853688i | \(0.674360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.20381 | 0.128772 | 0.0643859 | − | 0.997925i | \(-0.479491\pi\) | ||||
0.0643859 | + | 0.997925i | \(0.479491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.53088 | 0.221947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.1370 | −0.806773 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.3755 | 0.773783 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.42089 | −0.216145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0248650 | −0.000989858 0 | −0.000494929 | − | 1.00000i | \(-0.500158\pi\) | ||||
−0.000494929 | 1.00000i | \(0.500158\pi\) | ||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −42.0112 | −1.66980 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.16528 | −0.204656 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.968219 | −0.0383022 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.77145 | −0.385949 | −0.192975 | − | 0.981204i | \(-0.561813\pi\) | ||||
−0.192975 | + | 0.981204i | \(0.561813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.8211 | −1.45208 | −0.726041 | − | 0.687651i | \(-0.758642\pi\) | ||||
−0.726041 | + | 0.687651i | \(0.758642\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.5570 | 1.83034 | 0.915172 | − | 0.403064i | \(-0.132055\pi\) | ||||
0.915172 | + | 0.403064i | \(0.132055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.1274 | −0.593802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.3884 | 1.46537 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.76029 | −0.108018 | −0.0540092 | − | 0.998540i | \(-0.517200\pi\) | ||||
−0.0540092 | + | 0.998540i | \(0.517200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.44150 | 0.0952520 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.3922 | −1.53450 | −0.767252 | − | 0.641346i | \(-0.778376\pi\) | ||||
−0.767252 | + | 0.641346i | \(0.778376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7641 | −0.690943 | −0.345472 | − | 0.938429i | \(-0.612281\pi\) | ||||
−0.345472 | + | 0.938429i | \(0.612281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.5239 | −0.913593 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.61816 | −0.256256 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.1253 | 1.28070 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.5537 | −0.909280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.7072 | 0.913847 | 0.456923 | − | 0.889506i | \(-0.348951\pi\) | ||||
0.456923 | + | 0.889506i | \(0.348951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.3507 | −1.89670 | −0.948352 | − | 0.317221i | \(-0.897250\pi\) | ||||
−0.948352 | + | 0.317221i | \(0.897250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.9435 | −0.765361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7646 | 0.565779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6461 | 0.598682 | 0.299341 | − | 0.954146i | \(-0.403233\pi\) | ||||
0.299341 | + | 0.954146i | \(0.403233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.7341 | −1.78302 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.0325 | 1.10605 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.79498 | −0.144368 | −0.0721839 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721839 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.79005 | −0.105985 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.2945 | −0.806587 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −45.8887 | −1.73567 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.751725 | 0.0283923 | 0.0141961 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141961 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5467 | 0.397775 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.5599 | −0.773234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.52035 | 0.169765 | 0.0848827 | − | 0.996391i | \(-0.472948\pi\) | ||||
0.0848827 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.21044 | 0.157904 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.29732 | 0.310737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.2336 | −0.568910 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.6742 | 1.36772 | 0.683859 | − | 0.729614i | \(-0.260300\pi\) | ||||
0.683859 | + | 0.729614i | \(0.260300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.4820 | 1.35866 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.6574 | −0.917020 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.6449 | −1.24782 | −0.623910 | − | 0.781496i | \(-0.714457\pi\) | ||||
−0.623910 | + | 0.781496i | \(0.714457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8601 | 1.10593 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.563582 | 0.0208448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.5745 | −1.75720 | −0.878602 | − | 0.477555i | \(-0.841523\pi\) | ||||
−0.878602 | + | 0.477555i | \(0.841523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.10916 | −0.225034 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.8914 | −1.06279 | −0.531395 | − | 0.847124i | \(-0.678332\pi\) | ||||
−0.531395 | + | 0.847124i | \(0.678332\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.7672 | 1.68130 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.61970 | 0.132794 | 0.0663969 | − | 0.997793i | \(-0.478850\pi\) | ||||
0.0663969 | + | 0.997793i | \(0.478850\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.72443 | −0.0630936 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.2553 | 1.21512 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.2050 | −0.700801 | −0.350401 | − | 0.936600i | \(-0.613955\pi\) | ||||
−0.350401 | + | 0.936600i | \(0.613955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.1073 | −1.31582 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.6638 | 0.460275 | 0.230137 | − | 0.973158i | \(-0.426082\pi\) | ||||
0.230137 | + | 0.973158i | \(0.426082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.14481 | 0.114149 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.9053 | −1.41032 | −0.705159 | − | 0.709050i | \(-0.749124\pi\) | ||||
−0.705159 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.7138 | 1.40153 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.7326 | −1.29023 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.16816 | 0.150308 | 0.0751539 | − | 0.997172i | \(-0.476055\pi\) | ||||
0.0751539 | + | 0.997172i | \(0.476055\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.3003 | 0.659070 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.6030 | −0.956842 | −0.478421 | − | 0.878131i | \(-0.658791\pi\) | ||||
−0.478421 | + | 0.878131i | \(0.658791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.71358 | 0.276723 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.4297 | 1.48437 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.89716 | −0.139451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.6043 | −1.30813 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.7538 | 0.775440 | 0.387720 | − | 0.921777i | \(-0.373263\pi\) | ||||
0.387720 | + | 0.921777i | \(0.373263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.4100 | −0.370607 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.11351 | 0.146260 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.6366 | −1.97571 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.2490 | −0.363039 | −0.181519 | − | 0.983387i | \(-0.558102\pi\) | ||||
−0.181519 | + | 0.983387i | \(0.558102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.3381 | −1.28555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.49153 | −0.123367 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.82722 | 0.346795 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.3659 | 0.928123 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.0993 | 1.30434 | 0.652170 | − | 0.758072i | \(-0.273859\pi\) | ||||
0.652170 | + | 0.758072i | \(0.273859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.8084 | −1.25740 | −0.628701 | − | 0.777647i | \(-0.716413\pi\) | ||||
−0.628701 | + | 0.777647i | \(0.716413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.7869 | −1.32525 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.09648 | −0.0383610 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.59042 | −0.230288 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5343 | −0.751551 | −0.375775 | − | 0.926711i | \(-0.622624\pi\) | ||||
−0.375775 | + | 0.926711i | \(0.622624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.1466 | −1.43428 | −0.717140 | − | 0.696929i | \(-0.754549\pi\) | ||||
−0.717140 | + | 0.696929i | \(0.754549\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.48319 | −0.329763 | −0.164881 | − | 0.986313i | \(-0.552724\pi\) | ||||
−0.164881 | + | 0.986313i | \(0.552724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.0091 | 0.833872 | 0.416936 | − | 0.908936i | \(-0.363104\pi\) | ||||
0.416936 | + | 0.908936i | \(0.363104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.95088 | 0.310503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.48616 | −0.120788 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.8915 | 1.58624 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.89039 | −0.341454 | −0.170727 | − | 0.985318i | \(-0.554612\pi\) | ||||
−0.170727 | + | 0.985318i | \(0.554612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.8001 | 0.510348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50.2519 | 1.73077 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0781 | 0.689890 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.58017 | 0.0542314 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.71181 | 0.0586802 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.02358 | −0.172004 | −0.0860021 | − | 0.996295i | \(-0.527409\pi\) | ||||
−0.0860021 | + | 0.996295i | \(0.527409\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.8011 | 0.915509 | 0.457754 | − | 0.889079i | \(-0.348654\pi\) | ||||
0.457754 | + | 0.889079i | \(0.348654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.3018 | −0.931525 | −0.465763 | − | 0.884910i | \(-0.654220\pi\) | ||||
−0.465763 | + | 0.884910i | \(0.654220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.3007 | 1.03265 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.22910 | 0.0758796 | 0.0379398 | − | 0.999280i | \(-0.487920\pi\) | ||||
0.0379398 | + | 0.999280i | \(0.487920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.0375 | 0.374854 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.9474 | 0.574900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4305 | −0.488960 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.45797 | −0.117035 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.4517 | 1.56856 | 0.784280 | − | 0.620407i | \(-0.213032\pi\) | ||||
0.784280 | + | 0.620407i | \(0.213032\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.9980 | 0.741975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.6878 | −0.865444 | −0.432722 | − | 0.901527i | \(-0.642447\pi\) | ||||
−0.432722 | + | 0.901527i | \(0.642447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.8481 | 1.64387 | 0.821934 | − | 0.569582i | \(-0.192895\pi\) | ||||
0.821934 | + | 0.569582i | \(0.192895\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.1121 | 1.51472 | 0.757358 | − | 0.653000i | \(-0.226490\pi\) | ||||
0.757358 | + | 0.653000i | \(0.226490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.9667 | 0.870895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.4528 | 0.484185 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 70.6979 | 2.36581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.42840 | 0.248027 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.9130 | −1.83145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.5947 | 0.652792 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.801941 | −0.0266869 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.5516 | 0.516382 | 0.258191 | − | 0.966094i | \(-0.416874\pi\) | ||||
0.258191 | + | 0.966094i | \(0.416874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.56485 | −0.118239 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.1283 | 0.998195 | 0.499097 | − | 0.866546i | \(-0.333665\pi\) | ||||
0.499097 | + | 0.866546i | \(0.333665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.94096 | −0.229712 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.5602 | 0.877094 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.2483 | −1.12975 | −0.564874 | − | 0.825177i | \(-0.691075\pi\) | ||||
−0.564874 | + | 0.825177i | \(0.691075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.80452 | −0.191265 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.20553 | −0.303004 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.32556 | 0.207759 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.6989 | −1.79461 | −0.897307 | − | 0.441408i | \(-0.854479\pi\) | ||||
−0.897307 | + | 0.441408i | \(0.854479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.78252 | 0.222288 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.8312 | −0.747462 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1635 | 0.397364 | 0.198682 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198682 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.6308 | −0.542725 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.9048 | −0.909672 | −0.454836 | − | 0.890575i | \(-0.650302\pi\) | ||||
−0.454836 | + | 0.890575i | \(0.650302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.72440 | 0.218977 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.5104 | −0.341541 | −0.170770 | − | 0.985311i | \(-0.554626\pi\) | ||||
−0.170770 | + | 0.985311i | \(0.554626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.2130 | 0.753527 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.7916 | 1.64703 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.7005 | −0.379017 | −0.189508 | − | 0.981879i | \(-0.560689\pi\) | ||||
−0.189508 | + | 0.981879i | \(0.560689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.8129 | −0.672784 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −59.7738 | −1.93020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8455 | 1.22082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.76609 | 0.185810 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7133 | −0.376673 | −0.188337 | − | 0.982105i | \(-0.560310\pi\) | ||||
−0.188337 | + | 0.982105i | \(0.560310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.8892 | 0.992304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8963 | 1.21615 | 0.608075 | − | 0.793879i | \(-0.291942\pi\) | ||||
0.608075 | + | 0.793879i | \(0.291942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.9090 | −1.47178 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.83500 | −0.0906997 | −0.0453499 | − | 0.998971i | \(-0.514440\pi\) | ||||
−0.0453499 | + | 0.998971i | \(0.514440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0537 | −0.449158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.71253 | 0.214314 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.47696 | 0.142793 | 0.0713964 | − | 0.997448i | \(-0.477254\pi\) | ||||
0.0713964 | + | 0.997448i | \(0.477254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.7068 | 1.64584 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.177968 | −0.00565906 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.2466 | 1.02435 | 0.512173 | − | 0.858882i | \(-0.328841\pi\) | ||||
0.512173 | + | 0.858882i | \(0.328841\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.3777 | 0.487996 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.5708 | −0.873177 | −0.436589 | − | 0.899661i | \(-0.643813\pi\) | ||||
−0.436589 | + | 0.899661i | \(0.643813\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.46784 | 0.299549 |
(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 | 9200.2.a.cz.1.3 | 7 | ||
4.3 | odd | 2 | 4600.2.a.bi.1.5 | 7 | |||
5.2 | odd | 4 | 1840.2.e.g.369.11 | 14 | |||
5.3 | odd | 4 | 1840.2.e.g.369.4 | 14 | |||
5.4 | even | 2 | 9200.2.a.dc.1.5 | 7 | |||
20.3 | even | 4 | 920.2.e.b.369.11 | yes | 14 | ||
20.7 | even | 4 | 920.2.e.b.369.4 | ✓ | 14 | ||
20.19 | odd | 2 | 4600.2.a.bh.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.4 | ✓ | 14 | 20.7 | even | 4 | ||
920.2.e.b.369.11 | yes | 14 | 20.3 | even | 4 | ||
1840.2.e.g.369.4 | 14 | 5.3 | odd | 4 | |||
1840.2.e.g.369.11 | 14 | 5.2 | odd | 4 | |||
4600.2.a.bh.1.3 | 7 | 20.19 | odd | 2 | |||
4600.2.a.bi.1.5 | 7 | 4.3 | odd | 2 | |||
9200.2.a.cz.1.3 | 7 | 1.1 | even | 1 | trivial | ||
9200.2.a.dc.1.5 | 7 | 5.4 | even | 2 |