Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [670,2,Mod(171,670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(670, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("670.171");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 670 = 2 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 670.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: | \(5.34997693543\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 17 x^{10} - 18 x^{9} + 172 x^{8} - 170 x^{7} + 887 x^{6} - 312 x^{5} + 2516 x^{4} + \cdots + 289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 431.6 | ||
Root | \(-1.42828 - 2.47386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 670.431 |
Dual form | 670.2.e.j.171.6 |
$q$-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 \(\left(\mathbb{Z}/670\mathbb{Z}\right)^\times\).
\(n\) | \(471\) | \(537\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 2.85656 | 1.64924 | 0.824619 | − | 0.565688i | \(-0.191390\pi\) | ||||
0.824619 | + | 0.565688i | \(0.191390\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.42828 | − | 2.47386i | 0.583094 | − | 1.00995i | ||||
\(7\) | 2.24706 | + | 3.89203i | 0.849310 | + | 1.47105i | 0.881825 | + | 0.471576i | \(0.156315\pi\) |
−0.0325157 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.15996 | 1.71999 | ||||||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −1.57998 | − | 2.73660i | −0.476382 | − | 0.825117i | 0.523252 | − | 0.852178i | \(-0.324719\pi\) |
−0.999634 | + | 0.0270607i | \(0.991385\pi\) | |||||||
\(12\) | −1.42828 | − | 2.47386i | −0.412310 | − | 0.714141i | ||||
\(13\) | 0.503666 | − | 0.872375i | 0.139692 | − | 0.241953i | −0.787688 | − | 0.616074i | \(-0.788722\pi\) |
0.927380 | + | 0.374121i | \(0.122056\pi\) | |||||||
\(14\) | 4.49412 | 1.20111 | ||||||||
\(15\) | −2.85656 | −0.737562 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.38990 | − | 4.13942i | 0.579635 | − | 1.00396i | −0.415886 | − | 0.909417i | \(-0.636528\pi\) |
0.995521 | − | 0.0945409i | \(-0.0301383\pi\) | |||||||
\(18\) | 2.57998 | − | 4.46866i | 0.608107 | − | 1.05327i | ||||
\(19\) | 1.11836 | − | 1.93706i | 0.256570 | − | 0.444393i | −0.708751 | − | 0.705459i | \(-0.750741\pi\) |
0.965321 | + | 0.261067i | \(0.0840742\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 6.41888 | + | 11.1178i | 1.40071 | + | 2.42611i | ||||
\(22\) | −3.15996 | −0.673705 | ||||||||
\(23\) | −1.98966 | + | 3.44620i | −0.414874 | + | 0.718583i | −0.995415 | − | 0.0956482i | \(-0.969508\pi\) |
0.580541 | + | 0.814231i | \(0.302841\pi\) | |||||||
\(24\) | −2.85656 | −0.583094 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.503666 | − | 0.872375i | −0.0987770 | − | 0.171087i | ||||
\(27\) | 6.17006 | 1.18743 | ||||||||
\(28\) | 2.24706 | − | 3.89203i | 0.424655 | − | 0.735524i | ||||
\(29\) | 2.41428 | + | 4.18166i | 0.448321 | + | 0.776514i | 0.998277 | − | 0.0586792i | \(-0.0186889\pi\) |
−0.549956 | + | 0.835194i | \(0.685356\pi\) | |||||||
\(30\) | −1.42828 | + | 2.47386i | −0.260767 | + | 0.451662i | ||||
\(31\) | 3.72420 | + | 6.45050i | 0.668886 | + | 1.15854i | 0.978216 | + | 0.207590i | \(0.0665619\pi\) |
−0.309330 | + | 0.950955i | \(0.600105\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −4.51331 | − | 7.81729i | −0.785667 | − | 1.36081i | ||||
\(34\) | −2.38990 | − | 4.13942i | −0.409864 | − | 0.709905i | ||||
\(35\) | −2.24706 | − | 3.89203i | −0.379823 | − | 0.657872i | ||||
\(36\) | −2.57998 | − | 4.46866i | −0.429997 | − | 0.744776i | ||||
\(37\) | 0.280396 | − | 0.485660i | 0.0460968 | − | 0.0798419i | −0.842056 | − | 0.539389i | \(-0.818655\pi\) |
0.888153 | + | 0.459548i | \(0.151988\pi\) | |||||||
\(38\) | −1.11836 | − | 1.93706i | −0.181423 | − | 0.314233i | ||||
\(39\) | 1.43875 | − | 2.49199i | 0.230385 | − | 0.399038i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.45574 | − | 4.25347i | −0.383522 | − | 0.664280i | 0.608041 | − | 0.793906i | \(-0.291956\pi\) |
−0.991563 | + | 0.129626i | \(0.958622\pi\) | |||||||
\(42\) | 12.8378 | 1.98091 | ||||||||
\(43\) | −9.06529 | −1.38244 | −0.691222 | − | 0.722643i | \(-0.742927\pi\) | ||||
−0.691222 | + | 0.722643i | \(0.742927\pi\) | |||||||
\(44\) | −1.57998 | + | 2.73660i | −0.238191 | + | 0.412559i | ||||
\(45\) | −5.15996 | −0.769201 | ||||||||
\(46\) | 1.98966 | + | 3.44620i | 0.293360 | + | 0.508115i | ||||
\(47\) | −6.34989 | − | 10.9983i | −0.926227 | − | 1.60427i | −0.789575 | − | 0.613654i | \(-0.789699\pi\) |
−0.136652 | − | 0.990619i | \(-0.543634\pi\) | |||||||
\(48\) | −1.42828 | + | 2.47386i | −0.206155 | + | 0.357071i | ||||
\(49\) | −6.59858 | + | 11.4291i | −0.942654 | + | 1.63272i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 6.82690 | − | 11.8245i | 0.955957 | − | 1.65577i | ||||
\(52\) | −1.00733 | −0.139692 | ||||||||
\(53\) | −3.55346 | −0.488105 | −0.244053 | − | 0.969762i | \(-0.578477\pi\) | ||||
−0.244053 | + | 0.969762i | \(0.578477\pi\) | |||||||
\(54\) | 3.08503 | − | 5.34343i | 0.419819 | − | 0.727148i | ||||
\(55\) | 1.57998 | + | 2.73660i | 0.213044 | + | 0.369004i | ||||
\(56\) | −2.24706 | − | 3.89203i | −0.300276 | − | 0.520094i | ||||
\(57\) | 3.19468 | − | 5.53334i | 0.423145 | − | 0.732909i | ||||
\(58\) | 4.82856 | 0.634021 | ||||||||
\(59\) | −3.55022 | −0.462200 | −0.231100 | − | 0.972930i | \(-0.574232\pi\) | ||||
−0.231100 | + | 0.972930i | \(0.574232\pi\) | |||||||
\(60\) | 1.42828 | + | 2.47386i | 0.184390 | + | 0.319374i | ||||
\(61\) | −6.68053 | + | 11.5710i | −0.855354 | + | 1.48152i | 0.0209616 | + | 0.999780i | \(0.493327\pi\) |
−0.876316 | + | 0.481737i | \(0.840006\pi\) | |||||||
\(62\) | 7.44840 | 0.945948 | ||||||||
\(63\) | 11.5947 | + | 20.0827i | 1.46080 | + | 2.53018i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.503666 | + | 0.872375i | −0.0624720 | + | 0.108205i | ||||
\(66\) | −9.02662 | −1.11110 | ||||||||
\(67\) | 4.23827 | − | 7.00265i | 0.517787 | − | 0.855509i | ||||
\(68\) | −4.77980 | −0.579635 | ||||||||
\(69\) | −5.68361 | + | 9.84429i | −0.684226 | + | 1.18511i | ||||
\(70\) | −4.49412 | −0.537151 | ||||||||
\(71\) | −1.95128 | − | 3.37972i | −0.231574 | − | 0.401099i | 0.726697 | − | 0.686958i | \(-0.241054\pi\) |
−0.958272 | + | 0.285859i | \(0.907721\pi\) | |||||||
\(72\) | −5.15996 | −0.608107 | ||||||||
\(73\) | −6.32323 | + | 10.9522i | −0.740078 | + | 1.28185i | 0.212381 | + | 0.977187i | \(0.431878\pi\) |
−0.952459 | + | 0.304666i | \(0.901455\pi\) | |||||||
\(74\) | −0.280396 | − | 0.485660i | −0.0325953 | − | 0.0564568i | ||||
\(75\) | 2.85656 | 0.329848 | ||||||||
\(76\) | −2.23673 | −0.256570 | ||||||||
\(77\) | 7.10062 | − | 12.2986i | 0.809191 | − | 1.40156i | ||||
\(78\) | −1.43875 | − | 2.49199i | −0.162907 | − | 0.282163i | ||||
\(79\) | −6.08596 | − | 10.5412i | −0.684724 | − | 1.18598i | −0.973523 | − | 0.228587i | \(-0.926589\pi\) |
0.288800 | − | 0.957390i | \(-0.406744\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 2.14530 | 0.238366 | ||||||||
\(82\) | −4.91148 | −0.542382 | ||||||||
\(83\) | −6.82278 | + | 11.8174i | −0.748897 | + | 1.29713i | 0.199455 | + | 0.979907i | \(0.436083\pi\) |
−0.948352 | + | 0.317220i | \(0.897250\pi\) | |||||||
\(84\) | 6.41888 | − | 11.1178i | 0.700357 | − | 1.21305i | ||||
\(85\) | −2.38990 | + | 4.13942i | −0.259221 | + | 0.448984i | ||||
\(86\) | −4.53264 | + | 7.85077i | −0.488768 | + | 0.846570i | ||||
\(87\) | 6.89655 | + | 11.9452i | 0.739388 | + | 1.28066i | ||||
\(88\) | 1.57998 | + | 2.73660i | 0.168426 | + | 0.291723i | ||||
\(89\) | −3.52240 | −0.373373 | −0.186687 | − | 0.982419i | \(-0.559775\pi\) | ||||
−0.186687 | + | 0.982419i | \(0.559775\pi\) | |||||||
\(90\) | −2.57998 | + | 4.46866i | −0.271954 | + | 0.471038i | ||||
\(91\) | 4.52707 | 0.474566 | ||||||||
\(92\) | 3.97933 | 0.414874 | ||||||||
\(93\) | 10.6384 | + | 18.4263i | 1.10315 | + | 1.91072i | ||||
\(94\) | −12.6998 | −1.30988 | ||||||||
\(95\) | −1.11836 | + | 1.93706i | −0.114742 | + | 0.198738i | ||||
\(96\) | 1.42828 | + | 2.47386i | 0.145773 | + | 0.252487i | ||||
\(97\) | 0.642699 | − | 1.11319i | 0.0652562 | − | 0.113027i | −0.831551 | − | 0.555448i | \(-0.812547\pi\) |
0.896808 | + | 0.442421i | \(0.145880\pi\) | |||||||
\(98\) | 6.59858 | + | 11.4291i | 0.666557 | + | 1.15451i | ||||
\(99\) | −8.15263 | − | 14.1208i | −0.819370 | − | 1.41919i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.72580 | − | 6.45328i | −0.370731 | − | 0.642125i | 0.618947 | − | 0.785433i | \(-0.287559\pi\) |
−0.989678 | + | 0.143308i | \(0.954226\pi\) | |||||||
\(102\) | −6.82690 | − | 11.8245i | −0.675963 | − | 1.17080i | ||||
\(103\) | −4.74340 | − | 8.21580i | −0.467381 | − | 0.809527i | 0.531925 | − | 0.846792i | \(-0.321469\pi\) |
−0.999305 | + | 0.0372645i | \(0.988136\pi\) | |||||||
\(104\) | −0.503666 | + | 0.872375i | −0.0493885 | + | 0.0855434i | ||||
\(105\) | −6.41888 | − | 11.1178i | −0.626418 | − | 1.08499i | ||||
\(106\) | −1.77673 | + | 3.07739i | −0.172571 | + | 0.298902i | ||||
\(107\) | 9.34497 | 0.903412 | 0.451706 | − | 0.892167i | \(-0.350816\pi\) | ||||
0.451706 | + | 0.892167i | \(0.350816\pi\) | |||||||
\(108\) | −3.08503 | − | 5.34343i | −0.296857 | − | 0.514172i | ||||
\(109\) | 13.3672 | 1.28035 | 0.640173 | − | 0.768231i | \(-0.278863\pi\) | ||||
0.640173 | + | 0.768231i | \(0.278863\pi\) | |||||||
\(110\) | 3.15996 | 0.301290 | ||||||||
\(111\) | 0.800968 | − | 1.38732i | 0.0760245 | − | 0.131678i | ||||
\(112\) | −4.49412 | −0.424655 | ||||||||
\(113\) | 3.75547 | + | 6.50466i | 0.353285 | + | 0.611907i | 0.986823 | − | 0.161804i | \(-0.0517314\pi\) |
−0.633538 | + | 0.773711i | \(0.718398\pi\) | |||||||
\(114\) | −3.19468 | − | 5.53334i | −0.299209 | − | 0.518245i | ||||
\(115\) | 1.98966 | − | 3.44620i | 0.185537 | − | 0.321360i | ||||
\(116\) | 2.41428 | − | 4.18166i | 0.224160 | − | 0.388257i | ||||
\(117\) | 2.59889 | − | 4.50142i | 0.240268 | − | 0.416156i | ||||
\(118\) | −1.77511 | + | 3.07458i | −0.163412 | + | 0.283038i | ||||
\(119\) | 21.4810 | 1.96916 | ||||||||
\(120\) | 2.85656 | 0.260767 | ||||||||
\(121\) | 0.507331 | − | 0.878724i | 0.0461210 | − | 0.0798840i | ||||
\(122\) | 6.68053 | + | 11.5710i | 0.604827 | + | 1.04759i | ||||
\(123\) | −7.01498 | − | 12.1503i | −0.632519 | − | 1.09556i | ||||
\(124\) | 3.72420 | − | 6.45050i | 0.334443 | − | 0.579272i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 23.1895 | 2.06588 | ||||||||
\(127\) | −0.0732391 | − | 0.126854i | −0.00649892 | − | 0.0112565i | 0.862758 | − | 0.505618i | \(-0.168735\pi\) |
−0.869257 | + | 0.494361i | \(0.835402\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −25.8956 | −2.27998 | ||||||||
\(130\) | 0.503666 | + | 0.872375i | 0.0441744 | + | 0.0765123i | ||||
\(131\) | 11.0212 | 0.962922 | 0.481461 | − | 0.876467i | \(-0.340106\pi\) | ||||
0.481461 | + | 0.876467i | \(0.340106\pi\) | |||||||
\(132\) | −4.51331 | + | 7.81729i | −0.392833 | + | 0.680407i | ||||
\(133\) | 10.0521 | 0.871630 | ||||||||
\(134\) | −3.94533 | − | 7.17177i | −0.340825 | − | 0.619547i | ||||
\(135\) | −6.17006 | −0.531034 | ||||||||
\(136\) | −2.38990 | + | 4.13942i | −0.204932 | + | 0.354953i | ||||
\(137\) | −14.8683 | −1.27028 | −0.635141 | − | 0.772396i | \(-0.719058\pi\) | ||||
−0.635141 | + | 0.772396i | \(0.719058\pi\) | |||||||
\(138\) | 5.68361 | + | 9.84429i | 0.483821 | + | 0.838002i | ||||
\(139\) | 6.42920 | 0.545318 | 0.272659 | − | 0.962111i | \(-0.412097\pi\) | ||||
0.272659 | + | 0.962111i | \(0.412097\pi\) | |||||||
\(140\) | −2.24706 | + | 3.89203i | −0.189911 | + | 0.328936i | ||||
\(141\) | −18.1389 | − | 31.4175i | −1.52757 | − | 2.64583i | ||||
\(142\) | −3.90256 | −0.327496 | ||||||||
\(143\) | −3.18313 | −0.266186 | ||||||||
\(144\) | −2.57998 | + | 4.46866i | −0.214998 | + | 0.372388i | ||||
\(145\) | −2.41428 | − | 4.18166i | −0.200495 | − | 0.347268i | ||||
\(146\) | 6.32323 | + | 10.9522i | 0.523314 | + | 0.906407i | ||||
\(147\) | −18.8493 | + | 32.6479i | −1.55466 | + | 2.69275i | ||||
\(148\) | −0.560791 | −0.0460968 | ||||||||
\(149\) | 14.1698 | 1.16083 | 0.580417 | − | 0.814319i | \(-0.302890\pi\) | ||||
0.580417 | + | 0.814319i | \(0.302890\pi\) | |||||||
\(150\) | 1.42828 | − | 2.47386i | 0.116619 | − | 0.201990i | ||||
\(151\) | −3.43807 | + | 5.95492i | −0.279786 | + | 0.484604i | −0.971332 | − | 0.237729i | \(-0.923597\pi\) |
0.691545 | + | 0.722333i | \(0.256930\pi\) | |||||||
\(152\) | −1.11836 | + | 1.93706i | −0.0907113 | + | 0.157117i | ||||
\(153\) | 12.3318 | − | 21.3593i | 0.996965 | − | 1.72679i | ||||
\(154\) | −7.10062 | − | 12.2986i | −0.572184 | − | 0.991053i | ||||
\(155\) | −3.72420 | − | 6.45050i | −0.299135 | − | 0.518117i | ||||
\(156\) | −2.87751 | −0.230385 | ||||||||
\(157\) | 10.0454 | − | 17.3991i | 0.801707 | − | 1.38860i | −0.116785 | − | 0.993157i | \(-0.537259\pi\) |
0.918492 | − | 0.395440i | \(-0.129408\pi\) | |||||||
\(158\) | −12.1719 | −0.968346 | ||||||||
\(159\) | −10.1507 | −0.805002 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −17.8836 | −1.40943 | ||||||||
\(162\) | 1.07265 | − | 1.85788i | 0.0842752 | − | 0.145969i | ||||
\(163\) | 2.03273 | + | 3.52080i | 0.159216 | + | 0.275770i | 0.934586 | − | 0.355737i | \(-0.115770\pi\) |
−0.775370 | + | 0.631507i | \(0.782437\pi\) | |||||||
\(164\) | −2.45574 | + | 4.25347i | −0.191761 | + | 0.332140i | ||||
\(165\) | 4.51331 | + | 7.81729i | 0.351361 | + | 0.608575i | ||||
\(166\) | 6.82278 | + | 11.8174i | 0.529550 | + | 0.917208i | ||||
\(167\) | 8.13469 | + | 14.0897i | 0.629481 | + | 1.09029i | 0.987656 | + | 0.156639i | \(0.0500660\pi\) |
−0.358174 | + | 0.933655i | \(0.616601\pi\) | |||||||
\(168\) | −6.41888 | − | 11.1178i | −0.495227 | − | 0.857758i | ||||
\(169\) | 5.99264 | + | 10.3796i | 0.460972 | + | 0.798428i | ||||
\(170\) | 2.38990 | + | 4.13942i | 0.183297 | + | 0.317479i | ||||
\(171\) | 5.77071 | − | 9.99516i | 0.441297 | − | 0.764349i | ||||
\(172\) | 4.53264 | + | 7.85077i | 0.345611 | + | 0.598616i | ||||
\(173\) | 7.64982 | − | 13.2499i | 0.581605 | − | 1.00737i | −0.413685 | − | 0.910420i | \(-0.635758\pi\) |
0.995289 | − | 0.0969488i | \(-0.0309083\pi\) | |||||||
\(174\) | 13.7931 | 1.04565 | ||||||||
\(175\) | 2.24706 | + | 3.89203i | 0.169862 | + | 0.294209i | ||||
\(176\) | 3.15996 | 0.238191 | ||||||||
\(177\) | −10.1414 | −0.762277 | ||||||||
\(178\) | −1.76120 | + | 3.05049i | −0.132007 | + | 0.228644i | ||||
\(179\) | −0.218731 | −0.0163488 | −0.00817438 | − | 0.999967i | \(-0.502602\pi\) | ||||
−0.00817438 | + | 0.999967i | \(0.502602\pi\) | |||||||
\(180\) | 2.57998 | + | 4.46866i | 0.192300 | + | 0.333074i | ||||
\(181\) | 11.3277 | + | 19.6202i | 0.841984 | + | 1.45836i | 0.888215 | + | 0.459428i | \(0.151946\pi\) |
−0.0462307 | + | 0.998931i | \(0.514721\pi\) | |||||||
\(182\) | 2.26354 | − | 3.92056i | 0.167784 | − | 0.290611i | ||||
\(183\) | −19.0834 | + | 33.0534i | −1.41068 | + | 2.44337i | ||||
\(184\) | 1.98966 | − | 3.44620i | 0.146680 | − | 0.254057i | ||||
\(185\) | −0.280396 | + | 0.485660i | −0.0206151 | + | 0.0357064i | ||||
\(186\) | 21.2768 | 1.56009 | ||||||||
\(187\) | −15.1040 | −1.10451 | ||||||||
\(188\) | −6.34989 | + | 10.9983i | −0.463114 | + | 0.802136i | ||||
\(189\) | 13.8645 | + | 24.0140i | 1.00849 | + | 1.74676i | ||||
\(190\) | 1.11836 | + | 1.93706i | 0.0811346 | + | 0.140529i | ||||
\(191\) | −0.588841 | + | 1.01990i | −0.0426070 | + | 0.0737975i | −0.886542 | − | 0.462647i | \(-0.846900\pi\) |
0.843935 | + | 0.536445i | \(0.180233\pi\) | |||||||
\(192\) | 2.85656 | 0.206155 | ||||||||
\(193\) | −8.71036 | −0.626985 | −0.313493 | − | 0.949591i | \(-0.601499\pi\) | ||||
−0.313493 | + | 0.949591i | \(0.601499\pi\) | |||||||
\(194\) | −0.642699 | − | 1.11319i | −0.0461431 | − | 0.0799222i | ||||
\(195\) | −1.43875 | + | 2.49199i | −0.103031 | + | 0.178455i | ||||
\(196\) | 13.1972 | 0.942654 | ||||||||
\(197\) | 8.00919 | + | 13.8723i | 0.570631 | + | 0.988362i | 0.996501 | + | 0.0835779i | \(0.0266348\pi\) |
−0.425870 | + | 0.904784i | \(0.640032\pi\) | |||||||
\(198\) | −16.3053 | −1.15876 | ||||||||
\(199\) | −6.98114 | + | 12.0917i | −0.494880 | + | 0.857157i | −0.999983 | − | 0.00590199i | \(-0.998121\pi\) |
0.505103 | + | 0.863059i | \(0.331455\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 12.1069 | − | 20.0035i | 0.853954 | − | 1.41094i | ||||
\(202\) | −7.45160 | −0.524293 | ||||||||
\(203\) | −10.8501 | + | 18.7929i | −0.761526 | + | 1.31900i | ||||
\(204\) | −13.6538 | −0.955957 | ||||||||
\(205\) | 2.45574 | + | 4.25347i | 0.171516 | + | 0.297075i | ||||
\(206\) | −9.48679 | −0.660976 | ||||||||
\(207\) | −10.2666 | + | 17.7823i | −0.713577 | + | 1.23595i | ||||
\(208\) | 0.503666 | + | 0.872375i | 0.0349229 | + | 0.0604883i | ||||
\(209\) | −7.06796 | −0.488901 | ||||||||
\(210\) | −12.8378 | −0.885889 | ||||||||
\(211\) | 8.38955 | − | 14.5311i | 0.577560 | − | 1.00036i | −0.418198 | − | 0.908356i | \(-0.637338\pi\) |
0.995758 | − | 0.0920078i | \(-0.0293285\pi\) | |||||||
\(212\) | 1.77673 | + | 3.07739i | 0.122026 | + | 0.211356i | ||||
\(213\) | −5.57396 | − | 9.65438i | −0.381921 | − | 0.661507i | ||||
\(214\) | 4.67249 | − | 8.09298i | 0.319405 | − | 0.553225i | ||||
\(215\) | 9.06529 | 0.618248 | ||||||||
\(216\) | −6.17006 | −0.419819 | ||||||||
\(217\) | −16.7370 | + | 28.9894i | −1.13618 | + | 1.96793i | ||||
\(218\) | 6.68361 | − | 11.5763i | 0.452671 | − | 0.784049i | ||||
\(219\) | −18.0627 | + | 31.2855i | −1.22057 | + | 2.11408i | ||||
\(220\) | 1.57998 | − | 2.73660i | 0.106522 | − | 0.184502i | ||||
\(221\) | −2.40742 | − | 4.16977i | −0.161941 | − | 0.280489i | ||||
\(222\) | −0.800968 | − | 1.38732i | −0.0537575 | − | 0.0931107i | ||||
\(223\) | −16.4544 | −1.10187 | −0.550933 | − | 0.834549i | \(-0.685728\pi\) | ||||
−0.550933 | + | 0.834549i | \(0.685728\pi\) | |||||||
\(224\) | −2.24706 | + | 3.89203i | −0.150138 | + | 0.260047i | ||||
\(225\) | 5.15996 | 0.343997 | ||||||||
\(226\) | 7.51094 | 0.499620 | ||||||||
\(227\) | −5.76358 | − | 9.98282i | −0.382543 | − | 0.662583i | 0.608882 | − | 0.793260i | \(-0.291618\pi\) |
−0.991425 | + | 0.130677i | \(0.958285\pi\) | |||||||
\(228\) | −6.38935 | −0.423145 | ||||||||
\(229\) | 14.1846 | − | 24.5685i | 0.937345 | − | 1.62353i | 0.166947 | − | 0.985966i | \(-0.446609\pi\) |
0.770398 | − | 0.637564i | \(-0.220058\pi\) | |||||||
\(230\) | −1.98966 | − | 3.44620i | −0.131195 | − | 0.227236i | ||||
\(231\) | 20.2834 | − | 35.1319i | 1.33455 | − | 2.31151i | ||||
\(232\) | −2.41428 | − | 4.18166i | −0.158505 | − | 0.274539i | ||||
\(233\) | −1.39110 | − | 2.40945i | −0.0911339 | − | 0.157848i | 0.816855 | − | 0.576844i | \(-0.195716\pi\) |
−0.907989 | + | 0.418995i | \(0.862382\pi\) | |||||||
\(234\) | −2.59889 | − | 4.50142i | −0.169895 | − | 0.294267i | ||||
\(235\) | 6.34989 | + | 10.9983i | 0.414221 | + | 0.717453i | ||||
\(236\) | 1.77511 | + | 3.07458i | 0.115550 | + | 0.200138i | ||||
\(237\) | −17.3849 | − | 30.1116i | −1.12927 | − | 1.95596i | ||||
\(238\) | 10.7405 | − | 18.6031i | 0.696203 | − | 1.20586i | ||||
\(239\) | −12.1378 | − | 21.0233i | −0.785130 | − | 1.35989i | −0.928921 | − | 0.370277i | \(-0.879263\pi\) |
0.143791 | − | 0.989608i | \(-0.454071\pi\) | |||||||
\(240\) | 1.42828 | − | 2.47386i | 0.0921952 | − | 0.159687i | ||||
\(241\) | 6.93147 | 0.446495 | 0.223248 | − | 0.974762i | \(-0.428334\pi\) | ||||
0.223248 | + | 0.974762i | \(0.428334\pi\) | |||||||
\(242\) | −0.507331 | − | 0.878724i | −0.0326125 | − | 0.0564865i | ||||
\(243\) | −12.3820 | −0.794306 | ||||||||
\(244\) | 13.3611 | 0.855354 | ||||||||
\(245\) | 6.59858 | − | 11.4291i | 0.421568 | − | 0.730176i | ||||
\(246\) | −14.0300 | −0.894517 | ||||||||
\(247\) | −1.12656 | − | 1.95126i | −0.0716815 | − | 0.124156i | ||||
\(248\) | −3.72420 | − | 6.45050i | −0.236487 | − | 0.409607i | ||||
\(249\) | −19.4897 | + | 33.7571i | −1.23511 | + | 2.13927i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 5.02058 | − | 8.69590i | 0.316896 | − | 0.548880i | −0.662942 | − | 0.748670i | \(-0.730693\pi\) |
0.979839 | + | 0.199790i | \(0.0640260\pi\) | |||||||
\(252\) | 11.5947 | − | 20.0827i | 0.730400 | − | 1.26509i | ||||
\(253\) | 12.5745 | 0.790553 | ||||||||
\(254\) | −0.146478 | −0.00919086 | ||||||||
\(255\) | −6.82690 | + | 11.8245i | −0.427517 | + | 0.740481i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 9.76190 | + | 16.9081i | 0.608930 | + | 1.05470i | 0.991417 | + | 0.130737i | \(0.0417344\pi\) |
−0.382487 | + | 0.923961i | \(0.624932\pi\) | |||||||
\(258\) | −12.9478 | + | 22.4262i | −0.806094 | + | 1.39620i | ||||
\(259\) | 2.52027 | 0.156602 | ||||||||
\(260\) | 1.00733 | 0.0624720 | ||||||||
\(261\) | 12.4576 | + | 21.5772i | 0.771105 | + | 1.33559i | ||||
\(262\) | 5.51058 | − | 9.54460i | 0.340445 | − | 0.589667i | ||||
\(263\) | 2.78647 | 0.171821 | 0.0859105 | − | 0.996303i | \(-0.472620\pi\) | ||||
0.0859105 | + | 0.996303i | \(0.472620\pi\) | |||||||
\(264\) | 4.51331 | + | 7.81729i | 0.277775 | + | 0.481121i | ||||
\(265\) | 3.55346 | 0.218287 | ||||||||
\(266\) | 5.02606 | − | 8.70540i | 0.308168 | − | 0.533762i | ||||
\(267\) | −10.0620 | −0.615782 | ||||||||
\(268\) | −8.18361 | − | 0.169127i | −0.499893 | − | 0.0103311i | ||||
\(269\) | 24.1857 | 1.47463 | 0.737313 | − | 0.675551i | \(-0.236094\pi\) | ||||
0.737313 | + | 0.675551i | \(0.236094\pi\) | |||||||
\(270\) | −3.08503 | + | 5.34343i | −0.187749 | + | 0.325191i | ||||
\(271\) | −27.6341 | −1.67865 | −0.839325 | − | 0.543630i | \(-0.817050\pi\) | ||||
−0.839325 | + | 0.543630i | \(0.817050\pi\) | |||||||
\(272\) | 2.38990 | + | 4.13942i | 0.144909 | + | 0.250989i | ||||
\(273\) | 12.9319 | 0.782673 | ||||||||
\(274\) | −7.43414 | + | 12.8763i | −0.449113 | + | 0.777886i | ||||
\(275\) | −1.57998 | − | 2.73660i | −0.0952763 | − | 0.165023i | ||||
\(276\) | 11.3672 | 0.684226 | ||||||||
\(277\) | 27.2038 | 1.63452 | 0.817258 | − | 0.576272i | \(-0.195493\pi\) | ||||
0.817258 | + | 0.576272i | \(0.195493\pi\) | |||||||
\(278\) | 3.21460 | − | 5.56785i | 0.192799 | − | 0.333938i | ||||
\(279\) | 19.2167 | + | 33.2843i | 1.15047 | + | 1.99268i | ||||
\(280\) | 2.24706 | + | 3.89203i | 0.134288 | + | 0.232593i | ||||
\(281\) | 15.4913 | − | 26.8317i | 0.924133 | − | 1.60065i | 0.131183 | − | 0.991358i | \(-0.458122\pi\) |
0.792950 | − | 0.609287i | \(-0.208544\pi\) | |||||||
\(282\) | −36.2778 | −2.16031 | ||||||||
\(283\) | −4.86433 | −0.289154 | −0.144577 | − | 0.989494i | \(-0.546182\pi\) | ||||
−0.144577 | + | 0.989494i | \(0.546182\pi\) | |||||||
\(284\) | −1.95128 | + | 3.37972i | −0.115787 | + | 0.200549i | ||||
\(285\) | −3.19468 | + | 5.53334i | −0.189236 | + | 0.327767i | ||||
\(286\) | −1.59156 | + | 2.75667i | −0.0941111 | + | 0.163005i | ||||
\(287\) | 11.0364 | − | 19.1156i | 0.651458 | − | 1.12836i | ||||
\(288\) | 2.57998 | + | 4.46866i | 0.152027 | + | 0.263318i | ||||
\(289\) | −2.92322 | − | 5.06317i | −0.171954 | − | 0.297834i | ||||
\(290\) | −4.82856 | −0.283543 | ||||||||
\(291\) | 1.83591 | − | 3.17989i | 0.107623 | − | 0.186409i | ||||
\(292\) | 12.6465 | 0.740078 | ||||||||
\(293\) | 7.34574 | 0.429143 | 0.214571 | − | 0.976708i | \(-0.431165\pi\) | ||||
0.214571 | + | 0.976708i | \(0.431165\pi\) | |||||||
\(294\) | 18.8493 | + | 32.6479i | 1.09931 | + | 1.90406i | ||||
\(295\) | 3.55022 | 0.206702 | ||||||||
\(296\) | −0.280396 | + | 0.485660i | −0.0162977 | + | 0.0282284i | ||||
\(297\) | −9.74857 | − | 16.8850i | −0.565669 | − | 0.979768i | ||||
\(298\) | 7.08489 | − | 12.2714i | 0.410417 | − | 0.710863i | ||||
\(299\) | 2.00425 | + | 3.47147i | 0.115909 | + | 0.200760i | ||||
\(300\) | −1.42828 | − | 2.47386i | −0.0824619 | − | 0.142828i | ||||
\(301\) | −20.3703 | − | 35.2823i | −1.17412 | − | 2.03364i | ||||
\(302\) | 3.43807 | + | 5.95492i | 0.197839 | + | 0.342667i | ||||
\(303\) | −10.6430 | − | 18.4342i | −0.611424 | − | 1.05902i | ||||
\(304\) | 1.11836 | + | 1.93706i | 0.0641425 | + | 0.111098i | ||||
\(305\) | 6.68053 | − | 11.5710i | 0.382526 | − | 0.662555i | ||||
\(306\) | −12.3318 | − | 21.3593i | −0.704961 | − | 1.22103i | ||||
\(307\) | −3.21456 | + | 5.56779i | −0.183465 | + | 0.317770i | −0.943058 | − | 0.332628i | \(-0.892065\pi\) |
0.759593 | + | 0.650398i | \(0.225398\pi\) | |||||||
\(308\) | −14.2012 | −0.809191 | ||||||||
\(309\) | −13.5498 | − | 23.4690i | −0.770822 | − | 1.33510i | ||||
\(310\) | −7.44840 | −0.423041 | ||||||||
\(311\) | 22.7484 | 1.28994 | 0.644970 | − | 0.764208i | \(-0.276870\pi\) | ||||
0.644970 | + | 0.764208i | \(0.276870\pi\) | |||||||
\(312\) | −1.43875 | + | 2.49199i | −0.0814534 | + | 0.141081i | ||||
\(313\) | −10.4667 | −0.591611 | −0.295806 | − | 0.955248i | \(-0.595588\pi\) | ||||
−0.295806 | + | 0.955248i | \(0.595588\pi\) | |||||||
\(314\) | −10.0454 | − | 17.3991i | −0.566892 | − | 0.981886i | ||||
\(315\) | −11.5947 | − | 20.0827i | −0.653290 | − | 1.13153i | ||||
\(316\) | −6.08596 | + | 10.5412i | −0.342362 | + | 0.592988i | ||||
\(317\) | −16.6592 | + | 28.8545i | −0.935673 | + | 1.62063i | −0.162243 | + | 0.986751i | \(0.551873\pi\) |
−0.773430 | + | 0.633882i | \(0.781460\pi\) | |||||||
\(318\) | −5.07534 | + | 8.79075i | −0.284611 | + | 0.492961i | ||||
\(319\) | 7.62903 | − | 13.2139i | 0.427144 | − | 0.739834i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 26.6945 | 1.48994 | ||||||||
\(322\) | −8.94180 | + | 15.4877i | −0.498307 | + | 0.863093i | ||||
\(323\) | −5.34555 | − | 9.25876i | −0.297434 | − | 0.515171i | ||||
\(324\) | −1.07265 | − | 1.85788i | −0.0595915 | − | 0.103216i | ||||
\(325\) | 0.503666 | − | 0.872375i | 0.0279383 | − | 0.0483906i | ||||
\(326\) | 4.06547 | 0.225165 | ||||||||
\(327\) | 38.1843 | 2.11160 | ||||||||
\(328\) | 2.45574 | + | 4.25347i | 0.135596 | + | 0.234858i | ||||
\(329\) | 28.5372 | − | 49.4279i | 1.57331 | − | 2.72505i | ||||
\(330\) | 9.02662 | 0.496899 | ||||||||
\(331\) | 10.8376 | + | 18.7713i | 0.595691 | + | 1.03177i | 0.993449 | + | 0.114276i | \(0.0364549\pi\) |
−0.397758 | + | 0.917490i | \(0.630212\pi\) | |||||||
\(332\) | 13.6456 | 0.748897 | ||||||||
\(333\) | 1.44683 | − | 2.50598i | 0.0792858 | − | 0.137327i | ||||
\(334\) | 16.2694 | 0.890221 | ||||||||
\(335\) | −4.23827 | + | 7.00265i | −0.231561 | + | 0.382595i | ||||
\(336\) | −12.8378 | −0.700357 | ||||||||
\(337\) | 11.0932 | − | 19.2140i | 0.604286 | − | 1.04665i | −0.387878 | − | 0.921711i | \(-0.626792\pi\) |
0.992164 | − | 0.124944i | \(-0.0398750\pi\) | |||||||
\(338\) | 11.9853 | 0.651913 | ||||||||
\(339\) | 10.7277 | + | 18.5810i | 0.582651 | + | 1.00918i | ||||
\(340\) | 4.77980 | 0.259221 | ||||||||
\(341\) | 11.7683 | − | 20.3833i | 0.637290 | − | 1.10382i | ||||
\(342\) | −5.77071 | − | 9.99516i | −0.312044 | − | 0.540476i | ||||
\(343\) | −27.8508 | −1.50380 | ||||||||
\(344\) | 9.06529 | 0.488768 | ||||||||
\(345\) | 5.68361 | − | 9.84429i | 0.305995 | − | 0.529999i | ||||
\(346\) | −7.64982 | − | 13.2499i | −0.411257 | − | 0.712317i | ||||
\(347\) | −8.82651 | − | 15.2880i | −0.473832 | − | 0.820701i | 0.525719 | − | 0.850658i | \(-0.323796\pi\) |
−0.999551 | + | 0.0299571i | \(0.990463\pi\) | |||||||
\(348\) | 6.89655 | − | 11.9452i | 0.369694 | − | 0.640328i | ||||
\(349\) | −23.0772 | −1.23530 | −0.617648 | − | 0.786455i | \(-0.711914\pi\) | ||||
−0.617648 | + | 0.786455i | \(0.711914\pi\) | |||||||
\(350\) | 4.49412 | 0.240221 | ||||||||
\(351\) | 3.10765 | − | 5.38260i | 0.165874 | − | 0.287302i | ||||
\(352\) | 1.57998 | − | 2.73660i | 0.0842132 | − | 0.145861i | ||||
\(353\) | 13.5950 | − | 23.5472i | 0.723587 | − | 1.25329i | −0.235967 | − | 0.971761i | \(-0.575826\pi\) |
0.959553 | − | 0.281528i | \(-0.0908411\pi\) | |||||||
\(354\) | −5.07072 | + | 8.78274i | −0.269506 | + | 0.466798i | ||||
\(355\) | 1.95128 | + | 3.37972i | 0.103563 | + | 0.179377i | ||||
\(356\) | 1.76120 | + | 3.05049i | 0.0933434 | + | 0.161675i | ||||
\(357\) | 61.3618 | 3.24761 | ||||||||
\(358\) | −0.109366 | + | 0.189427i | −0.00578016 | + | 0.0100115i | ||||
\(359\) | −26.9813 | −1.42402 | −0.712010 | − | 0.702170i | \(-0.752215\pi\) | ||||
−0.712010 | + | 0.702170i | \(0.752215\pi\) | |||||||
\(360\) | 5.15996 | 0.271954 | ||||||||
\(361\) | 6.99853 | + | 12.1218i | 0.368343 | + | 0.637990i | ||||
\(362\) | 22.6555 | 1.19075 | ||||||||
\(363\) | 1.44922 | − | 2.51013i | 0.0760646 | − | 0.131748i | ||||
\(364\) | −2.26354 | − | 3.92056i | −0.118642 | − | 0.205493i | ||||
\(365\) | 6.32323 | − | 10.9522i | 0.330973 | − | 0.573262i | ||||
\(366\) | 19.0834 | + | 33.0534i | 0.997503 | + | 1.72773i | ||||
\(367\) | 13.3557 | + | 23.1327i | 0.697161 | + | 1.20752i | 0.969447 | + | 0.245301i | \(0.0788869\pi\) |
−0.272286 | + | 0.962216i | \(0.587780\pi\) | |||||||
\(368\) | −1.98966 | − | 3.44620i | −0.103718 | − | 0.179646i | ||||
\(369\) | −12.6715 | − | 21.9477i | −0.659653 | − | 1.14255i | ||||
\(370\) | 0.280396 | + | 0.485660i | 0.0145771 | + | 0.0252482i | ||||
\(371\) | −7.98484 | − | 13.8302i | −0.414552 | − | 0.718026i | ||||
\(372\) | 10.6384 | − | 18.4263i | 0.551576 | − | 0.955358i | ||||
\(373\) | −2.35596 | − | 4.08065i | −0.121987 | − | 0.211288i | 0.798564 | − | 0.601910i | \(-0.205593\pi\) |
−0.920551 | + | 0.390622i | \(0.872260\pi\) | |||||||
\(374\) | −7.55198 | + | 13.0804i | −0.390503 | + | 0.676372i | ||||
\(375\) | −2.85656 | −0.147512 | ||||||||
\(376\) | 6.34989 | + | 10.9983i | 0.327471 | + | 0.567196i | ||||
\(377\) | 4.86396 | 0.250507 | ||||||||
\(378\) | 27.7290 | 1.42623 | ||||||||
\(379\) | 9.10210 | − | 15.7653i | 0.467544 | − | 0.809809i | −0.531769 | − | 0.846890i | \(-0.678472\pi\) |
0.999312 | + | 0.0370802i | \(0.0118057\pi\) | |||||||
\(380\) | 2.23673 | 0.114742 | ||||||||
\(381\) | −0.209212 | − | 0.362366i | −0.0107183 | − | 0.0185646i | ||||
\(382\) | 0.588841 | + | 1.01990i | 0.0301277 | + | 0.0521827i | ||||
\(383\) | −3.84384 | + | 6.65773i | −0.196411 | + | 0.340194i | −0.947362 | − | 0.320164i | \(-0.896262\pi\) |
0.750951 | + | 0.660358i | \(0.229595\pi\) | |||||||
\(384\) | 1.42828 | − | 2.47386i | 0.0728867 | − | 0.126243i | ||||
\(385\) | −7.10062 | + | 12.2986i | −0.361881 | + | 0.626797i | ||||
\(386\) | −4.35518 | + | 7.54339i | −0.221673 | + | 0.383949i | ||||
\(387\) | −46.7765 | −2.37778 | ||||||||
\(388\) | −1.28540 | −0.0652562 | ||||||||
\(389\) | −9.94332 | + | 17.2223i | −0.504146 | + | 0.873207i | 0.495842 | + | 0.868413i | \(0.334859\pi\) |
−0.999989 | + | 0.00479424i | \(0.998474\pi\) | |||||||
\(390\) | 1.43875 | + | 2.49199i | 0.0728541 | + | 0.126187i | ||||
\(391\) | 9.51019 | + | 16.4721i | 0.480951 | + | 0.833032i | ||||
\(392\) | 6.59858 | − | 11.4291i | 0.333278 | − | 0.577255i | ||||
\(393\) | 31.4826 | 1.58809 | ||||||||
\(394\) | 16.0184 | 0.806994 | ||||||||
\(395\) | 6.08596 | + | 10.5412i | 0.306218 | + | 0.530385i | ||||
\(396\) | −8.15263 | + | 14.1208i | −0.409685 | + | 0.709595i | ||||
\(397\) | −31.5129 | −1.58159 | −0.790793 | − | 0.612083i | \(-0.790332\pi\) | ||||
−0.790793 | + | 0.612083i | \(0.790332\pi\) | |||||||
\(398\) | 6.98114 | + | 12.0917i | 0.349933 | + | 0.606102i | ||||
\(399\) | 28.7145 | 1.43753 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −8.92203 | −0.445545 | −0.222772 | − | 0.974870i | \(-0.571511\pi\) | ||||
−0.222772 | + | 0.974870i | \(0.571511\pi\) | |||||||
\(402\) | −11.2701 | − | 20.4866i | −0.562101 | − | 1.02178i | ||||
\(403\) | 7.50301 | 0.373751 | ||||||||
\(404\) | −3.72580 | + | 6.45328i | −0.185365 | + | 0.321062i | ||||
\(405\) | −2.14530 | −0.106601 | ||||||||
\(406\) | 10.8501 | + | 18.7929i | 0.538480 | + | 0.932675i | ||||
\(407\) | −1.77208 | −0.0878386 | ||||||||
\(408\) | −6.82690 | + | 11.8245i | −0.337982 | + | 0.585402i | ||||
\(409\) | −9.88689 | − | 17.1246i | −0.488875 | − | 0.846757i | 0.511043 | − | 0.859555i | \(-0.329259\pi\) |
−0.999918 | + | 0.0127982i | \(0.995926\pi\) | |||||||
\(410\) | 4.91148 | 0.242561 | ||||||||
\(411\) | −42.4722 | −2.09500 | ||||||||
\(412\) | −4.74340 | + | 8.21580i | −0.233690 | + | 0.404764i | ||||
\(413\) | −7.97757 | − | 13.8176i | −0.392551 | − | 0.679918i | ||||
\(414\) | 10.2666 | + | 17.7823i | 0.504575 | + | 0.873950i | ||||
\(415\) | 6.82278 | − | 11.8174i | 0.334917 | − | 0.580093i | ||||
\(416\) | 1.00733 | 0.0493885 | ||||||||
\(417\) | 18.3654 | 0.899359 | ||||||||
\(418\) | −3.53398 | + | 6.12104i | −0.172853 | + | 0.299390i | ||||
\(419\) | 7.41294 | − | 12.8396i | 0.362146 | − | 0.627255i | −0.626168 | − | 0.779688i | \(-0.715378\pi\) |
0.988314 | + | 0.152433i | \(0.0487110\pi\) | |||||||
\(420\) | −6.41888 | + | 11.1178i | −0.313209 | + | 0.542494i | ||||
\(421\) | 3.25445 | − | 5.63687i | 0.158612 | − | 0.274724i | −0.775756 | − | 0.631033i | \(-0.782631\pi\) |
0.934368 | + | 0.356308i | \(0.115965\pi\) | |||||||
\(422\) | −8.38955 | − | 14.5311i | −0.408397 | − | 0.707364i | ||||
\(423\) | −32.7652 | − | 56.7510i | −1.59310 | − | 2.75933i | ||||
\(424\) | 3.55346 | 0.172571 | ||||||||
\(425\) | 2.38990 | − | 4.13942i | 0.115927 | − | 0.200792i | ||||
\(426\) | −11.1479 | −0.540118 | ||||||||
\(427\) | −60.0463 | −2.90584 | ||||||||
\(428\) | −4.67249 | − | 8.09298i | −0.225853 | − | 0.391189i | ||||
\(429\) | −9.09280 | −0.439005 | ||||||||
\(430\) | 4.53264 | − | 7.85077i | 0.218584 | − | 0.378598i | ||||
\(431\) | 1.51593 | + | 2.62567i | 0.0730198 | + | 0.126474i | 0.900223 | − | 0.435428i | \(-0.143403\pi\) |
−0.827204 | + | 0.561902i | \(0.810070\pi\) | |||||||
\(432\) | −3.08503 | + | 5.34343i | −0.148429 | + | 0.257086i | ||||
\(433\) | 9.74939 | + | 16.8864i | 0.468526 | + | 0.811510i | 0.999353 | − | 0.0359697i | \(-0.0114520\pi\) |
−0.530827 | + | 0.847480i | \(0.678119\pi\) | |||||||
\(434\) | 16.7370 | + | 28.9894i | 0.803402 | + | 1.39153i | ||||
\(435\) | −6.89655 | − | 11.9452i | −0.330664 | − | 0.572727i | ||||
\(436\) | −6.68361 | − | 11.5763i | −0.320087 | − | 0.554406i | ||||
\(437\) | 4.45034 | + | 7.70821i | 0.212888 | + | 0.368734i | ||||
\(438\) | 18.0627 | + | 31.2855i | 0.863070 | + | 1.49488i | ||||
\(439\) | −2.73228 | + | 4.73244i | −0.130404 | + | 0.225867i | −0.923833 | − | 0.382797i | \(-0.874961\pi\) |
0.793428 | + | 0.608664i | \(0.208294\pi\) | |||||||
\(440\) | −1.57998 | − | 2.73660i | −0.0753226 | − | 0.130462i | ||||
\(441\) | −34.0484 | + | 58.9735i | −1.62135 | + | 2.80826i | ||||
\(442\) | −4.81484 | −0.229019 | ||||||||
\(443\) | 14.2350 | + | 24.6557i | 0.676324 | + | 1.17143i | 0.976080 | + | 0.217412i | \(0.0697614\pi\) |
−0.299756 | + | 0.954016i | \(0.596905\pi\) | |||||||
\(444\) | −1.60194 | −0.0760245 | ||||||||
\(445\) | 3.52240 | 0.166978 | ||||||||
\(446\) | −8.22719 | + | 14.2499i | −0.389569 | + | 0.674752i | ||||
\(447\) | 40.4769 | 1.91449 | ||||||||
\(448\) | 2.24706 | + | 3.89203i | 0.106164 | + | 0.183881i | ||||
\(449\) | −8.24126 | − | 14.2743i | −0.388929 | − | 0.673645i | 0.603377 | − | 0.797456i | \(-0.293822\pi\) |
−0.992306 | + | 0.123811i | \(0.960488\pi\) | |||||||
\(450\) | 2.57998 | − | 4.46866i | 0.121621 | − | 0.210654i | ||||
\(451\) | −7.76004 | + | 13.4408i | −0.365406 | + | 0.632901i | ||||
\(452\) | 3.75547 | − | 6.50466i | 0.176642 | − | 0.305954i | ||||
\(453\) | −9.82108 | + | 17.0106i | −0.461434 | + | 0.799228i | ||||
\(454\) | −11.5272 | −0.540997 | ||||||||
\(455\) | −4.52707 | −0.212232 | ||||||||
\(456\) | −3.19468 | + | 5.53334i | −0.149604 | + | 0.259123i | ||||
\(457\) | 7.52000 | + | 13.0250i | 0.351771 | + | 0.609285i | 0.986560 | − | 0.163400i | \(-0.0522463\pi\) |
−0.634789 | + | 0.772686i | \(0.718913\pi\) | |||||||
\(458\) | −14.1846 | − | 24.5685i | −0.662803 | − | 1.14801i | ||||
\(459\) | 14.7458 | − | 25.5405i | 0.688276 | − | 1.19213i | ||||
\(460\) | −3.97933 | −0.185537 | ||||||||
\(461\) | −3.06250 | −0.142635 | −0.0713175 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713175 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(462\) | −20.2834 | − | 35.1319i | −0.943668 | − | 1.63448i | ||||
\(463\) | −20.9244 | + | 36.2422i | −0.972440 | + | 1.68432i | −0.284304 | + | 0.958734i | \(0.591762\pi\) |
−0.688136 | + | 0.725581i | \(0.741571\pi\) | |||||||
\(464\) | −4.82856 | −0.224160 | ||||||||
\(465\) | −10.6384 | − | 18.4263i | −0.493345 | − | 0.854498i | ||||
\(466\) | −2.78220 | −0.128883 | ||||||||
\(467\) | 3.88008 | − | 6.72050i | 0.179549 | − | 0.310988i | −0.762177 | − | 0.647368i | \(-0.775870\pi\) |
0.941726 | + | 0.336381i | \(0.109203\pi\) | |||||||
\(468\) | −5.19779 | −0.240268 | ||||||||
\(469\) | 36.7781 | + | 0.760080i | 1.69826 | + | 0.0350972i | ||||
\(470\) | 12.6998 | 0.585798 | ||||||||
\(471\) | 28.6952 | − | 49.7016i | 1.32221 | − | 2.29013i | ||||
\(472\) | 3.55022 | 0.163412 | ||||||||
\(473\) | 14.3230 | + | 24.8081i | 0.658571 | + | 1.14068i | ||||
\(474\) | −34.7699 | −1.59703 | ||||||||
\(475\) | 1.11836 | − | 1.93706i | 0.0513140 | − | 0.0888785i | ||||
\(476\) | −10.7405 | − | 18.6031i | −0.492290 | − | 0.852671i | ||||
\(477\) | −18.3357 | −0.839534 | ||||||||
\(478\) | −24.2756 | −1.11034 | ||||||||
\(479\) | −2.69733 | + | 4.67192i | −0.123244 | + | 0.213465i | −0.921045 | − | 0.389455i | \(-0.872663\pi\) |
0.797801 | + | 0.602921i | \(0.205997\pi\) | |||||||
\(480\) | −1.42828 | − | 2.47386i | −0.0651919 | − | 0.112916i | ||||
\(481\) | −0.282451 | − | 0.489220i | −0.0128787 | − | 0.0223065i | ||||
\(482\) | 3.46574 | − | 6.00283i | 0.157860 | − | 0.273421i | ||||
\(483\) | −51.0857 | −2.32448 | ||||||||
\(484\) | −1.01466 | −0.0461210 | ||||||||
\(485\) | −0.642699 | + | 1.11319i | −0.0291835 | + | 0.0505473i | ||||
\(486\) | −6.19100 | + | 10.7231i | −0.280830 | + | 0.486411i | ||||
\(487\) | 0.707213 | − | 1.22493i | 0.0320469 | − | 0.0555069i | −0.849557 | − | 0.527497i | \(-0.823131\pi\) |
0.881604 | + | 0.471990i | \(0.156464\pi\) | |||||||
\(488\) | 6.68053 | − | 11.5710i | 0.302413 | − | 0.523795i | ||||
\(489\) | 5.80663 | + | 10.0574i | 0.262585 | + | 0.454811i | ||||
\(490\) | −6.59858 | − | 11.4291i | −0.298093 | − | 0.516313i | ||||
\(491\) | −39.4245 | −1.77920 | −0.889601 | − | 0.456739i | \(-0.849017\pi\) | ||||
−0.889601 | + | 0.456739i | \(0.849017\pi\) | |||||||
\(492\) | −7.01498 | + | 12.1503i | −0.316260 | + | 0.547778i | ||||
\(493\) | 23.0795 | 1.03945 | ||||||||
\(494\) | −2.25313 | −0.101373 | ||||||||
\(495\) | 8.15263 | + | 14.1208i | 0.366433 | + | 0.634681i | ||||
\(496\) | −7.44840 | −0.334443 | ||||||||
\(497\) | 8.76930 | − | 15.1889i | 0.393357 | − | 0.681314i | ||||
\(498\) | 19.4897 | + | 33.7571i | 0.873354 | + | 1.51269i | ||||
\(499\) | 11.6957 | − | 20.2575i | 0.523570 | − | 0.906851i | −0.476053 | − | 0.879416i | \(-0.657933\pi\) |
0.999624 | − | 0.0274341i | \(-0.00873364\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 23.2373 | + | 40.2481i | 1.03816 | + | 1.79815i | ||||
\(502\) | −5.02058 | − | 8.69590i | −0.224080 | − | 0.388117i | ||||
\(503\) | 10.6927 | + | 18.5203i | 0.476765 | + | 0.825781i | 0.999645 | − | 0.0266247i | \(-0.00847591\pi\) |
−0.522880 | + | 0.852406i | \(0.675143\pi\) | |||||||
\(504\) | −11.5947 | − | 20.0827i | −0.516471 | − | 0.894554i | ||||
\(505\) | 3.72580 | + | 6.45328i | 0.165796 | + | 0.287167i | ||||
\(506\) | 6.28726 | − | 10.8899i | 0.279503 | − | 0.484113i | ||||
\(507\) | 17.1184 | + | 29.6499i | 0.760253 | + | 1.31680i | ||||
\(508\) | −0.0732391 | + | 0.126854i | −0.00324946 | + | 0.00562823i | ||||
\(509\) | 15.8720 | 0.703514 | 0.351757 | − | 0.936091i | \(-0.385584\pi\) | ||||
0.351757 | + | 0.936091i | \(0.385584\pi\) | |||||||
\(510\) | 6.82690 | + | 11.8245i | 0.302300 | + | 0.523599i | ||||
\(511\) | −56.8348 | −2.51422 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.90037 | − | 11.9518i | 0.304659 | − | 0.527684i | ||||
\(514\) | 19.5238 | 0.861157 | ||||||||
\(515\) | 4.74340 | + | 8.21580i | 0.209019 | + | 0.362032i | ||||
\(516\) | 12.9478 | + | 22.4262i | 0.569995 | + | 0.987260i | ||||
\(517\) | −20.0654 | + | 34.7543i | −0.882475 | + | 1.52849i | ||||
\(518\) | 1.26013 | − | 2.18261i | 0.0553671 | − | 0.0958986i | ||||
\(519\) | 21.8522 | − | 37.8491i | 0.959205 | − | 1.66139i | ||||
\(520\) | 0.503666 | − | 0.872375i | 0.0220872 | − | 0.0382562i | ||||
\(521\) | −15.6199 | −0.684322 | −0.342161 | − | 0.939641i | \(-0.611159\pi\) | ||||
−0.342161 | + | 0.939641i | \(0.611159\pi\) | |||||||
\(522\) | 24.9152 | 1.09051 | ||||||||
\(523\) | 14.2957 | − | 24.7608i | 0.625105 | − | 1.08271i | −0.363415 | − | 0.931627i | \(-0.618389\pi\) |
0.988521 | − | 0.151087i | \(-0.0482773\pi\) | |||||||
\(524\) | −5.51058 | − | 9.54460i | −0.240731 | − | 0.416958i | ||||
\(525\) | 6.41888 | + | 11.1178i | 0.280143 | + | 0.485221i | ||||
\(526\) | 1.39323 | − | 2.41315i | 0.0607479 | − | 0.105218i | ||||
\(527\) | 35.6018 | 1.55084 | ||||||||
\(528\) | 9.02662 | 0.392833 | ||||||||
\(529\) | 3.58247 | + | 6.20502i | 0.155759 | + | 0.269783i | ||||
\(530\) | 1.77673 | − | 3.07739i | 0.0771762 | − | 0.133673i | ||||
\(531\) | −18.3190 | −0.794977 | ||||||||
\(532\) | −5.02606 | − | 8.70540i | −0.217908 | − | 0.377427i | ||||
\(533\) | −4.94749 | −0.214299 | ||||||||
\(534\) | −5.03098 | + | 8.71391i | −0.217712 | + | 0.377088i | ||||
\(535\) | −9.34497 | −0.404018 | ||||||||
\(536\) | −4.23827 | + | 7.00265i | −0.183065 | + | 0.302468i | ||||
\(537\) | −0.624820 | −0.0269630 | ||||||||
\(538\) | 12.0928 | − | 20.9454i | 0.521359 | − | 0.903021i | ||||
\(539\) | 41.7024 | 1.79625 | ||||||||
\(540\) | 3.08503 | + | 5.34343i | 0.132759 | + | 0.229945i | ||||
\(541\) | 5.96241 | 0.256344 | 0.128172 | − | 0.991752i | \(-0.459089\pi\) | ||||
0.128172 | + | 0.991752i | \(0.459089\pi\) | |||||||
\(542\) | −13.8170 | + | 23.9318i | −0.593493 | + | 1.02796i | ||||
\(543\) | 32.3584 | + | 56.0464i | 1.38863 | + | 2.40518i | ||||
\(544\) | 4.77980 | 0.204932 | ||||||||
\(545\) | −13.3672 | −0.572588 | ||||||||
\(546\) | 6.46594 | − | 11.1993i | 0.276717 | − | 0.479287i | ||||
\(547\) | 4.02806 | + | 6.97681i | 0.172228 | + | 0.298307i | 0.939198 | − | 0.343375i | \(-0.111570\pi\) |
−0.766971 | + | 0.641682i | \(0.778237\pi\) | |||||||
\(548\) | 7.43414 | + | 12.8763i | 0.317571 | + | 0.550049i | ||||
\(549\) | −34.4713 | + | 59.7060i | −1.47120 | + | 2.54819i | ||||
\(550\) | −3.15996 | −0.134741 | ||||||||
\(551\) | 10.8002 | 0.460103 | ||||||||
\(552\) | 5.68361 | − | 9.84429i | 0.241910 | − | 0.419001i | ||||
\(553\) | 27.3511 | − | 47.3734i | 1.16309 | − | 2.01452i | ||||
\(554\) | 13.6019 | − | 23.5592i | 0.577889 | − | 1.00093i | ||||
\(555\) | −0.800968 | + | 1.38732i | −0.0339992 | + | 0.0588884i | ||||
\(556\) | −3.21460 | − | 5.56785i | −0.136329 | − | 0.236130i | ||||
\(557\) | −10.2351 | − | 17.7276i | −0.433673 | − | 0.751144i | 0.563513 | − | 0.826107i | \(-0.309449\pi\) |
−0.997186 | + | 0.0749630i | \(0.976116\pi\) | |||||||
\(558\) | 38.4334 | 1.62702 | ||||||||
\(559\) | −4.56588 | + | 7.90833i | −0.193116 | + | 0.334487i | ||||
\(560\) | 4.49412 | 0.189911 | ||||||||
\(561\) | −43.1454 | −1.82160 | ||||||||
\(562\) | −15.4913 | − | 26.8317i | −0.653461 | − | 1.13183i | ||||
\(563\) | 22.9616 | 0.967716 | 0.483858 | − | 0.875146i | \(-0.339235\pi\) | ||||
0.483858 | + | 0.875146i | \(0.339235\pi\) | |||||||
\(564\) | −18.1389 | + | 31.4175i | −0.763785 | + | 1.32291i | ||||
\(565\) | −3.75547 | − | 6.50466i | −0.157994 | − | 0.273653i | ||||
\(566\) | −2.43216 | + | 4.21263i | −0.102231 | + | 0.177070i | ||||
\(567\) | 4.82061 | + | 8.34954i | 0.202447 | + | 0.350648i | ||||
\(568\) | 1.95128 | + | 3.37972i | 0.0818739 | + | 0.141810i | ||||
\(569\) | −13.5246 | − | 23.4252i | −0.566979 | − | 0.982036i | −0.996863 | − | 0.0791521i | \(-0.974779\pi\) |
0.429884 | − | 0.902884i | \(-0.358555\pi\) | |||||||
\(570\) | 3.19468 | + | 5.53334i | 0.133810 | + | 0.231766i | ||||
\(571\) | 3.51800 | + | 6.09335i | 0.147224 | + | 0.254999i | 0.930200 | − | 0.367052i | \(-0.119633\pi\) |
−0.782977 | + | 0.622051i | \(0.786300\pi\) | |||||||
\(572\) | 1.59156 | + | 2.75667i | 0.0665466 | + | 0.115262i | ||||
\(573\) | −1.68206 | + | 2.91341i | −0.0702691 | + | 0.121710i | ||||
\(574\) | −11.0364 | − | 19.1156i | −0.460650 | − | 0.797870i | ||||
\(575\) | −1.98966 | + | 3.44620i | −0.0829748 | + | 0.143717i | ||||
\(576\) | 5.15996 | 0.214998 | ||||||||
\(577\) | 20.0029 | + | 34.6461i | 0.832733 | + | 1.44234i | 0.895863 | + | 0.444330i | \(0.146558\pi\) |
−0.0631308 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(578\) | −5.84645 | −0.243180 | ||||||||
\(579\) | −24.8817 | −1.03405 | ||||||||
\(580\) | −2.41428 | + | 4.18166i | −0.100248 | + | 0.173634i | ||||
\(581\) | −61.3248 | −2.54418 | ||||||||
\(582\) | −1.83591 | − | 3.17989i | −0.0761010 | − | 0.131811i | ||||
\(583\) | 5.61439 | + | 9.72441i | 0.232524 | + | 0.402744i | ||||
\(584\) | 6.32323 | − | 10.9522i | 0.261657 | − | 0.453203i | ||||
\(585\) | −2.59889 | + | 4.50142i | −0.107451 | + | 0.186111i | ||||
\(586\) | 3.67287 | − | 6.36160i | 0.151725 | − | 0.262795i | ||||
\(587\) | 17.3079 | − | 29.9782i | 0.714375 | − | 1.23733i | −0.248825 | − | 0.968548i | \(-0.580044\pi\) |
0.963200 | − | 0.268786i | \(-0.0866223\pi\) | |||||||
\(588\) | 37.6985 | 1.55466 | ||||||||
\(589\) | 16.6600 | 0.686465 | ||||||||
\(590\) | 1.77511 | − | 3.07458i | 0.0730802 | − | 0.126579i | ||||
\(591\) | 22.8788 | + | 39.6272i | 0.941107 | + | 1.63004i | ||||
\(592\) | 0.280396 | + | 0.485660i | 0.0115242 | + | 0.0199605i | ||||
\(593\) | 5.11485 | − | 8.85918i | 0.210042 | − | 0.363803i | −0.741686 | − | 0.670748i | \(-0.765973\pi\) |
0.951727 | + | 0.306945i | \(0.0993067\pi\) | |||||||
\(594\) | −19.4971 | −0.799977 | ||||||||
\(595\) | −21.4810 | −0.880635 | ||||||||
\(596\) | −7.08489 | − | 12.2714i | −0.290209 | − | 0.502656i | ||||
\(597\) | −19.9421 | + | 34.5407i | −0.816175 | + | 1.41366i | ||||
\(598\) | 4.00850 | 0.163920 | ||||||||
\(599\) | 9.96932 | + | 17.2674i | 0.407336 | + | 0.705526i | 0.994590 | − | 0.103876i | \(-0.0331246\pi\) |
−0.587255 | + | 0.809402i | \(0.699791\pi\) | |||||||
\(600\) | −2.85656 | −0.116619 | ||||||||
\(601\) | 11.4181 | − | 19.7767i | 0.465752 | − | 0.806707i | −0.533483 | − | 0.845811i | \(-0.679117\pi\) |
0.999235 | + | 0.0391041i | \(0.0124504\pi\) | |||||||
\(602\) | −40.7405 | −1.66046 | ||||||||
\(603\) | 21.8693 | − | 36.1334i | 0.890587 | − | 1.47146i | ||||
\(604\) | 6.87615 | 0.279786 | ||||||||
\(605\) | −0.507331 | + | 0.878724i | −0.0206260 | + | 0.0357252i | ||||
\(606\) | −21.2860 | −0.864684 | ||||||||
\(607\) | 6.11278 | + | 10.5877i | 0.248110 | + | 0.429740i | 0.963001 | − | 0.269496i | \(-0.0868571\pi\) |
−0.714891 | + | 0.699236i | \(0.753524\pi\) | |||||||
\(608\) | 2.23673 | 0.0907113 | ||||||||
\(609\) | −30.9939 | + | 53.6831i | −1.25594 | + | 2.17535i | ||||
\(610\) | −6.68053 | − | 11.5710i | −0.270487 | − | 0.468497i | ||||
\(611\) | −12.7929 | −0.517545 | ||||||||
\(612\) | −24.6635 | −0.996965 | ||||||||
\(613\) | 5.64908 | − | 9.78449i | 0.228164 | − | 0.395192i | −0.729100 | − | 0.684407i | \(-0.760061\pi\) |
0.957264 | + | 0.289215i | \(0.0933944\pi\) | |||||||
\(614\) | 3.21456 | + | 5.56779i | 0.129729 | + | 0.224698i | ||||
\(615\) | 7.01498 | + | 12.1503i | 0.282871 | + | 0.489947i | ||||
\(616\) | −7.10062 | + | 12.2986i | −0.286092 | + | 0.495526i | ||||
\(617\) | 14.7010 | 0.591838 | 0.295919 | − | 0.955213i | \(-0.404374\pi\) | ||||
0.295919 | + | 0.955213i | \(0.404374\pi\) | |||||||
\(618\) | −27.0996 | −1.09011 | ||||||||
\(619\) | −5.29906 | + | 9.17825i | −0.212987 | + | 0.368905i | −0.952648 | − | 0.304075i | \(-0.901653\pi\) |
0.739661 | + | 0.672980i | \(0.234986\pi\) | |||||||
\(620\) | −3.72420 | + | 6.45050i | −0.149567 | + | 0.259058i | ||||
\(621\) | −12.2764 | + | 21.2633i | −0.492633 | + | 0.853265i | ||||
\(622\) | 11.3742 | − | 19.7006i | 0.456063 | − | 0.789924i | ||||
\(623\) | −7.91505 | − | 13.7093i | −0.317110 | − | 0.549250i | ||||
\(624\) | 1.43875 | + | 2.49199i | 0.0575962 | + | 0.0997596i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.23333 | + | 9.06440i | −0.209166 | + | 0.362286i | ||||
\(627\) | −20.1901 | −0.806315 | ||||||||
\(628\) | −20.0907 | −0.801707 | ||||||||
\(629\) | −1.34023 | − | 2.32135i | −0.0534386 | − | 0.0925584i | ||||
\(630\) | −23.1895 | −0.923892 | ||||||||
\(631\) | 5.99862 | − | 10.3899i | 0.238801 | − | 0.413616i | −0.721569 | − | 0.692342i | \(-0.756579\pi\) |
0.960371 | + | 0.278726i | \(0.0899122\pi\) | |||||||
\(632\) | 6.08596 | + | 10.5412i | 0.242086 | + | 0.419306i | ||||
\(633\) | 23.9653 | − | 41.5091i | 0.952534 | − | 1.64984i | ||||
\(634\) | 16.6592 | + | 28.8545i | 0.661621 | + | 1.14596i | ||||
\(635\) | 0.0732391 | + | 0.126854i | 0.00290641 | + | 0.00503404i | ||||
\(636\) | 5.07534 | + | 8.79075i | 0.201250 | + | 0.348576i | ||||
\(637\) | 6.64695 | + | 11.5129i | 0.263362 | + | 0.456156i | ||||
\(638\) | −7.62903 | − | 13.2139i | −0.302036 | − | 0.523142i | ||||
\(639\) | −10.0685 | − | 17.4392i | −0.398305 | − | 0.689884i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 10.9639 | + | 18.9901i | 0.433049 | + | 0.750062i | 0.997134 | − | 0.0756541i | \(-0.0241045\pi\) |
−0.564085 | + | 0.825716i | \(0.690771\pi\) | |||||||
\(642\) | 13.3473 | − | 23.1181i | 0.526774 | − | 0.912400i | ||||
\(643\) | −10.7513 | −0.423990 | −0.211995 | − | 0.977271i | \(-0.567996\pi\) | ||||
−0.211995 | + | 0.977271i | \(0.567996\pi\) | |||||||
\(644\) | 8.94180 | + | 15.4877i | 0.352356 | + | 0.610299i | ||||
\(645\) | 25.8956 | 1.01964 | ||||||||
\(646\) | −10.6911 | −0.420636 | ||||||||
\(647\) | −10.6281 | + | 18.4085i | −0.417835 | + | 0.723712i | −0.995721 | − | 0.0924055i | \(-0.970544\pi\) |
0.577886 | + | 0.816117i | \(0.303878\pi\) | |||||||
\(648\) | −2.14530 | −0.0842752 | ||||||||
\(649\) | 5.60928 | + | 9.71555i | 0.220183 | + | 0.381369i | ||||
\(650\) | −0.503666 | − | 0.872375i | −0.0197554 | − | 0.0342173i | ||||
\(651\) | −47.8104 | + | 82.8100i | −1.87384 | + | 3.24558i | ||||
\(652\) | 2.03273 | − | 3.52080i | 0.0796080 | − | 0.137885i | ||||
\(653\) | 17.3614 | − | 30.0708i | 0.679402 | − | 1.17676i | −0.295759 | − | 0.955263i | \(-0.595572\pi\) |
0.975161 | − | 0.221497i | \(-0.0710942\pi\) | |||||||
\(654\) | 19.0921 | − | 33.0686i | 0.746562 | − | 1.29308i | ||||
\(655\) | −11.0212 | −0.430632 | ||||||||
\(656\) | 4.91148 | 0.191761 | ||||||||
\(657\) | −32.6276 | + | 56.5127i | −1.27292 | + | 2.20477i | ||||
\(658\) | −28.5372 | − | 49.4279i | −1.11250 | − | 1.92690i | ||||
\(659\) | 7.23113 | + | 12.5247i | 0.281685 | + | 0.487893i | 0.971800 | − | 0.235807i | \(-0.0757734\pi\) |
−0.690115 | + | 0.723700i | \(0.742440\pi\) | |||||||
\(660\) | 4.51331 | − | 7.81729i | 0.175680 | − | 0.304287i | ||||
\(661\) | 36.1436 | 1.40582 | 0.702912 | − | 0.711277i | \(-0.251883\pi\) | ||||
0.702912 | + | 0.711277i | \(0.251883\pi\) | |||||||
\(662\) | 21.6753 | 0.842434 | ||||||||
\(663\) | −6.87695 | − | 11.9112i | −0.267079 | − | 0.462594i | ||||
\(664\) | 6.82278 | − | 11.8174i | 0.264775 | − | 0.458604i | ||||
\(665\) | −10.0521 | −0.389805 | ||||||||
\(666\) | −1.44683 | − | 2.50598i | −0.0560635 | − | 0.0971049i | ||||
\(667\) | −19.2144 | −0.743986 | ||||||||
\(668\) | 8.13469 | − | 14.0897i | 0.314741 | − | 0.545147i | ||||
\(669\) | −47.0030 | −1.81724 | ||||||||
\(670\) | 3.94533 | + | 7.17177i | 0.152422 | + | 0.277070i | ||||
\(671\) | 42.2204 | 1.62990 | ||||||||
\(672\) | −6.41888 | + | 11.1178i | −0.247614 | + | 0.428879i | ||||
\(673\) | −32.6383 | −1.25811 | −0.629057 | − | 0.777359i | \(-0.716559\pi\) | ||||
−0.629057 | + | 0.777359i | \(0.716559\pi\) | |||||||
\(674\) | −11.0932 | − | 19.2140i | −0.427295 | − | 0.740096i | ||||
\(675\) | 6.17006 | 0.237486 | ||||||||
\(676\) | 5.99264 | − | 10.3796i | 0.230486 | − | 0.399214i | ||||
\(677\) | 22.0062 | + | 38.1158i | 0.845767 | + | 1.46491i | 0.884954 | + | 0.465679i | \(0.154190\pi\) |
−0.0391873 | + | 0.999232i | \(0.512477\pi\) | |||||||
\(678\) | 21.4555 | 0.823992 | ||||||||
\(679\) | 5.77674 | 0.221691 | ||||||||
\(680\) | 2.38990 | − | 4.13942i | 0.0916484 | − | 0.158740i | ||||
\(681\) | −16.4640 | − | 28.5166i | −0.630904 | − | 1.09276i | ||||
\(682\) | −11.7683 | − | 20.3833i | −0.450632 | − | 0.780518i | ||||
\(683\) | −17.4542 | + | 30.2315i | −0.667866 | + | 1.15678i | 0.310634 | + | 0.950530i | \(0.399459\pi\) |
−0.978500 | + | 0.206248i | \(0.933875\pi\) | |||||||
\(684\) | −11.5414 | −0.441297 | ||||||||
\(685\) | 14.8683 | 0.568088 | ||||||||
\(686\) | −13.9254 | + | 24.1195i | −0.531674 | + | 0.920886i | ||||
\(687\) | 40.5192 | − | 70.1814i | 1.54591 | − | 2.67759i | ||||
\(688\) | 4.53264 | − | 7.85077i | 0.172805 | − | 0.299308i | ||||
\(689\) | −1.78976 | + | 3.09995i | −0.0681843 | + | 0.118099i | ||||
\(690\) | −5.68361 | − | 9.84429i | −0.216371 | − | 0.374766i | ||||
\(691\) | 1.76647 | + | 3.05961i | 0.0671995 | + | 0.116393i | 0.897668 | − | 0.440673i | \(-0.145260\pi\) |
−0.830468 | + | 0.557066i | \(0.811927\pi\) | |||||||
\(692\) | −15.2996 | −0.581605 | ||||||||
\(693\) | 36.6389 | − | 63.4605i | 1.39180 | − | 2.41066i | ||||
\(694\) | −17.6530 | −0.670100 | ||||||||
\(695\) | −6.42920 | −0.243874 | ||||||||
\(696\) | −6.89655 | − | 11.9452i | −0.261413 | − | 0.452781i | ||||
\(697\) | −23.4759 | −0.889212 | ||||||||
\(698\) | −11.5386 | + | 19.9855i | −0.436743 | + | 0.756461i | ||||
\(699\) | −3.97376 | − | 6.88276i | −0.150301 | − | 0.260330i | ||||
\(700\) | 2.24706 | − | 3.89203i | 0.0849310 | − | 0.147105i | ||||
\(701\) | −0.779963 | − | 1.35094i | −0.0294588 | − | 0.0510242i | 0.850920 | − | 0.525295i | \(-0.176045\pi\) |
−0.880379 | + | 0.474271i | \(0.842712\pi\) | |||||||
\(702\) | −3.10765 | − | 5.38260i | −0.117291 | − | 0.203153i | ||||
\(703\) | −0.627169 | − | 1.08629i | −0.0236541 | − | 0.0409701i | ||||
\(704\) | −1.57998 | − | 2.73660i | −0.0595477 | − | 0.103140i | ||||
\(705\) | 18.1389 | + | 31.4175i | 0.683150 | + | 1.18325i | ||||
\(706\) | −13.5950 | − | 23.5472i | −0.511653 | − | 0.886209i | ||||
\(707\) | 16.7442 | − | 29.0018i | 0.629731 | − | 1.09073i | ||||
\(708\) | 5.07072 | + | 8.78274i | 0.190569 | + | 0.330076i | ||||
\(709\) | −10.0334 | + | 17.3783i | −0.376812 | + | 0.652657i | −0.990596 | − | 0.136816i | \(-0.956313\pi\) |
0.613785 | + | 0.789474i | \(0.289646\pi\) | |||||||
\(710\) | 3.90256 | 0.146461 | ||||||||
\(711\) | −31.4033 | − | 54.3921i | −1.17772 | − | 2.03986i | ||||
\(712\) | 3.52240 | 0.132007 | ||||||||
\(713\) | −29.6396 | −1.11001 | ||||||||
\(714\) | 30.6809 | − | 53.1409i | 1.14820 | − | 1.98875i | ||||
\(715\) | 3.18313 | 0.119042 | ||||||||
\(716\) | 0.109366 | + | 0.189427i | 0.00408719 | + | 0.00707922i | ||||
\(717\) | −34.6724 | − | 60.0544i | −1.29487 | − | 2.24277i | ||||
\(718\) | −13.4907 | + | 23.3665i | −0.503467 | + | 0.872030i | ||||
\(719\) | 6.76392 | − | 11.7154i | 0.252252 | − | 0.436912i | −0.711894 | − | 0.702287i | \(-0.752162\pi\) |
0.964145 | + | 0.265375i | \(0.0854956\pi\) | |||||||
\(720\) | 2.57998 | − | 4.46866i | 0.0961501 | − | 0.166537i | ||||
\(721\) | 21.3174 | − | 36.9228i | 0.793902 | − | 1.37508i | ||||
\(722\) | 13.9971 | 0.520916 | ||||||||
\(723\) | 19.8002 | 0.736377 | ||||||||
\(724\) | 11.3277 | − | 19.6202i | 0.420992 | − | 0.729180i | ||||
\(725\) | 2.41428 | + | 4.18166i | 0.0896642 | + | 0.155303i | ||||
\(726\) | −1.44922 | − | 2.51013i | −0.0537858 | − | 0.0931597i | ||||
\(727\) | 7.73333 | − | 13.3945i | 0.286813 | − | 0.496775i | −0.686234 | − | 0.727381i | \(-0.740737\pi\) |
0.973047 | + | 0.230606i | \(0.0740707\pi\) | |||||||
\(728\) | −4.52707 | −0.167784 | ||||||||
\(729\) | −41.8059 | −1.54837 | ||||||||
\(730\) | −6.32323 | − | 10.9522i | −0.234033 | − | 0.405357i | ||||
\(731\) | −21.6651 | + | 37.5251i | −0.801313 | + | 1.38792i | ||||
\(732\) | 38.1667 | 1.41068 | ||||||||
\(733\) | −14.8715 | − | 25.7581i | −0.549290 | − | 0.951398i | −0.998323 | − | 0.0578832i | \(-0.981565\pi\) |
0.449033 | − | 0.893515i | \(-0.351768\pi\) | |||||||
\(734\) | 26.7114 | 0.985934 | ||||||||
\(735\) | 18.8493 | − | 32.6479i | 0.695265 | − | 1.20423i | ||||
\(736\) | −3.97933 | −0.146680 | ||||||||
\(737\) | −25.8599 | − | 0.534436i | −0.952560 | − | 0.0196862i | ||||
\(738\) | −25.3430 | −0.932890 | ||||||||
\(739\) | −11.4606 | + | 19.8504i | −0.421586 | + | 0.730208i | −0.996095 | − | 0.0882902i | \(-0.971860\pi\) |
0.574509 | + | 0.818498i | \(0.305193\pi\) | |||||||
\(740\) | 0.560791 | 0.0206151 | ||||||||
\(741\) | −3.21810 | − | 5.57391i | −0.118220 | − | 0.204763i | ||||
\(742\) | −15.9697 | −0.586266 | ||||||||
\(743\) | −25.0187 | + | 43.3336i | −0.917845 | + | 1.58975i | −0.115164 | + | 0.993346i | \(0.536739\pi\) |
−0.802681 | + | 0.596408i | \(0.796594\pi\) | |||||||
\(744\) | −10.6384 | − | 18.4263i | −0.390023 | − | 0.675540i | ||||
\(745\) | −14.1698 | −0.519141 | ||||||||
\(746\) | −4.71193 | −0.172516 | ||||||||
\(747\) | −35.2052 | + | 60.9773i | −1.28809 | + | 2.23104i | ||||
\(748\) | 7.55198 | + | 13.0804i | 0.276128 | + | 0.478267i | ||||
\(749\) | 20.9987 | + | 36.3709i | 0.767277 | + | 1.32896i | ||||
\(750\) | −1.42828 | + | 2.47386i | −0.0521535 | + | 0.0903325i | ||||
\(751\) | 2.20927 | 0.0806174 | 0.0403087 | − | 0.999187i | \(-0.487166\pi\) | ||||
0.0403087 | + | 0.999187i | \(0.487166\pi\) | |||||||
\(752\) | 12.6998 | 0.463114 | ||||||||
\(753\) | 14.3416 | − | 24.8404i | 0.522637 | − | 0.905235i | ||||
\(754\) | 2.43198 | − | 4.21232i | 0.0885675 | − | 0.153403i | ||||
\(755\) | 3.43807 | − | 5.95492i | 0.125124 | − | 0.216722i | ||||
\(756\) | 13.8645 | − | 24.0140i | 0.504247 | − | 0.873382i | ||||
\(757\) | −19.9564 | − | 34.5655i | −0.725329 | − | 1.25631i | −0.958839 | − | 0.283952i | \(-0.908354\pi\) |
0.233510 | − | 0.972354i | \(-0.424979\pi\) | |||||||
\(758\) | −9.10210 | − | 15.7653i | −0.330603 | − | 0.572622i | ||||
\(759\) | 35.9199 | 1.30381 | ||||||||
\(760\) | 1.11836 | − | 1.93706i | 0.0405673 | − | 0.0702646i | ||||
\(761\) | −7.91877 | −0.287055 | −0.143528 | − | 0.989646i | \(-0.545845\pi\) | ||||
−0.143528 | + | 0.989646i | \(0.545845\pi\) | |||||||
\(762\) | −0.418425 | −0.0151579 | ||||||||
\(763\) | 30.0370 | + | 52.0255i | 1.08741 | + | 1.88345i | ||||
\(764\) | 1.17768 | 0.0426070 | ||||||||
\(765\) | −12.3318 | + | 21.3593i | −0.445856 | + | 0.772246i | ||||
\(766\) | 3.84384 | + | 6.65773i | 0.138884 | + | 0.240554i | ||||
\(767\) | −1.78813 | + | 3.09712i | −0.0645655 | + | 0.111831i | ||||
\(768\) | −1.42828 | − | 2.47386i | −0.0515387 | − | 0.0892676i | ||||
\(769\) | −16.8633 | − | 29.2081i | −0.608106 | − | 1.05327i | −0.991552 | − | 0.129708i | \(-0.958596\pi\) |
0.383446 | − | 0.923563i | \(-0.374737\pi\) | |||||||
\(770\) | 7.10062 | + | 12.2986i | 0.255889 | + | 0.443212i | ||||
\(771\) | 27.8855 | + | 48.2991i | 1.00427 | + | 1.73945i | ||||
\(772\) | 4.35518 | + | 7.54339i | 0.156746 | + | 0.271493i | ||||
\(773\) | 7.89567 | + | 13.6757i | 0.283988 | + | 0.491881i | 0.972363 | − | 0.233474i | \(-0.0750092\pi\) |
−0.688376 | + | 0.725354i | \(0.741676\pi\) | |||||||
\(774\) | −23.3883 | + | 40.5097i | −0.840674 | + | 1.45609i | ||||
\(775\) | 3.72420 | + | 6.45050i | 0.133777 | + | 0.231709i | ||||
\(776\) | −0.642699 | + | 1.11319i | −0.0230716 | + | 0.0399611i | ||||
\(777\) | 7.19930 | 0.258274 | ||||||||
\(778\) | 9.94332 | + | 17.2223i | 0.356485 | + | 0.617450i | ||||
\(779\) | −10.9856 | −0.393601 | ||||||||
\(780\) | 2.87751 | 0.103031 | ||||||||
\(781\) | −6.16597 | + | 10.6798i | −0.220636 | + | 0.382152i | ||||
\(782\) | 19.0204 | 0.680168 | ||||||||
\(783\) | 14.8963 | + | 25.8011i | 0.532349 | + | 0.922055i | ||||
\(784\) | −6.59858 | − | 11.4291i | −0.235663 | − | 0.408181i | ||||
\(785\) | −10.0454 | + | 17.3991i | −0.358534 | + | 0.620999i | ||||
\(786\) | 15.7413 | − | 27.2648i | 0.561474 | − | 0.972502i | ||||
\(787\) | −6.50152 | + | 11.2610i | −0.231754 | + | 0.401410i | −0.958324 | − | 0.285682i | \(-0.907780\pi\) |
0.726570 | + | 0.687092i | \(0.241113\pi\) | |||||||
\(788\) | 8.00919 | − | 13.8723i | 0.285316 | − | 0.494181i | ||||
\(789\) | 7.95972 | 0.283374 | ||||||||
\(790\) | 12.1719 | 0.433057 | ||||||||
\(791\) | −16.8775 | + | 29.2328i | −0.600096 | + | 1.03940i | ||||
\(792\) | 8.15263 | + | 14.1208i | 0.289691 | + | 0.501760i | ||||
\(793\) | 6.72951 | + | 11.6559i | 0.238972 | + | 0.413911i | ||||
\(794\) | −15.7564 | + | 27.2910i | −0.559175 | + | 0.968520i | ||||
\(795\) | 10.1507 | 0.360008 | ||||||||
\(796\) | 13.9623 | 0.494880 | ||||||||
\(797\) | −24.9444 | − | 43.2049i | −0.883575 | − | 1.53040i | −0.847338 | − | 0.531053i | \(-0.821796\pi\) |
−0.0362366 | − | 0.999343i | \(-0.511537\pi\) | |||||||
\(798\) | 14.3573 | − | 24.8675i | 0.508242 | − | 0.880301i | ||||
\(799\) | −60.7024 | −2.14750 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −18.1754 | −0.642197 | ||||||||
\(802\) | −4.46102 | + | 7.72671i | −0.157524 | + | 0.272839i | ||||
\(803\) | 39.9623 | 1.41024 | ||||||||
\(804\) | −23.3770 | − | 0.483123i | −0.824443 | − | 0.0170384i | ||||
\(805\) | 17.8836 | 0.630314 | ||||||||
\(806\) | 3.75150 | − | 6.49780i | 0.132141 | − | 0.228875i | ||||
\(807\) | 69.0879 | 2.43201 | ||||||||
\(808\) | 3.72580 | + | 6.45328i | 0.131073 | + | 0.227025i | ||||
\(809\) | 14.9279 | 0.524835 | 0.262418 | − | 0.964954i | \(-0.415480\pi\) | ||||
0.262418 | + | 0.964954i | \(0.415480\pi\) | |||||||
\(810\) | −1.07265 | + | 1.85788i | −0.0376890 | + | 0.0652793i | ||||
\(811\) | −11.1930 | − | 19.3868i | −0.393038 | − | 0.680761i | 0.599811 | − | 0.800142i | \(-0.295242\pi\) |
−0.992849 | + | 0.119381i | \(0.961909\pi\) | |||||||
\(812\) | 21.7002 | 0.761526 | ||||||||
\(813\) | −78.9385 | −2.76849 | ||||||||
\(814\) | −0.886039 | + | 1.53466i | −0.0310556 | + | 0.0537900i | ||||
\(815\) | −2.03273 | − | 3.52080i | −0.0712035 | − | 0.123328i | ||||
\(816\) | 6.82690 | + | 11.8245i | 0.238989 | + | 0.413941i | ||||
\(817\) | −10.1383 | + | 17.5600i | −0.354694 | + | 0.614348i | ||||
\(818\) | −19.7738 | −0.691374 | ||||||||
\(819\) | 23.3595 | 0.816247 | ||||||||
\(820\) | 2.45574 | − | 4.25347i | 0.0857582 | − | 0.148537i | ||||
\(821\) | −9.21305 | + | 15.9575i | −0.321538 | + | 0.556919i | −0.980805 | − | 0.194989i | \(-0.937533\pi\) |
0.659268 | + | 0.751908i | \(0.270866\pi\) | |||||||
\(822\) | −21.2361 | + | 36.7820i | −0.740694 | + | 1.28292i | ||||
\(823\) | −22.3242 | + | 38.6666i | −0.778173 | + | 1.34783i | 0.154821 | + | 0.987943i | \(0.450520\pi\) |
−0.932994 | + | 0.359892i | \(0.882813\pi\) | |||||||
\(824\) | 4.74340 | + | 8.21580i | 0.165244 | + | 0.286211i | ||||
\(825\) | −4.51331 | − | 7.81729i | −0.157133 | − | 0.272163i | ||||
\(826\) | −15.9551 | −0.555150 | ||||||||
\(827\) | 6.54846 | − | 11.3423i | 0.227712 | − | 0.394409i | −0.729418 | − | 0.684069i | \(-0.760209\pi\) |
0.957130 | + | 0.289660i | \(0.0935421\pi\) | |||||||
\(828\) | 20.5332 | 0.713577 | ||||||||
\(829\) | 39.0237 | 1.35535 | 0.677675 | − | 0.735362i | \(-0.262988\pi\) | ||||
0.677675 | + | 0.735362i | \(0.262988\pi\) | |||||||
\(830\) | −6.82278 | − | 11.8174i | −0.236822 | − | 0.410188i | ||||
\(831\) | 77.7093 | 2.69571 | ||||||||
\(832\) | 0.503666 | − | 0.872375i | 0.0174615 | − | 0.0302441i | ||||
\(833\) | 31.5398 | + | 54.6286i | 1.09279 | + | 1.89277i | ||||
\(834\) | 9.18272 | − | 15.9049i | 0.317971 | − | 0.550743i | ||||
\(835\) | −8.13469 | − | 14.0897i | −0.281513 | − | 0.487594i | ||||
\(836\) | 3.53398 | + | 6.12104i | 0.122225 | + | 0.211700i | ||||
\(837\) | 22.9785 | + | 39.8000i | 0.794254 | + | 1.37569i | ||||
\(838\) | −7.41294 | − | 12.8396i | −0.256076 | − | 0.443536i | ||||
\(839\) | −6.65497 | − | 11.5267i | −0.229755 | − | 0.397948i | 0.727980 | − | 0.685598i | \(-0.240459\pi\) |
−0.957735 | + | 0.287650i | \(0.907126\pi\) | |||||||
\(840\) | 6.41888 | + | 11.1178i | 0.221472 | + | 0.383601i | ||||
\(841\) | 2.84249 | − | 4.92334i | 0.0980170 | − | 0.169770i | ||||
\(842\) | −3.25445 | − | 5.63687i | −0.112156 | − | 0.194259i | ||||
\(843\) | 44.2519 | − | 76.6465i | 1.52412 | − | 2.63984i | ||||
\(844\) | −16.7791 | −0.577560 | ||||||||
\(845\) | −5.99264 | − | 10.3796i | −0.206153 | − | 0.357068i | ||||
\(846\) | −65.5304 | −2.25298 | ||||||||
\(847\) | 4.56002 | 0.156684 | ||||||||
\(848\) | 1.77673 | − | 3.07739i | 0.0610132 | − | 0.105678i | ||||
\(849\) | −13.8953 | −0.476884 | ||||||||
\(850\) | −2.38990 | − | 4.13942i | −0.0819728 | − | 0.141981i | ||||
\(851\) | 1.11579 | + | 1.93260i | 0.0382487 | + | 0.0662487i | ||||
\(852\) | −5.57396 | + | 9.65438i | −0.190961 | + | 0.330754i | ||||
\(853\) | −3.80971 | + | 6.59861i | −0.130442 | + | 0.225932i | −0.923847 | − | 0.382762i | \(-0.874973\pi\) |
0.793405 | + | 0.608694i | \(0.208306\pi\) | |||||||
\(854\) | −30.0231 | + | 52.0016i | −1.02737 | + | 1.77946i | ||||
\(855\) | −5.77071 | + | 9.99516i | −0.197354 | + | 0.341827i | ||||
\(856\) | −9.34497 | −0.319405 | ||||||||
\(857\) | 3.07051 | 0.104886 | 0.0524432 | − | 0.998624i | \(-0.483299\pi\) | ||||
0.0524432 | + | 0.998624i | \(0.483299\pi\) | |||||||
\(858\) | −4.54640 | + | 7.87460i | −0.155212 | + | 0.268834i | ||||
\(859\) | 17.8682 | + | 30.9487i | 0.609656 | + | 1.05596i | 0.991297 | + | 0.131644i | \(0.0420257\pi\) |
−0.381641 | + | 0.924311i | \(0.624641\pi\) | |||||||
\(860\) | −4.53264 | − | 7.85077i | −0.154562 | − | 0.267709i | ||||
\(861\) | 31.5262 | − | 54.6049i | 1.07441 | − | 1.86093i | ||||
\(862\) | 3.03186 | 0.103266 | ||||||||
\(863\) | −8.07597 | −0.274909 | −0.137455 | − | 0.990508i | \(-0.543892\pi\) | ||||
−0.137455 | + | 0.990508i | \(0.543892\pi\) | |||||||
\(864\) | 3.08503 | + | 5.34343i | 0.104955 | + | 0.181787i | ||||
\(865\) | −7.64982 | + | 13.2499i | −0.260102 | + | 0.450509i | ||||
\(866\) | 19.4988 | 0.662596 | ||||||||
\(867\) | −8.35037 | − | 14.4633i | −0.283594 | − | 0.491198i | ||||
\(868\) | 33.4740 | 1.13618 | ||||||||
\(869\) | −19.2314 | + | 33.3097i | −0.652380 | + | 1.12996i | ||||
\(870\) | −13.7931 | −0.467630 | ||||||||
\(871\) | −3.97426 | − | 7.22435i | −0.134663 | − | 0.244788i | ||||
\(872\) | −13.3672 | −0.452671 | ||||||||
\(873\) | 3.31630 | − | 5.74400i | 0.112240 | − | 0.194405i | ||||
\(874\) | 8.90067 | 0.301070 | ||||||||
\(875\) | −2.24706 | − | 3.89203i | −0.0759646 | − | 0.131574i | ||||
\(876\) | 36.1254 | 1.22057 | ||||||||
\(877\) | −11.2332 | + | 19.4564i | −0.379317 | + | 0.656997i | −0.990963 | − | 0.134135i | \(-0.957174\pi\) |
0.611646 | + | 0.791132i | \(0.290508\pi\) | |||||||
\(878\) | 2.73228 | + | 4.73244i | 0.0922099 | + | 0.159712i | ||||
\(879\) | 20.9836 | 0.707758 | ||||||||
\(880\) | −3.15996 | −0.106522 | ||||||||
\(881\) | −16.2695 | + | 28.1796i | −0.548134 | + | 0.949395i | 0.450269 | + | 0.892893i | \(0.351328\pi\) |
−0.998402 | + | 0.0565023i | \(0.982005\pi\) | |||||||
\(882\) | 34.0484 | + | 58.9735i | 1.14647 | + | 1.98574i | ||||
\(883\) | −9.77152 | − | 16.9248i | −0.328838 | − | 0.569564i | 0.653444 | − | 0.756975i | \(-0.273324\pi\) |
−0.982282 | + | 0.187411i | \(0.939990\pi\) | |||||||
\(884\) | −2.40742 | + | 4.16977i | −0.0809703 | + | 0.140245i | ||||
\(885\) | 10.1414 | 0.340901 | ||||||||
\(886\) | 28.4699 | 0.956467 | ||||||||
\(887\) | −8.98005 | + | 15.5539i | −0.301520 | + | 0.522249i | −0.976481 | − | 0.215606i | \(-0.930827\pi\) |
0.674960 | + | 0.737854i | \(0.264161\pi\) | |||||||
\(888\) | −0.800968 | + | 1.38732i | −0.0268787 | + | 0.0465553i | ||||
\(889\) | 0.329146 | − | 0.570097i | 0.0110392 | − | 0.0191204i | ||||
\(890\) | 1.76120 | − | 3.05049i | 0.0590355 | − | 0.102253i | ||||
\(891\) | −3.38952 | − | 5.87082i | −0.113553 | − | 0.196680i | ||||
\(892\) | 8.22719 | + | 14.2499i | 0.275467 | + | 0.477122i | ||||
\(893\) | −28.4060 | −0.950569 | ||||||||
\(894\) | 20.2385 | − | 35.0540i | 0.676875 | − | 1.17238i | ||||
\(895\) | 0.218731 | 0.00731139 | ||||||||
\(896\) | 4.49412 | 0.150138 | ||||||||
\(897\) | 5.72527 | + | 9.91647i | 0.191161 | + | 0.331101i | ||||
\(898\) | −16.4825 | −0.550029 | ||||||||
\(899\) | −17.9825 | + | 31.1467i | −0.599751 | + | 1.03880i | ||||
\(900\) | −2.57998 | − | 4.46866i | −0.0859993 | − | 0.148955i | ||||
\(901\) | −8.49241 | + | 14.7093i | −0.282923 | + | 0.490037i | ||||
\(902\) | 7.76004 | + | 13.4408i | 0.258381 | + | 0.447529i | ||||
\(903\) | −58.1890 | − | 100.786i | −1.93641 | − | 3.35396i | ||||
\(904\) | −3.75547 | − | 6.50466i | −0.124905 | − | 0.216342i | ||||
\(905\) | −11.3277 | − | 19.6202i | −0.376547 | − | 0.652198i | ||||
\(906\) | 9.82108 | + | 17.0106i | 0.326283 | + | 0.565139i | ||||
\(907\) | 7.17966 | + | 12.4355i | 0.238397 | + | 0.412915i | 0.960254 | − | 0.279126i | \(-0.0900448\pi\) |
−0.721858 | + | 0.692041i | \(0.756712\pi\) | |||||||
\(908\) | −5.76358 | + | 9.98282i | −0.191271 | + | 0.331292i | ||||
\(909\) | −19.2250 | − | 33.2986i | −0.637652 | − | 1.10445i | ||||
\(910\) | −2.26354 | + | 3.92056i | −0.0750355 | + | 0.129965i | ||||
\(911\) | −36.7883 | −1.21885 | −0.609425 | − | 0.792844i | \(-0.708600\pi\) | ||||
−0.609425 | + | 0.792844i | \(0.708600\pi\) | |||||||
\(912\) | 3.19468 | + | 5.53334i | 0.105786 | + | 0.183227i | ||||
\(913\) | 43.1194 | 1.42704 | ||||||||
\(914\) | 15.0400 | 0.497479 | ||||||||
\(915\) | 19.0834 | − | 33.0534i | 0.630877 | − | 1.09271i | ||||
\(916\) | −28.3692 | −0.937345 | ||||||||
\(917\) | 24.7652 | + | 42.8946i | 0.817819 | + | 1.41650i | ||||
\(918\) | −14.7458 | − | 25.5405i | −0.486684 | − | 0.842962i | ||||
\(919\) | 24.5733 | − | 42.5623i | 0.810599 | − | 1.40400i | −0.101846 | − | 0.994800i | \(-0.532475\pi\) |
0.912445 | − | 0.409199i | \(-0.134192\pi\) | |||||||
\(920\) | −1.98966 | + | 3.44620i | −0.0655973 | + | 0.113618i | ||||
\(921\) | −9.18260 | + | 15.9047i | −0.302577 | + | 0.524079i | ||||
\(922\) | −1.53125 | + | 2.65220i | −0.0504291 | + | 0.0873457i | ||||
\(923\) | −3.93117 | −0.129396 | ||||||||
\(924\) | −40.5668 | −1.33455 | ||||||||
\(925\) | 0.280396 | − | 0.485660i | 0.00921935 | − | 0.0159684i | ||||
\(926\) | 20.9244 | + | 36.2422i | 0.687619 | + | 1.19099i | ||||
\(927\) | −24.4757 | − | 42.3932i | −0.803888 | − | 1.39238i | ||||
\(928\) | −2.41428 | + | 4.18166i | −0.0792527 | + | 0.137270i | ||||
\(929\) | −47.2750 | −1.55104 | −0.775521 | − | 0.631322i | \(-0.782513\pi\) | ||||
−0.775521 | + | 0.631322i | \(0.782513\pi\) | |||||||
\(930\) | −21.2768 | −0.697695 | ||||||||
\(931\) | 14.7592 | + | 25.5637i | 0.483714 | + | 0.837817i | ||||
\(932\) | −1.39110 | + | 2.40945i | −0.0455669 | + | 0.0789242i | ||||
\(933\) | 64.9821 | 2.12742 | ||||||||
\(934\) | −3.88008 | − | 6.72050i | −0.126960 | − | 0.219902i | ||||
\(935\) | 15.1040 | 0.493952 | ||||||||
\(936\) | −2.59889 | + | 4.50142i | −0.0849475 | + | 0.147133i | ||||
\(937\) | −35.0244 | −1.14420 | −0.572098 | − | 0.820185i | \(-0.693870\pi\) | ||||
−0.572098 | + | 0.820185i | \(0.693870\pi\) | |||||||
\(938\) | 19.0473 | − | 31.4708i | 0.621917 | − | 1.02756i | ||||
\(939\) | −29.8987 | −0.975708 | ||||||||
\(940\) | 6.34989 | − | 10.9983i | 0.207111 | − | 0.358726i | ||||
\(941\) | 55.6740 | 1.81492 | 0.907460 | − | 0.420139i | \(-0.138019\pi\) | ||||
0.907460 | + | 0.420139i | \(0.138019\pi\) | |||||||
\(942\) | −28.6952 | − | 49.7016i | −0.934940 | − | 1.61936i | ||||
\(943\) | 19.5444 | 0.636453 | ||||||||
\(944\) | 1.77511 | − | 3.07458i | 0.0577749 | − | 0.100069i | ||||
\(945\) | −13.8645 | − | 24.0140i | −0.451012 | − | 0.781176i | ||||
\(946\) | 28.6459 | 0.931360 | ||||||||
\(947\) | 17.4537 | 0.567168 | 0.283584 | − | 0.958947i | \(-0.408476\pi\) | ||||
0.283584 | + | 0.958947i | \(0.408476\pi\) | |||||||
\(948\) | −17.3849 | + | 30.1116i | −0.564636 | + | 0.977979i | ||||
\(949\) | 6.36959 | + | 11.0325i | 0.206766 | + | 0.358129i | ||||
\(950\) | −1.11836 | − | 1.93706i | −0.0362845 | − | 0.0628466i | ||||
\(951\) | −47.5880 | + | 82.4249i | −1.54315 | + | 2.67281i | ||||
\(952\) | −21.4810 | −0.696203 | ||||||||
\(953\) | −7.64184 | −0.247543 | −0.123772 | − | 0.992311i | \(-0.539499\pi\) | ||||
−0.123772 | + | 0.992311i | \(0.539499\pi\) | |||||||
\(954\) | −9.16785 | + | 15.8792i | −0.296820 | + | 0.514108i | ||||
\(955\) | 0.588841 | − | 1.01990i | 0.0190544 | − | 0.0330032i | ||||
\(956\) | −12.1378 | + | 21.0233i | −0.392565 | + | 0.679943i | ||||
\(957\) | 21.7928 | − | 37.7463i | 0.704461 | − | 1.22016i | ||||
\(958\) | 2.69733 | + | 4.67192i | 0.0871469 | + | 0.150943i | ||||
\(959\) | −33.4099 | − | 57.8677i | −1.07886 | − | 1.86865i | ||||
\(960\) | −2.85656 | −0.0921952 | ||||||||
\(961\) | −12.2393 | + | 21.1991i | −0.394817 | + | 0.683843i | ||||
\(962\) | −0.564903 | −0.0182132 | ||||||||
\(963\) | 48.2197 | 1.55386 | ||||||||
\(964\) | −3.46574 | − | 6.00283i | −0.111624 | − | 0.193338i | ||||
\(965\) | 8.71036 | 0.280396 | ||||||||
\(966\) | −25.5428 | + | 44.2415i | −0.821827 | + | 1.42345i | ||||
\(967\) | 3.89292 | + | 6.74274i | 0.125188 | + | 0.216832i | 0.921806 | − | 0.387651i | \(-0.126713\pi\) |
−0.796618 | + | 0.604482i | \(0.793380\pi\) | |||||||
\(968\) | −0.507331 | + | 0.878724i | −0.0163063 | + | 0.0282433i | ||||
\(969\) | −15.2699 | − | 26.4482i | −0.490540 | − | 0.849640i | ||||
\(970\) | 0.642699 | + | 1.11319i | 0.0206358 | + | 0.0357423i | ||||
\(971\) | −17.9921 | − | 31.1632i | −0.577394 | − | 1.00008i | −0.995777 | − | 0.0918054i | \(-0.970736\pi\) |
0.418383 | − | 0.908271i | \(-0.362597\pi\) | |||||||
\(972\) | 6.19100 | + | 10.7231i | 0.198576 | + | 0.343945i | ||||
\(973\) | 14.4468 | + | 25.0226i | 0.463144 | + | 0.802189i | ||||
\(974\) | −0.707213 | − | 1.22493i | −0.0226606 | − | 0.0392493i | ||||
\(975\) | 1.43875 | − | 2.49199i | 0.0460770 | − | 0.0798077i | ||||
\(976\) | −6.68053 | − | 11.5710i | −0.213839 | − | 0.370379i | ||||
\(977\) | 9.67400 | − | 16.7559i | 0.309499 | − | 0.536067i | −0.668754 | − | 0.743484i | \(-0.733172\pi\) |
0.978253 | + | 0.207416i | \(0.0665054\pi\) | |||||||
\(978\) | 11.6133 | 0.371351 | ||||||||
\(979\) | 5.56532 | + | 9.63941i | 0.177868 | + | 0.308077i | ||||
\(980\) | −13.1972 | −0.421568 | ||||||||
\(981\) | 68.9743 | 2.20218 | ||||||||
\(982\) | −19.7122 | + | 34.1426i | −0.629043 | + | 1.08953i | ||||
\(983\) | −48.9508 | −1.56129 | −0.780643 | − | 0.624977i | \(-0.785108\pi\) | ||||
−0.780643 | + | 0.624977i | \(0.785108\pi\) | |||||||
\(984\) | 7.01498 | + | 12.1503i | 0.223629 | + | 0.387337i | ||||
\(985\) | −8.00919 | − | 13.8723i | −0.255194 | − | 0.442009i | ||||
\(986\) | 11.5398 | − | 19.9875i | 0.367501 | − | 0.636531i | ||||
\(987\) | 81.5184 | − | 141.194i | 2.59476 | − | 4.49425i | ||||
\(988\) | −1.12656 | + | 1.95126i | −0.0358407 | + | 0.0620780i | ||||
\(989\) | 18.0369 | − | 31.2408i | 0.573540 | − | 0.993400i | ||||
\(990\) | 16.3053 | 0.518215 | ||||||||
\(991\) | −7.45780 | −0.236905 | −0.118452 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118452 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(992\) | −3.72420 | + | 6.45050i | −0.118243 | + | 0.204804i | ||||
\(993\) | 30.9584 | + | 53.6215i | 0.982436 | + | 1.70163i | ||||
\(994\) | −8.76930 | − | 15.1889i | −0.278145 | − | 0.481762i | ||||
\(995\) | 6.98114 | − | 12.0917i | 0.221317 | − | 0.383332i | ||||
\(996\) | 38.9794 | 1.23511 | ||||||||
\(997\) | −39.7859 | −1.26003 | −0.630017 | − | 0.776582i | \(-0.716952\pi\) | ||||
−0.630017 | + | 0.776582i | \(0.716952\pi\) | |||||||
\(998\) | −11.6957 | − | 20.2575i | −0.370220 | − | 0.641240i | ||||
\(999\) | 1.73006 | − | 2.99655i | 0.0547366 | − | 0.0948066i |
(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 | 670.2.e.j.431.6 | yes | 12 | |
67.37 | even | 3 | inner | 670.2.e.j.171.6 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
670.2.e.j.171.6 | ✓ | 12 | 67.37 | even | 3 | inner | |
670.2.e.j.431.6 | yes | 12 | 1.1 | even | 1 | trivial |