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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(2.73861 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.b.7.2 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 1.00000 | ||||||||
\(3\) | 1.23861 | + | 0.715113i | 0.412871 | + | 0.238371i | 0.692023 | − | 0.721876i | \(-0.256720\pi\) |
−0.279152 | + | 0.960247i | \(0.590053\pi\) | |||||||
\(4\) | 4.00000 | 1.00000 | ||||||||
\(5\) | −3.73861 | + | 6.47547i | −0.747723 | + | 1.29509i | 0.201189 | + | 0.979552i | \(0.435519\pi\) |
−0.948912 | + | 0.315541i | \(0.897814\pi\) | |||||||
\(6\) | 2.47723 | + | 1.43023i | 0.412871 | + | 0.238371i | ||||
\(7\) | − | 3.76593i | − | 0.537989i | −0.963142 | − | 0.268995i | \(-0.913309\pi\) | ||
0.963142 | − | 0.268995i | \(-0.0866914\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | −3.47723 | − | 6.02273i | −0.386358 | − | 0.669192i | ||||
\(10\) | −7.47723 | + | 12.9509i | −0.747723 | + | 1.29509i | ||||
\(11\) | − | 14.0793i | − | 1.27994i | −0.768400 | − | 0.639970i | \(-0.778947\pi\) | ||
0.768400 | − | 0.639970i | \(-0.221053\pi\) | |||||||
\(12\) | 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 | \(0.907458\pi\) | |||||||
\(14\) | − | 7.53185i | − | 0.537989i | ||||||
\(15\) | −9.26139 | + | 5.34706i | −0.617426 | + | 0.356471i | ||||
\(16\) | 16.0000 | 1.00000 | ||||||||
\(17\) | −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 | ||||
\(22\) | − | 28.1587i | − | 1.27994i | ||||||
\(23\) | −21.6475 | + | 12.4982i | −0.941196 | + | 0.543400i | −0.890335 | − | 0.455306i | \(-0.849530\pi\) |
−0.0508612 | + | 0.998706i | \(0.516197\pi\) | |||||||
\(24\) | 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 | ||||||
\(28\) | − | 15.0637i | − | 0.537989i | ||||||
\(29\) | 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 | \(0.219575\pi\) | ||||
−0.771364 | + | 0.636394i | \(0.780425\pi\) | |||||||
\(32\) | 32.0000 | 1.00000 | ||||||||
\(33\) | 10.0683 | − | 17.4388i | 0.305101 | − | 0.528450i | ||||
\(34\) | −26.9545 | + | 46.6865i | −0.792778 | + | 1.37313i | ||||
\(35\) | 24.3861 | + | 14.0793i | 0.696747 | + | 0.402267i | ||||
\(36\) | −13.9089 | − | 24.0909i | −0.386358 | − | 0.669192i | ||||
\(37\) | 3.38613 | 0.0915170 | 0.0457585 | − | 0.998953i | \(-0.485430\pi\) | ||||
0.0457585 | + | 0.998953i | \(0.485430\pi\) | |||||||
\(38\) | 37.4317 | − | 6.54749i | 0.985044 | − | 0.172302i | ||||
\(39\) | − | 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 | \(0.201318\pi\) | |||||||
\(42\) | 5.38613 | − | 9.32905i | 0.128241 | − | 0.222120i | ||||
\(43\) | −45.3861 | − | 26.2037i | −1.05549 | − | 0.609388i | −0.131310 | − | 0.991341i | \(-0.541918\pi\) |
−0.924182 | + | 0.381953i | \(0.875252\pi\) | |||||||
\(44\) | − | 56.3173i | − | 1.27994i | ||||||
\(45\) | 52.0000 | 1.15556 | ||||||||
\(46\) | −43.2950 | + | 24.9964i | −0.941196 | + | 0.543400i | ||||
\(47\) | 19.1703 | − | 11.0680i | 0.407879 | − | 0.235489i | −0.281999 | − | 0.959415i | \(-0.590998\pi\) |
0.689878 | + | 0.723926i | \(0.257664\pi\) | |||||||
\(48\) | 19.8178 | + | 11.4418i | 0.412871 | + | 0.238371i | ||||
\(49\) | 34.8178 | 0.710567 | ||||||||
\(50\) | −30.9089 | − | 53.5358i | −0.618178 | − | 1.07072i | ||||
\(51\) | −33.3861 | + | 19.2755i | −0.654630 | + | 0.377951i | ||||
\(52\) | −12.0000 | − | 20.7846i | −0.230769 | − | 0.399704i | ||||
\(53\) | 41.9545 | + | 72.6672i | 0.791593 | + | 1.37108i | 0.924980 | + | 0.380016i | \(0.124081\pi\) |
−0.133387 | + | 0.991064i | \(0.542585\pi\) | |||||||
\(54\) | − | 45.6370i | − | 0.845129i | ||||||
\(55\) | 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 | 0.299554 | − | 0.954079i | \(-0.403162\pi\) |
−0.676480 | + | 0.736461i | \(0.736495\pi\) | |||||||
\(60\) | −37.0455 | + | 21.3883i | −0.617426 | + | 0.356471i | ||||
\(61\) | −13.7386 | − | 23.7960i | −0.225223 | − | 0.390098i | 0.731163 | − | 0.682203i | \(-0.238978\pi\) |
−0.956386 | + | 0.292105i | \(0.905644\pi\) | |||||||
\(62\) | 78.9129i | 1.27279i | ||||||||
\(63\) | −22.6812 | + | 13.0950i | −0.360018 | + | 0.207857i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 44.8634 | 0.690205 | ||||||||
\(66\) | 20.1366 | − | 34.8777i | 0.305101 | − | 0.528450i | ||||
\(67\) | 32.0109 | − | 18.4815i | 0.477774 | − | 0.275843i | −0.241714 | − | 0.970347i | \(-0.577710\pi\) |
0.719488 | + | 0.694504i | \(0.244376\pi\) | |||||||
\(68\) | −53.9089 | + | 93.3730i | −0.792778 | + | 1.37313i | ||||
\(69\) | −35.7505 | −0.518123 | ||||||||
\(70\) | 48.7723 | + | 28.1587i | 0.696747 | + | 0.402267i | ||||
\(71\) | 89.3406 | + | 51.5808i | 1.25832 | + | 0.726490i | 0.972747 | − | 0.231867i | \(-0.0744836\pi\) |
0.285571 | + | 0.958358i | \(0.407817\pi\) | |||||||
\(72\) | −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 | \(0.147231\pi\) | |||||||
\(74\) | 6.77226 | 0.0915170 | ||||||||
\(75\) | − | 44.2067i | − | 0.589423i | ||||||
\(76\) | 74.8634 | − | 13.0950i | 0.985044 | − | 0.172302i | ||||
\(77\) | −53.0217 | −0.688594 | ||||||||
\(78\) | − | 17.1627i | − | 0.220035i | ||||||
\(79\) | −111.909 | − | 64.6106i | −1.41657 | − | 0.817856i | −0.420573 | − | 0.907259i | \(-0.638171\pi\) |
−0.995996 | + | 0.0894026i | \(0.971504\pi\) | |||||||
\(80\) | −59.8178 | + | 103.607i | −0.747723 | + | 1.29509i | ||||
\(81\) | −14.9772 | + | 25.9413i | −0.184904 | + | 0.320263i | ||||
\(82\) | −8.90890 | + | 15.4307i | −0.108645 | + | 0.188179i | ||||
\(83\) | − | 27.1743i | − | 0.327401i | −0.986510 | − | 0.163701i | \(-0.947657\pi\) | ||
0.986510 | − | 0.163701i | \(-0.0523431\pi\) | |||||||
\(84\) | 10.7723 | − | 18.6581i | 0.128241 | − | 0.222120i | ||||
\(85\) | −100.772 | − | 174.543i | −1.18556 | − | 2.05344i | ||||
\(86\) | −90.7723 | − | 52.4074i | −1.05549 | − | 0.609388i | ||||
\(87\) | 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 | \(-0.423400\pi\) | |||||||
\(90\) | 104.000 | 1.15556 | ||||||||
\(91\) | −19.5683 | + | 11.2978i | −0.215037 | + | 0.124151i | ||||
\(92\) | −86.5901 | + | 49.9928i | −0.941196 | + | 0.543400i | ||||
\(93\) | −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 | \(0.982578\pi\) | |||||||
\(98\) | 69.6356 | 0.710567 | ||||||||
\(99\) | −84.7961 | + | 48.9570i | −0.856526 | + | 0.494515i | ||||
\(100\) | −61.8178 | − | 107.072i | −0.618178 | − | 1.07072i | ||||
\(101\) | 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 | \(-0.832481\pi\) | ||
0.864684 | − | 0.502316i | \(-0.167519\pi\) | |||||||
\(104\) | −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 | \(-0.897405\pi\) | ||
0.948506 | − | 0.316760i | \(-0.102595\pi\) | |||||||
\(108\) | − | 91.2739i | − | 0.845129i | ||||||
\(109\) | 24.8634 | − | 43.0646i | 0.228104 | − | 0.395088i | −0.729142 | − | 0.684362i | \(-0.760081\pi\) |
0.957246 | + | 0.289274i | \(0.0934140\pi\) | |||||||
\(110\) | 182.341 | + | 105.274i | 1.65764 | + | 0.957040i | ||||
\(111\) | 4.19410 | + | 2.42147i | 0.0377847 | + | 0.0218150i | ||||
\(112\) | − | 60.2548i | − | 0.537989i | ||||||
\(113\) | −70.9089 | −0.627512 | −0.313756 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313756 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(114\) | 51.0455 | + | 18.6581i | 0.447768 | + | 0.163667i | ||||
\(115\) | − | 186.904i | − | 1.62525i | ||||||
\(116\) | 6.95445 | + | 12.0455i | 0.0599522 | + | 0.103840i | ||||
\(117\) | −20.8634 | + | 36.1364i | −0.178319 | + | 0.308858i | ||||
\(118\) | −44.4772 | − | 25.6789i | −0.376926 | − | 0.217618i | ||||
\(119\) | 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 | ||||
\(124\) | 157.826i | 1.27279i | ||||||||
\(125\) | 44.1822 | 0.353458 | ||||||||
\(126\) | −45.3623 | + | 26.1899i | −0.360018 | + | 0.207857i | ||||
\(127\) | 20.2039 | − | 11.6647i | 0.159086 | − | 0.0918484i | −0.418343 | − | 0.908289i | \(-0.637389\pi\) |
0.577430 | + | 0.816441i | \(0.304056\pi\) | |||||||
\(128\) | 128.000 | 1.00000 | ||||||||
\(129\) | −37.4772 | − | 64.9125i | −0.290521 | − | 0.503197i | ||||
\(130\) | 89.7267 | 0.690205 | ||||||||
\(131\) | 23.9436 | + | 13.8238i | 0.182775 | + | 0.105525i | 0.588596 | − | 0.808427i | \(-0.299681\pi\) |
−0.405821 | + | 0.913953i | \(0.633014\pi\) | |||||||
\(132\) | 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 | \(0.574890\pi\) | |||||||
\(138\) | −71.5010 | −0.518123 | ||||||||
\(139\) | 232.738 | − | 134.371i | 1.67437 | − | 0.966699i | 0.709227 | − | 0.704981i | \(-0.249044\pi\) |
0.965144 | − | 0.261718i | \(-0.0842891\pi\) | |||||||
\(140\) | 97.5445 | + | 56.3173i | 0.696747 | + | 0.402267i | ||||
\(141\) | 31.6594 | 0.224535 | ||||||||
\(142\) | 178.681 | + | 103.162i | 1.25832 | + | 0.726490i | ||||
\(143\) | −73.1584 | + | 42.2380i | −0.511597 | + | 0.295371i | ||||
\(144\) | −55.6356 | − | 96.3637i | −0.386358 | − | 0.669192i | ||||
\(145\) | −26.0000 | −0.179310 | ||||||||
\(146\) | 8.90890 | − | 15.4307i | 0.0610199 | − | 0.105690i | ||||
\(147\) | 43.1258 | + | 24.8987i | 0.293373 | + | 0.169379i | ||||
\(148\) | 13.5445 | 0.0915170 | ||||||||
\(149\) | 36.2158 | − | 62.7277i | 0.243059 | − | 0.420991i | −0.718525 | − | 0.695501i | \(-0.755182\pi\) |
0.961584 | + | 0.274510i | \(0.0885157\pi\) | |||||||
\(150\) | − | 88.4135i | − | 0.589423i | ||||||
\(151\) | 39.4565i | 0.261301i | 0.991428 | + | 0.130651i | \(0.0417066\pi\) | ||||
−0.991428 | + | 0.130651i | \(0.958293\pi\) | |||||||
\(152\) | 149.727 | − | 26.1899i | 0.985044 | − | 0.172302i | ||||
\(153\) | 187.453 | 1.22519 | ||||||||
\(154\) | −106.043 | −0.688594 | ||||||||
\(155\) | −255.499 | − | 147.512i | −1.64838 | − | 0.951693i | ||||
\(156\) | − | 34.3254i | − | 0.220035i | ||||||
\(157\) | −50.9545 | + | 88.2557i | −0.324551 | + | 0.562138i | −0.981421 | − | 0.191865i | \(-0.938546\pi\) |
0.656871 | + | 0.754003i | \(0.271880\pi\) | |||||||
\(158\) | −223.818 | − | 129.221i | −1.41657 | − | 0.817856i | ||||
\(159\) | 120.009i | 0.754772i | ||||||||
\(160\) | −119.636 | + | 207.215i | −0.747723 | + | 1.29509i | ||||
\(161\) | 47.0673 | + | 81.5229i | 0.292343 | + | 0.506354i | ||||
\(162\) | −29.9545 | + | 51.8826i | −0.184904 | + | 0.320263i | ||||
\(163\) | 190.563i | 1.16910i | 0.811358 | + | 0.584550i | \(0.198729\pi\) | ||||
−0.811358 | + | 0.584550i | \(0.801271\pi\) | |||||||
\(164\) | −17.8178 | + | 30.8613i | −0.108645 | + | 0.188179i | ||||
\(165\) | 75.2831 | + | 130.394i | 0.456261 | + | 0.790268i | ||||
\(166\) | − | 54.3486i | − | 0.327401i | ||||||
\(167\) | −256.681 | + | 148.195i | −1.53701 | + | 0.887395i | −0.538001 | + | 0.842944i | \(0.680820\pi\) |
−0.999012 | + | 0.0444508i | \(0.985846\pi\) | |||||||
\(168\) | 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 | \(-0.0620024\pi\) | |||||||
\(174\) | 9.94644i | 0.0571635i | ||||||||
\(175\) | −100.806 | + | 58.2003i | −0.576034 | + | 0.332573i | ||||
\(176\) | − | 225.269i | − | 1.27994i | ||||||
\(177\) | −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 | \(-0.738285\pi\) | ||
0.680610 | − | 0.732646i | \(-0.261715\pi\) | |||||||
\(180\) | 208.000 | 1.15556 | ||||||||
\(181\) | −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 | ||||
\(186\) | −56.4317 | + | 97.7425i | −0.303396 | + | 0.525497i | ||||
\(187\) | 328.657 | + | 189.750i | 1.75753 | + | 1.01471i | ||||
\(188\) | 76.6812 | − | 44.2719i | 0.407879 | − | 0.235489i | ||||
\(189\) | −85.9327 | −0.454670 | ||||||||
\(190\) | −97.5445 | + | 266.866i | −0.513392 | + | 1.40456i | ||||
\(191\) | 233.144i | 1.22065i | 0.792151 | + | 0.610325i | \(0.208961\pi\) | ||||
−0.792151 | + | 0.610325i | \(0.791039\pi\) | |||||||
\(192\) | 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 | \(0.0634759\pi\) | |||||||
\(194\) | −106.046 | + | 183.676i | −0.546627 | + | 0.946785i | ||||
\(195\) | 55.5683 | + | 32.0824i | 0.284966 | + | 0.164525i | ||||
\(196\) | 139.271 | 0.710567 | ||||||||
\(197\) | −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 | −0.715074 | − | 0.699049i | \(-0.753607\pi\) |
0.247857 | + | 0.968797i | \(0.420274\pi\) | |||||||
\(200\) | −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 | ||||
\(204\) | −133.545 | + | 77.1020i | −0.654630 | + | 0.377951i | ||||
\(205\) | −33.3069 | − | 57.6893i | −0.162473 | − | 0.281411i | ||||
\(206\) | − | 206.954i | − | 1.00463i | ||||||
\(207\) | 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 | 0.195794 | − | 0.980645i | \(-0.437271\pi\) |
−0.751366 | + | 0.659885i | \(0.770605\pi\) | |||||||
\(212\) | 167.818 | + | 290.669i | 0.791593 | + | 1.37108i | ||||
\(213\) | 73.7723 | + | 127.777i | 0.346349 | + | 0.599893i | ||||
\(214\) | − | 135.573i | − | 0.633520i | ||||||
\(215\) | 339.362 | − | 195.931i | 1.57843 | − | 0.911307i | ||||
\(216\) | − | 182.548i | − | 0.845129i | ||||||
\(217\) | 148.590 | 0.684747 | ||||||||
\(218\) | 49.7267 | − | 86.1292i | 0.228104 | − | 0.395088i | ||||
\(219\) | 11.0347 | − | 6.37088i | 0.0503867 | − | 0.0290908i | ||||
\(220\) | 364.681 | + | 210.549i | 1.65764 | + | 0.957040i | ||||
\(221\) | 161.727 | 0.731795 | ||||||||
\(222\) | 8.38820 | + | 4.84293i | 0.0377847 | + | 0.0218150i | ||||
\(223\) | −118.943 | − | 68.6715i | −0.533375 | − | 0.307944i | 0.209015 | − | 0.977912i | \(-0.432974\pi\) |
−0.742390 | + | 0.669968i | \(0.766308\pi\) | |||||||
\(224\) | − | 120.510i | − | 0.537989i | ||||||
\(225\) | −107.477 | + | 186.156i | −0.477677 | + | 0.827360i | ||||
\(226\) | −141.818 | −0.627512 | ||||||||
\(227\) | 92.9922i | 0.409657i | 0.978798 | + | 0.204829i | \(0.0656637\pi\) | ||||
−0.978798 | + | 0.204829i | \(0.934336\pi\) | |||||||
\(228\) | 102.091 | + | 37.3162i | 0.447768 | + | 0.163667i | ||||
\(229\) | −164.182 | −0.716953 | −0.358476 | − | 0.933539i | \(-0.616704\pi\) | ||||
−0.358476 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(230\) | − | 373.807i | − | 1.62525i | ||||||
\(231\) | −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 | \(0.204010\pi\) | |||||||
\(234\) | −41.7267 | + | 72.2728i | −0.178319 | + | 0.308858i | ||||
\(235\) | 165.515i | 0.704321i | ||||||||
\(236\) | −88.9545 | − | 51.3579i | −0.376926 | − | 0.217618i | ||||
\(237\) | −92.4079 | − | 160.055i | −0.389907 | − | 0.675338i | ||||
\(238\) | 175.818 | + | 101.508i | 0.738730 | + | 0.426506i | ||||
\(239\) | − | 285.524i | − | 1.19466i | −0.801995 | − | 0.597331i | \(-0.796228\pi\) | ||
0.801995 | − | 0.597331i | \(-0.203772\pi\) | |||||||
\(240\) | −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 | \(0.714514\pi\) | |||||||
\(242\) | −154.455 | −0.638246 | ||||||||
\(243\) | −214.954 | + | 124.104i | −0.884586 | + | 0.510716i | ||||
\(244\) | −54.9545 | − | 95.1839i | −0.225223 | − | 0.390098i | ||||
\(245\) | −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 | ||||
\(250\) | 88.3644 | 0.353458 | ||||||||
\(251\) | 140.124 | − | 80.9005i | 0.558262 | − | 0.322313i | −0.194186 | − | 0.980965i | \(-0.562206\pi\) |
0.752448 | + | 0.658652i | \(0.228873\pi\) | |||||||
\(252\) | −90.7246 | + | 52.3799i | −0.360018 | + | 0.207857i | ||||
\(253\) | 175.966 | + | 304.783i | 0.695519 | + | 1.20467i | ||||
\(254\) | 40.4079 | − | 23.3295i | 0.159086 | − | 0.0918484i | ||||
\(255\) | − | 288.254i | − | 1.13041i | ||||||
\(256\) | 256.000 | 1.00000 | ||||||||
\(257\) | 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 | ||||||
\(260\) | 179.453 | 0.690205 | ||||||||
\(261\) | 12.0911 | − | 20.9424i | 0.0463260 | − | 0.0802391i | ||||
\(262\) | 47.8872 | + | 27.6477i | 0.182775 | + | 0.105525i | ||||
\(263\) | −171.238 | − | 98.8641i | −0.651093 | − | 0.375909i | 0.137782 | − | 0.990463i | \(-0.456003\pi\) |
−0.788875 | + | 0.614554i | \(0.789336\pi\) | |||||||
\(264\) | 80.5466 | − | 139.511i | 0.305101 | − | 0.528450i | ||||
\(265\) | −627.406 | −2.36757 | ||||||||
\(266\) | −24.6573 | − | 140.965i | −0.0926968 | − | 0.529943i | ||||
\(267\) | − | 183.783i | − | 0.688325i | ||||||
\(268\) | 128.043 | − | 73.9259i | 0.477774 | − | 0.275843i | ||||
\(269\) | 77.6356 | − | 134.469i | 0.288608 | − | 0.499884i | −0.684870 | − | 0.728666i | \(-0.740141\pi\) |
0.973478 | + | 0.228782i | \(0.0734742\pi\) | |||||||
\(270\) | 295.521 | + | 170.619i | 1.09452 | + | 0.631922i | ||||
\(271\) | 52.0098 | + | 30.0279i | 0.191918 | + | 0.110804i | 0.592880 | − | 0.805291i | \(-0.297991\pi\) |
−0.400962 | + | 0.916095i | \(0.631324\pi\) | |||||||
\(272\) | −215.636 | + | 373.492i | −0.792778 | + | 1.37313i | ||||
\(273\) | −32.3168 | −0.118376 | ||||||||
\(274\) | 198.818 | + | 344.363i | 0.725612 | + | 1.25680i | ||||
\(275\) | −376.874 | + | 217.588i | −1.37045 | + | 0.791231i | ||||
\(276\) | −143.002 | −0.518123 | ||||||||
\(277\) | 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 | \(-0.469898\pi\) | |||||||
\(282\) | 63.3188 | 0.224535 | ||||||||
\(283\) | 362.237 | + | 209.137i | 1.27999 | + | 0.739001i | 0.976846 | − | 0.213944i | \(-0.0686311\pi\) |
0.303142 | + | 0.952945i | \(0.401964\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | −111.271 | − | 192.727i | −0.386358 | − | 0.669192i | ||||
\(289\) | −218.771 | − | 378.923i | −0.756994 | − | 1.31115i | ||||
\(290\) | −52.0000 | −0.179310 | ||||||||
\(291\) | −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 | \(0.567754\pi\) | |||||||
\(294\) | 86.2516 | + | 49.7974i | 0.293373 | + | 0.169379i | ||||
\(295\) | 166.283 | − | 96.0036i | 0.563672 | − | 0.325436i | ||||
\(296\) | 27.0890 | 0.0915170 | ||||||||
\(297\) | −321.269 | −1.08171 | ||||||||
\(298\) | 72.4317 | − | 125.455i | 0.243059 | − | 0.420991i | ||||
\(299\) | 129.885 | + | 74.9892i | 0.434398 | + | 0.250800i | ||||
\(300\) | − | 176.827i | − | 0.589423i | ||||||
\(301\) | −98.6812 | + | 170.921i | −0.327844 | + | 0.567843i | ||||
\(302\) | 78.9129i | 0.261301i | ||||||||
\(303\) | 191.486i | 0.631967i | ||||||||
\(304\) | 299.453 | − | 52.3799i | 0.985044 | − | 0.172302i | ||||
\(305\) | 205.453 | 0.673618 | ||||||||
\(306\) | 374.907 | 1.22519 | ||||||||
\(307\) | −146.783 | − | 84.7453i | −0.478121 | − | 0.276043i | 0.241512 | − | 0.970398i | \(-0.422357\pi\) |
−0.719633 | + | 0.694355i | \(0.755690\pi\) | |||||||
\(308\) | −212.087 | −0.688594 | ||||||||
\(309\) | 73.9979 | − | 128.168i | 0.239475 | − | 0.414784i | ||||
\(310\) | −510.998 | − | 295.025i | −1.64838 | − | 0.951693i | ||||
\(311\) | − | 407.488i | − | 1.31025i | −0.755520 | − | 0.655125i | \(-0.772616\pi\) | ||
0.755520 | − | 0.655125i | \(-0.227384\pi\) | |||||||
\(312\) | − | 68.6509i | − | 0.220035i | ||||||
\(313\) | 286.361 | + | 495.992i | 0.914892 | + | 1.58464i | 0.807059 | + | 0.590471i | \(0.201058\pi\) |
0.107833 | + | 0.994169i | \(0.465609\pi\) | |||||||
\(314\) | −101.909 | + | 176.511i | −0.324551 | + | 0.562138i | ||||
\(315\) | − | 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 | \(-0.480759\pi\) | |||||||
\(318\) | 240.018i | 0.754772i | ||||||||
\(319\) | 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 | ||||
\(326\) | 381.126i | 1.16910i | ||||||||
\(327\) | 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 | \(-0.971463\pi\) | ||
0.995984 | − | 0.0895324i | \(-0.0285373\pi\) | |||||||
\(332\) | − | 108.697i | − | 0.327401i | ||||||
\(333\) | −11.7743 | − | 20.3937i | −0.0353583 | − | 0.0612425i | ||||
\(334\) | −513.362 | + | 296.390i | −1.53701 | + | 0.887395i | ||||
\(335\) | 276.380i | 0.825016i | ||||||||
\(336\) | 43.0890 | − | 74.6324i | 0.128241 | − | 0.222120i | ||||
\(337\) | −135.203 | + | 234.178i | −0.401196 | + | 0.694891i | −0.993870 | − | 0.110551i | \(-0.964739\pi\) |
0.592675 | + | 0.805442i | \(0.298072\pi\) | |||||||
\(338\) | 133.000 | − | 230.363i | 0.393491 | − | 0.681547i | ||||
\(339\) | −87.8287 | − | 50.7079i | −0.259082 | − | 0.149581i | ||||
\(340\) | −403.089 | − | 698.171i | −1.18556 | − | 2.05344i | ||||
\(341\) | 555.521 | 1.62909 | ||||||||
\(342\) | −169.592 | − | 202.674i | −0.495883 | − | 0.592614i | ||||
\(343\) | − | 315.652i | − | 0.920267i | ||||||
\(344\) | −363.089 | − | 209.630i | −1.05549 | − | 0.609388i | ||||
\(345\) | 133.657 | − | 231.501i | 0.387413 | − | 0.671018i | ||||
\(346\) | 227.727 | − | 394.434i | 0.658170 | − | 1.13998i | ||||
\(347\) | 292.649 | + | 168.961i | 0.843368 | + | 0.486919i | 0.858407 | − | 0.512968i | \(-0.171454\pi\) |
−0.0150399 | + | 0.999887i | \(0.504788\pi\) | |||||||
\(348\) | 19.8929i | 0.0571635i | ||||||||
\(349\) | −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 | ||||
\(352\) | − | 450.539i | − | 1.27994i | ||||||
\(353\) | 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 | ||||
\(356\) | −256.998 | − | 445.133i | −0.721904 | − | 1.25037i | ||||
\(357\) | 72.5901 | + | 125.730i | 0.203334 | + | 0.352184i | ||||
\(358\) | − | 524.575i | − | 1.46529i | ||||||
\(359\) | 71.7148 | + | 41.4046i | 0.199763 | + | 0.115333i | 0.596545 | − | 0.802580i | \(-0.296540\pi\) |
−0.396782 | + | 0.917913i | \(0.629873\pi\) | |||||||
\(360\) | 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 | ||||
\(364\) | −78.2733 | + | 45.1911i | −0.215037 | + | 0.124151i | ||||
\(365\) | 33.3069 | + | 57.6893i | 0.0912519 | + | 0.158053i | ||||
\(366\) | − | 78.5973i | − | 0.214747i | ||||||
\(367\) | −261.398 | + | 150.918i | −0.712256 | + | 0.411221i | −0.811896 | − | 0.583802i | \(-0.801564\pi\) |
0.0996397 | + | 0.995024i | \(0.468231\pi\) | |||||||
\(368\) | −346.360 | + | 199.971i | −0.941196 | + | 0.543400i | ||||
\(369\) | 61.9565 | 0.167904 | ||||||||
\(370\) | −25.3188 | + | 43.8535i | −0.0684293 | + | 0.118523i | ||||
\(371\) | 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 | \(0.367375\pi\) | |||||||
\(374\) | 657.315 | + | 379.501i | 1.75753 | + | 1.01471i | ||||
\(375\) | 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 | ||||
\(378\) | −171.865 | −0.454670 | ||||||||
\(379\) | 498.042i | 1.31409i | 0.753850 | + | 0.657047i | \(0.228195\pi\) | ||||
−0.753850 | + | 0.657047i | \(0.771805\pi\) | |||||||
\(380\) | −195.089 | + | 533.732i | −0.513392 | + | 1.40456i | ||||
\(381\) | 33.3665 | 0.0875760 | ||||||||
\(382\) | 466.289i | 1.22065i | ||||||||
\(383\) | −30.0771 | − | 17.3650i | −0.0785303 | − | 0.0453395i | 0.460221 | − | 0.887805i | \(-0.347770\pi\) |
−0.538751 | + | 0.842465i | \(0.681104\pi\) | |||||||
\(384\) | 158.542 | + | 91.5345i | 0.412871 | + | 0.238371i | ||||
\(385\) | 198.228 | − | 343.341i | 0.514877 | − | 0.891794i | ||||
\(386\) | 122.954 | − | 212.963i | 0.318535 | − | 0.551719i | ||||
\(387\) | 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 | \(0.994870\pi\) | |||||||
\(390\) | 111.137 | + | 64.1648i | 0.284966 | + | 0.164525i | ||||
\(391\) | − | 673.764i | − | 1.72318i | ||||||
\(392\) | 278.542 | 0.710567 | ||||||||
\(393\) | 19.7712 | + | 34.2448i | 0.0503084 | + | 0.0871368i | ||||
\(394\) | −308.317 | −0.782530 | ||||||||
\(395\) | 836.768 | − | 483.108i | 2.11840 | − | 1.22306i | ||||
\(396\) | −339.184 | + | 195.828i | −0.856526 | + | 0.494515i | ||||
\(397\) | −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 | \(0.981775\pi\) | |||||||
\(402\) | 105.731 | 0.263012 | ||||||||
\(403\) | 205.022 | − | 118.369i | 0.508739 | − | 0.293720i | ||||
\(404\) | 267.770 | + | 463.792i | 0.662797 | + | 1.14800i | ||||
\(405\) | −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 | ||||||||
\(412\) | − | 413.909i | − | 1.00463i | ||||||
\(413\) | −48.3525 | + | 83.7490i | −0.117076 | + | 0.202782i | ||||
\(414\) | 301.093 | + | 173.836i | 0.727278 | + | 0.419894i | ||||
\(415\) | 175.966 | + | 101.594i | 0.424015 | + | 0.244805i | ||||
\(416\) | −96.0000 | − | 166.277i | −0.230769 | − | 0.399704i | ||||
\(417\) | 384.362 | 0.921732 | ||||||||
\(418\) | −92.1843 | − | 527.013i | −0.220537 | − | 1.26080i | ||||
\(419\) | 431.538i | 1.02992i | 0.857213 | + | 0.514961i | \(0.172194\pi\) | ||||
−0.857213 | + | 0.514961i | \(0.827806\pi\) | |||||||
\(420\) | 80.5466 | + | 139.511i | 0.191778 | + | 0.332169i | ||||
\(421\) | 27.0357 | − | 46.8272i | 0.0642179 | − | 0.111229i | −0.832129 | − | 0.554582i | \(-0.812878\pi\) |
0.896347 | + | 0.443354i | \(0.146211\pi\) | |||||||
\(422\) | −234.451 | − | 135.361i | −0.555572 | − | 0.320760i | ||||
\(423\) | −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 | ||||
\(428\) | − | 271.147i | − | 0.633520i | ||||||
\(429\) | −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 | \(0.731402\pi\) |
−0.979391 | + | 0.201973i | \(0.935265\pi\) | |||||||
\(432\) | − | 365.096i | − | 0.845129i | ||||||
\(433\) | 186.863 | + | 323.657i | 0.431555 | + | 0.747475i | 0.997007 | − | 0.0773056i | \(-0.0246317\pi\) |
−0.565452 | + | 0.824781i | \(0.691298\pi\) | |||||||
\(434\) | 297.180 | 0.684747 | ||||||||
\(435\) | −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 | 0.208159 | − | 0.978095i | \(-0.433253\pi\) |
−0.742975 | + | 0.669319i | \(0.766586\pi\) | |||||||
\(440\) | 729.362 | + | 421.098i | 1.65764 | + | 0.957040i | ||||
\(441\) | −121.069 | − | 209.698i | −0.274534 | − | 0.475506i | ||||
\(442\) | 323.453 | 0.731795 | ||||||||
\(443\) | 379.351 | − | 219.019i | 0.856324 | − | 0.494399i | −0.00645570 | − | 0.999979i | \(-0.502055\pi\) |
0.862780 | + | 0.505580i | \(0.168722\pi\) | |||||||
\(444\) | 16.7764 | + | 9.68586i | 0.0377847 | + | 0.0218150i | ||||
\(445\) | 960.816 | 2.15914 | ||||||||
\(446\) | −237.885 | − | 137.343i | −0.533375 | − | 0.307944i | ||||
\(447\) | 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 | \(0.790359\pi\) | |||||||
\(450\) | −214.954 | + | 372.312i | −0.477677 | + | 0.827360i | ||||
\(451\) | 108.627 | + | 62.7157i | 0.240858 | + | 0.139059i | ||||
\(452\) | −283.636 | −0.627512 | ||||||||
\(453\) | −28.2158 | + | 48.8713i | −0.0622866 | + | 0.107884i | ||||
\(454\) | 185.984i | 0.409657i | ||||||||
\(455\) | − | 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 | \(0.385774\pi\) | |||||||
\(458\) | −328.364 | −0.716953 | ||||||||
\(459\) | 532.657 | + | 307.530i | 1.16047 | + | 0.670000i | ||||
\(460\) | − | 747.615i | − | 1.62525i | ||||||
\(461\) | −415.907 | + | 720.372i | −0.902184 | + | 1.56263i | −0.0775307 | + | 0.996990i | \(0.524704\pi\) |
−0.824653 | + | 0.565639i | \(0.808630\pi\) | |||||||
\(462\) | −131.347 | − | 75.8331i | −0.284300 | − | 0.164141i | ||||
\(463\) | 231.176i | 0.499299i | 0.968336 | + | 0.249650i | \(0.0803155\pi\) | ||||
−0.968336 | + | 0.249650i | \(0.919685\pi\) | |||||||
\(464\) | 27.8178 | + | 48.1819i | 0.0599522 | + | 0.103840i | ||||
\(465\) | −210.976 | − | 365.421i | −0.453712 | − | 0.785853i | ||||
\(466\) | −54.5445 | + | 94.4739i | −0.117048 | + | 0.202734i | ||||
\(467\) | − | 327.762i | − | 0.701846i | −0.936404 | − | 0.350923i | \(-0.885868\pi\) | ||
0.936404 | − | 0.350923i | \(-0.114132\pi\) | |||||||
\(468\) | −83.4534 | + | 144.546i | −0.178319 | + | 0.308858i | ||||
\(469\) | −69.5999 | − | 120.551i | −0.148401 | − | 0.257037i | ||||
\(470\) | 331.031i | 0.704321i | ||||||||
\(471\) | −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 | ||||
\(478\) | − | 571.048i | − | 1.19466i | ||||||
\(479\) | 67.8178 | − | 39.1546i | 0.141582 | − | 0.0817424i | −0.427536 | − | 0.903998i | \(-0.640618\pi\) |
0.569118 | + | 0.822256i | \(0.307285\pi\) | |||||||
\(480\) | −296.364 | + | 171.106i | −0.617426 | + | 0.356471i | ||||
\(481\) | −10.1584 | − | 17.5948i | −0.0211193 | − | 0.0365797i | ||||
\(482\) | 175.772 | + | 304.446i | 0.364673 | + | 0.631632i | ||||
\(483\) | 134.634i | 0.278745i | ||||||||
\(484\) | −308.911 | −0.638246 | ||||||||
\(485\) | −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 | \(-0.995664\pi\) | ||
0.999907 | − | 0.0136206i | \(-0.00433572\pi\) | |||||||
\(488\) | −109.909 | − | 190.368i | −0.225223 | − | 0.390098i | ||||
\(489\) | −136.274 | + | 236.034i | −0.278680 | + | 0.482687i | ||||
\(490\) | −260.341 | + | 450.923i | −0.531307 | + | 0.920251i | ||||
\(491\) | −139.069 | − | 80.2917i | −0.283237 | − | 0.163527i | 0.351651 | − | 0.936131i | \(-0.385620\pi\) |
−0.634888 | + | 0.772604i | \(0.718954\pi\) | |||||||
\(492\) | −44.1387 | + | 25.4835i | −0.0897128 | + | 0.0517957i | ||||
\(493\) | −93.7267 | −0.190115 | ||||||||
\(494\) | −146.317 | − | 174.858i | −0.296188 | − | 0.353964i | ||||
\(495\) | − | 732.126i | − | 1.47904i | ||||||
\(496\) | 631.303i | 1.27279i | ||||||||
\(497\) | 194.249 | − | 336.450i | 0.390844 | − | 0.676962i | ||||
\(498\) | 38.8654 | − | 67.3169i | 0.0780430 | − | 0.135174i | ||||
\(499\) | −522.621 | − | 301.735i | −1.04734 | − | 0.604680i | −0.125434 | − | 0.992102i | \(-0.540032\pi\) |
−0.921902 | + | 0.387422i | \(0.873366\pi\) | |||||||
\(500\) | 176.729 | 0.353458 | ||||||||
\(501\) | −423.905 | −0.846117 | ||||||||
\(502\) | 280.247 | − | 161.801i | 0.558262 | − | 0.322313i | ||||
\(503\) | −220.170 | + | 127.115i | −0.437714 | + | 0.252714i | −0.702628 | − | 0.711558i | \(-0.747990\pi\) |
0.264913 | + | 0.964272i | \(0.414657\pi\) | |||||||
\(504\) | −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 | ||||
\(508\) | 80.8157 | − | 46.6590i | 0.159086 | − | 0.0918484i | ||||
\(509\) | 49.0455 | + | 84.9494i | 0.0963567 | + | 0.166895i | 0.910174 | − | 0.414226i | \(-0.135948\pi\) |
−0.813817 | + | 0.581121i | \(0.802614\pi\) | |||||||
\(510\) | − | 576.509i | − | 1.13041i | ||||||
\(511\) | −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 | ||||
\(516\) | −149.909 | − | 259.650i | −0.290521 | − | 0.503197i | ||||
\(517\) | −155.830 | − | 269.905i | −0.301411 | − | 0.522060i | ||||
\(518\) | − | 25.5038i | − | 0.0492352i | ||||||
\(519\) | 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 | \(0.656292\pi\) | |||||||
\(522\) | 24.1822 | − | 41.8848i | 0.0463260 | − | 0.0802391i | ||||
\(523\) | −399.564 | + | 230.688i | −0.763985 | + | 0.441087i | −0.830725 | − | 0.556683i | \(-0.812074\pi\) |
0.0667397 | + | 0.997770i | \(0.478740\pi\) | |||||||
\(524\) | 95.7743 | + | 55.2953i | 0.182775 | + | 0.105525i | ||||
\(525\) | −166.479 | −0.317103 | ||||||||
\(526\) | −342.475 | − | 197.728i | −0.651093 | − | 0.375909i | ||||
\(527\) | −921.041 | − | 531.763i | −1.74771 | − | 1.00904i | ||||
\(528\) | 161.093 | − | 279.022i | 0.305101 | − | 0.528450i | ||||
\(529\) | 47.9099 | − | 82.9824i | 0.0905670 | − | 0.156867i | ||||
\(530\) | −1254.81 | −2.36757 | ||||||||
\(531\) | 178.583i | 0.336314i | ||||||||
\(532\) | −49.3147 | − | 281.930i | −0.0926968 | − | 0.529943i | ||||
\(533\) | 53.4534 | 0.100288 | ||||||||
\(534\) | − | 367.565i | − | 0.688325i | ||||||
\(535\) | 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 | ||||
\(538\) | 155.271 | − | 268.938i | 0.288608 | − | 0.499884i | ||||
\(539\) | − | 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 | \(0.855817\pi\) | |||||||
\(542\) | 104.020 | + | 60.0558i | 0.191918 | + | 0.110804i | ||||
\(543\) | − | 114.254i | − | 0.210412i | ||||||
\(544\) | −431.271 | + | 746.984i | −0.792778 | + | 1.37313i | ||||
\(545\) | 185.909 | + | 322.004i | 0.341117 | + | 0.590832i | ||||
\(546\) | −64.6335 | −0.118376 | ||||||||
\(547\) | −181.521 | + | 104.801i | −0.331848 | + | 0.191592i | −0.656661 | − | 0.754186i | \(-0.728032\pi\) |
0.324813 | + | 0.945778i | \(0.394698\pi\) | |||||||
\(548\) | 397.636 | + | 688.725i | 0.725612 | + | 1.25680i | ||||
\(549\) | −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 | ||||
\(554\) | 798.859 | 1.44198 | ||||||||
\(555\) | −31.3602 | + | 18.1058i | −0.0565049 | + | 0.0326231i | ||||
\(556\) | 930.950 | − | 537.484i | 1.67437 | − | 0.966699i | ||||
\(557\) | 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 | ||||||||
\(560\) | 390.178 | + | 225.269i | 0.696747 | + | 0.402267i | ||||
\(561\) | 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 | \(0.141418\pi\) | ||||
−0.902921 | + | 0.429807i | \(0.858582\pi\) | |||||||
\(564\) | 126.638 | 0.224535 | ||||||||
\(565\) | 265.101 | − | 459.168i | 0.469205 | − | 0.812687i | ||||
\(566\) | 724.473 | + | 418.275i | 1.27999 | + | 0.739001i | ||||
\(567\) | 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 | \(0.481821\pi\) | |||||||
\(570\) | −311.659 | + | 260.788i | −0.546771 | + | 0.457523i | ||||
\(571\) | 553.718i | 0.969733i | 0.874588 | + | 0.484867i | \(0.161132\pi\) | ||||
−0.874588 | + | 0.484867i | \(0.838868\pi\) | |||||||
\(572\) | −292.634 | + | 168.952i | −0.511597 | + | 0.295371i | ||||
\(573\) | −166.725 | + | 288.776i | −0.290968 | + | 0.503971i | ||||
\(574\) | 58.1108 | + | 33.5503i | 0.101238 | + | 0.0584499i | ||||
\(575\) | 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 | ||||
\(580\) | −104.000 | −0.179310 | ||||||||
\(581\) | −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 | ||||
\(586\) | −247.588 | −0.422505 | ||||||||
\(587\) | −838.432 | − | 484.069i | −1.42833 | − | 0.824649i | −0.431344 | − | 0.902188i | \(-0.641960\pi\) |
−0.996989 | + | 0.0775389i | \(0.975294\pi\) | |||||||
\(588\) | 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 | ||||
\(592\) | 54.1780 | 0.0915170 | ||||||||
\(593\) | 64.8188 | + | 112.270i | 0.109307 | + | 0.189325i | 0.915490 | − | 0.402342i | \(-0.131804\pi\) |
−0.806183 | + | 0.591666i | \(0.798470\pi\) | |||||||
\(594\) | −642.538 | −1.08171 | ||||||||
\(595\) | −657.315 | + | 379.501i | −1.10473 | + | 0.637816i | ||||
\(596\) | 144.863 | − | 250.911i | 0.243059 | − | 0.420991i | ||||
\(597\) | −153.549 | −0.257200 | ||||||||
\(598\) | 259.770 | + | 149.978i | 0.434398 | + | 0.250800i | ||||
\(599\) | 636.142 | − | 367.277i | 1.06201 | − | 0.613150i | 0.136020 | − | 0.990706i | \(-0.456569\pi\) |
0.925987 | + | 0.377556i | \(0.123235\pi\) | |||||||
\(600\) | − | 353.654i | − | 0.589423i | ||||||
\(601\) | 964.041 | 1.60406 | 0.802031 | − | 0.597282i | \(-0.203753\pi\) | ||||
0.802031 | + | 0.597282i | \(0.203753\pi\) | |||||||
\(602\) | −197.362 | + | 341.842i | −0.327844 | + | 0.567843i | ||||
\(603\) | −222.618 | − | 128.529i | −0.369184 | − | 0.213149i | ||||
\(604\) | 157.826i | 0.261301i | ||||||||
\(605\) | 288.725 | − | 500.086i | 0.477231 | − | 0.826588i | ||||
\(606\) | 382.972i | 0.631967i | ||||||||
\(607\) | 526.372i | 0.867170i | 0.901113 | + | 0.433585i | \(0.142752\pi\) | ||||
−0.901113 | + | 0.433585i | \(0.857248\pi\) | |||||||
\(608\) | 598.907 | − | 104.760i | 0.985044 | − | 0.172302i | ||||
\(609\) | 18.7288 | 0.0307533 | ||||||||
\(610\) | 410.907 | 0.673618 | ||||||||
\(611\) | −115.022 | − | 66.4078i | −0.188252 | − | 0.108687i | ||||
\(612\) | 749.814 | 1.22519 | ||||||||
\(613\) | 38.9565 | − | 67.4747i | 0.0635506 | − | 0.110073i | −0.832500 | − | 0.554026i | \(-0.813091\pi\) |
0.896050 | + | 0.443953i | \(0.146424\pi\) | |||||||
\(614\) | −293.566 | − | 169.491i | −0.478121 | − | 0.276043i | ||||
\(615\) | − | 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 | \(0.782073\pi\) | |||||||
\(618\) | 147.996 | − | 256.336i | 0.239475 | − | 0.414784i | ||||
\(619\) | 86.1017i | 0.139098i | 0.997579 | + | 0.0695490i | \(0.0221560\pi\) | ||||
−0.997579 | + | 0.0695490i | \(0.977844\pi\) | |||||||
\(620\) | −1022.00 | − | 590.050i | −1.64838 | − | 0.951693i | ||||
\(621\) | 285.190 | + | 493.963i | 0.459243 | + | 0.795432i | ||||
\(622\) | − | 814.976i | − | 1.31025i | ||||||
\(623\) | −419.085 | + | 241.959i | −0.672688 | + | 0.388377i | ||||
\(624\) | − | 137.302i | − | 0.220035i | ||||||
\(625\) | 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 | ||||
\(630\) | − | 391.656i | − | 0.621677i | ||||||
\(631\) | 367.717 | − | 212.301i | 0.582753 | − | 0.336452i | −0.179474 | − | 0.983763i | \(-0.557440\pi\) |
0.762227 | + | 0.647310i | \(0.224106\pi\) | |||||||
\(632\) | −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 | ||||||||
\(636\) | 480.035i | 0.754772i | ||||||||
\(637\) | −104.453 | − | 180.919i | −0.163977 | − | 0.284017i | ||||
\(638\) | 84.7961 | − | 48.9570i | 0.132909 | − | 0.0767352i | ||||
\(639\) | − | 717.432i | − | 1.12274i | ||||||
\(640\) | −478.542 | + | 828.860i | −0.747723 | + | 1.29509i | ||||
\(641\) | 131.637 | − | 228.001i | 0.205361 | − | 0.355696i | −0.744886 | − | 0.667191i | \(-0.767496\pi\) |
0.950248 | + | 0.311495i | \(0.100830\pi\) | |||||||
\(642\) | 96.9503 | − | 167.923i | 0.151013 | − | 0.261562i | ||||
\(643\) | 71.3256 | + | 41.1798i | 0.110926 | + | 0.0640433i | 0.554437 | − | 0.832226i | \(-0.312934\pi\) |
−0.443510 | + | 0.896269i | \(0.646267\pi\) | |||||||
\(644\) | 188.269 | + | 326.092i | 0.292343 | + | 0.506354i | ||||
\(645\) | 560.451 | 0.868917 | ||||||||
\(646\) | −351.636 | + | 962.019i | −0.544328 | + | 1.48919i | ||||
\(647\) | 149.354i | 0.230841i | 0.993317 | + | 0.115421i | \(0.0368216\pi\) | ||||
−0.993317 | + | 0.115421i | \(0.963178\pi\) | |||||||
\(648\) | −119.818 | + | 207.531i | −0.184904 | + | 0.320263i | ||||
\(649\) | −180.771 | + | 313.105i | −0.278538 | + | 0.482442i | ||||
\(650\) | −185.453 | + | 321.215i | −0.285313 | + | 0.494177i | ||||
\(651\) | 184.046 | + | 106.259i | 0.282712 | + | 0.163224i | ||||
\(652\) | 762.253i | 1.16910i | ||||||||
\(653\) | 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 | ||||
\(656\) | −71.2712 | + | 123.445i | −0.108645 | + | 0.188179i | ||||
\(657\) | −61.9565 | −0.0943022 | ||||||||
\(658\) | −83.3623 | − | 144.388i | −0.126690 | − | 0.219434i | ||||
\(659\) | 741.636 | − | 428.184i | 1.12540 | − | 0.649747i | 0.182623 | − | 0.983183i | \(-0.441541\pi\) |
0.942773 | + | 0.333436i | \(0.108208\pi\) | |||||||
\(660\) | 301.132 | + | 521.577i | 0.456261 | + | 0.790268i | ||||
\(661\) | 115.830 | + | 200.623i | 0.175234 | + | 0.303514i | 0.940242 | − | 0.340506i | \(-0.110598\pi\) |
−0.765008 | + | 0.644021i | \(0.777265\pi\) | |||||||
\(662\) | − | 118.541i | − | 0.179065i | ||||||
\(663\) | 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 | ||||
\(668\) | −1026.72 | + | 592.780i | −1.53701 | + | 0.887395i | ||||
\(669\) | −98.2158 | − | 170.115i | −0.146810 | − | 0.254282i | ||||
\(670\) | 552.761i | 0.825016i | ||||||||
\(671\) | −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 | \(0.442523\pi\) | |||||||
\(674\) | −270.406 | + | 468.357i | −0.401196 | + | 0.694891i | ||||
\(675\) | −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 | \(0.286270\pi\) | |||||||
\(678\) | −175.657 | − | 101.416i | −0.259082 | − | 0.149581i | ||||
\(679\) | 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 | ||||
\(682\) | 1111.04 | 1.62909 | ||||||||
\(683\) | − | 469.540i | − | 0.687467i | −0.939067 | − | 0.343734i | \(-0.888308\pi\) | ||
0.939067 | − | 0.343734i | \(-0.111692\pi\) | |||||||
\(684\) | −339.184 | − | 405.348i | −0.495883 | − | 0.592614i | ||||
\(685\) | −1486.61 | −2.17023 | ||||||||
\(686\) | − | 631.303i | − | 0.920267i | ||||||
\(687\) | −203.358 | − | 117.409i | −0.296009 | − | 0.170901i | ||||
\(688\) | −726.178 | − | 419.259i | −1.05549 | − | 0.609388i | ||||
\(689\) | 251.727 | − | 436.003i | 0.365351 | − | 0.632806i | ||||
\(690\) | 267.315 | − | 463.003i | 0.387413 | − | 0.671018i | ||||
\(691\) | 627.366i | 0.907910i | 0.891025 | + | 0.453955i | \(0.149987\pi\) | ||||
−0.891025 | + | 0.453955i | \(0.850013\pi\) | |||||||
\(692\) | 455.453 | − | 788.868i | 0.658170 | − | 1.13998i | ||||
\(693\) | 184.369 | + | 319.336i | 0.266044 | + | 0.460802i | ||||
\(694\) | 585.297 | + | 337.921i | 0.843368 | + | 0.486919i | ||||
\(695\) | 2009.45i | 2.89129i | ||||||||
\(696\) | 39.7858i | 0.0571635i | ||||||||
\(697\) | −120.067 | − | 207.963i | −0.172263 | − | 0.298368i | ||||
\(698\) | −313.458 | −0.449080 | ||||||||
\(699\) | −67.5595 | + | 39.0055i | −0.0966517 | + | 0.0558019i | ||||
\(700\) | −403.224 | + | 232.801i | −0.576034 | + | 0.332573i | ||||
\(701\) | 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 | ||||
\(706\) | 27.5445 | 0.0390149 | ||||||||
\(707\) | 436.651 | − | 252.101i | 0.617611 | − | 0.356578i | ||||
\(708\) | −73.4534 | − | 127.225i | −0.103748 | − | 0.179696i | ||||
\(709\) | 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 | ||||||
\(716\) | − | 1049.15i | − | 1.46529i | ||||||
\(717\) | 204.182 | − | 353.654i | 0.284773 | − | 0.493241i | ||||
\(718\) | 143.430 | + | 82.8091i | 0.199763 | + | 0.115333i | ||||
\(719\) | −517.610 | − | 298.842i | −0.719902 | − | 0.415636i | 0.0948144 | − | 0.995495i | \(-0.469774\pi\) |
−0.814717 | + | 0.579859i | \(0.803108\pi\) | |||||||
\(720\) | 832.000 | 1.15556 | ||||||||
\(721\) | −389.687 | −0.540482 | ||||||||
\(722\) | 679.130 | − | 245.083i | 0.940624 | − | 0.339451i | ||||
\(723\) | 251.394i | 0.347710i | ||||||||
\(724\) | −159.770 | − | 276.730i | −0.220677 | − | 0.382224i | ||||
\(725\) | 53.7386 | − | 93.0780i | 0.0741222 | − | 0.128383i | ||||
\(726\) | −191.311 | − | 110.453i | −0.263513 | − | 0.152139i | ||||
\(727\) | −209.050 | − | 120.695i | −0.287551 | − | 0.166018i | 0.349286 | − | 0.937016i | \(-0.386424\pi\) |
−0.636837 | + | 0.770998i | \(0.719758\pi\) | |||||||
\(728\) | −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 | ||||
\(732\) | − | 157.195i | − | 0.214747i | ||||||
\(733\) | 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 | ||||
\(736\) | −692.720 | + | 399.942i | −0.941196 | + | 0.543400i | ||||
\(737\) | −260.207 | − | 450.692i | −0.353062 | − | 0.611522i | ||||
\(738\) | 123.913 | 0.167904 | ||||||||
\(739\) | −258.757 | − | 149.394i | −0.350145 | − | 0.202156i | 0.314604 | − | 0.949223i | \(-0.398128\pi\) |
−0.664749 | + | 0.747067i | \(0.731462\pi\) | |||||||
\(740\) | −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 | 0.115049 | − | 0.993360i | \(-0.463298\pi\) |
−0.802750 | + | 0.596315i | \(0.796631\pi\) | |||||||
\(744\) | −225.727 | + | 390.970i | −0.303396 | + | 0.525497i | ||||
\(745\) | 270.794 | + | 469.029i | 0.363482 | + | 0.629569i | ||||
\(746\) | 603.818 | 0.809407 | ||||||||
\(747\) | −163.664 | + | 94.4912i | −0.219094 | + | 0.126494i | ||||
\(748\) | 1314.63 | + | 759.002i | 1.75753 | + | 1.01471i | ||||
\(749\) | −255.280 | −0.340827 | ||||||||
\(750\) | 109.449 | + | 63.1906i | 0.145932 | + | 0.0842541i | ||||
\(751\) | −360.208 | + | 207.966i | −0.479638 | + | 0.276919i | −0.720266 | − | 0.693698i | \(-0.755980\pi\) |
0.240628 | + | 0.970617i | \(0.422647\pi\) | |||||||
\(752\) | 306.725 | − | 177.088i | 0.407879 | − | 0.235489i | ||||
\(753\) | 231.412 | 0.307320 | ||||||||
\(754\) | 20.8634 | − | 36.1364i | 0.0276702 | − | 0.0479262i | ||||
\(755\) | −255.499 | − | 147.512i | −0.338409 | − | 0.195381i | ||||
\(756\) | −343.731 | −0.454670 | ||||||||
\(757\) | −94.9565 | + | 164.470i | −0.125438 | + | 0.217265i | −0.921904 | − | 0.387418i | \(-0.873367\pi\) |
0.796466 | + | 0.604683i | \(0.206700\pi\) | |||||||
\(758\) | 996.083i | 1.31409i | ||||||||
\(759\) | 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 | \(0.588665\pi\) | |||||||
\(762\) | 66.7329 | 0.0875760 | ||||||||
\(763\) | −162.178 | − | 93.6335i | −0.212553 | − | 0.122718i | ||||
\(764\) | 932.577i | 1.22065i | ||||||||
\(765\) | −700.816 | + | 1213.85i | −0.916099 | + | 1.58673i | ||||
\(766\) | −60.1542 | − | 34.7301i | −0.0785303 | − | 0.0453395i | ||||
\(767\) | 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 | \(0.844435\pi\) | |||||||
\(770\) | 396.455 | − | 686.681i | 0.514877 | − | 0.891794i | ||||
\(771\) | 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 | \(0.947643\pi\) | |||||||
\(774\) | 728.929i | 0.941769i | ||||||||
\(775\) | 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 | ||||
\(782\) | − | 1347.53i | − | 1.72318i | ||||||
\(783\) | 68.7148 | − | 39.6725i | 0.0877584 | − | 0.0506673i | ||||
\(784\) | 557.085 | 0.710567 | ||||||||
\(785\) | −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 | \(-0.787076\pi\) | ||
0.784492 | − | 0.620138i | \(-0.212924\pi\) | |||||||
\(788\) | −616.634 | −0.782530 | ||||||||
\(789\) | −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 | ||||
\(794\) | −161.065 | + | 278.973i | −0.202853 | + | 0.351352i | ||||
\(795\) | −777.113 | − | 448.666i | −0.977500 | − | 0.564360i | ||||
\(796\) | −371.905 | + | 214.719i | −0.467217 | + | 0.269748i | ||||
\(797\) | −596.606 | −0.748564 | −0.374282 | − | 0.927315i | \(-0.622111\pi\) | ||||
−0.374282 | + | 0.927315i | \(0.622111\pi\) | |||||||
\(798\) | 70.2650 | − | 192.234i | 0.0880514 | − | 0.240894i | ||||
\(799\) | 596.662i | 0.746761i | ||||||||
\(800\) | −494.542 | − | 856.573i | −0.618178 | − | 1.07072i | ||||
\(801\) | −446.820 | + | 773.915i | −0.557828 | + | 0.966186i | ||||
\(802\) | −440.089 | + | 762.257i | −0.548739 | + | 0.950445i | ||||
\(803\) | −108.627 | − | 62.7157i | −0.135276 | − | 0.0781018i | ||||
\(804\) | 211.462 | 0.263012 | ||||||||
\(805\) | −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 | −0.122166 | − | 0.992510i | \(-0.538984\pi\) |
0.798456 | + | 0.602054i | \(0.205651\pi\) | |||||||
\(812\) | 45.3623 | − | 26.1899i | 0.0558649 | − | 0.0322536i | ||||
\(813\) | 42.9467 | + | 74.3859i | 0.0528250 | + | 0.0914955i | ||||
\(814\) | − | 95.3489i | − | 0.117136i | ||||||
\(815\) | −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 | ||||
\(820\) | −133.228 | − | 230.757i | −0.162473 | − | 0.281411i | ||||
\(821\) | 390.770 | + | 676.834i | 0.475969 | + | 0.824402i | 0.999621 | − | 0.0275303i | \(-0.00876427\pi\) |
−0.523652 | + | 0.851932i | \(0.675431\pi\) | |||||||
\(822\) | 568.709i | 0.691860i | ||||||||
\(823\) | −117.748 | + | 67.9821i | −0.143072 | + | 0.0826028i | −0.569827 | − | 0.821764i | \(-0.692990\pi\) |
0.426755 | + | 0.904367i | \(0.359657\pi\) | |||||||
\(824\) | − | 827.817i | − | 1.00463i | ||||||
\(825\) | −622.402 | −0.754426 | ||||||||
\(826\) | −96.7050 | + | 167.498i | −0.117076 | + | 0.202782i | ||||
\(827\) | 447.466 | − | 258.345i | 0.541072 | − | 0.312388i | −0.204441 | − | 0.978879i | \(-0.565538\pi\) |
0.745513 | + | 0.666491i | \(0.232204\pi\) | |||||||
\(828\) | 602.186 | + | 347.672i | 0.727278 | + | 0.419894i | ||||
\(829\) | −1147.72 | −1.38447 | −0.692233 | − | 0.721674i | \(-0.743373\pi\) | ||||
−0.692233 | + | 0.721674i | \(0.743373\pi\) | |||||||
\(830\) | 351.933 | + | 203.188i | 0.424015 | + | 0.244805i | ||||
\(831\) | 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 | ||||
\(834\) | 768.725 | 0.921732 | ||||||||
\(835\) | − | 2216.17i | − | 2.65410i | ||||||
\(836\) | −184.369 | − | 1054.03i | −0.220537 | − | 1.26080i | ||||
\(837\) | 900.336 | 1.07567 | ||||||||
\(838\) | 863.075i | 1.02992i | ||||||||
\(839\) | −166.461 | − | 96.1064i | −0.198404 | − | 0.114549i | 0.397507 | − | 0.917599i | \(-0.369876\pi\) |
−0.595911 | + | 0.803051i | \(0.703209\pi\) | |||||||
\(840\) | 161.093 | + | 279.022i | 0.191778 | + | 0.332169i | ||||
\(841\) | 414.454 | − | 717.856i | 0.492811 | − | 0.853575i | ||||
\(842\) | 54.0714 | − | 93.6545i | 0.0642179 | − | 0.111229i | ||||
\(843\) | − | 655.041i | − | 0.777036i | ||||||
\(844\) | −468.903 | − | 270.721i | −0.555572 | − | 0.320760i | ||||
\(845\) | 497.236 | + | 861.237i | 0.588444 | + | 1.01922i | ||||
\(846\) | −266.638 | − | 153.943i | −0.315175 | − | 0.181966i | ||||
\(847\) | 290.834i | 0.343369i | ||||||||
\(848\) | 671.271 | + | 1162.68i | 0.791593 | + | 1.37108i | ||||
\(849\) | 299.114 | + | 518.080i | 0.352313 | + | 0.610224i | ||||
\(850\) | 1666.26 | 1.96031 | ||||||||
\(851\) | −73.3013 | + | 42.3205i | −0.0861354 | + | 0.0497303i | ||||
\(852\) | 295.089 | + | 511.109i | 0.346349 | + | 0.599893i | ||||
\(853\) | 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 | \(0.190071\pi\) | |||||||
\(858\) | −241.640 | −0.281631 | ||||||||
\(859\) | −503.551 | + | 290.725i | −0.586206 | + | 0.338446i | −0.763596 | − | 0.645694i | \(-0.776568\pi\) |
0.177390 | + | 0.984141i | \(0.443235\pi\) | |||||||
\(860\) | 1357.45 | − | 783.724i | 1.57843 | − | 0.911307i | ||||
\(861\) | 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 | \(0.445657\pi\) | ||||
−0.169894 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(864\) | − | 730.192i | − | 0.845129i | ||||||
\(865\) | 851.382 | + | 1474.64i | 0.984257 | + | 1.70478i | ||||
\(866\) | 373.727 | + | 647.314i | 0.431555 | + | 0.747475i | ||||
\(867\) | − | 625.785i | − | 0.721782i | ||||||
\(868\) | 594.360 | 0.684747 | ||||||||
\(869\) | −909.675 | + | 1575.60i | −1.04681 | + | 1.81312i | ||||
\(870\) | −64.4079 | − | 37.1859i | −0.0740320 | − | 0.0427424i | ||||
\(871\) | −192.065 | − | 110.889i | −0.220511 | − | 0.127312i | ||||
\(872\) | 198.907 | − | 344.517i | 0.228104 | − | 0.395088i | ||||
\(873\) | 737.489 | 0.844775 | ||||||||
\(874\) | −728.471 | + | 609.565i | −0.833491 | + | 0.697443i | ||||
\(875\) | − | 166.387i | − | 0.190156i | ||||||
\(876\) | 44.1387 | − | 25.4835i | 0.0503867 | − | 0.0290908i | ||||
\(877\) | −36.2417 | + | 62.7725i | −0.0413247 | + | 0.0715764i | −0.885948 | − | 0.463785i | \(-0.846491\pi\) |
0.844623 | + | 0.535361i | \(0.179824\pi\) | |||||||
\(878\) | −469.568 | − | 271.105i | −0.534816 | − | 0.308776i | ||||
\(879\) | −153.333 | − | 88.5267i | −0.174440 | − | 0.100713i | ||||
\(880\) | 1458.72 | + | 842.195i | 1.65764 | + | 0.957040i | ||||
\(881\) | 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 | −0.00952321 | − | 0.999955i | \(-0.503031\pi\) |
0.861225 | + | 0.508225i | \(0.169698\pi\) | |||||||
\(884\) | 646.907 | 0.731795 | ||||||||
\(885\) | 274.614 | 0.310298 | ||||||||
\(886\) | 758.703 | − | 438.037i | 0.856324 | − | 0.494399i | ||||
\(887\) | −511.770 | + | 295.471i | −0.576968 | + | 0.333112i | −0.759927 | − | 0.650008i | \(-0.774766\pi\) |
0.182960 | + | 0.983120i | \(0.441432\pi\) | |||||||
\(888\) | 33.5528 | + | 19.3717i | 0.0377847 | + | 0.0218150i | ||||
\(889\) | −43.9286 | − | 76.0865i | −0.0494135 | − | 0.0855866i | ||||
\(890\) | 1921.63 | 2.15914 | ||||||||
\(891\) | 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 | ||||
\(896\) | − | 482.038i | − | 0.537989i | ||||||
\(897\) | 107.252 | + | 185.765i | 0.119567 | + | 0.207096i | ||||
\(898\) | −1420.36 | −1.58169 | ||||||||
\(899\) | −118.818 | + | 68.5995i | −0.132167 | + | 0.0763064i | ||||
\(900\) | −429.909 | + | 744.624i | −0.477677 | + | 0.827360i | ||||
\(901\) | −2261.72 | −2.51023 | ||||||||
\(902\) | 217.254 | + | 125.431i | 0.240858 | + | 0.139059i | ||||
\(903\) | −244.455 | + | 141.136i | −0.270715 | + | 0.156297i | ||||
\(904\) | −567.271 | −0.627512 | ||||||||
\(905\) | 597.319 | 0.660021 | ||||||||
\(906\) | −56.4317 | + | 97.7425i | −0.0622866 | + | 0.107884i | ||||
\(907\) | 774.413 | + | 447.107i | 0.853818 | + | 0.492952i | 0.861937 | − | 0.507015i | \(-0.169251\pi\) |
−0.00811954 | + | 0.999967i | \(0.502585\pi\) | |||||||
\(908\) | 371.969i | 0.409657i | ||||||||
\(909\) | 465.549 | − | 806.354i | 0.512155 | − | 0.887078i | ||||
\(910\) | − | 337.904i | − | 0.371323i | ||||||
\(911\) | − | 1132.77i | − | 1.24343i | −0.783242 | − | 0.621717i | \(-0.786436\pi\) | ||
0.783242 | − | 0.621717i | \(-0.213564\pi\) | |||||||
\(912\) | 408.364 | + | 149.265i | 0.447768 | + | 0.163667i | ||||
\(913\) | −382.596 | −0.419054 | ||||||||
\(914\) | 641.992 | 0.702398 | ||||||||
\(915\) | 254.477 | + | 146.922i | 0.278117 | + | 0.160571i | ||||
\(916\) | −656.729 | −0.716953 | ||||||||
\(917\) | 52.0595 | − | 90.1697i | 0.0567716 | − | 0.0983312i | ||||
\(918\) | 1065.31 | + | 615.060i | 1.16047 | + | 0.670000i | ||||
\(919\) | − | 103.477i | − | 0.112598i | −0.998414 | − | 0.0562988i | \(-0.982070\pi\) | ||
0.998414 | − | 0.0562988i | \(-0.0179299\pi\) | |||||||
\(920\) | − | 1495.23i | − | 1.62525i | ||||||
\(921\) | −121.205 | − | 209.933i | −0.131601 | − | 0.227940i | ||||
\(922\) | −831.814 | + | 1440.74i | −0.902184 | + | 1.56263i | ||||
\(923\) | − | 618.970i | − | 0.670606i | ||||||
\(924\) | −262.694 | − | 151.666i | −0.284300 | − | 0.164141i | ||||
\(925\) | −52.3307 | − | 90.6395i | −0.0565738 | − | 0.0979887i | ||||
\(926\) | 462.351i | 0.499299i | ||||||||
\(927\) | −623.215 | + | 359.814i | −0.672293 | + | 0.388148i | ||||
\(928\) | 55.6356 | + | 96.3637i | 0.0599522 | + | 0.103840i | ||||
\(929\) | 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 | ||||
\(934\) | − | 655.524i | − | 0.701846i | ||||||
\(935\) | −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 | ||||||||
\(940\) | 662.062i | 0.704321i | ||||||||
\(941\) | −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 | ||||||
\(944\) | −355.818 | − | 205.432i | −0.376926 | − | 0.217618i | ||||
\(945\) | 321.269 | − | 556.454i | 0.339967 | − | 0.588841i | ||||
\(946\) | −737.861 | + | 1278.01i | −0.779980 | + | 1.35097i | ||||
\(947\) | 918.950 | + | 530.556i | 0.970380 | + | 0.560249i | 0.899352 | − | 0.437225i | \(-0.144039\pi\) |
0.0710283 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(948\) | −369.631 | − | 640.220i | −0.389907 | − | 0.675338i | ||||
\(949\) | −53.4534 | −0.0563260 | ||||||||
\(950\) | −753.748 | − | 900.779i | −0.793419 | − | 0.948189i | ||||
\(951\) | − | 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 | \(0.928064\pi\) | |||||||
\(954\) | 583.540 | − | 1010.72i | 0.611678 | − | 1.05946i | ||||
\(955\) | −1509.72 | − | 871.636i | −1.58086 | − | 0.912708i | ||||
\(956\) | − | 1142.10i | − | 1.19466i | ||||||
\(957\) | 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 | ||||
\(964\) | 351.545 | + | 608.893i | 0.364673 | + | 0.631632i | ||||
\(965\) | 459.679 | + | 796.188i | 0.476351 | + | 0.825065i | ||||
\(966\) | 269.268i | 0.278745i | ||||||||
\(967\) | −312.980 | − | 180.699i | −0.323661 | − | 0.186866i | 0.329362 | − | 0.944204i | \(-0.393166\pi\) |
−0.653023 | + | 0.757338i | \(0.726500\pi\) | |||||||
\(968\) | −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 | −0.368726 | − | 0.929538i | \(-0.620206\pi\) |
−0.989367 | + | 0.145443i | \(0.953539\pi\) | |||||||
\(972\) | −859.818 | + | 496.416i | −0.884586 | + | 0.510716i | ||||
\(973\) | −506.032 | − | 876.472i | −0.520074 | − | 0.900794i | ||||
\(974\) | − | 26.5330i | − | 0.0272413i | ||||||
\(975\) | −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 | \(0.502067\pi\) | |||||||
\(978\) | −272.549 | + | 472.068i | −0.278680 | + | 0.482687i | ||||
\(979\) | −1566.80 | + | 904.590i | −1.60040 | + | 0.923994i | ||||
\(980\) | −520.681 | + | 901.846i | −0.531307 | + | 0.920251i | ||||
\(981\) | −345.822 | −0.352520 | ||||||||
\(982\) | −278.139 | − | 160.583i | −0.283237 | − | 0.163527i | ||||
\(983\) | 726.273 | + | 419.314i | 0.738833 | + | 0.426566i | 0.821645 | − | 0.570000i | \(-0.193057\pi\) |
−0.0828116 | + | 0.996565i | \(0.526390\pi\) | |||||||
\(984\) | −88.2774 | + | 50.9670i | −0.0897128 | + | 0.0517957i | ||||
\(985\) | 576.339 | − | 998.248i | 0.585115 | − | 1.01345i | ||||
\(986\) | −187.453 | −0.190115 | ||||||||
\(987\) | − | 119.227i | − | 0.120797i | ||||||
\(988\) | −292.634 | − | 349.716i | −0.296188 | − | 0.353964i | ||||
\(989\) | 1310.00 | 1.32457 | ||||||||
\(990\) | − | 1464.25i | − | 1.47904i | ||||||
\(991\) | 1478.90 | + | 853.842i | 1.49233 | + | 0.861597i | 0.999961 | − | 0.00879022i | \(-0.00279805\pi\) |
0.492368 | + | 0.870387i | \(0.336131\pi\) | |||||||
\(992\) | 1262.61i | 1.27279i | ||||||||
\(993\) | 42.3851 | − | 73.4131i | 0.0426839 | − | 0.0739306i | ||||
\(994\) | 388.499 | − | 672.900i | 0.390844 | − | 0.676962i | ||||
\(995\) | − | 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 | \(0.726040\pi\) | |||||||
\(998\) | −1045.24 | − | 603.470i | −1.04734 | − | 0.604680i | ||||
\(999\) | − | 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.b.11.2 | yes | 4 | |
4.3 | odd | 2 | 76.3.g.a.11.1 | yes | 4 | ||
19.7 | even | 3 | 76.3.g.a.7.1 | ✓ | 4 | ||
76.7 | odd | 6 | inner | 76.3.g.b.7.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.a.7.1 | ✓ | 4 | 19.7 | even | 3 | ||
76.3.g.a.11.1 | yes | 4 | 4.3 | odd | 2 | ||
76.3.g.b.7.2 | yes | 4 | 76.7 | odd | 6 | inner | |
76.3.g.b.11.2 | yes | 4 | 1.1 | even | 1 | trivial |