Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3432,2,Mod(1,3432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3432, 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("3432.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3432.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: | \(27.4046579737\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.65544\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3432.1 |
$q$-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 | ||||||||
\(5\) | −2.39593 | −1.07149 | −0.535747 | − | 0.844379i | \(-0.679970\pi\) | ||||
−0.535747 | + | 0.844379i | \(0.679970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05137 | 0.397382 | 0.198691 | − | 0.980062i | \(-0.436331\pi\) | ||||
0.198691 | + | 0.980062i | \(0.436331\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.39593 | −0.618627 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.96633 | −1.44705 | −0.723523 | − | 0.690300i | \(-0.757479\pi\) | ||||
−0.723523 | + | 0.690300i | \(0.757479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.05137 | −1.15886 | −0.579432 | − | 0.815020i | \(-0.696726\pi\) | ||||
−0.579432 | + | 0.815020i | \(0.696726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05137 | 0.229429 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.15412 | 1.90877 | 0.954383 | − | 0.298584i | \(-0.0965144\pi\) | ||||
0.954383 | + | 0.298584i | \(0.0965144\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.740489 | 0.148098 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.65544 | −0.493103 | −0.246552 | − | 0.969130i | \(-0.579297\pi\) | ||||
−0.246552 | + | 0.969130i | \(0.579297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.70682 | −1.74340 | −0.871698 | − | 0.490044i | \(-0.836981\pi\) | ||||
−0.871698 | + | 0.490044i | \(0.836981\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.51902 | −0.425792 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.51902 | −0.742922 | −0.371461 | − | 0.928448i | \(-0.621143\pi\) | ||||
−0.371461 | + | 0.928448i | \(0.621143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57040 | 0.557602 | 0.278801 | − | 0.960349i | \(-0.410063\pi\) | ||||
0.278801 | + | 0.960349i | \(0.410063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.96633 | 1.21485 | 0.607427 | − | 0.794376i | \(-0.292202\pi\) | ||||
0.607427 | + | 0.794376i | \(0.292202\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.39593 | −0.357164 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.20814 | −0.176225 | −0.0881124 | − | 0.996111i | \(-0.528083\pi\) | ||||
−0.0881124 | + | 0.996111i | \(0.528083\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.89461 | −0.842087 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.96633 | −0.835453 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.689115 | −0.0946573 | −0.0473286 | − | 0.998879i | \(-0.515071\pi\) | ||||
−0.0473286 | + | 0.998879i | \(0.515071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.39593 | −0.323067 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.05137 | −0.669071 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4136 | 1.48593 | 0.742964 | − | 0.669331i | \(-0.233419\pi\) | ||||
0.742964 | + | 0.669331i | \(0.233419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.89461 | −0.882765 | −0.441382 | − | 0.897319i | \(-0.645512\pi\) | ||||
−0.441382 | + | 0.897319i | \(0.645512\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.05137 | 0.132461 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.39593 | −0.297179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.2258 | −1.73796 | −0.868981 | − | 0.494845i | \(-0.835225\pi\) | ||||
−0.868981 | + | 0.494845i | \(0.835225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.15412 | 1.10203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.10275 | −0.961619 | −0.480810 | − | 0.876825i | \(-0.659657\pi\) | ||||
−0.480810 | + | 0.876825i | \(0.659657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.25951 | 0.264456 | 0.132228 | − | 0.991219i | \(-0.457787\pi\) | ||||
0.132228 | + | 0.991219i | \(0.457787\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.740489 | 0.0855044 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.05137 | 0.119815 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4473 | −1.28792 | −0.643961 | − | 0.765058i | \(-0.722710\pi\) | ||||
−0.643961 | + | 0.765058i | \(0.722710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.4136 | 1.69187 | 0.845933 | − | 0.533289i | \(-0.179044\pi\) | ||||
0.845933 | + | 0.533289i | \(0.179044\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.2949 | 1.55050 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.65544 | −0.284693 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8096 | −1.25181 | −0.625906 | − | 0.779899i | \(-0.715271\pi\) | ||||
−0.625906 | + | 0.779899i | \(0.715271\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.05137 | 0.110214 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.70682 | −1.00655 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.1027 | 1.24172 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.1027 | −1.43192 | −0.715959 | − | 0.698143i | \(-0.754010\pi\) | ||||
−0.715959 | + | 0.698143i | \(0.754010\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.17446 | −0.912893 | −0.456447 | − | 0.889751i | \(-0.650878\pi\) | ||||
−0.456447 | + | 0.889751i | \(0.650878\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.62177 | 0.258331 | 0.129165 | − | 0.991623i | \(-0.458770\pi\) | ||||
0.129165 | + | 0.991623i | \(0.458770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.51902 | −0.245831 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.37559 | 0.616352 | 0.308176 | − | 0.951329i | \(-0.400281\pi\) | ||||
0.308176 | + | 0.951329i | \(0.400281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.22147 | −0.116995 | −0.0584977 | − | 0.998288i | \(-0.518631\pi\) | ||||
−0.0584977 | + | 0.998288i | \(0.518631\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.51902 | −0.428926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4136 | 1.26185 | 0.630924 | − | 0.775844i | \(-0.282676\pi\) | ||||
0.630924 | + | 0.775844i | \(0.282676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.9327 | −2.04523 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.27284 | −0.575031 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.57040 | 0.321932 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2055 | 0.912807 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.06908 | 0.716015 | 0.358007 | − | 0.933719i | \(-0.383456\pi\) | ||||
0.358007 | + | 0.933719i | \(0.383456\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.96633 | 0.701396 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.3082 | −1.59960 | −0.799799 | − | 0.600267i | \(-0.795061\pi\) | ||||
−0.799799 | + | 0.600267i | \(0.795061\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.31088 | −0.460512 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.39593 | −0.206209 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.2258 | −1.55714 | −0.778569 | − | 0.627559i | \(-0.784054\pi\) | ||||
−0.778569 | + | 0.627559i | \(0.784054\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.65544 | −0.394869 | −0.197435 | − | 0.980316i | \(-0.563261\pi\) | ||||
−0.197435 | + | 0.980316i | \(0.563261\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.20814 | −0.101743 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.36226 | 0.528357 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.89461 | −0.486179 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7759 | 0.964719 | 0.482359 | − | 0.875973i | \(-0.339780\pi\) | ||||
0.482359 | + | 0.875973i | \(0.339780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6351 | −1.84202 | −0.921009 | − | 0.389541i | \(-0.872634\pi\) | ||||
−0.921009 | + | 0.389541i | \(0.872634\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.96633 | −0.482349 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.2569 | 1.86804 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.259511 | 0.0207112 | 0.0103556 | − | 0.999946i | \(-0.496704\pi\) | ||||
0.0103556 | + | 0.999946i | \(0.496704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.689115 | −0.0546504 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.62441 | 0.758510 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.60143 | 0.203760 | 0.101880 | − | 0.994797i | \(-0.467514\pi\) | ||||
0.101880 | + | 0.994797i | \(0.467514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.39593 | −0.186523 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.06471 | −0.701448 | −0.350724 | − | 0.936479i | \(-0.614064\pi\) | ||||
−0.350724 | + | 0.936479i | \(0.614064\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.05137 | −0.386288 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.8990 | −1.36083 | −0.680417 | − | 0.732825i | \(-0.738201\pi\) | ||||
−0.680417 | + | 0.732825i | \(0.738201\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.778532 | 0.0588515 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.4136 | 0.857901 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.8813 | −0.962792 | −0.481396 | − | 0.876503i | \(-0.659870\pi\) | ||||
−0.481396 | + | 0.876503i | \(0.659870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.84324 | −0.434324 | −0.217162 | − | 0.976136i | \(-0.569680\pi\) | ||||
−0.217162 | + | 0.976136i | \(0.569680\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.89461 | −0.509664 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8273 | 0.796036 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.96633 | −0.436301 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.05137 | 0.0764762 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.82991 | −0.711267 | −0.355634 | − | 0.934625i | \(-0.615735\pi\) | ||||
−0.355634 | + | 0.934625i | \(0.615735\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.0868 | −1.22993 | −0.614967 | − | 0.788553i | \(-0.710831\pi\) | ||||
−0.614967 | + | 0.788553i | \(0.710831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.39593 | −0.171576 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.74049 | −0.408993 | −0.204496 | − | 0.978867i | \(-0.565556\pi\) | ||||
−0.204496 | + | 0.978867i | \(0.565556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2055 | 1.14878 | 0.574389 | − | 0.818583i | \(-0.305240\pi\) | ||||
0.574389 | + | 0.818583i | \(0.305240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.2258 | −1.00341 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.79186 | −0.195950 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.55442 | −0.597467 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.15412 | 0.636256 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.05137 | −0.349411 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.27721 | 0.363298 | 0.181649 | − | 0.983363i | \(-0.441856\pi\) | ||||
0.181649 | + | 0.983363i | \(0.441856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.10275 | −0.555191 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.0868 | −1.30171 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.2055 | −0.692794 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.25951 | 0.152684 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.96633 | −0.401339 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.0824 | −1.34482 | −0.672409 | − | 0.740180i | \(-0.734740\pi\) | ||||
−0.672409 | + | 0.740180i | \(0.734740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.740489 | 0.0493660 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.25687 | −0.348911 | −0.174455 | − | 0.984665i | \(-0.555816\pi\) | ||||
−0.174455 | + | 0.984665i | \(0.555816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.7919 | −1.10964 | −0.554819 | − | 0.831971i | \(-0.687212\pi\) | ||||
−0.554819 | + | 0.831971i | \(0.687212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.05137 | 0.0691753 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.93092 | 0.388548 | 0.194274 | − | 0.980947i | \(-0.437765\pi\) | ||||
0.194274 | + | 0.980947i | \(0.437765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.89461 | 0.188824 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.4473 | −0.743582 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.3977 | −1.31942 | −0.659708 | − | 0.751522i | \(-0.729320\pi\) | ||||
−0.659708 | + | 0.751522i | \(0.729320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.1001 | 1.10151 | 0.550757 | − | 0.834665i | \(-0.314339\pi\) | ||||
0.550757 | + | 0.834665i | \(0.314339\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.1231 | 0.902291 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.05137 | −0.321411 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4136 | 0.976799 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.997361 | −0.0629528 | −0.0314764 | − | 0.999504i | \(-0.510021\pi\) | ||||
−0.0314764 | + | 0.999504i | \(0.510021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.15412 | 0.575515 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.2949 | 0.895182 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.3463 | 1.83057 | 0.915286 | − | 0.402806i | \(-0.131965\pi\) | ||||
0.915286 | + | 0.402806i | \(0.131965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.75118 | −0.295224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.65544 | −0.164368 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.2029 | −1.55407 | −0.777037 | − | 0.629454i | \(-0.783278\pi\) | ||||
−0.777037 | + | 0.629454i | \(0.783278\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.65107 | 0.101425 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8096 | −0.722734 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.68912 | 0.285900 | 0.142950 | − | 0.989730i | \(-0.454341\pi\) | ||||
0.142950 | + | 0.989730i | \(0.454341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.465007 | 0.0282472 | 0.0141236 | − | 0.999900i | \(-0.495504\pi\) | ||||
0.0141236 | + | 0.999900i | \(0.495504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.05137 | 0.0636321 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.740489 | 0.0446532 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3082 | 1.22020 | 0.610102 | − | 0.792323i | \(-0.291128\pi\) | ||||
0.610102 | + | 0.792323i | \(0.291128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.70682 | −0.581132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4003 | 1.03801 | 0.519007 | − | 0.854770i | \(-0.326302\pi\) | ||||
0.519007 | + | 0.854770i | \(0.326302\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.1692 | 1.85282 | 0.926408 | − | 0.376522i | \(-0.122880\pi\) | ||||
0.926408 | + | 0.376522i | \(0.122880\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.1027 | 0.716905 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.75382 | 0.221581 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.5971 | 1.09394 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1027 | −0.826718 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8432 | 1.15925 | 0.579627 | − | 0.814882i | \(-0.303198\pi\) | ||||
0.579627 | + | 0.814882i | \(0.303198\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.3463 | −1.59216 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.15412 | 0.529397 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.37559 | 0.482761 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.17446 | −0.527059 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5190 | 0.945876 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5704 | −0.774503 | −0.387252 | − | 0.921974i | \(-0.626576\pi\) | ||||
−0.387252 | + | 0.921974i | \(0.626576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.62177 | 0.149147 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3216 | −1.37915 | −0.689575 | − | 0.724214i | \(-0.742203\pi\) | ||||
−0.689575 | + | 0.724214i | \(0.742203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6084 | 1.05181 | 0.525906 | − | 0.850543i | \(-0.323727\pi\) | ||||
0.525906 | + | 0.850543i | \(0.323727\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.51902 | −0.141931 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.6395 | 1.44006 | 0.720028 | − | 0.693945i | \(-0.244129\pi\) | ||||
0.720028 | + | 0.693945i | \(0.244129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.65544 | −0.148676 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.37559 | 0.355851 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.1382 | 1.67693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.740489 | 0.0410750 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.22147 | −0.0675474 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.27020 | −0.0700286 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.7422 | 1.85464 | 0.927320 | − | 0.374269i | \(-0.122106\pi\) | ||||
0.927320 | + | 0.374269i | \(0.122106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.51902 | −0.247641 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.0841 | 1.86222 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1701 | 0.662947 | 0.331474 | − | 0.943464i | \(-0.392454\pi\) | ||||
0.331474 | + | 0.943464i | \(0.392454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.4136 | 0.728529 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.70682 | −0.525654 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5571 | −0.732013 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.9327 | −1.18081 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.4490 | 1.25881 | 0.629405 | − | 0.777077i | \(-0.283299\pi\) | ||||
0.629405 | + | 0.777077i | \(0.283299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.8946 | 1.11846 | 0.559231 | − | 0.829012i | \(-0.311096\pi\) | ||||
0.559231 | + | 0.829012i | \(0.311096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.97966 | 0.211816 | 0.105908 | − | 0.994376i | \(-0.466225\pi\) | ||||
0.105908 | + | 0.994376i | \(0.466225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4136 | 1.03037 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.27284 | −0.331994 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.9433 | 1.94980 | 0.974898 | − | 0.222654i | \(-0.0714719\pi\) | ||||
0.974898 | + | 0.222654i | \(0.0714719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.51638 | 0.342967 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.41363 | −0.283363 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.8946 | −0.777492 | −0.388746 | − | 0.921345i | \(-0.627092\pi\) | ||||
−0.388746 | + | 0.921345i | \(0.627092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.57040 | 0.185867 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.724518 | −0.0376151 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2462 | −0.530527 | −0.265264 | − | 0.964176i | \(-0.585459\pi\) | ||||
−0.265264 | + | 0.964176i | \(0.585459\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2055 | 0.527010 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.65544 | −0.136762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.6395 | −1.83068 | −0.915338 | − | 0.402686i | \(-0.868077\pi\) | ||||
−0.915338 | + | 0.402686i | \(0.868077\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.06908 | 0.413391 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.9327 | −1.22290 | −0.611451 | − | 0.791282i | \(-0.709414\pi\) | ||||
−0.611451 | + | 0.791282i | \(0.709414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.51902 | −0.128381 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.96633 | 0.404951 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.45168 | −0.327113 | −0.163556 | − | 0.986534i | \(-0.552297\pi\) | ||||
−0.163556 | + | 0.986534i | \(0.552297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.6165 | −2.76207 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.3082 | −0.923529 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.4270 | 1.38000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.51902 | −0.226803 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.31088 | −0.265877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.33123 | 0.0664782 | 0.0332391 | − | 0.999447i | \(-0.489418\pi\) | ||||
0.0332391 | + | 0.999447i | \(0.489418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.70682 | −0.483531 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.39593 | −0.119055 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.51902 | −0.224000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4650 | 0.715249 | 0.357624 | − | 0.933866i | \(-0.383587\pi\) | ||||
0.357624 | + | 0.933866i | \(0.383587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.2258 | −0.899014 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | 0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.9300 | −1.81282 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.65544 | −0.227978 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.156762 | 0.00765833 | 0.00382916 | − | 0.999993i | \(-0.498781\pi\) | ||||
0.00382916 | + | 0.999993i | \(0.498781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8973 | 0.774785 | 0.387392 | − | 0.921915i | \(-0.373376\pi\) | ||||
0.387392 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.20814 | −0.0587416 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.41800 | −0.214305 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.24882 | −0.350795 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.69175 | −0.0814889 | −0.0407445 | − | 0.999170i | \(-0.512973\pi\) | ||||
−0.0407445 | + | 0.999170i | \(0.512973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.16745 | −0.440560 | −0.220280 | − | 0.975437i | \(-0.570697\pi\) | ||||
−0.220280 | + | 0.975437i | \(0.570697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.36226 | 0.305047 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −46.2409 | −2.21200 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.5208 | −0.883947 | −0.441974 | − | 0.897028i | \(-0.645722\pi\) | ||||
−0.441974 | + | 0.897028i | \(0.645722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.89461 | −0.280696 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.03804 | 0.239365 | 0.119682 | − | 0.992812i | \(-0.461812\pi\) | ||||
0.119682 | + | 0.992812i | \(0.461812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.2949 | 1.34131 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.7759 | 0.556981 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.70946 | −0.127867 | −0.0639336 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639336 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.57040 | 0.168123 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.6351 | −1.06349 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.51902 | −0.118094 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8973 | 0.930754 | 0.465377 | − | 0.885113i | \(-0.345919\pi\) | ||||
0.465377 | + | 0.885113i | \(0.345919\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.96633 | −0.278484 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.4624 | −1.27905 | −0.639525 | − | 0.768770i | \(-0.720869\pi\) | ||||
−0.639525 | + | 0.768770i | \(0.720869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0470050 | −0.00218451 | −0.00109225 | − | 0.999999i | \(-0.500348\pi\) | ||||
−0.00109225 | + | 0.999999i | \(0.500348\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.2569 | 1.07851 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.2188 | −1.21326 | −0.606631 | − | 0.794983i | \(-0.707480\pi\) | ||||
−0.606631 | + | 0.794983i | \(0.707480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9567 | −0.690635 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.259511 | 0.0119576 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.96633 | 0.366292 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.74049 | −0.171625 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.689115 | −0.0315524 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.6351 | −1.39975 | −0.699877 | − | 0.714264i | \(-0.746762\pi\) | ||||
−0.699877 | + | 0.714264i | \(0.746762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.51902 | −0.206050 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.62441 | 0.437926 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.7892 | 1.53429 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3553 | 0.469241 | 0.234621 | − | 0.972087i | \(-0.424615\pi\) | ||||
0.234621 | + | 0.972087i | \(0.424615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.60143 | 0.117641 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.48098 | 0.427871 | 0.213935 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213935 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.8432 | 0.713544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.39593 | −0.107689 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.51902 | −0.382130 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.2879 | 1.98260 | 0.991299 | − | 0.131626i | \(-0.0420198\pi\) | ||||
0.991299 | + | 0.131626i | \(0.0420198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.06471 | −0.404981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.1115 | 1.61013 | 0.805066 | − | 0.593186i | \(-0.202130\pi\) | ||||
0.805066 | + | 0.593186i | \(0.202130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.9814 | 0.978159 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.80957 | 0.346153 | 0.173076 | − | 0.984908i | \(-0.444629\pi\) | ||||
0.173076 | + | 0.984908i | \(0.444629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.37559 | 0.105090 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.05137 | −0.223024 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.28158 | −0.276800 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.20814 | −0.0531338 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.8990 | −0.785678 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7512 | −0.821504 | −0.410752 | − | 0.911747i | \(-0.634734\pi\) | ||||
−0.410752 | + | 0.911747i | \(0.634734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.92829 | −0.128045 | −0.0640225 | − | 0.997948i | \(-0.520393\pi\) | ||||
−0.0640225 | + | 0.997948i | \(0.520393\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.778532 | 0.0339779 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 57.9140 | 2.52278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.7980 | 2.64339 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4136 | 0.495309 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.57040 | 0.154651 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.2755 | −0.660417 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.8813 | −0.555868 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.89461 | −0.253899 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.0380 | −1.16246 | −0.581228 | − | 0.813741i | \(-0.697428\pi\) | ||||
−0.581228 | + | 0.813741i | \(0.697428\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.84324 | −0.250757 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.92656 | 0.125360 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.5588 | 1.60590 | 0.802949 | − | 0.596048i | \(-0.203263\pi\) | ||||
0.802949 | + | 0.596048i | \(0.203263\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.89461 | −0.294255 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4136 | 0.571440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0354 | −0.511797 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.8273 | 0.459592 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.1161 | 0.682860 | 0.341430 | − | 0.939907i | \(-0.389089\pi\) | ||||
0.341430 | + | 0.939907i | \(0.389089\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.96633 | 0.336940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.96633 | −0.251899 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.10275 | −0.0886203 | −0.0443101 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443101 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.1382 | −1.35206 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.05137 | 0.0441536 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9663 | 1.08857 | 0.544283 | − | 0.838902i | \(-0.316802\pi\) | ||||
0.544283 | + | 0.838902i | \(0.316802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.54742 | 0.274001 | 0.137000 | − | 0.990571i | \(-0.456254\pi\) | ||||
0.137000 | + | 0.990571i | \(0.456254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.82991 | −0.410650 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.77853 | 0.282684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.3082 | −1.01197 | −0.505983 | − | 0.862544i | \(-0.668870\pi\) | ||||
−0.505983 | + | 0.862544i | \(0.668870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.0868 | −0.710102 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.2055 | 0.672317 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.689115 | −0.0285402 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.39593 | −0.0990596 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.00264 | −0.123932 | −0.0619661 | − | 0.998078i | \(-0.519737\pi\) | ||||
−0.0619661 | + | 0.998078i | \(0.519737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.0328 | 2.02036 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.74049 | −0.236132 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.7733 | −1.34584 | −0.672918 | − | 0.739717i | \(-0.734959\pi\) | ||||
−0.672918 | + | 0.739717i | \(0.734959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0293 | 0.616141 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.2055 | 0.663247 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0354 | 0.573471 | 0.286736 | − | 0.958010i | \(-0.407430\pi\) | ||||
0.286736 | + | 0.958010i | \(0.407430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.3730 | 1.03498 | 0.517492 | − | 0.855688i | \(-0.326866\pi\) | ||||
0.517492 | + | 0.855688i | \(0.326866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.2258 | −0.579321 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.39593 | −0.0974085 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.5855 | −1.85026 | −0.925128 | − | 0.379655i | \(-0.876043\pi\) | ||||
−0.925128 | + | 0.379655i | \(0.876043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.79186 | −0.113132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.20814 | −0.0488760 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.71383 | 0.230779 | 0.115390 | − | 0.993320i | \(-0.463188\pi\) | ||||
0.115390 | + | 0.993320i | \(0.463188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.55442 | −0.344948 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.4606 | −0.783456 | −0.391728 | − | 0.920081i | \(-0.628123\pi\) | ||||
−0.391728 | + | 0.920081i | \(0.628123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3259 | −0.455228 | −0.227614 | − | 0.973751i | \(-0.573092\pi\) | ||||
−0.227614 | + | 0.973751i | \(0.573092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.15412 | 0.367342 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.4163 | −0.497447 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1541 | −1.12616 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.05137 | −0.201732 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.9620 | 1.07504 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7068 | −0.466041 | −0.233021 | − | 0.972472i | \(-0.574861\pi\) | ||||
−0.233021 | + | 0.972472i | \(0.574861\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.27721 | 0.209750 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.3330 | −0.767205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.89461 | −0.233553 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.10275 | −0.320540 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.7245 | 0.897564 | 0.448782 | − | 0.893641i | \(-0.351858\pi\) | ||||
0.448782 | + | 0.893641i | \(0.351858\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.4340 | −1.16076 | −0.580381 | − | 0.814345i | \(-0.697096\pi\) | ||||
−0.580381 | + | 0.814345i | \(0.697096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.0868 | −0.751541 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.3170 | 1.74228 | 0.871140 | − | 0.491034i | \(-0.163381\pi\) | ||||
0.871140 | + | 0.491034i | \(0.163381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4136 | 0.448024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.2055 | −0.399985 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.7245 | −0.732747 | −0.366374 | − | 0.930468i | \(-0.619401\pi\) | ||||
−0.366374 | + | 0.930468i | \(0.619401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.8653 | 1.71396 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.25951 | 0.0881519 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.72716 | 0.378916 | 0.189458 | − | 0.981889i | \(-0.439327\pi\) | ||||
0.189458 | + | 0.981889i | \(0.439327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.7980 | 1.93692 | 0.968458 | − | 0.249176i | \(-0.0801599\pi\) | ||||
0.968458 | + | 0.249176i | \(0.0801599\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.96633 | −0.231713 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7245 | 0.493436 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.3082 | −0.941219 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.0824 | −0.776431 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.89461 | −0.266164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.41627 | 0.247329 | 0.123665 | − | 0.992324i | \(-0.460535\pi\) | ||||
0.123665 | + | 0.992324i | \(0.460535\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.740489 | 0.0285015 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.7315 | 0.796777 | 0.398389 | − | 0.917217i | \(-0.369570\pi\) | ||||
0.398389 | + | 0.917217i | \(0.369570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.8273 | −0.569018 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.25687 | −0.201444 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.85921 | 0.262460 | 0.131230 | − | 0.991352i | \(-0.458107\pi\) | ||||
0.131230 | + | 0.991352i | \(0.458107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.6679 | 1.66846 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.7919 | −0.640650 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.689115 | −0.0262532 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.8183 | 1.51476 | 0.757380 | − | 0.652975i | \(-0.226479\pi\) | ||||
0.757380 | + | 0.652975i | \(0.226479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.05137 | 0.0399384 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.1541 | 0.423100 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.3021 | −0.806876 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.93092 | 0.224328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.1985 | 1.14058 | 0.570291 | − | 0.821443i | \(-0.306831\pi\) | ||||
0.570291 | + | 0.821443i | \(0.306831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.8273 | 0.860947 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.89461 | 0.109017 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.64579 | −0.362767 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.7219 | −1.11623 | −0.558114 | − | 0.829764i | \(-0.688475\pi\) | ||||
−0.558114 | + | 0.829764i | \(0.688475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4473 | −0.429308 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −88.8574 | −3.32774 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.39593 | −0.0896028 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.3977 | −0.761765 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.44904 | −0.352390 | −0.176195 | − | 0.984355i | \(-0.556379\pi\) | ||||
−0.176195 | + | 0.984355i | \(0.556379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.75646 | 0.102656 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.1001 | 0.635960 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.96633 | −0.0730276 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.3436 | −1.64461 | −0.822307 | − | 0.569043i | \(-0.807314\pi\) | ||||
−0.822307 | + | 0.569043i | \(0.807314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.5297 | −1.75795 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.77325 | −0.324047 | −0.162024 | − | 0.986787i | \(-0.551802\pi\) | ||||
−0.162024 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.1231 | 0.520938 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.2258 | −0.524015 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.3863 | −1.15456 | −0.577282 | − | 0.816545i | \(-0.695886\pi\) | ||||
−0.577282 | + | 0.816545i | \(0.695886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.05137 | −0.185567 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.5164 | −0.642614 | −0.321307 | − | 0.946975i | \(-0.604122\pi\) | ||||
−0.321307 | + | 0.946975i | \(0.604122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.2142 | −1.03369 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.4136 | 0.563955 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.70313 | 0.244927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.1382 | 1.75659 | 0.878293 | − | 0.478123i | \(-0.158683\pi\) | ||||
0.878293 | + | 0.478123i | \(0.158683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.997361 | −0.0363458 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.2322 | 1.97371 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0868 | 0.693721 | 0.346860 | − | 0.937917i | \(-0.387248\pi\) | ||||
0.346860 | + | 0.937917i | \(0.387248\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.15412 | 0.332274 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.1895 | 1.27562 | 0.637810 | − | 0.770194i | \(-0.279841\pi\) | ||||
0.637810 | + | 0.770194i | \(0.279841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.28422 | −0.0464919 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.2949 | 0.516834 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.4136 | 0.412122 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.1088 | −1.55454 | −0.777272 | − | 0.629164i | \(-0.783397\pi\) | ||||
−0.777272 | + | 0.629164i | \(0.783397\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.3463 | 1.05688 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.8069 | 0.460633 | 0.230317 | − | 0.973116i | \(-0.426024\pi\) | ||||
0.230317 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.18780 | −0.258193 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.75118 | −0.170448 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.0354 | −0.646185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.10275 | −0.289939 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.65544 | −0.0948978 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.621770 | −0.0221919 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.50569 | −0.303195 | −0.151598 | − | 0.988442i | \(-0.548442\pi\) | ||||
−0.151598 | + | 0.988442i | \(0.548442\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.2029 | −0.897245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.1027 | 0.501436 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.89461 | −0.244835 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.65107 | 0.0585575 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.129413 | 0.00458404 | 0.00229202 | − | 0.999997i | \(-0.499270\pi\) | ||||
0.00229202 | + | 0.999997i | \(0.499270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.20814 | 0.255006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.8096 | −0.417270 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.25951 | 0.0797364 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.0594 | −0.812738 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.68912 | 0.165065 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.9610 | 1.12369 | 0.561845 | − | 0.827242i | \(-0.310092\pi\) | ||||
0.561845 | + | 0.827242i | \(0.310092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.4243 | 1.27903 | 0.639516 | − | 0.768778i | \(-0.279135\pi\) | ||||
0.639516 | + | 0.768778i | \(0.279135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.465007 | 0.0163085 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.23285 | −0.218327 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.2409 | −1.40785 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.05137 | 0.0367380 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.09206 | −0.107913 | −0.0539567 | − | 0.998543i | \(-0.517183\pi\) | ||||
−0.0539567 | + | 0.998543i | \(0.517183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.1001 | −0.386925 | −0.193463 | − | 0.981108i | \(-0.561972\pi\) | ||||
−0.193463 | + | 0.981108i | \(0.561972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.740489 | 0.0257805 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.6998 | 1.10231 | 0.551155 | − | 0.834403i | \(-0.314187\pi\) | ||||
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0328 | −0.452647 | −0.226323 | − | 0.974052i | \(-0.572671\pi\) | ||||
−0.226323 | + | 0.974052i | \(0.572671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.3082 | 0.704485 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.1692 | 1.21854 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.7184 | 0.751597 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.70682 | −0.335517 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.93529 | 0.101338 | 0.0506688 | − | 0.998716i | \(-0.483865\pi\) | ||||
0.0506688 | + | 0.998716i | \(0.483865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9486 | −0.756849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.4003 | 0.599298 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.39593 | −0.0824226 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.05137 | 0.0361256 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.1692 | 1.06972 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.3677 | −1.41807 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.4757 | 1.35162 | 0.675811 | − | 0.737075i | \(-0.263794\pi\) | ||||
0.675811 | + | 0.737075i | \(0.263794\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.1027 | 0.413905 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.4534 | 1.45018 | 0.725090 | − | 0.688654i | \(-0.241798\pi\) | ||||
0.725090 | + | 0.688654i | \(0.241798\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1329 | −1.30108 | −0.650538 | − | 0.759473i | \(-0.725457\pi\) | ||||
−0.650538 | + | 0.759473i | \(0.725457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.75382 | 0.127930 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.3489 | −0.624605 | −0.312302 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312302 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.8847 | 1.45812 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.5971 | 0.631589 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.4473 | −0.388323 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.2258 | −0.482024 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.1027 | −0.477306 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.7298 | 0.362733 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.7599 | −0.971154 | −0.485577 | − | 0.874194i | \(-0.661390\pi\) | ||||
−0.485577 | + | 0.874194i | \(0.661390\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.8432 | 0.669296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.5251 | −1.39902 | −0.699508 | − | 0.714624i | \(-0.746598\pi\) | ||||
−0.699508 | + | 0.714624i | \(0.746598\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.03804 | −0.0349329 | −0.0174664 | − | 0.999847i | \(-0.505560\pi\) | ||||
−0.0174664 | + | 0.999847i | \(0.505560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.3463 | −0.919235 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.1329 | 1.34753 | 0.673765 | − | 0.738946i | \(-0.264676\pi\) | ||||
0.673765 | + | 0.738946i | \(0.264676\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.48362 | 0.284531 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.10275 | 0.204221 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.8627 | 1.03163 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.15412 | 0.305647 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.7759 | 0.859674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.11149 | 0.136973 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.37559 | 0.278722 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.2676 | −0.606565 | −0.303282 | − | 0.952901i | \(-0.598083\pi\) | ||||
−0.303282 | + | 0.952901i | \(0.598083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.17446 | −0.304298 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5430 | 1.11133 | 0.555665 | − | 0.831406i | \(-0.312464\pi\) | ||||
0.555665 | + | 0.831406i | \(0.312464\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.4136 | 0.510117 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.5190 | 0.546102 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.2488 | −0.635652 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.6200 | 0.482271 | 0.241135 | − | 0.970492i | \(-0.422480\pi\) | ||||
0.241135 | + | 0.970492i | \(0.422480\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5704 | −0.447160 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.10275 | −0.266705 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.34629 | −0.110025 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.62177 | 0.0861102 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.2879 | 0.403153 | 0.201577 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201577 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.7759 | 0.975865 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.3216 | −0.796253 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.2949 | 0.467494 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.930015 | 0.0303823 | 0.0151911 | − | 0.999885i | \(-0.495164\pi\) | ||||
0.0151911 | + | 0.999885i | \(0.495164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.6084 | 0.607263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.3277 | −1.15165 | −0.575825 | − | 0.817573i | \(-0.695319\pi\) | ||||
−0.575825 | + | 0.817573i | \(0.695319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.6838 | 1.06433 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.51902 | −0.0819438 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.65107 | 0.248626 | 0.124313 | − | 0.992243i | \(-0.460327\pi\) | ||||
0.124313 | + | 0.992243i | \(0.460327\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.25951 | 0.0733468 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.6395 | 0.831417 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.3507 | 1.82538 | 0.912688 | − | 0.408656i | \(-0.134002\pi\) | ||||
0.912688 | + | 0.408656i | \(0.134002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.5518 | 0.762118 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.65544 | −0.0858383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.1622 | −0.618779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.2223 | 2.03943 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.37559 | 0.205451 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40.9388 | 1.31787 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.5625 | 1.30440 | 0.652201 | − | 0.758046i | \(-0.273846\pi\) | ||||
0.652201 | + | 0.758046i | \(0.273846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.1382 | 0.968177 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.33296 | 0.299509 | 0.149754 | − | 0.988723i | \(-0.452152\pi\) | ||||
0.149754 | + | 0.988723i | \(0.452152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.89461 | −0.156914 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.740489 | 0.0237146 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.5634 | −1.64966 | −0.824829 | − | 0.565382i | \(-0.808729\pi\) | ||||
−0.824829 | + | 0.565382i | \(0.808729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.8096 | −0.377435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.22147 | −0.0389985 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3463 | 0.872211 | 0.436106 | − | 0.899896i | \(-0.356357\pi\) | ||||
0.436106 | + | 0.899896i | \(0.356357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.7538 | 0.438233 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.27020 | −0.0404310 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 72.9247 | 2.31887 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.8679 | −0.599360 | −0.299680 | − | 0.954040i | \(-0.596880\pi\) | ||||
−0.299680 | + | 0.954040i | \(0.596880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.7422 | 1.07078 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.8273 | −1.23091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.41891 | −0.108278 | −0.0541390 | − | 0.998533i | \(-0.517241\pi\) | ||||
−0.0541390 | + | 0.998533i | \(0.517241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.51902 | −0.142975 |
(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 | 3432.2.a.n.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 6864.2.a.bn.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.n.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
6864.2.a.bn.1.2 | 3 | 4.3 | odd | 2 |