Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7440,2,Mod(1,7440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, 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("7440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.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: | \(59.4086991038\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 5x + 3 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 465) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7440.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.485863 | −0.183639 | −0.0918195 | − | 0.995776i | \(-0.529268\pi\) | ||||
−0.0918195 | + | 0.995776i | \(0.529268\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.02827 | −1.51608 | −0.758041 | − | 0.652207i | \(-0.773843\pi\) | ||||
−0.758041 | + | 0.652207i | \(0.773843\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.51414 | 0.974646 | 0.487323 | − | 0.873222i | \(-0.337973\pi\) | ||||
0.487323 | + | 0.873222i | \(0.337973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.32088 | −0.320362 | −0.160181 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160181 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.64177 | 1.52373 | 0.761863 | − | 0.647738i | \(-0.224285\pi\) | ||||
0.761863 | + | 0.647738i | \(0.224285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.485863 | −0.106024 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.292611 | −0.0610135 | −0.0305068 | − | 0.999535i | \(-0.509712\pi\) | ||||
−0.0305068 | + | 0.999535i | \(0.509712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.86330 | −1.83157 | −0.915784 | − | 0.401671i | \(-0.868429\pi\) | ||||
−0.915784 | + | 0.401671i | \(0.868429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.02827 | −0.875310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.485863 | 0.0821258 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.51414 | 0.906519 | 0.453259 | − | 0.891379i | \(-0.350261\pi\) | ||||
0.453259 | + | 0.891379i | \(0.350261\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.51414 | 0.562712 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.02827 | −1.09763 | −0.548816 | − | 0.835943i | \(-0.684921\pi\) | ||||
−0.548816 | + | 0.835943i | \(0.684921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.02827 | 0.156810 | 0.0784051 | − | 0.996922i | \(-0.475017\pi\) | ||||
0.0784051 | + | 0.996922i | \(0.475017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.93438 | 1.01148 | 0.505742 | − | 0.862685i | \(-0.331219\pi\) | ||||
0.505742 | + | 0.862685i | \(0.331219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.76394 | −0.966277 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.32088 | −0.184961 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.70739 | −0.234528 | −0.117264 | − | 0.993101i | \(-0.537412\pi\) | ||||
−0.117264 | + | 0.993101i | \(0.537412\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.02827 | 0.678012 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.64177 | 0.879724 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.19325 | 0.285537 | 0.142769 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142769 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.485863 | −0.0612130 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.51414 | −0.435875 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.12763 | −1.11512 | −0.557559 | − | 0.830137i | \(-0.688262\pi\) | ||||
−0.557559 | + | 0.830137i | \(0.688262\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.292611 | −0.0352262 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4768 | −1.59940 | −0.799700 | − | 0.600399i | \(-0.795008\pi\) | ||||
−0.799700 | + | 0.600399i | \(0.795008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5424 | 1.46798 | 0.733989 | − | 0.679161i | \(-0.237656\pi\) | ||||
0.733989 | + | 0.679161i | \(0.237656\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.44305 | 0.278412 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.349158 | 0.0392834 | 0.0196417 | − | 0.999807i | \(-0.493747\pi\) | ||||
0.0196417 | + | 0.999807i | \(0.493747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9344 | −1.20020 | −0.600102 | − | 0.799923i | \(-0.704873\pi\) | ||||
−0.600102 | + | 0.799923i | \(0.704873\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.32088 | 0.143270 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.86330 | −1.05746 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.03374 | 0.533575 | 0.266788 | − | 0.963755i | \(-0.414038\pi\) | ||||
0.266788 | + | 0.963755i | \(0.414038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.70739 | −0.178983 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.64177 | −0.681431 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4431 | 1.06033 | 0.530166 | − | 0.847894i | \(-0.322130\pi\) | ||||
0.530166 | + | 0.847894i | \(0.322130\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.02827 | −0.505361 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6135 | −1.15559 | −0.577793 | − | 0.816183i | \(-0.696086\pi\) | ||||
−0.577793 | + | 0.816183i | \(0.696086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.76940 | 0.371410 | 0.185705 | − | 0.982606i | \(-0.440543\pi\) | ||||
0.185705 | + | 0.982606i | \(0.440543\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.485863 | 0.0474154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.73566 | 0.651161 | 0.325581 | − | 0.945514i | \(-0.394440\pi\) | ||||
0.325581 | + | 0.945514i | \(0.394440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.90611 | −0.374137 | −0.187069 | − | 0.982347i | \(-0.559899\pi\) | ||||
−0.187069 | + | 0.982347i | \(0.559899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.51414 | 0.523379 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0848 | −1.41906 | −0.709530 | − | 0.704675i | \(-0.751093\pi\) | ||||
−0.709530 | + | 0.704675i | \(0.751093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.292611 | 0.0272861 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.51414 | 0.324882 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.641769 | 0.0588309 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.2835 | 1.29850 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.02827 | −0.633718 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.25526 | 0.555065 | 0.277532 | − | 0.960716i | \(-0.410483\pi\) | ||||
0.277532 | + | 0.960716i | \(0.410483\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.02827 | 0.0905345 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.1186 | 1.93251 | 0.966254 | − | 0.257592i | \(-0.0829291\pi\) | ||||
0.966254 | + | 0.257592i | \(0.0829291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.22699 | −0.279816 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6044 | −1.24774 | −0.623870 | − | 0.781528i | \(-0.714441\pi\) | ||||
−0.623870 | + | 0.781528i | \(0.714441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.8970 | −1.09391 | −0.546956 | − | 0.837161i | \(-0.684214\pi\) | ||||
−0.546956 | + | 0.837161i | \(0.684214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.93438 | 0.583980 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6700 | −1.47764 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.86330 | 0.819102 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.76394 | −0.557880 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.3118 | 1.33632 | 0.668158 | − | 0.744020i | \(-0.267083\pi\) | ||||
0.668158 | + | 0.744020i | \(0.267083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.3774 | −1.57691 | −0.788457 | − | 0.615090i | \(-0.789119\pi\) | ||||
−0.788457 | + | 0.615090i | \(0.789119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.32088 | −0.106787 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.80128 | −0.303375 | −0.151688 | − | 0.988428i | \(-0.548471\pi\) | ||||
−0.151688 | + | 0.988428i | \(0.548471\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.70739 | −0.135405 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.142169 | 0.0112045 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.5424 | −0.982397 | −0.491199 | − | 0.871048i | \(-0.663441\pi\) | ||||
−0.491199 | + | 0.871048i | \(0.663441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.02827 | 0.391451 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.2553 | −1.72216 | −0.861082 | − | 0.508466i | \(-0.830213\pi\) | ||||
−0.861082 | + | 0.508466i | \(0.830213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.650842 | −0.0500647 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.64177 | 0.507909 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9717 | −0.834165 | −0.417082 | − | 0.908869i | \(-0.636947\pi\) | ||||
−0.417082 | + | 0.908869i | \(0.636947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.485863 | −0.0367278 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.19325 | 0.164855 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9253 | 1.19031 | 0.595157 | − | 0.803610i | \(-0.297090\pi\) | ||||
0.595157 | + | 0.803610i | \(0.297090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.05655 | −0.598838 | −0.299419 | − | 0.954122i | \(-0.596793\pi\) | ||||
−0.299419 | + | 0.954122i | \(0.596793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.51414 | −0.405407 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.64177 | 0.485694 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.485863 | −0.0353413 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.19325 | −0.448128 | −0.224064 | − | 0.974574i | \(-0.571932\pi\) | ||||
−0.224064 | + | 0.974574i | \(0.571932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.25526 | −0.162337 | −0.0811687 | − | 0.996700i | \(-0.525865\pi\) | ||||
−0.0811687 | + | 0.996700i | \(0.525865\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.51414 | −0.251653 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.32088 | 0.664086 | 0.332043 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332043 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5479 | −1.17305 | −0.586524 | − | 0.809932i | \(-0.699504\pi\) | ||||
−0.586524 | + | 0.809932i | \(0.699504\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.12763 | −0.643814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.79221 | 0.336347 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.02827 | 0.490876 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.292611 | −0.0203378 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33.3966 | −2.31009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0101 | −1.72177 | −0.860884 | − | 0.508801i | \(-0.830089\pi\) | ||||
−0.860884 | + | 0.508801i | \(0.830089\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.4768 | −0.923414 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.02827 | −0.0701277 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.485863 | 0.0329825 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.5424 | 0.847538 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.64177 | −0.312239 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.2835 | −1.29132 | −0.645661 | − | 0.763625i | \(-0.723418\pi\) | ||||
−0.645661 | + | 0.763625i | \(0.723418\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4340 | −1.55537 | −0.777684 | − | 0.628655i | \(-0.783606\pi\) | ||||
−0.777684 | + | 0.628655i | \(0.783606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.0283 | −1.65391 | −0.826957 | − | 0.562265i | \(-0.809930\pi\) | ||||
−0.826957 | + | 0.562265i | \(0.809930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44305 | 0.160741 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7175 | 1.22623 | 0.613113 | − | 0.789995i | \(-0.289917\pi\) | ||||
0.613113 | + | 0.789995i | \(0.289917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.93438 | −0.452349 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.349158 | 0.0226803 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.86876 | 0.250249 | 0.125125 | − | 0.992141i | \(-0.460067\pi\) | ||||
0.125125 | + | 0.992141i | \(0.460067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.61350 | −0.103934 | −0.0519672 | − | 0.998649i | \(-0.516549\pi\) | ||||
−0.0519672 | + | 0.998649i | \(0.516549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.76394 | 0.432132 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.3401 | 1.48509 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9344 | −0.692938 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.4713 | 1.60774 | 0.803868 | − | 0.594808i | \(-0.202772\pi\) | ||||
0.803868 | + | 0.594808i | \(0.202772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.47133 | 0.0925015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.32088 | 0.0827170 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0192 | 1.12401 | 0.562003 | − | 0.827135i | \(-0.310031\pi\) | ||||
0.562003 | + | 0.827135i | \(0.310031\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.67912 | −0.166472 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.86330 | −0.610523 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.15951 | −0.0714987 | −0.0357494 | − | 0.999361i | \(-0.511382\pi\) | ||||
−0.0357494 | + | 0.999361i | \(0.511382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.70739 | 0.104884 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.03374 | 0.308060 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.80675 | −0.475986 | −0.237993 | − | 0.971267i | \(-0.576489\pi\) | ||||
−0.237993 | + | 0.971267i | \(0.576489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.7831 | −1.08025 | −0.540124 | − | 0.841585i | \(-0.681623\pi\) | ||||
−0.540124 | + | 0.841585i | \(0.681623\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.70739 | −0.103336 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.02827 | −0.303216 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.9390 | 1.55853 | 0.779263 | − | 0.626697i | \(-0.215594\pi\) | ||||
0.779263 | + | 0.626697i | \(0.215594\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0283 | −0.777202 | −0.388601 | − | 0.921406i | \(-0.627041\pi\) | ||||
−0.388601 | + | 0.921406i | \(0.627041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9006 | −0.945195 | −0.472598 | − | 0.881278i | \(-0.656684\pi\) | ||||
−0.472598 | + | 0.881278i | \(0.656684\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.64177 | −0.393424 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.41478 | 0.201568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2553 | −0.897368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4431 | 0.612183 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.4340 | −1.71955 | −0.859776 | − | 0.510672i | \(-0.829397\pi\) | ||||
−0.859776 | + | 0.510672i | \(0.829397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.19325 | −0.127696 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.02827 | −0.291770 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.02827 | −0.0594666 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.499600 | −0.0287965 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.6135 | −0.667178 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.96812 | −0.568911 | −0.284455 | − | 0.958689i | \(-0.591813\pi\) | ||||
−0.284455 | + | 0.958689i | \(0.591813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.76940 | 0.214434 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9945 | −0.906967 | −0.453483 | − | 0.891265i | \(-0.649819\pi\) | ||||
−0.453483 | + | 0.891265i | \(0.649819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.8542 | −1.29180 | −0.645899 | − | 0.763423i | \(-0.723517\pi\) | ||||
−0.645899 | + | 0.763423i | \(0.723517\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.485863 | 0.0273753 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6044 | 0.820266 | 0.410133 | − | 0.912026i | \(-0.365482\pi\) | ||||
0.410133 | + | 0.912026i | \(0.365482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 49.5953 | 2.77681 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.73566 | 0.375948 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.77301 | −0.488143 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.51414 | 0.194929 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.90611 | −0.216008 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.36916 | −0.185748 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.16137 | 0.448589 | 0.224295 | − | 0.974521i | \(-0.427992\pi\) | ||||
0.224295 | + | 0.974521i | \(0.427992\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.51414 | 0.302173 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.12763 | 0.498696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8825 | −0.647281 | −0.323640 | − | 0.946180i | \(-0.604907\pi\) | ||||
−0.323640 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.0848 | −0.819295 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02827 | 0.272296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.68739 | 0.361085 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.292611 | 0.0157536 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3684 | 0.986065 | 0.493033 | − | 0.870011i | \(-0.335888\pi\) | ||||
0.493033 | + | 0.870011i | \(0.335888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2462 | 0.601995 | 0.300997 | − | 0.953625i | \(-0.402680\pi\) | ||||
0.300997 | + | 0.953625i | \(0.402680\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.51414 | 0.187571 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.3593 | 1.34974 | 0.674869 | − | 0.737937i | \(-0.264200\pi\) | ||||
0.674869 | + | 0.737937i | \(0.264200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.4768 | 0.715274 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.641769 | 0.0339660 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2890 | −0.806923 | −0.403461 | − | 0.914997i | \(-0.632193\pi\) | ||||
−0.403461 | + | 0.914997i | \(0.632193\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.1131 | 1.32174 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.2835 | 0.749691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.5424 | −0.656500 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.05655 | −0.316149 | −0.158075 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158075 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.02827 | −0.365877 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.829557 | 0.0430685 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.06748 | 0.417718 | 0.208859 | − | 0.977946i | \(-0.433025\pi\) | ||||
0.208859 | + | 0.977946i | \(0.433025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.6610 | −1.78513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.8114 | 1.89088 | 0.945438 | − | 0.325803i | \(-0.105635\pi\) | ||||
0.945438 | + | 0.325803i | \(0.105635\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.25526 | 0.320467 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.63270 | 0.185622 | 0.0928111 | − | 0.995684i | \(-0.470415\pi\) | ||||
0.0928111 | + | 0.995684i | \(0.470415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.44305 | −0.124509 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.02827 | 0.0522701 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2781 | 0.774629 | 0.387315 | − | 0.921948i | \(-0.373403\pi\) | ||||
0.387315 | + | 0.921948i | \(0.373403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.386505 | 0.0195464 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.1186 | 1.11573 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.349158 | −0.0175681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5852 | −0.932766 | −0.466383 | − | 0.884583i | \(-0.654443\pi\) | ||||
−0.466383 | + | 0.884583i | \(0.654443\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.22699 | −0.161552 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.19325 | 0.309276 | 0.154638 | − | 0.987971i | \(-0.450579\pi\) | ||||
0.154638 | + | 0.987971i | \(0.450579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.51414 | −0.175052 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.7266 | −1.37436 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.0565 | −1.58509 | −0.792547 | − | 0.609811i | \(-0.791245\pi\) | ||||
−0.792547 | + | 0.609811i | \(0.791245\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6044 | −0.720383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.06562 | −0.0524357 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.9344 | 0.536748 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.8970 | −0.631570 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.78860 | −0.478205 | −0.239102 | − | 0.970994i | \(-0.576853\pi\) | ||||
−0.239102 | + | 0.970994i | \(0.576853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2745 | −0.695695 | −0.347847 | − | 0.937551i | \(-0.613087\pi\) | ||||
−0.347847 | + | 0.937551i | \(0.613087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.93438 | 0.337161 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.32088 | −0.0640723 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.971726 | 0.0470251 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6700 | −0.853118 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.8350 | 1.09992 | 0.549962 | − | 0.835190i | \(-0.314642\pi\) | ||||
0.549962 | + | 0.835190i | \(0.314642\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8259 | 0.664433 | 0.332216 | − | 0.943203i | \(-0.392204\pi\) | ||||
0.332216 | + | 0.943203i | \(0.392204\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.86330 | 0.472909 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.94345 | −0.0929679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.8506 | −1.90197 | −0.950983 | − | 0.309243i | \(-0.899924\pi\) | ||||
−0.950983 | + | 0.309243i | \(0.899924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.76394 | −0.322092 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.1504 | 0.482262 | 0.241131 | − | 0.970493i | \(-0.422482\pi\) | ||||
0.241131 | + | 0.970493i | \(0.422482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.03374 | −0.238622 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.3118 | 0.771522 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.75020 | −0.176983 | −0.0884914 | − | 0.996077i | \(-0.528205\pi\) | ||||
−0.0884914 | + | 0.996077i | \(0.528205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.3401 | 1.66410 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.3774 | −0.910431 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.70739 | 0.0800436 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.70193 | −0.0796127 | −0.0398064 | − | 0.999207i | \(-0.512674\pi\) | ||||
−0.0398064 | + | 0.999207i | \(0.512674\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.32088 | −0.0616536 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.40931 | 0.345086 | 0.172543 | − | 0.985002i | \(-0.444802\pi\) | ||||
0.172543 | + | 0.985002i | \(0.444802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3865 | 1.41218 | 0.706090 | − | 0.708122i | \(-0.250457\pi\) | ||||
0.706090 | + | 0.708122i | \(0.250457\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1040 | −0.791480 | −0.395740 | − | 0.918363i | \(-0.629512\pi\) | ||||
−0.395740 | + | 0.918363i | \(0.629512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.43478 | 0.204779 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.80128 | −0.175154 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.17044 | −0.237737 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.64177 | 0.304745 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.70739 | −0.0781760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2890 | −0.972719 | −0.486360 | − | 0.873759i | \(-0.661676\pi\) | ||||
−0.486360 | + | 0.873759i | \(0.661676\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.3774 | 0.883535 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.142169 | 0.00646890 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4431 | −0.474195 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.4996 | −0.928926 | −0.464463 | − | 0.885593i | \(-0.653753\pi\) | ||||
−0.464463 | + | 0.885593i | \(0.653753\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.5424 | −0.567187 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.0667 | 1.40202 | 0.701010 | − | 0.713152i | \(-0.252733\pi\) | ||||
0.701010 | + | 0.713152i | \(0.252733\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0283 | 0.586764 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.02827 | 0.226004 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.54787 | 0.293712 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3401 | −0.686717 | −0.343358 | − | 0.939205i | \(-0.611565\pi\) | ||||
−0.343358 | + | 0.939205i | \(0.611565\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.2553 | −0.994292 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9344 | 0.665891 | 0.332946 | − | 0.942946i | \(-0.391957\pi\) | ||||
0.332946 | + | 0.942946i | \(0.391957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6135 | 0.516794 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.650842 | −0.0289049 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.22153 | −0.0541432 | −0.0270716 | − | 0.999633i | \(-0.508618\pi\) | ||||
−0.0270716 | + | 0.999633i | \(0.508618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.09389 | −0.269578 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.64177 | 0.293241 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.76940 | −0.166100 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.8680 | −1.53349 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.9717 | −0.481605 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.57429 | 0.200403 | 0.100202 | − | 0.994967i | \(-0.468051\pi\) | ||||
0.100202 | + | 0.994967i | \(0.468051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.7831 | 1.30233 | 0.651163 | − | 0.758938i | \(-0.274281\pi\) | ||||
0.651163 | + | 0.758938i | \(0.274281\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.485863 | −0.0212048 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.32088 | 0.0575386 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9144 | −0.996277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.19325 | 0.0951790 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.6983 | −1.06980 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.73566 | −0.291208 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.9253 | 0.687228 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.0109 | 1.46495 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.04748 | −0.131021 | −0.0655106 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655106 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.05655 | −0.345740 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.90611 | 0.167319 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.82595 | −0.420127 | −0.210064 | − | 0.977688i | \(-0.567367\pi\) | ||||
−0.210064 | + | 0.977688i | \(0.567367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −65.5097 | −2.79081 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.169643 | −0.00721396 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.51414 | −0.234062 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.7922 | −1.64368 | −0.821839 | − | 0.569719i | \(-0.807052\pi\) | ||||
−0.821839 | + | 0.569719i | \(0.807052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.61350 | 0.152835 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.64177 | 0.280416 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.73566 | −0.115294 | −0.0576472 | − | 0.998337i | \(-0.518360\pi\) | ||||
−0.0576472 | + | 0.998337i | \(0.518360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.0848 | 0.634623 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.485863 | −0.0204043 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.39197 | 0.184121 | 0.0920605 | − | 0.995753i | \(-0.470655\pi\) | ||||
0.0920605 | + | 0.995753i | \(0.470655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.67004 | −0.404679 | −0.202339 | − | 0.979315i | \(-0.564854\pi\) | ||||
−0.202339 | + | 0.979315i | \(0.564854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.19325 | −0.258727 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.292611 | −0.0122027 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.4148 | 1.30781 | 0.653907 | − | 0.756575i | \(-0.273129\pi\) | ||||
0.653907 | + | 0.756575i | \(0.273129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.25526 | −0.0937256 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.31261 | 0.220404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.58522 | 0.355564 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.51414 | −0.145292 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.2161 | 1.12333 | 0.561664 | − | 0.827366i | \(-0.310162\pi\) | ||||
0.561664 | + | 0.827366i | \(0.310162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.64177 | −0.273669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.32088 | 0.383410 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.5561 | 1.33692 | 0.668460 | − | 0.743748i | \(-0.266954\pi\) | ||||
0.668460 | + | 0.743748i | \(0.266954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.641769 | −0.0263100 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.5479 | −0.677259 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.8067 | −1.13615 | −0.568076 | − | 0.822976i | \(-0.692312\pi\) | ||||
−0.568076 | + | 0.822976i | \(0.692312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6519 | 0.720036 | 0.360018 | − | 0.932945i | \(-0.382771\pi\) | ||||
0.360018 | + | 0.932945i | \(0.382771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.12763 | −0.371706 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.2835 | −0.580708 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.9673 | −1.82517 | −0.912584 | − | 0.408890i | \(-0.865916\pi\) | ||||
−0.912584 | + | 0.408890i | \(0.865916\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.79221 | 0.194190 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.3684 | 0.985838 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.7694 | 1.36393 | 0.681967 | − | 0.731383i | \(-0.261125\pi\) | ||||
0.681967 | + | 0.731383i | \(0.261125\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.02827 | 0.283407 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.1131 | −1.05127 | −0.525637 | − | 0.850709i | \(-0.676173\pi\) | ||||
−0.525637 | + | 0.850709i | \(0.676173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8597 | 0.838422 | 0.419211 | − | 0.907889i | \(-0.362307\pi\) | ||||
0.419211 | + | 0.907889i | \(0.362307\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.292611 | −0.0117421 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.44571 | −0.0979852 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −33.3966 | −1.33373 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.28354 | −0.290414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5105 | 0.816511 | 0.408256 | − | 0.912868i | \(-0.366137\pi\) | ||||
0.408256 | + | 0.912868i | \(0.366137\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.0101 | −0.994063 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.25526 | −0.248233 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.7694 | −0.941778 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.4768 | −0.533134 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.9945 | 0.947727 | 0.473864 | − | 0.880598i | \(-0.342859\pi\) | ||||
0.473864 | + | 0.880598i | \(0.342859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6700 | 0.539094 | 0.269547 | − | 0.962987i | \(-0.413126\pi\) | ||||
0.269547 | + | 0.962987i | \(0.413126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.02827 | −0.0404882 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.1523 | 0.438442 | 0.219221 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219221 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.0283 | −0.432898 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.485863 | 0.0190425 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.1896 | −1.53361 | −0.766805 | − | 0.641881i | \(-0.778154\pi\) | ||||
−0.766805 | + | 0.641881i | \(0.778154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.1186 | −0.864244 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.5424 | 0.489326 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.6464 | 1.23277 | 0.616385 | − | 0.787445i | \(-0.288597\pi\) | ||||
0.616385 | + | 0.787445i | \(0.288597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.59535 | −0.139843 | −0.0699215 | − | 0.997553i | \(-0.522275\pi\) | ||||
−0.0699215 | + | 0.997553i | \(0.522275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.64177 | −0.180271 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.22699 | 0.125137 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.88611 | 0.111750 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.2835 | −0.745545 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0565 | 0.388229 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.24073 | −0.279110 | −0.139555 | − | 0.990214i | \(-0.544567\pi\) | ||||
−0.139555 | + | 0.990214i | \(0.544567\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.5188 | 1.48040 | 0.740199 | − | 0.672388i | \(-0.234731\pi\) | ||||
0.740199 | + | 0.672388i | \(0.234731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.07389 | −0.194718 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.4340 | −0.897992 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.0192 | −1.53129 | −0.765646 | − | 0.643262i | \(-0.777581\pi\) | ||||
−0.765646 | + | 0.643262i | \(0.777581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6044 | 0.558006 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.0283 | −0.954888 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.8013 | 0.448942 | 0.224471 | − | 0.974481i | \(-0.427935\pi\) | ||||
0.224471 | + | 0.974481i | \(0.427935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.44305 | 0.0928039 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.8970 | 0.489212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.28354 | 0.351639 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.7175 | 0.707962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.17044 | 0.195285 | 0.0976425 | − | 0.995222i | \(-0.468870\pi\) | ||||
0.0976425 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.6236 | 1.38129 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.93438 | −0.261164 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.64257 | 0.212211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.7722 | 1.79412 | 0.897062 | − | 0.441906i | \(-0.145697\pi\) | ||||
0.897062 | + | 0.441906i | \(0.145697\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.349158 | 0.0130945 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.292611 | 0.0109584 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.6700 | 0.660822 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.86876 | 0.144481 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.0848 | −0.860919 | −0.430459 | − | 0.902610i | \(-0.641648\pi\) | ||||
−0.430459 | + | 0.902610i | \(0.641648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.83141 | −0.0682054 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.61350 | −0.0600065 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.86330 | −0.366314 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2125 | 0.823814 | 0.411907 | − | 0.911226i | \(-0.364863\pi\) | ||||
0.411907 | + | 0.911226i | \(0.364863\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.35823 | −0.0502360 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.9072 | −1.62175 | −0.810874 | − | 0.585221i | \(-0.801008\pi\) | ||||
−0.810874 | + | 0.585221i | \(0.801008\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.76394 | 0.249492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.8962 | 1.69061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.86690 | −0.252603 | −0.126302 | − | 0.991992i | \(-0.540311\pi\) | ||||
−0.126302 | + | 0.991992i | \(0.540311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.3401 | 0.857419 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.2726 | −1.07391 | −0.536954 | − | 0.843612i | \(-0.680425\pi\) | ||||
−0.536954 | + | 0.843612i | \(0.680425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3118 | −0.597619 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.9344 | −0.400068 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.27261 | −0.119579 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.67004 | −0.352865 | −0.176432 | − | 0.984313i | \(-0.556456\pi\) | ||||
−0.176432 | + | 0.984313i | \(0.556456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.4713 | 0.928227 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.3774 | 0.705217 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.4104 | −1.79585 | −0.897925 | − | 0.440148i | \(-0.854926\pi\) | ||||
−0.897925 | + | 0.440148i | \(0.854926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.47133 | 0.0534058 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.2599 | 1.71317 | 0.856586 | − | 0.516005i | \(-0.172581\pi\) | ||||
0.856586 | + | 0.516005i | \(0.172581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.89783 | 0.0687062 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.32088 | 0.0477567 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.70739 | 0.278298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.49053 | 0.342237 | 0.171119 | − | 0.985250i | \(-0.445262\pi\) | ||||
0.171119 | + | 0.985250i | \(0.445262\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0192 | 0.648946 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.7567 | 1.50188 | 0.750942 | − | 0.660368i | \(-0.229600\pi\) | ||||
0.750942 | + | 0.660368i | \(0.229600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.67912 | −0.0961127 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −46.6802 | −1.67249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.7650 | 2.42482 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.86330 | −0.352485 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.80128 | 0.135674 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.0950 | 1.42923 | 0.714615 | − | 0.699518i | \(-0.246602\pi\) | ||||
0.714615 | + | 0.699518i | \(0.246602\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.15951 | −0.0412798 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.32916 | 0.260595 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.02827 | −0.249581 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.70739 | 0.0605549 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.1150 | −1.10215 | −0.551074 | − | 0.834456i | \(-0.685782\pi\) | ||||
−0.551074 | + | 0.834456i | \(0.685782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.15951 | −0.324040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.03374 | 0.177858 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −63.0667 | −2.22557 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.142169 | −0.00501079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.80675 | −0.274811 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.6291 | 1.63939 | 0.819696 | − | 0.572799i | \(-0.194143\pi\) | ||||
0.819696 | + | 0.572799i | \(0.194143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0283 | 1.65139 | 0.825693 | − | 0.564120i | \(-0.190784\pi\) | ||||
0.825693 | + | 0.564120i | \(0.190784\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.7831 | −0.623682 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5424 | 0.439341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.82956 | 0.238936 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.70739 | −0.0596610 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.3912 | 1.23516 | 0.617580 | − | 0.786508i | \(-0.288113\pi\) | ||||
0.617580 | + | 0.786508i | \(0.288113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.2161 | 0.600114 | 0.300057 | − | 0.953921i | \(-0.402994\pi\) | ||||
0.300057 | + | 0.953921i | \(0.402994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.02827 | −0.175062 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.3310 | −0.567885 | −0.283942 | − | 0.958841i | \(-0.591642\pi\) | ||||
−0.283942 | + | 0.958841i | \(0.591642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.0667 | −1.00953 | −0.504764 | − | 0.863258i | \(-0.668420\pi\) | ||||
−0.504764 | + | 0.863258i | \(0.668420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.9390 | 0.899815 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.93438 | 0.309558 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.2553 | 0.770175 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.6646 | −0.955087 | −0.477544 | − | 0.878608i | \(-0.658473\pi\) | ||||
−0.477544 | + | 0.878608i | \(0.658473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 68.2846 | 2.35464 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.0283 | −0.448718 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.650842 | 0.0223896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.93984 | −0.238456 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.9006 | −0.545709 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.61350 | −0.0553099 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.5105 | 1.11314 | 0.556570 | − | 0.830801i | \(-0.312117\pi\) | ||||
0.556570 | + | 0.830801i | \(0.312117\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.64177 | −0.227144 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.9144 | −1.56841 | −0.784203 | − | 0.620505i | \(-0.786928\pi\) | ||||
−0.784203 | + | 0.620505i | \(0.786928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.6026 | 0.668831 | 0.334415 | − | 0.942426i | \(-0.391461\pi\) | ||||
0.334415 | + | 0.942426i | \(0.391461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.41478 | 0.116375 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.1696 | −1.57163 | −0.785816 | − | 0.618460i | \(-0.787757\pi\) | ||||
−0.785816 | + | 0.618460i | \(0.787757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9717 | 0.373050 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.2553 | −0.518096 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.75566 | −0.0595568 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.0757 | −1.08685 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.4431 | 0.353444 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.485863 | 0.0164252 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3017 | 0.381631 | 0.190815 | − | 0.981626i | \(-0.438887\pi\) | ||||
0.190815 | + | 0.981626i | \(0.438887\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.4340 | −0.992784 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.60803 | −0.323703 | −0.161851 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161851 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.5279 | 1.12830 | 0.564151 | − | 0.825671i | \(-0.309203\pi\) | ||||
0.564151 | + | 0.825671i | \(0.309203\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.19325 | −0.0737254 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.76394 | 0.327841 | 0.163920 | − | 0.986474i | \(-0.447586\pi\) | ||||
0.163920 | + | 0.986474i | \(0.447586\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.03920 | −0.101932 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.02827 | −0.168454 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.0565 | 1.54122 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.9253 | −0.532324 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.02827 | −0.0343331 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.86330 | 0.328959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.25526 | 0.0751337 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.499600 | −0.0166257 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.05655 | 0.267809 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.18418 | 0.304956 | 0.152478 | − | 0.988307i | \(-0.451275\pi\) | ||||
0.152478 | + | 0.988307i | \(0.451275\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.6135 | −0.385195 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2553 | 0.406035 | 0.203018 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203018 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.9811 | 1.81961 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.7466 | −0.354884 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.5663 | 1.56907 | 0.784533 | − | 0.620087i | \(-0.212903\pi\) | ||||
0.784533 | + | 0.620087i | \(0.212903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.96812 | −0.328461 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47.3593 | −1.55885 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.51414 | 0.181304 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.76940 | 0.123803 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.5333 | 0.772104 | 0.386052 | − | 0.922477i | \(-0.373839\pi\) | ||||
0.386052 | + | 0.922477i | \(0.373839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.9245 | −1.47234 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.9945 | −0.523638 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.64177 | −0.217209 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.7258 | −1.85315 | −0.926575 | − | 0.376109i | \(-0.877262\pi\) | ||||
−0.926575 | + | 0.376109i | \(0.877262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.8542 | −0.745819 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.5333 | −1.09316 | −0.546578 | − | 0.837408i | \(-0.684070\pi\) | ||||
−0.546578 | + | 0.837408i | \(0.684070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.05655 | 0.0669704 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.485863 | 0.0158051 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.0685 | 1.69200 | 0.846000 | − | 0.533183i | \(-0.179004\pi\) | ||||
0.846000 | + | 0.533183i | \(0.179004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.0757 | 1.43076 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.6044 | 0.473581 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.1896 | −0.362468 | −0.181234 | − | 0.983440i | \(-0.558009\pi\) | ||||
−0.181234 | + | 0.983440i | \(0.558009\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.19325 | 0.200409 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.5953 | 1.60319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.09575 | 0.229134 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.73566 | 0.217054 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.25526 | 0.0725995 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.8296 | −1.18436 | −0.592179 | − | 0.805806i | \(-0.701732\pi\) | ||||
−0.592179 | + | 0.805806i | \(0.701732\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.77301 | −0.281830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7494 | −0.601697 | −0.300848 | − | 0.953672i | \(-0.597270\pi\) | ||||
−0.300848 | + | 0.953672i | \(0.597270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.26619 | 0.200885 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.51414 | 0.112542 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.2262 | −1.60688 | −0.803439 | − | 0.595387i | \(-0.796999\pi\) | ||||
−0.803439 | + | 0.595387i | \(0.796999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.3110 | −0.808943 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.90611 | −0.124712 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.5279 | −0.495262 | −0.247631 | − | 0.968854i | \(-0.579652\pi\) | ||||
−0.247631 | + | 0.968854i | \(0.579652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.32088 | −0.296988 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.36916 | −0.107242 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.300884 | −0.00956755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.1022 | 0.638566 | 0.319283 | − | 0.947659i | \(-0.396558\pi\) | ||||
0.319283 | + | 0.947659i | \(0.396558\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.16137 | 0.258993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.5479 | 0.524603 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.8186 | −0.659333 | −0.329666 | − | 0.944098i | \(-0.606936\pi\) | ||||
−0.329666 | + | 0.944098i | \(0.606936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.51414 | 0.174460 |
(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 | 7440.2.a.bs.1.3 | 3 | ||
4.3 | odd | 2 | 465.2.a.e.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 1395.2.a.j.1.1 | 3 | |||
20.3 | even | 4 | 2325.2.c.k.1024.1 | 6 | |||
20.7 | even | 4 | 2325.2.c.k.1024.6 | 6 | |||
20.19 | odd | 2 | 2325.2.a.r.1.1 | 3 | |||
60.59 | even | 2 | 6975.2.a.bf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.a.e.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
1395.2.a.j.1.1 | 3 | 12.11 | even | 2 | |||
2325.2.a.r.1.1 | 3 | 20.19 | odd | 2 | |||
2325.2.c.k.1024.1 | 6 | 20.3 | even | 4 | |||
2325.2.c.k.1024.6 | 6 | 20.7 | even | 4 | |||
6975.2.a.bf.1.3 | 3 | 60.59 | even | 2 | |||
7440.2.a.bs.1.3 | 3 | 1.1 | even | 1 | trivial |