Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.52892\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.52892 | 1.13097 | 0.565483 | − | 0.824760i | \(-0.308690\pi\) | ||||
0.565483 | + | 0.824760i | \(0.308690\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.86651 | −0.562773 | −0.281387 | − | 0.959594i | \(-0.590794\pi\) | ||||
−0.281387 | + | 0.959594i | \(0.590794\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.66241 | −0.738420 | −0.369210 | − | 0.929346i | \(-0.620372\pi\) | ||||
−0.369210 | + | 0.929346i | \(0.620372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.52892 | 0.652964 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.92434 | −1.19433 | −0.597164 | − | 0.802119i | \(-0.703706\pi\) | ||||
−0.597164 | + | 0.802119i | \(0.703706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.13349 | −0.489457 | −0.244728 | − | 0.969592i | \(-0.578699\pi\) | ||||
−0.244728 | + | 0.969592i | \(0.578699\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.39543 | 0.279085 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.86651 | −0.694445 | −0.347223 | − | 0.937783i | \(-0.612875\pi\) | ||||
−0.347223 | + | 0.937783i | \(0.612875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.86651 | −0.324917 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.52892 | −0.427465 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.05784 | 0.338306 | 0.169153 | − | 0.985590i | \(-0.445897\pi\) | ||||
0.169153 | + | 0.985590i | \(0.445897\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.66241 | −0.426327 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.79085 | 1.21673 | 0.608363 | − | 0.793659i | \(-0.291826\pi\) | ||||
0.608363 | + | 0.793659i | \(0.291826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.72025 | −0.872329 | −0.436165 | − | 0.899867i | \(-0.643663\pi\) | ||||
−0.436165 | + | 0.899867i | \(0.643663\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.52892 | 0.376989 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.92434 | −0.864154 | −0.432077 | − | 0.901837i | \(-0.642219\pi\) | ||||
−0.432077 | + | 0.901837i | \(0.642219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.92434 | −0.689546 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.45326 | −1.16114 | −0.580572 | − | 0.814209i | \(-0.697171\pi\) | ||||
−0.580572 | + | 0.814209i | \(0.697171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.72025 | −0.636478 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.13349 | −0.282588 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.1863 | −1.84690 | −0.923448 | − | 0.383723i | \(-0.874642\pi\) | ||||
−0.923448 | + | 0.383723i | \(0.874642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.26193 | −0.161574 | −0.0807871 | − | 0.996731i | \(-0.525743\pi\) | ||||
−0.0807871 | + | 0.996731i | \(0.525743\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.73302 | −0.835128 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2441 | 1.37369 | 0.686844 | − | 0.726805i | \(-0.258996\pi\) | ||||
0.686844 | + | 0.726805i | \(0.258996\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26193 | 0.149764 | 0.0748820 | − | 0.997192i | \(-0.476142\pi\) | ||||
0.0748820 | + | 0.997192i | \(0.476142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7730 | 1.72905 | 0.864526 | − | 0.502588i | \(-0.167619\pi\) | ||||
0.864526 | + | 0.502588i | \(0.167619\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.39543 | 0.161130 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.86651 | 0.212708 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9822 | −1.79814 | −0.899068 | − | 0.437809i | \(-0.855755\pi\) | ||||
−0.899068 | + | 0.437809i | \(0.855755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.8309 | 1.95719 | 0.978596 | − | 0.205791i | \(-0.0659766\pi\) | ||||
0.978596 | + | 0.205791i | \(0.0659766\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4533 | −1.35075 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.26193 | −0.133765 | −0.0668824 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668824 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.66241 | 0.279096 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.86651 | −0.400938 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.39543 | −0.553559 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3248 | −1.25140 | −0.625698 | − | 0.780065i | \(-0.715186\pi\) | ||||
−0.625698 | + | 0.780065i | \(0.715186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.86651 | −0.187591 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.66241 | 0.762438 | 0.381219 | − | 0.924485i | \(-0.375504\pi\) | ||||
0.381219 | + | 0.924485i | \(0.375504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2492 | −1.50254 | −0.751272 | − | 0.659992i | \(-0.770560\pi\) | ||||
−0.751272 | + | 0.659992i | \(0.770560\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.52892 | −0.246797 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.47108 | −0.432236 | −0.216118 | − | 0.976367i | \(-0.569340\pi\) | ||||
−0.216118 | + | 0.976367i | \(0.569340\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3776 | −1.76026 | −0.880128 | − | 0.474737i | \(-0.842543\pi\) | ||||
−0.880128 | + | 0.474737i | \(0.842543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.05784 | 0.195321 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.85374 | 0.550673 | 0.275337 | − | 0.961348i | \(-0.411211\pi\) | ||||
0.275337 | + | 0.961348i | \(0.411211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.52892 | 0.235823 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.66241 | −0.246140 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.92434 | 0.451414 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.51615 | −0.683286 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.79085 | 0.702477 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.11567 | −0.815330 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.5689 | −1.20405 | −0.602024 | − | 0.798478i | \(-0.705639\pi\) | ||||
−0.602024 | + | 0.798478i | \(0.705639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.72025 | −0.503640 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9243 | −1.65343 | −0.826714 | − | 0.562623i | \(-0.809792\pi\) | ||||
−0.826714 | + | 0.562623i | \(0.809792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.13349 | 0.184997 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.52892 | 0.217655 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0000 | −1.11066 | −0.555332 | − | 0.831628i | \(-0.687409\pi\) | ||||
−0.555332 | + | 0.831628i | \(0.687409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.1685 | −1.62585 | −0.812924 | − | 0.582370i | \(-0.802125\pi\) | ||||
−0.812924 | + | 0.582370i | \(0.802125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.92434 | −0.498920 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.96941 | 0.415563 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.6446 | 1.05008 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.05784 | 0.250508 | 0.125254 | − | 0.992125i | \(-0.460025\pi\) | ||||
0.125254 | + | 0.992125i | \(0.460025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.04002 | 0.654287 | 0.327144 | − | 0.944975i | \(-0.393914\pi\) | ||||
0.327144 | + | 0.944975i | \(0.393914\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.92434 | −0.398110 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.77808 | −0.785394 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.67518 | 0.373120 | 0.186560 | − | 0.982444i | \(-0.440266\pi\) | ||||
0.186560 | + | 0.982444i | \(0.440266\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.45326 | −0.670387 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.6624 | −1.07012 | −0.535061 | − | 0.844813i | \(-0.679711\pi\) | ||||
−0.535061 | + | 0.844813i | \(0.679711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.72025 | −0.367471 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3070 | 0.874962 | 0.437481 | − | 0.899228i | \(-0.355871\pi\) | ||||
0.437481 | + | 0.899228i | \(0.355871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.91157 | −0.454736 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.13349 | −0.163152 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8887 | −1.43608 | −0.718041 | − | 0.696001i | \(-0.754961\pi\) | ||||
−0.718041 | + | 0.696001i | \(0.754961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.39543 | −0.105484 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.1863 | −1.06631 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5868 | −1.16501 | −0.582504 | − | 0.812828i | \(-0.697927\pi\) | ||||
−0.582504 | + | 0.812828i | \(0.697927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.5740 | 1.60358 | 0.801791 | − | 0.597605i | \(-0.203881\pi\) | ||||
0.801791 | + | 0.597605i | \(0.203881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.26193 | −0.0932849 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.20410 | 0.382613 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.19133 | 0.672136 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.5239 | −1.34034 | −0.670170 | − | 0.742208i | \(-0.733779\pi\) | ||||
−0.670170 | + | 0.742208i | \(0.733779\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.07566 | −0.293372 | −0.146686 | − | 0.989183i | \(-0.546861\pi\) | ||||
−0.146686 | + | 0.989183i | \(0.546861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.73302 | −0.482161 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.9771 | 1.28082 | 0.640409 | − | 0.768034i | \(-0.278765\pi\) | ||||
0.640409 | + | 0.768034i | \(0.278765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.2841 | 1.79234 | 0.896172 | − | 0.443706i | \(-0.146337\pi\) | ||||
0.896172 | + | 0.443706i | \(0.146337\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2441 | 0.793099 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.7024 | 1.37608 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.98218 | 0.275453 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.19133 | 0.632757 | 0.316379 | − | 0.948633i | \(-0.397533\pi\) | ||||
0.316379 | + | 0.948633i | \(0.397533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.26193 | 0.0864663 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.4660 | −0.986575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.86651 | 0.262476 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.7730 | 0.998269 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.1106 | 0.881916 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.51110 | 0.636910 | 0.318455 | − | 0.947938i | \(-0.396836\pi\) | ||||
0.318455 | + | 0.947938i | \(0.396836\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.39543 | 0.0930284 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.68023 | −0.310638 | −0.155319 | − | 0.987864i | \(-0.549641\pi\) | ||||
−0.155319 | + | 0.987864i | \(0.549641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.45326 | −0.294280 | −0.147140 | − | 0.989116i | \(-0.547007\pi\) | ||||
−0.147140 | + | 0.989116i | \(0.547007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.86651 | 0.122807 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.72025 | 0.440258 | 0.220129 | − | 0.975471i | \(-0.429352\pi\) | ||||
0.220129 | + | 0.975471i | \(0.429352\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.9822 | −0.977330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.9822 | −1.03815 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5689 | 0.683647 | 0.341824 | − | 0.939764i | \(-0.388955\pi\) | ||||
0.341824 | + | 0.939764i | \(0.388955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.74312 | 0.176700 | 0.0883498 | − | 0.996090i | \(-0.471841\pi\) | ||||
0.0883498 | + | 0.996090i | \(0.471841\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.52892 | 0.161567 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.68023 | 0.361424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.8309 | 1.12999 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.9243 | −1.76257 | −0.881284 | − | 0.472586i | \(-0.843321\pi\) | ||||
−0.881284 | + | 0.472586i | \(0.843321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.86651 | −0.117346 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.4533 | −0.779854 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.9065 | 1.42887 | 0.714435 | − | 0.699702i | \(-0.246684\pi\) | ||||
0.714435 | + | 0.699702i | \(0.246684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.05784 | −0.127868 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5918 | −0.653119 | −0.326559 | − | 0.945177i | \(-0.605889\pi\) | ||||
−0.326559 | + | 0.945177i | \(0.605889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.3776 | −1.31322 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.26193 | −0.0772291 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.0272 | 1.83079 | 0.915397 | − | 0.402553i | \(-0.131877\pi\) | ||||
0.915397 | + | 0.402553i | \(0.131877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.80867 | 0.170615 | 0.0853073 | − | 0.996355i | \(-0.472813\pi\) | ||||
0.0853073 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.66241 | 0.161136 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.60457 | −0.157062 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2619 | 0.676664 | 0.338332 | − | 0.941027i | \(-0.390137\pi\) | ||||
0.338332 | + | 0.941027i | \(0.390137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.86651 | −0.231482 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.39038 | −0.440873 | −0.220436 | − | 0.975401i | \(-0.570748\pi\) | ||||
−0.220436 | + | 0.975401i | \(0.570748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.337590 | 0.0200676 | 0.0100338 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100338 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.39543 | −0.319597 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.79085 | −0.459879 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.24916 | 0.426421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.3248 | −0.722494 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.3147 | −1.12838 | −0.564189 | − | 0.825646i | \(-0.690811\pi\) | ||||
−0.564189 | + | 0.825646i | \(0.690811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −35.8759 | −2.08878 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.86651 | −0.108306 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.66241 | −0.153971 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.72025 | 0.329709 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.66241 | 0.440194 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.19133 | −0.182735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0800 | 1.20310 | 0.601550 | − | 0.798835i | \(-0.294550\pi\) | ||||
0.601550 | + | 0.798835i | \(0.294550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.2492 | −0.867495 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.72797 | 0.381508 | 0.190754 | − | 0.981638i | \(-0.438907\pi\) | ||||
0.190754 | + | 0.981638i | \(0.438907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.8964 | −1.40723 | −0.703615 | − | 0.710582i | \(-0.748432\pi\) | ||||
−0.703615 | + | 0.710582i | \(0.748432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.52892 | −0.142488 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.26193 | 0.351705 | 0.175853 | − | 0.984417i | \(-0.443732\pi\) | ||||
0.175853 | + | 0.984417i | \(0.443732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.33254 | −0.522522 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.47108 | −0.249551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5060 | 0.584572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.71520 | −0.206082 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.3776 | −1.01628 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.92434 | 0.326620 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.266984 | 0.0146748 | 0.00733738 | − | 0.999973i | \(-0.497664\pi\) | ||||
0.00733738 | + | 0.999973i | \(0.497664\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.05784 | 0.112769 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.4354 | 1.55359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00505 | −0.272642 | −0.136321 | − | 0.990665i | \(-0.543528\pi\) | ||||
−0.136321 | + | 0.990665i | \(0.543528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.85374 | 0.317931 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.21687 | 0.390815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.52892 | 0.136152 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.85879 | −0.475565 | −0.237782 | − | 0.971318i | \(-0.576420\pi\) | ||||
−0.237782 | + | 0.971318i | \(0.576420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8615 | −0.581401 | −0.290700 | − | 0.956814i | \(-0.593888\pi\) | ||||
−0.290700 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.66241 | −0.142109 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7075 | 1.10215 | 0.551074 | − | 0.834456i | \(-0.314218\pi\) | ||||
0.551074 | + | 0.834456i | \(0.314218\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.19133 | 0.169378 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.92434 | 0.260624 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.4933 | 1.60937 | 0.804687 | − | 0.593700i | \(-0.202333\pi\) | ||||
0.804687 | + | 0.593700i | \(0.202333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4482 | −0.760432 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.51615 | −0.394495 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.3598 | 1.95550 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.4533 | −0.911053 | −0.455526 | − | 0.890222i | \(-0.650549\pi\) | ||||
−0.455526 | + | 0.890222i | \(0.650549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.79085 | 0.405576 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.45326 | 0.438871 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.99228 | −0.413825 | −0.206912 | − | 0.978360i | \(-0.566341\pi\) | ||||
−0.206912 | + | 0.978360i | \(0.566341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.11567 | −0.470731 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.3120 | −0.685605 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.5639 | 1.36450 | 0.682248 | − | 0.731121i | \(-0.261003\pi\) | ||||
0.682248 | + | 0.731121i | \(0.261003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5689 | −0.695158 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.8309 | −1.52429 | −0.762143 | − | 0.647409i | \(-0.775853\pi\) | ||||
−0.762143 | + | 0.647409i | \(0.775853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.72025 | 0.240566 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.72025 | −0.290776 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.5417 | 0.635889 | 0.317944 | − | 0.948109i | \(-0.397007\pi\) | ||||
0.317944 | + | 0.948109i | \(0.397007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.92434 | −0.249035 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.9243 | −0.954607 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −40.4176 | −2.03363 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4405 | −0.574182 | −0.287091 | − | 0.957903i | \(-0.592688\pi\) | ||||
−0.287091 | + | 0.957903i | \(0.592688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.13349 | 0.106808 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.92434 | 0.345785 | 0.172893 | − | 0.984941i | \(-0.444689\pi\) | ||||
0.172893 | + | 0.984941i | \(0.444689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2942 | 0.512792 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.52892 | 0.125663 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.84097 | −0.190390 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1456 | 1.54005 | 0.770025 | − | 0.638014i | \(-0.220244\pi\) | ||||
0.770025 | + | 0.638014i | \(0.220244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.0000 | −0.641243 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.1863 | 0.698061 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.0928 | 2.21352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.1685 | −0.938683 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.987230 | −0.0482293 | −0.0241147 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241147 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.08071 | −0.247618 | −0.123809 | − | 0.992306i | \(-0.539511\pi\) | ||||
−0.123809 | + | 0.992306i | \(0.539511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.92434 | −0.288051 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.87156 | −0.333320 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.26193 | 0.0610693 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.96941 | 0.239925 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2186 | 1.84092 | 0.920462 | − | 0.390832i | \(-0.127813\pi\) | ||||
0.920462 | + | 0.390832i | \(0.127813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8887 | 1.05190 | 0.525952 | − | 0.850514i | \(-0.323709\pi\) | ||||
0.525952 | + | 0.850514i | \(0.323709\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.6446 | 0.606262 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.13349 | −0.102059 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.71520 | 0.0818618 | 0.0409309 | − | 0.999162i | \(-0.486968\pi\) | ||||
0.0409309 | + | 0.999162i | \(0.486968\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.7152 | −0.509094 | −0.254547 | − | 0.967060i | \(-0.581926\pi\) | ||||
−0.254547 | + | 0.967060i | \(0.581926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.19133 | −0.151283 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.05784 | 0.144631 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.977130 | 0.0461136 | 0.0230568 | − | 0.999734i | \(-0.492660\pi\) | ||||
0.0230568 | + | 0.999734i | \(0.492660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.5417 | −0.684741 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.04002 | 0.377753 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.73302 | 0.315649 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1863 | −0.570050 | −0.285025 | − | 0.958520i | \(-0.592002\pi\) | ||||
−0.285025 | + | 0.958520i | \(0.592002\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.92434 | −0.229849 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.71015 | 0.405672 | 0.202836 | − | 0.979213i | \(-0.434984\pi\) | ||||
0.202836 | + | 0.979213i | \(0.434984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.3827 | 1.55142 | 0.775712 | − | 0.631087i | \(-0.217391\pi\) | ||||
0.775712 | + | 0.631087i | \(0.217391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.77808 | −0.453448 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.46603 | −0.391761 | −0.195881 | − | 0.980628i | \(-0.562757\pi\) | ||||
−0.195881 | + | 0.980628i | \(0.562757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.2441 | −0.519205 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.67518 | 0.215421 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.6769 | 0.490924 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.97713 | −0.136600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.45326 | −0.387048 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.5861 | 1.39751 | 0.698757 | − | 0.715359i | \(-0.253737\pi\) | ||||
0.698757 | + | 0.715359i | \(0.253737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.47880 | −0.249812 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.1685 | −1.41529 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0477 | −0.636564 | −0.318282 | − | 0.947996i | \(-0.603106\pi\) | ||||
−0.318282 | + | 0.947996i | \(0.603106\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.6624 | −0.617836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.9015 | −1.62021 | −0.810105 | − | 0.586284i | \(-0.800590\pi\) | ||||
−0.810105 | + | 0.586284i | \(0.800590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.6217 | −1.10891 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.72025 | −0.212159 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.26193 | −0.0566055 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.75589 | 0.123370 | 0.0616852 | − | 0.998096i | \(-0.480353\pi\) | ||||
0.0616852 | + | 0.998096i | \(0.480353\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3070 | 0.505159 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.6745 | −1.27853 | −0.639267 | − | 0.768985i | \(-0.720762\pi\) | ||||
−0.639267 | + | 0.768985i | \(0.720762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.3776 | 0.862292 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.91157 | −0.262542 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.01010 | −0.0890961 | −0.0445480 | − | 0.999007i | \(-0.514185\pi\) | ||||
−0.0445480 | + | 0.999007i | \(0.514185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.7730 | −0.653520 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.13349 | −0.0941960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.5639 | −1.69933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0578 | 0.486323 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8887 | −0.829122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.58170 | −0.156917 | −0.0784587 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784587 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.53397 | 0.110803 | 0.0554013 | − | 0.998464i | \(-0.482356\pi\) | ||||
0.0554013 | + | 0.998464i | \(0.482356\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.39543 | −0.0609014 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.0400 | 0.829396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.1863 | −0.615632 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.7424 | −0.898455 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3070 | −0.488844 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5868 | −0.672618 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.86651 | −0.0803962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.28918 | 0.141413 | 0.0707064 | − | 0.997497i | \(-0.477475\pi\) | ||||
0.0707064 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.5740 | 0.925828 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −46.4755 | −1.99079 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.64021 | 0.198401 | 0.0992006 | − | 0.995067i | \(-0.468371\pi\) | ||||
0.0992006 | + | 0.995067i | \(0.468371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.26193 | −0.0538580 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6675 | −0.454449 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9822 | 0.679631 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.20410 | 0.220902 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0222 | −0.467025 | −0.233513 | − | 0.972354i | \(-0.575022\pi\) | ||||
−0.233513 | + | 0.972354i | \(0.575022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2296 | 0.644145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.19133 | 0.388058 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.8837 | −0.964431 | −0.482216 | − | 0.876053i | \(-0.660168\pi\) | ||||
−0.482216 | + | 0.876053i | \(0.660168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.8036 | 0.622793 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0979 | 0.465246 | 0.232623 | − | 0.972567i | \(-0.425269\pi\) | ||||
0.232623 | + | 0.972567i | \(0.425269\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.9109 | 1.67022 | 0.835110 | − | 0.550084i | \(-0.185404\pi\) | ||||
0.835110 | + | 0.550084i | \(0.185404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.5239 | −0.773846 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.39543 | 0.0581933 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.1634 | 1.54713 | 0.773566 | − | 0.633715i | \(-0.218471\pi\) | ||||
0.773566 | + | 0.633715i | \(0.218471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.07566 | −0.169378 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.8309 | −0.739749 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7781 | 0.653461 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.73302 | −0.278376 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.29757 | 0.136105 | 0.0680527 | − | 0.997682i | \(-0.478321\pi\) | ||||
0.0680527 | + | 0.997682i | \(0.478321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.24916 | 0.339901 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.9771 | 0.739480 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.7374 | −1.22117 | −0.610584 | − | 0.791951i | \(-0.709065\pi\) | ||||
−0.610584 | + | 0.791951i | \(0.709065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4533 | 0.510534 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.2841 | 1.03481 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.14626 | 0.0468350 | 0.0234175 | − | 0.999726i | \(-0.492545\pi\) | ||||
0.0234175 | + | 0.999726i | \(0.492545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9516 | −1.18096 | −0.590480 | − | 0.807052i | \(-0.701062\pi\) | ||||
−0.590480 | + | 0.807052i | \(0.701062\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.2441 | 0.457896 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.0077 | −0.772774 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.7858 | 1.29015 | 0.645073 | − | 0.764121i | \(-0.276827\pi\) | ||||
0.645073 | + | 0.764121i | \(0.276827\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00000 | −0.202610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.7730 | 0.638109 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0477 | 1.05206 | 0.526029 | − | 0.850467i | \(-0.323680\pi\) | ||||
0.526029 | + | 0.850467i | \(0.323680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.7024 | 0.794478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.5511 | −0.988391 | −0.494195 | − | 0.869351i | \(-0.664537\pi\) | ||||
−0.494195 | + | 0.869351i | \(0.664537\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.72797 | 0.350807 | 0.175403 | − | 0.984497i | \(-0.443877\pi\) | ||||
0.175403 | + | 0.984497i | \(0.443877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.26193 | 0.0505583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0299 | −1.20120 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.98218 | 0.159033 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1335 | −0.404049 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.621720 | 0.0247503 | 0.0123751 | − | 0.999923i | \(-0.496061\pi\) | ||||
0.0123751 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.19133 | 0.365322 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.3147 | −1.36174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.66241 | −0.105489 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.26193 | 0.0499213 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.0094 | 0.987813 | 0.493906 | − | 0.869515i | \(-0.335569\pi\) | ||||
0.493906 | + | 0.869515i | \(0.335569\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.4933 | 1.16310 | 0.581551 | − | 0.813510i | \(-0.302446\pi\) | ||||
0.581551 | + | 0.813510i | \(0.302446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4660 | −0.569599 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7424 | 1.24792 | 0.623962 | − | 0.781455i | \(-0.285522\pi\) | ||||
0.623962 | + | 0.781455i | \(0.285522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.4788 | 1.03938 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.86651 | 0.151540 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.4253 | −0.525374 | −0.262687 | − | 0.964881i | \(-0.584609\pi\) | ||||
−0.262687 | + | 0.964881i | \(0.584609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.8581 | −1.86997 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.7730 | 0.576351 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.3171 | 0.674578 | 0.337289 | − | 0.941401i | \(-0.390490\pi\) | ||||
0.337289 | + | 0.941401i | \(0.390490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.5740 | 1.46146 | 0.730729 | − | 0.682667i | \(-0.239180\pi\) | ||||
0.730729 | + | 0.682667i | \(0.239180\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.1106 | 0.509174 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.39543 | 0.209226 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.00000 | 0.193601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.51110 | 0.367720 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.35541 | 0.0909296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.9644 | −1.42487 | −0.712436 | − | 0.701737i | \(-0.752408\pi\) | ||||
−0.712436 | + | 0.701737i | \(0.752408\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.39543 | 0.0537100 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.4576 | 1.74708 | 0.873539 | − | 0.486753i | \(-0.161819\pi\) | ||||
0.873539 | + | 0.486753i | \(0.161819\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.3248 | 0.472983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.68023 | −0.179347 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.9566 | −1.60543 | −0.802713 | − | 0.596365i | \(-0.796611\pi\) | ||||
−0.802713 | + | 0.596365i | \(0.796611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.8759 | −1.25612 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.45326 | −0.169903 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.5060 | 0.857412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3120 | 0.734665 | 0.367332 | − | 0.930090i | \(-0.380271\pi\) | ||||
0.367332 | + | 0.930090i | \(0.380271\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.86651 | 0.0709028 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −48.4755 | −1.83878 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.3648 | −1.45317 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.72025 | 0.254183 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.4533 | 0.772509 | 0.386255 | − | 0.922392i | \(-0.373769\pi\) | ||||
0.386255 | + | 0.922392i | \(0.373769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.39038 | −0.165586 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.9822 | −0.564262 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.66241 | −0.288175 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.2008 | −1.77266 | −0.886331 | − | 0.463053i | \(-0.846754\pi\) | ||||
−0.886331 | + | 0.463053i | \(0.846754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.9822 | −0.599379 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.86651 | −0.144802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5672 | 0.469988 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.5689 | 0.394704 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.38266 | −0.126152 | −0.0630759 | − | 0.998009i | \(-0.520091\pi\) | ||||
−0.0630759 | + | 0.998009i | \(0.520091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2492 | 0.567909 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.74312 | 0.102018 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.97713 | 0.259124 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.516148 | −0.0191429 | −0.00957143 | − | 0.999954i | \(-0.503047\pi\) | ||||
−0.00957143 | + | 0.999954i | \(0.503047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.1685 | 1.04185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.4405 | −1.67838 | −0.839191 | − | 0.543836i | \(-0.816971\pi\) | ||||
−0.839191 | + | 0.543836i | \(0.816971\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.52892 | 0.0932805 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.9872 | −0.773075 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9243 | 0.843286 | 0.421643 | − | 0.906762i | \(-0.361454\pi\) | ||||
0.421643 | + | 0.906762i | \(0.361454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.68023 | 0.208668 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7781 | 0.578842 | 0.289421 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289421 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.73302 | 0.283316 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.8309 | 0.652397 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.47108 | 0.163370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.7680 | 1.81606 | 0.908030 | − | 0.418906i | \(-0.137586\pi\) | ||||
0.908030 | + | 0.418906i | \(0.137586\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.9243 | −1.01762 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.3325 | 0.739977 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.5740 | 0.784120 | 0.392060 | − | 0.919940i | \(-0.371763\pi\) | ||||
0.392060 | + | 0.919940i | \(0.371763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.86651 | −0.0677500 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.1957 | −1.09459 | −0.547297 | − | 0.836939i | \(-0.684343\pi\) | ||||
−0.547297 | + | 0.836939i | \(0.684343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.3776 | 0.665314 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.4533 | −0.450249 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.7697 | 1.36378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5417 | −0.560448 | −0.280224 | − | 0.959935i | \(-0.590409\pi\) | ||||
−0.280224 | + | 0.959935i | \(0.590409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.9065 | 0.824958 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.5663 | −1.09939 | −0.549696 | − | 0.835365i | \(-0.685256\pi\) | ||||
−0.549696 | + | 0.835365i | \(0.685256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.39543 | −0.193809 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.05784 | −0.0738245 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.6217 | −0.595535 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.35541 | −0.0842832 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8231 | 0.421986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.9415 | −0.817776 | −0.408888 | − | 0.912585i | \(-0.634083\pi\) | ||||
−0.408888 | + | 0.912585i | \(0.634083\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5918 | −0.377078 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.85374 | −0.208135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.35979 | 0.119309 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.3776 | −0.758186 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −49.0878 | −1.73878 | −0.869389 | − | 0.494129i | \(-0.835487\pi\) | ||||
−0.869389 | + | 0.494129i | \(0.835487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.1735 | 1.03208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.26193 | −0.0445882 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.5740 | −0.973065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.52892 | −0.0891326 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.0272 | 1.05701 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.5767 | −1.00470 | −0.502351 | − | 0.864664i | \(-0.667531\pi\) | ||||
−0.502351 | + | 0.864664i | \(0.667531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.3369 | −0.819470 | −0.409735 | − | 0.912205i | \(-0.634379\pi\) | ||||
−0.409735 | + | 0.912205i | \(0.634379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.80867 | 0.0985044 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.5511 | −1.21027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.2041 | 0.426967 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.66241 | 0.0930321 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.74312 | 0.130636 | 0.0653178 | − | 0.997865i | \(-0.479194\pi\) | ||||
0.0653178 | + | 0.997865i | \(0.479194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6089 | 0.927530 | 0.463765 | − | 0.885958i | \(-0.346498\pi\) | ||||
0.463765 | + | 0.885958i | \(0.346498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.60457 | −0.0906796 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 56.6389 | 1.96953 | 0.984763 | − | 0.173901i | \(-0.0556372\pi\) | ||||
0.984763 | + | 0.173901i | \(0.0556372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.9465 | −1.17901 | −0.589506 | − | 0.807764i | \(-0.700678\pi\) | ||||
−0.589506 | + | 0.807764i | \(0.700678\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2619 | 0.390672 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.92434 | −0.170618 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.5945 | 0.989553 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.86651 | −0.133646 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.64459 | 0.263921 | 0.131960 | − | 0.991255i | \(-0.457873\pi\) | ||||
0.131960 | + | 0.991255i | \(0.457873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.39038 | −0.254538 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.9499 | −0.514292 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.51615 | 0.258258 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.337590 | 0.0115861 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.05784 | 0.0705417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.8887 | 1.70816 | 0.854078 | − | 0.520144i | \(-0.174122\pi\) | ||||
0.854078 | + | 0.520144i | \(0.174122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.39543 | −0.184520 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.6217 | −0.943540 | −0.471770 | − | 0.881722i | \(-0.656385\pi\) | ||||
−0.471770 | + | 0.881722i | \(0.656385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.44821 | −0.220010 | −0.110005 | − | 0.993931i | \(-0.535087\pi\) | ||||
−0.110005 | + | 0.993931i | \(0.535087\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.79085 | −0.265512 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.7196 | −1.72651 | −0.863257 | − | 0.504764i | \(-0.831579\pi\) | ||||
−0.863257 | + | 0.504764i | \(0.831579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.7680 | −1.62416 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.24916 | 0.246195 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.8309 | 1.01194 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.9364 | −1.01436 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.3248 | −0.417132 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.11567 | 0.308166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2993 | −0.854296 | −0.427148 | − | 0.904182i | \(-0.640482\pi\) | ||||
−0.427148 | + | 0.904182i | \(0.640482\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.3147 | −0.651469 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.7075 | −1.60731 | −0.803653 | − | 0.595098i | \(-0.797113\pi\) | ||||
−0.803653 | + | 0.595098i | \(0.797113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.0851 | 1.11340 | 0.556701 | − | 0.830713i | \(-0.312067\pi\) | ||||
0.556701 | + | 0.830713i | \(0.312067\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.8759 | −1.20596 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.7347 | −1.80424 | −0.902118 | − | 0.431490i | \(-0.857988\pi\) | ||||
−0.902118 | + | 0.431490i | \(0.857988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.5689 | 0.455087 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.86651 | −0.0625304 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.6395 | 0.422966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.4176 | −1.31759 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.66241 | −0.0888953 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.3325 | −0.644776 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.6268 | 1.38679 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.72025 | 0.190358 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 54.5588 | 1.81360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.1207 | 0.668098 | 0.334049 | − | 0.942556i | \(-0.391585\pi\) | ||||
0.334049 | + | 0.942556i | \(0.391585\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.66241 | 0.254146 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.9721 | −1.15868 | −0.579338 | − | 0.815087i | \(-0.696689\pi\) | ||||
−0.579338 | + | 0.815087i | \(0.696689\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.2815 | −1.10146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.19133 | −0.105502 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.9243 | 0.624937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.30700 | −0.109088 | −0.0545439 | − | 0.998511i | \(-0.517370\pi\) | ||||
−0.0545439 | + | 0.998511i | \(0.517370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.0800 | 0.694611 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.35979 | −0.110589 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.87156 | 0.0944162 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.2492 | −0.500848 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.7959 | −0.747909 | −0.373955 | − | 0.927447i | \(-0.621998\pi\) | ||||
−0.373955 | + | 0.927447i | \(0.621998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.13349 | −0.0699224 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.72797 | 0.220264 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.2441 | 0.760164 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7653 | 0.907053 | 0.453527 | − | 0.891243i | \(-0.350166\pi\) | ||||
0.453527 | + | 0.891243i | \(0.350166\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.8964 | −0.812464 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.8309 | 1.85263 | 0.926317 | − | 0.376746i | \(-0.122957\pi\) | ||||
0.926317 | + | 0.376746i | \(0.122957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.79085 | 0.253705 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.52892 | −0.0822657 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.59952 | 0.214456 | 0.107228 | − | 0.994234i | \(-0.465803\pi\) | ||||
0.107228 | + | 0.994234i | \(0.465803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.3319 | −1.27677 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.26193 | 0.203057 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.4354 | −1.11547 | −0.557737 | − | 0.830018i | \(-0.688330\pi\) | ||||
−0.557737 | + | 0.830018i | \(0.688330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.8453 | −1.51588 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.33254 | −0.301678 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.0000 | 0.419792 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0501 | −0.517746 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.47108 | −0.144079 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.3070 | −0.331794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.03230 | −0.161828 | −0.0809139 | − | 0.996721i | \(-0.525784\pi\) | ||||
−0.0809139 | + | 0.996721i | \(0.525784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5060 | 0.337503 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.5969 | −0.789351 | −0.394675 | − | 0.918821i | \(-0.629143\pi\) | ||||
−0.394675 | + | 0.918821i | \(0.629143\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.1685 | 0.614513 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.71520 | −0.118981 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.4176 | −1.19710 | −0.598548 | − | 0.801087i | \(-0.704255\pi\) | ||||
−0.598548 | + | 0.801087i | \(0.704255\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.35541 | 0.0752792 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.3776 | −0.586752 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.6796 | −1.32937 | −0.664686 | − | 0.747123i | \(-0.731435\pi\) | ||||
−0.664686 | + | 0.747123i | \(0.731435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.4627 | 1.44856 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.92434 | 0.188574 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.72025 | −0.181893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.44889 | −0.173090 | −0.0865448 | − | 0.996248i | \(-0.527583\pi\) | ||||
−0.0865448 | + | 0.996248i | \(0.527583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.266984 | 0.00847248 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 63.9415 | 2.02708 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.2815 | 1.49742 | 0.748709 | − | 0.662898i | \(-0.230674\pi\) | ||||
0.748709 | + | 0.662898i | \(0.230674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.05784 | 0.0651070 |
(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 | 7728.2.a.bx.1.3 | 3 | ||
4.3 | odd | 2 | 3864.2.a.m.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.m.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
7728.2.a.bx.1.3 | 3 | 1.1 | even | 1 | trivial |