Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(197,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.c (of order \(2\), degree \(1\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.8 | ||
Root | \(-2.33939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.197 |
Dual form | 462.2.c.a.197.7 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.806630 | + | 1.53276i | 0.465708 | + | 0.884938i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.86104i | 1.72671i | 0.504597 | + | 0.863355i | \(0.331641\pi\) | ||||
−0.504597 | + | 0.863355i | \(0.668359\pi\) | |||||||
\(6\) | −0.806630 | − | 1.53276i | −0.329305 | − | 0.625746i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.69870 | + | 2.47274i | −0.566232 | + | 0.824246i | ||||
\(10\) | − | 3.86104i | − | 1.22097i | ||||||
\(11\) | −1.72613 | − | 2.83205i | −0.520447 | − | 0.853894i | ||||
\(12\) | 0.806630 | + | 1.53276i | 0.232854 | + | 0.442469i | ||||
\(13\) | 5.06552i | 1.40492i | 0.711722 | + | 0.702461i | \(0.247915\pi\) | ||||
−0.711722 | + | 0.702461i | \(0.752085\pi\) | |||||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | −5.91804 | + | 3.11443i | −1.52803 | + | 0.804143i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.69769 | 0.654287 | 0.327143 | − | 0.944975i | \(-0.393914\pi\) | ||||
0.327143 | + | 0.944975i | \(0.393914\pi\) | |||||||
\(18\) | 1.69870 | − | 2.47274i | 0.400386 | − | 0.582830i | ||||
\(19\) | − | 7.70835i | − | 1.76842i | −0.467093 | − | 0.884208i | \(-0.654699\pi\) | ||
0.467093 | − | 0.884208i | \(-0.345301\pi\) | |||||||
\(20\) | 3.86104i | 0.863355i | ||||||||
\(21\) | −1.53276 | + | 0.806630i | −0.334475 | + | 0.176021i | ||||
\(22\) | 1.72613 | + | 2.83205i | 0.368012 | + | 0.603794i | ||||
\(23\) | − | 3.49322i | − | 0.728386i | −0.931323 | − | 0.364193i | \(-0.881345\pi\) | ||
0.931323 | − | 0.364193i | \(-0.118655\pi\) | |||||||
\(24\) | −0.806630 | − | 1.53276i | −0.164653 | − | 0.312873i | ||||
\(25\) | −9.90764 | −1.98153 | ||||||||
\(26\) | − | 5.06552i | − | 0.993430i | ||||||
\(27\) | −5.16033 | − | 0.609106i | −0.993106 | − | 0.117222i | ||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 0.831472 | 0.154400 | 0.0772002 | − | 0.997016i | \(-0.475402\pi\) | ||||
0.0772002 | + | 0.997016i | \(0.475402\pi\) | |||||||
\(30\) | 5.91804 | − | 3.11443i | 1.08048 | − | 0.568615i | ||||
\(31\) | 9.19326 | 1.65116 | 0.825579 | − | 0.564287i | \(-0.190849\pi\) | ||||
0.825579 | + | 0.564287i | \(0.190849\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.94849 | − | 4.93015i | 0.513267 | − | 0.858229i | ||||
\(34\) | −2.69769 | −0.462651 | ||||||||
\(35\) | −3.86104 | −0.652635 | ||||||||
\(36\) | −1.69870 | + | 2.47274i | −0.283116 | + | 0.412123i | ||||
\(37\) | 3.04331 | 0.500316 | 0.250158 | − | 0.968205i | \(-0.419517\pi\) | ||||
0.250158 | + | 0.968205i | \(0.419517\pi\) | |||||||
\(38\) | 7.70835i | 1.25046i | ||||||||
\(39\) | −7.76421 | + | 4.08600i | −1.24327 | + | 0.654283i | ||||
\(40\) | − | 3.86104i | − | 0.610484i | ||||||
\(41\) | −5.28064 | −0.824698 | −0.412349 | − | 0.911026i | \(-0.635292\pi\) | ||||
−0.412349 | + | 0.911026i | \(0.635292\pi\) | |||||||
\(42\) | 1.53276 | − | 0.806630i | 0.236510 | − | 0.124466i | ||||
\(43\) | 12.5717i | 1.91717i | 0.284805 | + | 0.958586i | \(0.408071\pi\) | ||||
−0.284805 | + | 0.958586i | \(0.591929\pi\) | |||||||
\(44\) | −1.72613 | − | 2.83205i | −0.260224 | − | 0.426947i | ||||
\(45\) | −9.54734 | − | 6.55874i | −1.42323 | − | 0.977719i | ||||
\(46\) | 3.49322i | 0.515047i | ||||||||
\(47\) | 4.96439i | 0.724131i | 0.932153 | + | 0.362066i | \(0.117928\pi\) | ||||
−0.932153 | + | 0.362066i | \(0.882072\pi\) | |||||||
\(48\) | 0.806630 | + | 1.53276i | 0.116427 | + | 0.221235i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 9.90764 | 1.40115 | ||||||||
\(51\) | 2.17604 | + | 4.13491i | 0.304707 | + | 0.579004i | ||||
\(52\) | 5.06552i | 0.702461i | ||||||||
\(53\) | 0.602608i | 0.0827746i | 0.999143 | + | 0.0413873i | \(0.0131777\pi\) | ||||
−0.999143 | + | 0.0413873i | \(0.986822\pi\) | |||||||
\(54\) | 5.16033 | + | 0.609106i | 0.702232 | + | 0.0828888i | ||||
\(55\) | 10.9346 | − | 6.66465i | 1.47443 | − | 0.898662i | ||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 11.8150 | − | 6.21778i | 1.56494 | − | 0.823566i | ||||
\(58\) | −0.831472 | −0.109178 | ||||||||
\(59\) | − | 0.161004i | − | 0.0209609i | −0.999945 | − | 0.0104804i | \(-0.996664\pi\) | ||
0.999945 | − | 0.0104804i | \(-0.00333609\pi\) | |||||||
\(60\) | −5.91804 | + | 3.11443i | −0.764016 | + | 0.402071i | ||||
\(61\) | 4.61360i | 0.590711i | 0.955387 | + | 0.295355i | \(0.0954381\pi\) | ||||
−0.955387 | + | 0.295355i | \(0.904562\pi\) | |||||||
\(62\) | −9.19326 | −1.16754 | ||||||||
\(63\) | −2.47274 | − | 1.69870i | −0.311536 | − | 0.214016i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −19.5582 | −2.42589 | ||||||||
\(66\) | −2.94849 | + | 4.93015i | −0.362935 | + | 0.606860i | ||||
\(67\) | −4.22686 | −0.516393 | −0.258197 | − | 0.966092i | \(-0.583128\pi\) | ||||
−0.258197 | + | 0.966092i | \(0.583128\pi\) | |||||||
\(68\) | 2.69769 | 0.327143 | ||||||||
\(69\) | 5.35426 | − | 2.81774i | 0.644577 | − | 0.339215i | ||||
\(70\) | 3.86104 | 0.461483 | ||||||||
\(71\) | 12.0213i | 1.42667i | 0.700825 | + | 0.713333i | \(0.252815\pi\) | ||||
−0.700825 | + | 0.713333i | \(0.747185\pi\) | |||||||
\(72\) | 1.69870 | − | 2.47274i | 0.200193 | − | 0.291415i | ||||
\(73\) | 6.15308i | 0.720163i | 0.932921 | + | 0.360082i | \(0.117251\pi\) | ||||
−0.932921 | + | 0.360082i | \(0.882749\pi\) | |||||||
\(74\) | −3.04331 | −0.353777 | ||||||||
\(75\) | −7.99180 | − | 15.1860i | −0.922814 | − | 1.75353i | ||||
\(76\) | − | 7.70835i | − | 0.884208i | ||||||
\(77\) | 2.83205 | − | 1.72613i | 0.322742 | − | 0.196711i | ||||
\(78\) | 7.76421 | − | 4.08600i | 0.879124 | − | 0.462648i | ||||
\(79\) | − | 2.49556i | − | 0.280773i | −0.990097 | − | 0.140386i | \(-0.955166\pi\) | ||
0.990097 | − | 0.140386i | \(-0.0448345\pi\) | |||||||
\(80\) | 3.86104i | 0.431678i | ||||||||
\(81\) | −3.22886 | − | 8.40086i | −0.358763 | − | 0.933429i | ||||
\(82\) | 5.28064 | 0.583150 | ||||||||
\(83\) | 3.53635 | 0.388165 | 0.194082 | − | 0.980985i | \(-0.437827\pi\) | ||||
0.194082 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(84\) | −1.53276 | + | 0.806630i | −0.167238 | + | 0.0880106i | ||||
\(85\) | 10.4159i | 1.12976i | ||||||||
\(86\) | − | 12.5717i | − | 1.35564i | ||||||
\(87\) | 0.670690 | + | 1.27445i | 0.0719055 | + | 0.136635i | ||||
\(88\) | 1.72613 | + | 2.83205i | 0.184006 | + | 0.301897i | ||||
\(89\) | − | 7.35755i | − | 0.779899i | −0.920836 | − | 0.389950i | \(-0.872492\pi\) | ||
0.920836 | − | 0.389950i | \(-0.127508\pi\) | |||||||
\(90\) | 9.54734 | + | 6.55874i | 1.00638 | + | 0.691351i | ||||
\(91\) | −5.06552 | −0.531010 | ||||||||
\(92\) | − | 3.49322i | − | 0.364193i | ||||||
\(93\) | 7.41556 | + | 14.0910i | 0.768957 | + | 1.46117i | ||||
\(94\) | − | 4.96439i | − | 0.512038i | ||||||
\(95\) | 29.7622 | 3.05354 | ||||||||
\(96\) | −0.806630 | − | 1.53276i | −0.0823263 | − | 0.156436i | ||||
\(97\) | 12.0650 | 1.22501 | 0.612505 | − | 0.790467i | \(-0.290162\pi\) | ||||
0.612505 | + | 0.790467i | \(0.290162\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 9.93507 | + | 0.542522i | 0.998512 | + | 0.0545255i | ||||
\(100\) | −9.90764 | −0.990764 | ||||||||
\(101\) | 10.4799 | 1.04279 | 0.521396 | − | 0.853315i | \(-0.325411\pi\) | ||||
0.521396 | + | 0.853315i | \(0.325411\pi\) | |||||||
\(102\) | −2.17604 | − | 4.13491i | −0.215460 | − | 0.409417i | ||||
\(103\) | −4.76959 | −0.469961 | −0.234981 | − | 0.972000i | \(-0.575503\pi\) | ||||
−0.234981 | + | 0.972000i | \(0.575503\pi\) | |||||||
\(104\) | − | 5.06552i | − | 0.496715i | ||||||
\(105\) | −3.11443 | − | 5.91804i | −0.303937 | − | 0.577542i | ||||
\(106\) | − | 0.602608i | − | 0.0585305i | ||||||
\(107\) | 5.70706 | 0.551722 | 0.275861 | − | 0.961198i | \(-0.411037\pi\) | ||||
0.275861 | + | 0.961198i | \(0.411037\pi\) | |||||||
\(108\) | −5.16033 | − | 0.609106i | −0.496553 | − | 0.0586112i | ||||
\(109\) | − | 0.152695i | − | 0.0146255i | −0.999973 | − | 0.00731277i | \(-0.997672\pi\) | ||
0.999973 | − | 0.00731277i | \(-0.00232775\pi\) | |||||||
\(110\) | −10.9346 | + | 6.66465i | −1.04258 | + | 0.635450i | ||||
\(111\) | 2.45482 | + | 4.66465i | 0.233001 | + | 0.442749i | ||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − | 5.39852i | − | 0.507850i | −0.967224 | − | 0.253925i | \(-0.918278\pi\) | ||
0.967224 | − | 0.253925i | \(-0.0817216\pi\) | |||||||
\(114\) | −11.8150 | + | 6.21778i | −1.10658 | + | 0.582349i | ||||
\(115\) | 13.4875 | 1.25771 | ||||||||
\(116\) | 0.831472 | 0.0772002 | ||||||||
\(117\) | −12.5257 | − | 8.60477i | −1.15800 | − | 0.795512i | ||||
\(118\) | 0.161004i | 0.0148216i | ||||||||
\(119\) | 2.69769i | 0.247297i | ||||||||
\(120\) | 5.91804 | − | 3.11443i | 0.540241 | − | 0.284307i | ||||
\(121\) | −5.04096 | + | 9.77695i | −0.458269 | + | 0.888813i | ||||
\(122\) | − | 4.61360i | − | 0.417696i | ||||||
\(123\) | −4.25953 | − | 8.09395i | −0.384069 | − | 0.729807i | ||||
\(124\) | 9.19326 | 0.825579 | ||||||||
\(125\) | − | 18.9486i | − | 1.69481i | ||||||
\(126\) | 2.47274 | + | 1.69870i | 0.220289 | + | 0.151332i | ||||
\(127\) | − | 14.2439i | − | 1.26394i | −0.774993 | − | 0.631970i | \(-0.782246\pi\) | ||
0.774993 | − | 0.631970i | \(-0.217754\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −19.2694 | + | 10.1407i | −1.69658 | + | 0.892842i | ||||
\(130\) | 19.5582 | 1.71536 | ||||||||
\(131\) | 17.0775 | 1.49207 | 0.746034 | − | 0.665908i | \(-0.231956\pi\) | ||||
0.746034 | + | 0.665908i | \(0.231956\pi\) | |||||||
\(132\) | 2.94849 | − | 4.93015i | 0.256633 | − | 0.429115i | ||||
\(133\) | 7.70835 | 0.668398 | ||||||||
\(134\) | 4.22686 | 0.365145 | ||||||||
\(135\) | 2.35178 | − | 19.9242i | 0.202409 | − | 1.71481i | ||||
\(136\) | −2.69769 | −0.231325 | ||||||||
\(137\) | − | 10.9911i | − | 0.939035i | −0.882923 | − | 0.469518i | \(-0.844428\pi\) | ||
0.882923 | − | 0.469518i | \(-0.155572\pi\) | |||||||
\(138\) | −5.35426 | + | 2.81774i | −0.455785 | + | 0.239862i | ||||
\(139\) | 8.67348i | 0.735675i | 0.929890 | + | 0.367837i | \(0.119902\pi\) | ||||
−0.929890 | + | 0.367837i | \(0.880098\pi\) | |||||||
\(140\) | −3.86104 | −0.326318 | ||||||||
\(141\) | −7.60921 | + | 4.00443i | −0.640811 | + | 0.337234i | ||||
\(142\) | − | 12.0213i | − | 1.00881i | ||||||
\(143\) | 14.3458 | − | 8.74373i | 1.19965 | − | 0.731188i | ||||
\(144\) | −1.69870 | + | 2.47274i | −0.141558 | + | 0.206061i | ||||
\(145\) | 3.21035i | 0.266605i | ||||||||
\(146\) | − | 6.15308i | − | 0.509232i | ||||||
\(147\) | −0.806630 | − | 1.53276i | −0.0665297 | − | 0.126420i | ||||
\(148\) | 3.04331 | 0.250158 | ||||||||
\(149\) | −3.59764 | −0.294730 | −0.147365 | − | 0.989082i | \(-0.547079\pi\) | ||||
−0.147365 | + | 0.989082i | \(0.547079\pi\) | |||||||
\(150\) | 7.99180 | + | 15.1860i | 0.652528 | + | 1.23993i | ||||
\(151\) | − | 17.5295i | − | 1.42653i | −0.700892 | − | 0.713267i | \(-0.747215\pi\) | ||
0.700892 | − | 0.713267i | \(-0.252785\pi\) | |||||||
\(152\) | 7.70835i | 0.625229i | ||||||||
\(153\) | −4.58256 | + | 6.67069i | −0.370478 | + | 0.539293i | ||||
\(154\) | −2.83205 | + | 1.72613i | −0.228213 | + | 0.139095i | ||||
\(155\) | 35.4955i | 2.85107i | ||||||||
\(156\) | −7.76421 | + | 4.08600i | −0.621635 | + | 0.327142i | ||||
\(157\) | −7.25956 | −0.579376 | −0.289688 | − | 0.957121i | \(-0.593551\pi\) | ||||
−0.289688 | + | 0.957121i | \(0.593551\pi\) | |||||||
\(158\) | 2.49556i | 0.198536i | ||||||||
\(159\) | −0.923652 | + | 0.486082i | −0.0732504 | + | 0.0385488i | ||||
\(160\) | − | 3.86104i | − | 0.305242i | ||||||
\(161\) | 3.49322 | 0.275304 | ||||||||
\(162\) | 3.22886 | + | 8.40086i | 0.253683 | + | 0.660034i | ||||
\(163\) | 15.4886 | 1.21316 | 0.606580 | − | 0.795023i | \(-0.292541\pi\) | ||||
0.606580 | + | 0.795023i | \(0.292541\pi\) | |||||||
\(164\) | −5.28064 | −0.412349 | ||||||||
\(165\) | 19.0355 | + | 11.3843i | 1.48191 | + | 0.886263i | ||||
\(166\) | −3.53635 | −0.274474 | ||||||||
\(167\) | −3.94198 | −0.305040 | −0.152520 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152520 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(168\) | 1.53276 | − | 0.806630i | 0.118255 | − | 0.0622329i | ||||
\(169\) | −12.6595 | −0.973804 | ||||||||
\(170\) | − | 10.4159i | − | 0.798864i | ||||||
\(171\) | 19.0607 | + | 13.0941i | 1.45761 | + | 1.00133i | ||||
\(172\) | 12.5717i | 0.958586i | ||||||||
\(173\) | −5.16603 | −0.392766 | −0.196383 | − | 0.980527i | \(-0.562920\pi\) | ||||
−0.196383 | + | 0.980527i | \(0.562920\pi\) | |||||||
\(174\) | −0.670690 | − | 1.27445i | −0.0508449 | − | 0.0966155i | ||||
\(175\) | − | 9.90764i | − | 0.748947i | ||||||
\(176\) | −1.72613 | − | 2.83205i | −0.130112 | − | 0.213473i | ||||
\(177\) | 0.246779 | − | 0.129870i | 0.0185491 | − | 0.00976165i | ||||
\(178\) | 7.35755i | 0.551472i | ||||||||
\(179\) | 5.01937i | 0.375166i | 0.982249 | + | 0.187583i | \(0.0600653\pi\) | ||||
−0.982249 | + | 0.187583i | \(0.939935\pi\) | |||||||
\(180\) | −9.54734 | − | 6.55874i | −0.711617 | − | 0.488859i | ||||
\(181\) | −9.50810 | −0.706732 | −0.353366 | − | 0.935485i | \(-0.614963\pi\) | ||||
−0.353366 | + | 0.935485i | \(0.614963\pi\) | |||||||
\(182\) | 5.06552 | 0.375481 | ||||||||
\(183\) | −7.07153 | + | 3.72147i | −0.522743 | + | 0.275099i | ||||
\(184\) | 3.49322i | 0.257524i | ||||||||
\(185\) | 11.7503i | 0.863901i | ||||||||
\(186\) | −7.41556 | − | 14.0910i | −0.543735 | − | 1.03321i | ||||
\(187\) | −4.65657 | − | 7.63999i | −0.340522 | − | 0.558692i | ||||
\(188\) | 4.96439i | 0.362066i | ||||||||
\(189\) | 0.609106 | − | 5.16033i | 0.0443059 | − | 0.375359i | ||||
\(190\) | −29.7622 | −2.15918 | ||||||||
\(191\) | − | 8.73096i | − | 0.631750i | −0.948801 | − | 0.315875i | \(-0.897702\pi\) | ||
0.948801 | − | 0.315875i | \(-0.102298\pi\) | |||||||
\(192\) | 0.806630 | + | 1.53276i | 0.0582135 | + | 0.110617i | ||||
\(193\) | 11.2644i | 0.810830i | 0.914133 | + | 0.405415i | \(0.132873\pi\) | ||||
−0.914133 | + | 0.405415i | \(0.867127\pi\) | |||||||
\(194\) | −12.0650 | −0.866213 | ||||||||
\(195\) | −15.7762 | − | 29.9779i | −1.12976 | − | 2.14677i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 26.1013 | 1.85964 | 0.929820 | − | 0.368016i | \(-0.119963\pi\) | ||||
0.929820 | + | 0.368016i | \(0.119963\pi\) | |||||||
\(198\) | −9.93507 | − | 0.542522i | −0.706055 | − | 0.0385553i | ||||
\(199\) | −20.1620 | −1.42925 | −0.714625 | − | 0.699508i | \(-0.753402\pi\) | ||||
−0.714625 | + | 0.699508i | \(0.753402\pi\) | |||||||
\(200\) | 9.90764 | 0.700576 | ||||||||
\(201\) | −3.40951 | − | 6.47875i | −0.240488 | − | 0.456976i | ||||
\(202\) | −10.4799 | −0.737366 | ||||||||
\(203\) | 0.831472i | 0.0583579i | ||||||||
\(204\) | 2.17604 | + | 4.13491i | 0.152353 | + | 0.289502i | ||||
\(205\) | − | 20.3888i | − | 1.42401i | ||||||
\(206\) | 4.76959 | 0.332313 | ||||||||
\(207\) | 8.63781 | + | 5.93392i | 0.600370 | + | 0.412436i | ||||
\(208\) | 5.06552i | 0.351230i | ||||||||
\(209\) | −21.8304 | + | 13.3056i | −1.51004 | + | 0.920367i | ||||
\(210\) | 3.11443 | + | 5.91804i | 0.214916 | + | 0.408384i | ||||
\(211\) | 20.1922i | 1.39009i | 0.718968 | + | 0.695043i | \(0.244615\pi\) | ||||
−0.718968 | + | 0.695043i | \(0.755385\pi\) | |||||||
\(212\) | 0.602608i | 0.0413873i | ||||||||
\(213\) | −18.4258 | + | 9.69674i | −1.26251 | + | 0.664410i | ||||
\(214\) | −5.70706 | −0.390126 | ||||||||
\(215\) | −48.5400 | −3.31040 | ||||||||
\(216\) | 5.16033 | + | 0.609106i | 0.351116 | + | 0.0414444i | ||||
\(217\) | 9.19326i | 0.624079i | ||||||||
\(218\) | 0.152695i | 0.0103418i | ||||||||
\(219\) | −9.43118 | + | 4.96326i | −0.637300 | + | 0.335386i | ||||
\(220\) | 10.9346 | − | 6.66465i | 0.737214 | − | 0.449331i | ||||
\(221\) | 13.6652i | 0.919222i | ||||||||
\(222\) | −2.45482 | − | 4.66465i | −0.164757 | − | 0.313071i | ||||
\(223\) | −0.163853 | −0.0109724 | −0.00548620 | − | 0.999985i | \(-0.501746\pi\) | ||||
−0.00548620 | + | 0.999985i | \(0.501746\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 16.8301 | − | 24.4990i | 1.12200 | − | 1.63327i | ||||
\(226\) | 5.39852i | 0.359104i | ||||||||
\(227\) | 9.14938 | 0.607266 | 0.303633 | − | 0.952789i | \(-0.401800\pi\) | ||||
0.303633 | + | 0.952789i | \(0.401800\pi\) | |||||||
\(228\) | 11.8150 | − | 6.21778i | 0.782470 | − | 0.411783i | ||||
\(229\) | 9.97390 | 0.659094 | 0.329547 | − | 0.944139i | \(-0.393104\pi\) | ||||
0.329547 | + | 0.944139i | \(0.393104\pi\) | |||||||
\(230\) | −13.4875 | −0.889337 | ||||||||
\(231\) | 4.93015 | + | 2.94849i | 0.324380 | + | 0.193997i | ||||
\(232\) | −0.831472 | −0.0545888 | ||||||||
\(233\) | −2.49984 | −0.163770 | −0.0818849 | − | 0.996642i | \(-0.526094\pi\) | ||||
−0.0818849 | + | 0.996642i | \(0.526094\pi\) | |||||||
\(234\) | 12.5257 | + | 8.60477i | 0.818830 | + | 0.562512i | ||||
\(235\) | −19.1677 | −1.25036 | ||||||||
\(236\) | − | 0.161004i | − | 0.0104804i | ||||||
\(237\) | 3.82509 | − | 2.01300i | 0.248467 | − | 0.130758i | ||||
\(238\) | − | 2.69769i | − | 0.174866i | ||||||
\(239\) | 8.25748 | 0.534132 | 0.267066 | − | 0.963678i | \(-0.413946\pi\) | ||||
0.267066 | + | 0.963678i | \(0.413946\pi\) | |||||||
\(240\) | −5.91804 | + | 3.11443i | −0.382008 | + | 0.201036i | ||||
\(241\) | − | 15.0943i | − | 0.972309i | −0.873873 | − | 0.486155i | \(-0.838399\pi\) | ||
0.873873 | − | 0.486155i | \(-0.161601\pi\) | |||||||
\(242\) | 5.04096 | − | 9.77695i | 0.324045 | − | 0.628486i | ||||
\(243\) | 10.2720 | − | 11.7255i | 0.658948 | − | 0.752188i | ||||
\(244\) | 4.61360i | 0.295355i | ||||||||
\(245\) | − | 3.86104i | − | 0.246673i | ||||||
\(246\) | 4.25953 | + | 8.09395i | 0.271577 | + | 0.516051i | ||||
\(247\) | 39.0468 | 2.48449 | ||||||||
\(248\) | −9.19326 | −0.583772 | ||||||||
\(249\) | 2.85253 | + | 5.42037i | 0.180772 | + | 0.343502i | ||||
\(250\) | 18.9486i | 1.19841i | ||||||||
\(251\) | 13.7304i | 0.866655i | 0.901237 | + | 0.433327i | \(0.142661\pi\) | ||||
−0.901237 | + | 0.433327i | \(0.857339\pi\) | |||||||
\(252\) | −2.47274 | − | 1.69870i | −0.155768 | − | 0.107008i | ||||
\(253\) | −9.89295 | + | 6.02974i | −0.621965 | + | 0.379087i | ||||
\(254\) | 14.2439i | 0.893741i | ||||||||
\(255\) | −15.9651 | + | 8.40178i | −0.999771 | + | 0.526140i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.93347i | 0.370120i | 0.982727 | + | 0.185060i | \(0.0592479\pi\) | ||||
−0.982727 | + | 0.185060i | \(0.940752\pi\) | |||||||
\(258\) | 19.2694 | − | 10.1407i | 1.19966 | − | 0.631335i | ||||
\(259\) | 3.04331i | 0.189102i | ||||||||
\(260\) | −19.5582 | −1.21295 | ||||||||
\(261\) | −1.41242 | + | 2.05601i | −0.0874265 | + | 0.127264i | ||||
\(262\) | −17.0775 | −1.05505 | ||||||||
\(263\) | −20.1194 | −1.24062 | −0.620308 | − | 0.784359i | \(-0.712992\pi\) | ||||
−0.620308 | + | 0.784359i | \(0.712992\pi\) | |||||||
\(264\) | −2.94849 | + | 4.93015i | −0.181467 | + | 0.303430i | ||||
\(265\) | −2.32669 | −0.142928 | ||||||||
\(266\) | −7.70835 | −0.472629 | ||||||||
\(267\) | 11.2774 | − | 5.93482i | 0.690163 | − | 0.363205i | ||||
\(268\) | −4.22686 | −0.258197 | ||||||||
\(269\) | 23.5034i | 1.43303i | 0.697571 | + | 0.716515i | \(0.254264\pi\) | ||||
−0.697571 | + | 0.716515i | \(0.745736\pi\) | |||||||
\(270\) | −2.35178 | + | 19.9242i | −0.143125 | + | 1.21255i | ||||
\(271\) | − | 30.2007i | − | 1.83456i | −0.398243 | − | 0.917280i | \(-0.630380\pi\) | ||
0.398243 | − | 0.917280i | \(-0.369620\pi\) | |||||||
\(272\) | 2.69769 | 0.163572 | ||||||||
\(273\) | −4.08600 | − | 7.76421i | −0.247296 | − | 0.469912i | ||||
\(274\) | 10.9911i | 0.663998i | ||||||||
\(275\) | 17.1019 | + | 28.0589i | 1.03128 | + | 1.69201i | ||||
\(276\) | 5.35426 | − | 2.81774i | 0.322289 | − | 0.169608i | ||||
\(277\) | − | 3.10788i | − | 0.186735i | −0.995632 | − | 0.0933673i | \(-0.970237\pi\) | ||
0.995632 | − | 0.0933673i | \(-0.0297631\pi\) | |||||||
\(278\) | − | 8.67348i | − | 0.520201i | ||||||
\(279\) | −15.6165 | + | 22.7325i | −0.934938 | + | 1.36096i | ||||
\(280\) | 3.86104 | 0.230741 | ||||||||
\(281\) | −1.17009 | −0.0698016 | −0.0349008 | − | 0.999391i | \(-0.511112\pi\) | ||||
−0.0349008 | + | 0.999391i | \(0.511112\pi\) | |||||||
\(282\) | 7.60921 | − | 4.00443i | 0.453122 | − | 0.238460i | ||||
\(283\) | − | 32.3497i | − | 1.92299i | −0.274826 | − | 0.961494i | \(-0.588620\pi\) | ||
0.274826 | − | 0.961494i | \(-0.411380\pi\) | |||||||
\(284\) | 12.0213i | 0.713333i | ||||||||
\(285\) | 24.0071 | + | 45.6183i | 1.42206 | + | 2.70220i | ||||
\(286\) | −14.3458 | + | 8.74373i | −0.848283 | + | 0.517028i | ||||
\(287\) | − | 5.28064i | − | 0.311707i | ||||||
\(288\) | 1.69870 | − | 2.47274i | 0.100097 | − | 0.145707i | ||||
\(289\) | −9.72245 | −0.571909 | ||||||||
\(290\) | − | 3.21035i | − | 0.188518i | ||||||
\(291\) | 9.73195 | + | 18.4927i | 0.570497 | + | 1.08406i | ||||
\(292\) | 6.15308i | 0.360082i | ||||||||
\(293\) | 10.6481 | 0.622070 | 0.311035 | − | 0.950398i | \(-0.399324\pi\) | ||||
0.311035 | + | 0.950398i | \(0.399324\pi\) | |||||||
\(294\) | 0.806630 | + | 1.53276i | 0.0470436 | + | 0.0893923i | ||||
\(295\) | 0.621641 | 0.0361934 | ||||||||
\(296\) | −3.04331 | −0.176889 | ||||||||
\(297\) | 7.18237 | + | 15.6657i | 0.416764 | + | 0.909015i | ||||
\(298\) | 3.59764 | 0.208405 | ||||||||
\(299\) | 17.6950 | 1.02333 | ||||||||
\(300\) | −7.99180 | − | 15.1860i | −0.461407 | − | 0.876765i | ||||
\(301\) | −12.5717 | −0.724623 | ||||||||
\(302\) | 17.5295i | 1.00871i | ||||||||
\(303\) | 8.45343 | + | 16.0632i | 0.485637 | + | 0.922807i | ||||
\(304\) | − | 7.70835i | − | 0.442104i | ||||||
\(305\) | −17.8133 | −1.01999 | ||||||||
\(306\) | 4.58256 | − | 6.67069i | 0.261968 | − | 0.381338i | ||||
\(307\) | − | 14.4447i | − | 0.824401i | −0.911093 | − | 0.412200i | \(-0.864760\pi\) | ||
0.911093 | − | 0.412200i | \(-0.135240\pi\) | |||||||
\(308\) | 2.83205 | − | 1.72613i | 0.161371 | − | 0.0983553i | ||||
\(309\) | −3.84729 | − | 7.31063i | −0.218865 | − | 0.415887i | ||||
\(310\) | − | 35.4955i | − | 2.01601i | ||||||
\(311\) | − | 27.8091i | − | 1.57691i | −0.615094 | − | 0.788454i | \(-0.710882\pi\) | ||
0.615094 | − | 0.788454i | \(-0.289118\pi\) | |||||||
\(312\) | 7.76421 | − | 4.08600i | 0.439562 | − | 0.231324i | ||||
\(313\) | 14.5554 | 0.822719 | 0.411359 | − | 0.911473i | \(-0.365054\pi\) | ||||
0.411359 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(314\) | 7.25956 | 0.409681 | ||||||||
\(315\) | 6.55874 | − | 9.54734i | 0.369543 | − | 0.537932i | ||||
\(316\) | − | 2.49556i | − | 0.140386i | ||||||
\(317\) | 1.42646i | 0.0801177i | 0.999197 | + | 0.0400589i | \(0.0127545\pi\) | ||||
−0.999197 | + | 0.0400589i | \(0.987245\pi\) | |||||||
\(318\) | 0.923652 | − | 0.486082i | 0.0517959 | − | 0.0272581i | ||||
\(319\) | −1.43523 | − | 2.35477i | −0.0803573 | − | 0.131842i | ||||
\(320\) | 3.86104i | 0.215839i | ||||||||
\(321\) | 4.60348 | + | 8.74754i | 0.256941 | + | 0.488240i | ||||
\(322\) | −3.49322 | −0.194669 | ||||||||
\(323\) | − | 20.7948i | − | 1.15705i | ||||||
\(324\) | −3.22886 | − | 8.40086i | −0.179381 | − | 0.466714i | ||||
\(325\) | − | 50.1873i | − | 2.78389i | ||||||
\(326\) | −15.4886 | −0.857833 | ||||||||
\(327\) | 0.234045 | − | 0.123169i | 0.0129427 | − | 0.00681123i | ||||
\(328\) | 5.28064 | 0.291575 | ||||||||
\(329\) | −4.96439 | −0.273696 | ||||||||
\(330\) | −19.0355 | − | 11.3843i | −1.04787 | − | 0.626683i | ||||
\(331\) | 7.00503 | 0.385031 | 0.192516 | − | 0.981294i | \(-0.438335\pi\) | ||||
0.192516 | + | 0.981294i | \(0.438335\pi\) | |||||||
\(332\) | 3.53635 | 0.194082 | ||||||||
\(333\) | −5.16965 | + | 7.52530i | −0.283295 | + | 0.412384i | ||||
\(334\) | 3.94198 | 0.215696 | ||||||||
\(335\) | − | 16.3201i | − | 0.891661i | ||||||
\(336\) | −1.53276 | + | 0.806630i | −0.0836188 | + | 0.0440053i | ||||
\(337\) | 15.1925i | 0.827589i | 0.910370 | + | 0.413795i | \(0.135797\pi\) | ||||
−0.910370 | + | 0.413795i | \(0.864203\pi\) | |||||||
\(338\) | 12.6595 | 0.688584 | ||||||||
\(339\) | 8.27462 | − | 4.35460i | 0.449416 | − | 0.236510i | ||||
\(340\) | 10.4159i | 0.564882i | ||||||||
\(341\) | −15.8687 | − | 26.0357i | −0.859340 | − | 1.40991i | ||||
\(342\) | −19.0607 | − | 13.0941i | −1.03069 | − | 0.708050i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 12.5717i | − | 0.677822i | ||||||
\(345\) | 10.8794 | + | 20.6730i | 0.585727 | + | 1.11300i | ||||
\(346\) | 5.16603 | 0.277728 | ||||||||
\(347\) | 17.4151 | 0.934893 | 0.467446 | − | 0.884021i | \(-0.345174\pi\) | ||||
0.467446 | + | 0.884021i | \(0.345174\pi\) | |||||||
\(348\) | 0.670690 | + | 1.27445i | 0.0359528 | + | 0.0683174i | ||||
\(349\) | 12.0560i | 0.645341i | 0.946511 | + | 0.322670i | \(0.104581\pi\) | ||||
−0.946511 | + | 0.322670i | \(0.895419\pi\) | |||||||
\(350\) | 9.90764i | 0.529586i | ||||||||
\(351\) | 3.08544 | − | 26.1397i | 0.164688 | − | 1.39524i | ||||
\(352\) | 1.72613 | + | 2.83205i | 0.0920029 | + | 0.150949i | ||||
\(353\) | − | 23.4434i | − | 1.24776i | −0.781518 | − | 0.623882i | \(-0.785555\pi\) | ||
0.781518 | − | 0.623882i | \(-0.214445\pi\) | |||||||
\(354\) | −0.246779 | + | 0.129870i | −0.0131162 | + | 0.00690253i | ||||
\(355\) | −46.4148 | −2.46344 | ||||||||
\(356\) | − | 7.35755i | − | 0.389950i | ||||||
\(357\) | −4.13491 | + | 2.17604i | −0.218843 | + | 0.115168i | ||||
\(358\) | − | 5.01937i | − | 0.265282i | ||||||
\(359\) | 5.26816 | 0.278043 | 0.139021 | − | 0.990289i | \(-0.455604\pi\) | ||||
0.139021 | + | 0.990289i | \(0.455604\pi\) | |||||||
\(360\) | 9.54734 | + | 6.55874i | 0.503189 | + | 0.345676i | ||||
\(361\) | −40.4186 | −2.12729 | ||||||||
\(362\) | 9.50810 | 0.499735 | ||||||||
\(363\) | −19.0519 | + | 0.159802i | −0.999965 | + | 0.00838745i | ||||
\(364\) | −5.06552 | −0.265505 | ||||||||
\(365\) | −23.7573 | −1.24351 | ||||||||
\(366\) | 7.07153 | − | 3.72147i | 0.369635 | − | 0.194524i | ||||
\(367\) | 19.4642 | 1.01602 | 0.508012 | − | 0.861350i | \(-0.330380\pi\) | ||||
0.508012 | + | 0.861350i | \(0.330380\pi\) | |||||||
\(368\) | − | 3.49322i | − | 0.182097i | ||||||
\(369\) | 8.97021 | − | 13.0576i | 0.466970 | − | 0.679754i | ||||
\(370\) | − | 11.7503i | − | 0.610871i | ||||||
\(371\) | −0.602608 | −0.0312858 | ||||||||
\(372\) | 7.41556 | + | 14.0910i | 0.384479 | + | 0.730586i | ||||
\(373\) | 5.38807i | 0.278984i | 0.990223 | + | 0.139492i | \(0.0445469\pi\) | ||||
−0.990223 | + | 0.139492i | \(0.955453\pi\) | |||||||
\(374\) | 4.65657 | + | 7.63999i | 0.240785 | + | 0.395055i | ||||
\(375\) | 29.0436 | − | 15.2845i | 1.49981 | − | 0.789289i | ||||
\(376\) | − | 4.96439i | − | 0.256019i | ||||||
\(377\) | 4.21183i | 0.216921i | ||||||||
\(378\) | −0.609106 | + | 5.16033i | −0.0313290 | + | 0.265419i | ||||
\(379\) | −8.29732 | −0.426205 | −0.213102 | − | 0.977030i | \(-0.568357\pi\) | ||||
−0.213102 | + | 0.977030i | \(0.568357\pi\) | |||||||
\(380\) | 29.7622 | 1.52677 | ||||||||
\(381\) | 21.8324 | − | 11.4895i | 1.11851 | − | 0.588627i | ||||
\(382\) | 8.73096i | 0.446715i | ||||||||
\(383\) | 27.2636i | 1.39311i | 0.717506 | + | 0.696553i | \(0.245284\pi\) | ||||
−0.717506 | + | 0.696553i | \(0.754716\pi\) | |||||||
\(384\) | −0.806630 | − | 1.53276i | −0.0411632 | − | 0.0782182i | ||||
\(385\) | 6.66465 | + | 10.9346i | 0.339662 | + | 0.557281i | ||||
\(386\) | − | 11.2644i | − | 0.573343i | ||||||
\(387\) | −31.0866 | − | 21.3555i | −1.58022 | − | 1.08556i | ||||
\(388\) | 12.0650 | 0.612505 | ||||||||
\(389\) | − | 26.4139i | − | 1.33924i | −0.742705 | − | 0.669619i | \(-0.766457\pi\) | ||
0.742705 | − | 0.669619i | \(-0.233543\pi\) | |||||||
\(390\) | 15.7762 | + | 29.9779i | 0.798859 | + | 1.51799i | ||||
\(391\) | − | 9.42364i | − | 0.476574i | ||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 13.7752 | + | 26.1757i | 0.694868 | + | 1.32039i | ||||
\(394\) | −26.1013 | −1.31496 | ||||||||
\(395\) | 9.63547 | 0.484813 | ||||||||
\(396\) | 9.93507 | + | 0.542522i | 0.499256 | + | 0.0272627i | ||||
\(397\) | 2.10425 | 0.105609 | 0.0528047 | − | 0.998605i | \(-0.483184\pi\) | ||||
0.0528047 | + | 0.998605i | \(0.483184\pi\) | |||||||
\(398\) | 20.1620 | 1.01063 | ||||||||
\(399\) | 6.21778 | + | 11.8150i | 0.311279 | + | 0.591491i | ||||
\(400\) | −9.90764 | −0.495382 | ||||||||
\(401\) | − | 18.9795i | − | 0.947793i | −0.880581 | − | 0.473896i | \(-0.842847\pi\) | ||
0.880581 | − | 0.473896i | \(-0.157153\pi\) | |||||||
\(402\) | 3.40951 | + | 6.47875i | 0.170051 | + | 0.323131i | ||||
\(403\) | 46.5686i | 2.31975i | ||||||||
\(404\) | 10.4799 | 0.521396 | ||||||||
\(405\) | 32.4361 | − | 12.4668i | 1.61176 | − | 0.619479i | ||||
\(406\) | − | 0.831472i | − | 0.0412653i | ||||||
\(407\) | −5.25314 | − | 8.61878i | −0.260388 | − | 0.427217i | ||||
\(408\) | −2.17604 | − | 4.13491i | −0.107730 | − | 0.204709i | ||||
\(409\) | 5.10349i | 0.252352i | 0.992008 | + | 0.126176i | \(0.0402703\pi\) | ||||
−0.992008 | + | 0.126176i | \(0.959730\pi\) | |||||||
\(410\) | 20.3888i | 1.00693i | ||||||||
\(411\) | 16.8467 | − | 8.86577i | 0.830988 | − | 0.437316i | ||||
\(412\) | −4.76959 | −0.234981 | ||||||||
\(413\) | 0.161004 | 0.00792246 | ||||||||
\(414\) | −8.63781 | − | 5.93392i | −0.424525 | − | 0.291636i | ||||
\(415\) | 13.6540i | 0.670248i | ||||||||
\(416\) | − | 5.06552i | − | 0.248357i | ||||||
\(417\) | −13.2943 | + | 6.99629i | −0.651027 | + | 0.342610i | ||||
\(418\) | 21.8304 | − | 13.3056i | 1.06776 | − | 0.650798i | ||||
\(419\) | − | 6.15406i | − | 0.300645i | −0.988637 | − | 0.150323i | \(-0.951969\pi\) | ||
0.988637 | − | 0.150323i | \(-0.0480313\pi\) | |||||||
\(420\) | −3.11443 | − | 5.91804i | −0.151969 | − | 0.288771i | ||||
\(421\) | 18.8837 | 0.920334 | 0.460167 | − | 0.887832i | \(-0.347790\pi\) | ||||
0.460167 | + | 0.887832i | \(0.347790\pi\) | |||||||
\(422\) | − | 20.1922i | − | 0.982940i | ||||||
\(423\) | −12.2756 | − | 8.43299i | −0.596862 | − | 0.410026i | ||||
\(424\) | − | 0.602608i | − | 0.0292652i | ||||||
\(425\) | −26.7278 | −1.29649 | ||||||||
\(426\) | 18.4258 | − | 9.69674i | 0.892731 | − | 0.469809i | ||||
\(427\) | −4.61360 | −0.223268 | ||||||||
\(428\) | 5.70706 | 0.275861 | ||||||||
\(429\) | 24.9738 | + | 14.9356i | 1.20574 | + | 0.721100i | ||||
\(430\) | 48.5400 | 2.34081 | ||||||||
\(431\) | −4.81981 | −0.232162 | −0.116081 | − | 0.993240i | \(-0.537033\pi\) | ||||
−0.116081 | + | 0.993240i | \(0.537033\pi\) | |||||||
\(432\) | −5.16033 | − | 0.609106i | −0.248276 | − | 0.0293056i | ||||
\(433\) | −18.0162 | −0.865802 | −0.432901 | − | 0.901441i | \(-0.642510\pi\) | ||||
−0.432901 | + | 0.901441i | \(0.642510\pi\) | |||||||
\(434\) | − | 9.19326i | − | 0.441290i | ||||||
\(435\) | −4.92069 | + | 2.58956i | −0.235929 | + | 0.124160i | ||||
\(436\) | − | 0.152695i | − | 0.00731277i | ||||||
\(437\) | −26.9269 | −1.28809 | ||||||||
\(438\) | 9.43118 | − | 4.96326i | 0.450639 | − | 0.237154i | ||||
\(439\) | − | 10.9524i | − | 0.522729i | −0.965240 | − | 0.261364i | \(-0.915828\pi\) | ||
0.965240 | − | 0.261364i | \(-0.0841724\pi\) | |||||||
\(440\) | −10.9346 | + | 6.66465i | −0.521289 | + | 0.317725i | ||||
\(441\) | 1.69870 | − | 2.47274i | 0.0808903 | − | 0.117749i | ||||
\(442\) | − | 13.6652i | − | 0.649988i | ||||||
\(443\) | 3.51803i | 0.167147i | 0.996502 | + | 0.0835734i | \(0.0266333\pi\) | ||||
−0.996502 | + | 0.0835734i | \(0.973367\pi\) | |||||||
\(444\) | 2.45482 | + | 4.66465i | 0.116501 | + | 0.221375i | ||||
\(445\) | 28.4078 | 1.34666 | ||||||||
\(446\) | 0.163853 | 0.00775866 | ||||||||
\(447\) | −2.90196 | − | 5.51431i | −0.137258 | − | 0.260818i | ||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | 10.5334i | 0.497102i | 0.968619 | + | 0.248551i | \(0.0799543\pi\) | ||||
−0.968619 | + | 0.248551i | \(0.920046\pi\) | |||||||
\(450\) | −16.8301 | + | 24.4990i | −0.793377 | + | 1.15489i | ||||
\(451\) | 9.11507 | + | 14.9550i | 0.429212 | + | 0.704205i | ||||
\(452\) | − | 5.39852i | − | 0.253925i | ||||||
\(453\) | 26.8686 | − | 14.1399i | 1.26240 | − | 0.664349i | ||||
\(454\) | −9.14938 | −0.429402 | ||||||||
\(455\) | − | 19.5582i | − | 0.916901i | ||||||
\(456\) | −11.8150 | + | 6.21778i | −0.553290 | + | 0.291174i | ||||
\(457\) | − | 3.05021i | − | 0.142683i | −0.997452 | − | 0.0713414i | \(-0.977272\pi\) | ||
0.997452 | − | 0.0713414i | \(-0.0227280\pi\) | |||||||
\(458\) | −9.97390 | −0.466050 | ||||||||
\(459\) | −13.9210 | − | 1.64318i | −0.649776 | − | 0.0766971i | ||||
\(460\) | 13.4875 | 0.628856 | ||||||||
\(461\) | 41.6488 | 1.93978 | 0.969888 | − | 0.243551i | \(-0.0783122\pi\) | ||||
0.969888 | + | 0.243551i | \(0.0783122\pi\) | |||||||
\(462\) | −4.93015 | − | 2.94849i | −0.229371 | − | 0.137176i | ||||
\(463\) | −1.06374 | −0.0494362 | −0.0247181 | − | 0.999694i | \(-0.507869\pi\) | ||||
−0.0247181 | + | 0.999694i | \(0.507869\pi\) | |||||||
\(464\) | 0.831472 | 0.0386001 | ||||||||
\(465\) | −54.4061 | + | 28.6318i | −2.52302 | + | 1.32777i | ||||
\(466\) | 2.49984 | 0.115803 | ||||||||
\(467\) | − | 19.4950i | − | 0.902121i | −0.892493 | − | 0.451060i | \(-0.851046\pi\) | ||
0.892493 | − | 0.451060i | \(-0.148954\pi\) | |||||||
\(468\) | −12.5257 | − | 8.60477i | −0.579000 | − | 0.397756i | ||||
\(469\) | − | 4.22686i | − | 0.195178i | ||||||
\(470\) | 19.1677 | 0.884141 | ||||||||
\(471\) | −5.85578 | − | 11.1271i | −0.269820 | − | 0.512712i | ||||
\(472\) | 0.161004i | 0.00741079i | ||||||||
\(473\) | 35.6037 | − | 21.7004i | 1.63706 | − | 0.997786i | ||||
\(474\) | −3.82509 | + | 2.01300i | −0.175692 | + | 0.0924600i | ||||
\(475\) | 76.3715i | 3.50417i | ||||||||
\(476\) | 2.69769i | 0.123649i | ||||||||
\(477\) | −1.49009 | − | 1.02365i | −0.0682266 | − | 0.0468696i | ||||
\(478\) | −8.25748 | −0.377689 | ||||||||
\(479\) | −7.07807 | −0.323405 | −0.161703 | − | 0.986840i | \(-0.551699\pi\) | ||||
−0.161703 | + | 0.986840i | \(0.551699\pi\) | |||||||
\(480\) | 5.91804 | − | 3.11443i | 0.270120 | − | 0.142154i | ||||
\(481\) | 15.4159i | 0.702905i | ||||||||
\(482\) | 15.0943i | 0.687527i | ||||||||
\(483\) | 2.81774 | + | 5.35426i | 0.128211 | + | 0.243627i | ||||
\(484\) | −5.04096 | + | 9.77695i | −0.229135 | + | 0.444407i | ||||
\(485\) | 46.5833i | 2.11524i | ||||||||
\(486\) | −10.2720 | + | 11.7255i | −0.465947 | + | 0.531877i | ||||
\(487\) | 30.7305 | 1.39253 | 0.696266 | − | 0.717784i | \(-0.254843\pi\) | ||||
0.696266 | + | 0.717784i | \(0.254843\pi\) | |||||||
\(488\) | − | 4.61360i | − | 0.208848i | ||||||
\(489\) | 12.4936 | + | 23.7403i | 0.564978 | + | 1.07357i | ||||
\(490\) | 3.86104i | 0.174424i | ||||||||
\(491\) | −12.6920 | −0.572781 | −0.286391 | − | 0.958113i | \(-0.592456\pi\) | ||||
−0.286391 | + | 0.958113i | \(0.592456\pi\) | |||||||
\(492\) | −4.25953 | − | 8.09395i | −0.192034 | − | 0.364903i | ||||
\(493\) | 2.24306 | 0.101022 | ||||||||
\(494\) | −39.0468 | −1.75680 | ||||||||
\(495\) | −2.09470 | + | 38.3597i | −0.0941497 | + | 1.72414i | ||||
\(496\) | 9.19326 | 0.412789 | ||||||||
\(497\) | −12.0213 | −0.539229 | ||||||||
\(498\) | −2.85253 | − | 5.42037i | −0.127825 | − | 0.242893i | ||||
\(499\) | −25.1145 | −1.12428 | −0.562140 | − | 0.827042i | \(-0.690022\pi\) | ||||
−0.562140 | + | 0.827042i | \(0.690022\pi\) | |||||||
\(500\) | − | 18.9486i | − | 0.847407i | ||||||
\(501\) | −3.17972 | − | 6.04211i | −0.142060 | − | 0.269942i | ||||
\(502\) | − | 13.7304i | − | 0.612817i | ||||||
\(503\) | 2.25842 | 0.100698 | 0.0503489 | − | 0.998732i | \(-0.483967\pi\) | ||||
0.0503489 | + | 0.998732i | \(0.483967\pi\) | |||||||
\(504\) | 2.47274 | + | 1.69870i | 0.110144 | + | 0.0756659i | ||||
\(505\) | 40.4635i | 1.80060i | ||||||||
\(506\) | 9.89295 | − | 6.02974i | 0.439795 | − | 0.268055i | ||||
\(507\) | −10.2115 | − | 19.4039i | −0.453509 | − | 0.861757i | ||||
\(508\) | − | 14.2439i | − | 0.631970i | ||||||
\(509\) | 38.1220i | 1.68973i | 0.534982 | + | 0.844863i | \(0.320318\pi\) | ||||
−0.534982 | + | 0.844863i | \(0.679682\pi\) | |||||||
\(510\) | 15.9651 | − | 8.40178i | 0.706945 | − | 0.372037i | ||||
\(511\) | −6.15308 | −0.272196 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.69520 | + | 39.7776i | −0.207298 | + | 1.75622i | ||||
\(514\) | − | 5.93347i | − | 0.261714i | ||||||
\(515\) | − | 18.4156i | − | 0.811487i | ||||||
\(516\) | −19.2694 | + | 10.1407i | −0.848289 | + | 0.446421i | ||||
\(517\) | 14.0594 | − | 8.56918i | 0.618331 | − | 0.376872i | ||||
\(518\) | − | 3.04331i | − | 0.133715i | ||||||
\(519\) | −4.16708 | − | 7.91828i | −0.182914 | − | 0.347574i | ||||
\(520\) | 19.5582 | 0.857682 | ||||||||
\(521\) | − | 28.2110i | − | 1.23595i | −0.786199 | − | 0.617974i | \(-0.787954\pi\) | ||
0.786199 | − | 0.617974i | \(-0.212046\pi\) | |||||||
\(522\) | 1.41242 | − | 2.05601i | 0.0618198 | − | 0.0899892i | ||||
\(523\) | 0.946140i | 0.0413718i | 0.999786 | + | 0.0206859i | \(0.00658500\pi\) | ||||
−0.999786 | + | 0.0206859i | \(0.993415\pi\) | |||||||
\(524\) | 17.0775 | 0.746034 | ||||||||
\(525\) | 15.1860 | − | 7.99180i | 0.662772 | − | 0.348791i | ||||
\(526\) | 20.1194 | 0.877248 | ||||||||
\(527\) | 24.8006 | 1.08033 | ||||||||
\(528\) | 2.94849 | − | 4.93015i | 0.128317 | − | 0.214557i | ||||
\(529\) | 10.7974 | 0.469453 | ||||||||
\(530\) | 2.32669 | 0.101065 | ||||||||
\(531\) | 0.398119 | + | 0.273496i | 0.0172769 | + | 0.0118687i | ||||
\(532\) | 7.70835 | 0.334199 | ||||||||
\(533\) | − | 26.7492i | − | 1.15864i | ||||||
\(534\) | −11.2774 | + | 5.93482i | −0.488019 | + | 0.256825i | ||||
\(535\) | 22.0352i | 0.952664i | ||||||||
\(536\) | 4.22686 | 0.182573 | ||||||||
\(537\) | −7.69349 | + | 4.04878i | −0.331998 | + | 0.174718i | ||||
\(538\) | − | 23.5034i | − | 1.01331i | ||||||
\(539\) | 1.72613 | + | 2.83205i | 0.0743496 | + | 0.121985i | ||||
\(540\) | 2.35178 | − | 19.9242i | 0.101205 | − | 0.857403i | ||||
\(541\) | − | 13.1089i | − | 0.563597i | −0.959474 | − | 0.281799i | \(-0.909069\pi\) | ||
0.959474 | − | 0.281799i | \(-0.0909310\pi\) | |||||||
\(542\) | 30.2007i | 1.29723i | ||||||||
\(543\) | −7.66952 | − | 14.5736i | −0.329131 | − | 0.625414i | ||||
\(544\) | −2.69769 | −0.115663 | ||||||||
\(545\) | 0.589562 | 0.0252541 | ||||||||
\(546\) | 4.08600 | + | 7.76421i | 0.174865 | + | 0.332278i | ||||
\(547\) | − | 18.6449i | − | 0.797198i | −0.917125 | − | 0.398599i | \(-0.869497\pi\) | ||
0.917125 | − | 0.398599i | \(-0.130503\pi\) | |||||||
\(548\) | − | 10.9911i | − | 0.469518i | ||||||
\(549\) | −11.4082 | − | 7.83710i | −0.486891 | − | 0.334479i | ||||
\(550\) | −17.1019 | − | 28.0589i | −0.729226 | − | 1.19643i | ||||
\(551\) | − | 6.40927i | − | 0.273044i | ||||||
\(552\) | −5.35426 | + | 2.81774i | −0.227892 | + | 0.119931i | ||||
\(553\) | 2.49556 | 0.106122 | ||||||||
\(554\) | 3.10788i | 0.132041i | ||||||||
\(555\) | −18.0104 | + | 9.47817i | −0.764500 | + | 0.402326i | ||||
\(556\) | 8.67348i | 0.367837i | ||||||||
\(557\) | −32.6578 | −1.38376 | −0.691878 | − | 0.722015i | \(-0.743216\pi\) | ||||
−0.691878 | + | 0.722015i | \(0.743216\pi\) | |||||||
\(558\) | 15.6165 | − | 22.7325i | 0.661101 | − | 0.962344i | ||||
\(559\) | −63.6823 | −2.69347 | ||||||||
\(560\) | −3.86104 | −0.163159 | ||||||||
\(561\) | 7.95414 | − | 13.3000i | 0.335824 | − | 0.561528i | ||||
\(562\) | 1.17009 | 0.0493572 | ||||||||
\(563\) | −42.8575 | −1.80623 | −0.903114 | − | 0.429400i | \(-0.858725\pi\) | ||||
−0.903114 | + | 0.429400i | \(0.858725\pi\) | |||||||
\(564\) | −7.60921 | + | 4.00443i | −0.320406 | + | 0.168617i | ||||
\(565\) | 20.8439 | 0.876909 | ||||||||
\(566\) | 32.3497i | 1.35976i | ||||||||
\(567\) | 8.40086 | − | 3.22886i | 0.352803 | − | 0.135600i | ||||
\(568\) | − | 12.0213i | − | 0.504403i | ||||||
\(569\) | −9.63357 | −0.403860 | −0.201930 | − | 0.979400i | \(-0.564721\pi\) | ||||
−0.201930 | + | 0.979400i | \(0.564721\pi\) | |||||||
\(570\) | −24.0071 | − | 45.6183i | −1.00555 | − | 1.91074i | ||||
\(571\) | 10.6965i | 0.447634i | 0.974631 | + | 0.223817i | \(0.0718518\pi\) | ||||
−0.974631 | + | 0.223817i | \(0.928148\pi\) | |||||||
\(572\) | 14.3458 | − | 8.74373i | 0.599827 | − | 0.365594i | ||||
\(573\) | 13.3824 | − | 7.04265i | 0.559060 | − | 0.294211i | ||||
\(574\) | 5.28064i | 0.220410i | ||||||||
\(575\) | 34.6096i | 1.44332i | ||||||||
\(576\) | −1.69870 | + | 2.47274i | −0.0707790 | + | 0.103031i | ||||
\(577\) | −30.7639 | −1.28072 | −0.640359 | − | 0.768076i | \(-0.721214\pi\) | ||||
−0.640359 | + | 0.768076i | \(0.721214\pi\) | |||||||
\(578\) | 9.72245 | 0.404400 | ||||||||
\(579\) | −17.2656 | + | 9.08621i | −0.717535 | + | 0.377610i | ||||
\(580\) | 3.21035i | 0.133302i | ||||||||
\(581\) | 3.53635i | 0.146713i | ||||||||
\(582\) | −9.73195 | − | 18.4927i | −0.403402 | − | 0.766545i | ||||
\(583\) | 1.70661 | − | 1.04018i | 0.0706807 | − | 0.0430798i | ||||
\(584\) | − | 6.15308i | − | 0.254616i | ||||||
\(585\) | 33.2234 | − | 48.3622i | 1.37362 | − | 1.99953i | ||||
\(586\) | −10.6481 | −0.439870 | ||||||||
\(587\) | − | 4.00060i | − | 0.165122i | −0.996586 | − | 0.0825612i | \(-0.973690\pi\) | ||
0.996586 | − | 0.0825612i | \(-0.0263100\pi\) | |||||||
\(588\) | −0.806630 | − | 1.53276i | −0.0332649 | − | 0.0632099i | ||||
\(589\) | − | 70.8648i | − | 2.91993i | ||||||
\(590\) | −0.621641 | −0.0255926 | ||||||||
\(591\) | 21.0541 | + | 40.0070i | 0.866049 | + | 1.64567i | ||||
\(592\) | 3.04331 | 0.125079 | ||||||||
\(593\) | 35.7449 | 1.46787 | 0.733933 | − | 0.679222i | \(-0.237683\pi\) | ||||
0.733933 | + | 0.679222i | \(0.237683\pi\) | |||||||
\(594\) | −7.18237 | − | 15.6657i | −0.294696 | − | 0.642771i | ||||
\(595\) | −10.4159 | −0.427011 | ||||||||
\(596\) | −3.59764 | −0.147365 | ||||||||
\(597\) | −16.2633 | − | 30.9035i | −0.665613 | − | 1.26480i | ||||
\(598\) | −17.6950 | −0.723601 | ||||||||
\(599\) | 18.2841i | 0.747066i | 0.927617 | + | 0.373533i | \(0.121854\pi\) | ||||
−0.927617 | + | 0.373533i | \(0.878146\pi\) | |||||||
\(600\) | 7.99180 | + | 15.1860i | 0.326264 | + | 0.619967i | ||||
\(601\) | 3.92580i | 0.160137i | 0.996789 | + | 0.0800683i | \(0.0255138\pi\) | ||||
−0.996789 | + | 0.0800683i | \(0.974486\pi\) | |||||||
\(602\) | 12.5717 | 0.512386 | ||||||||
\(603\) | 7.18015 | − | 10.4519i | 0.292398 | − | 0.425635i | ||||
\(604\) | − | 17.5295i | − | 0.713267i | ||||||
\(605\) | −37.7492 | − | 19.4634i | −1.53472 | − | 0.791298i | ||||
\(606\) | −8.45343 | − | 16.0632i | −0.343397 | − | 0.652523i | ||||
\(607\) | 0.684969i | 0.0278020i | 0.999903 | + | 0.0139010i | \(0.00442497\pi\) | ||||
−0.999903 | + | 0.0139010i | \(0.995575\pi\) | |||||||
\(608\) | 7.70835i | 0.312615i | ||||||||
\(609\) | −1.27445 | + | 0.670690i | −0.0516431 | + | 0.0271777i | ||||
\(610\) | 17.8133 | 0.721239 | ||||||||
\(611\) | −25.1472 | −1.01735 | ||||||||
\(612\) | −4.58256 | + | 6.67069i | −0.185239 | + | 0.269647i | ||||
\(613\) | − | 13.9389i | − | 0.562987i | −0.959563 | − | 0.281494i | \(-0.909170\pi\) | ||
0.959563 | − | 0.281494i | \(-0.0908298\pi\) | |||||||
\(614\) | 14.4447i | 0.582939i | ||||||||
\(615\) | 31.2511 | − | 16.4462i | 1.26017 | − | 0.663175i | ||||
\(616\) | −2.83205 | + | 1.72613i | −0.114106 | + | 0.0695477i | ||||
\(617\) | 2.06877i | 0.0832854i | 0.999133 | + | 0.0416427i | \(0.0132591\pi\) | ||||
−0.999133 | + | 0.0416427i | \(0.986741\pi\) | |||||||
\(618\) | 3.84729 | + | 7.31063i | 0.154761 | + | 0.294077i | ||||
\(619\) | −32.1629 | −1.29274 | −0.646368 | − | 0.763026i | \(-0.723713\pi\) | ||||
−0.646368 | + | 0.763026i | \(0.723713\pi\) | |||||||
\(620\) | 35.4955i | 1.42554i | ||||||||
\(621\) | −2.12774 | + | 18.0262i | −0.0853833 | + | 0.723365i | ||||
\(622\) | 27.8091i | 1.11504i | ||||||||
\(623\) | 7.35755 | 0.294774 | ||||||||
\(624\) | −7.76421 | + | 4.08600i | −0.310817 | + | 0.163571i | ||||
\(625\) | 23.6231 | 0.944925 | ||||||||
\(626\) | −14.5554 | −0.581750 | ||||||||
\(627\) | −38.0033 | − | 22.7280i | −1.51771 | − | 0.907669i | ||||
\(628\) | −7.25956 | −0.289688 | ||||||||
\(629\) | 8.20991 | 0.327351 | ||||||||
\(630\) | −6.55874 | + | 9.54734i | −0.261306 | + | 0.380375i | ||||
\(631\) | 30.5134 | 1.21472 | 0.607359 | − | 0.794428i | \(-0.292229\pi\) | ||||
0.607359 | + | 0.794428i | \(0.292229\pi\) | |||||||
\(632\) | 2.49556i | 0.0992682i | ||||||||
\(633\) | −30.9497 | + | 16.2876i | −1.23014 | + | 0.647375i | ||||
\(634\) | − | 1.42646i | − | 0.0566518i | ||||||
\(635\) | 54.9962 | 2.18246 | ||||||||
\(636\) | −0.923652 | + | 0.486082i | −0.0366252 | + | 0.0192744i | ||||
\(637\) | − | 5.06552i | − | 0.200703i | ||||||
\(638\) | 1.43523 | + | 2.35477i | 0.0568212 | + | 0.0932261i | ||||
\(639\) | −29.7255 | − | 20.4205i | −1.17592 | − | 0.807824i | ||||
\(640\) | − | 3.86104i | − | 0.152621i | ||||||
\(641\) | − | 5.28722i | − | 0.208833i | −0.994534 | − | 0.104416i | \(-0.966703\pi\) | ||
0.994534 | − | 0.104416i | \(-0.0332974\pi\) | |||||||
\(642\) | −4.60348 | − | 8.74754i | −0.181685 | − | 0.345238i | ||||
\(643\) | 33.0075 | 1.30169 | 0.650845 | − | 0.759211i | \(-0.274415\pi\) | ||||
0.650845 | + | 0.759211i | \(0.274415\pi\) | |||||||
\(644\) | 3.49322 | 0.137652 | ||||||||
\(645\) | −39.1538 | − | 74.4000i | −1.54168 | − | 2.92950i | ||||
\(646\) | 20.7948i | 0.818159i | ||||||||
\(647\) | 19.8311i | 0.779640i | 0.920891 | + | 0.389820i | \(0.127463\pi\) | ||||
−0.920891 | + | 0.389820i | \(0.872537\pi\) | |||||||
\(648\) | 3.22886 | + | 8.40086i | 0.126842 | + | 0.330017i | ||||
\(649\) | −0.455969 | + | 0.277913i | −0.0178984 | + | 0.0109090i | ||||
\(650\) | 50.1873i | 1.96851i | ||||||||
\(651\) | −14.0910 | + | 7.41556i | −0.552271 | + | 0.290639i | ||||
\(652\) | 15.4886 | 0.606580 | ||||||||
\(653\) | 25.9231i | 1.01445i | 0.861814 | + | 0.507225i | \(0.169329\pi\) | ||||
−0.861814 | + | 0.507225i | \(0.830671\pi\) | |||||||
\(654\) | −0.234045 | + | 0.123169i | −0.00915188 | + | 0.00481627i | ||||
\(655\) | 65.9369i | 2.57637i | ||||||||
\(656\) | −5.28064 | −0.206175 | ||||||||
\(657\) | −15.2149 | − | 10.4522i | −0.593592 | − | 0.407780i | ||||
\(658\) | 4.96439 | 0.193532 | ||||||||
\(659\) | −20.2139 | −0.787421 | −0.393710 | − | 0.919235i | \(-0.628809\pi\) | ||||
−0.393710 | + | 0.919235i | \(0.628809\pi\) | |||||||
\(660\) | 19.0355 | + | 11.3843i | 0.740956 | + | 0.443132i | ||||
\(661\) | 26.7459 | 1.04029 | 0.520147 | − | 0.854077i | \(-0.325877\pi\) | ||||
0.520147 | + | 0.854077i | \(0.325877\pi\) | |||||||
\(662\) | −7.00503 | −0.272258 | ||||||||
\(663\) | −20.9455 | + | 11.0228i | −0.813455 | + | 0.428089i | ||||
\(664\) | −3.53635 | −0.137237 | ||||||||
\(665\) | 29.7622i | 1.15413i | ||||||||
\(666\) | 5.16965 | − | 7.52530i | 0.200320 | − | 0.291599i | ||||
\(667\) | − | 2.90451i | − | 0.112463i | ||||||
\(668\) | −3.94198 | −0.152520 | ||||||||
\(669\) | −0.132169 | − | 0.251147i | −0.00510993 | − | 0.00970990i | ||||
\(670\) | 16.3201i | 0.630500i | ||||||||
\(671\) | 13.0659 | − | 7.96367i | 0.504404 | − | 0.307434i | ||||
\(672\) | 1.53276 | − | 0.806630i | 0.0591274 | − | 0.0311164i | ||||
\(673\) | − | 38.6571i | − | 1.49012i | −0.666996 | − | 0.745061i | \(-0.732420\pi\) | ||
0.666996 | − | 0.745061i | \(-0.267580\pi\) | |||||||
\(674\) | − | 15.1925i | − | 0.585194i | ||||||
\(675\) | 51.1267 | + | 6.03480i | 1.96787 | + | 0.232280i | ||||
\(676\) | −12.6595 | −0.486902 | ||||||||
\(677\) | 7.55254 | 0.290268 | 0.145134 | − | 0.989412i | \(-0.453639\pi\) | ||||
0.145134 | + | 0.989412i | \(0.453639\pi\) | |||||||
\(678\) | −8.27462 | + | 4.35460i | −0.317785 | + | 0.167238i | ||||
\(679\) | 12.0650i | 0.463010i | ||||||||
\(680\) | − | 10.4159i | − | 0.399432i | ||||||
\(681\) | 7.38017 | + | 14.0238i | 0.282809 | + | 0.537393i | ||||
\(682\) | 15.8687 | + | 26.0357i | 0.607645 | + | 0.996959i | ||||
\(683\) | − | 9.59137i | − | 0.367004i | −0.983019 | − | 0.183502i | \(-0.941257\pi\) | ||
0.983019 | − | 0.183502i | \(-0.0587433\pi\) | |||||||
\(684\) | 19.0607 | + | 13.0941i | 0.728805 | + | 0.500667i | ||||
\(685\) | 42.4372 | 1.62144 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 8.04525 | + | 15.2876i | 0.306945 | + | 0.583257i | ||||
\(688\) | 12.5717i | 0.479293i | ||||||||
\(689\) | −3.05252 | −0.116292 | ||||||||
\(690\) | −10.8794 | − | 20.6730i | −0.414171 | − | 0.787008i | ||||
\(691\) | 11.3824 | 0.433008 | 0.216504 | − | 0.976282i | \(-0.430535\pi\) | ||||
0.216504 | + | 0.976282i | \(0.430535\pi\) | |||||||
\(692\) | −5.16603 | −0.196383 | ||||||||
\(693\) | −0.542522 | + | 9.93507i | −0.0206087 | + | 0.377402i | ||||
\(694\) | −17.4151 | −0.661069 | ||||||||
\(695\) | −33.4887 | −1.27030 | ||||||||
\(696\) | −0.670690 | − | 1.27445i | −0.0254224 | − | 0.0483077i | ||||
\(697\) | −14.2456 | −0.539589 | ||||||||
\(698\) | − | 12.0560i | − | 0.456325i | ||||||
\(699\) | −2.01644 | − | 3.83165i | −0.0762689 | − | 0.144926i | ||||
\(700\) | − | 9.90764i | − | 0.374474i | ||||||
\(701\) | −36.0942 | −1.36326 | −0.681630 | − | 0.731697i | \(-0.738729\pi\) | ||||
−0.681630 | + | 0.731697i | \(0.738729\pi\) | |||||||
\(702\) | −3.08544 | + | 26.1397i | −0.116452 | + | 0.986581i | ||||
\(703\) | − | 23.4589i | − | 0.884768i | ||||||
\(704\) | −1.72613 | − | 2.83205i | −0.0650559 | − | 0.106737i | ||||
\(705\) | −15.4613 | − | 29.3795i | −0.582305 | − | 1.10650i | ||||
\(706\) | 23.4434i | 0.882303i | ||||||||
\(707\) | 10.4799i | 0.394139i | ||||||||
\(708\) | 0.246779 | − | 0.129870i | 0.00927454 | − | 0.00488082i | ||||
\(709\) | −10.7092 | −0.402192 | −0.201096 | − | 0.979571i | \(-0.564450\pi\) | ||||
−0.201096 | + | 0.979571i | \(0.564450\pi\) | |||||||
\(710\) | 46.4148 | 1.74191 | ||||||||
\(711\) | 6.17087 | + | 4.23920i | 0.231426 | + | 0.158983i | ||||
\(712\) | 7.35755i | 0.275736i | ||||||||
\(713\) | − | 32.1141i | − | 1.20268i | ||||||
\(714\) | 4.13491 | − | 2.17604i | 0.154745 | − | 0.0814363i | ||||
\(715\) | 33.7599 | + | 55.3896i | 1.26255 | + | 2.07145i | ||||
\(716\) | 5.01937i | 0.187583i | ||||||||
\(717\) | 6.66073 | + | 12.6567i | 0.248750 | + | 0.472674i | ||||
\(718\) | −5.26816 | −0.196606 | ||||||||
\(719\) | 48.6552i | 1.81453i | 0.420556 | + | 0.907267i | \(0.361835\pi\) | ||||
−0.420556 | + | 0.907267i | \(0.638165\pi\) | |||||||
\(720\) | −9.54734 | − | 6.55874i | −0.355808 | − | 0.244430i | ||||
\(721\) | − | 4.76959i | − | 0.177629i | ||||||
\(722\) | 40.4186 | 1.50422 | ||||||||
\(723\) | 23.1359 | − | 12.1755i | 0.860434 | − | 0.452812i | ||||
\(724\) | −9.50810 | −0.353366 | ||||||||
\(725\) | −8.23792 | −0.305949 | ||||||||
\(726\) | 19.0519 | − | 0.159802i | 0.707082 | − | 0.00593082i | ||||
\(727\) | 3.44225 | 0.127666 | 0.0638329 | − | 0.997961i | \(-0.479668\pi\) | ||||
0.0638329 | + | 0.997961i | \(0.479668\pi\) | |||||||
\(728\) | 5.06552 | 0.187741 | ||||||||
\(729\) | 26.2580 | + | 6.28637i | 0.972518 | + | 0.232829i | ||||
\(730\) | 23.7573 | 0.879297 | ||||||||
\(731\) | 33.9147i | 1.25438i | ||||||||
\(732\) | −7.07153 | + | 3.72147i | −0.261371 | + | 0.137549i | ||||
\(733\) | − | 1.65107i | − | 0.0609837i | −0.999535 | − | 0.0304919i | \(-0.990293\pi\) | ||
0.999535 | − | 0.0304919i | \(-0.00970737\pi\) | |||||||
\(734\) | −19.4642 | −0.718438 | ||||||||
\(735\) | 5.91804 | − | 3.11443i | 0.218290 | − | 0.114878i | ||||
\(736\) | 3.49322i | 0.128762i | ||||||||
\(737\) | 7.29610 | + | 11.9707i | 0.268755 | + | 0.440945i | ||||
\(738\) | −8.97021 | + | 13.0576i | −0.330198 | + | 0.480659i | ||||
\(739\) | − | 21.9281i | − | 0.806639i | −0.915059 | − | 0.403319i | \(-0.867856\pi\) | ||
0.915059 | − | 0.403319i | \(-0.132144\pi\) | |||||||
\(740\) | 11.7503i | 0.431951i | ||||||||
\(741\) | 31.4963 | + | 59.8492i | 1.15704 | + | 2.19862i | ||||
\(742\) | 0.602608 | 0.0221224 | ||||||||
\(743\) | −34.8682 | −1.27919 | −0.639596 | − | 0.768712i | \(-0.720898\pi\) | ||||
−0.639596 | + | 0.768712i | \(0.720898\pi\) | |||||||
\(744\) | −7.41556 | − | 14.0910i | −0.271868 | − | 0.516603i | ||||
\(745\) | − | 13.8906i | − | 0.508913i | ||||||
\(746\) | − | 5.38807i | − | 0.197271i | ||||||
\(747\) | −6.00718 | + | 8.74447i | −0.219791 | + | 0.319943i | ||||
\(748\) | −4.65657 | − | 7.63999i | −0.170261 | − | 0.279346i | ||||
\(749\) | 5.70706i | 0.208531i | ||||||||
\(750\) | −29.0436 | + | 15.2845i | −1.06052 | + | 0.558111i | ||||
\(751\) | 25.6297 | 0.935239 | 0.467620 | − | 0.883930i | \(-0.345112\pi\) | ||||
0.467620 | + | 0.883930i | \(0.345112\pi\) | |||||||
\(752\) | 4.96439i | 0.181033i | ||||||||
\(753\) | −21.0454 | + | 11.0753i | −0.766936 | + | 0.403608i | ||||
\(754\) | − | 4.21183i | − | 0.153386i | ||||||
\(755\) | 67.6823 | 2.46321 | ||||||||
\(756\) | 0.609106 | − | 5.16033i | 0.0221530 | − | 0.187679i | ||||
\(757\) | −28.8949 | −1.05020 | −0.525102 | − | 0.851039i | \(-0.675973\pi\) | ||||
−0.525102 | + | 0.851039i | \(0.675973\pi\) | |||||||
\(758\) | 8.29732 | 0.301372 | ||||||||
\(759\) | −17.2221 | − | 10.2997i | −0.625122 | − | 0.373857i | ||||
\(760\) | −29.7622 | −1.07959 | ||||||||
\(761\) | −11.0225 | −0.399565 | −0.199782 | − | 0.979840i | \(-0.564024\pi\) | ||||
−0.199782 | + | 0.979840i | \(0.564024\pi\) | |||||||
\(762\) | −21.8324 | + | 11.4895i | −0.790906 | + | 0.416222i | ||||
\(763\) | 0.152695 | 0.00552794 | ||||||||
\(764\) | − | 8.73096i | − | 0.315875i | ||||||
\(765\) | −25.7558 | − | 17.6935i | −0.931203 | − | 0.639708i | ||||
\(766\) | − | 27.2636i | − | 0.985074i | ||||||
\(767\) | 0.815566 | 0.0294484 | ||||||||
\(768\) | 0.806630 | + | 1.53276i | 0.0291068 | + | 0.0553087i | ||||
\(769\) | − | 31.5094i | − | 1.13626i | −0.822939 | − | 0.568129i | \(-0.807667\pi\) | ||
0.822939 | − | 0.568129i | \(-0.192333\pi\) | |||||||
\(770\) | −6.66465 | − | 10.9346i | −0.240177 | − | 0.394057i | ||||
\(771\) | −9.09458 | + | 4.78612i | −0.327533 | + | 0.172368i | ||||
\(772\) | 11.2644i | 0.405415i | ||||||||
\(773\) | − | 46.5070i | − | 1.67274i | −0.548164 | − | 0.836371i | \(-0.684673\pi\) | ||
0.548164 | − | 0.836371i | \(-0.315327\pi\) | |||||||
\(774\) | 31.0866 | + | 21.3555i | 1.11738 | + | 0.767609i | ||||
\(775\) | −91.0835 | −3.27182 | ||||||||
\(776\) | −12.0650 | −0.433106 | ||||||||
\(777\) | −4.66465 | + | 2.45482i | −0.167343 | + | 0.0880663i | ||||
\(778\) | 26.4139i | 0.946984i | ||||||||
\(779\) | 40.7050i | 1.45841i | ||||||||
\(780\) | −15.7762 | − | 29.9779i | −0.564879 | − | 1.07338i | ||||
\(781\) | 34.0449 | − | 20.7503i | 1.21822 | − | 0.742505i | ||||
\(782\) | 9.42364i | 0.336989i | ||||||||
\(783\) | −4.29067 | − | 0.506454i | −0.153336 | − | 0.0180992i | ||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | − | 28.0295i | − | 1.00041i | ||||||
\(786\) | −13.7752 | − | 26.1757i | −0.491346 | − | 0.933655i | ||||
\(787\) | − | 28.8312i | − | 1.02772i | −0.857874 | − | 0.513860i | \(-0.828215\pi\) | ||
0.857874 | − | 0.513860i | \(-0.171785\pi\) | |||||||
\(788\) | 26.1013 | 0.929820 | ||||||||
\(789\) | −16.2289 | − | 30.8382i | −0.577765 | − | 1.09787i | ||||
\(790\) | −9.63547 | −0.342815 | ||||||||
\(791\) | 5.39852 | 0.191949 | ||||||||
\(792\) | −9.93507 | − | 0.542522i | −0.353027 | − | 0.0192777i | ||||
\(793\) | −23.3703 | −0.829903 | ||||||||
\(794\) | −2.10425 | −0.0746771 | ||||||||
\(795\) | −1.87678 | − | 3.56626i | −0.0665626 | − | 0.126482i | ||||
\(796\) | −20.1620 | −0.714625 | ||||||||
\(797\) | − | 21.2458i | − | 0.752566i | −0.926505 | − | 0.376283i | \(-0.877202\pi\) | ||
0.926505 | − | 0.376283i | \(-0.122798\pi\) | |||||||
\(798\) | −6.21778 | − | 11.8150i | −0.220107 | − | 0.418248i | ||||
\(799\) | 13.3924i | 0.473790i | ||||||||
\(800\) | 9.90764 | 0.350288 | ||||||||
\(801\) | 18.1933 | + | 12.4982i | 0.642829 | + | 0.441604i | ||||
\(802\) | 18.9795i | 0.670191i | ||||||||
\(803\) | 17.4258 | − | 10.6210i | 0.614943 | − | 0.374807i | ||||
\(804\) | −3.40951 | − | 6.47875i | −0.120244 | − | 0.228488i | ||||
\(805\) | 13.4875i | 0.475371i | ||||||||
\(806\) | − | 46.5686i | − | 1.64031i | ||||||
\(807\) | −36.0251 | + | 18.9586i | −1.26814 | + | 0.667374i | ||||
\(808\) | −10.4799 | −0.368683 | ||||||||
\(809\) | −37.3877 | −1.31448 | −0.657241 | − | 0.753681i | \(-0.728276\pi\) | ||||
−0.657241 | + | 0.753681i | \(0.728276\pi\) | |||||||
\(810\) | −32.4361 | + | 12.4668i | −1.13969 | + | 0.438038i | ||||
\(811\) | − | 19.8659i | − | 0.697588i | −0.937200 | − | 0.348794i | \(-0.886591\pi\) | ||
0.937200 | − | 0.348794i | \(-0.113409\pi\) | |||||||
\(812\) | 0.831472i | 0.0291789i | ||||||||
\(813\) | 46.2903 | − | 24.3608i | 1.62347 | − | 0.854369i | ||||
\(814\) | 5.25314 | + | 8.61878i | 0.184122 | + | 0.302088i | ||||
\(815\) | 59.8021i | 2.09478i | ||||||||
\(816\) | 2.17604 | + | 4.13491i | 0.0761767 | + | 0.144751i | ||||
\(817\) | 96.9073 | 3.39036 | ||||||||
\(818\) | − | 5.10349i | − | 0.178439i | ||||||
\(819\) | 8.60477 | − | 12.5257i | 0.300675 | − | 0.437683i | ||||
\(820\) | − | 20.3888i | − | 0.712007i | ||||||
\(821\) | −19.1112 | −0.666986 | −0.333493 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333493 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(822\) | −16.8467 | + | 8.86577i | −0.587597 | + | 0.309229i | ||||
\(823\) | −7.36922 | −0.256875 | −0.128437 | − | 0.991718i | \(-0.540996\pi\) | ||||
−0.128437 | + | 0.991718i | \(0.540996\pi\) | |||||||
\(824\) | 4.76959 | 0.166156 | ||||||||
\(825\) | −29.2126 | + | 48.8462i | −1.01705 | + | 1.70060i | ||||
\(826\) | −0.161004 | −0.00560203 | ||||||||
\(827\) | −0.0610377 | −0.00212249 | −0.00106124 | − | 0.999999i | \(-0.500338\pi\) | ||||
−0.00106124 | + | 0.999999i | \(0.500338\pi\) | |||||||
\(828\) | 8.63781 | + | 5.93392i | 0.300185 | + | 0.206218i | ||||
\(829\) | 44.7995 | 1.55595 | 0.777975 | − | 0.628295i | \(-0.216247\pi\) | ||||
0.777975 | + | 0.628295i | \(0.216247\pi\) | |||||||
\(830\) | − | 13.6540i | − | 0.473937i | ||||||
\(831\) | 4.76364 | − | 2.50691i | 0.165249 | − | 0.0869638i | ||||
\(832\) | 5.06552i | 0.175615i | ||||||||
\(833\) | −2.69769 | −0.0934696 | ||||||||
\(834\) | 13.2943 | − | 6.99629i | 0.460346 | − | 0.242262i | ||||
\(835\) | − | 15.2202i | − | 0.526716i | ||||||
\(836\) | −21.8304 | + | 13.3056i | −0.755020 | + | 0.460184i | ||||
\(837\) | −47.4402 | − | 5.59967i | −1.63977 | − | 0.193553i | ||||
\(838\) | 6.15406i | 0.212588i | ||||||||
\(839\) | − | 37.9316i | − | 1.30954i | −0.755826 | − | 0.654772i | \(-0.772765\pi\) | ||
0.755826 | − | 0.654772i | \(-0.227235\pi\) | |||||||
\(840\) | 3.11443 | + | 5.91804i | 0.107458 | + | 0.204192i | ||||
\(841\) | −28.3087 | −0.976161 | ||||||||
\(842\) | −18.8837 | −0.650774 | ||||||||
\(843\) | −0.943828 | − | 1.79346i | −0.0325072 | − | 0.0617701i | ||||
\(844\) | 20.1922i | 0.695043i | ||||||||
\(845\) | − | 48.8787i | − | 1.68148i | ||||||
\(846\) | 12.2756 | + | 8.43299i | 0.422045 | + | 0.289932i | ||||
\(847\) | −9.77695 | − | 5.04096i | −0.335940 | − | 0.173210i | ||||
\(848\) | 0.602608i | 0.0206936i | ||||||||
\(849\) | 49.5842 | − | 26.0942i | 1.70173 | − | 0.895551i | ||||
\(850\) | 26.7278 | 0.916755 | ||||||||
\(851\) | − | 10.6309i | − | 0.364424i | ||||||
\(852\) | −18.4258 | + | 9.69674i | −0.631256 | + | 0.332205i | ||||
\(853\) | 7.86879i | 0.269422i | 0.990885 | + | 0.134711i | \(0.0430106\pi\) | ||||
−0.990885 | + | 0.134711i | \(0.956989\pi\) | |||||||
\(854\) | 4.61360 | 0.157874 | ||||||||
\(855\) | −50.5570 | + | 73.5942i | −1.72901 | + | 2.51687i | ||||
\(856\) | −5.70706 | −0.195063 | ||||||||
\(857\) | 31.4422 | 1.07404 | 0.537022 | − | 0.843568i | \(-0.319549\pi\) | ||||
0.537022 | + | 0.843568i | \(0.319549\pi\) | |||||||
\(858\) | −24.9738 | − | 14.9356i | −0.852590 | − | 0.509895i | ||||
\(859\) | 22.2235 | 0.758257 | 0.379129 | − | 0.925344i | \(-0.376224\pi\) | ||||
0.379129 | + | 0.925344i | \(0.376224\pi\) | |||||||
\(860\) | −48.5400 | −1.65520 | ||||||||
\(861\) | 8.09395 | − | 4.25953i | 0.275841 | − | 0.145164i | ||||
\(862\) | 4.81981 | 0.164163 | ||||||||
\(863\) | − | 56.2253i | − | 1.91393i | −0.290198 | − | 0.956967i | \(-0.593721\pi\) | ||
0.290198 | − | 0.956967i | \(-0.406279\pi\) | |||||||
\(864\) | 5.16033 | + | 0.609106i | 0.175558 | + | 0.0207222i | ||||
\(865\) | − | 19.9463i | − | 0.678193i | ||||||
\(866\) | 18.0162 | 0.612214 | ||||||||
\(867\) | −7.84242 | − | 14.9022i | −0.266342 | − | 0.506104i | ||||
\(868\) | 9.19326i | 0.312039i | ||||||||
\(869\) | −7.06755 | + | 4.30766i | −0.239750 | + | 0.146127i | ||||
\(870\) | 4.92069 | − | 2.58956i | 0.166827 | − | 0.0877944i | ||||
\(871\) | − | 21.4112i | − | 0.725492i | ||||||
\(872\) | 0.152695i | 0.00517091i | ||||||||
\(873\) | −20.4947 | + | 29.8335i | −0.693640 | + | 1.00971i | ||||
\(874\) | 26.9269 | 0.910817 | ||||||||
\(875\) | 18.9486 | 0.640580 | ||||||||
\(876\) | −9.43118 | + | 4.96326i | −0.318650 | + | 0.167693i | ||||
\(877\) | 8.04833i | 0.271773i | 0.990724 | + | 0.135886i | \(0.0433882\pi\) | ||||
−0.990724 | + | 0.135886i | \(0.956612\pi\) | |||||||
\(878\) | 10.9524i | 0.369625i | ||||||||
\(879\) | 8.58910 | + | 16.3210i | 0.289703 | + | 0.550494i | ||||
\(880\) | 10.9346 | − | 6.66465i | 0.368607 | − | 0.224665i | ||||
\(881\) | 38.6483i | 1.30210i | 0.759037 | + | 0.651048i | \(0.225670\pi\) | ||||
−0.759037 | + | 0.651048i | \(0.774330\pi\) | |||||||
\(882\) | −1.69870 | + | 2.47274i | −0.0571981 | + | 0.0832614i | ||||
\(883\) | 22.6170 | 0.761123 | 0.380561 | − | 0.924756i | \(-0.375731\pi\) | ||||
0.380561 | + | 0.924756i | \(0.375731\pi\) | |||||||
\(884\) | 13.6652i | 0.459611i | ||||||||
\(885\) | 0.501434 | + | 0.952826i | 0.0168555 | + | 0.0320289i | ||||
\(886\) | − | 3.51803i | − | 0.118191i | ||||||
\(887\) | 31.5870 | 1.06059 | 0.530294 | − | 0.847814i | \(-0.322082\pi\) | ||||
0.530294 | + | 0.847814i | \(0.322082\pi\) | |||||||
\(888\) | −2.45482 | − | 4.66465i | −0.0823784 | − | 0.156535i | ||||
\(889\) | 14.2439 | 0.477725 | ||||||||
\(890\) | −28.4078 | −0.952232 | ||||||||
\(891\) | −18.2182 | + | 23.6452i | −0.610332 | + | 0.792146i | ||||
\(892\) | −0.163853 | −0.00548620 | ||||||||
\(893\) | 38.2673 | 1.28057 | ||||||||
\(894\) | 2.90196 | + | 5.51431i | 0.0970561 | + | 0.184426i | ||||
\(895\) | −19.3800 | −0.647802 | ||||||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | 14.2733 | + | 27.1221i | 0.476571 | + | 0.905580i | ||||
\(898\) | − | 10.5334i | − | 0.351504i | ||||||
\(899\) | 7.64393 | 0.254939 | ||||||||
\(900\) | 16.8301 | − | 24.4990i | 0.561002 | − | 0.816633i | ||||
\(901\) | 1.62565i | 0.0541583i | ||||||||
\(902\) | −9.11507 | − | 14.9550i | −0.303499 | − | 0.497948i | ||||
\(903\) | −10.1407 | − | 19.2694i | −0.337463 | − | 0.641246i | ||||
\(904\) | 5.39852i | 0.179552i | ||||||||
\(905\) | − | 36.7112i | − | 1.22032i | ||||||
\(906\) | −26.8686 | + | 14.1399i | −0.892648 | + | 0.469765i | ||||
\(907\) | −28.7146 | −0.953454 | −0.476727 | − | 0.879051i | \(-0.658177\pi\) | ||||
−0.476727 | + | 0.879051i | \(0.658177\pi\) | |||||||
\(908\) | 9.14938 | 0.303633 | ||||||||
\(909\) | −17.8022 | + | 25.9141i | −0.590463 | + | 0.859518i | ||||
\(910\) | 19.5582i | 0.648347i | ||||||||
\(911\) | − | 2.44106i | − | 0.0808758i | −0.999182 | − | 0.0404379i | \(-0.987125\pi\) | ||
0.999182 | − | 0.0404379i | \(-0.0128753\pi\) | |||||||
\(912\) | 11.8150 | − | 6.21778i | 0.391235 | − | 0.205891i | ||||
\(913\) | −6.10419 | − | 10.0151i | −0.202019 | − | 0.331452i | ||||
\(914\) | 3.05021i | 0.100892i | ||||||||
\(915\) | −14.3687 | − | 27.3035i | −0.475016 | − | 0.902625i | ||||
\(916\) | 9.97390 | 0.329547 | ||||||||
\(917\) | 17.0775i | 0.563948i | ||||||||
\(918\) | 13.9210 | + | 1.64318i | 0.459461 | + | 0.0542331i | ||||
\(919\) | 41.7704i | 1.37788i | 0.724819 | + | 0.688939i | \(0.241923\pi\) | ||||
−0.724819 | + | 0.688939i | \(0.758077\pi\) | |||||||
\(920\) | −13.4875 | −0.444668 | ||||||||
\(921\) | 22.1402 | − | 11.6515i | 0.729544 | − | 0.383930i | ||||
\(922\) | −41.6488 | −1.37163 | ||||||||
\(923\) | −60.8941 | −2.00435 | ||||||||
\(924\) | 4.93015 | + | 2.94849i | 0.162190 | + | 0.0969983i | ||||
\(925\) | −30.1520 | −0.991391 | ||||||||
\(926\) | 1.06374 | 0.0349566 | ||||||||
\(927\) | 8.10208 | − | 11.7939i | 0.266107 | − | 0.387364i | ||||
\(928\) | −0.831472 | −0.0272944 | ||||||||
\(929\) | 24.5494i | 0.805441i | 0.915323 | + | 0.402721i | \(0.131935\pi\) | ||||
−0.915323 | + | 0.402721i | \(0.868065\pi\) | |||||||
\(930\) | 54.4061 | − | 28.6318i | 1.78405 | − | 0.938873i | ||||
\(931\) | 7.70835i | 0.252631i | ||||||||
\(932\) | −2.49984 | −0.0818849 | ||||||||
\(933\) | 42.6246 | − | 22.4316i | 1.39547 | − | 0.734379i | ||||
\(934\) | 19.4950i | 0.637896i | ||||||||
\(935\) | 29.4983 | − | 17.9792i | 0.964698 | − | 0.587983i | ||||
\(936\) | 12.5257 | + | 8.60477i | 0.409415 | + | 0.281256i | ||||
\(937\) | 44.9563i | 1.46866i | 0.678794 | + | 0.734328i | \(0.262503\pi\) | ||||
−0.678794 | + | 0.734328i | \(0.737497\pi\) | |||||||
\(938\) | 4.22686i | 0.138012i | ||||||||
\(939\) | 11.7408 | + | 22.3099i | 0.383147 | + | 0.728055i | ||||
\(940\) | −19.1677 | −0.625182 | ||||||||
\(941\) | 58.9543 | 1.92185 | 0.960927 | − | 0.276801i | \(-0.0892744\pi\) | ||||
0.960927 | + | 0.276801i | \(0.0892744\pi\) | |||||||
\(942\) | 5.85578 | + | 11.1271i | 0.190792 | + | 0.362542i | ||||
\(943\) | 18.4464i | 0.600699i | ||||||||
\(944\) | − | 0.161004i | − | 0.00524022i | ||||||
\(945\) | 19.9242 | + | 2.35178i | 0.648136 | + | 0.0765035i | ||||
\(946\) | −35.6037 | + | 21.7004i | −1.15758 | + | 0.705542i | ||||
\(947\) | 15.3478i | 0.498735i | 0.968409 | + | 0.249368i | \(0.0802227\pi\) | ||||
−0.968409 | + | 0.249368i | \(0.919777\pi\) | |||||||
\(948\) | 3.82509 | − | 2.01300i | 0.124233 | − | 0.0653791i | ||||
\(949\) | −31.1685 | −1.01177 | ||||||||
\(950\) | − | 76.3715i | − | 2.47782i | ||||||
\(951\) | −2.18641 | + | 1.15062i | −0.0708993 | + | 0.0373115i | ||||
\(952\) | − | 2.69769i | − | 0.0874328i | ||||||
\(953\) | −20.9482 | −0.678579 | −0.339290 | − | 0.940682i | \(-0.610187\pi\) | ||||
−0.339290 | + | 0.940682i | \(0.610187\pi\) | |||||||
\(954\) | 1.49009 | + | 1.02365i | 0.0482435 | + | 0.0331418i | ||||
\(955\) | 33.7106 | 1.09085 | ||||||||
\(956\) | 8.25748 | 0.267066 | ||||||||
\(957\) | 2.45159 | − | 4.09928i | 0.0792486 | − | 0.132511i | ||||
\(958\) | 7.07807 | 0.228682 | ||||||||
\(959\) | 10.9911 | 0.354922 | ||||||||
\(960\) | −5.91804 | + | 3.11443i | −0.191004 | + | 0.100518i | ||||
\(961\) | 53.5160 | 1.72632 | ||||||||
\(962\) | − | 15.4159i | − | 0.497029i | ||||||
\(963\) | −9.69455 | + | 14.1121i | −0.312403 | + | 0.454755i | ||||
\(964\) | − | 15.0943i | − | 0.486155i | ||||||
\(965\) | −43.4924 | −1.40007 | ||||||||
\(966\) | −2.81774 | − | 5.35426i | −0.0906591 | − | 0.172271i | ||||
\(967\) | 4.00123i | 0.128671i | 0.997928 | + | 0.0643354i | \(0.0204928\pi\) | ||||
−0.997928 | + | 0.0643354i | \(0.979507\pi\) | |||||||
\(968\) | 5.04096 | − | 9.77695i | 0.162023 | − | 0.314243i | ||||
\(969\) | 31.8733 | − | 16.7737i | 1.02392 | − | 0.538848i | ||||
\(970\) | − | 46.5833i | − | 1.49570i | ||||||
\(971\) | − | 26.3379i | − | 0.845223i | −0.906311 | − | 0.422611i | \(-0.861114\pi\) | ||
0.906311 | − | 0.422611i | \(-0.138886\pi\) | |||||||
\(972\) | 10.2720 | − | 11.7255i | 0.329474 | − | 0.376094i | ||||
\(973\) | −8.67348 | −0.278059 | ||||||||
\(974\) | −30.7305 | −0.984669 | ||||||||
\(975\) | 76.9250 | − | 40.4826i | 2.46357 | − | 1.29648i | ||||
\(976\) | 4.61360i | 0.147678i | ||||||||
\(977\) | 48.9097i | 1.56476i | 0.622801 | + | 0.782381i | \(0.285995\pi\) | ||||
−0.622801 | + | 0.782381i | \(0.714005\pi\) | |||||||
\(978\) | −12.4936 | − | 23.7403i | −0.399500 | − | 0.759130i | ||||
\(979\) | −20.8369 | + | 12.7001i | −0.665951 | + | 0.405896i | ||||
\(980\) | − | 3.86104i | − | 0.123336i | ||||||
\(981\) | 0.377575 | + | 0.259383i | 0.0120550 | + | 0.00828145i | ||||
\(982\) | 12.6920 | 0.405018 | ||||||||
\(983\) | − | 15.8828i | − | 0.506582i | −0.967390 | − | 0.253291i | \(-0.918487\pi\) | ||
0.967390 | − | 0.253291i | \(-0.0815130\pi\) | |||||||
\(984\) | 4.25953 | + | 8.09395i | 0.135789 | + | 0.258026i | ||||
\(985\) | 100.778i | 3.21106i | ||||||||
\(986\) | −2.24306 | −0.0714335 | ||||||||
\(987\) | −4.00443 | − | 7.60921i | −0.127462 | − | 0.242204i | ||||
\(988\) | 39.0468 | 1.24224 | ||||||||
\(989\) | 43.9158 | 1.39644 | ||||||||
\(990\) | 2.09470 | − | 38.3597i | 0.0665739 | − | 1.21915i | ||||
\(991\) | 43.0978 | 1.36905 | 0.684523 | − | 0.728991i | \(-0.260011\pi\) | ||||
0.684523 | + | 0.728991i | \(0.260011\pi\) | |||||||
\(992\) | −9.19326 | −0.291886 | ||||||||
\(993\) | 5.65047 | + | 10.7370i | 0.179312 | + | 0.340729i | ||||
\(994\) | 12.0213 | 0.381293 | ||||||||
\(995\) | − | 77.8465i | − | 2.46790i | ||||||
\(996\) | 2.85253 | + | 5.42037i | 0.0903858 | + | 0.171751i | ||||
\(997\) | 21.3314i | 0.675571i | 0.941223 | + | 0.337785i | \(0.109678\pi\) | ||||
−0.941223 | + | 0.337785i | \(0.890322\pi\) | |||||||
\(998\) | 25.1145 | 0.794986 | ||||||||
\(999\) | −15.7045 | − | 1.85370i | −0.496867 | − | 0.0586483i |
(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 | 462.2.c.a.197.8 | yes | 12 | |
3.2 | odd | 2 | 462.2.c.b.197.7 | yes | 12 | ||
11.10 | odd | 2 | 462.2.c.b.197.8 | yes | 12 | ||
33.32 | even | 2 | inner | 462.2.c.a.197.7 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.c.a.197.7 | ✓ | 12 | 33.32 | even | 2 | inner | |
462.2.c.a.197.8 | yes | 12 | 1.1 | even | 1 | trivial | |
462.2.c.b.197.7 | yes | 12 | 3.2 | odd | 2 | ||
462.2.c.b.197.8 | yes | 12 | 11.10 | odd | 2 |