Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.6498455769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 445.4 | ||
Root | \(-0.186817 - 0.323577i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.445 |
Dual form | 546.2.k.d.373.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.651388 | + | 1.12824i | 0.291309 | + | 0.504563i | 0.974120 | − | 0.226033i | \(-0.0725757\pi\) |
−0.682810 | + | 0.730596i | \(0.739242\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | 2.21184 | + | 1.45181i | 0.835997 | + | 0.548734i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.30278 | 0.411974 | ||||||||
\(11\) | 2.11879 | 0.638839 | 0.319419 | − | 0.947613i | \(-0.396512\pi\) | ||||
0.319419 | + | 0.947613i | \(0.396512\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 0.0315412 | + | 3.60541i | 0.00874794 | + | 0.999962i | ||||
\(14\) | 2.36323 | − | 1.18960i | 0.631599 | − | 0.317935i | ||||
\(15\) | 0.651388 | + | 1.12824i | 0.168188 | + | 0.291309i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.243381 | + | 0.421549i | 0.0590286 | + | 0.102241i | 0.894030 | − | 0.448008i | \(-0.147866\pi\) |
−0.835001 | + | 0.550248i | \(0.814533\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −6.27630 | −1.43988 | −0.719941 | − | 0.694035i | \(-0.755831\pi\) | ||||
−0.719941 | + | 0.694035i | \(0.755831\pi\) | |||||||
\(20\) | 0.651388 | − | 1.12824i | 0.145655 | − | 0.252281i | ||||
\(21\) | 2.21184 | + | 1.45181i | 0.482663 | + | 0.316812i | ||||
\(22\) | 1.05939 | − | 1.83493i | 0.225864 | − | 0.391207i | ||||
\(23\) | 2.39477 | − | 4.14786i | 0.499344 | − | 0.864889i | −0.500656 | − | 0.865646i | \(-0.666908\pi\) |
1.00000 | 0.000757495i | \(0.000241118\pi\) | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.65139 | − | 2.86029i | 0.330278 | − | 0.572058i | ||||
\(26\) | 3.13815 | + | 1.77539i | 0.615442 | + | 0.348183i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.151388 | − | 2.64142i | 0.0286096 | − | 0.499181i | ||||
\(29\) | 1.74338 | + | 3.01962i | 0.323738 | + | 0.560730i | 0.981256 | − | 0.192708i | \(-0.0617271\pi\) |
−0.657518 | + | 0.753439i | \(0.728394\pi\) | |||||||
\(30\) | 1.30278 | 0.237853 | ||||||||
\(31\) | 2.24338 | − | 3.88565i | 0.402923 | − | 0.697883i | −0.591154 | − | 0.806559i | \(-0.701328\pi\) |
0.994077 | + | 0.108675i | \(0.0346609\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.11879 | 0.368834 | ||||||||
\(34\) | 0.486762 | 0.0834790 | ||||||||
\(35\) | −0.197224 | + | 3.44117i | −0.0333370 | + | 0.581664i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 0.578756 | − | 1.00243i | 0.0951468 | − | 0.164799i | −0.814523 | − | 0.580131i | \(-0.803001\pi\) |
0.909670 | + | 0.415332i | \(0.136335\pi\) | |||||||
\(38\) | −3.13815 | + | 5.43544i | −0.509075 | + | 0.881744i | ||||
\(39\) | 0.0315412 | + | 3.60541i | 0.00505063 | + | 0.577328i | ||||
\(40\) | −0.651388 | − | 1.12824i | −0.102993 | − | 0.178390i | ||||
\(41\) | −6.31845 | − | 10.9439i | −0.986776 | − | 1.70915i | −0.633762 | − | 0.773528i | \(-0.718490\pi\) |
−0.353014 | − | 0.935618i | \(-0.614843\pi\) | |||||||
\(42\) | 2.36323 | − | 1.18960i | 0.364654 | − | 0.183560i | ||||
\(43\) | −4.01356 | + | 6.95169i | −0.612062 | + | 1.06012i | 0.378831 | + | 0.925466i | \(0.376326\pi\) |
−0.990892 | + | 0.134656i | \(0.957007\pi\) | |||||||
\(44\) | −1.05939 | − | 1.83493i | −0.159710 | − | 0.276625i | ||||
\(45\) | 0.651388 | + | 1.12824i | 0.0971032 | + | 0.168188i | ||||
\(46\) | −2.39477 | − | 4.14786i | −0.353089 | − | 0.611569i | ||||
\(47\) | −3.98570 | − | 6.90344i | −0.581375 | − | 1.00697i | −0.995317 | − | 0.0966674i | \(-0.969182\pi\) |
0.413942 | − | 0.910303i | \(-0.364152\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 2.78447 | + | 6.42236i | 0.397782 | + | 0.917480i | ||||
\(50\) | −1.65139 | − | 2.86029i | −0.233542 | − | 0.404506i | ||||
\(51\) | 0.243381 | + | 0.421549i | 0.0340802 | + | 0.0590286i | ||||
\(52\) | 3.10661 | − | 1.83002i | 0.430809 | − | 0.253778i | ||||
\(53\) | 4.29060 | − | 7.43153i | 0.589359 | − | 1.02080i | −0.404958 | − | 0.914335i | \(-0.632714\pi\) |
0.994317 | − | 0.106464i | \(-0.0339528\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 1.38015 | + | 2.39050i | 0.186100 | + | 0.322334i | ||||
\(56\) | −2.21184 | − | 1.45181i | −0.295570 | − | 0.194007i | ||||
\(57\) | −6.27630 | −0.831316 | ||||||||
\(58\) | 3.48676 | 0.457834 | ||||||||
\(59\) | 4.57507 | + | 7.92425i | 0.595623 | + | 1.03165i | 0.993459 | + | 0.114193i | \(0.0364281\pi\) |
−0.397836 | + | 0.917457i | \(0.630239\pi\) | |||||||
\(60\) | 0.651388 | − | 1.12824i | 0.0840938 | − | 0.145655i | ||||
\(61\) | −10.1846 | −1.30401 | −0.652004 | − | 0.758216i | \(-0.726071\pi\) | ||||
−0.652004 | + | 0.758216i | \(0.726071\pi\) | |||||||
\(62\) | −2.24338 | − | 3.88565i | −0.284910 | − | 0.493478i | ||||
\(63\) | 2.21184 | + | 1.45181i | 0.278666 | + | 0.182911i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.04721 | + | 2.38411i | −0.501995 | + | 0.295712i | ||||
\(66\) | 1.05939 | − | 1.83493i | 0.130402 | − | 0.225864i | ||||
\(67\) | −3.35848 | −0.410304 | −0.205152 | − | 0.978730i | \(-0.565769\pi\) | ||||
−0.205152 | + | 0.978730i | \(0.565769\pi\) | |||||||
\(68\) | 0.243381 | − | 0.421549i | 0.0295143 | − | 0.0511203i | ||||
\(69\) | 2.39477 | − | 4.14786i | 0.288296 | − | 0.499344i | ||||
\(70\) | 2.88153 | + | 1.89139i | 0.344409 | + | 0.226064i | ||||
\(71\) | 1.46740 | − | 2.54161i | 0.174148 | − | 0.301634i | −0.765718 | − | 0.643177i | \(-0.777616\pi\) |
0.939866 | + | 0.341543i | \(0.110949\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.09337 | + | 14.0181i | −0.947257 | + | 1.64070i | −0.196090 | + | 0.980586i | \(0.562825\pi\) |
−0.751167 | + | 0.660112i | \(0.770509\pi\) | |||||||
\(74\) | −0.578756 | − | 1.00243i | −0.0672790 | − | 0.116531i | ||||
\(75\) | 1.65139 | − | 2.86029i | 0.190686 | − | 0.330278i | ||||
\(76\) | 3.13815 | + | 5.43544i | 0.359971 | + | 0.623487i | ||||
\(77\) | 4.68642 | + | 3.07609i | 0.534067 | + | 0.350553i | ||||
\(78\) | 3.13815 | + | 1.77539i | 0.355326 | + | 0.201023i | ||||
\(79\) | −7.16738 | − | 12.4143i | −0.806393 | − | 1.39671i | −0.915346 | − | 0.402667i | \(-0.868083\pi\) |
0.108953 | − | 0.994047i | \(-0.465250\pi\) | |||||||
\(80\) | −1.30278 | −0.145655 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.6369 | −1.39551 | ||||||||
\(83\) | 3.48676 | 0.382722 | 0.191361 | − | 0.981520i | \(-0.438710\pi\) | ||||
0.191361 | + | 0.981520i | \(0.438710\pi\) | |||||||
\(84\) | 0.151388 | − | 2.64142i | 0.0165178 | − | 0.288202i | ||||
\(85\) | −0.317071 | + | 0.549183i | −0.0343912 | + | 0.0595673i | ||||
\(86\) | 4.01356 | + | 6.95169i | 0.432793 | + | 0.749620i | ||||
\(87\) | 1.74338 | + | 3.01962i | 0.186910 | + | 0.323738i | ||||
\(88\) | −2.11879 | −0.225864 | ||||||||
\(89\) | −4.69860 | + | 8.13822i | −0.498051 | + | 0.862649i | −0.999997 | − | 0.00224923i | \(-0.999284\pi\) |
0.501947 | + | 0.864899i | \(0.332617\pi\) | |||||||
\(90\) | 1.30278 | 0.137325 | ||||||||
\(91\) | −5.16463 | + | 8.02039i | −0.541400 | + | 0.840765i | ||||
\(92\) | −4.78954 | −0.499344 | ||||||||
\(93\) | 2.24338 | − | 3.88565i | 0.232628 | − | 0.402923i | ||||
\(94\) | −7.97141 | −0.822188 | ||||||||
\(95\) | −4.08831 | − | 7.08115i | −0.419451 | − | 0.726511i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 0.698602 | − | 1.21001i | 0.0709323 | − | 0.122858i | −0.828378 | − | 0.560170i | \(-0.810736\pi\) |
0.899310 | + | 0.437311i | \(0.144069\pi\) | |||||||
\(98\) | 6.95416 | + | 0.799757i | 0.702477 | + | 0.0807876i | ||||
\(99\) | 2.11879 | 0.212946 | ||||||||
\(100\) | −3.30278 | −0.330278 | ||||||||
\(101\) | −6.03449 | −0.600454 | −0.300227 | − | 0.953868i | \(-0.597062\pi\) | ||||
−0.300227 | + | 0.953868i | \(0.597062\pi\) | |||||||
\(102\) | 0.486762 | 0.0481966 | ||||||||
\(103\) | 5.64770 | + | 9.78210i | 0.556484 | + | 0.963859i | 0.997786 | + | 0.0665006i | \(0.0211834\pi\) |
−0.441302 | + | 0.897359i | \(0.645483\pi\) | |||||||
\(104\) | −0.0315412 | − | 3.60541i | −0.00309287 | − | 0.353540i | ||||
\(105\) | −0.197224 | + | 3.44117i | −0.0192471 | + | 0.335824i | ||||
\(106\) | −4.29060 | − | 7.43153i | −0.416739 | − | 0.721814i | ||||
\(107\) | 7.01462 | − | 12.1497i | 0.678128 | − | 1.17455i | −0.297415 | − | 0.954748i | \(-0.596125\pi\) |
0.975544 | − | 0.219805i | \(-0.0705420\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 2.76031 | 0.263185 | ||||||||
\(111\) | 0.578756 | − | 1.00243i | 0.0549331 | − | 0.0951468i | ||||
\(112\) | −2.36323 | + | 1.18960i | −0.223304 | + | 0.112407i | ||||
\(113\) | 3.56552 | − | 6.17566i | 0.335416 | − | 0.580957i | −0.648149 | − | 0.761514i | \(-0.724457\pi\) |
0.983565 | + | 0.180557i | \(0.0577899\pi\) | |||||||
\(114\) | −3.13815 | + | 5.43544i | −0.293915 | + | 0.509075i | ||||
\(115\) | 6.23969 | 0.581854 | ||||||||
\(116\) | 1.74338 | − | 3.01962i | 0.161869 | − | 0.280365i | ||||
\(117\) | 0.0315412 | + | 3.60541i | 0.00291598 | + | 0.333321i | ||||
\(118\) | 9.15014 | 0.842338 | ||||||||
\(119\) | −0.0736899 | + | 1.28574i | −0.00675514 | + | 0.117864i | ||||
\(120\) | −0.651388 | − | 1.12824i | −0.0594633 | − | 0.102993i | ||||
\(121\) | −6.51073 | −0.591885 | ||||||||
\(122\) | −5.09231 | + | 8.82015i | −0.461036 | + | 0.798538i | ||||
\(123\) | −6.31845 | − | 10.9439i | −0.569715 | − | 0.986776i | ||||
\(124\) | −4.48676 | −0.402923 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | 2.36323 | − | 1.18960i | 0.210533 | − | 0.105978i | ||||
\(127\) | 2.59305 | + | 4.49130i | 0.230096 | + | 0.398538i | 0.957836 | − | 0.287315i | \(-0.0927626\pi\) |
−0.727740 | + | 0.685853i | \(0.759429\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −4.01356 | + | 6.95169i | −0.353374 | + | 0.612062i | ||||
\(130\) | 0.0410911 | + | 4.69704i | 0.00360392 | + | 0.411958i | ||||
\(131\) | 4.03186 | + | 6.98339i | 0.352265 | + | 0.610142i | 0.986646 | − | 0.162879i | \(-0.0520781\pi\) |
−0.634381 | + | 0.773021i | \(0.718745\pi\) | |||||||
\(132\) | −1.05939 | − | 1.83493i | −0.0922085 | − | 0.159710i | ||||
\(133\) | −13.8822 | − | 9.11202i | −1.20374 | − | 0.790112i | ||||
\(134\) | −1.67924 | + | 2.90853i | −0.145064 | + | 0.251259i | ||||
\(135\) | 0.651388 | + | 1.12824i | 0.0560625 | + | 0.0971032i | ||||
\(136\) | −0.243381 | − | 0.421549i | −0.0208698 | − | 0.0361475i | ||||
\(137\) | 3.39583 | + | 5.88174i | 0.290125 | + | 0.502511i | 0.973839 | − | 0.227239i | \(-0.0729698\pi\) |
−0.683714 | + | 0.729750i | \(0.739636\pi\) | |||||||
\(138\) | −2.39477 | − | 4.14786i | −0.203856 | − | 0.353089i | ||||
\(139\) | 6.45522 | − | 11.1808i | 0.547525 | − | 0.948341i | −0.450919 | − | 0.892565i | \(-0.648904\pi\) |
0.998443 | − | 0.0557755i | \(-0.0177631\pi\) | |||||||
\(140\) | 3.07876 | − | 1.54979i | 0.260202 | − | 0.130981i | ||||
\(141\) | −3.98570 | − | 6.90344i | −0.335657 | − | 0.581375i | ||||
\(142\) | −1.46740 | − | 2.54161i | −0.123142 | − | 0.213287i | ||||
\(143\) | 0.0668291 | + | 7.63911i | 0.00558853 | + | 0.638814i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −2.27123 | + | 3.93389i | −0.188616 | + | 0.326692i | ||||
\(146\) | 8.09337 | + | 14.0181i | 0.669812 | + | 1.16015i | ||||
\(147\) | 2.78447 | + | 6.42236i | 0.229659 | + | 0.529707i | ||||
\(148\) | −1.15751 | −0.0951468 | ||||||||
\(149\) | −23.3640 | −1.91405 | −0.957026 | − | 0.290001i | \(-0.906345\pi\) | ||||
−0.957026 | + | 0.290001i | \(0.906345\pi\) | |||||||
\(150\) | −1.65139 | − | 2.86029i | −0.134835 | − | 0.233542i | ||||
\(151\) | −2.93692 | + | 5.08689i | −0.239003 | + | 0.413965i | −0.960428 | − | 0.278527i | \(-0.910154\pi\) |
0.721425 | + | 0.692492i | \(0.243487\pi\) | |||||||
\(152\) | 6.27630 | 0.509075 | ||||||||
\(153\) | 0.243381 | + | 0.421549i | 0.0196762 | + | 0.0340802i | ||||
\(154\) | 5.00718 | − | 2.52052i | 0.403490 | − | 0.203109i | ||||
\(155\) | 5.84524 | 0.469501 | ||||||||
\(156\) | 3.10661 | − | 1.83002i | 0.248728 | − | 0.146519i | ||||
\(157\) | −3.12248 | + | 5.40829i | −0.249201 | + | 0.431628i | −0.963304 | − | 0.268412i | \(-0.913501\pi\) |
0.714104 | + | 0.700040i | \(0.246835\pi\) | |||||||
\(158\) | −14.3348 | −1.14041 | ||||||||
\(159\) | 4.29060 | − | 7.43153i | 0.340266 | − | 0.589359i | ||||
\(160\) | −0.651388 | + | 1.12824i | −0.0514967 | + | 0.0891950i | ||||
\(161\) | 11.3188 | − | 5.69765i | 0.892044 | − | 0.449037i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −2.60767 | −0.204248 | −0.102124 | − | 0.994772i | \(-0.532564\pi\) | ||||
−0.102124 | + | 0.994772i | \(0.532564\pi\) | |||||||
\(164\) | −6.31845 | + | 10.9439i | −0.493388 | + | 0.854573i | ||||
\(165\) | 1.38015 | + | 2.39050i | 0.107445 | + | 0.186100i | ||||
\(166\) | 1.74338 | − | 3.01962i | 0.135313 | − | 0.234368i | ||||
\(167\) | −3.45416 | − | 5.98279i | −0.267291 | − | 0.462962i | 0.700870 | − | 0.713289i | \(-0.252795\pi\) |
−0.968161 | + | 0.250327i | \(0.919462\pi\) | |||||||
\(168\) | −2.21184 | − | 1.45181i | −0.170647 | − | 0.112010i | ||||
\(169\) | −12.9980 | + | 0.227438i | −0.999847 | + | 0.0174952i | ||||
\(170\) | 0.317071 | + | 0.549183i | 0.0243182 | + | 0.0421204i | ||||
\(171\) | −6.27630 | −0.479961 | ||||||||
\(172\) | 8.02712 | 0.612062 | ||||||||
\(173\) | −7.72710 | −0.587480 | −0.293740 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293740 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(174\) | 3.48676 | 0.264331 | ||||||||
\(175\) | 7.80521 | − | 3.92899i | 0.590019 | − | 0.297004i | ||||
\(176\) | −1.05939 | + | 1.83493i | −0.0798549 | + | 0.138313i | ||||
\(177\) | 4.57507 | + | 7.92425i | 0.343883 | + | 0.595623i | ||||
\(178\) | 4.69860 | + | 8.13822i | 0.352175 | + | 0.609985i | ||||
\(179\) | 19.1508 | 1.43140 | 0.715698 | − | 0.698410i | \(-0.246109\pi\) | ||||
0.715698 | + | 0.698410i | \(0.246109\pi\) | |||||||
\(180\) | 0.651388 | − | 1.12824i | 0.0485516 | − | 0.0840938i | ||||
\(181\) | 13.0972 | 0.973506 | 0.486753 | − | 0.873540i | \(-0.338181\pi\) | ||||
0.486753 | + | 0.873540i | \(0.338181\pi\) | |||||||
\(182\) | 4.36355 | + | 8.48289i | 0.323448 | + | 0.628794i | ||||
\(183\) | −10.1846 | −0.752869 | ||||||||
\(184\) | −2.39477 | + | 4.14786i | −0.176545 | + | 0.305784i | ||||
\(185\) | 1.50798 | 0.110869 | ||||||||
\(186\) | −2.24338 | − | 3.88565i | −0.164493 | − | 0.284910i | ||||
\(187\) | 0.515673 | + | 0.893172i | 0.0377098 | + | 0.0653152i | ||||
\(188\) | −3.98570 | + | 6.90344i | −0.290687 | + | 0.503485i | ||||
\(189\) | 2.21184 | + | 1.45181i | 0.160888 | + | 0.105604i | ||||
\(190\) | −8.17661 | −0.593194 | ||||||||
\(191\) | −11.4889 | −0.831306 | −0.415653 | − | 0.909523i | \(-0.636447\pi\) | ||||
−0.415653 | + | 0.909523i | \(0.636447\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −0.276300 | −0.0198885 | −0.00994426 | − | 0.999951i | \(-0.503165\pi\) | ||||
−0.00994426 | + | 0.999951i | \(0.503165\pi\) | |||||||
\(194\) | −0.698602 | − | 1.21001i | −0.0501567 | − | 0.0868740i | ||||
\(195\) | −4.04721 | + | 2.38411i | −0.289827 | + | 0.170730i | ||||
\(196\) | 4.16969 | − | 5.62260i | 0.297835 | − | 0.401615i | ||||
\(197\) | −6.63552 | − | 11.4931i | −0.472761 | − | 0.818846i | 0.526753 | − | 0.850019i | \(-0.323409\pi\) |
−0.999514 | + | 0.0311721i | \(0.990076\pi\) | |||||||
\(198\) | 1.05939 | − | 1.83493i | 0.0752879 | − | 0.130402i | ||||
\(199\) | −9.51093 | − | 16.4734i | −0.674212 | − | 1.16777i | −0.976699 | − | 0.214616i | \(-0.931150\pi\) |
0.302487 | − | 0.953154i | \(-0.402183\pi\) | |||||||
\(200\) | −1.65139 | + | 2.86029i | −0.116771 | + | 0.202253i | ||||
\(201\) | −3.35848 | −0.236889 | ||||||||
\(202\) | −3.01725 | + | 5.22602i | −0.212293 | + | 0.367702i | ||||
\(203\) | −0.527853 | + | 9.20999i | −0.0370480 | + | 0.646415i | ||||
\(204\) | 0.243381 | − | 0.421549i | 0.0170401 | − | 0.0295143i | ||||
\(205\) | 8.23152 | − | 14.2574i | 0.574914 | − | 0.995781i | ||||
\(206\) | 11.2954 | 0.786988 | ||||||||
\(207\) | 2.39477 | − | 4.14786i | 0.166448 | − | 0.288296i | ||||
\(208\) | −3.13815 | − | 1.77539i | −0.217592 | − | 0.123101i | ||||
\(209\) | −13.2982 | −0.919853 | ||||||||
\(210\) | 2.88153 | + | 1.89139i | 0.198845 | + | 0.130518i | ||||
\(211\) | −1.98750 | − | 3.44245i | −0.136825 | − | 0.236988i | 0.789468 | − | 0.613792i | \(-0.210357\pi\) |
−0.926293 | + | 0.376804i | \(0.877023\pi\) | |||||||
\(212\) | −8.58119 | −0.589359 | ||||||||
\(213\) | 1.46740 | − | 2.54161i | 0.100545 | − | 0.174148i | ||||
\(214\) | −7.01462 | − | 12.1497i | −0.479509 | − | 0.830534i | ||||
\(215\) | −10.4575 | −0.713198 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.6032 | − | 5.33746i | 0.719795 | − | 0.362331i | ||||
\(218\) | 5.50000 | + | 9.52628i | 0.372507 | + | 0.645201i | ||||
\(219\) | −8.09337 | + | 14.0181i | −0.546899 | + | 0.947257i | ||||
\(220\) | 1.38015 | − | 2.39050i | 0.0930499 | − | 0.161167i | ||||
\(221\) | −1.51218 | + | 0.890786i | −0.101720 | + | 0.0599207i | ||||
\(222\) | −0.578756 | − | 1.00243i | −0.0388435 | − | 0.0672790i | ||||
\(223\) | 9.58013 | + | 16.5933i | 0.641533 | + | 1.11117i | 0.985091 | + | 0.172036i | \(0.0550347\pi\) |
−0.343557 | + | 0.939132i | \(0.611632\pi\) | |||||||
\(224\) | −0.151388 | + | 2.64142i | −0.0101150 | + | 0.176487i | ||||
\(225\) | 1.65139 | − | 2.86029i | 0.110093 | − | 0.190686i | ||||
\(226\) | −3.56552 | − | 6.17566i | −0.237175 | − | 0.410799i | ||||
\(227\) | 0.591256 | + | 1.02409i | 0.0392430 | + | 0.0679709i | 0.884980 | − | 0.465629i | \(-0.154172\pi\) |
−0.845737 | + | 0.533600i | \(0.820839\pi\) | |||||||
\(228\) | 3.13815 | + | 5.43544i | 0.207829 | + | 0.359971i | ||||
\(229\) | 7.51599 | + | 13.0181i | 0.496671 | + | 0.860259i | 0.999993 | − | 0.00383994i | \(-0.00122229\pi\) |
−0.503322 | + | 0.864099i | \(0.667889\pi\) | |||||||
\(230\) | 3.11985 | − | 5.40373i | 0.205717 | − | 0.356312i | ||||
\(231\) | 4.68642 | + | 3.07609i | 0.308344 | + | 0.202392i | ||||
\(232\) | −1.74338 | − | 3.01962i | −0.114459 | − | 0.198248i | ||||
\(233\) | −2.59706 | − | 4.49824i | −0.170139 | − | 0.294689i | 0.768329 | − | 0.640055i | \(-0.221088\pi\) |
−0.938468 | + | 0.345365i | \(0.887755\pi\) | |||||||
\(234\) | 3.13815 | + | 1.77539i | 0.205147 | + | 0.116061i | ||||
\(235\) | 5.19248 | − | 8.99364i | 0.338720 | − | 0.586680i | ||||
\(236\) | 4.57507 | − | 7.92425i | 0.297812 | − | 0.515825i | ||||
\(237\) | −7.16738 | − | 12.4143i | −0.465571 | − | 0.806393i | ||||
\(238\) | 1.07664 | + | 0.706688i | 0.0697882 | + | 0.0458078i | ||||
\(239\) | 25.3978 | 1.64285 | 0.821425 | − | 0.570317i | \(-0.193179\pi\) | ||||
0.821425 | + | 0.570317i | \(0.193179\pi\) | |||||||
\(240\) | −1.30278 | −0.0840938 | ||||||||
\(241\) | 5.92875 | + | 10.2689i | 0.381904 | + | 0.661477i | 0.991334 | − | 0.131362i | \(-0.0419351\pi\) |
−0.609430 | + | 0.792840i | \(0.708602\pi\) | |||||||
\(242\) | −3.25537 | + | 5.63846i | −0.209263 | + | 0.362454i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.09231 | + | 8.82015i | 0.326002 | + | 0.564652i | ||||
\(245\) | −5.43217 | + | 7.32499i | −0.347049 | + | 0.467977i | ||||
\(246\) | −12.6369 | −0.805699 | ||||||||
\(247\) | −0.197962 | − | 22.6287i | −0.0125960 | − | 1.43983i | ||||
\(248\) | −2.24338 | + | 3.88565i | −0.142455 | + | 0.246739i | ||||
\(249\) | 3.48676 | 0.220965 | ||||||||
\(250\) | 5.40833 | − | 9.36750i | 0.342053 | − | 0.592453i | ||||
\(251\) | 10.7397 | − | 18.6017i | 0.677883 | − | 1.17413i | −0.297734 | − | 0.954649i | \(-0.596231\pi\) |
0.975617 | − | 0.219480i | \(-0.0704359\pi\) | |||||||
\(252\) | 0.151388 | − | 2.64142i | 0.00953654 | − | 0.166394i | ||||
\(253\) | 5.07401 | − | 8.78844i | 0.319000 | − | 0.552525i | ||||
\(254\) | 5.18610 | 0.325405 | ||||||||
\(255\) | −0.317071 | + | 0.549183i | −0.0198558 | + | 0.0343912i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.42294 | − | 5.92871i | 0.213517 | − | 0.369823i | −0.739296 | − | 0.673381i | \(-0.764841\pi\) |
0.952813 | + | 0.303558i | \(0.0981747\pi\) | |||||||
\(258\) | 4.01356 | + | 6.95169i | 0.249873 | + | 0.432793i | ||||
\(259\) | 2.73546 | − | 1.37698i | 0.169973 | − | 0.0855613i | ||||
\(260\) | 4.08831 | + | 2.31294i | 0.253546 | + | 0.143442i | ||||
\(261\) | 1.74338 | + | 3.01962i | 0.107913 | + | 0.186910i | ||||
\(262\) | 8.06372 | 0.498178 | ||||||||
\(263\) | 15.4000 | 0.949602 | 0.474801 | − | 0.880093i | \(-0.342520\pi\) | ||||
0.474801 | + | 0.880093i | \(0.342520\pi\) | |||||||
\(264\) | −2.11879 | −0.130402 | ||||||||
\(265\) | 11.1794 | 0.686743 | ||||||||
\(266\) | −14.8323 | + | 7.46630i | −0.909428 | + | 0.457788i | ||||
\(267\) | −4.69860 | + | 8.13822i | −0.287550 | + | 0.498051i | ||||
\(268\) | 1.67924 | + | 2.90853i | 0.102576 | + | 0.177667i | ||||
\(269\) | 5.86566 | + | 10.1596i | 0.357636 | + | 0.619443i | 0.987565 | − | 0.157209i | \(-0.0502496\pi\) |
−0.629930 | + | 0.776652i | \(0.716916\pi\) | |||||||
\(270\) | 1.30278 | 0.0792844 | ||||||||
\(271\) | 13.0428 | − | 22.5908i | 0.792293 | − | 1.37229i | −0.132251 | − | 0.991216i | \(-0.542220\pi\) |
0.924544 | − | 0.381075i | \(-0.124446\pi\) | |||||||
\(272\) | −0.486762 | −0.0295143 | ||||||||
\(273\) | −5.16463 | + | 8.02039i | −0.312577 | + | 0.485416i | ||||
\(274\) | 6.79165 | 0.410299 | ||||||||
\(275\) | 3.49894 | − | 6.06035i | 0.210994 | − | 0.365453i | ||||
\(276\) | −4.78954 | −0.288296 | ||||||||
\(277\) | −11.7153 | − | 20.2916i | −0.703906 | − | 1.21920i | −0.967085 | − | 0.254454i | \(-0.918104\pi\) |
0.263179 | − | 0.964747i | \(-0.415229\pi\) | |||||||
\(278\) | −6.45522 | − | 11.1808i | −0.387158 | − | 0.670578i | ||||
\(279\) | 2.24338 | − | 3.88565i | 0.134308 | − | 0.232628i | ||||
\(280\) | 0.197224 | − | 3.44117i | 0.0117864 | − | 0.205649i | ||||
\(281\) | 6.15751 | 0.367326 | 0.183663 | − | 0.982989i | \(-0.441204\pi\) | ||||
0.183663 | + | 0.982989i | \(0.441204\pi\) | |||||||
\(282\) | −7.97141 | −0.474691 | ||||||||
\(283\) | 21.9323 | 1.30374 | 0.651870 | − | 0.758331i | \(-0.273985\pi\) | ||||
0.651870 | + | 0.758331i | \(0.273985\pi\) | |||||||
\(284\) | −2.93480 | −0.174148 | ||||||||
\(285\) | −4.08831 | − | 7.08115i | −0.242170 | − | 0.419451i | ||||
\(286\) | 6.64908 | + | 3.76168i | 0.393168 | + | 0.222433i | ||||
\(287\) | 1.91307 | − | 33.3793i | 0.112925 | − | 1.97032i | ||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 8.38153 | − | 14.5172i | 0.493031 | − | 0.853955i | ||||
\(290\) | 2.27123 | + | 3.93389i | 0.133371 | + | 0.231006i | ||||
\(291\) | 0.698602 | − | 1.21001i | 0.0409528 | − | 0.0709323i | ||||
\(292\) | 16.1867 | 0.947257 | ||||||||
\(293\) | −8.74075 | + | 15.1394i | −0.510640 | + | 0.884455i | 0.489284 | + | 0.872125i | \(0.337258\pi\) |
−0.999924 | + | 0.0123300i | \(0.996075\pi\) | |||||||
\(294\) | 6.95416 | + | 0.799757i | 0.405575 | + | 0.0466428i | ||||
\(295\) | −5.96029 | + | 10.3235i | −0.347021 | + | 0.601059i | ||||
\(296\) | −0.578756 | + | 1.00243i | −0.0336395 | + | 0.0582653i | ||||
\(297\) | 2.11879 | 0.122945 | ||||||||
\(298\) | −11.6820 | + | 20.2338i | −0.676720 | + | 1.17211i | ||||
\(299\) | 15.0303 | + | 8.50330i | 0.869224 | + | 0.491759i | ||||
\(300\) | −3.30278 | −0.190686 | ||||||||
\(301\) | −18.9699 | + | 9.54908i | −1.09341 | + | 0.550400i | ||||
\(302\) | 2.93692 | + | 5.08689i | 0.169001 | + | 0.292718i | ||||
\(303\) | −6.03449 | −0.346672 | ||||||||
\(304\) | 3.13815 | − | 5.43544i | 0.179985 | − | 0.311744i | ||||
\(305\) | −6.63414 | − | 11.4907i | −0.379870 | − | 0.657954i | ||||
\(306\) | 0.486762 | 0.0278263 | ||||||||
\(307\) | −12.0673 | −0.688718 | −0.344359 | − | 0.938838i | \(-0.611904\pi\) | ||||
−0.344359 | + | 0.938838i | \(0.611904\pi\) | |||||||
\(308\) | 0.320759 | − | 5.59660i | 0.0182769 | − | 0.318896i | ||||
\(309\) | 5.64770 | + | 9.78210i | 0.321286 | + | 0.556484i | ||||
\(310\) | 2.92262 | − | 5.06213i | 0.165994 | − | 0.287510i | ||||
\(311\) | 0.755881 | − | 1.30923i | 0.0428621 | − | 0.0742393i | −0.843798 | − | 0.536660i | \(-0.819686\pi\) |
0.886661 | + | 0.462421i | \(0.153019\pi\) | |||||||
\(312\) | −0.0315412 | − | 3.60541i | −0.00178567 | − | 0.204116i | ||||
\(313\) | −0.862908 | − | 1.49460i | −0.0487744 | − | 0.0844798i | 0.840607 | − | 0.541645i | \(-0.182198\pi\) |
−0.889382 | + | 0.457165i | \(0.848865\pi\) | |||||||
\(314\) | 3.12248 | + | 5.40829i | 0.176212 | + | 0.305207i | ||||
\(315\) | −0.197224 | + | 3.44117i | −0.0111123 | + | 0.193888i | ||||
\(316\) | −7.16738 | + | 12.4143i | −0.403197 | + | 0.698357i | ||||
\(317\) | −10.6520 | − | 18.4499i | −0.598278 | − | 1.03625i | −0.993075 | − | 0.117479i | \(-0.962519\pi\) |
0.394798 | − | 0.918768i | \(-0.370815\pi\) | |||||||
\(318\) | −4.29060 | − | 7.43153i | −0.240605 | − | 0.416739i | ||||
\(319\) | 3.69386 | + | 6.39795i | 0.206816 | + | 0.358216i | ||||
\(320\) | 0.651388 | + | 1.12824i | 0.0364137 | + | 0.0630704i | ||||
\(321\) | 7.01462 | − | 12.1497i | 0.391518 | − | 0.678128i | ||||
\(322\) | 0.725078 | − | 12.6512i | 0.0404070 | − | 0.705022i | ||||
\(323\) | −1.52753 | − | 2.64576i | −0.0849942 | − | 0.147214i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 10.3646 | + | 5.86372i | 0.574925 | + | 0.325261i | ||||
\(326\) | −1.30383 | + | 2.25831i | −0.0722126 | + | 0.125076i | ||||
\(327\) | −5.50000 | + | 9.52628i | −0.304151 | + | 0.526804i | ||||
\(328\) | 6.31845 | + | 10.9439i | 0.348878 | + | 0.604274i | ||||
\(329\) | 1.20677 | − | 21.0558i | 0.0665316 | − | 1.16084i | ||||
\(330\) | 2.76031 | 0.151950 | ||||||||
\(331\) | 16.4338 | 0.903284 | 0.451642 | − | 0.892199i | \(-0.350838\pi\) | ||||
0.451642 | + | 0.892199i | \(0.350838\pi\) | |||||||
\(332\) | −1.74338 | − | 3.01962i | −0.0956805 | − | 0.165723i | ||||
\(333\) | 0.578756 | − | 1.00243i | 0.0317156 | − | 0.0549331i | ||||
\(334\) | −6.90833 | −0.378007 | ||||||||
\(335\) | −2.18767 | − | 3.78916i | −0.119525 | − | 0.207024i | ||||
\(336\) | −2.36323 | + | 1.18960i | −0.128925 | + | 0.0648981i | ||||
\(337\) | −12.9178 | −0.703678 | −0.351839 | − | 0.936060i | \(-0.614444\pi\) | ||||
−0.351839 | + | 0.936060i | \(0.614444\pi\) | |||||||
\(338\) | −6.30204 | + | 11.3703i | −0.342786 | + | 0.618464i | ||||
\(339\) | 3.56552 | − | 6.17566i | 0.193652 | − | 0.335416i | ||||
\(340\) | 0.634142 | 0.0343912 | ||||||||
\(341\) | 4.75325 | − | 8.23287i | 0.257403 | − | 0.445835i | ||||
\(342\) | −3.13815 | + | 5.43544i | −0.169692 | + | 0.293915i | ||||
\(343\) | −3.16527 | + | 18.2478i | −0.170908 | + | 0.985287i | ||||
\(344\) | 4.01356 | − | 6.95169i | 0.216397 | − | 0.374810i | ||||
\(345\) | 6.23969 | 0.335934 | ||||||||
\(346\) | −3.86355 | + | 6.69186i | −0.207706 | + | 0.359757i | ||||
\(347\) | 8.01936 | + | 13.8899i | 0.430502 | + | 0.745651i | 0.996917 | − | 0.0784693i | \(-0.0250033\pi\) |
−0.566415 | + | 0.824120i | \(0.691670\pi\) | |||||||
\(348\) | 1.74338 | − | 3.01962i | 0.0934550 | − | 0.161869i | ||||
\(349\) | −3.81951 | − | 6.61558i | −0.204453 | − | 0.354124i | 0.745505 | − | 0.666500i | \(-0.232208\pi\) |
−0.949958 | + | 0.312376i | \(0.898875\pi\) | |||||||
\(350\) | 0.500000 | − | 8.72401i | 0.0267261 | − | 0.466318i | ||||
\(351\) | 0.0315412 | + | 3.60541i | 0.00168354 | + | 0.192443i | ||||
\(352\) | 1.05939 | + | 1.83493i | 0.0564659 | + | 0.0978018i | ||||
\(353\) | −32.3911 | −1.72400 | −0.862002 | − | 0.506904i | \(-0.830790\pi\) | ||||
−0.862002 | + | 0.506904i | \(0.830790\pi\) | |||||||
\(354\) | 9.15014 | 0.486324 | ||||||||
\(355\) | 3.82339 | 0.202924 | ||||||||
\(356\) | 9.39720 | 0.498051 | ||||||||
\(357\) | −0.0736899 | + | 1.28574i | −0.00390008 | + | 0.0680487i | ||||
\(358\) | 9.57539 | − | 16.5851i | 0.506075 | − | 0.876548i | ||||
\(359\) | 1.57507 | + | 2.72810i | 0.0831289 | + | 0.143983i | 0.904592 | − | 0.426278i | \(-0.140175\pi\) |
−0.821463 | + | 0.570261i | \(0.806842\pi\) | |||||||
\(360\) | −0.651388 | − | 1.12824i | −0.0343312 | − | 0.0594633i | ||||
\(361\) | 20.3919 | 1.07326 | ||||||||
\(362\) | 6.54859 | − | 11.3425i | 0.344186 | − | 0.596148i | ||||
\(363\) | −6.51073 | −0.341725 | ||||||||
\(364\) | 9.52817 | + | 0.462502i | 0.499412 | + | 0.0242417i | ||||
\(365\) | −21.0877 | −1.10378 | ||||||||
\(366\) | −5.09231 | + | 8.82015i | −0.266179 | + | 0.461036i | ||||
\(367\) | −4.46926 | −0.233293 | −0.116647 | − | 0.993173i | \(-0.537214\pi\) | ||||
−0.116647 | + | 0.993173i | \(0.537214\pi\) | |||||||
\(368\) | 2.39477 | + | 4.14786i | 0.124836 | + | 0.216222i | ||||
\(369\) | −6.31845 | − | 10.9439i | −0.328925 | − | 0.569715i | ||||
\(370\) | 0.753989 | − | 1.30595i | 0.0391980 | − | 0.0678929i | ||||
\(371\) | 20.2793 | − | 10.2082i | 1.05285 | − | 0.529984i | ||||
\(372\) | −4.48676 | −0.232628 | ||||||||
\(373\) | 4.95231 | 0.256421 | 0.128210 | − | 0.991747i | \(-0.459077\pi\) | ||||
0.128210 | + | 0.991747i | \(0.459077\pi\) | |||||||
\(374\) | 1.03135 | 0.0533297 | ||||||||
\(375\) | 10.8167 | 0.558570 | ||||||||
\(376\) | 3.98570 | + | 6.90344i | 0.205547 | + | 0.356018i | ||||
\(377\) | −10.8320 | + | 6.38085i | −0.557877 | + | 0.328631i | ||||
\(378\) | 2.36323 | − | 1.18960i | 0.121551 | − | 0.0611866i | ||||
\(379\) | 6.55920 | + | 11.3609i | 0.336923 | + | 0.583569i | 0.983852 | − | 0.178982i | \(-0.0572803\pi\) |
−0.646929 | + | 0.762550i | \(0.723947\pi\) | |||||||
\(380\) | −4.08831 | + | 7.08115i | −0.209726 | + | 0.363255i | ||||
\(381\) | 2.59305 | + | 4.49130i | 0.132846 | + | 0.230096i | ||||
\(382\) | −5.74444 | + | 9.94966i | −0.293911 | + | 0.509069i | ||||
\(383\) | −12.1800 | −0.622369 | −0.311185 | − | 0.950349i | \(-0.600726\pi\) | ||||
−0.311185 | + | 0.950349i | \(0.600726\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −0.417877 | + | 7.29112i | −0.0212970 | + | 0.371590i | ||||
\(386\) | −0.138150 | + | 0.239283i | −0.00703165 | + | 0.0121792i | ||||
\(387\) | −4.01356 | + | 6.95169i | −0.204021 | + | 0.353374i | ||||
\(388\) | −1.39720 | −0.0709323 | ||||||||
\(389\) | 3.34598 | − | 5.79541i | 0.169648 | − | 0.293839i | −0.768648 | − | 0.639672i | \(-0.779070\pi\) |
0.938296 | + | 0.345833i | \(0.112404\pi\) | |||||||
\(390\) | 0.0410911 | + | 4.69704i | 0.00208073 | + | 0.237844i | ||||
\(391\) | 2.33137 | 0.117902 | ||||||||
\(392\) | −2.78447 | − | 6.42236i | −0.140637 | − | 0.324378i | ||||
\(393\) | 4.03186 | + | 6.98339i | 0.203381 | + | 0.352265i | ||||
\(394\) | −13.2710 | −0.668585 | ||||||||
\(395\) | 9.33749 | − | 16.1730i | 0.469820 | − | 0.813752i | ||||
\(396\) | −1.05939 | − | 1.83493i | −0.0532366 | − | 0.0922085i | ||||
\(397\) | 24.5825 | 1.23376 | 0.616879 | − | 0.787058i | \(-0.288397\pi\) | ||||
0.616879 | + | 0.787058i | \(0.288397\pi\) | |||||||
\(398\) | −19.0219 | −0.953479 | ||||||||
\(399\) | −13.8822 | − | 9.11202i | −0.694978 | − | 0.456172i | ||||
\(400\) | 1.65139 | + | 2.86029i | 0.0825694 | + | 0.143014i | ||||
\(401\) | −17.3273 | + | 30.0117i | −0.865282 | + | 1.49871i | 0.00148462 | + | 0.999999i | \(0.499527\pi\) |
−0.866767 | + | 0.498714i | \(0.833806\pi\) | |||||||
\(402\) | −1.67924 | + | 2.90853i | −0.0837529 | + | 0.145064i | ||||
\(403\) | 14.0801 | + | 7.96576i | 0.701381 | + | 0.396803i | ||||
\(404\) | 3.01725 | + | 5.22602i | 0.150114 | + | 0.260004i | ||||
\(405\) | 0.651388 | + | 1.12824i | 0.0323677 | + | 0.0560625i | ||||
\(406\) | 7.71216 | + | 5.06213i | 0.382748 | + | 0.251229i | ||||
\(407\) | 1.22626 | − | 2.12395i | 0.0607835 | − | 0.105280i | ||||
\(408\) | −0.243381 | − | 0.421549i | −0.0120492 | − | 0.0208698i | ||||
\(409\) | 11.9545 | + | 20.7058i | 0.591111 | + | 1.02383i | 0.994083 | + | 0.108622i | \(0.0346439\pi\) |
−0.402972 | + | 0.915212i | \(0.632023\pi\) | |||||||
\(410\) | −8.23152 | − | 14.2574i | −0.406526 | − | 0.704123i | ||||
\(411\) | 3.39583 | + | 5.88174i | 0.167504 | + | 0.290125i | ||||
\(412\) | 5.64770 | − | 9.78210i | 0.278242 | − | 0.481930i | ||||
\(413\) | −1.38522 | + | 24.1693i | −0.0681622 | + | 1.18929i | ||||
\(414\) | −2.39477 | − | 4.14786i | −0.117696 | − | 0.203856i | ||||
\(415\) | 2.27123 | + | 3.93389i | 0.111491 | + | 0.193107i | ||||
\(416\) | −3.10661 | + | 1.83002i | −0.152314 | + | 0.0897242i | ||||
\(417\) | 6.45522 | − | 11.1808i | 0.316114 | − | 0.547525i | ||||
\(418\) | −6.64908 | + | 11.5165i | −0.325217 | + | 0.563292i | ||||
\(419\) | −6.09738 | − | 10.5610i | −0.297876 | − | 0.515937i | 0.677773 | − | 0.735271i | \(-0.262945\pi\) |
−0.975650 | + | 0.219334i | \(0.929612\pi\) | |||||||
\(420\) | 3.07876 | − | 1.54979i | 0.150228 | − | 0.0756218i | ||||
\(421\) | 14.0504 | 0.684777 | 0.342388 | − | 0.939558i | \(-0.388764\pi\) | ||||
0.342388 | + | 0.939558i | \(0.388764\pi\) | |||||||
\(422\) | −3.97500 | −0.193500 | ||||||||
\(423\) | −3.98570 | − | 6.90344i | −0.193792 | − | 0.335657i | ||||
\(424\) | −4.29060 | + | 7.43153i | −0.208370 | + | 0.360907i | ||||
\(425\) | 1.60767 | 0.0779833 | ||||||||
\(426\) | −1.46740 | − | 2.54161i | −0.0710958 | − | 0.123142i | ||||
\(427\) | −22.5268 | − | 14.7862i | −1.09015 | − | 0.715554i | ||||
\(428\) | −14.0292 | −0.678128 | ||||||||
\(429\) | 0.0668291 | + | 7.63911i | 0.00322654 | + | 0.368820i | ||||
\(430\) | −5.22877 | + | 9.05649i | −0.252153 | + | 0.436743i | ||||
\(431\) | 17.3034 | 0.833476 | 0.416738 | − | 0.909027i | \(-0.363173\pi\) | ||||
0.416738 | + | 0.909027i | \(0.363173\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 10.1803 | − | 17.6328i | 0.489234 | − | 0.847378i | −0.510689 | − | 0.859765i | \(-0.670610\pi\) |
0.999923 | + | 0.0123873i | \(0.00394309\pi\) | |||||||
\(434\) | 0.679241 | − | 11.8514i | 0.0326046 | − | 0.568886i | ||||
\(435\) | −2.27123 | + | 3.93389i | −0.108897 | + | 0.188616i | ||||
\(436\) | 11.0000 | 0.526804 | ||||||||
\(437\) | −15.0303 | + | 26.0332i | −0.718996 | + | 1.24534i | ||||
\(438\) | 8.09337 | + | 14.0181i | 0.386716 | + | 0.669812i | ||||
\(439\) | −2.02199 | + | 3.50219i | −0.0965044 | + | 0.167150i | −0.910235 | − | 0.414091i | \(-0.864100\pi\) |
0.813731 | + | 0.581242i | \(0.197433\pi\) | |||||||
\(440\) | −1.38015 | − | 2.39050i | −0.0657962 | − | 0.113962i | ||||
\(441\) | 2.78447 | + | 6.42236i | 0.132594 | + | 0.305827i | ||||
\(442\) | 0.0153530 | + | 1.75498i | 0.000730270 | + | 0.0834758i | ||||
\(443\) | 10.1092 | + | 17.5097i | 0.480304 | + | 0.831912i | 0.999745 | − | 0.0225951i | \(-0.00719285\pi\) |
−0.519440 | + | 0.854507i | \(0.673860\pi\) | |||||||
\(444\) | −1.15751 | −0.0549331 | ||||||||
\(445\) | −12.2424 | −0.580348 | ||||||||
\(446\) | 19.1603 | 0.907265 | ||||||||
\(447\) | −23.3640 | −1.10508 | ||||||||
\(448\) | 2.21184 | + | 1.45181i | 0.104500 | + | 0.0685918i | ||||
\(449\) | −19.8059 | + | 34.3047i | −0.934696 | + | 1.61894i | −0.159521 | + | 0.987195i | \(0.550995\pi\) |
−0.775175 | + | 0.631746i | \(0.782338\pi\) | |||||||
\(450\) | −1.65139 | − | 2.86029i | −0.0778472 | − | 0.134835i | ||||
\(451\) | −13.3875 | − | 23.1878i | −0.630391 | − | 1.09187i | ||||
\(452\) | −7.13104 | −0.335416 | ||||||||
\(453\) | −2.93692 | + | 5.08689i | −0.137988 | + | 0.239003i | ||||
\(454\) | 1.18251 | 0.0554980 | ||||||||
\(455\) | −12.4131 | − | 0.602537i | −0.581934 | − | 0.0282474i | ||||
\(456\) | 6.27630 | 0.293915 | ||||||||
\(457\) | 3.32371 | − | 5.75683i | 0.155477 | − | 0.269293i | −0.777756 | − | 0.628566i | \(-0.783642\pi\) |
0.933232 | + | 0.359273i | \(0.116975\pi\) | |||||||
\(458\) | 15.0320 | 0.702399 | ||||||||
\(459\) | 0.243381 | + | 0.421549i | 0.0113601 | + | 0.0196762i | ||||
\(460\) | −3.11985 | − | 5.40373i | −0.145464 | − | 0.251950i | ||||
\(461\) | −10.2371 | + | 17.7311i | −0.476788 | + | 0.825820i | −0.999646 | − | 0.0265991i | \(-0.991532\pi\) |
0.522859 | + | 0.852419i | \(0.324866\pi\) | |||||||
\(462\) | 5.00718 | − | 2.52052i | 0.232955 | − | 0.117265i | ||||
\(463\) | 17.2668 | 0.802457 | 0.401228 | − | 0.915978i | \(-0.368583\pi\) | ||||
0.401228 | + | 0.915978i | \(0.368583\pi\) | |||||||
\(464\) | −3.48676 | −0.161869 | ||||||||
\(465\) | 5.84524 | 0.271067 | ||||||||
\(466\) | −5.19412 | −0.240613 | ||||||||
\(467\) | 4.37922 | + | 7.58503i | 0.202646 | + | 0.350994i | 0.949380 | − | 0.314129i | \(-0.101713\pi\) |
−0.746734 | + | 0.665123i | \(0.768379\pi\) | |||||||
\(468\) | 3.10661 | − | 1.83002i | 0.143603 | − | 0.0845928i | ||||
\(469\) | −7.42843 | − | 4.87589i | −0.343013 | − | 0.225148i | ||||
\(470\) | −5.19248 | − | 8.99364i | −0.239511 | − | 0.414846i | ||||
\(471\) | −3.12248 | + | 5.40829i | −0.143876 | + | 0.249201i | ||||
\(472\) | −4.57507 | − | 7.92425i | −0.210585 | − | 0.364743i | ||||
\(473\) | −8.50388 | + | 14.7292i | −0.391009 | + | 0.677247i | ||||
\(474\) | −14.3348 | −0.658417 | ||||||||
\(475\) | −10.3646 | + | 17.9520i | −0.475561 | + | 0.823695i | ||||
\(476\) | 1.15033 | − | 0.579054i | 0.0527253 | − | 0.0265409i | ||||
\(477\) | 4.29060 | − | 7.43153i | 0.196453 | − | 0.340266i | ||||
\(478\) | 12.6989 | − | 21.9952i | 0.580835 | − | 1.00604i | ||||
\(479\) | −27.0253 | −1.23482 | −0.617408 | − | 0.786643i | \(-0.711817\pi\) | ||||
−0.617408 | + | 0.786643i | \(0.711817\pi\) | |||||||
\(480\) | −0.651388 | + | 1.12824i | −0.0297317 | + | 0.0514967i | ||||
\(481\) | 3.63244 | + | 2.05504i | 0.165625 | + | 0.0937015i | ||||
\(482\) | 11.8575 | 0.540094 | ||||||||
\(483\) | 11.3188 | − | 5.69765i | 0.515022 | − | 0.259252i | ||||
\(484\) | 3.25537 | + | 5.63846i | 0.147971 | + | 0.256294i | ||||
\(485\) | 1.82024 | 0.0826530 | ||||||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −10.9717 | − | 19.0036i | −0.497177 | − | 0.861135i | 0.502818 | − | 0.864392i | \(-0.332297\pi\) |
−0.999995 | + | 0.00325721i | \(0.998963\pi\) | |||||||
\(488\) | 10.1846 | 0.461036 | ||||||||
\(489\) | −2.60767 | −0.117923 | ||||||||
\(490\) | 3.62754 | + | 8.36689i | 0.163876 | + | 0.377978i | ||||
\(491\) | −7.09020 | − | 12.2806i | −0.319976 | − | 0.554215i | 0.660507 | − | 0.750820i | \(-0.270342\pi\) |
−0.980483 | + | 0.196605i | \(0.937008\pi\) | |||||||
\(492\) | −6.31845 | + | 10.9439i | −0.284858 | + | 0.493388i | ||||
\(493\) | −0.848612 | + | 1.46984i | −0.0382196 | + | 0.0661982i | ||||
\(494\) | −19.6960 | − | 11.1429i | −0.886164 | − | 0.501342i | ||||
\(495\) | 1.38015 | + | 2.39050i | 0.0620333 | + | 0.107445i | ||||
\(496\) | 2.24338 | + | 3.88565i | 0.100731 | + | 0.174471i | ||||
\(497\) | 6.93561 | − | 3.49125i | 0.311104 | − | 0.156604i | ||||
\(498\) | 1.74338 | − | 3.01962i | 0.0781228 | − | 0.135313i | ||||
\(499\) | 14.7488 | + | 25.5456i | 0.660245 | + | 1.14358i | 0.980551 | + | 0.196264i | \(0.0628811\pi\) |
−0.320306 | + | 0.947314i | \(0.603786\pi\) | |||||||
\(500\) | −5.40833 | − | 9.36750i | −0.241868 | − | 0.418927i | ||||
\(501\) | −3.45416 | − | 5.98279i | −0.154321 | − | 0.267291i | ||||
\(502\) | −10.7397 | − | 18.6017i | −0.479336 | − | 0.830234i | ||||
\(503\) | −7.49400 | + | 12.9800i | −0.334141 | + | 0.578749i | −0.983319 | − | 0.181887i | \(-0.941780\pi\) |
0.649178 | + | 0.760636i | \(0.275113\pi\) | |||||||
\(504\) | −2.21184 | − | 1.45181i | −0.0985232 | − | 0.0646689i | ||||
\(505\) | −3.93079 | − | 6.80834i | −0.174918 | − | 0.302967i | ||||
\(506\) | −5.07401 | − | 8.78844i | −0.225567 | − | 0.390694i | ||||
\(507\) | −12.9980 | + | 0.227438i | −0.577262 | + | 0.0101009i | ||||
\(508\) | 2.59305 | − | 4.49130i | 0.115048 | − | 0.199269i | ||||
\(509\) | −20.9837 | + | 36.3449i | −0.930087 | + | 1.61096i | −0.146918 | + | 0.989149i | \(0.546935\pi\) |
−0.783169 | + | 0.621809i | \(0.786398\pi\) | |||||||
\(510\) | 0.317071 | + | 0.549183i | 0.0140401 | + | 0.0243182i | ||||
\(511\) | −38.2530 | + | 19.2558i | −1.69221 | + | 0.851826i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.27630 | −0.277105 | ||||||||
\(514\) | −3.42294 | − | 5.92871i | −0.150980 | − | 0.261504i | ||||
\(515\) | −7.35769 | + | 12.7439i | −0.324218 | + | 0.561563i | ||||
\(516\) | 8.02712 | 0.353374 | ||||||||
\(517\) | −8.44487 | − | 14.6269i | −0.371405 | − | 0.643292i | ||||
\(518\) | 0.175233 | − | 3.05747i | 0.00769930 | − | 0.134337i | ||||
\(519\) | −7.72710 | −0.339182 | ||||||||
\(520\) | 4.04721 | − | 2.38411i | 0.177482 | − | 0.104550i | ||||
\(521\) | −8.68748 | + | 15.0472i | −0.380605 | + | 0.659228i | −0.991149 | − | 0.132755i | \(-0.957618\pi\) |
0.610544 | + | 0.791983i | \(0.290951\pi\) | |||||||
\(522\) | 3.48676 | 0.152611 | ||||||||
\(523\) | −16.5017 | + | 28.5818i | −0.721569 | + | 1.24979i | 0.238802 | + | 0.971068i | \(0.423245\pi\) |
−0.960371 | + | 0.278726i | \(0.910088\pi\) | |||||||
\(524\) | 4.03186 | − | 6.98339i | 0.176133 | − | 0.305071i | ||||
\(525\) | 7.80521 | − | 3.92899i | 0.340647 | − | 0.171475i | ||||
\(526\) | 7.69998 | − | 13.3368i | 0.335735 | − | 0.581510i | ||||
\(527\) | 2.18399 | 0.0951360 | ||||||||
\(528\) | −1.05939 | + | 1.83493i | −0.0461042 | + | 0.0798549i | ||||
\(529\) | 0.0301633 | + | 0.0522443i | 0.00131145 | + | 0.00227149i | ||||
\(530\) | 5.58968 | − | 9.68162i | 0.242800 | − | 0.420543i | ||||
\(531\) | 4.57507 | + | 7.92425i | 0.198541 | + | 0.343883i | ||||
\(532\) | −0.950155 | + | 16.5783i | −0.0411945 | + | 0.718761i | ||||
\(533\) | 39.2579 | − | 23.1258i | 1.70045 | − | 1.00169i | ||||
\(534\) | 4.69860 | + | 8.13822i | 0.203328 | + | 0.352175i | ||||
\(535\) | 18.2769 | 0.790181 | ||||||||
\(536\) | 3.35848 | 0.145064 | ||||||||
\(537\) | 19.1508 | 0.826417 | ||||||||
\(538\) | 11.7313 | 0.505773 | ||||||||
\(539\) | 5.89971 | + | 13.6076i | 0.254118 | + | 0.586122i | ||||
\(540\) | 0.651388 | − | 1.12824i | 0.0280313 | − | 0.0485516i | ||||
\(541\) | −8.93967 | − | 15.4840i | −0.384347 | − | 0.665708i | 0.607332 | − | 0.794448i | \(-0.292240\pi\) |
−0.991678 | + | 0.128741i | \(0.958907\pi\) | |||||||
\(542\) | −13.0428 | − | 22.5908i | −0.560236 | − | 0.970357i | ||||
\(543\) | 13.0972 | 0.562054 | ||||||||
\(544\) | −0.243381 | + | 0.421549i | −0.0104349 | + | 0.0180737i | ||||
\(545\) | −14.3305 | −0.613853 | ||||||||
\(546\) | 4.36355 | + | 8.48289i | 0.186743 | + | 0.363034i | ||||
\(547\) | 11.4550 | 0.489782 | 0.244891 | − | 0.969551i | \(-0.421248\pi\) | ||||
0.244891 | + | 0.969551i | \(0.421248\pi\) | |||||||
\(548\) | 3.39583 | − | 5.88174i | 0.145063 | − | 0.251256i | ||||
\(549\) | −10.1846 | −0.434669 | ||||||||
\(550\) | −3.49894 | − | 6.06035i | −0.149195 | − | 0.258414i | ||||
\(551\) | −10.9420 | − | 18.9521i | −0.466144 | − | 0.807385i | ||||
\(552\) | −2.39477 | + | 4.14786i | −0.101928 | + | 0.176545i | ||||
\(553\) | 2.17011 | − | 37.8641i | 0.0922824 | − | 1.61014i | ||||
\(554\) | −23.4307 | −0.995474 | ||||||||
\(555\) | 1.50798 | 0.0640101 | ||||||||
\(556\) | −12.9104 | −0.547525 | ||||||||
\(557\) | 40.6243 | 1.72131 | 0.860654 | − | 0.509190i | \(-0.170055\pi\) | ||||
0.860654 | + | 0.509190i | \(0.170055\pi\) | |||||||
\(558\) | −2.24338 | − | 3.88565i | −0.0949699 | − | 0.164493i | ||||
\(559\) | −25.1903 | − | 14.2513i | −1.06544 | − | 0.602765i | ||||
\(560\) | −2.88153 | − | 1.89139i | −0.121767 | − | 0.0799257i | ||||
\(561\) | 0.515673 | + | 0.893172i | 0.0217717 | + | 0.0377098i | ||||
\(562\) | 3.07876 | − | 5.33256i | 0.129869 | − | 0.224941i | ||||
\(563\) | −16.5928 | − | 28.7395i | −0.699301 | − | 1.21123i | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.269408 | − | 0.963026i | \(-0.413172\pi\) | |||||||
\(564\) | −3.98570 | + | 6.90344i | −0.167828 | + | 0.290687i | ||||
\(565\) | 9.29014 | 0.390839 | ||||||||
\(566\) | 10.9661 | − | 18.9939i | 0.460942 | − | 0.798374i | ||||
\(567\) | 2.21184 | + | 1.45181i | 0.0928885 | + | 0.0609705i | ||||
\(568\) | −1.46740 | + | 2.54161i | −0.0615708 | + | 0.106644i | ||||
\(569\) | −0.0339767 | + | 0.0588494i | −0.00142438 | + | 0.00246710i | −0.866737 | − | 0.498766i | \(-0.833787\pi\) |
0.865312 | + | 0.501233i | \(0.167120\pi\) | |||||||
\(570\) | −8.17661 | −0.342481 | ||||||||
\(571\) | −10.2822 | + | 17.8092i | −0.430295 | + | 0.745293i | −0.996899 | − | 0.0786977i | \(-0.974924\pi\) |
0.566603 | + | 0.823991i | \(0.308257\pi\) | |||||||
\(572\) | 6.58225 | − | 3.87743i | 0.275218 | − | 0.162124i | ||||
\(573\) | −11.4889 | −0.479955 | ||||||||
\(574\) | −27.9508 | − | 18.3464i | −1.16664 | − | 0.765765i | ||||
\(575\) | −7.90938 | − | 13.6995i | −0.329844 | − | 0.571307i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.7814 | − | 39.4586i | 0.948403 | − | 1.64268i | 0.199613 | − | 0.979875i | \(-0.436031\pi\) |
0.748790 | − | 0.662808i | \(-0.230635\pi\) | |||||||
\(578\) | −8.38153 | − | 14.5172i | −0.348626 | − | 0.603837i | ||||
\(579\) | −0.276300 | −0.0114826 | ||||||||
\(580\) | 4.54247 | 0.188616 | ||||||||
\(581\) | 7.71216 | + | 5.06213i | 0.319954 | + | 0.210013i | ||||
\(582\) | −0.698602 | − | 1.21001i | −0.0289580 | − | 0.0501567i | ||||
\(583\) | 9.09087 | − | 15.7458i | 0.376505 | − | 0.652126i | ||||
\(584\) | 8.09337 | − | 14.0181i | 0.334906 | − | 0.580074i | ||||
\(585\) | −4.04721 | + | 2.38411i | −0.167332 | + | 0.0985707i | ||||
\(586\) | 8.74075 | + | 15.1394i | 0.361077 | + | 0.625404i | ||||
\(587\) | 2.71527 | + | 4.70298i | 0.112071 | + | 0.194113i | 0.916605 | − | 0.399794i | \(-0.130918\pi\) |
−0.804534 | + | 0.593906i | \(0.797585\pi\) | |||||||
\(588\) | 4.16969 | − | 5.62260i | 0.171955 | − | 0.231872i | ||||
\(589\) | −14.0801 | + | 24.3875i | −0.580162 | + | 1.00487i | ||||
\(590\) | 5.96029 | + | 10.3235i | 0.245381 | + | 0.425013i | ||||
\(591\) | −6.63552 | − | 11.4931i | −0.272949 | − | 0.472761i | ||||
\(592\) | 0.578756 | + | 1.00243i | 0.0237867 | + | 0.0411998i | ||||
\(593\) | −2.77524 | − | 4.80686i | −0.113966 | − | 0.197394i | 0.803400 | − | 0.595439i | \(-0.203022\pi\) |
−0.917366 | + | 0.398045i | \(0.869689\pi\) | |||||||
\(594\) | 1.05939 | − | 1.83493i | 0.0434675 | − | 0.0752879i | ||||
\(595\) | −1.49862 | + | 0.754377i | −0.0614375 | + | 0.0309264i | ||||
\(596\) | 11.6820 | + | 20.2338i | 0.478513 | + | 0.828809i | ||||
\(597\) | −9.51093 | − | 16.4734i | −0.389256 | − | 0.674212i | ||||
\(598\) | 14.8792 | − | 8.76496i | 0.608457 | − | 0.358426i | ||||
\(599\) | −7.94019 | + | 13.7528i | −0.324427 | + | 0.561925i | −0.981396 | − | 0.191993i | \(-0.938505\pi\) |
0.656969 | + | 0.753918i | \(0.271838\pi\) | |||||||
\(600\) | −1.65139 | + | 2.86029i | −0.0674176 | + | 0.116771i | ||||
\(601\) | 19.1239 | + | 33.1235i | 0.780078 | + | 1.35114i | 0.931896 | + | 0.362727i | \(0.118154\pi\) |
−0.151817 | + | 0.988409i | \(0.548513\pi\) | |||||||
\(602\) | −1.21521 | + | 21.2030i | −0.0495282 | + | 0.864168i | ||||
\(603\) | −3.35848 | −0.136768 | ||||||||
\(604\) | 5.87384 | 0.239003 | ||||||||
\(605\) | −4.24101 | − | 7.34565i | −0.172422 | − | 0.298643i | ||||
\(606\) | −3.01725 | + | 5.22602i | −0.122567 | + | 0.212293i | ||||
\(607\) | −19.3219 | −0.784251 | −0.392125 | − | 0.919912i | \(-0.628260\pi\) | ||||
−0.392125 | + | 0.919912i | \(0.628260\pi\) | |||||||
\(608\) | −3.13815 | − | 5.43544i | −0.127269 | − | 0.220436i | ||||
\(609\) | −0.527853 | + | 9.20999i | −0.0213897 | + | 0.373208i | ||||
\(610\) | −13.2683 | −0.537217 | ||||||||
\(611\) | 24.7641 | − | 14.5879i | 1.00185 | − | 0.590161i | ||||
\(612\) | 0.243381 | − | 0.421549i | 0.00983810 | − | 0.0170401i | ||||
\(613\) | −30.5251 | −1.23290 | −0.616448 | − | 0.787395i | \(-0.711429\pi\) | ||||
−0.616448 | + | 0.787395i | \(0.711429\pi\) | |||||||
\(614\) | −6.03366 | + | 10.4506i | −0.243499 | + | 0.421752i | ||||
\(615\) | 8.23152 | − | 14.2574i | 0.331927 | − | 0.574914i | ||||
\(616\) | −4.68642 | − | 3.07609i | −0.188821 | − | 0.123939i | ||||
\(617\) | −12.5446 | + | 21.7279i | −0.505026 | + | 0.874731i | 0.494957 | + | 0.868917i | \(0.335184\pi\) |
−0.999983 | + | 0.00581322i | \(0.998150\pi\) | |||||||
\(618\) | 11.2954 | 0.454368 | ||||||||
\(619\) | 9.35717 | − | 16.2071i | 0.376096 | − | 0.651418i | −0.614394 | − | 0.788999i | \(-0.710599\pi\) |
0.990490 | + | 0.137581i | \(0.0439328\pi\) | |||||||
\(620\) | −2.92262 | − | 5.06213i | −0.117375 | − | 0.203300i | ||||
\(621\) | 2.39477 | − | 4.14786i | 0.0960988 | − | 0.166448i | ||||
\(622\) | −0.755881 | − | 1.30923i | −0.0303081 | − | 0.0524951i | ||||
\(623\) | −22.2077 | + | 11.1789i | −0.889734 | + | 0.447875i | ||||
\(624\) | −3.13815 | − | 1.77539i | −0.125627 | − | 0.0710725i | ||||
\(625\) | −1.21110 | − | 2.09769i | −0.0484441 | − | 0.0839076i | ||||
\(626\) | −1.72582 | −0.0689774 | ||||||||
\(627\) | −13.2982 | −0.531077 | ||||||||
\(628\) | 6.24495 | 0.249201 | ||||||||
\(629\) | 0.563433 | 0.0224655 | ||||||||
\(630\) | 2.88153 | + | 1.89139i | 0.114803 | + | 0.0753547i | ||||
\(631\) | −14.4362 | + | 25.0042i | −0.574695 | + | 0.995401i | 0.421379 | + | 0.906884i | \(0.361546\pi\) |
−0.996075 | + | 0.0885169i | \(0.971787\pi\) | |||||||
\(632\) | 7.16738 | + | 12.4143i | 0.285103 | + | 0.493813i | ||||
\(633\) | −1.98750 | − | 3.44245i | −0.0789960 | − | 0.136825i | ||||
\(634\) | −21.3041 | −0.846092 | ||||||||
\(635\) | −3.37816 | + | 5.85115i | −0.134058 | + | 0.232196i | ||||
\(636\) | −8.58119 | −0.340266 | ||||||||
\(637\) | −23.0674 | + | 10.2417i | −0.913965 | + | 0.405793i | ||||
\(638\) | 7.38771 | 0.292482 | ||||||||
\(639\) | 1.46740 | − | 2.54161i | 0.0580495 | − | 0.100545i | ||||
\(640\) | 1.30278 | 0.0514967 | ||||||||
\(641\) | −1.09911 | − | 1.90371i | −0.0434121 | − | 0.0751920i | 0.843503 | − | 0.537125i | \(-0.180490\pi\) |
−0.886915 | + | 0.461933i | \(0.847156\pi\) | |||||||
\(642\) | −7.01462 | − | 12.1497i | −0.276845 | − | 0.479509i | ||||
\(643\) | 8.74713 | − | 15.1505i | 0.344953 | − | 0.597476i | −0.640392 | − | 0.768048i | \(-0.721228\pi\) |
0.985345 | + | 0.170572i | \(0.0545615\pi\) | |||||||
\(644\) | −10.5937 | − | 6.95352i | −0.417450 | − | 0.274007i | ||||
\(645\) | −10.4575 | −0.411765 | ||||||||
\(646\) | −3.05507 | −0.120200 | ||||||||
\(647\) | 32.1735 | 1.26487 | 0.632436 | − | 0.774612i | \(-0.282055\pi\) | ||||
0.632436 | + | 0.774612i | \(0.282055\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 9.69360 | + | 16.7898i | 0.380507 | + | 0.659058i | ||||
\(650\) | 10.2604 | − | 6.04415i | 0.402447 | − | 0.237071i | ||||
\(651\) | 10.6032 | − | 5.33746i | 0.415574 | − | 0.209192i | ||||
\(652\) | 1.30383 | + | 2.25831i | 0.0510621 | + | 0.0884421i | ||||
\(653\) | −23.7831 | + | 41.1935i | −0.930703 | + | 1.61203i | −0.148581 | + | 0.988900i | \(0.547471\pi\) |
−0.782122 | + | 0.623125i | \(0.785863\pi\) | |||||||
\(654\) | 5.50000 | + | 9.52628i | 0.215067 | + | 0.372507i | ||||
\(655\) | −5.25261 | + | 9.09779i | −0.205236 | + | 0.355480i | ||||
\(656\) | 12.6369 | 0.493388 | ||||||||
\(657\) | −8.09337 | + | 14.0181i | −0.315752 | + | 0.546899i | ||||
\(658\) | −17.6315 | − | 11.5730i | −0.687347 | − | 0.451163i | ||||
\(659\) | −3.69892 | + | 6.40672i | −0.144090 | + | 0.249570i | −0.929033 | − | 0.369997i | \(-0.879359\pi\) |
0.784943 | + | 0.619568i | \(0.212692\pi\) | |||||||
\(660\) | 1.38015 | − | 2.39050i | 0.0537224 | − | 0.0930499i | ||||
\(661\) | 12.2297 | 0.475680 | 0.237840 | − | 0.971304i | \(-0.423561\pi\) | ||||
0.237840 | + | 0.971304i | \(0.423561\pi\) | |||||||
\(662\) | 8.21691 | − | 14.2321i | 0.319359 | − | 0.553146i | ||||
\(663\) | −1.51218 | + | 0.890786i | −0.0587282 | + | 0.0345953i | ||||
\(664\) | −3.48676 | −0.135313 | ||||||||
\(665\) | 1.23784 | − | 21.5978i | 0.0480013 | − | 0.837528i | ||||
\(666\) | −0.578756 | − | 1.00243i | −0.0224263 | − | 0.0388435i | ||||
\(667\) | 16.7000 | 0.646626 | ||||||||
\(668\) | −3.45416 | + | 5.98279i | −0.133646 | + | 0.231481i | ||||
\(669\) | 9.58013 | + | 16.5933i | 0.370389 | + | 0.641533i | ||||
\(670\) | −4.37535 | −0.169034 | ||||||||
\(671\) | −21.5791 | −0.833051 | ||||||||
\(672\) | −0.151388 | + | 2.64142i | −0.00583991 | + | 0.101895i | ||||
\(673\) | 24.4511 | + | 42.3506i | 0.942521 | + | 1.63249i | 0.760640 | + | 0.649174i | \(0.224885\pi\) |
0.181882 | + | 0.983320i | \(0.441781\pi\) | |||||||
\(674\) | −6.45891 | + | 11.1872i | −0.248788 | + | 0.430913i | ||||
\(675\) | 1.65139 | − | 2.86029i | 0.0635619 | − | 0.110093i | ||||
\(676\) | 6.69597 | + | 11.1429i | 0.257537 | + | 0.428573i | ||||
\(677\) | −9.74027 | − | 16.8707i | −0.374349 | − | 0.648392i | 0.615880 | − | 0.787840i | \(-0.288801\pi\) |
−0.990229 | + | 0.139448i | \(0.955467\pi\) | |||||||
\(678\) | −3.56552 | − | 6.17566i | −0.136933 | − | 0.237175i | ||||
\(679\) | 3.30191 | − | 1.66212i | 0.126716 | − | 0.0637862i | ||||
\(680\) | 0.317071 | − | 0.549183i | 0.0121591 | − | 0.0210602i | ||||
\(681\) | 0.591256 | + | 1.02409i | 0.0226570 | + | 0.0392430i | ||||
\(682\) | −4.75325 | − | 8.23287i | −0.182011 | − | 0.315253i | ||||
\(683\) | 9.08013 | + | 15.7273i | 0.347442 | + | 0.601787i | 0.985794 | − | 0.167958i | \(-0.0537171\pi\) |
−0.638353 | + | 0.769744i | \(0.720384\pi\) | |||||||
\(684\) | 3.13815 | + | 5.43544i | 0.119990 | + | 0.207829i | ||||
\(685\) | −4.42400 | + | 7.66259i | −0.169032 | + | 0.292773i | ||||
\(686\) | 14.2204 | + | 11.8651i | 0.542937 | + | 0.453011i | ||||
\(687\) | 7.51599 | + | 13.0181i | 0.286753 | + | 0.496671i | ||||
\(688\) | −4.01356 | − | 6.95169i | −0.153015 | − | 0.265031i | ||||
\(689\) | 26.9291 | + | 15.2350i | 1.02592 | + | 0.580406i | ||||
\(690\) | 3.11985 | − | 5.40373i | 0.118771 | − | 0.205717i | ||||
\(691\) | −18.5024 | + | 32.0472i | −0.703866 | + | 1.21913i | 0.263233 | + | 0.964732i | \(0.415211\pi\) |
−0.967099 | + | 0.254399i | \(0.918122\pi\) | |||||||
\(692\) | 3.86355 | + | 6.69186i | 0.146870 | + | 0.254386i | ||||
\(693\) | 4.68642 | + | 3.07609i | 0.178022 | + | 0.116851i | ||||
\(694\) | 16.0387 | 0.608822 | ||||||||
\(695\) | 16.8194 | 0.637997 | ||||||||
\(696\) | −1.74338 | − | 3.01962i | −0.0660827 | − | 0.114459i | ||||
\(697\) | 3.07558 | − | 5.32707i | 0.116496 | − | 0.201777i | ||||
\(698\) | −7.63901 | −0.289141 | ||||||||
\(699\) | −2.59706 | − | 4.49824i | −0.0982298 | − | 0.170139i | ||||
\(700\) | −7.30521 | − | 4.79502i | −0.276111 | − | 0.181235i | ||||
\(701\) | 36.3972 | 1.37470 | 0.687352 | − | 0.726325i | \(-0.258773\pi\) | ||||
0.687352 | + | 0.726325i | \(0.258773\pi\) | |||||||
\(702\) | 3.13815 | + | 1.77539i | 0.118442 | + | 0.0670078i | ||||
\(703\) | −3.63244 | + | 6.29158i | −0.137000 | + | 0.237291i | ||||
\(704\) | 2.11879 | 0.0798549 | ||||||||
\(705\) | 5.19248 | − | 8.99364i | 0.195560 | − | 0.338720i | ||||
\(706\) | −16.1956 | + | 28.0515i | −0.609528 | + | 1.05573i | ||||
\(707\) | −13.3473 | − | 8.76096i | −0.501978 | − | 0.329490i | ||||
\(708\) | 4.57507 | − | 7.92425i | 0.171942 | − | 0.297812i | ||||
\(709\) | −0.331366 | −0.0124447 | −0.00622236 | − | 0.999981i | \(-0.501981\pi\) | ||||
−0.00622236 | + | 0.999981i | \(0.501981\pi\) | |||||||
\(710\) | 1.91169 | − | 3.31115i | 0.0717446 | − | 0.124265i | ||||
\(711\) | −7.16738 | − | 12.4143i | −0.268798 | − | 0.465571i | ||||
\(712\) | 4.69860 | − | 8.13822i | 0.176088 | − | 0.304993i | ||||
\(713\) | −10.7448 | − | 18.6105i | −0.402394 | − | 0.696968i | ||||
\(714\) | 1.07664 | + | 0.706688i | 0.0402922 | + | 0.0264471i | ||||
\(715\) | −8.57519 | + | 5.05142i | −0.320694 | + | 0.188912i | ||||
\(716\) | −9.57539 | − | 16.5851i | −0.357849 | − | 0.619813i | ||||
\(717\) | 25.3978 | 0.948500 | ||||||||
\(718\) | 3.15014 | 0.117562 | ||||||||
\(719\) | 47.5862 | 1.77467 | 0.887333 | − | 0.461130i | \(-0.152556\pi\) | ||||
0.887333 | + | 0.461130i | \(0.152556\pi\) | |||||||
\(720\) | −1.30278 | −0.0485516 | ||||||||
\(721\) | −1.70999 | + | 29.8359i | −0.0636832 | + | 1.11115i | ||||
\(722\) | 10.1960 | − | 17.6599i | 0.379455 | − | 0.657235i | ||||
\(723\) | 5.92875 | + | 10.2689i | 0.220492 | + | 0.381904i | ||||
\(724\) | −6.54859 | − | 11.3425i | −0.243377 | − | 0.421540i | ||||
\(725\) | 11.5160 | 0.427693 | ||||||||
\(726\) | −3.25537 | + | 5.63846i | −0.120818 | + | 0.209263i | ||||
\(727\) | −32.9021 | −1.22027 | −0.610136 | − | 0.792297i | \(-0.708885\pi\) | ||||
−0.610136 | + | 0.792297i | \(0.708885\pi\) | |||||||
\(728\) | 5.16463 | − | 8.02039i | 0.191414 | − | 0.297255i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.5438 | + | 18.2625i | −0.390245 | + | 0.675925i | ||||
\(731\) | −3.90730 | −0.144517 | ||||||||
\(732\) | 5.09231 | + | 8.82015i | 0.188217 | + | 0.326002i | ||||
\(733\) | −10.5040 | − | 18.1935i | −0.387974 | − | 0.671991i | 0.604203 | − | 0.796831i | \(-0.293492\pi\) |
−0.992177 | + | 0.124839i | \(0.960158\pi\) | |||||||
\(734\) | −2.23463 | + | 3.87049i | −0.0824816 | + | 0.142862i | ||||
\(735\) | −5.43217 | + | 7.32499i | −0.200369 | + | 0.270186i | ||||
\(736\) | 4.78954 | 0.176545 | ||||||||
\(737\) | −7.11592 | −0.262118 | ||||||||
\(738\) | −12.6369 | −0.465171 | ||||||||
\(739\) | 6.52170 | 0.239905 | 0.119952 | − | 0.992780i | \(-0.461726\pi\) | ||||
0.119952 | + | 0.992780i | \(0.461726\pi\) | |||||||
\(740\) | −0.753989 | − | 1.30595i | −0.0277172 | − | 0.0480076i | ||||
\(741\) | −0.197962 | − | 22.6287i | −0.00727231 | − | 0.831284i | ||||
\(742\) | 1.29909 | − | 22.6665i | 0.0476910 | − | 0.832113i | ||||
\(743\) | −8.64802 | − | 14.9788i | −0.317265 | − | 0.549519i | 0.662651 | − | 0.748928i | \(-0.269431\pi\) |
−0.979916 | + | 0.199409i | \(0.936098\pi\) | |||||||
\(744\) | −2.24338 | + | 3.88565i | −0.0822463 | + | 0.142455i | ||||
\(745\) | −15.2190 | − | 26.3601i | −0.557582 | − | 0.965760i | ||||
\(746\) | 2.47615 | − | 4.28883i | 0.0906585 | − | 0.157025i | ||||
\(747\) | 3.48676 | 0.127574 | ||||||||
\(748\) | 0.515673 | − | 0.893172i | 0.0188549 | − | 0.0326576i | ||||
\(749\) | 33.1543 | − | 16.6892i | 1.21143 | − | 0.609810i | ||||
\(750\) | 5.40833 | − | 9.36750i | 0.197484 | − | 0.342053i | ||||
\(751\) | 4.81213 | − | 8.33486i | 0.175597 | − | 0.304143i | −0.764771 | − | 0.644303i | \(-0.777148\pi\) |
0.940368 | + | 0.340159i | \(0.110481\pi\) | |||||||
\(752\) | 7.97141 | 0.290687 | ||||||||
\(753\) | 10.7397 | − | 18.6017i | 0.391376 | − | 0.677883i | ||||
\(754\) | 0.109977 | + | 12.5712i | 0.00400511 | + | 0.457817i | ||||
\(755\) | −7.65229 | −0.278495 | ||||||||
\(756\) | 0.151388 | − | 2.64142i | 0.00550592 | − | 0.0960674i | ||||
\(757\) | −19.5740 | − | 33.9032i | −0.711429 | − | 1.23223i | −0.964321 | − | 0.264737i | \(-0.914715\pi\) |
0.252891 | − | 0.967495i | \(-0.418619\pi\) | |||||||
\(758\) | 13.1184 | 0.476482 | ||||||||
\(759\) | 5.07401 | − | 8.78844i | 0.184175 | − | 0.319000i | ||||
\(760\) | 4.08831 | + | 7.08115i | 0.148298 | + | 0.256860i | ||||
\(761\) | −10.3776 | −0.376187 | −0.188094 | − | 0.982151i | \(-0.560231\pi\) | ||||
−0.188094 | + | 0.982151i | \(0.560231\pi\) | |||||||
\(762\) | 5.18610 | 0.187873 | ||||||||
\(763\) | −25.9955 | + | 13.0856i | −0.941100 | + | 0.473732i | ||||
\(764\) | 5.74444 | + | 9.94966i | 0.207827 | + | 0.359966i | ||||
\(765\) | −0.317071 | + | 0.549183i | −0.0114637 | + | 0.0198558i | ||||
\(766\) | −6.09000 | + | 10.5482i | −0.220041 | + | 0.381122i | ||||
\(767\) | −28.4259 | + | 16.7450i | −1.02640 | + | 0.604625i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 17.5102 | + | 30.3285i | 0.631434 | + | 1.09368i | 0.987259 | + | 0.159123i | \(0.0508665\pi\) |
−0.355825 | + | 0.934553i | \(0.615800\pi\) | |||||||
\(770\) | 6.10536 | + | 4.00745i | 0.220022 | + | 0.144419i | ||||
\(771\) | 3.42294 | − | 5.92871i | 0.123274 | − | 0.213517i | ||||
\(772\) | 0.138150 | + | 0.239283i | 0.00497213 | + | 0.00861198i | ||||
\(773\) | −10.0617 | − | 17.4274i | −0.361894 | − | 0.626819i | 0.626378 | − | 0.779519i | \(-0.284537\pi\) |
−0.988273 | + | 0.152700i | \(0.951203\pi\) | |||||||
\(774\) | 4.01356 | + | 6.95169i | 0.144264 | + | 0.249873i | ||||
\(775\) | −7.40938 | − | 12.8334i | −0.266153 | − | 0.460990i | ||||
\(776\) | −0.698602 | + | 1.21001i | −0.0250784 | + | 0.0434370i | ||||
\(777\) | 2.73546 | − | 1.37698i | 0.0981342 | − | 0.0493988i | ||||
\(778\) | −3.34598 | − | 5.79541i | −0.119959 | − | 0.207776i | ||||
\(779\) | 39.6565 | + | 68.6870i | 1.42084 | + | 2.46097i | ||||
\(780\) | 4.08831 | + | 2.31294i | 0.146385 | + | 0.0828164i | ||||
\(781\) | 3.10911 | − | 5.38514i | 0.111253 | − | 0.192696i | ||||
\(782\) | 1.16568 | − | 2.01902i | 0.0416847 | − | 0.0722001i | ||||
\(783\) | 1.74338 | + | 3.01962i | 0.0623034 | + | 0.107913i | ||||
\(784\) | −6.95416 | − | 0.799757i | −0.248363 | − | 0.0285627i | ||||
\(785\) | −8.13577 | −0.290378 | ||||||||
\(786\) | 8.06372 | 0.287623 | ||||||||
\(787\) | −0.951533 | − | 1.64810i | −0.0339185 | − | 0.0587486i | 0.848568 | − | 0.529087i | \(-0.177465\pi\) |
−0.882486 | + | 0.470338i | \(0.844132\pi\) | |||||||
\(788\) | −6.63552 | + | 11.4931i | −0.236381 | + | 0.409423i | ||||
\(789\) | 15.4000 | 0.548253 | ||||||||
\(790\) | −9.33749 | − | 16.1730i | −0.332213 | − | 0.575410i | ||||
\(791\) | 16.8523 | − | 8.48310i | 0.599197 | − | 0.301624i | ||||
\(792\) | −2.11879 | −0.0752879 | ||||||||
\(793\) | −0.321235 | − | 36.7198i | −0.0114074 | − | 1.30396i | ||||
\(794\) | 12.2912 | − | 21.2890i | 0.436200 | − | 0.755520i | ||||
\(795\) | 11.1794 | 0.396491 | ||||||||
\(796\) | −9.51093 | + | 16.4734i | −0.337106 | + | 0.583885i | ||||
\(797\) | 10.9112 | − | 18.8987i | 0.386494 | − | 0.669427i | −0.605481 | − | 0.795859i | \(-0.707019\pi\) |
0.991975 | + | 0.126433i | \(0.0403527\pi\) | |||||||
\(798\) | −14.8323 | + | 7.46630i | −0.525059 | + | 0.264304i | ||||
\(799\) | 1.94009 | − | 3.36034i | 0.0686355 | − | 0.118880i | ||||
\(800\) | 3.30278 | 0.116771 | ||||||||
\(801\) | −4.69860 | + | 8.13822i | −0.166017 | + | 0.287550i | ||||
\(802\) | 17.3273 | + | 30.0117i | 0.611847 | + | 1.05975i | ||||
\(803\) | −17.1481 | + | 29.7015i | −0.605145 | + | 1.04814i | ||||
\(804\) | 1.67924 | + | 2.90853i | 0.0592223 | + | 0.102576i | ||||
\(805\) | 13.8012 | + | 9.05887i | 0.486428 | + | 0.319283i | ||||
\(806\) | 13.9386 | − | 8.21087i | 0.490967 | − | 0.289216i | ||||
\(807\) | 5.86566 | + | 10.1596i | 0.206481 | + | 0.357636i | ||||
\(808\) | 6.03449 | 0.212293 | ||||||||
\(809\) | 45.9037 | 1.61389 | 0.806944 | − | 0.590628i | \(-0.201120\pi\) | ||||
0.806944 | + | 0.590628i | \(0.201120\pi\) | |||||||
\(810\) | 1.30278 | 0.0457749 | ||||||||
\(811\) | 3.66652 | 0.128749 | 0.0643744 | − | 0.997926i | \(-0.479495\pi\) | ||||
0.0643744 | + | 0.997926i | \(0.479495\pi\) | |||||||
\(812\) | 8.24001 | − | 4.14786i | 0.289168 | − | 0.145561i | ||||
\(813\) | 13.0428 | − | 22.5908i | 0.457431 | − | 0.792293i | ||||
\(814\) | −1.22626 | − | 2.12395i | −0.0429804 | − | 0.0744443i | ||||
\(815\) | −1.69860 | − | 2.94207i | −0.0594994 | − | 0.103056i | ||||
\(816\) | −0.486762 | −0.0170401 | ||||||||
\(817\) | 25.1903 | − | 43.6309i | 0.881297 | − | 1.52645i | ||||
\(818\) | 23.9090 | 0.835957 | ||||||||
\(819\) | −5.16463 | + | 8.02039i | −0.180467 | + | 0.280255i | ||||
\(820\) | −16.4630 | −0.574914 | ||||||||
\(821\) | 10.1742 | − | 17.6222i | 0.355081 | − | 0.615019i | −0.632051 | − | 0.774927i | \(-0.717787\pi\) |
0.987132 | + | 0.159908i | \(0.0511199\pi\) | |||||||
\(822\) | 6.79165 | 0.236886 | ||||||||
\(823\) | −13.8672 | − | 24.0188i | −0.483381 | − | 0.837241i | 0.516436 | − | 0.856326i | \(-0.327258\pi\) |
−0.999818 | + | 0.0190843i | \(0.993925\pi\) | |||||||
\(824\) | −5.64770 | − | 9.78210i | −0.196747 | − | 0.340776i | ||||
\(825\) | 3.49894 | − | 6.06035i | 0.121818 | − | 0.210994i | ||||
\(826\) | 20.2386 | + | 13.2843i | 0.704192 | + | 0.462220i | ||||
\(827\) | 36.6640 | 1.27493 | 0.637466 | − | 0.770478i | \(-0.279983\pi\) | ||||
0.637466 | + | 0.770478i | \(0.279983\pi\) | |||||||
\(828\) | −4.78954 | −0.166448 | ||||||||
\(829\) | 14.4624 | 0.502300 | 0.251150 | − | 0.967948i | \(-0.419191\pi\) | ||||
0.251150 | + | 0.967948i | \(0.419191\pi\) | |||||||
\(830\) | 4.54247 | 0.157671 | ||||||||
\(831\) | −11.7153 | − | 20.2916i | −0.406400 | − | 0.703906i | ||||
\(832\) | 0.0315412 | + | 3.60541i | 0.00109349 | + | 0.124995i | ||||
\(833\) | −2.02965 | + | 2.73687i | −0.0703232 | + | 0.0948270i | ||||
\(834\) | −6.45522 | − | 11.1808i | −0.223526 | − | 0.387158i | ||||
\(835\) | 4.50000 | − | 7.79423i | 0.155729 | − | 0.269730i | ||||
\(836\) | 6.64908 | + | 11.5165i | 0.229963 | + | 0.398308i | ||||
\(837\) | 2.24338 | − | 3.88565i | 0.0775426 | − | 0.134308i | ||||
\(838\) | −12.1948 | −0.421261 | ||||||||
\(839\) | −2.51779 | + | 4.36094i | −0.0869237 | + | 0.150556i | −0.906209 | − | 0.422829i | \(-0.861037\pi\) |
0.819286 | + | 0.573386i | \(0.194370\pi\) | |||||||
\(840\) | 0.197224 | − | 3.44117i | 0.00680489 | − | 0.118732i | ||||
\(841\) | 8.42124 | − | 14.5860i | 0.290388 | − | 0.502966i | ||||
\(842\) | 7.02522 | − | 12.1680i | 0.242105 | − | 0.419338i | ||||
\(843\) | 6.15751 | 0.212076 | ||||||||
\(844\) | −1.98750 | + | 3.44245i | −0.0684126 | + | 0.118494i | ||||
\(845\) | −8.72335 | − | 14.5167i | −0.300092 | − | 0.499389i | ||||
\(846\) | −7.97141 | −0.274063 | ||||||||
\(847\) | −14.4007 | − | 9.45237i | −0.494814 | − | 0.324787i | ||||
\(848\) | 4.29060 | + | 7.43153i | 0.147340 | + | 0.255200i | ||||
\(849\) | 21.9323 | 0.752715 | ||||||||
\(850\) | 0.803833 | − | 1.39228i | 0.0275713 | − | 0.0477548i | ||||
\(851\) | −2.77197 | − | 4.80120i | −0.0950220 | − | 0.164583i | ||||
\(852\) | −2.93480 | −0.100545 | ||||||||
\(853\) | 21.9833 | 0.752693 | 0.376346 | − | 0.926479i | \(-0.377180\pi\) | ||||
0.376346 | + | 0.926479i | \(0.377180\pi\) | |||||||
\(854\) | −24.0686 | + | 12.1157i | −0.823610 | + | 0.414589i | ||||
\(855\) | −4.08831 | − | 7.08115i | −0.139817 | − | 0.242170i | ||||
\(856\) | −7.01462 | + | 12.1497i | −0.239755 | + | 0.415267i | ||||
\(857\) | 21.6450 | − | 37.4902i | 0.739378 | − | 1.28064i | −0.213397 | − | 0.976965i | \(-0.568453\pi\) |
0.952776 | − | 0.303675i | \(-0.0982137\pi\) | |||||||
\(858\) | 6.64908 | + | 3.76168i | 0.226996 | + | 0.128422i | ||||
\(859\) | 22.6834 | + | 39.2888i | 0.773947 | + | 1.34052i | 0.935385 | + | 0.353632i | \(0.115054\pi\) |
−0.161438 | + | 0.986883i | \(0.551613\pi\) | |||||||
\(860\) | 5.22877 | + | 9.05649i | 0.178299 | + | 0.308824i | ||||
\(861\) | 1.91307 | − | 33.3793i | 0.0651973 | − | 1.13756i | ||||
\(862\) | 8.65171 | − | 14.9852i | 0.294678 | − | 0.510398i | ||||
\(863\) | −6.76755 | − | 11.7217i | −0.230370 | − | 0.399012i | 0.727547 | − | 0.686058i | \(-0.240660\pi\) |
−0.957917 | + | 0.287045i | \(0.907327\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −5.03334 | − | 8.71799i | −0.171139 | − | 0.296421i | ||||
\(866\) | −10.1803 | − | 17.6328i | −0.345941 | − | 0.599187i | ||||
\(867\) | 8.38153 | − | 14.5172i | 0.284652 | − | 0.493031i | ||||
\(868\) | −9.92400 | − | 6.51394i | −0.336843 | − | 0.221098i | ||||
\(869\) | −15.1862 | − | 26.3032i | −0.515155 | − | 0.892275i | ||||
\(870\) | 2.27123 | + | 3.93389i | 0.0770021 | + | 0.133371i | ||||
\(871\) | −0.105930 | − | 12.1087i | −0.00358932 | − | 0.410288i | ||||
\(872\) | 5.50000 | − | 9.52628i | 0.186254 | − | 0.322601i | ||||
\(873\) | 0.698602 | − | 1.21001i | 0.0236441 | − | 0.0409528i | ||||
\(874\) | 15.0303 | + | 26.0332i | 0.508407 | + | 0.880587i | ||||
\(875\) | 23.9247 | + | 15.7038i | 0.808803 | + | 0.530884i | ||||
\(876\) | 16.1867 | 0.546899 | ||||||||
\(877\) | 19.4218 | 0.655828 | 0.327914 | − | 0.944708i | \(-0.393654\pi\) | ||||
0.327914 | + | 0.944708i | \(0.393654\pi\) | |||||||
\(878\) | 2.02199 | + | 3.50219i | 0.0682389 | + | 0.118193i | ||||
\(879\) | −8.74075 | + | 15.1394i | −0.294818 | + | 0.510640i | ||||
\(880\) | −2.76031 | −0.0930499 | ||||||||
\(881\) | −2.77059 | − | 4.79881i | −0.0933437 | − | 0.161676i | 0.815572 | − | 0.578655i | \(-0.196422\pi\) |
−0.908916 | + | 0.416979i | \(0.863089\pi\) | |||||||
\(882\) | 6.95416 | + | 0.799757i | 0.234159 | + | 0.0269292i | ||||
\(883\) | 51.6940 | 1.73964 | 0.869821 | − | 0.493367i | \(-0.164234\pi\) | ||||
0.869821 | + | 0.493367i | \(0.164234\pi\) | |||||||
\(884\) | 1.52753 | + | 0.864193i | 0.0513765 | + | 0.0290660i | ||||
\(885\) | −5.96029 | + | 10.3235i | −0.200353 | + | 0.347021i | ||||
\(886\) | 20.2185 | 0.679253 | ||||||||
\(887\) | 1.77418 | − | 3.07298i | 0.0595713 | − | 0.103181i | −0.834702 | − | 0.550702i | \(-0.814360\pi\) |
0.894273 | + | 0.447522i | \(0.147693\pi\) | |||||||
\(888\) | −0.578756 | + | 1.00243i | −0.0194218 | + | 0.0336395i | ||||
\(889\) | −0.785113 | + | 13.6987i | −0.0263318 | + | 0.459438i | ||||
\(890\) | −6.12122 | + | 10.6023i | −0.205184 | + | 0.355389i | ||||
\(891\) | 2.11879 | 0.0709821 | ||||||||
\(892\) | 9.58013 | − | 16.5933i | 0.320767 | − | 0.555584i | ||||
\(893\) | 25.0155 | + | 43.3281i | 0.837111 | + | 1.44992i | ||||
\(894\) | −11.6820 | + | 20.2338i | −0.390704 | + | 0.676720i | ||||
\(895\) | 12.4746 | + | 21.6066i | 0.416979 | + | 0.722229i | ||||
\(896\) | 2.36323 | − | 1.18960i | 0.0789499 | − | 0.0397418i | ||||
\(897\) | 15.0303 | + | 8.50330i | 0.501847 | + | 0.283917i | ||||
\(898\) | 19.8059 | + | 34.3047i | 0.660930 | + | 1.14476i | ||||
\(899\) | 15.6443 | 0.521766 | ||||||||
\(900\) | −3.30278 | −0.110093 | ||||||||
\(901\) | 4.17700 | 0.139156 | ||||||||
\(902\) | −26.7749 | −0.891507 | ||||||||
\(903\) | −18.9699 | + | 9.54908i | −0.631279 | + | 0.317773i | ||||
\(904\) | −3.56552 | + | 6.17566i | −0.118587 | + | 0.205399i | ||||
\(905\) | 8.53135 | + | 14.7767i | 0.283592 | + | 0.491195i | ||||
\(906\) | 2.93692 | + | 5.08689i | 0.0975726 | + | 0.169001i | ||||
\(907\) | −43.6906 | −1.45072 | −0.725362 | − | 0.688368i | \(-0.758327\pi\) | ||||
−0.725362 | + | 0.688368i | \(0.758327\pi\) | |||||||
\(908\) | 0.591256 | − | 1.02409i | 0.0196215 | − | 0.0339855i | ||||
\(909\) | −6.03449 | −0.200151 | ||||||||
\(910\) | −6.72835 | + | 10.4488i | −0.223043 | + | 0.346373i | ||||
\(911\) | −5.97013 | −0.197799 | −0.0988996 | − | 0.995097i | \(-0.531532\pi\) | ||||
−0.0988996 | + | 0.995097i | \(0.531532\pi\) | |||||||
\(912\) | 3.13815 | − | 5.43544i | 0.103915 | − | 0.179985i | ||||
\(913\) | 7.38771 | 0.244498 | ||||||||
\(914\) | −3.32371 | − | 5.75683i | −0.109939 | − | 0.190419i | ||||
\(915\) | −6.63414 | − | 11.4907i | −0.219318 | − | 0.379870i | ||||
\(916\) | 7.51599 | − | 13.0181i | 0.248335 | − | 0.430130i | ||||
\(917\) | −1.22075 | + | 21.2997i | −0.0403127 | + | 0.703376i | ||||
\(918\) | 0.486762 | 0.0160655 | ||||||||
\(919\) | −57.6579 | −1.90196 | −0.950980 | − | 0.309254i | \(-0.899921\pi\) | ||||
−0.950980 | + | 0.309254i | \(0.899921\pi\) | |||||||
\(920\) | −6.23969 | −0.205717 | ||||||||
\(921\) | −12.0673 | −0.397631 | ||||||||
\(922\) | 10.2371 | + | 17.7311i | 0.337140 | + | 0.583943i | ||||
\(923\) | 9.20985 | + | 5.21042i | 0.303146 | + | 0.171503i | ||||
\(924\) | 0.320759 | − | 5.59660i | 0.0105522 | − | 0.184115i | ||||
\(925\) | −1.91150 | − | 3.31081i | −0.0628497 | − | 0.108859i | ||||
\(926\) | 8.63340 | − | 14.9535i | 0.283711 | − | 0.491402i | ||||
\(927\) | 5.64770 | + | 9.78210i | 0.185495 | + | 0.321286i | ||||
\(928\) | −1.74338 | + | 3.01962i | −0.0572293 | + | 0.0991240i | ||||
\(929\) | 4.11918 | 0.135146 | 0.0675729 | − | 0.997714i | \(-0.478474\pi\) | ||||
0.0675729 | + | 0.997714i | \(0.478474\pi\) | |||||||
\(930\) | 2.92262 | − | 5.06213i | 0.0958366 | − | 0.165994i | ||||
\(931\) | −17.4762 | − | 40.3087i | −0.572759 | − | 1.32106i | ||||
\(932\) | −2.59706 | + | 4.49824i | −0.0850695 | + | 0.147345i | ||||
\(933\) | 0.755881 | − | 1.30923i | 0.0247464 | − | 0.0428621i | ||||
\(934\) | 8.75844 | 0.286585 | ||||||||
\(935\) | −0.671807 | + | 1.16360i | −0.0219704 | + | 0.0380539i | ||||
\(936\) | −0.0315412 | − | 3.60541i | −0.00103096 | − | 0.117847i | ||||
\(937\) | 22.6483 | 0.739888 | 0.369944 | − | 0.929054i | \(-0.379377\pi\) | ||||
0.369944 | + | 0.929054i | \(0.379377\pi\) | |||||||
\(938\) | −7.93686 | + | 3.99526i | −0.259148 | + | 0.130450i | ||||
\(939\) | −0.862908 | − | 1.49460i | −0.0281599 | − | 0.0487744i | ||||
\(940\) | −10.3850 | −0.338720 | ||||||||
\(941\) | 10.0011 | − | 17.3223i | 0.326025 | − | 0.564692i | −0.655694 | − | 0.755027i | \(-0.727624\pi\) |
0.981719 | + | 0.190334i | \(0.0609572\pi\) | |||||||
\(942\) | 3.12248 | + | 5.40829i | 0.101736 | + | 0.176212i | ||||
\(943\) | −60.5249 | −1.97096 | ||||||||
\(944\) | −9.15014 | −0.297812 | ||||||||
\(945\) | −0.197224 | + | 3.44117i | −0.00641571 | + | 0.111941i | ||||
\(946\) | 8.50388 | + | 14.7292i | 0.276485 | + | 0.478886i | ||||
\(947\) | −3.76592 | + | 6.52276i | −0.122376 | + | 0.211961i | −0.920704 | − | 0.390261i | \(-0.872385\pi\) |
0.798328 | + | 0.602222i | \(0.205718\pi\) | |||||||
\(948\) | −7.16738 | + | 12.4143i | −0.232786 | + | 0.403197i | ||||
\(949\) | −50.7964 | − | 28.7378i | −1.64892 | − | 0.932868i | ||||
\(950\) | 10.3646 | + | 17.9520i | 0.336272 | + | 0.582441i | ||||
\(951\) | −10.6520 | − | 18.4499i | −0.345416 | − | 0.598278i | ||||
\(952\) | 0.0736899 | − | 1.28574i | 0.00238830 | − | 0.0416711i | ||||
\(953\) | −2.65075 | + | 4.59123i | −0.0858661 | + | 0.148724i | −0.905760 | − | 0.423791i | \(-0.860699\pi\) |
0.819894 | + | 0.572516i | \(0.194032\pi\) | |||||||
\(954\) | −4.29060 | − | 7.43153i | −0.138913 | − | 0.240605i | ||||
\(955\) | −7.48371 | − | 12.9622i | −0.242167 | − | 0.419446i | ||||
\(956\) | −12.6989 | − | 21.9952i | −0.410713 | − | 0.711375i | ||||
\(957\) | 3.69386 | + | 6.39795i | 0.119405 | + | 0.206816i | ||||
\(958\) | −13.5126 | + | 23.4046i | −0.436573 | + | 0.756167i | ||||
\(959\) | −1.02817 | + | 17.9396i | −0.0332015 | + | 0.579299i | ||||
\(960\) | 0.651388 | + | 1.12824i | 0.0210235 | + | 0.0364137i | ||||
\(961\) | 5.43448 | + | 9.41280i | 0.175306 | + | 0.303639i | ||||
\(962\) | 3.59593 | − | 2.11827i | 0.115938 | − | 0.0682958i | ||||
\(963\) | 7.01462 | − | 12.1497i | 0.226043 | − | 0.391518i | ||||
\(964\) | 5.92875 | − | 10.2689i | 0.190952 | − | 0.330739i | ||||
\(965\) | −0.179979 | − | 0.311732i | −0.00579372 | − | 0.0100350i | ||||
\(966\) | 0.725078 | − | 12.6512i | 0.0233290 | − | 0.407045i | ||||
\(967\) | −7.46926 | −0.240195 | −0.120098 | − | 0.992762i | \(-0.538321\pi\) | ||||
−0.120098 | + | 0.992762i | \(0.538321\pi\) | |||||||
\(968\) | 6.51073 | 0.209263 | ||||||||
\(969\) | −1.52753 | − | 2.64576i | −0.0490714 | − | 0.0849942i | ||||
\(970\) | 0.910122 | − | 1.57638i | 0.0292223 | − | 0.0506144i | ||||
\(971\) | −3.28791 | −0.105514 | −0.0527570 | − | 0.998607i | \(-0.516801\pi\) | ||||
−0.0527570 | + | 0.998607i | \(0.516801\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 30.5103 | − | 15.3583i | 0.978116 | − | 0.492364i | ||||
\(974\) | −21.9435 | −0.703114 | ||||||||
\(975\) | 10.3646 | + | 5.86372i | 0.331933 | + | 0.187789i | ||||
\(976\) | 5.09231 | − | 8.82015i | 0.163001 | − | 0.282326i | ||||
\(977\) | −0.832998 | −0.0266500 | −0.0133250 | − | 0.999911i | \(-0.504242\pi\) | ||||
−0.0133250 | + | 0.999911i | \(0.504242\pi\) | |||||||
\(978\) | −1.30383 | + | 2.25831i | −0.0416920 | + | 0.0722126i | ||||
\(979\) | −9.95535 | + | 17.2432i | −0.318174 | + | 0.551094i | ||||
\(980\) | 9.05971 | + | 1.04190i | 0.289402 | + | 0.0332824i | ||||
\(981\) | −5.50000 | + | 9.52628i | −0.175601 | + | 0.304151i | ||||
\(982\) | −14.1804 | −0.452515 | ||||||||
\(983\) | 20.9860 | − | 36.3487i | 0.669348 | − | 1.15934i | −0.308739 | − | 0.951147i | \(-0.599907\pi\) |
0.978087 | − | 0.208198i | \(-0.0667598\pi\) | |||||||
\(984\) | 6.31845 | + | 10.9439i | 0.201425 | + | 0.348878i | ||||
\(985\) | 8.64459 | − | 14.9729i | 0.275440 | − | 0.477075i | ||||
\(986\) | 0.848612 | + | 1.46984i | 0.0270253 | + | 0.0468092i | ||||
\(987\) | 1.20677 | − | 21.0558i | 0.0384120 | − | 0.670214i | ||||
\(988\) | −19.4980 | + | 11.4858i | −0.620314 | + | 0.365411i | ||||
\(989\) | 19.2231 | + | 33.2954i | 0.611259 | + | 1.05873i | ||||
\(990\) | 2.76031 | 0.0877283 | ||||||||
\(991\) | −51.9215 | −1.64934 | −0.824670 | − | 0.565614i | \(-0.808639\pi\) | ||||
−0.824670 | + | 0.565614i | \(0.808639\pi\) | |||||||
\(992\) | 4.48676 | 0.142455 | ||||||||
\(993\) | 16.4338 | 0.521511 | ||||||||
\(994\) | 0.444293 | − | 7.75204i | 0.0140921 | − | 0.245880i | ||||
\(995\) | 12.3906 | − | 21.4612i | 0.392809 | − | 0.680364i | ||||
\(996\) | −1.74338 | − | 3.01962i | −0.0552411 | − | 0.0956805i | ||||
\(997\) | 24.2587 | + | 42.0173i | 0.768281 | + | 1.33070i | 0.938494 | + | 0.345294i | \(0.112221\pi\) |
−0.170214 | + | 0.985407i | \(0.554446\pi\) | |||||||
\(998\) | 29.4975 | 0.933728 | ||||||||
\(999\) | 0.578756 | − | 1.00243i | 0.0183110 | − | 0.0317156i |
(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 | 546.2.k.d.445.4 | yes | 8 | |
3.2 | odd | 2 | 1638.2.p.g.991.2 | 8 | |||
7.2 | even | 3 | 546.2.j.b.289.3 | ✓ | 8 | ||
13.9 | even | 3 | 546.2.j.b.529.3 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.m.i.289.1 | 8 | |||
39.35 | odd | 6 | 1638.2.m.i.1621.1 | 8 | |||
91.9 | even | 3 | inner | 546.2.k.d.373.4 | yes | 8 | |
273.191 | odd | 6 | 1638.2.p.g.919.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.b.289.3 | ✓ | 8 | 7.2 | even | 3 | ||
546.2.j.b.529.3 | yes | 8 | 13.9 | even | 3 | ||
546.2.k.d.373.4 | yes | 8 | 91.9 | even | 3 | inner | |
546.2.k.d.445.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1638.2.m.i.289.1 | 8 | 21.2 | odd | 6 | |||
1638.2.m.i.1621.1 | 8 | 39.35 | odd | 6 | |||
1638.2.p.g.919.2 | 8 | 273.191 | odd | 6 | |||
1638.2.p.g.991.2 | 8 | 3.2 | odd | 2 |