Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [161,4,Mod(93,161)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(161, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("161.93");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 161 = 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 161.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.49930751092\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 93.5 | ||
Character | \(\chi\) | \(=\) | 161.93 |
Dual form | 161.4.e.a.116.5 |
$q$-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 \(\left(\mathbb{Z}/161\mathbb{Z}\right)^\times\).
\(n\) | \(24\) | \(120\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86723 | + | 3.23414i | −0.660166 | + | 1.14344i | 0.320405 | + | 0.947280i | \(0.396181\pi\) |
−0.980572 | + | 0.196161i | \(0.937152\pi\) | |||||||
\(3\) | 1.89237 | + | 3.27768i | 0.364187 | + | 0.630791i | 0.988645 | − | 0.150268i | \(-0.0480135\pi\) |
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(4\) | −2.97311 | − | 5.14958i | −0.371639 | − | 0.643698i | ||||
\(5\) | 5.27939 | − | 9.14417i | 0.472203 | − | 0.817880i | −0.527291 | − | 0.849685i | \(-0.676792\pi\) |
0.999494 | + | 0.0318051i | \(0.0101256\pi\) | |||||||
\(6\) | −14.1340 | −0.961696 | ||||||||
\(7\) | 18.0686 | − | 4.06535i | 0.975611 | − | 0.219508i | ||||
\(8\) | −7.66976 | −0.338959 | ||||||||
\(9\) | 6.33786 | − | 10.9775i | 0.234735 | − | 0.406574i | ||||
\(10\) | 19.7157 | + | 34.1486i | 0.623465 | + | 1.07987i | ||||
\(11\) | 32.8419 | + | 56.8838i | 0.900200 | + | 1.55919i | 0.827234 | + | 0.561857i | \(0.189913\pi\) |
0.0729654 | + | 0.997334i | \(0.476754\pi\) | |||||||
\(12\) | 11.2525 | − | 19.4898i | 0.270692 | − | 0.468853i | ||||
\(13\) | 32.1382 | 0.685656 | 0.342828 | − | 0.939398i | \(-0.388615\pi\) | ||||
0.342828 | + | 0.939398i | \(0.388615\pi\) | |||||||
\(14\) | −20.5903 | + | 66.0272i | −0.393071 | + | 1.26047i | ||||
\(15\) | 39.9623 | 0.687881 | ||||||||
\(16\) | 38.1061 | − | 66.0017i | 0.595408 | − | 1.03128i | ||||
\(17\) | 3.45319 | + | 5.98111i | 0.0492660 | + | 0.0853312i | 0.889607 | − | 0.456727i | \(-0.150978\pi\) |
−0.840341 | + | 0.542058i | \(0.817645\pi\) | |||||||
\(18\) | 23.6685 | + | 40.9951i | 0.309929 | + | 0.536813i | ||||
\(19\) | −14.7296 | + | 25.5125i | −0.177853 | + | 0.308051i | −0.941145 | − | 0.338003i | \(-0.890249\pi\) |
0.763292 | + | 0.646054i | \(0.223582\pi\) | |||||||
\(20\) | −62.7849 | −0.701956 | ||||||||
\(21\) | 47.5174 | + | 51.5299i | 0.493768 | + | 0.535464i | ||||
\(22\) | −245.294 | −2.37713 | ||||||||
\(23\) | 11.5000 | − | 19.9186i | 0.104257 | − | 0.180579i | ||||
\(24\) | −14.5140 | − | 25.1390i | −0.123444 | − | 0.213812i | ||||
\(25\) | 6.75608 | + | 11.7019i | 0.0540486 | + | 0.0936150i | ||||
\(26\) | −60.0094 | + | 103.939i | −0.452647 | + | 0.784007i | ||||
\(27\) | 150.162 | 1.07032 | ||||||||
\(28\) | −74.6547 | − | 80.9588i | −0.503872 | − | 0.546420i | ||||
\(29\) | −89.9938 | −0.576256 | −0.288128 | − | 0.957592i | \(-0.593033\pi\) | ||||
−0.288128 | + | 0.957592i | \(0.593033\pi\) | |||||||
\(30\) | −74.6188 | + | 129.244i | −0.454116 | + | 0.786552i | ||||
\(31\) | −104.152 | − | 180.396i | −0.603425 | − | 1.04516i | −0.992298 | − | 0.123872i | \(-0.960469\pi\) |
0.388873 | − | 0.921291i | \(-0.372864\pi\) | |||||||
\(32\) | 111.627 | + | 193.343i | 0.616657 | + | 1.06808i | ||||
\(33\) | −124.298 | + | 215.291i | −0.655682 | + | 1.13567i | ||||
\(34\) | −25.7917 | −0.130095 | ||||||||
\(35\) | 58.2168 | − | 186.685i | 0.281155 | − | 0.901584i | ||||
\(36\) | −75.3726 | −0.348947 | ||||||||
\(37\) | −166.574 | + | 288.515i | −0.740126 | + | 1.28194i | 0.212312 | + | 0.977202i | \(0.431901\pi\) |
−0.952438 | + | 0.304733i | \(0.901433\pi\) | |||||||
\(38\) | −55.0073 | − | 95.2754i | −0.234825 | − | 0.406729i | ||||
\(39\) | 60.8174 | + | 105.339i | 0.249707 | + | 0.432505i | ||||
\(40\) | −40.4916 | + | 70.1336i | −0.160057 | + | 0.277227i | ||||
\(41\) | −309.362 | −1.17839 | −0.589197 | − | 0.807989i | \(-0.700556\pi\) | ||||
−0.589197 | + | 0.807989i | \(0.700556\pi\) | |||||||
\(42\) | −255.381 | + | 57.4596i | −0.938241 | + | 0.211100i | ||||
\(43\) | 251.681 | 0.892583 | 0.446291 | − | 0.894888i | \(-0.352745\pi\) | ||||
0.446291 | + | 0.894888i | \(0.352745\pi\) | |||||||
\(44\) | 195.285 | − | 338.244i | 0.669099 | − | 1.15891i | ||||
\(45\) | −66.9201 | − | 115.909i | −0.221686 | − | 0.383971i | ||||
\(46\) | 42.9463 | + | 74.3852i | 0.137654 | + | 0.238424i | ||||
\(47\) | −26.9415 | + | 46.6640i | −0.0836131 | + | 0.144822i | −0.904799 | − | 0.425838i | \(-0.859979\pi\) |
0.821186 | + | 0.570660i | \(0.193313\pi\) | |||||||
\(48\) | 288.444 | 0.867360 | ||||||||
\(49\) | 309.946 | − | 146.910i | 0.903632 | − | 0.428309i | ||||
\(50\) | −50.4607 | −0.142724 | ||||||||
\(51\) | −13.0694 | + | 22.6370i | −0.0358841 | + | 0.0621531i | ||||
\(52\) | −95.5504 | − | 165.498i | −0.254816 | − | 0.441355i | ||||
\(53\) | 165.232 | + | 286.190i | 0.428232 | + | 0.741720i | 0.996716 | − | 0.0809742i | \(-0.0258031\pi\) |
−0.568484 | + | 0.822694i | \(0.692470\pi\) | |||||||
\(54\) | −280.388 | + | 485.646i | −0.706592 | + | 1.22385i | ||||
\(55\) | 693.540 | 1.70031 | ||||||||
\(56\) | −138.581 | + | 31.1802i | −0.330692 | + | 0.0744042i | ||||
\(57\) | −111.496 | −0.259087 | ||||||||
\(58\) | 168.039 | − | 291.053i | 0.380425 | − | 0.658915i | ||||
\(59\) | 106.027 | + | 183.645i | 0.233959 | + | 0.405229i | 0.958970 | − | 0.283509i | \(-0.0914985\pi\) |
−0.725011 | + | 0.688738i | \(0.758165\pi\) | |||||||
\(60\) | −118.812 | − | 205.789i | −0.255643 | − | 0.442787i | ||||
\(61\) | 181.518 | − | 314.398i | 0.380999 | − | 0.659910i | −0.610206 | − | 0.792243i | \(-0.708913\pi\) |
0.991205 | + | 0.132332i | \(0.0422466\pi\) | |||||||
\(62\) | 777.901 | 1.59344 | ||||||||
\(63\) | 69.8887 | − | 224.113i | 0.139764 | − | 0.448184i | ||||
\(64\) | −224.035 | −0.437569 | ||||||||
\(65\) | 169.670 | − | 293.877i | 0.323769 | − | 0.560784i | ||||
\(66\) | −464.187 | − | 803.995i | −0.865719 | − | 1.49947i | ||||
\(67\) | −109.534 | − | 189.718i | −0.199726 | − | 0.345936i | 0.748713 | − | 0.662894i | \(-0.230672\pi\) |
−0.948440 | + | 0.316958i | \(0.897339\pi\) | |||||||
\(68\) | 20.5335 | − | 35.5650i | 0.0366183 | − | 0.0634248i | ||||
\(69\) | 87.0491 | 0.151877 | ||||||||
\(70\) | 495.060 | + | 536.865i | 0.845300 | + | 0.916680i | ||||
\(71\) | 591.325 | 0.988413 | 0.494207 | − | 0.869344i | \(-0.335459\pi\) | ||||
0.494207 | + | 0.869344i | \(0.335459\pi\) | |||||||
\(72\) | −48.6098 | + | 84.1947i | −0.0795656 | + | 0.137812i | ||||
\(73\) | −509.826 | − | 883.044i | −0.817405 | − | 1.41579i | −0.907588 | − | 0.419862i | \(-0.862078\pi\) |
0.0901826 | − | 0.995925i | \(-0.471255\pi\) | |||||||
\(74\) | −622.066 | − | 1077.45i | −0.977212 | − | 1.69258i | ||||
\(75\) | −25.5700 | + | 44.2886i | −0.0393676 | + | 0.0681867i | ||||
\(76\) | 175.171 | 0.264389 | ||||||||
\(77\) | 824.658 | + | 894.295i | 1.22050 | + | 1.32356i | ||||
\(78\) | −454.241 | −0.659392 | ||||||||
\(79\) | −168.304 | + | 291.510i | −0.239692 | + | 0.415158i | −0.960626 | − | 0.277846i | \(-0.910380\pi\) |
0.720934 | + | 0.693004i | \(0.243713\pi\) | |||||||
\(80\) | −402.354 | − | 696.898i | −0.562307 | − | 0.973944i | ||||
\(81\) | 113.041 | + | 195.793i | 0.155063 | + | 0.268577i | ||||
\(82\) | 577.650 | − | 1000.52i | 0.777936 | − | 1.34743i | ||||
\(83\) | −415.472 | −0.549446 | −0.274723 | − | 0.961523i | \(-0.588586\pi\) | ||||
−0.274723 | + | 0.961523i | \(0.588586\pi\) | |||||||
\(84\) | 124.083 | − | 397.899i | 0.161173 | − | 0.516837i | ||||
\(85\) | 72.9230 | 0.0930542 | ||||||||
\(86\) | −469.948 | + | 813.973i | −0.589253 | + | 1.02062i | ||||
\(87\) | −170.302 | − | 294.971i | −0.209865 | − | 0.363497i | ||||
\(88\) | −251.889 | − | 436.285i | −0.305130 | − | 0.528501i | ||||
\(89\) | −300.116 | + | 519.817i | −0.357441 | + | 0.619107i | −0.987533 | − | 0.157414i | \(-0.949684\pi\) |
0.630091 | + | 0.776521i | \(0.283017\pi\) | |||||||
\(90\) | 499.821 | 0.585397 | ||||||||
\(91\) | 580.690 | − | 130.653i | 0.668933 | − | 0.150507i | ||||
\(92\) | −136.763 | −0.154984 | ||||||||
\(93\) | 394.187 | − | 682.752i | 0.439519 | − | 0.761270i | ||||
\(94\) | −100.612 | − | 174.265i | −0.110397 | − | 0.191213i | ||||
\(95\) | 155.527 | + | 269.381i | 0.167966 | + | 0.290925i | ||||
\(96\) | −422.479 | + | 731.755i | −0.449157 | + | 0.777963i | ||||
\(97\) | 612.267 | 0.640889 | 0.320445 | − | 0.947267i | \(-0.396168\pi\) | ||||
0.320445 | + | 0.947267i | \(0.396168\pi\) | |||||||
\(98\) | −103.613 | + | 1276.72i | −0.106801 | + | 1.31601i | ||||
\(99\) | 832.588 | 0.845235 | ||||||||
\(100\) | 40.1732 | − | 69.5819i | 0.0401732 | − | 0.0695819i | ||||
\(101\) | 436.405 | + | 755.876i | 0.429940 | + | 0.744678i | 0.996867 | − | 0.0790898i | \(-0.0252014\pi\) |
−0.566928 | + | 0.823768i | \(0.691868\pi\) | |||||||
\(102\) | −48.8074 | − | 84.5369i | −0.0473789 | − | 0.0820627i | ||||
\(103\) | 961.229 | − | 1664.90i | 0.919541 | − | 1.59269i | 0.119427 | − | 0.992843i | \(-0.461894\pi\) |
0.800114 | − | 0.599848i | \(-0.204772\pi\) | |||||||
\(104\) | −246.492 | −0.232409 | ||||||||
\(105\) | 722.061 | − | 162.461i | 0.671104 | − | 0.150995i | ||||
\(106\) | −1234.10 | −1.13082 | ||||||||
\(107\) | −123.633 | + | 214.138i | −0.111701 | + | 0.193472i | −0.916456 | − | 0.400135i | \(-0.868963\pi\) |
0.804755 | + | 0.593607i | \(0.202297\pi\) | |||||||
\(108\) | −446.450 | − | 773.273i | −0.397774 | − | 0.688965i | ||||
\(109\) | 50.7507 | + | 87.9028i | 0.0445967 | + | 0.0772437i | 0.887462 | − | 0.460881i | \(-0.152466\pi\) |
−0.842865 | + | 0.538124i | \(0.819133\pi\) | |||||||
\(110\) | −1295.00 | + | 2243.01i | −1.12249 | + | 1.94420i | ||||
\(111\) | −1260.88 | −1.07818 | ||||||||
\(112\) | 420.203 | − | 1347.47i | 0.354513 | − | 1.13682i | ||||
\(113\) | −1652.92 | −1.37605 | −0.688026 | − | 0.725686i | \(-0.741522\pi\) | ||||
−0.688026 | + | 0.725686i | \(0.741522\pi\) | |||||||
\(114\) | 208.188 | − | 360.593i | 0.171041 | − | 0.296251i | ||||
\(115\) | −121.426 | − | 210.316i | −0.0984611 | − | 0.170540i | ||||
\(116\) | 267.562 | + | 463.430i | 0.214159 | + | 0.370935i | ||||
\(117\) | 203.687 | − | 352.796i | 0.160948 | − | 0.278770i | ||||
\(118\) | −791.910 | −0.617807 | ||||||||
\(119\) | 86.7095 | + | 94.0315i | 0.0667954 | + | 0.0724358i | ||||
\(120\) | −306.501 | −0.233163 | ||||||||
\(121\) | −1491.68 | + | 2583.66i | −1.12072 | + | 1.94114i | ||||
\(122\) | 677.872 | + | 1174.11i | 0.503046 | + | 0.871301i | ||||
\(123\) | −585.427 | − | 1013.99i | −0.429156 | − | 0.743320i | ||||
\(124\) | −619.309 | + | 1072.67i | −0.448512 | + | 0.776846i | ||||
\(125\) | 1462.52 | 1.04649 | ||||||||
\(126\) | 594.315 | + | 644.501i | 0.420205 | + | 0.455688i | ||||
\(127\) | −1617.35 | −1.13005 | −0.565026 | − | 0.825073i | \(-0.691134\pi\) | ||||
−0.565026 | + | 0.825073i | \(0.691134\pi\) | |||||||
\(128\) | −474.689 | + | 822.185i | −0.327789 | + | 0.567747i | ||||
\(129\) | 476.275 | + | 824.932i | 0.325067 | + | 0.563033i | ||||
\(130\) | 633.626 | + | 1097.47i | 0.427482 | + | 0.740421i | ||||
\(131\) | −1097.18 | + | 1900.37i | −0.731765 | + | 1.26745i | 0.224363 | + | 0.974506i | \(0.427970\pi\) |
−0.956128 | + | 0.292949i | \(0.905364\pi\) | |||||||
\(132\) | 1478.21 | 0.974708 | ||||||||
\(133\) | −162.426 | + | 520.855i | −0.105896 | + | 0.339578i | ||||
\(134\) | 818.098 | 0.527410 | ||||||||
\(135\) | 792.766 | − | 1373.11i | 0.505411 | − | 0.875397i | ||||
\(136\) | −26.4851 | − | 45.8736i | −0.0166991 | − | 0.0289238i | ||||
\(137\) | −1087.44 | − | 1883.50i | −0.678149 | − | 1.17459i | −0.975538 | − | 0.219831i | \(-0.929449\pi\) |
0.297389 | − | 0.954756i | \(-0.403884\pi\) | |||||||
\(138\) | −162.541 | + | 281.529i | −0.100264 | + | 0.173662i | ||||
\(139\) | −342.050 | −0.208722 | −0.104361 | − | 0.994540i | \(-0.533280\pi\) | ||||
−0.104361 | + | 0.994540i | \(0.533280\pi\) | |||||||
\(140\) | −1134.43 | + | 255.242i | −0.684836 | + | 0.154085i | ||||
\(141\) | −203.933 | −0.121803 | ||||||||
\(142\) | −1104.14 | + | 1912.43i | −0.652517 | + | 1.13019i | ||||
\(143\) | 1055.48 | + | 1828.14i | 0.617227 | + | 1.06907i | ||||
\(144\) | −483.022 | − | 836.619i | −0.279527 | − | 0.484155i | ||||
\(145\) | −475.112 | + | 822.919i | −0.272110 | + | 0.471308i | ||||
\(146\) | 3807.85 | 2.15849 | ||||||||
\(147\) | 1068.06 | + | 737.896i | 0.599265 | + | 0.414018i | ||||
\(148\) | 1980.98 | 1.10024 | ||||||||
\(149\) | 379.214 | − | 656.817i | 0.208499 | − | 0.361131i | −0.742743 | − | 0.669577i | \(-0.766475\pi\) |
0.951242 | + | 0.308446i | \(0.0998088\pi\) | |||||||
\(150\) | −95.4904 | − | 165.394i | −0.0519784 | − | 0.0900292i | ||||
\(151\) | −1512.38 | − | 2619.52i | −0.815071 | − | 1.41174i | −0.909277 | − | 0.416191i | \(-0.863365\pi\) |
0.0942065 | − | 0.995553i | \(-0.469969\pi\) | |||||||
\(152\) | 112.973 | − | 195.674i | 0.0602848 | − | 0.104416i | ||||
\(153\) | 87.5434 | 0.0462579 | ||||||||
\(154\) | −4432.10 | + | 997.204i | −2.31915 | + | 0.521798i | ||||
\(155\) | −2199.43 | −1.13976 | ||||||||
\(156\) | 361.634 | − | 626.368i | 0.185602 | − | 0.321472i | ||||
\(157\) | −1684.65 | − | 2917.91i | −0.856370 | − | 1.48328i | −0.875368 | − | 0.483457i | \(-0.839381\pi\) |
0.0189983 | − | 0.999820i | \(-0.493952\pi\) | |||||||
\(158\) | −628.524 | − | 1088.63i | −0.316473 | − | 0.548146i | ||||
\(159\) | −625.360 | + | 1083.15i | −0.311913 | + | 0.540250i | ||||
\(160\) | 2357.29 | 1.16475 | ||||||||
\(161\) | 126.813 | − | 406.652i | 0.0620759 | − | 0.199060i | ||||
\(162\) | −844.295 | −0.409469 | ||||||||
\(163\) | 2047.38 | − | 3546.16i | 0.983821 | − | 1.70403i | 0.336760 | − | 0.941590i | \(-0.390669\pi\) |
0.647061 | − | 0.762438i | \(-0.275998\pi\) | |||||||
\(164\) | 919.767 | + | 1593.08i | 0.437937 | + | 0.758530i | ||||
\(165\) | 1312.44 | + | 2273.21i | 0.619230 | + | 1.07254i | ||||
\(166\) | 775.783 | − | 1343.70i | 0.362725 | − | 0.628259i | ||||
\(167\) | 487.681 | 0.225975 | 0.112988 | − | 0.993596i | \(-0.463958\pi\) | ||||
0.112988 | + | 0.993596i | \(0.463958\pi\) | |||||||
\(168\) | −364.447 | − | 395.222i | −0.167367 | − | 0.181500i | ||||
\(169\) | −1164.14 | −0.529876 | ||||||||
\(170\) | −136.164 | + | 235.843i | −0.0614313 | + | 0.106402i | ||||
\(171\) | 186.709 | + | 323.389i | 0.0834969 | + | 0.144621i | ||||
\(172\) | −748.277 | − | 1296.05i | −0.331718 | − | 0.574553i | ||||
\(173\) | 1323.85 | − | 2292.98i | 0.581795 | − | 1.00770i | −0.413471 | − | 0.910517i | \(-0.635684\pi\) |
0.995267 | − | 0.0971820i | \(-0.0309829\pi\) | |||||||
\(174\) | 1271.97 | 0.554183 | ||||||||
\(175\) | 169.645 | + | 183.970i | 0.0732797 | + | 0.0794677i | ||||
\(176\) | 5005.90 | 2.14394 | ||||||||
\(177\) | −401.286 | + | 695.048i | −0.170410 | + | 0.295158i | ||||
\(178\) | −1120.77 | − | 1941.24i | −0.471942 | − | 0.817427i | ||||
\(179\) | −135.500 | − | 234.693i | −0.0565796 | − | 0.0979988i | 0.836348 | − | 0.548198i | \(-0.184686\pi\) |
−0.892928 | + | 0.450200i | \(0.851353\pi\) | |||||||
\(180\) | −397.922 | + | 689.220i | −0.164774 | + | 0.285397i | ||||
\(181\) | 4414.00 | 1.81265 | 0.906327 | − | 0.422577i | \(-0.138874\pi\) | ||||
0.906327 | + | 0.422577i | \(0.138874\pi\) | |||||||
\(182\) | −661.734 | + | 2121.99i | −0.269511 | + | 0.864245i | ||||
\(183\) | 1374.00 | 0.555020 | ||||||||
\(184\) | −88.2022 | + | 152.771i | −0.0353389 | + | 0.0612087i | ||||
\(185\) | 1758.82 | + | 3046.37i | 0.698979 | + | 1.21067i | ||||
\(186\) | 1472.08 | + | 2549.71i | 0.580312 | + | 1.00513i | ||||
\(187\) | −226.819 | + | 392.861i | −0.0886985 | + | 0.153630i | ||||
\(188\) | 320.400 | 0.124296 | ||||||||
\(189\) | 2713.22 | − | 610.462i | 1.04422 | − | 0.234945i | ||||
\(190\) | −1161.62 | −0.443541 | ||||||||
\(191\) | 591.727 | − | 1024.90i | 0.224167 | − | 0.388268i | −0.731902 | − | 0.681409i | \(-0.761367\pi\) |
0.956069 | + | 0.293141i | \(0.0947007\pi\) | |||||||
\(192\) | −423.958 | − | 734.317i | −0.159357 | − | 0.276014i | ||||
\(193\) | −555.607 | − | 962.340i | −0.207220 | − | 0.358916i | 0.743618 | − | 0.668605i | \(-0.233108\pi\) |
−0.950838 | + | 0.309689i | \(0.899775\pi\) | |||||||
\(194\) | −1143.24 | + | 1980.16i | −0.423093 | + | 0.732819i | ||||
\(195\) | 1284.31 | 0.471650 | ||||||||
\(196\) | −1678.03 | − | 1159.31i | −0.611526 | − | 0.422490i | ||||
\(197\) | −4927.09 | −1.78193 | −0.890967 | − | 0.454068i | \(-0.849972\pi\) | ||||
−0.890967 | + | 0.454068i | \(0.849972\pi\) | |||||||
\(198\) | −1554.64 | + | 2692.71i | −0.557996 | + | 0.966477i | ||||
\(199\) | −1240.22 | − | 2148.12i | −0.441793 | − | 0.765207i | 0.556030 | − | 0.831162i | \(-0.312324\pi\) |
−0.997823 | + | 0.0659549i | \(0.978991\pi\) | |||||||
\(200\) | −51.8175 | − | 89.7505i | −0.0183202 | − | 0.0317316i | ||||
\(201\) | 414.556 | − | 718.033i | 0.145475 | − | 0.251971i | ||||
\(202\) | −3259.48 | −1.13533 | ||||||||
\(203\) | −1626.06 | + | 365.856i | −0.562202 | + | 0.126493i | ||||
\(204\) | 155.428 | 0.0533437 | ||||||||
\(205\) | −1633.24 | + | 2828.86i | −0.556442 | + | 0.963785i | ||||
\(206\) | 3589.67 | + | 6217.50i | 1.21410 | + | 2.10288i | ||||
\(207\) | −145.771 | − | 252.482i | −0.0489457 | − | 0.0847765i | ||||
\(208\) | 1224.66 | − | 2121.17i | 0.408245 | − | 0.707101i | ||||
\(209\) | −1934.99 | −0.640413 | ||||||||
\(210\) | −822.835 | + | 2638.60i | −0.270386 | + | 0.867050i | ||||
\(211\) | −2729.88 | −0.890676 | −0.445338 | − | 0.895362i | \(-0.646917\pi\) | ||||
−0.445338 | + | 0.895362i | \(0.646917\pi\) | |||||||
\(212\) | 982.504 | − | 1701.75i | 0.318296 | − | 0.551304i | ||||
\(213\) | 1119.01 | + | 1938.18i | 0.359967 | + | 0.623482i | ||||
\(214\) | −461.702 | − | 799.691i | −0.147483 | − | 0.255448i | ||||
\(215\) | 1328.72 | − | 2301.42i | 0.421480 | − | 0.730025i | ||||
\(216\) | −1151.71 | −0.362796 | ||||||||
\(217\) | −2615.24 | − | 2836.08i | −0.818130 | − | 0.887215i | ||||
\(218\) | −379.053 | −0.117765 | ||||||||
\(219\) | 1929.56 | − | 3342.09i | 0.595377 | − | 1.03122i | ||||
\(220\) | −2061.97 | − | 3571.44i | −0.631901 | − | 1.09448i | ||||
\(221\) | 110.979 | + | 192.222i | 0.0337795 | + | 0.0585079i | ||||
\(222\) | 2354.36 | − | 4077.87i | 0.711776 | − | 1.23283i | ||||
\(223\) | 4010.07 | 1.20419 | 0.602094 | − | 0.798425i | \(-0.294333\pi\) | ||||
0.602094 | + | 0.798425i | \(0.294333\pi\) | |||||||
\(224\) | 2802.95 | + | 3039.64i | 0.836070 | + | 0.906670i | ||||
\(225\) | 171.276 | 0.0507485 | ||||||||
\(226\) | 3086.39 | − | 5345.78i | 0.908423 | − | 1.57343i | ||||
\(227\) | −2416.92 | − | 4186.23i | −0.706681 | − | 1.22401i | −0.966081 | − | 0.258238i | \(-0.916858\pi\) |
0.259400 | − | 0.965770i | \(-0.416475\pi\) | |||||||
\(228\) | 331.489 | + | 574.156i | 0.0962869 | + | 0.166774i | ||||
\(229\) | −2718.97 | + | 4709.39i | −0.784605 | + | 1.35898i | 0.144630 | + | 0.989486i | \(0.453801\pi\) |
−0.929235 | + | 0.369490i | \(0.879532\pi\) | |||||||
\(230\) | 906.922 | 0.260003 | ||||||||
\(231\) | −1370.66 | + | 4395.31i | −0.390401 | + | 1.25190i | ||||
\(232\) | 690.231 | 0.195327 | ||||||||
\(233\) | 2059.93 | − | 3567.90i | 0.579186 | − | 1.00318i | −0.416387 | − | 0.909187i | \(-0.636704\pi\) |
0.995573 | − | 0.0939917i | \(-0.0299627\pi\) | |||||||
\(234\) | 760.662 | + | 1317.51i | 0.212505 | + | 0.368069i | ||||
\(235\) | 284.469 | + | 492.715i | 0.0789647 | + | 0.136771i | ||||
\(236\) | 630.462 | − | 1091.99i | 0.173896 | − | 0.301198i | ||||
\(237\) | −1273.97 | −0.349170 | ||||||||
\(238\) | −466.018 | + | 104.852i | −0.126922 | + | 0.0285569i | ||||
\(239\) | −599.850 | −0.162348 | −0.0811738 | − | 0.996700i | \(-0.525867\pi\) | ||||
−0.0811738 | + | 0.996700i | \(0.525867\pi\) | |||||||
\(240\) | 1522.81 | − | 2637.58i | 0.409570 | − | 0.709396i | ||||
\(241\) | 1191.55 | + | 2063.83i | 0.318484 | + | 0.551631i | 0.980172 | − | 0.198148i | \(-0.0634928\pi\) |
−0.661688 | + | 0.749780i | \(0.730159\pi\) | |||||||
\(242\) | −5570.61 | − | 9648.59i | −1.47972 | − | 2.56295i | ||||
\(243\) | 1599.36 | − | 2770.18i | 0.422218 | − | 0.731304i | ||||
\(244\) | −2158.69 | −0.566377 | ||||||||
\(245\) | 292.955 | − | 3609.79i | 0.0763928 | − | 0.941311i | ||||
\(246\) | 4372.52 | 1.13326 | ||||||||
\(247\) | −473.383 | + | 819.924i | −0.121946 | + | 0.211217i | ||||
\(248\) | 798.817 | + | 1383.59i | 0.204536 | + | 0.354267i | ||||
\(249\) | −786.228 | − | 1361.79i | −0.200101 | − | 0.346585i | ||||
\(250\) | −2730.86 | + | 4729.99i | −0.690860 | + | 1.19660i | ||||
\(251\) | −3857.12 | −0.969956 | −0.484978 | − | 0.874526i | \(-0.661172\pi\) | ||||
−0.484978 | + | 0.874526i | \(0.661172\pi\) | |||||||
\(252\) | −1361.88 | + | 306.416i | −0.340437 | + | 0.0765968i | ||||
\(253\) | 1510.73 | 0.375409 | ||||||||
\(254\) | 3019.97 | − | 5230.74i | 0.746022 | − | 1.29215i | ||||
\(255\) | 137.997 | + | 239.019i | 0.0338892 | + | 0.0586977i | ||||
\(256\) | −2668.85 | − | 4622.58i | −0.651575 | − | 1.12856i | ||||
\(257\) | −2417.01 | + | 4186.39i | −0.586650 | + | 1.01611i | 0.408018 | + | 0.912974i | \(0.366220\pi\) |
−0.994668 | + | 0.103133i | \(0.967113\pi\) | |||||||
\(258\) | −3557.26 | −0.858393 | ||||||||
\(259\) | −1836.84 | + | 5890.24i | −0.440679 | + | 1.41313i | ||||
\(260\) | −2017.79 | −0.481300 | ||||||||
\(261\) | −570.368 | + | 987.906i | −0.135268 | + | 0.234291i | ||||
\(262\) | −4097.39 | − | 7096.88i | −0.966173 | − | 1.67346i | ||||
\(263\) | −263.698 | − | 456.738i | −0.0618262 | − | 0.107086i | 0.833456 | − | 0.552587i | \(-0.186359\pi\) |
−0.895282 | + | 0.445500i | \(0.853026\pi\) | |||||||
\(264\) | 953.336 | − | 1651.23i | 0.222249 | − | 0.384947i | ||||
\(265\) | 3489.29 | 0.808850 | ||||||||
\(266\) | −1381.23 | − | 1497.87i | −0.318378 | − | 0.345263i | ||||
\(267\) | −2271.73 | −0.520702 | ||||||||
\(268\) | −651.311 | + | 1128.10i | −0.148452 | + | 0.257126i | ||||
\(269\) | 130.674 | + | 226.334i | 0.0296184 | + | 0.0513005i | 0.880455 | − | 0.474130i | \(-0.157237\pi\) |
−0.850836 | + | 0.525431i | \(0.823904\pi\) | |||||||
\(270\) | 2960.56 | + | 5127.83i | 0.667310 | + | 1.15581i | ||||
\(271\) | −1368.85 | + | 2370.92i | −0.306833 | + | 0.531450i | −0.977668 | − | 0.210157i | \(-0.932603\pi\) |
0.670835 | + | 0.741607i | \(0.265936\pi\) | |||||||
\(272\) | 526.351 | 0.117334 | ||||||||
\(273\) | 1527.12 | + | 1656.08i | 0.338555 | + | 0.367144i | ||||
\(274\) | 8122.02 | 1.79076 | ||||||||
\(275\) | −443.765 | + | 768.623i | −0.0973091 | + | 0.168544i | ||||
\(276\) | −258.807 | − | 448.266i | −0.0564432 | − | 0.0977625i | ||||
\(277\) | 2049.83 | + | 3550.41i | 0.444629 | + | 0.770120i | 0.998026 | − | 0.0627972i | \(-0.0200021\pi\) |
−0.553397 | + | 0.832918i | \(0.686669\pi\) | |||||||
\(278\) | 638.687 | − | 1106.24i | 0.137791 | − | 0.238661i | ||||
\(279\) | −2640.39 | −0.566581 | ||||||||
\(280\) | −446.508 | + | 1431.83i | −0.0952999 | + | 0.305600i | ||||
\(281\) | 1600.73 | 0.339828 | 0.169914 | − | 0.985459i | \(-0.445651\pi\) | ||||
0.169914 | + | 0.985459i | \(0.445651\pi\) | |||||||
\(282\) | 380.790 | − | 659.548i | 0.0804104 | − | 0.139275i | ||||
\(283\) | 2903.21 | + | 5028.51i | 0.609816 | + | 1.05623i | 0.991270 | + | 0.131845i | \(0.0420901\pi\) |
−0.381454 | + | 0.924388i | \(0.624577\pi\) | |||||||
\(284\) | −1758.07 | − | 3045.07i | −0.367333 | − | 0.636239i | ||||
\(285\) | −588.630 | + | 1019.54i | −0.122342 | + | 0.211902i | ||||
\(286\) | −7883.29 | −1.62989 | ||||||||
\(287\) | −5589.72 | + | 1257.66i | −1.14965 | + | 0.258667i | ||||
\(288\) | 2829.90 | 0.579005 | ||||||||
\(289\) | 2432.65 | − | 4213.47i | 0.495146 | − | 0.857618i | ||||
\(290\) | −1774.29 | − | 3073.16i | −0.359276 | − | 0.622284i | ||||
\(291\) | 1158.64 | + | 2006.82i | 0.233404 | + | 0.404267i | ||||
\(292\) | −3031.54 | + | 5250.78i | −0.607559 | + | 1.05232i | ||||
\(293\) | 727.432 | 0.145041 | 0.0725205 | − | 0.997367i | \(-0.476896\pi\) | ||||
0.0725205 | + | 0.997367i | \(0.476896\pi\) | |||||||
\(294\) | −4380.77 | + | 2076.42i | −0.869020 | + | 0.411903i | ||||
\(295\) | 2239.04 | 0.441904 | ||||||||
\(296\) | 1277.58 | − | 2212.84i | 0.250872 | − | 0.434523i | ||||
\(297\) | 4931.61 | + | 8541.81i | 0.963506 | + | 1.66884i | ||||
\(298\) | 1416.16 | + | 2452.86i | 0.275288 | + | 0.476813i | ||||
\(299\) | 369.589 | − | 640.147i | 0.0714845 | − | 0.123815i | ||||
\(300\) | 304.090 | 0.0585222 | ||||||||
\(301\) | 4547.52 | − | 1023.17i | 0.870813 | − | 0.195929i | ||||
\(302\) | 11295.9 | 2.15233 | ||||||||
\(303\) | −1651.68 | + | 2860.80i | −0.313157 | + | 0.542404i | ||||
\(304\) | 1122.58 | + | 1944.36i | 0.211790 | + | 0.366832i | ||||
\(305\) | −1916.61 | − | 3319.66i | −0.359818 | − | 0.623223i | ||||
\(306\) | −163.464 | + | 283.128i | −0.0305379 | + | 0.0528932i | ||||
\(307\) | −6262.33 | −1.16420 | −0.582101 | − | 0.813117i | \(-0.697769\pi\) | ||||
−0.582101 | + | 0.813117i | \(0.697769\pi\) | |||||||
\(308\) | 2153.44 | − | 6905.48i | 0.398389 | − | 1.27752i | ||||
\(309\) | 7276.01 | 1.33954 | ||||||||
\(310\) | 4106.84 | − | 7113.26i | 0.752429 | − | 1.30324i | ||||
\(311\) | 2839.84 | + | 4918.75i | 0.517790 | + | 0.896839i | 0.999786 | + | 0.0206654i | \(0.00657847\pi\) |
−0.481996 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(312\) | −466.454 | − | 807.923i | −0.0846403 | − | 0.146601i | ||||
\(313\) | 581.100 | − | 1006.49i | 0.104938 | − | 0.181758i | −0.808775 | − | 0.588119i | \(-0.799869\pi\) |
0.913713 | + | 0.406360i | \(0.133202\pi\) | |||||||
\(314\) | 12582.6 | 2.26139 | ||||||||
\(315\) | −1680.36 | − | 1822.25i | −0.300564 | − | 0.325944i | ||||
\(316\) | 2001.54 | 0.356315 | ||||||||
\(317\) | −3871.48 | + | 6705.61i | −0.685944 | + | 1.18809i | 0.287195 | + | 0.957872i | \(0.407277\pi\) |
−0.973139 | + | 0.230218i | \(0.926056\pi\) | |||||||
\(318\) | −2335.38 | − | 4045.00i | −0.411829 | − | 0.713310i | ||||
\(319\) | −2955.56 | − | 5119.19i | −0.518746 | − | 0.898494i | ||||
\(320\) | −1182.77 | + | 2048.62i | −0.206621 | + | 0.357879i | ||||
\(321\) | −935.836 | −0.162721 | ||||||||
\(322\) | 1078.38 | + | 1169.44i | 0.186633 | + | 0.202393i | ||||
\(323\) | −203.457 | −0.0350485 | ||||||||
\(324\) | 672.167 | − | 1164.23i | 0.115255 | − | 0.199627i | ||||
\(325\) | 217.128 | + | 376.077i | 0.0370588 | + | 0.0641876i | ||||
\(326\) | 7645.85 | + | 13243.0i | 1.29897 | + | 2.24988i | ||||
\(327\) | −192.078 | + | 332.690i | −0.0324831 | + | 0.0562623i | ||||
\(328\) | 2372.73 | 0.399427 | ||||||||
\(329\) | −297.088 | + | 952.677i | −0.0497842 | + | 0.159644i | ||||
\(330\) | −9802.49 | −1.63518 | ||||||||
\(331\) | −3301.74 | + | 5718.78i | −0.548278 | + | 0.949645i | 0.450115 | + | 0.892971i | \(0.351383\pi\) |
−0.998393 | + | 0.0566743i | \(0.981950\pi\) | |||||||
\(332\) | 1235.24 | + | 2139.51i | 0.204195 | + | 0.353677i | ||||
\(333\) | 2111.45 | + | 3657.14i | 0.347468 | + | 0.601831i | ||||
\(334\) | −910.614 | + | 1577.23i | −0.149181 | + | 0.258390i | ||||
\(335\) | −2313.08 | −0.377245 | ||||||||
\(336\) | 5211.76 | − | 1172.62i | 0.846205 | − | 0.190392i | ||||
\(337\) | −5975.53 | −0.965898 | −0.482949 | − | 0.875648i | \(-0.660434\pi\) | ||||
−0.482949 | + | 0.875648i | \(0.660434\pi\) | |||||||
\(338\) | 2173.72 | − | 3764.99i | 0.349806 | − | 0.605883i | ||||
\(339\) | −3127.94 | − | 5417.76i | −0.501140 | − | 0.868000i | ||||
\(340\) | −216.808 | − | 375.523i | −0.0345826 | − | 0.0598988i | ||||
\(341\) | 6841.07 | − | 11849.1i | 1.08641 | − | 1.88171i | ||||
\(342\) | −1394.51 | −0.220487 | ||||||||
\(343\) | 5003.04 | − | 3914.49i | 0.787576 | − | 0.616217i | ||||
\(344\) | −1930.34 | −0.302549 | ||||||||
\(345\) | 459.566 | − | 795.992i | 0.0717166 | − | 0.124217i | ||||
\(346\) | 4943.88 | + | 8563.05i | 0.768163 | + | 1.33050i | ||||
\(347\) | −1867.29 | − | 3234.23i | −0.288879 | − | 0.500354i | 0.684663 | − | 0.728860i | \(-0.259949\pi\) |
−0.973543 | + | 0.228506i | \(0.926616\pi\) | |||||||
\(348\) | −1012.65 | + | 1753.96i | −0.155988 | + | 0.270179i | ||||
\(349\) | 4115.40 | 0.631210 | 0.315605 | − | 0.948891i | \(-0.397792\pi\) | ||||
0.315605 | + | 0.948891i | \(0.397792\pi\) | |||||||
\(350\) | −911.752 | + | 205.140i | −0.139243 | + | 0.0313292i | ||||
\(351\) | 4825.94 | 0.733874 | ||||||||
\(352\) | −7332.07 | + | 12699.5i | −1.11023 | + | 1.92297i | ||||
\(353\) | −2374.92 | − | 4113.48i | −0.358085 | − | 0.620222i | 0.629556 | − | 0.776955i | \(-0.283237\pi\) |
−0.987641 | + | 0.156734i | \(0.949904\pi\) | |||||||
\(354\) | −1498.59 | − | 2595.63i | −0.224997 | − | 0.389707i | ||||
\(355\) | 3121.83 | − | 5407.18i | 0.466732 | − | 0.808403i | ||||
\(356\) | 3569.12 | 0.531357 | ||||||||
\(357\) | −144.119 | + | 462.149i | −0.0213658 | + | 0.0685141i | ||||
\(358\) | 1012.04 | 0.149408 | ||||||||
\(359\) | −854.496 | + | 1480.03i | −0.125623 | + | 0.217585i | −0.921976 | − | 0.387247i | \(-0.873426\pi\) |
0.796353 | + | 0.604832i | \(0.206760\pi\) | |||||||
\(360\) | 513.261 | + | 888.993i | 0.0751422 | + | 0.130150i | ||||
\(361\) | 2995.58 | + | 5188.49i | 0.436737 | + | 0.756450i | ||||
\(362\) | −8241.97 | + | 14275.5i | −1.19665 | + | 2.07266i | ||||
\(363\) | −11291.2 | −1.63261 | ||||||||
\(364\) | −2399.26 | − | 2601.87i | −0.345483 | − | 0.374656i | ||||
\(365\) | −10766.3 | −1.54392 | ||||||||
\(366\) | −2565.57 | + | 4443.70i | −0.366406 | + | 0.634633i | ||||
\(367\) | −755.329 | − | 1308.27i | −0.107433 | − | 0.186079i | 0.807297 | − | 0.590146i | \(-0.200930\pi\) |
−0.914730 | + | 0.404067i | \(0.867596\pi\) | |||||||
\(368\) | −876.440 | − | 1518.04i | −0.124151 | − | 0.215036i | ||||
\(369\) | −1960.69 | + | 3396.02i | −0.276611 | + | 0.479104i | ||||
\(370\) | −13136.5 | −1.84577 | ||||||||
\(371\) | 4148.96 | + | 4499.31i | 0.580602 | + | 0.629630i | ||||
\(372\) | −4687.85 | −0.653370 | ||||||||
\(373\) | −6328.35 | + | 10961.0i | −0.878471 | + | 1.52156i | −0.0254526 | + | 0.999676i | \(0.508103\pi\) |
−0.853019 | + | 0.521881i | \(0.825231\pi\) | |||||||
\(374\) | −847.046 | − | 1467.13i | −0.117112 | − | 0.202843i | ||||
\(375\) | 2767.63 | + | 4793.68i | 0.381120 | + | 0.660118i | ||||
\(376\) | 206.634 | − | 357.901i | 0.0283414 | − | 0.0490887i | ||||
\(377\) | −2892.24 | −0.395113 | ||||||||
\(378\) | −3091.89 | + | 9914.81i | −0.420713 | + | 1.34911i | ||||
\(379\) | −9215.14 | −1.24894 | −0.624472 | − | 0.781047i | \(-0.714686\pi\) | ||||
−0.624472 | + | 0.781047i | \(0.714686\pi\) | |||||||
\(380\) | 924.798 | − | 1601.80i | 0.124845 | − | 0.216238i | ||||
\(381\) | −3060.63 | − | 5301.16i | −0.411550 | − | 0.712826i | ||||
\(382\) | 2209.78 | + | 3827.45i | 0.295975 | + | 0.512643i | ||||
\(383\) | 306.679 | − | 531.183i | 0.0409153 | − | 0.0708674i | −0.844843 | − | 0.535015i | \(-0.820306\pi\) |
0.885758 | + | 0.464148i | \(0.153639\pi\) | |||||||
\(384\) | −3593.15 | −0.477506 | ||||||||
\(385\) | 12531.3 | − | 2819.48i | 1.65884 | − | 0.373231i | ||||
\(386\) | 4149.79 | 0.547199 | ||||||||
\(387\) | 1595.12 | − | 2762.83i | 0.209521 | − | 0.362901i | ||||
\(388\) | −1820.34 | − | 3152.92i | −0.238179 | − | 0.412539i | ||||
\(389\) | −584.829 | − | 1012.95i | −0.0762263 | − | 0.132028i | 0.825393 | − | 0.564559i | \(-0.190954\pi\) |
−0.901619 | + | 0.432531i | \(0.857620\pi\) | |||||||
\(390\) | −2398.11 | + | 4153.65i | −0.311367 | + | 0.539304i | ||||
\(391\) | 158.847 | 0.0205453 | ||||||||
\(392\) | −2377.21 | + | 1126.76i | −0.306294 | + | 0.145179i | ||||
\(393\) | −8305.10 | −1.06600 | ||||||||
\(394\) | 9200.03 | − | 15934.9i | 1.17637 | − | 2.03754i | ||||
\(395\) | 1777.08 | + | 3077.99i | 0.226366 | + | 0.392078i | ||||
\(396\) | −2475.38 | − | 4287.48i | −0.314122 | − | 0.544076i | ||||
\(397\) | 3233.76 | − | 5601.04i | 0.408811 | − | 0.708081i | −0.585946 | − | 0.810350i | \(-0.699277\pi\) |
0.994757 | + | 0.102269i | \(0.0326103\pi\) | |||||||
\(398\) | 9263.10 | 1.16663 | ||||||||
\(399\) | −2014.57 | + | 453.269i | −0.252768 | + | 0.0568718i | ||||
\(400\) | 1029.79 | 0.128724 | ||||||||
\(401\) | −84.7378 | + | 146.770i | −0.0105526 | + | 0.0182777i | −0.871253 | − | 0.490833i | \(-0.836692\pi\) |
0.860701 | + | 0.509111i | \(0.170026\pi\) | |||||||
\(402\) | 1548.15 | + | 2681.47i | 0.192076 | + | 0.332685i | ||||
\(403\) | −3347.24 | − | 5797.59i | −0.413742 | − | 0.716622i | ||||
\(404\) | 2594.96 | − | 4494.61i | 0.319565 | − | 0.553503i | ||||
\(405\) | 2387.15 | 0.292885 | ||||||||
\(406\) | 1853.00 | − | 5942.04i | 0.226509 | − | 0.726351i | ||||
\(407\) | −21882.4 | −2.66504 | ||||||||
\(408\) | 100.239 | − | 173.620i | 0.0121632 | − | 0.0210673i | ||||
\(409\) | 3294.12 | + | 5705.59i | 0.398249 | + | 0.689788i | 0.993510 | − | 0.113745i | \(-0.0362846\pi\) |
−0.595261 | + | 0.803533i | \(0.702951\pi\) | |||||||
\(410\) | −6099.28 | − | 10564.3i | −0.734688 | − | 1.27252i | ||||
\(411\) | 4115.69 | − | 7128.58i | 0.493946 | − | 0.855539i | ||||
\(412\) | −11431.4 | −1.36695 | ||||||||
\(413\) | 2662.34 | + | 2887.16i | 0.317204 | + | 0.343990i | ||||
\(414\) | 1088.75 | 0.129249 | ||||||||
\(415\) | −2193.44 | + | 3799.15i | −0.259450 | + | 0.449380i | ||||
\(416\) | 3587.48 | + | 6213.70i | 0.422814 | + | 0.732336i | ||||
\(417\) | −647.286 | − | 1121.13i | −0.0760137 | − | 0.131660i | ||||
\(418\) | 3613.08 | − | 6258.05i | 0.422779 | − | 0.732275i | ||||
\(419\) | 4312.62 | 0.502829 | 0.251414 | − | 0.967880i | \(-0.419104\pi\) | ||||
0.251414 | + | 0.967880i | \(0.419104\pi\) | |||||||
\(420\) | −2983.37 | − | 3235.30i | −0.346604 | − | 0.375872i | ||||
\(421\) | 7210.67 | 0.834742 | 0.417371 | − | 0.908736i | \(-0.362952\pi\) | ||||
0.417371 | + | 0.908736i | \(0.362952\pi\) | |||||||
\(422\) | 5097.32 | − | 8828.82i | 0.587995 | − | 1.01844i | ||||
\(423\) | 341.502 | + | 591.499i | 0.0392539 | + | 0.0679898i | ||||
\(424\) | −1267.29 | − | 2195.01i | −0.145153 | − | 0.251412i | ||||
\(425\) | −46.6601 | + | 80.8176i | −0.00532552 | + | 0.00922407i | ||||
\(426\) | −8357.78 | −0.950553 | ||||||||
\(427\) | 2001.63 | − | 6418.65i | 0.226851 | − | 0.727448i | ||||
\(428\) | 1470.30 | 0.166050 | ||||||||
\(429\) | −3994.71 | + | 6919.04i | −0.449572 | + | 0.778682i | ||||
\(430\) | 4962.07 | + | 8594.56i | 0.556494 | + | 0.963876i | ||||
\(431\) | 4952.65 | + | 8578.24i | 0.553505 | + | 0.958700i | 0.998018 | + | 0.0629270i | \(0.0200435\pi\) |
−0.444513 | + | 0.895773i | \(0.646623\pi\) | |||||||
\(432\) | 5722.11 | − | 9910.98i | 0.637280 | − | 1.10380i | ||||
\(433\) | −3132.44 | −0.347657 | −0.173829 | − | 0.984776i | \(-0.555614\pi\) | ||||
−0.173829 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(434\) | 14055.5 | − | 3162.44i | 1.55458 | − | 0.349774i | ||||
\(435\) | −3596.36 | −0.396396 | ||||||||
\(436\) | 301.775 | − | 522.690i | 0.0331477 | − | 0.0574135i | ||||
\(437\) | 338.782 | + | 586.787i | 0.0370849 | + | 0.0642330i | ||||
\(438\) | 7205.87 | + | 12480.9i | 0.786095 | + | 1.36156i | ||||
\(439\) | 2151.11 | − | 3725.83i | 0.233865 | − | 0.405066i | −0.725077 | − | 0.688668i | \(-0.758196\pi\) |
0.958942 | + | 0.283601i | \(0.0915293\pi\) | |||||||
\(440\) | −5319.28 | −0.576334 | ||||||||
\(441\) | 351.690 | − | 4333.52i | 0.0379754 | − | 0.467933i | ||||
\(442\) | −828.896 | −0.0892004 | ||||||||
\(443\) | −2474.22 | + | 4285.47i | −0.265358 | + | 0.459613i | −0.967657 | − | 0.252268i | \(-0.918823\pi\) |
0.702299 | + | 0.711882i | \(0.252157\pi\) | |||||||
\(444\) | 3748.74 | + | 6493.01i | 0.400693 | + | 0.694020i | ||||
\(445\) | 3168.86 | + | 5488.63i | 0.337570 | + | 0.584688i | ||||
\(446\) | −7487.72 | + | 12969.1i | −0.794964 | + | 1.37692i | ||||
\(447\) | 2870.45 | 0.303731 | ||||||||
\(448\) | −4048.00 | + | 910.782i | −0.426897 | + | 0.0960500i | ||||
\(449\) | 7606.44 | 0.799488 | 0.399744 | − | 0.916627i | \(-0.369099\pi\) | ||||
0.399744 | + | 0.916627i | \(0.369099\pi\) | |||||||
\(450\) | −319.813 | + | 553.932i | −0.0335025 | + | 0.0580280i | ||||
\(451\) | −10160.0 | − | 17597.7i | −1.06079 | − | 1.83734i | ||||
\(452\) | 4914.32 | + | 8511.86i | 0.511394 | + | 0.885761i | ||||
\(453\) | 5723.97 | − | 9914.20i | 0.593676 | − | 1.02828i | ||||
\(454\) | 18051.8 | 1.86611 | ||||||||
\(455\) | 1870.98 | − | 5999.70i | 0.192776 | − | 0.618177i | ||||
\(456\) | 855.145 | 0.0878198 | ||||||||
\(457\) | −1603.02 | + | 2776.52i | −0.164084 | + | 0.284202i | −0.936330 | − | 0.351122i | \(-0.885800\pi\) |
0.772246 | + | 0.635324i | \(0.219133\pi\) | |||||||
\(458\) | −10153.9 | − | 17587.1i | −1.03594 | − | 1.79430i | ||||
\(459\) | 518.540 | + | 898.137i | 0.0527306 | + | 0.0913321i | ||||
\(460\) | −722.026 | + | 1250.59i | −0.0731840 | + | 0.126758i | ||||
\(461\) | 11181.4 | 1.12965 | 0.564825 | − | 0.825211i | \(-0.308944\pi\) | ||||
0.564825 | + | 0.825211i | \(0.308944\pi\) | |||||||
\(462\) | −11655.7 | − | 12640.0i | −1.17375 | − | 1.27287i | ||||
\(463\) | −2334.72 | −0.234349 | −0.117174 | − | 0.993111i | \(-0.537384\pi\) | ||||
−0.117174 | + | 0.993111i | \(0.537384\pi\) | |||||||
\(464\) | −3429.31 | + | 5939.75i | −0.343108 | + | 0.594280i | ||||
\(465\) | −4162.13 | − | 7209.03i | −0.415085 | − | 0.718948i | ||||
\(466\) | 7692.72 | + | 13324.2i | 0.764718 | + | 1.32453i | ||||
\(467\) | 7306.43 | − | 12655.1i | 0.723986 | − | 1.25398i | −0.235404 | − | 0.971898i | \(-0.575641\pi\) |
0.959390 | − | 0.282083i | \(-0.0910253\pi\) | |||||||
\(468\) | −2422.34 | −0.239258 | ||||||||
\(469\) | −2750.38 | − | 2982.63i | −0.270791 | − | 0.293657i | ||||
\(470\) | −2124.68 | −0.208519 | ||||||||
\(471\) | 6375.99 | − | 11043.5i | 0.623758 | − | 1.08038i | ||||
\(472\) | −813.203 | − | 1408.51i | −0.0793024 | − | 0.137356i | ||||
\(473\) | 8265.69 | + | 14316.6i | 0.803503 | + | 1.39171i | ||||
\(474\) | 2378.80 | − | 4120.20i | 0.230510 | − | 0.399256i | ||||
\(475\) | −398.058 | −0.0384509 | ||||||||
\(476\) | 226.426 | − | 726.084i | 0.0218030 | − | 0.0699160i | ||||
\(477\) | 4188.86 | 0.402085 | ||||||||
\(478\) | 1120.06 | − | 1940.00i | 0.107176 | − | 0.185635i | ||||
\(479\) | −6026.15 | − | 10437.6i | −0.574827 | − | 0.995629i | −0.996060 | − | 0.0886769i | \(-0.971736\pi\) |
0.421234 | − | 0.906952i | \(-0.361597\pi\) | |||||||
\(480\) | 4460.86 | + | 7726.44i | 0.424187 | + | 0.734713i | ||||
\(481\) | −5353.39 | + | 9272.35i | −0.507471 | + | 0.878966i | ||||
\(482\) | −8899.63 | −0.841011 | ||||||||
\(483\) | 1572.85 | − | 353.885i | 0.148172 | − | 0.0333381i | ||||
\(484\) | 17739.7 | 1.66601 | ||||||||
\(485\) | 3232.39 | − | 5598.67i | 0.302630 | − | 0.524170i | ||||
\(486\) | 5972.76 | + | 10345.1i | 0.557469 | + | 0.965564i | ||||
\(487\) | −9112.51 | − | 15783.3i | −0.847900 | − | 1.46861i | −0.883079 | − | 0.469225i | \(-0.844533\pi\) |
0.0351786 | − | 0.999381i | \(-0.488800\pi\) | |||||||
\(488\) | −1392.20 | + | 2411.36i | −0.129143 | + | 0.223682i | ||||
\(489\) | 15497.6 | 1.43318 | ||||||||
\(490\) | 11127.6 | + | 7687.78i | 1.02590 | + | 0.708773i | ||||
\(491\) | −3903.86 | −0.358816 | −0.179408 | − | 0.983775i | \(-0.557418\pi\) | ||||
−0.179408 | + | 0.983775i | \(0.557418\pi\) | |||||||
\(492\) | −3481.08 | + | 6029.41i | −0.318982 | + | 0.552494i | ||||
\(493\) | −310.766 | − | 538.262i | −0.0283898 | − | 0.0491727i | ||||
\(494\) | −1767.83 | − | 3061.98i | −0.161009 | − | 0.278876i | ||||
\(495\) | 4395.56 | − | 7613.33i | 0.399123 | − | 0.691301i | ||||
\(496\) | −15875.2 | −1.43714 | ||||||||
\(497\) | 10684.4 | − | 2403.94i | 0.964306 | − | 0.216965i | ||||
\(498\) | 5872.28 | 0.528400 | ||||||||
\(499\) | −9922.49 | + | 17186.3i | −0.890163 | + | 1.54181i | −0.0504848 | + | 0.998725i | \(0.516077\pi\) |
−0.839679 | + | 0.543084i | \(0.817257\pi\) | |||||||
\(500\) | −4348.23 | − | 7531.36i | −0.388918 | − | 0.673625i | ||||
\(501\) | 922.874 | + | 1598.46i | 0.0822973 | + | 0.142543i | ||||
\(502\) | 7202.13 | − | 12474.5i | 0.640332 | − | 1.10909i | ||||
\(503\) | 9819.27 | 0.870417 | 0.435208 | − | 0.900330i | \(-0.356675\pi\) | ||||
0.435208 | + | 0.900330i | \(0.356675\pi\) | |||||||
\(504\) | −536.029 | + | 1718.89i | −0.0473743 | + | 0.151916i | ||||
\(505\) | 9215.81 | 0.812076 | ||||||||
\(506\) | −2820.88 | + | 4885.90i | −0.247832 | + | 0.429258i | ||||
\(507\) | −2202.98 | − | 3815.68i | −0.192974 | − | 0.334241i | ||||
\(508\) | 4808.56 | + | 8328.67i | 0.419971 | + | 0.727411i | ||||
\(509\) | −8586.30 | + | 14871.9i | −0.747704 | + | 1.29506i | 0.201217 | + | 0.979547i | \(0.435510\pi\) |
−0.948921 | + | 0.315514i | \(0.897823\pi\) | |||||||
\(510\) | −1030.69 | −0.0894899 | ||||||||
\(511\) | −12801.7 | − | 13882.7i | −1.10825 | − | 1.20183i | ||||
\(512\) | 12338.4 | 1.06501 | ||||||||
\(513\) | −2211.84 | + | 3831.01i | −0.190361 | + | 0.329714i | ||||
\(514\) | −9026.24 | − | 15633.9i | −0.774573 | − | 1.34160i | ||||
\(515\) | −10149.4 | − | 17579.3i | −0.868420 | − | 1.50415i | ||||
\(516\) | 2832.04 | − | 4905.23i | 0.241615 | − | 0.418490i | ||||
\(517\) | −3539.23 | −0.301074 | ||||||||
\(518\) | −15620.0 | − | 16939.1i | −1.32491 | − | 1.43679i | ||||
\(519\) | 10020.9 | 0.847530 | ||||||||
\(520\) | −1301.33 | + | 2253.96i | −0.109744 | + | 0.190082i | ||||
\(521\) | −4924.97 | − | 8530.31i | −0.414140 | − | 0.717312i | 0.581198 | − | 0.813762i | \(-0.302584\pi\) |
−0.995338 | + | 0.0964507i | \(0.969251\pi\) | |||||||
\(522\) | −2130.02 | − | 3689.30i | −0.178598 | − | 0.309342i | ||||
\(523\) | 5103.26 | − | 8839.10i | 0.426673 | − | 0.739019i | −0.569902 | − | 0.821712i | \(-0.693019\pi\) |
0.996575 | + | 0.0826937i | \(0.0263523\pi\) | |||||||
\(524\) | 13048.2 | 1.08781 | ||||||||
\(525\) | −281.965 | + | 904.182i | −0.0234399 | + | 0.0751652i | ||||
\(526\) | 1969.54 | 0.163262 | ||||||||
\(527\) | 719.311 | − | 1245.88i | 0.0594567 | − | 0.102982i | ||||
\(528\) | 9473.03 | + | 16407.8i | 0.780797 | + | 1.35238i | ||||
\(529\) | −264.500 | − | 458.127i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −6515.31 | + | 11284.9i | −0.533976 | + | 0.924873i | ||||
\(531\) | 2687.94 | 0.219674 | ||||||||
\(532\) | 3165.09 | − | 712.132i | 0.257940 | − | 0.0580354i | ||||
\(533\) | −9942.32 | −0.807973 | ||||||||
\(534\) | 4241.84 | − | 7347.09i | 0.343750 | − | 0.595393i | ||||
\(535\) | 1305.41 | + | 2261.04i | 0.105491 | + | 0.182716i | ||||
\(536\) | 840.096 | + | 1455.09i | 0.0676989 | + | 0.117258i | ||||
\(537\) | 512.833 | − | 888.253i | 0.0412112 | − | 0.0713798i | ||||
\(538\) | −975.995 | −0.0782122 | ||||||||
\(539\) | 18536.0 | + | 12806.1i | 1.48127 | + | 1.02337i | ||||
\(540\) | −9427.93 | −0.751321 | ||||||||
\(541\) | −4695.10 | + | 8132.14i | −0.373120 | + | 0.646263i | −0.990044 | − | 0.140760i | \(-0.955045\pi\) |
0.616924 | + | 0.787023i | \(0.288379\pi\) | |||||||
\(542\) | −5111.92 | − | 8854.10i | −0.405121 | − | 0.701691i | ||||
\(543\) | 8352.94 | + | 14467.7i | 0.660145 | + | 1.14341i | ||||
\(544\) | −770.938 | + | 1335.30i | −0.0607605 | + | 0.105240i | ||||
\(545\) | 1071.73 | 0.0842347 | ||||||||
\(546\) | −8207.47 | + | 1846.65i | −0.643310 | + | 0.144742i | ||||
\(547\) | 18781.7 | 1.46809 | 0.734047 | − | 0.679099i | \(-0.237629\pi\) | ||||
0.734047 | + | 0.679099i | \(0.237629\pi\) | |||||||
\(548\) | −6466.17 | + | 11199.7i | −0.504053 | + | 0.873045i | ||||
\(549\) | −2300.87 | − | 3985.22i | −0.178868 | − | 0.309809i | ||||
\(550\) | −1657.22 | − | 2870.39i | −0.128480 | − | 0.222535i | ||||
\(551\) | 1325.58 | − | 2295.96i | 0.102489 | − | 0.177516i | ||||
\(552\) | −667.645 | −0.0514798 | ||||||||
\(553\) | −1855.91 | + | 5951.39i | −0.142715 | + | 0.457647i | ||||
\(554\) | −15310.0 | −1.17412 | ||||||||
\(555\) | −6656.69 | + | 11529.7i | −0.509118 | + | 0.881819i | ||||
\(556\) | 1016.95 | + | 1761.41i | 0.0775691 | + | 0.134354i | ||||
\(557\) | −10532.7 | − | 18243.2i | −0.801229 | − | 1.38777i | −0.918807 | − | 0.394706i | \(-0.870846\pi\) |
0.117578 | − | 0.993064i | \(-0.462487\pi\) | |||||||
\(558\) | 4930.22 | − | 8539.40i | 0.374038 | − | 0.647852i | ||||
\(559\) | 8088.58 | 0.612004 | ||||||||
\(560\) | −10103.1 | − | 10956.2i | −0.762381 | − | 0.826759i | ||||
\(561\) | −1716.90 | −0.129211 | ||||||||
\(562\) | −2988.94 | + | 5177.00i | −0.224343 | + | 0.388574i | ||||
\(563\) | −980.682 | − | 1698.59i | −0.0734117 | − | 0.127153i | 0.826983 | − | 0.562227i | \(-0.190055\pi\) |
−0.900394 | + | 0.435074i | \(0.856722\pi\) | |||||||
\(564\) | 606.316 | + | 1050.17i | 0.0452668 | + | 0.0784044i | ||||
\(565\) | −8726.42 | + | 15114.6i | −0.649776 | + | 1.12544i | ||||
\(566\) | −21683.9 | −1.61032 | ||||||||
\(567\) | 2838.45 | + | 3078.14i | 0.210236 | + | 0.227989i | ||||
\(568\) | −4535.32 | −0.335031 | ||||||||
\(569\) | −9982.48 | + | 17290.2i | −0.735478 | + | 1.27389i | 0.219035 | + | 0.975717i | \(0.429709\pi\) |
−0.954513 | + | 0.298169i | \(0.903624\pi\) | |||||||
\(570\) | −2198.22 | − | 3807.42i | −0.161532 | − | 0.279781i | ||||
\(571\) | 5325.77 | + | 9224.51i | 0.390327 | + | 0.676066i | 0.992493 | − | 0.122305i | \(-0.0390287\pi\) |
−0.602166 | + | 0.798371i | \(0.705695\pi\) | |||||||
\(572\) | 6276.10 | − | 10870.5i | 0.458771 | − | 0.794615i | ||||
\(573\) | 4479.07 | 0.326555 | ||||||||
\(574\) | 6369.85 | − | 20426.3i | 0.463192 | − | 1.48533i | ||||
\(575\) | 310.780 | 0.0225398 | ||||||||
\(576\) | −1419.90 | + | 2459.35i | −0.102713 | + | 0.177904i | ||||
\(577\) | 7918.21 | + | 13714.7i | 0.571299 | + | 0.989519i | 0.996433 | + | 0.0843885i | \(0.0268937\pi\) |
−0.425134 | + | 0.905130i | \(0.639773\pi\) | |||||||
\(578\) | 9084.65 | + | 15735.1i | 0.653757 | + | 1.13234i | ||||
\(579\) | 2102.83 | − | 3642.21i | 0.150934 | − | 0.261425i | ||||
\(580\) | 5650.25 | 0.404507 | ||||||||
\(581\) | −7506.98 | + | 1689.04i | −0.536045 | + | 0.120608i | ||||
\(582\) | −8653.77 | −0.616341 | ||||||||
\(583\) | −10853.0 | + | 18798.0i | −0.770989 | + | 1.33539i | ||||
\(584\) | 3910.24 | + | 6772.73i | 0.277067 | + | 0.479893i | ||||
\(585\) | −2150.69 | − | 3725.10i | −0.152000 | − | 0.263272i | ||||
\(586\) | −1358.28 | + | 2352.62i | −0.0957512 | + | 0.165846i | ||||
\(587\) | 12834.5 | 0.902444 | 0.451222 | − | 0.892412i | \(-0.350988\pi\) | ||||
0.451222 | + | 0.892412i | \(0.350988\pi\) | |||||||
\(588\) | 624.404 | − | 7693.90i | 0.0437925 | − | 0.539610i | ||||
\(589\) | 6136.46 | 0.429284 | ||||||||
\(590\) | −4180.80 | + | 7241.36i | −0.291730 | + | 0.505292i | ||||
\(591\) | −9323.90 | − | 16149.5i | −0.648957 | − | 1.12403i | ||||
\(592\) | 12695.0 | + | 21988.4i | 0.881353 | + | 1.52655i | ||||
\(593\) | 6525.01 | − | 11301.6i | 0.451855 | − | 0.782636i | −0.546646 | − | 0.837364i | \(-0.684096\pi\) |
0.998501 | + | 0.0547278i | \(0.0174291\pi\) | |||||||
\(594\) | −36833.9 | −2.54430 | ||||||||
\(595\) | 1317.61 | − | 296.457i | 0.0907847 | − | 0.0204262i | ||||
\(596\) | −4509.78 | −0.309946 | ||||||||
\(597\) | 4693.91 | − | 8130.09i | 0.321790 | − | 0.557357i | ||||
\(598\) | 1380.22 | + | 2390.61i | 0.0943834 | + | 0.163477i | ||||
\(599\) | −136.649 | − | 236.683i | −0.00932109 | − | 0.0161446i | 0.861327 | − | 0.508051i | \(-0.169634\pi\) |
−0.870648 | + | 0.491906i | \(0.836300\pi\) | |||||||
\(600\) | 196.116 | − | 339.683i | 0.0133440 | − | 0.0231125i | ||||
\(601\) | 4002.62 | 0.271665 | 0.135832 | − | 0.990732i | \(-0.456629\pi\) | ||||
0.135832 | + | 0.990732i | \(0.456629\pi\) | |||||||
\(602\) | −5182.19 | + | 16617.8i | −0.350848 | + | 1.12507i | ||||
\(603\) | −2776.83 | −0.187531 | ||||||||
\(604\) | −8992.94 | + | 15576.2i | −0.605824 | + | 1.04932i | ||||
\(605\) | 15750.3 | + | 27280.3i | 1.05841 | + | 1.83323i | ||||
\(606\) | −6168.15 | − | 10683.5i | −0.413472 | − | 0.716154i | ||||
\(607\) | −7427.06 | + | 12864.1i | −0.496631 | + | 0.860191i | −0.999992 | − | 0.00388537i | \(-0.998763\pi\) |
0.503361 | + | 0.864076i | \(0.332097\pi\) | |||||||
\(608\) | −6576.89 | −0.438698 | ||||||||
\(609\) | −4276.27 | − | 4637.37i | −0.284537 | − | 0.308564i | ||||
\(610\) | 14315.0 | 0.950159 | ||||||||
\(611\) | −865.849 | + | 1499.69i | −0.0573298 | + | 0.0992981i | ||||
\(612\) | −260.276 | − | 450.812i | −0.0171912 | − | 0.0297761i | ||||
\(613\) | 14931.8 | + | 25862.7i | 0.983834 | + | 1.70405i | 0.647005 | + | 0.762485i | \(0.276021\pi\) |
0.336829 | + | 0.941566i | \(0.390646\pi\) | |||||||
\(614\) | 11693.2 | − | 20253.2i | 0.768566 | − | 1.33120i | ||||
\(615\) | −12362.8 | −0.810595 | ||||||||
\(616\) | −6324.92 | − | 6859.02i | −0.413699 | − | 0.448633i | ||||
\(617\) | −16055.1 | −1.04758 | −0.523789 | − | 0.851848i | \(-0.675482\pi\) | ||||
−0.523789 | + | 0.851848i | \(0.675482\pi\) | |||||||
\(618\) | −13586.0 | + | 23531.6i | −0.884319 | + | 1.53168i | ||||
\(619\) | −9893.35 | − | 17135.8i | −0.642403 | − | 1.11267i | −0.984895 | − | 0.173154i | \(-0.944604\pi\) |
0.342492 | − | 0.939521i | \(-0.388729\pi\) | |||||||
\(620\) | 6539.14 | + | 11326.1i | 0.423578 | + | 0.733658i | ||||
\(621\) | 1726.87 | − | 2991.02i | 0.111589 | − | 0.193278i | ||||
\(622\) | −21210.6 | −1.36731 | ||||||||
\(623\) | −3309.44 | + | 10612.4i | −0.212825 | + | 0.682468i | ||||
\(624\) | 9270.05 | 0.594710 | ||||||||
\(625\) | 6876.70 | − | 11910.8i | 0.440109 | − | 0.762291i | ||||
\(626\) | 2170.10 | + | 3758.72i | 0.138553 | + | 0.239982i | ||||
\(627\) | −3661.73 | − | 6342.30i | −0.233230 | − | 0.403967i | ||||
\(628\) | −10017.3 | + | 17350.5i | −0.636521 | + | 1.10249i | ||||
\(629\) | −2300.85 | −0.145852 | ||||||||
\(630\) | 9031.05 | − | 2031.95i | 0.571120 | − | 0.128499i | ||||
\(631\) | −1044.43 | −0.0658927 | −0.0329463 | − | 0.999457i | \(-0.510489\pi\) | ||||
−0.0329463 | + | 0.999457i | \(0.510489\pi\) | |||||||
\(632\) | 1290.85 | − | 2235.81i | 0.0812455 | − | 0.140721i | ||||
\(633\) | −5165.95 | − | 8947.69i | −0.324373 | − | 0.561830i | ||||
\(634\) | −14457.9 | − | 25041.9i | −0.905674 | − | 1.56867i | ||||
\(635\) | −8538.62 | + | 14789.3i | −0.533614 | + | 0.924246i | ||||
\(636\) | 7437.05 | 0.463677 | ||||||||
\(637\) | 9961.09 | − | 4721.42i | 0.619581 | − | 0.293672i | ||||
\(638\) | 22074.9 | 1.36983 | ||||||||
\(639\) | 3747.73 | − | 6491.26i | 0.232016 | − | 0.401863i | ||||
\(640\) | 5012.14 | + | 8681.27i | 0.309566 | + | 0.536184i | ||||
\(641\) | −7026.86 | − | 12170.9i | −0.432987 | − | 0.749955i | 0.564142 | − | 0.825678i | \(-0.309207\pi\) |
−0.997129 | + | 0.0757228i | \(0.975874\pi\) | |||||||
\(642\) | 1747.42 | − | 3026.63i | 0.107423 | − | 0.186061i | ||||
\(643\) | −14339.0 | −0.879431 | −0.439715 | − | 0.898137i | \(-0.644921\pi\) | ||||
−0.439715 | + | 0.898137i | \(0.644921\pi\) | |||||||
\(644\) | −2471.11 | + | 555.990i | −0.151204 | + | 0.0340203i | ||||
\(645\) | 10057.8 | 0.613991 | ||||||||
\(646\) | 379.902 | − | 658.009i | 0.0231378 | − | 0.0400759i | ||||
\(647\) | 8368.35 | + | 14494.4i | 0.508491 | + | 0.880732i | 0.999952 | + | 0.00983244i | \(0.00312981\pi\) |
−0.491461 | + | 0.870900i | \(0.663537\pi\) | |||||||
\(648\) | −866.996 | − | 1501.68i | −0.0525599 | − | 0.0910365i | ||||
\(649\) | −6964.27 | + | 12062.5i | −0.421219 | + | 0.729574i | ||||
\(650\) | −1621.71 | −0.0978598 | ||||||||
\(651\) | 4346.77 | − | 13938.9i | 0.261695 | − | 0.839181i | ||||
\(652\) | −24348.3 | −1.46251 | ||||||||
\(653\) | 15313.9 | − | 26524.5i | 0.917733 | − | 1.58956i | 0.114883 | − | 0.993379i | \(-0.463351\pi\) |
0.802850 | − | 0.596181i | \(-0.203316\pi\) | |||||||
\(654\) | −717.310 | − | 1242.42i | −0.0428884 | − | 0.0742850i | ||||
\(655\) | 11584.9 | + | 20065.6i | 0.691083 | + | 1.19699i | ||||
\(656\) | −11788.6 | + | 20418.4i | −0.701626 | + | 1.21525i | ||||
\(657\) | −12924.8 | −0.767496 | ||||||||
\(658\) | −2526.36 | − | 2739.69i | −0.149677 | − | 0.162317i | ||||
\(659\) | −9716.61 | −0.574363 | −0.287182 | − | 0.957876i | \(-0.592718\pi\) | ||||
−0.287182 | + | 0.957876i | \(0.592718\pi\) | |||||||
\(660\) | 7804.04 | − | 13517.0i | 0.460260 | − | 0.797194i | ||||
\(661\) | −2548.38 | − | 4413.93i | −0.149955 | − | 0.259730i | 0.781255 | − | 0.624212i | \(-0.214580\pi\) |
−0.931211 | + | 0.364481i | \(0.881246\pi\) | |||||||
\(662\) | −12330.2 | − | 21356.6i | −0.723909 | − | 1.25385i | ||||
\(663\) | −420.028 | + | 727.510i | −0.0246041 | + | 0.0426156i | ||||
\(664\) | 3186.57 | 0.186239 | ||||||||
\(665\) | 3905.27 | + | 4235.05i | 0.227729 | + | 0.246960i | ||||
\(666\) | −15770.3 | −0.917545 | ||||||||
\(667\) | −1034.93 | + | 1792.55i | −0.0600789 | + | 0.104060i | ||||
\(668\) | −1449.93 | − | 2511.35i | −0.0839812 | − | 0.145460i | ||||
\(669\) | 7588.54 | + | 13143.7i | 0.438550 | + | 0.759590i | ||||
\(670\) | 4319.06 | − | 7480.83i | 0.249044 | − | 0.431358i | ||||
\(671\) | 23845.5 | 1.37190 | ||||||||
\(672\) | −4658.75 | + | 14939.3i | −0.267433 | + | 0.857583i | ||||
\(673\) | 18211.9 | 1.04311 | 0.521557 | − | 0.853216i | \(-0.325351\pi\) | ||||
0.521557 | + | 0.853216i | \(0.325351\pi\) | |||||||
\(674\) | 11157.7 | − | 19325.7i | 0.637654 | − | 1.10445i | ||||
\(675\) | 1014.51 | + | 1757.18i | 0.0578496 | + | 0.100198i | ||||
\(676\) | 3461.11 | + | 5994.82i | 0.196923 | + | 0.341080i | ||||
\(677\) | −12346.0 | + | 21383.9i | −0.700879 | + | 1.21396i | 0.267280 | + | 0.963619i | \(0.413875\pi\) |
−0.968158 | + | 0.250339i | \(0.919458\pi\) | |||||||
\(678\) | 23362.4 | 1.32334 | ||||||||
\(679\) | 11062.8 | − | 2489.08i | 0.625258 | − | 0.140680i | ||||
\(680\) | −559.302 | −0.0315415 | ||||||||
\(681\) | 9147.42 | − | 15843.8i | 0.514728 | − | 0.891536i | ||||
\(682\) | 25547.7 | + | 44249.9i | 1.43442 | + | 2.48448i | ||||
\(683\) | −8687.76 | − | 15047.6i | −0.486717 | − | 0.843019i | 0.513166 | − | 0.858289i | \(-0.328473\pi\) |
−0.999883 | + | 0.0152701i | \(0.995139\pi\) | |||||||
\(684\) | 1110.21 | − | 1922.94i | 0.0620614 | − | 0.107493i | ||||
\(685\) | −22964.1 | −1.28090 | ||||||||
\(686\) | 3318.18 | + | 23489.8i | 0.184677 | + | 1.30735i | ||||
\(687\) | −20581.2 | −1.14297 | ||||||||
\(688\) | 9590.60 | − | 16611.4i | 0.531451 | − | 0.920500i | ||||
\(689\) | 5310.24 | + | 9197.61i | 0.293620 | + | 0.508565i | ||||
\(690\) | 1716.23 | + | 2972.60i | 0.0946897 | + | 0.164007i | ||||
\(691\) | 5712.94 | − | 9895.10i | 0.314516 | − | 0.544757i | −0.664819 | − | 0.747005i | \(-0.731491\pi\) |
0.979334 | + | 0.202247i | \(0.0648245\pi\) | |||||||
\(692\) | −15743.8 | −0.864871 | ||||||||
\(693\) | 15043.7 | − | 3384.76i | 0.824621 | − | 0.185536i | ||||
\(694\) | 13946.6 | 0.762834 | ||||||||
\(695\) | −1805.82 | + | 3127.76i | −0.0985590 | + | 0.170709i | ||||
\(696\) | 1306.17 | + | 2262.36i | 0.0711356 | + | 0.123210i | ||||
\(697\) | −1068.29 | − | 1850.33i | −0.0580548 | − | 0.100554i | ||||
\(698\) | −7684.41 | + | 13309.8i | −0.416704 | + | 0.721752i | ||||
\(699\) | 15592.6 | 0.843728 | ||||||||
\(700\) | 442.996 | − | 1420.56i | 0.0239196 | − | 0.0767032i | ||||
\(701\) | 19974.7 | 1.07623 | 0.538114 | − | 0.842872i | \(-0.319137\pi\) | ||||
0.538114 | + | 0.842872i | \(0.319137\pi\) | |||||||
\(702\) | −9011.16 | + | 15607.8i | −0.484479 | + | 0.839142i | ||||
\(703\) | −4907.16 | − | 8499.44i | −0.263267 | − | 0.455992i | ||||
\(704\) | −7357.74 | − | 12744.0i | −0.393900 | − | 0.682254i | ||||
\(705\) | −1076.64 | + | 1864.80i | −0.0575159 | + | 0.0996204i | ||||
\(706\) | 17738.1 | 0.945583 | ||||||||
\(707\) | 10958.1 | + | 11883.5i | 0.582917 | + | 0.632140i | ||||
\(708\) | 4772.27 | 0.253323 | ||||||||
\(709\) | 8646.62 | − | 14976.4i | 0.458012 | − | 0.793301i | −0.540843 | − | 0.841123i | \(-0.681895\pi\) |
0.998856 | + | 0.0478226i | \(0.0152282\pi\) | |||||||
\(710\) | 11658.4 | + | 20192.9i | 0.616241 | + | 1.06736i | ||||
\(711\) | 2133.37 | + | 3695.10i | 0.112528 | + | 0.194905i | ||||
\(712\) | 2301.82 | − | 3986.87i | 0.121158 | − | 0.209852i | ||||
\(713\) | −4790.97 | −0.251646 | ||||||||
\(714\) | −1225.55 | − | 1329.04i | −0.0642368 | − | 0.0696612i | ||||
\(715\) | 22289.1 | 1.16583 | ||||||||
\(716\) | −805.714 | + | 1395.54i | −0.0420544 | + | 0.0728404i | ||||
\(717\) | −1135.14 | − | 1966.12i | −0.0591249 | − | 0.102407i | ||||
\(718\) | −3191.08 | − | 5527.12i | −0.165864 | − | 0.287285i | ||||
\(719\) | −13617.6 | + | 23586.4i | −0.706332 | + | 1.22340i | 0.259877 | + | 0.965642i | \(0.416318\pi\) |
−0.966209 | + | 0.257760i | \(0.917015\pi\) | |||||||
\(720\) | −10200.3 | −0.527973 | ||||||||
\(721\) | 10599.6 | − | 33990.0i | 0.547505 | − | 1.75569i | ||||
\(722\) | −22373.7 | −1.15327 | ||||||||
\(723\) | −4509.73 | + | 7811.08i | −0.231976 | + | 0.401794i | ||||
\(724\) | −13123.3 | − | 22730.3i | −0.673653 | − | 1.16680i | ||||
\(725\) | −608.005 | − | 1053.10i | −0.0311459 | − | 0.0539462i | ||||
\(726\) | 21083.3 | − | 36517.4i | 1.07779 | − | 1.86679i | ||||
\(727\) | 33672.5 | 1.71780 | 0.858901 | − | 0.512141i | \(-0.171148\pi\) | ||||
0.858901 | + | 0.512141i | \(0.171148\pi\) | |||||||
\(728\) | −4453.75 | + | 1002.08i | −0.226741 | + | 0.0510156i | ||||
\(729\) | 18210.6 | 0.925192 | ||||||||
\(730\) | 20103.1 | − | 34819.6i | 1.01925 | − | 1.76539i | ||||
\(731\) | 869.104 | + | 1505.33i | 0.0439740 | + | 0.0761652i | ||||
\(732\) | −4085.04 | − | 7075.50i | −0.206267 | − | 0.357265i | ||||
\(733\) | −13840.0 | + | 23971.5i | −0.697396 | + | 1.20793i | 0.271970 | + | 0.962306i | \(0.412325\pi\) |
−0.969366 | + | 0.245620i | \(0.921009\pi\) | |||||||
\(734\) | 5641.50 | 0.283694 | ||||||||
\(735\) | 12386.1 | − | 5870.86i | 0.621592 | − | 0.294626i | ||||
\(736\) | 5134.84 | 0.257164 | ||||||||
\(737\) | 7194.57 | − | 12461.4i | 0.359587 | − | 0.622823i | ||||
\(738\) | −7322.13 | − | 12682.3i | −0.365219 | − | 0.632577i | ||||
\(739\) | 10075.5 | + | 17451.3i | 0.501535 | + | 0.868684i | 0.999998 | + | 0.00177310i | \(0.000564397\pi\) |
−0.498464 | + | 0.866911i | \(0.666102\pi\) | |||||||
\(740\) | 10458.3 | − | 18114.4i | 0.519536 | − | 0.899862i | ||||
\(741\) | −3583.27 | −0.177645 | ||||||||
\(742\) | −22298.5 | + | 5017.06i | −1.10324 | + | 0.248224i | ||||
\(743\) | 13758.0 | 0.679315 | 0.339658 | − | 0.940549i | \(-0.389689\pi\) | ||||
0.339658 | + | 0.940549i | \(0.389689\pi\) | |||||||
\(744\) | −3023.32 | + | 5236.54i | −0.148979 | + | 0.258039i | ||||
\(745\) | −4004.03 | − | 6935.19i | −0.196908 | − | 0.341055i | ||||
\(746\) | −23633.0 | − | 40933.6i | −1.15987 | − | 2.00896i | ||||
\(747\) | −2633.20 | + | 4560.84i | −0.128974 | + | 0.223390i | ||||
\(748\) | 2697.43 | 0.131855 | ||||||||
\(749\) | −1363.32 | + | 4371.78i | −0.0665082 | + | 0.213273i | ||||
\(750\) | −20671.2 | −1.00641 | ||||||||
\(751\) | −15544.2 | + | 26923.3i | −0.755279 | + | 1.30818i | 0.189957 | + | 0.981792i | \(0.439165\pi\) |
−0.945236 | + | 0.326389i | \(0.894168\pi\) | |||||||
\(752\) | 2053.27 | + | 3556.36i | 0.0995678 | + | 0.172456i | ||||
\(753\) | −7299.10 | − | 12642.4i | −0.353246 | − | 0.611839i | ||||
\(754\) | 5400.48 | − | 9353.90i | 0.260840 | − | 0.451789i | ||||
\(755\) | −31937.8 | −1.53952 | ||||||||
\(756\) | −11210.3 | − | 12157.0i | −0.539306 | − | 0.584847i | ||||
\(757\) | 16596.6 | 0.796847 | 0.398423 | − | 0.917202i | \(-0.369557\pi\) | ||||
0.398423 | + | 0.917202i | \(0.369557\pi\) | |||||||
\(758\) | 17206.8 | − | 29803.0i | 0.824511 | − | 1.42809i | ||||
\(759\) | 2858.86 | + | 4951.68i | 0.136719 | + | 0.236805i | ||||
\(760\) | −1192.85 | − | 2066.08i | −0.0569334 | − | 0.0986115i | ||||
\(761\) | 8613.00 | − | 14918.1i | 0.410277 | − | 0.710621i | −0.584643 | − | 0.811291i | \(-0.698765\pi\) |
0.994920 | + | 0.100670i | \(0.0320987\pi\) | |||||||
\(762\) | 22859.6 | 1.08677 | ||||||||
\(763\) | 1274.35 | + | 1381.96i | 0.0604646 | + | 0.0655705i | ||||
\(764\) | −7037.08 | −0.333236 | ||||||||
\(765\) | 462.176 | − | 800.512i | 0.0218431 | − | 0.0378334i | ||||
\(766\) | 1145.28 | + | 1983.68i | 0.0540218 | + | 0.0935685i | ||||
\(767\) | 3407.52 | + | 5902.00i | 0.160415 | + | 0.277847i | ||||
\(768\) | 10100.9 | − | 17495.3i | 0.474590 | − | 0.822014i | ||||
\(769\) | −7949.04 | −0.372757 | −0.186378 | − | 0.982478i | \(-0.559675\pi\) | ||||
−0.186378 | + | 0.982478i | \(0.559675\pi\) | |||||||
\(770\) | −14280.2 | + | 45792.5i | −0.668341 | + | 2.14318i | ||||
\(771\) | −18295.5 | −0.854601 | ||||||||
\(772\) | −3303.76 | + | 5722.29i | −0.154022 | + | 0.266774i | ||||
\(773\) | −11989.8 | − | 20767.0i | −0.557884 | − | 0.966284i | −0.997673 | − | 0.0681828i | \(-0.978280\pi\) |
0.439788 | − | 0.898101i | \(-0.355053\pi\) | |||||||
\(774\) | 5956.92 | + | 10317.7i | 0.276637 | + | 0.479150i | ||||
\(775\) | 1407.31 | − | 2437.54i | 0.0652286 | − | 0.112979i | ||||
\(776\) | −4695.94 | −0.217235 | ||||||||
\(777\) | −22782.3 | + | 5125.92i | −1.05188 | + | 0.236669i | ||||
\(778\) | 4368.05 | 0.201288 | ||||||||
\(779\) | 4556.78 | − | 7892.58i | 0.209581 | − | 0.363005i | ||||
\(780\) | −3818.41 | − | 6613.68i | −0.175283 | − | 0.303600i | ||||
\(781\) | 19420.2 | + | 33636.8i | 0.889769 | + | 1.54113i | ||||
\(782\) | −296.604 | + | 513.733i | −0.0135633 | + | 0.0234924i | ||||
\(783\) | −13513.7 | −0.616781 | ||||||||
\(784\) | 2114.52 | − | 26055.1i | 0.0963248 | − | 1.18691i | ||||
\(785\) | −35575.8 | −1.61752 | ||||||||
\(786\) | 15507.6 | − | 26859.9i | 0.703736 | − | 1.21891i | ||||
\(787\) | 3448.66 | + | 5973.26i | 0.156203 | + | 0.270551i | 0.933496 | − | 0.358587i | \(-0.116741\pi\) |
−0.777294 | + | 0.629138i | \(0.783408\pi\) | |||||||
\(788\) | 14648.8 | + | 25372.5i | 0.662236 | + | 1.14703i | ||||
\(789\) | 998.028 | − | 1728.64i | 0.0450326 | − | 0.0779988i | ||||
\(790\) | −13272.9 | −0.597757 | ||||||||
\(791\) | −29865.9 | + | 6719.70i | −1.34249 | + | 0.302055i | ||||
\(792\) | −6385.75 | −0.286500 | ||||||||
\(793\) | 5833.65 | − | 10104.2i | 0.261234 | − | 0.452471i | ||||
\(794\) | 12076.4 | + | 20916.9i | 0.539766 | + | 0.934903i | ||||
\(795\) | 6603.03 | + | 11436.8i | 0.294573 | + | 0.510215i | ||||
\(796\) | −7374.61 | + | 12773.2i | −0.328375 | + | 0.568762i | ||||
\(797\) | −23415.9 | −1.04070 | −0.520348 | − | 0.853954i | \(-0.674198\pi\) | ||||
−0.520348 | + | 0.853954i | \(0.674198\pi\) | |||||||
\(798\) | 2295.73 | − | 7361.76i | 0.101840 | − | 0.326571i | ||||
\(799\) | −372.136 | −0.0164771 | ||||||||
\(800\) | −1508.32 | + | 2612.49i | −0.0666590 | + | 0.115457i | ||||
\(801\) | 3804.19 | + | 6589.05i | 0.167808 | + | 0.290653i | ||||
\(802\) | −316.450 | − | 548.108i | −0.0139330 | − | 0.0241326i | ||||
\(803\) | 33487.3 | − | 58001.6i | 1.47166 | − | 2.54898i | ||||
\(804\) | −4930.09 | −0.216257 | ||||||||
\(805\) | −3049.00 | − | 3306.47i | −0.133495 | − | 0.144767i | ||||
\(806\) | 25000.3 | 1.09255 | ||||||||
\(807\) | −494.568 | + | 856.617i | −0.0215733 | + | 0.0373660i | ||||
\(808\) | −3347.12 | − | 5797.38i | −0.145732 | − | 0.252415i | ||||
\(809\) | −16714.7 | − | 28950.7i | −0.726399 | − | 1.25816i | −0.958396 | − | 0.285443i | \(-0.907859\pi\) |
0.231997 | − | 0.972716i | \(-0.425474\pi\) | |||||||
\(810\) | −4457.36 | + | 7720.38i | −0.193353 | + | 0.334897i | ||||
\(811\) | −8822.63 | −0.382003 | −0.191001 | − | 0.981590i | \(-0.561174\pi\) | ||||
−0.191001 | + | 0.981590i | \(0.561174\pi\) | |||||||
\(812\) | 6718.46 | + | 7285.79i | 0.290359 | + | 0.314878i | ||||
\(813\) | −10361.5 | −0.446978 | ||||||||
\(814\) | 40859.6 | − | 70770.9i | 1.75937 | − | 3.04732i | ||||
\(815\) | −21617.8 | − | 37443.1i | −0.929127 | − | 1.60929i | ||||
\(816\) | 996.052 | + | 1725.21i | 0.0427314 | + | 0.0740129i | ||||
\(817\) | −3707.17 | + | 6421.01i | −0.158749 | + | 0.274961i | ||||
\(818\) | −24603.6 | −1.05164 | ||||||||
\(819\) | 2246.09 | − | 7202.58i | 0.0958301 | − | 0.307300i | ||||
\(820\) | 19423.2 | 0.827181 | ||||||||
\(821\) | −13854.7 | + | 23997.1i | −0.588956 | + | 1.02010i | 0.405413 | + | 0.914134i | \(0.367128\pi\) |
−0.994369 | + | 0.105969i | \(0.966206\pi\) | |||||||
\(822\) | 15369.9 | + | 26621.4i | 0.652173 | + | 1.12960i | ||||
\(823\) | −6054.26 | − | 10486.3i | −0.256425 | − | 0.444142i | 0.708856 | − | 0.705353i | \(-0.249211\pi\) |
−0.965282 | + | 0.261211i | \(0.915878\pi\) | |||||||
\(824\) | −7372.39 | + | 12769.4i | −0.311686 | + | 0.539856i | ||||
\(825\) | −3359.07 | −0.141755 | ||||||||
\(826\) | −14308.7 | + | 3219.39i | −0.602739 | + | 0.135614i | ||||
\(827\) | 16709.2 | 0.702583 | 0.351292 | − | 0.936266i | \(-0.385743\pi\) | ||||
0.351292 | + | 0.936266i | \(0.385743\pi\) | |||||||
\(828\) | −866.785 | + | 1501.32i | −0.0363803 | + | 0.0630125i | ||||
\(829\) | 18843.8 | + | 32638.5i | 0.789474 | + | 1.36741i | 0.926290 | + | 0.376812i | \(0.122980\pi\) |
−0.136816 | + | 0.990597i | \(0.543687\pi\) | |||||||
\(830\) | −8191.32 | − | 14187.8i | −0.342560 | − | 0.593331i | ||||
\(831\) | −7758.08 | + | 13437.4i | −0.323856 | + | 0.560936i | ||||
\(832\) | −7200.09 | −0.300022 | ||||||||
\(833\) | 1948.99 | + | 1346.51i | 0.0810665 | + | 0.0560070i | ||||
\(834\) | 4834.53 | 0.200727 | ||||||||
\(835\) | 2574.66 | − | 4459.44i | 0.106706 | − | 0.184821i | ||||
\(836\) | 5752.95 | + | 9964.41i | 0.238003 | + | 0.412232i | ||||
\(837\) | −15639.7 | − | 27088.7i | −0.645861 | − | 1.11866i | ||||
\(838\) | −8052.66 | + | 13947.6i | −0.331950 | + | 0.574955i | ||||
\(839\) | 4982.49 | 0.205023 | 0.102512 | − | 0.994732i | \(-0.467312\pi\) | ||||
0.102512 | + | 0.994732i | \(0.467312\pi\) | |||||||
\(840\) | −5538.03 | + | 1246.03i | −0.227476 | + | 0.0511812i | ||||
\(841\) | −16290.1 | −0.667929 | ||||||||
\(842\) | −13464.0 | + | 23320.3i | −0.551068 | + | 0.954479i | ||||
\(843\) | 3029.18 | + | 5246.70i | 0.123761 | + | 0.214360i | ||||
\(844\) | 8116.24 | + | 14057.7i | 0.331010 | + | 0.573326i | ||||
\(845\) | −6145.94 | + | 10645.1i | −0.250209 | + | 0.433375i | ||||
\(846\) | −2550.66 | −0.103656 | ||||||||
\(847\) | −16449.0 | + | 52747.2i | −0.667289 | + | 2.13981i | ||||
\(848\) | 25185.3 | 1.01989 | ||||||||
\(849\) | −10987.9 | + | 19031.6i | −0.444175 | + | 0.769333i | ||||
\(850\) | −174.250 | − | 301.811i | −0.00703146 | − | 0.0121788i | ||||
\(851\) | 3831.21 | + | 6635.85i | 0.154327 | + | 0.267302i | ||||
\(852\) | 6653.86 | − | 11524.8i | 0.267556 | − | 0.463420i | ||||
\(853\) | 20816.1 | 0.835557 | 0.417778 | − | 0.908549i | \(-0.362809\pi\) | ||||
0.417778 | + | 0.908549i | \(0.362809\pi\) | |||||||
\(854\) | 17021.3 | + | 18458.7i | 0.682035 | + | 0.739628i | ||||
\(855\) | 3942.83 | 0.157710 | ||||||||
\(856\) | 948.233 | − | 1642.39i | 0.0378621 | − | 0.0655790i | ||||
\(857\) | −8612.45 | − | 14917.2i | −0.343286 | − | 0.594588i | 0.641755 | − | 0.766910i | \(-0.278207\pi\) |
−0.985041 | + | 0.172321i | \(0.944873\pi\) | |||||||
\(858\) | −14918.1 | − | 25838.9i | −0.593585 | − | 1.02812i | ||||
\(859\) | 22307.1 | − | 38637.0i | 0.886039 | − | 1.53466i | 0.0415208 | − | 0.999138i | \(-0.486780\pi\) |
0.844518 | − | 0.535527i | \(-0.179887\pi\) | |||||||
\(860\) | −15801.8 | −0.626554 | ||||||||
\(861\) | −14700.1 | − | 15941.4i | −0.581854 | − | 0.630988i | ||||
\(862\) | −36991.0 | −1.46162 | ||||||||
\(863\) | −5735.38 | + | 9933.97i | −0.226228 | + | 0.391838i | −0.956687 | − | 0.291118i | \(-0.905973\pi\) |
0.730459 | + | 0.682956i | \(0.239306\pi\) | |||||||
\(864\) | 16762.2 | + | 29032.9i | 0.660023 | + | 1.14319i | ||||
\(865\) | −13978.3 | − | 24211.1i | −0.549451 | − | 0.951677i | ||||
\(866\) | 5849.00 | − | 10130.8i | 0.229512 | − | 0.397526i | ||||
\(867\) | 18413.9 | 0.721303 | ||||||||
\(868\) | −6829.22 | + | 21899.4i | −0.267049 | + | 0.856352i | ||||
\(869\) | −22109.6 | −0.863081 | ||||||||
\(870\) | 6715.23 | − | 11631.1i | 0.261687 | − | 0.453255i | ||||
\(871\) | −3520.21 | − | 6097.18i | −0.136943 | − | 0.237193i | ||||
\(872\) | −389.246 | − | 674.193i | −0.0151164 | − | 0.0261824i | ||||
\(873\) | 3880.46 | − | 6721.15i | 0.150439 | − | 0.260569i | ||||
\(874\) | −2530.34 | −0.0979289 | ||||||||
\(875\) | 26425.6 | − | 5945.65i | 1.02097 | − | 0.229714i | ||||
\(876\) | −22947.2 | −0.885061 | ||||||||
\(877\) | 5950.84 | − | 10307.2i | 0.229129 | − | 0.396862i | −0.728422 | − | 0.685129i | \(-0.759746\pi\) |
0.957550 | + | 0.288267i | \(0.0930790\pi\) | |||||||
\(878\) | 8033.23 | + | 13914.0i | 0.308780 | + | 0.534822i | ||||
\(879\) | 1376.57 | + | 2384.29i | 0.0528221 | + | 0.0914905i | ||||
\(880\) | 26428.1 | − | 45774.8i | 1.01238 | − | 1.75349i | ||||
\(881\) | 3538.35 | 0.135312 | 0.0676561 | − | 0.997709i | \(-0.478448\pi\) | ||||
0.0676561 | + | 0.997709i | \(0.478448\pi\) | |||||||
\(882\) | 13358.5 | + | 9229.11i | 0.509983 | + | 0.352336i | ||||
\(883\) | −7915.33 | −0.301667 | −0.150834 | − | 0.988559i | \(-0.548196\pi\) | ||||
−0.150834 | + | 0.988559i | \(0.548196\pi\) | |||||||
\(884\) | 659.908 | − | 1142.99i | 0.0251076 | − | 0.0434876i | ||||
\(885\) | 4237.09 | + | 7338.86i | 0.160936 | + | 0.278749i | ||||
\(886\) | −9239.87 | − | 16003.9i | −0.350361 | − | 0.606843i | ||||
\(887\) | −13364.5 | + | 23148.0i | −0.505903 | + | 0.876251i | 0.494073 | + | 0.869420i | \(0.335507\pi\) |
−0.999977 | + | 0.00683020i | \(0.997826\pi\) | |||||||
\(888\) | 9670.66 | 0.365457 | ||||||||
\(889\) | −29223.2 | + | 6575.09i | −1.10249 | + | 0.248055i | ||||
\(890\) | −23668.0 | −0.891409 | ||||||||
\(891\) | −7424.95 | + | 12860.4i | −0.279175 | + | 0.483546i | ||||
\(892\) | −11922.4 | − | 20650.2i | −0.447523 | − | 0.775133i | ||||
\(893\) | −793.675 | − | 1374.69i | −0.0297417 | − | 0.0515141i | ||||
\(894\) | −5359.80 | + | 9283.45i | −0.200513 | + | 0.347299i | ||||
\(895\) | −2861.43 | −0.106868 | ||||||||
\(896\) | −5234.48 | + | 16785.5i | −0.195169 | + | 0.625852i | ||||
\(897\) | 2797.60 | 0.104135 | ||||||||
\(898\) | −14203.0 | + | 24600.3i | −0.527795 | + | 0.914168i | ||||
\(899\) | 9373.00 | + | 16234.5i | 0.347727 | + | 0.602282i | ||||
\(900\) | −509.224 | − | 882.001i | −0.0188601 | − | 0.0326667i | ||||
\(901\) | −1141.15 | + | 1976.54i | −0.0421946 | + | 0.0730832i | ||||
\(902\) | 75884.5 | 2.80119 | ||||||||
\(903\) | 11959.2 | + | 12969.1i | 0.440729 | + | 0.477946i | ||||
\(904\) | 12677.5 | 0.466425 | ||||||||
\(905\) | 23303.3 | − | 40362.4i | 0.855941 | − | 1.48253i | ||||
\(906\) | 21376.0 | + | 37024.2i | 0.783850 | + | 1.35767i | ||||
\(907\) | 18971.8 | + | 32860.1i | 0.694541 | + | 1.20298i | 0.970335 | + | 0.241764i | \(0.0777259\pi\) |
−0.275794 | + | 0.961217i | \(0.588941\pi\) | |||||||
\(908\) | −14371.5 | + | 24892.2i | −0.525260 | + | 0.909778i | ||||
\(909\) | 11063.5 | 0.403689 | ||||||||
\(910\) | 15910.3 | + | 17253.8i | 0.579585 | + | 0.628527i | ||||
\(911\) | 28622.9 | 1.04097 | 0.520483 | − | 0.853872i | \(-0.325752\pi\) | ||||
0.520483 | + | 0.853872i | \(0.325752\pi\) | |||||||
\(912\) | −4248.67 | + | 7358.91i | −0.154263 | + | 0.267191i | ||||
\(913\) | −13644.9 | − | 23633.6i | −0.494611 | − | 0.856691i | ||||
\(914\) | −5986.44 | − | 10368.8i | −0.216645 | − | 0.375241i | ||||
\(915\) | 7253.86 | − | 12564.1i | 0.262082 | − | 0.453940i | ||||
\(916\) | 32335.2 | 1.16636 | ||||||||
\(917\) | −12098.8 | + | 38797.5i | −0.435701 | + | 1.39717i | ||||
\(918\) | −3872.94 | −0.139244 | ||||||||
\(919\) | 3113.01 | − | 5391.90i | 0.111740 | − | 0.193539i | −0.804732 | − | 0.593638i | \(-0.797691\pi\) |
0.916472 | + | 0.400099i | \(0.131024\pi\) | |||||||
\(920\) | 931.308 | + | 1613.07i | 0.0333742 | + | 0.0578059i | ||||
\(921\) | −11850.6 | − | 20525.9i | −0.423987 | − | 0.734367i | ||||
\(922\) | −20878.2 | + | 36162.1i | −0.745756 | + | 1.29169i | ||||
\(923\) | 19004.1 | 0.677711 | ||||||||
\(924\) | 26709.1 | − | 6009.43i | 0.950936 | − | 0.213956i | ||||
\(925\) | −4501.56 | −0.160011 | ||||||||
\(926\) | 4359.46 | − | 7550.81i | 0.154709 | − | 0.267964i | ||||
\(927\) | −12184.3 | − | 21103.8i | −0.431698 | − | 0.747722i | ||||
\(928\) | −10045.7 | − | 17399.7i | −0.355353 | − | 0.615489i | ||||
\(929\) | −15455.2 | + | 26769.2i | −0.545822 | + | 0.945391i | 0.452733 | + | 0.891646i | \(0.350449\pi\) |
−0.998555 | + | 0.0537450i | \(0.982884\pi\) | |||||||
\(930\) | 31086.7 | 1.09610 | ||||||||
\(931\) | −817.353 | + | 10071.4i | −0.0287730 | + | 0.354541i | ||||
\(932\) | −24497.6 | −0.860992 | ||||||||
\(933\) | −10748.1 | + | 18616.2i | −0.377145 | + | 0.653234i | ||||
\(934\) | 27285.6 | + | 47260.1i | 0.955902 | + | 1.65567i | ||||
\(935\) | 2394.93 | + | 4148.14i | 0.0837674 | + | 0.145089i | ||||
\(936\) | −1562.23 | + | 2705.86i | −0.0545546 | + | 0.0944914i | ||||
\(937\) | −24419.6 | −0.851390 | −0.425695 | − | 0.904867i | \(-0.639970\pi\) | ||||
−0.425695 | + | 0.904867i | \(0.639970\pi\) | |||||||
\(938\) | 14781.9 | − | 3325.85i | 0.514547 | − | 0.115771i | ||||
\(939\) | 4398.63 | 0.152869 | ||||||||
\(940\) | 1691.52 | − | 2929.79i | 0.0586927 | − | 0.101659i | ||||
\(941\) | −27851.7 | − | 48240.5i | −0.964865 | − | 1.67120i | −0.709977 | − | 0.704225i | \(-0.751295\pi\) |
−0.254888 | − | 0.966970i | \(-0.582039\pi\) | |||||||
\(942\) | 23810.9 | + | 41241.7i | 0.823568 | + | 1.42646i | ||||
\(943\) | −3557.66 | + | 6162.05i | −0.122856 | + | 0.212793i | ||||
\(944\) | 16161.1 | 0.557204 | ||||||||
\(945\) | 8741.97 | − | 28033.0i | 0.300927 | − | 0.964988i | ||||
\(946\) | −61735.8 | −2.12178 | ||||||||
\(947\) | 14811.5 | − | 25654.2i | 0.508245 | − | 0.880306i | −0.491710 | − | 0.870759i | \(-0.663628\pi\) |
0.999954 | − | 0.00954673i | \(-0.00303887\pi\) | |||||||
\(948\) | 3787.66 | + | 6560.42i | 0.129765 | + | 0.224760i | ||||
\(949\) | −16384.9 | − | 28379.4i | −0.560459 | − | 0.970743i | ||||
\(950\) | 743.267 | − | 1287.38i | 0.0253840 | − | 0.0439663i | ||||
\(951\) | −29305.2 | −0.999248 | ||||||||
\(952\) | −665.041 | − | 721.199i | −0.0226409 | − | 0.0245527i | ||||
\(953\) | 21996.3 | 0.747671 | 0.373835 | − | 0.927495i | \(-0.378043\pi\) | ||||
0.373835 | + | 0.927495i | \(0.378043\pi\) | |||||||
\(954\) | −7821.57 | + | 13547.4i | −0.265443 | + | 0.459761i | ||||
\(955\) | −6247.91 | − | 10821.7i | −0.211704 | − | 0.366683i | ||||
\(956\) | 1783.42 | + | 3088.98i | 0.0603347 | + | 0.104503i | ||||
\(957\) | 11186.1 | − | 19374.8i | 0.377841 | − | 0.654440i | ||||
\(958\) | 45008.9 | 1.51792 | ||||||||
\(959\) | −27305.6 | − | 29611.4i | −0.919441 | − | 0.997081i | ||||
\(960\) | −8952.96 | −0.300995 | ||||||||
\(961\) | −6799.60 | + | 11777.3i | −0.228244 | + | 0.395329i | ||||
\(962\) | −19992.1 | − | 34627.3i | −0.670031 | − | 1.16053i | ||||
\(963\) | 1567.13 | + | 2714.35i | 0.0524405 | + | 0.0908295i | ||||
\(964\) | 7085.25 | − | 12272.0i | 0.236722 | − | 0.410015i | ||||
\(965\) | −11733.1 | −0.391400 | ||||||||
\(966\) | −1792.37 | + | 5747.61i | −0.0596982 | + | 0.191435i | ||||
\(967\) | −25243.2 | −0.839470 | −0.419735 | − | 0.907647i | \(-0.637877\pi\) | ||||
−0.419735 | + | 0.907647i | \(0.637877\pi\) | |||||||
\(968\) | 11440.8 | − | 19816.0i | 0.379877 | − | 0.657967i | ||||
\(969\) | −385.016 | − | 666.868i | −0.0127642 | − | 0.0221082i | ||||
\(970\) | 12071.3 | + | 20908.0i | 0.399572 | + | 0.692079i | ||||
\(971\) | 25647.0 | − | 44421.8i | 0.847632 | − | 1.46814i | −0.0356846 | − | 0.999363i | \(-0.511361\pi\) |
0.883316 | − | 0.468778i | \(-0.155305\pi\) | |||||||
\(972\) | −19020.3 | −0.627651 | ||||||||
\(973\) | −6180.35 | + | 1390.55i | −0.203631 | + | 0.0458161i | ||||
\(974\) | 68060.7 | 2.23902 | ||||||||
\(975\) | −821.774 | + | 1423.35i | −0.0269926 | + | 0.0467526i | ||||
\(976\) | −13833.9 | − | 23961.0i | −0.453700 | − | 0.785832i | ||||
\(977\) | −4815.82 | − | 8341.24i | −0.157699 | − | 0.273142i | 0.776340 | − | 0.630315i | \(-0.217074\pi\) |
−0.934038 | + | 0.357173i | \(0.883741\pi\) | |||||||
\(978\) | −28937.6 | + | 50121.4i | −0.946137 | + | 1.63876i | ||||
\(979\) | −39425.5 | −1.28707 | ||||||||
\(980\) | −19459.9 | + | 9223.72i | −0.634310 | + | 0.300654i | ||||
\(981\) | 1286.60 | 0.0418737 | ||||||||
\(982\) | 7289.41 | − | 12625.6i | 0.236878 | − | 0.410285i | ||||
\(983\) | −17510.9 | − | 30329.8i | −0.568170 | − | 0.984099i | −0.996747 | − | 0.0805940i | \(-0.974318\pi\) |
0.428577 | − | 0.903505i | \(-0.359015\pi\) | |||||||
\(984\) | 4490.09 | + | 7777.06i | 0.145466 | + | 0.251955i | ||||
\(985\) | −26012.1 | + | 45054.2i | −0.841435 | + | 1.45741i | ||||
\(986\) | 2321.09 | 0.0749681 | ||||||||
\(987\) | −3684.78 | + | 829.058i | −0.118833 | + | 0.0267368i | ||||
\(988\) | 5629.69 | 0.181280 | ||||||||
\(989\) | 2894.34 | − | 5013.14i | 0.0930582 | − | 0.161181i | ||||
\(990\) | 16415.1 | + | 28431.7i | 0.526975 | + | 0.912747i | ||||
\(991\) | 24574.2 | + | 42563.8i | 0.787714 | + | 1.36436i | 0.927364 | + | 0.374160i | \(0.122069\pi\) |
−0.139650 | + | 0.990201i | \(0.544598\pi\) | |||||||
\(992\) | 23252.2 | − | 40274.0i | 0.744213 | − | 1.28901i | ||||
\(993\) | −24992.5 | −0.798703 | ||||||||
\(994\) | −12175.6 | + | 39043.5i | −0.388516 | + | 1.24586i | ||||
\(995\) | −26190.4 | −0.834463 | ||||||||
\(996\) | −4675.08 | + | 8097.48i | −0.148731 | + | 0.257609i | ||||
\(997\) | 9314.55 | + | 16133.3i | 0.295883 | + | 0.512484i | 0.975190 | − | 0.221370i | \(-0.0710530\pi\) |
−0.679307 | + | 0.733854i | \(0.737720\pi\) | |||||||
\(998\) | −37055.2 | − | 64181.4i | −1.17531 | − | 2.03570i | ||||
\(999\) | −25013.2 | + | 43324.1i | −0.792175 | + | 1.37209i |
(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 | 161.4.e.a.93.5 | ✓ | 44 | |
7.2 | even | 3 | 1127.4.a.l.1.18 | 22 | |||
7.4 | even | 3 | inner | 161.4.e.a.116.5 | yes | 44 | |
7.5 | odd | 6 | 1127.4.a.k.1.18 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.4.e.a.93.5 | ✓ | 44 | 1.1 | even | 1 | trivial | |
161.4.e.a.116.5 | yes | 44 | 7.4 | even | 3 | inner | |
1127.4.a.k.1.18 | 22 | 7.5 | odd | 6 | |||
1127.4.a.l.1.18 | 22 | 7.2 | even | 3 |