Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(93,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.e (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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.310217769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 93.3 | ||
Root | \(0.882007 + 1.52768i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.93 |
Dual form | 322.2.e.a.277.3 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0.0985631 | + | 0.170716i | 0.0569055 | + | 0.0985631i | 0.893075 | − | 0.449908i | \(-0.148543\pi\) |
−0.836169 | + | 0.548471i | \(0.815210\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.154437 | − | 0.267494i | 0.0690665 | − | 0.119627i | −0.829424 | − | 0.558619i | \(-0.811331\pi\) |
0.898491 | + | 0.438993i | \(0.144665\pi\) | |||||||
\(6\) | −0.197126 | −0.0804765 | ||||||||
\(7\) | −1.71031 | − | 2.01862i | −0.646437 | − | 0.762967i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.48057 | − | 2.56442i | 0.493524 | − | 0.854808i | ||||
\(10\) | 0.154437 | + | 0.267494i | 0.0488374 | + | 0.0845889i | ||||
\(11\) | −0.184881 | − | 0.320224i | −0.0557438 | − | 0.0965510i | 0.836807 | − | 0.547498i | \(-0.184420\pi\) |
−0.892551 | + | 0.450947i | \(0.851086\pi\) | |||||||
\(12\) | 0.0985631 | − | 0.170716i | 0.0284527 | − | 0.0492816i | ||||
\(13\) | 6.29639 | 1.74630 | 0.873152 | − | 0.487448i | \(-0.162072\pi\) | ||||
0.873152 | + | 0.487448i | \(0.162072\pi\) | |||||||
\(14\) | 2.60333 | − | 0.471863i | 0.695770 | − | 0.126111i | ||||
\(15\) | 0.0608874 | 0.0157211 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.30670 | − | 3.99533i | −0.559458 | − | 0.969009i | −0.997542 | − | 0.0700753i | \(-0.977676\pi\) |
0.438084 | − | 0.898934i | \(-0.355657\pi\) | |||||||
\(18\) | 1.48057 | + | 2.56442i | 0.348974 | + | 0.604440i | ||||
\(19\) | 0.176466 | − | 0.305648i | 0.0404841 | − | 0.0701205i | −0.845073 | − | 0.534650i | \(-0.820443\pi\) |
0.885557 | + | 0.464530i | \(0.153777\pi\) | |||||||
\(20\) | −0.308875 | −0.0690665 | ||||||||
\(21\) | 0.176038 | − | 0.490940i | 0.0384147 | − | 0.107132i | ||||
\(22\) | 0.369762 | 0.0788336 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 0.0985631 | + | 0.170716i | 0.0201191 | + | 0.0348473i | ||||
\(25\) | 2.45230 | + | 4.24750i | 0.490460 | + | 0.849501i | ||||
\(26\) | −3.14819 | + | 5.45283i | −0.617412 | + | 1.06939i | ||||
\(27\) | 1.17510 | 0.226148 | ||||||||
\(28\) | −0.893022 | + | 2.49048i | −0.168765 | + | 0.470657i | ||||
\(29\) | 1.74199 | 0.323479 | 0.161739 | − | 0.986834i | \(-0.448290\pi\) | ||||
0.161739 | + | 0.986834i | \(0.448290\pi\) | |||||||
\(30\) | −0.0304437 | + | 0.0527300i | −0.00555823 | + | 0.00962714i | ||||
\(31\) | −1.46739 | − | 2.54159i | −0.263550 | − | 0.456482i | 0.703633 | − | 0.710564i | \(-0.251560\pi\) |
−0.967183 | + | 0.254082i | \(0.918227\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.0364449 | − | 0.0631245i | 0.00634425 | − | 0.0109886i | ||||
\(34\) | 4.61341 | 0.791193 | ||||||||
\(35\) | −0.804105 | + | 0.145747i | −0.135918 | + | 0.0246357i | ||||
\(36\) | −2.96114 | −0.493524 | ||||||||
\(37\) | 3.18965 | − | 5.52464i | 0.524375 | − | 0.908245i | −0.475222 | − | 0.879866i | \(-0.657632\pi\) |
0.999597 | − | 0.0283789i | \(-0.00903451\pi\) | |||||||
\(38\) | 0.176466 | + | 0.305648i | 0.0286266 | + | 0.0495827i | ||||
\(39\) | 0.620592 | + | 1.07490i | 0.0993742 | + | 0.172121i | ||||
\(40\) | 0.154437 | − | 0.267494i | 0.0244187 | − | 0.0422944i | ||||
\(41\) | −1.90213 | −0.297064 | −0.148532 | − | 0.988908i | \(-0.547455\pi\) | ||||
−0.148532 | + | 0.988908i | \(0.547455\pi\) | |||||||
\(42\) | 0.337147 | + | 0.397923i | 0.0520230 | + | 0.0614009i | ||||
\(43\) | 6.55252 | 0.999250 | 0.499625 | − | 0.866242i | \(-0.333471\pi\) | ||||
0.499625 | + | 0.866242i | \(0.333471\pi\) | |||||||
\(44\) | −0.184881 | + | 0.320224i | −0.0278719 | + | 0.0482755i | ||||
\(45\) | −0.457311 | − | 0.792086i | −0.0681719 | − | 0.118077i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | −5.86735 | + | 10.1625i | −0.855841 | + | 1.48236i | 0.0200221 | + | 0.999800i | \(0.493626\pi\) |
−0.875863 | + | 0.482560i | \(0.839707\pi\) | |||||||
\(48\) | −0.197126 | −0.0284527 | ||||||||
\(49\) | −1.14967 | + | 6.90495i | −0.164238 | + | 0.986421i | ||||
\(50\) | −4.90460 | −0.693615 | ||||||||
\(51\) | 0.454712 | − | 0.787584i | 0.0636724 | − | 0.110284i | ||||
\(52\) | −3.14819 | − | 5.45283i | −0.436576 | − | 0.756172i | ||||
\(53\) | −2.95230 | − | 5.11353i | −0.405529 | − | 0.702397i | 0.588854 | − | 0.808240i | \(-0.299579\pi\) |
−0.994383 | + | 0.105842i | \(0.966246\pi\) | |||||||
\(54\) | −0.587549 | + | 1.01766i | −0.0799553 | + | 0.138487i | ||||
\(55\) | −0.114210 | −0.0154001 | ||||||||
\(56\) | −1.71031 | − | 2.01862i | −0.228550 | − | 0.269750i | ||||
\(57\) | 0.0695722 | 0.00921506 | ||||||||
\(58\) | −0.870993 | + | 1.50860i | −0.114367 | + | 0.198089i | ||||
\(59\) | 1.14602 | + | 1.98497i | 0.149199 | + | 0.258421i | 0.930932 | − | 0.365193i | \(-0.118997\pi\) |
−0.781732 | + | 0.623614i | \(0.785664\pi\) | |||||||
\(60\) | −0.0304437 | − | 0.0527300i | −0.00393026 | − | 0.00680742i | ||||
\(61\) | −3.39396 | + | 5.87851i | −0.434552 | + | 0.752667i | −0.997259 | − | 0.0739899i | \(-0.976427\pi\) |
0.562707 | + | 0.826657i | \(0.309760\pi\) | |||||||
\(62\) | 2.93477 | 0.372716 | ||||||||
\(63\) | −7.70884 | + | 1.39725i | −0.971222 | + | 0.176037i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.972398 | − | 1.68424i | 0.120611 | − | 0.208905i | ||||
\(66\) | 0.0364449 | + | 0.0631245i | 0.00448606 | + | 0.00777009i | ||||
\(67\) | −6.37212 | − | 11.0368i | −0.778478 | − | 1.34836i | −0.932819 | − | 0.360346i | \(-0.882659\pi\) |
0.154340 | − | 0.988018i | \(-0.450675\pi\) | |||||||
\(68\) | −2.30670 | + | 3.99533i | −0.279729 | + | 0.484505i | ||||
\(69\) | 0.197126 | 0.0237312 | ||||||||
\(70\) | 0.275832 | − | 0.769248i | 0.0329682 | − | 0.0919427i | ||||
\(71\) | 0.492118 | 0.0584037 | 0.0292018 | − | 0.999574i | \(-0.490703\pi\) | ||||
0.0292018 | + | 0.999574i | \(0.490703\pi\) | |||||||
\(72\) | 1.48057 | − | 2.56442i | 0.174487 | − | 0.302220i | ||||
\(73\) | −2.99976 | − | 5.19573i | −0.351095 | − | 0.608114i | 0.635347 | − | 0.772227i | \(-0.280857\pi\) |
−0.986442 | + | 0.164113i | \(0.947524\pi\) | |||||||
\(74\) | 3.18965 | + | 5.52464i | 0.370789 | + | 0.642226i | ||||
\(75\) | −0.483412 | + | 0.837295i | −0.0558197 | + | 0.0966825i | ||||
\(76\) | −0.352932 | −0.0404841 | ||||||||
\(77\) | −0.330206 | + | 0.920887i | −0.0376304 | + | 0.104945i | ||||
\(78\) | −1.24118 | −0.140536 | ||||||||
\(79\) | −0.333075 | + | 0.576902i | −0.0374738 | + | 0.0649066i | −0.884154 | − | 0.467196i | \(-0.845264\pi\) |
0.846680 | + | 0.532102i | \(0.178598\pi\) | |||||||
\(80\) | 0.154437 | + | 0.267494i | 0.0172666 | + | 0.0299067i | ||||
\(81\) | −4.32589 | − | 7.49266i | −0.480655 | − | 0.832518i | ||||
\(82\) | 0.951067 | − | 1.64730i | 0.105028 | − | 0.181914i | ||||
\(83\) | −6.44785 | −0.707744 | −0.353872 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353872 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(84\) | −0.513186 | + | 0.0930165i | −0.0559931 | + | 0.0101489i | ||||
\(85\) | −1.42497 | −0.154559 | ||||||||
\(86\) | −3.27626 | + | 5.67465i | −0.353288 | + | 0.611913i | ||||
\(87\) | 0.171696 | + | 0.297386i | 0.0184077 | + | 0.0318831i | ||||
\(88\) | −0.184881 | − | 0.320224i | −0.0197084 | − | 0.0341359i | ||||
\(89\) | −5.81105 | + | 10.0650i | −0.615970 | + | 1.06689i | 0.374244 | + | 0.927330i | \(0.377902\pi\) |
−0.990214 | + | 0.139560i | \(0.955431\pi\) | |||||||
\(90\) | 0.914622 | 0.0964097 | ||||||||
\(91\) | −10.7688 | − | 12.7100i | −1.12888 | − | 1.33237i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0.289260 | − | 0.501013i | 0.0299949 | − | 0.0519527i | ||||
\(94\) | −5.86735 | − | 10.1625i | −0.605171 | − | 1.04819i | ||||
\(95\) | −0.0545060 | − | 0.0944071i | −0.00559219 | − | 0.00968596i | ||||
\(96\) | 0.0985631 | − | 0.170716i | 0.0100596 | − | 0.0174237i | ||||
\(97\) | 4.96548 | 0.504168 | 0.252084 | − | 0.967705i | \(-0.418884\pi\) | ||||
0.252084 | + | 0.967705i | \(0.418884\pi\) | |||||||
\(98\) | −5.40502 | − | 4.44811i | −0.545990 | − | 0.449327i | ||||
\(99\) | −1.09492 | −0.110043 | ||||||||
\(100\) | 2.45230 | − | 4.24750i | 0.245230 | − | 0.424750i | ||||
\(101\) | 6.67745 | + | 11.5657i | 0.664432 | + | 1.15083i | 0.979439 | + | 0.201740i | \(0.0646596\pi\) |
−0.315008 | + | 0.949089i | \(0.602007\pi\) | |||||||
\(102\) | 0.454712 | + | 0.787584i | 0.0450232 | + | 0.0779825i | ||||
\(103\) | −0.439355 | + | 0.760986i | −0.0432910 | + | 0.0749821i | −0.886859 | − | 0.462040i | \(-0.847118\pi\) |
0.843568 | + | 0.537022i | \(0.180451\pi\) | |||||||
\(104\) | 6.29639 | 0.617412 | ||||||||
\(105\) | −0.104136 | − | 0.122909i | −0.0101627 | − | 0.0119946i | ||||
\(106\) | 5.90460 | 0.573505 | ||||||||
\(107\) | −7.15055 | + | 12.3851i | −0.691270 | + | 1.19731i | 0.280152 | + | 0.959956i | \(0.409615\pi\) |
−0.971422 | + | 0.237359i | \(0.923718\pi\) | |||||||
\(108\) | −0.587549 | − | 1.01766i | −0.0565369 | − | 0.0979248i | ||||
\(109\) | 7.56040 | + | 13.0950i | 0.724155 | + | 1.25427i | 0.959321 | + | 0.282318i | \(0.0911034\pi\) |
−0.235166 | + | 0.971955i | \(0.575563\pi\) | |||||||
\(110\) | 0.0571052 | − | 0.0989090i | 0.00544476 | − | 0.00943061i | ||||
\(111\) | 1.25753 | 0.119359 | ||||||||
\(112\) | 2.60333 | − | 0.471863i | 0.245992 | − | 0.0445868i | ||||
\(113\) | 7.57075 | 0.712196 | 0.356098 | − | 0.934449i | \(-0.384107\pi\) | ||||
0.356098 | + | 0.934449i | \(0.384107\pi\) | |||||||
\(114\) | −0.0347861 | + | 0.0602513i | −0.00325802 | + | 0.00564305i | ||||
\(115\) | −0.154437 | − | 0.267494i | −0.0144014 | − | 0.0249439i | ||||
\(116\) | −0.870993 | − | 1.50860i | −0.0808697 | − | 0.140070i | ||||
\(117\) | 9.32225 | − | 16.1466i | 0.861842 | − | 1.49275i | ||||
\(118\) | −2.29204 | −0.211000 | ||||||||
\(119\) | −4.11987 | + | 11.4896i | −0.377668 | + | 1.05325i | ||||
\(120\) | 0.0608874 | 0.00555823 | ||||||||
\(121\) | 5.43164 | − | 9.40787i | 0.493785 | − | 0.855261i | ||||
\(122\) | −3.39396 | − | 5.87851i | −0.307275 | − | 0.532216i | ||||
\(123\) | −0.187480 | − | 0.324726i | −0.0169045 | − | 0.0292795i | ||||
\(124\) | −1.46739 | + | 2.54159i | −0.131775 | + | 0.228241i | ||||
\(125\) | 3.05928 | 0.273630 | ||||||||
\(126\) | 2.64436 | − | 7.37468i | 0.235579 | − | 0.656988i | ||||
\(127\) | 16.0215 | 1.42168 | 0.710841 | − | 0.703353i | \(-0.248315\pi\) | ||||
0.710841 | + | 0.703353i | \(0.248315\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.645837 | + | 1.11862i | 0.0568628 | + | 0.0984892i | ||||
\(130\) | 0.972398 | + | 1.68424i | 0.0852850 | + | 0.147718i | ||||
\(131\) | −9.15897 | + | 15.8638i | −0.800223 | + | 1.38603i | 0.119247 | + | 0.992865i | \(0.461952\pi\) |
−0.919469 | + | 0.393161i | \(0.871381\pi\) | |||||||
\(132\) | −0.0728899 | −0.00634425 | ||||||||
\(133\) | −0.918800 | + | 0.166535i | −0.0796701 | + | 0.0144405i | ||||
\(134\) | 12.7442 | 1.10093 | ||||||||
\(135\) | 0.181479 | − | 0.314331i | 0.0156192 | − | 0.0270533i | ||||
\(136\) | −2.30670 | − | 3.99533i | −0.197798 | − | 0.342597i | ||||
\(137\) | 4.61681 | + | 7.99655i | 0.394441 | + | 0.683191i | 0.993030 | − | 0.117865i | \(-0.0376050\pi\) |
−0.598589 | + | 0.801056i | \(0.704272\pi\) | |||||||
\(138\) | −0.0985631 | + | 0.170716i | −0.00839025 | + | 0.0145323i | ||||
\(139\) | −17.2940 | −1.46686 | −0.733430 | − | 0.679765i | \(-0.762082\pi\) | ||||
−0.733430 | + | 0.679765i | \(0.762082\pi\) | |||||||
\(140\) | 0.528272 | + | 0.623502i | 0.0446472 | + | 0.0526955i | ||||
\(141\) | −2.31322 | −0.194808 | ||||||||
\(142\) | −0.246059 | + | 0.426187i | −0.0206488 | + | 0.0357648i | ||||
\(143\) | −1.16408 | − | 2.01625i | −0.0973455 | − | 0.168607i | ||||
\(144\) | 1.48057 | + | 2.56442i | 0.123381 | + | 0.213702i | ||||
\(145\) | 0.269028 | − | 0.465970i | 0.0223416 | − | 0.0386967i | ||||
\(146\) | 5.99951 | 0.496523 | ||||||||
\(147\) | −1.29210 | + | 0.484306i | −0.106571 | + | 0.0399449i | ||||
\(148\) | −6.37930 | −0.524375 | ||||||||
\(149\) | 7.37742 | − | 12.7781i | 0.604382 | − | 1.04682i | −0.387767 | − | 0.921757i | \(-0.626753\pi\) |
0.992149 | − | 0.125063i | \(-0.0399132\pi\) | |||||||
\(150\) | −0.483412 | − | 0.837295i | −0.0394705 | − | 0.0683648i | ||||
\(151\) | 10.6213 | + | 18.3966i | 0.864348 | + | 1.49710i | 0.867693 | + | 0.497101i | \(0.165602\pi\) |
−0.00334456 | + | 0.999994i | \(0.501065\pi\) | |||||||
\(152\) | 0.176466 | − | 0.305648i | 0.0143133 | − | 0.0247913i | ||||
\(153\) | −13.6610 | −1.10442 | ||||||||
\(154\) | −0.632409 | − | 0.746410i | −0.0509610 | − | 0.0601475i | ||||
\(155\) | −0.906477 | −0.0728100 | ||||||||
\(156\) | 0.620592 | − | 1.07490i | 0.0496871 | − | 0.0860606i | ||||
\(157\) | 6.82206 | + | 11.8162i | 0.544460 | + | 0.943032i | 0.998641 | + | 0.0521224i | \(0.0165986\pi\) |
−0.454181 | + | 0.890909i | \(0.650068\pi\) | |||||||
\(158\) | −0.333075 | − | 0.576902i | −0.0264980 | − | 0.0458959i | ||||
\(159\) | 0.581976 | − | 1.00801i | 0.0461537 | − | 0.0799405i | ||||
\(160\) | −0.308875 | −0.0244187 | ||||||||
\(161\) | −2.60333 | + | 0.471863i | −0.205171 | + | 0.0371880i | ||||
\(162\) | 8.65178 | 0.679748 | ||||||||
\(163\) | 9.56734 | − | 16.5711i | 0.749372 | − | 1.29795i | −0.198752 | − | 0.980050i | \(-0.563689\pi\) |
0.948124 | − | 0.317901i | \(-0.102978\pi\) | |||||||
\(164\) | 0.951067 | + | 1.64730i | 0.0742659 | + | 0.128632i | ||||
\(165\) | −0.0112569 | − | 0.0194976i | −0.000876351 | − | 0.00151788i | ||||
\(166\) | 3.22393 | − | 5.58400i | 0.250225 | − | 0.433403i | ||||
\(167\) | 5.31322 | 0.411149 | 0.205575 | − | 0.978641i | \(-0.434094\pi\) | ||||
0.205575 | + | 0.978641i | \(0.434094\pi\) | |||||||
\(168\) | 0.176038 | − | 0.490940i | 0.0135816 | − | 0.0378768i | ||||
\(169\) | 26.6445 | 2.04958 | ||||||||
\(170\) | 0.712483 | − | 1.23406i | 0.0546450 | − | 0.0946478i | ||||
\(171\) | −0.522541 | − | 0.905068i | −0.0399597 | − | 0.0692122i | ||||
\(172\) | −3.27626 | − | 5.67465i | −0.249812 | − | 0.432688i | ||||
\(173\) | 2.61269 | − | 4.52531i | 0.198639 | − | 0.344053i | −0.749448 | − | 0.662063i | \(-0.769681\pi\) |
0.948087 | + | 0.318010i | \(0.103015\pi\) | |||||||
\(174\) | −0.343391 | −0.0260324 | ||||||||
\(175\) | 4.37991 | − | 12.2148i | 0.331090 | − | 0.923354i | ||||
\(176\) | 0.369762 | 0.0278719 | ||||||||
\(177\) | −0.225911 | + | 0.391290i | −0.0169805 | + | 0.0294111i | ||||
\(178\) | −5.81105 | − | 10.0650i | −0.435556 | − | 0.754406i | ||||
\(179\) | 5.20161 | + | 9.00945i | 0.388786 | + | 0.673398i | 0.992287 | − | 0.123965i | \(-0.0395611\pi\) |
−0.603500 | + | 0.797363i | \(0.706228\pi\) | |||||||
\(180\) | −0.457311 | + | 0.792086i | −0.0340860 | + | 0.0590386i | ||||
\(181\) | 7.39945 | 0.549997 | 0.274998 | − | 0.961445i | \(-0.411323\pi\) | ||||
0.274998 | + | 0.961445i | \(0.411323\pi\) | |||||||
\(182\) | 16.3916 | − | 2.97103i | 1.21503 | − | 0.220227i | ||||
\(183\) | −1.33808 | −0.0989136 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −0.985203 | − | 1.70642i | −0.0724336 | − | 0.125459i | ||||
\(186\) | 0.289260 | + | 0.501013i | 0.0212096 | + | 0.0367361i | ||||
\(187\) | −0.852932 | + | 1.47732i | −0.0623726 | + | 0.108032i | ||||
\(188\) | 11.7347 | 0.855841 | ||||||||
\(189\) | −2.00978 | − | 2.37208i | −0.146190 | − | 0.172543i | ||||
\(190\) | 0.109012 | 0.00790855 | ||||||||
\(191\) | 1.99976 | − | 3.46368i | 0.144697 | − | 0.250623i | −0.784563 | − | 0.620050i | \(-0.787112\pi\) |
0.929260 | + | 0.369426i | \(0.120446\pi\) | |||||||
\(192\) | 0.0985631 | + | 0.170716i | 0.00711318 | + | 0.0123204i | ||||
\(193\) | −0.226630 | − | 0.392534i | −0.0163132 | − | 0.0282552i | 0.857754 | − | 0.514061i | \(-0.171860\pi\) |
−0.874067 | + | 0.485806i | \(0.838526\pi\) | |||||||
\(194\) | −2.48274 | + | 4.30023i | −0.178250 | + | 0.308739i | ||||
\(195\) | 0.383370 | 0.0274537 | ||||||||
\(196\) | 6.55469 | − | 2.45683i | 0.468192 | − | 0.175488i | ||||
\(197\) | −6.07584 | −0.432885 | −0.216443 | − | 0.976295i | \(-0.569445\pi\) | ||||
−0.216443 | + | 0.976295i | \(0.569445\pi\) | |||||||
\(198\) | 0.547459 | − | 0.948227i | 0.0389062 | − | 0.0673876i | ||||
\(199\) | 12.9633 | + | 22.4530i | 0.918941 | + | 1.59165i | 0.801027 | + | 0.598628i | \(0.204287\pi\) |
0.117914 | + | 0.993024i | \(0.462379\pi\) | |||||||
\(200\) | 2.45230 | + | 4.24750i | 0.173404 | + | 0.300344i | ||||
\(201\) | 1.25611 | − | 2.17565i | 0.0885993 | − | 0.153459i | ||||
\(202\) | −13.3549 | −0.939648 | ||||||||
\(203\) | −2.97934 | − | 3.51641i | −0.209109 | − | 0.246804i | ||||
\(204\) | −0.909424 | −0.0636724 | ||||||||
\(205\) | −0.293761 | + | 0.508809i | −0.0205171 | + | 0.0355367i | ||||
\(206\) | −0.439355 | − | 0.760986i | −0.0306113 | − | 0.0530204i | ||||
\(207\) | −1.48057 | − | 2.56442i | −0.102907 | − | 0.178240i | ||||
\(208\) | −3.14819 | + | 5.45283i | −0.218288 | + | 0.378086i | ||||
\(209\) | −0.130501 | −0.00902694 | ||||||||
\(210\) | 0.158510 | − | 0.0287305i | 0.0109382 | − | 0.00198259i | ||||
\(211\) | −14.9365 | −1.02827 | −0.514137 | − | 0.857708i | \(-0.671888\pi\) | ||||
−0.514137 | + | 0.857708i | \(0.671888\pi\) | |||||||
\(212\) | −2.95230 | + | 5.11353i | −0.202765 | + | 0.351199i | ||||
\(213\) | 0.0485047 | + | 0.0840126i | 0.00332349 | + | 0.00575645i | ||||
\(214\) | −7.15055 | − | 12.3851i | −0.488802 | − | 0.846629i | ||||
\(215\) | 1.01195 | − | 1.75276i | 0.0690147 | − | 0.119537i | ||||
\(216\) | 1.17510 | 0.0799553 | ||||||||
\(217\) | −2.62081 | + | 7.30900i | −0.177912 | + | 0.496167i | ||||
\(218\) | −15.1208 | −1.02411 | ||||||||
\(219\) | 0.591331 | − | 1.02422i | 0.0399585 | − | 0.0692101i | ||||
\(220\) | 0.0571052 | + | 0.0989090i | 0.00385003 | + | 0.00666845i | ||||
\(221\) | −14.5239 | − | 25.1561i | −0.976983 | − | 1.69218i | ||||
\(222\) | −0.628764 | + | 1.08905i | −0.0421999 | + | 0.0730924i | ||||
\(223\) | −5.36408 | −0.359205 | −0.179603 | − | 0.983739i | \(-0.557481\pi\) | ||||
−0.179603 | + | 0.983739i | \(0.557481\pi\) | |||||||
\(224\) | −0.893022 | + | 2.49048i | −0.0596675 | + | 0.166402i | ||||
\(225\) | 14.5232 | 0.968213 | ||||||||
\(226\) | −3.78537 | + | 6.55646i | −0.251799 | + | 0.436129i | ||||
\(227\) | −14.0894 | − | 24.4035i | −0.935146 | − | 1.61972i | −0.774374 | − | 0.632729i | \(-0.781935\pi\) |
−0.160772 | − | 0.986992i | \(-0.551398\pi\) | |||||||
\(228\) | −0.0347861 | − | 0.0602513i | −0.00230377 | − | 0.00399024i | ||||
\(229\) | −7.91864 | + | 13.7155i | −0.523278 | + | 0.906345i | 0.476355 | + | 0.879253i | \(0.341958\pi\) |
−0.999633 | + | 0.0270914i | \(0.991375\pi\) | |||||||
\(230\) | 0.308875 | 0.0203666 | ||||||||
\(231\) | −0.189757 | + | 0.0343940i | −0.0124851 | + | 0.00226296i | ||||
\(232\) | 1.74199 | 0.114367 | ||||||||
\(233\) | −12.7090 | + | 22.0127i | −0.832596 | + | 1.44210i | 0.0633771 | + | 0.997990i | \(0.479813\pi\) |
−0.895973 | + | 0.444109i | \(0.853520\pi\) | |||||||
\(234\) | 9.32225 | + | 16.1466i | 0.609414 | + | 1.05554i | ||||
\(235\) | 1.81228 | + | 3.13896i | 0.118220 | + | 0.204763i | ||||
\(236\) | 1.14602 | − | 1.98497i | 0.0745997 | − | 0.129210i | ||||
\(237\) | −0.131316 | −0.00852986 | ||||||||
\(238\) | −7.89037 | − | 9.31272i | −0.511456 | − | 0.603654i | ||||
\(239\) | 8.59412 | 0.555907 | 0.277954 | − | 0.960595i | \(-0.410344\pi\) | ||||
0.277954 | + | 0.960595i | \(0.410344\pi\) | |||||||
\(240\) | −0.0304437 | + | 0.0527300i | −0.00196513 | + | 0.00340371i | ||||
\(241\) | −4.69442 | − | 8.13098i | −0.302394 | − | 0.523762i | 0.674283 | − | 0.738473i | \(-0.264453\pi\) |
−0.976678 | + | 0.214710i | \(0.931119\pi\) | |||||||
\(242\) | 5.43164 | + | 9.40787i | 0.349159 | + | 0.604761i | ||||
\(243\) | 2.61539 | − | 4.52999i | 0.167778 | − | 0.290599i | ||||
\(244\) | 6.78792 | 0.434552 | ||||||||
\(245\) | 1.66948 | + | 1.37391i | 0.106659 | + | 0.0877759i | ||||
\(246\) | 0.374961 | 0.0239066 | ||||||||
\(247\) | 1.11110 | − | 1.92448i | 0.0706975 | − | 0.122452i | ||||
\(248\) | −1.46739 | − | 2.54159i | −0.0931790 | − | 0.161391i | ||||
\(249\) | −0.635520 | − | 1.10075i | −0.0402745 | − | 0.0697574i | ||||
\(250\) | −1.52964 | + | 2.64942i | −0.0967430 | + | 0.167564i | ||||
\(251\) | −3.13763 | −0.198046 | −0.0990229 | − | 0.995085i | \(-0.531572\pi\) | ||||
−0.0990229 | + | 0.995085i | \(0.531572\pi\) | |||||||
\(252\) | 5.06447 | + | 5.97742i | 0.319032 | + | 0.376542i | ||||
\(253\) | −0.369762 | −0.0232468 | ||||||||
\(254\) | −8.01077 | + | 13.8751i | −0.502641 | + | 0.870599i | ||||
\(255\) | −0.140449 | − | 0.243265i | −0.00879527 | − | 0.0152338i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 13.4913 | − | 23.3677i | 0.841567 | − | 1.45764i | −0.0470028 | − | 0.998895i | \(-0.514967\pi\) |
0.888570 | − | 0.458742i | \(-0.151700\pi\) | |||||||
\(258\) | −1.29167 | −0.0804161 | ||||||||
\(259\) | −16.6075 | + | 3.01015i | −1.03194 | + | 0.187042i | ||||
\(260\) | −1.94480 | −0.120611 | ||||||||
\(261\) | 2.57913 | − | 4.46719i | 0.159644 | − | 0.276512i | ||||
\(262\) | −9.15897 | − | 15.8638i | −0.565843 | − | 0.980068i | ||||
\(263\) | 5.36612 | + | 9.29439i | 0.330889 | + | 0.573117i | 0.982686 | − | 0.185277i | \(-0.0593181\pi\) |
−0.651797 | + | 0.758393i | \(0.725985\pi\) | |||||||
\(264\) | 0.0364449 | − | 0.0631245i | 0.00224303 | − | 0.00388504i | ||||
\(265\) | −1.82378 | −0.112034 | ||||||||
\(266\) | 0.315176 | − | 0.878972i | 0.0193247 | − | 0.0538932i | ||||
\(267\) | −2.29102 | −0.140208 | ||||||||
\(268\) | −6.37212 | + | 11.0368i | −0.389239 | + | 0.674182i | ||||
\(269\) | 7.93807 | + | 13.7491i | 0.483992 | + | 0.838300i | 0.999831 | − | 0.0183863i | \(-0.00585286\pi\) |
−0.515838 | + | 0.856686i | \(0.672520\pi\) | |||||||
\(270\) | 0.181479 | + | 0.314331i | 0.0110445 | + | 0.0191296i | ||||
\(271\) | −7.19021 | + | 12.4538i | −0.436774 | + | 0.756515i | −0.997439 | − | 0.0715280i | \(-0.977212\pi\) |
0.560664 | + | 0.828043i | \(0.310546\pi\) | |||||||
\(272\) | 4.61341 | 0.279729 | ||||||||
\(273\) | 1.10840 | − | 3.09115i | 0.0670837 | − | 0.187085i | ||||
\(274\) | −9.23362 | −0.557823 | ||||||||
\(275\) | 0.906767 | − | 1.57057i | 0.0546801 | − | 0.0947088i | ||||
\(276\) | −0.0985631 | − | 0.170716i | −0.00593280 | − | 0.0102759i | ||||
\(277\) | −5.81799 | − | 10.0771i | −0.349569 | − | 0.605471i | 0.636604 | − | 0.771191i | \(-0.280339\pi\) |
−0.986173 | + | 0.165720i | \(0.947005\pi\) | |||||||
\(278\) | 8.64701 | − | 14.9771i | 0.518613 | − | 0.898264i | ||||
\(279\) | −8.69027 | −0.520273 | ||||||||
\(280\) | −0.804105 | + | 0.145747i | −0.0480544 | + | 0.00871002i | ||||
\(281\) | −25.2062 | −1.50367 | −0.751837 | − | 0.659349i | \(-0.770832\pi\) | ||||
−0.751837 | + | 0.659349i | \(0.770832\pi\) | |||||||
\(282\) | 1.15661 | − | 2.00331i | 0.0688750 | − | 0.119295i | ||||
\(283\) | 1.78808 | + | 3.09704i | 0.106290 | + | 0.184100i | 0.914265 | − | 0.405118i | \(-0.132769\pi\) |
−0.807974 | + | 0.589218i | \(0.799436\pi\) | |||||||
\(284\) | −0.246059 | − | 0.426187i | −0.0146009 | − | 0.0252895i | ||||
\(285\) | 0.0107446 | − | 0.0186101i | 0.000636453 | − | 0.00110237i | ||||
\(286\) | 2.32817 | 0.137667 | ||||||||
\(287\) | 3.25324 | + | 3.83969i | 0.192033 | + | 0.226650i | ||||
\(288\) | −2.96114 | −0.174487 | ||||||||
\(289\) | −2.14176 | + | 3.70964i | −0.125986 | + | 0.218214i | ||||
\(290\) | 0.269028 | + | 0.465970i | 0.0157979 | + | 0.0273627i | ||||
\(291\) | 0.489414 | + | 0.847689i | 0.0286899 | + | 0.0496924i | ||||
\(292\) | −2.99976 | + | 5.19573i | −0.175548 | + | 0.304057i | ||||
\(293\) | −4.03243 | −0.235577 | −0.117788 | − | 0.993039i | \(-0.537580\pi\) | ||||
−0.117788 | + | 0.993039i | \(0.537580\pi\) | |||||||
\(294\) | 0.226630 | − | 1.36115i | 0.0132173 | − | 0.0793837i | ||||
\(295\) | 0.707955 | 0.0412187 | ||||||||
\(296\) | 3.18965 | − | 5.52464i | 0.185395 | − | 0.321113i | ||||
\(297\) | −0.217253 | − | 0.376294i | −0.0126063 | − | 0.0218348i | ||||
\(298\) | 7.37742 | + | 12.7781i | 0.427363 | + | 0.740214i | ||||
\(299\) | 3.14819 | − | 5.45283i | 0.182065 | − | 0.315345i | ||||
\(300\) | 0.966825 | 0.0558197 | ||||||||
\(301\) | −11.2069 | − | 13.2271i | −0.645952 | − | 0.762395i | ||||
\(302\) | −21.2426 | −1.22237 | ||||||||
\(303\) | −1.31630 | + | 2.27990i | −0.0756196 | + | 0.130977i | ||||
\(304\) | 0.176466 | + | 0.305648i | 0.0101210 | + | 0.0175301i | ||||
\(305\) | 1.04831 | + | 1.81573i | 0.0600261 | + | 0.103968i | ||||
\(306\) | 6.83048 | − | 11.8307i | 0.390472 | − | 0.676318i | ||||
\(307\) | −1.35937 | −0.0775831 | −0.0387915 | − | 0.999247i | \(-0.512351\pi\) | ||||
−0.0387915 | + | 0.999247i | \(0.512351\pi\) | |||||||
\(308\) | 0.962615 | − | 0.174477i | 0.0548501 | − | 0.00994175i | ||||
\(309\) | −0.173217 | −0.00985397 | ||||||||
\(310\) | 0.453239 | − | 0.785032i | 0.0257422 | − | 0.0445868i | ||||
\(311\) | −7.38172 | − | 12.7855i | −0.418579 | − | 0.725000i | 0.577218 | − | 0.816590i | \(-0.304138\pi\) |
−0.995797 | + | 0.0915904i | \(0.970805\pi\) | |||||||
\(312\) | 0.620592 | + | 1.07490i | 0.0351341 | + | 0.0608540i | ||||
\(313\) | 11.6470 | − | 20.1732i | 0.658328 | − | 1.14026i | −0.322720 | − | 0.946494i | \(-0.604597\pi\) |
0.981048 | − | 0.193763i | \(-0.0620693\pi\) | |||||||
\(314\) | −13.6441 | −0.769982 | ||||||||
\(315\) | −0.816778 | + | 2.27785i | −0.0460202 | + | 0.128342i | ||||
\(316\) | 0.666150 | 0.0374738 | ||||||||
\(317\) | −9.66087 | + | 16.7331i | −0.542608 | + | 0.939825i | 0.456145 | + | 0.889906i | \(0.349230\pi\) |
−0.998753 | + | 0.0499197i | \(0.984103\pi\) | |||||||
\(318\) | 0.581976 | + | 1.00801i | 0.0326356 | + | 0.0565265i | ||||
\(319\) | −0.322060 | − | 0.557825i | −0.0180319 | − | 0.0312322i | ||||
\(320\) | 0.154437 | − | 0.267494i | 0.00863332 | − | 0.0149533i | ||||
\(321\) | −2.81912 | −0.157348 | ||||||||
\(322\) | 0.893022 | − | 2.49048i | 0.0497662 | − | 0.138789i | ||||
\(323\) | −1.62822 | −0.0905966 | ||||||||
\(324\) | −4.32589 | + | 7.49266i | −0.240327 | + | 0.416259i | ||||
\(325\) | 15.4406 | + | 26.7439i | 0.856491 | + | 1.48349i | ||||
\(326\) | 9.56734 | + | 16.5711i | 0.529886 | + | 0.917790i | ||||
\(327\) | −1.49035 | + | 2.58137i | −0.0824168 | + | 0.142750i | ||||
\(328\) | −1.90213 | −0.105028 | ||||||||
\(329\) | 30.5493 | − | 5.53716i | 1.68424 | − | 0.305274i | ||||
\(330\) | 0.0225139 | 0.00123935 | ||||||||
\(331\) | 2.00407 | − | 3.47116i | 0.110154 | − | 0.190792i | −0.805678 | − | 0.592353i | \(-0.798199\pi\) |
0.915832 | + | 0.401561i | \(0.131532\pi\) | |||||||
\(332\) | 3.22393 | + | 5.58400i | 0.176936 | + | 0.306462i | ||||
\(333\) | −9.44501 | − | 16.3592i | −0.517583 | − | 0.896481i | ||||
\(334\) | −2.65661 | + | 4.60138i | −0.145363 | + | 0.251776i | ||||
\(335\) | −3.93638 | −0.215067 | ||||||||
\(336\) | 0.337147 | + | 0.397923i | 0.0183929 | + | 0.0217085i | ||||
\(337\) | −18.7242 | −1.01997 | −0.509986 | − | 0.860183i | \(-0.670349\pi\) | ||||
−0.509986 | + | 0.860183i | \(0.670349\pi\) | |||||||
\(338\) | −13.3222 | + | 23.0748i | −0.724635 | + | 1.25510i | ||||
\(339\) | 0.746197 | + | 1.29245i | 0.0405278 | + | 0.0701963i | ||||
\(340\) | 0.712483 | + | 1.23406i | 0.0386398 | + | 0.0669261i | ||||
\(341\) | −0.542584 | + | 0.939783i | −0.0293826 | + | 0.0508921i | ||||
\(342\) | 1.04508 | 0.0565116 | ||||||||
\(343\) | 15.9048 | − | 9.48887i | 0.858776 | − | 0.512351i | ||||
\(344\) | 6.55252 | 0.353288 | ||||||||
\(345\) | 0.0304437 | − | 0.0527300i | 0.00163903 | − | 0.00283889i | ||||
\(346\) | 2.61269 | + | 4.52531i | 0.140459 | + | 0.243282i | ||||
\(347\) | −2.62469 | − | 4.54610i | −0.140901 | − | 0.244047i | 0.786935 | − | 0.617036i | \(-0.211667\pi\) |
−0.927836 | + | 0.372988i | \(0.878333\pi\) | |||||||
\(348\) | 0.171696 | − | 0.297386i | 0.00920385 | − | 0.0159415i | ||||
\(349\) | −29.3789 | −1.57262 | −0.786309 | − | 0.617834i | \(-0.788010\pi\) | ||||
−0.786309 | + | 0.617834i | \(0.788010\pi\) | |||||||
\(350\) | 8.38839 | + | 9.90052i | 0.448378 | + | 0.529205i | ||||
\(351\) | 7.39887 | 0.394922 | ||||||||
\(352\) | −0.184881 | + | 0.320224i | −0.00985420 | + | 0.0170680i | ||||
\(353\) | −1.88815 | − | 3.27037i | −0.100496 | − | 0.174064i | 0.811393 | − | 0.584501i | \(-0.198710\pi\) |
−0.911889 | + | 0.410437i | \(0.865376\pi\) | |||||||
\(354\) | −0.225911 | − | 0.391290i | −0.0120070 | − | 0.0207968i | ||||
\(355\) | 0.0760015 | − | 0.131638i | 0.00403374 | − | 0.00698664i | ||||
\(356\) | 11.6221 | 0.615970 | ||||||||
\(357\) | −2.36753 | + | 0.429123i | −0.125303 | + | 0.0227116i | ||||
\(358\) | −10.4032 | −0.549827 | ||||||||
\(359\) | 9.28414 | − | 16.0806i | 0.489998 | − | 0.848702i | −0.509935 | − | 0.860213i | \(-0.670331\pi\) |
0.999934 | + | 0.0115107i | \(0.00366406\pi\) | |||||||
\(360\) | −0.457311 | − | 0.792086i | −0.0241024 | − | 0.0417466i | ||||
\(361\) | 9.43772 | + | 16.3466i | 0.496722 | + | 0.860348i | ||||
\(362\) | −3.69973 | + | 6.40811i | −0.194453 | + | 0.336803i | ||||
\(363\) | 2.14144 | 0.112396 | ||||||||
\(364\) | −5.62281 | + | 15.6811i | −0.294715 | + | 0.821911i | ||||
\(365\) | −1.85310 | −0.0969957 | ||||||||
\(366\) | 0.669039 | − | 1.15881i | 0.0349712 | − | 0.0605720i | ||||
\(367\) | −7.66138 | − | 13.2699i | −0.399921 | − | 0.692683i | 0.593795 | − | 0.804616i | \(-0.297629\pi\) |
−0.993716 | + | 0.111933i | \(0.964296\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | −2.81624 | + | 4.87788i | −0.146608 | + | 0.253932i | ||||
\(370\) | 1.97041 | 0.102437 | ||||||||
\(371\) | −5.27293 | + | 14.7053i | −0.273757 | + | 0.763461i | ||||
\(372\) | −0.578520 | −0.0299949 | ||||||||
\(373\) | −2.03891 | + | 3.53149i | −0.105571 | + | 0.182854i | −0.913971 | − | 0.405779i | \(-0.867000\pi\) |
0.808401 | + | 0.588633i | \(0.200334\pi\) | |||||||
\(374\) | −0.852932 | − | 1.47732i | −0.0441041 | − | 0.0763905i | ||||
\(375\) | 0.301532 | + | 0.522270i | 0.0155711 | + | 0.0269699i | ||||
\(376\) | −5.86735 | + | 10.1625i | −0.302585 | + | 0.524093i | ||||
\(377\) | 10.9682 | 0.564892 | ||||||||
\(378\) | 3.05917 | − | 0.554485i | 0.157347 | − | 0.0285196i | ||||
\(379\) | 27.4392 | 1.40946 | 0.704729 | − | 0.709477i | \(-0.251069\pi\) | ||||
0.704729 | + | 0.709477i | \(0.251069\pi\) | |||||||
\(380\) | −0.0545060 | + | 0.0944071i | −0.00279610 | + | 0.00484298i | ||||
\(381\) | 1.57913 | + | 2.73514i | 0.0809015 | + | 0.140125i | ||||
\(382\) | 1.99976 | + | 3.46368i | 0.102316 | + | 0.177217i | ||||
\(383\) | 0.302361 | − | 0.523705i | 0.0154499 | − | 0.0267601i | −0.858197 | − | 0.513320i | \(-0.828415\pi\) |
0.873647 | + | 0.486560i | \(0.161749\pi\) | |||||||
\(384\) | −0.197126 | −0.0100596 | ||||||||
\(385\) | 0.195335 | + | 0.230547i | 0.00995521 | + | 0.0117498i | ||||
\(386\) | 0.453259 | 0.0230703 | ||||||||
\(387\) | 9.70147 | − | 16.8034i | 0.493153 | − | 0.854167i | ||||
\(388\) | −2.48274 | − | 4.30023i | −0.126042 | − | 0.218311i | ||||
\(389\) | 4.05062 | + | 7.01588i | 0.205375 | + | 0.355719i | 0.950252 | − | 0.311482i | \(-0.100825\pi\) |
−0.744877 | + | 0.667201i | \(0.767492\pi\) | |||||||
\(390\) | −0.191685 | + | 0.332009i | −0.00970636 | + | 0.0168119i | ||||
\(391\) | −4.61341 | −0.233310 | ||||||||
\(392\) | −1.14967 | + | 6.90495i | −0.0580670 | + | 0.348752i | ||||
\(393\) | −3.61095 | −0.182148 | ||||||||
\(394\) | 3.03792 | − | 5.26183i | 0.153048 | − | 0.265087i | ||||
\(395\) | 0.102878 | + | 0.178191i | 0.00517638 | + | 0.00896575i | ||||
\(396\) | 0.547459 | + | 0.948227i | 0.0275109 | + | 0.0476502i | ||||
\(397\) | 6.42365 | − | 11.1261i | 0.322394 | − | 0.558402i | −0.658588 | − | 0.752504i | \(-0.728846\pi\) |
0.980981 | + | 0.194102i | \(0.0621791\pi\) | |||||||
\(398\) | −25.9265 | −1.29958 | ||||||||
\(399\) | −0.118990 | − | 0.140440i | −0.00595696 | − | 0.00703079i | ||||
\(400\) | −4.90460 | −0.245230 | ||||||||
\(401\) | −4.03550 | + | 6.98970i | −0.201523 | + | 0.349049i | −0.949019 | − | 0.315217i | \(-0.897923\pi\) |
0.747496 | + | 0.664266i | \(0.231256\pi\) | |||||||
\(402\) | 1.25611 | + | 2.17565i | 0.0626492 | + | 0.108512i | ||||
\(403\) | −9.23922 | − | 16.0028i | −0.460239 | − | 0.797157i | ||||
\(404\) | 6.67745 | − | 11.5657i | 0.332216 | − | 0.575415i | ||||
\(405\) | −2.67232 | −0.132789 | ||||||||
\(406\) | 4.53497 | − | 0.821978i | 0.225067 | − | 0.0407941i | ||||
\(407\) | −2.35883 | −0.116923 | ||||||||
\(408\) | 0.454712 | − | 0.787584i | 0.0225116 | − | 0.0389912i | ||||
\(409\) | 8.67087 | + | 15.0184i | 0.428747 | + | 0.742612i | 0.996762 | − | 0.0804065i | \(-0.0256218\pi\) |
−0.568015 | + | 0.823018i | \(0.692289\pi\) | |||||||
\(410\) | −0.293761 | − | 0.508809i | −0.0145078 | − | 0.0251283i | ||||
\(411\) | −0.910095 | + | 1.57633i | −0.0448917 | + | 0.0777546i | ||||
\(412\) | 0.878711 | 0.0432910 | ||||||||
\(413\) | 2.04685 | − | 5.70830i | 0.100719 | − | 0.280887i | ||||
\(414\) | 2.96114 | 0.145532 | ||||||||
\(415\) | −0.995790 | + | 1.72476i | −0.0488814 | + | 0.0846651i | ||||
\(416\) | −3.14819 | − | 5.45283i | −0.154353 | − | 0.267347i | ||||
\(417\) | −1.70455 | − | 2.95237i | −0.0834723 | − | 0.144578i | ||||
\(418\) | 0.0652505 | − | 0.113017i | 0.00319151 | − | 0.00552785i | ||||
\(419\) | 15.7626 | 0.770054 | 0.385027 | − | 0.922905i | \(-0.374192\pi\) | ||||
0.385027 | + | 0.922905i | \(0.374192\pi\) | |||||||
\(420\) | −0.0543738 | + | 0.151639i | −0.00265317 | + | 0.00739923i | ||||
\(421\) | −16.4898 | −0.803661 | −0.401831 | − | 0.915714i | \(-0.631626\pi\) | ||||
−0.401831 | + | 0.915714i | \(0.631626\pi\) | |||||||
\(422\) | 7.46827 | − | 12.9354i | 0.363550 | − | 0.629686i | ||||
\(423\) | 17.3740 | + | 30.0927i | 0.844755 | + | 1.46316i | ||||
\(424\) | −2.95230 | − | 5.11353i | −0.143376 | − | 0.248335i | ||||
\(425\) | 11.3135 | − | 19.5955i | 0.548783 | − | 0.950520i | ||||
\(426\) | −0.0970094 | −0.00470012 | ||||||||
\(427\) | 17.6712 | − | 3.20297i | 0.855171 | − | 0.155002i | ||||
\(428\) | 14.3011 | 0.691270 | ||||||||
\(429\) | 0.229471 | − | 0.397456i | 0.0110790 | − | 0.0191894i | ||||
\(430\) | 1.01195 | + | 1.75276i | 0.0488008 | + | 0.0845254i | ||||
\(431\) | −5.47285 | − | 9.47926i | −0.263618 | − | 0.456600i | 0.703583 | − | 0.710614i | \(-0.251583\pi\) |
−0.967201 | + | 0.254014i | \(0.918249\pi\) | |||||||
\(432\) | −0.587549 | + | 1.01766i | −0.0282685 | + | 0.0489624i | ||||
\(433\) | −28.0699 | −1.34896 | −0.674478 | − | 0.738295i | \(-0.735631\pi\) | ||||
−0.674478 | + | 0.738295i | \(0.735631\pi\) | |||||||
\(434\) | −5.01937 | − | 5.92419i | −0.240938 | − | 0.284370i | ||||
\(435\) | 0.106065 | 0.00508543 | ||||||||
\(436\) | 7.56040 | − | 13.0950i | 0.362078 | − | 0.627137i | ||||
\(437\) | −0.176466 | − | 0.305648i | −0.00844152 | − | 0.0146211i | ||||
\(438\) | 0.591331 | + | 1.02422i | 0.0282549 | + | 0.0489389i | ||||
\(439\) | 4.54122 | − | 7.86562i | 0.216740 | − | 0.375405i | −0.737069 | − | 0.675817i | \(-0.763791\pi\) |
0.953810 | + | 0.300412i | \(0.0971242\pi\) | |||||||
\(440\) | −0.114210 | −0.00544476 | ||||||||
\(441\) | 16.0050 | + | 13.1715i | 0.762145 | + | 0.627214i | ||||
\(442\) | 29.0478 | 1.38166 | ||||||||
\(443\) | 15.3899 | − | 26.6560i | 0.731194 | − | 1.26647i | −0.225179 | − | 0.974317i | \(-0.572297\pi\) |
0.956373 | − | 0.292148i | \(-0.0943699\pi\) | |||||||
\(444\) | −0.628764 | − | 1.08905i | −0.0298398 | − | 0.0516841i | ||||
\(445\) | 1.79489 | + | 3.10883i | 0.0850858 | + | 0.147373i | ||||
\(446\) | 2.68204 | − | 4.64543i | 0.126998 | − | 0.219967i | ||||
\(447\) | 2.90857 | 0.137571 | ||||||||
\(448\) | −1.71031 | − | 2.01862i | −0.0808046 | − | 0.0953709i | ||||
\(449\) | −30.9015 | −1.45833 | −0.729166 | − | 0.684337i | \(-0.760092\pi\) | ||||
−0.729166 | + | 0.684337i | \(0.760092\pi\) | |||||||
\(450\) | −7.26160 | + | 12.5775i | −0.342315 | + | 0.592907i | ||||
\(451\) | 0.351669 | + | 0.609108i | 0.0165594 | + | 0.0286818i | ||||
\(452\) | −3.78537 | − | 6.55646i | −0.178049 | − | 0.308390i | ||||
\(453\) | −2.09374 | + | 3.62646i | −0.0983723 | + | 0.170386i | ||||
\(454\) | 28.1788 | 1.32250 | ||||||||
\(455\) | −5.06295 | + | 0.917677i | −0.237355 | + | 0.0430213i | ||||
\(456\) | 0.0695722 | 0.00325802 | ||||||||
\(457\) | −20.3512 | + | 35.2492i | −0.951987 | + | 1.64889i | −0.210870 | + | 0.977514i | \(0.567630\pi\) |
−0.741117 | + | 0.671376i | \(0.765704\pi\) | |||||||
\(458\) | −7.91864 | − | 13.7155i | −0.370014 | − | 0.640882i | ||||
\(459\) | −2.71060 | − | 4.69490i | −0.126520 | − | 0.219139i | ||||
\(460\) | −0.154437 | + | 0.267494i | −0.00720068 | + | 0.0124720i | ||||
\(461\) | 22.0792 | 1.02833 | 0.514166 | − | 0.857691i | \(-0.328102\pi\) | ||||
0.514166 | + | 0.857691i | \(0.328102\pi\) | |||||||
\(462\) | 0.0650922 | − | 0.181531i | 0.00302837 | − | 0.00844559i | ||||
\(463\) | 16.3672 | 0.760648 | 0.380324 | − | 0.924853i | \(-0.375813\pi\) | ||||
0.380324 | + | 0.924853i | \(0.375813\pi\) | |||||||
\(464\) | −0.870993 | + | 1.50860i | −0.0404348 | + | 0.0700352i | ||||
\(465\) | −0.0893452 | − | 0.154750i | −0.00414329 | − | 0.00717638i | ||||
\(466\) | −12.7090 | − | 22.0127i | −0.588734 | − | 1.01972i | ||||
\(467\) | 15.0234 | − | 26.0213i | 0.695201 | − | 1.20412i | −0.274912 | − | 0.961469i | \(-0.588649\pi\) |
0.970113 | − | 0.242654i | \(-0.0780181\pi\) | |||||||
\(468\) | −18.6445 | −0.861842 | ||||||||
\(469\) | −11.3809 | + | 31.7393i | −0.525520 | + | 1.46559i | ||||
\(470\) | −3.62455 | −0.167188 | ||||||||
\(471\) | −1.34481 | + | 2.32927i | −0.0619655 | + | 0.107327i | ||||
\(472\) | 1.14602 | + | 1.98497i | 0.0527500 | + | 0.0913656i | ||||
\(473\) | −1.21144 | − | 2.09827i | −0.0557020 | − | 0.0964786i | ||||
\(474\) | 0.0656578 | − | 0.113723i | 0.00301576 | − | 0.00522345i | ||||
\(475\) | 1.73099 | 0.0794233 | ||||||||
\(476\) | 12.0102 | − | 2.17689i | 0.550488 | − | 0.0997778i | ||||
\(477\) | −17.4843 | −0.800553 | ||||||||
\(478\) | −4.29706 | + | 7.44272i | −0.196543 | + | 0.340422i | ||||
\(479\) | 4.04609 | + | 7.00803i | 0.184871 | + | 0.320205i | 0.943533 | − | 0.331279i | \(-0.107480\pi\) |
−0.758662 | + | 0.651484i | \(0.774147\pi\) | |||||||
\(480\) | −0.0304437 | − | 0.0527300i | −0.00138956 | − | 0.00240678i | ||||
\(481\) | 20.0833 | − | 34.7853i | 0.915719 | − | 1.58607i | ||||
\(482\) | 9.38884 | 0.427650 | ||||||||
\(483\) | −0.337147 | − | 0.397923i | −0.0153407 | − | 0.0181061i | ||||
\(484\) | −10.8633 | −0.493785 | ||||||||
\(485\) | 0.766857 | − | 1.32823i | 0.0348212 | − | 0.0603120i | ||||
\(486\) | 2.61539 | + | 4.52999i | 0.118637 | + | 0.205485i | ||||
\(487\) | −3.29781 | − | 5.71198i | −0.149438 | − | 0.258834i | 0.781582 | − | 0.623803i | \(-0.214413\pi\) |
−0.931020 | + | 0.364968i | \(0.881080\pi\) | |||||||
\(488\) | −3.39396 | + | 5.87851i | −0.153637 | + | 0.266108i | ||||
\(489\) | 3.77195 | 0.170573 | ||||||||
\(490\) | −2.02458 | + | 0.758854i | −0.0914612 | + | 0.0342815i | ||||
\(491\) | −12.7040 | −0.573323 | −0.286661 | − | 0.958032i | \(-0.592545\pi\) | ||||
−0.286661 | + | 0.958032i | \(0.592545\pi\) | |||||||
\(492\) | −0.187480 | + | 0.324726i | −0.00845227 | + | 0.0146398i | ||||
\(493\) | −4.01825 | − | 6.95981i | −0.180973 | − | 0.313454i | ||||
\(494\) | 1.11110 | + | 1.92448i | 0.0499907 | + | 0.0865864i | ||||
\(495\) | −0.169096 | + | 0.292884i | −0.00760032 | + | 0.0131641i | ||||
\(496\) | 2.93477 | 0.131775 | ||||||||
\(497\) | −0.841675 | − | 0.993400i | −0.0377543 | − | 0.0445601i | ||||
\(498\) | 1.27104 | 0.0569567 | ||||||||
\(499\) | 3.34489 | − | 5.79352i | 0.149738 | − | 0.259354i | −0.781393 | − | 0.624040i | \(-0.785490\pi\) |
0.931131 | + | 0.364686i | \(0.118824\pi\) | |||||||
\(500\) | −1.52964 | − | 2.64942i | −0.0684076 | − | 0.118485i | ||||
\(501\) | 0.523687 | + | 0.907053i | 0.0233966 | + | 0.0405242i | ||||
\(502\) | 1.56882 | − | 2.71727i | 0.0700197 | − | 0.121278i | ||||
\(503\) | 42.8269 | 1.90956 | 0.954779 | − | 0.297316i | \(-0.0960913\pi\) | ||||
0.954779 | + | 0.297316i | \(0.0960913\pi\) | |||||||
\(504\) | −7.70884 | + | 1.39725i | −0.343379 | + | 0.0622385i | ||||
\(505\) | 4.12500 | 0.183560 | ||||||||
\(506\) | 0.184881 | − | 0.320224i | 0.00821897 | − | 0.0142357i | ||||
\(507\) | 2.62616 | + | 4.54865i | 0.116632 | + | 0.202013i | ||||
\(508\) | −8.01077 | − | 13.8751i | −0.355421 | − | 0.615606i | ||||
\(509\) | 13.9892 | − | 24.2300i | 0.620059 | − | 1.07397i | −0.369415 | − | 0.929264i | \(-0.620442\pi\) |
0.989474 | − | 0.144709i | \(-0.0462247\pi\) | |||||||
\(510\) | 0.280898 | 0.0124384 | ||||||||
\(511\) | −5.35770 | + | 14.9417i | −0.237011 | + | 0.660982i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.207365 | − | 0.359167i | 0.00915538 | − | 0.0158576i | ||||
\(514\) | 13.4913 | + | 23.3677i | 0.595078 | + | 1.03070i | ||||
\(515\) | 0.135706 | + | 0.235049i | 0.00597991 | + | 0.0103575i | ||||
\(516\) | 0.645837 | − | 1.11862i | 0.0284314 | − | 0.0492446i | ||||
\(517\) | 4.33905 | 0.190831 | ||||||||
\(518\) | 5.69686 | − | 15.8876i | 0.250306 | − | 0.698059i | ||||
\(519\) | 1.03006 | 0.0452146 | ||||||||
\(520\) | 0.972398 | − | 1.68424i | 0.0426425 | − | 0.0738589i | ||||
\(521\) | 2.01361 | + | 3.48768i | 0.0882180 | + | 0.152798i | 0.906758 | − | 0.421652i | \(-0.138549\pi\) |
−0.818540 | + | 0.574450i | \(0.805216\pi\) | |||||||
\(522\) | 2.57913 | + | 4.46719i | 0.112886 | + | 0.195524i | ||||
\(523\) | −17.3396 | + | 30.0331i | −0.758209 | + | 1.31326i | 0.185554 | + | 0.982634i | \(0.440592\pi\) |
−0.943763 | + | 0.330623i | \(0.892741\pi\) | |||||||
\(524\) | 18.3179 | 0.800223 | ||||||||
\(525\) | 2.51697 | − | 0.456209i | 0.109849 | − | 0.0199106i | ||||
\(526\) | −10.7322 | −0.467948 | ||||||||
\(527\) | −6.76965 | + | 11.7254i | −0.294890 | + | 0.510765i | ||||
\(528\) | 0.0364449 | + | 0.0631245i | 0.00158606 | + | 0.00274714i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 0.911891 | − | 1.57944i | 0.0396100 | − | 0.0686066i | ||||
\(531\) | 6.78707 | 0.294534 | ||||||||
\(532\) | 0.603624 | + | 0.712436i | 0.0261704 | + | 0.0308880i | ||||
\(533\) | −11.9766 | −0.518763 | ||||||||
\(534\) | 1.14551 | − | 1.98408i | 0.0495711 | − | 0.0858596i | ||||
\(535\) | 2.20863 | + | 3.82545i | 0.0954872 | + | 0.165389i | ||||
\(536\) | −6.37212 | − | 11.0368i | −0.275234 | − | 0.476719i | ||||
\(537\) | −1.02537 | + | 1.77600i | −0.0442481 | + | 0.0766400i | ||||
\(538\) | −15.8761 | −0.684469 | ||||||||
\(539\) | 2.42368 | − | 0.908444i | 0.104395 | − | 0.0391294i | ||||
\(540\) | −0.362958 | −0.0156192 | ||||||||
\(541\) | 13.3296 | − | 23.0875i | 0.573084 | − | 0.992610i | −0.423163 | − | 0.906053i | \(-0.639080\pi\) |
0.996247 | − | 0.0865564i | \(-0.0275863\pi\) | |||||||
\(542\) | −7.19021 | − | 12.4538i | −0.308846 | − | 0.534937i | ||||
\(543\) | 0.729313 | + | 1.26321i | 0.0312978 | + | 0.0542094i | ||||
\(544\) | −2.30670 | + | 3.99533i | −0.0988991 | + | 0.171298i | ||||
\(545\) | 4.67044 | 0.200060 | ||||||||
\(546\) | 2.12281 | + | 2.50548i | 0.0908479 | + | 0.107225i | ||||
\(547\) | −5.21015 | −0.222770 | −0.111385 | − | 0.993777i | \(-0.535529\pi\) | ||||
−0.111385 | + | 0.993777i | \(0.535529\pi\) | |||||||
\(548\) | 4.61681 | − | 7.99655i | 0.197220 | − | 0.341596i | ||||
\(549\) | 10.0500 | + | 17.4071i | 0.428924 | + | 0.742917i | ||||
\(550\) | 0.906767 | + | 1.57057i | 0.0386647 | + | 0.0669692i | ||||
\(551\) | 0.307401 | − | 0.532435i | 0.0130957 | − | 0.0226825i | ||||
\(552\) | 0.197126 | 0.00839025 | ||||||||
\(553\) | 1.73421 | − | 0.314331i | 0.0737461 | − | 0.0133667i | ||||
\(554\) | 11.6360 | 0.494365 | ||||||||
\(555\) | 0.194210 | − | 0.336381i | 0.00824373 | − | 0.0142786i | ||||
\(556\) | 8.64701 | + | 14.9771i | 0.366715 | + | 0.635169i | ||||
\(557\) | −23.3278 | − | 40.4050i | −0.988431 | − | 1.71201i | −0.625564 | − | 0.780172i | \(-0.715131\pi\) |
−0.362867 | − | 0.931841i | \(-0.618202\pi\) | |||||||
\(558\) | 4.34513 | − | 7.52599i | 0.183944 | − | 0.318601i | ||||
\(559\) | 41.2572 | 1.74499 | ||||||||
\(560\) | 0.275832 | − | 0.769248i | 0.0116560 | − | 0.0325067i | ||||
\(561\) | −0.336271 | −0.0141974 | ||||||||
\(562\) | 12.6031 | − | 21.8292i | 0.531629 | − | 0.920809i | ||||
\(563\) | −20.9007 | − | 36.2010i | −0.880859 | − | 1.52569i | −0.850388 | − | 0.526156i | \(-0.823633\pi\) |
−0.0304709 | − | 0.999536i | \(-0.509701\pi\) | |||||||
\(564\) | 1.15661 | + | 2.00331i | 0.0487020 | + | 0.0843544i | ||||
\(565\) | 1.16921 | − | 2.02513i | 0.0491889 | − | 0.0851977i | ||||
\(566\) | −3.57615 | −0.150317 | ||||||||
\(567\) | −7.72623 | + | 21.5471i | −0.324471 | + | 0.904894i | ||||
\(568\) | 0.492118 | 0.0206488 | ||||||||
\(569\) | 5.68959 | − | 9.85467i | 0.238520 | − | 0.413129i | −0.721770 | − | 0.692133i | \(-0.756671\pi\) |
0.960290 | + | 0.279004i | \(0.0900043\pi\) | |||||||
\(570\) | 0.0107446 | + | 0.0186101i | 0.000450040 | + | 0.000779492i | ||||
\(571\) | −10.6530 | − | 18.4516i | −0.445815 | − | 0.772174i | 0.552294 | − | 0.833649i | \(-0.313753\pi\) |
−0.998109 | + | 0.0614758i | \(0.980419\pi\) | |||||||
\(572\) | −1.16408 | + | 2.01625i | −0.0486728 | + | 0.0843037i | ||||
\(573\) | 0.788410 | 0.0329363 | ||||||||
\(574\) | −4.95189 | + | 0.897546i | −0.206688 | + | 0.0374629i | ||||
\(575\) | 4.90460 | 0.204536 | ||||||||
\(576\) | 1.48057 | − | 2.56442i | 0.0616904 | − | 0.106851i | ||||
\(577\) | 8.62124 | + | 14.9324i | 0.358907 | + | 0.621645i | 0.987779 | − | 0.155864i | \(-0.0498162\pi\) |
−0.628872 | + | 0.777509i | \(0.716483\pi\) | |||||||
\(578\) | −2.14176 | − | 3.70964i | −0.0890857 | − | 0.154301i | ||||
\(579\) | 0.0446747 | − | 0.0773788i | 0.00185662 | − | 0.00321575i | ||||
\(580\) | −0.538056 | −0.0223416 | ||||||||
\(581\) | 11.0278 | + | 13.0158i | 0.457512 | + | 0.539985i | ||||
\(582\) | −0.978827 | −0.0405737 | ||||||||
\(583\) | −1.09165 | + | 1.89079i | −0.0452115 | + | 0.0783086i | ||||
\(584\) | −2.99976 | − | 5.19573i | −0.124131 | − | 0.215001i | ||||
\(585\) | −2.87941 | − | 4.98728i | −0.119049 | − | 0.206199i | ||||
\(586\) | 2.01621 | − | 3.49218i | 0.0832890 | − | 0.144261i | ||||
\(587\) | −3.94485 | −0.162821 | −0.0814107 | − | 0.996681i | \(-0.525943\pi\) | ||||
−0.0814107 | + | 0.996681i | \(0.525943\pi\) | |||||||
\(588\) | 1.06547 | + | 0.876840i | 0.0439393 | + | 0.0361603i | ||||
\(589\) | −1.03577 | −0.0426784 | ||||||||
\(590\) | −0.353978 | + | 0.613107i | −0.0145730 | + | 0.0252412i | ||||
\(591\) | −0.598854 | − | 1.03724i | −0.0246335 | − | 0.0426666i | ||||
\(592\) | 3.18965 | + | 5.52464i | 0.131094 | + | 0.227061i | ||||
\(593\) | −4.52179 | + | 7.83196i | −0.185687 | + | 0.321620i | −0.943808 | − | 0.330494i | \(-0.892785\pi\) |
0.758120 | + | 0.652115i | \(0.226118\pi\) | |||||||
\(594\) | 0.434507 | 0.0178280 | ||||||||
\(595\) | 2.43714 | + | 2.87647i | 0.0999128 | + | 0.117924i | ||||
\(596\) | −14.7548 | −0.604382 | ||||||||
\(597\) | −2.55540 | + | 4.42608i | −0.104585 | + | 0.181147i | ||||
\(598\) | 3.14819 | + | 5.45283i | 0.128739 | + | 0.222983i | ||||
\(599\) | 15.0419 | + | 26.0534i | 0.614597 | + | 1.06451i | 0.990455 | + | 0.137836i | \(0.0440147\pi\) |
−0.375858 | + | 0.926677i | \(0.622652\pi\) | |||||||
\(600\) | −0.483412 | + | 0.837295i | −0.0197352 | + | 0.0341824i | ||||
\(601\) | −25.0873 | −1.02333 | −0.511665 | − | 0.859185i | \(-0.670971\pi\) | ||||
−0.511665 | + | 0.859185i | \(0.670971\pi\) | |||||||
\(602\) | 17.0584 | − | 3.09189i | 0.695248 | − | 0.126016i | ||||
\(603\) | −37.7375 | −1.53679 | ||||||||
\(604\) | 10.6213 | − | 18.3966i | 0.432174 | − | 0.748548i | ||||
\(605\) | −1.67770 | − | 2.90586i | −0.0682081 | − | 0.118140i | ||||
\(606\) | −1.31630 | − | 2.27990i | −0.0534711 | − | 0.0926147i | ||||
\(607\) | −19.0622 | + | 33.0168i | −0.773713 | + | 1.34011i | 0.161802 | + | 0.986823i | \(0.448269\pi\) |
−0.935515 | + | 0.353287i | \(0.885064\pi\) | |||||||
\(608\) | −0.352932 | −0.0143133 | ||||||||
\(609\) | 0.306656 | − | 0.855211i | 0.0124263 | − | 0.0346549i | ||||
\(610\) | −2.09662 | −0.0848897 | ||||||||
\(611\) | −36.9431 | + | 63.9873i | −1.49456 | + | 2.58865i | ||||
\(612\) | 6.83048 | + | 11.8307i | 0.276106 | + | 0.478229i | ||||
\(613\) | 15.8375 | + | 27.4314i | 0.639670 | + | 1.10794i | 0.985505 | + | 0.169646i | \(0.0542625\pi\) |
−0.345835 | + | 0.938296i | \(0.612404\pi\) | |||||||
\(614\) | 0.679683 | − | 1.17725i | 0.0274298 | − | 0.0475097i | ||||
\(615\) | −0.115816 | −0.00467015 | ||||||||
\(616\) | −0.330206 | + | 0.920887i | −0.0133044 | + | 0.0371036i | ||||
\(617\) | −39.9083 | −1.60665 | −0.803324 | − | 0.595543i | \(-0.796937\pi\) | ||||
−0.803324 | + | 0.595543i | \(0.796937\pi\) | |||||||
\(618\) | 0.0866085 | − | 0.150010i | 0.00348390 | − | 0.00603430i | ||||
\(619\) | 5.69093 | + | 9.85698i | 0.228738 | + | 0.396185i | 0.957434 | − | 0.288651i | \(-0.0932068\pi\) |
−0.728696 | + | 0.684837i | \(0.759873\pi\) | |||||||
\(620\) | 0.453239 | + | 0.785032i | 0.0182025 | + | 0.0315276i | ||||
\(621\) | 0.587549 | − | 1.01766i | 0.0235775 | − | 0.0408375i | ||||
\(622\) | 14.7634 | 0.591960 | ||||||||
\(623\) | 30.2562 | − | 5.48403i | 1.21219 | − | 0.219713i | ||||
\(624\) | −1.24118 | −0.0496871 | ||||||||
\(625\) | −11.7890 | + | 20.4192i | −0.471561 | + | 0.816767i | ||||
\(626\) | 11.6470 | + | 20.1732i | 0.465508 | + | 0.806284i | ||||
\(627\) | −0.0128626 | − | 0.0222787i | −0.000513682 | − | 0.000889724i | ||||
\(628\) | 6.82206 | − | 11.8162i | 0.272230 | − | 0.471516i | ||||
\(629\) | −29.4303 | −1.17346 | ||||||||
\(630\) | −1.56429 | − | 1.84628i | −0.0623228 | − | 0.0735574i | ||||
\(631\) | 28.3119 | 1.12708 | 0.563539 | − | 0.826089i | \(-0.309439\pi\) | ||||
0.563539 | + | 0.826089i | \(0.309439\pi\) | |||||||
\(632\) | −0.333075 | + | 0.576902i | −0.0132490 | + | 0.0229479i | ||||
\(633\) | −1.47219 | − | 2.54991i | −0.0585144 | − | 0.101350i | ||||
\(634\) | −9.66087 | − | 16.7331i | −0.383682 | − | 0.664557i | ||||
\(635\) | 2.47433 | − | 4.28566i | 0.0981907 | − | 0.170071i | ||||
\(636\) | −1.16395 | −0.0461537 | ||||||||
\(637\) | −7.23875 | + | 43.4762i | −0.286810 | + | 1.72259i | ||||
\(638\) | 0.644121 | 0.0255010 | ||||||||
\(639\) | 0.728615 | − | 1.26200i | 0.0288236 | − | 0.0499239i | ||||
\(640\) | 0.154437 | + | 0.267494i | 0.00610468 | + | 0.0105736i | ||||
\(641\) | 1.16446 | + | 2.01691i | 0.0459935 | + | 0.0796632i | 0.888106 | − | 0.459639i | \(-0.152021\pi\) |
−0.842112 | + | 0.539302i | \(0.818688\pi\) | |||||||
\(642\) | 1.40956 | − | 2.44143i | 0.0556310 | − | 0.0963556i | ||||
\(643\) | −5.03301 | −0.198482 | −0.0992412 | − | 0.995063i | \(-0.531642\pi\) | ||||
−0.0992412 | + | 0.995063i | \(0.531642\pi\) | |||||||
\(644\) | 1.71031 | + | 2.01862i | 0.0673957 | + | 0.0795448i | ||||
\(645\) | 0.398966 | 0.0157093 | ||||||||
\(646\) | 0.814110 | − | 1.41008i | 0.0320307 | − | 0.0554788i | ||||
\(647\) | 17.9635 | + | 31.1137i | 0.706218 | + | 1.22321i | 0.966250 | + | 0.257605i | \(0.0829335\pi\) |
−0.260032 | + | 0.965600i | \(0.583733\pi\) | |||||||
\(648\) | −4.32589 | − | 7.49266i | −0.169937 | − | 0.294340i | ||||
\(649\) | 0.423756 | − | 0.733967i | 0.0166339 | − | 0.0288107i | ||||
\(650\) | −30.8812 | −1.21126 | ||||||||
\(651\) | −1.50608 | + | 0.272982i | −0.0590280 | + | 0.0106990i | ||||
\(652\) | −19.1347 | −0.749372 | ||||||||
\(653\) | 11.9554 | − | 20.7073i | 0.467849 | − | 0.810338i | −0.531476 | − | 0.847073i | \(-0.678362\pi\) |
0.999325 | + | 0.0367350i | \(0.0116957\pi\) | |||||||
\(654\) | −1.49035 | − | 2.58137i | −0.0582775 | − | 0.100940i | ||||
\(655\) | 2.82897 | + | 4.89993i | 0.110537 | + | 0.191456i | ||||
\(656\) | 0.951067 | − | 1.64730i | 0.0371329 | − | 0.0643161i | ||||
\(657\) | −17.7654 | −0.693095 | ||||||||
\(658\) | −10.4793 | + | 29.2251i | −0.408527 | + | 1.13931i | ||||
\(659\) | 25.6645 | 0.999749 | 0.499874 | − | 0.866098i | \(-0.333380\pi\) | ||||
0.499874 | + | 0.866098i | \(0.333380\pi\) | |||||||
\(660\) | −0.0112569 | + | 0.0194976i | −0.000438175 | + | 0.000758942i | ||||
\(661\) | −0.221521 | − | 0.383685i | −0.00861616 | − | 0.0149236i | 0.861685 | − | 0.507443i | \(-0.169409\pi\) |
−0.870301 | + | 0.492520i | \(0.836076\pi\) | |||||||
\(662\) | 2.00407 | + | 3.47116i | 0.0778905 | + | 0.134910i | ||||
\(663\) | 2.86304 | − | 4.95894i | 0.111191 | − | 0.192589i | ||||
\(664\) | −6.44785 | −0.250225 | ||||||||
\(665\) | −0.0973500 | + | 0.271492i | −0.00377507 | + | 0.0105280i | ||||
\(666\) | 18.8900 | 0.731973 | ||||||||
\(667\) | 0.870993 | − | 1.50860i | 0.0337250 | − | 0.0584134i | ||||
\(668\) | −2.65661 | − | 4.60138i | −0.102787 | − | 0.178033i | ||||
\(669\) | −0.528700 | − | 0.915736i | −0.0204407 | − | 0.0354044i | ||||
\(670\) | 1.96819 | − | 3.40900i | 0.0760377 | − | 0.131701i | ||||
\(671\) | 2.50992 | 0.0968943 | ||||||||
\(672\) | −0.513186 | + | 0.0930165i | −0.0197966 | + | 0.00358819i | ||||
\(673\) | 27.3836 | 1.05556 | 0.527781 | − | 0.849381i | \(-0.323024\pi\) | ||||
0.527781 | + | 0.849381i | \(0.323024\pi\) | |||||||
\(674\) | 9.36209 | − | 16.2156i | 0.360614 | − | 0.624602i | ||||
\(675\) | 2.88169 | + | 4.99123i | 0.110916 | + | 0.192113i | ||||
\(676\) | −13.3222 | − | 23.0748i | −0.512394 | − | 0.887493i | ||||
\(677\) | −19.3292 | + | 33.4792i | −0.742882 | + | 1.28671i | 0.208296 | + | 0.978066i | \(0.433208\pi\) |
−0.951178 | + | 0.308644i | \(0.900125\pi\) | |||||||
\(678\) | −1.49239 | −0.0573150 | ||||||||
\(679\) | −8.49253 | − | 10.0234i | −0.325913 | − | 0.384664i | ||||
\(680\) | −1.42497 | −0.0546450 | ||||||||
\(681\) | 2.77739 | − | 4.81058i | 0.106430 | − | 0.184342i | ||||
\(682\) | −0.542584 | − | 0.939783i | −0.0207766 | − | 0.0359861i | ||||
\(683\) | −19.0423 | − | 32.9822i | −0.728633 | − | 1.26203i | −0.957461 | − | 0.288562i | \(-0.906823\pi\) |
0.228828 | − | 0.973467i | \(-0.426511\pi\) | |||||||
\(684\) | −0.522541 | + | 0.905068i | −0.0199799 | + | 0.0346061i | ||||
\(685\) | 2.85203 | 0.108971 | ||||||||
\(686\) | 0.265219 | + | 18.5184i | 0.0101261 | + | 0.707034i | ||||
\(687\) | −3.12194 | −0.119110 | ||||||||
\(688\) | −3.27626 | + | 5.67465i | −0.124906 | + | 0.216344i | ||||
\(689\) | −18.5888 | − | 32.1968i | −0.708177 | − | 1.22660i | ||||
\(690\) | 0.0304437 | + | 0.0527300i | 0.00115897 | + | 0.00200740i | ||||
\(691\) | 10.0832 | − | 17.4646i | 0.383582 | − | 0.664384i | −0.607989 | − | 0.793945i | \(-0.708024\pi\) |
0.991571 | + | 0.129562i | \(0.0413570\pi\) | |||||||
\(692\) | −5.22538 | −0.198639 | ||||||||
\(693\) | 1.87265 | + | 2.21023i | 0.0711362 | + | 0.0839596i | ||||
\(694\) | 5.24938 | 0.199264 | ||||||||
\(695\) | −2.67084 | + | 4.62604i | −0.101311 | + | 0.175476i | ||||
\(696\) | 0.171696 | + | 0.297386i | 0.00650811 | + | 0.0112724i | ||||
\(697\) | 4.38766 | + | 7.59965i | 0.166195 | + | 0.287857i | ||||
\(698\) | 14.6895 | − | 25.4429i | 0.556004 | − | 0.963027i | ||||
\(699\) | −5.01057 | −0.189517 | ||||||||
\(700\) | −12.7683 | + | 2.31430i | −0.482596 | + | 0.0874722i | ||||
\(701\) | −21.0182 | −0.793847 | −0.396924 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396924 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(702\) | −3.69944 | + | 6.40761i | −0.139626 | + | 0.241840i | ||||
\(703\) | −1.12573 | − | 1.94982i | −0.0424577 | − | 0.0735390i | ||||
\(704\) | −0.184881 | − | 0.320224i | −0.00696797 | − | 0.0120689i | ||||
\(705\) | −0.357247 | + | 0.618771i | −0.0134547 | + | 0.0233043i | ||||
\(706\) | 3.77629 | 0.142123 | ||||||||
\(707\) | 11.9262 | − | 33.2602i | 0.448532 | − | 1.25088i | ||||
\(708\) | 0.451822 | 0.0169805 | ||||||||
\(709\) | −4.15409 | + | 7.19509i | −0.156010 | + | 0.270217i | −0.933426 | − | 0.358769i | \(-0.883197\pi\) |
0.777416 | + | 0.628986i | \(0.216530\pi\) | |||||||
\(710\) | 0.0760015 | + | 0.131638i | 0.00285228 | + | 0.00494030i | ||||
\(711\) | 0.986281 | + | 1.70829i | 0.0369884 | + | 0.0640659i | ||||
\(712\) | −5.81105 | + | 10.0650i | −0.217778 | + | 0.377203i | ||||
\(713\) | −2.93477 | −0.109908 | ||||||||
\(714\) | 0.812135 | − | 2.26491i | 0.0303934 | − | 0.0847620i | ||||
\(715\) | −0.719112 | −0.0268933 | ||||||||
\(716\) | 5.20161 | − | 9.00945i | 0.194393 | − | 0.336699i | ||||
\(717\) | 0.847063 | + | 1.46716i | 0.0316342 | + | 0.0547920i | ||||
\(718\) | 9.28414 | + | 16.0806i | 0.346481 | + | 0.600123i | ||||
\(719\) | −16.2182 | + | 28.0908i | −0.604838 | + | 1.04761i | 0.387239 | + | 0.921980i | \(0.373429\pi\) |
−0.992077 | + | 0.125631i | \(0.959904\pi\) | |||||||
\(720\) | 0.914622 | 0.0340860 | ||||||||
\(721\) | 2.28758 | − | 0.414631i | 0.0851938 | − | 0.0154417i | ||||
\(722\) | −18.8754 | −0.702471 | ||||||||
\(723\) | 0.925394 | − | 1.60283i | 0.0344158 | − | 0.0596099i | ||||
\(724\) | −3.69973 | − | 6.40811i | −0.137499 | − | 0.238156i | ||||
\(725\) | 4.27187 | + | 7.39910i | 0.158653 | + | 0.274796i | ||||
\(726\) | −1.07072 | + | 1.85454i | −0.0397381 | + | 0.0688284i | ||||
\(727\) | −17.1339 | −0.635460 | −0.317730 | − | 0.948181i | \(-0.602921\pi\) | ||||
−0.317730 | + | 0.948181i | \(0.602921\pi\) | |||||||
\(728\) | −10.7688 | − | 12.7100i | −0.399118 | − | 0.471065i | ||||
\(729\) | −24.9242 | −0.923119 | ||||||||
\(730\) | 0.926550 | − | 1.60483i | 0.0342932 | − | 0.0593975i | ||||
\(731\) | −15.1147 | − | 26.1795i | −0.559038 | − | 0.968283i | ||||
\(732\) | 0.669039 | + | 1.15881i | 0.0247284 | + | 0.0428308i | ||||
\(733\) | 3.43584 | − | 5.95105i | 0.126906 | − | 0.219807i | −0.795571 | − | 0.605861i | \(-0.792829\pi\) |
0.922476 | + | 0.386054i | \(0.126162\pi\) | |||||||
\(734\) | 15.3228 | 0.565573 | ||||||||
\(735\) | −0.0700002 | + | 0.420424i | −0.00258200 | + | 0.0155076i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −2.35617 | + | 4.08101i | −0.0867906 | + | 0.150326i | ||||
\(738\) | −2.81624 | − | 4.87788i | −0.103667 | − | 0.179557i | ||||
\(739\) | 5.63174 | + | 9.75446i | 0.207167 | + | 0.358823i | 0.950821 | − | 0.309741i | \(-0.100242\pi\) |
−0.743654 | + | 0.668565i | \(0.766909\pi\) | |||||||
\(740\) | −0.985203 | + | 1.70642i | −0.0362168 | + | 0.0627293i | ||||
\(741\) | 0.438054 | 0.0160923 | ||||||||
\(742\) | −10.0987 | − | 11.9191i | −0.370735 | − | 0.437566i | ||||
\(743\) | −23.7565 | −0.871540 | −0.435770 | − | 0.900058i | \(-0.643524\pi\) | ||||
−0.435770 | + | 0.900058i | \(0.643524\pi\) | |||||||
\(744\) | 0.289260 | − | 0.501013i | 0.0106048 | − | 0.0183680i | ||||
\(745\) | −2.27870 | − | 3.94683i | −0.0834851 | − | 0.144601i | ||||
\(746\) | −2.03891 | − | 3.53149i | −0.0746497 | − | 0.129297i | ||||
\(747\) | −9.54650 | + | 16.5350i | −0.349288 | + | 0.604985i | ||||
\(748\) | 1.70586 | 0.0623726 | ||||||||
\(749\) | 37.2305 | − | 6.74815i | 1.36037 | − | 0.246572i | ||||
\(750\) | −0.603065 | −0.0220208 | ||||||||
\(751\) | 16.9977 | − | 29.4409i | 0.620256 | − | 1.07431i | −0.369182 | − | 0.929357i | \(-0.620362\pi\) |
0.989438 | − | 0.144957i | \(-0.0463045\pi\) | |||||||
\(752\) | −5.86735 | − | 10.1625i | −0.213960 | − | 0.370590i | ||||
\(753\) | −0.309255 | − | 0.535646i | −0.0112699 | − | 0.0195200i | ||||
\(754\) | −5.48411 | + | 9.49876i | −0.199720 | + | 0.345924i | ||||
\(755\) | 6.56130 | 0.238790 | ||||||||
\(756\) | −1.04939 | + | 2.92656i | −0.0381659 | + | 0.106438i | ||||
\(757\) | −40.7166 | −1.47987 | −0.739935 | − | 0.672679i | \(-0.765144\pi\) | ||||
−0.739935 | + | 0.672679i | \(0.765144\pi\) | |||||||
\(758\) | −13.7196 | + | 23.7631i | −0.498319 | + | 0.863113i | ||||
\(759\) | −0.0364449 | − | 0.0631245i | −0.00132287 | − | 0.00229127i | ||||
\(760\) | −0.0545060 | − | 0.0944071i | −0.00197714 | − | 0.00342450i | ||||
\(761\) | −19.0121 | + | 32.9300i | −0.689189 | + | 1.19371i | 0.282911 | + | 0.959146i | \(0.408700\pi\) |
−0.972101 | + | 0.234565i | \(0.924634\pi\) | |||||||
\(762\) | −3.15827 | −0.114412 | ||||||||
\(763\) | 13.5032 | − | 37.6581i | 0.488849 | − | 1.36332i | ||||
\(764\) | −3.99951 | −0.144697 | ||||||||
\(765\) | −2.10976 | + | 3.65422i | −0.0762786 | + | 0.132118i | ||||
\(766\) | 0.302361 | + | 0.523705i | 0.0109248 | + | 0.0189222i | ||||
\(767\) | 7.21580 | + | 12.4981i | 0.260547 | + | 0.451281i | ||||
\(768\) | 0.0985631 | − | 0.170716i | 0.00355659 | − | 0.00616020i | ||||
\(769\) | −18.1567 | −0.654746 | −0.327373 | − | 0.944895i | \(-0.606163\pi\) | ||||
−0.327373 | + | 0.944895i | \(0.606163\pi\) | |||||||
\(770\) | −0.297328 | + | 0.0538916i | −0.0107149 | + | 0.00194212i | ||||
\(771\) | 5.31900 | 0.191559 | ||||||||
\(772\) | −0.226630 | + | 0.392534i | −0.00815658 | + | 0.0141276i | ||||
\(773\) | −12.8258 | − | 22.2150i | −0.461313 | − | 0.799018i | 0.537714 | − | 0.843128i | \(-0.319288\pi\) |
−0.999027 | + | 0.0441098i | \(0.985955\pi\) | |||||||
\(774\) | 9.70147 | + | 16.8034i | 0.348712 | + | 0.603987i | ||||
\(775\) | 7.19693 | − | 12.4655i | 0.258521 | − | 0.447772i | ||||
\(776\) | 4.96548 | 0.178250 | ||||||||
\(777\) | −2.15077 | − | 2.53847i | −0.0771583 | − | 0.0910673i | ||||
\(778\) | −8.10124 | −0.290443 | ||||||||
\(779\) | −0.335662 | + | 0.581384i | −0.0120263 | + | 0.0208302i | ||||
\(780\) | −0.191685 | − | 0.332009i | −0.00686343 | − | 0.0118878i | ||||
\(781\) | −0.0909833 | − | 0.157588i | −0.00325564 | − | 0.00563893i | ||||
\(782\) | 2.30670 | − | 3.99533i | 0.0824876 | − | 0.142873i | ||||
\(783\) | 2.04700 | 0.0731540 | ||||||||
\(784\) | −5.40502 | − | 4.44811i | −0.193037 | − | 0.158861i | ||||
\(785\) | 4.21433 | 0.150416 | ||||||||
\(786\) | 1.80547 | − | 3.12717i | 0.0643991 | − | 0.111542i | ||||
\(787\) | −13.5264 | − | 23.4284i | −0.482165 | − | 0.835134i | 0.517626 | − | 0.855607i | \(-0.326816\pi\) |
−0.999790 | + | 0.0204733i | \(0.993483\pi\) | |||||||
\(788\) | 3.03792 | + | 5.26183i | 0.108221 | + | 0.187445i | ||||
\(789\) | −1.05780 | + | 1.83217i | −0.0376588 | + | 0.0652269i | ||||
\(790\) | −0.205757 | −0.00732050 | ||||||||
\(791\) | −12.9483 | − | 15.2825i | −0.460390 | − | 0.543382i | ||||
\(792\) | −1.09492 | −0.0389062 | ||||||||
\(793\) | −21.3697 | + | 37.0134i | −0.758860 | + | 1.31438i | ||||
\(794\) | 6.42365 | + | 11.1261i | 0.227967 | + | 0.394850i | ||||
\(795\) | −0.179758 | − | 0.311349i | −0.00637535 | − | 0.0110424i | ||||
\(796\) | 12.9633 | − | 22.4530i | 0.459470 | − | 0.795826i | ||||
\(797\) | 28.6420 | 1.01455 | 0.507276 | − | 0.861783i | \(-0.330652\pi\) | ||||
0.507276 | + | 0.861783i | \(0.330652\pi\) | |||||||
\(798\) | 0.181120 | − | 0.0328285i | 0.00641157 | − | 0.00116212i | ||||
\(799\) | 54.1369 | 1.91523 | ||||||||
\(800\) | 2.45230 | − | 4.24750i | 0.0867018 | − | 0.150172i | ||||
\(801\) | 17.2073 | + | 29.8040i | 0.607991 | + | 1.05307i | ||||
\(802\) | −4.03550 | − | 6.98970i | −0.142499 | − | 0.246815i | ||||
\(803\) | −1.10920 | + | 1.92119i | −0.0391427 | + | 0.0677972i | ||||
\(804\) | −2.51222 | −0.0885993 | ||||||||
\(805\) | −0.275832 | + | 0.769248i | −0.00972180 | + | 0.0271124i | ||||
\(806\) | 18.4784 | 0.650876 | ||||||||
\(807\) | −1.56480 | + | 2.71032i | −0.0550836 | + | 0.0954076i | ||||
\(808\) | 6.67745 | + | 11.5657i | 0.234912 | + | 0.406880i | ||||
\(809\) | −21.0580 | − | 36.4736i | −0.740360 | − | 1.28234i | −0.952331 | − | 0.305066i | \(-0.901322\pi\) |
0.211971 | − | 0.977276i | \(-0.432012\pi\) | |||||||
\(810\) | 1.33616 | − | 2.31430i | 0.0469478 | − | 0.0813161i | ||||
\(811\) | 3.28555 | 0.115371 | 0.0576856 | − | 0.998335i | \(-0.481628\pi\) | ||||
0.0576856 | + | 0.998335i | \(0.481628\pi\) | |||||||
\(812\) | −1.55563 | + | 4.33839i | −0.0545920 | + | 0.152248i | ||||
\(813\) | −2.83476 | −0.0994194 | ||||||||
\(814\) | 1.17941 | − | 2.04280i | 0.0413384 | − | 0.0716002i | ||||
\(815\) | −2.95511 | − | 5.11841i | −0.103513 | − | 0.179290i | ||||
\(816\) | 0.454712 | + | 0.787584i | 0.0159181 | + | 0.0275710i | ||||
\(817\) | 1.15630 | − | 2.00277i | 0.0404537 | − | 0.0700679i | ||||
\(818\) | −17.3417 | −0.606340 | ||||||||
\(819\) | −48.5378 | + | 8.79764i | −1.69605 | + | 0.307414i | ||||
\(820\) | 0.587522 | 0.0205171 | ||||||||
\(821\) | −16.4529 | + | 28.4973i | −0.574211 | + | 0.994562i | 0.421916 | + | 0.906635i | \(0.361358\pi\) |
−0.996127 | + | 0.0879271i | \(0.971976\pi\) | |||||||
\(822\) | −0.910095 | − | 1.57633i | −0.0317432 | − | 0.0549808i | ||||
\(823\) | 20.6346 | + | 35.7402i | 0.719278 | + | 1.24583i | 0.961286 | + | 0.275552i | \(0.0888605\pi\) |
−0.242008 | + | 0.970274i | \(0.577806\pi\) | |||||||
\(824\) | −0.439355 | + | 0.760986i | −0.0153057 | + | 0.0265102i | ||||
\(825\) | 0.357495 | 0.0124464 | ||||||||
\(826\) | 3.92011 | + | 4.62677i | 0.136398 | + | 0.160986i | ||||
\(827\) | 8.07826 | 0.280909 | 0.140454 | − | 0.990087i | \(-0.455144\pi\) | ||||
0.140454 | + | 0.990087i | \(0.455144\pi\) | |||||||
\(828\) | −1.48057 | + | 2.56442i | −0.0514534 | + | 0.0891199i | ||||
\(829\) | −8.07798 | − | 13.9915i | −0.280560 | − | 0.485944i | 0.690963 | − | 0.722890i | \(-0.257187\pi\) |
−0.971523 | + | 0.236946i | \(0.923853\pi\) | |||||||
\(830\) | −0.995790 | − | 1.72476i | −0.0345644 | − | 0.0598672i | ||||
\(831\) | 1.14688 | − | 1.98645i | 0.0397848 | − | 0.0689092i | ||||
\(832\) | 6.29639 | 0.218288 | ||||||||
\(833\) | 30.2395 | − | 11.3344i | 1.04774 | − | 0.392712i | ||||
\(834\) | 3.40911 | 0.118048 | ||||||||
\(835\) | 0.820560 | − | 1.42125i | 0.0283966 | − | 0.0491844i | ||||
\(836\) | 0.0652505 | + | 0.113017i | 0.00225674 | + | 0.00390878i | ||||
\(837\) | −1.72432 | − | 2.98661i | −0.0596012 | − | 0.103232i | ||||
\(838\) | −7.88131 | + | 13.6508i | −0.272255 | + | 0.471560i | ||||
\(839\) | 28.5777 | 0.986613 | 0.493306 | − | 0.869856i | \(-0.335788\pi\) | ||||
0.493306 | + | 0.869856i | \(0.335788\pi\) | |||||||
\(840\) | −0.104136 | − | 0.122909i | −0.00359305 | − | 0.00424075i | ||||
\(841\) | −25.9655 | −0.895362 | ||||||||
\(842\) | 8.24488 | − | 14.2805i | 0.284137 | − | 0.492140i | ||||
\(843\) | −2.48440 | − | 4.30311i | −0.0855673 | − | 0.148207i | ||||
\(844\) | 7.46827 | + | 12.9354i | 0.257068 | + | 0.445256i | ||||
\(845\) | 4.11491 | − | 7.12723i | 0.141557 | − | 0.245184i | ||||
\(846\) | −34.7481 | −1.19466 | ||||||||
\(847\) | −28.2807 | + | 5.12597i | −0.971737 | + | 0.176131i | ||||
\(848\) | 5.90460 | 0.202765 | ||||||||
\(849\) | −0.352477 | + | 0.610508i | −0.0120970 | + | 0.0209526i | ||||
\(850\) | 11.3135 | + | 19.5955i | 0.388048 | + | 0.672119i | ||||
\(851\) | −3.18965 | − | 5.52464i | −0.109340 | − | 0.189382i | ||||
\(852\) | 0.0485047 | − | 0.0840126i | 0.00166174 | − | 0.00287822i | ||||
\(853\) | −11.7746 | −0.403154 | −0.201577 | − | 0.979473i | \(-0.564607\pi\) | ||||
−0.201577 | + | 0.979473i | \(0.564607\pi\) | |||||||
\(854\) | −6.06176 | + | 16.9052i | −0.207429 | + | 0.578485i | ||||
\(855\) | −0.322800 | −0.0110395 | ||||||||
\(856\) | −7.15055 | + | 12.3851i | −0.244401 | + | 0.423315i | ||||
\(857\) | 16.4006 | + | 28.4066i | 0.560232 | + | 0.970351i | 0.997476 | + | 0.0710077i | \(0.0226215\pi\) |
−0.437243 | + | 0.899343i | \(0.644045\pi\) | |||||||
\(858\) | 0.229471 | + | 0.397456i | 0.00783403 | + | 0.0135689i | ||||
\(859\) | 12.3157 | − | 21.3315i | 0.420207 | − | 0.727820i | −0.575752 | − | 0.817624i | \(-0.695291\pi\) |
0.995959 | + | 0.0898038i | \(0.0286240\pi\) | |||||||
\(860\) | −2.02391 | −0.0690147 | ||||||||
\(861\) | −0.334848 | + | 0.933834i | −0.0114116 | + | 0.0318250i | ||||
\(862\) | 10.9457 | 0.372812 | ||||||||
\(863\) | −15.2591 | + | 26.4296i | −0.519426 | + | 0.899673i | 0.480319 | + | 0.877094i | \(0.340521\pi\) |
−0.999745 | + | 0.0225789i | \(0.992812\pi\) | |||||||
\(864\) | −0.587549 | − | 1.01766i | −0.0199888 | − | 0.0346216i | ||||
\(865\) | −0.806994 | − | 1.39775i | −0.0274386 | − | 0.0475251i | ||||
\(866\) | 14.0350 | − | 24.3093i | 0.476928 | − | 0.826063i | ||||
\(867\) | −0.844396 | −0.0286772 | ||||||||
\(868\) | 7.64019 | − | 1.38481i | 0.259325 | − | 0.0470035i | ||||
\(869\) | 0.246317 | 0.00835573 | ||||||||
\(870\) | −0.0530325 | + | 0.0918550i | −0.00179797 | + | 0.00311417i | ||||
\(871\) | −40.1213 | − | 69.4922i | −1.35946 | − | 2.35465i | ||||
\(872\) | 7.56040 | + | 13.0950i | 0.256028 | + | 0.443453i | ||||
\(873\) | 7.35175 | − | 12.7336i | 0.248819 | − | 0.430967i | ||||
\(874\) | 0.352932 | 0.0119381 | ||||||||
\(875\) | −5.23233 | − | 6.17553i | −0.176885 | − | 0.208771i | ||||
\(876\) | −1.18266 | −0.0399585 | ||||||||
\(877\) | 20.9763 | − | 36.3320i | 0.708319 | − | 1.22684i | −0.257161 | − | 0.966368i | \(-0.582787\pi\) |
0.965480 | − | 0.260476i | \(-0.0838795\pi\) | |||||||
\(878\) | 4.54122 | + | 7.86562i | 0.153259 | + | 0.265452i | ||||
\(879\) | −0.397449 | − | 0.688401i | −0.0134056 | − | 0.0232192i | ||||
\(880\) | 0.0571052 | − | 0.0989090i | 0.00192501 | − | 0.00333422i | ||||
\(881\) | 38.4289 | 1.29470 | 0.647352 | − | 0.762192i | \(-0.275877\pi\) | ||||
0.647352 | + | 0.762192i | \(0.275877\pi\) | |||||||
\(882\) | −19.4094 | + | 7.27503i | −0.653547 | + | 0.244963i | ||||
\(883\) | 44.5679 | 1.49983 | 0.749914 | − | 0.661536i | \(-0.230095\pi\) | ||||
0.749914 | + | 0.661536i | \(0.230095\pi\) | |||||||
\(884\) | −14.5239 | + | 25.1561i | −0.488492 | + | 0.846092i | ||||
\(885\) | 0.0697783 | + | 0.120860i | 0.00234557 | + | 0.00406265i | ||||
\(886\) | 15.3899 | + | 26.6560i | 0.517032 | + | 0.895526i | ||||
\(887\) | 4.21548 | − | 7.30142i | 0.141542 | − | 0.245158i | −0.786536 | − | 0.617545i | \(-0.788127\pi\) |
0.928077 | + | 0.372387i | \(0.121461\pi\) | |||||||
\(888\) | 1.25753 | 0.0421999 | ||||||||
\(889\) | −27.4018 | − | 32.3414i | −0.919028 | − | 1.08470i | ||||
\(890\) | −3.58977 | −0.120329 | ||||||||
\(891\) | −1.59955 | + | 2.77050i | −0.0535870 | + | 0.0928154i | ||||
\(892\) | 2.68204 | + | 4.64543i | 0.0898013 | + | 0.155540i | ||||
\(893\) | 2.07078 | + | 3.58669i | 0.0692959 | + | 0.120024i | ||||
\(894\) | −1.45428 | + | 2.51889i | −0.0486385 | + | 0.0842444i | ||||
\(895\) | 3.21329 | 0.107408 | ||||||||
\(896\) | 2.60333 | − | 0.471863i | 0.0869713 | − | 0.0157638i | ||||
\(897\) | 1.24118 | 0.0414419 | ||||||||
\(898\) | 15.4507 | − | 26.7615i | 0.515598 | − | 0.893042i | ||||
\(899\) | −2.55616 | − | 4.42741i | −0.0852529 | − | 0.147662i | ||||
\(900\) | −7.26160 | − | 12.5775i | −0.242053 | − | 0.419249i | ||||
\(901\) | −13.6202 | + | 23.5908i | −0.453753 | + | 0.785923i | ||||
\(902\) | −0.703338 | −0.0234186 | ||||||||
\(903\) | 1.15349 | − | 3.21689i | 0.0383858 | − | 0.107052i | ||||
\(904\) | 7.57075 | 0.251799 | ||||||||
\(905\) | 1.14275 | − | 1.97931i | 0.0379864 | − | 0.0657943i | ||||
\(906\) | −2.09374 | − | 3.62646i | −0.0695597 | − | 0.120481i | ||||
\(907\) | 5.55314 | + | 9.61832i | 0.184389 | + | 0.319371i | 0.943370 | − | 0.331741i | \(-0.107636\pi\) |
−0.758982 | + | 0.651112i | \(0.774303\pi\) | |||||||
\(908\) | −14.0894 | + | 24.4035i | −0.467573 | + | 0.809860i | ||||
\(909\) | 39.5458 | 1.31165 | ||||||||
\(910\) | 1.73675 | − | 4.84348i | 0.0575726 | − | 0.160560i | ||||
\(911\) | 18.4884 | 0.612548 | 0.306274 | − | 0.951943i | \(-0.400918\pi\) | ||||
0.306274 | + | 0.951943i | \(0.400918\pi\) | |||||||
\(912\) | −0.0347861 | + | 0.0602513i | −0.00115188 | + | 0.00199512i | ||||
\(913\) | 1.19209 | + | 2.06475i | 0.0394523 | + | 0.0683334i | ||||
\(914\) | −20.3512 | − | 35.2492i | −0.673157 | − | 1.16594i | ||||
\(915\) | −0.206649 | + | 0.357927i | −0.00683162 | + | 0.0118327i | ||||
\(916\) | 15.8373 | 0.523278 | ||||||||
\(917\) | 47.6877 | − | 8.64355i | 1.57479 | − | 0.285435i | ||||
\(918\) | 5.42120 | 0.178926 | ||||||||
\(919\) | −2.91435 | + | 5.04781i | −0.0961356 | + | 0.166512i | −0.910082 | − | 0.414428i | \(-0.863982\pi\) |
0.813946 | + | 0.580940i | \(0.197315\pi\) | |||||||
\(920\) | −0.154437 | − | 0.267494i | −0.00509165 | − | 0.00881900i | ||||
\(921\) | −0.133983 | − | 0.232066i | −0.00441490 | − | 0.00764683i | ||||
\(922\) | −11.0396 | + | 19.1212i | −0.363570 | + | 0.629722i | ||||
\(923\) | 3.09857 | 0.101991 | ||||||||
\(924\) | 0.124664 | + | 0.147137i | 0.00410116 | + | 0.00484045i | ||||
\(925\) | 31.2879 | 1.02874 | ||||||||
\(926\) | −8.18359 | + | 14.1744i | −0.268930 | + | 0.465800i | ||||
\(927\) | 1.30099 | + | 2.25339i | 0.0427302 | + | 0.0740109i | ||||
\(928\) | −0.870993 | − | 1.50860i | −0.0285918 | − | 0.0495224i | ||||
\(929\) | 12.6140 | − | 21.8481i | 0.413852 | − | 0.716813i | −0.581455 | − | 0.813578i | \(-0.697516\pi\) |
0.995307 | + | 0.0967658i | \(0.0308498\pi\) | |||||||
\(930\) | 0.178690 | 0.00585949 | ||||||||
\(931\) | 1.90761 | + | 1.56988i | 0.0625193 | + | 0.0514508i | ||||
\(932\) | 25.4180 | 0.832596 | ||||||||
\(933\) | 1.45513 | − | 2.52036i | 0.0476388 | − | 0.0825129i | ||||
\(934\) | 15.0234 | + | 26.0213i | 0.491581 | + | 0.851444i | ||||
\(935\) | 0.263449 | + | 0.456308i | 0.00861572 | + | 0.0149229i | ||||
\(936\) | 9.32225 | − | 16.1466i | 0.304707 | − | 0.527768i | ||||
\(937\) | 31.9205 | 1.04280 | 0.521399 | − | 0.853313i | \(-0.325410\pi\) | ||||
0.521399 | + | 0.853313i | \(0.325410\pi\) | |||||||
\(938\) | −21.7966 | − | 25.7258i | −0.711685 | − | 0.839977i | ||||
\(939\) | 4.59186 | 0.149850 | ||||||||
\(940\) | 1.81228 | − | 3.13896i | 0.0591100 | − | 0.102381i | ||||
\(941\) | −26.0129 | − | 45.0557i | −0.847998 | − | 1.46878i | −0.882992 | − | 0.469388i | \(-0.844475\pi\) |
0.0349945 | − | 0.999388i | \(-0.488859\pi\) | |||||||
\(942\) | −1.34481 | − | 2.32927i | −0.0438162 | − | 0.0758919i | ||||
\(943\) | −0.951067 | + | 1.64730i | −0.0309710 | + | 0.0536434i | ||||
\(944\) | −2.29204 | −0.0745997 | ||||||||
\(945\) | −0.944901 | + | 0.171266i | −0.0307376 | + | 0.00557130i | ||||
\(946\) | 2.42288 | 0.0787745 | ||||||||
\(947\) | 12.2772 | − | 21.2647i | 0.398955 | − | 0.691011i | −0.594642 | − | 0.803990i | \(-0.702706\pi\) |
0.993597 | + | 0.112980i | \(0.0360396\pi\) | |||||||
\(948\) | 0.0656578 | + | 0.113723i | 0.00213247 | + | 0.00369354i | ||||
\(949\) | −18.8876 | − | 32.7143i | −0.613119 | − | 1.06195i | ||||
\(950\) | −0.865495 | + | 1.49908i | −0.0280804 | + | 0.0486366i | ||||
\(951\) | −3.80882 | −0.123510 | ||||||||
\(952\) | −4.11987 | + | 11.4896i | −0.133526 | + | 0.372381i | ||||
\(953\) | 37.5355 | 1.21589 | 0.607947 | − | 0.793977i | \(-0.291993\pi\) | ||||
0.607947 | + | 0.793977i | \(0.291993\pi\) | |||||||
\(954\) | 8.74217 | − | 15.1419i | 0.283038 | − | 0.490237i | ||||
\(955\) | −0.617675 | − | 1.06984i | −0.0199875 | − | 0.0346194i | ||||
\(956\) | −4.29706 | − | 7.44272i | −0.138977 | − | 0.240715i | ||||
\(957\) | 0.0634866 | − | 0.109962i | 0.00205223 | − | 0.00355457i | ||||
\(958\) | −8.09218 | −0.261447 | ||||||||
\(959\) | 8.24582 | − | 22.9962i | 0.266272 | − | 0.742585i | ||||
\(960\) | 0.0608874 | 0.00196513 | ||||||||
\(961\) | 11.1936 | − | 19.3878i | 0.361083 | − | 0.625413i | ||||
\(962\) | 20.0833 | + | 34.7853i | 0.647511 | + | 1.12152i | ||||
\(963\) | 21.1738 | + | 36.6741i | 0.682316 | + | 1.18181i | ||||
\(964\) | −4.69442 | + | 8.13098i | −0.151197 | + | 0.261881i | ||||
\(965\) | −0.140000 | −0.00450677 | ||||||||
\(966\) | 0.513186 | − | 0.0930165i | 0.0165115 | − | 0.00299276i | ||||
\(967\) | −25.6889 | −0.826100 | −0.413050 | − | 0.910708i | \(-0.635537\pi\) | ||||
−0.413050 | + | 0.910708i | \(0.635537\pi\) | |||||||
\(968\) | 5.43164 | − | 9.40787i | 0.174579 | − | 0.302380i | ||||
\(969\) | −0.160482 | − | 0.277964i | −0.00515544 | − | 0.00892948i | ||||
\(970\) | 0.766857 | + | 1.32823i | 0.0246223 | + | 0.0426471i | ||||
\(971\) | −26.4915 | + | 45.8847i | −0.850154 | + | 1.47251i | 0.0309157 | + | 0.999522i | \(0.490158\pi\) |
−0.881069 | + | 0.472987i | \(0.843176\pi\) | |||||||
\(972\) | −5.23079 | −0.167778 | ||||||||
\(973\) | 29.5782 | + | 34.9101i | 0.948233 | + | 1.11917i | ||||
\(974\) | 6.59563 | 0.211337 | ||||||||
\(975\) | −3.04375 | + | 5.27193i | −0.0974781 | + | 0.168837i | ||||
\(976\) | −3.39396 | − | 5.87851i | −0.108638 | − | 0.188167i | ||||
\(977\) | 25.6548 | + | 44.4355i | 0.820771 | + | 1.42162i | 0.905109 | + | 0.425180i | \(0.139789\pi\) |
−0.0843381 | + | 0.996437i | \(0.526878\pi\) | |||||||
\(978\) | −1.88598 | + | 3.26660i | −0.0603068 | + | 0.104454i | ||||
\(979\) | 4.29741 | 0.137346 | ||||||||
\(980\) | 0.355103 | − | 2.13276i | 0.0113434 | − | 0.0681287i | ||||
\(981\) | 44.7748 | 1.42955 | ||||||||
\(982\) | 6.35199 | − | 11.0020i | 0.202700 | − | 0.351087i | ||||
\(983\) | −0.842694 | − | 1.45959i | −0.0268778 | − | 0.0465536i | 0.852274 | − | 0.523096i | \(-0.175223\pi\) |
−0.879151 | + | 0.476543i | \(0.841890\pi\) | |||||||
\(984\) | −0.187480 | − | 0.324726i | −0.00597666 | − | 0.0103519i | ||||
\(985\) | −0.938337 | + | 1.62525i | −0.0298979 | + | 0.0517847i | ||||
\(986\) | 8.03649 | 0.255934 | ||||||||
\(987\) | 3.95632 | + | 4.66951i | 0.125931 | + | 0.148632i | ||||
\(988\) | −2.22220 | −0.0706975 | ||||||||
\(989\) | 3.27626 | − | 5.67465i | 0.104179 | − | 0.180443i | ||||
\(990\) | −0.169096 | − | 0.292884i | −0.00537424 | − | 0.00930845i | ||||
\(991\) | −9.49397 | − | 16.4440i | −0.301586 | − | 0.522362i | 0.674909 | − | 0.737901i | \(-0.264183\pi\) |
−0.976495 | + | 0.215539i | \(0.930849\pi\) | |||||||
\(992\) | −1.46739 | + | 2.54159i | −0.0465895 | + | 0.0806954i | ||||
\(993\) | 0.790111 | 0.0250734 | ||||||||
\(994\) | 1.28115 | − | 0.232212i | 0.0406355 | − | 0.00736532i | ||||
\(995\) | 8.00805 | 0.253872 | ||||||||
\(996\) | −0.635520 | + | 1.10075i | −0.0201372 | + | 0.0348787i | ||||
\(997\) | 24.5349 | + | 42.4957i | 0.777029 | + | 1.34585i | 0.933647 | + | 0.358194i | \(0.116607\pi\) |
−0.156619 | + | 0.987659i | \(0.550059\pi\) | |||||||
\(998\) | 3.34489 | + | 5.79352i | 0.105881 | + | 0.183391i | ||||
\(999\) | 3.74815 | − | 6.49199i | 0.118586 | − | 0.205397i |
(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 | 322.2.e.a.93.3 | ✓ | 8 | |
7.2 | even | 3 | 2254.2.a.z.1.2 | 4 | |||
7.4 | even | 3 | inner | 322.2.e.a.277.3 | yes | 8 | |
7.5 | odd | 6 | 2254.2.a.x.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.a.93.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
322.2.e.a.277.3 | yes | 8 | 7.4 | even | 3 | inner | |
2254.2.a.x.1.3 | 4 | 7.5 | odd | 6 | |||
2254.2.a.z.1.2 | 4 | 7.2 | even | 3 |