Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-2.73861 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(3\) | −1.23861 | − | 0.715113i | −0.412871 | − | 0.238371i | 0.279152 | − | 0.960247i | \(-0.409947\pi\) |
−0.692023 | + | 0.721876i | \(0.743280\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(5\) | −3.73861 | + | 6.47547i | −0.747723 | + | 1.29509i | 0.201189 | + | 0.979552i | \(0.435519\pi\) |
−0.948912 | + | 0.315541i | \(0.897814\pi\) | |||||||
\(6\) | 2.86045i | 0.476742i | ||||||||
\(7\) | 3.76593i | 0.537989i | 0.963142 | + | 0.268995i | \(0.0866914\pi\) | ||||
−0.963142 | + | 0.268995i | \(0.913309\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | −3.47723 | − | 6.02273i | −0.386358 | − | 0.669192i | ||||
\(10\) | 14.9545 | 1.49545 | ||||||||
\(11\) | 14.0793i | 1.27994i | 0.768400 | + | 0.639970i | \(0.221053\pi\) | ||||
−0.768400 | + | 0.639970i | \(0.778947\pi\) | |||||||
\(12\) | 4.95445 | − | 2.86045i | 0.412871 | − | 0.238371i | ||||
\(13\) | −3.00000 | − | 5.19615i | −0.230769 | − | 0.399704i | 0.727265 | − | 0.686356i | \(-0.240791\pi\) |
−0.958035 | + | 0.286652i | \(0.907458\pi\) | |||||||
\(14\) | 6.52277 | − | 3.76593i | 0.465912 | − | 0.268995i | ||||
\(15\) | 9.26139 | − | 5.34706i | 0.617426 | − | 0.356471i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(17\) | −13.4772 | + | 23.3432i | −0.792778 | + | 1.37313i | 0.131463 | + | 0.991321i | \(0.458033\pi\) |
−0.924241 | + | 0.381811i | \(0.875301\pi\) | |||||||
\(18\) | −6.95445 | + | 12.0455i | −0.386358 | + | 0.669192i | ||||
\(19\) | −18.7158 | + | 3.27374i | −0.985044 | + | 0.172302i | ||||
\(20\) | −14.9545 | − | 25.9019i | −0.747723 | − | 1.29509i | ||||
\(21\) | 2.69306 | − | 4.66452i | 0.128241 | − | 0.222120i | ||||
\(22\) | 24.3861 | − | 14.0793i | 1.10846 | − | 0.639970i | ||||
\(23\) | 21.6475 | − | 12.4982i | 0.941196 | − | 0.543400i | 0.0508612 | − | 0.998706i | \(-0.483803\pi\) |
0.890335 | + | 0.455306i | \(0.150470\pi\) | |||||||
\(24\) | −9.90890 | − | 5.72091i | −0.412871 | − | 0.238371i | ||||
\(25\) | −15.4545 | − | 26.7679i | −0.618178 | − | 1.07072i | ||||
\(26\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(27\) | 22.8185i | 0.845129i | ||||||||
\(28\) | −13.0455 | − | 7.53185i | −0.465912 | − | 0.268995i | ||||
\(29\) | 1.73861 | + | 3.01137i | 0.0599522 | + | 0.103840i | 0.894444 | − | 0.447181i | \(-0.147572\pi\) |
−0.834492 | + | 0.551021i | \(0.814239\pi\) | |||||||
\(30\) | −18.5228 | − | 10.6941i | −0.617426 | − | 0.356471i | ||||
\(31\) | − | 39.4565i | − | 1.27279i | −0.771364 | − | 0.636394i | \(-0.780425\pi\) | ||
0.771364 | − | 0.636394i | \(-0.219575\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.500000 | + | 0.866025i | ||||
\(33\) | 10.0683 | − | 17.4388i | 0.305101 | − | 0.528450i | ||||
\(34\) | 53.9089 | 1.58556 | ||||||||
\(35\) | −24.3861 | − | 14.0793i | −0.696747 | − | 0.402267i | ||||
\(36\) | 27.8178 | 0.772717 | ||||||||
\(37\) | 3.38613 | 0.0915170 | 0.0457585 | − | 0.998953i | \(-0.485430\pi\) | ||||
0.0457585 | + | 0.998953i | \(0.485430\pi\) | |||||||
\(38\) | 24.3861 | + | 29.1430i | 0.641740 | + | 0.766922i | ||||
\(39\) | 8.58136i | 0.220035i | ||||||||
\(40\) | −29.9089 | + | 51.8037i | −0.747723 | + | 1.29509i | ||||
\(41\) | −4.45445 | + | 7.71534i | −0.108645 | + | 0.188179i | −0.915222 | − | 0.402951i | \(-0.867985\pi\) |
0.806576 | + | 0.591130i | \(0.201318\pi\) | |||||||
\(42\) | −10.7723 | −0.256482 | ||||||||
\(43\) | 45.3861 | + | 26.2037i | 1.05549 | + | 0.609388i | 0.924182 | − | 0.381953i | \(-0.124748\pi\) |
0.131310 | + | 0.991341i | \(0.458082\pi\) | |||||||
\(44\) | −48.7723 | − | 28.1587i | −1.10846 | − | 0.639970i | ||||
\(45\) | 52.0000 | 1.15556 | ||||||||
\(46\) | −43.2950 | − | 24.9964i | −0.941196 | − | 0.543400i | ||||
\(47\) | −19.1703 | + | 11.0680i | −0.407879 | + | 0.235489i | −0.689878 | − | 0.723926i | \(-0.742336\pi\) |
0.281999 | + | 0.959415i | \(0.409002\pi\) | |||||||
\(48\) | 22.8836i | 0.476742i | ||||||||
\(49\) | 34.8178 | 0.710567 | ||||||||
\(50\) | −30.9089 | + | 53.5358i | −0.618178 | + | 1.07072i | ||||
\(51\) | 33.3861 | − | 19.2755i | 0.654630 | − | 0.377951i | ||||
\(52\) | 24.0000 | 0.461538 | ||||||||
\(53\) | 41.9545 | + | 72.6672i | 0.791593 | + | 1.37108i | 0.924980 | + | 0.380016i | \(0.124081\pi\) |
−0.133387 | + | 0.991064i | \(0.542585\pi\) | |||||||
\(54\) | 39.5228 | − | 22.8185i | 0.731903 | − | 0.422565i | ||||
\(55\) | −91.1703 | − | 52.6372i | −1.65764 | − | 0.957040i | ||||
\(56\) | 30.1274i | 0.537989i | ||||||||
\(57\) | 25.5228 | + | 9.32905i | 0.447768 | + | 0.163667i | ||||
\(58\) | 3.47723 | − | 6.02273i | 0.0599522 | − | 0.103840i | ||||
\(59\) | 22.2386 | + | 12.8395i | 0.376926 | + | 0.217618i | 0.676480 | − | 0.736461i | \(-0.263505\pi\) |
−0.299554 | + | 0.954079i | \(0.596838\pi\) | |||||||
\(60\) | 42.7765i | 0.712942i | ||||||||
\(61\) | −13.7386 | − | 23.7960i | −0.225223 | − | 0.390098i | 0.731163 | − | 0.682203i | \(-0.238978\pi\) |
−0.956386 | + | 0.292105i | \(0.905644\pi\) | |||||||
\(62\) | −68.3406 | + | 39.4565i | −1.10227 | + | 0.636394i | ||||
\(63\) | 22.6812 | − | 13.0950i | 0.360018 | − | 0.207857i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 44.8634 | 0.690205 | ||||||||
\(66\) | −40.2733 | −0.610201 | ||||||||
\(67\) | −32.0109 | + | 18.4815i | −0.477774 | + | 0.275843i | −0.719488 | − | 0.694504i | \(-0.755624\pi\) |
0.241714 | + | 0.970347i | \(0.422290\pi\) | |||||||
\(68\) | −53.9089 | − | 93.3730i | −0.792778 | − | 1.37313i | ||||
\(69\) | −35.7505 | −0.518123 | ||||||||
\(70\) | 56.3173i | 0.804534i | ||||||||
\(71\) | −89.3406 | − | 51.5808i | −1.25832 | − | 0.726490i | −0.285571 | − | 0.958358i | \(-0.592183\pi\) |
−0.972747 | + | 0.231867i | \(0.925516\pi\) | |||||||
\(72\) | −27.8178 | − | 48.1819i | −0.386358 | − | 0.669192i | ||||
\(73\) | 4.45445 | − | 7.71534i | 0.0610199 | − | 0.105690i | −0.833902 | − | 0.551913i | \(-0.813898\pi\) |
0.894922 | + | 0.446224i | \(0.147231\pi\) | |||||||
\(74\) | −3.38613 | − | 5.86495i | −0.0457585 | − | 0.0792560i | ||||
\(75\) | 44.2067i | 0.589423i | ||||||||
\(76\) | 26.0911 | − | 71.3811i | 0.343304 | − | 0.939224i | ||||
\(77\) | −53.0217 | −0.688594 | ||||||||
\(78\) | 14.8634 | − | 8.58136i | 0.190556 | − | 0.110017i | ||||
\(79\) | 111.909 | + | 64.6106i | 1.41657 | + | 0.817856i | 0.995996 | − | 0.0894026i | \(-0.0284958\pi\) |
0.420573 | + | 0.907259i | \(0.361829\pi\) | |||||||
\(80\) | 119.636 | 1.49545 | ||||||||
\(81\) | −14.9772 | + | 25.9413i | −0.184904 | + | 0.320263i | ||||
\(82\) | 17.8178 | 0.217290 | ||||||||
\(83\) | 27.1743i | 0.327401i | 0.986510 | + | 0.163701i | \(0.0523431\pi\) | ||||
−0.986510 | + | 0.163701i | \(0.947657\pi\) | |||||||
\(84\) | 10.7723 | + | 18.6581i | 0.128241 | + | 0.222120i | ||||
\(85\) | −100.772 | − | 174.543i | −1.18556 | − | 2.05344i | ||||
\(86\) | − | 104.815i | − | 1.21878i | ||||||
\(87\) | − | 4.97322i | − | 0.0571635i | ||||||
\(88\) | 112.635i | 1.27994i | ||||||||
\(89\) | −64.2495 | − | 111.283i | −0.721904 | − | 1.25037i | −0.960236 | − | 0.279191i | \(-0.909934\pi\) |
0.238331 | − | 0.971184i | \(-0.423400\pi\) | |||||||
\(90\) | −52.0000 | − | 90.0666i | −0.577778 | − | 1.00074i | ||||
\(91\) | 19.5683 | − | 11.2978i | 0.215037 | − | 0.124151i | ||||
\(92\) | 99.9856i | 1.08680i | ||||||||
\(93\) | −28.2158 | + | 48.8713i | −0.303396 | + | 0.525497i | ||||
\(94\) | 38.3406 | + | 22.1359i | 0.407879 | + | 0.235489i | ||||
\(95\) | 48.7723 | − | 133.433i | 0.513392 | − | 1.40456i | ||||
\(96\) | 39.6356 | − | 22.8836i | 0.412871 | − | 0.238371i | ||||
\(97\) | −53.0228 | + | 91.8381i | −0.546627 | + | 0.946785i | 0.451876 | + | 0.892081i | \(0.350755\pi\) |
−0.998503 | + | 0.0547042i | \(0.982578\pi\) | |||||||
\(98\) | −34.8178 | − | 60.3062i | −0.355284 | − | 0.615369i | ||||
\(99\) | 84.7961 | − | 48.9570i | 0.856526 | − | 0.494515i | ||||
\(100\) | 123.636 | 1.23636 | ||||||||
\(101\) | 66.9425 | + | 115.948i | 0.662797 | + | 1.14800i | 0.979877 | + | 0.199600i | \(0.0639643\pi\) |
−0.317080 | + | 0.948399i | \(0.602702\pi\) | |||||||
\(102\) | −66.7723 | − | 38.5510i | −0.654630 | − | 0.377951i | ||||
\(103\) | 103.477i | 1.00463i | 0.864684 | + | 0.502316i | \(0.167519\pi\) | ||||
−0.864684 | + | 0.502316i | \(0.832481\pi\) | |||||||
\(104\) | −24.0000 | − | 41.5692i | −0.230769 | − | 0.399704i | ||||
\(105\) | 20.1366 | + | 34.8777i | 0.191778 | + | 0.332169i | ||||
\(106\) | 83.9089 | − | 145.334i | 0.791593 | − | 1.37108i | ||||
\(107\) | 67.7867i | 0.633520i | 0.948506 | + | 0.316760i | \(0.102595\pi\) | ||||
−0.948506 | + | 0.316760i | \(0.897405\pi\) | |||||||
\(108\) | −79.0455 | − | 45.6370i | −0.731903 | − | 0.422565i | ||||
\(109\) | 24.8634 | − | 43.0646i | 0.228104 | − | 0.395088i | −0.729142 | − | 0.684362i | \(-0.760081\pi\) |
0.957246 | + | 0.289274i | \(0.0934140\pi\) | |||||||
\(110\) | 210.549i | 1.91408i | ||||||||
\(111\) | −4.19410 | − | 2.42147i | −0.0377847 | − | 0.0218150i | ||||
\(112\) | 52.1822 | − | 30.1274i | 0.465912 | − | 0.268995i | ||||
\(113\) | −70.9089 | −0.627512 | −0.313756 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313756 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(114\) | −9.36439 | − | 53.5358i | −0.0821438 | − | 0.469612i | ||||
\(115\) | 186.904i | 1.62525i | ||||||||
\(116\) | −13.9089 | −0.119904 | ||||||||
\(117\) | −20.8634 | + | 36.1364i | −0.178319 | + | 0.308858i | ||||
\(118\) | − | 51.3579i | − | 0.435236i | ||||||
\(119\) | −87.9089 | − | 50.7542i | −0.738730 | − | 0.426506i | ||||
\(120\) | 74.0911 | − | 42.7765i | 0.617426 | − | 0.356471i | ||||
\(121\) | −77.2277 | −0.638246 | ||||||||
\(122\) | −27.4772 | + | 47.5920i | −0.225223 | + | 0.390098i | ||||
\(123\) | 11.0347 | − | 6.37088i | 0.0897128 | − | 0.0517957i | ||||
\(124\) | 136.681 | + | 78.9129i | 1.10227 | + | 0.636394i | ||||
\(125\) | 44.1822 | 0.353458 | ||||||||
\(126\) | −45.3623 | − | 26.1899i | −0.360018 | − | 0.207857i | ||||
\(127\) | −20.2039 | + | 11.6647i | −0.159086 | + | 0.0918484i | −0.577430 | − | 0.816441i | \(-0.695944\pi\) |
0.418343 | + | 0.908289i | \(0.362611\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.500000 | − | 0.866025i | ||||
\(129\) | −37.4772 | − | 64.9125i | −0.290521 | − | 0.503197i | ||||
\(130\) | −44.8634 | − | 77.7056i | −0.345103 | − | 0.597735i | ||||
\(131\) | −23.9436 | − | 13.8238i | −0.182775 | − | 0.105525i | 0.405821 | − | 0.913953i | \(-0.366986\pi\) |
−0.588596 | + | 0.808427i | \(0.700319\pi\) | |||||||
\(132\) | 40.2733 | + | 69.7554i | 0.305101 | + | 0.528450i | ||||
\(133\) | −12.3287 | − | 70.4825i | −0.0926968 | − | 0.529943i | ||||
\(134\) | 64.0217 | + | 36.9630i | 0.477774 | + | 0.275843i | ||||
\(135\) | −147.760 | − | 85.3095i | −1.09452 | − | 0.631922i | ||||
\(136\) | −107.818 | + | 186.746i | −0.792778 | + | 1.37313i | ||||
\(137\) | 99.4089 | + | 172.181i | 0.725612 | + | 1.25680i | 0.958721 | + | 0.284347i | \(0.0917768\pi\) |
−0.233109 | + | 0.972451i | \(0.574890\pi\) | |||||||
\(138\) | 35.7505 | + | 61.9217i | 0.259062 | + | 0.448708i | ||||
\(139\) | −232.738 | + | 134.371i | −1.67437 | + | 0.966699i | −0.709227 | + | 0.704981i | \(0.750956\pi\) |
−0.965144 | + | 0.261718i | \(0.915711\pi\) | |||||||
\(140\) | 97.5445 | − | 56.3173i | 0.696747 | − | 0.402267i | ||||
\(141\) | 31.6594 | 0.224535 | ||||||||
\(142\) | 206.323i | 1.45298i | ||||||||
\(143\) | 73.1584 | − | 42.2380i | 0.511597 | − | 0.295371i | ||||
\(144\) | −55.6356 | + | 96.3637i | −0.386358 | + | 0.669192i | ||||
\(145\) | −26.0000 | −0.179310 | ||||||||
\(146\) | −17.8178 | −0.122040 | ||||||||
\(147\) | −43.1258 | − | 24.8987i | −0.293373 | − | 0.169379i | ||||
\(148\) | −6.77226 | + | 11.7299i | −0.0457585 | + | 0.0792560i | ||||
\(149\) | 36.2158 | − | 62.7277i | 0.243059 | − | 0.420991i | −0.718525 | − | 0.695501i | \(-0.755182\pi\) |
0.961584 | + | 0.274510i | \(0.0885157\pi\) | |||||||
\(150\) | 76.5683 | − | 44.2067i | 0.510455 | − | 0.294712i | ||||
\(151\) | − | 39.4565i | − | 0.261301i | −0.991428 | − | 0.130651i | \(-0.958293\pi\) | ||
0.991428 | − | 0.130651i | \(-0.0417066\pi\) | |||||||
\(152\) | −149.727 | + | 26.1899i | −0.985044 | + | 0.172302i | ||||
\(153\) | 187.453 | 1.22519 | ||||||||
\(154\) | 53.0217 | + | 91.8363i | 0.344297 | + | 0.596340i | ||||
\(155\) | 255.499 | + | 147.512i | 1.64838 | + | 0.951693i | ||||
\(156\) | −29.7267 | − | 17.1627i | −0.190556 | − | 0.110017i | ||||
\(157\) | −50.9545 | + | 88.2557i | −0.324551 | + | 0.562138i | −0.981421 | − | 0.191865i | \(-0.938546\pi\) |
0.656871 | + | 0.754003i | \(0.271880\pi\) | |||||||
\(158\) | − | 258.443i | − | 1.63571i | ||||||
\(159\) | − | 120.009i | − | 0.754772i | ||||||
\(160\) | −119.636 | − | 207.215i | −0.747723 | − | 1.29509i | ||||
\(161\) | 47.0673 | + | 81.5229i | 0.292343 | + | 0.506354i | ||||
\(162\) | 59.9089 | 0.369808 | ||||||||
\(163\) | − | 190.563i | − | 1.16910i | −0.811358 | − | 0.584550i | \(-0.801271\pi\) | ||
0.811358 | − | 0.584550i | \(-0.198729\pi\) | |||||||
\(164\) | −17.8178 | − | 30.8613i | −0.108645 | − | 0.188179i | ||||
\(165\) | 75.2831 | + | 130.394i | 0.456261 | + | 0.790268i | ||||
\(166\) | 47.0673 | − | 27.1743i | 0.283538 | − | 0.163701i | ||||
\(167\) | 256.681 | − | 148.195i | 1.53701 | − | 0.887395i | 0.538001 | − | 0.842944i | \(-0.319180\pi\) |
0.999012 | − | 0.0444508i | \(-0.0141538\pi\) | |||||||
\(168\) | 21.5445 | − | 37.3162i | 0.128241 | − | 0.222120i | ||||
\(169\) | 66.5000 | − | 115.181i | 0.393491 | − | 0.681547i | ||||
\(170\) | −201.545 | + | 349.085i | −1.18556 | + | 2.05344i | ||||
\(171\) | 84.7961 | + | 101.337i | 0.495883 | + | 0.592614i | ||||
\(172\) | −181.545 | + | 104.815i | −1.05549 | + | 0.609388i | ||||
\(173\) | 113.863 | − | 197.217i | 0.658170 | − | 1.13998i | −0.322919 | − | 0.946426i | \(-0.604664\pi\) |
0.981089 | − | 0.193557i | \(-0.0620024\pi\) | |||||||
\(174\) | −8.61387 | + | 4.97322i | −0.0495050 | + | 0.0285817i | ||||
\(175\) | 100.806 | − | 58.2003i | 0.576034 | − | 0.332573i | ||||
\(176\) | 195.089 | − | 112.635i | 1.10846 | − | 0.639970i | ||||
\(177\) | −18.3634 | − | 31.8063i | −0.103748 | − | 0.179696i | ||||
\(178\) | −128.499 | + | 222.567i | −0.721904 | + | 1.25037i | ||||
\(179\) | 262.287i | 1.46529i | 0.680610 | + | 0.732646i | \(0.261715\pi\) | ||||
−0.680610 | + | 0.732646i | \(0.738285\pi\) | |||||||
\(180\) | −104.000 | + | 180.133i | −0.577778 | + | 1.00074i | ||||
\(181\) | −39.9425 | − | 69.1825i | −0.220677 | − | 0.382224i | 0.734337 | − | 0.678785i | \(-0.237493\pi\) |
−0.955014 | + | 0.296562i | \(0.904160\pi\) | |||||||
\(182\) | −39.1366 | − | 22.5956i | −0.215037 | − | 0.124151i | ||||
\(183\) | 39.2987i | 0.214747i | ||||||||
\(184\) | 173.180 | − | 99.9856i | 0.941196 | − | 0.543400i | ||||
\(185\) | −12.6594 | + | 21.9268i | −0.0684293 | + | 0.118523i | ||||
\(186\) | 112.863 | 0.606792 | ||||||||
\(187\) | −328.657 | − | 189.750i | −1.75753 | − | 1.01471i | ||||
\(188\) | − | 88.5438i | − | 0.470978i | ||||||
\(189\) | −85.9327 | −0.454670 | ||||||||
\(190\) | −279.885 | + | 48.9570i | −1.47308 | + | 0.257669i | ||||
\(191\) | − | 233.144i | − | 1.22065i | −0.792151 | − | 0.610325i | \(-0.791039\pi\) | ||
0.792151 | − | 0.610325i | \(-0.208961\pi\) | |||||||
\(192\) | −79.2712 | − | 45.7673i | −0.412871 | − | 0.238371i | ||||
\(193\) | 61.4772 | − | 106.482i | 0.318535 | − | 0.551719i | −0.661648 | − | 0.749815i | \(-0.730143\pi\) |
0.980183 | + | 0.198096i | \(0.0634759\pi\) | |||||||
\(194\) | 212.091 | 1.09325 | ||||||||
\(195\) | −55.5683 | − | 32.0824i | −0.284966 | − | 0.164525i | ||||
\(196\) | −69.6356 | + | 120.612i | −0.355284 | + | 0.615369i | ||||
\(197\) | −154.158 | −0.782530 | −0.391265 | − | 0.920278i | \(-0.627962\pi\) | ||||
−0.391265 | + | 0.920278i | \(0.627962\pi\) | |||||||
\(198\) | −169.592 | − | 97.9141i | −0.856526 | − | 0.494515i | ||||
\(199\) | 92.9762 | − | 53.6798i | 0.467217 | − | 0.269748i | −0.247857 | − | 0.968797i | \(-0.579726\pi\) |
0.715074 | + | 0.699049i | \(0.246393\pi\) | |||||||
\(200\) | −123.636 | − | 214.143i | −0.618178 | − | 1.07072i | ||||
\(201\) | 52.8654 | 0.263012 | ||||||||
\(202\) | 133.885 | − | 231.896i | 0.662797 | − | 1.14800i | ||||
\(203\) | −11.3406 | + | 6.54749i | −0.0558649 | + | 0.0322536i | ||||
\(204\) | 154.204i | 0.755902i | ||||||||
\(205\) | −33.3069 | − | 57.6893i | −0.162473 | − | 0.281411i | ||||
\(206\) | 179.228 | − | 103.477i | 0.870038 | − | 0.502316i | ||||
\(207\) | −150.547 | − | 86.9181i | −0.727278 | − | 0.419894i | ||||
\(208\) | −48.0000 | + | 83.1384i | −0.230769 | + | 0.399704i | ||||
\(209\) | −46.0921 | − | 263.507i | −0.220537 | − | 1.26080i | ||||
\(210\) | 40.2733 | − | 69.7554i | 0.191778 | − | 0.332169i | ||||
\(211\) | 117.226 | + | 67.6803i | 0.555572 | + | 0.320760i | 0.751366 | − | 0.659885i | \(-0.229395\pi\) |
−0.195794 | + | 0.980645i | \(0.562729\pi\) | |||||||
\(212\) | −335.636 | −1.58319 | ||||||||
\(213\) | 73.7723 | + | 127.777i | 0.346349 | + | 0.599893i | ||||
\(214\) | 117.410 | − | 67.7867i | 0.548645 | − | 0.316760i | ||||
\(215\) | −339.362 | + | 195.931i | −1.57843 | + | 0.911307i | ||||
\(216\) | 182.548i | 0.845129i | ||||||||
\(217\) | 148.590 | 0.684747 | ||||||||
\(218\) | −99.4534 | −0.456208 | ||||||||
\(219\) | −11.0347 | + | 6.37088i | −0.0503867 | + | 0.0290908i | ||||
\(220\) | 364.681 | − | 210.549i | 1.65764 | − | 0.957040i | ||||
\(221\) | 161.727 | 0.731795 | ||||||||
\(222\) | 9.68586i | 0.0436300i | ||||||||
\(223\) | 118.943 | + | 68.6715i | 0.533375 | + | 0.307944i | 0.742390 | − | 0.669968i | \(-0.233692\pi\) |
−0.209015 | + | 0.977912i | \(0.567026\pi\) | |||||||
\(224\) | −104.364 | − | 60.2548i | −0.465912 | − | 0.268995i | ||||
\(225\) | −107.477 | + | 186.156i | −0.477677 | + | 0.827360i | ||||
\(226\) | 70.9089 | + | 122.818i | 0.313756 | + | 0.543442i | ||||
\(227\) | − | 92.9922i | − | 0.409657i | −0.978798 | − | 0.204829i | \(-0.934336\pi\) | ||
0.978798 | − | 0.204829i | \(-0.0656637\pi\) | |||||||
\(228\) | −83.3623 | + | 69.7554i | −0.365624 | + | 0.305945i | ||||
\(229\) | −164.182 | −0.716953 | −0.358476 | − | 0.933539i | \(-0.616704\pi\) | ||||
−0.358476 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(230\) | 323.727 | − | 186.904i | 1.40751 | − | 0.812625i | ||||
\(231\) | 65.6734 | + | 37.9166i | 0.284300 | + | 0.164141i | ||||
\(232\) | 13.9089 | + | 24.0909i | 0.0599522 | + | 0.103840i | ||||
\(233\) | −27.2723 | + | 47.2369i | −0.117048 | + | 0.202734i | −0.918597 | − | 0.395196i | \(-0.870677\pi\) |
0.801548 | + | 0.597930i | \(0.204010\pi\) | |||||||
\(234\) | 83.4534 | 0.356639 | ||||||||
\(235\) | − | 165.515i | − | 0.704321i | ||||||
\(236\) | −88.9545 | + | 51.3579i | −0.376926 | + | 0.217618i | ||||
\(237\) | −92.4079 | − | 160.055i | −0.389907 | − | 0.675338i | ||||
\(238\) | 203.017i | 0.853012i | ||||||||
\(239\) | 285.524i | 1.19466i | 0.801995 | + | 0.597331i | \(0.203772\pi\) | ||||
−0.801995 | + | 0.597331i | \(0.796228\pi\) | |||||||
\(240\) | −148.182 | − | 85.5530i | −0.617426 | − | 0.356471i | ||||
\(241\) | 87.8861 | + | 152.223i | 0.364673 | + | 0.631632i | 0.988724 | − | 0.149752i | \(-0.0478475\pi\) |
−0.624051 | + | 0.781384i | \(0.714514\pi\) | |||||||
\(242\) | 77.2277 | + | 133.762i | 0.319123 | + | 0.552737i | ||||
\(243\) | 214.954 | − | 124.104i | 0.884586 | − | 0.510716i | ||||
\(244\) | 109.909 | 0.450446 | ||||||||
\(245\) | −130.170 | + | 225.462i | −0.531307 | + | 0.920251i | ||||
\(246\) | −22.0694 | − | 12.7418i | −0.0897128 | − | 0.0517957i | ||||
\(247\) | 73.1584 | + | 87.4291i | 0.296188 | + | 0.353964i | ||||
\(248\) | − | 315.652i | − | 1.27279i | ||||||
\(249\) | 19.4327 | − | 33.6584i | 0.0780430 | − | 0.135174i | ||||
\(250\) | −44.1822 | − | 76.5258i | −0.176729 | − | 0.306103i | ||||
\(251\) | −140.124 | + | 80.9005i | −0.558262 | + | 0.322313i | −0.752448 | − | 0.658652i | \(-0.771127\pi\) |
0.194186 | + | 0.980965i | \(0.437794\pi\) | |||||||
\(252\) | 104.760i | 0.415713i | ||||||||
\(253\) | 175.966 | + | 304.783i | 0.695519 | + | 1.20467i | ||||
\(254\) | 40.4079 | + | 23.3295i | 0.159086 | + | 0.0918484i | ||||
\(255\) | 288.254i | 1.13041i | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.500000 | + | 0.866025i | ||||
\(257\) | 154.862 | + | 268.229i | 0.602577 | + | 1.04369i | 0.992429 | + | 0.122817i | \(0.0391927\pi\) |
−0.389852 | + | 0.920877i | \(0.627474\pi\) | |||||||
\(258\) | −74.9545 | + | 129.825i | −0.290521 | + | 0.503197i | ||||
\(259\) | 12.7519i | 0.0492352i | ||||||||
\(260\) | −89.7267 | + | 155.411i | −0.345103 | + | 0.597735i | ||||
\(261\) | 12.0911 | − | 20.9424i | 0.0463260 | − | 0.0802391i | ||||
\(262\) | 55.2953i | 0.211051i | ||||||||
\(263\) | 171.238 | + | 98.8641i | 0.651093 | + | 0.375909i | 0.788875 | − | 0.614554i | \(-0.210664\pi\) |
−0.137782 | + | 0.990463i | \(0.543997\pi\) | |||||||
\(264\) | 80.5466 | − | 139.511i | 0.305101 | − | 0.528450i | ||||
\(265\) | −627.406 | −2.36757 | ||||||||
\(266\) | −109.751 | + | 91.8363i | −0.412596 | + | 0.345249i | ||||
\(267\) | 183.783i | 0.688325i | ||||||||
\(268\) | − | 147.852i | − | 0.551686i | ||||||
\(269\) | 77.6356 | − | 134.469i | 0.288608 | − | 0.499884i | −0.684870 | − | 0.728666i | \(-0.740141\pi\) |
0.973478 | + | 0.228782i | \(0.0734742\pi\) | |||||||
\(270\) | 341.238i | 1.26384i | ||||||||
\(271\) | −52.0098 | − | 30.0279i | −0.191918 | − | 0.110804i | 0.400962 | − | 0.916095i | \(-0.368676\pi\) |
−0.592880 | + | 0.805291i | \(0.702009\pi\) | |||||||
\(272\) | 431.271 | 1.58556 | ||||||||
\(273\) | −32.3168 | −0.118376 | ||||||||
\(274\) | 198.818 | − | 344.363i | 0.725612 | − | 1.25680i | ||||
\(275\) | 376.874 | − | 217.588i | 1.37045 | − | 0.791231i | ||||
\(276\) | 71.5010 | − | 123.843i | 0.259062 | − | 0.448708i | ||||
\(277\) | 399.430 | 1.44198 | 0.720992 | − | 0.692943i | \(-0.243686\pi\) | ||||
0.720992 | + | 0.692943i | \(0.243686\pi\) | |||||||
\(278\) | 465.475 | + | 268.742i | 1.67437 | + | 0.966699i | ||||
\(279\) | −237.636 | + | 137.199i | −0.851741 | + | 0.491753i | ||||
\(280\) | −195.089 | − | 112.635i | −0.696747 | − | 0.402267i | ||||
\(281\) | −228.999 | − | 396.638i | −0.814943 | − | 1.41152i | −0.909369 | − | 0.415991i | \(-0.863435\pi\) |
0.0944260 | − | 0.995532i | \(-0.469898\pi\) | |||||||
\(282\) | −31.6594 | − | 54.8357i | −0.112267 | − | 0.194453i | ||||
\(283\) | −362.237 | − | 209.137i | −1.27999 | − | 0.739001i | −0.303142 | − | 0.952945i | \(-0.598036\pi\) |
−0.976846 | + | 0.213944i | \(0.931369\pi\) | |||||||
\(284\) | 357.362 | − | 206.323i | 1.25832 | − | 0.726490i | ||||
\(285\) | −155.830 | + | 130.394i | −0.546771 | + | 0.457523i | ||||
\(286\) | −146.317 | − | 84.4760i | −0.511597 | − | 0.295371i | ||||
\(287\) | −29.0554 | − | 16.7751i | −0.101238 | − | 0.0584499i | ||||
\(288\) | 222.542 | 0.772717 | ||||||||
\(289\) | −218.771 | − | 378.923i | −0.756994 | − | 1.31115i | ||||
\(290\) | 26.0000 | + | 45.0333i | 0.0896552 | + | 0.155287i | ||||
\(291\) | 131.349 | − | 75.8346i | 0.451372 | − | 0.260600i | ||||
\(292\) | 17.8178 | + | 30.8613i | 0.0610199 | + | 0.105690i | ||||
\(293\) | −123.794 | −0.422505 | −0.211253 | − | 0.977432i | \(-0.567754\pi\) | ||||
−0.211253 | + | 0.977432i | \(0.567754\pi\) | |||||||
\(294\) | 99.5947i | 0.338758i | ||||||||
\(295\) | −166.283 | + | 96.0036i | −0.563672 | + | 0.325436i | ||||
\(296\) | 27.0890 | 0.0915170 | ||||||||
\(297\) | −321.269 | −1.08171 | ||||||||
\(298\) | −144.863 | −0.486119 | ||||||||
\(299\) | −129.885 | − | 74.9892i | −0.434398 | − | 0.250800i | ||||
\(300\) | −153.137 | − | 88.4135i | −0.510455 | − | 0.294712i | ||||
\(301\) | −98.6812 | + | 170.921i | −0.327844 | + | 0.567843i | ||||
\(302\) | −68.3406 | + | 39.4565i | −0.226293 | + | 0.130651i | ||||
\(303\) | − | 191.486i | − | 0.631967i | ||||||
\(304\) | 195.089 | + | 233.144i | 0.641740 | + | 0.766922i | ||||
\(305\) | 205.453 | 0.673618 | ||||||||
\(306\) | −187.453 | − | 324.679i | −0.612593 | − | 1.06104i | ||||
\(307\) | 146.783 | + | 84.7453i | 0.478121 | + | 0.276043i | 0.719633 | − | 0.694355i | \(-0.244310\pi\) |
−0.241512 | + | 0.970398i | \(0.577643\pi\) | |||||||
\(308\) | 106.043 | − | 183.673i | 0.344297 | − | 0.596340i | ||||
\(309\) | 73.9979 | − | 128.168i | 0.239475 | − | 0.414784i | ||||
\(310\) | − | 590.050i | − | 1.90339i | ||||||
\(311\) | 407.488i | 1.31025i | 0.755520 | + | 0.655125i | \(0.227384\pi\) | ||||
−0.755520 | + | 0.655125i | \(0.772616\pi\) | |||||||
\(312\) | 68.6509i | 0.220035i | ||||||||
\(313\) | 286.361 | + | 495.992i | 0.914892 | + | 1.58464i | 0.807059 | + | 0.590471i | \(0.201058\pi\) |
0.107833 | + | 0.994169i | \(0.465609\pi\) | |||||||
\(314\) | 203.818 | 0.649101 | ||||||||
\(315\) | 195.828i | 0.621677i | ||||||||
\(316\) | −447.636 | + | 258.443i | −1.41657 | + | 0.817856i | ||||
\(317\) | −264.453 | − | 458.047i | −0.834238 | − | 1.44494i | −0.894649 | − | 0.446769i | \(-0.852575\pi\) |
0.0604115 | − | 0.998174i | \(-0.480759\pi\) | |||||||
\(318\) | −207.861 | + | 120.009i | −0.653652 | + | 0.377386i | ||||
\(319\) | −42.3980 | + | 24.4785i | −0.132909 | + | 0.0767352i | ||||
\(320\) | −239.271 | + | 414.430i | −0.747723 | + | 1.29509i | ||||
\(321\) | 48.4752 | − | 83.9614i | 0.151013 | − | 0.261562i | ||||
\(322\) | 94.1346 | − | 163.046i | 0.292343 | − | 0.506354i | ||||
\(323\) | 175.818 | − | 481.009i | 0.544328 | − | 1.48919i | ||||
\(324\) | −59.9089 | − | 103.765i | −0.184904 | − | 0.320263i | ||||
\(325\) | −92.7267 | + | 160.607i | −0.285313 | + | 0.494177i | ||||
\(326\) | −330.065 | + | 190.563i | −1.01247 | + | 0.584550i | ||||
\(327\) | −61.5921 | + | 35.5602i | −0.188355 | + | 0.108747i | ||||
\(328\) | −35.6356 | + | 61.7227i | −0.108645 | + | 0.188179i | ||||
\(329\) | −41.6812 | − | 72.1939i | −0.126690 | − | 0.219434i | ||||
\(330\) | 150.566 | − | 260.788i | 0.456261 | − | 0.790268i | ||||
\(331\) | 59.2704i | 0.179065i | 0.995984 | + | 0.0895324i | \(0.0285373\pi\) | ||||
−0.995984 | + | 0.0895324i | \(0.971463\pi\) | |||||||
\(332\) | −94.1346 | − | 54.3486i | −0.283538 | − | 0.163701i | ||||
\(333\) | −11.7743 | − | 20.3937i | −0.0353583 | − | 0.0612425i | ||||
\(334\) | −513.362 | − | 296.390i | −1.53701 | − | 0.887395i | ||||
\(335\) | − | 276.380i | − | 0.825016i | ||||||
\(336\) | −86.1780 | −0.256482 | ||||||||
\(337\) | −135.203 | + | 234.178i | −0.401196 | + | 0.694891i | −0.993870 | − | 0.110551i | \(-0.964739\pi\) |
0.592675 | + | 0.805442i | \(0.298072\pi\) | |||||||
\(338\) | −266.000 | −0.786982 | ||||||||
\(339\) | 87.8287 | + | 50.7079i | 0.259082 | + | 0.149581i | ||||
\(340\) | 806.178 | 2.37111 | ||||||||
\(341\) | 555.521 | 1.62909 | ||||||||
\(342\) | 90.7246 | − | 248.208i | 0.265277 | − | 0.725754i | ||||
\(343\) | 315.652i | 0.920267i | ||||||||
\(344\) | 363.089 | + | 209.630i | 1.05549 | + | 0.609388i | ||||
\(345\) | 133.657 | − | 231.501i | 0.387413 | − | 0.671018i | ||||
\(346\) | −455.453 | −1.31634 | ||||||||
\(347\) | −292.649 | − | 168.961i | −0.843368 | − | 0.486919i | 0.0150399 | − | 0.999887i | \(-0.495212\pi\) |
−0.858407 | + | 0.512968i | \(0.828546\pi\) | |||||||
\(348\) | 17.2277 | + | 9.94644i | 0.0495050 | + | 0.0285817i | ||||
\(349\) | −156.729 | −0.449080 | −0.224540 | − | 0.974465i | \(-0.572088\pi\) | ||||
−0.224540 | + | 0.974465i | \(0.572088\pi\) | |||||||
\(350\) | −201.612 | − | 116.401i | −0.576034 | − | 0.332573i | ||||
\(351\) | 118.568 | − | 68.4555i | 0.337801 | − | 0.195030i | ||||
\(352\) | −390.178 | − | 225.269i | −1.10846 | − | 0.639970i | ||||
\(353\) | 13.7723 | 0.0390149 | 0.0195074 | − | 0.999810i | \(-0.493790\pi\) | ||||
0.0195074 | + | 0.999810i | \(0.493790\pi\) | |||||||
\(354\) | −36.7267 | + | 63.6125i | −0.103748 | + | 0.179696i | ||||
\(355\) | 668.020 | − | 385.681i | 1.88175 | − | 1.08643i | ||||
\(356\) | 513.996 | 1.44381 | ||||||||
\(357\) | 72.5901 | + | 125.730i | 0.203334 | + | 0.352184i | ||||
\(358\) | 454.295 | − | 262.287i | 1.26898 | − | 0.732646i | ||||
\(359\) | −71.7148 | − | 41.4046i | −0.199763 | − | 0.115333i | 0.396782 | − | 0.917913i | \(-0.370127\pi\) |
−0.596545 | + | 0.802580i | \(0.703460\pi\) | |||||||
\(360\) | 416.000 | 1.15556 | ||||||||
\(361\) | 339.565 | − | 122.542i | 0.940624 | − | 0.339451i | ||||
\(362\) | −79.8851 | + | 138.365i | −0.220677 | + | 0.382224i | ||||
\(363\) | 95.6553 | + | 55.2266i | 0.263513 | + | 0.152139i | ||||
\(364\) | 90.3822i | 0.248303i | ||||||||
\(365\) | 33.3069 | + | 57.6893i | 0.0912519 | + | 0.158053i | ||||
\(366\) | 68.0673 | − | 39.2987i | 0.185976 | − | 0.107373i | ||||
\(367\) | 261.398 | − | 150.918i | 0.712256 | − | 0.411221i | −0.0996397 | − | 0.995024i | \(-0.531769\pi\) |
0.811896 | + | 0.583802i | \(0.198436\pi\) | |||||||
\(368\) | −346.360 | − | 199.971i | −0.941196 | − | 0.543400i | ||||
\(369\) | 61.9565 | 0.167904 | ||||||||
\(370\) | 50.6377 | 0.136859 | ||||||||
\(371\) | −273.659 | + | 157.997i | −0.737626 | + | 0.425869i | ||||
\(372\) | −112.863 | − | 195.485i | −0.303396 | − | 0.525497i | ||||
\(373\) | 301.909 | 0.809407 | 0.404704 | − | 0.914448i | \(-0.367375\pi\) | ||||
0.404704 | + | 0.914448i | \(0.367375\pi\) | |||||||
\(374\) | 759.002i | 2.02942i | ||||||||
\(375\) | −54.7246 | − | 31.5953i | −0.145932 | − | 0.0842541i | ||||
\(376\) | −153.362 | + | 88.5438i | −0.407879 | + | 0.235489i | ||||
\(377\) | 10.4317 | − | 18.0682i | 0.0276702 | − | 0.0479262i | ||||
\(378\) | 85.9327 | + | 148.840i | 0.227335 | + | 0.393756i | ||||
\(379\) | − | 498.042i | − | 1.31409i | −0.753850 | − | 0.657047i | \(-0.771805\pi\) | ||
0.753850 | − | 0.657047i | \(-0.228195\pi\) | |||||||
\(380\) | 364.681 | + | 435.818i | 0.959687 | + | 1.14689i | ||||
\(381\) | 33.3665 | 0.0875760 | ||||||||
\(382\) | −403.818 | + | 233.144i | −1.05711 | + | 0.610325i | ||||
\(383\) | 30.0771 | + | 17.3650i | 0.0785303 | + | 0.0453395i | 0.538751 | − | 0.842465i | \(-0.318896\pi\) |
−0.460221 | + | 0.887805i | \(0.652230\pi\) | |||||||
\(384\) | 183.069i | 0.476742i | ||||||||
\(385\) | 198.228 | − | 343.341i | 0.514877 | − | 0.891794i | ||||
\(386\) | −245.909 | −0.637070 | ||||||||
\(387\) | − | 364.465i | − | 0.941769i | ||||||
\(388\) | −212.091 | − | 367.353i | −0.546627 | − | 0.946785i | ||||
\(389\) | −189.046 | − | 327.436i | −0.485978 | − | 0.841739i | 0.513892 | − | 0.857855i | \(-0.328203\pi\) |
−0.999870 | + | 0.0161159i | \(0.994870\pi\) | |||||||
\(390\) | 128.330i | 0.329050i | ||||||||
\(391\) | 673.764i | 1.72318i | ||||||||
\(392\) | 278.542 | 0.710567 | ||||||||
\(393\) | 19.7712 | + | 34.2448i | 0.0503084 | + | 0.0871368i | ||||
\(394\) | 154.158 | + | 267.010i | 0.391265 | + | 0.677691i | ||||
\(395\) | −836.768 | + | 483.108i | −2.11840 | + | 1.22306i | ||||
\(396\) | 391.656i | 0.989031i | ||||||||
\(397\) | −80.5326 | + | 139.487i | −0.202853 | + | 0.351352i | −0.949447 | − | 0.313929i | \(-0.898355\pi\) |
0.746594 | + | 0.665280i | \(0.231688\pi\) | |||||||
\(398\) | −185.952 | − | 107.360i | −0.467217 | − | 0.269748i | ||||
\(399\) | −35.1325 | + | 96.1169i | −0.0880514 | + | 0.240894i | ||||
\(400\) | −247.271 | + | 428.286i | −0.618178 | + | 1.07072i | ||||
\(401\) | −220.045 | + | 381.128i | −0.548739 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572256i | \(0.981775\pi\) | |||||||
\(402\) | −52.8654 | − | 91.5656i | −0.131506 | − | 0.227775i | ||||
\(403\) | −205.022 | + | 118.369i | −0.508739 | + | 0.293720i | ||||
\(404\) | −535.540 | −1.32559 | ||||||||
\(405\) | −111.988 | − | 193.969i | −0.276514 | − | 0.478936i | ||||
\(406\) | 22.6812 | + | 13.0950i | 0.0558649 | + | 0.0322536i | ||||
\(407\) | 47.6744i | 0.117136i | ||||||||
\(408\) | 267.089 | − | 154.204i | 0.654630 | − | 0.377951i | ||||
\(409\) | 110.068 | + | 190.644i | 0.269116 | + | 0.466122i | 0.968634 | − | 0.248493i | \(-0.0799353\pi\) |
−0.699518 | + | 0.714615i | \(0.746602\pi\) | |||||||
\(410\) | −66.6139 | + | 115.379i | −0.162473 | + | 0.281411i | ||||
\(411\) | − | 284.355i | − | 0.691860i | ||||||
\(412\) | −358.455 | − | 206.954i | −0.870038 | − | 0.502316i | ||||
\(413\) | −48.3525 | + | 83.7490i | −0.117076 | + | 0.202782i | ||||
\(414\) | 347.672i | 0.839789i | ||||||||
\(415\) | −175.966 | − | 101.594i | −0.424015 | − | 0.244805i | ||||
\(416\) | 192.000 | 0.461538 | ||||||||
\(417\) | 384.362 | 0.921732 | ||||||||
\(418\) | −410.315 | + | 343.341i | −0.981614 | + | 0.821389i | ||||
\(419\) | − | 431.538i | − | 1.02992i | −0.857213 | − | 0.514961i | \(-0.827806\pi\) | ||
0.857213 | − | 0.514961i | \(-0.172194\pi\) | |||||||
\(420\) | −161.093 | −0.383555 | ||||||||
\(421\) | 27.0357 | − | 46.8272i | 0.0642179 | − | 0.111229i | −0.832129 | − | 0.554582i | \(-0.812878\pi\) |
0.896347 | + | 0.443354i | \(0.146211\pi\) | |||||||
\(422\) | − | 270.721i | − | 0.641519i | ||||||
\(423\) | 133.319 | + | 76.9717i | 0.315175 | + | 0.181966i | ||||
\(424\) | 335.636 | + | 581.338i | 0.791593 | + | 1.37108i | ||||
\(425\) | 833.132 | 1.96031 | ||||||||
\(426\) | 147.545 | − | 255.555i | 0.346349 | − | 0.599893i | ||||
\(427\) | 89.6139 | − | 51.7386i | 0.209869 | − | 0.121168i | ||||
\(428\) | −234.820 | − | 135.573i | −0.548645 | − | 0.316760i | ||||
\(429\) | −120.820 | −0.281631 | ||||||||
\(430\) | 678.725 | + | 391.862i | 1.57843 | + | 0.911307i | ||||
\(431\) | 708.564 | − | 409.090i | 1.64400 | − | 0.949164i | 0.664609 | − | 0.747191i | \(-0.268598\pi\) |
0.979391 | − | 0.201973i | \(-0.0647353\pi\) | |||||||
\(432\) | 316.182 | − | 182.548i | 0.731903 | − | 0.422565i | ||||
\(433\) | 186.863 | + | 323.657i | 0.431555 | + | 0.747475i | 0.997007 | − | 0.0773056i | \(-0.0246317\pi\) |
−0.565452 | + | 0.824781i | \(0.691298\pi\) | |||||||
\(434\) | −148.590 | − | 257.366i | −0.342373 | − | 0.593008i | ||||
\(435\) | 32.2039 | + | 18.5929i | 0.0740320 | + | 0.0427424i | ||||
\(436\) | 99.4534 | + | 172.258i | 0.228104 | + | 0.395088i | ||||
\(437\) | −364.236 | + | 304.783i | −0.833491 | + | 0.697443i | ||||
\(438\) | 22.0694 | + | 12.7418i | 0.0503867 | + | 0.0290908i | ||||
\(439\) | 234.784 | + | 135.553i | 0.534816 | + | 0.308776i | 0.742975 | − | 0.669319i | \(-0.233414\pi\) |
−0.208159 | + | 0.978095i | \(0.566747\pi\) | |||||||
\(440\) | −729.362 | − | 421.098i | −1.65764 | − | 0.957040i | ||||
\(441\) | −121.069 | − | 209.698i | −0.274534 | − | 0.475506i | ||||
\(442\) | −161.727 | − | 280.119i | −0.365898 | − | 0.633753i | ||||
\(443\) | −379.351 | + | 219.019i | −0.856324 | + | 0.494399i | −0.862780 | − | 0.505580i | \(-0.831278\pi\) |
0.00645570 | + | 0.999979i | \(0.497945\pi\) | |||||||
\(444\) | 16.7764 | − | 9.68586i | 0.0377847 | − | 0.0218150i | ||||
\(445\) | 960.816 | 2.15914 | ||||||||
\(446\) | − | 274.686i | − | 0.615888i | ||||||
\(447\) | −89.7148 | + | 51.7969i | −0.200704 | + | 0.115877i | ||||
\(448\) | 241.019i | 0.537989i | ||||||||
\(449\) | −710.180 | −1.58169 | −0.790846 | − | 0.612015i | \(-0.790359\pi\) | ||||
−0.790846 | + | 0.612015i | \(0.790359\pi\) | |||||||
\(450\) | 429.909 | 0.955353 | ||||||||
\(451\) | −108.627 | − | 62.7157i | −0.240858 | − | 0.139059i | ||||
\(452\) | 141.818 | − | 245.636i | 0.313756 | − | 0.543442i | ||||
\(453\) | −28.2158 | + | 48.8713i | −0.0622866 | + | 0.107884i | ||||
\(454\) | −161.067 | + | 92.9922i | −0.354774 | + | 0.204829i | ||||
\(455\) | 168.952i | 0.371323i | ||||||||
\(456\) | 204.182 | + | 74.6324i | 0.447768 | + | 0.163667i | ||||
\(457\) | 320.996 | 0.702398 | 0.351199 | − | 0.936301i | \(-0.385774\pi\) | ||||
0.351199 | + | 0.936301i | \(0.385774\pi\) | |||||||
\(458\) | 164.182 | + | 284.372i | 0.358476 | + | 0.620899i | ||||
\(459\) | −532.657 | − | 307.530i | −1.16047 | − | 0.670000i | ||||
\(460\) | −647.453 | − | 373.807i | −1.40751 | − | 0.812625i | ||||
\(461\) | −415.907 | + | 720.372i | −0.902184 | + | 1.56263i | −0.0775307 | + | 0.996990i | \(0.524704\pi\) |
−0.824653 | + | 0.565639i | \(0.808630\pi\) | |||||||
\(462\) | − | 151.666i | − | 0.328282i | ||||||
\(463\) | − | 231.176i | − | 0.499299i | −0.968336 | − | 0.249650i | \(-0.919685\pi\) | ||
0.968336 | − | 0.249650i | \(-0.0803155\pi\) | |||||||
\(464\) | 27.8178 | − | 48.1819i | 0.0599522 | − | 0.103840i | ||||
\(465\) | −210.976 | − | 365.421i | −0.453712 | − | 0.785853i | ||||
\(466\) | 109.089 | 0.234097 | ||||||||
\(467\) | 327.762i | 0.701846i | 0.936404 | + | 0.350923i | \(0.114132\pi\) | ||||
−0.936404 | + | 0.350923i | \(0.885868\pi\) | |||||||
\(468\) | −83.4534 | − | 144.546i | −0.178319 | − | 0.308858i | ||||
\(469\) | −69.5999 | − | 120.551i | −0.148401 | − | 0.257037i | ||||
\(470\) | −286.681 | + | 165.515i | −0.609960 | + | 0.352161i | ||||
\(471\) | 126.226 | − | 72.8764i | 0.267995 | − | 0.154727i | ||||
\(472\) | 177.909 | + | 102.716i | 0.376926 | + | 0.217618i | ||||
\(473\) | −368.931 | + | 639.007i | −0.779980 | + | 1.35097i | ||||
\(474\) | −184.816 | + | 320.110i | −0.389907 | + | 0.675338i | ||||
\(475\) | 376.874 | + | 450.390i | 0.793419 | + | 0.948189i | ||||
\(476\) | 351.636 | − | 203.017i | 0.738730 | − | 0.426506i | ||||
\(477\) | 291.770 | − | 505.361i | 0.611678 | − | 1.05946i | ||||
\(478\) | 494.542 | − | 285.524i | 1.03461 | − | 0.597331i | ||||
\(479\) | −67.8178 | + | 39.1546i | −0.141582 | + | 0.0817424i | −0.569118 | − | 0.822256i | \(-0.692715\pi\) |
0.427536 | + | 0.903998i | \(0.359382\pi\) | |||||||
\(480\) | 342.212i | 0.712942i | ||||||||
\(481\) | −10.1584 | − | 17.5948i | −0.0211193 | − | 0.0365797i | ||||
\(482\) | 175.772 | − | 304.446i | 0.364673 | − | 0.631632i | ||||
\(483\) | − | 134.634i | − | 0.278745i | ||||||
\(484\) | 154.455 | − | 267.525i | 0.319123 | − | 0.552737i | ||||
\(485\) | −396.463 | − | 686.694i | −0.817450 | − | 1.41586i | ||||
\(486\) | −429.909 | − | 248.208i | −0.884586 | − | 0.510716i | ||||
\(487\) | 13.2665i | 0.0272413i | 0.999907 | + | 0.0136206i | \(0.00433572\pi\) | ||||
−0.999907 | + | 0.0136206i | \(0.995664\pi\) | |||||||
\(488\) | −109.909 | − | 190.368i | −0.225223 | − | 0.390098i | ||||
\(489\) | −136.274 | + | 236.034i | −0.278680 | + | 0.482687i | ||||
\(490\) | 520.681 | 1.06261 | ||||||||
\(491\) | 139.069 | + | 80.2917i | 0.283237 | + | 0.163527i | 0.634888 | − | 0.772604i | \(-0.281046\pi\) |
−0.351651 | + | 0.936131i | \(0.614380\pi\) | |||||||
\(492\) | 50.9670i | 0.103591i | ||||||||
\(493\) | −93.7267 | −0.190115 | ||||||||
\(494\) | 78.2733 | − | 214.143i | 0.158448 | − | 0.433488i | ||||
\(495\) | 732.126i | 1.47904i | ||||||||
\(496\) | −546.725 | + | 315.652i | −1.10227 | + | 0.636394i | ||||
\(497\) | 194.249 | − | 336.450i | 0.390844 | − | 0.676962i | ||||
\(498\) | −77.7309 | −0.156086 | ||||||||
\(499\) | 522.621 | + | 301.735i | 1.04734 | + | 0.604680i | 0.921902 | − | 0.387422i | \(-0.126634\pi\) |
0.125434 | + | 0.992102i | \(0.459968\pi\) | |||||||
\(500\) | −88.3644 | + | 153.052i | −0.176729 | + | 0.306103i | ||||
\(501\) | −423.905 | −0.846117 | ||||||||
\(502\) | 280.247 | + | 161.801i | 0.558262 | + | 0.322313i | ||||
\(503\) | 220.170 | − | 127.115i | 0.437714 | − | 0.252714i | −0.264913 | − | 0.964272i | \(-0.585343\pi\) |
0.702628 | + | 0.711558i | \(0.252010\pi\) | |||||||
\(504\) | 181.449 | − | 104.760i | 0.360018 | − | 0.207857i | ||||
\(505\) | −1001.09 | −1.98235 | ||||||||
\(506\) | 351.933 | − | 609.565i | 0.695519 | − | 1.20467i | ||||
\(507\) | −164.736 | + | 95.1101i | −0.324922 | + | 0.187594i | ||||
\(508\) | − | 93.3180i | − | 0.183697i | ||||||
\(509\) | 49.0455 | + | 84.9494i | 0.0963567 | + | 0.166895i | 0.910174 | − | 0.414226i | \(-0.135948\pi\) |
−0.813817 | + | 0.581121i | \(0.802614\pi\) | |||||||
\(510\) | 499.271 | − | 288.254i | 0.978963 | − | 0.565205i | ||||
\(511\) | 29.0554 | + | 16.7751i | 0.0568598 | + | 0.0328280i | ||||
\(512\) | 512.000 | 1.00000 | ||||||||
\(513\) | −74.7019 | − | 427.067i | −0.145618 | − | 0.832489i | ||||
\(514\) | 309.725 | − | 536.459i | 0.602577 | − | 1.04369i | ||||
\(515\) | −670.063 | − | 386.861i | −1.30109 | − | 0.751187i | ||||
\(516\) | 299.818 | 0.581042 | ||||||||
\(517\) | −155.830 | − | 269.905i | −0.301411 | − | 0.522060i | ||||
\(518\) | 22.0869 | − | 12.7519i | 0.0426389 | − | 0.0246176i | ||||
\(519\) | −282.065 | + | 162.850i | −0.543478 | + | 0.313777i | ||||
\(520\) | 358.907 | 0.690205 | ||||||||
\(521\) | −491.317 | −0.943026 | −0.471513 | − | 0.881859i | \(-0.656292\pi\) | ||||
−0.471513 | + | 0.881859i | \(0.656292\pi\) | |||||||
\(522\) | −48.3644 | −0.0926521 | ||||||||
\(523\) | 399.564 | − | 230.688i | 0.763985 | − | 0.441087i | −0.0667397 | − | 0.997770i | \(-0.521260\pi\) |
0.830725 | + | 0.556683i | \(0.187926\pi\) | |||||||
\(524\) | 95.7743 | − | 55.2953i | 0.182775 | − | 0.105525i | ||||
\(525\) | −166.479 | −0.317103 | ||||||||
\(526\) | − | 395.456i | − | 0.751818i | ||||||
\(527\) | 921.041 | + | 531.763i | 1.74771 | + | 1.00904i | ||||
\(528\) | −322.186 | −0.610201 | ||||||||
\(529\) | 47.9099 | − | 82.9824i | 0.0905670 | − | 0.156867i | ||||
\(530\) | 627.406 | + | 1086.70i | 1.18378 | + | 2.05037i | ||||
\(531\) | − | 178.583i | − | 0.336314i | ||||||
\(532\) | 268.816 | + | 98.2571i | 0.505293 | + | 0.184694i | ||||
\(533\) | 53.4534 | 0.100288 | ||||||||
\(534\) | 318.321 | − | 183.783i | 0.596107 | − | 0.344162i | ||||
\(535\) | −438.950 | − | 253.428i | −0.820468 | − | 0.473697i | ||||
\(536\) | −256.087 | + | 147.852i | −0.477774 | + | 0.275843i | ||||
\(537\) | 187.565 | − | 324.872i | 0.349283 | − | 0.604977i | ||||
\(538\) | −310.542 | −0.577216 | ||||||||
\(539\) | 490.212i | 0.909484i | ||||||||
\(540\) | 591.041 | − | 341.238i | 1.09452 | − | 0.631922i | ||||
\(541\) | −38.1822 | − | 66.1335i | −0.0705771 | − | 0.122243i | 0.828577 | − | 0.559875i | \(-0.189151\pi\) |
−0.899154 | + | 0.437632i | \(0.855817\pi\) | |||||||
\(542\) | 120.112i | 0.221608i | ||||||||
\(543\) | 114.254i | 0.210412i | ||||||||
\(544\) | −431.271 | − | 746.984i | −0.792778 | − | 1.37313i | ||||
\(545\) | 185.909 | + | 322.004i | 0.341117 | + | 0.590832i | ||||
\(546\) | 32.3168 | + | 55.9743i | 0.0591882 | + | 0.102517i | ||||
\(547\) | 181.521 | − | 104.801i | 0.331848 | − | 0.191592i | −0.324813 | − | 0.945778i | \(-0.605302\pi\) |
0.656661 | + | 0.754186i | \(0.271968\pi\) | |||||||
\(548\) | −795.271 | −1.45122 | ||||||||
\(549\) | −95.5445 | + | 165.488i | −0.174034 | + | 0.301435i | ||||
\(550\) | −753.748 | − | 435.177i | −1.37045 | − | 0.791231i | ||||
\(551\) | −42.3980 | − | 50.6685i | −0.0769474 | − | 0.0919573i | ||||
\(552\) | −286.004 | −0.518123 | ||||||||
\(553\) | −243.319 | + | 421.441i | −0.439998 | + | 0.762099i | ||||
\(554\) | −399.430 | − | 691.832i | −0.720992 | − | 1.24879i | ||||
\(555\) | 31.3602 | − | 18.1058i | 0.0565049 | − | 0.0326231i | ||||
\(556\) | − | 1074.97i | − | 1.93340i | ||||||
\(557\) | 91.1801 | + | 157.929i | 0.163699 | + | 0.283534i | 0.936192 | − | 0.351488i | \(-0.114324\pi\) |
−0.772494 | + | 0.635022i | \(0.780991\pi\) | |||||||
\(558\) | 475.271 | + | 274.398i | 0.851741 | + | 0.491753i | ||||
\(559\) | − | 314.444i | − | 0.562512i | ||||||
\(560\) | 450.539i | 0.804534i | ||||||||
\(561\) | 271.386 | + | 470.055i | 0.483754 | + | 0.837887i | ||||
\(562\) | −457.998 | + | 793.276i | −0.814943 | + | 1.41152i | ||||
\(563\) | − | 483.962i | − | 0.859613i | −0.902921 | − | 0.429807i | \(-0.858582\pi\) | ||
0.902921 | − | 0.429807i | \(-0.141418\pi\) | |||||||
\(564\) | −63.3188 | + | 109.671i | −0.112267 | + | 0.194453i | ||||
\(565\) | 265.101 | − | 459.168i | 0.469205 | − | 0.812687i | ||||
\(566\) | 836.549i | 1.47800i | ||||||||
\(567\) | −97.6931 | − | 56.4031i | −0.172298 | − | 0.0994764i | ||||
\(568\) | −714.725 | − | 412.646i | −1.25832 | − | 0.726490i | ||||
\(569\) | 64.9586 | 0.114163 | 0.0570814 | − | 0.998370i | \(-0.481821\pi\) | ||||
0.0570814 | + | 0.998370i | \(0.481821\pi\) | |||||||
\(570\) | 381.679 | + | 139.511i | 0.669612 | + | 0.244756i | ||||
\(571\) | − | 553.718i | − | 0.969733i | −0.874588 | − | 0.484867i | \(-0.838868\pi\) | ||
0.874588 | − | 0.484867i | \(-0.161132\pi\) | |||||||
\(572\) | 337.904i | 0.590741i | ||||||||
\(573\) | −166.725 | + | 288.776i | −0.290968 | + | 0.503971i | ||||
\(574\) | 67.1005i | 0.116900i | ||||||||
\(575\) | −669.101 | − | 386.306i | −1.16365 | − | 0.671836i | ||||
\(576\) | −222.542 | − | 385.455i | −0.386358 | − | 0.669192i | ||||
\(577\) | −21.9979 | −0.0381247 | −0.0190623 | − | 0.999818i | \(-0.506068\pi\) | ||||
−0.0190623 | + | 0.999818i | \(0.506068\pi\) | |||||||
\(578\) | −437.542 | + | 757.846i | −0.756994 | + | 1.31115i | ||||
\(579\) | −152.293 | + | 87.9264i | −0.263028 | + | 0.151859i | ||||
\(580\) | 52.0000 | − | 90.0666i | 0.0896552 | − | 0.155287i | ||||
\(581\) | −102.336 | −0.176138 | ||||||||
\(582\) | −262.699 | − | 151.669i | −0.451372 | − | 0.260600i | ||||
\(583\) | −1023.11 | + | 590.691i | −1.75490 | + | 1.01319i | ||||
\(584\) | 35.6356 | − | 61.7227i | 0.0610199 | − | 0.105690i | ||||
\(585\) | −156.000 | − | 270.200i | −0.266667 | − | 0.461880i | ||||
\(586\) | 123.794 | + | 214.417i | 0.211253 | + | 0.365900i | ||||
\(587\) | 838.432 | + | 484.069i | 1.42833 | + | 0.824649i | 0.996989 | − | 0.0775389i | \(-0.0247062\pi\) |
0.431344 | + | 0.902188i | \(0.358040\pi\) | |||||||
\(588\) | 172.503 | − | 99.5947i | 0.293373 | − | 0.169379i | ||||
\(589\) | 129.170 | + | 738.461i | 0.219304 | + | 1.25375i | ||||
\(590\) | 332.566 | + | 192.007i | 0.563672 | + | 0.325436i | ||||
\(591\) | 190.943 | + | 110.241i | 0.323084 | + | 0.186533i | ||||
\(592\) | −27.0890 | − | 46.9196i | −0.0457585 | − | 0.0792560i | ||||
\(593\) | 64.8188 | + | 112.270i | 0.109307 | + | 0.189325i | 0.915490 | − | 0.402342i | \(-0.131804\pi\) |
−0.806183 | + | 0.591666i | \(0.798470\pi\) | |||||||
\(594\) | 321.269 | + | 556.454i | 0.540857 | + | 0.936792i | ||||
\(595\) | 657.315 | − | 379.501i | 1.10473 | − | 0.637816i | ||||
\(596\) | 144.863 | + | 250.911i | 0.243059 | + | 0.420991i | ||||
\(597\) | −153.549 | −0.257200 | ||||||||
\(598\) | 299.957i | 0.501600i | ||||||||
\(599\) | −636.142 | + | 367.277i | −1.06201 | + | 0.613150i | −0.925987 | − | 0.377556i | \(-0.876765\pi\) |
−0.136020 | + | 0.990706i | \(0.543431\pi\) | |||||||
\(600\) | 353.654i | 0.589423i | ||||||||
\(601\) | 964.041 | 1.60406 | 0.802031 | − | 0.597282i | \(-0.203753\pi\) | ||||
0.802031 | + | 0.597282i | \(0.203753\pi\) | |||||||
\(602\) | 394.725 | 0.655689 | ||||||||
\(603\) | 222.618 | + | 128.529i | 0.369184 | + | 0.213149i | ||||
\(604\) | 136.681 | + | 78.9129i | 0.226293 | + | 0.130651i | ||||
\(605\) | 288.725 | − | 500.086i | 0.477231 | − | 0.826588i | ||||
\(606\) | −331.664 | + | 191.486i | −0.547300 | + | 0.315984i | ||||
\(607\) | − | 526.372i | − | 0.867170i | −0.901113 | − | 0.433585i | \(-0.857248\pi\) | ||
0.901113 | − | 0.433585i | \(-0.142752\pi\) | |||||||
\(608\) | 208.729 | − | 571.048i | 0.343304 | − | 0.939224i | ||||
\(609\) | 18.7288 | 0.0307533 | ||||||||
\(610\) | −205.453 | − | 355.856i | −0.336809 | − | 0.583370i | ||||
\(611\) | 115.022 | + | 66.4078i | 0.188252 | + | 0.108687i | ||||
\(612\) | −374.907 | + | 649.358i | −0.612593 | + | 1.06104i | ||||
\(613\) | 38.9565 | − | 67.4747i | 0.0635506 | − | 0.110073i | −0.832500 | − | 0.554026i | \(-0.813091\pi\) |
0.896050 | + | 0.443953i | \(0.146424\pi\) | |||||||
\(614\) | − | 338.981i | − | 0.552086i | ||||||
\(615\) | 95.2729i | 0.154915i | ||||||||
\(616\) | −424.174 | −0.688594 | ||||||||
\(617\) | 98.9317 | + | 171.355i | 0.160343 | + | 0.277722i | 0.934992 | − | 0.354669i | \(-0.115407\pi\) |
−0.774649 | + | 0.632392i | \(0.782073\pi\) | |||||||
\(618\) | −295.992 | −0.478951 | ||||||||
\(619\) | − | 86.1017i | − | 0.139098i | −0.997579 | − | 0.0695490i | \(-0.977844\pi\) | ||
0.997579 | − | 0.0695490i | \(-0.0221560\pi\) | |||||||
\(620\) | −1022.00 | + | 590.050i | −1.64838 | + | 0.951693i | ||||
\(621\) | 285.190 | + | 493.963i | 0.459243 | + | 0.795432i | ||||
\(622\) | 705.790 | − | 407.488i | 1.13471 | − | 0.655125i | ||||
\(623\) | 419.085 | − | 241.959i | 0.672688 | − | 0.388377i | ||||
\(624\) | 118.907 | − | 68.6509i | 0.190556 | − | 0.110017i | ||||
\(625\) | 221.181 | − | 383.097i | 0.353890 | − | 0.612955i | ||||
\(626\) | 572.723 | − | 991.985i | 0.914892 | − | 1.58464i | ||||
\(627\) | −131.347 | + | 359.344i | −0.209485 | + | 0.573116i | ||||
\(628\) | −203.818 | − | 353.023i | −0.324551 | − | 0.562138i | ||||
\(629\) | −45.6356 | + | 79.0432i | −0.0725526 | + | 0.125665i | ||||
\(630\) | 339.184 | − | 195.828i | 0.538388 | − | 0.310838i | ||||
\(631\) | −367.717 | + | 212.301i | −0.582753 | + | 0.336452i | −0.762227 | − | 0.647310i | \(-0.775894\pi\) |
0.179474 | + | 0.983763i | \(0.442560\pi\) | |||||||
\(632\) | 895.271 | + | 516.885i | 1.41657 | + | 0.817856i | ||||
\(633\) | −96.7981 | − | 167.659i | −0.152920 | − | 0.264865i | ||||
\(634\) | −528.907 | + | 916.093i | −0.834238 | + | 1.44494i | ||||
\(635\) | − | 174.440i | − | 0.274708i | ||||||
\(636\) | 415.723 | + | 240.018i | 0.653652 | + | 0.377386i | ||||
\(637\) | −104.453 | − | 180.919i | −0.163977 | − | 0.284017i | ||||
\(638\) | 84.7961 | + | 48.9570i | 0.132909 | + | 0.0767352i | ||||
\(639\) | 717.432i | 1.12274i | ||||||||
\(640\) | 957.085 | 1.49545 | ||||||||
\(641\) | 131.637 | − | 228.001i | 0.205361 | − | 0.355696i | −0.744886 | − | 0.667191i | \(-0.767496\pi\) |
0.950248 | + | 0.311495i | \(0.100830\pi\) | |||||||
\(642\) | −193.901 | −0.302026 | ||||||||
\(643\) | −71.3256 | − | 41.1798i | −0.110926 | − | 0.0640433i | 0.443510 | − | 0.896269i | \(-0.353733\pi\) |
−0.554437 | + | 0.832226i | \(0.687066\pi\) | |||||||
\(644\) | −376.538 | −0.584687 | ||||||||
\(645\) | 560.451 | 0.868917 | ||||||||
\(646\) | −1008.95 | + | 176.484i | −1.56184 | + | 0.273195i | ||||
\(647\) | − | 149.354i | − | 0.230841i | −0.993317 | − | 0.115421i | \(-0.963178\pi\) | ||
0.993317 | − | 0.115421i | \(-0.0368216\pi\) | |||||||
\(648\) | −119.818 | + | 207.531i | −0.184904 | + | 0.320263i | ||||
\(649\) | −180.771 | + | 313.105i | −0.278538 | + | 0.482442i | ||||
\(650\) | 370.907 | 0.570626 | ||||||||
\(651\) | −184.046 | − | 106.259i | −0.282712 | − | 0.163224i | ||||
\(652\) | 660.130 | + | 381.126i | 1.01247 | + | 0.584550i | ||||
\(653\) | 335.540 | 0.513844 | 0.256922 | − | 0.966432i | \(-0.417292\pi\) | ||||
0.256922 | + | 0.966432i | \(0.417292\pi\) | |||||||
\(654\) | 123.184 | + | 71.1205i | 0.188355 | + | 0.108747i | ||||
\(655\) | 179.032 | − | 103.364i | 0.273331 | − | 0.157808i | ||||
\(656\) | 142.542 | 0.217290 | ||||||||
\(657\) | −61.9565 | −0.0943022 | ||||||||
\(658\) | −83.3623 | + | 144.388i | −0.126690 | + | 0.219434i | ||||
\(659\) | −741.636 | + | 428.184i | −1.12540 | + | 0.649747i | −0.942773 | − | 0.333436i | \(-0.891792\pi\) |
−0.182623 | + | 0.983183i | \(0.558459\pi\) | |||||||
\(660\) | −602.265 | −0.912523 | ||||||||
\(661\) | 115.830 | + | 200.623i | 0.175234 | + | 0.303514i | 0.940242 | − | 0.340506i | \(-0.110598\pi\) |
−0.765008 | + | 0.644021i | \(0.777265\pi\) | |||||||
\(662\) | 102.659 | − | 59.2704i | 0.155075 | − | 0.0895324i | ||||
\(663\) | −200.317 | − | 115.653i | −0.302137 | − | 0.174439i | ||||
\(664\) | 217.394i | 0.327401i | ||||||||
\(665\) | 502.499 | + | 183.673i | 0.755638 | + | 0.276200i | ||||
\(666\) | −23.5487 | + | 40.7875i | −0.0353583 | + | 0.0612425i | ||||
\(667\) | 75.2733 | + | 43.4591i | 0.112854 | + | 0.0651560i | ||||
\(668\) | 1185.56i | 1.77479i | ||||||||
\(669\) | −98.2158 | − | 170.115i | −0.146810 | − | 0.254282i | ||||
\(670\) | −478.705 | + | 276.380i | −0.714485 | + | 0.412508i | ||||
\(671\) | 335.032 | − | 193.431i | 0.499302 | − | 0.288272i | ||||
\(672\) | 86.1780 | + | 149.265i | 0.128241 | + | 0.222120i | ||||
\(673\) | 241.727 | 0.359178 | 0.179589 | − | 0.983742i | \(-0.442523\pi\) | ||||
0.179589 | + | 0.983742i | \(0.442523\pi\) | |||||||
\(674\) | 540.812 | 0.802391 | ||||||||
\(675\) | 610.803 | − | 352.647i | 0.904893 | − | 0.522440i | ||||
\(676\) | 266.000 | + | 460.726i | 0.393491 | + | 0.681547i | ||||
\(677\) | 842.356 | 1.24425 | 0.622124 | − | 0.782919i | \(-0.286270\pi\) | ||||
0.622124 | + | 0.782919i | \(0.286270\pi\) | |||||||
\(678\) | − | 202.832i | − | 0.299162i | ||||||
\(679\) | −345.856 | − | 199.680i | −0.509360 | − | 0.294079i | ||||
\(680\) | −806.178 | − | 1396.34i | −1.18556 | − | 2.05344i | ||||
\(681\) | −66.5000 | + | 115.181i | −0.0976505 | + | 0.169136i | ||||
\(682\) | −555.521 | − | 962.190i | −0.814546 | − | 1.41084i | ||||
\(683\) | 469.540i | 0.687467i | 0.939067 | + | 0.343734i | \(0.111692\pi\) | ||||
−0.939067 | + | 0.343734i | \(0.888308\pi\) | |||||||
\(684\) | −520.634 | + | 91.0683i | −0.761160 | + | 0.133141i | ||||
\(685\) | −1486.61 | −2.17023 | ||||||||
\(686\) | 546.725 | − | 315.652i | 0.796975 | − | 0.460134i | ||||
\(687\) | 203.358 | + | 117.409i | 0.296009 | + | 0.170901i | ||||
\(688\) | − | 838.518i | − | 1.21878i | ||||||
\(689\) | 251.727 | − | 436.003i | 0.365351 | − | 0.632806i | ||||
\(690\) | −534.629 | −0.774825 | ||||||||
\(691\) | − | 627.366i | − | 0.907910i | −0.891025 | − | 0.453955i | \(-0.850013\pi\) | ||
0.891025 | − | 0.453955i | \(-0.149987\pi\) | |||||||
\(692\) | 455.453 | + | 788.868i | 0.658170 | + | 1.13998i | ||||
\(693\) | 184.369 | + | 319.336i | 0.266044 | + | 0.460802i | ||||
\(694\) | 675.843i | 0.973837i | ||||||||
\(695\) | − | 2009.45i | − | 2.89129i | ||||||
\(696\) | − | 39.7858i | − | 0.0571635i | ||||||
\(697\) | −120.067 | − | 207.963i | −0.172263 | − | 0.298368i | ||||
\(698\) | 156.729 | + | 271.462i | 0.224540 | + | 0.388914i | ||||
\(699\) | 67.5595 | − | 39.0055i | 0.0966517 | − | 0.0558019i | ||||
\(700\) | 465.603i | 0.665146i | ||||||||
\(701\) | 440.075 | − | 762.232i | 0.627782 | − | 1.08735i | −0.360214 | − | 0.932870i | \(-0.617296\pi\) |
0.987996 | − | 0.154480i | \(-0.0493703\pi\) | |||||||
\(702\) | −237.137 | − | 136.911i | −0.337801 | − | 0.195030i | ||||
\(703\) | −63.3742 | + | 11.0853i | −0.0901483 | + | 0.0157686i | ||||
\(704\) | 901.078i | 1.27994i | ||||||||
\(705\) | −118.362 | + | 205.010i | −0.167890 | + | 0.290794i | ||||
\(706\) | −13.7723 | − | 23.8542i | −0.0195074 | − | 0.0337879i | ||||
\(707\) | −436.651 | + | 252.101i | −0.617611 | + | 0.356578i | ||||
\(708\) | 146.907 | 0.207496 | ||||||||
\(709\) | 533.689 | + | 924.376i | 0.752735 | + | 1.30377i | 0.946493 | + | 0.322725i | \(0.104599\pi\) |
−0.193758 | + | 0.981049i | \(0.562068\pi\) | |||||||
\(710\) | −1336.04 | − | 771.363i | −1.88175 | − | 1.08643i | ||||
\(711\) | − | 898.663i | − | 1.26394i | ||||||
\(712\) | −513.996 | − | 890.267i | −0.721904 | − | 1.25037i | ||||
\(713\) | −493.135 | − | 854.134i | −0.691633 | − | 1.19794i | ||||
\(714\) | 145.180 | − | 251.459i | 0.203334 | − | 0.352184i | ||||
\(715\) | 631.646i | 0.883421i | ||||||||
\(716\) | −908.590 | − | 524.575i | −1.26898 | − | 0.732646i | ||||
\(717\) | 204.182 | − | 353.654i | 0.284773 | − | 0.493241i | ||||
\(718\) | 165.618i | 0.230666i | ||||||||
\(719\) | 517.610 | + | 298.842i | 0.719902 | + | 0.415636i | 0.814717 | − | 0.579859i | \(-0.196892\pi\) |
−0.0948144 | + | 0.995495i | \(0.530226\pi\) | |||||||
\(720\) | −416.000 | − | 720.533i | −0.577778 | − | 1.00074i | ||||
\(721\) | −389.687 | −0.540482 | ||||||||
\(722\) | −551.814 | − | 465.603i | −0.764285 | − | 0.644879i | ||||
\(723\) | − | 251.394i | − | 0.347710i | ||||||
\(724\) | 319.540 | 0.441354 | ||||||||
\(725\) | 53.7386 | − | 93.0780i | 0.0741222 | − | 0.128383i | ||||
\(726\) | − | 220.906i | − | 0.304279i | ||||||
\(727\) | 209.050 | + | 120.695i | 0.287551 | + | 0.166018i | 0.636837 | − | 0.770998i | \(-0.280242\pi\) |
−0.349286 | + | 0.937016i | \(0.613576\pi\) | |||||||
\(728\) | 156.547 | − | 90.3822i | 0.215037 | − | 0.124151i | ||||
\(729\) | −85.4037 | −0.117152 | ||||||||
\(730\) | 66.6139 | − | 115.379i | 0.0912519 | − | 0.158053i | ||||
\(731\) | −1223.36 | + | 706.306i | −1.67354 | + | 0.966219i | ||||
\(732\) | −136.135 | − | 78.5973i | −0.185976 | − | 0.107373i | ||||
\(733\) | 201.525 | 0.274932 | 0.137466 | − | 0.990507i | \(-0.456104\pi\) | ||||
0.137466 | + | 0.990507i | \(0.456104\pi\) | |||||||
\(734\) | −522.796 | − | 301.836i | −0.712256 | − | 0.411221i | ||||
\(735\) | 322.461 | − | 186.173i | 0.438723 | − | 0.253297i | ||||
\(736\) | 799.885i | 1.08680i | ||||||||
\(737\) | −260.207 | − | 450.692i | −0.353062 | − | 0.611522i | ||||
\(738\) | −61.9565 | − | 107.312i | −0.0839519 | − | 0.145409i | ||||
\(739\) | 258.757 | + | 149.394i | 0.350145 | + | 0.202156i | 0.664749 | − | 0.747067i | \(-0.268538\pi\) |
−0.314604 | + | 0.949223i | \(0.601872\pi\) | |||||||
\(740\) | −50.6377 | − | 87.7070i | −0.0684293 | − | 0.118523i | ||||
\(741\) | −28.0932 | − | 160.607i | −0.0379125 | − | 0.216744i | ||||
\(742\) | 547.319 | + | 315.995i | 0.737626 | + | 0.425869i | ||||
\(743\) | 510.962 | + | 295.004i | 0.687701 | + | 0.397045i | 0.802750 | − | 0.596315i | \(-0.203369\pi\) |
−0.115049 | + | 0.993360i | \(0.536702\pi\) | |||||||
\(744\) | −225.727 | + | 390.970i | −0.303396 | + | 0.525497i | ||||
\(745\) | 270.794 | + | 469.029i | 0.363482 | + | 0.629569i | ||||
\(746\) | −301.909 | − | 522.922i | −0.404704 | − | 0.700967i | ||||
\(747\) | 163.664 | − | 94.4912i | 0.219094 | − | 0.126494i | ||||
\(748\) | 1314.63 | − | 759.002i | 1.75753 | − | 1.01471i | ||||
\(749\) | −255.280 | −0.340827 | ||||||||
\(750\) | 126.381i | 0.168508i | ||||||||
\(751\) | 360.208 | − | 207.966i | 0.479638 | − | 0.276919i | −0.240628 | − | 0.970617i | \(-0.577353\pi\) |
0.720266 | + | 0.693698i | \(0.244020\pi\) | |||||||
\(752\) | 306.725 | + | 177.088i | 0.407879 | + | 0.235489i | ||||
\(753\) | 231.412 | 0.307320 | ||||||||
\(754\) | −41.7267 | −0.0553405 | ||||||||
\(755\) | 255.499 | + | 147.512i | 0.338409 | + | 0.195381i | ||||
\(756\) | 171.865 | − | 297.680i | 0.227335 | − | 0.393756i | ||||
\(757\) | −94.9565 | + | 164.470i | −0.125438 | + | 0.217265i | −0.921904 | − | 0.387418i | \(-0.873367\pi\) |
0.796466 | + | 0.604683i | \(0.206700\pi\) | |||||||
\(758\) | −862.634 | + | 498.042i | −1.13804 | + | 0.657047i | ||||
\(759\) | − | 503.344i | − | 0.663167i | ||||||
\(760\) | 390.178 | − | 1067.46i | 0.513392 | − | 1.40456i | ||||
\(761\) | −418.493 | −0.549925 | −0.274962 | − | 0.961455i | \(-0.588665\pi\) | ||||
−0.274962 | + | 0.961455i | \(0.588665\pi\) | |||||||
\(762\) | −33.3665 | − | 57.7924i | −0.0437880 | − | 0.0758431i | ||||
\(763\) | 162.178 | + | 93.6335i | 0.212553 | + | 0.122718i | ||||
\(764\) | 807.636 | + | 466.289i | 1.05711 | + | 0.610325i | ||||
\(765\) | −700.816 | + | 1213.85i | −0.916099 | + | 1.58673i | ||||
\(766\) | − | 69.4601i | − | 0.0906790i | ||||||
\(767\) | − | 154.074i | − | 0.200878i | ||||||
\(768\) | 317.085 | − | 183.069i | 0.412871 | − | 0.238371i | ||||
\(769\) | −26.8157 | − | 46.4462i | −0.0348709 | − | 0.0603982i | 0.848063 | − | 0.529895i | \(-0.177769\pi\) |
−0.882934 | + | 0.469497i | \(0.844435\pi\) | |||||||
\(770\) | −792.911 | −1.02975 | ||||||||
\(771\) | − | 442.976i | − | 0.574548i | ||||||
\(772\) | 245.909 | + | 425.927i | 0.318535 | + | 0.551719i | ||||
\(773\) | −271.667 | − | 470.541i | −0.351445 | − | 0.608721i | 0.635058 | − | 0.772465i | \(-0.280976\pi\) |
−0.986503 | + | 0.163744i | \(0.947643\pi\) | |||||||
\(774\) | −631.271 | + | 364.465i | −0.815596 | + | 0.470885i | ||||
\(775\) | −1056.17 | + | 609.778i | −1.36280 | + | 0.786810i | ||||
\(776\) | −424.182 | + | 734.705i | −0.546627 | + | 0.946785i | ||||
\(777\) | 9.11906 | − | 15.7947i | 0.0117362 | − | 0.0203278i | ||||
\(778\) | −378.091 | + | 654.873i | −0.485978 | + | 0.841739i | ||||
\(779\) | 58.1108 | − | 158.982i | 0.0745966 | − | 0.204084i | ||||
\(780\) | 222.273 | − | 128.330i | 0.284966 | − | 0.164525i | ||||
\(781\) | 726.224 | − | 1257.86i | 0.929864 | − | 1.61057i | ||||
\(782\) | 1166.99 | − | 673.764i | 1.49232 | − | 0.861591i | ||||
\(783\) | −68.7148 | + | 39.6725i | −0.0877584 | + | 0.0506673i | ||||
\(784\) | −278.542 | − | 482.450i | −0.355284 | − | 0.615369i | ||||
\(785\) | −380.998 | − | 659.908i | −0.485348 | − | 0.840647i | ||||
\(786\) | 39.5424 | − | 68.4895i | 0.0503084 | − | 0.0871368i | ||||
\(787\) | 976.098i | 1.24028i | 0.784492 | + | 0.620138i | \(0.212924\pi\) | ||||
−0.784492 | + | 0.620138i | \(0.787076\pi\) | |||||||
\(788\) | 308.317 | − | 534.020i | 0.391265 | − | 0.677691i | ||||
\(789\) | −141.398 | − | 244.909i | −0.179212 | − | 0.310404i | ||||
\(790\) | 1673.54 | + | 966.217i | 2.11840 | + | 1.22306i | ||||
\(791\) | − | 267.038i | − | 0.337595i | ||||||
\(792\) | 678.369 | − | 391.656i | 0.856526 | − | 0.494515i | ||||
\(793\) | −82.4317 | + | 142.776i | −0.103949 | + | 0.180045i | ||||
\(794\) | 322.130 | 0.405706 | ||||||||
\(795\) | 777.113 | + | 448.666i | 0.977500 | + | 0.564360i | ||||
\(796\) | 429.439i | 0.539496i | ||||||||
\(797\) | −596.606 | −0.748564 | −0.374282 | − | 0.927315i | \(-0.622111\pi\) | ||||
−0.374282 | + | 0.927315i | \(0.622111\pi\) | |||||||
\(798\) | 201.612 | − | 35.2656i | 0.252646 | − | 0.0441925i | ||||
\(799\) | − | 596.662i | − | 0.746761i | ||||||
\(800\) | 989.085 | 1.23636 | ||||||||
\(801\) | −446.820 | + | 773.915i | −0.557828 | + | 0.966186i | ||||
\(802\) | 880.178 | 1.09748 | ||||||||
\(803\) | 108.627 | + | 62.7157i | 0.135276 | + | 0.0781018i | ||||
\(804\) | −105.731 | + | 183.131i | −0.131506 | + | 0.227775i | ||||
\(805\) | −703.865 | −0.874367 | ||||||||
\(806\) | 410.043 | + | 236.739i | 0.508739 | + | 0.293720i | ||||
\(807\) | −192.321 | + | 111.037i | −0.238316 | + | 0.137592i | ||||
\(808\) | 535.540 | + | 927.583i | 0.662797 | + | 1.14800i | ||||
\(809\) | 718.128 | 0.887674 | 0.443837 | − | 0.896108i | \(-0.353617\pi\) | ||||
0.443837 | + | 0.896108i | \(0.353617\pi\) | |||||||
\(810\) | −223.976 | + | 387.938i | −0.276514 | + | 0.478936i | ||||
\(811\) | −548.471 | + | 316.660i | −0.676290 | + | 0.390456i | −0.798456 | − | 0.602054i | \(-0.794349\pi\) |
0.122166 | + | 0.992510i | \(0.461016\pi\) | |||||||
\(812\) | − | 52.3799i | − | 0.0645073i | ||||||
\(813\) | 42.9467 | + | 74.3859i | 0.0528250 | + | 0.0914955i | ||||
\(814\) | 82.5745 | − | 47.6744i | 0.101443 | − | 0.0585681i | ||||
\(815\) | 1233.99 | + | 712.442i | 1.51409 | + | 0.874162i | ||||
\(816\) | −534.178 | − | 308.408i | −0.654630 | − | 0.377951i | ||||
\(817\) | −935.224 | − | 341.842i | −1.14470 | − | 0.418411i | ||||
\(818\) | 220.137 | − | 381.288i | 0.269116 | − | 0.466122i | ||||
\(819\) | −136.087 | − | 78.5698i | −0.166162 | − | 0.0959339i | ||||
\(820\) | 266.455 | 0.324946 | ||||||||
\(821\) | 390.770 | + | 676.834i | 0.475969 | + | 0.824402i | 0.999621 | − | 0.0275303i | \(-0.00876427\pi\) |
−0.523652 | + | 0.851932i | \(0.675431\pi\) | |||||||
\(822\) | −492.517 | + | 284.355i | −0.599169 | + | 0.345930i | ||||
\(823\) | 117.748 | − | 67.9821i | 0.143072 | − | 0.0826028i | −0.426755 | − | 0.904367i | \(-0.640343\pi\) |
0.569827 | + | 0.821764i | \(0.307010\pi\) | |||||||
\(824\) | 827.817i | 1.00463i | ||||||||
\(825\) | −622.402 | −0.754426 | ||||||||
\(826\) | 193.410 | 0.234152 | ||||||||
\(827\) | −447.466 | + | 258.345i | −0.541072 | + | 0.312388i | −0.745513 | − | 0.666491i | \(-0.767796\pi\) |
0.204441 | + | 0.978879i | \(0.434462\pi\) | |||||||
\(828\) | 602.186 | − | 347.672i | 0.727278 | − | 0.419894i | ||||
\(829\) | −1147.72 | −1.38447 | −0.692233 | − | 0.721674i | \(-0.743373\pi\) | ||||
−0.692233 | + | 0.721674i | \(0.743373\pi\) | |||||||
\(830\) | 406.377i | 0.489611i | ||||||||
\(831\) | −494.739 | − | 285.637i | −0.595353 | − | 0.343727i | ||||
\(832\) | −192.000 | − | 332.554i | −0.230769 | − | 0.399704i | ||||
\(833\) | −469.247 | + | 812.760i | −0.563322 | + | 0.975703i | ||||
\(834\) | −384.362 | − | 665.735i | −0.460866 | − | 0.798243i | ||||
\(835\) | 2216.17i | 2.65410i | ||||||||
\(836\) | 1005.00 | + | 367.345i | 1.20215 | + | 0.439408i | ||||
\(837\) | 900.336 | 1.07567 | ||||||||
\(838\) | −747.445 | + | 431.538i | −0.891939 | + | 0.514961i | ||||
\(839\) | 166.461 | + | 96.1064i | 0.198404 | + | 0.114549i | 0.595911 | − | 0.803051i | \(-0.296791\pi\) |
−0.397507 | + | 0.917599i | \(0.630124\pi\) | |||||||
\(840\) | 161.093 | + | 279.022i | 0.191778 | + | 0.332169i | ||||
\(841\) | 414.454 | − | 717.856i | 0.492811 | − | 0.853575i | ||||
\(842\) | −108.143 | −0.128436 | ||||||||
\(843\) | 655.041i | 0.777036i | ||||||||
\(844\) | −468.903 | + | 270.721i | −0.555572 | + | 0.320760i | ||||
\(845\) | 497.236 | + | 861.237i | 0.588444 | + | 1.01922i | ||||
\(846\) | − | 307.887i | − | 0.363932i | ||||||
\(847\) | − | 290.834i | − | 0.343369i | ||||||
\(848\) | 671.271 | − | 1162.68i | 0.791593 | − | 1.37108i | ||||
\(849\) | 299.114 | + | 518.080i | 0.352313 | + | 0.610224i | ||||
\(850\) | −833.132 | − | 1443.03i | −0.980156 | − | 1.69768i | ||||
\(851\) | 73.3013 | − | 42.3205i | 0.0861354 | − | 0.0497303i | ||||
\(852\) | −590.178 | −0.692697 | ||||||||
\(853\) | 449.317 | − | 778.239i | 0.526749 | − | 0.912356i | −0.472765 | − | 0.881188i | \(-0.656744\pi\) |
0.999514 | − | 0.0311674i | \(-0.00992250\pi\) | |||||||
\(854\) | −179.228 | − | 103.477i | −0.209869 | − | 0.121168i | ||||
\(855\) | −973.224 | + | 170.235i | −1.13827 | + | 0.199105i | ||||
\(856\) | 542.293i | 0.633520i | ||||||||
\(857\) | −62.9555 | + | 109.042i | −0.0734603 | + | 0.127237i | −0.900416 | − | 0.435031i | \(-0.856738\pi\) |
0.826955 | + | 0.562268i | \(0.190071\pi\) | |||||||
\(858\) | 120.820 | + | 209.266i | 0.140816 | + | 0.243900i | ||||
\(859\) | 503.551 | − | 290.725i | 0.586206 | − | 0.338446i | −0.177390 | − | 0.984141i | \(-0.556765\pi\) |
0.763596 | + | 0.645694i | \(0.223432\pi\) | |||||||
\(860\) | − | 1567.45i | − | 1.82261i | ||||||
\(861\) | 23.9922 | + | 41.5558i | 0.0278656 | + | 0.0482646i | ||||
\(862\) | −1417.13 | − | 818.179i | −1.64400 | − | 0.949164i | ||||
\(863\) | − | 1700.91i | − | 1.97092i | −0.169894 | − | 0.985462i | \(-0.554343\pi\) | ||
0.169894 | − | 0.985462i | \(-0.445657\pi\) | |||||||
\(864\) | −632.364 | − | 365.096i | −0.731903 | − | 0.422565i | ||||
\(865\) | 851.382 | + | 1474.64i | 0.984257 | + | 1.70478i | ||||
\(866\) | 373.727 | − | 647.314i | 0.431555 | − | 0.747475i | ||||
\(867\) | 625.785i | 0.721782i | ||||||||
\(868\) | −297.180 | + | 514.731i | −0.342373 | + | 0.593008i | ||||
\(869\) | −909.675 | + | 1575.60i | −1.04681 | + | 1.81312i | ||||
\(870\) | − | 74.3718i | − | 0.0854848i | ||||||
\(871\) | 192.065 | + | 110.889i | 0.220511 | + | 0.127312i | ||||
\(872\) | 198.907 | − | 344.517i | 0.228104 | − | 0.395088i | ||||
\(873\) | 737.489 | 0.844775 | ||||||||
\(874\) | 892.135 | + | 326.092i | 1.02075 | + | 0.373103i | ||||
\(875\) | 166.387i | 0.190156i | ||||||||
\(876\) | − | 50.9670i | − | 0.0581815i | ||||||
\(877\) | −36.2417 | + | 62.7725i | −0.0413247 | + | 0.0715764i | −0.885948 | − | 0.463785i | \(-0.846491\pi\) |
0.844623 | + | 0.535361i | \(0.179824\pi\) | |||||||
\(878\) | − | 542.211i | − | 0.617552i | ||||||
\(879\) | 153.333 | + | 88.5267i | 0.174440 | + | 0.100713i | ||||
\(880\) | 1684.39i | 1.91408i | ||||||||
\(881\) | 201.998 | 0.229283 | 0.114641 | − | 0.993407i | \(-0.463428\pi\) | ||||
0.114641 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(882\) | −242.139 | + | 419.397i | −0.274534 | + | 0.475506i | ||||
\(883\) | −752.052 | + | 434.198i | −0.851701 | + | 0.491730i | −0.861225 | − | 0.508225i | \(-0.830302\pi\) |
0.00952321 | + | 0.999955i | \(0.496969\pi\) | |||||||
\(884\) | −323.453 | + | 560.238i | −0.365898 | + | 0.633753i | ||||
\(885\) | 274.614 | 0.310298 | ||||||||
\(886\) | 758.703 | + | 438.037i | 0.856324 | + | 0.494399i | ||||
\(887\) | 511.770 | − | 295.471i | 0.576968 | − | 0.333112i | −0.182960 | − | 0.983120i | \(-0.558568\pi\) |
0.759927 | + | 0.650008i | \(0.225234\pi\) | |||||||
\(888\) | −33.5528 | − | 19.3717i | −0.0377847 | − | 0.0218150i | ||||
\(889\) | −43.9286 | − | 76.0865i | −0.0494135 | − | 0.0855866i | ||||
\(890\) | −960.816 | − | 1664.18i | −1.07957 | − | 1.86987i | ||||
\(891\) | −365.237 | − | 210.869i | −0.409918 | − | 0.236666i | ||||
\(892\) | −475.770 | + | 274.686i | −0.533375 | + | 0.307944i | ||||
\(893\) | 322.554 | − | 269.905i | 0.361203 | − | 0.302245i | ||||
\(894\) | 179.430 | + | 103.594i | 0.200704 | + | 0.115877i | ||||
\(895\) | −1698.43 | − | 980.591i | −1.89769 | − | 1.09563i | ||||
\(896\) | 417.458 | − | 241.019i | 0.465912 | − | 0.268995i | ||||
\(897\) | 107.252 | + | 185.765i | 0.119567 | + | 0.207096i | ||||
\(898\) | 710.180 | + | 1230.07i | 0.790846 | + | 1.36979i | ||||
\(899\) | 118.818 | − | 68.5995i | 0.132167 | − | 0.0763064i | ||||
\(900\) | −429.909 | − | 744.624i | −0.477677 | − | 0.827360i | ||||
\(901\) | −2261.72 | −2.51023 | ||||||||
\(902\) | 250.863i | 0.278118i | ||||||||
\(903\) | 244.455 | − | 141.136i | 0.270715 | − | 0.156297i | ||||
\(904\) | −567.271 | −0.627512 | ||||||||
\(905\) | 597.319 | 0.660021 | ||||||||
\(906\) | 112.863 | 0.124573 | ||||||||
\(907\) | −774.413 | − | 447.107i | −0.853818 | − | 0.492952i | 0.00811954 | − | 0.999967i | \(-0.497415\pi\) |
−0.861937 | + | 0.507015i | \(0.830749\pi\) | |||||||
\(908\) | 322.135 | + | 185.984i | 0.354774 | + | 0.204829i | ||||
\(909\) | 465.549 | − | 806.354i | 0.512155 | − | 0.887078i | ||||
\(910\) | 292.634 | − | 168.952i | 0.321575 | − | 0.185662i | ||||
\(911\) | 1132.77i | 1.24343i | 0.783242 | + | 0.621717i | \(0.213564\pi\) | ||||
−0.783242 | + | 0.621717i | \(0.786436\pi\) | |||||||
\(912\) | −74.9151 | − | 428.286i | −0.0821438 | − | 0.469612i | ||||
\(913\) | −382.596 | −0.419054 | ||||||||
\(914\) | −320.996 | − | 555.981i | −0.351199 | − | 0.608294i | ||||
\(915\) | −254.477 | − | 146.922i | −0.278117 | − | 0.160571i | ||||
\(916\) | 328.364 | − | 568.744i | 0.358476 | − | 0.620899i | ||||
\(917\) | 52.0595 | − | 90.1697i | 0.0567716 | − | 0.0983312i | ||||
\(918\) | 1230.12i | 1.34000i | ||||||||
\(919\) | 103.477i | 0.112598i | 0.998414 | + | 0.0562988i | \(0.0179299\pi\) | ||||
−0.998414 | + | 0.0562988i | \(0.982070\pi\) | |||||||
\(920\) | 1495.23i | 1.62525i | ||||||||
\(921\) | −121.205 | − | 209.933i | −0.131601 | − | 0.227940i | ||||
\(922\) | 1663.63 | 1.80437 | ||||||||
\(923\) | 618.970i | 0.670606i | ||||||||
\(924\) | −262.694 | + | 151.666i | −0.284300 | + | 0.164141i | ||||
\(925\) | −52.3307 | − | 90.6395i | −0.0565738 | − | 0.0979887i | ||||
\(926\) | −400.408 | + | 231.176i | −0.432406 | + | 0.249650i | ||||
\(927\) | 623.215 | − | 359.814i | 0.672293 | − | 0.388148i | ||||
\(928\) | −111.271 | −0.119904 | ||||||||
\(929\) | 622.997 | − | 1079.06i | 0.670610 | − | 1.16153i | −0.307121 | − | 0.951670i | \(-0.599366\pi\) |
0.977731 | − | 0.209861i | \(-0.0673010\pi\) | |||||||
\(930\) | −421.952 | + | 730.843i | −0.453712 | + | 0.785853i | ||||
\(931\) | −651.644 | + | 113.985i | −0.699940 | + | 0.122432i | ||||
\(932\) | −109.089 | − | 188.948i | −0.117048 | − | 0.202734i | ||||
\(933\) | 291.400 | − | 504.720i | 0.312326 | − | 0.540964i | ||||
\(934\) | 567.701 | − | 327.762i | 0.607817 | − | 0.350923i | ||||
\(935\) | 2457.45 | − | 1418.81i | 2.62828 | − | 1.51744i | ||||
\(936\) | −166.907 | + | 289.091i | −0.178319 | + | 0.308858i | ||||
\(937\) | −831.676 | − | 1440.51i | −0.887594 | − | 1.53736i | −0.842711 | − | 0.538366i | \(-0.819042\pi\) |
−0.0448835 | − | 0.998992i | \(-0.514292\pi\) | |||||||
\(938\) | −139.200 | + | 241.101i | −0.148401 | + | 0.257037i | ||||
\(939\) | − | 819.123i | − | 0.872336i | ||||||
\(940\) | 573.362 | + | 331.031i | 0.609960 | + | 0.352161i | ||||
\(941\) | −156.636 | − | 271.301i | −0.166457 | − | 0.288311i | 0.770715 | − | 0.637180i | \(-0.219899\pi\) |
−0.937172 | + | 0.348869i | \(0.886566\pi\) | |||||||
\(942\) | −252.451 | − | 145.753i | −0.267995 | − | 0.154727i | ||||
\(943\) | 222.690i | 0.236151i | ||||||||
\(944\) | − | 410.863i | − | 0.435236i | ||||||
\(945\) | 321.269 | − | 556.454i | 0.339967 | − | 0.588841i | ||||
\(946\) | 1475.72 | 1.55996 | ||||||||
\(947\) | −918.950 | − | 530.556i | −0.970380 | − | 0.560249i | −0.0710283 | − | 0.997474i | \(-0.522628\pi\) |
−0.899352 | + | 0.437225i | \(0.855961\pi\) | |||||||
\(948\) | 739.263 | 0.779813 | ||||||||
\(949\) | −53.4534 | −0.0563260 | ||||||||
\(950\) | 403.224 | − | 1103.15i | 0.424446 | − | 1.16122i | ||||
\(951\) | 756.457i | 0.795433i | ||||||||
\(952\) | −703.271 | − | 406.034i | −0.738730 | − | 0.426506i | ||||
\(953\) | −649.318 | + | 1124.65i | −0.681341 | + | 1.18012i | 0.293231 | + | 0.956042i | \(0.405269\pi\) |
−0.974572 | + | 0.224075i | \(0.928064\pi\) | |||||||
\(954\) | −1167.08 | −1.22336 | ||||||||
\(955\) | 1509.72 | + | 871.636i | 1.58086 | + | 0.912708i | ||||
\(956\) | −989.085 | − | 571.048i | −1.03461 | − | 0.597331i | ||||
\(957\) | 70.0197 | 0.0731658 | ||||||||
\(958\) | 135.636 | + | 78.3093i | 0.141582 | + | 0.0817424i | ||||
\(959\) | −648.422 | + | 374.367i | −0.676144 | + | 0.390372i | ||||
\(960\) | 592.729 | − | 342.212i | 0.617426 | − | 0.356471i | ||||
\(961\) | −595.812 | −0.619991 | ||||||||
\(962\) | −20.3168 | + | 35.1897i | −0.0211193 | + | 0.0365797i | ||||
\(963\) | 408.261 | − | 235.710i | 0.423947 | − | 0.244766i | ||||
\(964\) | −703.089 | −0.729345 | ||||||||
\(965\) | 459.679 | + | 796.188i | 0.476351 | + | 0.825065i | ||||
\(966\) | −233.193 | + | 134.634i | −0.241400 | + | 0.139372i | ||||
\(967\) | 312.980 | + | 180.699i | 0.323661 | + | 0.186866i | 0.653023 | − | 0.757338i | \(-0.273500\pi\) |
−0.329362 | + | 0.944204i | \(0.606834\pi\) | |||||||
\(968\) | −617.822 | −0.638246 | ||||||||
\(969\) | −561.746 | + | 470.055i | −0.579718 | + | 0.485092i | ||||
\(970\) | −792.926 | + | 1373.39i | −0.817450 | + | 1.41586i | ||||
\(971\) | 1318.71 | + | 761.356i | 1.35809 | + | 0.784095i | 0.989367 | − | 0.145443i | \(-0.0464609\pi\) |
0.368726 | + | 0.929538i | \(0.379794\pi\) | |||||||
\(972\) | 992.832i | 1.02143i | ||||||||
\(973\) | −506.032 | − | 876.472i | −0.520074 | − | 0.900794i | ||||
\(974\) | 22.9783 | − | 13.2665i | 0.0235916 | − | 0.0136206i | ||||
\(975\) | 229.705 | − | 132.620i | 0.235595 | − | 0.136021i | ||||
\(976\) | −219.818 | + | 380.736i | −0.225223 | + | 0.390098i | ||||
\(977\) | −12.6874 | −0.0129861 | −0.00649303 | − | 0.999979i | \(-0.502067\pi\) | ||||
−0.00649303 | + | 0.999979i | \(0.502067\pi\) | |||||||
\(978\) | 545.097 | 0.557359 | ||||||||
\(979\) | 1566.80 | − | 904.590i | 1.60040 | − | 0.923994i | ||||
\(980\) | −520.681 | − | 901.846i | −0.531307 | − | 0.920251i | ||||
\(981\) | −345.822 | −0.352520 | ||||||||
\(982\) | − | 321.167i | − | 0.327054i | ||||||
\(983\) | −726.273 | − | 419.314i | −0.738833 | − | 0.426566i | 0.0828116 | − | 0.996565i | \(-0.473610\pi\) |
−0.821645 | + | 0.570000i | \(0.806943\pi\) | |||||||
\(984\) | 88.2774 | − | 50.9670i | 0.0897128 | − | 0.0517957i | ||||
\(985\) | 576.339 | − | 998.248i | 0.585115 | − | 1.01345i | ||||
\(986\) | 93.7267 | + | 162.339i | 0.0950575 | + | 0.164644i | ||||
\(987\) | 119.227i | 0.120797i | ||||||||
\(988\) | −449.180 | + | 78.5698i | −0.454636 | + | 0.0795241i | ||||
\(989\) | 1310.00 | 1.32457 | ||||||||
\(990\) | 1268.08 | − | 732.126i | 1.28089 | − | 0.739521i | ||||
\(991\) | −1478.90 | − | 853.842i | −1.49233 | − | 0.861597i | −0.492368 | − | 0.870387i | \(-0.663869\pi\) |
−0.999961 | + | 0.00879022i | \(0.997202\pi\) | |||||||
\(992\) | 1093.45 | + | 631.303i | 1.10227 | + | 0.636394i | ||||
\(993\) | 42.3851 | − | 73.4131i | 0.0426839 | − | 0.0739306i | ||||
\(994\) | −776.998 | −0.781688 | ||||||||
\(995\) | 802.752i | 0.806786i | ||||||||
\(996\) | 77.7309 | + | 134.634i | 0.0780430 | + | 0.135174i | ||||
\(997\) | 329.734 | + | 571.117i | 0.330727 | + | 0.572835i | 0.982655 | − | 0.185446i | \(-0.0593729\pi\) |
−0.651928 | + | 0.758281i | \(0.726040\pi\) | |||||||
\(998\) | − | 1206.94i | − | 1.20936i | ||||||
\(999\) | 77.2663i | 0.0773436i |
(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 | 76.3.g.a.11.1 | yes | 4 | |
4.3 | odd | 2 | 76.3.g.b.11.2 | yes | 4 | ||
19.7 | even | 3 | 76.3.g.b.7.2 | yes | 4 | ||
76.7 | odd | 6 | inner | 76.3.g.a.7.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.a.7.1 | ✓ | 4 | 76.7 | odd | 6 | inner | |
76.3.g.a.11.1 | yes | 4 | 1.1 | even | 1 | trivial | |
76.3.g.b.7.2 | yes | 4 | 19.7 | even | 3 | ||
76.3.g.b.11.2 | yes | 4 | 4.3 | odd | 2 |