Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.2 | ||
Root | \(-3.11681 - 1.79949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.607 |
Dual form | 1050.2.bc.f.493.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | 0.258819 | − | 0.965926i | 0.149429 | − | 0.557678i | ||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.63306 | − | 0.258819i | 0.995204 | − | 0.0978244i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54487 | − | 4.40784i | −0.767307 | − | 1.32901i | −0.939018 | − | 0.343867i | \(-0.888263\pi\) |
0.171712 | − | 0.985147i | \(-0.445070\pi\) | |||||||
\(12\) | −0.258819 | − | 0.965926i | −0.0747146 | − | 0.278839i | ||||
\(13\) | 2.02443 | + | 2.02443i | 0.561475 | + | 0.561475i | 0.929726 | − | 0.368251i | \(-0.120043\pi\) |
−0.368251 | + | 0.929726i | \(0.620043\pi\) | |||||||
\(14\) | −2.47635 | + | 0.931486i | −0.661834 | + | 0.248950i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 6.71580 | + | 1.79949i | 1.62882 | + | 0.436441i | 0.953576 | − | 0.301152i | \(-0.0973712\pi\) |
0.675245 | + | 0.737593i | \(0.264038\pi\) | |||||||
\(18\) | 0.965926 | + | 0.258819i | 0.227671 | + | 0.0610042i | ||||
\(19\) | −1.79751 | + | 3.11338i | −0.412378 | + | 0.714259i | −0.995149 | − | 0.0983771i | \(-0.968635\pi\) |
0.582772 | + | 0.812636i | \(0.301968\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.431486 | − | 2.61033i | 0.0941581 | − | 0.569621i | ||||
\(22\) | 3.59899 | + | 3.59899i | 0.767307 | + | 0.767307i | ||||
\(23\) | −1.79949 | − | 6.71580i | −0.375220 | − | 1.40034i | −0.853023 | − | 0.521874i | \(-0.825233\pi\) |
0.477802 | − | 0.878467i | \(-0.341434\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.47941 | − | 1.43149i | −0.486252 | − | 0.280738i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.15089 | − | 1.54067i | 0.406480 | − | 0.291160i | ||||
\(29\) | − | 8.81568i | − | 1.63703i | −0.574484 | − | 0.818516i | \(-0.694797\pi\) | ||
0.574484 | − | 0.818516i | \(-0.305203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61338 | − | 0.931486i | 0.289772 | − | 0.167300i | −0.348067 | − | 0.937470i | \(-0.613162\pi\) |
0.637839 | + | 0.770170i | \(0.279829\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | −4.91631 | + | 1.31732i | −0.855819 | + | 0.229316i | ||||
\(34\) | −6.95271 | −1.19238 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 7.50959 | − | 2.01219i | 1.23457 | − | 0.330802i | 0.418212 | − | 0.908350i | \(-0.362657\pi\) |
0.816357 | + | 0.577548i | \(0.195990\pi\) | |||||||
\(38\) | 0.930461 | − | 3.47253i | 0.150941 | − | 0.563318i | ||||
\(39\) | 2.47941 | − | 1.43149i | 0.397023 | − | 0.229221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.13703i | 0.646095i | 0.946383 | + | 0.323048i | \(0.104707\pi\) | ||||
−0.946383 | + | 0.323048i | \(0.895293\pi\) | |||||||
\(42\) | 0.258819 | + | 2.63306i | 0.0399366 | + | 0.406290i | ||||
\(43\) | −7.84163 | + | 7.84163i | −1.19584 | + | 1.19584i | −0.220436 | + | 0.975402i | \(0.570748\pi\) |
−0.975402 | + | 0.220436i | \(0.929252\pi\) | |||||||
\(44\) | −4.40784 | − | 2.54487i | −0.664507 | − | 0.383653i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.47635 | + | 6.02122i | 0.512561 | + | 0.887781i | ||||
\(47\) | 0.482173 | + | 1.79949i | 0.0703321 | + | 0.262483i | 0.992134 | − | 0.125177i | \(-0.0399500\pi\) |
−0.921802 | + | 0.387660i | \(0.873283\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 6.86603 | − | 1.36297i | 0.980861 | − | 0.194710i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.47635 | − | 6.02122i | 0.486787 | − | 0.843140i | ||||
\(52\) | 2.76542 | + | 0.740992i | 0.383495 | + | 0.102757i | ||||
\(53\) | 0.879247 | + | 0.235593i | 0.120774 | + | 0.0323613i | 0.318700 | − | 0.947856i | \(-0.396754\pi\) |
−0.197926 | + | 0.980217i | \(0.563421\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.67884 | + | 2.04487i | −0.224345 | + | 0.273257i | ||||
\(57\) | 2.54207 | + | 2.54207i | 0.336705 | + | 0.336705i | ||||
\(58\) | 2.28167 | + | 8.51530i | 0.299597 | + | 1.11811i | ||||
\(59\) | −2.08974 | − | 3.61953i | −0.272061 | − | 0.471223i | 0.697329 | − | 0.716751i | \(-0.254372\pi\) |
−0.969389 | + | 0.245529i | \(0.921038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.08277 | − | 2.93454i | −0.650782 | − | 0.375729i | 0.137974 | − | 0.990436i | \(-0.455941\pi\) |
−0.788756 | + | 0.614707i | \(0.789274\pi\) | |||||||
\(62\) | −1.31732 | + | 1.31732i | −0.167300 | + | 0.167300i | ||||
\(63\) | −2.40971 | − | 1.09239i | −0.303595 | − | 0.137628i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.40784 | − | 2.54487i | 0.542568 | − | 0.313252i | ||||
\(67\) | 0.762637 | − | 2.84620i | 0.0931710 | − | 0.347719i | −0.903565 | − | 0.428451i | \(-0.859059\pi\) |
0.996736 | + | 0.0807326i | \(0.0257260\pi\) | |||||||
\(68\) | 6.71580 | − | 1.79949i | 0.814411 | − | 0.218221i | ||||
\(69\) | −6.95271 | −0.837008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.86297 | 0.933163 | 0.466582 | − | 0.884478i | \(-0.345485\pi\) | ||||
0.466582 | + | 0.884478i | \(0.345485\pi\) | |||||||
\(72\) | 0.965926 | − | 0.258819i | 0.113835 | − | 0.0305021i | ||||
\(73\) | 3.50165 | − | 13.0683i | 0.409837 | − | 1.52953i | −0.385120 | − | 0.922867i | \(-0.625840\pi\) |
0.794957 | − | 0.606666i | \(-0.207493\pi\) | |||||||
\(74\) | −6.73291 | + | 3.88725i | −0.782685 | + | 0.451883i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.59502i | 0.412378i | ||||||||
\(77\) | −7.84163 | − | 10.9475i | −0.893636 | − | 1.24758i | ||||
\(78\) | −2.02443 | + | 2.02443i | −0.229221 | + | 0.229221i | ||||
\(79\) | −10.4700 | − | 6.04487i | −1.17797 | − | 0.680101i | −0.222425 | − | 0.974950i | \(-0.571397\pi\) |
−0.955544 | + | 0.294849i | \(0.904731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.07074 | − | 3.99606i | −0.118244 | − | 0.441291i | ||||
\(83\) | −1.99099 | − | 1.99099i | −0.218539 | − | 0.218539i | 0.589343 | − | 0.807883i | \(-0.299387\pi\) |
−0.807883 | + | 0.589343i | \(0.799387\pi\) | |||||||
\(84\) | −0.931486 | − | 2.47635i | −0.101634 | − | 0.270192i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.54487 | − | 9.60399i | 0.597919 | − | 1.03563i | ||||
\(87\) | −8.51530 | − | 2.28167i | −0.912935 | − | 0.244620i | ||||
\(88\) | 4.91631 | + | 1.31732i | 0.524080 | + | 0.140427i | ||||
\(89\) | 3.82507 | − | 6.62522i | 0.405457 | − | 0.702272i | −0.588918 | − | 0.808193i | \(-0.700446\pi\) |
0.994375 | + | 0.105921i | \(0.0337792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.85440 | + | 4.80648i | 0.613708 | + | 0.503856i | ||||
\(92\) | −4.91631 | − | 4.91631i | −0.512561 | − | 0.512561i | ||||
\(93\) | −0.482173 | − | 1.79949i | −0.0499990 | − | 0.186599i | ||||
\(94\) | −0.931486 | − | 1.61338i | −0.0960755 | − | 0.166408i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 13.4951 | − | 13.4951i | 1.37022 | − | 1.37022i | 0.510101 | − | 0.860115i | \(-0.329608\pi\) |
0.860115 | − | 0.510101i | \(-0.170392\pi\) | |||||||
\(98\) | −6.27931 | + | 3.09359i | −0.634306 | + | 0.312500i | ||||
\(99\) | 5.08974i | 0.511538i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.18108 | − | 0.681895i | 0.117522 | − | 0.0678511i | −0.440087 | − | 0.897955i | \(-0.645052\pi\) |
0.557609 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(102\) | −1.79949 | + | 6.71580i | −0.178176 | + | 0.664963i | ||||
\(103\) | 0.351395 | − | 0.0941560i | 0.0346240 | − | 0.00927747i | −0.241465 | − | 0.970409i | \(-0.577628\pi\) |
0.276089 | + | 0.961132i | \(0.410961\pi\) | |||||||
\(104\) | −2.86297 | −0.280738 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.910263 | −0.0884126 | ||||||||
\(107\) | 0.205579 | − | 0.0550849i | 0.0198741 | − | 0.00532525i | −0.248868 | − | 0.968537i | \(-0.580059\pi\) |
0.268742 | + | 0.963212i | \(0.413392\pi\) | |||||||
\(108\) | −0.258819 | + | 0.965926i | −0.0249049 | + | 0.0929463i | ||||
\(109\) | 1.35135 | − | 0.780202i | 0.129436 | − | 0.0747298i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.77450i | − | 0.737923i | ||||||
\(112\) | 1.09239 | − | 2.40971i | 0.103221 | − | 0.227696i | ||||
\(113\) | 0.0300140 | − | 0.0300140i | 0.00282348 | − | 0.00282348i | −0.705694 | − | 0.708517i | \(-0.749364\pi\) |
0.708517 | + | 0.705694i | \(0.249364\pi\) | |||||||
\(114\) | −3.11338 | − | 1.79751i | −0.291595 | − | 0.168352i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.40784 | − | 7.63460i | −0.409258 | − | 0.708855i | ||||
\(117\) | −0.740992 | − | 2.76542i | −0.0685047 | − | 0.255663i | ||||
\(118\) | 2.95533 | + | 2.95533i | 0.272061 | + | 0.272061i | ||||
\(119\) | 18.1489 | + | 3.00000i | 1.66370 | + | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.45271 | + | 12.9085i | −0.677519 | + | 1.17350i | ||||
\(122\) | 5.66909 | + | 1.51903i | 0.513256 | + | 0.137526i | ||||
\(123\) | 3.99606 | + | 1.07074i | 0.360313 | + | 0.0965455i | ||||
\(124\) | 0.931486 | − | 1.61338i | 0.0836500 | − | 0.144886i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.61033 | + | 0.431486i | 0.232547 | + | 0.0384399i | ||||
\(127\) | −1.42723 | − | 1.42723i | −0.126646 | − | 0.126646i | 0.640943 | − | 0.767589i | \(-0.278544\pi\) |
−0.767589 | + | 0.640943i | \(0.778544\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | 5.54487 | + | 9.60399i | 0.488198 | + | 0.845584i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.59216 | − | 2.65128i | −0.401219 | − | 0.231644i | 0.285791 | − | 0.958292i | \(-0.407744\pi\) |
−0.687010 | + | 0.726648i | \(0.741077\pi\) | |||||||
\(132\) | −3.59899 | + | 3.59899i | −0.313252 | + | 0.313252i | ||||
\(133\) | −3.92716 | + | 8.66296i | −0.340528 | + | 0.751174i | ||||
\(134\) | 2.94660i | 0.254548i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.02122 | + | 3.47635i | −0.516316 | + | 0.298095i | ||||
\(137\) | −5.68916 | + | 21.2322i | −0.486058 | + | 1.81399i | 0.0891925 | + | 0.996014i | \(0.471571\pi\) |
−0.575250 | + | 0.817978i | \(0.695095\pi\) | |||||||
\(138\) | 6.71580 | − | 1.79949i | 0.571687 | − | 0.153183i | ||||
\(139\) | 16.5902 | 1.40716 | 0.703580 | − | 0.710616i | \(-0.251584\pi\) | ||||
0.703580 | + | 0.710616i | \(0.251584\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.86297 | 0.156891 | ||||||||
\(142\) | −7.59505 | + | 2.03509i | −0.637362 | + | 0.170781i | ||||
\(143\) | 3.77145 | − | 14.0753i | 0.315385 | − | 1.17703i | ||||
\(144\) | −0.866025 | + | 0.500000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.5293i | 1.11970i | ||||||||
\(147\) | 0.460527 | − | 6.98483i | 0.0379837 | − | 0.576099i | ||||
\(148\) | 5.49740 | − | 5.49740i | 0.451883 | − | 0.451883i | ||||
\(149\) | −8.60723 | − | 4.96939i | −0.705132 | − | 0.407108i | 0.104124 | − | 0.994564i | \(-0.466796\pi\) |
−0.809256 | + | 0.587456i | \(0.800129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.65825 | + | 13.2645i | 0.623220 | + | 1.07945i | 0.988882 | + | 0.148701i | \(0.0475090\pi\) |
−0.365663 | + | 0.930747i | \(0.619158\pi\) | |||||||
\(152\) | −0.930461 | − | 3.47253i | −0.0754703 | − | 0.281659i | ||||
\(153\) | −4.91631 | − | 4.91631i | −0.397460 | − | 0.397460i | ||||
\(154\) | 10.4078 | + | 8.54487i | 0.838688 | + | 0.688565i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.43149 | − | 2.47941i | 0.114611 | − | 0.198511i | ||||
\(157\) | 15.7881 | + | 4.23040i | 1.26003 | + | 0.337623i | 0.826201 | − | 0.563375i | \(-0.190497\pi\) |
0.433824 | + | 0.900998i | \(0.357164\pi\) | |||||||
\(158\) | 11.6778 | + | 3.12905i | 0.929035 | + | 0.248934i | ||||
\(159\) | 0.455132 | − | 0.788311i | 0.0360943 | − | 0.0625171i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.47635 | − | 17.2174i | −0.510408 | − | 1.35692i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 1.93977 | + | 7.23934i | 0.151935 | + | 0.567029i | 0.999348 | + | 0.0360951i | \(0.0114919\pi\) |
−0.847413 | + | 0.530933i | \(0.821841\pi\) | |||||||
\(164\) | 2.06851 | + | 3.58277i | 0.161524 | + | 0.279767i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.43845 | + | 1.40784i | 0.189261 | + | 0.109270i | ||||
\(167\) | −12.7880 | + | 12.7880i | −0.989561 | + | 0.989561i | −0.999946 | − | 0.0103848i | \(-0.996694\pi\) |
0.0103848 | + | 0.999946i | \(0.496694\pi\) | |||||||
\(168\) | 1.54067 | + | 2.15089i | 0.118866 | + | 0.165945i | ||||
\(169\) | − | 4.80339i | − | 0.369491i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.11338 | − | 1.79751i | 0.238086 | − | 0.137459i | ||||
\(172\) | −2.87024 | + | 10.7119i | −0.218853 | + | 0.816772i | ||||
\(173\) | −15.6282 | + | 4.18756i | −1.18819 | + | 0.318374i | −0.798169 | − | 0.602433i | \(-0.794198\pi\) |
−0.390018 | + | 0.920807i | \(0.627531\pi\) | |||||||
\(174\) | 8.81568 | 0.668315 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.08974 | −0.383653 | ||||||||
\(177\) | −4.03706 | + | 1.08173i | −0.303444 | + | 0.0813076i | ||||
\(178\) | −1.98000 | + | 7.38947i | −0.148407 | + | 0.553864i | ||||
\(179\) | −8.60723 | + | 4.96939i | −0.643335 | + | 0.371430i | −0.785898 | − | 0.618356i | \(-0.787799\pi\) |
0.142563 | + | 0.989786i | \(0.454466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.60285i | 0.193468i | 0.995310 | + | 0.0967342i | \(0.0308397\pi\) | ||||
−0.995310 | + | 0.0967342i | \(0.969160\pi\) | |||||||
\(182\) | −6.89893 | − | 3.12747i | −0.511383 | − | 0.231824i | ||||
\(183\) | −4.15006 | + | 4.15006i | −0.306782 | + | 0.306782i | ||||
\(184\) | 6.02122 | + | 3.47635i | 0.443890 | + | 0.256280i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.931486 | + | 1.61338i | 0.0682999 | + | 0.118299i | ||||
\(187\) | −9.15895 | − | 34.1817i | −0.669769 | − | 2.49961i | ||||
\(188\) | 1.31732 | + | 1.31732i | 0.0960755 | + | 0.0960755i | ||||
\(189\) | −1.67884 | + | 2.04487i | −0.122118 | + | 0.148742i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.06851 | + | 3.58277i | −0.149672 | + | 0.259240i | −0.931106 | − | 0.364748i | \(-0.881155\pi\) |
0.781434 | + | 0.623988i | \(0.214489\pi\) | |||||||
\(192\) | −0.965926 | − | 0.258819i | −0.0697097 | − | 0.0186787i | ||||
\(193\) | 12.5114 | + | 3.35241i | 0.900587 | + | 0.241312i | 0.679268 | − | 0.733890i | \(-0.262297\pi\) |
0.221319 | + | 0.975202i | \(0.428964\pi\) | |||||||
\(194\) | −9.54245 | + | 16.5280i | −0.685108 | + | 1.18664i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.26467 | − | 4.61338i | 0.376048 | − | 0.329527i | ||||
\(197\) | 0.876148 | + | 0.876148i | 0.0624229 | + | 0.0624229i | 0.737629 | − | 0.675206i | \(-0.235945\pi\) |
−0.675206 | + | 0.737629i | \(0.735945\pi\) | |||||||
\(198\) | −1.31732 | − | 4.91631i | −0.0936179 | − | 0.349387i | ||||
\(199\) | 8.63155 | + | 14.9503i | 0.611875 | + | 1.05980i | 0.990924 | + | 0.134421i | \(0.0429176\pi\) |
−0.379050 | + | 0.925376i | \(0.623749\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.55183 | − | 1.47330i | −0.179993 | − | 0.103919i | ||||
\(202\) | −0.964346 | + | 0.964346i | −0.0678511 | + | 0.0678511i | ||||
\(203\) | −2.28167 | − | 23.2122i | −0.160142 | − | 1.62918i | ||||
\(204\) | − | 6.95271i | − | 0.486787i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.315052 | + | 0.181895i | −0.0219507 | + | 0.0126733i | ||||
\(207\) | −1.79949 | + | 6.71580i | −0.125073 | + | 0.466780i | ||||
\(208\) | 2.76542 | − | 0.740992i | 0.191747 | − | 0.0513785i | ||||
\(209\) | 18.2977 | 1.26568 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.40460 | −0.509754 | −0.254877 | − | 0.966974i | \(-0.582035\pi\) | ||||
−0.254877 | + | 0.966974i | \(0.582035\pi\) | |||||||
\(212\) | 0.879247 | − | 0.235593i | 0.0603869 | − | 0.0161806i | ||||
\(213\) | 2.03509 | − | 7.59505i | 0.139442 | − | 0.520404i | ||||
\(214\) | −0.184318 | + | 0.106416i | −0.0125997 | + | 0.00727443i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 4.00705 | − | 2.87024i | 0.272016 | − | 0.194844i | ||||
\(218\) | −1.10337 | + | 1.10337i | −0.0747298 | + | 0.0747298i | ||||
\(219\) | −11.7167 | − | 6.76467i | −0.791744 | − | 0.457114i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.95271 | + | 17.2386i | 0.669492 | + | 1.15959i | ||||
\(222\) | 2.01219 | + | 7.50959i | 0.135049 | + | 0.504011i | ||||
\(223\) | −2.69809 | − | 2.69809i | −0.180678 | − | 0.180678i | 0.610973 | − | 0.791651i | \(-0.290778\pi\) |
−0.791651 | + | 0.610973i | \(0.790778\pi\) | |||||||
\(224\) | −0.431486 | + | 2.61033i | −0.0288299 | + | 0.174410i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0212231 | + | 0.0367595i | −0.00141174 | + | 0.00244520i | ||||
\(227\) | −19.0216 | − | 5.09682i | −1.26251 | − | 0.338288i | −0.435351 | − | 0.900261i | \(-0.643376\pi\) |
−0.827155 | + | 0.561973i | \(0.810042\pi\) | |||||||
\(228\) | 3.47253 | + | 0.930461i | 0.229974 | + | 0.0616213i | ||||
\(229\) | −11.4884 | + | 19.8985i | −0.759173 | + | 1.31493i | 0.184099 | + | 0.982908i | \(0.441063\pi\) |
−0.943273 | + | 0.332019i | \(0.892270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.6040 | + | 4.74102i | −0.829282 | + | 0.311936i | ||||
\(232\) | 6.23363 | + | 6.23363i | 0.409258 | + | 0.409258i | ||||
\(233\) | 3.42652 | + | 12.7880i | 0.224479 | + | 0.837766i | 0.982613 | + | 0.185667i | \(0.0594447\pi\) |
−0.758134 | + | 0.652099i | \(0.773889\pi\) | |||||||
\(234\) | 1.43149 | + | 2.47941i | 0.0935792 | + | 0.162084i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.61953 | − | 2.08974i | −0.235611 | − | 0.136030i | ||||
\(237\) | −8.54873 | + | 8.54873i | −0.555300 | + | 0.555300i | ||||
\(238\) | −18.3069 | + | 1.79949i | −1.18666 | + | 0.116644i | ||||
\(239\) | 1.65014i | 0.106739i | 0.998575 | + | 0.0533694i | \(0.0169961\pi\) | ||||
−0.998575 | + | 0.0533694i | \(0.983004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.9564 | + | 6.32570i | −0.705766 | + | 0.407474i | −0.809491 | − | 0.587132i | \(-0.800257\pi\) |
0.103725 | + | 0.994606i | \(0.466924\pi\) | |||||||
\(242\) | 3.85781 | − | 14.3975i | 0.247989 | − | 0.925508i | ||||
\(243\) | 0.965926 | − | 0.258819i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | −5.86908 | −0.375729 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.13703 | −0.263767 | ||||||||
\(247\) | −9.94175 | + | 2.66388i | −0.632578 | + | 0.169499i | ||||
\(248\) | −0.482173 | + | 1.79949i | −0.0306180 | + | 0.114268i | ||||
\(249\) | −2.43845 | + | 1.40784i | −0.154531 | + | 0.0892183i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.45189i | 0.470359i | 0.971952 | + | 0.235180i | \(0.0755678\pi\) | ||||
−0.971952 | + | 0.235180i | \(0.924432\pi\) | |||||||
\(252\) | −2.63306 | + | 0.258819i | −0.165867 | + | 0.0163041i | ||||
\(253\) | −25.0227 | + | 25.0227i | −1.57316 | + | 1.57316i | ||||
\(254\) | 1.74799 | + | 1.00920i | 0.109678 | + | 0.0633229i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.30494 | + | 16.0662i | 0.268535 | + | 1.00218i | 0.960051 | + | 0.279824i | \(0.0902762\pi\) |
−0.691517 | + | 0.722361i | \(0.743057\pi\) | |||||||
\(258\) | −7.84163 | − | 7.84163i | −0.488198 | − | 0.488198i | ||||
\(259\) | 19.2524 | − | 7.24184i | 1.19629 | − | 0.449986i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.40784 | + | 7.63460i | −0.272839 | + | 0.472570i | ||||
\(262\) | 5.12189 | + | 1.37241i | 0.316431 | + | 0.0847875i | ||||
\(263\) | 10.6709 | + | 2.85925i | 0.657994 | + | 0.176309i | 0.572340 | − | 0.820016i | \(-0.306036\pi\) |
0.0856532 | + | 0.996325i | \(0.472702\pi\) | |||||||
\(264\) | 2.54487 | − | 4.40784i | 0.156626 | − | 0.271284i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.55120 | − | 9.38420i | 0.0951104 | − | 0.575382i | ||||
\(267\) | −5.40947 | − | 5.40947i | −0.331054 | − | 0.331054i | ||||
\(268\) | −0.762637 | − | 2.84620i | −0.0465855 | − | 0.173859i | ||||
\(269\) | 13.3014 | + | 23.0387i | 0.811002 | + | 1.40470i | 0.912163 | + | 0.409827i | \(0.134411\pi\) |
−0.101161 | + | 0.994870i | \(0.532256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5946 | − | 10.1583i | −1.06880 | − | 0.617070i | −0.140944 | − | 0.990018i | \(-0.545014\pi\) |
−0.927852 | + | 0.372948i | \(0.878347\pi\) | |||||||
\(272\) | 4.91631 | − | 4.91631i | 0.298095 | − | 0.298095i | ||||
\(273\) | 6.15794 | − | 4.41091i | 0.372695 | − | 0.266960i | ||||
\(274\) | − | 21.9812i | − | 1.32793i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.02122 | + | 3.47635i | −0.362435 | + | 0.209252i | ||||
\(277\) | −2.60623 | + | 9.72658i | −0.156593 | + | 0.584414i | 0.842370 | + | 0.538899i | \(0.181160\pi\) |
−0.998964 | + | 0.0455149i | \(0.985507\pi\) | |||||||
\(278\) | −16.0249 | + | 4.29385i | −0.961109 | + | 0.257528i | ||||
\(279\) | −1.86297 | −0.111533 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2268 | 0.908353 | 0.454176 | − | 0.890912i | \(-0.349934\pi\) | ||||
0.454176 | + | 0.890912i | \(0.349934\pi\) | |||||||
\(282\) | −1.79949 | + | 0.482173i | −0.107158 | + | 0.0287130i | ||||
\(283\) | 3.83878 | − | 14.3265i | 0.228192 | − | 0.851623i | −0.752909 | − | 0.658125i | \(-0.771350\pi\) |
0.981101 | − | 0.193498i | \(-0.0619834\pi\) | |||||||
\(284\) | 6.80953 | − | 3.93149i | 0.404072 | − | 0.233291i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.5718i | 0.861647i | ||||||||
\(287\) | 1.07074 | + | 10.8930i | 0.0632039 | + | 0.642996i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 27.1414 | + | 15.6701i | 1.59655 | + | 0.921770i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.54245 | − | 16.5280i | −0.559388 | − | 0.968889i | ||||
\(292\) | −3.50165 | − | 13.0683i | −0.204918 | − | 0.764766i | ||||
\(293\) | 18.7009 | + | 18.7009i | 1.09252 | + | 1.09252i | 0.995259 | + | 0.0972583i | \(0.0310073\pi\) |
0.0972583 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(294\) | 1.36297 | + | 6.86603i | 0.0794902 | + | 0.400435i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.88725 | + | 6.73291i | −0.225942 | + | 0.391343i | ||||
\(297\) | 4.91631 | + | 1.31732i | 0.285273 | + | 0.0764387i | ||||
\(298\) | 9.60012 | + | 2.57234i | 0.556120 | + | 0.149012i | ||||
\(299\) | 9.95271 | − | 17.2386i | 0.575580 | − | 0.996934i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6179 | + | 22.6771i | −1.07312 | + | 1.30708i | ||||
\(302\) | −10.8304 | − | 10.8304i | −0.623220 | − | 0.623220i | ||||
\(303\) | −0.352975 | − | 1.31732i | −0.0202779 | − | 0.0756781i | ||||
\(304\) | 1.79751 | + | 3.11338i | 0.103094 | + | 0.178565i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.02122 | + | 3.47635i | 0.344210 | + | 0.198730i | ||||
\(307\) | −22.4937 | + | 22.4937i | −1.28378 | + | 1.28378i | −0.345282 | + | 0.938499i | \(0.612217\pi\) |
−0.938499 | + | 0.345282i | \(0.887783\pi\) | |||||||
\(308\) | −12.2648 | − | 5.55996i | −0.698851 | − | 0.316808i | ||||
\(309\) | − | 0.363791i | − | 0.0206953i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2598 | − | 8.23291i | 0.808600 | − | 0.466846i | −0.0378693 | − | 0.999283i | \(-0.512057\pi\) |
0.846470 | + | 0.532437i | \(0.178724\pi\) | |||||||
\(312\) | −0.740992 | + | 2.76542i | −0.0419504 | + | 0.156561i | ||||
\(313\) | 3.26105 | − | 0.873796i | 0.184325 | − | 0.0493899i | −0.165476 | − | 0.986214i | \(-0.552916\pi\) |
0.349801 | + | 0.936824i | \(0.386249\pi\) | |||||||
\(314\) | −16.3450 | −0.922403 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0897 | −0.680101 | ||||||||
\(317\) | 13.3465 | − | 3.57619i | 0.749614 | − | 0.200859i | 0.136267 | − | 0.990672i | \(-0.456489\pi\) |
0.613347 | + | 0.789814i | \(0.289823\pi\) | |||||||
\(318\) | −0.235593 | + | 0.879247i | −0.0132114 | + | 0.0493057i | ||||
\(319\) | −38.8581 | + | 22.4348i | −2.17564 | + | 1.25610i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.212832i | − | 0.0118791i | ||||||
\(322\) | 10.7119 | + | 14.9545i | 0.596949 | + | 0.833382i | ||||
\(323\) | −17.6742 | + | 17.6742i | −0.983421 | + | 0.983421i | ||||
\(324\) | 0.866025 | + | 0.500000i | 0.0481125 | + | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.74736 | − | 6.49061i | −0.207547 | − | 0.359482i | ||||
\(327\) | −0.403862 | − | 1.50724i | −0.0223336 | − | 0.0833503i | ||||
\(328\) | −2.92532 | − | 2.92532i | −0.161524 | − | 0.161524i | ||||
\(329\) | 1.73533 | + | 4.61338i | 0.0956721 | + | 0.254344i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.41481 | − | 4.18257i | 0.132730 | − | 0.229895i | −0.791998 | − | 0.610524i | \(-0.790959\pi\) |
0.924728 | + | 0.380629i | \(0.124292\pi\) | |||||||
\(332\) | −2.71974 | − | 0.728752i | −0.149265 | − | 0.0399955i | ||||
\(333\) | −7.50959 | − | 2.01219i | −0.411523 | − | 0.110267i | ||||
\(334\) | 9.04245 | − | 15.6620i | 0.494781 | − | 0.856985i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.04487 | − | 1.67884i | −0.111557 | − | 0.0915884i | ||||
\(337\) | −6.52431 | − | 6.52431i | −0.355402 | − | 0.355402i | 0.506713 | − | 0.862115i | \(-0.330860\pi\) |
−0.862115 | + | 0.506713i | \(0.830860\pi\) | |||||||
\(338\) | 1.24321 | + | 4.63971i | 0.0676216 | + | 0.252367i | ||||
\(339\) | −0.0212231 | − | 0.0367595i | −0.00115268 | − | 0.00199650i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.21169 | − | 4.74102i | −0.444688 | − | 0.256741i | ||||
\(342\) | −2.54207 | + | 2.54207i | −0.137459 | + | 0.137459i | ||||
\(343\) | 17.7259 | − | 5.36585i | 0.957109 | − | 0.289729i | ||||
\(344\) | − | 11.0897i | − | 0.597919i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0118 | − | 8.08974i | 0.753281 | − | 0.434907i | ||||
\(347\) | −8.13952 | + | 30.3771i | −0.436952 | + | 1.63073i | 0.299399 | + | 0.954128i | \(0.403214\pi\) |
−0.736351 | + | 0.676600i | \(0.763453\pi\) | |||||||
\(348\) | −8.51530 | + | 2.28167i | −0.456468 | + | 0.122310i | ||||
\(349\) | −28.5083 | −1.52601 | −0.763006 | − | 0.646391i | \(-0.776278\pi\) | ||||
−0.763006 | + | 0.646391i | \(0.776278\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.86297 | −0.152814 | ||||||||
\(352\) | 4.91631 | − | 1.31732i | 0.262040 | − | 0.0702134i | ||||
\(353\) | −6.04935 | + | 22.5765i | −0.321974 | + | 1.20162i | 0.595345 | + | 0.803471i | \(0.297016\pi\) |
−0.917319 | + | 0.398154i | \(0.869651\pi\) | |||||||
\(354\) | 3.61953 | − | 2.08974i | 0.192376 | − | 0.111068i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7.65014i | − | 0.405457i | ||||||
\(357\) | 7.59505 | − | 16.7540i | 0.401973 | − | 0.886716i | ||||
\(358\) | 7.02778 | − | 7.02778i | 0.371430 | − | 0.371430i | ||||
\(359\) | −14.5889 | − | 8.42292i | −0.769974 | − | 0.444545i | 0.0628915 | − | 0.998020i | \(-0.479968\pi\) |
−0.832865 | + | 0.553476i | \(0.813301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.03790 | + | 5.26180i | 0.159890 | + | 0.276937i | ||||
\(362\) | −0.673667 | − | 2.51416i | −0.0354072 | − | 0.132141i | ||||
\(363\) | 10.5397 | + | 10.5397i | 0.553192 | + | 0.553192i | ||||
\(364\) | 7.47330 | + | 1.23533i | 0.391707 | + | 0.0647491i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.93454 | − | 5.08277i | 0.153391 | − | 0.265681i | ||||
\(367\) | 26.0453 | + | 6.97882i | 1.35955 | + | 0.364291i | 0.863653 | − | 0.504088i | \(-0.168171\pi\) |
0.495901 | + | 0.868379i | \(0.334838\pi\) | |||||||
\(368\) | −6.71580 | − | 1.79949i | −0.350085 | − | 0.0938051i | ||||
\(369\) | 2.06851 | − | 3.58277i | 0.107683 | − | 0.186512i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.37609 | + | 0.392766i | 0.123360 | + | 0.0203914i | ||||
\(372\) | −1.31732 | − | 1.31732i | −0.0682999 | − | 0.0682999i | ||||
\(373\) | 2.66388 | + | 9.94175i | 0.137931 | + | 0.514764i | 0.999969 | + | 0.00792053i | \(0.00252121\pi\) |
−0.862038 | + | 0.506844i | \(0.830812\pi\) | |||||||
\(374\) | 17.6937 | + | 30.6464i | 0.914921 | + | 1.58469i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.61338 | − | 0.931486i | −0.0832038 | − | 0.0480377i | ||||
\(377\) | 17.8467 | − | 17.8467i | 0.919152 | − | 0.919152i | ||||
\(378\) | 1.09239 | − | 2.40971i | 0.0561863 | − | 0.123942i | ||||
\(379\) | − | 24.4633i | − | 1.25659i | −0.777974 | − | 0.628297i | \(-0.783752\pi\) | ||
0.777974 | − | 0.628297i | \(-0.216248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.74799 | + | 1.00920i | −0.0895521 | + | 0.0517029i | ||||
\(382\) | 1.07074 | − | 3.99606i | 0.0547839 | − | 0.204456i | ||||
\(383\) | −5.96013 | + | 1.59701i | −0.304549 | + | 0.0816036i | −0.407857 | − | 0.913046i | \(-0.633724\pi\) |
0.103308 | + | 0.994649i | \(0.467057\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.9527 | −0.659276 | ||||||||
\(387\) | 10.7119 | − | 2.87024i | 0.544515 | − | 0.145902i | ||||
\(388\) | 4.93953 | − | 18.4346i | 0.250767 | − | 0.935875i | ||||
\(389\) | 11.9344 | − | 6.89034i | 0.605099 | − | 0.349354i | −0.165946 | − | 0.986135i | \(-0.553068\pi\) |
0.771045 | + | 0.636781i | \(0.219734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 48.3402i | − | 2.44467i | ||||||
\(392\) | −3.89125 | + | 5.81878i | −0.196538 | + | 0.293893i | ||||
\(393\) | −3.74948 | + | 3.74948i | −0.189136 | + | 0.189136i | ||||
\(394\) | −1.07306 | − | 0.619530i | −0.0540599 | − | 0.0312115i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.54487 | + | 4.40784i | 0.127884 | + | 0.221502i | ||||
\(397\) | −0.298482 | − | 1.11395i | −0.0149804 | − | 0.0559075i | 0.958031 | − | 0.286664i | \(-0.0925465\pi\) |
−0.973011 | + | 0.230757i | \(0.925880\pi\) | |||||||
\(398\) | −12.2069 | − | 12.2069i | −0.611875 | − | 0.611875i | ||||
\(399\) | 7.35135 | + | 6.03548i | 0.368028 | + | 0.302152i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.13703 | + | 7.16554i | −0.206593 | + | 0.357830i | −0.950639 | − | 0.310298i | \(-0.899571\pi\) |
0.744046 | + | 0.668128i | \(0.232904\pi\) | |||||||
\(402\) | 2.84620 | + | 0.762637i | 0.141956 | + | 0.0380369i | ||||
\(403\) | 5.15190 | + | 1.38045i | 0.256634 | + | 0.0687650i | ||||
\(404\) | 0.681895 | − | 1.18108i | 0.0339256 | − | 0.0587608i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.21169 | + | 21.8308i | 0.407539 | + | 1.08344i | ||||
\(407\) | −27.9803 | − | 27.9803i | −1.38693 | − | 1.38693i | ||||
\(408\) | 1.79949 | + | 6.71580i | 0.0890882 | + | 0.332482i | ||||
\(409\) | −18.2355 | − | 31.5849i | −0.901690 | − | 1.56177i | −0.825300 | − | 0.564694i | \(-0.808994\pi\) |
−0.0763896 | − | 0.997078i | \(-0.524339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.0363 | + | 10.9906i | 0.938991 | + | 0.542127i | ||||
\(412\) | 0.257239 | − | 0.257239i | 0.0126733 | − | 0.0126733i | ||||
\(413\) | −6.43921 | − | 8.98958i | −0.316853 | − | 0.442348i | ||||
\(414\) | − | 6.95271i | − | 0.341707i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.47941 | + | 1.43149i | −0.121563 | + | 0.0701844i | ||||
\(417\) | 4.29385 | − | 16.0249i | 0.210271 | − | 0.784742i | ||||
\(418\) | −17.6742 | + | 4.73580i | −0.864476 | + | 0.231636i | ||||
\(419\) | −9.05638 | −0.442433 | −0.221217 | − | 0.975225i | \(-0.571003\pi\) | ||||
−0.221217 | + | 0.975225i | \(0.571003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.3149 | 0.502716 | 0.251358 | − | 0.967894i | \(-0.419123\pi\) | ||||
0.251358 | + | 0.967894i | \(0.419123\pi\) | |||||||
\(422\) | 7.15230 | − | 1.91645i | 0.348168 | − | 0.0932914i | ||||
\(423\) | 0.482173 | − | 1.79949i | 0.0234440 | − | 0.0874944i | ||||
\(424\) | −0.788311 | + | 0.455132i | −0.0382838 | + | 0.0221031i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.86297i | 0.380962i | ||||||||
\(427\) | −14.1428 | − | 6.41130i | −0.684416 | − | 0.310265i | ||||
\(428\) | 0.150495 | − | 0.150495i | 0.00727443 | − | 0.00727443i | ||||
\(429\) | −12.6195 | − | 7.28589i | −0.609277 | − | 0.351766i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4441 | + | 19.8218i | 0.551245 | + | 0.954784i | 0.998185 | + | 0.0602202i | \(0.0191803\pi\) |
−0.446940 | + | 0.894564i | \(0.647486\pi\) | |||||||
\(432\) | 0.258819 | + | 0.965926i | 0.0124524 | + | 0.0464731i | ||||
\(433\) | 17.2780 | + | 17.2780i | 0.830327 | + | 0.830327i | 0.987561 | − | 0.157235i | \(-0.0502579\pi\) |
−0.157235 | + | 0.987561i | \(0.550258\pi\) | |||||||
\(434\) | −3.12764 | + | 3.80953i | −0.150131 | + | 0.182863i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.780202 | − | 1.35135i | 0.0373649 | − | 0.0647179i | ||||
\(437\) | 24.1435 | + | 6.46922i | 1.15494 | + | 0.309465i | ||||
\(438\) | 13.0683 | + | 3.50165i | 0.624429 | + | 0.167315i | ||||
\(439\) | −2.48269 | + | 4.30015i | −0.118492 | + | 0.205235i | −0.919170 | − | 0.393860i | \(-0.871139\pi\) |
0.800678 | + | 0.599095i | \(0.204473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.62764 | − | 2.25264i | −0.315602 | − | 0.107269i | ||||
\(442\) | −14.0753 | − | 14.0753i | −0.669492 | − | 0.669492i | ||||
\(443\) | −3.36339 | − | 12.5524i | −0.159800 | − | 0.596380i | −0.998646 | − | 0.0520128i | \(-0.983436\pi\) |
0.838847 | − | 0.544368i | \(-0.183230\pi\) | |||||||
\(444\) | −3.88725 | − | 6.73291i | −0.184481 | − | 0.319530i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.30448 | + | 1.90784i | 0.156472 | + | 0.0903389i | ||||
\(447\) | −7.02778 | + | 7.02778i | −0.332402 | + | 0.332402i | ||||
\(448\) | −0.258819 | − | 2.63306i | −0.0122281 | − | 0.124400i | ||||
\(449\) | − | 15.0710i | − | 0.711243i | −0.934630 | − | 0.355621i | \(-0.884269\pi\) | ||
0.934630 | − | 0.355621i | \(-0.115731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2354 | − | 10.5282i | 0.858669 | − | 0.495753i | ||||
\(452\) | 0.0109859 | − | 0.0409999i | 0.000516733 | − | 0.00192847i | ||||
\(453\) | 14.7946 | − | 3.96420i | 0.695111 | − | 0.186254i | ||||
\(454\) | 19.6926 | 0.924219 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.59502 | −0.168352 | ||||||||
\(457\) | −25.0167 | + | 6.70321i | −1.17023 | + | 0.313563i | −0.791046 | − | 0.611757i | \(-0.790463\pi\) |
−0.379187 | + | 0.925320i | \(0.623796\pi\) | |||||||
\(458\) | 5.94682 | − | 22.1938i | 0.277877 | − | 1.03705i | ||||
\(459\) | −6.02122 | + | 3.47635i | −0.281047 | + | 0.162262i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.9054i | − | 0.927088i | −0.886074 | − | 0.463544i | \(-0.846578\pi\) | ||
0.886074 | − | 0.463544i | \(-0.153422\pi\) | |||||||
\(462\) | 10.9475 | − | 7.84163i | 0.509322 | − | 0.364826i | ||||
\(463\) | 29.0870 | − | 29.0870i | 1.35179 | − | 1.35179i | 0.468121 | − | 0.883664i | \(-0.344931\pi\) |
0.883664 | − | 0.468121i | \(-0.155069\pi\) | |||||||
\(464\) | −7.63460 | − | 4.40784i | −0.354428 | − | 0.204629i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.61953 | − | 11.4654i | −0.306644 | − | 0.531123i | ||||
\(467\) | 7.37127 | + | 27.5100i | 0.341102 | + | 1.27301i | 0.897101 | + | 0.441826i | \(0.145669\pi\) |
−0.555999 | + | 0.831183i | \(0.687664\pi\) | |||||||
\(468\) | −2.02443 | − | 2.02443i | −0.0935792 | − | 0.0935792i | ||||
\(469\) | 1.27142 | − | 7.69161i | 0.0587087 | − | 0.355165i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.17251 | − | 14.1552i | 0.376569 | − | 0.652237i | ||||
\(472\) | 4.03706 | + | 1.08173i | 0.185821 | + | 0.0497905i | ||||
\(473\) | 54.5206 | + | 14.6087i | 2.50686 | + | 0.671711i | ||||
\(474\) | 6.04487 | − | 10.4700i | 0.277650 | − | 0.480904i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.2174 | − | 6.47635i | 0.789157 | − | 0.296843i | ||||
\(477\) | −0.643653 | − | 0.643653i | −0.0294709 | − | 0.0294709i | ||||
\(478\) | −0.427088 | − | 1.59391i | −0.0195346 | − | 0.0729039i | ||||
\(479\) | 4.79770 | + | 8.30986i | 0.219212 | + | 0.379687i | 0.954567 | − | 0.297995i | \(-0.0963179\pi\) |
−0.735355 | + | 0.677682i | \(0.762985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.2761 | + | 11.1291i | 0.878917 | + | 0.507443i | ||||
\(482\) | 8.94589 | − | 8.94589i | 0.407474 | − | 0.407474i | ||||
\(483\) | −18.3069 | + | 1.79949i | −0.832993 | + | 0.0818798i | ||||
\(484\) | 14.9054i | 0.677519i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 3.22698 | − | 12.0433i | 0.146229 | − | 0.545733i | −0.853469 | − | 0.521144i | \(-0.825506\pi\) |
0.999698 | − | 0.0245890i | \(-0.00782772\pi\) | |||||||
\(488\) | 5.66909 | − | 1.51903i | 0.256628 | − | 0.0687632i | ||||
\(489\) | 7.49471 | 0.338923 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3288 | 1.63950 | 0.819748 | − | 0.572725i | \(-0.194114\pi\) | ||||
0.819748 | + | 0.572725i | \(0.194114\pi\) | |||||||
\(492\) | 3.99606 | − | 1.07074i | 0.180156 | − | 0.0482728i | ||||
\(493\) | 15.8638 | − | 59.2044i | 0.714468 | − | 2.66643i | ||||
\(494\) | 8.91353 | − | 5.14623i | 0.401039 | − | 0.231540i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.86297i | − | 0.0836500i | ||||||
\(497\) | 20.7037 | − | 2.03509i | 0.928687 | − | 0.0912861i | ||||
\(498\) | 1.99099 | − | 1.99099i | 0.0892183 | − | 0.0892183i | ||||
\(499\) | −2.42441 | − | 1.39973i | −0.108531 | − | 0.0626606i | 0.444752 | − | 0.895654i | \(-0.353292\pi\) |
−0.553283 | + | 0.832993i | \(0.686625\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.04245 | + | 15.6620i | 0.403987 | + | 0.699725i | ||||
\(502\) | −1.92869 | − | 7.19797i | −0.0860817 | − | 0.321261i | ||||
\(503\) | 12.1725 | + | 12.1725i | 0.542743 | + | 0.542743i | 0.924332 | − | 0.381589i | \(-0.124623\pi\) |
−0.381589 | + | 0.924332i | \(0.624623\pi\) | |||||||
\(504\) | 2.47635 | − | 0.931486i | 0.110306 | − | 0.0414917i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.6937 | − | 30.6464i | 0.786582 | − | 1.36240i | ||||
\(507\) | −4.63971 | − | 1.24321i | −0.206057 | − | 0.0552128i | ||||
\(508\) | −1.94963 | − | 0.522401i | −0.0865007 | − | 0.0231778i | ||||
\(509\) | −10.4503 | + | 18.1004i | −0.463201 | + | 0.802287i | −0.999118 | − | 0.0419830i | \(-0.986632\pi\) |
0.535917 | + | 0.844270i | \(0.319966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.83772 | − | 35.3160i | 0.258246 | − | 1.56229i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −0.930461 | − | 3.47253i | −0.0410808 | − | 0.153316i | ||||
\(514\) | −8.31650 | − | 14.4046i | −0.366825 | − | 0.635360i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.60399 | + | 5.54487i | 0.422792 | + | 0.244099i | ||||
\(517\) | 6.70482 | − | 6.70482i | 0.294877 | − | 0.294877i | ||||
\(518\) | −16.7221 | + | 11.9780i | −0.734726 | + | 0.526282i | ||||
\(519\) | 16.1795i | 0.710200i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.3985 | + | 12.3544i | −0.937483 | + | 0.541256i | −0.889170 | − | 0.457576i | \(-0.848718\pi\) |
−0.0483128 | + | 0.998832i | \(0.515384\pi\) | |||||||
\(522\) | 2.28167 | − | 8.51530i | 0.0998658 | − | 0.372704i | ||||
\(523\) | −29.0889 | + | 7.79435i | −1.27197 | + | 0.340823i | −0.830785 | − | 0.556594i | \(-0.812108\pi\) |
−0.441184 | + | 0.897417i | \(0.645441\pi\) | |||||||
\(524\) | −5.30257 | −0.231644 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0473 | −0.481685 | ||||||||
\(527\) | 12.5114 | − | 3.35241i | 0.545003 | − | 0.146033i | ||||
\(528\) | −1.31732 | + | 4.91631i | −0.0573290 | + | 0.213955i | ||||
\(529\) | −21.9452 | + | 12.6701i | −0.954140 | + | 0.550873i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.17947i | 0.181374i | ||||||||
\(532\) | 0.930461 | + | 9.46592i | 0.0403406 | + | 0.410400i | ||||
\(533\) | −8.37511 | + | 8.37511i | −0.362766 | + | 0.362766i | ||||
\(534\) | 6.62522 | + | 3.82507i | 0.286701 | + | 0.165527i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.47330 | + | 2.55183i | 0.0636370 | + | 0.110222i | ||||
\(537\) | 2.57234 | + | 9.60012i | 0.111005 | + | 0.414276i | ||||
\(538\) | −18.8111 | − | 18.8111i | −0.811002 | − | 0.811002i | ||||
\(539\) | −23.4809 | − | 26.7958i | −1.01139 | − | 1.15418i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0506 | + | 34.7286i | −0.862041 | + | 1.49310i | 0.00791517 | + | 0.999969i | \(0.497480\pi\) |
−0.869956 | + | 0.493130i | \(0.835853\pi\) | |||||||
\(542\) | 19.6242 | + | 5.25830i | 0.842933 | + | 0.225863i | ||||
\(543\) | 2.51416 | + | 0.673667i | 0.107893 | + | 0.0289098i | ||||
\(544\) | −3.47635 | + | 6.02122i | −0.149047 | + | 0.258158i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.80648 | + | 5.85440i | −0.205698 | + | 0.250545i | ||||
\(547\) | 26.5205 | + | 26.5205i | 1.13394 | + | 1.13394i | 0.989516 | + | 0.144420i | \(0.0461317\pi\) |
0.144420 | + | 0.989516i | \(0.453868\pi\) | |||||||
\(548\) | 5.68916 | + | 21.2322i | 0.243029 | + | 0.906996i | ||||
\(549\) | 2.93454 | + | 5.08277i | 0.125243 | + | 0.216927i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.4466 | + | 15.8463i | 1.16926 | + | 0.675075i | ||||
\(552\) | 4.91631 | − | 4.91631i | 0.209252 | − | 0.209252i | ||||
\(553\) | −29.1327 | − | 13.2067i | −1.23885 | − | 0.561605i | ||||
\(554\) | − | 10.0697i | − | 0.427821i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.3675 | − | 8.29509i | 0.609318 | − | 0.351790i | ||||
\(557\) | −1.34960 | + | 5.03679i | −0.0571845 | + | 0.213416i | −0.988606 | − | 0.150527i | \(-0.951903\pi\) |
0.931421 | + | 0.363943i | \(0.118570\pi\) | |||||||
\(558\) | 1.79949 | − | 0.482173i | 0.0761786 | − | 0.0204120i | ||||
\(559\) | −31.7496 | −1.34287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.3875 | −1.49406 | ||||||||
\(562\) | −14.7079 | + | 3.94098i | −0.620416 | + | 0.166240i | ||||
\(563\) | 4.01426 | − | 14.9814i | 0.169181 | − | 0.631392i | −0.828289 | − | 0.560301i | \(-0.810685\pi\) |
0.997470 | − | 0.0710904i | \(-0.0226479\pi\) | |||||||
\(564\) | 1.61338 | − | 0.931486i | 0.0679356 | − | 0.0392227i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.8319i | 0.623431i | ||||||||
\(567\) | 1.54067 | + | 2.15089i | 0.0647023 | + | 0.0903288i | ||||
\(568\) | −5.55996 | + | 5.55996i | −0.233291 | + | 0.233291i | ||||
\(569\) | −23.8369 | − | 13.7622i | −0.999295 | − | 0.576943i | −0.0912554 | − | 0.995828i | \(-0.529088\pi\) |
−0.908040 | + | 0.418884i | \(0.862421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.46210 | − | 2.53243i | −0.0611869 | − | 0.105979i | 0.833809 | − | 0.552053i | \(-0.186155\pi\) |
−0.894996 | + | 0.446074i | \(0.852822\pi\) | |||||||
\(572\) | −3.77145 | − | 14.0753i | −0.157692 | − | 0.588516i | ||||
\(573\) | 2.92532 | + | 2.92532i | 0.122207 | + | 0.122207i | ||||
\(574\) | −3.85358 | − | 10.2447i | −0.160846 | − | 0.427607i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −3.36119 | − | 0.900627i | −0.139928 | − | 0.0374936i | 0.188175 | − | 0.982135i | \(-0.439743\pi\) |
−0.328103 | + | 0.944642i | \(0.606409\pi\) | |||||||
\(578\) | −30.2723 | − | 8.11143i | −1.25916 | − | 0.337391i | ||||
\(579\) | 6.47635 | − | 11.2174i | 0.269148 | − | 0.466178i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.75770 | − | 4.72709i | −0.238870 | − | 0.196113i | ||||
\(582\) | 13.4951 | + | 13.4951i | 0.559388 | + | 0.559388i | ||||
\(583\) | −1.19911 | − | 4.47514i | −0.0496620 | − | 0.185341i | ||||
\(584\) | 6.76467 | + | 11.7167i | 0.279924 | + | 0.484842i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.9038 | − | 13.2235i | −0.946148 | − | 0.546259i | ||||
\(587\) | 29.2873 | − | 29.2873i | 1.20882 | − | 1.20882i | 0.237407 | − | 0.971410i | \(-0.423702\pi\) |
0.971410 | − | 0.237407i | \(-0.0762975\pi\) | |||||||
\(588\) | −3.09359 | − | 6.27931i | −0.127577 | − | 0.258954i | ||||
\(589\) | 6.69743i | 0.275963i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.07306 | − | 0.619530i | 0.0441397 | − | 0.0254841i | ||||
\(592\) | 2.01219 | − | 7.50959i | 0.0827004 | − | 0.308642i | ||||
\(593\) | 12.1553 | − | 3.25700i | 0.499158 | − | 0.133749i | −0.000451399 | − | 1.00000i | \(-0.500144\pi\) |
0.499609 | + | 0.866251i | \(0.333477\pi\) | |||||||
\(594\) | −5.08974 | −0.208834 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.93878 | −0.407108 | ||||||||
\(597\) | 16.6749 | − | 4.46802i | 0.682457 | − | 0.182864i | ||||
\(598\) | −5.15190 | + | 19.2272i | −0.210677 | + | 0.786257i | ||||
\(599\) | −41.1024 | + | 23.7305i | −1.67940 | + | 0.969602i | −0.717355 | + | 0.696708i | \(0.754647\pi\) |
−0.962044 | + | 0.272894i | \(0.912019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.1953i | − | 1.59881i | −0.600792 | − | 0.799405i | \(-0.705148\pi\) | ||
0.600792 | − | 0.799405i | \(-0.294852\pi\) | |||||||
\(602\) | 12.1143 | − | 26.7230i | 0.493741 | − | 1.08915i | ||||
\(603\) | −2.08356 | + | 2.08356i | −0.0848493 | + | 0.0848493i | ||||
\(604\) | 13.2645 | + | 7.65825i | 0.539724 | + | 0.311610i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.681895 | + | 1.18108i | 0.0277001 | + | 0.0479780i | ||||
\(607\) | 3.46559 | + | 12.9338i | 0.140664 | + | 0.524965i | 0.999910 | + | 0.0134030i | \(0.00426642\pi\) |
−0.859246 | + | 0.511562i | \(0.829067\pi\) | |||||||
\(608\) | −2.54207 | − | 2.54207i | −0.103094 | − | 0.103094i | ||||
\(609\) | −23.0118 | − | 3.80385i | −0.932487 | − | 0.154140i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.66682 | + | 4.61907i | −0.107888 | + | 0.186868i | ||||
\(612\) | −6.71580 | − | 1.79949i | −0.271470 | − | 0.0727402i | ||||
\(613\) | −19.9559 | − | 5.34717i | −0.806012 | − | 0.215970i | −0.167790 | − | 0.985823i | \(-0.553663\pi\) |
−0.638222 | + | 0.769853i | \(0.720330\pi\) | |||||||
\(614\) | 15.9054 | − | 27.5490i | 0.641890 | − | 1.11179i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.2859 | + | 2.19615i | 0.535304 | + | 0.0884855i | ||||
\(617\) | −3.22631 | − | 3.22631i | −0.129886 | − | 0.129886i | 0.639175 | − | 0.769061i | \(-0.279276\pi\) |
−0.769061 | + | 0.639175i | \(0.779276\pi\) | |||||||
\(618\) | 0.0941560 | + | 0.351395i | 0.00378751 | + | 0.0141352i | ||||
\(619\) | −2.10527 | − | 3.64644i | −0.0846181 | − | 0.146563i | 0.820610 | − | 0.571488i | \(-0.193634\pi\) |
−0.905228 | + | 0.424925i | \(0.860300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.02122 | + | 3.47635i | 0.241623 | + | 0.139501i | ||||
\(622\) | −11.6431 | + | 11.6431i | −0.466846 | + | 0.466846i | ||||
\(623\) | 8.35691 | − | 18.4346i | 0.334813 | − | 0.738567i | ||||
\(624\) | − | 2.86297i | − | 0.114611i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.92378 | + | 1.68804i | −0.116858 | + | 0.0674678i | ||||
\(627\) | 4.73580 | − | 17.6742i | 0.189130 | − | 0.705841i | ||||
\(628\) | 15.7881 | − | 4.23040i | 0.630013 | − | 0.168811i | ||||
\(629\) | 54.0538 | 2.15527 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.1730 | 1.40021 | 0.700107 | − | 0.714038i | \(-0.253135\pi\) | ||||
0.700107 | + | 0.714038i | \(0.253135\pi\) | |||||||
\(632\) | 11.6778 | − | 3.12905i | 0.464517 | − | 0.124467i | ||||
\(633\) | −1.91645 | + | 7.15230i | −0.0761721 | + | 0.284278i | ||||
\(634\) | −11.9661 | + | 6.90866i | −0.475236 | + | 0.274378i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 0.910263i | − | 0.0360943i | ||||||
\(637\) | 16.6590 | + | 11.1405i | 0.660054 | + | 0.441404i | ||||
\(638\) | 31.7275 | − | 31.7275i | 1.25610 | − | 1.25610i | ||||
\(639\) | −6.80953 | − | 3.93149i | −0.269381 | − | 0.155527i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.56609 | − | 9.64075i | −0.219847 | − | 0.380787i | 0.734914 | − | 0.678161i | \(-0.237223\pi\) |
−0.954761 | + | 0.297374i | \(0.903889\pi\) | |||||||
\(642\) | 0.0550849 | + | 0.205579i | 0.00217403 | + | 0.00811358i | ||||
\(643\) | 20.3659 | + | 20.3659i | 0.803153 | + | 0.803153i | 0.983587 | − | 0.180434i | \(-0.0577502\pi\) |
−0.180434 | + | 0.983587i | \(0.557750\pi\) | |||||||
\(644\) | −14.2174 | − | 11.6725i | −0.560243 | − | 0.459961i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4976 | − | 21.6464i | 0.491711 | − | 0.851668i | ||||
\(647\) | −11.0379 | − | 2.95760i | −0.433946 | − | 0.116275i | 0.0352321 | − | 0.999379i | \(-0.488783\pi\) |
−0.469178 | + | 0.883104i | \(0.655450\pi\) | |||||||
\(648\) | −0.965926 | − | 0.258819i | −0.0379452 | − | 0.0101674i | ||||
\(649\) | −10.6362 | + | 18.4225i | −0.417508 | + | 0.723145i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.73533 | − | 4.61338i | −0.0680131 | − | 0.180813i | ||||
\(652\) | 5.29956 | + | 5.29956i | 0.207547 | + | 0.207547i | ||||
\(653\) | 3.66128 | + | 13.6641i | 0.143277 | + | 0.534717i | 0.999826 | + | 0.0186516i | \(0.00593735\pi\) |
−0.856549 | + | 0.516066i | \(0.827396\pi\) | |||||||
\(654\) | 0.780202 | + | 1.35135i | 0.0305083 | + | 0.0528420i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.58277 | + | 2.06851i | 0.139884 | + | 0.0807619i | ||||
\(657\) | −9.56668 | + | 9.56668i | −0.373232 | + | 0.373232i | ||||
\(658\) | −2.87024 | − | 4.00705i | −0.111893 | − | 0.156211i | ||||
\(659\) | − | 11.7840i | − | 0.459038i | −0.973304 | − | 0.229519i | \(-0.926285\pi\) | ||
0.973304 | − | 0.229519i | \(-0.0737153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.3181 | − | 23.8550i | 1.60709 | − | 0.927853i | 0.617072 | − | 0.786907i | \(-0.288319\pi\) |
0.990017 | − | 0.140946i | \(-0.0450145\pi\) | |||||||
\(662\) | −1.25000 | + | 4.66505i | −0.0485825 | + | 0.181312i | ||||
\(663\) | 19.2272 | − | 5.15190i | 0.746721 | − | 0.200083i | ||||
\(664\) | 2.81568 | 0.109270 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.77450 | 0.301256 | ||||||||
\(667\) | −59.2044 | + | 15.8638i | −2.29240 | + | 0.614247i | ||||
\(668\) | −4.68071 | + | 17.4687i | −0.181102 | + | 0.675883i | ||||
\(669\) | −3.30448 | + | 1.90784i | −0.127758 | + | 0.0737614i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.8721i | 1.15320i | ||||||||
\(672\) | 2.40971 | + | 1.09239i | 0.0929565 | + | 0.0421397i | ||||
\(673\) | −23.3048 | + | 23.3048i | −0.898334 | + | 0.898334i | −0.995289 | − | 0.0969544i | \(-0.969090\pi\) |
0.0969544 | + | 0.995289i | \(0.469090\pi\) | |||||||
\(674\) | 7.99061 | + | 4.61338i | 0.307787 | + | 0.177701i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.40169 | − | 4.15985i | −0.0923728 | − | 0.159994i | ||||
\(677\) | −1.58293 | − | 5.90757i | −0.0608369 | − | 0.227046i | 0.928813 | − | 0.370548i | \(-0.120830\pi\) |
−0.989650 | + | 0.143502i | \(0.954164\pi\) | |||||||
\(678\) | 0.0300140 | + | 0.0300140i | 0.00115268 | + | 0.00115268i | ||||
\(679\) | 32.0405 | − | 39.0261i | 1.22960 | − | 1.49768i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.84629 | + | 17.0543i | −0.377311 | + | 0.653521i | ||||
\(682\) | 9.15895 | + | 2.45413i | 0.350714 | + | 0.0939736i | ||||
\(683\) | −27.6574 | − | 7.41077i | −1.05828 | − | 0.283565i | −0.312610 | − | 0.949882i | \(-0.601203\pi\) |
−0.745669 | + | 0.666316i | \(0.767870\pi\) | |||||||
\(684\) | 1.79751 | − | 3.11338i | 0.0687296 | − | 0.119043i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7331 | + | 9.77081i | −0.600693 | + | 0.373051i | ||||
\(687\) | 16.2470 | + | 16.2470i | 0.619862 | + | 0.619862i | ||||
\(688\) | 2.87024 | + | 10.7119i | 0.109427 | + | 0.408386i | ||||
\(689\) | 1.30303 | + | 2.25691i | 0.0496415 | + | 0.0859816i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.56043 | − | 4.94237i | −0.325654 | − | 0.188016i | 0.328256 | − | 0.944589i | \(-0.393539\pi\) |
−0.653910 | + | 0.756572i | \(0.726873\pi\) | |||||||
\(692\) | −11.4406 | + | 11.4406i | −0.434907 | + | 0.434907i | ||||
\(693\) | 1.31732 | + | 13.4016i | 0.0500409 | + | 0.509084i | ||||
\(694\) | − | 31.4487i | − | 1.19378i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.63460 | − | 4.40784i | 0.289389 | − | 0.167079i | ||||
\(697\) | −7.44455 | + | 27.7835i | −0.281983 | + | 1.05237i | ||||
\(698\) | 27.5369 | − | 7.37848i | 1.04229 | − | 0.279280i | ||||
\(699\) | 13.2391 | 0.500747 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.4772 | −0.848952 | −0.424476 | − | 0.905439i | \(-0.639542\pi\) | ||||
−0.424476 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(702\) | 2.76542 | − | 0.740992i | 0.104374 | − | 0.0279669i | ||||
\(703\) | −7.23386 | + | 26.9971i | −0.272830 | + | 1.01822i | ||||
\(704\) | −4.40784 | + | 2.54487i | −0.166127 | + | 0.0959133i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 23.3729i | − | 0.879650i | ||||||
\(707\) | 2.93336 | − | 2.10116i | 0.110320 | − | 0.0790222i | ||||
\(708\) | −2.95533 | + | 2.95533i | −0.111068 | + | 0.111068i | ||||
\(709\) | −6.12307 | − | 3.53516i | −0.229957 | − | 0.132766i | 0.380595 | − | 0.924742i | \(-0.375719\pi\) |
−0.610552 | + | 0.791976i | \(0.709052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.04487 | + | 10.4700i | 0.226700 | + | 0.392656i | ||||
\(712\) | 1.98000 | + | 7.38947i | 0.0742037 | + | 0.276932i | ||||
\(713\) | −9.15895 | − | 9.15895i | −0.343005 | − | 0.343005i | ||||
\(714\) | −3.00000 | + | 18.1489i | −0.112272 | + | 0.679204i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.96939 | + | 8.60723i | −0.185715 | + | 0.321667i | ||||
\(717\) | 1.59391 | + | 0.427088i | 0.0595258 | + | 0.0159499i | ||||
\(718\) | 16.2718 | + | 4.36002i | 0.607259 | + | 0.162715i | ||||
\(719\) | 18.1121 | − | 31.3711i | 0.675467 | − | 1.16994i | −0.300865 | − | 0.953667i | \(-0.597275\pi\) |
0.976332 | − | 0.216277i | \(-0.0693914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.900875 | − | 0.338866i | 0.0335503 | − | 0.0126200i | ||||
\(722\) | −4.29624 | − | 4.29624i | −0.159890 | − | 0.159890i | ||||
\(723\) | 3.27442 | + | 12.2203i | 0.121777 | + | 0.454478i | ||||
\(724\) | 1.30143 | + | 2.25414i | 0.0483671 | + | 0.0837743i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.9085 | − | 7.45271i | −0.479078 | − | 0.276596i | ||||
\(727\) | 8.46215 | − | 8.46215i | 0.313844 | − | 0.313844i | −0.532553 | − | 0.846397i | \(-0.678767\pi\) |
0.846397 | + | 0.532553i | \(0.178767\pi\) | |||||||
\(728\) | −7.53838 | + | 0.740992i | −0.279391 | + | 0.0274630i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −66.7738 | + | 38.5519i | −2.46972 | + | 1.42589i | ||||
\(732\) | −1.51903 | + | 5.66909i | −0.0561449 | + | 0.209536i | ||||
\(733\) | −4.51455 | + | 1.20967i | −0.166749 | + | 0.0446802i | −0.341228 | − | 0.939981i | \(-0.610843\pi\) |
0.174479 | + | 0.984661i | \(0.444176\pi\) | |||||||
\(734\) | −26.9641 | −0.995262 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.95271 | 0.256280 | ||||||||
\(737\) | −14.4864 | + | 3.88162i | −0.533614 | + | 0.142981i | ||||
\(738\) | −1.07074 | + | 3.99606i | −0.0394145 | + | 0.147097i | ||||
\(739\) | 22.4673 | − | 12.9715i | 0.826474 | − | 0.477165i | −0.0261702 | − | 0.999658i | \(-0.508331\pi\) |
0.852644 | + | 0.522493i | \(0.174998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2925i | 0.378103i | ||||||||
\(742\) | −2.39678 | + | 0.235593i | −0.0879885 | + | 0.00864891i | ||||
\(743\) | 33.8328 | − | 33.8328i | 1.24121 | − | 1.24121i | 0.281704 | − | 0.959501i | \(-0.409101\pi\) |
0.959501 | − | 0.281704i | \(-0.0908995\pi\) | |||||||
\(744\) | 1.61338 | + | 0.931486i | 0.0591494 | + | 0.0341500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.14623 | − | 8.91353i | −0.188417 | − | 0.326347i | ||||
\(747\) | 0.728752 | + | 2.71974i | 0.0266637 | + | 0.0995101i | ||||
\(748\) | −25.0227 | − | 25.0227i | −0.914921 | − | 0.914921i | ||||
\(749\) | 0.527046 | − | 0.198250i | 0.0192579 | − | 0.00724389i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.00811 | + | 8.67430i | −0.182748 | + | 0.316530i | −0.942816 | − | 0.333315i | \(-0.891833\pi\) |
0.760067 | + | 0.649845i | \(0.225166\pi\) | |||||||
\(752\) | 1.79949 | + | 0.482173i | 0.0656208 | + | 0.0175830i | ||||
\(753\) | 7.19797 | + | 1.92869i | 0.262309 | + | 0.0702854i | ||||
\(754\) | −12.6195 | + | 21.8577i | −0.459576 | + | 0.796009i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.431486 | + | 2.61033i | −0.0156930 | + | 0.0949368i | ||||
\(757\) | 2.56404 | + | 2.56404i | 0.0931915 | + | 0.0931915i | 0.752166 | − | 0.658974i | \(-0.229009\pi\) |
−0.658974 | + | 0.752166i | \(0.729009\pi\) | |||||||
\(758\) | 6.33156 | + | 23.6297i | 0.229973 | + | 0.858269i | ||||
\(759\) | 17.6937 | + | 30.6464i | 0.642242 | + | 1.11240i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.98202 | + | 1.14432i | 0.0718481 | + | 0.0414815i | 0.535494 | − | 0.844539i | \(-0.320126\pi\) |
−0.463646 | + | 0.886021i | \(0.653459\pi\) | |||||||
\(762\) | 1.42723 | − | 1.42723i | 0.0517029 | − | 0.0517029i | ||||
\(763\) | 3.35626 | − | 2.40408i | 0.121505 | − | 0.0870334i | ||||
\(764\) | 4.13703i | 0.149672i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.34371 | − | 3.08519i | 0.193076 | − | 0.111473i | ||||
\(767\) | 3.09696 | − | 11.5580i | 0.111825 | − | 0.417335i | ||||
\(768\) | −0.965926 | + | 0.258819i | −0.0348548 | + | 0.00933933i | ||||
\(769\) | 8.35895 | 0.301431 | 0.150716 | − | 0.988577i | \(-0.451842\pi\) | ||||
0.150716 | + | 0.988577i | \(0.451842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6330 | 0.599023 | ||||||||
\(772\) | 12.5114 | − | 3.35241i | 0.450294 | − | 0.120656i | ||||
\(773\) | −2.81515 | + | 10.5063i | −0.101254 | + | 0.377885i | −0.997893 | − | 0.0648769i | \(-0.979335\pi\) |
0.896639 | + | 0.442762i | \(0.146001\pi\) | |||||||
\(774\) | −9.60399 | + | 5.54487i | −0.345208 | + | 0.199306i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 19.0849i | 0.685108i | ||||||||
\(777\) | −2.01219 | − | 20.4707i | −0.0721868 | − | 0.734383i | ||||
\(778\) | −9.74442 | + | 9.74442i | −0.349354 | + | 0.349354i | ||||
\(779\) | −12.8801 | − | 7.43636i | −0.461479 | − | 0.266435i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0102 | − | 34.6587i | −0.716022 | − | 1.24019i | ||||
\(782\) | 12.5114 | + | 46.6930i | 0.447405 | + | 1.66974i | ||||
\(783\) | 6.23363 | + | 6.23363i | 0.222772 | + | 0.222772i | ||||
\(784\) | 2.25264 | − | 6.62764i | 0.0804516 | − | 0.236701i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.65128 | − | 4.59216i | 0.0945682 | − | 0.163797i | ||||
\(787\) | −20.0907 | − | 5.38330i | −0.716158 | − | 0.191894i | −0.117701 | − | 0.993049i | \(-0.537552\pi\) |
−0.598457 | + | 0.801155i | \(0.704219\pi\) | |||||||
\(788\) | 1.19684 | + | 0.320692i | 0.0426357 | + | 0.0114242i | ||||
\(789\) | 5.52365 | − | 9.56723i | 0.196647 | − | 0.340603i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0712605 | − | 0.0867969i | 0.00253373 | − | 0.00308614i | ||||
\(792\) | −3.59899 | − | 3.59899i | −0.127884 | − | 0.127884i | ||||
\(793\) | −4.34894 | − | 16.2305i | −0.154435 | − | 0.576361i | ||||
\(794\) | 0.576622 | + | 0.998739i | 0.0204636 | + | 0.0354439i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9503 | + | 8.63155i | 0.529899 | + | 0.305937i | ||||
\(797\) | −8.60761 | + | 8.60761i | −0.304897 | + | 0.304897i | −0.842926 | − | 0.538029i | \(-0.819169\pi\) |
0.538029 | + | 0.842926i | \(0.319169\pi\) | |||||||
\(798\) | −8.66296 | − | 3.92716i | −0.306665 | − | 0.139020i | ||||
\(799\) | 12.9527i | 0.458234i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.62522 | + | 3.82507i | −0.234091 | + | 0.135152i | ||||
\(802\) | 2.14148 | − | 7.99212i | 0.0756184 | − | 0.282212i | ||||
\(803\) | −66.5144 | + | 17.8225i | −2.34724 | + | 0.628941i | ||||
\(804\) | −2.94660 | −0.103919 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.33364 | −0.187869 | ||||||||
\(807\) | 25.6964 | − | 6.88532i | 0.904555 | − | 0.242375i | ||||
\(808\) | −0.352975 | + | 1.31732i | −0.0124176 | + | 0.0463432i | ||||
\(809\) | −13.8034 | + | 7.96939i | −0.485301 | + | 0.280189i | −0.722623 | − | 0.691242i | \(-0.757064\pi\) |
0.237322 | + | 0.971431i | \(0.423730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.3056i | − | 0.818369i | −0.912452 | − | 0.409184i | \(-0.865813\pi\) | ||
0.912452 | − | 0.409184i | \(-0.134187\pi\) | |||||||
\(812\) | −13.5821 | − | 18.9616i | −0.476638 | − | 0.665420i | ||||
\(813\) | −14.3659 | + | 14.3659i | −0.503835 | + | 0.503835i | ||||
\(814\) | 34.2687 | + | 19.7851i | 1.20112 | + | 0.693466i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.47635 | − | 6.02122i | −0.121697 | − | 0.210785i | ||||
\(817\) | −10.3186 | − | 38.5094i | −0.361001 | − | 1.34727i | ||||
\(818\) | 25.7890 | + | 25.7890i | 0.901690 | + | 0.901690i | ||||
\(819\) | −2.66682 | − | 7.08974i | −0.0931862 | − | 0.247735i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.12149 | − | 7.13863i | 0.143841 | − | 0.249140i | −0.785099 | − | 0.619370i | \(-0.787388\pi\) |
0.928940 | + | 0.370230i | \(0.120721\pi\) | |||||||
\(822\) | −21.2322 | − | 5.68916i | −0.740559 | − | 0.198432i | ||||
\(823\) | −31.3528 | − | 8.40095i | −1.09289 | − | 0.292839i | −0.333023 | − | 0.942919i | \(-0.608069\pi\) |
−0.759866 | + | 0.650080i | \(0.774736\pi\) | |||||||
\(824\) | −0.181895 | + | 0.315052i | −0.00633663 | + | 0.0109754i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.54647 | + | 7.01668i | 0.297370 | + | 0.244141i | ||||
\(827\) | −7.75116 | − | 7.75116i | −0.269534 | − | 0.269534i | 0.559378 | − | 0.828913i | \(-0.311040\pi\) |
−0.828913 | + | 0.559378i | \(0.811040\pi\) | |||||||
\(828\) | 1.79949 | + | 6.71580i | 0.0625367 | + | 0.233390i | ||||
\(829\) | 2.65278 | + | 4.59474i | 0.0921347 | + | 0.159582i | 0.908409 | − | 0.418082i | \(-0.137298\pi\) |
−0.816274 | + | 0.577664i | \(0.803964\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.72062 | + | 5.03485i | 0.302515 | + | 0.174657i | ||||
\(832\) | 2.02443 | − | 2.02443i | 0.0701844 | − | 0.0701844i | ||||
\(833\) | 48.5635 | + | 3.20191i | 1.68263 | + | 0.110940i | ||||
\(834\) | 16.5902i | 0.574471i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.8463 | − | 9.14886i | 0.548056 | − | 0.316420i | ||||
\(837\) | −0.482173 | + | 1.79949i | −0.0166663 | + | 0.0621996i | ||||
\(838\) | 8.74779 | − | 2.34396i | 0.302187 | − | 0.0809709i | ||||
\(839\) | −2.31971 | −0.0800852 | −0.0400426 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400426 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −48.7163 | −1.67987 | ||||||||
\(842\) | −9.96339 | + | 2.66968i | −0.343361 | + | 0.0920034i | ||||
\(843\) | 3.94098 | − | 14.7079i | 0.135734 | − | 0.506568i | ||||
\(844\) | −6.41257 | + | 3.70230i | −0.220730 | + | 0.127438i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.86297i | 0.0640503i | ||||||||
\(847\) | −16.2825 | + | 35.9177i | −0.559473 | + | 1.23415i | ||||
\(848\) | 0.643653 | − | 0.643653i | 0.0221031 | − | 0.0221031i | ||||
\(849\) | −12.8448 | − | 7.41595i | −0.440832 | − | 0.254515i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.0269 | − | 46.8120i | −0.926471 | − | 1.60469i | ||||
\(852\) | −2.03509 | − | 7.59505i | −0.0697209 | − | 0.260202i | ||||
\(853\) | −25.8556 | − | 25.8556i | −0.885278 | − | 0.885278i | 0.108787 | − | 0.994065i | \(-0.465303\pi\) |
−0.994065 | + | 0.108787i | \(0.965303\pi\) | |||||||
\(854\) | 15.3202 | + | 2.53243i | 0.524247 | + | 0.0866579i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.106416 | + | 0.184318i | −0.00363722 | + | 0.00629984i | ||||
\(857\) | 37.0519 | + | 9.92803i | 1.26567 | + | 0.339135i | 0.828370 | − | 0.560181i | \(-0.189269\pi\) |
0.437299 | + | 0.899316i | \(0.355935\pi\) | |||||||
\(858\) | 14.0753 | + | 3.77145i | 0.480521 | + | 0.128755i | ||||
\(859\) | −10.5922 | + | 18.3462i | −0.361400 | + | 0.625963i | −0.988191 | − | 0.153224i | \(-0.951034\pi\) |
0.626792 | + | 0.779187i | \(0.284368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7990 | + | 1.78507i | 0.368029 | + | 0.0608351i | ||||
\(862\) | −16.1845 | − | 16.1845i | −0.551245 | − | 0.551245i | ||||
\(863\) | −6.19036 | − | 23.1027i | −0.210722 | − | 0.786426i | −0.987629 | − | 0.156810i | \(-0.949879\pi\) |
0.776906 | − | 0.629616i | \(-0.216788\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.1611 | − | 12.2174i | −0.719084 | − | 0.415163i | ||||
\(867\) | 22.1608 | − | 22.1608i | 0.752622 | − | 0.752622i | ||||
\(868\) | 2.03509 | − | 4.48922i | 0.0690754 | − | 0.152374i | ||||
\(869\) | 61.5336i | 2.08738i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.30583 | − | 4.21802i | 0.247549 | − | 0.142922i | ||||
\(872\) | −0.403862 | + | 1.50724i | −0.0136765 | + | 0.0510414i | ||||
\(873\) | −18.4346 | + | 4.93953i | −0.623916 | + | 0.167178i | ||||
\(874\) | −24.9952 | −0.845474 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.5293 | −0.457114 | ||||||||
\(877\) | −50.9006 | + | 13.6388i | −1.71879 | + | 0.460549i | −0.977553 | − | 0.210691i | \(-0.932429\pi\) |
−0.741240 | + | 0.671240i | \(0.765762\pi\) | |||||||
\(878\) | 1.28514 | − | 4.79619i | 0.0433712 | − | 0.161864i | ||||
\(879\) | 22.9038 | − | 13.2235i | 0.772527 | − | 0.446018i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.86297i | − | 0.264910i | −0.991189 | − | 0.132455i | \(-0.957714\pi\) | ||
0.991189 | − | 0.132455i | \(-0.0422860\pi\) | |||||||
\(882\) | 6.98483 | + | 0.460527i | 0.235192 | + | 0.0155068i | ||||
\(883\) | −16.6993 | + | 16.6993i | −0.561977 | + | 0.561977i | −0.929869 | − | 0.367892i | \(-0.880080\pi\) |
0.367892 | + | 0.929869i | \(0.380080\pi\) | |||||||
\(884\) | 17.2386 | + | 9.95271i | 0.579797 | + | 0.334746i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.49758 | + | 11.2541i | 0.218290 | + | 0.378090i | ||||
\(887\) | 10.8924 | + | 40.6509i | 0.365730 | + | 1.36492i | 0.866428 | + | 0.499301i | \(0.166410\pi\) |
−0.500698 | + | 0.865622i | \(0.666923\pi\) | |||||||
\(888\) | 5.49740 | + | 5.49740i | 0.184481 | + | 0.184481i | ||||
\(889\) | −4.12736 | − | 3.38858i | −0.138427 | − | 0.113649i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.54487 | − | 4.40784i | 0.0852563 | − | 0.147668i | ||||
\(892\) | −3.68567 | − | 0.987571i | −0.123405 | − | 0.0330663i | ||||
\(893\) | −6.46922 | − | 1.73342i | −0.216484 | − | 0.0580068i | ||||
\(894\) | 4.96939 | − | 8.60723i | 0.166201 | − | 0.287869i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.931486 | + | 2.47635i | 0.0311188 | + | 0.0827292i | ||||
\(897\) | −14.0753 | − | 14.0753i | −0.469959 | − | 0.469959i | ||||
\(898\) | 3.90065 | + | 14.5574i | 0.130166 | + | 0.485788i | ||||
\(899\) | −8.21169 | − | 14.2231i | −0.273875 | − | 0.474366i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.48090 | + | 3.16440i | 0.182595 | + | 0.105421i | ||||
\(902\) | −14.8891 | + | 14.8891i | −0.495753 | + | 0.495753i | ||||
\(903\) | 17.0857 | + | 23.8528i | 0.568576 | + | 0.793771i | ||||
\(904\) | 0.0424462i | 0.00141174i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.2645 | + | 7.65825i | −0.440683 | + | 0.254428i | ||||
\(907\) | 11.6250 | − | 43.3851i | 0.386002 | − | 1.44058i | −0.450580 | − | 0.892736i | \(-0.648783\pi\) |
0.836582 | − | 0.547842i | \(-0.184550\pi\) | |||||||
\(908\) | −19.0216 | + | 5.09682i | −0.631253 | + | 0.169144i | ||||
\(909\) | −1.36379 | −0.0452341 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.6738 | −0.585559 | −0.292780 | − | 0.956180i | \(-0.594580\pi\) | ||||
−0.292780 | + | 0.956180i | \(0.594580\pi\) | |||||||
\(912\) | 3.47253 | − | 0.930461i | 0.114987 | − | 0.0308106i | ||||
\(913\) | −3.70916 | + | 13.8428i | −0.122755 | + | 0.458129i | ||||
\(914\) | 22.4294 | − | 12.9496i | 0.741898 | − | 0.428335i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.9768i | 0.759173i | ||||||||
\(917\) | −12.7776 | − | 5.79246i | −0.421955 | − | 0.191284i | ||||
\(918\) | 4.91631 | − | 4.91631i | 0.162262 | − | 0.162262i | ||||
\(919\) | 49.9117 | + | 28.8165i | 1.64643 | + | 0.950569i | 0.978473 | + | 0.206373i | \(0.0661662\pi\) |
0.667961 | + | 0.744196i | \(0.267167\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9054 | + | 27.5490i | 0.524101 | + | 0.907770i | ||||
\(922\) | 5.15190 | + | 19.2272i | 0.169669 | + | 0.633213i | ||||
\(923\) | 15.9180 | + | 15.9180i | 0.523948 | + | 0.523948i | ||||
\(924\) | −8.54487 | + | 10.4078i | −0.281106 | + | 0.342393i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.5676 | + | 35.6241i | −0.675893 | + | 1.17068i | ||||
\(927\) | −0.351395 | − | 0.0941560i | −0.0115413 | − | 0.00309249i | ||||
\(928\) | 8.51530 | + | 2.28167i | 0.279528 | + | 0.0748994i | ||||
\(929\) | 22.7211 | − | 39.3541i | 0.745455 | − | 1.29117i | −0.204527 | − | 0.978861i | \(-0.565566\pi\) |
0.949982 | − | 0.312305i | \(-0.101101\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.09831 | + | 23.8265i | −0.265411 | + | 0.780883i | ||||
\(932\) | 9.36143 | + | 9.36143i | 0.306644 | + | 0.306644i | ||||
\(933\) | −4.26167 | − | 15.9048i | −0.139521 | − | 0.520699i | ||||
\(934\) | −14.2402 | − | 24.6648i | −0.465954 | − | 0.807055i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.47941 | + | 1.43149i | 0.0810420 | + | 0.0467896i | ||||
\(937\) | −2.46056 | + | 2.46056i | −0.0803830 | + | 0.0803830i | −0.746155 | − | 0.665772i | \(-0.768102\pi\) |
0.665772 | + | 0.746155i | \(0.268102\pi\) | |||||||
\(938\) | 0.762637 | + | 7.75859i | 0.0249010 | + | 0.253327i | ||||
\(939\) | − | 3.37609i | − | 0.110174i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.6954 | − | 7.90702i | 0.446456 | − | 0.257762i | −0.259876 | − | 0.965642i | \(-0.583682\pi\) |
0.706332 | + | 0.707880i | \(0.250348\pi\) | |||||||
\(942\) | −4.23040 | + | 15.7881i | −0.137834 | + | 0.514403i | ||||
\(943\) | 27.7835 | − | 7.44455i | 0.904754 | − | 0.242428i | ||||
\(944\) | −4.17947 | −0.136030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −56.4438 | −1.83515 | ||||||||
\(947\) | 5.56306 | − | 1.49062i | 0.180775 | − | 0.0484386i | −0.167296 | − | 0.985907i | \(-0.553503\pi\) |
0.348071 | + | 0.937468i | \(0.386837\pi\) | |||||||
\(948\) | −3.12905 | + | 11.6778i | −0.101627 | + | 0.379277i | ||||
\(949\) | 33.5447 | − | 19.3671i | 1.08891 | − | 0.628681i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 13.8173i | − | 0.448057i | ||||||
\(952\) | −14.9545 | + | 10.7119i | −0.484678 | + | 0.347173i | ||||
\(953\) | −33.0749 | + | 33.0749i | −1.07140 | + | 1.07140i | −0.0741531 | + | 0.997247i | \(0.523625\pi\) |
−0.997247 | + | 0.0741531i | \(0.976375\pi\) | |||||||
\(954\) | 0.788311 | + | 0.455132i | 0.0255225 | + | 0.0147354i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.825071 | + | 1.42906i | 0.0266847 | + | 0.0462192i | ||||
\(957\) | 11.6131 | + | 43.3406i | 0.375398 | + | 1.40100i | ||||
\(958\) | −6.78497 | − | 6.78497i | −0.219212 | − | 0.219212i | ||||
\(959\) | −9.48460 | + | 57.3782i | −0.306274 | + | 1.85284i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7647 | + | 23.8411i | −0.444021 | + | 0.769068i | ||||
\(962\) | −21.4997 | − | 5.76084i | −0.693180 | − | 0.185737i | ||||
\(963\) | −0.205579 | − | 0.0550849i | −0.00662471 | − | 0.00177508i | ||||
\(964\) | −6.32570 | + | 10.9564i | −0.203737 | + | 0.352883i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 17.2174 | − | 6.47635i | 0.553960 | − | 0.208373i | ||||
\(967\) | 12.8181 | + | 12.8181i | 0.412203 | + | 0.412203i | 0.882505 | − | 0.470302i | \(-0.155855\pi\) |
−0.470302 | + | 0.882505i | \(0.655855\pi\) | |||||||
\(968\) | −3.85781 | − | 14.3975i | −0.123995 | − | 0.462754i | ||||
\(969\) | 12.4976 | + | 21.6464i | 0.401480 | + | 0.695384i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.40830 | + | 1.96778i | 0.109378 | + | 0.0631492i | 0.553691 | − | 0.832722i | \(-0.313219\pi\) |
−0.444313 | + | 0.895872i | \(0.646552\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 43.6830 | − | 4.29385i | 1.40041 | − | 0.137655i | ||||
\(974\) | 12.4681i | 0.399504i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.08277 | + | 2.93454i | −0.162696 | + | 0.0939323i | ||||
\(977\) | 4.38709 | − | 16.3729i | 0.140356 | − | 0.523814i | −0.859563 | − | 0.511030i | \(-0.829264\pi\) |
0.999918 | − | 0.0127838i | \(-0.00406931\pi\) | |||||||
\(978\) | −7.23934 | + | 1.93977i | −0.231488 | + | 0.0620271i | ||||
\(979\) | −38.9372 | −1.24444 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.56040 | −0.0498199 | ||||||||
\(982\) | −35.0909 | + | 9.40258i | −1.11980 | + | 0.300049i | ||||
\(983\) | −1.27255 | + | 4.74921i | −0.0405879 | + | 0.151476i | −0.983246 | − | 0.182284i | \(-0.941651\pi\) |
0.942658 | + | 0.333760i | \(0.108318\pi\) | |||||||
\(984\) | −3.58277 | + | 2.06851i | −0.114215 | + | 0.0659418i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 61.2929i | 1.95196i | ||||||||
\(987\) | 4.90532 | − | 0.482173i | 0.156138 | − | 0.0153477i | ||||
\(988\) | −7.27787 | + | 7.27787i | −0.231540 | + | 0.231540i | ||||
\(989\) | 66.7738 | + | 38.5519i | 2.12328 | + | 1.22588i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.32540 | − | 2.29565i | −0.0421026 | − | 0.0729238i | 0.844206 | − | 0.536019i | \(-0.180072\pi\) |
−0.886309 | + | 0.463095i | \(0.846739\pi\) | |||||||
\(992\) | 0.482173 | + | 1.79949i | 0.0153090 | + | 0.0571340i | ||||
\(993\) | −3.41505 | − | 3.41505i | −0.108373 | − | 0.108373i | ||||
\(994\) | −19.4715 | + | 7.32425i | −0.617599 | + | 0.232311i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.40784 | + | 2.43845i | −0.0446092 | + | 0.0772653i | ||||
\(997\) | 13.6569 | + | 3.65936i | 0.432518 | + | 0.115893i | 0.468508 | − | 0.883459i | \(-0.344792\pi\) |
−0.0359897 | + | 0.999352i | \(0.511458\pi\) | |||||||
\(998\) | 2.70408 | + | 0.724555i | 0.0855960 | + | 0.0229354i | ||||
\(999\) | −3.88725 | + | 6.73291i | −0.122987 | + | 0.213020i |
(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 | 1050.2.bc.f.607.2 | yes | 16 | |
5.2 | odd | 4 | 1050.2.bc.e.943.2 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.e.943.3 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.2.bc.f.607.3 | yes | 16 | |
7.3 | odd | 6 | 1050.2.bc.e.157.4 | yes | 16 | ||
35.3 | even | 12 | inner | 1050.2.bc.f.493.2 | yes | 16 | |
35.17 | even | 12 | inner | 1050.2.bc.f.493.3 | yes | 16 | |
35.24 | odd | 6 | 1050.2.bc.e.157.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.e.157.1 | ✓ | 16 | 35.24 | odd | 6 | ||
1050.2.bc.e.157.4 | yes | 16 | 7.3 | odd | 6 | ||
1050.2.bc.e.943.2 | yes | 16 | 5.2 | odd | 4 | ||
1050.2.bc.e.943.3 | yes | 16 | 5.3 | odd | 4 | ||
1050.2.bc.f.493.2 | yes | 16 | 35.3 | even | 12 | inner | |
1050.2.bc.f.493.3 | yes | 16 | 35.17 | even | 12 | inner | |
1050.2.bc.f.607.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.2.bc.f.607.3 | yes | 16 | 5.4 | even | 2 | inner |