Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.173309020416.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Root | \(-1.61272 + 2.45863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.n.415.2 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.739514 | − | 1.28088i | −0.330721 | − | 0.572825i | 0.651933 | − | 0.758277i | \(-0.273959\pi\) |
−0.982653 | + | 0.185452i | \(0.940625\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.32288 | − | 2.29129i | 0.500000 | − | 0.866025i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.739514 | − | 1.28088i | 0.233855 | − | 0.405049i | ||||
\(11\) | −2.85224 | + | 4.94022i | −0.859982 | + | 1.48953i | 0.0119622 | + | 0.999928i | \(0.496192\pi\) |
−0.871945 | + | 0.489605i | \(0.837141\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 6.35023 | 1.76124 | 0.880618 | − | 0.473826i | \(-0.157128\pi\) | ||||
0.880618 | + | 0.473826i | \(0.157128\pi\) | |||||||
\(14\) | 2.64575 | 0.707107 | ||||||||
\(15\) | −1.47903 | −0.381884 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.06239 | − | 3.57216i | 0.500203 | − | 0.866377i | −0.499797 | − | 0.866143i | \(-0.666592\pi\) |
1.00000 | 0.000234490i | \(-7.46404e-5\pi\) | ||||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −1.69609 | − | 2.93771i | −0.389109 | − | 0.673956i | 0.603221 | − | 0.797574i | \(-0.293884\pi\) |
−0.992330 | + | 0.123618i | \(0.960550\pi\) | |||||||
\(20\) | 1.47903 | 0.330721 | ||||||||
\(21\) | −1.32288 | − | 2.29129i | −0.288675 | − | 0.500000i | ||||
\(22\) | −5.70448 | −1.21620 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 1.40624 | − | 2.43567i | 0.281247 | − | 0.487135i | ||||
\(26\) | 3.17511 | + | 5.49946i | 0.622691 | + | 1.07853i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.32288 | + | 2.29129i | 0.250000 | + | 0.433013i | ||||
\(29\) | 2.39217 | 0.444215 | 0.222108 | − | 0.975022i | \(-0.428706\pi\) | ||||
0.222108 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(30\) | −0.739514 | − | 1.28088i | −0.135016 | − | 0.233855i | ||||
\(31\) | 3.90624 | − | 6.76580i | 0.701581 | − | 1.21517i | −0.266330 | − | 0.963882i | \(-0.585811\pi\) |
0.967911 | − | 0.251292i | \(-0.0808554\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 2.85224 | + | 4.94022i | 0.496511 | + | 0.859982i | ||||
\(34\) | 4.12478 | 0.707394 | ||||||||
\(35\) | −3.91314 | −0.661442 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.17511 | − | 7.23151i | −0.686385 | − | 1.18885i | −0.973000 | − | 0.230807i | \(-0.925863\pi\) |
0.286615 | − | 0.958046i | \(-0.407470\pi\) | |||||||
\(38\) | 1.69609 | − | 2.93771i | 0.275141 | − | 0.476559i | ||||
\(39\) | 3.17511 | − | 5.49946i | 0.508425 | − | 0.880618i | ||||
\(40\) | 0.739514 | + | 1.28088i | 0.116927 | + | 0.202524i | ||||
\(41\) | 7.39217 | 1.15446 | 0.577232 | − | 0.816580i | \(-0.304133\pi\) | ||||
0.577232 | + | 0.816580i | \(0.304133\pi\) | |||||||
\(42\) | 1.32288 | − | 2.29129i | 0.204124 | − | 0.353553i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −2.85224 | − | 4.94022i | −0.429991 | − | 0.744767i | ||||
\(45\) | −0.739514 | + | 1.28088i | −0.110240 | + | 0.190942i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | −5.11071 | − | 8.85202i | −0.745474 | − | 1.29120i | −0.949973 | − | 0.312333i | \(-0.898890\pi\) |
0.204499 | − | 0.978867i | \(-0.434444\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | 2.81247 | 0.397744 | ||||||||
\(51\) | −2.06239 | − | 3.57216i | −0.288792 | − | 0.500203i | ||||
\(52\) | −3.17511 | + | 5.49946i | −0.440309 | + | 0.762638i | ||||
\(53\) | −0.260486 | + | 0.451174i | −0.0357804 | + | 0.0619736i | −0.883361 | − | 0.468693i | \(-0.844725\pi\) |
0.847581 | + | 0.530667i | \(0.178058\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 8.43709 | 1.13766 | ||||||||
\(56\) | −1.32288 | + | 2.29129i | −0.176777 | + | 0.306186i | ||||
\(57\) | −3.39217 | −0.449304 | ||||||||
\(58\) | 1.19609 | + | 2.07168i | 0.157054 | + | 0.272025i | ||||
\(59\) | −3.68918 | + | 6.38985i | −0.480290 | + | 0.831887i | −0.999744 | − | 0.0226111i | \(-0.992802\pi\) |
0.519454 | + | 0.854498i | \(0.326135\pi\) | |||||||
\(60\) | 0.739514 | − | 1.28088i | 0.0954709 | − | 0.165360i | ||||
\(61\) | 2.52097 | + | 4.36645i | 0.322777 | + | 0.559067i | 0.981060 | − | 0.193704i | \(-0.0620502\pi\) |
−0.658283 | + | 0.752771i | \(0.728717\pi\) | |||||||
\(62\) | 7.81247 | 0.992185 | ||||||||
\(63\) | −2.64575 | −0.333333 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.69609 | − | 8.13386i | −0.582478 | − | 1.00888i | ||||
\(66\) | −2.85224 | + | 4.94022i | −0.351086 | + | 0.608099i | ||||
\(67\) | −7.70448 | + | 13.3445i | −0.941252 | + | 1.63030i | −0.178164 | + | 0.984001i | \(0.557016\pi\) |
−0.763088 | + | 0.646295i | \(0.776318\pi\) | |||||||
\(68\) | 2.06239 | + | 3.57216i | 0.250102 | + | 0.433189i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.95657 | − | 3.38888i | −0.233855 | − | 0.405049i | ||||
\(71\) | 9.87120 | 1.17150 | 0.585748 | − | 0.810493i | \(-0.300801\pi\) | ||||
0.585748 | + | 0.810493i | \(0.300801\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −4.46496 | + | 7.73354i | −0.522584 | + | 0.905143i | 0.477070 | + | 0.878865i | \(0.341699\pi\) |
−0.999655 | + | 0.0262776i | \(0.991635\pi\) | |||||||
\(74\) | 4.17511 | − | 7.23151i | 0.485347 | − | 0.840646i | ||||
\(75\) | −1.40624 | − | 2.43567i | −0.162378 | − | 0.281247i | ||||
\(76\) | 3.39217 | 0.389109 | ||||||||
\(77\) | 7.54631 | + | 13.0706i | 0.859982 | + | 1.48953i | ||||
\(78\) | 6.35023 | 0.719022 | ||||||||
\(79\) | 6.71505 | + | 11.6308i | 0.755502 | + | 1.30857i | 0.945124 | + | 0.326710i | \(0.105940\pi\) |
−0.189623 | + | 0.981857i | \(0.560726\pi\) | |||||||
\(80\) | −0.739514 | + | 1.28088i | −0.0826802 | + | 0.143206i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.69609 | + | 6.40181i | 0.408164 | + | 0.706961i | ||||
\(83\) | −9.22143 | −1.01218 | −0.506092 | − | 0.862480i | \(-0.668910\pi\) | ||||
−0.506092 | + | 0.862480i | \(0.668910\pi\) | |||||||
\(84\) | 2.64575 | 0.288675 | ||||||||
\(85\) | −6.10067 | −0.661710 | ||||||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | 1.19609 | − | 2.07168i | 0.128234 | − | 0.222108i | ||||
\(88\) | 2.85224 | − | 4.94022i | 0.304050 | − | 0.526629i | ||||
\(89\) | 3.21706 | + | 5.57211i | 0.341007 | + | 0.590642i | 0.984620 | − | 0.174709i | \(-0.0558986\pi\) |
−0.643613 | + | 0.765351i | \(0.722565\pi\) | |||||||
\(90\) | −1.47903 | −0.155903 | ||||||||
\(91\) | 8.40056 | − | 14.5502i | 0.880618 | − | 1.52528i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −3.90624 | − | 6.76580i | −0.405058 | − | 0.701581i | ||||
\(94\) | 5.11071 | − | 8.85202i | 0.527130 | − | 0.913016i | ||||
\(95\) | −2.50856 | + | 4.34495i | −0.257373 | + | 0.445783i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −10.3640 | −1.05231 | −0.526154 | − | 0.850389i | \(-0.676367\pi\) | ||||
−0.526154 | + | 0.850389i | \(0.676367\pi\) | |||||||
\(98\) | 3.50000 | − | 6.06218i | 0.353553 | − | 0.612372i | ||||
\(99\) | 5.70448 | 0.573322 | ||||||||
\(100\) | 1.40624 | + | 2.43567i | 0.140624 | + | 0.243567i | ||||
\(101\) | −1.40624 | + | 2.43567i | −0.139926 | + | 0.242359i | −0.927468 | − | 0.373902i | \(-0.878020\pi\) |
0.787543 | + | 0.616260i | \(0.211353\pi\) | |||||||
\(102\) | 2.06239 | − | 3.57216i | 0.204207 | − | 0.353697i | ||||
\(103\) | 6.27945 | + | 10.8763i | 0.618732 | + | 1.07168i | 0.989717 | + | 0.143037i | \(0.0456868\pi\) |
−0.370985 | + | 0.928639i | \(0.620980\pi\) | |||||||
\(104\) | −6.35023 | −0.622691 | ||||||||
\(105\) | −1.95657 | + | 3.38888i | −0.190942 | + | 0.330721i | ||||
\(106\) | −0.520971 | −0.0506012 | ||||||||
\(107\) | 2.61071 | + | 4.52189i | 0.252387 | + | 0.437148i | 0.964183 | − | 0.265239i | \(-0.0854510\pi\) |
−0.711795 | + | 0.702387i | \(0.752118\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 4.23750 | − | 7.33957i | 0.405879 | − | 0.703004i | −0.588544 | − | 0.808465i | \(-0.700299\pi\) |
0.994423 | + | 0.105462i | \(0.0336320\pi\) | |||||||
\(110\) | 4.21854 | + | 7.30673i | 0.402222 | + | 0.696669i | ||||
\(111\) | −8.35023 | −0.792569 | ||||||||
\(112\) | −2.64575 | −0.250000 | ||||||||
\(113\) | 0.725281 | 0.0682287 | 0.0341144 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341144 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(114\) | −1.69609 | − | 2.93771i | −0.158853 | − | 0.275141i | ||||
\(115\) | −0.739514 | + | 1.28088i | −0.0689601 | + | 0.119442i | ||||
\(116\) | −1.19609 | + | 2.07168i | −0.111054 | + | 0.192351i | ||||
\(117\) | −3.17511 | − | 5.49946i | −0.293539 | − | 0.508425i | ||||
\(118\) | −7.37836 | −0.679233 | ||||||||
\(119\) | −5.45657 | − | 9.45106i | −0.500203 | − | 0.866377i | ||||
\(120\) | 1.47903 | 0.135016 | ||||||||
\(121\) | −10.7705 | − | 18.6551i | −0.979139 | − | 1.69592i | ||||
\(122\) | −2.52097 | + | 4.36645i | −0.228238 | + | 0.395320i | ||||
\(123\) | 3.69609 | − | 6.40181i | 0.333265 | − | 0.577232i | ||||
\(124\) | 3.90624 | + | 6.76580i | 0.350790 | + | 0.607587i | ||||
\(125\) | −11.5549 | −1.03350 | ||||||||
\(126\) | −1.32288 | − | 2.29129i | −0.117851 | − | 0.204124i | ||||
\(127\) | 0.0138109 | 0.00122552 | 0.000612760 | − | 1.00000i | \(-0.499805\pi\) | ||||
0.000612760 | 1.00000i | \(0.499805\pi\) | ||||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | 4.69609 | − | 8.13386i | 0.411874 | − | 0.713387i | ||||
\(131\) | 7.24807 | + | 12.5540i | 0.633267 | + | 1.09685i | 0.986879 | + | 0.161459i | \(0.0516199\pi\) |
−0.353612 | + | 0.935392i | \(0.615047\pi\) | |||||||
\(132\) | −5.70448 | −0.496511 | ||||||||
\(133\) | −8.97484 | −0.778217 | ||||||||
\(134\) | −15.4090 | −1.33113 | ||||||||
\(135\) | 0.739514 | + | 1.28088i | 0.0636473 | + | 0.110240i | ||||
\(136\) | −2.06239 | + | 3.57216i | −0.176848 | + | 0.306311i | ||||
\(137\) | −4.01206 | + | 6.94908i | −0.342773 | + | 0.593700i | −0.984947 | − | 0.172859i | \(-0.944700\pi\) |
0.642174 | + | 0.766559i | \(0.278033\pi\) | |||||||
\(138\) | −0.500000 | − | 0.866025i | −0.0425628 | − | 0.0737210i | ||||
\(139\) | 14.2214 | 1.20625 | 0.603123 | − | 0.797648i | \(-0.293923\pi\) | ||||
0.603123 | + | 0.797648i | \(0.293923\pi\) | |||||||
\(140\) | 1.95657 | − | 3.38888i | 0.165360 | − | 0.286413i | ||||
\(141\) | −10.2214 | −0.860800 | ||||||||
\(142\) | 4.93560 | + | 8.54871i | 0.414186 | + | 0.717392i | ||||
\(143\) | −18.1124 | + | 31.3715i | −1.51463 | + | 2.62342i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.76905 | − | 3.06408i | −0.146911 | − | 0.254458i | ||||
\(146\) | −8.92993 | −0.739046 | ||||||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | 8.35023 | 0.686385 | ||||||||
\(149\) | 11.6417 | + | 20.1641i | 0.953728 | + | 1.65190i | 0.737253 | + | 0.675617i | \(0.236123\pi\) |
0.216475 | + | 0.976288i | \(0.430544\pi\) | |||||||
\(150\) | 1.40624 | − | 2.43567i | 0.114819 | − | 0.198872i | ||||
\(151\) | 3.00691 | − | 5.20811i | 0.244698 | − | 0.423830i | −0.717348 | − | 0.696715i | \(-0.754644\pi\) |
0.962047 | + | 0.272884i | \(0.0879777\pi\) | |||||||
\(152\) | 1.69609 | + | 2.93771i | 0.137571 | + | 0.238279i | ||||
\(153\) | −4.12478 | −0.333469 | ||||||||
\(154\) | −7.54631 | + | 13.0706i | −0.608099 | + | 1.05326i | ||||
\(155\) | −11.5549 | −0.928110 | ||||||||
\(156\) | 3.17511 | + | 5.49946i | 0.254213 | + | 0.440309i | ||||
\(157\) | 8.93359 | − | 15.4734i | 0.712978 | − | 1.23491i | −0.250756 | − | 0.968050i | \(-0.580679\pi\) |
0.963734 | − | 0.266864i | \(-0.0859875\pi\) | |||||||
\(158\) | −6.71505 | + | 11.6308i | −0.534220 | + | 0.925297i | ||||
\(159\) | 0.260486 | + | 0.451174i | 0.0206579 | + | 0.0357804i | ||||
\(160\) | −1.47903 | −0.116927 | ||||||||
\(161\) | −2.64575 | −0.208514 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −6.93560 | − | 12.0128i | −0.543238 | − | 0.940916i | −0.998716 | − | 0.0506687i | \(-0.983865\pi\) |
0.455477 | − | 0.890247i | \(-0.349469\pi\) | |||||||
\(164\) | −3.69609 | + | 6.40181i | −0.288616 | + | 0.499897i | ||||
\(165\) | 4.21854 | − | 7.30673i | 0.328413 | − | 0.568828i | ||||
\(166\) | −4.61071 | − | 7.98599i | −0.357861 | − | 0.619833i | ||||
\(167\) | 5.07551 | 0.392755 | 0.196377 | − | 0.980528i | \(-0.437082\pi\) | ||||
0.196377 | + | 0.980528i | \(0.437082\pi\) | |||||||
\(168\) | 1.32288 | + | 2.29129i | 0.102062 | + | 0.176777i | ||||
\(169\) | 27.3254 | 2.10195 | ||||||||
\(170\) | −3.05033 | − | 5.28333i | −0.233950 | − | 0.405213i | ||||
\(171\) | −1.69609 | + | 2.93771i | −0.129703 | + | 0.224652i | ||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | −1.46496 | − | 2.53739i | −0.111379 | − | 0.192914i | 0.804947 | − | 0.593346i | \(-0.202193\pi\) |
−0.916327 | + | 0.400432i | \(0.868860\pi\) | |||||||
\(174\) | 2.39217 | 0.181350 | ||||||||
\(175\) | −3.72055 | − | 6.44419i | −0.281247 | − | 0.487135i | ||||
\(176\) | 5.70448 | 0.429991 | ||||||||
\(177\) | 3.68918 | + | 6.38985i | 0.277296 | + | 0.480290i | ||||
\(178\) | −3.21706 | + | 5.57211i | −0.241129 | + | 0.417647i | ||||
\(179\) | 3.97187 | − | 6.87948i | 0.296871 | − | 0.514196i | −0.678547 | − | 0.734557i | \(-0.737390\pi\) |
0.975418 | + | 0.220361i | \(0.0707234\pi\) | |||||||
\(180\) | −0.739514 | − | 1.28088i | −0.0551201 | − | 0.0954709i | ||||
\(181\) | −7.39950 | −0.550000 | −0.275000 | − | 0.961444i | \(-0.588678\pi\) | ||||
−0.275000 | + | 0.961444i | \(0.588678\pi\) | |||||||
\(182\) | 16.8011 | 1.24538 | ||||||||
\(183\) | 5.04194 | 0.372711 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | −6.17511 | + | 10.6956i | −0.454003 | + | 0.786357i | ||||
\(186\) | 3.90624 | − | 6.76580i | 0.286419 | − | 0.496093i | ||||
\(187\) | 11.7649 | + | 20.3773i | 0.860332 | + | 1.49014i | ||||
\(188\) | 10.2214 | 0.745474 | ||||||||
\(189\) | −1.32288 | + | 2.29129i | −0.0962250 | + | 0.166667i | ||||
\(190\) | −5.01712 | −0.363980 | ||||||||
\(191\) | −10.0883 | − | 17.4734i | −0.729961 | − | 1.26433i | −0.956899 | − | 0.290420i | \(-0.906205\pi\) |
0.226939 | − | 0.973909i | \(-0.427128\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −6.44399 | + | 11.1613i | −0.463849 | + | 0.803409i | −0.999149 | − | 0.0412525i | \(-0.986865\pi\) |
0.535300 | + | 0.844662i | \(0.320199\pi\) | |||||||
\(194\) | −5.18202 | − | 8.97552i | −0.372047 | − | 0.644405i | ||||
\(195\) | −9.39217 | −0.672587 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | −9.80410 | −0.698513 | −0.349257 | − | 0.937027i | \(-0.613566\pi\) | ||||
−0.349257 | + | 0.937027i | \(0.613566\pi\) | |||||||
\(198\) | 2.85224 | + | 4.94022i | 0.202700 | + | 0.351086i | ||||
\(199\) | −1.65781 | + | 2.87141i | −0.117519 | + | 0.203549i | −0.918784 | − | 0.394761i | \(-0.870827\pi\) |
0.801265 | + | 0.598310i | \(0.204161\pi\) | |||||||
\(200\) | −1.40624 | + | 2.43567i | −0.0994360 | + | 0.172228i | ||||
\(201\) | 7.70448 | + | 13.3445i | 0.543432 | + | 0.941252i | ||||
\(202\) | −2.81247 | −0.197885 | ||||||||
\(203\) | 3.16454 | − | 5.48115i | 0.222108 | − | 0.384702i | ||||
\(204\) | 4.12478 | 0.288792 | ||||||||
\(205\) | −5.46662 | − | 9.46846i | −0.381805 | − | 0.661306i | ||||
\(206\) | −6.27945 | + | 10.8763i | −0.437510 | + | 0.757789i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | −3.17511 | − | 5.49946i | −0.220155 | − | 0.381319i | ||||
\(209\) | 19.3506 | 1.33851 | ||||||||
\(210\) | −3.91314 | −0.270032 | ||||||||
\(211\) | −17.9638 | −1.23668 | −0.618340 | − | 0.785910i | \(-0.712195\pi\) | ||||
−0.618340 | + | 0.785910i | \(0.712195\pi\) | |||||||
\(212\) | −0.260486 | − | 0.451174i | −0.0178902 | − | 0.0309868i | ||||
\(213\) | 4.93560 | − | 8.54871i | 0.338182 | − | 0.585748i | ||||
\(214\) | −2.61071 | + | 4.52189i | −0.178465 | + | 0.309110i | ||||
\(215\) | −1.47903 | − | 2.56175i | −0.100869 | − | 0.174710i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.3349 | − | 17.9006i | −0.701581 | − | 1.21517i | ||||
\(218\) | 8.47501 | 0.574000 | ||||||||
\(219\) | 4.46496 | + | 7.73354i | 0.301714 | + | 0.522584i | ||||
\(220\) | −4.21854 | + | 7.30673i | −0.284414 | + | 0.492620i | ||||
\(221\) | 13.0966 | − | 22.6841i | 0.880976 | − | 1.52590i | ||||
\(222\) | −4.17511 | − | 7.23151i | −0.280215 | − | 0.485347i | ||||
\(223\) | −1.22947 | −0.0823313 | −0.0411657 | − | 0.999152i | \(-0.513107\pi\) | ||||
−0.0411657 | + | 0.999152i | \(0.513107\pi\) | |||||||
\(224\) | −1.32288 | − | 2.29129i | −0.0883883 | − | 0.153093i | ||||
\(225\) | −2.81247 | −0.187498 | ||||||||
\(226\) | 0.362641 | + | 0.628112i | 0.0241225 | + | 0.0417814i | ||||
\(227\) | −8.20649 | + | 14.2141i | −0.544684 | + | 0.943420i | 0.453943 | + | 0.891031i | \(0.350017\pi\) |
−0.998627 | + | 0.0523891i | \(0.983316\pi\) | |||||||
\(228\) | 1.69609 | − | 2.93771i | 0.112326 | − | 0.194554i | ||||
\(229\) | 12.7081 | + | 22.0111i | 0.839778 | + | 1.45454i | 0.890080 | + | 0.455803i | \(0.150648\pi\) |
−0.0503028 | + | 0.998734i | \(0.516019\pi\) | |||||||
\(230\) | −1.47903 | −0.0975243 | ||||||||
\(231\) | 15.0926 | 0.993022 | ||||||||
\(232\) | −2.39217 | −0.157054 | ||||||||
\(233\) | −0.275783 | − | 0.477670i | −0.0180671 | − | 0.0312932i | 0.856850 | − | 0.515565i | \(-0.172418\pi\) |
−0.874918 | + | 0.484272i | \(0.839085\pi\) | |||||||
\(234\) | 3.17511 | − | 5.49946i | 0.207564 | − | 0.359511i | ||||
\(235\) | −7.55889 | + | 13.0924i | −0.493088 | + | 0.854053i | ||||
\(236\) | −3.68918 | − | 6.38985i | −0.240145 | − | 0.415944i | ||||
\(237\) | 13.4301 | 0.872378 | ||||||||
\(238\) | 5.45657 | − | 9.45106i | 0.353697 | − | 0.612621i | ||||
\(239\) | −11.2634 | −0.728567 | −0.364283 | − | 0.931288i | \(-0.618686\pi\) | ||||
−0.364283 | + | 0.931288i | \(0.618686\pi\) | |||||||
\(240\) | 0.739514 | + | 1.28088i | 0.0477354 | + | 0.0826802i | ||||
\(241\) | 14.1642 | − | 24.5331i | 0.912396 | − | 1.58032i | 0.101725 | − | 0.994813i | \(-0.467564\pi\) |
0.810670 | − | 0.585503i | \(-0.199103\pi\) | |||||||
\(242\) | 10.7705 | − | 18.6551i | 0.692356 | − | 1.19920i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.04194 | −0.322777 | ||||||||
\(245\) | −5.17660 | + | 8.96614i | −0.330721 | + | 0.572825i | ||||
\(246\) | 7.39217 | 0.471308 | ||||||||
\(247\) | −10.7705 | − | 18.6551i | −0.685313 | − | 1.18700i | ||||
\(248\) | −3.90624 | + | 6.76580i | −0.248046 | + | 0.429629i | ||||
\(249\) | −4.61071 | + | 7.98599i | −0.292192 | + | 0.506092i | ||||
\(250\) | −5.77744 | − | 10.0068i | −0.365397 | − | 0.632886i | ||||
\(251\) | −7.83659 | −0.494641 | −0.247320 | − | 0.968934i | \(-0.579550\pi\) | ||||
−0.247320 | + | 0.968934i | \(0.579550\pi\) | |||||||
\(252\) | 1.32288 | − | 2.29129i | 0.0833333 | − | 0.144338i | ||||
\(253\) | 5.70448 | 0.358637 | ||||||||
\(254\) | 0.00690545 | + | 0.0119606i | 0.000433287 | + | 0.000750475i | ||||
\(255\) | −3.05033 | + | 5.28333i | −0.191019 | + | 0.330855i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.86281 | − | 3.22648i | −0.116199 | − | 0.201262i | 0.802060 | − | 0.597244i | \(-0.203738\pi\) |
−0.918258 | + | 0.395982i | \(0.870404\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | −22.0926 | −1.37277 | ||||||||
\(260\) | 9.39217 | 0.582478 | ||||||||
\(261\) | −1.19609 | − | 2.07168i | −0.0740358 | − | 0.128234i | ||||
\(262\) | −7.24807 | + | 12.5540i | −0.447787 | + | 0.775591i | ||||
\(263\) | −14.4331 | + | 24.9988i | −0.889981 | + | 1.54149i | −0.0500850 | + | 0.998745i | \(0.515949\pi\) |
−0.839896 | + | 0.542747i | \(0.817384\pi\) | |||||||
\(264\) | −2.85224 | − | 4.94022i | −0.175543 | − | 0.304050i | ||||
\(265\) | 0.770531 | 0.0473334 | ||||||||
\(266\) | −4.48742 | − | 7.77244i | −0.275141 | − | 0.476559i | ||||
\(267\) | 6.43411 | 0.393761 | ||||||||
\(268\) | −7.70448 | − | 13.3445i | −0.470626 | − | 0.815148i | ||||
\(269\) | 0.241001 | − | 0.417426i | 0.0146941 | − | 0.0254509i | −0.858585 | − | 0.512671i | \(-0.828656\pi\) |
0.873279 | + | 0.487221i | \(0.161989\pi\) | |||||||
\(270\) | −0.739514 | + | 1.28088i | −0.0450054 | + | 0.0779517i | ||||
\(271\) | 2.44801 | + | 4.24008i | 0.148706 | + | 0.257567i | 0.930750 | − | 0.365657i | \(-0.119156\pi\) |
−0.782043 | + | 0.623224i | \(0.785822\pi\) | |||||||
\(272\) | −4.12478 | −0.250102 | ||||||||
\(273\) | −8.40056 | − | 14.5502i | −0.508425 | − | 0.880618i | ||||
\(274\) | −8.02411 | −0.484754 | ||||||||
\(275\) | 8.02185 | + | 13.8942i | 0.483736 | + | 0.837855i | ||||
\(276\) | 0.500000 | − | 0.866025i | 0.0300965 | − | 0.0521286i | ||||
\(277\) | −7.76320 | + | 13.4463i | −0.466446 | + | 0.807908i | −0.999265 | − | 0.0383211i | \(-0.987799\pi\) |
0.532820 | + | 0.846229i | \(0.321132\pi\) | |||||||
\(278\) | 7.11071 | + | 12.3161i | 0.426472 | + | 0.738672i | ||||
\(279\) | −7.81247 | −0.467721 | ||||||||
\(280\) | 3.91314 | 0.233855 | ||||||||
\(281\) | 13.2003 | 0.787463 | 0.393732 | − | 0.919225i | \(-0.371184\pi\) | ||||
0.393732 | + | 0.919225i | \(0.371184\pi\) | |||||||
\(282\) | −5.11071 | − | 8.85202i | −0.304339 | − | 0.527130i | ||||
\(283\) | 1.37836 | − | 2.38739i | 0.0819350 | − | 0.141916i | −0.822146 | − | 0.569277i | \(-0.807223\pi\) |
0.904081 | + | 0.427361i | \(0.140557\pi\) | |||||||
\(284\) | −4.93560 | + | 8.54871i | −0.292874 | + | 0.507273i | ||||
\(285\) | 2.50856 | + | 4.34495i | 0.148594 | + | 0.257373i | ||||
\(286\) | −36.2247 | −2.14201 | ||||||||
\(287\) | 9.77892 | − | 16.9376i | 0.577232 | − | 0.999794i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −0.00690545 | − | 0.0119606i | −0.000406203 | − | 0.000703565i | ||||
\(290\) | 1.76905 | − | 3.06408i | 0.103882 | − | 0.179929i | ||||
\(291\) | −5.18202 | + | 8.97552i | −0.303775 | + | 0.526154i | ||||
\(292\) | −4.46496 | − | 7.73354i | −0.261292 | − | 0.452571i | ||||
\(293\) | 0.0976957 | 0.00570745 | 0.00285372 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285372 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(294\) | −3.50000 | − | 6.06218i | −0.204124 | − | 0.353553i | ||||
\(295\) | 10.9128 | 0.635368 | ||||||||
\(296\) | 4.17511 | + | 7.23151i | 0.242674 | + | 0.420323i | ||||
\(297\) | 2.85224 | − | 4.94022i | 0.165504 | − | 0.286661i | ||||
\(298\) | −11.6417 | + | 20.1641i | −0.674387 | + | 1.16807i | ||||
\(299\) | −3.17511 | − | 5.49946i | −0.183622 | − | 0.318042i | ||||
\(300\) | 2.81247 | 0.162378 | ||||||||
\(301\) | 2.64575 | − | 4.58258i | 0.152499 | − | 0.264135i | ||||
\(302\) | 6.01381 | 0.346056 | ||||||||
\(303\) | 1.40624 | + | 2.43567i | 0.0807862 | + | 0.139926i | ||||
\(304\) | −1.69609 | + | 2.93771i | −0.0972772 | + | 0.168489i | ||||
\(305\) | 3.72859 | − | 6.45811i | 0.213498 | − | 0.369790i | ||||
\(306\) | −2.06239 | − | 3.57216i | −0.117899 | − | 0.204207i | ||||
\(307\) | −24.9467 | −1.42378 | −0.711892 | − | 0.702289i | \(-0.752161\pi\) | ||||
−0.711892 | + | 0.702289i | \(0.752161\pi\) | |||||||
\(308\) | −15.0926 | −0.859982 | ||||||||
\(309\) | 12.5589 | 0.714450 | ||||||||
\(310\) | −5.77744 | − | 10.0068i | −0.328136 | − | 0.568349i | ||||
\(311\) | −13.2439 | + | 22.9391i | −0.750992 | + | 1.30076i | 0.196351 | + | 0.980534i | \(0.437091\pi\) |
−0.947342 | + | 0.320222i | \(0.896242\pi\) | |||||||
\(312\) | −3.17511 | + | 5.49946i | −0.179755 | + | 0.311346i | ||||
\(313\) | 9.61911 | + | 16.6608i | 0.543704 | + | 0.941723i | 0.998687 | + | 0.0512230i | \(0.0163119\pi\) |
−0.454983 | + | 0.890500i | \(0.650355\pi\) | |||||||
\(314\) | 17.8672 | 1.00830 | ||||||||
\(315\) | 1.95657 | + | 3.38888i | 0.110240 | + | 0.190942i | ||||
\(316\) | −13.4301 | −0.755502 | ||||||||
\(317\) | −12.6892 | − | 21.9783i | −0.712695 | − | 1.23442i | −0.963842 | − | 0.266475i | \(-0.914141\pi\) |
0.251146 | − | 0.967949i | \(-0.419192\pi\) | |||||||
\(318\) | −0.260486 | + | 0.451174i | −0.0146073 | + | 0.0253006i | ||||
\(319\) | −6.82304 | + | 11.8179i | −0.382017 | + | 0.661673i | ||||
\(320\) | −0.739514 | − | 1.28088i | −0.0413401 | − | 0.0716032i | ||||
\(321\) | 5.22143 | 0.291432 | ||||||||
\(322\) | −1.32288 | − | 2.29129i | −0.0737210 | − | 0.127688i | ||||
\(323\) | −13.9920 | −0.778533 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 8.92993 | − | 15.4671i | 0.495343 | − | 0.857960i | ||||
\(326\) | 6.93560 | − | 12.0128i | 0.384127 | − | 0.665328i | ||||
\(327\) | −4.23750 | − | 7.33957i | −0.234335 | − | 0.405879i | ||||
\(328\) | −7.39217 | −0.408164 | ||||||||
\(329\) | −27.0434 | −1.49095 | ||||||||
\(330\) | 8.43709 | 0.464446 | ||||||||
\(331\) | −1.42137 | − | 2.46188i | −0.0781254 | − | 0.135317i | 0.824316 | − | 0.566130i | \(-0.191560\pi\) |
−0.902441 | + | 0.430813i | \(0.858227\pi\) | |||||||
\(332\) | 4.61071 | − | 7.98599i | 0.253046 | − | 0.438288i | ||||
\(333\) | −4.17511 | + | 7.23151i | −0.228795 | + | 0.396284i | ||||
\(334\) | 2.53775 | + | 4.39552i | 0.138860 | + | 0.240512i | ||||
\(335\) | 22.7903 | 1.24517 | ||||||||
\(336\) | −1.32288 | + | 2.29129i | −0.0721688 | + | 0.125000i | ||||
\(337\) | 26.7793 | 1.45876 | 0.729380 | − | 0.684109i | \(-0.239809\pi\) | ||||
0.729380 | + | 0.684109i | \(0.239809\pi\) | |||||||
\(338\) | 13.6627 | + | 23.6645i | 0.743153 | + | 1.28718i | ||||
\(339\) | 0.362641 | − | 0.628112i | 0.0196959 | − | 0.0341144i | ||||
\(340\) | 3.05033 | − | 5.28333i | 0.165428 | − | 0.286529i | ||||
\(341\) | 22.2830 | + | 38.5954i | 1.20669 | + | 2.09006i | ||||
\(342\) | −3.39217 | −0.183428 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0.739514 | + | 1.28088i | 0.0398141 | + | 0.0689601i | ||||
\(346\) | 1.46496 | − | 2.53739i | 0.0787569 | − | 0.136411i | ||||
\(347\) | 2.81247 | − | 4.87135i | 0.150982 | − | 0.261508i | −0.780607 | − | 0.625022i | \(-0.785090\pi\) |
0.931589 | + | 0.363514i | \(0.118423\pi\) | |||||||
\(348\) | 1.19609 | + | 2.07168i | 0.0641169 | + | 0.111054i | ||||
\(349\) | 20.8011 | 1.11346 | 0.556729 | − | 0.830694i | \(-0.312056\pi\) | ||||
0.556729 | + | 0.830694i | \(0.312056\pi\) | |||||||
\(350\) | 3.72055 | − | 6.44419i | 0.198872 | − | 0.344456i | ||||
\(351\) | −6.35023 | −0.338950 | ||||||||
\(352\) | 2.85224 | + | 4.94022i | 0.152025 | + | 0.263315i | ||||
\(353\) | 17.3546 | − | 30.0591i | 0.923692 | − | 1.59988i | 0.130041 | − | 0.991509i | \(-0.458489\pi\) |
0.793651 | − | 0.608373i | \(-0.208178\pi\) | |||||||
\(354\) | −3.68918 | + | 6.38985i | −0.196078 | + | 0.339617i | ||||
\(355\) | −7.29989 | − | 12.6438i | −0.387438 | − | 0.671063i | ||||
\(356\) | −6.43411 | −0.341007 | ||||||||
\(357\) | −10.9131 | −0.577585 | ||||||||
\(358\) | 7.94374 | 0.419840 | ||||||||
\(359\) | 2.89200 | + | 5.00910i | 0.152634 | + | 0.264370i | 0.932195 | − | 0.361956i | \(-0.117891\pi\) |
−0.779561 | + | 0.626326i | \(0.784558\pi\) | |||||||
\(360\) | 0.739514 | − | 1.28088i | 0.0389758 | − | 0.0675081i | ||||
\(361\) | 3.74659 | − | 6.48928i | 0.197189 | − | 0.341541i | ||||
\(362\) | −3.69975 | − | 6.40815i | −0.194455 | − | 0.336805i | ||||
\(363\) | −21.5411 | −1.13061 | ||||||||
\(364\) | 8.40056 | + | 14.5502i | 0.440309 | + | 0.762638i | ||||
\(365\) | 13.2076 | 0.691318 | ||||||||
\(366\) | 2.52097 | + | 4.36645i | 0.131773 | + | 0.228238i | ||||
\(367\) | −0.334931 | + | 0.580118i | −0.0174833 | + | 0.0302819i | −0.874635 | − | 0.484783i | \(-0.838899\pi\) |
0.857151 | + | 0.515065i | \(0.172232\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | −3.69609 | − | 6.40181i | −0.192411 | − | 0.333265i | ||||
\(370\) | −12.3502 | −0.642058 | ||||||||
\(371\) | 0.689180 | + | 1.19369i | 0.0357804 | + | 0.0619736i | ||||
\(372\) | 7.81247 | 0.405058 | ||||||||
\(373\) | 4.90004 | + | 8.48712i | 0.253714 | + | 0.439446i | 0.964546 | − | 0.263916i | \(-0.0850143\pi\) |
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(374\) | −11.7649 | + | 20.3773i | −0.608346 | + | 1.05369i | ||||
\(375\) | −5.77744 | + | 10.0068i | −0.298346 | + | 0.516750i | ||||
\(376\) | 5.11071 | + | 8.85202i | 0.263565 | + | 0.456508i | ||||
\(377\) | 15.1908 | 0.782368 | ||||||||
\(378\) | −2.64575 | −0.136083 | ||||||||
\(379\) | −0.742065 | −0.0381173 | −0.0190587 | − | 0.999818i | \(-0.506067\pi\) | ||||
−0.0190587 | + | 0.999818i | \(0.506067\pi\) | |||||||
\(380\) | −2.50856 | − | 4.34495i | −0.128686 | − | 0.222891i | ||||
\(381\) | 0.00690545 | − | 0.0119606i | 0.000353777 | − | 0.000612760i | ||||
\(382\) | 10.0883 | − | 17.4734i | 0.516160 | − | 0.894016i | ||||
\(383\) | −15.2057 | − | 26.3371i | −0.776975 | − | 1.34576i | −0.933677 | − | 0.358115i | \(-0.883420\pi\) |
0.156702 | − | 0.987646i | \(-0.449914\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 11.1612 | − | 19.3318i | 0.568828 | − | 0.985239i | ||||
\(386\) | −12.8880 | −0.655981 | ||||||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 5.18202 | − | 8.97552i | 0.263077 | − | 0.455663i | ||||
\(389\) | 0.337465 | − | 0.584506i | 0.0171102 | − | 0.0296357i | −0.857344 | − | 0.514745i | \(-0.827887\pi\) |
0.874454 | + | 0.485109i | \(0.161220\pi\) | |||||||
\(390\) | −4.69609 | − | 8.13386i | −0.237796 | − | 0.411874i | ||||
\(391\) | −4.12478 | −0.208599 | ||||||||
\(392\) | 3.50000 | + | 6.06218i | 0.176777 | + | 0.306186i | ||||
\(393\) | 14.4961 | 0.731234 | ||||||||
\(394\) | −4.90205 | − | 8.49060i | −0.246962 | − | 0.427750i | ||||
\(395\) | 9.93175 | − | 17.2023i | 0.499720 | − | 0.865541i | ||||
\(396\) | −2.85224 | + | 4.94022i | −0.143330 | + | 0.248256i | ||||
\(397\) | −4.21304 | − | 7.29719i | −0.211446 | − | 0.366236i | 0.740721 | − | 0.671813i | \(-0.234484\pi\) |
−0.952167 | + | 0.305577i | \(0.901151\pi\) | |||||||
\(398\) | −3.31561 | −0.166197 | ||||||||
\(399\) | −4.48742 | + | 7.77244i | −0.224652 | + | 0.389109i | ||||
\(400\) | −2.81247 | −0.140624 | ||||||||
\(401\) | −17.5596 | − | 30.4141i | −0.876885 | − | 1.51881i | −0.854741 | − | 0.519054i | \(-0.826284\pi\) |
−0.0221432 | − | 0.999755i | \(-0.507049\pi\) | |||||||
\(402\) | −7.70448 | + | 13.3445i | −0.384264 | + | 0.665565i | ||||
\(403\) | 24.8055 | − | 42.9644i | 1.23565 | − | 2.14021i | ||||
\(404\) | −1.40624 | − | 2.43567i | −0.0699629 | − | 0.121179i | ||||
\(405\) | 1.47903 | 0.0734935 | ||||||||
\(406\) | 6.32909 | 0.314107 | ||||||||
\(407\) | 47.6337 | 2.36111 | ||||||||
\(408\) | 2.06239 | + | 3.57216i | 0.102104 | + | 0.176848i | ||||
\(409\) | −9.86404 | + | 17.0850i | −0.487745 | + | 0.844800i | −0.999901 | − | 0.0140931i | \(-0.995514\pi\) |
0.512155 | + | 0.858893i | \(0.328847\pi\) | |||||||
\(410\) | 5.46662 | − | 9.46846i | 0.269977 | − | 0.467614i | ||||
\(411\) | 4.01206 | + | 6.94908i | 0.197900 | + | 0.342773i | ||||
\(412\) | −12.5589 | −0.618732 | ||||||||
\(413\) | 9.76065 | + | 16.9059i | 0.480290 | + | 0.831887i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 6.81938 | + | 11.8115i | 0.334750 | + | 0.579804i | ||||
\(416\) | 3.17511 | − | 5.49946i | 0.155673 | − | 0.269633i | ||||
\(417\) | 7.11071 | − | 12.3161i | 0.348213 | − | 0.603123i | ||||
\(418\) | 9.67528 | + | 16.7581i | 0.473234 | + | 0.819664i | ||||
\(419\) | 7.26739 | 0.355035 | 0.177518 | − | 0.984118i | \(-0.443193\pi\) | ||||
0.177518 | + | 0.984118i | \(0.443193\pi\) | |||||||
\(420\) | −1.95657 | − | 3.38888i | −0.0954709 | − | 0.165360i | ||||
\(421\) | 3.82277 | 0.186311 | 0.0931553 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931553 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(422\) | −8.98191 | − | 15.5571i | −0.437233 | − | 0.757309i | ||||
\(423\) | −5.11071 | + | 8.85202i | −0.248491 | + | 0.430400i | ||||
\(424\) | 0.260486 | − | 0.451174i | 0.0126503 | − | 0.0219110i | ||||
\(425\) | −5.80042 | − | 10.0466i | −0.281362 | − | 0.487333i | ||||
\(426\) | 9.87120 | 0.478261 | ||||||||
\(427\) | 13.3397 | 0.645555 | ||||||||
\(428\) | −5.22143 | −0.252387 | ||||||||
\(429\) | 18.1124 | + | 31.3715i | 0.874473 | + | 1.51463i | ||||
\(430\) | 1.47903 | − | 2.56175i | 0.0713251 | − | 0.123539i | ||||
\(431\) | 0.986189 | − | 1.70813i | 0.0475031 | − | 0.0822777i | −0.841296 | − | 0.540574i | \(-0.818207\pi\) |
0.888799 | + | 0.458297i | \(0.151540\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −31.3929 | −1.50865 | −0.754323 | − | 0.656504i | \(-0.772035\pi\) | ||||
−0.754323 | + | 0.656504i | \(0.772035\pi\) | |||||||
\(434\) | 10.3349 | − | 17.9006i | 0.496093 | − | 0.859258i | ||||
\(435\) | −3.53809 | −0.169638 | ||||||||
\(436\) | 4.23750 | + | 7.33957i | 0.202940 | + | 0.351502i | ||||
\(437\) | −1.69609 | + | 2.93771i | −0.0811348 | + | 0.140530i | ||||
\(438\) | −4.46496 | + | 7.73354i | −0.213344 | + | 0.369523i | ||||
\(439\) | 17.8603 | + | 30.9349i | 0.852424 | + | 1.47644i | 0.879014 | + | 0.476796i | \(0.158202\pi\) |
−0.0265896 | + | 0.999646i | \(0.508465\pi\) | |||||||
\(440\) | −8.43709 | −0.402222 | ||||||||
\(441\) | −3.50000 | + | 6.06218i | −0.166667 | + | 0.288675i | ||||
\(442\) | 26.1933 | 1.24589 | ||||||||
\(443\) | 0.0572397 | + | 0.0991421i | 0.00271954 | + | 0.00471038i | 0.867382 | − | 0.497643i | \(-0.165801\pi\) |
−0.864662 | + | 0.502353i | \(0.832468\pi\) | |||||||
\(444\) | 4.17511 | − | 7.23151i | 0.198142 | − | 0.343192i | ||||
\(445\) | 4.75812 | − | 8.24130i | 0.225557 | − | 0.390675i | ||||
\(446\) | −0.614734 | − | 1.06475i | −0.0291085 | − | 0.0504174i | ||||
\(447\) | 23.2835 | 1.10127 | ||||||||
\(448\) | 1.32288 | − | 2.29129i | 0.0625000 | − | 0.108253i | ||||
\(449\) | −9.26006 | −0.437009 | −0.218505 | − | 0.975836i | \(-0.570118\pi\) | ||||
−0.218505 | + | 0.975836i | \(0.570118\pi\) | |||||||
\(450\) | −1.40624 | − | 2.43567i | −0.0662906 | − | 0.114819i | ||||
\(451\) | −21.0842 | + | 36.5190i | −0.992818 | + | 1.71961i | ||||
\(452\) | −0.362641 | + | 0.628112i | −0.0170572 | + | 0.0295439i | ||||
\(453\) | −3.00691 | − | 5.20811i | −0.141277 | − | 0.244698i | ||||
\(454\) | −16.4130 | −0.770299 | ||||||||
\(455\) | −24.8493 | −1.16496 | ||||||||
\(456\) | 3.39217 | 0.158853 | ||||||||
\(457\) | −2.91865 | − | 5.05525i | −0.136529 | − | 0.236475i | 0.789652 | − | 0.613555i | \(-0.210261\pi\) |
−0.926180 | + | 0.377081i | \(0.876928\pi\) | |||||||
\(458\) | −12.7081 | + | 22.0111i | −0.593812 | + | 1.02851i | ||||
\(459\) | −2.06239 | + | 3.57216i | −0.0962641 | + | 0.166734i | ||||
\(460\) | −0.739514 | − | 1.28088i | −0.0344800 | − | 0.0597212i | ||||
\(461\) | 23.1660 | 1.07895 | 0.539474 | − | 0.842002i | \(-0.318623\pi\) | ||||
0.539474 | + | 0.842002i | \(0.318623\pi\) | |||||||
\(462\) | 7.54631 | + | 13.0706i | 0.351086 | + | 0.608099i | ||||
\(463\) | 0.140148 | 0.00651322 | 0.00325661 | − | 0.999995i | \(-0.498963\pi\) | ||||
0.00325661 | + | 0.999995i | \(0.498963\pi\) | |||||||
\(464\) | −1.19609 | − | 2.07168i | −0.0555269 | − | 0.0961754i | ||||
\(465\) | −5.77744 | + | 10.0068i | −0.267922 | + | 0.464055i | ||||
\(466\) | 0.275783 | − | 0.477670i | 0.0127754 | − | 0.0221276i | ||||
\(467\) | −7.75848 | − | 13.4381i | −0.359019 | − | 0.621840i | 0.628778 | − | 0.777585i | \(-0.283555\pi\) |
−0.987797 | + | 0.155745i | \(0.950222\pi\) | |||||||
\(468\) | 6.35023 | 0.293539 | ||||||||
\(469\) | 20.3841 | + | 35.3064i | 0.941252 | + | 1.63030i | ||||
\(470\) | −15.1178 | −0.697332 | ||||||||
\(471\) | −8.93359 | − | 15.4734i | −0.411638 | − | 0.712978i | ||||
\(472\) | 3.68918 | − | 6.38985i | 0.169808 | − | 0.294117i | ||||
\(473\) | −5.70448 | + | 9.88044i | −0.262292 | + | 0.454303i | ||||
\(474\) | 6.71505 | + | 11.6308i | 0.308432 | + | 0.534220i | ||||
\(475\) | −9.54039 | −0.437743 | ||||||||
\(476\) | 10.9131 | 0.500203 | ||||||||
\(477\) | 0.520971 | 0.0238536 | ||||||||
\(478\) | −5.63169 | − | 9.75437i | −0.257587 | − | 0.446154i | ||||
\(479\) | −7.69609 | + | 13.3300i | −0.351643 | + | 0.609064i | −0.986538 | − | 0.163535i | \(-0.947710\pi\) |
0.634894 | + | 0.772599i | \(0.281044\pi\) | |||||||
\(480\) | −0.739514 | + | 1.28088i | −0.0337541 | + | 0.0584637i | ||||
\(481\) | −26.5129 | − | 45.9217i | −1.20889 | − | 2.09385i | ||||
\(482\) | 28.3284 | 1.29032 | ||||||||
\(483\) | −1.32288 | + | 2.29129i | −0.0601929 | + | 0.104257i | ||||
\(484\) | 21.5411 | 0.979139 | ||||||||
\(485\) | 7.66436 | + | 13.2751i | 0.348021 | + | 0.602789i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 0.277269 | − | 0.480245i | 0.0125643 | − | 0.0217620i | −0.859675 | − | 0.510842i | \(-0.829334\pi\) |
0.872239 | + | 0.489080i | \(0.162667\pi\) | |||||||
\(488\) | −2.52097 | − | 4.36645i | −0.114119 | − | 0.197660i | ||||
\(489\) | −13.8712 | −0.627277 | ||||||||
\(490\) | −10.3532 | −0.467710 | ||||||||
\(491\) | 43.1966 | 1.94944 | 0.974718 | − | 0.223440i | \(-0.0717286\pi\) | ||||
0.974718 | + | 0.223440i | \(0.0717286\pi\) | |||||||
\(492\) | 3.69609 | + | 6.40181i | 0.166632 | + | 0.288616i | ||||
\(493\) | 4.93359 | − | 8.54523i | 0.222198 | − | 0.384858i | ||||
\(494\) | 10.7705 | − | 18.6551i | 0.484589 | − | 0.839333i | ||||
\(495\) | −4.21854 | − | 7.30673i | −0.189609 | − | 0.328413i | ||||
\(496\) | −7.81247 | −0.350790 | ||||||||
\(497\) | 13.0584 | − | 22.6178i | 0.585748 | − | 1.01455i | ||||
\(498\) | −9.22143 | −0.413222 | ||||||||
\(499\) | 10.4471 | + | 18.0950i | 0.467678 | + | 0.810042i | 0.999318 | − | 0.0369286i | \(-0.0117574\pi\) |
−0.531640 | + | 0.846970i | \(0.678424\pi\) | |||||||
\(500\) | 5.77744 | − | 10.0068i | 0.258375 | − | 0.447518i | ||||
\(501\) | 2.53775 | − | 4.39552i | 0.113379 | − | 0.196377i | ||||
\(502\) | −3.91829 | − | 6.78668i | −0.174882 | − | 0.302904i | ||||
\(503\) | −10.1657 | −0.453265 | −0.226633 | − | 0.973980i | \(-0.572772\pi\) | ||||
−0.226633 | + | 0.973980i | \(0.572772\pi\) | |||||||
\(504\) | 2.64575 | 0.117851 | ||||||||
\(505\) | 4.15973 | 0.185106 | ||||||||
\(506\) | 2.85224 | + | 4.94022i | 0.126797 | + | 0.219620i | ||||
\(507\) | 13.6627 | − | 23.6645i | 0.606782 | − | 1.05098i | ||||
\(508\) | −0.00690545 | + | 0.0119606i | −0.000306380 | + | 0.000530666i | ||||
\(509\) | 6.86595 | + | 11.8922i | 0.304328 | + | 0.527111i | 0.977111 | − | 0.212728i | \(-0.0682348\pi\) |
−0.672784 | + | 0.739839i | \(0.734902\pi\) | |||||||
\(510\) | −6.10067 | −0.270142 | ||||||||
\(511\) | 11.8132 | + | 20.4610i | 0.522584 | + | 0.905143i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.69609 | + | 2.93771i | 0.0748840 | + | 0.129703i | ||||
\(514\) | 1.86281 | − | 3.22648i | 0.0821649 | − | 0.142314i | ||||
\(515\) | 9.28748 | − | 16.0864i | 0.409255 | − | 0.708851i | ||||
\(516\) | 1.00000 | + | 1.73205i | 0.0440225 | + | 0.0762493i | ||||
\(517\) | 58.3079 | 2.56438 | ||||||||
\(518\) | −11.0463 | − | 19.1328i | −0.485347 | − | 0.840646i | ||||
\(519\) | −2.92993 | −0.128609 | ||||||||
\(520\) | 4.69609 | + | 8.13386i | 0.205937 | + | 0.356693i | ||||
\(521\) | 1.81247 | − | 3.13930i | 0.0794059 | − | 0.137535i | −0.823588 | − | 0.567189i | \(-0.808031\pi\) |
0.902994 | + | 0.429654i | \(0.141364\pi\) | |||||||
\(522\) | 1.19609 | − | 2.07168i | 0.0523512 | − | 0.0906750i | ||||
\(523\) | 14.4710 | + | 25.0645i | 0.632772 | + | 1.09599i | 0.986982 | + | 0.160828i | \(0.0514164\pi\) |
−0.354210 | + | 0.935166i | \(0.615250\pi\) | |||||||
\(524\) | −14.4961 | −0.633267 | ||||||||
\(525\) | −7.44111 | −0.324757 | ||||||||
\(526\) | −28.8661 | −1.25862 | ||||||||
\(527\) | −16.1124 | − | 27.9074i | −0.701866 | − | 1.21567i | ||||
\(528\) | 2.85224 | − | 4.94022i | 0.124128 | − | 0.214996i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 0.385266 | + | 0.667300i | 0.0167349 | + | 0.0289857i | ||||
\(531\) | 7.37836 | 0.320194 | ||||||||
\(532\) | 4.48742 | − | 7.77244i | 0.194554 | − | 0.336978i | ||||
\(533\) | 46.9420 | 2.03328 | ||||||||
\(534\) | 3.21706 | + | 5.57211i | 0.139216 | + | 0.241129i | ||||
\(535\) | 3.86132 | − | 6.68801i | 0.166939 | − | 0.289148i | ||||
\(536\) | 7.70448 | − | 13.3445i | 0.332783 | − | 0.576397i | ||||
\(537\) | −3.97187 | − | 6.87948i | −0.171399 | − | 0.296871i | ||||
\(538\) | 0.482002 | 0.0207806 | ||||||||
\(539\) | 39.9313 | 1.71996 | ||||||||
\(540\) | −1.47903 | −0.0636473 | ||||||||
\(541\) | 16.5086 | + | 28.5937i | 0.709758 | + | 1.22934i | 0.964947 | + | 0.262446i | \(0.0845292\pi\) |
−0.255188 | + | 0.966891i | \(0.582137\pi\) | |||||||
\(542\) | −2.44801 | + | 4.24008i | −0.105151 | + | 0.182127i | ||||
\(543\) | −3.69975 | + | 6.40815i | −0.158771 | + | 0.275000i | ||||
\(544\) | −2.06239 | − | 3.57216i | −0.0884242 | − | 0.153155i | ||||
\(545\) | −12.5348 | −0.536931 | ||||||||
\(546\) | 8.40056 | − | 14.5502i | 0.359511 | − | 0.622691i | ||||
\(547\) | 36.6891 | 1.56871 | 0.784357 | − | 0.620310i | \(-0.212993\pi\) | ||||
0.784357 | + | 0.620310i | \(0.212993\pi\) | |||||||
\(548\) | −4.01206 | − | 6.94908i | −0.171387 | − | 0.296850i | ||||
\(549\) | 2.52097 | − | 4.36645i | 0.107592 | − | 0.186356i | ||||
\(550\) | −8.02185 | + | 13.8942i | −0.342053 | + | 0.592453i | ||||
\(551\) | −4.05733 | − | 7.02750i | −0.172848 | − | 0.299381i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 35.5327 | 1.51100 | ||||||||
\(554\) | −15.5264 | −0.659654 | ||||||||
\(555\) | 6.17511 | + | 10.6956i | 0.262119 | + | 0.454003i | ||||
\(556\) | −7.11071 | + | 12.3161i | −0.301561 | + | 0.522320i | ||||
\(557\) | −15.4681 | + | 26.7915i | −0.655405 | + | 1.13519i | 0.326388 | + | 0.945236i | \(0.394169\pi\) |
−0.981792 | + | 0.189958i | \(0.939165\pi\) | |||||||
\(558\) | −3.90624 | − | 6.76580i | −0.165364 | − | 0.286419i | ||||
\(559\) | 12.7005 | 0.537172 | ||||||||
\(560\) | 1.95657 | + | 3.38888i | 0.0826802 | + | 0.143206i | ||||
\(561\) | 23.5297 | 0.993425 | ||||||||
\(562\) | 6.60014 | + | 11.4318i | 0.278410 | + | 0.482221i | ||||
\(563\) | −0.276561 | + | 0.479018i | −0.0116557 | + | 0.0201882i | −0.871794 | − | 0.489872i | \(-0.837044\pi\) |
0.860139 | + | 0.510060i | \(0.170377\pi\) | |||||||
\(564\) | 5.11071 | − | 8.85202i | 0.215200 | − | 0.372737i | ||||
\(565\) | −0.536356 | − | 0.928996i | −0.0225647 | − | 0.0390831i | ||||
\(566\) | 2.75672 | 0.115874 | ||||||||
\(567\) | 1.32288 | + | 2.29129i | 0.0555556 | + | 0.0962250i | ||||
\(568\) | −9.87120 | −0.414186 | ||||||||
\(569\) | −1.19083 | − | 2.06259i | −0.0499224 | − | 0.0864681i | 0.839984 | − | 0.542611i | \(-0.182564\pi\) |
−0.889907 | + | 0.456143i | \(0.849231\pi\) | |||||||
\(570\) | −2.50856 | + | 4.34495i | −0.105072 | + | 0.181990i | ||||
\(571\) | −13.2831 | + | 23.0070i | −0.555881 | + | 0.962814i | 0.441954 | + | 0.897038i | \(0.354286\pi\) |
−0.997834 | + | 0.0657760i | \(0.979048\pi\) | |||||||
\(572\) | −18.1124 | − | 31.3715i | −0.757316 | − | 1.31171i | ||||
\(573\) | −20.1765 | −0.842886 | ||||||||
\(574\) | 19.5578 | 0.816329 | ||||||||
\(575\) | −2.81247 | −0.117288 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 2.86158 | − | 4.95640i | 0.119129 | − | 0.206337i | −0.800294 | − | 0.599608i | \(-0.795323\pi\) |
0.919423 | + | 0.393271i | \(0.128656\pi\) | |||||||
\(578\) | 0.00690545 | − | 0.0119606i | 0.000287229 | − | 0.000497495i | ||||
\(579\) | 6.44399 | + | 11.1613i | 0.267803 | + | 0.463849i | ||||
\(580\) | 3.53809 | 0.146911 | ||||||||
\(581\) | −12.1988 | + | 21.1289i | −0.506092 | + | 0.876576i | ||||
\(582\) | −10.3640 | −0.429603 | ||||||||
\(583\) | −1.48593 | − | 2.57371i | −0.0615411 | − | 0.106592i | ||||
\(584\) | 4.46496 | − | 7.73354i | 0.184761 | − | 0.320016i | ||||
\(585\) | −4.69609 | + | 8.13386i | −0.194159 | + | 0.336294i | ||||
\(586\) | 0.0488479 | + | 0.0846070i | 0.00201789 | + | 0.00349508i | ||||
\(587\) | 19.2323 | 0.793801 | 0.396900 | − | 0.917862i | \(-0.370086\pi\) | ||||
0.396900 | + | 0.917862i | \(0.370086\pi\) | |||||||
\(588\) | 3.50000 | − | 6.06218i | 0.144338 | − | 0.250000i | ||||
\(589\) | −26.5012 | −1.09196 | ||||||||
\(590\) | 5.45640 | + | 9.45077i | 0.224637 | + | 0.389082i | ||||
\(591\) | −4.90205 | + | 8.49060i | −0.201643 | + | 0.349257i | ||||
\(592\) | −4.17511 | + | 7.23151i | −0.171596 | + | 0.297213i | ||||
\(593\) | 10.3429 | + | 17.9144i | 0.424732 | + | 0.735657i | 0.996395 | − | 0.0848308i | \(-0.0270350\pi\) |
−0.571663 | + | 0.820488i | \(0.693702\pi\) | |||||||
\(594\) | 5.70448 | 0.234058 | ||||||||
\(595\) | −8.07043 | + | 13.9784i | −0.330855 | + | 0.573058i | ||||
\(596\) | −23.2835 | −0.953728 | ||||||||
\(597\) | 1.65781 | + | 2.87141i | 0.0678495 | + | 0.117519i | ||||
\(598\) | 3.17511 | − | 5.49946i | 0.129840 | − | 0.224890i | ||||
\(599\) | 9.80977 | − | 16.9910i | 0.400816 | − | 0.694234i | −0.593008 | − | 0.805196i | \(-0.702060\pi\) |
0.993825 | + | 0.110962i | \(0.0353932\pi\) | |||||||
\(600\) | 1.40624 | + | 2.43567i | 0.0574094 | + | 0.0994360i | ||||
\(601\) | −8.88798 | −0.362548 | −0.181274 | − | 0.983433i | \(-0.558022\pi\) | ||||
−0.181274 | + | 0.983433i | \(0.558022\pi\) | |||||||
\(602\) | 5.29150 | 0.215666 | ||||||||
\(603\) | 15.4090 | 0.627501 | ||||||||
\(604\) | 3.00691 | + | 5.20811i | 0.122349 | + | 0.211915i | ||||
\(605\) | −15.9299 | + | 27.5914i | −0.647644 | + | 1.12175i | ||||
\(606\) | −1.40624 | + | 2.43567i | −0.0571245 | + | 0.0989425i | ||||
\(607\) | 5.88945 | + | 10.2008i | 0.239046 | + | 0.414039i | 0.960441 | − | 0.278485i | \(-0.0898321\pi\) |
−0.721395 | + | 0.692524i | \(0.756499\pi\) | |||||||
\(608\) | −3.39217 | −0.137571 | ||||||||
\(609\) | −3.16454 | − | 5.48115i | −0.128234 | − | 0.222108i | ||||
\(610\) | 7.45718 | 0.301932 | ||||||||
\(611\) | −32.4542 | − | 56.2123i | −1.31296 | − | 2.27411i | ||||
\(612\) | 2.06239 | − | 3.57216i | 0.0833672 | − | 0.144396i | ||||
\(613\) | −12.3593 | + | 21.4070i | −0.499188 | + | 0.864619i | −1.00000 | 0.000937480i | \(-0.999702\pi\) | |
0.500812 | + | 0.865556i | \(0.333035\pi\) | |||||||
\(614\) | −12.4734 | − | 21.6045i | −0.503384 | − | 0.871886i | ||||
\(615\) | −10.9332 | −0.440871 | ||||||||
\(616\) | −7.54631 | − | 13.0706i | −0.304050 | − | 0.526629i | ||||
\(617\) | −19.0580 | −0.767247 | −0.383623 | − | 0.923490i | \(-0.625324\pi\) | ||||
−0.383623 | + | 0.923490i | \(0.625324\pi\) | |||||||
\(618\) | 6.27945 | + | 10.8763i | 0.252596 | + | 0.437510i | ||||
\(619\) | 9.75481 | − | 16.8958i | 0.392079 | − | 0.679101i | −0.600645 | − | 0.799516i | \(-0.705089\pi\) |
0.992724 | + | 0.120415i | \(0.0384227\pi\) | |||||||
\(620\) | 5.77744 | − | 10.0068i | 0.232027 | − | 0.401883i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | −26.4878 | −1.06206 | ||||||||
\(623\) | 17.0231 | 0.682015 | ||||||||
\(624\) | −6.35023 | −0.254213 | ||||||||
\(625\) | 1.51381 | + | 2.62200i | 0.0605524 | + | 0.104880i | ||||
\(626\) | −9.61911 | + | 16.6608i | −0.384457 | + | 0.665899i | ||||
\(627\) | 9.67528 | − | 16.7581i | 0.386394 | − | 0.669253i | ||||
\(628\) | 8.93359 | + | 15.4734i | 0.356489 | + | 0.617457i | ||||
\(629\) | −34.4429 | −1.37333 | ||||||||
\(630\) | −1.95657 | + | 3.38888i | −0.0779517 | + | 0.135016i | ||||
\(631\) | −46.6443 | −1.85688 | −0.928441 | − | 0.371481i | \(-0.878850\pi\) | ||||
−0.928441 | + | 0.371481i | \(0.878850\pi\) | |||||||
\(632\) | −6.71505 | − | 11.6308i | −0.267110 | − | 0.462648i | ||||
\(633\) | −8.98191 | + | 15.5571i | −0.356999 | + | 0.618340i | ||||
\(634\) | 12.6892 | − | 21.9783i | 0.503952 | − | 0.872870i | ||||
\(635\) | −0.0102134 | − | 0.0176901i | −0.000405305 | − | 0.000702009i | ||||
\(636\) | −0.520971 | −0.0206579 | ||||||||
\(637\) | −22.2258 | − | 38.4962i | −0.880618 | − | 1.52528i | ||||
\(638\) | −13.6461 | −0.540254 | ||||||||
\(639\) | −4.93560 | − | 8.54871i | −0.195249 | − | 0.338182i | ||||
\(640\) | 0.739514 | − | 1.28088i | 0.0292319 | − | 0.0506311i | ||||
\(641\) | 13.2670 | − | 22.9792i | 0.524016 | − | 0.907623i | −0.475593 | − | 0.879666i | \(-0.657766\pi\) |
0.999609 | − | 0.0279574i | \(-0.00890028\pi\) | |||||||
\(642\) | 2.61071 | + | 4.52189i | 0.103037 | + | 0.178465i | ||||
\(643\) | 1.53826 | 0.0606632 | 0.0303316 | − | 0.999540i | \(-0.490344\pi\) | ||||
0.0303316 | + | 0.999540i | \(0.490344\pi\) | |||||||
\(644\) | 1.32288 | − | 2.29129i | 0.0521286 | − | 0.0902894i | ||||
\(645\) | −2.95806 | −0.116473 | ||||||||
\(646\) | −6.99598 | − | 12.1174i | −0.275253 | − | 0.476752i | ||||
\(647\) | −18.5310 | + | 32.0967i | −0.728529 | + | 1.26185i | 0.228975 | + | 0.973432i | \(0.426463\pi\) |
−0.957505 | + | 0.288418i | \(0.906871\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −21.0448 | − | 36.4507i | −0.826082 | − | 1.43082i | ||||
\(650\) | 17.8599 | 0.700521 | ||||||||
\(651\) | −20.6699 | −0.810116 | ||||||||
\(652\) | 13.8712 | 0.543238 | ||||||||
\(653\) | −4.09542 | − | 7.09347i | −0.160266 | − | 0.277589i | 0.774698 | − | 0.632331i | \(-0.217902\pi\) |
−0.934964 | + | 0.354742i | \(0.884569\pi\) | |||||||
\(654\) | 4.23750 | − | 7.33957i | 0.165700 | − | 0.287000i | ||||
\(655\) | 10.7201 | − | 18.5678i | 0.418869 | − | 0.725503i | ||||
\(656\) | −3.69609 | − | 6.40181i | −0.144308 | − | 0.249949i | ||||
\(657\) | 8.92993 | 0.348390 | ||||||||
\(658\) | −13.5217 | − | 23.4202i | −0.527130 | − | 0.913016i | ||||
\(659\) | 24.2174 | 0.943376 | 0.471688 | − | 0.881765i | \(-0.343645\pi\) | ||||
0.471688 | + | 0.881765i | \(0.343645\pi\) | |||||||
\(660\) | 4.21854 | + | 7.30673i | 0.164207 | + | 0.284414i | ||||
\(661\) | 18.7964 | − | 32.5563i | 0.731095 | − | 1.26629i | −0.225320 | − | 0.974285i | \(-0.572343\pi\) |
0.956416 | − | 0.292009i | \(-0.0943238\pi\) | |||||||
\(662\) | 1.42137 | − | 2.46188i | 0.0552430 | − | 0.0956837i | ||||
\(663\) | −13.0966 | − | 22.6841i | −0.508632 | − | 0.880976i | ||||
\(664\) | 9.22143 | 0.357861 | ||||||||
\(665\) | 6.63702 | + | 11.4957i | 0.257373 | + | 0.445783i | ||||
\(666\) | −8.35023 | −0.323565 | ||||||||
\(667\) | −1.19609 | − | 2.07168i | −0.0463126 | − | 0.0802158i | ||||
\(668\) | −2.53775 | + | 4.39552i | −0.0981887 | + | 0.170068i | ||||
\(669\) | −0.614734 | + | 1.06475i | −0.0237670 | + | 0.0411657i | ||||
\(670\) | 11.3951 | + | 19.7370i | 0.440233 | + | 0.762506i | ||||
\(671\) | −28.7616 | −1.11033 | ||||||||
\(672\) | −2.64575 | −0.102062 | ||||||||
\(673\) | 4.15939 | 0.160333 | 0.0801664 | − | 0.996781i | \(-0.474455\pi\) | ||||
0.0801664 | + | 0.996781i | \(0.474455\pi\) | |||||||
\(674\) | 13.3896 | + | 23.1915i | 0.515750 | + | 0.893304i | ||||
\(675\) | −1.40624 | + | 2.43567i | −0.0541261 | + | 0.0937491i | ||||
\(676\) | −13.6627 | + | 23.6645i | −0.525489 | + | 0.910173i | ||||
\(677\) | −6.17258 | − | 10.6912i | −0.237232 | − | 0.410897i | 0.722687 | − | 0.691175i | \(-0.242907\pi\) |
−0.959919 | + | 0.280278i | \(0.909573\pi\) | |||||||
\(678\) | 0.725281 | 0.0278543 | ||||||||
\(679\) | −13.7103 | + | 23.7470i | −0.526154 | + | 0.911326i | ||||
\(680\) | 6.10067 | 0.233950 | ||||||||
\(681\) | 8.20649 | + | 14.2141i | 0.314473 | + | 0.544684i | ||||
\(682\) | −22.2830 | + | 38.5954i | −0.853262 | + | 1.47789i | ||||
\(683\) | −20.5731 | + | 35.6337i | −0.787209 | + | 1.36349i | 0.140461 | + | 0.990086i | \(0.455142\pi\) |
−0.927670 | + | 0.373401i | \(0.878192\pi\) | |||||||
\(684\) | −1.69609 | − | 2.93771i | −0.0648515 | − | 0.112326i | ||||
\(685\) | 11.8679 | 0.453449 | ||||||||
\(686\) | −9.26013 | − | 16.0390i | −0.353553 | − | 0.612372i | ||||
\(687\) | 25.4163 | 0.969692 | ||||||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | −1.65414 | + | 2.86506i | −0.0630178 | + | 0.109150i | ||||
\(690\) | −0.739514 | + | 1.28088i | −0.0281528 | + | 0.0487621i | ||||
\(691\) | 3.08118 | + | 5.33677i | 0.117214 | + | 0.203020i | 0.918663 | − | 0.395043i | \(-0.129270\pi\) |
−0.801449 | + | 0.598063i | \(0.795937\pi\) | |||||||
\(692\) | 2.92993 | 0.111379 | ||||||||
\(693\) | 7.54631 | − | 13.0706i | 0.286661 | − | 0.496511i | ||||
\(694\) | 5.62495 | 0.213520 | ||||||||
\(695\) | −10.5170 | − | 18.2159i | −0.398931 | − | 0.690968i | ||||
\(696\) | −1.19609 | + | 2.07168i | −0.0453375 | + | 0.0785269i | ||||
\(697\) | 15.2455 | − | 26.4061i | 0.577466 | − | 1.00020i | ||||
\(698\) | 10.4006 | + | 18.0143i | 0.393667 | + | 0.681851i | ||||
\(699\) | −0.551566 | −0.0208621 | ||||||||
\(700\) | 7.44111 | 0.281247 | ||||||||
\(701\) | −27.6447 | −1.04413 | −0.522063 | − | 0.852907i | \(-0.674837\pi\) | ||||
−0.522063 | + | 0.852907i | \(0.674837\pi\) | |||||||
\(702\) | −3.17511 | − | 5.49946i | −0.119837 | − | 0.207564i | ||||
\(703\) | −14.1627 | + | 24.5305i | −0.534156 | + | 0.925186i | ||||
\(704\) | −2.85224 | + | 4.94022i | −0.107498 | + | 0.186192i | ||||
\(705\) | 7.55889 | + | 13.0924i | 0.284684 | + | 0.493088i | ||||
\(706\) | 34.7092 | 1.30630 | ||||||||
\(707\) | 3.72055 | + | 6.44419i | 0.139926 | + | 0.242359i | ||||
\(708\) | −7.37836 | −0.277296 | ||||||||
\(709\) | −12.6213 | − | 21.8607i | −0.474002 | − | 0.820996i | 0.525555 | − | 0.850760i | \(-0.323858\pi\) |
−0.999557 | + | 0.0297638i | \(0.990524\pi\) | |||||||
\(710\) | 7.29989 | − | 12.6438i | 0.273960 | − | 0.474513i | ||||
\(711\) | 6.71505 | − | 11.6308i | 0.251834 | − | 0.436189i | ||||
\(712\) | −3.21706 | − | 5.57211i | −0.120564 | − | 0.208823i | ||||
\(713\) | −7.81247 | −0.292579 | ||||||||
\(714\) | −5.45657 | − | 9.45106i | −0.204207 | − | 0.353697i | ||||
\(715\) | 53.5774 | 2.00368 | ||||||||
\(716\) | 3.97187 | + | 6.87948i | 0.148436 | + | 0.257098i | ||||
\(717\) | −5.63169 | + | 9.75437i | −0.210319 | + | 0.364283i | ||||
\(718\) | −2.89200 | + | 5.00910i | −0.107929 | + | 0.186938i | ||||
\(719\) | −19.7038 | − | 34.1279i | −0.734826 | − | 1.27276i | −0.954799 | − | 0.297251i | \(-0.903930\pi\) |
0.219973 | − | 0.975506i | \(-0.429403\pi\) | |||||||
\(720\) | 1.47903 | 0.0551201 | ||||||||
\(721\) | 33.2277 | 1.23746 | ||||||||
\(722\) | 7.49317 | 0.278867 | ||||||||
\(723\) | −14.1642 | − | 24.5331i | −0.526772 | − | 0.912396i | ||||
\(724\) | 3.69975 | − | 6.40815i | 0.137500 | − | 0.238157i | ||||
\(725\) | 3.36396 | − | 5.82655i | 0.124934 | − | 0.216393i | ||||
\(726\) | −10.7705 | − | 18.6551i | −0.399732 | − | 0.692356i | ||||
\(727\) | 33.9963 | 1.26085 | 0.630427 | − | 0.776248i | \(-0.282880\pi\) | ||||
0.630427 | + | 0.776248i | \(0.282880\pi\) | |||||||
\(728\) | −8.40056 | + | 14.5502i | −0.311346 | + | 0.539266i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.60381 | + | 11.4381i | 0.244418 | + | 0.423344i | ||||
\(731\) | 4.12478 | − | 7.14433i | 0.152561 | − | 0.264243i | ||||
\(732\) | −2.52097 | + | 4.36645i | −0.0931778 | + | 0.161389i | ||||
\(733\) | 1.24590 | + | 2.15796i | 0.0460182 | + | 0.0797059i | 0.888117 | − | 0.459617i | \(-0.152013\pi\) |
−0.842099 | + | 0.539323i | \(0.818680\pi\) | |||||||
\(734\) | −0.669863 | −0.0247251 | ||||||||
\(735\) | 5.17660 | + | 8.96614i | 0.190942 | + | 0.330721i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −43.9500 | − | 76.1237i | −1.61892 | − | 2.80405i | ||||
\(738\) | 3.69609 | − | 6.40181i | 0.136055 | − | 0.235654i | ||||
\(739\) | −23.6488 | + | 40.9609i | −0.869935 | + | 1.50677i | −0.00787354 | + | 0.999969i | \(0.502506\pi\) |
−0.862062 | + | 0.506803i | \(0.830827\pi\) | |||||||
\(740\) | −6.17511 | − | 10.6956i | −0.227002 | − | 0.393179i | ||||
\(741\) | −21.5411 | −0.791331 | ||||||||
\(742\) | −0.689180 | + | 1.19369i | −0.0253006 | + | 0.0438219i | ||||
\(743\) | 44.5435 | 1.63414 | 0.817072 | − | 0.576536i | \(-0.195596\pi\) | ||||
0.817072 | + | 0.576536i | \(0.195596\pi\) | |||||||
\(744\) | 3.90624 | + | 6.76580i | 0.143210 | + | 0.248046i | ||||
\(745\) | 17.2185 | − | 29.8232i | 0.630835 | − | 1.09264i | ||||
\(746\) | −4.90004 | + | 8.48712i | −0.179403 | + | 0.310735i | ||||
\(747\) | 4.61071 | + | 7.98599i | 0.168697 | + | 0.292192i | ||||
\(748\) | −23.5297 | −0.860332 | ||||||||
\(749\) | 13.8146 | 0.504775 | ||||||||
\(750\) | −11.5549 | −0.421924 | ||||||||
\(751\) | 6.75523 | + | 11.7004i | 0.246502 | + | 0.426954i | 0.962553 | − | 0.271094i | \(-0.0873855\pi\) |
−0.716051 | + | 0.698048i | \(0.754052\pi\) | |||||||
\(752\) | −5.11071 | + | 8.85202i | −0.186369 | + | 0.322800i | ||||
\(753\) | −3.91829 | + | 6.78668i | −0.142791 | + | 0.247320i | ||||
\(754\) | 7.59542 | + | 13.1556i | 0.276609 | + | 0.479100i | ||||
\(755\) | −8.89460 | −0.323708 | ||||||||
\(756\) | −1.32288 | − | 2.29129i | −0.0481125 | − | 0.0833333i | ||||
\(757\) | −24.9895 | −0.908259 | −0.454129 | − | 0.890936i | \(-0.650050\pi\) | ||||
−0.454129 | + | 0.890936i | \(0.650050\pi\) | |||||||
\(758\) | −0.371032 | − | 0.642647i | −0.0134765 | − | 0.0233420i | ||||
\(759\) | 2.85224 | − | 4.94022i | 0.103530 | − | 0.179319i | ||||
\(760\) | 2.50856 | − | 4.34495i | 0.0909950 | − | 0.157608i | ||||
\(761\) | 1.26930 | + | 2.19849i | 0.0460121 | + | 0.0796953i | 0.888114 | − | 0.459623i | \(-0.152015\pi\) |
−0.842102 | + | 0.539318i | \(0.818682\pi\) | |||||||
\(762\) | 0.0138109 | 0.000500316 | ||||||||
\(763\) | −11.2114 | − | 19.4187i | −0.405879 | − | 0.703004i | ||||
\(764\) | 20.1765 | 0.729961 | ||||||||
\(765\) | 3.05033 | + | 5.28333i | 0.110285 | + | 0.191019i | ||||
\(766\) | 15.2057 | − | 26.3371i | 0.549405 | − | 0.951597i | ||||
\(767\) | −23.4271 | + | 40.5770i | −0.845905 | + | 1.46515i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −7.59435 | −0.273859 | −0.136930 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136930 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(770\) | 22.3224 | 0.804445 | ||||||||
\(771\) | −3.72562 | −0.134175 | ||||||||
\(772\) | −6.44399 | − | 11.1613i | −0.231924 | − | 0.401705i | ||||
\(773\) | 10.7843 | − | 18.6790i | 0.387886 | − | 0.671838i | −0.604279 | − | 0.796773i | \(-0.706539\pi\) |
0.992165 | + | 0.124935i | \(0.0398721\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | −10.9862 | − | 19.0286i | −0.394636 | − | 0.683529i | ||||
\(776\) | 10.3640 | 0.372047 | ||||||||
\(777\) | −11.0463 | + | 19.1328i | −0.396284 | + | 0.686385i | ||||
\(778\) | 0.674930 | 0.0241974 | ||||||||
\(779\) | −12.5378 | − | 21.7160i | −0.449212 | − | 0.778057i | ||||
\(780\) | 4.69609 | − | 8.13386i | 0.168147 | − | 0.291239i | ||||
\(781\) | −28.1550 | + | 48.7659i | −1.00747 | + | 1.74498i | ||||
\(782\) | −2.06239 | − | 3.57216i | −0.0737509 | − | 0.127740i | ||||
\(783\) | −2.39217 | −0.0854892 | ||||||||
\(784\) | −3.50000 | + | 6.06218i | −0.125000 | + | 0.216506i | ||||
\(785\) | −26.4261 | −0.943187 | ||||||||
\(786\) | 7.24807 | + | 12.5540i | 0.258530 | + | 0.447787i | ||||
\(787\) | 22.6096 | − | 39.1609i | 0.805944 | − | 1.39594i | −0.109707 | − | 0.993964i | \(-0.534991\pi\) |
0.915652 | − | 0.401973i | \(-0.131675\pi\) | |||||||
\(788\) | 4.90205 | − | 8.49060i | 0.174628 | − | 0.302465i | ||||
\(789\) | 14.4331 | + | 24.9988i | 0.513831 | + | 0.889981i | ||||
\(790\) | 19.8635 | 0.706711 | ||||||||
\(791\) | 0.959457 | − | 1.66183i | 0.0341144 | − | 0.0590878i | ||||
\(792\) | −5.70448 | −0.202700 | ||||||||
\(793\) | 16.0087 | + | 27.7280i | 0.568487 | + | 0.984649i | ||||
\(794\) | 4.21304 | − | 7.29719i | 0.149515 | − | 0.258968i | ||||
\(795\) | 0.385266 | − | 0.667300i | 0.0136640 | − | 0.0236667i | ||||
\(796\) | −1.65781 | − | 2.87141i | −0.0587594 | − | 0.101774i | ||||
\(797\) | 26.6028 | 0.942318 | 0.471159 | − | 0.882048i | \(-0.343836\pi\) | ||||
0.471159 | + | 0.882048i | \(0.343836\pi\) | |||||||
\(798\) | −8.97484 | −0.317706 | ||||||||
\(799\) | −42.1611 | −1.49155 | ||||||||
\(800\) | −1.40624 | − | 2.43567i | −0.0497180 | − | 0.0861141i | ||||
\(801\) | 3.21706 | − | 5.57211i | 0.113669 | − | 0.196881i | ||||
\(802\) | 17.5596 | − | 30.4141i | 0.620051 | − | 1.07396i | ||||
\(803\) | −25.4703 | − | 44.1158i | −0.898827 | − | 1.55681i | ||||
\(804\) | −15.4090 | −0.543432 | ||||||||
\(805\) | 1.95657 | + | 3.38888i | 0.0689601 | + | 0.119442i | ||||
\(806\) | 49.6110 | 1.74747 | ||||||||
\(807\) | −0.241001 | − | 0.417426i | −0.00848363 | − | 0.0146941i | ||||
\(808\) | 1.40624 | − | 2.43567i | 0.0494712 | − | 0.0856867i | ||||
\(809\) | 20.2791 | − | 35.1244i | 0.712975 | − | 1.23491i | −0.250761 | − | 0.968049i | \(-0.580681\pi\) |
0.963735 | − | 0.266860i | \(-0.0859860\pi\) | |||||||
\(810\) | 0.739514 | + | 1.28088i | 0.0259839 | + | 0.0450054i | ||||
\(811\) | 17.7894 | 0.624672 | 0.312336 | − | 0.949972i | \(-0.398889\pi\) | ||||
0.312336 | + | 0.949972i | \(0.398889\pi\) | |||||||
\(812\) | 3.16454 | + | 5.48115i | 0.111054 | + | 0.192351i | ||||
\(813\) | 4.89602 | 0.171711 | ||||||||
\(814\) | 23.8168 | + | 41.2520i | 0.834780 | + | 1.44588i | ||||
\(815\) | −10.2580 | + | 17.7673i | −0.359320 | + | 0.622361i | ||||
\(816\) | −2.06239 | + | 3.57216i | −0.0721981 | + | 0.125051i | ||||
\(817\) | −3.39217 | − | 5.87541i | −0.118677 | − | 0.205555i | ||||
\(818\) | −19.7281 | −0.689776 | ||||||||
\(819\) | −16.8011 | −0.587079 | ||||||||
\(820\) | 10.9332 | 0.381805 | ||||||||
\(821\) | −1.72003 | − | 2.97918i | −0.0600294 | − | 0.103974i | 0.834449 | − | 0.551085i | \(-0.185786\pi\) |
−0.894478 | + | 0.447111i | \(0.852453\pi\) | |||||||
\(822\) | −4.01206 | + | 6.94908i | −0.139937 | + | 0.242377i | ||||
\(823\) | −3.64244 | + | 6.30890i | −0.126968 | + | 0.219914i | −0.922500 | − | 0.385996i | \(-0.873858\pi\) |
0.795533 | + | 0.605911i | \(0.207191\pi\) | |||||||
\(824\) | −6.27945 | − | 10.8763i | −0.218755 | − | 0.378895i | ||||
\(825\) | 16.0437 | 0.558570 | ||||||||
\(826\) | −9.76065 | + | 16.9059i | −0.339617 | + | 0.588233i | ||||
\(827\) | −25.4665 | −0.885556 | −0.442778 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442778 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | −0.00330791 | + | 0.00572947i | −0.000114889 | + | 0.000198993i | −0.866083 | − | 0.499901i | \(-0.833370\pi\) |
0.865968 | + | 0.500099i | \(0.166703\pi\) | |||||||
\(830\) | −6.81938 | + | 11.8115i | −0.236704 | + | 0.409984i | ||||
\(831\) | 7.76320 | + | 13.4463i | 0.269303 | + | 0.466446i | ||||
\(832\) | 6.35023 | 0.220155 | ||||||||
\(833\) | −28.8735 | −1.00041 | ||||||||
\(834\) | 14.2214 | 0.492448 | ||||||||
\(835\) | −3.75341 | − | 6.50110i | −0.129892 | − | 0.224980i | ||||
\(836\) | −9.67528 | + | 16.7581i | −0.334627 | + | 0.579590i | ||||
\(837\) | −3.90624 | + | 6.76580i | −0.135019 | + | 0.233860i | ||||
\(838\) | 3.63370 | + | 6.29375i | 0.125524 | + | 0.217414i | ||||
\(839\) | 14.8092 | 0.511269 | 0.255635 | − | 0.966773i | \(-0.417716\pi\) | ||||
0.255635 | + | 0.966773i | \(0.417716\pi\) | |||||||
\(840\) | 1.95657 | − | 3.38888i | 0.0675081 | − | 0.116927i | ||||
\(841\) | −23.2775 | −0.802673 | ||||||||
\(842\) | 1.91139 | + | 3.31062i | 0.0658708 | + | 0.114091i | ||||
\(843\) | 6.60014 | − | 11.4318i | 0.227321 | − | 0.393732i | ||||
\(844\) | 8.98191 | − | 15.5571i | 0.309170 | − | 0.535499i | ||||
\(845\) | −20.2075 | − | 35.0005i | −0.695160 | − | 1.20405i | ||||
\(846\) | −10.2214 | −0.351420 | ||||||||
\(847\) | −56.9923 | −1.95828 | ||||||||
\(848\) | 0.520971 | 0.0178902 | ||||||||
\(849\) | −1.37836 | − | 2.38739i | −0.0473052 | − | 0.0819350i | ||||
\(850\) | 5.80042 | − | 10.0466i | 0.198953 | − | 0.344596i | ||||
\(851\) | −4.17511 | + | 7.23151i | −0.143121 | + | 0.247893i | ||||
\(852\) | 4.93560 | + | 8.54871i | 0.169091 | + | 0.292874i | ||||
\(853\) | −13.5264 | −0.463135 | −0.231568 | − | 0.972819i | \(-0.574385\pi\) | ||||
−0.231568 | + | 0.972819i | \(0.574385\pi\) | |||||||
\(854\) | 6.66986 | + | 11.5525i | 0.228238 | + | 0.395320i | ||||
\(855\) | 5.01712 | 0.171582 | ||||||||
\(856\) | −2.61071 | − | 4.52189i | −0.0892324 | − | 0.154555i | ||||
\(857\) | −4.31371 | + | 7.47156i | −0.147353 | + | 0.255224i | −0.930248 | − | 0.366930i | \(-0.880409\pi\) |
0.782895 | + | 0.622154i | \(0.213742\pi\) | |||||||
\(858\) | −18.1124 | + | 31.3715i | −0.618346 | + | 1.07101i | ||||
\(859\) | −12.1537 | − | 21.0509i | −0.414680 | − | 0.718246i | 0.580715 | − | 0.814107i | \(-0.302773\pi\) |
−0.995395 | + | 0.0958607i | \(0.969440\pi\) | |||||||
\(860\) | 2.95806 | 0.100869 | ||||||||
\(861\) | −9.77892 | − | 16.9376i | −0.333265 | − | 0.577232i | ||||
\(862\) | 1.97238 | 0.0671795 | ||||||||
\(863\) | 7.38981 | + | 12.7995i | 0.251552 | + | 0.435701i | 0.963953 | − | 0.266072i | \(-0.0857258\pi\) |
−0.712401 | + | 0.701772i | \(0.752392\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −2.16672 | + | 3.75287i | −0.0736708 | + | 0.127602i | ||||
\(866\) | −15.6964 | − | 27.1870i | −0.533387 | − | 0.923853i | ||||
\(867\) | −0.0138109 | −0.000469043 | ||||||||
\(868\) | 20.6699 | 0.701581 | ||||||||
\(869\) | −76.6117 | −2.59887 | ||||||||
\(870\) | −1.76905 | − | 3.06408i | −0.0599762 | − | 0.103882i | ||||
\(871\) | −48.9252 | + | 84.7409i | −1.65777 | + | 2.87134i | ||||
\(872\) | −4.23750 | + | 7.33957i | −0.143500 | + | 0.248549i | ||||
\(873\) | 5.18202 | + | 8.97552i | 0.175385 | + | 0.303775i | ||||
\(874\) | −3.39217 | −0.114742 | ||||||||
\(875\) | −15.2857 | + | 26.4755i | −0.516750 | + | 0.895037i | ||||
\(876\) | −8.92993 | −0.301714 | ||||||||
\(877\) | 26.3546 | + | 45.6475i | 0.889932 | + | 1.54141i | 0.839955 | + | 0.542656i | \(0.182581\pi\) |
0.0499769 | + | 0.998750i | \(0.484085\pi\) | |||||||
\(878\) | −17.8603 | + | 30.9349i | −0.602755 | + | 1.04400i | ||||
\(879\) | 0.0488479 | − | 0.0846070i | 0.00164760 | − | 0.00285372i | ||||
\(880\) | −4.21854 | − | 7.30673i | −0.142207 | − | 0.246310i | ||||
\(881\) | 35.2594 | 1.18792 | 0.593959 | − | 0.804495i | \(-0.297564\pi\) | ||||
0.593959 | + | 0.804495i | \(0.297564\pi\) | |||||||
\(882\) | −7.00000 | −0.235702 | ||||||||
\(883\) | 6.05906 | 0.203904 | 0.101952 | − | 0.994789i | \(-0.467491\pi\) | ||||
0.101952 | + | 0.994789i | \(0.467491\pi\) | |||||||
\(884\) | 13.0966 | + | 22.6841i | 0.440488 | + | 0.762948i | ||||
\(885\) | 5.45640 | − | 9.45077i | 0.183415 | − | 0.317684i | ||||
\(886\) | −0.0572397 | + | 0.0991421i | −0.00192301 | + | 0.00333074i | ||||
\(887\) | 2.45764 | + | 4.25675i | 0.0825193 | + | 0.142928i | 0.904331 | − | 0.426831i | \(-0.140370\pi\) |
−0.821812 | + | 0.569759i | \(0.807037\pi\) | |||||||
\(888\) | 8.35023 | 0.280215 | ||||||||
\(889\) | 0.0182701 | − | 0.0316448i | 0.000612760 | − | 0.00106133i | ||||
\(890\) | 9.51624 | 0.318985 | ||||||||
\(891\) | −2.85224 | − | 4.94022i | −0.0955536 | − | 0.165504i | ||||
\(892\) | 0.614734 | − | 1.06475i | 0.0205828 | − | 0.0356505i | ||||
\(893\) | −17.3364 | + | 30.0276i | −0.580141 | + | 1.00483i | ||||
\(894\) | 11.6417 | + | 20.1641i | 0.389358 | + | 0.674387i | ||||
\(895\) | −11.7490 | −0.392726 | ||||||||
\(896\) | 2.64575 | 0.0883883 | ||||||||
\(897\) | −6.35023 | −0.212028 | ||||||||
\(898\) | −4.63003 | − | 8.01945i | −0.154506 | − | 0.267613i | ||||
\(899\) | 9.34439 | − | 16.1850i | 0.311653 | − | 0.539798i | ||||
\(900\) | 1.40624 | − | 2.43567i | 0.0468746 | − | 0.0811891i | ||||
\(901\) | 1.07445 | + | 1.86099i | 0.0357950 | + | 0.0619987i | ||||
\(902\) | −42.1685 | −1.40406 | ||||||||
\(903\) | −2.64575 | − | 4.58258i | −0.0880451 | − | 0.152499i | ||||
\(904\) | −0.725281 | −0.0241225 | ||||||||
\(905\) | 5.47204 | + | 9.47784i | 0.181897 | + | 0.315054i | ||||
\(906\) | 3.00691 | − | 5.20811i | 0.0998977 | − | 0.173028i | ||||
\(907\) | −17.0769 | + | 29.5781i | −0.567029 | + | 0.982124i | 0.429828 | + | 0.902911i | \(0.358574\pi\) |
−0.996858 | + | 0.0792132i | \(0.974759\pi\) | |||||||
\(908\) | −8.20649 | − | 14.2141i | −0.272342 | − | 0.471710i | ||||
\(909\) | 2.81247 | 0.0932839 | ||||||||
\(910\) | −12.4247 | − | 21.5202i | −0.411874 | − | 0.713387i | ||||
\(911\) | −52.3590 | −1.73473 | −0.867365 | − | 0.497672i | \(-0.834188\pi\) | ||||
−0.867365 | + | 0.497672i | \(0.834188\pi\) | |||||||
\(912\) | 1.69609 | + | 2.93771i | 0.0561630 | + | 0.0972772i | ||||
\(913\) | 26.3017 | − | 45.5559i | 0.870460 | − | 1.50768i | ||||
\(914\) | 2.91865 | − | 5.05525i | 0.0965403 | − | 0.167213i | ||||
\(915\) | −3.72859 | − | 6.45811i | −0.123263 | − | 0.213498i | ||||
\(916\) | −25.4163 | −0.839778 | ||||||||
\(917\) | 38.3532 | 1.26653 | ||||||||
\(918\) | −4.12478 | −0.136138 | ||||||||
\(919\) | −18.2232 | − | 31.5635i | −0.601127 | − | 1.04118i | −0.992651 | − | 0.121015i | \(-0.961385\pi\) |
0.391523 | − | 0.920168i | \(-0.371948\pi\) | |||||||
\(920\) | 0.739514 | − | 1.28088i | 0.0243811 | − | 0.0422292i | ||||
\(921\) | −12.4734 | + | 21.6045i | −0.411011 | + | 0.711892i | ||||
\(922\) | 11.5830 | + | 20.0624i | 0.381466 | + | 0.660718i | ||||
\(923\) | 62.6844 | 2.06328 | ||||||||
\(924\) | −7.54631 | + | 13.0706i | −0.248256 | + | 0.429991i | ||||
\(925\) | −23.4848 | −0.772175 | ||||||||
\(926\) | 0.0700739 | + | 0.121372i | 0.00230277 | + | 0.00398852i | ||||
\(927\) | 6.27945 | − | 10.8763i | 0.206244 | − | 0.357225i | ||||
\(928\) | 1.19609 | − | 2.07168i | 0.0392634 | − | 0.0680063i | ||||
\(929\) | 27.7227 | + | 48.0171i | 0.909551 | + | 1.57539i | 0.814689 | + | 0.579898i | \(0.196908\pi\) |
0.0948619 | + | 0.995490i | \(0.469759\pi\) | |||||||
\(930\) | −11.5549 | −0.378899 | ||||||||
\(931\) | −11.8726 | + | 20.5639i | −0.389109 | + | 0.673956i | ||||
\(932\) | 0.551566 | 0.0180671 | ||||||||
\(933\) | 13.2439 | + | 22.9391i | 0.433585 | + | 0.750992i | ||||
\(934\) | 7.75848 | − | 13.4381i | 0.253865 | − | 0.439707i | ||||
\(935\) | 17.4006 | − | 30.1387i | 0.569059 | − | 0.985640i | ||||
\(936\) | 3.17511 | + | 5.49946i | 0.103782 | + | 0.179755i | ||||
\(937\) | −0.308796 | −0.0100879 | −0.00504396 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504396 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(938\) | −20.3841 | + | 35.3064i | −0.665565 | + | 1.15279i | ||||
\(939\) | 19.2382 | 0.627815 | ||||||||
\(940\) | −7.55889 | − | 13.0924i | −0.246544 | − | 0.427027i | ||||
\(941\) | 7.75228 | − | 13.4273i | 0.252717 | − | 0.437719i | −0.711556 | − | 0.702629i | \(-0.752009\pi\) |
0.964273 | + | 0.264911i | \(0.0853425\pi\) | |||||||
\(942\) | 8.93359 | − | 15.4734i | 0.291072 | − | 0.504152i | ||||
\(943\) | −3.69609 | − | 6.40181i | −0.120361 | − | 0.208472i | ||||
\(944\) | 7.37836 | 0.240145 | ||||||||
\(945\) | 3.91314 | 0.127295 | ||||||||
\(946\) | −11.4090 | −0.370937 | ||||||||
\(947\) | −29.3462 | − | 50.8291i | −0.953624 | − | 1.65172i | −0.737487 | − | 0.675362i | \(-0.763988\pi\) |
−0.216137 | − | 0.976363i | \(-0.569346\pi\) | |||||||
\(948\) | −6.71505 | + | 11.6308i | −0.218095 | + | 0.377751i | ||||
\(949\) | −28.3535 | + | 49.1098i | −0.920395 | + | 1.59417i | ||||
\(950\) | −4.77020 | − | 8.26222i | −0.154766 | − | 0.268062i | ||||
\(951\) | −25.3784 | −0.822950 | ||||||||
\(952\) | 5.45657 | + | 9.45106i | 0.176848 | + | 0.306311i | ||||
\(953\) | 28.6120 | 0.926835 | 0.463417 | − | 0.886140i | \(-0.346623\pi\) | ||||
0.463417 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(954\) | 0.260486 | + | 0.451174i | 0.00843353 | + | 0.0146073i | ||||
\(955\) | −14.9208 | + | 25.8436i | −0.482826 | + | 0.836280i | ||||
\(956\) | 5.63169 | − | 9.75437i | 0.182142 | − | 0.315479i | ||||
\(957\) | 6.82304 | + | 11.8179i | 0.220558 | + | 0.382017i | ||||
\(958\) | −15.3922 | −0.497298 | ||||||||
\(959\) | 10.6149 | + | 18.3855i | 0.342773 | + | 0.593700i | ||||
\(960\) | −1.47903 | −0.0477354 | ||||||||
\(961\) | −15.0174 | − | 26.0109i | −0.484431 | − | 0.839060i | ||||
\(962\) | 26.5129 | − | 45.9217i | 0.854811 | − | 1.48058i | ||||
\(963\) | 2.61071 | − | 4.52189i | 0.0841291 | − | 0.145716i | ||||
\(964\) | 14.1642 | + | 24.5331i | 0.456198 | + | 0.790158i | ||||
\(965\) | 19.0617 | 0.613618 | ||||||||
\(966\) | −2.64575 | −0.0851257 | ||||||||
\(967\) | −15.7059 | −0.505067 | −0.252534 | − | 0.967588i | \(-0.581264\pi\) | ||||
−0.252534 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(968\) | 10.7705 | + | 18.6551i | 0.346178 | + | 0.599598i | ||||
\(969\) | −6.99598 | + | 12.1174i | −0.224743 | + | 0.389267i | ||||
\(970\) | −7.66436 | + | 13.2751i | −0.246088 | + | 0.426236i | ||||
\(971\) | −8.38300 | − | 14.5198i | −0.269023 | − | 0.465962i | 0.699587 | − | 0.714548i | \(-0.253368\pi\) |
−0.968610 | + | 0.248586i | \(0.920034\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 18.8132 | − | 32.5854i | 0.603123 | − | 1.04464i | ||||
\(974\) | 0.554539 | 0.0177686 | ||||||||
\(975\) | −8.92993 | − | 15.4671i | −0.285987 | − | 0.495343i | ||||
\(976\) | 2.52097 | − | 4.36645i | 0.0806943 | − | 0.139767i | ||||
\(977\) | −8.68665 | + | 15.0457i | −0.277910 | + | 0.481355i | −0.970865 | − | 0.239626i | \(-0.922975\pi\) |
0.692955 | + | 0.720981i | \(0.256309\pi\) | |||||||
\(978\) | −6.93560 | − | 12.0128i | −0.221776 | − | 0.384127i | ||||
\(979\) | −36.7033 | −1.17304 | ||||||||
\(980\) | −5.17660 | − | 8.96614i | −0.165360 | − | 0.286413i | ||||
\(981\) | −8.47501 | −0.270586 | ||||||||
\(982\) | 21.5983 | + | 37.4094i | 0.689230 | + | 1.19378i | ||||
\(983\) | −12.0433 | + | 20.8597i | −0.384123 | + | 0.665320i | −0.991647 | − | 0.128981i | \(-0.958829\pi\) |
0.607524 | + | 0.794301i | \(0.292163\pi\) | |||||||
\(984\) | −3.69609 | + | 6.40181i | −0.117827 | + | 0.204082i | ||||
\(985\) | 7.25027 | + | 12.5578i | 0.231013 | + | 0.400126i | ||||
\(986\) | 9.86718 | 0.314235 | ||||||||
\(987\) | −13.5217 | + | 23.4202i | −0.430400 | + | 0.745474i | ||||
\(988\) | 21.5411 | 0.685313 | ||||||||
\(989\) | −1.00000 | − | 1.73205i | −0.0317982 | − | 0.0550760i | ||||
\(990\) | 4.21854 | − | 7.30673i | 0.134074 | − | 0.232223i | ||||
\(991\) | −28.3396 | + | 49.0857i | −0.900238 | + | 1.55926i | −0.0730538 | + | 0.997328i | \(0.523274\pi\) |
−0.827184 | + | 0.561930i | \(0.810059\pi\) | |||||||
\(992\) | −3.90624 | − | 6.76580i | −0.124023 | − | 0.214814i | ||||
\(993\) | −2.84273 | −0.0902114 | ||||||||
\(994\) | 26.1167 | 0.828373 | ||||||||
\(995\) | 4.90389 | 0.155464 | ||||||||
\(996\) | −4.61071 | − | 7.98599i | −0.146096 | − | 0.253046i | ||||
\(997\) | −20.7019 | + | 35.8567i | −0.655634 | + | 1.13559i | 0.326100 | + | 0.945335i | \(0.394265\pi\) |
−0.981734 | + | 0.190257i | \(0.939068\pi\) | |||||||
\(998\) | −10.4471 | + | 18.0950i | −0.330698 | + | 0.572786i | ||||
\(999\) | 4.17511 | + | 7.23151i | 0.132095 | + | 0.228795i |
(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 | 966.2.i.n.277.2 | ✓ | 8 | |
7.2 | even | 3 | inner | 966.2.i.n.415.2 | yes | 8 | |
7.3 | odd | 6 | 6762.2.a.ch.1.2 | 4 | |||
7.4 | even | 3 | 6762.2.a.cg.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.n.277.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
966.2.i.n.415.2 | yes | 8 | 7.2 | even | 3 | inner | |
6762.2.a.cg.1.3 | 4 | 7.4 | even | 3 | |||
6762.2.a.ch.1.2 | 4 | 7.3 | odd | 6 |