Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,4,Mod(7,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.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: | \(6.72621774065\) |
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 | 49.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.49 |
Dual form | 114.4.e.b.7.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(0.0801955\pi\) | |||||||
\(6\) | 3.00000 | + | 5.19615i | 0.204124 | + | 0.353553i | ||||
\(7\) | 19.0000 | 1.02590 | 0.512952 | − | 0.858417i | \(-0.328552\pi\) | ||||
0.512952 | + | 0.858417i | \(0.328552\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | −6.00000 | − | 10.3923i | −0.189737 | − | 0.328634i | ||||
\(11\) | 32.0000 | 0.877124 | 0.438562 | − | 0.898701i | \(-0.355488\pi\) | ||||
0.438562 | + | 0.898701i | \(0.355488\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −40.5000 | − | 70.1481i | −0.864052 | − | 1.49658i | −0.867985 | − | 0.496590i | \(-0.834585\pi\) |
0.00393295 | − | 0.999992i | \(-0.498748\pi\) | |||||||
\(14\) | 19.0000 | − | 32.9090i | 0.362712 | − | 0.628235i | ||||
\(15\) | 9.00000 | + | 15.5885i | 0.154919 | + | 0.268328i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 62.0000 | − | 107.387i | 0.884542 | − | 1.53207i | 0.0383036 | − | 0.999266i | \(-0.487805\pi\) |
0.846238 | − | 0.532805i | \(-0.178862\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 76.0000 | + | 32.9090i | 0.917663 | + | 0.397360i | ||||
\(20\) | −24.0000 | −0.268328 | ||||||||
\(21\) | −28.5000 | + | 49.3634i | −0.296153 | + | 0.512952i | ||||
\(22\) | 32.0000 | − | 55.4256i | 0.310110 | − | 0.537127i | ||||
\(23\) | −49.0000 | − | 84.8705i | −0.444226 | − | 0.769423i | 0.553772 | − | 0.832669i | \(-0.313188\pi\) |
−0.997998 | + | 0.0632460i | \(0.979855\pi\) | |||||||
\(24\) | 12.0000 | − | 20.7846i | 0.102062 | − | 0.176777i | ||||
\(25\) | 44.5000 | + | 77.0763i | 0.356000 | + | 0.616610i | ||||
\(26\) | −162.000 | −1.22195 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −38.0000 | − | 65.8179i | −0.256476 | − | 0.444229i | ||||
\(29\) | 150.000 | + | 259.808i | 0.960493 | + | 1.66362i | 0.721265 | + | 0.692660i | \(0.243561\pi\) |
0.239228 | + | 0.970963i | \(0.423106\pi\) | |||||||
\(30\) | 36.0000 | 0.219089 | ||||||||
\(31\) | −225.000 | −1.30359 | −0.651793 | − | 0.758397i | \(-0.725983\pi\) | ||||
−0.651793 | + | 0.758397i | \(0.725983\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −48.0000 | + | 83.1384i | −0.253204 | + | 0.438562i | ||||
\(34\) | −124.000 | − | 214.774i | −0.625465 | − | 1.08334i | ||||
\(35\) | 57.0000 | − | 98.7269i | 0.275279 | − | 0.476797i | ||||
\(36\) | −18.0000 | + | 31.1769i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −293.000 | −1.30186 | −0.650931 | − | 0.759137i | \(-0.725621\pi\) | ||||
−0.650931 | + | 0.759137i | \(0.725621\pi\) | |||||||
\(38\) | 133.000 | − | 98.7269i | 0.567775 | − | 0.421464i | ||||
\(39\) | 243.000 | 0.997722 | ||||||||
\(40\) | −24.0000 | + | 41.5692i | −0.0948683 | + | 0.164317i | ||||
\(41\) | −88.0000 | + | 152.420i | −0.335202 | + | 0.580587i | −0.983524 | − | 0.180779i | \(-0.942138\pi\) |
0.648321 | + | 0.761367i | \(0.275471\pi\) | |||||||
\(42\) | 57.0000 | + | 98.7269i | 0.209412 | + | 0.362712i | ||||
\(43\) | 55.5000 | − | 96.1288i | 0.196830 | − | 0.340919i | −0.750669 | − | 0.660678i | \(-0.770269\pi\) |
0.947499 | + | 0.319759i | \(0.103602\pi\) | |||||||
\(44\) | −64.0000 | − | 110.851i | −0.219281 | − | 0.379806i | ||||
\(45\) | −54.0000 | −0.178885 | ||||||||
\(46\) | −196.000 | −0.628231 | ||||||||
\(47\) | 275.000 | + | 476.314i | 0.853465 | + | 1.47825i | 0.878061 | + | 0.478548i | \(0.158837\pi\) |
−0.0245961 | + | 0.999697i | \(0.507830\pi\) | |||||||
\(48\) | −24.0000 | − | 41.5692i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 18.0000 | 0.0524781 | ||||||||
\(50\) | 178.000 | 0.503460 | ||||||||
\(51\) | 186.000 | + | 322.161i | 0.510690 | + | 0.884542i | ||||
\(52\) | −162.000 | + | 280.592i | −0.432026 | + | 0.748291i | ||||
\(53\) | 241.000 | + | 417.424i | 0.624602 | + | 1.08184i | 0.988618 | + | 0.150449i | \(0.0480720\pi\) |
−0.364016 | + | 0.931393i | \(0.618595\pi\) | |||||||
\(54\) | 27.0000 | − | 46.7654i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 96.0000 | − | 166.277i | 0.235357 | − | 0.407650i | ||||
\(56\) | −152.000 | −0.362712 | ||||||||
\(57\) | −199.500 | + | 148.090i | −0.463586 | + | 0.344124i | ||||
\(58\) | 600.000 | 1.35834 | ||||||||
\(59\) | 248.000 | − | 429.549i | 0.547235 | − | 0.947838i | −0.451228 | − | 0.892409i | \(-0.649014\pi\) |
0.998463 | − | 0.0554296i | \(-0.0176528\pi\) | |||||||
\(60\) | 36.0000 | − | 62.3538i | 0.0774597 | − | 0.134164i | ||||
\(61\) | −77.5000 | − | 134.234i | −0.162670 | − | 0.281752i | 0.773156 | − | 0.634216i | \(-0.218677\pi\) |
−0.935825 | + | 0.352464i | \(0.885344\pi\) | |||||||
\(62\) | −225.000 | + | 389.711i | −0.460888 | + | 0.798281i | ||||
\(63\) | −85.5000 | − | 148.090i | −0.170984 | − | 0.296153i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −486.000 | −0.927398 | ||||||||
\(66\) | 96.0000 | + | 166.277i | 0.179042 | + | 0.310110i | ||||
\(67\) | −232.500 | − | 402.702i | −0.423946 | − | 0.734296i | 0.572375 | − | 0.819992i | \(-0.306022\pi\) |
−0.996321 | + | 0.0856955i | \(0.972689\pi\) | |||||||
\(68\) | −496.000 | −0.884542 | ||||||||
\(69\) | 294.000 | 0.512948 | ||||||||
\(70\) | −114.000 | − | 197.454i | −0.194652 | − | 0.337146i | ||||
\(71\) | 55.0000 | − | 95.2628i | 0.0919338 | − | 0.159234i | −0.816391 | − | 0.577500i | \(-0.804029\pi\) |
0.908325 | + | 0.418266i | \(0.137362\pi\) | |||||||
\(72\) | 36.0000 | + | 62.3538i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −408.500 | + | 707.543i | −0.654949 | + | 1.13441i | 0.326957 | + | 0.945039i | \(0.393977\pi\) |
−0.981906 | + | 0.189366i | \(0.939357\pi\) | |||||||
\(74\) | −293.000 | + | 507.491i | −0.460278 | + | 0.797225i | ||||
\(75\) | −267.000 | −0.411073 | ||||||||
\(76\) | −38.0000 | − | 329.090i | −0.0573539 | − | 0.496700i | ||||
\(77\) | 608.000 | 0.899845 | ||||||||
\(78\) | 243.000 | − | 420.888i | 0.352748 | − | 0.610977i | ||||
\(79\) | −129.500 | + | 224.301i | −0.184429 | + | 0.319440i | −0.943384 | − | 0.331703i | \(-0.892377\pi\) |
0.758955 | + | 0.651143i | \(0.225710\pi\) | |||||||
\(80\) | 48.0000 | + | 83.1384i | 0.0670820 | + | 0.116190i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 176.000 | + | 304.841i | 0.237024 | + | 0.410537i | ||||
\(83\) | −56.0000 | −0.0740578 | −0.0370289 | − | 0.999314i | \(-0.511789\pi\) | ||||
−0.0370289 | + | 0.999314i | \(0.511789\pi\) | |||||||
\(84\) | 228.000 | 0.296153 | ||||||||
\(85\) | −372.000 | − | 644.323i | −0.474695 | − | 0.822196i | ||||
\(86\) | −111.000 | − | 192.258i | −0.139180 | − | 0.241066i | ||||
\(87\) | −900.000 | −1.10908 | ||||||||
\(88\) | −256.000 | −0.310110 | ||||||||
\(89\) | −154.000 | − | 266.736i | −0.183415 | − | 0.317685i | 0.759626 | − | 0.650360i | \(-0.225382\pi\) |
−0.943041 | + | 0.332675i | \(0.892049\pi\) | |||||||
\(90\) | −54.0000 | + | 93.5307i | −0.0632456 | + | 0.109545i | ||||
\(91\) | −769.500 | − | 1332.81i | −0.886434 | − | 1.53535i | ||||
\(92\) | −196.000 | + | 339.482i | −0.222113 | + | 0.384711i | ||||
\(93\) | 337.500 | − | 584.567i | 0.376313 | − | 0.651793i | ||||
\(94\) | 1100.00 | 1.20698 | ||||||||
\(95\) | 399.000 | − | 296.181i | 0.430911 | − | 0.319868i | ||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 575.000 | − | 995.929i | 0.601880 | − | 1.04249i | −0.390656 | − | 0.920537i | \(-0.627752\pi\) |
0.992536 | − | 0.121951i | \(-0.0389150\pi\) | |||||||
\(98\) | 18.0000 | − | 31.1769i | 0.0185538 | − | 0.0321362i | ||||
\(99\) | −144.000 | − | 249.415i | −0.146187 | − | 0.253204i | ||||
\(100\) | 178.000 | − | 308.305i | 0.178000 | − | 0.308305i | ||||
\(101\) | 289.000 | + | 500.563i | 0.284719 | + | 0.493147i | 0.972541 | − | 0.232732i | \(-0.0747665\pi\) |
−0.687822 | + | 0.725879i | \(0.741433\pi\) | |||||||
\(102\) | 744.000 | 0.722225 | ||||||||
\(103\) | 819.000 | 0.783480 | 0.391740 | − | 0.920076i | \(-0.371873\pi\) | ||||
0.391740 | + | 0.920076i | \(0.371873\pi\) | |||||||
\(104\) | 324.000 | + | 561.184i | 0.305489 | + | 0.529122i | ||||
\(105\) | 171.000 | + | 296.181i | 0.158932 | + | 0.275279i | ||||
\(106\) | 964.000 | 0.883320 | ||||||||
\(107\) | 262.000 | 0.236715 | 0.118357 | − | 0.992971i | \(-0.462237\pi\) | ||||
0.118357 | + | 0.992971i | \(0.462237\pi\) | |||||||
\(108\) | −54.0000 | − | 93.5307i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −517.000 | + | 895.470i | −0.454308 | + | 0.786885i | −0.998648 | − | 0.0519796i | \(-0.983447\pi\) |
0.544340 | + | 0.838865i | \(0.316780\pi\) | |||||||
\(110\) | −192.000 | − | 332.554i | −0.166423 | − | 0.288252i | ||||
\(111\) | 439.500 | − | 761.236i | 0.375815 | − | 0.650931i | ||||
\(112\) | −152.000 | + | 263.272i | −0.128238 | + | 0.222115i | ||||
\(113\) | −1324.00 | −1.10223 | −0.551113 | − | 0.834431i | \(-0.685797\pi\) | ||||
−0.551113 | + | 0.834431i | \(0.685797\pi\) | |||||||
\(114\) | 57.0000 | + | 493.634i | 0.0468293 | + | 0.405554i | ||||
\(115\) | −588.000 | −0.476794 | ||||||||
\(116\) | 600.000 | − | 1039.23i | 0.480247 | − | 0.831811i | ||||
\(117\) | −364.500 | + | 631.333i | −0.288017 | + | 0.498861i | ||||
\(118\) | −496.000 | − | 859.097i | −0.386953 | − | 0.670223i | ||||
\(119\) | 1178.00 | − | 2040.36i | 0.907454 | − | 1.57176i | ||||
\(120\) | −72.0000 | − | 124.708i | −0.0547723 | − | 0.0948683i | ||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | −310.000 | −0.230050 | ||||||||
\(123\) | −264.000 | − | 457.261i | −0.193529 | − | 0.335202i | ||||
\(124\) | 450.000 | + | 779.423i | 0.325897 | + | 0.564470i | ||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | −342.000 | −0.241808 | ||||||||
\(127\) | 718.000 | + | 1243.61i | 0.501671 | + | 0.868919i | 0.999998 | + | 0.00193040i | \(0.000614466\pi\) |
−0.498327 | + | 0.866989i | \(0.666052\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 166.500 | + | 288.386i | 0.113640 | + | 0.196830i | ||||
\(130\) | −486.000 | + | 841.777i | −0.327885 | + | 0.567913i | ||||
\(131\) | 189.000 | − | 327.358i | 0.126053 | − | 0.218331i | −0.796091 | − | 0.605177i | \(-0.793102\pi\) |
0.922144 | + | 0.386846i | \(0.126436\pi\) | |||||||
\(132\) | 384.000 | 0.253204 | ||||||||
\(133\) | 1444.00 | + | 625.270i | 0.941434 | + | 0.407653i | ||||
\(134\) | −930.000 | −0.599550 | ||||||||
\(135\) | 81.0000 | − | 140.296i | 0.0516398 | − | 0.0894427i | ||||
\(136\) | −496.000 | + | 859.097i | −0.312733 | + | 0.541669i | ||||
\(137\) | −531.000 | − | 919.719i | −0.331142 | − | 0.573554i | 0.651594 | − | 0.758568i | \(-0.274100\pi\) |
−0.982736 | + | 0.185014i | \(0.940767\pi\) | |||||||
\(138\) | 294.000 | − | 509.223i | 0.181355 | − | 0.314115i | ||||
\(139\) | 936.500 | + | 1622.07i | 0.571460 | + | 0.989797i | 0.996416 | + | 0.0845835i | \(0.0269560\pi\) |
−0.424957 | + | 0.905214i | \(0.639711\pi\) | |||||||
\(140\) | −456.000 | −0.275279 | ||||||||
\(141\) | −1650.00 | −0.985497 | ||||||||
\(142\) | −110.000 | − | 190.526i | −0.0650070 | − | 0.112595i | ||||
\(143\) | −1296.00 | − | 2244.74i | −0.757881 | − | 1.31269i | ||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 1800.00 | 1.03091 | ||||||||
\(146\) | 817.000 | + | 1415.09i | 0.463119 | + | 0.802146i | ||||
\(147\) | −27.0000 | + | 46.7654i | −0.0151491 | + | 0.0262391i | ||||
\(148\) | 586.000 | + | 1014.98i | 0.325466 | + | 0.563723i | ||||
\(149\) | −686.000 | + | 1188.19i | −0.377177 | + | 0.653289i | −0.990650 | − | 0.136426i | \(-0.956438\pi\) |
0.613474 | + | 0.789715i | \(0.289772\pi\) | |||||||
\(150\) | −267.000 | + | 462.458i | −0.145336 | + | 0.251730i | ||||
\(151\) | −3296.00 | −1.77632 | −0.888161 | − | 0.459532i | \(-0.848017\pi\) | ||||
−0.888161 | + | 0.459532i | \(0.848017\pi\) | |||||||
\(152\) | −608.000 | − | 263.272i | −0.324443 | − | 0.140488i | ||||
\(153\) | −1116.00 | −0.589694 | ||||||||
\(154\) | 608.000 | − | 1053.09i | 0.318143 | − | 0.551040i | ||||
\(155\) | −675.000 | + | 1169.13i | −0.349789 | + | 0.605852i | ||||
\(156\) | −486.000 | − | 841.777i | −0.249430 | − | 0.432026i | ||||
\(157\) | −883.500 | + | 1530.27i | −0.449114 | + | 0.777889i | −0.998329 | − | 0.0577925i | \(-0.981594\pi\) |
0.549214 | + | 0.835682i | \(0.314927\pi\) | |||||||
\(158\) | 259.000 | + | 448.601i | 0.130411 | + | 0.225878i | ||||
\(159\) | −1446.00 | −0.721228 | ||||||||
\(160\) | 192.000 | 0.0948683 | ||||||||
\(161\) | −931.000 | − | 1612.54i | −0.455733 | − | 0.789353i | ||||
\(162\) | 81.0000 | + | 140.296i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 1709.00 | 0.821222 | 0.410611 | − | 0.911811i | \(-0.365315\pi\) | ||||
0.410611 | + | 0.911811i | \(0.365315\pi\) | |||||||
\(164\) | 704.000 | 0.335202 | ||||||||
\(165\) | 288.000 | + | 498.831i | 0.135883 | + | 0.235357i | ||||
\(166\) | −56.0000 | + | 96.9948i | −0.0261834 | + | 0.0453510i | ||||
\(167\) | 1380.00 | + | 2390.23i | 0.639447 | + | 1.10755i | 0.985554 | + | 0.169359i | \(0.0541699\pi\) |
−0.346108 | + | 0.938195i | \(0.612497\pi\) | |||||||
\(168\) | 228.000 | − | 394.908i | 0.104706 | − | 0.181356i | ||||
\(169\) | −2182.00 | + | 3779.33i | −0.993173 | + | 1.72023i | ||||
\(170\) | −1488.00 | −0.671320 | ||||||||
\(171\) | −85.5000 | − | 740.452i | −0.0382360 | − | 0.331133i | ||||
\(172\) | −444.000 | −0.196830 | ||||||||
\(173\) | 738.000 | − | 1278.25i | 0.324330 | − | 0.561756i | −0.657046 | − | 0.753850i | \(-0.728194\pi\) |
0.981377 | + | 0.192094i | \(0.0615278\pi\) | |||||||
\(174\) | −900.000 | + | 1558.85i | −0.392120 | + | 0.679171i | ||||
\(175\) | 845.500 | + | 1464.45i | 0.365222 | + | 0.632582i | ||||
\(176\) | −256.000 | + | 443.405i | −0.109640 | + | 0.189903i | ||||
\(177\) | 744.000 | + | 1288.65i | 0.315946 | + | 0.547235i | ||||
\(178\) | −616.000 | −0.259388 | ||||||||
\(179\) | 26.0000 | 0.0108566 | 0.00542830 | − | 0.999985i | \(-0.498272\pi\) | ||||
0.00542830 | + | 0.999985i | \(0.498272\pi\) | |||||||
\(180\) | 108.000 | + | 187.061i | 0.0447214 | + | 0.0774597i | ||||
\(181\) | 1797.00 | + | 3112.50i | 0.737956 | + | 1.27818i | 0.953414 | + | 0.301664i | \(0.0975420\pi\) |
−0.215459 | + | 0.976513i | \(0.569125\pi\) | |||||||
\(182\) | −3078.00 | −1.25361 | ||||||||
\(183\) | 465.000 | 0.187835 | ||||||||
\(184\) | 392.000 | + | 678.964i | 0.157058 | + | 0.272032i | ||||
\(185\) | −879.000 | + | 1522.47i | −0.349326 | + | 0.605051i | ||||
\(186\) | −675.000 | − | 1169.13i | −0.266094 | − | 0.460888i | ||||
\(187\) | 1984.00 | − | 3436.39i | 0.775853 | − | 1.34382i | ||||
\(188\) | 1100.00 | − | 1905.26i | 0.426733 | − | 0.739123i | ||||
\(189\) | 513.000 | 0.197435 | ||||||||
\(190\) | −114.000 | − | 987.269i | −0.0435286 | − | 0.376969i | ||||
\(191\) | 314.000 | 0.118954 | 0.0594771 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594771 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(192\) | −96.0000 | + | 166.277i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 462.500 | − | 801.073i | 0.172495 | − | 0.298770i | −0.766797 | − | 0.641890i | \(-0.778151\pi\) |
0.939291 | + | 0.343120i | \(0.111484\pi\) | |||||||
\(194\) | −1150.00 | − | 1991.86i | −0.425594 | − | 0.737150i | ||||
\(195\) | 729.000 | − | 1262.67i | 0.267717 | − | 0.463699i | ||||
\(196\) | −36.0000 | − | 62.3538i | −0.0131195 | − | 0.0227237i | ||||
\(197\) | 1244.00 | 0.449905 | 0.224953 | − | 0.974370i | \(-0.427777\pi\) | ||||
0.224953 | + | 0.974370i | \(0.427777\pi\) | |||||||
\(198\) | −576.000 | −0.206740 | ||||||||
\(199\) | −1745.50 | − | 3023.29i | −0.621785 | − | 1.07696i | −0.989153 | − | 0.146888i | \(-0.953074\pi\) |
0.367368 | − | 0.930076i | \(-0.380259\pi\) | |||||||
\(200\) | −356.000 | − | 616.610i | −0.125865 | − | 0.218005i | ||||
\(201\) | 1395.00 | 0.489531 | ||||||||
\(202\) | 1156.00 | 0.402653 | ||||||||
\(203\) | 2850.00 | + | 4936.34i | 0.985373 | + | 1.70672i | ||||
\(204\) | 744.000 | − | 1288.65i | 0.255345 | − | 0.442271i | ||||
\(205\) | 528.000 | + | 914.523i | 0.179888 | + | 0.311576i | ||||
\(206\) | 819.000 | − | 1418.55i | 0.277002 | − | 0.479782i | ||||
\(207\) | −441.000 | + | 763.834i | −0.148075 | + | 0.256474i | ||||
\(208\) | 1296.00 | 0.432026 | ||||||||
\(209\) | 2432.00 | + | 1053.09i | 0.804904 | + | 0.348534i | ||||
\(210\) | 684.000 | 0.224764 | ||||||||
\(211\) | 2288.50 | − | 3963.80i | 0.746667 | − | 1.29327i | −0.202744 | − | 0.979232i | \(-0.564986\pi\) |
0.949412 | − | 0.314034i | \(-0.101681\pi\) | |||||||
\(212\) | 964.000 | − | 1669.70i | 0.312301 | − | 0.540921i | ||||
\(213\) | 165.000 | + | 285.788i | 0.0530780 | + | 0.0919338i | ||||
\(214\) | 262.000 | − | 453.797i | 0.0836914 | − | 0.144958i | ||||
\(215\) | −333.000 | − | 576.773i | −0.105630 | − | 0.182956i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −4275.00 | −1.33735 | ||||||||
\(218\) | 1034.00 | + | 1790.94i | 0.321245 | + | 0.556412i | ||||
\(219\) | −1225.50 | − | 2122.63i | −0.378135 | − | 0.654949i | ||||
\(220\) | −768.000 | −0.235357 | ||||||||
\(221\) | −10044.0 | −3.05716 | ||||||||
\(222\) | −879.000 | − | 1522.47i | −0.265742 | − | 0.460278i | ||||
\(223\) | −1147.50 | + | 1987.53i | −0.344584 | + | 0.596837i | −0.985278 | − | 0.170959i | \(-0.945313\pi\) |
0.640694 | + | 0.767796i | \(0.278647\pi\) | |||||||
\(224\) | 304.000 | + | 526.543i | 0.0906779 | + | 0.157059i | ||||
\(225\) | 400.500 | − | 693.686i | 0.118667 | − | 0.205537i | ||||
\(226\) | −1324.00 | + | 2293.24i | −0.389695 | + | 0.674972i | ||||
\(227\) | 2518.00 | 0.736236 | 0.368118 | − | 0.929779i | \(-0.380002\pi\) | ||||
0.368118 | + | 0.929779i | \(0.380002\pi\) | |||||||
\(228\) | 912.000 | + | 394.908i | 0.264906 | + | 0.114708i | ||||
\(229\) | 5401.00 | 1.55855 | 0.779275 | − | 0.626682i | \(-0.215587\pi\) | ||||
0.779275 | + | 0.626682i | \(0.215587\pi\) | |||||||
\(230\) | −588.000 | + | 1018.45i | −0.168572 | + | 0.291975i | ||||
\(231\) | −912.000 | + | 1579.63i | −0.259763 | + | 0.449922i | ||||
\(232\) | −1200.00 | − | 2078.46i | −0.339586 | − | 0.588180i | ||||
\(233\) | 3039.00 | − | 5263.70i | 0.854470 | − | 1.47999i | −0.0226658 | − | 0.999743i | \(-0.507215\pi\) |
0.877136 | − | 0.480242i | \(-0.159451\pi\) | |||||||
\(234\) | 729.000 | + | 1262.67i | 0.203659 | + | 0.352748i | ||||
\(235\) | 3300.00 | 0.916035 | ||||||||
\(236\) | −1984.00 | −0.547235 | ||||||||
\(237\) | −388.500 | − | 672.902i | −0.106480 | − | 0.184429i | ||||
\(238\) | −2356.00 | − | 4080.71i | −0.641667 | − | 1.11140i | ||||
\(239\) | 1062.00 | 0.287427 | 0.143714 | − | 0.989619i | \(-0.454096\pi\) | ||||
0.143714 | + | 0.989619i | \(0.454096\pi\) | |||||||
\(240\) | −288.000 | −0.0774597 | ||||||||
\(241\) | 2309.50 | + | 4000.17i | 0.617294 | + | 1.06919i | 0.989977 | + | 0.141227i | \(0.0451046\pi\) |
−0.372683 | + | 0.927959i | \(0.621562\pi\) | |||||||
\(242\) | −307.000 | + | 531.740i | −0.0815484 | + | 0.141246i | ||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −310.000 | + | 536.936i | −0.0813349 | + | 0.140876i | ||||
\(245\) | 54.0000 | − | 93.5307i | 0.0140814 | − | 0.0243896i | ||||
\(246\) | −1056.00 | −0.273691 | ||||||||
\(247\) | −769.500 | − | 6664.07i | −0.198227 | − | 1.71670i | ||||
\(248\) | 1800.00 | 0.460888 | ||||||||
\(249\) | 84.0000 | − | 145.492i | 0.0213786 | − | 0.0370289i | ||||
\(250\) | 1284.00 | − | 2223.95i | 0.324829 | − | 0.562621i | ||||
\(251\) | −1089.00 | − | 1886.20i | −0.273853 | − | 0.474327i | 0.695992 | − | 0.718049i | \(-0.254965\pi\) |
−0.969845 | + | 0.243722i | \(0.921631\pi\) | |||||||
\(252\) | −342.000 | + | 592.361i | −0.0854920 | + | 0.148076i | ||||
\(253\) | −1568.00 | − | 2715.86i | −0.389642 | − | 0.674879i | ||||
\(254\) | 2872.00 | 0.709470 | ||||||||
\(255\) | 2232.00 | 0.548130 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 315.000 | + | 545.596i | 0.0764559 | + | 0.132425i | 0.901718 | − | 0.432324i | \(-0.142306\pi\) |
−0.825263 | + | 0.564749i | \(0.808973\pi\) | |||||||
\(258\) | 666.000 | 0.160711 | ||||||||
\(259\) | −5567.00 | −1.33559 | ||||||||
\(260\) | 972.000 | + | 1683.55i | 0.231850 | + | 0.401575i | ||||
\(261\) | 1350.00 | − | 2338.27i | 0.320164 | − | 0.554541i | ||||
\(262\) | −378.000 | − | 654.715i | −0.0891333 | − | 0.154383i | ||||
\(263\) | −1371.00 | + | 2374.64i | −0.321443 | + | 0.556755i | −0.980786 | − | 0.195087i | \(-0.937501\pi\) |
0.659343 | + | 0.751842i | \(0.270834\pi\) | |||||||
\(264\) | 384.000 | − | 665.108i | 0.0895211 | − | 0.155055i | ||||
\(265\) | 2892.00 | 0.670393 | ||||||||
\(266\) | 2527.00 | − | 1875.81i | 0.582482 | − | 0.432381i | ||||
\(267\) | 924.000 | 0.211790 | ||||||||
\(268\) | −930.000 | + | 1610.81i | −0.211973 | + | 0.367148i | ||||
\(269\) | −1046.00 | + | 1811.73i | −0.237085 | + | 0.410642i | −0.959876 | − | 0.280423i | \(-0.909525\pi\) |
0.722792 | + | 0.691066i | \(0.242859\pi\) | |||||||
\(270\) | −162.000 | − | 280.592i | −0.0365148 | − | 0.0632456i | ||||
\(271\) | −2716.00 | + | 4704.25i | −0.608802 | + | 1.05448i | 0.382637 | + | 0.923899i | \(0.375016\pi\) |
−0.991438 | + | 0.130576i | \(0.958317\pi\) | |||||||
\(272\) | 992.000 | + | 1718.19i | 0.221135 | + | 0.383018i | ||||
\(273\) | 4617.00 | 1.02357 | ||||||||
\(274\) | −2124.00 | −0.468305 | ||||||||
\(275\) | 1424.00 | + | 2466.44i | 0.312256 | + | 0.540843i | ||||
\(276\) | −588.000 | − | 1018.45i | −0.128237 | − | 0.222113i | ||||
\(277\) | −2834.00 | −0.614724 | −0.307362 | − | 0.951593i | \(-0.599446\pi\) | ||||
−0.307362 | + | 0.951593i | \(0.599446\pi\) | |||||||
\(278\) | 3746.00 | 0.808166 | ||||||||
\(279\) | 1012.50 | + | 1753.70i | 0.217264 | + | 0.376313i | ||||
\(280\) | −456.000 | + | 789.815i | −0.0973258 | + | 0.168573i | ||||
\(281\) | −2845.00 | − | 4927.68i | −0.603980 | − | 1.04612i | −0.992212 | − | 0.124563i | \(-0.960247\pi\) |
0.388231 | − | 0.921562i | \(-0.373086\pi\) | |||||||
\(282\) | −1650.00 | + | 2857.88i | −0.348426 | + | 0.603491i | ||||
\(283\) | 2194.00 | − | 3800.12i | 0.460847 | − | 0.798211i | −0.538156 | − | 0.842845i | \(-0.680879\pi\) |
0.999003 | + | 0.0446343i | \(0.0142123\pi\) | |||||||
\(284\) | −440.000 | −0.0919338 | ||||||||
\(285\) | 171.000 | + | 1480.90i | 0.0355409 | + | 0.307794i | ||||
\(286\) | −5184.00 | −1.07181 | ||||||||
\(287\) | −1672.00 | + | 2895.99i | −0.343885 | + | 0.595627i | ||||
\(288\) | 144.000 | − | 249.415i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −5231.50 | − | 9061.22i | −1.06483 | − | 1.84434i | ||||
\(290\) | 1800.00 | − | 3117.69i | 0.364482 | − | 0.631301i | ||||
\(291\) | 1725.00 | + | 2987.79i | 0.347496 | + | 0.601880i | ||||
\(292\) | 3268.00 | 0.654949 | ||||||||
\(293\) | −1658.00 | −0.330585 | −0.165292 | − | 0.986245i | \(-0.552857\pi\) | ||||
−0.165292 | + | 0.986245i | \(0.552857\pi\) | |||||||
\(294\) | 54.0000 | + | 93.5307i | 0.0107121 | + | 0.0185538i | ||||
\(295\) | −1488.00 | − | 2577.29i | −0.293677 | − | 0.508663i | ||||
\(296\) | 2344.00 | 0.460278 | ||||||||
\(297\) | 864.000 | 0.168803 | ||||||||
\(298\) | 1372.00 | + | 2376.37i | 0.266704 | + | 0.461945i | ||||
\(299\) | −3969.00 | + | 6874.51i | −0.767670 | + | 1.32964i | ||||
\(300\) | 534.000 | + | 924.915i | 0.102768 | + | 0.178000i | ||||
\(301\) | 1054.50 | − | 1826.45i | 0.201928 | − | 0.349750i | ||||
\(302\) | −3296.00 | + | 5708.84i | −0.628025 | + | 1.08777i | ||||
\(303\) | −1734.00 | −0.328765 | ||||||||
\(304\) | −1064.00 | + | 789.815i | −0.200739 | + | 0.149010i | ||||
\(305\) | −930.000 | −0.174596 | ||||||||
\(306\) | −1116.00 | + | 1932.97i | −0.208488 | + | 0.361113i | ||||
\(307\) | −402.000 | + | 696.284i | −0.0747340 | + | 0.129443i | −0.900971 | − | 0.433880i | \(-0.857144\pi\) |
0.826237 | + | 0.563323i | \(0.190477\pi\) | |||||||
\(308\) | −1216.00 | − | 2106.17i | −0.224961 | − | 0.389644i | ||||
\(309\) | −1228.50 | + | 2127.82i | −0.226171 | + | 0.391740i | ||||
\(310\) | 1350.00 | + | 2338.27i | 0.247338 | + | 0.428402i | ||||
\(311\) | −3172.00 | −0.578352 | −0.289176 | − | 0.957276i | \(-0.593381\pi\) | ||||
−0.289176 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(312\) | −1944.00 | −0.352748 | ||||||||
\(313\) | −1917.00 | − | 3320.34i | −0.346183 | − | 0.599606i | 0.639385 | − | 0.768887i | \(-0.279189\pi\) |
−0.985568 | + | 0.169280i | \(0.945856\pi\) | |||||||
\(314\) | 1767.00 | + | 3060.53i | 0.317572 | + | 0.550051i | ||||
\(315\) | −1026.00 | −0.183519 | ||||||||
\(316\) | 1036.00 | 0.184429 | ||||||||
\(317\) | −1461.00 | − | 2530.53i | −0.258858 | − | 0.448355i | 0.707078 | − | 0.707135i | \(-0.250013\pi\) |
−0.965936 | + | 0.258780i | \(0.916679\pi\) | |||||||
\(318\) | −1446.00 | + | 2504.55i | −0.254993 | + | 0.441660i | ||||
\(319\) | 4800.00 | + | 8313.84i | 0.842471 | + | 1.45920i | ||||
\(320\) | 192.000 | − | 332.554i | 0.0335410 | − | 0.0580948i | ||||
\(321\) | −393.000 | + | 680.696i | −0.0683337 | + | 0.118357i | ||||
\(322\) | −3724.00 | −0.644504 | ||||||||
\(323\) | 8246.00 | − | 6121.07i | 1.42049 | − | 1.05444i | ||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 3604.50 | − | 6243.18i | 0.615205 | − | 1.06557i | ||||
\(326\) | 1709.00 | − | 2960.07i | 0.290346 | − | 0.502894i | ||||
\(327\) | −1551.00 | − | 2686.41i | −0.262295 | − | 0.454308i | ||||
\(328\) | 704.000 | − | 1219.36i | 0.118512 | − | 0.205269i | ||||
\(329\) | 5225.00 | + | 9049.97i | 0.875573 | + | 1.51654i | ||||
\(330\) | 1152.00 | 0.192168 | ||||||||
\(331\) | −4359.00 | −0.723844 | −0.361922 | − | 0.932208i | \(-0.617879\pi\) | ||||
−0.361922 | + | 0.932208i | \(0.617879\pi\) | |||||||
\(332\) | 112.000 | + | 193.990i | 0.0185145 | + | 0.0320680i | ||||
\(333\) | 1318.50 | + | 2283.71i | 0.216977 | + | 0.375815i | ||||
\(334\) | 5520.00 | 0.904314 | ||||||||
\(335\) | −2790.00 | −0.455027 | ||||||||
\(336\) | −456.000 | − | 789.815i | −0.0740382 | − | 0.128238i | ||||
\(337\) | −4364.50 | + | 7559.54i | −0.705488 | + | 1.22194i | 0.261027 | + | 0.965331i | \(0.415939\pi\) |
−0.966515 | + | 0.256610i | \(0.917395\pi\) | |||||||
\(338\) | 4364.00 | + | 7558.67i | 0.702279 | + | 1.21638i | ||||
\(339\) | 1986.00 | − | 3439.85i | 0.318185 | − | 0.551113i | ||||
\(340\) | −1488.00 | + | 2577.29i | −0.237347 | + | 0.411098i | ||||
\(341\) | −7200.00 | −1.14341 | ||||||||
\(342\) | −1368.00 | − | 592.361i | −0.216295 | − | 0.0936586i | ||||
\(343\) | −6175.00 | −0.972066 | ||||||||
\(344\) | −444.000 | + | 769.031i | −0.0695898 | + | 0.120533i | ||||
\(345\) | 882.000 | − | 1527.67i | 0.137639 | − | 0.238397i | ||||
\(346\) | −1476.00 | − | 2556.51i | −0.229336 | − | 0.397222i | ||||
\(347\) | −19.0000 | + | 32.9090i | −0.00293940 | + | 0.00509120i | −0.867491 | − | 0.497452i | \(-0.834269\pi\) |
0.864552 | + | 0.502543i | \(0.167602\pi\) | |||||||
\(348\) | 1800.00 | + | 3117.69i | 0.277270 | + | 0.480247i | ||||
\(349\) | 6103.00 | 0.936063 | 0.468032 | − | 0.883712i | \(-0.344963\pi\) | ||||
0.468032 | + | 0.883712i | \(0.344963\pi\) | |||||||
\(350\) | 3382.00 | 0.516501 | ||||||||
\(351\) | −1093.50 | − | 1894.00i | −0.166287 | − | 0.288017i | ||||
\(352\) | 512.000 | + | 886.810i | 0.0775275 | + | 0.134282i | ||||
\(353\) | −12198.0 | −1.83919 | −0.919595 | − | 0.392868i | \(-0.871483\pi\) | ||||
−0.919595 | + | 0.392868i | \(0.871483\pi\) | |||||||
\(354\) | 2976.00 | 0.446815 | ||||||||
\(355\) | −330.000 | − | 571.577i | −0.0493368 | − | 0.0854539i | ||||
\(356\) | −616.000 | + | 1066.94i | −0.0917077 | + | 0.158842i | ||||
\(357\) | 3534.00 | + | 6121.07i | 0.523919 | + | 0.907454i | ||||
\(358\) | 26.0000 | − | 45.0333i | 0.00383839 | − | 0.00664828i | ||||
\(359\) | −1494.00 | + | 2587.68i | −0.219639 | + | 0.380425i | −0.954698 | − | 0.297578i | \(-0.903821\pi\) |
0.735059 | + | 0.678003i | \(0.237155\pi\) | |||||||
\(360\) | 432.000 | 0.0632456 | ||||||||
\(361\) | 4693.00 | + | 5002.16i | 0.684211 | + | 0.729285i | ||||
\(362\) | 7188.00 | 1.04363 | ||||||||
\(363\) | 460.500 | − | 797.609i | 0.0665840 | − | 0.115327i | ||||
\(364\) | −3078.00 | + | 5331.25i | −0.443217 | + | 0.767675i | ||||
\(365\) | 2451.00 | + | 4245.26i | 0.351483 | + | 0.608786i | ||||
\(366\) | 465.000 | − | 805.404i | 0.0664097 | − | 0.115025i | ||||
\(367\) | −1052.50 | − | 1822.98i | −0.149700 | − | 0.259289i | 0.781416 | − | 0.624010i | \(-0.214498\pi\) |
−0.931117 | + | 0.364721i | \(0.881164\pi\) | |||||||
\(368\) | 1568.00 | 0.222113 | ||||||||
\(369\) | 1584.00 | 0.223468 | ||||||||
\(370\) | 1758.00 | + | 3044.95i | 0.247011 | + | 0.427836i | ||||
\(371\) | 4579.00 | + | 7931.06i | 0.640781 | + | 1.10987i | ||||
\(372\) | −2700.00 | −0.376313 | ||||||||
\(373\) | −2494.00 | −0.346205 | −0.173102 | − | 0.984904i | \(-0.555379\pi\) | ||||
−0.173102 | + | 0.984904i | \(0.555379\pi\) | |||||||
\(374\) | −3968.00 | − | 6872.78i | −0.548611 | − | 0.950222i | ||||
\(375\) | −1926.00 | + | 3335.93i | −0.265222 | + | 0.459378i | ||||
\(376\) | −2200.00 | − | 3810.51i | −0.301746 | − | 0.522639i | ||||
\(377\) | 12150.0 | − | 21044.4i | 1.65983 | − | 2.87491i | ||||
\(378\) | 513.000 | − | 888.542i | 0.0698039 | − | 0.120904i | ||||
\(379\) | 5729.00 | 0.776462 | 0.388231 | − | 0.921562i | \(-0.373086\pi\) | ||||
0.388231 | + | 0.921562i | \(0.373086\pi\) | |||||||
\(380\) | −1824.00 | − | 789.815i | −0.246235 | − | 0.106623i | ||||
\(381\) | −4308.00 | −0.579280 | ||||||||
\(382\) | 314.000 | − | 543.864i | 0.0420566 | − | 0.0728442i | ||||
\(383\) | 5008.00 | − | 8674.11i | 0.668138 | − | 1.15725i | −0.310286 | − | 0.950643i | \(-0.600425\pi\) |
0.978424 | − | 0.206606i | \(-0.0662418\pi\) | |||||||
\(384\) | 192.000 | + | 332.554i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 1824.00 | − | 3159.26i | 0.241454 | − | 0.418210i | ||||
\(386\) | −925.000 | − | 1602.15i | −0.121972 | − | 0.211262i | ||||
\(387\) | −999.000 | −0.131220 | ||||||||
\(388\) | −4600.00 | −0.601880 | ||||||||
\(389\) | −2909.00 | − | 5038.54i | −0.379157 | − | 0.656720i | 0.611783 | − | 0.791026i | \(-0.290453\pi\) |
−0.990940 | + | 0.134306i | \(0.957119\pi\) | |||||||
\(390\) | −1458.00 | − | 2525.33i | −0.189304 | − | 0.327885i | ||||
\(391\) | −12152.0 | −1.57175 | ||||||||
\(392\) | −144.000 | −0.0185538 | ||||||||
\(393\) | 567.000 | + | 982.073i | 0.0727770 | + | 0.126053i | ||||
\(394\) | 1244.00 | − | 2154.67i | 0.159066 | − | 0.275510i | ||||
\(395\) | 777.000 | + | 1345.80i | 0.0989750 | + | 0.171430i | ||||
\(396\) | −576.000 | + | 997.661i | −0.0730937 | + | 0.126602i | ||||
\(397\) | 2074.50 | − | 3593.14i | 0.262257 | − | 0.454243i | −0.704584 | − | 0.709621i | \(-0.748866\pi\) |
0.966841 | + | 0.255377i | \(0.0821997\pi\) | |||||||
\(398\) | −6982.00 | −0.879337 | ||||||||
\(399\) | −3790.50 | + | 2813.72i | −0.475595 | + | 0.353038i | ||||
\(400\) | −1424.00 | −0.178000 | ||||||||
\(401\) | −4536.00 | + | 7856.58i | −0.564880 | + | 0.978402i | 0.432180 | + | 0.901787i | \(0.357744\pi\) |
−0.997061 | + | 0.0766144i | \(0.975589\pi\) | |||||||
\(402\) | 1395.00 | − | 2416.21i | 0.173075 | − | 0.299775i | ||||
\(403\) | 9112.50 | + | 15783.3i | 1.12637 | + | 1.95093i | ||||
\(404\) | 1156.00 | − | 2002.25i | 0.142359 | − | 0.246574i | ||||
\(405\) | 243.000 | + | 420.888i | 0.0298142 | + | 0.0516398i | ||||
\(406\) | 11400.0 | 1.39353 | ||||||||
\(407\) | −9376.00 | −1.14189 | ||||||||
\(408\) | −1488.00 | − | 2577.29i | −0.180556 | − | 0.312733i | ||||
\(409\) | −4347.00 | − | 7529.22i | −0.525539 | − | 0.910260i | −0.999558 | − | 0.0297450i | \(-0.990530\pi\) |
0.474019 | − | 0.880515i | \(-0.342803\pi\) | |||||||
\(410\) | 2112.00 | 0.254401 | ||||||||
\(411\) | 3186.00 | 0.382369 | ||||||||
\(412\) | −1638.00 | − | 2837.10i | −0.195870 | − | 0.339257i | ||||
\(413\) | 4712.00 | − | 8161.42i | 0.561410 | − | 0.972391i | ||||
\(414\) | 882.000 | + | 1527.67i | 0.104705 | + | 0.181355i | ||||
\(415\) | −168.000 | + | 290.985i | −0.0198718 | + | 0.0344190i | ||||
\(416\) | 1296.00 | − | 2244.74i | 0.152744 | − | 0.264561i | ||||
\(417\) | −5619.00 | −0.659865 | ||||||||
\(418\) | 4256.00 | − | 3159.26i | 0.498009 | − | 0.369676i | ||||
\(419\) | −4392.00 | −0.512084 | −0.256042 | − | 0.966666i | \(-0.582419\pi\) | ||||
−0.256042 | + | 0.966666i | \(0.582419\pi\) | |||||||
\(420\) | 684.000 | − | 1184.72i | 0.0794661 | − | 0.137639i | ||||
\(421\) | −3455.00 | + | 5984.24i | −0.399968 | + | 0.692764i | −0.993721 | − | 0.111882i | \(-0.964312\pi\) |
0.593754 | + | 0.804647i | \(0.297645\pi\) | |||||||
\(422\) | −4577.00 | − | 7927.60i | −0.527974 | − | 0.914477i | ||||
\(423\) | 2475.00 | − | 4286.83i | 0.284488 | − | 0.492748i | ||||
\(424\) | −1928.00 | − | 3339.39i | −0.220830 | − | 0.382489i | ||||
\(425\) | 11036.0 | 1.25959 | ||||||||
\(426\) | 660.000 | 0.0750636 | ||||||||
\(427\) | −1472.50 | − | 2550.44i | −0.166884 | − | 0.289051i | ||||
\(428\) | −524.000 | − | 907.595i | −0.0591787 | − | 0.102501i | ||||
\(429\) | 7776.00 | 0.875125 | ||||||||
\(430\) | −1332.00 | −0.149383 | ||||||||
\(431\) | 4441.00 | + | 7692.04i | 0.496324 | + | 0.859658i | 0.999991 | − | 0.00424003i | \(-0.00134965\pi\) |
−0.503667 | + | 0.863898i | \(0.668016\pi\) | |||||||
\(432\) | −216.000 | + | 374.123i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −1849.50 | − | 3203.43i | −0.205269 | − | 0.355536i | 0.744950 | − | 0.667121i | \(-0.232473\pi\) |
−0.950218 | + | 0.311585i | \(0.899140\pi\) | |||||||
\(434\) | −4275.00 | + | 7404.52i | −0.472826 | + | 0.818959i | ||||
\(435\) | −2700.00 | + | 4676.54i | −0.297598 | + | 0.515455i | ||||
\(436\) | 4136.00 | 0.454308 | ||||||||
\(437\) | −931.000 | − | 8062.70i | −0.101913 | − | 0.882588i | ||||
\(438\) | −4902.00 | −0.534764 | ||||||||
\(439\) | 8453.50 | − | 14641.9i | 0.919051 | − | 1.59184i | 0.118192 | − | 0.992991i | \(-0.462290\pi\) |
0.800859 | − | 0.598853i | \(-0.204377\pi\) | |||||||
\(440\) | −768.000 | + | 1330.22i | −0.0832113 | + | 0.144126i | ||||
\(441\) | −81.0000 | − | 140.296i | −0.00874636 | − | 0.0151491i | ||||
\(442\) | −10044.0 | + | 17396.7i | −1.08087 | + | 1.87212i | ||||
\(443\) | 4986.00 | + | 8636.01i | 0.534745 | + | 0.926205i | 0.999176 | + | 0.0405959i | \(0.0129256\pi\) |
−0.464431 | + | 0.885609i | \(0.653741\pi\) | |||||||
\(444\) | −3516.00 | −0.375815 | ||||||||
\(445\) | −1848.00 | −0.196862 | ||||||||
\(446\) | 2295.00 | + | 3975.06i | 0.243658 | + | 0.422028i | ||||
\(447\) | −2058.00 | − | 3564.56i | −0.217763 | − | 0.377177i | ||||
\(448\) | 1216.00 | 0.128238 | ||||||||
\(449\) | −10368.0 | −1.08975 | −0.544873 | − | 0.838518i | \(-0.683422\pi\) | ||||
−0.544873 | + | 0.838518i | \(0.683422\pi\) | |||||||
\(450\) | −801.000 | − | 1387.37i | −0.0839100 | − | 0.145336i | ||||
\(451\) | −2816.00 | + | 4877.46i | −0.294014 | + | 0.509247i | ||||
\(452\) | 2648.00 | + | 4586.47i | 0.275556 | + | 0.477277i | ||||
\(453\) | 4944.00 | − | 8563.26i | 0.512780 | − | 0.888161i | ||||
\(454\) | 2518.00 | − | 4361.30i | 0.260299 | − | 0.450851i | ||||
\(455\) | −9234.00 | −0.951421 | ||||||||
\(456\) | 1596.00 | − | 1184.72i | 0.163903 | − | 0.121666i | ||||
\(457\) | 4481.00 | 0.458670 | 0.229335 | − | 0.973348i | \(-0.426345\pi\) | ||||
0.229335 | + | 0.973348i | \(0.426345\pi\) | |||||||
\(458\) | 5401.00 | − | 9354.81i | 0.551031 | − | 0.954414i | ||||
\(459\) | 1674.00 | − | 2899.45i | 0.170230 | − | 0.294847i | ||||
\(460\) | 1176.00 | + | 2036.89i | 0.119198 | + | 0.206458i | ||||
\(461\) | 1056.00 | − | 1829.05i | 0.106687 | − | 0.184788i | −0.807739 | − | 0.589540i | \(-0.799309\pi\) |
0.914426 | + | 0.404752i | \(0.132642\pi\) | |||||||
\(462\) | 1824.00 | + | 3159.26i | 0.183680 | + | 0.318143i | ||||
\(463\) | 5817.00 | 0.583885 | 0.291943 | − | 0.956436i | \(-0.405698\pi\) | ||||
0.291943 | + | 0.956436i | \(0.405698\pi\) | |||||||
\(464\) | −4800.00 | −0.480247 | ||||||||
\(465\) | −2025.00 | − | 3507.40i | −0.201951 | − | 0.349789i | ||||
\(466\) | −6078.00 | − | 10527.4i | −0.604202 | − | 1.04651i | ||||
\(467\) | 9100.00 | 0.901708 | 0.450854 | − | 0.892598i | \(-0.351119\pi\) | ||||
0.450854 | + | 0.892598i | \(0.351119\pi\) | |||||||
\(468\) | 2916.00 | 0.288017 | ||||||||
\(469\) | −4417.50 | − | 7651.33i | −0.434928 | − | 0.753317i | ||||
\(470\) | 3300.00 | − | 5715.77i | 0.323867 | − | 0.560955i | ||||
\(471\) | −2650.50 | − | 4590.80i | −0.259296 | − | 0.449114i | ||||
\(472\) | −1984.00 | + | 3436.39i | −0.193477 | + | 0.335111i | ||||
\(473\) | 1776.00 | − | 3076.12i | 0.172644 | − | 0.299028i | ||||
\(474\) | −1554.00 | −0.150586 | ||||||||
\(475\) | 845.500 | + | 7322.24i | 0.0816720 | + | 0.707300i | ||||
\(476\) | −9424.00 | −0.907454 | ||||||||
\(477\) | 2169.00 | − | 3756.82i | 0.208201 | − | 0.360614i | ||||
\(478\) | 1062.00 | − | 1839.44i | 0.101621 | − | 0.176012i | ||||
\(479\) | 15.0000 | + | 25.9808i | 0.00143083 | + | 0.00247827i | 0.866740 | − | 0.498760i | \(-0.166211\pi\) |
−0.865309 | + | 0.501239i | \(0.832878\pi\) | |||||||
\(480\) | −288.000 | + | 498.831i | −0.0273861 | + | 0.0474342i | ||||
\(481\) | 11866.5 | + | 20553.4i | 1.12488 | + | 1.94834i | ||||
\(482\) | 9238.00 | 0.872986 | ||||||||
\(483\) | 5586.00 | 0.526236 | ||||||||
\(484\) | 614.000 | + | 1063.48i | 0.0576634 | + | 0.0998760i | ||||
\(485\) | −3450.00 | − | 5975.58i | −0.323003 | − | 0.559458i | ||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −10924.0 | −1.01646 | −0.508228 | − | 0.861223i | \(-0.669699\pi\) | ||||
−0.508228 | + | 0.861223i | \(0.669699\pi\) | |||||||
\(488\) | 620.000 | + | 1073.87i | 0.0575125 | + | 0.0996145i | ||||
\(489\) | −2563.50 | + | 4440.11i | −0.237066 | + | 0.410611i | ||||
\(490\) | −108.000 | − | 187.061i | −0.00995703 | − | 0.0172461i | ||||
\(491\) | −3669.00 | + | 6354.89i | −0.337229 | + | 0.584099i | −0.983911 | − | 0.178662i | \(-0.942823\pi\) |
0.646681 | + | 0.762761i | \(0.276156\pi\) | |||||||
\(492\) | −1056.00 | + | 1829.05i | −0.0967645 | + | 0.167601i | ||||
\(493\) | 37200.0 | 3.39838 | ||||||||
\(494\) | −12312.0 | − | 5331.25i | −1.12134 | − | 0.485555i | ||||
\(495\) | −1728.00 | −0.156905 | ||||||||
\(496\) | 1800.00 | − | 3117.69i | 0.162948 | − | 0.282235i | ||||
\(497\) | 1045.00 | − | 1809.99i | 0.0943152 | − | 0.163359i | ||||
\(498\) | −168.000 | − | 290.985i | −0.0151170 | − | 0.0261834i | ||||
\(499\) | 4260.50 | − | 7379.40i | 0.382217 | − | 0.662019i | −0.609162 | − | 0.793046i | \(-0.708494\pi\) |
0.991379 | + | 0.131027i | \(0.0418274\pi\) | |||||||
\(500\) | −2568.00 | − | 4447.91i | −0.229689 | − | 0.397833i | ||||
\(501\) | −8280.00 | −0.738369 | ||||||||
\(502\) | −4356.00 | −0.387286 | ||||||||
\(503\) | 2750.00 | + | 4763.14i | 0.243770 | + | 0.422222i | 0.961785 | − | 0.273805i | \(-0.0882824\pi\) |
−0.718015 | + | 0.696028i | \(0.754949\pi\) | |||||||
\(504\) | 684.000 | + | 1184.72i | 0.0604519 | + | 0.104706i | ||||
\(505\) | 3468.00 | 0.305592 | ||||||||
\(506\) | −6272.00 | −0.551036 | ||||||||
\(507\) | −6546.00 | − | 11338.0i | −0.573408 | − | 0.993173i | ||||
\(508\) | 2872.00 | − | 4974.45i | 0.250835 | − | 0.434460i | ||||
\(509\) | −2969.00 | − | 5142.46i | −0.258543 | − | 0.447810i | 0.707309 | − | 0.706905i | \(-0.249909\pi\) |
−0.965852 | + | 0.259095i | \(0.916576\pi\) | |||||||
\(510\) | 2232.00 | − | 3865.94i | 0.193793 | − | 0.335660i | ||||
\(511\) | −7761.50 | + | 13443.3i | −0.671915 | + | 1.16379i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2052.00 | + | 888.542i | 0.176604 | + | 0.0764719i | ||||
\(514\) | 1260.00 | 0.108125 | ||||||||
\(515\) | 2457.00 | − | 4255.65i | 0.210230 | − | 0.364129i | ||||
\(516\) | 666.000 | − | 1153.55i | 0.0568198 | − | 0.0984148i | ||||
\(517\) | 8800.00 | + | 15242.0i | 0.748595 | + | 1.29660i | ||||
\(518\) | −5567.00 | + | 9642.33i | −0.472201 | + | 0.817876i | ||||
\(519\) | 2214.00 | + | 3834.76i | 0.187252 | + | 0.324330i | ||||
\(520\) | 3888.00 | 0.327885 | ||||||||
\(521\) | −2884.00 | −0.242515 | −0.121258 | − | 0.992621i | \(-0.538693\pi\) | ||||
−0.121258 | + | 0.992621i | \(0.538693\pi\) | |||||||
\(522\) | −2700.00 | − | 4676.54i | −0.226390 | − | 0.392120i | ||||
\(523\) | 5330.50 | + | 9232.70i | 0.445672 | + | 0.771927i | 0.998099 | − | 0.0616348i | \(-0.0196314\pi\) |
−0.552427 | + | 0.833561i | \(0.686298\pi\) | |||||||
\(524\) | −1512.00 | −0.126053 | ||||||||
\(525\) | −5073.00 | −0.421722 | ||||||||
\(526\) | 2742.00 | + | 4749.28i | 0.227294 | + | 0.393686i | ||||
\(527\) | −13950.0 | + | 24162.1i | −1.15308 | + | 1.99719i | ||||
\(528\) | −768.000 | − | 1330.22i | −0.0633010 | − | 0.109640i | ||||
\(529\) | 1281.50 | − | 2219.62i | 0.105326 | − | 0.182430i | ||||
\(530\) | 2892.00 | − | 5009.09i | 0.237020 | − | 0.410530i | ||||
\(531\) | −4464.00 | −0.364823 | ||||||||
\(532\) | −722.000 | − | 6252.70i | −0.0588396 | − | 0.509566i | ||||
\(533\) | 14256.0 | 1.15853 | ||||||||
\(534\) | 924.000 | − | 1600.41i | 0.0748790 | − | 0.129694i | ||||
\(535\) | 786.000 | − | 1361.39i | 0.0635173 | − | 0.110015i | ||||
\(536\) | 1860.00 | + | 3221.61i | 0.149888 | + | 0.259613i | ||||
\(537\) | −39.0000 | + | 67.5500i | −0.00313403 | + | 0.00542830i | ||||
\(538\) | 2092.00 | + | 3623.45i | 0.167644 | + | 0.290368i | ||||
\(539\) | 576.000 | 0.0460298 | ||||||||
\(540\) | −648.000 | −0.0516398 | ||||||||
\(541\) | −2942.50 | − | 5096.56i | −0.233841 | − | 0.405024i | 0.725094 | − | 0.688650i | \(-0.241796\pi\) |
−0.958935 | + | 0.283625i | \(0.908463\pi\) | |||||||
\(542\) | 5432.00 | + | 9408.50i | 0.430488 | + | 0.745627i | ||||
\(543\) | −10782.0 | −0.852118 | ||||||||
\(544\) | 3968.00 | 0.312733 | ||||||||
\(545\) | 3102.00 | + | 5372.82i | 0.243807 | + | 0.422287i | ||||
\(546\) | 4617.00 | − | 7996.88i | 0.361885 | − | 0.626804i | ||||
\(547\) | −818.500 | − | 1417.68i | −0.0639790 | − | 0.110815i | 0.832262 | − | 0.554383i | \(-0.187046\pi\) |
−0.896241 | + | 0.443568i | \(0.853712\pi\) | |||||||
\(548\) | −2124.00 | + | 3678.88i | −0.165571 | + | 0.286777i | ||||
\(549\) | −697.500 | + | 1208.11i | −0.0542233 | + | 0.0939175i | ||||
\(550\) | 5696.00 | 0.441597 | ||||||||
\(551\) | 2850.00 | + | 24681.7i | 0.220352 | + | 1.90831i | ||||
\(552\) | −2352.00 | −0.181355 | ||||||||
\(553\) | −2460.50 | + | 4261.71i | −0.189206 | + | 0.327715i | ||||
\(554\) | −2834.00 | + | 4908.63i | −0.217338 | + | 0.376440i | ||||
\(555\) | −2637.00 | − | 4567.42i | −0.201684 | − | 0.349326i | ||||
\(556\) | 3746.00 | − | 6488.26i | 0.285730 | − | 0.494899i | ||||
\(557\) | −3235.00 | − | 5603.18i | −0.246089 | − | 0.426238i | 0.716349 | − | 0.697743i | \(-0.245812\pi\) |
−0.962437 | + | 0.271505i | \(0.912479\pi\) | |||||||
\(558\) | 4050.00 | 0.307258 | ||||||||
\(559\) | −8991.00 | −0.680284 | ||||||||
\(560\) | 912.000 | + | 1579.63i | 0.0688197 | + | 0.119199i | ||||
\(561\) | 5952.00 | + | 10309.2i | 0.447939 | + | 0.775853i | ||||
\(562\) | −11380.0 | −0.854157 | ||||||||
\(563\) | 14898.0 | 1.11523 | 0.557616 | − | 0.830099i | \(-0.311716\pi\) | ||||
0.557616 | + | 0.830099i | \(0.311716\pi\) | |||||||
\(564\) | 3300.00 | + | 5715.77i | 0.246374 | + | 0.426733i | ||||
\(565\) | −3972.00 | + | 6879.71i | −0.295758 | + | 0.512268i | ||||
\(566\) | −4388.00 | − | 7600.24i | −0.325868 | − | 0.564420i | ||||
\(567\) | −769.500 | + | 1332.81i | −0.0569946 | + | 0.0987176i | ||||
\(568\) | −440.000 | + | 762.102i | −0.0325035 | + | 0.0562977i | ||||
\(569\) | −13260.0 | −0.976956 | −0.488478 | − | 0.872576i | \(-0.662448\pi\) | ||||
−0.488478 | + | 0.872576i | \(0.662448\pi\) | |||||||
\(570\) | 2736.00 | + | 1184.72i | 0.201050 | + | 0.0870572i | ||||
\(571\) | −6097.00 | −0.446850 | −0.223425 | − | 0.974721i | \(-0.571724\pi\) | ||||
−0.223425 | + | 0.974721i | \(0.571724\pi\) | |||||||
\(572\) | −5184.00 | + | 8978.95i | −0.378940 | + | 0.656344i | ||||
\(573\) | −471.000 | + | 815.796i | −0.0343391 | + | 0.0594771i | ||||
\(574\) | 3344.00 | + | 5791.98i | 0.243164 | + | 0.421172i | ||||
\(575\) | 4361.00 | − | 7553.47i | 0.316289 | − | 0.547829i | ||||
\(576\) | −288.000 | − | 498.831i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −5594.00 | −0.403607 | −0.201804 | − | 0.979426i | \(-0.564680\pi\) | ||||
−0.201804 | + | 0.979426i | \(0.564680\pi\) | |||||||
\(578\) | −20926.0 | −1.50589 | ||||||||
\(579\) | 1387.50 | + | 2403.22i | 0.0995899 | + | 0.172495i | ||||
\(580\) | −3600.00 | − | 6235.38i | −0.257727 | − | 0.446397i | ||||
\(581\) | −1064.00 | −0.0759762 | ||||||||
\(582\) | 6900.00 | 0.491433 | ||||||||
\(583\) | 7712.00 | + | 13357.6i | 0.547853 | + | 0.948910i | ||||
\(584\) | 3268.00 | − | 5660.34i | 0.231560 | − | 0.401073i | ||||
\(585\) | 2187.00 | + | 3788.00i | 0.154566 | + | 0.267717i | ||||
\(586\) | −1658.00 | + | 2871.74i | −0.116879 | + | 0.202441i | ||||
\(587\) | 9038.00 | − | 15654.3i | 0.635499 | − | 1.10072i | −0.350910 | − | 0.936409i | \(-0.614128\pi\) |
0.986409 | − | 0.164308i | \(-0.0525391\pi\) | |||||||
\(588\) | 216.000 | 0.0151491 | ||||||||
\(589\) | −17100.0 | − | 7404.52i | −1.19625 | − | 0.517993i | ||||
\(590\) | −5952.00 | −0.415322 | ||||||||
\(591\) | −1866.00 | + | 3232.01i | −0.129876 | + | 0.224953i | ||||
\(592\) | 2344.00 | − | 4059.93i | 0.162733 | − | 0.281861i | ||||
\(593\) | −11464.0 | − | 19856.2i | −0.793879 | − | 1.37504i | −0.923549 | − | 0.383481i | \(-0.874725\pi\) |
0.129670 | − | 0.991557i | \(-0.458608\pi\) | |||||||
\(594\) | 864.000 | − | 1496.49i | 0.0596807 | − | 0.103370i | ||||
\(595\) | −7068.00 | − | 12242.1i | −0.486991 | − | 0.843493i | ||||
\(596\) | 5488.00 | 0.377177 | ||||||||
\(597\) | 10473.0 | 0.717975 | ||||||||
\(598\) | 7938.00 | + | 13749.0i | 0.542824 | + | 0.940199i | ||||
\(599\) | 5896.00 | + | 10212.2i | 0.402177 | + | 0.696591i | 0.993988 | − | 0.109485i | \(-0.0349203\pi\) |
−0.591811 | + | 0.806076i | \(0.701587\pi\) | |||||||
\(600\) | 2136.00 | 0.145336 | ||||||||
\(601\) | −15585.0 | −1.05778 | −0.528890 | − | 0.848691i | \(-0.677391\pi\) | ||||
−0.528890 | + | 0.848691i | \(0.677391\pi\) | |||||||
\(602\) | −2109.00 | − | 3652.90i | −0.142785 | − | 0.247310i | ||||
\(603\) | −2092.50 | + | 3624.32i | −0.141315 | + | 0.244765i | ||||
\(604\) | 6592.00 | + | 11417.7i | 0.444081 | + | 0.769170i | ||||
\(605\) | −921.000 | + | 1595.22i | −0.0618909 | + | 0.107198i | ||||
\(606\) | −1734.00 | + | 3003.38i | −0.116236 | + | 0.201326i | ||||
\(607\) | −27181.0 | −1.81753 | −0.908767 | − | 0.417305i | \(-0.862975\pi\) | ||||
−0.908767 | + | 0.417305i | \(0.862975\pi\) | |||||||
\(608\) | 304.000 | + | 2632.72i | 0.0202777 | + | 0.175610i | ||||
\(609\) | −17100.0 | −1.13781 | ||||||||
\(610\) | −930.000 | + | 1610.81i | −0.0617289 | + | 0.106918i | ||||
\(611\) | 22275.0 | − | 38581.4i | 1.47488 | − | 2.55456i | ||||
\(612\) | 2232.00 | + | 3865.94i | 0.147424 | + | 0.255345i | ||||
\(613\) | −6913.00 | + | 11973.7i | −0.455487 | + | 0.788926i | −0.998716 | − | 0.0506581i | \(-0.983868\pi\) |
0.543229 | + | 0.839584i | \(0.317201\pi\) | |||||||
\(614\) | 804.000 | + | 1392.57i | 0.0528450 | + | 0.0915301i | ||||
\(615\) | −3168.00 | −0.207717 | ||||||||
\(616\) | −4864.00 | −0.318143 | ||||||||
\(617\) | 6222.00 | + | 10776.8i | 0.405978 | + | 0.703174i | 0.994435 | − | 0.105354i | \(-0.0335977\pi\) |
−0.588457 | + | 0.808529i | \(0.700264\pi\) | |||||||
\(618\) | 2457.00 | + | 4255.65i | 0.159927 | + | 0.277002i | ||||
\(619\) | −137.000 | −0.00889579 | −0.00444790 | − | 0.999990i | \(-0.501416\pi\) | ||||
−0.00444790 | + | 0.999990i | \(0.501416\pi\) | |||||||
\(620\) | 5400.00 | 0.349789 | ||||||||
\(621\) | −1323.00 | − | 2291.50i | −0.0854914 | − | 0.148075i | ||||
\(622\) | −3172.00 | + | 5494.07i | −0.204478 | + | 0.354167i | ||||
\(623\) | −2926.00 | − | 5067.98i | −0.188166 | − | 0.325914i | ||||
\(624\) | −1944.00 | + | 3367.11i | −0.124715 | + | 0.216013i | ||||
\(625\) | −1710.50 | + | 2962.67i | −0.109472 | + | 0.189611i | ||||
\(626\) | −7668.00 | −0.489577 | ||||||||
\(627\) | −6384.00 | + | 4738.89i | −0.406623 | + | 0.301839i | ||||
\(628\) | 7068.00 | 0.449114 | ||||||||
\(629\) | −18166.0 | + | 31464.4i | −1.15155 | + | 1.99455i | ||||
\(630\) | −1026.00 | + | 1777.08i | −0.0648838 | + | 0.112382i | ||||
\(631\) | 5130.50 | + | 8886.29i | 0.323680 | + | 0.560630i | 0.981244 | − | 0.192768i | \(-0.0617466\pi\) |
−0.657564 | + | 0.753398i | \(0.728413\pi\) | |||||||
\(632\) | 1036.00 | − | 1794.40i | 0.0652055 | − | 0.112939i | ||||
\(633\) | 6865.50 | + | 11891.4i | 0.431089 | + | 0.746667i | ||||
\(634\) | −5844.00 | −0.366080 | ||||||||
\(635\) | 8616.00 | 0.538450 | ||||||||
\(636\) | 2892.00 | + | 5009.09i | 0.180307 | + | 0.312301i | ||||
\(637\) | −729.000 | − | 1262.67i | −0.0453438 | − | 0.0785378i | ||||
\(638\) | 19200.0 | 1.19143 | ||||||||
\(639\) | −990.000 | −0.0612892 | ||||||||
\(640\) | −384.000 | − | 665.108i | −0.0237171 | − | 0.0410792i | ||||
\(641\) | 4625.00 | − | 8010.73i | 0.284987 | − | 0.493612i | −0.687619 | − | 0.726072i | \(-0.741344\pi\) |
0.972606 | + | 0.232460i | \(0.0746775\pi\) | |||||||
\(642\) | 786.000 | + | 1361.39i | 0.0483192 | + | 0.0836914i | ||||
\(643\) | 8264.50 | − | 14314.5i | 0.506874 | − | 0.877932i | −0.493094 | − | 0.869976i | \(-0.664134\pi\) |
0.999968 | − | 0.00795583i | \(-0.00253245\pi\) | |||||||
\(644\) | −3724.00 | + | 6450.16i | −0.227867 | + | 0.394677i | ||||
\(645\) | 1998.00 | 0.121971 | ||||||||
\(646\) | −2356.00 | − | 20403.6i | −0.143492 | − | 1.24267i | ||||
\(647\) | 13884.0 | 0.843642 | 0.421821 | − | 0.906679i | \(-0.361391\pi\) | ||||
0.421821 | + | 0.906679i | \(0.361391\pi\) | |||||||
\(648\) | 324.000 | − | 561.184i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 7936.00 | − | 13745.6i | 0.479993 | − | 0.831372i | ||||
\(650\) | −7209.00 | − | 12486.4i | −0.435016 | − | 0.753469i | ||||
\(651\) | 6412.50 | − | 11106.8i | 0.386061 | − | 0.668677i | ||||
\(652\) | −3418.00 | − | 5920.15i | −0.205306 | − | 0.355600i | ||||
\(653\) | −20538.0 | −1.23080 | −0.615401 | − | 0.788214i | \(-0.711006\pi\) | ||||
−0.615401 | + | 0.788214i | \(0.711006\pi\) | |||||||
\(654\) | −6204.00 | −0.370941 | ||||||||
\(655\) | −1134.00 | − | 1964.15i | −0.0676474 | − | 0.117169i | ||||
\(656\) | −1408.00 | − | 2438.73i | −0.0838006 | − | 0.145147i | ||||
\(657\) | 7353.00 | 0.436633 | ||||||||
\(658\) | 20900.0 | 1.23825 | ||||||||
\(659\) | −7624.00 | − | 13205.2i | −0.450666 | − | 0.780576i | 0.547762 | − | 0.836635i | \(-0.315480\pi\) |
−0.998428 | + | 0.0560582i | \(0.982147\pi\) | |||||||
\(660\) | 1152.00 | − | 1995.32i | 0.0679417 | − | 0.117679i | ||||
\(661\) | −12413.0 | − | 21499.9i | −0.730423 | − | 1.26513i | −0.956702 | − | 0.291068i | \(-0.905990\pi\) |
0.226279 | − | 0.974062i | \(-0.427344\pi\) | |||||||
\(662\) | −4359.00 | + | 7550.01i | −0.255917 | + | 0.443262i | ||||
\(663\) | 15066.0 | − | 26095.1i | 0.882526 | − | 1.52858i | ||||
\(664\) | 448.000 | 0.0261834 | ||||||||
\(665\) | 7581.00 | − | 5627.43i | 0.442073 | − | 0.328154i | ||||
\(666\) | 5274.00 | 0.306852 | ||||||||
\(667\) | 14700.0 | − | 25461.1i | 0.853353 | − | 1.47805i | ||||
\(668\) | 5520.00 | − | 9560.92i | 0.319723 | − | 0.553777i | ||||
\(669\) | −3442.50 | − | 5962.58i | −0.198946 | − | 0.344584i | ||||
\(670\) | −2790.00 | + | 4832.42i | −0.160876 | + | 0.278646i | ||||
\(671\) | −2480.00 | − | 4295.49i | −0.142682 | − | 0.247132i | ||||
\(672\) | −1824.00 | −0.104706 | ||||||||
\(673\) | 10907.0 | 0.624716 | 0.312358 | − | 0.949964i | \(-0.398881\pi\) | ||||
0.312358 | + | 0.949964i | \(0.398881\pi\) | |||||||
\(674\) | 8729.00 | + | 15119.1i | 0.498855 | + | 0.864043i | ||||
\(675\) | 1201.50 | + | 2081.06i | 0.0685122 | + | 0.118667i | ||||
\(676\) | 17456.0 | 0.993173 | ||||||||
\(677\) | 7386.00 | 0.419301 | 0.209651 | − | 0.977776i | \(-0.432767\pi\) | ||||
0.209651 | + | 0.977776i | \(0.432767\pi\) | |||||||
\(678\) | −3972.00 | − | 6879.71i | −0.224991 | − | 0.389695i | ||||
\(679\) | 10925.0 | − | 18922.7i | 0.617471 | − | 1.06949i | ||||
\(680\) | 2976.00 | + | 5154.58i | 0.167830 | + | 0.290690i | ||||
\(681\) | −3777.00 | + | 6541.96i | −0.212533 | + | 0.368118i | ||||
\(682\) | −7200.00 | + | 12470.8i | −0.404255 | + | 0.700191i | ||||
\(683\) | 16542.0 | 0.926738 | 0.463369 | − | 0.886165i | \(-0.346640\pi\) | ||||
0.463369 | + | 0.886165i | \(0.346640\pi\) | |||||||
\(684\) | −2394.00 | + | 1777.08i | −0.133826 | + | 0.0993399i | ||||
\(685\) | −6372.00 | −0.355418 | ||||||||
\(686\) | −6175.00 | + | 10695.4i | −0.343677 | + | 0.595266i | ||||
\(687\) | −8101.50 | + | 14032.2i | −0.449915 | + | 0.779275i | ||||
\(688\) | 888.000 | + | 1538.06i | 0.0492074 | + | 0.0852297i | ||||
\(689\) | 19521.0 | − | 33811.4i | 1.07938 | − | 1.86954i | ||||
\(690\) | −1764.00 | − | 3055.34i | −0.0973251 | − | 0.168572i | ||||
\(691\) | 1972.00 | 0.108565 | 0.0542825 | − | 0.998526i | \(-0.482713\pi\) | ||||
0.0542825 | + | 0.998526i | \(0.482713\pi\) | |||||||
\(692\) | −5904.00 | −0.324330 | ||||||||
\(693\) | −2736.00 | − | 4738.89i | −0.149974 | − | 0.259763i | ||||
\(694\) | 38.0000 | + | 65.8179i | 0.00207847 | + | 0.00360002i | ||||
\(695\) | 11238.0 | 0.613355 | ||||||||
\(696\) | 7200.00 | 0.392120 | ||||||||
\(697\) | 10912.0 | + | 18900.1i | 0.593001 | + | 1.02711i | ||||
\(698\) | 6103.00 | − | 10570.7i | 0.330948 | − | 0.573219i | ||||
\(699\) | 9117.00 | + | 15791.1i | 0.493328 | + | 0.854470i | ||||
\(700\) | 3382.00 | − | 5857.80i | 0.182611 | − | 0.316291i | ||||
\(701\) | 2207.00 | − | 3822.64i | 0.118912 | − | 0.205961i | −0.800425 | − | 0.599433i | \(-0.795393\pi\) |
0.919337 | + | 0.393472i | \(0.128726\pi\) | |||||||
\(702\) | −4374.00 | −0.235165 | ||||||||
\(703\) | −22268.0 | − | 9642.33i | −1.19467 | − | 0.517308i | ||||
\(704\) | 2048.00 | 0.109640 | ||||||||
\(705\) | −4950.00 | + | 8573.65i | −0.264437 | + | 0.458018i | ||||
\(706\) | −12198.0 | + | 21127.6i | −0.650252 | + | 1.12627i | ||||
\(707\) | 5491.00 | + | 9510.69i | 0.292094 | + | 0.505921i | ||||
\(708\) | 2976.00 | − | 5154.58i | 0.157973 | − | 0.273617i | ||||
\(709\) | −15344.5 | − | 26577.5i | −0.812799 | − | 1.40781i | −0.910897 | − | 0.412633i | \(-0.864609\pi\) |
0.0980979 | − | 0.995177i | \(-0.468724\pi\) | |||||||
\(710\) | −1320.00 | −0.0697728 | ||||||||
\(711\) | 2331.00 | 0.122953 | ||||||||
\(712\) | 1232.00 | + | 2133.89i | 0.0648471 | + | 0.112319i | ||||
\(713\) | 11025.0 | + | 19095.9i | 0.579088 | + | 1.00301i | ||||
\(714\) | 14136.0 | 0.740933 | ||||||||
\(715\) | −15552.0 | −0.813443 | ||||||||
\(716\) | −52.0000 | − | 90.0666i | −0.00271415 | − | 0.00470105i | ||||
\(717\) | −1593.00 | + | 2759.16i | −0.0829730 | + | 0.143714i | ||||
\(718\) | 2988.00 | + | 5175.37i | 0.155308 | + | 0.269001i | ||||
\(719\) | 10865.0 | − | 18818.7i | 0.563555 | − | 0.976106i | −0.433627 | − | 0.901092i | \(-0.642767\pi\) |
0.997182 | − | 0.0750138i | \(-0.0239001\pi\) | |||||||
\(720\) | 432.000 | − | 748.246i | 0.0223607 | − | 0.0387298i | ||||
\(721\) | 15561.0 | 0.803775 | ||||||||
\(722\) | 13357.0 | − | 3126.35i | 0.688499 | − | 0.161151i | ||||
\(723\) | −13857.0 | −0.712790 | ||||||||
\(724\) | 7188.00 | − | 12450.0i | 0.368978 | − | 0.639088i | ||||
\(725\) | −13350.0 | + | 23122.9i | −0.683871 | + | 1.18450i | ||||
\(726\) | −921.000 | − | 1595.22i | −0.0470820 | − | 0.0815484i | ||||
\(727\) | −1361.50 | + | 2358.19i | −0.0694570 | + | 0.120303i | −0.898662 | − | 0.438641i | \(-0.855460\pi\) |
0.829205 | + | 0.558944i | \(0.188793\pi\) | |||||||
\(728\) | 6156.00 | + | 10662.5i | 0.313402 | + | 0.542828i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 9804.00 | 0.497072 | ||||||||
\(731\) | −6882.00 | − | 11920.0i | −0.348208 | − | 0.603114i | ||||
\(732\) | −930.000 | − | 1610.81i | −0.0469587 | − | 0.0813349i | ||||
\(733\) | −26186.0 | −1.31951 | −0.659756 | − | 0.751480i | \(-0.729340\pi\) | ||||
−0.659756 | + | 0.751480i | \(0.729340\pi\) | |||||||
\(734\) | −4210.00 | −0.211708 | ||||||||
\(735\) | 162.000 | + | 280.592i | 0.00812988 | + | 0.0140814i | ||||
\(736\) | 1568.00 | − | 2715.86i | 0.0785289 | − | 0.136016i | ||||
\(737\) | −7440.00 | − | 12886.5i | −0.371853 | − | 0.644069i | ||||
\(738\) | 1584.00 | − | 2743.57i | 0.0790079 | − | 0.136846i | ||||
\(739\) | 4895.50 | − | 8479.25i | 0.243686 | − | 0.422076i | −0.718075 | − | 0.695965i | \(-0.754977\pi\) |
0.961761 | + | 0.273889i | \(0.0883101\pi\) | |||||||
\(740\) | 7032.00 | 0.349326 | ||||||||
\(741\) | 18468.0 | + | 7996.88i | 0.915572 | + | 0.396454i | ||||
\(742\) | 18316.0 | 0.906202 | ||||||||
\(743\) | −2766.00 | + | 4790.85i | −0.136574 | + | 0.236554i | −0.926198 | − | 0.377038i | \(-0.876943\pi\) |
0.789623 | + | 0.613592i | \(0.210276\pi\) | |||||||
\(744\) | −2700.00 | + | 4676.54i | −0.133047 | + | 0.230444i | ||||
\(745\) | 4116.00 | + | 7129.12i | 0.202414 | + | 0.350592i | ||||
\(746\) | −2494.00 | + | 4319.73i | −0.122402 | + | 0.212006i | ||||
\(747\) | 252.000 | + | 436.477i | 0.0123430 | + | 0.0213786i | ||||
\(748\) | −15872.0 | −0.775853 | ||||||||
\(749\) | 4978.00 | 0.242847 | ||||||||
\(750\) | 3852.00 | + | 6671.86i | 0.187540 | + | 0.324829i | ||||
\(751\) | −13965.5 | − | 24189.0i | −0.678573 | − | 1.17532i | −0.975411 | − | 0.220395i | \(-0.929265\pi\) |
0.296838 | − | 0.954928i | \(-0.404068\pi\) | |||||||
\(752\) | −8800.00 | −0.426733 | ||||||||
\(753\) | 6534.00 | 0.316218 | ||||||||
\(754\) | −24300.0 | − | 42088.8i | −1.17368 | − | 2.03287i | ||||
\(755\) | −9888.00 | + | 17126.5i | −0.476637 | + | 0.825560i | ||||
\(756\) | −1026.00 | − | 1777.08i | −0.0493588 | − | 0.0854920i | ||||
\(757\) | −12830.5 | + | 22223.1i | −0.616027 | + | 1.06699i | 0.374176 | + | 0.927358i | \(0.377925\pi\) |
−0.990203 | + | 0.139633i | \(0.955408\pi\) | |||||||
\(758\) | 5729.00 | − | 9922.92i | 0.274521 | − | 0.475484i | ||||
\(759\) | 9408.00 | 0.449919 | ||||||||
\(760\) | −3192.00 | + | 2369.45i | −0.152350 | + | 0.113091i | ||||
\(761\) | −16868.0 | −0.803501 | −0.401751 | − | 0.915749i | \(-0.631598\pi\) | ||||
−0.401751 | + | 0.915749i | \(0.631598\pi\) | |||||||
\(762\) | −4308.00 | + | 7461.67i | −0.204806 | + | 0.354735i | ||||
\(763\) | −9823.00 | + | 17013.9i | −0.466077 | + | 0.807268i | ||||
\(764\) | −628.000 | − | 1087.73i | −0.0297385 | − | 0.0515087i | ||||
\(765\) | −3348.00 | + | 5798.91i | −0.158232 | + | 0.274065i | ||||
\(766\) | −10016.0 | − | 17348.2i | −0.472445 | − | 0.818299i | ||||
\(767\) | −40176.0 | −1.89136 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −2845.50 | − | 4928.55i | −0.133435 | − | 0.231116i | 0.791564 | − | 0.611087i | \(-0.209267\pi\) |
−0.924998 | + | 0.379971i | \(0.875934\pi\) | |||||||
\(770\) | −3648.00 | − | 6318.52i | −0.170733 | − | 0.295719i | ||||
\(771\) | −1890.00 | −0.0882836 | ||||||||
\(772\) | −3700.00 | −0.172495 | ||||||||
\(773\) | 9459.00 | + | 16383.5i | 0.440125 | + | 0.762319i | 0.997698 | − | 0.0678089i | \(-0.0216008\pi\) |
−0.557573 | + | 0.830128i | \(0.688267\pi\) | |||||||
\(774\) | −999.000 | + | 1730.32i | −0.0463932 | + | 0.0803553i | ||||
\(775\) | −10012.5 | − | 17342.2i | −0.464077 | − | 0.803805i | ||||
\(776\) | −4600.00 | + | 7967.43i | −0.212797 | + | 0.368575i | ||||
\(777\) | 8350.50 | − | 14463.5i | 0.385550 | − | 0.667793i | ||||
\(778\) | −11636.0 | −0.536209 | ||||||||
\(779\) | −11704.0 | + | 8687.97i | −0.538305 | + | 0.399588i | ||||
\(780\) | −5832.00 | −0.267717 | ||||||||
\(781\) | 1760.00 | − | 3048.41i | 0.0806373 | − | 0.139668i | ||||
\(782\) | −12152.0 | + | 21047.9i | −0.555696 | + | 0.962495i | ||||
\(783\) | 4050.00 | + | 7014.81i | 0.184847 | + | 0.320164i | ||||
\(784\) | −144.000 | + | 249.415i | −0.00655977 | + | 0.0113618i | ||||
\(785\) | 5301.00 | + | 9181.60i | 0.241020 | + | 0.417459i | ||||
\(786\) | 2268.00 | 0.102922 | ||||||||
\(787\) | 29191.0 | 1.32217 | 0.661084 | − | 0.750312i | \(-0.270097\pi\) | ||||
0.661084 | + | 0.750312i | \(0.270097\pi\) | |||||||
\(788\) | −2488.00 | − | 4309.34i | −0.112476 | − | 0.194815i | ||||
\(789\) | −4113.00 | − | 7123.92i | −0.185585 | − | 0.321443i | ||||
\(790\) | 3108.00 | 0.139972 | ||||||||
\(791\) | −25156.0 | −1.13078 | ||||||||
\(792\) | 1152.00 | + | 1995.32i | 0.0516850 | + | 0.0895211i | ||||
\(793\) | −6277.50 | + | 10872.9i | −0.281110 | + | 0.486898i | ||||
\(794\) | −4149.00 | − | 7186.28i | −0.185444 | − | 0.321198i | ||||
\(795\) | −4338.00 | + | 7513.64i | −0.193526 | + | 0.335197i | ||||
\(796\) | −6982.00 | + | 12093.2i | −0.310892 | + | 0.538482i | ||||
\(797\) | 22594.0 | 1.00417 | 0.502083 | − | 0.864819i | \(-0.332567\pi\) | ||||
0.502083 | + | 0.864819i | \(0.332567\pi\) | |||||||
\(798\) | 1083.00 | + | 9379.06i | 0.0480423 | + | 0.416059i | ||||
\(799\) | 68200.0 | 3.01970 | ||||||||
\(800\) | −1424.00 | + | 2466.44i | −0.0629325 | + | 0.109002i | ||||
\(801\) | −1386.00 | + | 2400.62i | −0.0611385 | + | 0.105895i | ||||
\(802\) | 9072.00 | + | 15713.2i | 0.399431 | + | 0.691834i | ||||
\(803\) | −13072.0 | + | 22641.4i | −0.574472 | + | 0.995014i | ||||
\(804\) | −2790.00 | − | 4832.42i | −0.122383 | − | 0.211973i | ||||
\(805\) | −11172.0 | −0.489144 | ||||||||
\(806\) | 36450.0 | 1.59292 | ||||||||
\(807\) | −3138.00 | − | 5435.18i | −0.136881 | − | 0.237085i | ||||
\(808\) | −2312.00 | − | 4004.50i | −0.100663 | − | 0.174354i | ||||
\(809\) | 522.000 | 0.0226855 | 0.0113427 | − | 0.999936i | \(-0.496389\pi\) | ||||
0.0113427 | + | 0.999936i | \(0.496389\pi\) | |||||||
\(810\) | 972.000 | 0.0421637 | ||||||||
\(811\) | 6040.00 | + | 10461.6i | 0.261520 | + | 0.452967i | 0.966646 | − | 0.256116i | \(-0.0824428\pi\) |
−0.705126 | + | 0.709082i | \(0.749109\pi\) | |||||||
\(812\) | 11400.0 | − | 19745.4i | 0.492687 | − | 0.853358i | ||||
\(813\) | −8148.00 | − | 14112.7i | −0.351492 | − | 0.608802i | ||||
\(814\) | −9376.00 | + | 16239.7i | −0.403721 | + | 0.699265i | ||||
\(815\) | 5127.00 | − | 8880.22i | 0.220357 | − | 0.381670i | ||||
\(816\) | −5952.00 | −0.255345 | ||||||||
\(817\) | 7381.50 | − | 5479.34i | 0.316091 | − | 0.234636i | ||||
\(818\) | −17388.0 | −0.743224 | ||||||||
\(819\) | −6925.50 | + | 11995.3i | −0.295478 | + | 0.511783i | ||||
\(820\) | 2112.00 | − | 3658.09i | 0.0899442 | − | 0.155788i | ||||
\(821\) | 18234.0 | + | 31582.2i | 0.775117 | + | 1.34254i | 0.934729 | + | 0.355362i | \(0.115642\pi\) |
−0.159612 | + | 0.987180i | \(0.551024\pi\) | |||||||
\(822\) | 3186.00 | − | 5518.31i | 0.135188 | − | 0.234152i | ||||
\(823\) | −9344.00 | − | 16184.3i | −0.395761 | − | 0.685478i | 0.597437 | − | 0.801916i | \(-0.296186\pi\) |
−0.993198 | + | 0.116438i | \(0.962852\pi\) | |||||||
\(824\) | −6552.00 | −0.277002 | ||||||||
\(825\) | −8544.00 | −0.360562 | ||||||||
\(826\) | −9424.00 | − | 16322.8i | −0.396977 | − | 0.687584i | ||||
\(827\) | −2988.00 | − | 5175.37i | −0.125638 | − | 0.217612i | 0.796344 | − | 0.604844i | \(-0.206765\pi\) |
−0.921982 | + | 0.387232i | \(0.873431\pi\) | |||||||
\(828\) | 3528.00 | 0.148075 | ||||||||
\(829\) | −11167.0 | −0.467848 | −0.233924 | − | 0.972255i | \(-0.575157\pi\) | ||||
−0.233924 | + | 0.972255i | \(0.575157\pi\) | |||||||
\(830\) | 336.000 | + | 581.969i | 0.0140515 | + | 0.0243379i | ||||
\(831\) | 4251.00 | − | 7362.95i | 0.177456 | − | 0.307362i | ||||
\(832\) | −2592.00 | − | 4489.48i | −0.108007 | − | 0.187073i | ||||
\(833\) | 1116.00 | − | 1932.97i | 0.0464191 | − | 0.0804002i | ||||
\(834\) | −5619.00 | + | 9732.39i | −0.233297 | + | 0.404083i | ||||
\(835\) | 16560.0 | 0.686326 | ||||||||
\(836\) | −1216.00 | − | 10530.9i | −0.0503065 | − | 0.435667i | ||||
\(837\) | −6075.00 | −0.250875 | ||||||||
\(838\) | −4392.00 | + | 7607.17i | −0.181049 | + | 0.313586i | ||||
\(839\) | −10035.0 | + | 17381.1i | −0.412928 | + | 0.715212i | −0.995208 | − | 0.0977756i | \(-0.968827\pi\) |
0.582280 | + | 0.812988i | \(0.302161\pi\) | |||||||
\(840\) | −1368.00 | − | 2369.45i | −0.0561911 | − | 0.0973258i | ||||
\(841\) | −32805.5 | + | 56820.8i | −1.34509 | + | 2.32977i | ||||
\(842\) | 6910.00 | + | 11968.5i | 0.282820 | + | 0.489858i | ||||
\(843\) | 17070.0 | 0.697416 | ||||||||
\(844\) | −18308.0 | −0.746667 | ||||||||
\(845\) | 13092.0 | + | 22676.0i | 0.532992 | + | 0.923170i | ||||
\(846\) | −4950.00 | − | 8573.65i | −0.201164 | − | 0.348426i | ||||
\(847\) | −5833.00 | −0.236628 | ||||||||
\(848\) | −7712.00 | −0.312301 | ||||||||
\(849\) | 6582.00 | + | 11400.4i | 0.266070 | + | 0.460847i | ||||
\(850\) | 11036.0 | − | 19114.9i | 0.445331 | − | 0.771337i | ||||
\(851\) | 14357.0 | + | 24867.1i | 0.578322 | + | 1.00168i | ||||
\(852\) | 660.000 | − | 1143.15i | 0.0265390 | − | 0.0459669i | ||||
\(853\) | −5413.50 | + | 9376.46i | −0.217297 | + | 0.376370i | −0.953981 | − | 0.299868i | \(-0.903057\pi\) |
0.736683 | + | 0.676238i | \(0.236391\pi\) | |||||||
\(854\) | −5890.00 | −0.236009 | ||||||||
\(855\) | −4104.00 | − | 1777.08i | −0.164157 | − | 0.0710819i | ||||
\(856\) | −2096.00 | −0.0836914 | ||||||||
\(857\) | 11307.0 | − | 19584.3i | 0.450688 | − | 0.780615i | −0.547741 | − | 0.836648i | \(-0.684512\pi\) |
0.998429 | + | 0.0560333i | \(0.0178453\pi\) | |||||||
\(858\) | 7776.00 | − | 13468.4i | 0.309404 | − | 0.535903i | ||||
\(859\) | 13169.5 | + | 22810.2i | 0.523094 | + | 0.906025i | 0.999639 | + | 0.0268749i | \(0.00855558\pi\) |
−0.476545 | + | 0.879150i | \(0.658111\pi\) | |||||||
\(860\) | −1332.00 | + | 2307.09i | −0.0528149 | + | 0.0914781i | ||||
\(861\) | −5016.00 | − | 8687.97i | −0.198542 | − | 0.343885i | ||||
\(862\) | 17764.0 | 0.701907 | ||||||||
\(863\) | 20458.0 | 0.806951 | 0.403475 | − | 0.914991i | \(-0.367802\pi\) | ||||
0.403475 | + | 0.914991i | \(0.367802\pi\) | |||||||
\(864\) | 432.000 | + | 748.246i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −4428.00 | − | 7669.52i | −0.174054 | − | 0.301470i | ||||
\(866\) | −7398.00 | −0.290294 | ||||||||
\(867\) | 31389.0 | 1.22956 | ||||||||
\(868\) | 8550.00 | + | 14809.0i | 0.334339 | + | 0.579091i | ||||
\(869\) | −4144.00 | + | 7177.62i | −0.161767 | + | 0.280189i | ||||
\(870\) | 5400.00 | + | 9353.07i | 0.210434 | + | 0.364482i | ||||
\(871\) | −18832.5 | + | 32618.8i | −0.732623 | + | 1.26894i | ||||
\(872\) | 4136.00 | − | 7163.76i | 0.160622 | − | 0.278206i | ||||
\(873\) | −10350.0 | −0.401254 | ||||||||
\(874\) | −14896.0 | − | 6450.16i | −0.576504 | − | 0.249634i | ||||
\(875\) | 24396.0 | 0.942555 | ||||||||
\(876\) | −4902.00 | + | 8490.51i | −0.189068 | + | 0.327475i | ||||
\(877\) | 8160.50 | − | 14134.4i | 0.314208 | − | 0.544224i | −0.665061 | − | 0.746789i | \(-0.731594\pi\) |
0.979269 | + | 0.202565i | \(0.0649277\pi\) | |||||||
\(878\) | −16907.0 | − | 29283.8i | −0.649867 | − | 1.12560i | ||||
\(879\) | 2487.00 | − | 4307.61i | 0.0954317 | − | 0.165292i | ||||
\(880\) | 1536.00 | + | 2660.43i | 0.0588393 | + | 0.101913i | ||||
\(881\) | −15990.0 | −0.611483 | −0.305742 | − | 0.952115i | \(-0.598904\pi\) | ||||
−0.305742 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(882\) | −324.000 | −0.0123692 | ||||||||
\(883\) | −6412.50 | − | 11106.8i | −0.244392 | − | 0.423299i | 0.717569 | − | 0.696488i | \(-0.245255\pi\) |
−0.961960 | + | 0.273189i | \(0.911922\pi\) | |||||||
\(884\) | 20088.0 | + | 34793.4i | 0.764290 | + | 1.32379i | ||||
\(885\) | 8928.00 | 0.339109 | ||||||||
\(886\) | 19944.0 | 0.756244 | ||||||||
\(887\) | −11238.0 | − | 19464.8i | −0.425406 | − | 0.736825i | 0.571052 | − | 0.820914i | \(-0.306535\pi\) |
−0.996458 | + | 0.0840889i | \(0.973202\pi\) | |||||||
\(888\) | −3516.00 | + | 6089.89i | −0.132871 | + | 0.230139i | ||||
\(889\) | 13642.0 | + | 23628.6i | 0.514666 | + | 0.891428i | ||||
\(890\) | −1848.00 | + | 3200.83i | −0.0696012 | + | 0.120553i | ||||
\(891\) | −1296.00 | + | 2244.74i | −0.0487291 | + | 0.0844013i | ||||
\(892\) | 9180.00 | 0.344584 | ||||||||
\(893\) | 5225.00 | + | 45249.8i | 0.195798 | + | 1.69566i | ||||
\(894\) | −8232.00 | −0.307963 | ||||||||
\(895\) | 78.0000 | − | 135.100i | 0.00291313 | − | 0.00504569i | ||||
\(896\) | 1216.00 | − | 2106.17i | 0.0453390 | − | 0.0785294i | ||||
\(897\) | −11907.0 | − | 20623.5i | −0.443214 | − | 0.767670i | ||||
\(898\) | −10368.0 | + | 17957.9i | −0.385284 | + | 0.667331i | ||||
\(899\) | −33750.0 | − | 58456.7i | −1.25209 | − | 2.16868i | ||||
\(900\) | −3204.00 | −0.118667 | ||||||||
\(901\) | 59768.0 | 2.20995 | ||||||||
\(902\) | 5632.00 | + | 9754.91i | 0.207899 | + | 0.360092i | ||||
\(903\) | 3163.50 | + | 5479.34i | 0.116583 | + | 0.201928i | ||||
\(904\) | 10592.0 | 0.389695 | ||||||||
\(905\) | 21564.0 | 0.792057 | ||||||||
\(906\) | −9888.00 | − | 17126.5i | −0.362590 | − | 0.628025i | ||||
\(907\) | 1102.00 | − | 1908.72i | 0.0403432 | − | 0.0698765i | −0.845149 | − | 0.534531i | \(-0.820488\pi\) |
0.885492 | + | 0.464655i | \(0.153822\pi\) | |||||||
\(908\) | −5036.00 | − | 8722.61i | −0.184059 | − | 0.318799i | ||||
\(909\) | 2601.00 | − | 4505.06i | 0.0949062 | − | 0.164382i | ||||
\(910\) | −9234.00 | + | 15993.8i | −0.336378 | + | 0.582624i | ||||
\(911\) | −32472.0 | −1.18095 | −0.590475 | − | 0.807056i | \(-0.701060\pi\) | ||||
−0.590475 | + | 0.807056i | \(0.701060\pi\) | |||||||
\(912\) | −456.000 | − | 3949.08i | −0.0165567 | − | 0.143385i | ||||
\(913\) | −1792.00 | −0.0649579 | ||||||||
\(914\) | 4481.00 | − | 7761.32i | 0.162164 | − | 0.280877i | ||||
\(915\) | 1395.00 | − | 2416.21i | 0.0504014 | − | 0.0872978i | ||||
\(916\) | −10802.0 | − | 18709.6i | −0.389638 | − | 0.674872i | ||||
\(917\) | 3591.00 | − | 6219.79i | 0.129319 | − | 0.223987i | ||||
\(918\) | −3348.00 | − | 5798.91i | −0.120371 | − | 0.208488i | ||||
\(919\) | −6095.00 | −0.218776 | −0.109388 | − | 0.993999i | \(-0.534889\pi\) | ||||
−0.109388 | + | 0.993999i | \(0.534889\pi\) | |||||||
\(920\) | 4704.00 | 0.168572 | ||||||||
\(921\) | −1206.00 | − | 2088.85i | −0.0431477 | − | 0.0747340i | ||||
\(922\) | −2112.00 | − | 3658.09i | −0.0754393 | − | 0.130665i | ||||
\(923\) | −8910.00 | −0.317742 | ||||||||
\(924\) | 7296.00 | 0.259763 | ||||||||
\(925\) | −13038.5 | − | 22583.3i | −0.463463 | − | 0.802741i | ||||
\(926\) | 5817.00 | − | 10075.3i | 0.206435 | − | 0.357555i | ||||
\(927\) | −3685.50 | − | 6383.47i | −0.130580 | − | 0.226171i | ||||
\(928\) | −4800.00 | + | 8313.84i | −0.169793 | + | 0.294090i | ||||
\(929\) | −21993.0 | + | 38093.0i | −0.776714 | + | 1.34531i | 0.157113 | + | 0.987581i | \(0.449781\pi\) |
−0.933826 | + | 0.357727i | \(0.883552\pi\) | |||||||
\(930\) | −8100.00 | −0.285602 | ||||||||
\(931\) | 1368.00 | + | 592.361i | 0.0481572 | + | 0.0208527i | ||||
\(932\) | −24312.0 | −0.854470 | ||||||||
\(933\) | 4758.00 | − | 8241.10i | 0.166956 | − | 0.289176i | ||||
\(934\) | 9100.00 | − | 15761.7i | 0.318802 | − | 0.552181i | ||||
\(935\) | −11904.0 | − | 20618.3i | −0.416366 | − | 0.721167i | ||||
\(936\) | 2916.00 | − | 5050.66i | 0.101830 | − | 0.176374i | ||||
\(937\) | −11075.5 | − | 19183.3i | −0.386148 | − | 0.668828i | 0.605780 | − | 0.795632i | \(-0.292861\pi\) |
−0.991928 | + | 0.126804i | \(0.959528\pi\) | |||||||
\(938\) | −17670.0 | −0.615081 | ||||||||
\(939\) | 11502.0 | 0.399738 | ||||||||
\(940\) | −6600.00 | − | 11431.5i | −0.229009 | − | 0.396655i | ||||
\(941\) | −6700.00 | − | 11604.7i | −0.232108 | − | 0.402023i | 0.726320 | − | 0.687357i | \(-0.241229\pi\) |
−0.958428 | + | 0.285333i | \(0.907896\pi\) | |||||||
\(942\) | −10602.0 | −0.366700 | ||||||||
\(943\) | 17248.0 | 0.595623 | ||||||||
\(944\) | 3968.00 | + | 6872.78i | 0.136809 | + | 0.236960i | ||||
\(945\) | 1539.00 | − | 2665.63i | 0.0529774 | − | 0.0917596i | ||||
\(946\) | −3552.00 | − | 6152.24i | −0.122078 | − | 0.211445i | ||||
\(947\) | 27197.0 | − | 47106.6i | 0.933246 | − | 1.61643i | 0.155513 | − | 0.987834i | \(-0.450297\pi\) |
0.777733 | − | 0.628595i | \(-0.216370\pi\) | |||||||
\(948\) | −1554.00 | + | 2691.61i | −0.0532401 | + | 0.0922145i | ||||
\(949\) | 66177.0 | 2.26364 | ||||||||
\(950\) | 13528.0 | + | 5857.80i | 0.462007 | + | 0.200055i | ||||
\(951\) | 8766.00 | 0.298903 | ||||||||
\(952\) | −9424.00 | + | 16322.8i | −0.320834 | + | 0.555700i | ||||
\(953\) | −6828.00 | + | 11826.4i | −0.232089 | + | 0.401990i | −0.958423 | − | 0.285353i | \(-0.907889\pi\) |
0.726334 | + | 0.687342i | \(0.241223\pi\) | |||||||
\(954\) | −4338.00 | − | 7513.64i | −0.147220 | − | 0.254993i | ||||
\(955\) | 942.000 | − | 1631.59i | 0.0319187 | − | 0.0552849i | ||||
\(956\) | −2124.00 | − | 3678.88i | −0.0718568 | − | 0.124460i | ||||
\(957\) | −28800.0 | −0.972802 | ||||||||
\(958\) | 60.0000 | 0.00202350 | ||||||||
\(959\) | −10089.0 | − | 17474.7i | −0.339719 | − | 0.588411i | ||||
\(960\) | 576.000 | + | 997.661i | 0.0193649 | + | 0.0335410i | ||||
\(961\) | 20834.0 | 0.699339 | ||||||||
\(962\) | 47466.0 | 1.59082 | ||||||||
\(963\) | −1179.00 | − | 2042.09i | −0.0394525 | − | 0.0683337i | ||||
\(964\) | 9238.00 | − | 16000.7i | 0.308647 | − | 0.534593i | ||||
\(965\) | −2775.00 | − | 4806.44i | −0.0925704 | − | 0.160337i | ||||
\(966\) | 5586.00 | − | 9675.24i | 0.186052 | − | 0.322252i | ||||
\(967\) | −12340.5 | + | 21374.4i | −0.410386 | + | 0.710810i | −0.994932 | − | 0.100551i | \(-0.967940\pi\) |
0.584545 | + | 0.811361i | \(0.301273\pi\) | |||||||
\(968\) | 2456.00 | 0.0815484 | ||||||||
\(969\) | 3534.00 | + | 30605.3i | 0.117160 | + | 1.01464i | ||||
\(970\) | −13800.0 | −0.456795 | ||||||||
\(971\) | −23211.0 | + | 40202.6i | −0.767123 | + | 1.32870i | 0.171994 | + | 0.985098i | \(0.444979\pi\) |
−0.939117 | + | 0.343598i | \(0.888354\pi\) | |||||||
\(972\) | −486.000 | + | 841.777i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 17793.5 | + | 30819.2i | 0.586263 | + | 1.01544i | ||||
\(974\) | −10924.0 | + | 18920.9i | −0.359371 | + | 0.622449i | ||||
\(975\) | 10813.5 | + | 18729.5i | 0.355189 | + | 0.615205i | ||||
\(976\) | 2480.00 | 0.0813349 | ||||||||
\(977\) | 10266.0 | 0.336170 | 0.168085 | − | 0.985772i | \(-0.446242\pi\) | ||||
0.168085 | + | 0.985772i | \(0.446242\pi\) | |||||||
\(978\) | 5127.00 | + | 8880.22i | 0.167631 | + | 0.290346i | ||||
\(979\) | −4928.00 | − | 8535.55i | −0.160878 | − | 0.278649i | ||||
\(980\) | −432.000 | −0.0140814 | ||||||||
\(981\) | 9306.00 | 0.302872 | ||||||||
\(982\) | 7338.00 | + | 12709.8i | 0.238457 | + | 0.413020i | ||||
\(983\) | 14106.0 | − | 24432.3i | 0.457692 | − | 0.792746i | −0.541146 | − | 0.840928i | \(-0.682009\pi\) |
0.998839 | + | 0.0481822i | \(0.0153428\pi\) | |||||||
\(984\) | 2112.00 | + | 3658.09i | 0.0684229 | + | 0.118512i | ||||
\(985\) | 3732.00 | − | 6464.01i | 0.120722 | − | 0.209097i | ||||
\(986\) | 37200.0 | − | 64432.3i | 1.20151 | − | 2.08108i | ||||
\(987\) | −31350.0 | −1.01102 | ||||||||
\(988\) | −21546.0 | + | 15993.8i | −0.693795 | + | 0.515009i | ||||
\(989\) | −10878.0 | −0.349747 | ||||||||
\(990\) | −1728.00 | + | 2992.98i | −0.0554742 | + | 0.0960841i | ||||
\(991\) | −20448.5 | + | 35417.8i | −0.655467 | + | 1.13530i | 0.326309 | + | 0.945263i | \(0.394195\pi\) |
−0.981776 | + | 0.190039i | \(0.939138\pi\) | |||||||
\(992\) | −3600.00 | − | 6235.38i | −0.115222 | − | 0.199570i | ||||
\(993\) | 6538.50 | − | 11325.0i | 0.208956 | − | 0.361922i | ||||
\(994\) | −2090.00 | − | 3619.99i | −0.0666909 | − | 0.115512i | ||||
\(995\) | −20946.0 | −0.667370 | ||||||||
\(996\) | −672.000 | −0.0213786 | ||||||||
\(997\) | 7410.50 | + | 12835.4i | 0.235399 | + | 0.407723i | 0.959389 | − | 0.282088i | \(-0.0910270\pi\) |
−0.723990 | + | 0.689811i | \(0.757694\pi\) | |||||||
\(998\) | −8521.00 | − | 14758.8i | −0.270268 | − | 0.468118i | ||||
\(999\) | −7911.00 | −0.250544 |
(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 | 114.4.e.b.49.1 | yes | 2 | |
3.2 | odd | 2 | 342.4.g.a.163.1 | 2 | |||
19.7 | even | 3 | inner | 114.4.e.b.7.1 | ✓ | 2 | |
19.8 | odd | 6 | 2166.4.a.e.1.1 | 1 | |||
19.11 | even | 3 | 2166.4.a.b.1.1 | 1 | |||
57.26 | odd | 6 | 342.4.g.a.235.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.b.7.1 | ✓ | 2 | 19.7 | even | 3 | inner | |
114.4.e.b.49.1 | yes | 2 | 1.1 | even | 1 | trivial | |
342.4.g.a.163.1 | 2 | 3.2 | odd | 2 | |||
342.4.g.a.235.1 | 2 | 57.26 | odd | 6 | |||
2166.4.a.b.1.1 | 1 | 19.11 | even | 3 | |||
2166.4.a.e.1.1 | 1 | 19.8 | odd | 6 |