Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1472,2,Mod(1,1472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1472, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1472.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1472 = 2^{6} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1472.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: | \(11.7539791775\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 184) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1472.1 |
$q$-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 | ||||||||
\(3\) | 2.56155 | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235083\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12311 | −1.54467 | −0.772337 | − | 0.635213i | \(-0.780912\pi\) | ||||
−0.772337 | + | 0.635213i | \(0.780912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.56155 | −1.26515 | −0.632574 | − | 0.774500i | \(-0.718001\pi\) | ||||
−0.632574 | + | 0.774500i | \(0.718001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.12311 | −1.32278 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.12311 | −1.17532 | −0.587661 | − | 0.809108i | \(-0.699951\pi\) | ||||
−0.587661 | + | 0.809108i | \(0.699951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845 | 0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.561553 | 0.104278 | 0.0521389 | − | 0.998640i | \(-0.483396\pi\) | ||||
0.0521389 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.56155 | −1.17849 | −0.589245 | − | 0.807955i | \(-0.700575\pi\) | ||||
−0.589245 | + | 0.807955i | \(0.700575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.1231 | −2.28444 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24621 | 1.35567 | 0.677834 | − | 0.735215i | \(-0.262919\pi\) | ||||
0.677834 | + | 0.735215i | \(0.262919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.6847 | −1.87104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8078 | 1.68789 | 0.843945 | − | 0.536430i | \(-0.180228\pi\) | ||||
0.843945 | + | 0.536430i | \(0.180228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.12311 | −1.06185 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6847 | 1.70438 | 0.852191 | − | 0.523230i | \(-0.175273\pi\) | ||||
0.852191 | + | 0.523230i | \(0.175273\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | −1.12022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2462 | 1.38160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.1231 | −1.73820 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.24621 | 0.813187 | 0.406594 | − | 0.913609i | \(-0.366716\pi\) | ||||
0.406594 | + | 0.913609i | \(0.366716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2462 | −1.56797 | −0.783983 | − | 0.620782i | \(-0.786815\pi\) | ||||
−0.783983 | + | 0.620782i | \(0.786815\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.12311 | 1.13158 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.12311 | 0.625887 | 0.312943 | − | 0.949772i | \(-0.398685\pi\) | ||||
0.312943 | + | 0.949772i | \(0.398685\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.56155 | −0.308375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.43845 | 1.12014 | 0.560069 | − | 0.828446i | \(-0.310775\pi\) | ||||
0.560069 | + | 0.828446i | \(0.310775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.31534 | −0.270990 | −0.135495 | − | 0.990778i | \(-0.543263\pi\) | ||||
−0.135495 | + | 0.990778i | \(0.543263\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.12311 | −0.576394 | −0.288197 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288197 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.24621 | 0.246554 | 0.123277 | − | 0.992372i | \(-0.460660\pi\) | ||||
0.123277 | + | 0.992372i | \(0.460660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.24621 | 0.677497 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.43845 | 0.154218 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3693 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.8078 | −1.74288 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.2462 | 1.05124 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3693 | −1.35745 | −0.678724 | − | 0.734393i | \(-0.737467\pi\) | ||||
−0.678724 | + | 0.734393i | \(0.737467\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.2462 | −1.83381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24621 | 0.422514 | 0.211257 | − | 0.977431i | \(-0.432244\pi\) | ||||
0.211257 | + | 0.977431i | \(0.432244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.24621 | 0.221326 | 0.110663 | − | 0.993858i | \(-0.464703\pi\) | ||||
0.110663 | + | 0.993858i | \(0.464703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.87689 | −0.278120 | −0.139060 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139060 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.87689 | −0.467122 | −0.233561 | − | 0.972342i | \(-0.575038\pi\) | ||||
−0.233561 | + | 0.972342i | \(0.575038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1231 | 2.00492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.1231 | −1.04637 | −0.523187 | − | 0.852218i | \(-0.675257\pi\) | ||||
−0.523187 | + | 0.852218i | \(0.675257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.2462 | −1.50196 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 27.6847 | 2.49624 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6847 | −1.03685 | −0.518423 | − | 0.855124i | \(-0.673481\pi\) | ||||
−0.518423 | + | 0.855124i | \(0.673481\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.4924 | 1.80426 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6847 | −1.37037 | −0.685187 | − | 0.728367i | \(-0.740280\pi\) | ||||
−0.685187 | + | 0.728367i | \(0.740280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.87689 | −0.247604 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1231 | 1.29205 | 0.646027 | − | 0.763315i | \(-0.276429\pi\) | ||||
0.646027 | + | 0.763315i | \(0.276429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6847 | 1.33036 | 0.665178 | − | 0.746685i | \(-0.268356\pi\) | ||||
0.665178 | + | 0.746685i | \(0.268356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.9309 | 2.52063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.3693 | 1.95424 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.12311 | −0.0932688 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.9309 | −1.47891 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.75379 | 0.307522 | 0.153761 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153761 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5616 | −1.18500 | −0.592501 | − | 0.805570i | \(-0.701859\pi\) | ||||
−0.592501 | + | 0.805570i | \(0.701859\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.1231 | −0.899250 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.1231 | 1.05407 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.8769 | −1.02769 | −0.513844 | − | 0.857884i | \(-0.671779\pi\) | ||||
−0.513844 | + | 0.857884i | \(0.671779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.12311 | −0.406289 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.93087 | 0.777846 | 0.388923 | − | 0.921270i | \(-0.372847\pi\) | ||||
0.388923 | + | 0.921270i | \(0.372847\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26.2462 | 2.04326 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2462 | −1.39532 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000 | 0.760286 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | 1.20263 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.6847 | 1.17233 | 0.586163 | − | 0.810193i | \(-0.300638\pi\) | ||||
0.586163 | + | 0.810193i | \(0.300638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.2462 | −1.50489 | −0.752445 | − | 0.658656i | \(-0.771125\pi\) | ||||
−0.752445 | + | 0.658656i | \(0.771125\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −31.3693 | −2.31889 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.4924 | −1.21255 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000 | 1.17004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.630683 | 0.0456346 | 0.0228173 | − | 0.999740i | \(-0.492736\pi\) | ||||
0.0228173 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.56155 | −0.328348 | −0.164174 | − | 0.986431i | \(-0.552496\pi\) | ||||
−0.164174 | + | 0.986431i | \(0.552496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.3693 | 1.67351 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9309 | −0.850039 | −0.425020 | − | 0.905184i | \(-0.639733\pi\) | ||||
−0.425020 | + | 0.905184i | \(0.639733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.87689 | 0.203938 | 0.101969 | − | 0.994788i | \(-0.467486\pi\) | ||||
0.101969 | + | 0.994788i | \(0.467486\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.1231 | 0.925633 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.6155 | −1.50969 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.56155 | −0.247545 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.2462 | 1.81549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.1771 | 1.65659 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.93087 | −0.400771 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2462 | 0.958304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.49242 | 0.300835 | 0.150417 | − | 0.988623i | \(-0.451938\pi\) | ||||
0.150417 | + | 0.988623i | \(0.451938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.56155 | −0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2462 | −0.680065 | −0.340032 | − | 0.940414i | \(-0.610438\pi\) | ||||
−0.340032 | + | 0.940414i | \(0.610438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.1231 | −1.52802 | −0.764009 | − | 0.645206i | \(-0.776772\pi\) | ||||
−0.764009 | + | 0.645206i | \(0.776772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.0540 | 1.37929 | 0.689646 | − | 0.724147i | \(-0.257766\pi\) | ||||
0.689646 | + | 0.724147i | \(0.257766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.3693 | −1.52445 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.1231 | −0.852437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0540 | −0.715022 | −0.357511 | − | 0.933909i | \(-0.616375\pi\) | ||||
−0.357511 | + | 0.933909i | \(0.616375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.4924 | −1.70653 | −0.853263 | − | 0.521480i | \(-0.825380\pi\) | ||||
−0.853263 | + | 0.521480i | \(0.825380\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2462 | −1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.0000 | 0.894427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.3693 | 1.48695 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.75379 | 0.364632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2462 | −0.646735 | −0.323368 | − | 0.946273i | \(-0.604815\pi\) | ||||
−0.323368 | + | 0.946273i | \(0.604815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.12311 | 0.322087 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.0000 | 1.00196 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.6847 | −1.10314 | −0.551569 | − | 0.834129i | \(-0.685971\pi\) | ||||
−0.551569 | + | 0.834129i | \(0.685971\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.8769 | −0.670698 | −0.335349 | − | 0.942094i | \(-0.608854\pi\) | ||||
−0.335349 | + | 0.942094i | \(0.608854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −34.2462 | −2.09583 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.6847 | −1.56602 | −0.783011 | − | 0.622008i | \(-0.786317\pi\) | ||||
−0.783011 | + | 0.622008i | \(0.786317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.12311 | 0.308935 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.80776 | 0.168702 | 0.0843511 | − | 0.996436i | \(-0.473118\pi\) | ||||
0.0843511 | + | 0.996436i | \(0.473118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.3693 | −1.39908 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.12311 | −0.186309 | −0.0931544 | − | 0.995652i | \(-0.529695\pi\) | ||||
−0.0931544 | + | 0.995652i | \(0.529695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.12311 | 0.304537 | 0.152269 | − | 0.988339i | \(-0.451342\pi\) | ||||
0.152269 | + | 0.988339i | \(0.451342\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26.2462 | 1.55469 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.2462 | −2.00755 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.36932 | −0.547361 | −0.273681 | − | 0.961821i | \(-0.588241\pi\) | ||||
−0.273681 | + | 0.961821i | \(0.588241\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4924 | −0.727337 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.36932 | −0.427611 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.56155 | 0.263801 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.8769 | 0.624861 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.4924 | 1.40243 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.75379 | 0.100094 | 0.0500470 | − | 0.998747i | \(-0.484063\pi\) | ||||
0.0500470 | + | 0.998747i | \(0.484063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.75379 | 0.327322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.43845 | 0.0815669 | 0.0407834 | − | 0.999168i | \(-0.487015\pi\) | ||||
0.0407834 | + | 0.999168i | \(0.487015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.36932 | 0.529585 | 0.264793 | − | 0.964305i | \(-0.414697\pi\) | ||||
0.264793 | + | 0.964305i | \(0.414697\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.2462 | 1.13714 | 0.568570 | − | 0.822635i | \(-0.307497\pi\) | ||||
0.568570 | + | 0.822635i | \(0.307497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87689 | −0.161075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.36932 | −0.411315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000 | 0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.56155 | 0.253029 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.4924 | −0.690833 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4233 | 1.67222 | 0.836108 | − | 0.548565i | \(-0.184826\pi\) | ||||
0.836108 | + | 0.548565i | \(0.184826\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.3693 | 1.60943 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2462 | −0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.6155 | 1.06853 | 0.534263 | − | 0.845318i | \(-0.320589\pi\) | ||||
0.534263 | + | 0.845318i | \(0.320589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.4924 | −1.54750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.6155 | 1.82038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.12311 | 0.275819 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.4924 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.3153 | 1.19451 | 0.597256 | − | 0.802050i | \(-0.296257\pi\) | ||||
0.597256 | + | 0.802050i | \(0.296257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.56155 | −0.350230 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.4384 | 0.608807 | 0.304404 | − | 0.952543i | \(-0.401543\pi\) | ||||
0.304404 | + | 0.952543i | \(0.401543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.8769 | −1.00188 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.6155 | 0.929712 | 0.464856 | − | 0.885386i | \(-0.346106\pi\) | ||||
0.464856 | + | 0.885386i | \(0.346106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 39.0540 | 2.04980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.63068 | 0.242381 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.24621 | 0.117251 | 0.0586256 | − | 0.998280i | \(-0.481328\pi\) | ||||
0.0586256 | + | 0.998280i | \(0.481328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38.4924 | 2.00384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.4924 | −1.16461 | −0.582307 | − | 0.812969i | \(-0.697850\pi\) | ||||
−0.582307 | + | 0.812969i | \(0.697850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.7386 | 1.58734 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.56155 | −0.131927 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.4924 | −1.05263 | −0.526313 | − | 0.850291i | \(-0.676426\pi\) | ||||
−0.526313 | + | 0.850291i | \(0.676426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.9309 | −1.53340 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2462 | 1.34112 | 0.670559 | − | 0.741856i | \(-0.266054\pi\) | ||||
0.670559 | + | 0.741856i | \(0.266054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.4924 | 1.44835 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.36932 | −0.0694271 | −0.0347136 | − | 0.999397i | \(-0.511052\pi\) | ||||
−0.0347136 | + | 0.999397i | \(0.511052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.12311 | 0.157942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −40.1771 | −2.02667 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.2462 | 0.515543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.5616 | −1.03195 | −0.515977 | − | 0.856602i | \(-0.672571\pi\) | ||||
−0.515977 | + | 0.856602i | \(0.672571\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7538 | −0.586956 | −0.293478 | − | 0.955966i | \(-0.594813\pi\) | ||||
−0.293478 | + | 0.955966i | \(0.594813\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.9309 | 1.49096 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.0000 | 0.695666 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −42.2462 | −2.09407 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.3002 | −1.34991 | −0.674954 | − | 0.737860i | \(-0.735836\pi\) | ||||
−0.674954 | + | 0.737860i | \(0.735836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.7386 | 1.91084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.49242 | −0.220524 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.1771 | 1.96748 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4924 | 0.610295 | 0.305147 | − | 0.952305i | \(-0.401294\pi\) | ||||
0.305147 | + | 0.952305i | \(0.401294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.1231 | 1.32190 | 0.660950 | − | 0.750430i | \(-0.270154\pi\) | ||||
0.660950 | + | 0.750430i | \(0.270154\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 41.6155 | 2.02342 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.12311 | 0.151493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 59.8617 | 2.89015 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4924 | −1.37243 | −0.686216 | − | 0.727398i | \(-0.740729\pi\) | ||||
−0.686216 | + | 0.727398i | \(0.740729\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7386 | 1.18886 | 0.594431 | − | 0.804146i | \(-0.297377\pi\) | ||||
0.594431 | + | 0.804146i | \(0.297377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.87689 | −0.137937 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.12311 | 0.245071 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0540 | 0.527577 | 0.263789 | − | 0.964580i | \(-0.415028\pi\) | ||||
0.263789 | + | 0.964580i | \(0.415028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.9309 | −1.18718 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.06913 | 0.288353 | 0.144177 | − | 0.989552i | \(-0.453947\pi\) | ||||
0.144177 | + | 0.989552i | \(0.453947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.7386 | 1.26753 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.61553 | 0.454799 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.24621 | −0.389163 | −0.194581 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194581 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −55.3693 | −2.60724 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.3002 | −1.75252 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.36932 | −0.251166 | −0.125583 | − | 0.992083i | \(-0.540080\pi\) | ||||
−0.125583 | + | 0.992083i | \(0.540080\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.49242 | −0.209688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8078 | 0.503368 | 0.251684 | − | 0.967809i | \(-0.419016\pi\) | ||||
0.251684 | + | 0.967809i | \(0.419016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4924 | 0.580572 | 0.290286 | − | 0.956940i | \(-0.406250\pi\) | ||||
0.290286 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 33.6155 | 1.55888 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.3693 | 0.711207 | 0.355604 | − | 0.934637i | \(-0.384275\pi\) | ||||
0.355604 | + | 0.934637i | \(0.384275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.9848 | −1.51986 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.9848 | −1.88449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.12311 | 0.235064 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.12311 | −0.326145 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.2462 | 0.468161 | 0.234081 | − | 0.972217i | \(-0.424792\pi\) | ||||
0.234081 | + | 0.972217i | \(0.424792\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.6155 | −1.71512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.7386 | 1.21414 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.3153 | 0.558061 | 0.279031 | − | 0.960282i | \(-0.409987\pi\) | ||||
0.279031 | + | 0.960282i | \(0.409987\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.4384 | 1.15037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8078 | −0.578006 | −0.289003 | − | 0.957328i | \(-0.593324\pi\) | ||||
−0.289003 | + | 0.957328i | \(0.593324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.75379 | −0.0789867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.4924 | 1.64021 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0540 | 1.03204 | 0.516019 | − | 0.856577i | \(-0.327413\pi\) | ||||
0.516019 | + | 0.856577i | \(0.327413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.9848 | −1.83107 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.36932 | 0.328582 | 0.164291 | − | 0.986412i | \(-0.447466\pi\) | ||||
0.164291 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.49242 | −0.377908 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0000 | 0.888231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.3002 | 0.678169 | 0.339084 | − | 0.940756i | \(-0.389883\pi\) | ||||
0.339084 | + | 0.940756i | \(0.389883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.36932 | −0.325363 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.49242 | −0.197960 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −59.8617 | −2.63272 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.6155 | 1.12440 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.6155 | 0.859372 | 0.429686 | − | 0.902978i | \(-0.358624\pi\) | ||||
0.429686 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.75379 | −0.251596 | −0.125798 | − | 0.992056i | \(-0.540149\pi\) | ||||
−0.125798 | + | 0.992056i | \(0.540149\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4924 | 0.892664 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.2462 | 0.965403 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.3002 | −2.13543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.75379 | 0.248758 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.1771 | 1.73377 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.8617 | 1.54467 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.9309 | −1.54479 | −0.772394 | − | 0.635143i | \(-0.780941\pi\) | ||||
−0.772394 | + | 0.635143i | \(0.780941\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −51.8617 | −2.22560 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.75379 | 0.417806 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.5464 | −1.86191 | −0.930955 | − | 0.365135i | \(-0.881023\pi\) | ||||
−0.930955 | + | 0.365135i | \(0.881023\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43.6155 | −1.86147 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.87689 | −0.122560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −42.2462 | −1.79325 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.876894 | 0.0371552 | 0.0185776 | − | 0.999827i | \(-0.494086\pi\) | ||||
0.0185776 | + | 0.999827i | \(0.494086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.4924 | −1.54347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.9848 | 1.73038 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.75379 | −0.242493 | −0.121247 | − | 0.992622i | \(-0.538689\pi\) | ||||
−0.121247 | + | 0.992622i | \(0.538689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.2462 | 0.935905 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.24621 | −0.345699 | −0.172850 | − | 0.984948i | \(-0.555297\pi\) | ||||
−0.172850 | + | 0.984948i | \(0.555297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.5076 | 0.481577 | 0.240789 | − | 0.970578i | \(-0.422594\pi\) | ||||
0.240789 | + | 0.970578i | \(0.422594\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.61553 | 0.0674897 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.9309 | 0.663211 | 0.331605 | − | 0.943418i | \(-0.392410\pi\) | ||||
0.331605 | + | 0.943418i | \(0.392410\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.6847 | −0.485598 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2462 | 0.424355 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 32.4924 | 1.34340 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.0540 | 0.951539 | 0.475770 | − | 0.879570i | \(-0.342170\pi\) | ||||
0.475770 | + | 0.879570i | \(0.342170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.6155 | 1.38510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.5616 | −1.25713 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.7386 | −1.83720 | −0.918598 | − | 0.395194i | \(-0.870677\pi\) | ||||
−0.918598 | + | 0.395194i | \(0.870677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.36932 | 0.301606 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.8078 | −1.58300 | −0.791501 | − | 0.611168i | \(-0.790700\pi\) | ||||
−0.791501 | + | 0.611168i | \(0.790700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.2462 | 0.743043 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.4924 | −1.23969 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.7386 | −0.598223 | −0.299111 | − | 0.954218i | \(-0.596690\pi\) | ||||
−0.299111 | + | 0.954218i | \(0.596690\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.3002 | −2.15629 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.1080 | 1.13527 | 0.567635 | − | 0.823281i | \(-0.307859\pi\) | ||||
0.567635 | + | 0.823281i | \(0.307859\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −55.3693 | −2.23271 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.9848 | 1.40844 | 0.704218 | − | 0.709983i | \(-0.251298\pi\) | ||||
0.704218 | + | 0.709983i | \(0.251298\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.4924 | −1.14521 | −0.572604 | − | 0.819832i | \(-0.694067\pi\) | ||||
−0.572604 | + | 0.819832i | \(0.694067\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.43845 | −0.0577229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 67.2311 | 2.68495 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.7538 | −1.02687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.73863 | −0.268261 | −0.134130 | − | 0.990964i | \(-0.542824\pi\) | ||||
−0.134130 | + | 0.990964i | \(0.542824\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.2462 | 0.407250 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.3693 | 0.927383 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.9309 | 1.26515 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.6155 | 1.32981 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.3693 | −0.528056 | −0.264028 | − | 0.964515i | \(-0.585051\pi\) | ||||
−0.264028 | + | 0.964515i | \(0.585051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.3693 | 0.921596 | 0.460798 | − | 0.887505i | \(-0.347563\pi\) | ||||
0.460798 | + | 0.887505i | \(0.347563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.9848 | −1.61378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.3002 | −1.15191 | −0.575955 | − | 0.817482i | \(-0.695370\pi\) | ||||
−0.575955 | + | 0.817482i | \(0.695370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.0540 | −0.980438 | −0.490219 | − | 0.871599i | \(-0.663083\pi\) | ||||
−0.490219 | + | 0.871599i | \(0.663083\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.3693 | 1.22570 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.24621 | −0.321715 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.24621 | −0.0875000 | −0.0437500 | − | 0.999043i | \(-0.513930\pi\) | ||||
−0.0437500 | + | 0.999043i | \(0.513930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.246211 | 0.00957651 | 0.00478825 | − | 0.999989i | \(-0.498476\pi\) | ||||
0.00478825 | + | 0.999989i | \(0.498476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.4924 | 1.41725 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.561553 | −0.0217434 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5076 | 0.444909 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 62.7386 | 2.42200 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.94602 | −0.113561 | −0.0567805 | − | 0.998387i | \(-0.518084\pi\) | ||||
−0.0567805 | + | 0.998387i | \(0.518084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.43845 | −0.0553659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.9848 | 1.49831 | 0.749155 | − | 0.662395i | \(-0.230460\pi\) | ||||
0.749155 | + | 0.662395i | \(0.230460\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.2462 | −1.00576 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.3153 | −0.624289 | −0.312145 | − | 0.950035i | \(-0.601047\pi\) | ||||
−0.312145 | + | 0.950035i | \(0.601047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.2462 | −1.15565 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −59.2311 | −2.25981 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.12311 | 0.347563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.9848 | −0.798301 | −0.399151 | − | 0.916885i | \(-0.630695\pi\) | ||||
−0.399151 | + | 0.916885i | \(0.630695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.3693 | −1.18991 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.7538 | −1.27852 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 53.9309 | 2.03985 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.8617 | −1.12786 | −0.563931 | − | 0.825822i | \(-0.690712\pi\) | ||||
−0.563931 | + | 0.825822i | \(0.690712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.2462 | −1.59335 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −59.8617 | −2.25452 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3693 | 1.40343 | 0.701717 | − | 0.712456i | \(-0.252417\pi\) | ||||
0.701717 | + | 0.712456i | \(0.252417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.2462 | −0.684286 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.56155 | 0.245732 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −46.7386 | −1.74793 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.3153 | −1.05746 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.49242 | 0.167539 | 0.0837695 | − | 0.996485i | \(-0.473304\pi\) | ||||
0.0837695 | + | 0.996485i | \(0.473304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −67.8617 | −2.52381 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.561553 | −0.0208555 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3693 | −1.46013 | −0.730064 | − | 0.683379i | \(-0.760510\pi\) | ||||
−0.730064 | + | 0.683379i | \(0.760510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9848 | −0.924098 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.3693 | −1.82350 | −0.911749 | − | 0.410749i | \(-0.865267\pi\) | ||||
−0.911749 | + | 0.410749i | \(0.865267\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.8617 | 1.32278 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.2462 | −0.966792 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.315342 | −0.0116000 | −0.00580001 | − | 0.999983i | \(-0.501846\pi\) | ||||
−0.00580001 | + | 0.999983i | \(0.501846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 59.8617 | 2.19908 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.2462 | 1.25637 | 0.628186 | − | 0.778063i | \(-0.283798\pi\) | ||||
0.628186 | + | 0.778063i | \(0.283798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.50758 | −0.275056 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.9848 | 1.49556 | 0.747779 | − | 0.663948i | \(-0.231120\pi\) | ||||
0.747779 | + | 0.663948i | \(0.231120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.2462 | −0.956465 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.1231 | 1.05990 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50758 | 0.0547938 | 0.0273969 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273969 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.1231 | 0.476339 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3153 | −0.663931 | −0.331965 | − | 0.943292i | \(-0.607712\pi\) | ||||
−0.331965 | + | 0.943292i | \(0.607712\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.2462 | 0.804313 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.4924 | −1.02880 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.3002 | −1.63145 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.63068 | −0.0946191 | −0.0473095 | − | 0.998880i | \(-0.515065\pi\) | ||||
−0.0473095 | + | 0.998880i | \(0.515065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.56155 | 0.235698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.3693 | −1.98381 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.3542 | −1.73025 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.807764 | 0.0288671 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.7538 | 0.919192 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.2462 | 0.935576 | 0.467788 | − | 0.883841i | \(-0.345051\pi\) | ||||
0.467788 | + | 0.883841i | \(0.345051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.8617 | −0.991904 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.8617 | 1.98371 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.2462 | 0.363396 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.2462 | −0.433783 | −0.216892 | − | 0.976196i | \(-0.569592\pi\) | ||||
−0.216892 | + | 0.976196i | \(0.569592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.4924 | −1.29101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.6155 | −1.68241 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.8617 | 0.418592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −65.7926 | −2.31601 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.0000 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.9309 | −1.19147 | −0.595737 | − | 0.803180i | \(-0.703140\pi\) | ||||
−0.595737 | + | 0.803180i | \(0.703140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 61.4773 | 2.15610 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.8617 | −0.695726 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.9848 | −1.43388 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7386 | 0.863384 | 0.431692 | − | 0.902021i | \(-0.357917\pi\) | ||||
0.431692 | + | 0.902021i | \(0.357917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.4384 | 1.72332 | 0.861658 | − | 0.507489i | \(-0.169426\pi\) | ||||
0.861658 | + | 0.507489i | \(0.169426\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.1231 | 0.456888 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.49242 | −0.156217 | −0.0781084 | − | 0.996945i | \(-0.524888\pi\) | ||||
−0.0781084 | + | 0.996945i | \(0.524888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2462 | 0.703180 | 0.351590 | − | 0.936154i | \(-0.385641\pi\) | ||||
0.351590 | + | 0.936154i | \(0.385641\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.19224 | 0.249496 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.8617 | 0.757464 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000 | 1.10741 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.43845 | −0.326240 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.2462 | 1.73469 | 0.867346 | − | 0.497706i | \(-0.165824\pi\) | ||||
0.867346 | + | 0.497706i | \(0.165824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6847 | −0.989126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.00000 | −0.275535 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.6155 | −0.537190 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.1231 | 0.450384 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.24621 | −0.282676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.9848 | 1.19786 | 0.598929 | − | 0.800802i | \(-0.295593\pi\) | ||||
0.598929 | + | 0.800802i | \(0.295593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.4924 | 1.24801 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5616 | 0.565732 | 0.282866 | − | 0.959159i | \(-0.408715\pi\) | ||||
0.282866 | + | 0.959159i | \(0.408715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9460 | −0.578191 | −0.289095 | − | 0.957300i | \(-0.593354\pi\) | ||||
−0.289095 | + | 0.957300i | \(0.593354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.17708 | −0.278351 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.0000 | −0.680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.5616 | −0.630383 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.2462 | 0.890342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.3693 | −0.791839 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −47.6155 | −1.61154 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.9848 | −1.04628 | −0.523142 | − | 0.852246i | \(-0.675240\pi\) | ||||
−0.523142 | + | 0.852246i | \(0.675240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.87689 | 0.164307 | 0.0821534 | − | 0.996620i | \(-0.473820\pi\) | ||||
0.0821534 | + | 0.996620i | \(0.473820\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.9848 | −1.24464 | −0.622320 | − | 0.782763i | \(-0.713810\pi\) | ||||
−0.622320 | + | 0.782763i | \(0.713810\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.0000 | −1.07567 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.6847 | 0.660946 | 0.330473 | − | 0.943815i | \(-0.392792\pi\) | ||||
0.330473 | + | 0.943815i | \(0.392792\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.8617 | 1.20141 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −59.8617 | −2.00320 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3693 | −1.04856 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.6847 | 0.390139 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.68466 | −0.122890 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.24621 | 0.208091 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 40.4924 | 1.34601 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.8769 | −1.42370 | −0.711852 | − | 0.702330i | \(-0.752143\pi\) | ||||
−0.711852 | + | 0.702330i | \(0.752143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1231 | 0.501602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.1231 | −1.22994 | −0.614972 | − | 0.788549i | \(-0.710833\pi\) | ||||
−0.614972 | + | 0.788549i | \(0.710833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.5076 | −0.380845 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 62.7386 | 2.07408 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.7538 | 1.24538 | 0.622691 | − | 0.782468i | \(-0.286039\pi\) | ||||
0.622691 | + | 0.782468i | \(0.286039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.49242 | 0.148030 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.0540 | −1.41714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.24621 | −0.271134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.8078 | 1.14201 | 0.571003 | − | 0.820948i | \(-0.306555\pi\) | ||||
0.571003 | + | 0.820948i | \(0.306555\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.8617 | 1.17532 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.68466 | 0.120630 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.0000 | −1.04651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.7538 | 0.514654 | 0.257327 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257327 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.1231 | −1.27538 | −0.637688 | − | 0.770294i | \(-0.720109\pi\) | ||||
−0.637688 | + | 0.770294i | \(0.720109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.8078 | −0.351949 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.56155 | 0.0832393 | 0.0416196 | − | 0.999134i | \(-0.486748\pi\) | ||||
0.0416196 | + | 0.999134i | \(0.486748\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5616 | 0.342843 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51.8617 | 1.68173 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.2462 | 1.43328 | 0.716638 | − | 0.697446i | \(-0.245680\pi\) | ||||
0.716638 | + | 0.697446i | \(0.245680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.26137 | −0.0408169 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.36932 | −0.238216 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0540 | 0.388838 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.2462 | −0.330180 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.12311 | 0.293683 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.0540 | 1.12726 | 0.563630 | − | 0.826027i | \(-0.309404\pi\) | ||||
0.563630 | + | 0.826027i | \(0.309404\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40.9848 | 1.31662 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.3693 | −1.00669 | −0.503345 | − | 0.864086i | \(-0.667897\pi\) | ||||
−0.503345 | + | 0.864086i | \(0.667897\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.6847 | 0.374209 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.2311 | −1.83098 | −0.915492 | − | 0.402337i | \(-0.868198\pi\) | ||||
−0.915492 | + | 0.402337i | \(0.868198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.4924 | 2.18903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.3693 | −0.554560 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.1080 | 0.705134 | 0.352567 | − | 0.935787i | \(-0.385309\pi\) | ||||
0.352567 | + | 0.935787i | \(0.385309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.8617 | 0.760298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.98485 | 0.285413 | 0.142707 | − | 0.989765i | \(-0.454419\pi\) | ||||
0.142707 | + | 0.989765i | \(0.454419\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.9309 | 2.47306 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.75379 | −0.182407 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.8617 | 0.375289 |
(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 | 1472.2.a.u.1.2 | 2 | ||
4.3 | odd | 2 | 1472.2.a.p.1.1 | 2 | |||
8.3 | odd | 2 | 368.2.a.i.1.2 | 2 | |||
8.5 | even | 2 | 184.2.a.e.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 1656.2.a.j.1.1 | 2 | |||
24.11 | even | 2 | 3312.2.a.t.1.2 | 2 | |||
40.13 | odd | 4 | 4600.2.e.o.4049.1 | 4 | |||
40.19 | odd | 2 | 9200.2.a.br.1.1 | 2 | |||
40.29 | even | 2 | 4600.2.a.s.1.2 | 2 | |||
40.37 | odd | 4 | 4600.2.e.o.4049.4 | 4 | |||
56.13 | odd | 2 | 9016.2.a.w.1.2 | 2 | |||
184.45 | odd | 2 | 4232.2.a.o.1.1 | 2 | |||
184.91 | even | 2 | 8464.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.a.e.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
368.2.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
1472.2.a.p.1.1 | 2 | 4.3 | odd | 2 | |||
1472.2.a.u.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1656.2.a.j.1.1 | 2 | 24.5 | odd | 2 | |||
3312.2.a.t.1.2 | 2 | 24.11 | even | 2 | |||
4232.2.a.o.1.1 | 2 | 184.45 | odd | 2 | |||
4600.2.a.s.1.2 | 2 | 40.29 | even | 2 | |||
4600.2.e.o.4049.1 | 4 | 40.13 | odd | 4 | |||
4600.2.e.o.4049.4 | 4 | 40.37 | odd | 4 | |||
8464.2.a.bd.1.2 | 2 | 184.91 | even | 2 | |||
9016.2.a.w.1.2 | 2 | 56.13 | odd | 2 | |||
9200.2.a.br.1.1 | 2 | 40.19 | odd | 2 |