Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(239,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.g (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 437.5 | ||
Root | \(0.500000 - 2.00333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.437 |
Dual form | 1014.2.g.d.239.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.53819 | + | 0.796225i | −0.888074 | + | 0.459701i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.428520 | + | 0.428520i | −0.191640 | + | 0.191640i | −0.796404 | − | 0.604765i | \(-0.793267\pi\) |
0.604765 | + | 0.796404i | \(0.293267\pi\) | |||||||
\(6\) | −0.524648 | + | 1.65068i | −0.214186 | + | 0.673887i | ||||
\(7\) | −0.538189 | + | 0.538189i | −0.203416 | + | 0.203416i | −0.801462 | − | 0.598046i | \(-0.795944\pi\) |
0.598046 | + | 0.801462i | \(0.295944\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.73205 | − | 2.44949i | 0.577350 | − | 0.816497i | ||||
\(10\) | 0.606018i | 0.191640i | ||||||||
\(11\) | 2.97155 | + | 2.97155i | 0.895957 | + | 0.895957i | 0.995076 | − | 0.0991187i | \(-0.0316023\pi\) |
−0.0991187 | + | 0.995076i | \(0.531602\pi\) | |||||||
\(12\) | 0.796225 | + | 1.53819i | 0.229850 | + | 0.444037i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.761114i | 0.203416i | ||||||||
\(15\) | 0.317946 | − | 1.00034i | 0.0820933 | − | 0.258287i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.24723 | −1.27264 | −0.636320 | − | 0.771425i | \(-0.719544\pi\) | ||||
−0.636320 | + | 0.771425i | \(0.719544\pi\) | |||||||
\(18\) | −0.507306 | − | 2.95680i | −0.119573 | − | 0.696923i | ||||
\(19\) | −2.41216 | − | 2.41216i | −0.553387 | − | 0.553387i | 0.374030 | − | 0.927417i | \(-0.377976\pi\) |
−0.927417 | + | 0.374030i | \(0.877976\pi\) | |||||||
\(20\) | 0.428520 | + | 0.428520i | 0.0958199 | + | 0.0958199i | ||||
\(21\) | 0.399317 | − | 1.25636i | 0.0871381 | − | 0.274159i | ||||
\(22\) | 4.20241 | 0.895957 | ||||||||
\(23\) | 1.86661 | 0.389216 | 0.194608 | − | 0.980881i | \(-0.437657\pi\) | ||||
0.194608 | + | 0.980881i | \(0.437657\pi\) | |||||||
\(24\) | 1.65068 | + | 0.524648i | 0.336944 | + | 0.107093i | ||||
\(25\) | 4.63274i | 0.926548i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.713876 | + | 5.14688i | −0.137386 | + | 0.990518i | ||||
\(28\) | 0.538189 | + | 0.538189i | 0.101708 | + | 0.101708i | ||||
\(29\) | 8.70629i | 1.61672i | 0.588690 | + | 0.808359i | \(0.299644\pi\) | ||||
−0.588690 | + | 0.808359i | \(0.700356\pi\) | |||||||
\(30\) | −0.482527 | − | 0.932171i | −0.0880970 | − | 0.170190i | ||||
\(31\) | 2.68240 | + | 2.68240i | 0.481773 | + | 0.481773i | 0.905697 | − | 0.423925i | \(-0.139348\pi\) |
−0.423925 | + | 0.905697i | \(0.639348\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −6.93684 | − | 2.20478i | −1.20755 | − | 0.383804i | ||||
\(34\) | −3.71035 | + | 3.71035i | −0.636320 | + | 0.636320i | ||||
\(35\) | − | 0.461249i | − | 0.0779653i | ||||||
\(36\) | −2.44949 | − | 1.73205i | −0.408248 | − | 0.288675i | ||||
\(37\) | −4.15628 | + | 4.15628i | −0.683288 | + | 0.683288i | −0.960740 | − | 0.277452i | \(-0.910510\pi\) |
0.277452 | + | 0.960740i | \(0.410510\pi\) | |||||||
\(38\) | −3.41130 | −0.553387 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.606018 | 0.0958199 | ||||||||
\(41\) | 6.27128 | − | 6.27128i | 0.979409 | − | 0.979409i | −0.0203836 | − | 0.999792i | \(-0.506489\pi\) |
0.999792 | + | 0.0203836i | \(0.00648874\pi\) | |||||||
\(42\) | −0.606018 | − | 1.17074i | −0.0935107 | − | 0.180649i | ||||
\(43\) | 1.95035i | 0.297425i | 0.988880 | + | 0.148712i | \(0.0475129\pi\) | ||||
−0.988880 | + | 0.148712i | \(0.952487\pi\) | |||||||
\(44\) | 2.97155 | − | 2.97155i | 0.447978 | − | 0.447978i | ||||
\(45\) | 0.307437 | + | 1.79187i | 0.0458300 | + | 0.267117i | ||||
\(46\) | 1.31989 | − | 1.31989i | 0.194608 | − | 0.194608i | ||||
\(47\) | 5.73474 | + | 5.73474i | 0.836498 | + | 0.836498i | 0.988396 | − | 0.151898i | \(-0.0485386\pi\) |
−0.151898 | + | 0.988396i | \(0.548539\pi\) | |||||||
\(48\) | 1.53819 | − | 0.796225i | 0.222018 | − | 0.114925i | ||||
\(49\) | 6.42071i | 0.917244i | ||||||||
\(50\) | 3.27584 | + | 3.27584i | 0.463274 | + | 0.463274i | ||||
\(51\) | 8.07123 | − | 4.17798i | 1.13020 | − | 0.585034i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.01501i | 1.23831i | 0.785270 | + | 0.619153i | \(0.212524\pi\) | ||||
−0.785270 | + | 0.619153i | \(0.787476\pi\) | |||||||
\(54\) | 3.13461 | + | 4.14418i | 0.426566 | + | 0.563952i | ||||
\(55\) | −2.54674 | −0.343402 | ||||||||
\(56\) | 0.761114 | 0.101708 | ||||||||
\(57\) | 5.63097 | + | 1.78973i | 0.745841 | + | 0.237056i | ||||
\(58\) | 6.15628 | + | 6.15628i | 0.808359 | + | 0.808359i | ||||
\(59\) | 6.10925 | + | 6.10925i | 0.795357 | + | 0.795357i | 0.982359 | − | 0.187002i | \(-0.0598772\pi\) |
−0.187002 | + | 0.982359i | \(0.559877\pi\) | |||||||
\(60\) | −1.00034 | − | 0.317946i | −0.129144 | − | 0.0410467i | ||||
\(61\) | −8.13061 | −1.04102 | −0.520509 | − | 0.853856i | \(-0.674258\pi\) | ||||
−0.520509 | + | 0.853856i | \(0.674258\pi\) | |||||||
\(62\) | 3.79348 | 0.481773 | ||||||||
\(63\) | 0.386118 | + | 2.25046i | 0.0486463 | + | 0.283531i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.46410 | + | 3.34607i | −0.795676 | + | 0.411872i | ||||
\(67\) | −0.0740874 | − | 0.0740874i | −0.00905121 | − | 0.00905121i | 0.702567 | − | 0.711618i | \(-0.252037\pi\) |
−0.711618 | + | 0.702567i | \(0.752037\pi\) | |||||||
\(68\) | 5.24723i | 0.636320i | ||||||||
\(69\) | −2.87120 | + | 1.48624i | −0.345652 | + | 0.178923i | ||||
\(70\) | −0.326152 | − | 0.326152i | −0.0389827 | − | 0.0389827i | ||||
\(71\) | 7.37536 | − | 7.37536i | 0.875294 | − | 0.875294i | −0.117749 | − | 0.993043i | \(-0.537568\pi\) |
0.993043 | + | 0.117749i | \(0.0375679\pi\) | |||||||
\(72\) | −2.95680 | + | 0.507306i | −0.348462 | + | 0.0597866i | ||||
\(73\) | −5.57806 | + | 5.57806i | −0.652863 | + | 0.652863i | −0.953681 | − | 0.300819i | \(-0.902740\pi\) |
0.300819 | + | 0.953681i | \(0.402740\pi\) | |||||||
\(74\) | 5.87787i | 0.683288i | ||||||||
\(75\) | −3.68871 | − | 7.12603i | −0.425935 | − | 0.822843i | ||||
\(76\) | −2.41216 | + | 2.41216i | −0.276693 | + | 0.276693i | ||||
\(77\) | −3.19851 | −0.364505 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5805 | −1.52793 | −0.763963 | − | 0.645260i | \(-0.776749\pi\) | ||||
−0.763963 | + | 0.645260i | \(0.776749\pi\) | |||||||
\(80\) | 0.428520 | − | 0.428520i | 0.0479100 | − | 0.0479100i | ||||
\(81\) | −3.00000 | − | 8.48528i | −0.333333 | − | 0.942809i | ||||
\(82\) | − | 8.86892i | − | 0.979409i | ||||||
\(83\) | 0.996926 | − | 0.996926i | 0.109427 | − | 0.109427i | −0.650273 | − | 0.759700i | \(-0.725346\pi\) |
0.759700 | + | 0.650273i | \(0.225346\pi\) | |||||||
\(84\) | −1.25636 | − | 0.399317i | −0.137080 | − | 0.0435690i | ||||
\(85\) | 2.24854 | − | 2.24854i | 0.243889 | − | 0.243889i | ||||
\(86\) | 1.37910 | + | 1.37910i | 0.148712 | + | 0.148712i | ||||
\(87\) | −6.93217 | − | 13.3919i | −0.743207 | − | 1.43577i | ||||
\(88\) | − | 4.20241i | − | 0.447978i | ||||||
\(89\) | 4.62980 | + | 4.62980i | 0.490758 | + | 0.490758i | 0.908545 | − | 0.417787i | \(-0.137194\pi\) |
−0.417787 | + | 0.908545i | \(0.637194\pi\) | |||||||
\(90\) | 1.48444 | + | 1.04965i | 0.156473 | + | 0.110643i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1.86661i | − | 0.194608i | ||||||
\(93\) | −6.26182 | − | 1.99024i | −0.649321 | − | 0.206378i | ||||
\(94\) | 8.11015 | 0.836498 | ||||||||
\(95\) | 2.06731 | 0.212102 | ||||||||
\(96\) | 0.524648 | − | 1.65068i | 0.0535466 | − | 0.168472i | ||||
\(97\) | −11.1369 | − | 11.1369i | −1.13078 | − | 1.13078i | −0.990048 | − | 0.140730i | \(-0.955055\pi\) |
−0.140730 | − | 0.990048i | \(-0.544945\pi\) | |||||||
\(98\) | 4.54012 | + | 4.54012i | 0.458622 | + | 0.458622i | ||||
\(99\) | 12.4257 | − | 2.13191i | 1.24883 | − | 0.214265i | ||||
\(100\) | 4.63274 | 0.463274 | ||||||||
\(101\) | −3.27260 | −0.325636 | −0.162818 | − | 0.986656i | \(-0.552058\pi\) | ||||
−0.162818 | + | 0.986656i | \(0.552058\pi\) | |||||||
\(102\) | 2.75295 | − | 8.66150i | 0.272582 | − | 0.857616i | ||||
\(103\) | − | 4.79880i | − | 0.472840i | −0.971651 | − | 0.236420i | \(-0.924026\pi\) | ||
0.971651 | − | 0.236420i | \(-0.0759741\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.367258 | + | 0.709488i | 0.0358407 | + | 0.0692390i | ||||
\(106\) | 6.37457 | + | 6.37457i | 0.619153 | + | 0.619153i | ||||
\(107\) | 3.12505i | 0.302110i | 0.988525 | + | 0.151055i | \(0.0482671\pi\) | ||||
−0.988525 | + | 0.151055i | \(0.951733\pi\) | |||||||
\(108\) | 5.14688 | + | 0.713876i | 0.495259 | + | 0.0686928i | ||||
\(109\) | 0.913996 | + | 0.913996i | 0.0875449 | + | 0.0875449i | 0.749523 | − | 0.661978i | \(-0.230283\pi\) |
−0.661978 | + | 0.749523i | \(0.730283\pi\) | |||||||
\(110\) | −1.80082 | + | 1.80082i | −0.171701 | + | 0.171701i | ||||
\(111\) | 3.08381 | − | 9.70248i | 0.292702 | − | 0.920918i | ||||
\(112\) | 0.538189 | − | 0.538189i | 0.0508541 | − | 0.0508541i | ||||
\(113\) | 6.97128i | 0.655802i | 0.944712 | + | 0.327901i | \(0.106341\pi\) | ||||
−0.944712 | + | 0.327901i | \(0.893659\pi\) | |||||||
\(114\) | 5.24723 | − | 2.71617i | 0.491448 | − | 0.254392i | ||||
\(115\) | −0.799880 | + | 0.799880i | −0.0745892 | + | 0.0745892i | ||||
\(116\) | 8.70629 | 0.808359 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.63979 | 0.795357 | ||||||||
\(119\) | 2.82400 | − | 2.82400i | 0.258876 | − | 0.258876i | ||||
\(120\) | −0.932171 | + | 0.482527i | −0.0850952 | + | 0.0440485i | ||||
\(121\) | 6.66025i | 0.605478i | ||||||||
\(122\) | −5.74921 | + | 5.74921i | −0.520509 | + | 0.520509i | ||||
\(123\) | −4.65306 | + | 14.6398i | −0.419552 | + | 1.32002i | ||||
\(124\) | 2.68240 | − | 2.68240i | 0.240886 | − | 0.240886i | ||||
\(125\) | −4.12782 | − | 4.12782i | −0.369203 | − | 0.369203i | ||||
\(126\) | 1.86434 | + | 1.31829i | 0.166089 | + | 0.117442i | ||||
\(127\) | 2.23497i | 0.198321i | 0.995071 | + | 0.0991607i | \(0.0316158\pi\) | ||||
−0.995071 | + | 0.0991607i | \(0.968384\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −1.55291 | − | 3.00000i | −0.136726 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 22.0856i | − | 1.92963i | −0.262938 | − | 0.964813i | \(-0.584692\pi\) | ||
0.262938 | − | 0.964813i | \(-0.415308\pi\) | |||||||
\(132\) | −2.20478 | + | 6.93684i | −0.191902 | + | 0.603774i | ||||
\(133\) | 2.59639 | 0.225136 | ||||||||
\(134\) | −0.104775 | −0.00905121 | ||||||||
\(135\) | −1.89963 | − | 2.51145i | −0.163494 | − | 0.216151i | ||||
\(136\) | 3.71035 | + | 3.71035i | 0.318160 | + | 0.318160i | ||||
\(137\) | 7.05984 | + | 7.05984i | 0.603162 | + | 0.603162i | 0.941150 | − | 0.337988i | \(-0.109746\pi\) |
−0.337988 | + | 0.941150i | \(0.609746\pi\) | |||||||
\(138\) | −0.979314 | + | 3.08118i | −0.0833647 | + | 0.262287i | ||||
\(139\) | −3.76503 | −0.319346 | −0.159673 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159673 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(140\) | −0.461249 | −0.0389827 | ||||||||
\(141\) | −13.3873 | − | 4.25497i | −1.12741 | − | 0.358333i | ||||
\(142\) | − | 10.4303i | − | 0.875294i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.73205 | + | 2.44949i | −0.144338 | + | 0.204124i | ||||
\(145\) | −3.73082 | − | 3.73082i | −0.309828 | − | 0.309828i | ||||
\(146\) | 7.88857i | 0.652863i | ||||||||
\(147\) | −5.11233 | − | 9.87626i | −0.421658 | − | 0.814580i | ||||
\(148\) | 4.15628 | + | 4.15628i | 0.341644 | + | 0.341644i | ||||
\(149\) | 6.17093 | − | 6.17093i | 0.505542 | − | 0.505542i | −0.407613 | − | 0.913155i | \(-0.633639\pi\) |
0.913155 | + | 0.407613i | \(0.133639\pi\) | |||||||
\(150\) | −7.64717 | − | 2.43056i | −0.624389 | − | 0.198454i | ||||
\(151\) | 17.3671 | − | 17.3671i | 1.41331 | − | 1.41331i | 0.681429 | − | 0.731885i | \(-0.261359\pi\) |
0.731885 | − | 0.681429i | \(-0.238641\pi\) | |||||||
\(152\) | 3.41130i | 0.276693i | ||||||||
\(153\) | −9.08847 | + | 12.8530i | −0.734759 | + | 1.03911i | ||||
\(154\) | −2.26169 | + | 2.26169i | −0.182252 | + | 0.182252i | ||||
\(155\) | −2.29892 | −0.184654 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0713 | 0.883589 | 0.441794 | − | 0.897116i | \(-0.354342\pi\) | ||||
0.441794 | + | 0.897116i | \(0.354342\pi\) | |||||||
\(158\) | −9.60287 | + | 9.60287i | −0.763963 | + | 0.763963i | ||||
\(159\) | −7.17798 | − | 13.8668i | −0.569251 | − | 1.09971i | ||||
\(160\) | − | 0.606018i | − | 0.0479100i | ||||||
\(161\) | −1.00459 | + | 1.00459i | −0.0791728 | + | 0.0791728i | ||||
\(162\) | −8.12132 | − | 3.87868i | −0.638071 | − | 0.304738i | ||||
\(163\) | −3.71617 | + | 3.71617i | −0.291073 | + | 0.291073i | −0.837504 | − | 0.546431i | \(-0.815986\pi\) |
0.546431 | + | 0.837504i | \(0.315986\pi\) | |||||||
\(164\) | −6.27128 | − | 6.27128i | −0.489704 | − | 0.489704i | ||||
\(165\) | 3.91736 | − | 2.02778i | 0.304966 | − | 0.157862i | ||||
\(166\) | − | 1.40987i | − | 0.109427i | ||||||
\(167\) | −11.1219 | − | 11.1219i | −0.860635 | − | 0.860635i | 0.130777 | − | 0.991412i | \(-0.458253\pi\) |
−0.991412 | + | 0.130777i | \(0.958253\pi\) | |||||||
\(168\) | −1.17074 | + | 0.606018i | −0.0903244 | + | 0.0467553i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | − | 3.17992i | − | 0.243889i | ||||||
\(171\) | −10.0865 | + | 1.73057i | −0.771336 | + | 0.132340i | ||||
\(172\) | 1.95035 | 0.148712 | ||||||||
\(173\) | 5.42372 | 0.412358 | 0.206179 | − | 0.978514i | \(-0.433897\pi\) | ||||
0.206179 | + | 0.978514i | \(0.433897\pi\) | |||||||
\(174\) | −14.3713 | − | 4.56774i | −1.08949 | − | 0.346279i | ||||
\(175\) | −2.49329 | − | 2.49329i | −0.188475 | − | 0.188475i | ||||
\(176\) | −2.97155 | − | 2.97155i | −0.223989 | − | 0.223989i | ||||
\(177\) | −14.2615 | − | 4.53284i | −1.07196 | − | 0.340709i | ||||
\(178\) | 6.54753 | 0.490758 | ||||||||
\(179\) | 10.3808 | 0.775900 | 0.387950 | − | 0.921680i | \(-0.373183\pi\) | ||||
0.387950 | + | 0.921680i | \(0.373183\pi\) | |||||||
\(180\) | 1.79187 | − | 0.307437i | 0.133558 | − | 0.0229150i | ||||
\(181\) | 11.1172i | 0.826335i | 0.910655 | + | 0.413167i | \(0.135578\pi\) | ||||
−0.910655 | + | 0.413167i | \(0.864422\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5064 | − | 6.47380i | 0.924501 | − | 0.478557i | ||||
\(184\) | −1.31989 | − | 1.31989i | −0.0973039 | − | 0.0973039i | ||||
\(185\) | − | 3.56209i | − | 0.261890i | ||||||
\(186\) | −5.83509 | + | 3.02047i | −0.427850 | + | 0.221471i | ||||
\(187\) | −15.5924 | − | 15.5924i | −1.14023 | − | 1.14023i | ||||
\(188\) | 5.73474 | − | 5.73474i | 0.418249 | − | 0.418249i | ||||
\(189\) | −2.38579 | − | 3.15419i | −0.173541 | − | 0.229434i | ||||
\(190\) | 1.46181 | − | 1.46181i | 0.106051 | − | 0.106051i | ||||
\(191\) | 5.73244i | 0.414785i | 0.978258 | + | 0.207392i | \(0.0664977\pi\) | ||||
−0.978258 | + | 0.207392i | \(0.933502\pi\) | |||||||
\(192\) | −0.796225 | − | 1.53819i | −0.0574626 | − | 0.111009i | ||||
\(193\) | 8.02170 | − | 8.02170i | 0.577414 | − | 0.577414i | −0.356776 | − | 0.934190i | \(-0.616124\pi\) |
0.934190 | + | 0.356776i | \(0.116124\pi\) | |||||||
\(194\) | −15.7499 | −1.13078 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.42071 | 0.458622 | ||||||||
\(197\) | 3.31151 | − | 3.31151i | 0.235935 | − | 0.235935i | −0.579229 | − | 0.815165i | \(-0.696646\pi\) |
0.815165 | + | 0.579229i | \(0.196646\pi\) | |||||||
\(198\) | 7.27879 | − | 10.2938i | 0.517281 | − | 0.731546i | ||||
\(199\) | 12.9027i | 0.914648i | 0.889300 | + | 0.457324i | \(0.151192\pi\) | ||||
−0.889300 | + | 0.457324i | \(0.848808\pi\) | |||||||
\(200\) | 3.27584 | − | 3.27584i | 0.231637 | − | 0.231637i | ||||
\(201\) | 0.172951 | + | 0.0549702i | 0.0121990 | + | 0.00387730i | ||||
\(202\) | −2.31408 | + | 2.31408i | −0.162818 | + | 0.162818i | ||||
\(203\) | −4.68563 | − | 4.68563i | −0.328867 | − | 0.328867i | ||||
\(204\) | −4.17798 | − | 8.07123i | −0.292517 | − | 0.565099i | ||||
\(205\) | 5.37473i | 0.375387i | ||||||||
\(206\) | −3.39327 | − | 3.39327i | −0.236420 | − | 0.236420i | ||||
\(207\) | 3.23307 | − | 4.57225i | 0.224714 | − | 0.317793i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 14.3357i | − | 0.991621i | ||||||
\(210\) | 0.761375 | + | 0.241993i | 0.0525399 | + | 0.0166991i | ||||
\(211\) | −5.27958 | −0.363461 | −0.181731 | − | 0.983348i | \(-0.558170\pi\) | ||||
−0.181731 | + | 0.983348i | \(0.558170\pi\) | |||||||
\(212\) | 9.01501 | 0.619153 | ||||||||
\(213\) | −5.47225 | + | 17.2171i | −0.374952 | + | 1.17970i | ||||
\(214\) | 2.20975 | + | 2.20975i | 0.151055 | + | 0.151055i | ||||
\(215\) | −0.835761 | − | 0.835761i | −0.0569985 | − | 0.0569985i | ||||
\(216\) | 4.14418 | − | 3.13461i | 0.281976 | − | 0.213283i | ||||
\(217\) | −2.88727 | −0.196001 | ||||||||
\(218\) | 1.29259 | 0.0875449 | ||||||||
\(219\) | 4.13872 | − | 13.0215i | 0.279669 | − | 0.879912i | ||||
\(220\) | 2.54674i | 0.171701i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.68011 | − | 9.04127i | −0.314108 | − | 0.606810i | ||||
\(223\) | −2.51039 | − | 2.51039i | −0.168108 | − | 0.168108i | 0.618039 | − | 0.786147i | \(-0.287927\pi\) |
−0.786147 | + | 0.618039i | \(0.787927\pi\) | |||||||
\(224\) | − | 0.761114i | − | 0.0508541i | ||||||
\(225\) | 11.3479 | + | 8.02414i | 0.756524 | + | 0.534943i | ||||
\(226\) | 4.92944 | + | 4.92944i | 0.327901 | + | 0.327901i | ||||
\(227\) | −3.55443 | + | 3.55443i | −0.235916 | + | 0.235916i | −0.815157 | − | 0.579241i | \(-0.803349\pi\) |
0.579241 | + | 0.815157i | \(0.303349\pi\) | |||||||
\(228\) | 1.78973 | − | 5.63097i | 0.118528 | − | 0.372920i | ||||
\(229\) | −11.3889 | + | 11.3889i | −0.752602 | + | 0.752602i | −0.974964 | − | 0.222362i | \(-0.928623\pi\) |
0.222362 | + | 0.974964i | \(0.428623\pi\) | |||||||
\(230\) | 1.13120i | 0.0745892i | ||||||||
\(231\) | 4.91992 | − | 2.54674i | 0.323707 | − | 0.167563i | ||||
\(232\) | 6.15628 | − | 6.15628i | 0.404180 | − | 0.404180i | ||||
\(233\) | −22.3807 | −1.46621 | −0.733103 | − | 0.680117i | \(-0.761929\pi\) | ||||
−0.733103 | + | 0.680117i | \(0.761929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.91490 | −0.320613 | ||||||||
\(236\) | 6.10925 | − | 6.10925i | 0.397679 | − | 0.397679i | ||||
\(237\) | 20.8894 | − | 10.8131i | 1.35691 | − | 0.702389i | ||||
\(238\) | − | 3.99374i | − | 0.258876i | ||||||
\(239\) | −6.08236 | + | 6.08236i | −0.393435 | + | 0.393435i | −0.875910 | − | 0.482475i | \(-0.839738\pi\) |
0.482475 | + | 0.875910i | \(0.339738\pi\) | |||||||
\(240\) | −0.317946 | + | 1.00034i | −0.0205233 | + | 0.0645718i | ||||
\(241\) | 4.34556 | − | 4.34556i | 0.279922 | − | 0.279922i | −0.553156 | − | 0.833078i | \(-0.686577\pi\) |
0.833078 | + | 0.553156i | \(0.186577\pi\) | |||||||
\(242\) | 4.70951 | + | 4.70951i | 0.302739 | + | 0.302739i | ||||
\(243\) | 11.3708 | + | 10.6633i | 0.729435 | + | 0.684050i | ||||
\(244\) | 8.13061i | 0.520509i | ||||||||
\(245\) | −2.75140 | − | 2.75140i | −0.175780 | − | 0.175780i | ||||
\(246\) | 7.06166 | + | 13.6421i | 0.450235 | + | 0.869787i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 3.79348i | − | 0.240886i | ||||||
\(249\) | −0.739683 | + | 2.32724i | −0.0468755 | + | 0.147483i | ||||
\(250\) | −5.83762 | −0.369203 | ||||||||
\(251\) | 12.5562 | 0.792538 | 0.396269 | − | 0.918134i | \(-0.370305\pi\) | ||||
0.396269 | + | 0.918134i | \(0.370305\pi\) | |||||||
\(252\) | 2.25046 | − | 0.386118i | 0.141766 | − | 0.0243231i | ||||
\(253\) | 5.54674 | + | 5.54674i | 0.348720 | + | 0.348720i | ||||
\(254\) | 1.58036 | + | 1.58036i | 0.0991607 | + | 0.0991607i | ||||
\(255\) | −1.66834 | + | 5.24903i | −0.104475 | + | 0.328707i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.73782 | −0.295537 | −0.147768 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147768 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(258\) | −3.21940 | − | 1.02324i | −0.200431 | − | 0.0637044i | ||||
\(259\) | − | 4.47373i | − | 0.277984i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.3260 | + | 15.0797i | 1.32004 | + | 0.933413i | ||||
\(262\) | −15.6169 | − | 15.6169i | −0.964813 | − | 0.964813i | ||||
\(263\) | − | 5.66894i | − | 0.349562i | −0.984607 | − | 0.174781i | \(-0.944078\pi\) | ||
0.984607 | − | 0.174781i | \(-0.0559218\pi\) | |||||||
\(264\) | 3.34607 | + | 6.46410i | 0.205936 | + | 0.397838i | ||||
\(265\) | −3.86311 | − | 3.86311i | −0.237309 | − | 0.237309i | ||||
\(266\) | 1.83593 | − | 1.83593i | 0.112568 | − | 0.112568i | ||||
\(267\) | −10.8079 | − | 3.43514i | −0.661431 | − | 0.210227i | ||||
\(268\) | −0.0740874 | + | 0.0740874i | −0.00452561 | + | 0.00452561i | ||||
\(269\) | 7.30591i | 0.445449i | 0.974881 | + | 0.222725i | \(0.0714951\pi\) | ||||
−0.974881 | + | 0.222725i | \(0.928505\pi\) | |||||||
\(270\) | −3.11910 | − | 0.432622i | −0.189823 | − | 0.0263285i | ||||
\(271\) | 17.3439 | − | 17.3439i | 1.05356 | − | 1.05356i | 0.0550829 | − | 0.998482i | \(-0.482458\pi\) |
0.998482 | − | 0.0550829i | \(-0.0175423\pi\) | |||||||
\(272\) | 5.24723 | 0.318160 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.98412 | 0.603162 | ||||||||
\(275\) | −13.7664 | + | 13.7664i | −0.830147 | + | 0.830147i | ||||
\(276\) | 1.48624 | + | 2.87120i | 0.0894614 | + | 0.172826i | ||||
\(277\) | − | 8.74626i | − | 0.525512i | −0.964862 | − | 0.262756i | \(-0.915369\pi\) | ||
0.964862 | − | 0.262756i | \(-0.0846314\pi\) | |||||||
\(278\) | −2.66228 | + | 2.66228i | −0.159673 | + | 0.159673i | ||||
\(279\) | 11.2165 | − | 1.92446i | 0.671517 | − | 0.115214i | ||||
\(280\) | −0.326152 | + | 0.326152i | −0.0194913 | + | 0.0194913i | ||||
\(281\) | −9.49571 | − | 9.49571i | −0.566467 | − | 0.566467i | 0.364670 | − | 0.931137i | \(-0.381182\pi\) |
−0.931137 | + | 0.364670i | \(0.881182\pi\) | |||||||
\(282\) | −12.4749 | + | 6.45750i | −0.742872 | + | 0.384539i | ||||
\(283\) | − | 31.4361i | − | 1.86868i | −0.356378 | − | 0.934342i | \(-0.615988\pi\) | ||
0.356378 | − | 0.934342i | \(-0.384012\pi\) | |||||||
\(284\) | −7.37536 | − | 7.37536i | −0.437647 | − | 0.437647i | ||||
\(285\) | −3.17992 | + | 1.64605i | −0.188362 | + | 0.0975034i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.75026i | 0.398455i | ||||||||
\(288\) | 0.507306 | + | 2.95680i | 0.0298933 | + | 0.174231i | ||||
\(289\) | 10.5334 | 0.619614 | ||||||||
\(290\) | −5.27617 | −0.309828 | ||||||||
\(291\) | 25.9981 | + | 8.26316i | 1.52403 | + | 0.484395i | ||||
\(292\) | 5.57806 | + | 5.57806i | 0.326431 | + | 0.326431i | ||||
\(293\) | 1.48128 | + | 1.48128i | 0.0865371 | + | 0.0865371i | 0.749050 | − | 0.662513i | \(-0.230510\pi\) |
−0.662513 | + | 0.749050i | \(0.730510\pi\) | |||||||
\(294\) | −10.5985 | − | 3.36861i | −0.618119 | − | 0.196461i | ||||
\(295\) | −5.23587 | −0.304844 | ||||||||
\(296\) | 5.87787 | 0.341644 | ||||||||
\(297\) | −17.4155 | + | 13.1729i | −1.01055 | + | 0.764370i | ||||
\(298\) | − | 8.72701i | − | 0.505542i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.12603 | + | 3.68871i | −0.411422 | + | 0.212968i | ||||
\(301\) | −1.04965 | − | 1.04965i | −0.0605011 | − | 0.0605011i | ||||
\(302\) | − | 24.5608i | − | 1.41331i | ||||||
\(303\) | 5.03388 | − | 2.60573i | 0.289189 | − | 0.149695i | ||||
\(304\) | 2.41216 | + | 2.41216i | 0.138347 | + | 0.138347i | ||||
\(305\) | 3.48413 | − | 3.48413i | 0.199501 | − | 0.199501i | ||||
\(306\) | 2.66195 | + | 15.5150i | 0.152174 | + | 0.886933i | ||||
\(307\) | −1.91340 | + | 1.91340i | −0.109203 | + | 0.109203i | −0.759597 | − | 0.650394i | \(-0.774604\pi\) |
0.650394 | + | 0.759597i | \(0.274604\pi\) | |||||||
\(308\) | 3.19851i | 0.182252i | ||||||||
\(309\) | 3.82093 | + | 7.38147i | 0.217365 | + | 0.419917i | ||||
\(310\) | −1.62558 | + | 1.62558i | −0.0923268 | + | 0.0923268i | ||||
\(311\) | 7.19354 | 0.407908 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6520 | −0.828180 | −0.414090 | − | 0.910236i | \(-0.635900\pi\) | ||||
−0.414090 | + | 0.910236i | \(0.635900\pi\) | |||||||
\(314\) | 7.82861 | − | 7.82861i | 0.441794 | − | 0.441794i | ||||
\(315\) | −1.12983 | − | 0.798907i | −0.0636584 | − | 0.0450133i | ||||
\(316\) | 13.5805i | 0.763963i | ||||||||
\(317\) | −3.93077 | + | 3.93077i | −0.220774 | + | 0.220774i | −0.808824 | − | 0.588050i | \(-0.799896\pi\) |
0.588050 | + | 0.808824i | \(0.299896\pi\) | |||||||
\(318\) | −14.8809 | − | 4.72970i | −0.834479 | − | 0.265229i | ||||
\(319\) | −25.8712 | + | 25.8712i | −1.44851 | + | 1.44851i | ||||
\(320\) | −0.428520 | − | 0.428520i | −0.0239550 | − | 0.0239550i | ||||
\(321\) | −2.48825 | − | 4.80692i | −0.138880 | − | 0.268296i | ||||
\(322\) | 1.42071i | 0.0791728i | ||||||||
\(323\) | 12.6571 | + | 12.6571i | 0.704262 | + | 0.704262i | ||||
\(324\) | −8.48528 | + | 3.00000i | −0.471405 | + | 0.166667i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.25545i | 0.291073i | ||||||||
\(327\) | −2.13364 | − | 0.678152i | −0.117991 | − | 0.0375019i | ||||
\(328\) | −8.86892 | −0.489704 | ||||||||
\(329\) | −6.17275 | −0.340315 | ||||||||
\(330\) | 1.33614 | − | 4.20385i | 0.0735521 | − | 0.231414i | ||||
\(331\) | 13.9674 | + | 13.9674i | 0.767720 | + | 0.767720i | 0.977705 | − | 0.209985i | \(-0.0673414\pi\) |
−0.209985 | + | 0.977705i | \(0.567341\pi\) | |||||||
\(332\) | −0.996926 | − | 0.996926i | −0.0547134 | − | 0.0547134i | ||||
\(333\) | 2.98188 | + | 17.3797i | 0.163406 | + | 0.952399i | ||||
\(334\) | −15.7287 | −0.860635 | ||||||||
\(335\) | 0.0634958 | 0.00346915 | ||||||||
\(336\) | −0.399317 | + | 1.25636i | −0.0217845 | + | 0.0685398i | ||||
\(337\) | 16.3889i | 0.892762i | 0.894843 | + | 0.446381i | \(0.147287\pi\) | ||||
−0.894843 | + | 0.446381i | \(0.852713\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.55071 | − | 10.7231i | −0.301473 | − | 0.582401i | ||||
\(340\) | −2.24854 | − | 2.24854i | −0.121944 | − | 0.121944i | ||||
\(341\) | 15.9418i | 0.863295i | ||||||||
\(342\) | −5.90855 | + | 8.35596i | −0.319498 | + | 0.451838i | ||||
\(343\) | −7.22288 | − | 7.22288i | −0.389999 | − | 0.389999i | ||||
\(344\) | 1.37910 | − | 1.37910i | 0.0743562 | − | 0.0743562i | ||||
\(345\) | 0.593482 | − | 1.86725i | 0.0319520 | − | 0.100529i | ||||
\(346\) | 3.83515 | − | 3.83515i | 0.206179 | − | 0.206179i | ||||
\(347\) | 21.6243i | 1.16085i | 0.814312 | + | 0.580427i | \(0.197114\pi\) | ||||
−0.814312 | + | 0.580427i | \(0.802886\pi\) | |||||||
\(348\) | −13.3919 | + | 6.93217i | −0.717883 | + | 0.371603i | ||||
\(349\) | 1.37688 | − | 1.37688i | 0.0737029 | − | 0.0737029i | −0.669294 | − | 0.742997i | \(-0.733403\pi\) |
0.742997 | + | 0.669294i | \(0.233403\pi\) | |||||||
\(350\) | −3.52605 | −0.188475 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.20241 | −0.223989 | ||||||||
\(353\) | −16.4570 | + | 16.4570i | −0.875919 | + | 0.875919i | −0.993109 | − | 0.117191i | \(-0.962611\pi\) |
0.117191 | + | 0.993109i | \(0.462611\pi\) | |||||||
\(354\) | −13.2896 | + | 6.87922i | −0.706336 | + | 0.365626i | ||||
\(355\) | 6.32097i | 0.335482i | ||||||||
\(356\) | 4.62980 | − | 4.62980i | 0.245379 | − | 0.245379i | ||||
\(357\) | −2.09531 | + | 6.59239i | −0.110895 | + | 0.348906i | ||||
\(358\) | 7.34036 | − | 7.34036i | 0.387950 | − | 0.387950i | ||||
\(359\) | 15.8859 | + | 15.8859i | 0.838428 | + | 0.838428i | 0.988652 | − | 0.150224i | \(-0.0479996\pi\) |
−0.150224 | + | 0.988652i | \(0.548000\pi\) | |||||||
\(360\) | 1.04965 | − | 1.48444i | 0.0553216 | − | 0.0782366i | ||||
\(361\) | − | 7.36300i | − | 0.387526i | ||||||
\(362\) | 7.86104 | + | 7.86104i | 0.413167 | + | 0.413167i | ||||
\(363\) | −5.30306 | − | 10.2447i | −0.278339 | − | 0.537709i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.78062i | − | 0.250229i | ||||||
\(366\) | 4.26571 | − | 13.4210i | 0.222972 | − | 0.701529i | ||||
\(367\) | 0.601762 | 0.0314117 | 0.0157059 | − | 0.999877i | \(-0.495000\pi\) | ||||
0.0157059 | + | 0.999877i | \(0.495000\pi\) | |||||||
\(368\) | −1.86661 | −0.0973039 | ||||||||
\(369\) | −4.49926 | − | 26.2236i | −0.234222 | − | 1.36515i | ||||
\(370\) | −2.51878 | − | 2.51878i | −0.130945 | − | 0.130945i | ||||
\(371\) | −4.85178 | − | 4.85178i | −0.251892 | − | 0.251892i | ||||
\(372\) | −1.99024 | + | 6.26182i | −0.103189 | + | 0.324660i | ||||
\(373\) | 11.4157 | 0.591080 | 0.295540 | − | 0.955330i | \(-0.404500\pi\) | ||||
0.295540 | + | 0.955330i | \(0.404500\pi\) | |||||||
\(374\) | −22.0510 | −1.14023 | ||||||||
\(375\) | 9.63604 | + | 3.06269i | 0.497603 | + | 0.158157i | ||||
\(376\) | − | 8.11015i | − | 0.418249i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.91736 | − | 0.543341i | −0.201487 | − | 0.0279465i | ||||
\(379\) | 26.5622 | + | 26.5622i | 1.36441 | + | 1.36441i | 0.868211 | + | 0.496196i | \(0.165270\pi\) |
0.496196 | + | 0.868211i | \(0.334730\pi\) | |||||||
\(380\) | − | 2.06731i | − | 0.106051i | ||||||
\(381\) | −1.77954 | − | 3.43780i | −0.0911685 | − | 0.176124i | ||||
\(382\) | 4.05345 | + | 4.05345i | 0.207392 | + | 0.207392i | ||||
\(383\) | −8.93292 | + | 8.93292i | −0.456451 | + | 0.456451i | −0.897489 | − | 0.441038i | \(-0.854610\pi\) |
0.441038 | + | 0.897489i | \(0.354610\pi\) | |||||||
\(384\) | −1.65068 | − | 0.524648i | −0.0842359 | − | 0.0267733i | ||||
\(385\) | 1.37063 | − | 1.37063i | 0.0698536 | − | 0.0698536i | ||||
\(386\) | − | 11.3444i | − | 0.577414i | ||||||
\(387\) | 4.77735 | + | 3.37810i | 0.242846 | + | 0.171718i | ||||
\(388\) | −11.1369 | + | 11.1369i | −0.565389 | + | 0.565389i | ||||
\(389\) | 18.8229 | 0.954361 | 0.477180 | − | 0.878805i | \(-0.341659\pi\) | ||||
0.477180 | + | 0.878805i | \(0.341659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.79455 | −0.495332 | ||||||||
\(392\) | 4.54012 | − | 4.54012i | 0.229311 | − | 0.229311i | ||||
\(393\) | 17.5851 | + | 33.9718i | 0.887050 | + | 1.71365i | ||||
\(394\) | − | 4.68319i | − | 0.235935i | ||||||
\(395\) | 5.81951 | − | 5.81951i | 0.292812 | − | 0.292812i | ||||
\(396\) | −2.13191 | − | 12.4257i | −0.107132 | − | 0.624413i | ||||
\(397\) | 8.43859 | − | 8.43859i | 0.423521 | − | 0.423521i | −0.462893 | − | 0.886414i | \(-0.653189\pi\) |
0.886414 | + | 0.462893i | \(0.153189\pi\) | |||||||
\(398\) | 9.12358 | + | 9.12358i | 0.457324 | + | 0.457324i | ||||
\(399\) | −3.99374 | + | 2.06731i | −0.199937 | + | 0.103495i | ||||
\(400\) | − | 4.63274i | − | 0.231637i | ||||||
\(401\) | −17.1270 | − | 17.1270i | −0.855280 | − | 0.855280i | 0.135497 | − | 0.990778i | \(-0.456737\pi\) |
−0.990778 | + | 0.135497i | \(0.956737\pi\) | |||||||
\(402\) | 0.161164 | − | 0.0834248i | 0.00803815 | − | 0.00416085i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.27260i | 0.162818i | ||||||||
\(405\) | 4.92167 | + | 2.35055i | 0.244560 | + | 0.116800i | ||||
\(406\) | −6.62648 | −0.328867 | ||||||||
\(407\) | −24.7012 | −1.22439 | ||||||||
\(408\) | −8.66150 | − | 2.75295i | −0.428808 | − | 0.136291i | ||||
\(409\) | −18.9725 | − | 18.9725i | −0.938128 | − | 0.938128i | 0.0600662 | − | 0.998194i | \(-0.480869\pi\) |
−0.998194 | + | 0.0600662i | \(0.980869\pi\) | |||||||
\(410\) | 3.80051 | + | 3.80051i | 0.187694 | + | 0.187694i | ||||
\(411\) | −16.4806 | − | 5.23814i | −0.812927 | − | 0.258379i | ||||
\(412\) | −4.79880 | −0.236420 | ||||||||
\(413\) | −6.57587 | −0.323577 | ||||||||
\(414\) | −0.946944 | − | 5.51919i | −0.0465397 | − | 0.271253i | ||||
\(415\) | 0.854405i | 0.0419411i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.79133 | − | 2.99781i | 0.283603 | − | 0.146804i | ||||
\(418\) | −10.1369 | − | 10.1369i | −0.495811 | − | 0.495811i | ||||
\(419\) | − | 10.8367i | − | 0.529409i | −0.964330 | − | 0.264704i | \(-0.914726\pi\) | ||
0.964330 | − | 0.264704i | \(-0.0852743\pi\) | |||||||
\(420\) | 0.709488 | − | 0.367258i | 0.0346195 | − | 0.0179204i | ||||
\(421\) | 22.8984 | + | 22.8984i | 1.11600 | + | 1.11600i | 0.992323 | + | 0.123676i | \(0.0394684\pi\) |
0.123676 | + | 0.992323i | \(0.460532\pi\) | |||||||
\(422\) | −3.73322 | + | 3.73322i | −0.181731 | + | 0.181731i | ||||
\(423\) | 23.9801 | − | 4.11433i | 1.16595 | − | 0.200045i | ||||
\(424\) | 6.37457 | − | 6.37457i | 0.309577 | − | 0.309577i | ||||
\(425\) | − | 24.3091i | − | 1.17916i | ||||||
\(426\) | 8.30489 | + | 16.0438i | 0.402373 | + | 0.777326i | ||||
\(427\) | 4.37581 | − | 4.37581i | 0.211760 | − | 0.211760i | ||||
\(428\) | 3.12505 | 0.151055 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.18195 | −0.0569985 | ||||||||
\(431\) | 23.7339 | − | 23.7339i | 1.14322 | − | 1.14322i | 0.155362 | − | 0.987858i | \(-0.450346\pi\) |
0.987858 | − | 0.155362i | \(-0.0496544\pi\) | |||||||
\(432\) | 0.713876 | − | 5.14688i | 0.0343464 | − | 0.247629i | ||||
\(433\) | − | 23.7562i | − | 1.14165i | −0.821072 | − | 0.570825i | \(-0.806623\pi\) | ||
0.821072 | − | 0.570825i | \(-0.193377\pi\) | |||||||
\(434\) | −2.04161 | + | 2.04161i | −0.0980004 | + | 0.0980004i | ||||
\(435\) | 8.70927 | + | 2.76813i | 0.417578 | + | 0.132722i | ||||
\(436\) | 0.913996 | − | 0.913996i | 0.0437725 | − | 0.0437725i | ||||
\(437\) | −4.50256 | − | 4.50256i | −0.215387 | − | 0.215387i | ||||
\(438\) | −6.28108 | − | 12.1341i | −0.300122 | − | 0.579790i | ||||
\(439\) | − | 14.8663i | − | 0.709532i | −0.934955 | − | 0.354766i | \(-0.884561\pi\) | ||
0.934955 | − | 0.354766i | \(-0.115439\pi\) | |||||||
\(440\) | 1.80082 | + | 1.80082i | 0.0858505 | + | 0.0858505i | ||||
\(441\) | 15.7275 | + | 11.1210i | 0.748926 | + | 0.529571i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.3416i | 1.91669i | 0.285619 | + | 0.958343i | \(0.407801\pi\) | ||||
−0.285619 | + | 0.958343i | \(0.592199\pi\) | |||||||
\(444\) | −9.70248 | − | 3.08381i | −0.460459 | − | 0.146351i | ||||
\(445\) | −3.96792 | −0.188097 | ||||||||
\(446\) | −3.55022 | −0.168108 | ||||||||
\(447\) | −4.57860 | + | 14.4055i | −0.216560 | + | 0.681357i | ||||
\(448\) | −0.538189 | − | 0.538189i | −0.0254270 | − | 0.0254270i | ||||
\(449\) | −3.22808 | − | 3.22808i | −0.152343 | − | 0.152343i | 0.626821 | − | 0.779163i | \(-0.284356\pi\) |
−0.779163 | + | 0.626821i | \(0.784356\pi\) | |||||||
\(450\) | 13.6981 | − | 2.35022i | 0.645733 | − | 0.110790i | ||||
\(451\) | 37.2709 | 1.75502 | ||||||||
\(452\) | 6.97128 | 0.327901 | ||||||||
\(453\) | −12.8857 | + | 40.5420i | −0.605425 | + | 1.90483i | ||||
\(454\) | 5.02672i | 0.235916i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.71617 | − | 5.24723i | −0.127196 | − | 0.245724i | ||||
\(457\) | 18.5918 | + | 18.5918i | 0.869687 | + | 0.869687i | 0.992438 | − | 0.122750i | \(-0.0391714\pi\) |
−0.122750 | + | 0.992438i | \(0.539171\pi\) | |||||||
\(458\) | 16.1064i | 0.752602i | ||||||||
\(459\) | 3.74587 | − | 27.0069i | 0.174842 | − | 1.26057i | ||||
\(460\) | 0.799880 | + | 0.799880i | 0.0372946 | + | 0.0372946i | ||||
\(461\) | −10.6532 | + | 10.6532i | −0.496168 | + | 0.496168i | −0.910243 | − | 0.414075i | \(-0.864105\pi\) |
0.414075 | + | 0.910243i | \(0.364105\pi\) | |||||||
\(462\) | 1.67809 | − | 5.27972i | 0.0780719 | − | 0.245635i | ||||
\(463\) | 12.8578 | − | 12.8578i | 0.597552 | − | 0.597552i | −0.342108 | − | 0.939661i | \(-0.611141\pi\) |
0.939661 | + | 0.342108i | \(0.111141\pi\) | |||||||
\(464\) | − | 8.70629i | − | 0.404180i | ||||||
\(465\) | 3.53617 | − | 1.83046i | 0.163986 | − | 0.0848854i | ||||
\(466\) | −15.8255 | + | 15.8255i | −0.733103 | + | 0.733103i | ||||
\(467\) | 12.7104 | 0.588168 | 0.294084 | − | 0.955780i | \(-0.404985\pi\) | ||||
0.294084 | + | 0.955780i | \(0.404985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0797460 | 0.00368233 | ||||||||
\(470\) | −3.47536 | + | 3.47536i | −0.160306 | + | 0.160306i | ||||
\(471\) | −17.0298 | + | 8.81527i | −0.784692 | + | 0.406186i | ||||
\(472\) | − | 8.63979i | − | 0.397679i | ||||||
\(473\) | −5.79555 | + | 5.79555i | −0.266480 | + | 0.266480i | ||||
\(474\) | 7.12498 | − | 22.4171i | 0.327261 | − | 1.02965i | ||||
\(475\) | 11.1749 | − | 11.1749i | 0.512739 | − | 0.512739i | ||||
\(476\) | −2.82400 | − | 2.82400i | −0.129438 | − | 0.129438i | ||||
\(477\) | 22.0822 | + | 15.6145i | 1.01107 | + | 0.714937i | ||||
\(478\) | 8.60176i | 0.393435i | ||||||||
\(479\) | 25.3340 | + | 25.3340i | 1.15754 | + | 1.15754i | 0.985003 | + | 0.172535i | \(0.0551959\pi\) |
0.172535 | + | 0.985003i | \(0.444804\pi\) | |||||||
\(480\) | 0.482527 | + | 0.932171i | 0.0220242 | + | 0.0425476i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 6.14555i | − | 0.279922i | ||||||
\(483\) | 0.745370 | − | 2.34513i | 0.0339155 | − | 0.106707i | ||||
\(484\) | 6.66025 | 0.302739 | ||||||||
\(485\) | 9.54474 | 0.433404 | ||||||||
\(486\) | 15.5804 | − | 0.500258i | 0.706743 | − | 0.0226921i | ||||
\(487\) | 4.75849 | + | 4.75849i | 0.215628 | + | 0.215628i | 0.806653 | − | 0.591025i | \(-0.201277\pi\) |
−0.591025 | + | 0.806653i | \(0.701277\pi\) | |||||||
\(488\) | 5.74921 | + | 5.74921i | 0.260255 | + | 0.260255i | ||||
\(489\) | 2.75726 | − | 8.67507i | 0.124688 | − | 0.392300i | ||||
\(490\) | −3.89106 | −0.175780 | ||||||||
\(491\) | 29.8138 | 1.34548 | 0.672740 | − | 0.739879i | \(-0.265117\pi\) | ||||
0.672740 | + | 0.739879i | \(0.265117\pi\) | |||||||
\(492\) | 14.6398 | + | 4.65306i | 0.660011 | + | 0.209776i | ||||
\(493\) | − | 45.6839i | − | 2.05750i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.41108 | + | 6.23821i | −0.198263 | + | 0.280387i | ||||
\(496\) | −2.68240 | − | 2.68240i | −0.120443 | − | 0.120443i | ||||
\(497\) | 7.93867i | 0.356098i | ||||||||
\(498\) | 1.12257 | + | 2.16864i | 0.0503036 | + | 0.0971791i | ||||
\(499\) | −25.5487 | − | 25.5487i | −1.14372 | − | 1.14372i | −0.987764 | − | 0.155954i | \(-0.950155\pi\) |
−0.155954 | − | 0.987764i | \(-0.549845\pi\) | |||||||
\(500\) | −4.12782 | + | 4.12782i | −0.184602 | + | 0.184602i | ||||
\(501\) | 25.9630 | + | 8.25202i | 1.15994 | + | 0.368673i | ||||
\(502\) | 8.87855 | − | 8.87855i | 0.396269 | − | 0.396269i | ||||
\(503\) | − | 42.5984i | − | 1.89937i | −0.313210 | − | 0.949684i | \(-0.601404\pi\) | ||
0.313210 | − | 0.949684i | \(-0.398596\pi\) | |||||||
\(504\) | 1.31829 | − | 1.86434i | 0.0587212 | − | 0.0830444i | ||||
\(505\) | 1.40238 | − | 1.40238i | 0.0624049 | − | 0.0624049i | ||||
\(506\) | 7.84427 | 0.348720 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.23497 | 0.0991607 | ||||||||
\(509\) | −11.9455 | + | 11.9455i | −0.529477 | + | 0.529477i | −0.920416 | − | 0.390940i | \(-0.872150\pi\) |
0.390940 | + | 0.920416i | \(0.372150\pi\) | |||||||
\(510\) | 2.53193 | + | 4.89131i | 0.112116 | + | 0.216591i | ||||
\(511\) | − | 6.00410i | − | 0.265606i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 14.1371 | − | 10.6931i | 0.624167 | − | 0.472112i | ||||
\(514\) | −3.35014 | + | 3.35014i | −0.147768 | + | 0.147768i | ||||
\(515\) | 2.05638 | + | 2.05638i | 0.0906150 | + | 0.0906150i | ||||
\(516\) | −3.00000 | + | 1.55291i | −0.132068 | + | 0.0683632i | ||||
\(517\) | 34.0822i | 1.49893i | ||||||||
\(518\) | −3.16340 | − | 3.16340i | −0.138992 | − | 0.138992i | ||||
\(519\) | −8.34271 | + | 4.31851i | −0.366204 | + | 0.189561i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.8358i | 0.825213i | 0.910909 | + | 0.412607i | \(0.135382\pi\) | ||||
−0.910909 | + | 0.412607i | \(0.864618\pi\) | |||||||
\(522\) | 25.7427 | − | 4.41675i | 1.12673 | − | 0.193316i | ||||
\(523\) | −11.9533 | −0.522683 | −0.261342 | − | 0.965246i | \(-0.584165\pi\) | ||||
−0.261342 | + | 0.965246i | \(0.584165\pi\) | |||||||
\(524\) | −22.0856 | −0.964813 | ||||||||
\(525\) | 5.82037 | + | 1.84993i | 0.254022 | + | 0.0807376i | ||||
\(526\) | −4.00855 | − | 4.00855i | −0.174781 | − | 0.174781i | ||||
\(527\) | −14.0752 | − | 14.0752i | −0.613123 | − | 0.613123i | ||||
\(528\) | 6.93684 | + | 2.20478i | 0.301887 | + | 0.0959509i | ||||
\(529\) | −19.5158 | −0.848511 | ||||||||
\(530\) | −5.46326 | −0.237309 | ||||||||
\(531\) | 25.5461 | − | 4.38302i | 1.10861 | − | 0.190207i | ||||
\(532\) | − | 2.59639i | − | 0.112568i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −10.0713 | + | 5.21331i | −0.435829 | + | 0.225602i | ||||
\(535\) | −1.33915 | − | 1.33915i | −0.0578964 | − | 0.0578964i | ||||
\(536\) | 0.104775i | 0.00452561i | ||||||||
\(537\) | −15.9677 | + | 8.26548i | −0.689057 | + | 0.356682i | ||||
\(538\) | 5.16606 | + | 5.16606i | 0.222725 | + | 0.222725i | ||||
\(539\) | −19.0795 | + | 19.0795i | −0.821811 | + | 0.821811i | ||||
\(540\) | −2.51145 | + | 1.89963i | −0.108076 | + | 0.0817470i | ||||
\(541\) | −13.7056 | + | 13.7056i | −0.589250 | + | 0.589250i | −0.937428 | − | 0.348179i | \(-0.886800\pi\) |
0.348179 | + | 0.937428i | \(0.386800\pi\) | |||||||
\(542\) | − | 24.5279i | − | 1.05356i | ||||||
\(543\) | −8.85179 | − | 17.1003i | −0.379867 | − | 0.733846i | ||||
\(544\) | 3.71035 | − | 3.71035i | 0.159080 | − | 0.159080i | ||||
\(545\) | −0.783330 | −0.0335542 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6259 | −0.625359 | −0.312679 | − | 0.949859i | \(-0.601227\pi\) | ||||
−0.312679 | + | 0.949859i | \(0.601227\pi\) | |||||||
\(548\) | 7.05984 | − | 7.05984i | 0.301581 | − | 0.301581i | ||||
\(549\) | −14.0826 | + | 19.9159i | −0.601032 | + | 0.849988i | ||||
\(550\) | 19.4687i | 0.830147i | ||||||||
\(551\) | 21.0009 | − | 21.0009i | 0.894670 | − | 0.894670i | ||||
\(552\) | 3.08118 | + | 0.979314i | 0.131144 | + | 0.0416824i | ||||
\(553\) | 7.30888 | − | 7.30888i | 0.310805 | − | 0.310805i | ||||
\(554\) | −6.18454 | − | 6.18454i | −0.262756 | − | 0.262756i | ||||
\(555\) | 2.83623 | + | 5.47918i | 0.120391 | + | 0.232578i | ||||
\(556\) | 3.76503i | 0.159673i | ||||||||
\(557\) | −0.855215 | − | 0.855215i | −0.0362366 | − | 0.0362366i | 0.688756 | − | 0.724993i | \(-0.258157\pi\) |
−0.724993 | + | 0.688756i | \(0.758157\pi\) | |||||||
\(558\) | 6.57050 | − | 9.29209i | 0.278152 | − | 0.393366i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.461249i | 0.0194913i | ||||||||
\(561\) | 36.3992 | + | 11.5690i | 1.53677 | + | 0.488444i | ||||
\(562\) | −13.4290 | −0.566467 | ||||||||
\(563\) | 24.4117 | 1.02883 | 0.514416 | − | 0.857541i | \(-0.328009\pi\) | ||||
0.514416 | + | 0.857541i | \(0.328009\pi\) | |||||||
\(564\) | −4.25497 | + | 13.3873i | −0.179167 | + | 0.563705i | ||||
\(565\) | −2.98733 | − | 2.98733i | −0.125678 | − | 0.125678i | ||||
\(566\) | −22.2287 | − | 22.2287i | −0.934342 | − | 0.934342i | ||||
\(567\) | 6.18125 | + | 2.95212i | 0.259588 | + | 0.123977i | ||||
\(568\) | −10.4303 | −0.437647 | ||||||||
\(569\) | −5.97665 | −0.250554 | −0.125277 | − | 0.992122i | \(-0.539982\pi\) | ||||
−0.125277 | + | 0.992122i | \(0.539982\pi\) | |||||||
\(570\) | −1.08461 | + | 3.41247i | −0.0454293 | + | 0.142933i | ||||
\(571\) | 35.8068i | 1.49847i | 0.662307 | + | 0.749233i | \(0.269578\pi\) | ||||
−0.662307 | + | 0.749233i | \(0.730422\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.56431 | − | 8.81758i | −0.190677 | − | 0.368360i | ||||
\(574\) | 4.77316 | + | 4.77316i | 0.199228 | + | 0.199228i | ||||
\(575\) | 8.64753i | 0.360627i | ||||||||
\(576\) | 2.44949 | + | 1.73205i | 0.102062 | + | 0.0721688i | ||||
\(577\) | −13.8142 | − | 13.8142i | −0.575094 | − | 0.575094i | 0.358453 | − | 0.933548i | \(-0.383304\pi\) |
−0.933548 | + | 0.358453i | \(0.883304\pi\) | |||||||
\(578\) | 7.44826 | − | 7.44826i | 0.309807 | − | 0.309807i | ||||
\(579\) | −5.95181 | + | 18.7260i | −0.247349 | + | 0.778225i | ||||
\(580\) | −3.73082 | + | 3.73082i | −0.154914 | + | 0.154914i | ||||
\(581\) | 1.07307i | 0.0445184i | ||||||||
\(582\) | 24.2263 | − | 12.5405i | 1.00421 | − | 0.519820i | ||||
\(583\) | −26.7886 | + | 26.7886i | −1.10947 | + | 1.10947i | ||||
\(584\) | 7.88857 | 0.326431 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.09484 | 0.0865371 | ||||||||
\(587\) | 10.9112 | − | 10.9112i | 0.450353 | − | 0.450353i | −0.445119 | − | 0.895472i | \(-0.646838\pi\) |
0.895472 | + | 0.445119i | \(0.146838\pi\) | |||||||
\(588\) | −9.87626 | + | 5.11233i | −0.407290 | + | 0.210829i | ||||
\(589\) | − | 12.9407i | − | 0.533213i | ||||||
\(590\) | −3.70232 | + | 3.70232i | −0.152422 | + | 0.152422i | ||||
\(591\) | −2.45702 | + | 7.73044i | −0.101068 | + | 0.317988i | ||||
\(592\) | 4.15628 | − | 4.15628i | 0.170822 | − | 0.170822i | ||||
\(593\) | 19.1066 | + | 19.1066i | 0.784613 | + | 0.784613i | 0.980605 | − | 0.195992i | \(-0.0627927\pi\) |
−0.195992 | + | 0.980605i | \(0.562793\pi\) | |||||||
\(594\) | −3.00000 | + | 21.6293i | −0.123091 | + | 0.887461i | ||||
\(595\) | 2.42028i | 0.0992218i | ||||||||
\(596\) | −6.17093 | − | 6.17093i | −0.252771 | − | 0.252771i | ||||
\(597\) | −10.2734 | − | 19.8468i | −0.420464 | − | 0.812275i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 15.6579i | − | 0.639764i | −0.947457 | − | 0.319882i | \(-0.896357\pi\) | ||
0.947457 | − | 0.319882i | \(-0.103643\pi\) | |||||||
\(600\) | −2.43056 | + | 7.64717i | −0.0992271 | + | 0.312195i | ||||
\(601\) | −13.3171 | −0.543217 | −0.271609 | − | 0.962408i | \(-0.587556\pi\) | ||||
−0.271609 | + | 0.962408i | \(0.587556\pi\) | |||||||
\(602\) | −1.48444 | −0.0605011 | ||||||||
\(603\) | −0.309799 | + | 0.0531532i | −0.0126160 | + | 0.00216456i | ||||
\(604\) | −17.3671 | − | 17.3671i | −0.706657 | − | 0.706657i | ||||
\(605\) | −2.85405 | − | 2.85405i | −0.116034 | − | 0.116034i | ||||
\(606\) | 1.71696 | − | 5.40202i | 0.0697469 | − | 0.219442i | ||||
\(607\) | 12.2930 | 0.498957 | 0.249479 | − | 0.968380i | \(-0.419741\pi\) | ||||
0.249479 | + | 0.968380i | \(0.419741\pi\) | |||||||
\(608\) | 3.41130 | 0.138347 | ||||||||
\(609\) | 10.9382 | + | 3.47657i | 0.443238 | + | 0.140878i | ||||
\(610\) | − | 4.92730i | − | 0.199501i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12.8530 | + | 9.08847i | 0.519553 | + | 0.367380i | ||||
\(613\) | −7.60371 | − | 7.60371i | −0.307111 | − | 0.307111i | 0.536677 | − | 0.843788i | \(-0.319679\pi\) |
−0.843788 | + | 0.536677i | \(0.819679\pi\) | |||||||
\(614\) | 2.70595i | 0.109203i | ||||||||
\(615\) | −4.27950 | − | 8.26735i | −0.172566 | − | 0.333372i | ||||
\(616\) | 2.26169 | + | 2.26169i | 0.0911261 | + | 0.0911261i | ||||
\(617\) | 8.90722 | − | 8.90722i | 0.358591 | − | 0.358591i | −0.504702 | − | 0.863294i | \(-0.668398\pi\) |
0.863294 | + | 0.504702i | \(0.168398\pi\) | |||||||
\(618\) | 7.92129 | + | 2.51768i | 0.318641 | + | 0.101276i | ||||
\(619\) | 5.08096 | − | 5.08096i | 0.204221 | − | 0.204221i | −0.597585 | − | 0.801806i | \(-0.703873\pi\) |
0.801806 | + | 0.597585i | \(0.203873\pi\) | |||||||
\(620\) | 2.29892i | 0.0923268i | ||||||||
\(621\) | −1.33253 | + | 9.60723i | −0.0534726 | + | 0.385525i | ||||
\(622\) | 5.08660 | − | 5.08660i | 0.203954 | − | 0.203954i | ||||
\(623\) | −4.98342 | −0.199656 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.6260 | −0.785040 | ||||||||
\(626\) | −10.3605 | + | 10.3605i | −0.414090 | + | 0.414090i | ||||
\(627\) | 11.4144 | + | 22.0510i | 0.455849 | + | 0.880633i | ||||
\(628\) | − | 11.0713i | − | 0.441794i | ||||||
\(629\) | 21.8090 | − | 21.8090i | 0.869580 | − | 0.869580i | ||||
\(630\) | −1.36382 | + | 0.233994i | −0.0543359 | + | 0.00932256i | ||||
\(631\) | −17.5431 | + | 17.5431i | −0.698378 | + | 0.698378i | −0.964061 | − | 0.265682i | \(-0.914403\pi\) |
0.265682 | + | 0.964061i | \(0.414403\pi\) | |||||||
\(632\) | 9.60287 | + | 9.60287i | 0.381982 | + | 0.381982i | ||||
\(633\) | 8.12099 | − | 4.20373i | 0.322780 | − | 0.167083i | ||||
\(634\) | 5.55894i | 0.220774i | ||||||||
\(635\) | −0.957728 | − | 0.957728i | −0.0380063 | − | 0.0380063i | ||||
\(636\) | −13.8668 | + | 7.17798i | −0.549854 | + | 0.284625i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36.5874i | 1.44851i | ||||||||
\(639\) | −5.29137 | − | 30.8404i | −0.209323 | − | 1.22003i | ||||
\(640\) | −0.606018 | −0.0239550 | ||||||||
\(641\) | −11.8520 | −0.468127 | −0.234064 | − | 0.972221i | \(-0.575202\pi\) | ||||
−0.234064 | + | 0.972221i | \(0.575202\pi\) | |||||||
\(642\) | −5.15846 | − | 1.63955i | −0.203588 | − | 0.0647079i | ||||
\(643\) | 19.6347 | + | 19.6347i | 0.774319 | + | 0.774319i | 0.978858 | − | 0.204540i | \(-0.0655697\pi\) |
−0.204540 | + | 0.978858i | \(0.565570\pi\) | |||||||
\(644\) | 1.00459 | + | 1.00459i | 0.0395864 | + | 0.0395864i | ||||
\(645\) | 1.95101 | + | 0.620105i | 0.0768211 | + | 0.0244166i | ||||
\(646\) | 17.8999 | 0.704262 | ||||||||
\(647\) | −19.6923 | −0.774182 | −0.387091 | − | 0.922041i | \(-0.626520\pi\) | ||||
−0.387091 | + | 0.922041i | \(0.626520\pi\) | |||||||
\(648\) | −3.87868 | + | 8.12132i | −0.152369 | + | 0.319036i | ||||
\(649\) | 36.3079i | 1.42521i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44117 | − | 2.29892i | 0.174063 | − | 0.0901017i | ||||
\(652\) | 3.71617 | + | 3.71617i | 0.145536 | + | 0.145536i | ||||
\(653\) | − | 48.6132i | − | 1.90238i | −0.308602 | − | 0.951191i | \(-0.599861\pi\) | ||
0.308602 | − | 0.951191i | \(-0.400139\pi\) | |||||||
\(654\) | −1.98824 | + | 1.02919i | −0.0777464 | + | 0.0402445i | ||||
\(655\) | 9.46410 | + | 9.46410i | 0.369793 | + | 0.369793i | ||||
\(656\) | −6.27128 | + | 6.27128i | −0.244852 | + | 0.244852i | ||||
\(657\) | 4.00192 | + | 23.3249i | 0.156130 | + | 0.909991i | ||||
\(658\) | −4.36479 | + | 4.36479i | −0.170157 | + | 0.170157i | ||||
\(659\) | 3.70793i | 0.144440i | 0.997389 | + | 0.0722202i | \(0.0230084\pi\) | ||||
−0.997389 | + | 0.0722202i | \(0.976992\pi\) | |||||||
\(660\) | −2.02778 | − | 3.91736i | −0.0789311 | − | 0.152483i | ||||
\(661\) | −4.54658 | + | 4.54658i | −0.176842 | + | 0.176842i | −0.789977 | − | 0.613136i | \(-0.789908\pi\) |
0.613136 | + | 0.789977i | \(0.289908\pi\) | |||||||
\(662\) | 19.7529 | 0.767720 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.40987 | −0.0547134 | ||||||||
\(665\) | −1.11261 | + | 1.11261i | −0.0431450 | + | 0.0431450i | ||||
\(666\) | 14.3978 | + | 10.1808i | 0.557902 | + | 0.394497i | ||||
\(667\) | 16.2513i | 0.629252i | ||||||||
\(668\) | −11.1219 | + | 11.1219i | −0.430318 | + | 0.430318i | ||||
\(669\) | 5.86029 | + | 1.86262i | 0.226572 | + | 0.0720129i | ||||
\(670\) | 0.0448983 | − | 0.0448983i | 0.00173457 | − | 0.00173457i | ||||
\(671\) | −24.1605 | − | 24.1605i | −0.932708 | − | 0.932708i | ||||
\(672\) | 0.606018 | + | 1.17074i | 0.0233777 | + | 0.0451622i | ||||
\(673\) | − | 5.93825i | − | 0.228903i | −0.993429 | − | 0.114451i | \(-0.963489\pi\) | ||
0.993429 | − | 0.114451i | \(-0.0365110\pi\) | |||||||
\(674\) | 11.5887 | + | 11.5887i | 0.446381 | + | 0.446381i | ||||
\(675\) | −23.8442 | − | 3.30720i | −0.917763 | − | 0.127294i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.5297i | 0.942753i | 0.881932 | + | 0.471376i | \(0.156243\pi\) | ||||
−0.881932 | + | 0.471376i | \(0.843757\pi\) | |||||||
\(678\) | −11.5073 | − | 3.65746i | −0.441937 | − | 0.140464i | ||||
\(679\) | 11.9875 | 0.460037 | ||||||||
\(680\) | −3.17992 | −0.121944 | ||||||||
\(681\) | 2.63726 | − | 8.29751i | 0.101060 | − | 0.317961i | ||||
\(682\) | 11.2725 | + | 11.2725i | 0.431647 | + | 0.431647i | ||||
\(683\) | −18.9705 | − | 18.9705i | −0.725885 | − | 0.725885i | 0.243912 | − | 0.969797i | \(-0.421569\pi\) |
−0.969797 | + | 0.243912i | \(0.921569\pi\) | |||||||
\(684\) | 1.73057 | + | 10.0865i | 0.0661702 | + | 0.385668i | ||||
\(685\) | −6.05056 | −0.231180 | ||||||||
\(686\) | −10.2147 | −0.389999 | ||||||||
\(687\) | 8.45018 | − | 26.5865i | 0.322394 | − | 1.01434i | ||||
\(688\) | − | 1.95035i | − | 0.0743562i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.900691 | − | 1.74000i | −0.0342887 | − | 0.0662407i | ||||
\(691\) | −7.45140 | − | 7.45140i | −0.283464 | − | 0.283464i | 0.551025 | − | 0.834489i | \(-0.314237\pi\) |
−0.834489 | + | 0.551025i | \(0.814237\pi\) | |||||||
\(692\) | − | 5.42372i | − | 0.206179i | ||||||
\(693\) | −5.53999 | + | 7.83473i | −0.210447 | + | 0.297617i | ||||
\(694\) | 15.2907 | + | 15.2907i | 0.580427 | + | 0.580427i | ||||
\(695\) | 1.61339 | − | 1.61339i | 0.0611994 | − | 0.0611994i | ||||
\(696\) | −4.56774 | + | 14.3713i | −0.173140 | + | 0.544743i | ||||
\(697\) | −32.9068 | + | 32.9068i | −1.24644 | + | 1.24644i | ||||
\(698\) | − | 1.94721i | − | 0.0737029i | ||||||
\(699\) | 34.4257 | − | 17.8201i | 1.30210 | − | 0.674016i | ||||
\(700\) | −2.49329 | + | 2.49329i | −0.0942375 | + | 0.0942375i | ||||
\(701\) | 48.3500 | 1.82616 | 0.913078 | − | 0.407785i | \(-0.133699\pi\) | ||||
0.913078 | + | 0.407785i | \(0.133699\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0512 | 0.756245 | ||||||||
\(704\) | −2.97155 | + | 2.97155i | −0.111995 | + | 0.111995i | ||||
\(705\) | 7.56004 | − | 3.91337i | 0.284728 | − | 0.147386i | ||||
\(706\) | 23.2737i | 0.875919i | ||||||||
\(707\) | 1.76128 | − | 1.76128i | 0.0662397 | − | 0.0662397i | ||||
\(708\) | −4.53284 | + | 14.2615i | −0.170355 | + | 0.535981i | ||||
\(709\) | 20.8103 | − | 20.8103i | 0.781546 | − | 0.781546i | −0.198545 | − | 0.980092i | \(-0.563622\pi\) |
0.980092 | + | 0.198545i | \(0.0636217\pi\) | |||||||
\(710\) | 4.46960 | + | 4.46960i | 0.167741 | + | 0.167741i | ||||
\(711\) | −23.5221 | + | 33.2653i | −0.882149 | + | 1.24755i | ||||
\(712\) | − | 6.54753i | − | 0.245379i | ||||||
\(713\) | 5.00699 | + | 5.00699i | 0.187513 | + | 0.187513i | ||||
\(714\) | 3.17992 | + | 6.14313i | 0.119005 | + | 0.229901i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 10.3808i | − | 0.387950i | ||||||
\(717\) | 4.51289 | − | 14.1988i | 0.168537 | − | 0.530262i | ||||
\(718\) | 22.4661 | 0.838428 | ||||||||
\(719\) | −42.8472 | −1.59793 | −0.798966 | − | 0.601376i | \(-0.794619\pi\) | ||||
−0.798966 | + | 0.601376i | \(0.794619\pi\) | |||||||
\(720\) | −0.307437 | − | 1.79187i | −0.0114575 | − | 0.0667791i | ||||
\(721\) | 2.58266 | + | 2.58266i | 0.0961834 | + | 0.0961834i | ||||
\(722\) | −5.20643 | − | 5.20643i | −0.193763 | − | 0.193763i | ||||
\(723\) | −3.22425 | + | 10.1443i | −0.119911 | + | 0.377272i | ||||
\(724\) | 11.1172 | 0.413167 | ||||||||
\(725\) | −40.3340 | −1.49797 | ||||||||
\(726\) | −10.9939 | − | 3.49429i | −0.408024 | − | 0.129685i | ||||
\(727\) | − | 1.92620i | − | 0.0714389i | −0.999362 | − | 0.0357194i | \(-0.988628\pi\) | ||
0.999362 | − | 0.0357194i | \(-0.0113723\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9808 | − | 7.34847i | −0.962250 | − | 0.272166i | ||||
\(730\) | −3.38041 | − | 3.38041i | −0.125115 | − | 0.125115i | ||||
\(731\) | − | 10.2339i | − | 0.378515i | ||||||
\(732\) | −6.47380 | − | 12.5064i | −0.239279 | − | 0.462251i | ||||
\(733\) | 22.6065 | + | 22.6065i | 0.834990 | + | 0.834990i | 0.988195 | − | 0.153204i | \(-0.0489593\pi\) |
−0.153204 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(734\) | 0.425510 | − | 0.425510i | 0.0157059 | − | 0.0157059i | ||||
\(735\) | 6.42290 | + | 2.04144i | 0.236912 | + | 0.0752996i | ||||
\(736\) | −1.31989 | + | 1.31989i | −0.0486519 | + | 0.0486519i | ||||
\(737\) | − | 0.440309i | − | 0.0162190i | ||||||
\(738\) | −21.7243 | − | 15.3614i | −0.799684 | − | 0.565462i | ||||
\(739\) | 1.02751 | − | 1.02751i | 0.0377976 | − | 0.0377976i | −0.687955 | − | 0.725753i | \(-0.741492\pi\) |
0.725753 | + | 0.687955i | \(0.241492\pi\) | |||||||
\(740\) | −3.56209 | −0.130945 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.86145 | −0.251892 | ||||||||
\(743\) | −26.1830 | + | 26.1830i | −0.960561 | + | 0.960561i | −0.999251 | − | 0.0386900i | \(-0.987682\pi\) |
0.0386900 | + | 0.999251i | \(0.487682\pi\) | |||||||
\(744\) | 3.02047 | + | 5.83509i | 0.110736 | + | 0.213925i | ||||
\(745\) | 5.28873i | 0.193764i | ||||||||
\(746\) | 8.07209 | − | 8.07209i | 0.295540 | − | 0.295540i | ||||
\(747\) | −0.715233 | − | 4.16869i | −0.0261690 | − | 0.152524i | ||||
\(748\) | −15.5924 | + | 15.5924i | −0.570116 | + | 0.570116i | ||||
\(749\) | −1.68187 | − | 1.68187i | −0.0614542 | − | 0.0614542i | ||||
\(750\) | 8.97936 | − | 4.64806i | 0.327880 | − | 0.169723i | ||||
\(751\) | 15.3439i | 0.559906i | 0.960014 | + | 0.279953i | \(0.0903188\pi\) | ||||
−0.960014 | + | 0.279953i | \(0.909681\pi\) | |||||||
\(752\) | −5.73474 | − | 5.73474i | −0.209124 | − | 0.209124i | ||||
\(753\) | −19.3138 | + | 9.99753i | −0.703832 | + | 0.364330i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.8843i | 0.541694i | ||||||||
\(756\) | −3.15419 | + | 2.38579i | −0.114717 | + | 0.0867705i | ||||
\(757\) | 22.4708 | 0.816715 | 0.408357 | − | 0.912822i | \(-0.366102\pi\) | ||||
0.408357 | + | 0.912822i | \(0.366102\pi\) | |||||||
\(758\) | 37.5646 | 1.36441 | ||||||||
\(759\) | −12.9484 | − | 4.11548i | −0.469997 | − | 0.149382i | ||||
\(760\) | −1.46181 | − | 1.46181i | −0.0530255 | − | 0.0530255i | ||||
\(761\) | 0.574247 | + | 0.574247i | 0.0208164 | + | 0.0208164i | 0.717438 | − | 0.696622i | \(-0.245314\pi\) |
−0.696622 | + | 0.717438i | \(0.745314\pi\) | |||||||
\(762\) | −3.68922 | − | 1.17257i | −0.133646 | − | 0.0424777i | ||||
\(763\) | −0.983805 | −0.0356161 | ||||||||
\(764\) | 5.73244 | 0.207392 | ||||||||
\(765\) | −1.61319 | − | 9.40237i | −0.0583251 | − | 0.339943i | ||||
\(766\) | 12.6331i | 0.456451i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.53819 | + | 0.796225i | −0.0555046 | + | 0.0287313i | ||||
\(769\) | −8.84388 | − | 8.84388i | −0.318918 | − | 0.318918i | 0.529433 | − | 0.848352i | \(-0.322405\pi\) |
−0.848352 | + | 0.529433i | \(0.822405\pi\) | |||||||
\(770\) | − | 1.93836i | − | 0.0698536i | ||||||
\(771\) | 7.28766 | − | 3.77237i | 0.262458 | − | 0.135859i | ||||
\(772\) | −8.02170 | − | 8.02170i | −0.288707 | − | 0.288707i | ||||
\(773\) | −10.7358 | + | 10.7358i | −0.386139 | + | 0.386139i | −0.873308 | − | 0.487169i | \(-0.838030\pi\) |
0.487169 | + | 0.873308i | \(0.338030\pi\) | |||||||
\(774\) | 5.76677 | − | 0.989422i | 0.207282 | − | 0.0355640i | ||||
\(775\) | −12.4268 | + | 12.4268i | −0.446386 | + | 0.446386i | ||||
\(776\) | 15.7499i | 0.565389i | ||||||||
\(777\) | 3.56209 | + | 6.88144i | 0.127789 | + | 0.246870i | ||||
\(778\) | 13.3098 | − | 13.3098i | 0.477180 | − | 0.477180i | ||||
\(779\) | −30.2546 | −1.08398 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.8325 | 1.56845 | ||||||||
\(782\) | −6.92579 | + | 6.92579i | −0.247666 | + | 0.247666i | ||||
\(783\) | −44.8103 | − | 6.21521i | −1.60139 | − | 0.222114i | ||||
\(784\) | − | 6.42071i | − | 0.229311i | ||||||
\(785\) | −4.74428 | + | 4.74428i | −0.169331 | + | 0.169331i | ||||
\(786\) | 36.4562 | + | 11.5871i | 1.30035 | + | 0.413300i | ||||
\(787\) | −19.7245 | + | 19.7245i | −0.703104 | + | 0.703104i | −0.965076 | − | 0.261972i | \(-0.915627\pi\) |
0.261972 | + | 0.965076i | \(0.415627\pi\) | |||||||
\(788\) | −3.31151 | − | 3.31151i | −0.117968 | − | 0.117968i | ||||
\(789\) | 4.51376 | + | 8.71991i | 0.160694 | + | 0.310437i | ||||
\(790\) | − | 8.23004i | − | 0.292812i | ||||||
\(791\) | −3.75186 | − | 3.75186i | −0.133401 | − | 0.133401i | ||||
\(792\) | −10.2938 | − | 7.27879i | −0.365773 | − | 0.258640i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 11.9340i | − | 0.423521i | ||||||
\(795\) | 9.01810 | + | 2.86629i | 0.319839 | + | 0.101657i | ||||
\(796\) | 12.9027 | 0.457324 | ||||||||
\(797\) | 43.8082 | 1.55177 | 0.775883 | − | 0.630877i | \(-0.217305\pi\) | ||||
0.775883 | + | 0.630877i | \(0.217305\pi\) | |||||||
\(798\) | −1.36219 | + | 4.28581i | −0.0482210 | + | 0.151716i | ||||
\(799\) | −30.0915 | − | 30.0915i | −1.06456 | − | 1.06456i | ||||
\(800\) | −3.27584 | − | 3.27584i | −0.115819 | − | 0.115819i | ||||
\(801\) | 19.3597 | − | 3.32160i | 0.684041 | − | 0.117363i | ||||
\(802\) | −24.2212 | −0.855280 | ||||||||
\(803\) | −33.1510 | −1.16987 | ||||||||
\(804\) | 0.0549702 | − | 0.172951i | 0.00193865 | − | 0.00609950i | ||||
\(805\) | − | 0.860973i | − | 0.0303453i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.81715 | − | 11.2379i | −0.204773 | − | 0.395592i | ||||
\(808\) | 2.31408 | + | 2.31408i | 0.0814091 | + | 0.0814091i | ||||
\(809\) | − | 0.388416i | − | 0.0136560i | −0.999977 | − | 0.00682798i | \(-0.997827\pi\) | ||
0.999977 | − | 0.00682798i | \(-0.00217343\pi\) | |||||||
\(810\) | 5.14224 | − | 1.81805i | 0.180680 | − | 0.0638799i | ||||
\(811\) | 5.70744 | + | 5.70744i | 0.200415 | + | 0.200415i | 0.800178 | − | 0.599763i | \(-0.204738\pi\) |
−0.599763 | + | 0.800178i | \(0.704738\pi\) | |||||||
\(812\) | −4.68563 | + | 4.68563i | −0.164433 | + | 0.164433i | ||||
\(813\) | −12.8685 | + | 40.4878i | −0.451319 | + | 1.41997i | ||||
\(814\) | −17.4664 | + | 17.4664i | −0.612197 | + | 0.612197i | ||||
\(815\) | − | 3.18490i | − | 0.111562i | ||||||
\(816\) | −8.07123 | + | 4.17798i | −0.282550 | + | 0.146258i | ||||
\(817\) | 4.70454 | − | 4.70454i | 0.164591 | − | 0.164591i | ||||
\(818\) | −26.8311 | −0.938128 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.37473 | 0.187694 | ||||||||
\(821\) | 24.1892 | − | 24.1892i | 0.844207 | − | 0.844207i | −0.145196 | − | 0.989403i | \(-0.546381\pi\) |
0.989403 | + | 0.145196i | \(0.0463812\pi\) | |||||||
\(822\) | −15.3575 | + | 7.94960i | −0.535653 | + | 0.277274i | ||||
\(823\) | 37.3184i | 1.30084i | 0.759576 | + | 0.650418i | \(0.225406\pi\) | ||||
−0.759576 | + | 0.650418i | \(0.774594\pi\) | |||||||
\(824\) | −3.39327 | + | 3.39327i | −0.118210 | + | 0.118210i | ||||
\(825\) | 10.2142 | − | 32.1366i | 0.355613 | − | 1.11885i | ||||
\(826\) | −4.64984 | + | 4.64984i | −0.161789 | + | 0.161789i | ||||
\(827\) | −8.16295 | − | 8.16295i | −0.283854 | − | 0.283854i | 0.550790 | − | 0.834644i | \(-0.314326\pi\) |
−0.834644 | + | 0.550790i | \(0.814326\pi\) | |||||||
\(828\) | −4.57225 | − | 3.23307i | −0.158897 | − | 0.112357i | ||||
\(829\) | − | 32.5422i | − | 1.13024i | −0.825010 | − | 0.565118i | \(-0.808831\pi\) | ||
0.825010 | − | 0.565118i | \(-0.191169\pi\) | |||||||
\(830\) | 0.604155 | + | 0.604155i | 0.0209705 | + | 0.0209705i | ||||
\(831\) | 6.96399 | + | 13.4534i | 0.241578 | + | 0.466693i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 33.6909i | − | 1.16732i | ||||||
\(834\) | 1.97532 | − | 6.21486i | 0.0683996 | − | 0.215203i | ||||
\(835\) | 9.53187 | 0.329864 | ||||||||
\(836\) | −14.3357 | −0.495811 | ||||||||
\(837\) | −15.7209 | + | 11.8911i | −0.543393 | + | 0.411016i | ||||
\(838\) | −7.66272 | − | 7.66272i | −0.264704 | − | 0.264704i | ||||
\(839\) | −9.51383 | − | 9.51383i | −0.328454 | − | 0.328454i | 0.523544 | − | 0.851998i | \(-0.324609\pi\) |
−0.851998 | + | 0.523544i | \(0.824609\pi\) | |||||||
\(840\) | 0.241993 | − | 0.761375i | 0.00834956 | − | 0.0262699i | ||||
\(841\) | −46.7996 | −1.61378 | ||||||||
\(842\) | 32.3832 | 1.11600 | ||||||||
\(843\) | 22.1669 | + | 7.04547i | 0.763469 | + | 0.242659i | ||||
\(844\) | 5.27958i | 0.181731i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.0472 | − | 19.8657i | 0.482952 | − | 0.682998i | ||||
\(847\) | −3.58448 | − | 3.58448i | −0.123164 | − | 0.123164i | ||||
\(848\) | − | 9.01501i | − | 0.309577i | ||||||
\(849\) | 25.0302 | + | 48.3547i | 0.859035 | + | 1.65953i | ||||
\(850\) | −17.1891 | − | 17.1891i | −0.589581 | − | 0.589581i | ||||
\(851\) | −7.75816 | + | 7.75816i | −0.265946 | + | 0.265946i | ||||
\(852\) | 17.2171 | + | 5.47225i | 0.589850 | + | 0.187476i | ||||
\(853\) | 8.09779 | − | 8.09779i | 0.277263 | − | 0.277263i | −0.554752 | − | 0.832015i | \(-0.687187\pi\) |
0.832015 | + | 0.554752i | \(0.187187\pi\) | |||||||
\(854\) | − | 6.18833i | − | 0.211760i | ||||||
\(855\) | 3.58069 | − | 5.06386i | 0.122457 | − | 0.173180i | ||||
\(856\) | 2.20975 | − | 2.20975i | 0.0755276 | − | 0.0755276i | ||||
\(857\) | 2.81672 | 0.0962173 | 0.0481086 | − | 0.998842i | \(-0.484681\pi\) | ||||
0.0481086 | + | 0.998842i | \(0.484681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5174 | 0.631807 | 0.315903 | − | 0.948791i | \(-0.397692\pi\) | ||||
0.315903 | + | 0.948791i | \(0.397692\pi\) | |||||||
\(860\) | −0.835761 | + | 0.835761i | −0.0284992 | + | 0.0284992i | ||||
\(861\) | −5.37473 | − | 10.3832i | −0.183170 | − | 0.353858i | ||||
\(862\) | − | 33.5647i | − | 1.14322i | ||||||
\(863\) | −16.9992 | + | 16.9992i | −0.578658 | + | 0.578658i | −0.934534 | − | 0.355875i | \(-0.884183\pi\) |
0.355875 | + | 0.934534i | \(0.384183\pi\) | |||||||
\(864\) | −3.13461 | − | 4.14418i | −0.106642 | − | 0.140988i | ||||
\(865\) | −2.32417 | + | 2.32417i | −0.0790242 | + | 0.0790242i | ||||
\(866\) | −16.7982 | − | 16.7982i | −0.570825 | − | 0.570825i | ||||
\(867\) | −16.2024 | + | 8.38698i | −0.550263 | + | 0.284837i | ||||
\(868\) | 2.88727i | 0.0980004i | ||||||||
\(869\) | −40.3552 | − | 40.3552i | −1.36896 | − | 1.36896i | ||||
\(870\) | 8.11575 | − | 4.20102i | 0.275150 | − | 0.142428i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 1.29259i | − | 0.0437725i | ||||||
\(873\) | −46.5693 | + | 7.99003i | −1.57613 | + | 0.270421i | ||||
\(874\) | −6.36758 | −0.215387 | ||||||||
\(875\) | 4.44309 | 0.150204 | ||||||||
\(876\) | −13.0215 | − | 4.13872i | −0.439956 | − | 0.139834i | ||||
\(877\) | 21.8195 | + | 21.8195i | 0.736793 | + | 0.736793i | 0.971956 | − | 0.235163i | \(-0.0755623\pi\) |
−0.235163 | + | 0.971956i | \(0.575562\pi\) | |||||||
\(878\) | −10.5121 | − | 10.5121i | −0.354766 | − | 0.354766i | ||||
\(879\) | −3.45791 | − | 1.09905i | −0.116633 | − | 0.0370702i | ||||
\(880\) | 2.54674 | 0.0858505 | ||||||||
\(881\) | 46.2624 | 1.55862 | 0.779310 | − | 0.626638i | \(-0.215570\pi\) | ||||
0.779310 | + | 0.626638i | \(0.215570\pi\) | |||||||
\(882\) | 18.9847 | − | 3.25726i | 0.639249 | − | 0.109678i | ||||
\(883\) | − | 31.0867i | − | 1.04615i | −0.852286 | − | 0.523076i | \(-0.824784\pi\) | ||
0.852286 | − | 0.523076i | \(-0.175216\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.05376 | − | 4.16893i | 0.270724 | − | 0.140137i | ||||
\(886\) | 28.5258 | + | 28.5258i | 0.958343 | + | 0.958343i | ||||
\(887\) | − | 36.2495i | − | 1.21714i | −0.793500 | − | 0.608570i | \(-0.791744\pi\) | ||
0.793500 | − | 0.608570i | \(-0.208256\pi\) | |||||||
\(888\) | −9.04127 | + | 4.68011i | −0.303405 | + | 0.157054i | ||||
\(889\) | −1.20283 | − | 1.20283i | −0.0403418 | − | 0.0403418i | ||||
\(890\) | −2.80574 | + | 2.80574i | −0.0940487 | + | 0.0940487i | ||||
\(891\) | 16.2998 | − | 34.1291i | 0.546064 | − | 1.14337i | ||||
\(892\) | −2.51039 | + | 2.51039i | −0.0840540 | + | 0.0840540i | ||||
\(893\) | − | 27.6662i | − | 0.925814i | ||||||
\(894\) | 6.94866 | + | 13.4238i | 0.232398 | + | 0.448959i | ||||
\(895\) | −4.44839 | + | 4.44839i | −0.148693 | + | 0.148693i | ||||
\(896\) | −0.761114 | −0.0254270 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.56520 | −0.152343 | ||||||||
\(899\) | −23.3537 | + | 23.3537i | −0.778891 | + | 0.778891i | ||||
\(900\) | 8.02414 | − | 11.3479i | 0.267471 | − | 0.378262i | ||||
\(901\) | − | 47.3038i | − | 1.57592i | ||||||
\(902\) | 26.3545 | − | 26.3545i | 0.877508 | − | 0.877508i | ||||
\(903\) | 2.45033 | + | 0.778806i | 0.0815418 | + | 0.0259170i | ||||
\(904\) | 4.92944 | − | 4.92944i | 0.163951 | − | 0.163951i | ||||
\(905\) | −4.76394 | − | 4.76394i | −0.158359 | − | 0.158359i | ||||
\(906\) | 19.5559 | + | 37.7791i | 0.649701 | + | 1.25513i | ||||
\(907\) | 54.8347i | 1.82076i | 0.413777 | + | 0.910378i | \(0.364209\pi\) | ||||
−0.413777 | + | 0.910378i | \(0.635791\pi\) | |||||||
\(908\) | 3.55443 | + | 3.55443i | 0.117958 | + | 0.117958i | ||||
\(909\) | −5.66832 | + | 8.01621i | −0.188006 | + | 0.265881i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.4963i | − | 0.414022i | −0.978339 | − | 0.207011i | \(-0.933626\pi\) | ||
0.978339 | − | 0.207011i | \(-0.0663737\pi\) | |||||||
\(912\) | −5.63097 | − | 1.78973i | −0.186460 | − | 0.0592640i | ||||
\(913\) | 5.92484 | 0.196083 | ||||||||
\(914\) | 26.2928 | 0.869687 | ||||||||
\(915\) | −2.58510 | + | 8.13340i | −0.0854607 | + | 0.268882i | ||||
\(916\) | 11.3889 | + | 11.3889i | 0.376301 | + | 0.376301i | ||||
\(917\) | 11.8862 | + | 11.8862i | 0.392517 | + | 0.392517i | ||||
\(918\) | −16.4480 | − | 21.7455i | −0.542865 | − | 0.717708i | ||||
\(919\) | 30.4287 | 1.00375 | 0.501874 | − | 0.864941i | \(-0.332644\pi\) | ||||
0.501874 | + | 0.864941i | \(0.332644\pi\) | |||||||
\(920\) | 1.13120 | 0.0372946 | ||||||||
\(921\) | 1.41967 | − | 4.46666i | 0.0467797 | − | 0.147181i | ||||
\(922\) | 15.0659i | 0.496168i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.54674 | − | 4.91992i | −0.0837815 | − | 0.161853i | ||||
\(925\) | −19.2550 | − | 19.2550i | −0.633099 | − | 0.633099i | ||||
\(926\) | − | 18.1837i | − | 0.597552i | ||||||
\(927\) | −11.7546 | − | 8.31177i | −0.386072 | − | 0.272994i | ||||
\(928\) | −6.15628 | − | 6.15628i | −0.202090 | − | 0.202090i | ||||
\(929\) | −8.30768 | + | 8.30768i | −0.272566 | + | 0.272566i | −0.830132 | − | 0.557566i | \(-0.811735\pi\) |
0.557566 | + | 0.830132i | \(0.311735\pi\) | |||||||
\(930\) | 1.20612 | − | 3.79478i | 0.0395503 | − | 0.124436i | ||||
\(931\) | 15.4877 | − | 15.4877i | 0.507590 | − | 0.507590i | ||||
\(932\) | 22.3807i | 0.733103i | ||||||||
\(933\) | −11.0650 | + | 5.72768i | −0.362253 | + | 0.187516i | ||||
\(934\) | 8.98762 | − | 8.98762i | 0.294084 | − | 0.294084i | ||||
\(935\) | 13.3633 | 0.437027 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.30645 | 0.140686 | 0.0703429 | − | 0.997523i | \(-0.477591\pi\) | ||||
0.0703429 | + | 0.997523i | \(0.477591\pi\) | |||||||
\(938\) | 0.0563890 | − | 0.0563890i | 0.00184116 | − | 0.00184116i | ||||
\(939\) | 22.5375 | − | 11.6663i | 0.735485 | − | 0.380715i | ||||
\(940\) | 4.91490i | 0.160306i | ||||||||
\(941\) | −35.4161 | + | 35.4161i | −1.15453 | + | 1.15453i | −0.168897 | + | 0.985634i | \(0.554020\pi\) |
−0.985634 | + | 0.168897i | \(0.945980\pi\) | |||||||
\(942\) | −5.80855 | + | 18.2752i | −0.189253 | + | 0.595439i | ||||
\(943\) | 11.7060 | − | 11.7060i | 0.381201 | − | 0.381201i | ||||
\(944\) | −6.10925 | − | 6.10925i | −0.198839 | − | 0.198839i | ||||
\(945\) | 2.37399 | + | 0.329275i | 0.0772260 | + | 0.0107113i | ||||
\(946\) | 8.19615i | 0.266480i | ||||||||
\(947\) | −39.9302 | − | 39.9302i | −1.29756 | − | 1.29756i | −0.930001 | − | 0.367557i | \(-0.880194\pi\) |
−0.367557 | − | 0.930001i | \(-0.619806\pi\) | |||||||
\(948\) | −10.8131 | − | 20.8894i | −0.351195 | − | 0.678456i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 15.8037i | − | 0.512739i | ||||||
\(951\) | 2.91649 | − | 9.17604i | 0.0945735 | − | 0.297553i | ||||
\(952\) | −3.99374 | −0.129438 | ||||||||
\(953\) | −6.54349 | −0.211964 | −0.105982 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105982 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(954\) | 26.6555 | − | 4.57337i | 0.863005 | − | 0.148068i | ||||
\(955\) | −2.45646 | − | 2.45646i | −0.0794893 | − | 0.0794893i | ||||
\(956\) | 6.08236 | + | 6.08236i | 0.196718 | + | 0.196718i | ||||
\(957\) | 19.1955 | − | 60.3941i | 0.620502 | − | 1.95226i | ||||
\(958\) | 35.8276 | 1.15754 | ||||||||
\(959\) | −7.59905 | −0.245386 | ||||||||
\(960\) | 1.00034 | + | 0.317946i | 0.0322859 | + | 0.0102617i | ||||
\(961\) | − | 16.6095i | − | 0.535790i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.65478 | + | 5.41275i | 0.246672 | + | 0.174423i | ||||
\(964\) | −4.34556 | − | 4.34556i | −0.139961 | − | 0.139961i | ||||
\(965\) | 6.87491i | 0.221311i | ||||||||
\(966\) | −1.13120 | − | 2.18531i | −0.0363958 | − | 0.0703113i | ||||
\(967\) | 10.8941 | + | 10.8941i | 0.350332 | + | 0.350332i | 0.860233 | − | 0.509901i | \(-0.170318\pi\) |
−0.509901 | + | 0.860233i | \(0.670318\pi\) | |||||||
\(968\) | 4.70951 | − | 4.70951i | 0.151369 | − | 0.151369i | ||||
\(969\) | −29.5470 | − | 9.39114i | −0.949187 | − | 0.301687i | ||||
\(970\) | 6.74915 | − | 6.74915i | 0.216702 | − | 0.216702i | ||||
\(971\) | 2.39332i | 0.0768053i | 0.999262 | + | 0.0384027i | \(0.0122270\pi\) | ||||
−0.999262 | + | 0.0384027i | \(0.987773\pi\) | |||||||
\(972\) | 10.6633 | − | 11.3708i | 0.342025 | − | 0.364717i | ||||
\(973\) | 2.02630 | − | 2.02630i | 0.0649602 | − | 0.0649602i | ||||
\(974\) | 6.72951 | 0.215628 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.13061 | 0.260255 | ||||||||
\(977\) | −23.8091 | + | 23.8091i | −0.761722 | + | 0.761722i | −0.976633 | − | 0.214912i | \(-0.931054\pi\) |
0.214912 | + | 0.976633i | \(0.431054\pi\) | |||||||
\(978\) | −4.18452 | − | 8.08388i | −0.133806 | − | 0.258494i | ||||
\(979\) | 27.5154i | 0.879396i | ||||||||
\(980\) | −2.75140 | + | 2.75140i | −0.0878902 | + | 0.0878902i | ||||
\(981\) | 3.82191 | − | 0.655736i | 0.122024 | − | 0.0209360i | ||||
\(982\) | 21.0816 | − | 21.0816i | 0.672740 | − | 0.672740i | ||||
\(983\) | 26.5732 | + | 26.5732i | 0.847553 | + | 0.847553i | 0.989827 | − | 0.142274i | \(-0.0454415\pi\) |
−0.142274 | + | 0.989827i | \(0.545442\pi\) | |||||||
\(984\) | 13.6421 | − | 7.06166i | 0.434894 | − | 0.225117i | ||||
\(985\) | 2.83810i | 0.0904293i | ||||||||
\(986\) | −32.3034 | − | 32.3034i | −1.02875 | − | 1.02875i | ||||
\(987\) | 9.49485 | − | 4.91490i | 0.302225 | − | 0.156443i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.64054i | 0.115762i | ||||||||
\(990\) | 1.29198 | + | 7.53018i | 0.0410617 | + | 0.239325i | ||||
\(991\) | 21.7196 | 0.689947 | 0.344974 | − | 0.938612i | \(-0.387888\pi\) | ||||
0.344974 | + | 0.938612i | \(0.387888\pi\) | |||||||
\(992\) | −3.79348 | −0.120443 | ||||||||
\(993\) | −32.6058 | − | 10.3633i | −1.03471 | − | 0.328871i | ||||
\(994\) | 5.61349 | + | 5.61349i | 0.178049 | + | 0.178049i | ||||
\(995\) | −5.52906 | − | 5.52906i | −0.175283 | − | 0.175283i | ||||
\(996\) | 2.32724 | + | 0.739683i | 0.0737413 | + | 0.0234377i | ||||
\(997\) | −11.5522 | −0.365862 | −0.182931 | − | 0.983126i | \(-0.558559\pi\) | ||||
−0.182931 | + | 0.983126i | \(0.558559\pi\) | |||||||
\(998\) | −36.1314 | −1.14372 | ||||||||
\(999\) | −18.4248 | − | 24.3589i | −0.582935 | − | 0.770683i |
(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 | 1014.2.g.d.437.5 | 16 | ||
3.2 | odd | 2 | inner | 1014.2.g.d.437.1 | 16 | ||
13.5 | odd | 4 | inner | 1014.2.g.d.239.1 | 16 | ||
13.7 | odd | 12 | 78.2.k.a.41.4 | yes | 16 | ||
13.8 | odd | 4 | 1014.2.g.c.239.5 | 16 | |||
13.10 | even | 6 | 78.2.k.a.59.2 | yes | 16 | ||
13.12 | even | 2 | 1014.2.g.c.437.1 | 16 | |||
39.5 | even | 4 | inner | 1014.2.g.d.239.5 | 16 | ||
39.8 | even | 4 | 1014.2.g.c.239.1 | 16 | |||
39.20 | even | 12 | 78.2.k.a.41.2 | ✓ | 16 | ||
39.23 | odd | 6 | 78.2.k.a.59.4 | yes | 16 | ||
39.38 | odd | 2 | 1014.2.g.c.437.5 | 16 | |||
52.7 | even | 12 | 624.2.cn.d.353.1 | 16 | |||
52.23 | odd | 6 | 624.2.cn.d.449.2 | 16 | |||
156.23 | even | 6 | 624.2.cn.d.449.1 | 16 | |||
156.59 | odd | 12 | 624.2.cn.d.353.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.k.a.41.2 | ✓ | 16 | 39.20 | even | 12 | ||
78.2.k.a.41.4 | yes | 16 | 13.7 | odd | 12 | ||
78.2.k.a.59.2 | yes | 16 | 13.10 | even | 6 | ||
78.2.k.a.59.4 | yes | 16 | 39.23 | odd | 6 | ||
624.2.cn.d.353.1 | 16 | 52.7 | even | 12 | |||
624.2.cn.d.353.2 | 16 | 156.59 | odd | 12 | |||
624.2.cn.d.449.1 | 16 | 156.23 | even | 6 | |||
624.2.cn.d.449.2 | 16 | 52.23 | odd | 6 | |||
1014.2.g.c.239.1 | 16 | 39.8 | even | 4 | |||
1014.2.g.c.239.5 | 16 | 13.8 | odd | 4 | |||
1014.2.g.c.437.1 | 16 | 13.12 | even | 2 | |||
1014.2.g.c.437.5 | 16 | 39.38 | odd | 2 | |||
1014.2.g.d.239.1 | 16 | 13.5 | odd | 4 | inner | ||
1014.2.g.d.239.5 | 16 | 39.5 | even | 4 | inner | ||
1014.2.g.d.437.1 | 16 | 3.2 | odd | 2 | inner | ||
1014.2.g.d.437.5 | 16 | 1.1 | even | 1 | trivial |