Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,4,Mod(25,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("42.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.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: | \(2.47808022024\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 42.37 |
Dual form | 42.4.e.a.25.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 3.00000 | − | 5.19615i | 0.268328 | − | 0.464758i | −0.700102 | − | 0.714043i | \(-0.746862\pi\) |
0.968430 | + | 0.249285i | \(0.0801955\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −3.50000 | − | 18.1865i | −0.188982 | − | 0.981981i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −6.00000 | − | 10.3923i | −0.189737 | − | 0.328634i | ||||
\(11\) | 15.0000 | + | 25.9808i | 0.411152 | + | 0.712136i | 0.995016 | − | 0.0997155i | \(-0.0317933\pi\) |
−0.583864 | + | 0.811851i | \(0.698460\pi\) | |||||||
\(12\) | −6.00000 | + | 10.3923i | −0.144338 | + | 0.250000i | ||||
\(13\) | 53.0000 | 1.13074 | 0.565368 | − | 0.824839i | \(-0.308734\pi\) | ||||
0.565368 | + | 0.824839i | \(0.308734\pi\) | |||||||
\(14\) | −35.0000 | − | 12.1244i | −0.668153 | − | 0.231455i | ||||
\(15\) | −18.0000 | −0.309839 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 42.0000 | + | 72.7461i | 0.599206 | + | 1.03785i | 0.992939 | + | 0.118630i | \(0.0378502\pi\) |
−0.393733 | + | 0.919225i | \(0.628817\pi\) | |||||||
\(18\) | 9.00000 | + | 15.5885i | 0.117851 | + | 0.204124i | ||||
\(19\) | 48.5000 | − | 84.0045i | 0.585614 | − | 1.01431i | −0.409185 | − | 0.912452i | \(-0.634187\pi\) |
0.994799 | − | 0.101861i | \(-0.0324798\pi\) | |||||||
\(20\) | −24.0000 | −0.268328 | ||||||||
\(21\) | −42.0000 | + | 36.3731i | −0.436436 | + | 0.377964i | ||||
\(22\) | 60.0000 | 0.581456 | ||||||||
\(23\) | −42.0000 | + | 72.7461i | −0.380765 | + | 0.659505i | −0.991172 | − | 0.132583i | \(-0.957673\pi\) |
0.610406 | + | 0.792088i | \(0.291006\pi\) | |||||||
\(24\) | 12.0000 | + | 20.7846i | 0.102062 | + | 0.176777i | ||||
\(25\) | 44.5000 | + | 77.0763i | 0.356000 | + | 0.616610i | ||||
\(26\) | 53.0000 | − | 91.7987i | 0.399775 | − | 0.692431i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −56.0000 | + | 48.4974i | −0.377964 | + | 0.327327i | ||||
\(29\) | −180.000 | −1.15259 | −0.576296 | − | 0.817241i | \(-0.695502\pi\) | ||||
−0.576296 | + | 0.817241i | \(0.695502\pi\) | |||||||
\(30\) | −18.0000 | + | 31.1769i | −0.109545 | + | 0.189737i | ||||
\(31\) | −89.5000 | − | 155.019i | −0.518538 | − | 0.898134i | −0.999768 | − | 0.0215397i | \(-0.993143\pi\) |
0.481230 | − | 0.876594i | \(-0.340190\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 45.0000 | − | 77.9423i | 0.237379 | − | 0.411152i | ||||
\(34\) | 168.000 | 0.847405 | ||||||||
\(35\) | −105.000 | − | 36.3731i | −0.507093 | − | 0.175662i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 72.5000 | − | 125.574i | 0.322133 | − | 0.557951i | −0.658795 | − | 0.752323i | \(-0.728933\pi\) |
0.980928 | + | 0.194372i | \(0.0622668\pi\) | |||||||
\(38\) | −97.0000 | − | 168.009i | −0.414092 | − | 0.717228i | ||||
\(39\) | −79.5000 | − | 137.698i | −0.326415 | − | 0.565368i | ||||
\(40\) | −24.0000 | + | 41.5692i | −0.0948683 | + | 0.164317i | ||||
\(41\) | 126.000 | 0.479949 | 0.239974 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239974 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(42\) | 21.0000 | + | 109.119i | 0.0771517 | + | 0.400892i | ||||
\(43\) | −325.000 | −1.15261 | −0.576303 | − | 0.817236i | \(-0.695505\pi\) | ||||
−0.576303 | + | 0.817236i | \(0.695505\pi\) | |||||||
\(44\) | 60.0000 | − | 103.923i | 0.205576 | − | 0.356068i | ||||
\(45\) | 27.0000 | + | 46.7654i | 0.0894427 | + | 0.154919i | ||||
\(46\) | 84.0000 | + | 145.492i | 0.269242 | + | 0.466341i | ||||
\(47\) | 183.000 | − | 316.965i | 0.567942 | − | 0.983705i | −0.428827 | − | 0.903387i | \(-0.641073\pi\) |
0.996769 | − | 0.0803184i | \(-0.0255937\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −318.500 | + | 127.306i | −0.928571 | + | 0.371154i | ||||
\(50\) | 178.000 | 0.503460 | ||||||||
\(51\) | 126.000 | − | 218.238i | 0.345952 | − | 0.599206i | ||||
\(52\) | −106.000 | − | 183.597i | −0.282684 | − | 0.489623i | ||||
\(53\) | 384.000 | + | 665.108i | 0.995216 | + | 1.72376i | 0.582217 | + | 0.813034i | \(0.302186\pi\) |
0.413000 | + | 0.910731i | \(0.364481\pi\) | |||||||
\(54\) | 27.0000 | − | 46.7654i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 180.000 | 0.441294 | ||||||||
\(56\) | 28.0000 | + | 145.492i | 0.0668153 | + | 0.347183i | ||||
\(57\) | −291.000 | −0.676209 | ||||||||
\(58\) | −180.000 | + | 311.769i | −0.407503 | + | 0.705815i | ||||
\(59\) | 132.000 | + | 228.631i | 0.291270 | + | 0.504495i | 0.974110 | − | 0.226073i | \(-0.0725888\pi\) |
−0.682840 | + | 0.730568i | \(0.739255\pi\) | |||||||
\(60\) | 36.0000 | + | 62.3538i | 0.0774597 | + | 0.134164i | ||||
\(61\) | −409.000 | + | 708.409i | −0.858477 | + | 1.48693i | 0.0149048 | + | 0.999889i | \(0.495255\pi\) |
−0.873382 | + | 0.487036i | \(0.838078\pi\) | |||||||
\(62\) | −358.000 | −0.733323 | ||||||||
\(63\) | 157.500 | + | 54.5596i | 0.314970 | + | 0.109109i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 159.000 | − | 275.396i | 0.303408 | − | 0.525518i | ||||
\(66\) | −90.0000 | − | 155.885i | −0.167852 | − | 0.290728i | ||||
\(67\) | 261.500 | + | 452.931i | 0.476826 | + | 0.825886i | 0.999647 | − | 0.0265560i | \(-0.00845402\pi\) |
−0.522822 | + | 0.852442i | \(0.675121\pi\) | |||||||
\(68\) | 168.000 | − | 290.985i | 0.299603 | − | 0.518927i | ||||
\(69\) | 252.000 | 0.439670 | ||||||||
\(70\) | −168.000 | + | 145.492i | −0.286855 | + | 0.248424i | ||||
\(71\) | −342.000 | −0.571661 | −0.285831 | − | 0.958280i | \(-0.592269\pi\) | ||||
−0.285831 | + | 0.958280i | \(0.592269\pi\) | |||||||
\(72\) | 36.0000 | − | 62.3538i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 21.5000 | + | 37.2391i | 0.0344710 | + | 0.0597056i | 0.882746 | − | 0.469850i | \(-0.155692\pi\) |
−0.848275 | + | 0.529556i | \(0.822359\pi\) | |||||||
\(74\) | −145.000 | − | 251.147i | −0.227783 | − | 0.394531i | ||||
\(75\) | 133.500 | − | 231.229i | 0.205537 | − | 0.356000i | ||||
\(76\) | −388.000 | −0.585614 | ||||||||
\(77\) | 420.000 | − | 363.731i | 0.621603 | − | 0.538324i | ||||
\(78\) | −318.000 | −0.461621 | ||||||||
\(79\) | 585.500 | − | 1014.12i | 0.833847 | − | 1.44427i | −0.0611191 | − | 0.998130i | \(-0.519467\pi\) |
0.894966 | − | 0.446135i | \(-0.147200\pi\) | |||||||
\(80\) | 48.0000 | + | 83.1384i | 0.0670820 | + | 0.116190i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 126.000 | − | 218.238i | 0.169687 | − | 0.293907i | ||||
\(83\) | −810.000 | −1.07119 | −0.535597 | − | 0.844474i | \(-0.679913\pi\) | ||||
−0.535597 | + | 0.844474i | \(0.679913\pi\) | |||||||
\(84\) | 210.000 | + | 72.7461i | 0.272772 | + | 0.0944911i | ||||
\(85\) | 504.000 | 0.643135 | ||||||||
\(86\) | −325.000 | + | 562.917i | −0.407508 | + | 0.705824i | ||||
\(87\) | 270.000 | + | 467.654i | 0.332725 | + | 0.576296i | ||||
\(88\) | −120.000 | − | 207.846i | −0.145364 | − | 0.251778i | ||||
\(89\) | 300.000 | − | 519.615i | 0.357303 | − | 0.618866i | −0.630207 | − | 0.776428i | \(-0.717030\pi\) |
0.987509 | + | 0.157561i | \(0.0503631\pi\) | |||||||
\(90\) | 108.000 | 0.126491 | ||||||||
\(91\) | −185.500 | − | 963.886i | −0.213689 | − | 1.11036i | ||||
\(92\) | 336.000 | 0.380765 | ||||||||
\(93\) | −268.500 | + | 465.056i | −0.299378 | + | 0.518538i | ||||
\(94\) | −366.000 | − | 633.931i | −0.401596 | − | 0.695585i | ||||
\(95\) | −291.000 | − | 504.027i | −0.314273 | − | 0.544337i | ||||
\(96\) | 48.0000 | − | 83.1384i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 386.000 | 0.404045 | 0.202022 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202022 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(98\) | −98.0000 | + | 678.964i | −0.101015 | + | 0.699854i | ||||
\(99\) | −270.000 | −0.274101 | ||||||||
\(100\) | 178.000 | − | 308.305i | 0.178000 | − | 0.308305i | ||||
\(101\) | −309.000 | − | 535.204i | −0.304422 | − | 0.527275i | 0.672710 | − | 0.739906i | \(-0.265130\pi\) |
−0.977133 | + | 0.212631i | \(0.931797\pi\) | |||||||
\(102\) | −252.000 | − | 436.477i | −0.244625 | − | 0.423702i | ||||
\(103\) | −737.500 | + | 1277.39i | −0.705515 | + | 1.22199i | 0.260991 | + | 0.965341i | \(0.415951\pi\) |
−0.966505 | + | 0.256646i | \(0.917382\pi\) | |||||||
\(104\) | −424.000 | −0.399775 | ||||||||
\(105\) | 63.0000 | + | 327.358i | 0.0585540 | + | 0.304256i | ||||
\(106\) | 1536.00 | 1.40745 | ||||||||
\(107\) | −942.000 | + | 1631.59i | −0.851090 | + | 1.47413i | 0.0291364 | + | 0.999575i | \(0.490724\pi\) |
−0.880226 | + | 0.474555i | \(0.842609\pi\) | |||||||
\(108\) | −54.0000 | − | 93.5307i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −206.500 | − | 357.668i | −0.181460 | − | 0.314298i | 0.760918 | − | 0.648848i | \(-0.224749\pi\) |
−0.942378 | + | 0.334550i | \(0.891416\pi\) | |||||||
\(110\) | 180.000 | − | 311.769i | 0.156021 | − | 0.270237i | ||||
\(111\) | −435.000 | −0.371967 | ||||||||
\(112\) | 280.000 | + | 96.9948i | 0.236228 | + | 0.0818317i | ||||
\(113\) | −882.000 | −0.734262 | −0.367131 | − | 0.930169i | \(-0.619660\pi\) | ||||
−0.367131 | + | 0.930169i | \(0.619660\pi\) | |||||||
\(114\) | −291.000 | + | 504.027i | −0.239076 | + | 0.414092i | ||||
\(115\) | 252.000 | + | 436.477i | 0.204340 | + | 0.353928i | ||||
\(116\) | 360.000 | + | 623.538i | 0.288148 | + | 0.499087i | ||||
\(117\) | −238.500 | + | 413.094i | −0.188456 | + | 0.326415i | ||||
\(118\) | 528.000 | 0.411918 | ||||||||
\(119\) | 1176.00 | − | 1018.45i | 0.905914 | − | 0.784544i | ||||
\(120\) | 144.000 | 0.109545 | ||||||||
\(121\) | 215.500 | − | 373.257i | 0.161908 | − | 0.280433i | ||||
\(122\) | 818.000 | + | 1416.82i | 0.607035 | + | 1.05142i | ||||
\(123\) | −189.000 | − | 327.358i | −0.138549 | − | 0.239974i | ||||
\(124\) | −358.000 | + | 620.074i | −0.259269 | + | 0.449067i | ||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 252.000 | − | 218.238i | 0.178174 | − | 0.154303i | ||||
\(127\) | 2483.00 | 1.73489 | 0.867443 | − | 0.497536i | \(-0.165762\pi\) | ||||
0.867443 | + | 0.497536i | \(0.165762\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 487.500 | + | 844.375i | 0.332729 | + | 0.576303i | ||||
\(130\) | −318.000 | − | 550.792i | −0.214542 | − | 0.371597i | ||||
\(131\) | −1059.00 | + | 1834.24i | −0.706300 | + | 1.22335i | 0.259921 | + | 0.965630i | \(0.416304\pi\) |
−0.966220 | + | 0.257717i | \(0.917030\pi\) | |||||||
\(132\) | −360.000 | −0.237379 | ||||||||
\(133\) | −1697.50 | − | 588.031i | −1.10671 | − | 0.383374i | ||||
\(134\) | 1046.00 | 0.674333 | ||||||||
\(135\) | 81.0000 | − | 140.296i | 0.0516398 | − | 0.0894427i | ||||
\(136\) | −336.000 | − | 581.969i | −0.211851 | − | 0.366937i | ||||
\(137\) | −1506.00 | − | 2608.47i | −0.939170 | − | 1.62669i | −0.767024 | − | 0.641618i | \(-0.778263\pi\) |
−0.172146 | − | 0.985071i | \(-0.555070\pi\) | |||||||
\(138\) | 252.000 | − | 436.477i | 0.155447 | − | 0.269242i | ||||
\(139\) | −37.0000 | −0.0225777 | −0.0112888 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112888 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(140\) | 84.0000 | + | 436.477i | 0.0507093 | + | 0.263493i | ||||
\(141\) | −1098.00 | −0.655803 | ||||||||
\(142\) | −342.000 | + | 592.361i | −0.202113 | + | 0.350069i | ||||
\(143\) | 795.000 | + | 1376.98i | 0.464904 | + | 0.805237i | ||||
\(144\) | −72.0000 | − | 124.708i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −540.000 | + | 935.307i | −0.309273 | + | 0.535676i | ||||
\(146\) | 86.0000 | 0.0487494 | ||||||||
\(147\) | 808.500 | + | 636.529i | 0.453632 | + | 0.357143i | ||||
\(148\) | −580.000 | −0.322133 | ||||||||
\(149\) | 822.000 | − | 1423.75i | 0.451952 | − | 0.782804i | −0.546555 | − | 0.837423i | \(-0.684061\pi\) |
0.998507 | + | 0.0546191i | \(0.0173945\pi\) | |||||||
\(150\) | −267.000 | − | 462.458i | −0.145336 | − | 0.251730i | ||||
\(151\) | −544.000 | − | 942.236i | −0.293179 | − | 0.507802i | 0.681380 | − | 0.731930i | \(-0.261380\pi\) |
−0.974560 | + | 0.224128i | \(0.928047\pi\) | |||||||
\(152\) | −388.000 | + | 672.036i | −0.207046 | + | 0.358614i | ||||
\(153\) | −756.000 | −0.399470 | ||||||||
\(154\) | −210.000 | − | 1091.19i | −0.109885 | − | 0.570979i | ||||
\(155\) | −1074.00 | −0.556553 | ||||||||
\(156\) | −318.000 | + | 550.792i | −0.163208 | + | 0.282684i | ||||
\(157\) | −253.000 | − | 438.209i | −0.128609 | − | 0.222757i | 0.794529 | − | 0.607226i | \(-0.207718\pi\) |
−0.923138 | + | 0.384469i | \(0.874385\pi\) | |||||||
\(158\) | −1171.00 | − | 2028.23i | −0.589619 | − | 1.02125i | ||||
\(159\) | 1152.00 | − | 1995.32i | 0.574588 | − | 0.995216i | ||||
\(160\) | 192.000 | 0.0948683 | ||||||||
\(161\) | 1470.00 | + | 509.223i | 0.719579 | + | 0.249270i | ||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −922.000 | + | 1596.95i | −0.443047 | + | 0.767379i | −0.997914 | − | 0.0645596i | \(-0.979436\pi\) |
0.554867 | + | 0.831939i | \(0.312769\pi\) | |||||||
\(164\) | −252.000 | − | 436.477i | −0.119987 | − | 0.207824i | ||||
\(165\) | −270.000 | − | 467.654i | −0.127391 | − | 0.220647i | ||||
\(166\) | −810.000 | + | 1402.96i | −0.378724 | + | 0.655969i | ||||
\(167\) | 162.000 | 0.0750655 | 0.0375327 | − | 0.999295i | \(-0.488050\pi\) | ||||
0.0375327 | + | 0.999295i | \(0.488050\pi\) | |||||||
\(168\) | 336.000 | − | 290.985i | 0.154303 | − | 0.133631i | ||||
\(169\) | 612.000 | 0.278562 | ||||||||
\(170\) | 504.000 | − | 872.954i | 0.227383 | − | 0.393838i | ||||
\(171\) | 436.500 | + | 756.040i | 0.195205 | + | 0.338104i | ||||
\(172\) | 650.000 | + | 1125.83i | 0.288151 | + | 0.499093i | ||||
\(173\) | 1362.00 | − | 2359.05i | 0.598560 | − | 1.03674i | −0.394473 | − | 0.918907i | \(-0.629073\pi\) |
0.993034 | − | 0.117830i | \(-0.0375937\pi\) | |||||||
\(174\) | 1080.00 | 0.470544 | ||||||||
\(175\) | 1246.00 | − | 1079.07i | 0.538221 | − | 0.466113i | ||||
\(176\) | −480.000 | −0.205576 | ||||||||
\(177\) | 396.000 | − | 685.892i | 0.168165 | − | 0.291270i | ||||
\(178\) | −600.000 | − | 1039.23i | −0.252651 | − | 0.437605i | ||||
\(179\) | 627.000 | + | 1086.00i | 0.261811 | + | 0.453470i | 0.966723 | − | 0.255825i | \(-0.0823469\pi\) |
−0.704912 | + | 0.709295i | \(0.749014\pi\) | |||||||
\(180\) | 108.000 | − | 187.061i | 0.0447214 | − | 0.0774597i | ||||
\(181\) | −1807.00 | −0.742062 | −0.371031 | − | 0.928620i | \(-0.620996\pi\) | ||||
−0.371031 | + | 0.928620i | \(0.620996\pi\) | |||||||
\(182\) | −1855.00 | − | 642.591i | −0.755504 | − | 0.261714i | ||||
\(183\) | 2454.00 | 0.991284 | ||||||||
\(184\) | 336.000 | − | 581.969i | 0.134621 | − | 0.233170i | ||||
\(185\) | −435.000 | − | 753.442i | −0.172875 | − | 0.299428i | ||||
\(186\) | 537.000 | + | 930.111i | 0.211692 | + | 0.366662i | ||||
\(187\) | −1260.00 | + | 2182.38i | −0.492729 | + | 0.853432i | ||||
\(188\) | −1464.00 | −0.567942 | ||||||||
\(189\) | −94.5000 | − | 491.036i | −0.0363696 | − | 0.188982i | ||||
\(190\) | −1164.00 | −0.444450 | ||||||||
\(191\) | −357.000 | + | 618.342i | −0.135244 | + | 0.234250i | −0.925691 | − | 0.378281i | \(-0.876515\pi\) |
0.790447 | + | 0.612531i | \(0.209849\pi\) | |||||||
\(192\) | −96.0000 | − | 166.277i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 1854.50 | + | 3212.09i | 0.691657 | + | 1.19799i | 0.971295 | + | 0.237880i | \(0.0764524\pi\) |
−0.279637 | + | 0.960106i | \(0.590214\pi\) | |||||||
\(194\) | 386.000 | − | 668.572i | 0.142851 | − | 0.247426i | ||||
\(195\) | −954.000 | −0.350345 | ||||||||
\(196\) | 1078.00 | + | 848.705i | 0.392857 | + | 0.309295i | ||||
\(197\) | −1044.00 | −0.377573 | −0.188787 | − | 0.982018i | \(-0.560455\pi\) | ||||
−0.188787 | + | 0.982018i | \(0.560455\pi\) | |||||||
\(198\) | −270.000 | + | 467.654i | −0.0969094 | + | 0.167852i | ||||
\(199\) | 68.0000 | + | 117.779i | 0.0242231 | + | 0.0419556i | 0.877883 | − | 0.478875i | \(-0.158955\pi\) |
−0.853660 | + | 0.520831i | \(0.825622\pi\) | |||||||
\(200\) | −356.000 | − | 616.610i | −0.125865 | − | 0.218005i | ||||
\(201\) | 784.500 | − | 1358.79i | 0.275295 | − | 0.476826i | ||||
\(202\) | −1236.00 | −0.430518 | ||||||||
\(203\) | 630.000 | + | 3273.58i | 0.217819 | + | 1.13182i | ||||
\(204\) | −1008.00 | −0.345952 | ||||||||
\(205\) | 378.000 | − | 654.715i | 0.128784 | − | 0.223060i | ||||
\(206\) | 1475.00 | + | 2554.77i | 0.498874 | + | 0.864076i | ||||
\(207\) | −378.000 | − | 654.715i | −0.126922 | − | 0.219835i | ||||
\(208\) | −424.000 | + | 734.390i | −0.141342 | + | 0.244811i | ||||
\(209\) | 2910.00 | 0.963105 | ||||||||
\(210\) | 630.000 | + | 218.238i | 0.207020 | + | 0.0717137i | ||||
\(211\) | 1484.00 | 0.484184 | 0.242092 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242092 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(212\) | 1536.00 | − | 2660.43i | 0.497608 | − | 0.861882i | ||||
\(213\) | 513.000 | + | 888.542i | 0.165024 | + | 0.285831i | ||||
\(214\) | 1884.00 | + | 3263.18i | 0.601811 | + | 1.04237i | ||||
\(215\) | −975.000 | + | 1688.75i | −0.309277 | + | 0.535683i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −2506.00 | + | 2170.26i | −0.783956 | + | 0.678925i | ||||
\(218\) | −826.000 | −0.256623 | ||||||||
\(219\) | 64.5000 | − | 111.717i | 0.0199019 | − | 0.0344710i | ||||
\(220\) | −360.000 | − | 623.538i | −0.110324 | − | 0.191086i | ||||
\(221\) | 2226.00 | + | 3855.55i | 0.677543 | + | 1.17354i | ||||
\(222\) | −435.000 | + | 753.442i | −0.131510 | + | 0.227783i | ||||
\(223\) | −2032.00 | −0.610192 | −0.305096 | − | 0.952322i | \(-0.598689\pi\) | ||||
−0.305096 | + | 0.952322i | \(0.598689\pi\) | |||||||
\(224\) | 448.000 | − | 387.979i | 0.133631 | − | 0.115728i | ||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | −882.000 | + | 1527.67i | −0.259601 | + | 0.449642i | ||||
\(227\) | −3099.00 | − | 5367.63i | −0.906114 | − | 1.56944i | −0.819415 | − | 0.573201i | \(-0.805702\pi\) |
−0.0866989 | − | 0.996235i | \(-0.527632\pi\) | |||||||
\(228\) | 582.000 | + | 1008.05i | 0.169052 | + | 0.292807i | ||||
\(229\) | 2295.50 | − | 3975.92i | 0.662406 | − | 1.14732i | −0.317576 | − | 0.948233i | \(-0.602869\pi\) |
0.979982 | − | 0.199088i | \(-0.0637978\pi\) | |||||||
\(230\) | 1008.00 | 0.288981 | ||||||||
\(231\) | −1575.00 | − | 545.596i | −0.448603 | − | 0.155401i | ||||
\(232\) | 1440.00 | 0.407503 | ||||||||
\(233\) | −2265.00 | + | 3923.10i | −0.636846 | + | 1.10305i | 0.349275 | + | 0.937020i | \(0.386428\pi\) |
−0.986121 | + | 0.166029i | \(0.946905\pi\) | |||||||
\(234\) | 477.000 | + | 826.188i | 0.133258 | + | 0.230810i | ||||
\(235\) | −1098.00 | − | 1901.79i | −0.304790 | − | 0.527912i | ||||
\(236\) | 528.000 | − | 914.523i | 0.145635 | − | 0.252247i | ||||
\(237\) | −3513.00 | −0.962843 | ||||||||
\(238\) | −588.000 | − | 3055.34i | −0.160144 | − | 0.832135i | ||||
\(239\) | 1530.00 | 0.414090 | 0.207045 | − | 0.978331i | \(-0.433615\pi\) | ||||
0.207045 | + | 0.978331i | \(0.433615\pi\) | |||||||
\(240\) | 144.000 | − | 249.415i | 0.0387298 | − | 0.0670820i | ||||
\(241\) | −2767.00 | − | 4792.58i | −0.739577 | − | 1.28099i | −0.952686 | − | 0.303957i | \(-0.901692\pi\) |
0.213108 | − | 0.977029i | \(-0.431641\pi\) | |||||||
\(242\) | −431.000 | − | 746.514i | −0.114486 | − | 0.198296i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3272.00 | 0.858477 | ||||||||
\(245\) | −294.000 | + | 2036.89i | −0.0766652 | + | 0.531152i | ||||
\(246\) | −756.000 | −0.195938 | ||||||||
\(247\) | 2570.50 | − | 4452.24i | 0.662174 | − | 1.14692i | ||||
\(248\) | 716.000 | + | 1240.15i | 0.183331 | + | 0.317538i | ||||
\(249\) | 1215.00 | + | 2104.44i | 0.309227 | + | 0.535597i | ||||
\(250\) | 1284.00 | − | 2223.95i | 0.324829 | − | 0.562621i | ||||
\(251\) | −468.000 | −0.117689 | −0.0588444 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588444 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(252\) | −126.000 | − | 654.715i | −0.0314970 | − | 0.163663i | ||||
\(253\) | −2520.00 | −0.626210 | ||||||||
\(254\) | 2483.00 | − | 4300.68i | 0.613375 | − | 1.06240i | ||||
\(255\) | −756.000 | − | 1309.43i | −0.185657 | − | 0.321568i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1245.00 | − | 2156.40i | 0.302183 | − | 0.523396i | −0.674447 | − | 0.738323i | \(-0.735618\pi\) |
0.976630 | + | 0.214927i | \(0.0689514\pi\) | |||||||
\(258\) | 1950.00 | 0.470549 | ||||||||
\(259\) | −2537.50 | − | 879.016i | −0.608774 | − | 0.210886i | ||||
\(260\) | −1272.00 | −0.303408 | ||||||||
\(261\) | 810.000 | − | 1402.96i | 0.192099 | − | 0.332725i | ||||
\(262\) | 2118.00 | + | 3668.48i | 0.499429 | + | 0.865037i | ||||
\(263\) | −786.000 | − | 1361.39i | −0.184285 | − | 0.319190i | 0.759051 | − | 0.651032i | \(-0.225663\pi\) |
−0.943335 | + | 0.331841i | \(0.892330\pi\) | |||||||
\(264\) | −360.000 | + | 623.538i | −0.0839260 | + | 0.145364i | ||||
\(265\) | 4608.00 | 1.06818 | ||||||||
\(266\) | −2716.00 | + | 2352.12i | −0.626048 | + | 0.542173i | ||||
\(267\) | −1800.00 | −0.412578 | ||||||||
\(268\) | 1046.00 | − | 1811.73i | 0.238413 | − | 0.412943i | ||||
\(269\) | −903.000 | − | 1564.04i | −0.204672 | − | 0.354503i | 0.745356 | − | 0.666667i | \(-0.232280\pi\) |
−0.950028 | + | 0.312164i | \(0.898946\pi\) | |||||||
\(270\) | −162.000 | − | 280.592i | −0.0365148 | − | 0.0632456i | ||||
\(271\) | 3056.00 | − | 5293.15i | 0.685014 | − | 1.18648i | −0.288418 | − | 0.957504i | \(-0.593129\pi\) |
0.973432 | − | 0.228975i | \(-0.0735372\pi\) | |||||||
\(272\) | −1344.00 | −0.299603 | ||||||||
\(273\) | −2226.00 | + | 1927.77i | −0.493493 | + | 0.427378i | ||||
\(274\) | −6024.00 | −1.32819 | ||||||||
\(275\) | −1335.00 | + | 2312.29i | −0.292740 | + | 0.507041i | ||||
\(276\) | −504.000 | − | 872.954i | −0.109918 | − | 0.190383i | ||||
\(277\) | 2115.50 | + | 3664.15i | 0.458874 | + | 0.794793i | 0.998902 | − | 0.0468542i | \(-0.0149196\pi\) |
−0.540028 | + | 0.841647i | \(0.681586\pi\) | |||||||
\(278\) | −37.0000 | + | 64.0859i | −0.00798242 | + | 0.0138260i | ||||
\(279\) | 1611.00 | 0.345692 | ||||||||
\(280\) | 840.000 | + | 290.985i | 0.179284 | + | 0.0621059i | ||||
\(281\) | −3816.00 | −0.810119 | −0.405060 | − | 0.914290i | \(-0.632749\pi\) | ||||
−0.405060 | + | 0.914290i | \(0.632749\pi\) | |||||||
\(282\) | −1098.00 | + | 1901.79i | −0.231862 | + | 0.401596i | ||||
\(283\) | 1998.50 | + | 3461.50i | 0.419783 | + | 0.727085i | 0.995917 | − | 0.0902699i | \(-0.0287730\pi\) |
−0.576135 | + | 0.817355i | \(0.695440\pi\) | |||||||
\(284\) | 684.000 | + | 1184.72i | 0.142915 | + | 0.247536i | ||||
\(285\) | −873.000 | + | 1512.08i | −0.181446 | + | 0.314273i | ||||
\(286\) | 3180.00 | 0.657473 | ||||||||
\(287\) | −441.000 | − | 2291.50i | −0.0907018 | − | 0.471300i | ||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | 1080.00 | + | 1870.61i | 0.218689 | + | 0.378780i | ||||
\(291\) | −579.000 | − | 1002.86i | −0.116638 | − | 0.202022i | ||||
\(292\) | 86.0000 | − | 148.956i | 0.0172355 | − | 0.0298528i | ||||
\(293\) | 4608.00 | 0.918779 | 0.459389 | − | 0.888235i | \(-0.348068\pi\) | ||||
0.459389 | + | 0.888235i | \(0.348068\pi\) | |||||||
\(294\) | 1911.00 | − | 763.834i | 0.379088 | − | 0.151523i | ||||
\(295\) | 1584.00 | 0.312624 | ||||||||
\(296\) | −580.000 | + | 1004.59i | −0.113891 | + | 0.197265i | ||||
\(297\) | 405.000 | + | 701.481i | 0.0791262 | + | 0.137051i | ||||
\(298\) | −1644.00 | − | 2847.49i | −0.319578 | − | 0.553526i | ||||
\(299\) | −2226.00 | + | 3855.55i | −0.430545 | + | 0.745726i | ||||
\(300\) | −1068.00 | −0.205537 | ||||||||
\(301\) | 1137.50 | + | 5910.62i | 0.217822 | + | 1.13184i | ||||
\(302\) | −2176.00 | −0.414618 | ||||||||
\(303\) | −927.000 | + | 1605.61i | −0.175758 | + | 0.304422i | ||||
\(304\) | 776.000 | + | 1344.07i | 0.146403 | + | 0.253578i | ||||
\(305\) | 2454.00 | + | 4250.45i | 0.460707 | + | 0.797968i | ||||
\(306\) | −756.000 | + | 1309.43i | −0.141234 | + | 0.244625i | ||||
\(307\) | −631.000 | −0.117306 | −0.0586532 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586532 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(308\) | −2100.00 | − | 727.461i | −0.388502 | − | 0.134581i | ||||
\(309\) | 4425.00 | 0.814658 | ||||||||
\(310\) | −1074.00 | + | 1860.22i | −0.196771 | + | 0.340818i | ||||
\(311\) | −1947.00 | − | 3372.30i | −0.354998 | − | 0.614874i | 0.632120 | − | 0.774871i | \(-0.282185\pi\) |
−0.987118 | + | 0.159997i | \(0.948852\pi\) | |||||||
\(312\) | 636.000 | + | 1101.58i | 0.115405 | + | 0.199888i | ||||
\(313\) | 1092.50 | − | 1892.27i | 0.197290 | − | 0.341716i | −0.750359 | − | 0.661031i | \(-0.770119\pi\) |
0.947649 | + | 0.319314i | \(0.103453\pi\) | |||||||
\(314\) | −1012.00 | −0.181880 | ||||||||
\(315\) | 756.000 | − | 654.715i | 0.135225 | − | 0.117108i | ||||
\(316\) | −4684.00 | −0.833847 | ||||||||
\(317\) | −1752.00 | + | 3034.55i | −0.310417 | + | 0.537658i | −0.978453 | − | 0.206471i | \(-0.933802\pi\) |
0.668036 | + | 0.744129i | \(0.267135\pi\) | |||||||
\(318\) | −2304.00 | − | 3990.65i | −0.406295 | − | 0.703724i | ||||
\(319\) | −2700.00 | − | 4676.54i | −0.473890 | − | 0.820802i | ||||
\(320\) | 192.000 | − | 332.554i | 0.0335410 | − | 0.0580948i | ||||
\(321\) | 5652.00 | 0.982754 | ||||||||
\(322\) | 2352.00 | − | 2036.89i | 0.407055 | − | 0.352520i | ||||
\(323\) | 8148.00 | 1.40361 | ||||||||
\(324\) | −162.000 | + | 280.592i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 2358.50 | + | 4085.04i | 0.402542 | + | 0.697223i | ||||
\(326\) | 1844.00 | + | 3193.90i | 0.313281 | + | 0.542619i | ||||
\(327\) | −619.500 | + | 1073.01i | −0.104766 | + | 0.181460i | ||||
\(328\) | −1008.00 | −0.169687 | ||||||||
\(329\) | −6405.00 | − | 2218.76i | −1.07331 | − | 0.371806i | ||||
\(330\) | −1080.00 | −0.180158 | ||||||||
\(331\) | −1472.50 | + | 2550.44i | −0.244519 | + | 0.423520i | −0.961996 | − | 0.273062i | \(-0.911964\pi\) |
0.717477 | + | 0.696582i | \(0.245297\pi\) | |||||||
\(332\) | 1620.00 | + | 2805.92i | 0.267798 | + | 0.463840i | ||||
\(333\) | 652.500 | + | 1130.16i | 0.107378 | + | 0.185984i | ||||
\(334\) | 162.000 | − | 280.592i | 0.0265397 | − | 0.0459680i | ||||
\(335\) | 3138.00 | 0.511783 | ||||||||
\(336\) | −168.000 | − | 872.954i | −0.0272772 | − | 0.141737i | ||||
\(337\) | 4277.00 | 0.691344 | 0.345672 | − | 0.938355i | \(-0.387651\pi\) | ||||
0.345672 | + | 0.938355i | \(0.387651\pi\) | |||||||
\(338\) | 612.000 | − | 1060.02i | 0.0984864 | − | 0.170583i | ||||
\(339\) | 1323.00 | + | 2291.50i | 0.211963 | + | 0.367131i | ||||
\(340\) | −1008.00 | − | 1745.91i | −0.160784 | − | 0.278486i | ||||
\(341\) | 2685.00 | − | 4650.56i | 0.426396 | − | 0.738539i | ||||
\(342\) | 1746.00 | 0.276061 | ||||||||
\(343\) | 3430.00 | + | 5346.84i | 0.539949 | + | 0.841698i | ||||
\(344\) | 2600.00 | 0.407508 | ||||||||
\(345\) | 756.000 | − | 1309.43i | 0.117976 | − | 0.204340i | ||||
\(346\) | −2724.00 | − | 4718.11i | −0.423246 | − | 0.733084i | ||||
\(347\) | −3594.00 | − | 6224.99i | −0.556012 | − | 0.963040i | −0.997824 | − | 0.0659329i | \(-0.978998\pi\) |
0.441812 | − | 0.897107i | \(-0.354336\pi\) | |||||||
\(348\) | 1080.00 | − | 1870.61i | 0.166362 | − | 0.288148i | ||||
\(349\) | −9406.00 | −1.44267 | −0.721335 | − | 0.692587i | \(-0.756471\pi\) | ||||
−0.721335 | + | 0.692587i | \(0.756471\pi\) | |||||||
\(350\) | −623.000 | − | 3237.20i | −0.0951450 | − | 0.494388i | ||||
\(351\) | 1431.00 | 0.217610 | ||||||||
\(352\) | −480.000 | + | 831.384i | −0.0726821 | + | 0.125889i | ||||
\(353\) | −1695.00 | − | 2935.83i | −0.255569 | − | 0.442658i | 0.709481 | − | 0.704724i | \(-0.248929\pi\) |
−0.965050 | + | 0.262066i | \(0.915596\pi\) | |||||||
\(354\) | −792.000 | − | 1371.78i | −0.118911 | − | 0.205959i | ||||
\(355\) | −1026.00 | + | 1777.08i | −0.153393 | + | 0.265684i | ||||
\(356\) | −2400.00 | −0.357303 | ||||||||
\(357\) | −4410.00 | − | 1527.67i | −0.653787 | − | 0.226478i | ||||
\(358\) | 2508.00 | 0.370257 | ||||||||
\(359\) | 2406.00 | − | 4167.31i | 0.353715 | − | 0.612653i | −0.633182 | − | 0.774003i | \(-0.718251\pi\) |
0.986897 | + | 0.161350i | \(0.0515848\pi\) | |||||||
\(360\) | −216.000 | − | 374.123i | −0.0316228 | − | 0.0547723i | ||||
\(361\) | −1275.00 | − | 2208.36i | −0.185887 | − | 0.321966i | ||||
\(362\) | −1807.00 | + | 3129.82i | −0.262359 | + | 0.454418i | ||||
\(363\) | −1293.00 | −0.186956 | ||||||||
\(364\) | −2968.00 | + | 2570.36i | −0.427378 | + | 0.370120i | ||||
\(365\) | 258.000 | 0.0369982 | ||||||||
\(366\) | 2454.00 | − | 4250.45i | 0.350472 | − | 0.607035i | ||||
\(367\) | 3549.50 | + | 6147.91i | 0.504857 | + | 0.874437i | 0.999984 | + | 0.00561709i | \(0.00178798\pi\) |
−0.495128 | + | 0.868820i | \(0.664879\pi\) | |||||||
\(368\) | −672.000 | − | 1163.94i | −0.0951914 | − | 0.164876i | ||||
\(369\) | −567.000 | + | 982.073i | −0.0799914 | + | 0.138549i | ||||
\(370\) | −1740.00 | −0.244482 | ||||||||
\(371\) | 10752.0 | − | 9311.51i | 1.50463 | − | 1.30304i | ||||
\(372\) | 2148.00 | 0.299378 | ||||||||
\(373\) | −1481.50 | + | 2566.03i | −0.205655 | + | 0.356204i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) |
0.744687 | + | 0.667414i | \(0.232599\pi\) | |||||||
\(374\) | 2520.00 | + | 4364.77i | 0.348412 | + | 0.603467i | ||||
\(375\) | −1926.00 | − | 3335.93i | −0.265222 | − | 0.459378i | ||||
\(376\) | −1464.00 | + | 2535.72i | −0.200798 | + | 0.347792i | ||||
\(377\) | −9540.00 | −1.30328 | ||||||||
\(378\) | −945.000 | − | 327.358i | −0.128586 | − | 0.0445435i | ||||
\(379\) | −11899.0 | −1.61269 | −0.806346 | − | 0.591444i | \(-0.798558\pi\) | ||||
−0.806346 | + | 0.591444i | \(0.798558\pi\) | |||||||
\(380\) | −1164.00 | + | 2016.11i | −0.157137 | + | 0.272169i | ||||
\(381\) | −3724.50 | − | 6451.02i | −0.500819 | − | 0.867443i | ||||
\(382\) | 714.000 | + | 1236.68i | 0.0956320 | + | 0.165639i | ||||
\(383\) | −1284.00 | + | 2223.95i | −0.171304 | + | 0.296707i | −0.938876 | − | 0.344256i | \(-0.888131\pi\) |
0.767572 | + | 0.640963i | \(0.221465\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −630.000 | − | 3273.58i | −0.0833968 | − | 0.433343i | ||||
\(386\) | 7418.00 | 0.978151 | ||||||||
\(387\) | 1462.50 | − | 2533.12i | 0.192101 | − | 0.332729i | ||||
\(388\) | −772.000 | − | 1337.14i | −0.101011 | − | 0.174957i | ||||
\(389\) | 5073.00 | + | 8786.69i | 0.661212 | + | 1.14525i | 0.980298 | + | 0.197526i | \(0.0632908\pi\) |
−0.319086 | + | 0.947726i | \(0.603376\pi\) | |||||||
\(390\) | −954.000 | + | 1652.38i | −0.123866 | + | 0.214542i | ||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | 2548.00 | − | 1018.45i | 0.328300 | − | 0.131223i | ||||
\(393\) | 6354.00 | 0.815565 | ||||||||
\(394\) | −1044.00 | + | 1808.26i | −0.133492 | + | 0.231215i | ||||
\(395\) | −3513.00 | − | 6084.69i | −0.447489 | − | 0.775074i | ||||
\(396\) | 540.000 | + | 935.307i | 0.0685253 | + | 0.118689i | ||||
\(397\) | 3114.50 | − | 5394.47i | 0.393734 | − | 0.681967i | −0.599205 | − | 0.800596i | \(-0.704517\pi\) |
0.992939 | + | 0.118629i | \(0.0378499\pi\) | |||||||
\(398\) | 272.000 | 0.0342566 | ||||||||
\(399\) | 1018.50 | + | 5292.28i | 0.127791 | + | 0.664024i | ||||
\(400\) | −1424.00 | −0.178000 | ||||||||
\(401\) | 1236.00 | − | 2140.81i | 0.153922 | − | 0.266601i | −0.778744 | − | 0.627342i | \(-0.784143\pi\) |
0.932666 | + | 0.360741i | \(0.117476\pi\) | |||||||
\(402\) | −1569.00 | − | 2717.59i | −0.194663 | − | 0.337167i | ||||
\(403\) | −4743.50 | − | 8215.98i | −0.586329 | − | 1.01555i | ||||
\(404\) | −1236.00 | + | 2140.81i | −0.152211 | + | 0.263637i | ||||
\(405\) | −486.000 | −0.0596285 | ||||||||
\(406\) | 6300.00 | + | 2182.38i | 0.770108 | + | 0.266773i | ||||
\(407\) | 4350.00 | 0.529783 | ||||||||
\(408\) | −1008.00 | + | 1745.91i | −0.122312 | + | 0.211851i | ||||
\(409\) | 3537.50 | + | 6127.13i | 0.427673 | + | 0.740751i | 0.996666 | − | 0.0815915i | \(-0.0260003\pi\) |
−0.568993 | + | 0.822342i | \(0.692667\pi\) | |||||||
\(410\) | −756.000 | − | 1309.43i | −0.0910639 | − | 0.157727i | ||||
\(411\) | −4518.00 | + | 7825.41i | −0.542230 | + | 0.939170i | ||||
\(412\) | 5900.00 | 0.705515 | ||||||||
\(413\) | 3696.00 | − | 3200.83i | 0.440359 | − | 0.381362i | ||||
\(414\) | −1512.00 | −0.179495 | ||||||||
\(415\) | −2430.00 | + | 4208.88i | −0.287431 | + | 0.497846i | ||||
\(416\) | 848.000 | + | 1468.78i | 0.0999438 | + | 0.173108i | ||||
\(417\) | 55.5000 | + | 96.1288i | 0.00651762 | + | 0.0112888i | ||||
\(418\) | 2910.00 | − | 5040.27i | 0.340509 | − | 0.589779i | ||||
\(419\) | −4158.00 | −0.484801 | −0.242400 | − | 0.970176i | \(-0.577935\pi\) | ||||
−0.242400 | + | 0.970176i | \(0.577935\pi\) | |||||||
\(420\) | 1008.00 | − | 872.954i | 0.117108 | − | 0.101419i | ||||
\(421\) | −6595.00 | −0.763469 | −0.381735 | − | 0.924272i | \(-0.624673\pi\) | ||||
−0.381735 | + | 0.924272i | \(0.624673\pi\) | |||||||
\(422\) | 1484.00 | − | 2570.36i | 0.171185 | − | 0.296501i | ||||
\(423\) | 1647.00 | + | 2852.69i | 0.189314 | + | 0.327902i | ||||
\(424\) | −3072.00 | − | 5320.86i | −0.351862 | − | 0.609443i | ||||
\(425\) | −3738.00 | + | 6474.41i | −0.426634 | + | 0.738953i | ||||
\(426\) | 2052.00 | 0.233380 | ||||||||
\(427\) | 14315.0 | + | 4958.86i | 1.62237 | + | 0.562005i | ||||
\(428\) | 7536.00 | 0.851090 | ||||||||
\(429\) | 2385.00 | − | 4130.94i | 0.268412 | − | 0.464904i | ||||
\(430\) | 1950.00 | + | 3377.50i | 0.218692 | + | 0.378785i | ||||
\(431\) | −759.000 | − | 1314.63i | −0.0848254 | − | 0.146922i | 0.820491 | − | 0.571659i | \(-0.193700\pi\) |
−0.905317 | + | 0.424737i | \(0.860367\pi\) | |||||||
\(432\) | −216.000 | + | 374.123i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 8567.00 | 0.950817 | 0.475408 | − | 0.879765i | \(-0.342300\pi\) | ||||
0.475408 | + | 0.879765i | \(0.342300\pi\) | |||||||
\(434\) | 1253.00 | + | 6510.78i | 0.138585 | + | 0.720109i | ||||
\(435\) | 3240.00 | 0.357117 | ||||||||
\(436\) | −826.000 | + | 1430.67i | −0.0907299 | + | 0.157149i | ||||
\(437\) | 4074.00 | + | 7056.37i | 0.445963 | + | 0.772431i | ||||
\(438\) | −129.000 | − | 223.435i | −0.0140727 | − | 0.0243747i | ||||
\(439\) | −5320.00 | + | 9214.51i | −0.578382 | + | 1.00179i | 0.417283 | + | 0.908777i | \(0.362982\pi\) |
−0.995665 | + | 0.0930106i | \(0.970351\pi\) | |||||||
\(440\) | −1440.00 | −0.156021 | ||||||||
\(441\) | 441.000 | − | 3055.34i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 8904.00 | 0.958190 | ||||||||
\(443\) | −3516.00 | + | 6089.89i | −0.377088 | + | 0.653136i | −0.990637 | − | 0.136520i | \(-0.956408\pi\) |
0.613549 | + | 0.789657i | \(0.289741\pi\) | |||||||
\(444\) | 870.000 | + | 1506.88i | 0.0929918 | + | 0.161067i | ||||
\(445\) | −1800.00 | − | 3117.69i | −0.191749 | − | 0.332119i | ||||
\(446\) | −2032.00 | + | 3519.53i | −0.215735 | + | 0.373665i | ||||
\(447\) | −4932.00 | −0.521869 | ||||||||
\(448\) | −224.000 | − | 1163.94i | −0.0236228 | − | 0.122748i | ||||
\(449\) | −14814.0 | −1.55705 | −0.778525 | − | 0.627613i | \(-0.784032\pi\) | ||||
−0.778525 | + | 0.627613i | \(0.784032\pi\) | |||||||
\(450\) | −801.000 | + | 1387.37i | −0.0839100 | + | 0.145336i | ||||
\(451\) | 1890.00 | + | 3273.58i | 0.197332 | + | 0.341789i | ||||
\(452\) | 1764.00 | + | 3055.34i | 0.183565 | + | 0.317945i | ||||
\(453\) | −1632.00 | + | 2826.71i | −0.169267 | + | 0.293179i | ||||
\(454\) | −12396.0 | −1.28144 | ||||||||
\(455\) | −5565.00 | − | 1927.77i | −0.573387 | − | 0.198627i | ||||
\(456\) | 2328.00 | 0.239076 | ||||||||
\(457\) | 5625.50 | − | 9743.65i | 0.575820 | − | 0.997350i | −0.420132 | − | 0.907463i | \(-0.638016\pi\) |
0.995952 | − | 0.0898866i | \(-0.0286505\pi\) | |||||||
\(458\) | −4591.00 | − | 7951.85i | −0.468392 | − | 0.811278i | ||||
\(459\) | 1134.00 | + | 1964.15i | 0.115317 | + | 0.199735i | ||||
\(460\) | 1008.00 | − | 1745.91i | 0.102170 | − | 0.176964i | ||||
\(461\) | −3852.00 | −0.389166 | −0.194583 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194583 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(462\) | −2520.00 | + | 2182.38i | −0.253768 | + | 0.219770i | ||||
\(463\) | −475.000 | −0.0476784 | −0.0238392 | − | 0.999716i | \(-0.507589\pi\) | ||||
−0.0238392 | + | 0.999716i | \(0.507589\pi\) | |||||||
\(464\) | 1440.00 | − | 2494.15i | 0.144074 | − | 0.249543i | ||||
\(465\) | 1611.00 | + | 2790.33i | 0.160663 | + | 0.278277i | ||||
\(466\) | 4530.00 | + | 7846.19i | 0.450318 | + | 0.779974i | ||||
\(467\) | −2967.00 | + | 5138.99i | −0.293997 | + | 0.509217i | −0.974751 | − | 0.223295i | \(-0.928319\pi\) |
0.680754 | + | 0.732512i | \(0.261652\pi\) | |||||||
\(468\) | 1908.00 | 0.188456 | ||||||||
\(469\) | 7322.00 | − | 6341.04i | 0.720892 | − | 0.624311i | ||||
\(470\) | −4392.00 | −0.431038 | ||||||||
\(471\) | −759.000 | + | 1314.63i | −0.0742524 | + | 0.128609i | ||||
\(472\) | −1056.00 | − | 1829.05i | −0.102980 | − | 0.178366i | ||||
\(473\) | −4875.00 | − | 8443.75i | −0.473896 | − | 0.820812i | ||||
\(474\) | −3513.00 | + | 6084.69i | −0.340417 | + | 0.589619i | ||||
\(475\) | 8633.00 | 0.833914 | ||||||||
\(476\) | −5880.00 | − | 2036.89i | −0.566196 | − | 0.196136i | ||||
\(477\) | −6912.00 | −0.663477 | ||||||||
\(478\) | 1530.00 | − | 2650.04i | 0.146403 | − | 0.253577i | ||||
\(479\) | 6684.00 | + | 11577.0i | 0.637578 | + | 1.10432i | 0.985963 | + | 0.166966i | \(0.0533969\pi\) |
−0.348385 | + | 0.937352i | \(0.613270\pi\) | |||||||
\(480\) | −288.000 | − | 498.831i | −0.0273861 | − | 0.0474342i | ||||
\(481\) | 3842.50 | − | 6655.41i | 0.364247 | − | 0.630895i | ||||
\(482\) | −11068.0 | −1.04592 | ||||||||
\(483\) | −882.000 | − | 4583.01i | −0.0830898 | − | 0.431747i | ||||
\(484\) | −1724.00 | −0.161908 | ||||||||
\(485\) | 1158.00 | − | 2005.71i | 0.108417 | − | 0.187783i | ||||
\(486\) | 243.000 | + | 420.888i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −3326.50 | − | 5761.67i | −0.309524 | − | 0.536111i | 0.668734 | − | 0.743501i | \(-0.266836\pi\) |
−0.978258 | + | 0.207390i | \(0.933503\pi\) | |||||||
\(488\) | 3272.00 | − | 5667.27i | 0.303517 | − | 0.525708i | ||||
\(489\) | 5532.00 | 0.511586 | ||||||||
\(490\) | 3234.00 | + | 2546.11i | 0.298158 | + | 0.234738i | ||||
\(491\) | 15444.0 | 1.41951 | 0.709754 | − | 0.704450i | \(-0.248806\pi\) | ||||
0.709754 | + | 0.704450i | \(0.248806\pi\) | |||||||
\(492\) | −756.000 | + | 1309.43i | −0.0692746 | + | 0.119987i | ||||
\(493\) | −7560.00 | − | 13094.3i | −0.690640 | − | 1.19622i | ||||
\(494\) | −5141.00 | − | 8904.47i | −0.468228 | − | 0.810994i | ||||
\(495\) | −810.000 | + | 1402.96i | −0.0735491 | + | 0.127391i | ||||
\(496\) | 2864.00 | 0.259269 | ||||||||
\(497\) | 1197.00 | + | 6219.79i | 0.108034 | + | 0.561360i | ||||
\(498\) | 4860.00 | 0.437313 | ||||||||
\(499\) | −341.500 | + | 591.495i | −0.0306366 | + | 0.0530641i | −0.880937 | − | 0.473233i | \(-0.843087\pi\) |
0.850301 | + | 0.526297i | \(0.176420\pi\) | |||||||
\(500\) | −2568.00 | − | 4447.91i | −0.229689 | − | 0.397833i | ||||
\(501\) | −243.000 | − | 420.888i | −0.0216695 | − | 0.0375327i | ||||
\(502\) | −468.000 | + | 810.600i | −0.0416093 | + | 0.0720694i | ||||
\(503\) | 9882.00 | 0.875977 | 0.437989 | − | 0.898980i | \(-0.355691\pi\) | ||||
0.437989 | + | 0.898980i | \(0.355691\pi\) | |||||||
\(504\) | −1260.00 | − | 436.477i | −0.111359 | − | 0.0385758i | ||||
\(505\) | −3708.00 | −0.326740 | ||||||||
\(506\) | −2520.00 | + | 4364.77i | −0.221399 | + | 0.383474i | ||||
\(507\) | −918.000 | − | 1590.02i | −0.0804138 | − | 0.139281i | ||||
\(508\) | −4966.00 | − | 8601.36i | −0.433722 | − | 0.751228i | ||||
\(509\) | −2103.00 | + | 3642.50i | −0.183131 | + | 0.317193i | −0.942945 | − | 0.332948i | \(-0.891957\pi\) |
0.759814 | + | 0.650141i | \(0.225290\pi\) | |||||||
\(510\) | −3024.00 | −0.262559 | ||||||||
\(511\) | 602.000 | − | 521.347i | 0.0521153 | − | 0.0451332i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1309.50 | − | 2268.12i | 0.112701 | − | 0.195205i | ||||
\(514\) | −2490.00 | − | 4312.81i | −0.213675 | − | 0.370097i | ||||
\(515\) | 4425.00 | + | 7664.32i | 0.378619 | + | 0.655787i | ||||
\(516\) | 1950.00 | − | 3377.50i | 0.166364 | − | 0.288151i | ||||
\(517\) | 10980.0 | 0.934042 | ||||||||
\(518\) | −4060.00 | + | 3516.06i | −0.344375 | + | 0.298237i | ||||
\(519\) | −8172.00 | −0.691158 | ||||||||
\(520\) | −1272.00 | + | 2203.17i | −0.107271 | + | 0.185799i | ||||
\(521\) | −4530.00 | − | 7846.19i | −0.380927 | − | 0.659785i | 0.610268 | − | 0.792195i | \(-0.291062\pi\) |
−0.991195 | + | 0.132410i | \(0.957728\pi\) | |||||||
\(522\) | −1620.00 | − | 2805.92i | −0.135834 | − | 0.235272i | ||||
\(523\) | 7839.50 | − | 13578.4i | 0.655444 | − | 1.13526i | −0.326338 | − | 0.945253i | \(-0.605815\pi\) |
0.981782 | − | 0.190010i | \(-0.0608520\pi\) | |||||||
\(524\) | 8472.00 | 0.706300 | ||||||||
\(525\) | −4672.50 | − | 1618.60i | −0.388428 | − | 0.134555i | ||||
\(526\) | −3144.00 | −0.260618 | ||||||||
\(527\) | 7518.00 | − | 13021.6i | 0.621422 | − | 1.07633i | ||||
\(528\) | 720.000 | + | 1247.08i | 0.0593447 | + | 0.102788i | ||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | 4608.00 | − | 7981.29i | 0.377658 | − | 0.654123i | ||||
\(531\) | −2376.00 | −0.194180 | ||||||||
\(532\) | 1358.00 | + | 7056.37i | 0.110671 | + | 0.575061i | ||||
\(533\) | 6678.00 | 0.542695 | ||||||||
\(534\) | −1800.00 | + | 3117.69i | −0.145868 | + | 0.252651i | ||||
\(535\) | 5652.00 | + | 9789.55i | 0.456743 | + | 0.791101i | ||||
\(536\) | −2092.00 | − | 3623.45i | −0.168583 | − | 0.291995i | ||||
\(537\) | 1881.00 | − | 3257.99i | 0.151157 | − | 0.261811i | ||||
\(538\) | −3612.00 | −0.289451 | ||||||||
\(539\) | −8085.00 | − | 6365.29i | −0.646096 | − | 0.508668i | ||||
\(540\) | −648.000 | −0.0516398 | ||||||||
\(541\) | 3855.50 | − | 6677.92i | 0.306397 | − | 0.530696i | −0.671174 | − | 0.741300i | \(-0.734210\pi\) |
0.977571 | + | 0.210604i | \(0.0675431\pi\) | |||||||
\(542\) | −6112.00 | − | 10586.3i | −0.484378 | − | 0.838967i | ||||
\(543\) | 2710.50 | + | 4694.72i | 0.214215 | + | 0.371031i | ||||
\(544\) | −1344.00 | + | 2327.88i | −0.105926 | + | 0.183469i | ||||
\(545\) | −2478.00 | −0.194763 | ||||||||
\(546\) | 1113.00 | + | 5783.32i | 0.0872381 | + | 0.453302i | ||||
\(547\) | 4292.00 | 0.335489 | 0.167745 | − | 0.985830i | \(-0.446352\pi\) | ||||
0.167745 | + | 0.985830i | \(0.446352\pi\) | |||||||
\(548\) | −6024.00 | + | 10433.9i | −0.469585 | + | 0.813345i | ||||
\(549\) | −3681.00 | − | 6375.68i | −0.286159 | − | 0.495642i | ||||
\(550\) | 2670.00 | + | 4624.58i | 0.206999 | + | 0.358532i | ||||
\(551\) | −8730.00 | + | 15120.8i | −0.674974 | + | 1.16909i | ||||
\(552\) | −2016.00 | −0.155447 | ||||||||
\(553\) | −20492.5 | − | 7098.81i | −1.57582 | − | 0.545881i | ||||
\(554\) | 8462.00 | 0.648946 | ||||||||
\(555\) | −1305.00 | + | 2260.33i | −0.0998093 | + | 0.172875i | ||||
\(556\) | 74.0000 | + | 128.172i | 0.00564442 | + | 0.00977643i | ||||
\(557\) | 4929.00 | + | 8537.28i | 0.374952 | + | 0.649436i | 0.990320 | − | 0.138804i | \(-0.0443258\pi\) |
−0.615368 | + | 0.788240i | \(0.710992\pi\) | |||||||
\(558\) | 1611.00 | − | 2790.33i | 0.122221 | − | 0.211692i | ||||
\(559\) | −17225.0 | −1.30329 | ||||||||
\(560\) | 1344.00 | − | 1163.94i | 0.101419 | − | 0.0878310i | ||||
\(561\) | 7560.00 | 0.568954 | ||||||||
\(562\) | −3816.00 | + | 6609.51i | −0.286420 | + | 0.496095i | ||||
\(563\) | 6945.00 | + | 12029.1i | 0.519888 | + | 0.900472i | 0.999733 | + | 0.0231188i | \(0.00735960\pi\) |
−0.479845 | + | 0.877353i | \(0.659307\pi\) | |||||||
\(564\) | 2196.00 | + | 3803.58i | 0.163951 | + | 0.283971i | ||||
\(565\) | −2646.00 | + | 4583.01i | −0.197023 | + | 0.341254i | ||||
\(566\) | 7994.00 | 0.593662 | ||||||||
\(567\) | −1134.00 | + | 982.073i | −0.0839921 | + | 0.0727393i | ||||
\(568\) | 2736.00 | 0.202113 | ||||||||
\(569\) | −9519.00 | + | 16487.4i | −0.701331 | + | 1.21474i | 0.266669 | + | 0.963788i | \(0.414077\pi\) |
−0.967999 | + | 0.250952i | \(0.919256\pi\) | |||||||
\(570\) | 1746.00 | + | 3024.16i | 0.128302 | + | 0.222225i | ||||
\(571\) | 4026.50 | + | 6974.10i | 0.295103 | + | 0.511133i | 0.975009 | − | 0.222166i | \(-0.0713127\pi\) |
−0.679906 | + | 0.733299i | \(0.737979\pi\) | |||||||
\(572\) | 3180.00 | − | 5507.92i | 0.232452 | − | 0.402618i | ||||
\(573\) | 2142.00 | 0.156166 | ||||||||
\(574\) | −4410.00 | − | 1527.67i | −0.320679 | − | 0.111087i | ||||
\(575\) | −7476.00 | −0.542210 | ||||||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 8568.50 | + | 14841.1i | 0.618217 | + | 1.07078i | 0.989811 | + | 0.142388i | \(0.0454781\pi\) |
−0.371594 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(578\) | 2143.00 | + | 3711.78i | 0.154216 | + | 0.267111i | ||||
\(579\) | 5563.50 | − | 9636.26i | 0.399328 | − | 0.691657i | ||||
\(580\) | 4320.00 | 0.309273 | ||||||||
\(581\) | 2835.00 | + | 14731.1i | 0.202437 | + | 1.05189i | ||||
\(582\) | −2316.00 | −0.164951 | ||||||||
\(583\) | −11520.0 | + | 19953.2i | −0.818370 | + | 1.41746i | ||||
\(584\) | −172.000 | − | 297.913i | −0.0121873 | − | 0.0211091i | ||||
\(585\) | 1431.00 | + | 2478.56i | 0.101136 | + | 0.175173i | ||||
\(586\) | 4608.00 | − | 7981.29i | 0.324837 | − | 0.562635i | ||||
\(587\) | 18144.0 | 1.27578 | 0.637890 | − | 0.770127i | \(-0.279807\pi\) | ||||
0.637890 | + | 0.770127i | \(0.279807\pi\) | |||||||
\(588\) | 588.000 | − | 4073.78i | 0.0412393 | − | 0.285714i | ||||
\(589\) | −17363.0 | −1.21465 | ||||||||
\(590\) | 1584.00 | − | 2743.57i | 0.110529 | − | 0.191442i | ||||
\(591\) | 1566.00 | + | 2712.39i | 0.108996 | + | 0.188787i | ||||
\(592\) | 1160.00 | + | 2009.18i | 0.0805333 | + | 0.139488i | ||||
\(593\) | 12351.0 | − | 21392.6i | 0.855303 | − | 1.48143i | −0.0210603 | − | 0.999778i | \(-0.506704\pi\) |
0.876363 | − | 0.481650i | \(-0.159962\pi\) | |||||||
\(594\) | 1620.00 | 0.111901 | ||||||||
\(595\) | −1764.00 | − | 9166.01i | −0.121541 | − | 0.631546i | ||||
\(596\) | −6576.00 | −0.451952 | ||||||||
\(597\) | 204.000 | − | 353.338i | 0.0139852 | − | 0.0242231i | ||||
\(598\) | 4452.00 | + | 7711.09i | 0.304441 | + | 0.527308i | ||||
\(599\) | 1086.00 | + | 1881.01i | 0.0740781 | + | 0.128307i | 0.900685 | − | 0.434473i | \(-0.143065\pi\) |
−0.826607 | + | 0.562780i | \(0.809732\pi\) | |||||||
\(600\) | −1068.00 | + | 1849.83i | −0.0726682 | + | 0.125865i | ||||
\(601\) | 4175.00 | 0.283364 | 0.141682 | − | 0.989912i | \(-0.454749\pi\) | ||||
0.141682 | + | 0.989912i | \(0.454749\pi\) | |||||||
\(602\) | 11375.0 | + | 3940.42i | 0.770117 | + | 0.266776i | ||||
\(603\) | −4707.00 | −0.317884 | ||||||||
\(604\) | −2176.00 | + | 3768.94i | −0.146590 | + | 0.253901i | ||||
\(605\) | −1293.00 | − | 2239.54i | −0.0868891 | − | 0.150496i | ||||
\(606\) | 1854.00 | + | 3211.22i | 0.124280 | + | 0.215259i | ||||
\(607\) | −1130.50 | + | 1958.08i | −0.0755940 | + | 0.130933i | −0.901344 | − | 0.433103i | \(-0.857419\pi\) |
0.825750 | + | 0.564036i | \(0.190752\pi\) | |||||||
\(608\) | 3104.00 | 0.207046 | ||||||||
\(609\) | 7560.00 | − | 6547.15i | 0.503032 | − | 0.435639i | ||||
\(610\) | 9816.00 | 0.651538 | ||||||||
\(611\) | 9699.00 | − | 16799.2i | 0.642192 | − | 1.11231i | ||||
\(612\) | 1512.00 | + | 2618.86i | 0.0998676 | + | 0.172976i | ||||
\(613\) | 8159.00 | + | 14131.8i | 0.537584 | + | 0.931123i | 0.999033 | + | 0.0439561i | \(0.0139962\pi\) |
−0.461450 | + | 0.887166i | \(0.652670\pi\) | |||||||
\(614\) | −631.000 | + | 1092.92i | −0.0414741 | + | 0.0718352i | ||||
\(615\) | −2268.00 | −0.148707 | ||||||||
\(616\) | −3360.00 | + | 2909.85i | −0.219770 | + | 0.190326i | ||||
\(617\) | −26550.0 | −1.73235 | −0.866177 | − | 0.499737i | \(-0.833430\pi\) | ||||
−0.866177 | + | 0.499737i | \(0.833430\pi\) | |||||||
\(618\) | 4425.00 | − | 7664.32i | 0.288025 | − | 0.498874i | ||||
\(619\) | −9962.50 | − | 17255.6i | −0.646893 | − | 1.12045i | −0.983861 | − | 0.178935i | \(-0.942735\pi\) |
0.336968 | − | 0.941516i | \(-0.390599\pi\) | |||||||
\(620\) | 2148.00 | + | 3720.45i | 0.139138 | + | 0.240995i | ||||
\(621\) | −1134.00 | + | 1964.15i | −0.0732783 | + | 0.126922i | ||||
\(622\) | −7788.00 | −0.502042 | ||||||||
\(623\) | −10500.0 | − | 3637.31i | −0.675239 | − | 0.233909i | ||||
\(624\) | 2544.00 | 0.163208 | ||||||||
\(625\) | −1710.50 | + | 2962.67i | −0.109472 | + | 0.189611i | ||||
\(626\) | −2185.00 | − | 3784.53i | −0.139505 | − | 0.241630i | ||||
\(627\) | −4365.00 | − | 7560.40i | −0.278024 | − | 0.481552i | ||||
\(628\) | −1012.00 | + | 1752.84i | −0.0643045 | + | 0.111379i | ||||
\(629\) | 12180.0 | 0.772096 | ||||||||
\(630\) | −378.000 | − | 1964.15i | −0.0239046 | − | 0.124212i | ||||
\(631\) | −6832.00 | −0.431026 | −0.215513 | − | 0.976501i | \(-0.569142\pi\) | ||||
−0.215513 | + | 0.976501i | \(0.569142\pi\) | |||||||
\(632\) | −4684.00 | + | 8112.93i | −0.294809 | + | 0.510625i | ||||
\(633\) | −2226.00 | − | 3855.55i | −0.139772 | − | 0.242092i | ||||
\(634\) | 3504.00 | + | 6069.11i | 0.219498 | + | 0.380181i | ||||
\(635\) | 7449.00 | − | 12902.0i | 0.465519 | − | 0.806303i | ||||
\(636\) | −9216.00 | −0.574588 | ||||||||
\(637\) | −16880.5 | + | 6747.20i | −1.04997 | + | 0.419677i | ||||
\(638\) | −10800.0 | −0.670182 | ||||||||
\(639\) | 1539.00 | − | 2665.63i | 0.0952768 | − | 0.165024i | ||||
\(640\) | −384.000 | − | 665.108i | −0.0237171 | − | 0.0410792i | ||||
\(641\) | −5106.00 | − | 8843.85i | −0.314625 | − | 0.544947i | 0.664732 | − | 0.747082i | \(-0.268546\pi\) |
−0.979358 | + | 0.202134i | \(0.935212\pi\) | |||||||
\(642\) | 5652.00 | − | 9789.55i | 0.347456 | − | 0.601811i | ||||
\(643\) | 3779.00 | 0.231772 | 0.115886 | − | 0.993263i | \(-0.463029\pi\) | ||||
0.115886 | + | 0.993263i | \(0.463029\pi\) | |||||||
\(644\) | −1176.00 | − | 6110.68i | −0.0719579 | − | 0.373904i | ||||
\(645\) | 5850.00 | 0.357122 | ||||||||
\(646\) | 8148.00 | − | 14112.7i | 0.496252 | − | 0.859534i | ||||
\(647\) | −8499.00 | − | 14720.7i | −0.516430 | − | 0.894483i | −0.999818 | − | 0.0190767i | \(-0.993927\pi\) |
0.483388 | − | 0.875406i | \(-0.339406\pi\) | |||||||
\(648\) | 324.000 | + | 561.184i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −3960.00 | + | 6858.92i | −0.239512 | + | 0.414848i | ||||
\(650\) | 9434.00 | 0.569280 | ||||||||
\(651\) | 9397.50 | + | 3255.39i | 0.565771 | + | 0.195989i | ||||
\(652\) | 7376.00 | 0.443047 | ||||||||
\(653\) | 10875.0 | − | 18836.1i | 0.651718 | − | 1.12881i | −0.330988 | − | 0.943635i | \(-0.607382\pi\) |
0.982706 | − | 0.185173i | \(-0.0592846\pi\) | |||||||
\(654\) | 1239.00 | + | 2146.01i | 0.0740806 | + | 0.128311i | ||||
\(655\) | 6354.00 | + | 11005.5i | 0.379040 | + | 0.656517i | ||||
\(656\) | −1008.00 | + | 1745.91i | −0.0599936 | + | 0.103912i | ||||
\(657\) | −387.000 | −0.0229807 | ||||||||
\(658\) | −10248.0 | + | 8875.03i | −0.607156 | + | 0.525813i | ||||
\(659\) | −10944.0 | −0.646916 | −0.323458 | − | 0.946243i | \(-0.604845\pi\) | ||||
−0.323458 | + | 0.946243i | \(0.604845\pi\) | |||||||
\(660\) | −1080.00 | + | 1870.61i | −0.0636954 | + | 0.110324i | ||||
\(661\) | −5477.50 | − | 9487.31i | −0.322315 | − | 0.558266i | 0.658650 | − | 0.752449i | \(-0.271128\pi\) |
−0.980965 | + | 0.194184i | \(0.937794\pi\) | |||||||
\(662\) | 2945.00 | + | 5100.89i | 0.172901 | + | 0.299474i | ||||
\(663\) | 6678.00 | − | 11566.6i | 0.391180 | − | 0.677543i | ||||
\(664\) | 6480.00 | 0.378724 | ||||||||
\(665\) | −8148.00 | + | 7056.37i | −0.475137 | + | 0.411480i | ||||
\(666\) | 2610.00 | 0.151855 | ||||||||
\(667\) | 7560.00 | − | 13094.3i | 0.438867 | − | 0.760140i | ||||
\(668\) | −324.000 | − | 561.184i | −0.0187664 | − | 0.0325043i | ||||
\(669\) | 3048.00 | + | 5279.29i | 0.176147 | + | 0.305096i | ||||
\(670\) | 3138.00 | − | 5435.18i | 0.180943 | − | 0.313402i | ||||
\(671\) | −24540.0 | −1.41186 | ||||||||
\(672\) | −1680.00 | − | 581.969i | −0.0964396 | − | 0.0334077i | ||||
\(673\) | 25103.0 | 1.43782 | 0.718908 | − | 0.695106i | \(-0.244642\pi\) | ||||
0.718908 | + | 0.695106i | \(0.244642\pi\) | |||||||
\(674\) | 4277.00 | − | 7407.98i | 0.244427 | − | 0.423360i | ||||
\(675\) | 1201.50 | + | 2081.06i | 0.0685122 | + | 0.118667i | ||||
\(676\) | −1224.00 | − | 2120.03i | −0.0696404 | − | 0.120621i | ||||
\(677\) | 2802.00 | − | 4853.21i | 0.159069 | − | 0.275515i | −0.775464 | − | 0.631391i | \(-0.782484\pi\) |
0.934533 | + | 0.355876i | \(0.115817\pi\) | |||||||
\(678\) | 5292.00 | 0.299761 | ||||||||
\(679\) | −1351.00 | − | 7020.00i | −0.0763573 | − | 0.396764i | ||||
\(680\) | −4032.00 | −0.227383 | ||||||||
\(681\) | −9297.00 | + | 16102.9i | −0.523145 | + | 0.906114i | ||||
\(682\) | −5370.00 | − | 9301.11i | −0.301507 | − | 0.522226i | ||||
\(683\) | −5484.00 | − | 9498.57i | −0.307232 | − | 0.532141i | 0.670524 | − | 0.741888i | \(-0.266069\pi\) |
−0.977756 | + | 0.209747i | \(0.932736\pi\) | |||||||
\(684\) | 1746.00 | − | 3024.16i | 0.0976023 | − | 0.169052i | ||||
\(685\) | −18072.0 | −1.00802 | ||||||||
\(686\) | 12691.0 | − | 594.093i | 0.706333 | − | 0.0330650i | ||||
\(687\) | −13773.0 | −0.764880 | ||||||||
\(688\) | 2600.00 | − | 4503.33i | 0.144076 | − | 0.249546i | ||||
\(689\) | 20352.0 | + | 35250.7i | 1.12533 | + | 1.94912i | ||||
\(690\) | −1512.00 | − | 2618.86i | −0.0834215 | − | 0.144490i | ||||
\(691\) | −4202.50 | + | 7278.94i | −0.231361 | + | 0.400729i | −0.958209 | − | 0.286069i | \(-0.907651\pi\) |
0.726848 | + | 0.686799i | \(0.240985\pi\) | |||||||
\(692\) | −10896.0 | −0.598560 | ||||||||
\(693\) | 945.000 | + | 4910.36i | 0.0518003 | + | 0.269162i | ||||
\(694\) | −14376.0 | −0.786319 | ||||||||
\(695\) | −111.000 | + | 192.258i | −0.00605823 | + | 0.0104932i | ||||
\(696\) | −2160.00 | − | 3741.23i | −0.117636 | − | 0.203751i | ||||
\(697\) | 5292.00 | + | 9166.01i | 0.287588 | + | 0.498117i | ||||
\(698\) | −9406.00 | + | 16291.7i | −0.510061 | + | 0.883451i | ||||
\(699\) | 13590.0 | 0.735366 | ||||||||
\(700\) | −6230.00 | − | 2158.14i | −0.336388 | − | 0.116528i | ||||
\(701\) | 468.000 | 0.0252156 | 0.0126078 | − | 0.999921i | \(-0.495987\pi\) | ||||
0.0126078 | + | 0.999921i | \(0.495987\pi\) | |||||||
\(702\) | 1431.00 | − | 2478.56i | 0.0769368 | − | 0.133258i | ||||
\(703\) | −7032.50 | − | 12180.6i | −0.377291 | − | 0.653488i | ||||
\(704\) | 960.000 | + | 1662.77i | 0.0513940 | + | 0.0890170i | ||||
\(705\) | −3294.00 | + | 5705.38i | −0.175971 | + | 0.304790i | ||||
\(706\) | −6780.00 | −0.361429 | ||||||||
\(707\) | −8652.00 | + | 7492.85i | −0.460243 | + | 0.398582i | ||||
\(708\) | −3168.00 | −0.168165 | ||||||||
\(709\) | 12533.0 | − | 21707.8i | 0.663874 | − | 1.14986i | −0.315715 | − | 0.948854i | \(-0.602244\pi\) |
0.979589 | − | 0.201010i | \(-0.0644222\pi\) | |||||||
\(710\) | 2052.00 | + | 3554.17i | 0.108465 | + | 0.187867i | ||||
\(711\) | 5269.50 | + | 9127.04i | 0.277949 | + | 0.481422i | ||||
\(712\) | −2400.00 | + | 4156.92i | −0.126326 | + | 0.218802i | ||||
\(713\) | 15036.0 | 0.789765 | ||||||||
\(714\) | −7056.00 | + | 6110.68i | −0.369838 | + | 0.320289i | ||||
\(715\) | 9540.00 | 0.498987 | ||||||||
\(716\) | 2508.00 | − | 4343.98i | 0.130906 | − | 0.226735i | ||||
\(717\) | −2295.00 | − | 3975.06i | −0.119537 | − | 0.207045i | ||||
\(718\) | −4812.00 | − | 8334.63i | −0.250115 | − | 0.433211i | ||||
\(719\) | −5541.00 | + | 9597.29i | −0.287405 | + | 0.497801i | −0.973190 | − | 0.230004i | \(-0.926126\pi\) |
0.685784 | + | 0.727805i | \(0.259459\pi\) | |||||||
\(720\) | −864.000 | −0.0447214 | ||||||||
\(721\) | 25812.5 | + | 8941.71i | 1.33330 | + | 0.461868i | ||||
\(722\) | −5100.00 | −0.262884 | ||||||||
\(723\) | −8301.00 | + | 14377.8i | −0.426995 | + | 0.739577i | ||||
\(724\) | 3614.00 | + | 6259.63i | 0.185516 | + | 0.321322i | ||||
\(725\) | −8010.00 | − | 13873.7i | −0.410323 | − | 0.710700i | ||||
\(726\) | −1293.00 | + | 2239.54i | −0.0660988 | + | 0.114486i | ||||
\(727\) | 13481.0 | 0.687734 | 0.343867 | − | 0.939018i | \(-0.388263\pi\) | ||||
0.343867 | + | 0.939018i | \(0.388263\pi\) | |||||||
\(728\) | 1484.00 | + | 7711.09i | 0.0755504 | + | 0.392571i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 258.000 | − | 446.869i | 0.0130808 | − | 0.0226567i | ||||
\(731\) | −13650.0 | − | 23642.5i | −0.690648 | − | 1.19624i | ||||
\(732\) | −4908.00 | − | 8500.91i | −0.247821 | − | 0.429238i | ||||
\(733\) | −12158.5 | + | 21059.1i | −0.612666 | + | 1.06117i | 0.378123 | + | 0.925755i | \(0.376570\pi\) |
−0.990789 | + | 0.135414i | \(0.956764\pi\) | |||||||
\(734\) | 14198.0 | 0.713975 | ||||||||
\(735\) | 5733.00 | − | 2291.50i | 0.287707 | − | 0.114998i | ||||
\(736\) | −2688.00 | −0.134621 | ||||||||
\(737\) | −7845.00 | + | 13587.9i | −0.392095 | + | 0.679129i | ||||
\(738\) | 1134.00 | + | 1964.15i | 0.0565625 | + | 0.0979691i | ||||
\(739\) | 9108.50 | + | 15776.4i | 0.453399 | + | 0.785309i | 0.998595 | − | 0.0529992i | \(-0.0168781\pi\) |
−0.545196 | + | 0.838309i | \(0.683545\pi\) | |||||||
\(740\) | −1740.00 | + | 3013.77i | −0.0864374 | + | 0.149714i | ||||
\(741\) | −15423.0 | −0.764613 | ||||||||
\(742\) | −5376.00 | − | 27934.5i | −0.265983 | − | 1.38209i | ||||
\(743\) | 19782.0 | 0.976758 | 0.488379 | − | 0.872632i | \(-0.337588\pi\) | ||||
0.488379 | + | 0.872632i | \(0.337588\pi\) | |||||||
\(744\) | 2148.00 | − | 3720.45i | 0.105846 | − | 0.183331i | ||||
\(745\) | −4932.00 | − | 8542.47i | −0.242543 | − | 0.420097i | ||||
\(746\) | 2963.00 | + | 5132.07i | 0.145420 | + | 0.251874i | ||||
\(747\) | 3645.00 | − | 6313.33i | 0.178532 | − | 0.309227i | ||||
\(748\) | 10080.0 | 0.492729 | ||||||||
\(749\) | 32970.0 | + | 11421.1i | 1.60841 | + | 0.557169i | ||||
\(750\) | −7704.00 | −0.375080 | ||||||||
\(751\) | 2460.50 | − | 4261.71i | 0.119554 | − | 0.207073i | −0.800037 | − | 0.599951i | \(-0.795187\pi\) |
0.919591 | + | 0.392877i | \(0.128520\pi\) | |||||||
\(752\) | 2928.00 | + | 5071.44i | 0.141986 | + | 0.245926i | ||||
\(753\) | 702.000 | + | 1215.90i | 0.0339738 | + | 0.0588444i | ||||
\(754\) | −9540.00 | + | 16523.8i | −0.460778 | + | 0.798090i | ||||
\(755\) | −6528.00 | −0.314673 | ||||||||
\(756\) | −1512.00 | + | 1309.43i | −0.0727393 | + | 0.0629941i | ||||
\(757\) | 18098.0 | 0.868934 | 0.434467 | − | 0.900688i | \(-0.356937\pi\) | ||||
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(758\) | −11899.0 | + | 20609.7i | −0.570173 | + | 0.987569i | ||||
\(759\) | 3780.00 | + | 6547.15i | 0.180771 | + | 0.313105i | ||||
\(760\) | 2328.00 | + | 4032.21i | 0.111112 | + | 0.192452i | ||||
\(761\) | 12234.0 | − | 21189.9i | 0.582762 | − | 1.00937i | −0.412388 | − | 0.911008i | \(-0.635305\pi\) |
0.995150 | − | 0.0983657i | \(-0.0313615\pi\) | |||||||
\(762\) | −14898.0 | −0.708265 | ||||||||
\(763\) | −5782.00 | + | 5007.36i | −0.274341 | + | 0.237587i | ||||
\(764\) | 2856.00 | 0.135244 | ||||||||
\(765\) | −2268.00 | + | 3928.29i | −0.107189 | + | 0.185657i | ||||
\(766\) | 2568.00 | + | 4447.91i | 0.121130 | + | 0.209803i | ||||
\(767\) | 6996.00 | + | 12117.4i | 0.329349 | + | 0.570450i | ||||
\(768\) | −384.000 | + | 665.108i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 21719.0 | 1.01847 | 0.509237 | − | 0.860626i | \(-0.329928\pi\) | ||||
0.509237 | + | 0.860626i | \(0.329928\pi\) | |||||||
\(770\) | −6300.00 | − | 2182.38i | −0.294852 | − | 0.102140i | ||||
\(771\) | −7470.00 | −0.348931 | ||||||||
\(772\) | 7418.00 | − | 12848.4i | 0.345829 | − | 0.598993i | ||||
\(773\) | 15153.0 | + | 26245.8i | 0.705065 | + | 1.22121i | 0.966668 | + | 0.256033i | \(0.0824157\pi\) |
−0.261603 | + | 0.965176i | \(0.584251\pi\) | |||||||
\(774\) | −2925.00 | − | 5066.25i | −0.135836 | − | 0.235275i | ||||
\(775\) | 7965.50 | − | 13796.7i | 0.369199 | − | 0.639471i | ||||
\(776\) | −3088.00 | −0.142851 | ||||||||
\(777\) | 1522.50 | + | 7911.14i | 0.0702952 | + | 0.365265i | ||||
\(778\) | 20292.0 | 0.935094 | ||||||||
\(779\) | 6111.00 | − | 10584.6i | 0.281065 | − | 0.486818i | ||||
\(780\) | 1908.00 | + | 3304.75i | 0.0875864 | + | 0.151704i | ||||
\(781\) | −5130.00 | − | 8885.42i | −0.235039 | − | 0.407100i | ||||
\(782\) | −7056.00 | + | 12221.4i | −0.322662 | + | 0.558868i | ||||
\(783\) | −4860.00 | −0.221816 | ||||||||
\(784\) | 784.000 | − | 5431.71i | 0.0357143 | − | 0.247436i | ||||
\(785\) | −3036.00 | −0.138038 | ||||||||
\(786\) | 6354.00 | − | 11005.5i | 0.288346 | − | 0.499429i | ||||
\(787\) | −13648.0 | − | 23639.0i | −0.618169 | − | 1.07070i | −0.989820 | − | 0.142327i | \(-0.954542\pi\) |
0.371651 | − | 0.928372i | \(-0.378792\pi\) | |||||||
\(788\) | 2088.00 | + | 3616.52i | 0.0943933 | + | 0.163494i | ||||
\(789\) | −2358.00 | + | 4084.18i | −0.106397 | + | 0.184285i | ||||
\(790\) | −14052.0 | −0.632845 | ||||||||
\(791\) | 3087.00 | + | 16040.5i | 0.138762 | + | 0.721031i | ||||
\(792\) | 2160.00 | 0.0969094 | ||||||||
\(793\) | −21677.0 | + | 37545.7i | −0.970710 | + | 1.68132i | ||||
\(794\) | −6229.00 | − | 10788.9i | −0.278412 | − | 0.482223i | ||||
\(795\) | −6912.00 | − | 11971.9i | −0.308356 | − | 0.534089i | ||||
\(796\) | 272.000 | − | 471.118i | 0.0121115 | − | 0.0209778i | ||||
\(797\) | −35100.0 | −1.55998 | −0.779991 | − | 0.625791i | \(-0.784776\pi\) | ||||
−0.779991 | + | 0.625791i | \(0.784776\pi\) | |||||||
\(798\) | 10185.0 | + | 3528.19i | 0.451811 | + | 0.156512i | ||||
\(799\) | 30744.0 | 1.36126 | ||||||||
\(800\) | −1424.00 | + | 2466.44i | −0.0629325 | + | 0.109002i | ||||
\(801\) | 2700.00 | + | 4676.54i | 0.119101 | + | 0.206289i | ||||
\(802\) | −2472.00 | − | 4281.63i | −0.108840 | − | 0.188516i | ||||
\(803\) | −645.000 | + | 1117.17i | −0.0283456 | + | 0.0490961i | ||||
\(804\) | −6276.00 | −0.275295 | ||||||||
\(805\) | 7056.00 | − | 6110.68i | 0.308933 | − | 0.267544i | ||||
\(806\) | −18974.0 | −0.829194 | ||||||||
\(807\) | −2709.00 | + | 4692.13i | −0.118168 | + | 0.204672i | ||||
\(808\) | 2472.00 | + | 4281.63i | 0.107630 | + | 0.186420i | ||||
\(809\) | −22197.0 | − | 38446.3i | −0.964654 | − | 1.67083i | −0.710542 | − | 0.703655i | \(-0.751550\pi\) |
−0.254112 | − | 0.967175i | \(-0.581783\pi\) | |||||||
\(810\) | −486.000 | + | 841.777i | −0.0210819 | + | 0.0365148i | ||||
\(811\) | −8584.00 | −0.371671 | −0.185835 | − | 0.982581i | \(-0.559499\pi\) | ||||
−0.185835 | + | 0.982581i | \(0.559499\pi\) | |||||||
\(812\) | 10080.0 | − | 8729.54i | 0.435639 | − | 0.377274i | ||||
\(813\) | −18336.0 | −0.790986 | ||||||||
\(814\) | 4350.00 | − | 7534.42i | 0.187306 | − | 0.324424i | ||||
\(815\) | 5532.00 | + | 9581.71i | 0.237764 | + | 0.411819i | ||||
\(816\) | 2016.00 | + | 3491.81i | 0.0864879 | + | 0.149801i | ||||
\(817\) | −15762.5 | + | 27301.5i | −0.674982 | + | 1.16910i | ||||
\(818\) | 14150.0 | 0.604820 | ||||||||
\(819\) | 8347.50 | + | 2891.66i | 0.356148 | + | 0.123373i | ||||
\(820\) | −3024.00 | −0.128784 | ||||||||
\(821\) | 4917.00 | − | 8516.49i | 0.209019 | − | 0.362031i | −0.742387 | − | 0.669971i | \(-0.766306\pi\) |
0.951406 | + | 0.307940i | \(0.0996397\pi\) | |||||||
\(822\) | 9036.00 | + | 15650.8i | 0.383414 | + | 0.664093i | ||||
\(823\) | −21928.0 | − | 37980.4i | −0.928751 | − | 1.60864i | −0.785415 | − | 0.618970i | \(-0.787550\pi\) |
−0.143336 | − | 0.989674i | \(-0.545783\pi\) | |||||||
\(824\) | 5900.00 | − | 10219.1i | 0.249437 | − | 0.432038i | ||||
\(825\) | 8010.00 | 0.338027 | ||||||||
\(826\) | −1848.00 | − | 9602.49i | −0.0778452 | − | 0.404496i | ||||
\(827\) | 13266.0 | 0.557804 | 0.278902 | − | 0.960320i | \(-0.410030\pi\) | ||||
0.278902 | + | 0.960320i | \(0.410030\pi\) | |||||||
\(828\) | −1512.00 | + | 2618.86i | −0.0634609 | + | 0.109918i | ||||
\(829\) | −8726.50 | − | 15114.7i | −0.365602 | − | 0.633241i | 0.623271 | − | 0.782006i | \(-0.285803\pi\) |
−0.988873 | + | 0.148765i | \(0.952470\pi\) | |||||||
\(830\) | 4860.00 | + | 8417.77i | 0.203245 | + | 0.352030i | ||||
\(831\) | 6346.50 | − | 10992.5i | 0.264931 | − | 0.458874i | ||||
\(832\) | 3392.00 | 0.141342 | ||||||||
\(833\) | −22638.0 | − | 17822.8i | −0.941609 | − | 0.741325i | ||||
\(834\) | 222.000 | 0.00921730 | ||||||||
\(835\) | 486.000 | − | 841.777i | 0.0201422 | − | 0.0348873i | ||||
\(836\) | −5820.00 | − | 10080.5i | −0.240776 | − | 0.417037i | ||||
\(837\) | −2416.50 | − | 4185.50i | −0.0997927 | − | 0.172846i | ||||
\(838\) | −4158.00 | + | 7201.87i | −0.171403 | + | 0.296879i | ||||
\(839\) | −35172.0 | −1.44729 | −0.723643 | − | 0.690175i | \(-0.757534\pi\) | ||||
−0.723643 | + | 0.690175i | \(0.757534\pi\) | |||||||
\(840\) | −504.000 | − | 2618.86i | −0.0207020 | − | 0.107571i | ||||
\(841\) | 8011.00 | 0.328468 | ||||||||
\(842\) | −6595.00 | + | 11422.9i | −0.269927 | + | 0.467528i | ||||
\(843\) | 5724.00 | + | 9914.26i | 0.233861 | + | 0.405060i | ||||
\(844\) | −2968.00 | − | 5140.73i | −0.121046 | − | 0.209658i | ||||
\(845\) | 1836.00 | − | 3180.05i | 0.0747459 | − | 0.129464i | ||||
\(846\) | 6588.00 | 0.267731 | ||||||||
\(847\) | −7542.50 | − | 2612.80i | −0.305978 | − | 0.105994i | ||||
\(848\) | −12288.0 | −0.497608 | ||||||||
\(849\) | 5995.50 | − | 10384.5i | 0.242362 | − | 0.419783i | ||||
\(850\) | 7476.00 | + | 12948.8i | 0.301676 | + | 0.522518i | ||||
\(851\) | 6090.00 | + | 10548.2i | 0.245314 | + | 0.424897i | ||||
\(852\) | 2052.00 | − | 3554.17i | 0.0825122 | − | 0.142915i | ||||
\(853\) | 3503.00 | 0.140610 | 0.0703051 | − | 0.997526i | \(-0.477603\pi\) | ||||
0.0703051 | + | 0.997526i | \(0.477603\pi\) | |||||||
\(854\) | 22904.0 | − | 19835.4i | 0.917750 | − | 0.794795i | ||||
\(855\) | 5238.00 | 0.209516 | ||||||||
\(856\) | 7536.00 | − | 13052.7i | 0.300906 | − | 0.521184i | ||||
\(857\) | −11424.0 | − | 19786.9i | −0.455352 | − | 0.788692i | 0.543357 | − | 0.839502i | \(-0.317153\pi\) |
−0.998708 | + | 0.0508097i | \(0.983820\pi\) | |||||||
\(858\) | −4770.00 | − | 8261.88i | −0.189796 | − | 0.328737i | ||||
\(859\) | 6728.00 | − | 11653.2i | 0.267237 | − | 0.462868i | −0.700910 | − | 0.713249i | \(-0.747223\pi\) |
0.968147 | + | 0.250382i | \(0.0805561\pi\) | |||||||
\(860\) | 7800.00 | 0.309277 | ||||||||
\(861\) | −5292.00 | + | 4583.01i | −0.209467 | + | 0.181404i | ||||
\(862\) | −3036.00 | −0.119961 | ||||||||
\(863\) | −20355.0 | + | 35255.9i | −0.802888 | + | 1.39064i | 0.114820 | + | 0.993386i | \(0.463371\pi\) |
−0.917708 | + | 0.397256i | \(0.869962\pi\) | |||||||
\(864\) | 432.000 | + | 748.246i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −8172.00 | − | 14154.3i | −0.321221 | − | 0.556371i | ||||
\(866\) | 8567.00 | − | 14838.5i | 0.336165 | − | 0.582254i | ||||
\(867\) | 6429.00 | 0.251834 | ||||||||
\(868\) | 12530.0 | + | 4340.52i | 0.489972 | + | 0.169731i | ||||
\(869\) | 35130.0 | 1.37135 | ||||||||
\(870\) | 3240.00 | − | 5611.84i | 0.126260 | − | 0.218689i | ||||
\(871\) | 13859.5 | + | 24005.4i | 0.539163 | + | 0.933858i | ||||
\(872\) | 1652.00 | + | 2861.35i | 0.0641557 | + | 0.111121i | ||||
\(873\) | −1737.00 | + | 3008.57i | −0.0673408 | + | 0.116638i | ||||
\(874\) | 16296.0 | 0.630687 | ||||||||
\(875\) | −4494.00 | − | 23351.5i | −0.173628 | − | 0.902200i | ||||
\(876\) | −516.000 | −0.0199019 | ||||||||
\(877\) | −1453.00 | + | 2516.67i | −0.0559456 | + | 0.0969007i | −0.892642 | − | 0.450767i | \(-0.851151\pi\) |
0.836696 | + | 0.547667i | \(0.184484\pi\) | |||||||
\(878\) | 10640.0 | + | 18429.0i | 0.408978 | + | 0.708371i | ||||
\(879\) | −6912.00 | − | 11971.9i | −0.265229 | − | 0.459389i | ||||
\(880\) | −1440.00 | + | 2494.15i | −0.0551618 | + | 0.0955431i | ||||
\(881\) | −19188.0 | −0.733780 | −0.366890 | − | 0.930264i | \(-0.619577\pi\) | ||||
−0.366890 | + | 0.930264i | \(0.619577\pi\) | |||||||
\(882\) | −4851.00 | − | 3819.17i | −0.185195 | − | 0.145803i | ||||
\(883\) | −17251.0 | −0.657466 | −0.328733 | − | 0.944423i | \(-0.606622\pi\) | ||||
−0.328733 | + | 0.944423i | \(0.606622\pi\) | |||||||
\(884\) | 8904.00 | − | 15422.2i | 0.338771 | − | 0.586769i | ||||
\(885\) | −2376.00 | − | 4115.35i | −0.0902467 | − | 0.156312i | ||||
\(886\) | 7032.00 | + | 12179.8i | 0.266642 | + | 0.461837i | ||||
\(887\) | 1047.00 | − | 1813.46i | 0.0396334 | − | 0.0686471i | −0.845528 | − | 0.533931i | \(-0.820714\pi\) |
0.885162 | + | 0.465284i | \(0.154048\pi\) | |||||||
\(888\) | 3480.00 | 0.131510 | ||||||||
\(889\) | −8690.50 | − | 45157.2i | −0.327863 | − | 1.70362i | ||||
\(890\) | −7200.00 | −0.271174 | ||||||||
\(891\) | 1215.00 | − | 2104.44i | 0.0456835 | − | 0.0791262i | ||||
\(892\) | 4064.00 | + | 7039.05i | 0.152548 | + | 0.264221i | ||||
\(893\) | −17751.0 | − | 30745.6i | −0.665190 | − | 1.15214i | ||||
\(894\) | −4932.00 | + | 8542.47i | −0.184509 | + | 0.319578i | ||||
\(895\) | 7524.00 | 0.281005 | ||||||||
\(896\) | −2240.00 | − | 775.959i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | 13356.0 | 0.497150 | ||||||||
\(898\) | −14814.0 | + | 25658.6i | −0.550501 | + | 0.953495i | ||||
\(899\) | 16110.0 | + | 27903.3i | 0.597662 | + | 1.03518i | ||||
\(900\) | 1602.00 | + | 2774.75i | 0.0593333 | + | 0.102768i | ||||
\(901\) | −32256.0 | + | 55869.0i | −1.19268 | + | 2.06578i | ||||
\(902\) | 7560.00 | 0.279069 | ||||||||
\(903\) | 13650.0 | − | 11821.2i | 0.503038 | − | 0.435644i | ||||
\(904\) | 7056.00 | 0.259601 | ||||||||
\(905\) | −5421.00 | + | 9389.45i | −0.199116 | + | 0.344879i | ||||
\(906\) | 3264.00 | + | 5653.41i | 0.119690 | + | 0.207309i | ||||
\(907\) | 20133.5 | + | 34872.2i | 0.737069 | + | 1.27664i | 0.953809 | + | 0.300412i | \(0.0971242\pi\) |
−0.216740 | + | 0.976229i | \(0.569542\pi\) | |||||||
\(908\) | −12396.0 | + | 21470.5i | −0.453057 | + | 0.784718i | ||||
\(909\) | 5562.00 | 0.202948 | ||||||||
\(910\) | −8904.00 | + | 7711.09i | −0.324357 | + | 0.280901i | ||||
\(911\) | 17604.0 | 0.640227 | 0.320113 | − | 0.947379i | \(-0.396279\pi\) | ||||
0.320113 | + | 0.947379i | \(0.396279\pi\) | |||||||
\(912\) | 2328.00 | − | 4032.21i | 0.0845261 | − | 0.146403i | ||||
\(913\) | −12150.0 | − | 21044.4i | −0.440423 | − | 0.762835i | ||||
\(914\) | −11251.0 | − | 19487.3i | −0.407166 | − | 0.705233i | ||||
\(915\) | 7362.00 | − | 12751.4i | 0.265989 | − | 0.460707i | ||||
\(916\) | −18364.0 | −0.662406 | ||||||||
\(917\) | 37065.0 | + | 12839.7i | 1.33478 | + | 0.462382i | ||||
\(918\) | 4536.00 | 0.163083 | ||||||||
\(919\) | −1754.50 | + | 3038.88i | −0.0629767 | + | 0.109079i | −0.895795 | − | 0.444468i | \(-0.853393\pi\) |
0.832818 | + | 0.553547i | \(0.186726\pi\) | |||||||
\(920\) | −2016.00 | − | 3491.81i | −0.0722452 | − | 0.125132i | ||||
\(921\) | 946.500 | + | 1639.39i | 0.0338634 | + | 0.0586532i | ||||
\(922\) | −3852.00 | + | 6671.86i | −0.137591 | + | 0.238315i | ||||
\(923\) | −18126.0 | −0.646397 | ||||||||
\(924\) | 1260.00 | + | 6547.15i | 0.0448603 | + | 0.233101i | ||||
\(925\) | 12905.0 | 0.458718 | ||||||||
\(926\) | −475.000 | + | 822.724i | −0.0168569 | + | 0.0291970i | ||||
\(927\) | −6637.50 | − | 11496.5i | −0.235172 | − | 0.407329i | ||||
\(928\) | −2880.00 | − | 4988.31i | −0.101876 | − | 0.176454i | ||||
\(929\) | 17319.0 | − | 29997.4i | 0.611645 | − | 1.05940i | −0.379319 | − | 0.925266i | \(-0.623842\pi\) |
0.990963 | − | 0.134134i | \(-0.0428251\pi\) | |||||||
\(930\) | 6444.00 | 0.227212 | ||||||||
\(931\) | −4753.00 | + | 32929.7i | −0.167318 | + | 1.15921i | ||||
\(932\) | 18120.0 | 0.636846 | ||||||||
\(933\) | −5841.00 | + | 10116.9i | −0.204958 | + | 0.354998i | ||||
\(934\) | 5934.00 | + | 10278.0i | 0.207887 | + | 0.360071i | ||||
\(935\) | 7560.00 | + | 13094.3i | 0.264426 | + | 0.458000i | ||||
\(936\) | 1908.00 | − | 3304.75i | 0.0666292 | − | 0.115405i | ||||
\(937\) | −17353.0 | −0.605014 | −0.302507 | − | 0.953147i | \(-0.597824\pi\) | ||||
−0.302507 | + | 0.953147i | \(0.597824\pi\) | |||||||
\(938\) | −3661.00 | − | 19023.1i | −0.127437 | − | 0.662182i | ||||
\(939\) | −6555.00 | −0.227811 | ||||||||
\(940\) | −4392.00 | + | 7607.17i | −0.152395 | + | 0.263956i | ||||
\(941\) | 23460.0 | + | 40633.9i | 0.812725 | + | 1.40768i | 0.910950 | + | 0.412517i | \(0.135350\pi\) |
−0.0982252 | + | 0.995164i | \(0.531317\pi\) | |||||||
\(942\) | 1518.00 | + | 2629.25i | 0.0525044 | + | 0.0909402i | ||||
\(943\) | −5292.00 | + | 9166.01i | −0.182748 | + | 0.316529i | ||||
\(944\) | −4224.00 | −0.145635 | ||||||||
\(945\) | −2835.00 | − | 982.073i | −0.0975900 | − | 0.0338062i | ||||
\(946\) | −19500.0 | −0.670190 | ||||||||
\(947\) | −9177.00 | + | 15895.0i | −0.314902 | + | 0.545427i | −0.979417 | − | 0.201849i | \(-0.935305\pi\) |
0.664514 | + | 0.747275i | \(0.268638\pi\) | |||||||
\(948\) | 7026.00 | + | 12169.4i | 0.240711 | + | 0.416923i | ||||
\(949\) | 1139.50 | + | 1973.67i | 0.0389776 | + | 0.0675112i | ||||
\(950\) | 8633.00 | − | 14952.8i | 0.294833 | − | 0.510666i | ||||
\(951\) | 10512.0 | 0.358438 | ||||||||
\(952\) | −9408.00 | + | 8147.57i | −0.320289 | + | 0.277378i | ||||
\(953\) | 35568.0 | 1.20898 | 0.604491 | − | 0.796612i | \(-0.293376\pi\) | ||||
0.604491 | + | 0.796612i | \(0.293376\pi\) | |||||||
\(954\) | −6912.00 | + | 11971.9i | −0.234575 | + | 0.406295i | ||||
\(955\) | 2142.00 | + | 3710.05i | 0.0725796 | + | 0.125712i | ||||
\(956\) | −3060.00 | − | 5300.08i | −0.103522 | − | 0.179306i | ||||
\(957\) | −8100.00 | + | 14029.6i | −0.273601 | + | 0.473890i | ||||
\(958\) | 26736.0 | 0.901671 | ||||||||
\(959\) | −42168.0 | + | 36518.6i | −1.41989 | + | 1.22966i | ||||
\(960\) | −1152.00 | −0.0387298 | ||||||||
\(961\) | −1125.00 | + | 1948.56i | −0.0377631 | + | 0.0654076i | ||||
\(962\) | −7685.00 | − | 13310.8i | −0.257562 | − | 0.446110i | ||||
\(963\) | −8478.00 | − | 14684.3i | −0.283697 | − | 0.491377i | ||||
\(964\) | −11068.0 | + | 19170.3i | −0.369789 | + | 0.640493i | ||||
\(965\) | 22254.0 | 0.742364 | ||||||||
\(966\) | −8820.00 | − | 3055.34i | −0.293767 | − | 0.101764i | ||||
\(967\) | −27343.0 | −0.909298 | −0.454649 | − | 0.890671i | \(-0.650235\pi\) | ||||
−0.454649 | + | 0.890671i | \(0.650235\pi\) | |||||||
\(968\) | −1724.00 | + | 2986.06i | −0.0572432 | + | 0.0991482i | ||||
\(969\) | −12222.0 | − | 21169.1i | −0.405188 | − | 0.701806i | ||||
\(970\) | −2316.00 | − | 4011.43i | −0.0766621 | − | 0.132783i | ||||
\(971\) | −25512.0 | + | 44188.1i | −0.843171 | + | 1.46042i | 0.0440291 | + | 0.999030i | \(0.485981\pi\) |
−0.887200 | + | 0.461385i | \(0.847353\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 129.500 | + | 672.902i | 0.00426678 | + | 0.0221709i | ||||
\(974\) | −13306.0 | −0.437733 | ||||||||
\(975\) | 7075.50 | − | 12255.1i | 0.232408 | − | 0.402542i | ||||
\(976\) | −6544.00 | − | 11334.5i | −0.214619 | − | 0.371731i | ||||
\(977\) | 1113.00 | + | 1927.77i | 0.0364463 | + | 0.0631268i | 0.883673 | − | 0.468104i | \(-0.155063\pi\) |
−0.847227 | + | 0.531231i | \(0.821730\pi\) | |||||||
\(978\) | 5532.00 | − | 9581.71i | 0.180873 | − | 0.313281i | ||||
\(979\) | 18000.0 | 0.587623 | ||||||||
\(980\) | 7644.00 | − | 3055.34i | 0.249162 | − | 0.0995910i | ||||
\(981\) | 3717.00 | 0.120973 | ||||||||
\(982\) | 15444.0 | − | 26749.8i | 0.501872 | − | 0.869267i | ||||
\(983\) | −17652.0 | − | 30574.2i | −0.572748 | − | 0.992029i | −0.996282 | − | 0.0861487i | \(-0.972544\pi\) |
0.423534 | − | 0.905880i | \(-0.360789\pi\) | |||||||
\(984\) | 1512.00 | + | 2618.86i | 0.0489846 | + | 0.0848437i | ||||
\(985\) | −3132.00 | + | 5424.78i | −0.101314 | + | 0.175480i | ||||
\(986\) | −30240.0 | −0.976712 | ||||||||
\(987\) | 3843.00 | + | 19968.8i | 0.123935 | + | 0.643986i | ||||
\(988\) | −20564.0 | −0.662174 | ||||||||
\(989\) | 13650.0 | − | 23642.5i | 0.438872 | − | 0.760149i | ||||
\(990\) | 1620.00 | + | 2805.92i | 0.0520071 | + | 0.0900789i | ||||
\(991\) | 1170.50 | + | 2027.37i | 0.0375198 | + | 0.0649863i | 0.884176 | − | 0.467155i | \(-0.154721\pi\) |
−0.846656 | + | 0.532141i | \(0.821388\pi\) | |||||||
\(992\) | 2864.00 | − | 4960.59i | 0.0916654 | − | 0.158769i | ||||
\(993\) | 8835.00 | 0.282347 | ||||||||
\(994\) | 11970.0 | + | 4146.53i | 0.381957 | + | 0.132314i | ||||
\(995\) | 816.000 | 0.0259989 | ||||||||
\(996\) | 4860.00 | − | 8417.77i | 0.154613 | − | 0.267798i | ||||
\(997\) | −14507.5 | − | 25127.7i | −0.460840 | − | 0.798198i | 0.538163 | − | 0.842841i | \(-0.319118\pi\) |
−0.999003 | + | 0.0446429i | \(0.985785\pi\) | |||||||
\(998\) | 683.000 | + | 1182.99i | 0.0216633 | + | 0.0375220i | ||||
\(999\) | 1957.50 | − | 3390.49i | 0.0619946 | − | 0.107378i |
(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 | 42.4.e.a.37.1 | yes | 2 | |
3.2 | odd | 2 | 126.4.g.b.37.1 | 2 | |||
4.3 | odd | 2 | 336.4.q.f.289.1 | 2 | |||
7.2 | even | 3 | 294.4.a.d.1.1 | 1 | |||
7.3 | odd | 6 | 294.4.e.i.67.1 | 2 | |||
7.4 | even | 3 | inner | 42.4.e.a.25.1 | ✓ | 2 | |
7.5 | odd | 6 | 294.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 294.4.e.i.79.1 | 2 | |||
21.2 | odd | 6 | 882.4.a.o.1.1 | 1 | |||
21.5 | even | 6 | 882.4.a.l.1.1 | 1 | |||
21.11 | odd | 6 | 126.4.g.b.109.1 | 2 | |||
21.17 | even | 6 | 882.4.g.g.361.1 | 2 | |||
21.20 | even | 2 | 882.4.g.g.667.1 | 2 | |||
28.11 | odd | 6 | 336.4.q.f.193.1 | 2 | |||
28.19 | even | 6 | 2352.4.a.bf.1.1 | 1 | |||
28.23 | odd | 6 | 2352.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.a.25.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
42.4.e.a.37.1 | yes | 2 | 1.1 | even | 1 | trivial | |
126.4.g.b.37.1 | 2 | 3.2 | odd | 2 | |||
126.4.g.b.109.1 | 2 | 21.11 | odd | 6 | |||
294.4.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
294.4.a.d.1.1 | 1 | 7.2 | even | 3 | |||
294.4.e.i.67.1 | 2 | 7.3 | odd | 6 | |||
294.4.e.i.79.1 | 2 | 7.6 | odd | 2 | |||
336.4.q.f.193.1 | 2 | 28.11 | odd | 6 | |||
336.4.q.f.289.1 | 2 | 4.3 | odd | 2 | |||
882.4.a.l.1.1 | 1 | 21.5 | even | 6 | |||
882.4.a.o.1.1 | 1 | 21.2 | odd | 6 | |||
882.4.g.g.361.1 | 2 | 21.17 | even | 6 | |||
882.4.g.g.667.1 | 2 | 21.20 | even | 2 | |||
2352.4.a.f.1.1 | 1 | 28.23 | odd | 6 | |||
2352.4.a.bf.1.1 | 1 | 28.19 | even | 6 |