Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,4,Mod(2,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.e (of order \(4\), 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: | \(0.885028650086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.28356903014400.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 209x^{4} + 1600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(-1.18766 + 1.18766i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.8 |
Dual form | 15.4.e.a.2.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18766 | − | 1.18766i | −0.419903 | − | 0.419903i | 0.465267 | − | 0.885170i | \(-0.345958\pi\) |
−0.885170 | + | 0.465267i | \(0.845958\pi\) | |||||||
\(3\) | 5.11173 | − | 0.932827i | 0.983754 | − | 0.179523i | ||||
\(4\) | − | 5.17891i | − | 0.647364i | ||||||
\(5\) | −2.48157 | + | 10.9015i | −0.221958 | + | 0.975056i | ||||
\(6\) | −7.17891 | − | 4.96314i | −0.488463 | − | 0.337699i | ||||
\(7\) | −13.3578 | + | 13.3578i | −0.721254 | + | 0.721254i | −0.968861 | − | 0.247606i | \(-0.920356\pi\) |
0.247606 | + | 0.968861i | \(0.420356\pi\) | |||||||
\(8\) | −15.6521 | + | 15.6521i | −0.691732 | + | 0.691732i | ||||
\(9\) | 25.2597 | − | 9.53673i | 0.935543 | − | 0.353212i | ||||
\(10\) | 15.8945 | − | 10.0000i | 0.502630 | − | 0.316228i | ||||
\(11\) | − | 28.7164i | − | 0.787121i | −0.919299 | − | 0.393560i | \(-0.871243\pi\) | ||
0.919299 | − | 0.393560i | \(-0.128757\pi\) | |||||||
\(12\) | −4.83102 | − | 26.4732i | −0.116216 | − | 0.636846i | ||||
\(13\) | 14.1789 | + | 14.1789i | 0.302502 | + | 0.302502i | 0.841992 | − | 0.539490i | \(-0.181383\pi\) |
−0.539490 | + | 0.841992i | \(0.681383\pi\) | |||||||
\(14\) | 31.7292 | 0.605713 | ||||||||
\(15\) | −2.51595 | + | 58.0402i | −0.0433078 | + | 0.999062i | ||||
\(16\) | −4.25236 | −0.0664431 | ||||||||
\(17\) | −18.5587 | − | 18.5587i | −0.264773 | − | 0.264773i | 0.562217 | − | 0.826990i | \(-0.309949\pi\) |
−0.826990 | + | 0.562217i | \(0.809949\pi\) | |||||||
\(18\) | −41.3264 | − | 18.6736i | −0.541152 | − | 0.244522i | ||||
\(19\) | − | 49.0735i | − | 0.592538i | −0.955105 | − | 0.296269i | \(-0.904258\pi\) | ||
0.955105 | − | 0.296269i | \(-0.0957425\pi\) | |||||||
\(20\) | 56.4577 | + | 12.8518i | 0.631216 | + | 0.143688i | ||||
\(21\) | −55.8211 | + | 80.7421i | −0.580055 | + | 0.839018i | ||||
\(22\) | −34.1055 | + | 34.1055i | −0.330514 | + | 0.330514i | ||||
\(23\) | 37.7738 | − | 37.7738i | 0.342451 | − | 0.342451i | −0.514837 | − | 0.857288i | \(-0.672148\pi\) |
0.857288 | + | 0.514837i | \(0.172148\pi\) | |||||||
\(24\) | −65.4088 | + | 94.6102i | −0.556313 | + | 0.804676i | ||||
\(25\) | −112.684 | − | 54.1055i | −0.901469 | − | 0.432844i | ||||
\(26\) | − | 33.6796i | − | 0.254042i | ||||||
\(27\) | 120.225 | − | 72.3121i | 0.856935 | − | 0.515425i | ||||
\(28\) | 69.1789 | + | 69.1789i | 0.466914 | + | 0.466914i | ||||
\(29\) | −125.854 | −0.805882 | −0.402941 | − | 0.915226i | \(-0.632012\pi\) | ||||
−0.402941 | + | 0.915226i | \(0.632012\pi\) | |||||||
\(30\) | 71.9204 | − | 65.9442i | 0.437694 | − | 0.401324i | ||||
\(31\) | 247.367 | 1.43318 | 0.716588 | − | 0.697496i | \(-0.245703\pi\) | ||||
0.716588 | + | 0.697496i | \(0.245703\pi\) | |||||||
\(32\) | 130.267 | + | 130.267i | 0.719632 | + | 0.719632i | ||||
\(33\) | −26.7874 | − | 146.791i | −0.141306 | − | 0.774333i | ||||
\(34\) | 44.0829i | 0.222357i | ||||||||
\(35\) | −112.471 | − | 178.768i | −0.543175 | − | 0.863352i | ||||
\(36\) | −49.3898 | − | 130.818i | −0.228657 | − | 0.605637i | ||||
\(37\) | −127.463 | + | 127.463i | −0.566347 | + | 0.566347i | −0.931103 | − | 0.364756i | \(-0.881152\pi\) |
0.364756 | + | 0.931103i | \(0.381152\pi\) | |||||||
\(38\) | −58.2828 | + | 58.2828i | −0.248808 | + | 0.248808i | ||||
\(39\) | 85.7053 | + | 59.2524i | 0.351893 | + | 0.243281i | ||||
\(40\) | −131.789 | − | 209.473i | −0.520942 | − | 0.828014i | ||||
\(41\) | 390.328i | 1.48680i | 0.668845 | + | 0.743402i | \(0.266789\pi\) | ||||
−0.668845 | + | 0.743402i | \(0.733211\pi\) | |||||||
\(42\) | 162.191 | − | 29.5978i | 0.595873 | − | 0.108739i | ||||
\(43\) | −39.3993 | − | 39.3993i | −0.139729 | − | 0.139729i | 0.633783 | − | 0.773511i | \(-0.281501\pi\) |
−0.773511 | + | 0.633783i | \(0.781501\pi\) | |||||||
\(44\) | −148.720 | −0.509553 | ||||||||
\(45\) | 41.2806 | + | 299.033i | 0.136750 | + | 0.990606i | ||||
\(46\) | −89.7251 | −0.287592 | ||||||||
\(47\) | −124.560 | − | 124.560i | −0.386575 | − | 0.386575i | 0.486889 | − | 0.873464i | \(-0.338132\pi\) |
−0.873464 | + | 0.486889i | \(0.838132\pi\) | |||||||
\(48\) | −21.7369 | + | 3.96671i | −0.0653637 | + | 0.0119280i | ||||
\(49\) | − | 13.8625i | − | 0.0404155i | ||||||
\(50\) | 69.5712 | + | 198.089i | 0.196777 | + | 0.560281i | ||||
\(51\) | −112.179 | − | 77.5549i | −0.308004 | − | 0.212938i | ||||
\(52\) | 73.4313 | − | 73.4313i | 0.195829 | − | 0.195829i | ||||
\(53\) | 160.441 | − | 160.441i | 0.415816 | − | 0.415816i | −0.467943 | − | 0.883759i | \(-0.655005\pi\) |
0.883759 | + | 0.467943i | \(0.155005\pi\) | |||||||
\(54\) | −228.669 | − | 56.9040i | −0.576257 | − | 0.143401i | ||||
\(55\) | 313.051 | + | 71.2618i | 0.767487 | + | 0.174708i | ||||
\(56\) | − | 418.156i | − | 0.997830i | ||||||
\(57\) | −45.7770 | − | 250.850i | −0.106374 | − | 0.582912i | ||||
\(58\) | 149.473 | + | 149.473i | 0.338392 | + | 0.338392i | ||||
\(59\) | 729.423 | 1.60954 | 0.804769 | − | 0.593588i | \(-0.202289\pi\) | ||||
0.804769 | + | 0.593588i | \(0.202289\pi\) | |||||||
\(60\) | 300.585 | + | 13.0299i | 0.646756 | + | 0.0280359i | ||||
\(61\) | 2.00000 | 0.00419793 | 0.00209897 | − | 0.999998i | \(-0.499332\pi\) | ||||
0.00209897 | + | 0.999998i | \(0.499332\pi\) | |||||||
\(62\) | −293.789 | − | 293.789i | −0.601795 | − | 0.601795i | ||||
\(63\) | −210.024 | + | 464.804i | −0.420009 | + | 0.929520i | ||||
\(64\) | − | 275.409i | − | 0.537908i | ||||||
\(65\) | −189.757 | + | 119.385i | −0.362099 | + | 0.227813i | ||||
\(66\) | −142.524 | + | 206.153i | −0.265810 | + | 0.384479i | ||||
\(67\) | −329.987 | + | 329.987i | −0.601706 | + | 0.601706i | −0.940765 | − | 0.339059i | \(-0.889891\pi\) |
0.339059 | + | 0.940765i | \(0.389891\pi\) | |||||||
\(68\) | −96.1136 | + | 96.1136i | −0.171404 | + | 0.171404i | ||||
\(69\) | 157.853 | − | 228.326i | 0.275410 | − | 0.398365i | ||||
\(70\) | −78.7382 | + | 345.895i | −0.134443 | + | 0.590604i | ||||
\(71\) | − | 171.760i | − | 0.287100i | −0.989643 | − | 0.143550i | \(-0.954148\pi\) | ||
0.989643 | − | 0.143550i | \(-0.0458518\pi\) | |||||||
\(72\) | −246.097 | + | 544.637i | −0.402817 | + | 0.891474i | ||||
\(73\) | −279.927 | − | 279.927i | −0.448807 | − | 0.448807i | 0.446151 | − | 0.894958i | \(-0.352795\pi\) |
−0.894958 | + | 0.446151i | \(0.852795\pi\) | |||||||
\(74\) | 302.767 | 0.475621 | ||||||||
\(75\) | −626.480 | − | 171.458i | −0.964529 | − | 0.263978i | ||||
\(76\) | −254.147 | −0.383587 | ||||||||
\(77\) | 383.589 | + | 383.589i | 0.567714 | + | 0.567714i | ||||
\(78\) | −31.4172 | − | 172.161i | −0.0456064 | − | 0.249915i | ||||
\(79\) | − | 48.0189i | − | 0.0683866i | −0.999415 | − | 0.0341933i | \(-0.989114\pi\) | ||
0.999415 | − | 0.0341933i | \(-0.0108862\pi\) | |||||||
\(80\) | 10.5525 | − | 46.3569i | 0.0147476 | − | 0.0647858i | ||||
\(81\) | 547.102 | − | 481.789i | 0.750483 | − | 0.660890i | ||||
\(82\) | 463.578 | − | 463.578i | 0.624313 | − | 0.624313i | ||||
\(83\) | −144.451 | + | 144.451i | −0.191031 | + | 0.191031i | −0.796141 | − | 0.605111i | \(-0.793129\pi\) |
0.605111 | + | 0.796141i | \(0.293129\pi\) | |||||||
\(84\) | 418.156 | + | 289.092i | 0.543150 | + | 0.375507i | ||||
\(85\) | 248.371 | − | 156.262i | 0.316937 | − | 0.199400i | ||||
\(86\) | 93.5862i | 0.117345i | ||||||||
\(87\) | −643.334 | + | 117.400i | −0.792789 | + | 0.144674i | ||||
\(88\) | 449.473 | + | 449.473i | 0.544477 | + | 0.544477i | ||||
\(89\) | −1417.21 | −1.68790 | −0.843952 | − | 0.536419i | \(-0.819777\pi\) | ||||
−0.843952 | + | 0.536419i | \(0.819777\pi\) | |||||||
\(90\) | 306.124 | − | 404.179i | 0.358536 | − | 0.473380i | ||||
\(91\) | −378.799 | −0.436361 | ||||||||
\(92\) | −195.627 | − | 195.627i | −0.221690 | − | 0.221690i | ||||
\(93\) | 1264.48 | − | 230.751i | 1.40989 | − | 0.257288i | ||||
\(94\) | 295.872i | 0.324647i | ||||||||
\(95\) | 534.972 | + | 121.779i | 0.577758 | + | 0.131519i | ||||
\(96\) | 787.409 | + | 544.375i | 0.837131 | + | 0.578751i | ||||
\(97\) | 908.111 | − | 908.111i | 0.950564 | − | 0.950564i | −0.0482702 | − | 0.998834i | \(-0.515371\pi\) |
0.998834 | + | 0.0482702i | \(0.0153708\pi\) | |||||||
\(98\) | −16.4640 | + | 16.4640i | −0.0169706 | + | 0.0169706i | ||||
\(99\) | −273.861 | − | 725.367i | −0.278020 | − | 0.736385i | ||||
\(100\) | −280.207 | + | 583.578i | −0.280207 | + | 0.583578i | ||||
\(101\) | 337.668i | 0.332665i | 0.986070 | + | 0.166333i | \(0.0531926\pi\) | ||||
−0.986070 | + | 0.166333i | \(0.946807\pi\) | |||||||
\(102\) | 41.1217 | + | 225.340i | 0.0399182 | + | 0.218745i | ||||
\(103\) | −933.505 | − | 933.505i | −0.893019 | − | 0.893019i | 0.101787 | − | 0.994806i | \(-0.467544\pi\) |
−0.994806 | + | 0.101787i | \(0.967544\pi\) | |||||||
\(104\) | −443.860 | −0.418500 | ||||||||
\(105\) | −741.683 | − | 808.899i | −0.689342 | − | 0.751814i | ||||
\(106\) | −381.100 | −0.349205 | ||||||||
\(107\) | 596.188 | + | 596.188i | 0.538651 | + | 0.538651i | 0.923133 | − | 0.384481i | \(-0.125620\pi\) |
−0.384481 | + | 0.923133i | \(0.625620\pi\) | |||||||
\(108\) | −374.498 | − | 622.632i | −0.333667 | − | 0.554748i | ||||
\(109\) | 2074.60i | 1.82303i | 0.411264 | + | 0.911516i | \(0.365087\pi\) | ||||
−0.411264 | + | 0.911516i | \(0.634913\pi\) | |||||||
\(110\) | −287.164 | − | 456.434i | −0.248909 | − | 0.395630i | ||||
\(111\) | −532.657 | + | 770.460i | −0.455474 | + | 0.658818i | ||||
\(112\) | 56.8022 | − | 56.8022i | 0.0479224 | − | 0.0479224i | ||||
\(113\) | −271.193 | + | 271.193i | −0.225767 | + | 0.225767i | −0.810922 | − | 0.585154i | \(-0.801034\pi\) |
0.585154 | + | 0.810922i | \(0.301034\pi\) | |||||||
\(114\) | −243.558 | + | 352.294i | −0.200099 | + | 0.289433i | ||||
\(115\) | 318.051 | + | 505.527i | 0.257899 | + | 0.409919i | ||||
\(116\) | 651.788i | 0.521698i | ||||||||
\(117\) | 493.375 | + | 222.934i | 0.389851 | + | 0.176156i | ||||
\(118\) | −866.309 | − | 866.309i | −0.675849 | − | 0.675849i | ||||
\(119\) | 495.806 | 0.381937 | ||||||||
\(120\) | −869.073 | − | 947.833i | −0.661126 | − | 0.721041i | ||||
\(121\) | 506.367 | 0.380441 | ||||||||
\(122\) | −2.37533 | − | 2.37533i | −0.00176272 | − | 0.00176272i | ||||
\(123\) | 364.108 | + | 1995.25i | 0.266915 | + | 1.46265i | ||||
\(124\) | − | 1281.09i | − | 0.927786i | ||||||
\(125\) | 869.461 | − | 1094.15i | 0.622135 | − | 0.782910i | ||||
\(126\) | 801.469 | − | 302.593i | 0.566671 | − | 0.213945i | ||||
\(127\) | 105.588 | − | 105.588i | 0.0737747 | − | 0.0737747i | −0.669257 | − | 0.743031i | \(-0.733387\pi\) |
0.743031 | + | 0.669257i | \(0.233387\pi\) | |||||||
\(128\) | 715.045 | − | 715.045i | 0.493763 | − | 0.493763i | ||||
\(129\) | −238.151 | − | 164.646i | −0.162543 | − | 0.112374i | ||||
\(130\) | 367.156 | + | 83.5782i | 0.247706 | + | 0.0563868i | ||||
\(131\) | − | 1979.28i | − | 1.32008i | −0.751231 | − | 0.660039i | \(-0.770540\pi\) | ||
0.751231 | − | 0.660039i | \(-0.229460\pi\) | |||||||
\(132\) | −760.216 | + | 138.730i | −0.501275 | + | 0.0914763i | ||||
\(133\) | 655.514 | + | 655.514i | 0.427371 | + | 0.427371i | ||||
\(134\) | 783.827 | 0.505316 | ||||||||
\(135\) | 489.962 | + | 1490.07i | 0.312364 | + | 0.949962i | ||||
\(136\) | 580.964 | 0.366304 | ||||||||
\(137\) | −507.451 | − | 507.451i | −0.316456 | − | 0.316456i | 0.530948 | − | 0.847404i | \(-0.321836\pi\) |
−0.847404 | + | 0.530948i | \(0.821836\pi\) | |||||||
\(138\) | −458.651 | + | 83.6979i | −0.282920 | + | 0.0516293i | ||||
\(139\) | − | 68.4333i | − | 0.0417585i | −0.999782 | − | 0.0208793i | \(-0.993353\pi\) | ||
0.999782 | − | 0.0208793i | \(-0.00664656\pi\) | |||||||
\(140\) | −925.823 | + | 582.479i | −0.558903 | + | 0.351632i | ||||
\(141\) | −752.913 | − | 520.527i | −0.449693 | − | 0.310895i | ||||
\(142\) | −203.993 | + | 203.993i | −0.120554 | + | 0.120554i | ||||
\(143\) | 407.167 | − | 407.167i | 0.238105 | − | 0.238105i | ||||
\(144\) | −107.413 | + | 40.5536i | −0.0621604 | + | 0.0234685i | ||||
\(145\) | 312.316 | − | 1372.00i | 0.178872 | − | 0.785780i | ||||
\(146\) | 664.917i | 0.376911i | ||||||||
\(147\) | −12.9313 | − | 70.8616i | −0.00725550 | − | 0.0397590i | ||||
\(148\) | 660.121 | + | 660.121i | 0.366632 | + | 0.366632i | ||||
\(149\) | −363.356 | −0.199780 | −0.0998902 | − | 0.994998i | \(-0.531849\pi\) | ||||
−0.0998902 | + | 0.994998i | \(0.531849\pi\) | |||||||
\(150\) | 540.413 | + | 947.683i | 0.294163 | + | 0.515853i | ||||
\(151\) | −2083.14 | −1.12267 | −0.561337 | − | 0.827588i | \(-0.689713\pi\) | ||||
−0.561337 | + | 0.827588i | \(0.689713\pi\) | |||||||
\(152\) | 768.103 | + | 768.103i | 0.409878 | + | 0.409878i | ||||
\(153\) | −645.774 | − | 291.797i | −0.341227 | − | 0.154185i | ||||
\(154\) | − | 911.149i | − | 0.476769i | ||||||
\(155\) | −613.859 | + | 2696.66i | −0.318105 | + | 1.39743i | ||||
\(156\) | 306.863 | − | 443.860i | 0.157491 | − | 0.227803i | ||||
\(157\) | −1208.52 | + | 1208.52i | −0.614333 | + | 0.614333i | −0.944072 | − | 0.329739i | \(-0.893039\pi\) |
0.329739 | + | 0.944072i | \(0.393039\pi\) | |||||||
\(158\) | −57.0303 | + | 57.0303i | −0.0287157 | + | 0.0287157i | ||||
\(159\) | 670.468 | − | 969.795i | 0.334412 | − | 0.483709i | ||||
\(160\) | −1743.37 | + | 1096.84i | −0.861410 | + | 0.541953i | ||||
\(161\) | 1009.15i | 0.493989i | ||||||||
\(162\) | −1221.98 | − | 77.5696i | −0.592639 | − | 0.0376200i | ||||
\(163\) | 626.062 | + | 626.062i | 0.300840 | + | 0.300840i | 0.841343 | − | 0.540502i | \(-0.181766\pi\) |
−0.540502 | + | 0.841343i | \(0.681766\pi\) | |||||||
\(164\) | 2021.47 | 0.962502 | ||||||||
\(165\) | 1666.71 | + | 72.2492i | 0.786382 | + | 0.0340884i | ||||
\(166\) | 343.119 | 0.160429 | ||||||||
\(167\) | −3009.65 | − | 3009.65i | −1.39457 | − | 1.39457i | −0.814724 | − | 0.579848i | \(-0.803112\pi\) |
−0.579848 | − | 0.814724i | \(-0.696888\pi\) | |||||||
\(168\) | −390.067 | − | 2137.50i | −0.179133 | − | 0.981619i | ||||
\(169\) | − | 1794.92i | − | 0.816985i | ||||||
\(170\) | −480.568 | − | 109.395i | −0.216811 | − | 0.0493541i | ||||
\(171\) | −468.000 | − | 1239.58i | −0.209292 | − | 0.554345i | ||||
\(172\) | −204.045 | + | 204.045i | −0.0904552 | + | 0.0904552i | ||||
\(173\) | −1839.23 | + | 1839.23i | −0.808288 | + | 0.808288i | −0.984375 | − | 0.176086i | \(-0.943656\pi\) |
0.176086 | + | 0.984375i | \(0.443656\pi\) | |||||||
\(174\) | 903.497 | + | 624.633i | 0.393643 | + | 0.272145i | ||||
\(175\) | 2227.94 | − | 782.476i | 0.962379 | − | 0.337998i | ||||
\(176\) | 122.113i | 0.0522987i | ||||||||
\(177\) | 3728.61 | − | 680.425i | 1.58339 | − | 0.288948i | ||||
\(178\) | 1683.16 | + | 1683.16i | 0.708755 | + | 0.708755i | ||||
\(179\) | 821.582 | 0.343061 | 0.171530 | − | 0.985179i | \(-0.445129\pi\) | ||||
0.171530 | + | 0.985179i | \(0.445129\pi\) | |||||||
\(180\) | 1548.67 | − | 213.788i | 0.641282 | − | 0.0885269i | ||||
\(181\) | 2314.20 | 0.950350 | 0.475175 | − | 0.879891i | \(-0.342385\pi\) | ||||
0.475175 | + | 0.879891i | \(0.342385\pi\) | |||||||
\(182\) | 449.885 | + | 449.885i | 0.183229 | + | 0.183229i | ||||
\(183\) | 10.2235 | − | 1.86565i | 0.00412973 | − | 0.000753623i | ||||
\(184\) | 1182.48i | 0.473769i | ||||||||
\(185\) | −1073.23 | − | 1705.84i | −0.426515 | − | 0.677925i | ||||
\(186\) | −1775.83 | − | 1227.72i | −0.700053 | − | 0.483982i | ||||
\(187\) | −532.938 | + | 532.938i | −0.208408 | + | 0.208408i | ||||
\(188\) | −645.087 | + | 645.087i | −0.250254 | + | 0.250254i | ||||
\(189\) | −640.007 | + | 2571.87i | −0.246316 | + | 0.989820i | ||||
\(190\) | −490.735 | − | 780.000i | −0.187377 | − | 0.297827i | ||||
\(191\) | − | 931.167i | − | 0.352758i | −0.984322 | − | 0.176379i | \(-0.943562\pi\) | ||
0.984322 | − | 0.176379i | \(-0.0564385\pi\) | |||||||
\(192\) | −256.909 | − | 1407.82i | −0.0965666 | − | 0.529169i | ||||
\(193\) | −2623.28 | − | 2623.28i | −0.978382 | − | 0.978382i | 0.0213891 | − | 0.999771i | \(-0.493191\pi\) |
−0.999771 | + | 0.0213891i | \(0.993191\pi\) | |||||||
\(194\) | −2157.06 | −0.798289 | ||||||||
\(195\) | −858.621 | + | 787.274i | −0.315319 | + | 0.289117i | ||||
\(196\) | −71.7928 | −0.0261636 | ||||||||
\(197\) | 2995.05 | + | 2995.05i | 1.08319 | + | 1.08319i | 0.996210 | + | 0.0869796i | \(0.0277215\pi\) |
0.0869796 | + | 0.996210i | \(0.472279\pi\) | |||||||
\(198\) | −536.238 | + | 1186.75i | −0.192469 | + | 0.425952i | ||||
\(199\) | 109.458i | 0.0389912i | 0.999810 | + | 0.0194956i | \(0.00620603\pi\) | ||||
−0.999810 | + | 0.0194956i | \(0.993794\pi\) | |||||||
\(200\) | 2610.60 | − | 916.872i | 0.922987 | − | 0.324163i | ||||
\(201\) | −1378.98 | + | 1994.63i | −0.483911 | + | 0.699951i | ||||
\(202\) | 401.036 | − | 401.036i | 0.139687 | − | 0.139687i | ||||
\(203\) | 1681.14 | − | 1681.14i | 0.581246 | − | 0.581246i | ||||
\(204\) | −401.650 | + | 580.964i | −0.137849 | + | 0.199390i | ||||
\(205\) | −4255.14 | − | 968.625i | −1.44972 | − | 0.330008i | ||||
\(206\) | 2217.38i | 0.749962i | ||||||||
\(207\) | 593.915 | − | 1314.39i | 0.199420 | − | 0.441336i | ||||
\(208\) | −60.2938 | − | 60.2938i | −0.0200991 | − | 0.0200991i | ||||
\(209\) | −1409.21 | −0.466399 | ||||||||
\(210\) | −79.8292 | + | 1841.57i | −0.0262321 | + | 0.605145i | ||||
\(211\) | 2714.94 | 0.885801 | 0.442901 | − | 0.896571i | \(-0.353949\pi\) | ||||
0.442901 | + | 0.896571i | \(0.353949\pi\) | |||||||
\(212\) | −830.909 | − | 830.909i | −0.269184 | − | 0.269184i | ||||
\(213\) | −160.222 | − | 877.989i | −0.0515409 | − | 0.282436i | ||||
\(214\) | − | 1416.14i | − | 0.452362i | ||||||
\(215\) | 527.281 | − | 331.737i | 0.167257 | − | 0.105229i | ||||
\(216\) | −749.932 | + | 3013.61i | −0.236233 | + | 0.949305i | ||||
\(217\) | −3304.29 | + | 3304.29i | −1.03368 | + | 1.03368i | ||||
\(218\) | 2463.93 | − | 2463.93i | 0.765496 | − | 0.765496i | ||||
\(219\) | −1692.03 | − | 1169.79i | −0.522087 | − | 0.360945i | ||||
\(220\) | 369.058 | − | 1621.26i | 0.113100 | − | 0.496843i | ||||
\(221\) | − | 526.283i | − | 0.160188i | ||||||
\(222\) | 1547.67 | − | 282.429i | 0.467894 | − | 0.0853847i | ||||
\(223\) | 2830.49 | + | 2830.49i | 0.849971 | + | 0.849971i | 0.990129 | − | 0.140158i | \(-0.0447612\pi\) |
−0.140158 | + | 0.990129i | \(0.544761\pi\) | |||||||
\(224\) | −3480.17 | −1.03808 | ||||||||
\(225\) | −3362.34 | − | 292.053i | −0.996249 | − | 0.0865343i | ||||
\(226\) | 644.173 | 0.189601 | ||||||||
\(227\) | 1398.96 | + | 1398.96i | 0.409042 | + | 0.409042i | 0.881404 | − | 0.472362i | \(-0.156599\pi\) |
−0.472362 | + | 0.881404i | \(0.656599\pi\) | |||||||
\(228\) | −1299.13 | + | 237.075i | −0.377356 | + | 0.0688626i | ||||
\(229\) | 3930.38i | 1.13418i | 0.823656 | + | 0.567089i | \(0.191931\pi\) | ||||
−0.823656 | + | 0.567089i | \(0.808069\pi\) | |||||||
\(230\) | 222.659 | − | 978.134i | 0.0638335 | − | 0.280419i | ||||
\(231\) | 2318.63 | + | 1602.98i | 0.660408 | + | 0.456573i | ||||
\(232\) | 1969.89 | − | 1969.89i | 0.557454 | − | 0.557454i | ||||
\(233\) | 1980.71 | − | 1980.71i | 0.556912 | − | 0.556912i | −0.371515 | − | 0.928427i | \(-0.621162\pi\) |
0.928427 | + | 0.371515i | \(0.121162\pi\) | |||||||
\(234\) | −321.193 | − | 850.735i | −0.0897309 | − | 0.237668i | ||||
\(235\) | 1667.00 | − | 1048.79i | 0.462736 | − | 0.291129i | ||||
\(236\) | − | 3777.61i | − | 1.04196i | ||||||
\(237\) | −44.7933 | − | 245.460i | −0.0122769 | − | 0.0672756i | ||||
\(238\) | −588.851 | − | 588.851i | −0.160376 | − | 0.160376i | ||||
\(239\) | 2976.20 | 0.805500 | 0.402750 | − | 0.915310i | \(-0.368054\pi\) | ||||
0.402750 | + | 0.915310i | \(0.368054\pi\) | |||||||
\(240\) | 10.6987 | − | 246.808i | 0.00287750 | − | 0.0663808i | ||||
\(241\) | 1835.45 | 0.490587 | 0.245294 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245294 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(242\) | −601.394 | − | 601.394i | −0.159748 | − | 0.159748i | ||||
\(243\) | 2347.21 | − | 2973.13i | 0.619645 | − | 0.784882i | ||||
\(244\) | − | 10.3578i | − | 0.00271759i | ||||||
\(245\) | 151.122 | + | 34.4008i | 0.0394074 | + | 0.00897057i | ||||
\(246\) | 1937.25 | − | 2802.13i | 0.502092 | − | 0.726248i | ||||
\(247\) | 695.808 | − | 695.808i | 0.179244 | − | 0.179244i | ||||
\(248\) | −3871.82 | + | 3871.82i | −0.991374 | + | 0.991374i | ||||
\(249\) | −603.648 | + | 873.143i | −0.153633 | + | 0.222222i | ||||
\(250\) | −2332.11 | + | 266.855i | −0.589982 | + | 0.0675095i | ||||
\(251\) | 1542.14i | 0.387805i | 0.981021 | + | 0.193902i | \(0.0621145\pi\) | ||||
−0.981021 | + | 0.193902i | \(0.937885\pi\) | |||||||
\(252\) | 2407.18 | + | 1087.70i | 0.601738 | + | 0.271898i | ||||
\(253\) | −1084.73 | − | 1084.73i | −0.269550 | − | 0.269550i | ||||
\(254\) | −250.805 | −0.0619564 | ||||||||
\(255\) | 1123.84 | − | 1030.46i | 0.275991 | − | 0.253057i | ||||
\(256\) | −3901.74 | −0.952572 | ||||||||
\(257\) | 428.853 | + | 428.853i | 0.104090 | + | 0.104090i | 0.757234 | − | 0.653144i | \(-0.226550\pi\) |
−0.653144 | + | 0.757234i | \(0.726550\pi\) | |||||||
\(258\) | 87.2997 | + | 478.388i | 0.0210660 | + | 0.115438i | ||||
\(259\) | − | 3405.26i | − | 0.816960i | ||||||
\(260\) | 618.283 | + | 982.733i | 0.147478 | + | 0.234410i | ||||
\(261\) | −3179.04 | + | 1200.24i | −0.753937 | + | 0.284647i | ||||
\(262\) | −2350.72 | + | 2350.72i | −0.554304 | + | 0.554304i | ||||
\(263\) | −5256.99 | + | 5256.99i | −1.23255 | + | 1.23255i | −0.269565 | + | 0.962982i | \(0.586880\pi\) |
−0.962982 | + | 0.269565i | \(0.913120\pi\) | |||||||
\(264\) | 2716.87 | + | 1878.31i | 0.633377 | + | 0.437885i | ||||
\(265\) | 1350.89 | + | 2147.18i | 0.313150 | + | 0.497738i | ||||
\(266\) | − | 1557.06i | − | 0.358908i | ||||||
\(267\) | −7244.38 | + | 1322.01i | −1.66048 | + | 0.303017i | ||||
\(268\) | 1708.97 | + | 1708.97i | 0.389523 | + | 0.389523i | ||||
\(269\) | 1930.34 | 0.437528 | 0.218764 | − | 0.975778i | \(-0.429797\pi\) | ||||
0.218764 | + | 0.975778i | \(0.429797\pi\) | |||||||
\(270\) | 1187.79 | − | 2351.61i | 0.267729 | − | 0.530054i | ||||
\(271\) | −3261.67 | −0.731116 | −0.365558 | − | 0.930789i | \(-0.619122\pi\) | ||||
−0.365558 | + | 0.930789i | \(0.619122\pi\) | |||||||
\(272\) | 78.9180 | + | 78.9180i | 0.0175923 | + | 0.0175923i | ||||
\(273\) | −1936.32 | + | 353.353i | −0.429272 | + | 0.0783367i | ||||
\(274\) | 1205.36i | 0.265762i | ||||||||
\(275\) | −1553.72 | + | 3235.87i | −0.340700 | + | 0.709565i | ||||
\(276\) | −1182.48 | − | 817.507i | −0.257887 | − | 0.178290i | ||||
\(277\) | 4865.57 | − | 4865.57i | 1.05539 | − | 1.05539i | 0.0570194 | − | 0.998373i | \(-0.481840\pi\) |
0.998373 | − | 0.0570194i | \(-0.0181597\pi\) | |||||||
\(278\) | −81.2758 | + | 81.2758i | −0.0175345 | + | 0.0175345i | ||||
\(279\) | 6248.41 | − | 2359.07i | 1.34080 | − | 0.506215i | ||||
\(280\) | 4558.51 | + | 1037.68i | 0.972940 | + | 0.221477i | ||||
\(281\) | 3981.96i | 0.845351i | 0.906281 | + | 0.422676i | \(0.138909\pi\) | ||||
−0.906281 | + | 0.422676i | \(0.861091\pi\) | |||||||
\(282\) | 275.997 | + | 1512.42i | 0.0582815 | + | 0.319373i | ||||
\(283\) | −4092.66 | − | 4092.66i | −0.859658 | − | 0.859658i | 0.131640 | − | 0.991298i | \(-0.457976\pi\) |
−0.991298 | + | 0.131640i | \(0.957976\pi\) | |||||||
\(284\) | −889.527 | −0.185858 | ||||||||
\(285\) | 2848.24 | + | 123.467i | 0.591982 | + | 0.0256615i | ||||
\(286\) | −967.156 | −0.199962 | ||||||||
\(287\) | −5213.93 | − | 5213.93i | −1.07236 | − | 1.07236i | ||||
\(288\) | 4532.83 | + | 2048.19i | 0.927429 | + | 0.419064i | ||||
\(289\) | − | 4224.15i | − | 0.859791i | ||||||
\(290\) | −2000.40 | + | 1258.54i | −0.405060 | + | 0.254842i | ||||
\(291\) | 3794.91 | − | 5489.13i | 0.764473 | − | 1.10577i | ||||
\(292\) | −1449.71 | + | 1449.71i | −0.290541 | + | 0.290541i | ||||
\(293\) | 4515.35 | − | 4515.35i | 0.900305 | − | 0.900305i | −0.0951570 | − | 0.995462i | \(-0.530335\pi\) |
0.995462 | + | 0.0951570i | \(0.0303353\pi\) | |||||||
\(294\) | −68.8017 | + | 99.5179i | −0.0136483 | + | 0.0197415i | ||||
\(295\) | −1810.11 | + | 7951.77i | −0.357250 | + | 1.56939i | ||||
\(296\) | − | 3990.14i | − | 0.783521i | ||||||
\(297\) | −2076.54 | − | 3452.42i | −0.405701 | − | 0.674511i | ||||
\(298\) | 431.545 | + | 431.545i | 0.0838883 | + | 0.0838883i | ||||
\(299\) | 1071.18 | 0.207184 | ||||||||
\(300\) | −887.968 | + | 3244.48i | −0.170889 | + | 0.624401i | ||||
\(301\) | 1052.58 | 0.201560 | ||||||||
\(302\) | 2474.07 | + | 2474.07i | 0.471413 | + | 0.471413i | ||||
\(303\) | 314.986 | + | 1726.07i | 0.0597210 | + | 0.327261i | ||||
\(304\) | 208.678i | 0.0393701i | ||||||||
\(305\) | −4.96314 | + | 21.8029i | −0.000931766 | + | 0.00409322i | ||||
\(306\) | 420.406 | + | 1113.52i | 0.0785393 | + | 0.208025i | ||||
\(307\) | 1831.07 | − | 1831.07i | 0.340406 | − | 0.340406i | −0.516114 | − | 0.856520i | \(-0.672622\pi\) |
0.856520 | + | 0.516114i | \(0.172622\pi\) | |||||||
\(308\) | 1986.57 | − | 1986.57i | 0.367517 | − | 0.367517i | ||||
\(309\) | −5642.63 | − | 3901.03i | −1.03883 | − | 0.718194i | ||||
\(310\) | 3931.79 | − | 2473.67i | 0.720357 | − | 0.453210i | ||||
\(311\) | 4010.21i | 0.731184i | 0.930775 | + | 0.365592i | \(0.119134\pi\) | ||||
−0.930775 | + | 0.365592i | \(0.880866\pi\) | |||||||
\(312\) | −2268.89 | + | 414.044i | −0.411701 | + | 0.0751303i | ||||
\(313\) | 6072.69 | + | 6072.69i | 1.09664 | + | 1.09664i | 0.994801 | + | 0.101841i | \(0.0324733\pi\) |
0.101841 | + | 0.994801i | \(0.467527\pi\) | |||||||
\(314\) | 2870.63 | 0.515920 | ||||||||
\(315\) | −4545.85 | − | 3443.01i | −0.813110 | − | 0.615847i | ||||
\(316\) | −248.685 | −0.0442710 | ||||||||
\(317\) | −3112.10 | − | 3112.10i | −0.551397 | − | 0.551397i | 0.375447 | − | 0.926844i | \(-0.377489\pi\) |
−0.926844 | + | 0.375447i | \(0.877489\pi\) | |||||||
\(318\) | −1948.08 | + | 355.500i | −0.343531 | + | 0.0626901i | ||||
\(319\) | 3614.09i | 0.634326i | ||||||||
\(320\) | 3002.36 | + | 683.446i | 0.524490 | + | 0.119393i | ||||
\(321\) | 3603.70 | + | 2491.42i | 0.626600 | + | 0.433200i | ||||
\(322\) | 1198.53 | − | 1198.53i | 0.207427 | − | 0.207427i | ||||
\(323\) | −910.737 | + | 910.737i | −0.156888 | + | 0.156888i | ||||
\(324\) | −2495.14 | − | 2833.39i | −0.427836 | − | 0.485835i | ||||
\(325\) | −830.574 | − | 2364.89i | −0.141760 | − | 0.403632i | ||||
\(326\) | − | 1487.10i | − | 0.252647i | ||||||
\(327\) | 1935.24 | + | 10604.8i | 0.327275 | + | 1.79342i | ||||
\(328\) | −6109.45 | − | 6109.45i | −1.02847 | − | 1.02847i | ||||
\(329\) | 3327.71 | 0.557637 | ||||||||
\(330\) | −1893.68 | − | 2065.30i | −0.315890 | − | 0.344518i | ||||
\(331\) | −9589.47 | −1.59240 | −0.796201 | − | 0.605033i | \(-0.793160\pi\) | ||||
−0.796201 | + | 0.605033i | \(0.793160\pi\) | |||||||
\(332\) | 748.099 | + | 748.099i | 0.123666 | + | 0.123666i | ||||
\(333\) | −2004.10 | + | 4435.26i | −0.329801 | + | 0.729883i | ||||
\(334\) | 7148.90i | 1.17117i | ||||||||
\(335\) | −2778.45 | − | 4416.22i | −0.453144 | − | 0.720251i | ||||
\(336\) | 237.371 | − | 343.345i | 0.0385407 | − | 0.0557470i | ||||
\(337\) | −2561.34 | + | 2561.34i | −0.414021 | + | 0.414021i | −0.883137 | − | 0.469115i | \(-0.844573\pi\) |
0.469115 | + | 0.883137i | \(0.344573\pi\) | |||||||
\(338\) | −2131.76 | + | 2131.76i | −0.343054 | + | 0.343054i | ||||
\(339\) | −1133.29 | + | 1639.24i | −0.181569 | + | 0.262630i | ||||
\(340\) | −809.265 | − | 1286.29i | −0.129084 | − | 0.205173i | ||||
\(341\) | − | 7103.50i | − | 1.12808i | ||||||
\(342\) | −916.377 | + | 2028.03i | −0.144889 | + | 0.320653i | ||||
\(343\) | −4396.56 | − | 4396.56i | −0.692104 | − | 0.692104i | ||||
\(344\) | 1233.36 | 0.193310 | ||||||||
\(345\) | 2097.36 | + | 2287.44i | 0.327299 | + | 0.356960i | ||||
\(346\) | 4368.77 | 0.678805 | ||||||||
\(347\) | 8177.44 | + | 8177.44i | 1.26509 | + | 1.26509i | 0.948592 | + | 0.316503i | \(0.102509\pi\) |
0.316503 | + | 0.948592i | \(0.397491\pi\) | |||||||
\(348\) | 608.005 | + | 3331.77i | 0.0936566 | + | 0.513223i | ||||
\(349\) | − | 2766.04i | − | 0.424249i | −0.977243 | − | 0.212124i | \(-0.931962\pi\) | ||
0.977243 | − | 0.212124i | \(-0.0680382\pi\) | |||||||
\(350\) | −3575.36 | − | 1716.72i | −0.546032 | − | 0.262179i | ||||
\(351\) | 2729.96 | + | 679.347i | 0.415141 | + | 0.103307i | ||||
\(352\) | 3740.81 | − | 3740.81i | 0.566437 | − | 0.566437i | ||||
\(353\) | 6338.53 | − | 6338.53i | 0.955711 | − | 0.955711i | −0.0433491 | − | 0.999060i | \(-0.513803\pi\) |
0.999060 | + | 0.0433491i | \(0.0138028\pi\) | |||||||
\(354\) | −5236.46 | − | 3620.23i | −0.786199 | − | 0.543539i | ||||
\(355\) | 1872.43 | + | 426.233i | 0.279939 | + | 0.0637242i | ||||
\(356\) | 7339.58i | 1.09269i | ||||||||
\(357\) | 2534.43 | − | 462.501i | 0.375732 | − | 0.0685663i | ||||
\(358\) | −975.763 | − | 975.763i | −0.144052 | − | 0.144052i | ||||
\(359\) | −8827.47 | −1.29776 | −0.648880 | − | 0.760890i | \(-0.724762\pi\) | ||||
−0.648880 | + | 0.760890i | \(0.724762\pi\) | |||||||
\(360\) | −5326.63 | − | 4034.38i | −0.779828 | − | 0.590640i | ||||
\(361\) | 4450.80 | 0.648899 | ||||||||
\(362\) | −2748.50 | − | 2748.50i | −0.399055 | − | 0.399055i | ||||
\(363\) | 2588.42 | − | 472.353i | 0.374261 | − | 0.0682978i | ||||
\(364\) | 1961.76i | 0.282484i | ||||||||
\(365\) | 3746.27 | − | 2356.95i | 0.537229 | − | 0.337996i | ||||
\(366\) | −14.3578 | − | 9.92628i | −0.00205053 | − | 0.00141764i | ||||
\(367\) | 6191.27 | − | 6191.27i | 0.880605 | − | 0.880605i | −0.112991 | − | 0.993596i | \(-0.536043\pi\) |
0.993596 | + | 0.112991i | \(0.0360432\pi\) | |||||||
\(368\) | −160.628 | + | 160.628i | −0.0227535 | + | 0.0227535i | ||||
\(369\) | 3722.45 | + | 9859.55i | 0.525157 | + | 1.39097i | ||||
\(370\) | −751.338 | + | 3300.60i | −0.105568 | + | 0.463757i | ||||
\(371\) | 4286.28i | 0.599818i | ||||||||
\(372\) | −1195.04 | − | 6548.60i | −0.166559 | − | 0.912713i | ||||
\(373\) | 3584.46 | + | 3584.46i | 0.497577 | + | 0.497577i | 0.910683 | − | 0.413106i | \(-0.135556\pi\) |
−0.413106 | + | 0.910683i | \(0.635556\pi\) | |||||||
\(374\) | 1265.90 | 0.175022 | ||||||||
\(375\) | 3423.80 | − | 6404.06i | 0.471478 | − | 0.881878i | ||||
\(376\) | 3899.27 | 0.534812 | ||||||||
\(377\) | −1784.48 | − | 1784.48i | −0.243781 | − | 0.243781i | ||||
\(378\) | 3814.63 | − | 2294.40i | 0.519057 | − | 0.312200i | ||||
\(379\) | 7110.48i | 0.963695i | 0.876255 | + | 0.481848i | \(0.160034\pi\) | ||||
−0.876255 | + | 0.481848i | \(0.839966\pi\) | |||||||
\(380\) | 630.683 | − | 2770.57i | 0.0851404 | − | 0.374019i | ||||
\(381\) | 441.241 | − | 638.231i | 0.0593319 | − | 0.0858203i | ||||
\(382\) | −1105.91 | + | 1105.91i | −0.148124 | + | 0.148124i | ||||
\(383\) | −1695.77 | + | 1695.77i | −0.226240 | + | 0.226240i | −0.811120 | − | 0.584880i | \(-0.801142\pi\) |
0.584880 | + | 0.811120i | \(0.301142\pi\) | |||||||
\(384\) | 2988.11 | − | 4322.14i | 0.397100 | − | 0.574383i | ||||
\(385\) | −5133.58 | + | 3229.77i | −0.679562 | + | 0.427544i | ||||
\(386\) | 6231.15i | 0.821650i | ||||||||
\(387\) | −1370.95 | − | 619.472i | −0.180076 | − | 0.0813683i | ||||
\(388\) | −4703.02 | − | 4703.02i | −0.615361 | − | 0.615361i | ||||
\(389\) | −12362.2 | −1.61128 | −0.805640 | − | 0.592405i | \(-0.798178\pi\) | ||||
−0.805640 | + | 0.592405i | \(0.798178\pi\) | |||||||
\(390\) | 1954.77 | + | 84.7362i | 0.253804 | + | 0.0110020i | ||||
\(391\) | −1402.06 | −0.181343 | ||||||||
\(392\) | 216.978 | + | 216.978i | 0.0279567 | + | 0.0279567i | ||||
\(393\) | −1846.32 | − | 10117.5i | −0.236984 | − | 1.29863i | ||||
\(394\) | − | 7114.22i | − | 0.909668i | ||||||
\(395\) | 523.476 | + | 119.162i | 0.0666808 | + | 0.0151790i | ||||
\(396\) | −3756.61 | + | 1418.30i | −0.476709 | + | 0.179980i | ||||
\(397\) | −1340.12 | + | 1340.12i | −0.169417 | + | 0.169417i | −0.786723 | − | 0.617306i | \(-0.788224\pi\) |
0.617306 | + | 0.786723i | \(0.288224\pi\) | |||||||
\(398\) | 129.999 | − | 129.999i | 0.0163725 | − | 0.0163725i | ||||
\(399\) | 3962.30 | + | 2739.33i | 0.497150 | + | 0.343705i | ||||
\(400\) | 479.171 | + | 230.076i | 0.0598964 | + | 0.0287595i | ||||
\(401\) | − | 2281.30i | − | 0.284096i | −0.989860 | − | 0.142048i | \(-0.954631\pi\) | ||
0.989860 | − | 0.142048i | \(-0.0453688\pi\) | |||||||
\(402\) | 4006.72 | − | 731.175i | 0.497107 | − | 0.0907156i | ||||
\(403\) | 3507.40 | + | 3507.40i | 0.433538 | + | 0.433538i | ||||
\(404\) | 1748.75 | 0.215356 | ||||||||
\(405\) | 3894.53 | + | 7159.80i | 0.477829 | + | 0.878453i | ||||
\(406\) | −3993.26 | −0.488133 | ||||||||
\(407\) | 3660.29 | + | 3660.29i | 0.445783 | + | 0.445783i | ||||
\(408\) | 2969.74 | − | 541.939i | 0.360352 | − | 0.0657597i | ||||
\(409\) | − | 4614.82i | − | 0.557917i | −0.960303 | − | 0.278959i | \(-0.910011\pi\) | ||
0.960303 | − | 0.278959i | \(-0.0899892\pi\) | |||||||
\(410\) | 3903.28 | + | 6204.08i | 0.470169 | + | 0.747311i | ||||
\(411\) | −3067.32 | − | 2120.59i | −0.368126 | − | 0.254504i | ||||
\(412\) | −4834.54 | + | 4834.54i | −0.578108 | + | 0.578108i | ||||
\(413\) | −9743.49 | + | 9743.49i | −1.16089 | + | 1.16089i | ||||
\(414\) | −2266.43 | + | 855.683i | −0.269055 | + | 0.101581i | ||||
\(415\) | −1216.26 | − | 1933.19i | −0.143865 | − | 0.228667i | ||||
\(416\) | 3694.10i | 0.435380i | ||||||||
\(417\) | −63.8364 | − | 349.813i | −0.00749660 | − | 0.0410801i | ||||
\(418\) | 1673.67 | + | 1673.67i | 0.195842 | + | 0.195842i | ||||
\(419\) | −2142.28 | −0.249779 | −0.124889 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124889 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(420\) | −4189.21 | + | 3841.11i | −0.486697 | + | 0.446255i | ||||
\(421\) | −8889.30 | −1.02907 | −0.514534 | − | 0.857470i | \(-0.672035\pi\) | ||||
−0.514534 | + | 0.857470i | \(0.672035\pi\) | |||||||
\(422\) | −3224.43 | − | 3224.43i | −0.371950 | − | 0.371950i | ||||
\(423\) | −4334.26 | − | 1958.46i | −0.498200 | − | 0.225115i | ||||
\(424\) | 5022.48i | 0.575267i | ||||||||
\(425\) | 1087.13 | + | 3095.38i | 0.124079 | + | 0.353289i | ||||
\(426\) | −852.466 | + | 1233.05i | −0.0969534 | + | 0.140238i | ||||
\(427\) | −26.7156 | + | 26.7156i | −0.00302778 | + | 0.00302778i | ||||
\(428\) | 3087.60 | − | 3087.60i | 0.348703 | − | 0.348703i | ||||
\(429\) | 1701.52 | − | 2461.15i | 0.191492 | − | 0.276982i | ||||
\(430\) | −1020.23 | − | 232.241i | −0.114418 | − | 0.0260457i | ||||
\(431\) | − | 15707.3i | − | 1.75543i | −0.479179 | − | 0.877717i | \(-0.659065\pi\) | ||
0.479179 | − | 0.877717i | \(-0.340935\pi\) | |||||||
\(432\) | −511.238 | + | 307.497i | −0.0569374 | + | 0.0342464i | ||||
\(433\) | 5430.81 | + | 5430.81i | 0.602744 | + | 0.602744i | 0.941040 | − | 0.338296i | \(-0.109851\pi\) |
−0.338296 | + | 0.941040i | \(0.609851\pi\) | |||||||
\(434\) | 7848.76 | 0.868094 | ||||||||
\(435\) | 316.644 | − | 7304.62i | 0.0349009 | − | 0.805126i | ||||
\(436\) | 10744.2 | 1.18016 | ||||||||
\(437\) | −1853.69 | − | 1853.69i | −0.202915 | − | 0.202915i | ||||
\(438\) | 620.253 | + | 3398.88i | 0.0676640 | + | 0.370787i | ||||
\(439\) | − | 8221.92i | − | 0.893874i | −0.894565 | − | 0.446937i | \(-0.852515\pi\) | ||
0.894565 | − | 0.446937i | \(-0.147485\pi\) | |||||||
\(440\) | −6015.31 | + | 3784.51i | −0.651747 | + | 0.410044i | ||||
\(441\) | −132.203 | − | 350.163i | −0.0142753 | − | 0.0378105i | ||||
\(442\) | −625.047 | + | 625.047i | −0.0672635 | + | 0.0672635i | ||||
\(443\) | −1960.53 | + | 1960.53i | −0.210265 | + | 0.210265i | −0.804380 | − | 0.594115i | \(-0.797502\pi\) |
0.594115 | + | 0.804380i | \(0.297502\pi\) | |||||||
\(444\) | 3990.14 | + | 2758.58i | 0.426495 | + | 0.294857i | ||||
\(445\) | 3516.89 | − | 15449.6i | 0.374644 | − | 1.64580i | ||||
\(446\) | − | 6723.34i | − | 0.713810i | ||||||
\(447\) | −1857.38 | + | 338.948i | −0.196535 | + | 0.0358651i | ||||
\(448\) | 3678.86 | + | 3678.86i | 0.387968 | + | 0.387968i | ||||
\(449\) | 17849.2 | 1.87607 | 0.938036 | − | 0.346537i | \(-0.112643\pi\) | ||||
0.938036 | + | 0.346537i | \(0.112643\pi\) | |||||||
\(450\) | 3646.47 | + | 4340.19i | 0.381992 | + | 0.454664i | ||||
\(451\) | 11208.8 | 1.17029 | ||||||||
\(452\) | 1404.49 | + | 1404.49i | 0.146154 | + | 0.146154i | ||||
\(453\) | −10648.5 | + | 1943.21i | −1.10443 | + | 0.201545i | ||||
\(454\) | − | 3323.00i | − | 0.343516i | ||||||
\(455\) | 940.015 | − | 4129.46i | 0.0968540 | − | 0.425477i | ||||
\(456\) | 4642.85 | + | 3209.83i | 0.476801 | + | 0.329636i | ||||
\(457\) | −6346.80 | + | 6346.80i | −0.649652 | + | 0.649652i | −0.952909 | − | 0.303257i | \(-0.901926\pi\) |
0.303257 | + | 0.952909i | \(0.401926\pi\) | |||||||
\(458\) | 4667.97 | − | 4667.97i | 0.476245 | − | 0.476245i | ||||
\(459\) | −3573.22 | − | 889.192i | −0.363363 | − | 0.0904225i | ||||
\(460\) | 2618.08 | − | 1647.16i | 0.265366 | − | 0.166954i | ||||
\(461\) | − | 8848.20i | − | 0.893930i | −0.894552 | − | 0.446965i | \(-0.852505\pi\) | ||
0.894552 | − | 0.446965i | \(-0.147495\pi\) | |||||||
\(462\) | −849.944 | − | 4657.55i | −0.0855908 | − | 0.469024i | ||||
\(463\) | 1329.43 | + | 1329.43i | 0.133443 | + | 0.133443i | 0.770673 | − | 0.637230i | \(-0.219920\pi\) |
−0.637230 | + | 0.770673i | \(0.719920\pi\) | |||||||
\(464\) | 535.178 | 0.0535453 | ||||||||
\(465\) | −622.365 | + | 14357.3i | −0.0620677 | + | 1.43183i | ||||
\(466\) | −4704.83 | −0.467697 | ||||||||
\(467\) | −1479.96 | − | 1479.96i | −0.146647 | − | 0.146647i | 0.629971 | − | 0.776618i | \(-0.283067\pi\) |
−0.776618 | + | 0.629971i | \(0.783067\pi\) | |||||||
\(468\) | 1154.56 | − | 2555.14i | 0.114037 | − | 0.252375i | ||||
\(469\) | − | 8815.81i | − | 0.867966i | ||||||
\(470\) | −3225.44 | − | 734.227i | −0.316550 | − | 0.0720582i | ||||
\(471\) | −5050.29 | + | 7304.96i | −0.494066 | + | 0.714639i | ||||
\(472\) | −11417.0 | + | 11417.0i | −1.11337 | + | 1.11337i | ||||
\(473\) | −1131.41 | + | 1131.41i | −0.109983 | + | 0.109983i | ||||
\(474\) | −238.324 | + | 344.723i | −0.0230941 | + | 0.0334043i | ||||
\(475\) | −2655.14 | + | 5529.77i | −0.256476 | + | 0.534155i | ||||
\(476\) | − | 2567.73i | − | 0.247252i | ||||||
\(477\) | 2522.60 | − | 5582.76i | 0.242143 | − | 0.535885i | ||||
\(478\) | −3534.73 | − | 3534.73i | −0.338231 | − | 0.338231i | ||||
\(479\) | −5039.60 | −0.480720 | −0.240360 | − | 0.970684i | \(-0.577266\pi\) | ||||
−0.240360 | + | 0.970684i | \(0.577266\pi\) | |||||||
\(480\) | −7888.49 | + | 7233.00i | −0.750122 | + | 0.687791i | ||||
\(481\) | −3614.58 | −0.342642 | ||||||||
\(482\) | −2179.89 | − | 2179.89i | −0.205999 | − | 0.205999i | ||||
\(483\) | 941.362 | + | 5158.51i | 0.0886821 | + | 0.485963i | ||||
\(484\) | − | 2622.43i | − | 0.246284i | ||||||
\(485\) | 7646.20 | + | 12153.3i | 0.715868 | + | 1.13784i | ||||
\(486\) | −6318.78 | + | 743.377i | −0.589765 | + | 0.0693833i | ||||
\(487\) | 1292.93 | − | 1292.93i | 0.120305 | − | 0.120305i | −0.644391 | − | 0.764696i | \(-0.722889\pi\) |
0.764696 | + | 0.644391i | \(0.222889\pi\) | |||||||
\(488\) | −31.3042 | + | 31.3042i | −0.00290384 | + | 0.00290384i | ||||
\(489\) | 3784.27 | + | 2616.26i | 0.349961 | + | 0.241945i | ||||
\(490\) | −138.625 | − | 220.339i | −0.0127805 | − | 0.0203140i | ||||
\(491\) | 13865.7i | 1.27444i | 0.770681 | + | 0.637221i | \(0.219916\pi\) | ||||
−0.770681 | + | 0.637221i | \(0.780084\pi\) | |||||||
\(492\) | 10333.2 | − | 1885.68i | 0.946865 | − | 0.172791i | ||||
\(493\) | 2335.69 | + | 2335.69i | 0.213375 | + | 0.213375i | ||||
\(494\) | −1652.77 | −0.150530 | ||||||||
\(495\) | 8587.17 | − | 1185.43i | 0.779726 | − | 0.107639i | ||||
\(496\) | −1051.89 | −0.0952247 | ||||||||
\(497\) | 2294.33 | + | 2294.33i | 0.207072 | + | 0.207072i | ||||
\(498\) | 1753.93 | − | 320.070i | 0.157822 | − | 0.0288006i | ||||
\(499\) | 10884.3i | 0.976453i | 0.872717 | + | 0.488226i | \(0.162356\pi\) | ||||
−0.872717 | + | 0.488226i | \(0.837644\pi\) | |||||||
\(500\) | −5666.50 | − | 4502.86i | −0.506827 | − | 0.402748i | ||||
\(501\) | −18192.0 | − | 12577.0i | −1.62227 | − | 1.12156i | ||||
\(502\) | 1831.54 | − | 1831.54i | 0.162840 | − | 0.162840i | ||||
\(503\) | 7880.86 | − | 7880.86i | 0.698589 | − | 0.698589i | −0.265517 | − | 0.964106i | \(-0.585543\pi\) |
0.964106 | + | 0.265517i | \(0.0855427\pi\) | |||||||
\(504\) | −3987.84 | − | 10562.5i | −0.352445 | − | 0.933513i | ||||
\(505\) | −3681.07 | − | 837.946i | −0.324368 | − | 0.0738379i | ||||
\(506\) | 2576.58i | 0.226370i | ||||||||
\(507\) | −1674.35 | − | 9175.14i | −0.146667 | − | 0.803713i | ||||
\(508\) | −546.829 | − | 546.829i | −0.0477590 | − | 0.0477590i | ||||
\(509\) | −1788.46 | −0.155741 | −0.0778704 | − | 0.996963i | \(-0.524812\pi\) | ||||
−0.0778704 | + | 0.996963i | \(0.524812\pi\) | |||||||
\(510\) | −2558.58 | − | 110.911i | −0.222149 | − | 0.00962981i | ||||
\(511\) | 7478.42 | 0.647408 | ||||||||
\(512\) | −1086.41 | − | 1086.41i | −0.0937754 | − | 0.0937754i | ||||
\(513\) | −3548.60 | − | 5899.84i | −0.305409 | − | 0.507766i | ||||
\(514\) | − | 1018.67i | − | 0.0874153i | ||||||
\(515\) | 12493.1 | − | 7860.01i | 1.06896 | − | 0.672531i | ||||
\(516\) | −852.686 | + | 1233.36i | −0.0727469 | + | 0.105224i | ||||
\(517\) | −3576.93 | + | 3576.93i | −0.304281 | + | 0.304281i | ||||
\(518\) | −4044.31 | + | 4044.31i | −0.343044 | + | 0.343044i | ||||
\(519\) | −7685.96 | + | 11117.3i | −0.650051 | + | 0.940263i | ||||
\(520\) | 1101.47 | − | 4838.72i | 0.0928896 | − | 0.408061i | ||||
\(521\) | 18251.6i | 1.53478i | 0.641183 | + | 0.767388i | \(0.278444\pi\) | ||||
−0.641183 | + | 0.767388i | \(0.721556\pi\) | |||||||
\(522\) | 5201.11 | + | 2350.15i | 0.436104 | + | 0.197056i | ||||
\(523\) | −2125.69 | − | 2125.69i | −0.177725 | − | 0.177725i | 0.612639 | − | 0.790363i | \(-0.290108\pi\) |
−0.790363 | + | 0.612639i | \(0.790108\pi\) | |||||||
\(524\) | −10250.5 | −0.854570 | ||||||||
\(525\) | 10658.7 | − | 6078.09i | 0.886066 | − | 0.505276i | ||||
\(526\) | 12487.1 | 1.03510 | ||||||||
\(527\) | −4590.80 | − | 4590.80i | −0.379466 | − | 0.379466i | ||||
\(528\) | 113.910 | + | 624.207i | 0.00938880 | + | 0.0514491i | ||||
\(529\) | 9313.29i | 0.765455i | ||||||||
\(530\) | 945.725 | − | 4154.54i | 0.0775088 | − | 0.340494i | ||||
\(531\) | 18425.0 | − | 6956.30i | 1.50579 | − | 0.568508i | ||||
\(532\) | 3394.85 | − | 3394.85i | 0.276664 | − | 0.276664i | ||||
\(533\) | −5534.42 | + | 5534.42i | −0.449761 | + | 0.449761i | ||||
\(534\) | 10174.0 | + | 7033.79i | 0.824478 | + | 0.570003i | ||||
\(535\) | −7978.81 | + | 5019.84i | −0.644774 | + | 0.405657i | ||||
\(536\) | − | 10330.0i | − | 0.832439i | ||||||
\(537\) | 4199.71 | − | 766.393i | 0.337488 | − | 0.0615872i | ||||
\(538\) | −2292.60 | − | 2292.60i | −0.183719 | − | 0.183719i | ||||
\(539\) | −398.082 | −0.0318119 | ||||||||
\(540\) | 7716.94 | − | 2537.47i | 0.614971 | − | 0.202213i | ||||
\(541\) | −2214.16 | −0.175960 | −0.0879798 | − | 0.996122i | \(-0.528041\pi\) | ||||
−0.0879798 | + | 0.996122i | \(0.528041\pi\) | |||||||
\(542\) | 3873.77 | + | 3873.77i | 0.306998 | + | 0.306998i | ||||
\(543\) | 11829.6 | − | 2158.75i | 0.934911 | − | 0.170609i | ||||
\(544\) | − | 4835.17i | − | 0.381078i | ||||||
\(545\) | −22616.2 | − | 5148.26i | −1.77756 | − | 0.404637i | ||||
\(546\) | 2719.36 | + | 1880.03i | 0.213146 | + | 0.147359i | ||||
\(547\) | 12385.1 | − | 12385.1i | 0.968098 | − | 0.968098i | −0.0314090 | − | 0.999507i | \(-0.509999\pi\) |
0.999507 | + | 0.0314090i | \(0.00999944\pi\) | |||||||
\(548\) | −2628.04 | + | 2628.04i | −0.204862 | + | 0.204862i | ||||
\(549\) | 50.5193 | − | 19.0735i | 0.00392735 | − | 0.00148276i | ||||
\(550\) | 5688.42 | − | 1997.84i | 0.441009 | − | 0.154887i | ||||
\(551\) | 6176.11i | 0.477516i | ||||||||
\(552\) | 1103.05 | + | 6044.52i | 0.0850522 | + | 0.466072i | ||||
\(553\) | 641.427 | + | 641.427i | 0.0493242 | + | 0.0493242i | ||||
\(554\) | −11557.3 | −0.886324 | ||||||||
\(555\) | −7077.31 | − | 7718.69i | −0.541288 | − | 0.590343i | ||||
\(556\) | −354.410 | −0.0270329 | ||||||||
\(557\) | 8716.96 | + | 8716.96i | 0.663105 | + | 0.663105i | 0.956111 | − | 0.293006i | \(-0.0946555\pi\) |
−0.293006 | + | 0.956111i | \(0.594656\pi\) | |||||||
\(558\) | −10222.8 | − | 4619.23i | −0.775566 | − | 0.350444i | ||||
\(559\) | − | 1117.28i | − | 0.0845363i | ||||||
\(560\) | 478.268 | + | 760.186i | 0.0360902 | + | 0.0573638i | ||||
\(561\) | −2227.10 | + | 3221.38i | −0.167608 | + | 0.242436i | ||||
\(562\) | 4729.23 | − | 4729.23i | 0.354965 | − | 0.354965i | ||||
\(563\) | 11697.0 | − | 11697.0i | 0.875615 | − | 0.875615i | −0.117462 | − | 0.993077i | \(-0.537476\pi\) |
0.993077 | + | 0.117462i | \(0.0374759\pi\) | |||||||
\(564\) | −2695.76 | + | 3899.27i | −0.201262 | + | 0.291115i | ||||
\(565\) | −2283.42 | − | 3629.39i | −0.170025 | − | 0.270247i | ||||
\(566\) | 9721.40i | 0.721945i | ||||||||
\(567\) | −872.435 | + | 13743.7i | −0.0646188 | + | 1.01796i | ||||
\(568\) | 2688.40 | + | 2688.40i | 0.198596 | + | 0.198596i | ||||
\(569\) | 11517.5 | 0.848576 | 0.424288 | − | 0.905527i | \(-0.360524\pi\) | ||||
0.424288 | + | 0.905527i | \(0.360524\pi\) | |||||||
\(570\) | −3236.11 | − | 3529.38i | −0.237799 | − | 0.259350i | ||||
\(571\) | −11093.9 | −0.813072 | −0.406536 | − | 0.913635i | \(-0.633263\pi\) | ||||
−0.406536 | + | 0.913635i | \(0.633263\pi\) | |||||||
\(572\) | −2108.68 | − | 2108.68i | −0.154141 | − | 0.154141i | ||||
\(573\) | −868.617 | − | 4759.88i | −0.0633281 | − | 0.347027i | ||||
\(574\) | 12384.8i | 0.900577i | ||||||||
\(575\) | −6300.25 | + | 2212.72i | −0.456937 | + | 0.160481i | ||||
\(576\) | −2626.50 | − | 6956.73i | −0.189995 | − | 0.503236i | ||||
\(577\) | −14119.4 | + | 14119.4i | −1.01871 | + | 1.01871i | −0.0188920 | + | 0.999822i | \(0.506014\pi\) |
−0.999822 | + | 0.0188920i | \(0.993986\pi\) | |||||||
\(578\) | −5016.87 | + | 5016.87i | −0.361028 | + | 0.361028i | ||||
\(579\) | −15856.6 | − | 10962.4i | −1.13813 | − | 0.786846i | ||||
\(580\) | −7105.44 | − | 1617.46i | −0.508685 | − | 0.115795i | ||||
\(581\) | − | 3859.10i | − | 0.275564i | ||||||
\(582\) | −11026.3 | + | 2012.16i | −0.785320 | + | 0.143311i | ||||
\(583\) | −4607.29 | − | 4607.29i | −0.327297 | − | 0.327297i | ||||
\(584\) | 8762.89 | 0.620909 | ||||||||
\(585\) | −3654.65 | + | 4825.28i | −0.258293 | + | 0.341027i | ||||
\(586\) | −10725.4 | −0.756081 | ||||||||
\(587\) | 8524.33 | + | 8524.33i | 0.599381 | + | 0.599381i | 0.940148 | − | 0.340767i | \(-0.110687\pi\) |
−0.340767 | + | 0.940148i | \(0.610687\pi\) | |||||||
\(588\) | −366.986 | + | 66.9702i | −0.0257385 | + | 0.00469695i | ||||
\(589\) | − | 12139.2i | − | 0.849211i | ||||||
\(590\) | 11593.8 | − | 7294.23i | 0.809001 | − | 0.508981i | ||||
\(591\) | 18103.8 | + | 12516.0i | 1.26005 | + | 0.871135i | ||||
\(592\) | 542.020 | − | 542.020i | 0.0376298 | − | 0.0376298i | ||||
\(593\) | −4580.53 | + | 4580.53i | −0.317200 | + | 0.317200i | −0.847691 | − | 0.530491i | \(-0.822008\pi\) |
0.530491 | + | 0.847691i | \(0.322008\pi\) | |||||||
\(594\) | −1634.08 | + | 6566.55i | −0.112874 | + | 0.453584i | ||||
\(595\) | −1230.38 | + | 5405.01i | −0.0847740 | + | 0.372410i | ||||
\(596\) | 1881.79i | 0.129331i | ||||||||
\(597\) | 102.105 | + | 559.518i | 0.00699979 | + | 0.0383577i | ||||
\(598\) | −1272.20 | − | 1272.20i | −0.0869971 | − | 0.0869971i | ||||
\(599\) | −10195.8 | −0.695477 | −0.347738 | − | 0.937592i | \(-0.613050\pi\) | ||||
−0.347738 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(600\) | 12489.4 | − | 7122.05i | 0.849798 | − | 0.484594i | ||||
\(601\) | 18915.8 | 1.28385 | 0.641923 | − | 0.766769i | \(-0.278137\pi\) | ||||
0.641923 | + | 0.766769i | \(0.278137\pi\) | |||||||
\(602\) | −1250.11 | − | 1250.11i | −0.0846355 | − | 0.0846355i | ||||
\(603\) | −5188.36 | + | 11482.4i | −0.350392 | + | 0.775452i | ||||
\(604\) | 10788.4i | 0.726778i | ||||||||
\(605\) | −1256.59 | + | 5520.14i | −0.0844421 | + | 0.370952i | ||||
\(606\) | 1675.89 | − | 2424.09i | 0.112341 | − | 0.162495i | ||||
\(607\) | 12758.2 | − | 12758.2i | 0.853113 | − | 0.853113i | −0.137402 | − | 0.990515i | \(-0.543875\pi\) |
0.990515 | + | 0.137402i | \(0.0438753\pi\) | |||||||
\(608\) | 6392.67 | − | 6392.67i | 0.426409 | − | 0.426409i | ||||
\(609\) | 7025.33 | − | 10161.8i | 0.467456 | − | 0.676149i | ||||
\(610\) | 31.7891 | − | 20.0000i | 0.00211000 | − | 0.00132750i | ||||
\(611\) | − | 3532.26i | − | 0.233879i | ||||||
\(612\) | −1511.19 | + | 3344.41i | −0.0998140 | + | 0.220898i | ||||
\(613\) | 7340.02 | + | 7340.02i | 0.483622 | + | 0.483622i | 0.906286 | − | 0.422664i | \(-0.138905\pi\) |
−0.422664 | + | 0.906286i | \(0.638905\pi\) | |||||||
\(614\) | −4349.39 | −0.285875 | ||||||||
\(615\) | −22654.7 | − | 982.047i | −1.48541 | − | 0.0643902i | ||||
\(616\) | −12007.9 | −0.785412 | ||||||||
\(617\) | −17118.9 | − | 17118.9i | −1.11698 | − | 1.11698i | −0.992182 | − | 0.124803i | \(-0.960170\pi\) |
−0.124803 | − | 0.992182i | \(-0.539830\pi\) | |||||||
\(618\) | 2068.43 | + | 11334.7i | 0.134635 | + | 0.737778i | ||||
\(619\) | − | 3176.16i | − | 0.206237i | −0.994669 | − | 0.103118i | \(-0.967118\pi\) | ||
0.994669 | − | 0.103118i | \(-0.0328820\pi\) | |||||||
\(620\) | 13965.8 | + | 3179.12i | 0.904644 | + | 0.205930i | ||||
\(621\) | 1809.84 | − | 7272.84i | 0.116950 | − | 0.469966i | ||||
\(622\) | 4762.79 | − | 4762.79i | 0.307026 | − | 0.307026i | ||||
\(623\) | 18930.8 | − | 18930.8i | 1.21741 | − | 1.21741i | ||||
\(624\) | −364.450 | − | 251.962i | −0.0233809 | − | 0.0161644i | ||||
\(625\) | 9770.20 | + | 12193.6i | 0.625293 | + | 0.780390i | ||||
\(626\) | − | 14424.6i | − | 0.920965i | ||||||
\(627\) | −7203.53 | + | 1314.55i | −0.458822 | + | 0.0837291i | ||||
\(628\) | 6258.80 | + | 6258.80i | 0.397697 | + | 0.397697i | ||||
\(629\) | 4731.09 | 0.299906 | ||||||||
\(630\) | 1309.80 | + | 9488.09i | 0.0828312 | + | 0.600023i | ||||
\(631\) | −11467.2 | −0.723459 | −0.361729 | − | 0.932283i | \(-0.617814\pi\) | ||||
−0.361729 | + | 0.932283i | \(0.617814\pi\) | |||||||
\(632\) | 751.597 | + | 751.597i | 0.0473052 | + | 0.0473052i | ||||
\(633\) | 13878.0 | − | 2532.57i | 0.871410 | − | 0.159021i | ||||
\(634\) | 7392.26i | 0.463066i | ||||||||
\(635\) | 889.036 | + | 1413.08i | 0.0555596 | + | 0.0883094i | ||||
\(636\) | −5022.48 | − | 3472.29i | −0.313136 | − | 0.216486i | ||||
\(637\) | 196.556 | − | 196.556i | 0.0122258 | − | 0.0122258i | ||||
\(638\) | 4292.32 | − | 4292.32i | 0.266355 | − | 0.266355i | ||||
\(639\) | −1638.02 | − | 4338.59i | −0.101407 | − | 0.268595i | ||||
\(640\) | 6020.60 | + | 9569.47i | 0.371852 | + | 0.591042i | ||||
\(641\) | − | 12383.2i | − | 0.763035i | −0.924362 | − | 0.381518i | \(-0.875402\pi\) | ||
0.924362 | − | 0.381518i | \(-0.124598\pi\) | |||||||
\(642\) | −1321.02 | − | 7238.95i | −0.0812092 | − | 0.445013i | ||||
\(643\) | −11142.9 | − | 11142.9i | −0.683413 | − | 0.683413i | 0.277354 | − | 0.960768i | \(-0.410542\pi\) |
−0.960768 | + | 0.277354i | \(0.910542\pi\) | |||||||
\(644\) | 5226.29 | 0.319790 | ||||||||
\(645\) | 2385.87 | − | 2187.62i | 0.145649 | − | 0.133546i | ||||
\(646\) | 2163.30 | 0.131755 | ||||||||
\(647\) | −2391.21 | − | 2391.21i | −0.145299 | − | 0.145299i | 0.630716 | − | 0.776014i | \(-0.282761\pi\) |
−0.776014 | + | 0.630716i | \(0.782761\pi\) | |||||||
\(648\) | −1022.28 | + | 16104.3i | −0.0619738 | + | 0.976292i | ||||
\(649\) | − | 20946.4i | − | 1.26690i | ||||||
\(650\) | −1822.25 | + | 3795.13i | −0.109961 | + | 0.229011i | ||||
\(651\) | −13808.3 | + | 19973.0i | −0.831322 | + | 1.20246i | ||||
\(652\) | 3242.32 | − | 3242.32i | 0.194753 | − | 0.194753i | ||||
\(653\) | −16623.3 | + | 16623.3i | −0.996201 | + | 0.996201i | −0.999993 | − | 0.00379136i | \(-0.998793\pi\) |
0.00379136 | + | 0.999993i | \(0.498793\pi\) | |||||||
\(654\) | 10296.5 | − | 14893.4i | 0.615636 | − | 0.890484i | ||||
\(655\) | 21577.0 | + | 4911.71i | 1.28715 | + | 0.293002i | ||||
\(656\) | − | 1659.81i | − | 0.0987878i | ||||||
\(657\) | −9740.43 | − | 4401.27i | −0.578403 | − | 0.261354i | ||||
\(658\) | −3952.20 | − | 3952.20i | −0.234153 | − | 0.234153i | ||||
\(659\) | 20089.8 | 1.18754 | 0.593768 | − | 0.804636i | \(-0.297640\pi\) | ||||
0.593768 | + | 0.804636i | \(0.297640\pi\) | |||||||
\(660\) | 374.172 | − | 8631.73i | 0.0220676 | − | 0.509075i | ||||
\(661\) | 541.434 | 0.0318598 | 0.0159299 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159299 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(662\) | 11389.1 | + | 11389.1i | 0.668654 | + | 0.668654i | ||||
\(663\) | −490.931 | − | 2690.22i | −0.0287574 | − | 0.157586i | ||||
\(664\) | − | 4521.93i | − | 0.264284i | ||||||
\(665\) | −8772.76 | + | 5519.36i | −0.511569 | + | 0.321852i | ||||
\(666\) | 7647.80 | − | 2887.41i | 0.444964 | − | 0.167995i | ||||
\(667\) | −4753.99 | + | 4753.99i | −0.275975 | + | 0.275975i | ||||
\(668\) | −15586.7 | + | 15586.7i | −0.902796 | + | 0.902796i | ||||
\(669\) | 17109.1 | + | 11828.3i | 0.988751 | + | 0.683573i | ||||
\(670\) | −1945.12 | + | 8544.86i | −0.112159 | + | 0.492711i | ||||
\(671\) | − | 57.4328i | − | 0.00330428i | ||||||
\(672\) | −17789.7 | + | 3246.40i | −1.02121 | + | 0.186358i | ||||
\(673\) | −24314.3 | − | 24314.3i | −1.39264 | − | 1.39264i | −0.819354 | − | 0.573288i | \(-0.805668\pi\) |
−0.573288 | − | 0.819354i | \(-0.694332\pi\) | |||||||
\(674\) | 6084.03 | 0.347697 | ||||||||
\(675\) | −17459.8 | + | 1643.58i | −0.995599 | + | 0.0937207i | ||||
\(676\) | −9295.71 | −0.528887 | ||||||||
\(677\) | −14662.4 | − | 14662.4i | −0.832380 | − | 0.832380i | 0.155462 | − | 0.987842i | \(-0.450313\pi\) |
−0.987842 | + | 0.155462i | \(0.950313\pi\) | |||||||
\(678\) | 3292.84 | − | 600.902i | 0.186520 | − | 0.0340376i | ||||
\(679\) | 24260.8i | 1.37120i | ||||||||
\(680\) | −1441.70 | + | 6333.36i | −0.0813041 | + | 0.357166i | ||||
\(681\) | 8456.13 | + | 5846.14i | 0.475829 | + | 0.328964i | ||||
\(682\) | −8436.57 | + | 8436.57i | −0.473685 | + | 0.473685i | ||||
\(683\) | −15981.2 | + | 15981.2i | −0.895320 | + | 0.895320i | −0.995018 | − | 0.0996976i | \(-0.968212\pi\) |
0.0996976 | + | 0.995018i | \(0.468212\pi\) | |||||||
\(684\) | −6419.67 | + | 2423.73i | −0.358863 | + | 0.135488i | ||||
\(685\) | 6791.23 | − | 4272.68i | 0.378803 | − | 0.238322i | ||||
\(686\) | 10443.3i | 0.581233i | ||||||||
\(687\) | 3666.36 | + | 20091.1i | 0.203611 | + | 1.11575i | ||||
\(688\) | 167.540 | + | 167.540i | 0.00928400 | + | 0.00928400i | ||||
\(689\) | 4549.75 | 0.251570 | ||||||||
\(690\) | 225.744 | − | 5207.66i | 0.0124550 | − | 0.287322i | ||||
\(691\) | −16714.9 | −0.920209 | −0.460105 | − | 0.887865i | \(-0.652188\pi\) | ||||
−0.460105 | + | 0.887865i | \(0.652188\pi\) | |||||||
\(692\) | 9525.19 | + | 9525.19i | 0.523256 | + | 0.523256i | ||||
\(693\) | 13347.5 | + | 6031.14i | 0.731645 | + | 0.330598i | ||||
\(694\) | − | 19424.1i | − | 1.06243i | ||||||
\(695\) | 746.023 | + | 169.822i | 0.0407169 | + | 0.00926865i | ||||
\(696\) | 8231.98 | − | 11907.1i | 0.448322 | − | 0.648474i | ||||
\(697\) | 7243.96 | − | 7243.96i | 0.393665 | − | 0.393665i | ||||
\(698\) | −3285.13 | + | 3285.13i | −0.178143 | + | 0.178143i | ||||
\(699\) | 8277.19 | − | 11972.5i | 0.447886 | − | 0.647842i | ||||
\(700\) | −4052.37 | − | 11538.3i | −0.218808 | − | 0.623009i | ||||
\(701\) | − | 6990.49i | − | 0.376643i | −0.982107 | − | 0.188322i | \(-0.939695\pi\) | ||
0.982107 | − | 0.188322i | \(-0.0603048\pi\) | |||||||
\(702\) | −2435.44 | − | 4049.11i | −0.130940 | − | 0.217698i | ||||
\(703\) | 6255.06 | + | 6255.06i | 0.335582 | + | 0.335582i | ||||
\(704\) | −7908.75 | −0.423398 | ||||||||
\(705\) | 7542.91 | − | 6916.13i | 0.402954 | − | 0.369470i | ||||
\(706\) | −15056.1 | −0.802611 | ||||||||
\(707\) | −4510.51 | − | 4510.51i | −0.239936 | − | 0.239936i | ||||
\(708\) | −3523.86 | − | 19310.2i | −0.187055 | − | 1.02503i | ||||
\(709\) | 28175.0i | 1.49243i | 0.665705 | + | 0.746215i | \(0.268131\pi\) | ||||
−0.665705 | + | 0.746215i | \(0.731869\pi\) | |||||||
\(710\) | −1717.60 | − | 2730.04i | −0.0907890 | − | 0.144305i | ||||
\(711\) | −457.943 | − | 1212.94i | −0.0241550 | − | 0.0639787i | ||||
\(712\) | 22182.3 | − | 22182.3i | 1.16758 | − | 1.16758i | ||||
\(713\) | 9343.99 | − | 9343.99i | 0.490793 | − | 0.490793i | ||||
\(714\) | −3559.35 | − | 2460.75i | −0.186562 | − | 0.128980i | ||||
\(715\) | 3428.31 | + | 5449.13i | 0.179317 | + | 0.285015i | ||||
\(716\) | − | 4254.90i | − | 0.222085i | ||||||
\(717\) | 15213.6 | − | 2776.28i | 0.792414 | − | 0.144605i | ||||
\(718\) | 10484.1 | + | 10484.1i | 0.544933 | + | 0.544933i | ||||
\(719\) | −20143.8 | −1.04484 | −0.522418 | − | 0.852690i | \(-0.674970\pi\) | ||||
−0.522418 | + | 0.852690i | \(0.674970\pi\) | |||||||
\(720\) | −175.540 | − | 1271.60i | −0.00908609 | − | 0.0658189i | ||||
\(721\) | 24939.2 | 1.28819 | ||||||||
\(722\) | −5286.05 | − | 5286.05i | −0.272474 | − | 0.272474i | ||||
\(723\) | 9382.32 | − | 1712.15i | 0.482617 | − | 0.0880715i | ||||
\(724\) | − | 11985.0i | − | 0.615222i | ||||||
\(725\) | 14181.7 | + | 6809.41i | 0.726477 | + | 0.348821i | ||||
\(726\) | −3635.16 | − | 2513.17i | −0.185831 | − | 0.128475i | ||||
\(727\) | −9805.90 | + | 9805.90i | −0.500249 | + | 0.500249i | −0.911515 | − | 0.411267i | \(-0.865087\pi\) |
0.411267 | + | 0.911515i | \(0.365087\pi\) | |||||||
\(728\) | 5929.00 | − | 5929.00i | 0.301845 | − | 0.301845i | ||||
\(729\) | 9224.92 | − | 17387.4i | 0.468674 | − | 0.883371i | ||||
\(730\) | −7248.57 | − | 1650.04i | −0.367509 | − | 0.0836585i | ||||
\(731\) | 1462.39i | 0.0739926i | ||||||||
\(732\) | −9.66205 | − | 52.9464i | −0.000487868 | − | 0.00267344i | ||||
\(733\) | 16533.1 | + | 16533.1i | 0.833100 | + | 0.833100i | 0.987940 | − | 0.154840i | \(-0.0494861\pi\) |
−0.154840 | + | 0.987940i | \(0.549486\pi\) | |||||||
\(734\) | −14706.3 | −0.739536 | ||||||||
\(735\) | 804.585 | + | 34.8775i | 0.0403776 | + | 0.00175031i | ||||
\(736\) | 9841.37 | 0.492877 | ||||||||
\(737\) | 9476.04 | + | 9476.04i | 0.473615 | + | 0.473615i | ||||
\(738\) | 7288.81 | − | 16130.8i | 0.363557 | − | 0.804586i | ||||
\(739\) | 15250.1i | 0.759114i | 0.925168 | + | 0.379557i | \(0.123924\pi\) | ||||
−0.925168 | + | 0.379557i | \(0.876076\pi\) | |||||||
\(740\) | −8834.41 | + | 5558.14i | −0.438864 | + | 0.276110i | ||||
\(741\) | 2907.72 | − | 4205.85i | 0.144153 | − | 0.208510i | ||||
\(742\) | 5090.66 | − | 5090.66i | 0.251865 | − | 0.251865i | ||||
\(743\) | −5438.49 | + | 5438.49i | −0.268531 | + | 0.268531i | −0.828508 | − | 0.559977i | \(-0.810810\pi\) |
0.559977 | + | 0.828508i | \(0.310810\pi\) | |||||||
\(744\) | −16180.0 | + | 23403.5i | −0.797294 | + | 1.15324i | ||||
\(745\) | 901.693 | − | 3961.11i | 0.0443429 | − | 0.194797i | ||||
\(746\) | − | 8514.27i | − | 0.417868i | ||||||
\(747\) | −2271.20 | + | 5026.38i | −0.111243 | + | 0.246192i | ||||
\(748\) | 2760.04 | + | 2760.04i | 0.134916 | + | 0.134916i | ||||
\(749\) | −15927.5 | −0.777009 | ||||||||
\(750\) | −11672.2 | + | 3539.54i | −0.568278 | + | 0.172328i | ||||
\(751\) | 2087.82 | 0.101446 | 0.0507228 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507228 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(752\) | 529.676 | + | 529.676i | 0.0256852 | + | 0.0256852i | ||||
\(753\) | 1438.55 | + | 7883.01i | 0.0696197 | + | 0.381505i | ||||
\(754\) | 4238.72i | 0.204728i | ||||||||
\(755\) | 5169.46 | − | 22709.3i | 0.249187 | − | 1.09467i | ||||
\(756\) | 13319.5 | + | 3314.54i | 0.640774 | + | 0.159456i | ||||
\(757\) | −10258.6 | + | 10258.6i | −0.492546 | + | 0.492546i | −0.909107 | − | 0.416562i | \(-0.863235\pi\) |
0.416562 | + | 0.909107i | \(0.363235\pi\) | |||||||
\(758\) | 8444.86 | − | 8444.86i | 0.404658 | − | 0.404658i | ||||
\(759\) | −6556.70 | − | 4532.98i | −0.313561 | − | 0.216781i | ||||
\(760\) | −10279.5 | + | 6467.35i | −0.490629 | + | 0.308678i | ||||
\(761\) | 26879.5i | 1.28040i | 0.768210 | + | 0.640198i | \(0.221148\pi\) | ||||
−0.768210 | + | 0.640198i | \(0.778852\pi\) | |||||||
\(762\) | −1282.05 | + | 233.958i | −0.0609498 | + | 0.0111226i | ||||
\(763\) | −27712.1 | − | 27712.1i | −1.31487 | − | 1.31487i | ||||
\(764\) | −4822.43 | −0.228363 | ||||||||
\(765\) | 4783.54 | − | 6315.77i | 0.226078 | − | 0.298493i | ||||
\(766\) | 4028.02 | 0.189998 | ||||||||
\(767\) | 10342.4 | + | 10342.4i | 0.486888 | + | 0.486888i | ||||
\(768\) | −19944.6 | + | 3639.64i | −0.937097 | + | 0.171008i | ||||
\(769\) | − | 25180.9i | − | 1.18082i | −0.807105 | − | 0.590408i | \(-0.798967\pi\) | ||
0.807105 | − | 0.590408i | \(-0.201033\pi\) | |||||||
\(770\) | 9932.85 | + | 2261.08i | 0.464877 | + | 0.105823i | ||||
\(771\) | 2592.23 | + | 1792.14i | 0.121085 | + | 0.0837124i | ||||
\(772\) | −13585.7 | + | 13585.7i | −0.633369 | + | 0.633369i | ||||
\(773\) | 18871.2 | − | 18871.2i | 0.878072 | − | 0.878072i | −0.115263 | − | 0.993335i | \(-0.536771\pi\) |
0.993335 | + | 0.115263i | \(0.0367711\pi\) | |||||||
\(774\) | 892.506 | + | 2363.96i | 0.0414476 | + | 0.109781i | ||||
\(775\) | −27874.2 | − | 13383.9i | −1.29196 | − | 0.620341i | ||||
\(776\) | 28427.7i | 1.31507i | ||||||||
\(777\) | −3176.52 | − | 17406.8i | −0.146663 | − | 0.803688i | ||||
\(778\) | 14682.1 | + | 14682.1i | 0.676581 | + | 0.676581i | ||||
\(779\) | 19154.7 | 0.880988 | ||||||||
\(780\) | 4077.22 | + | 4446.72i | 0.187164 | + | 0.204126i | ||||
\(781\) | −4932.32 | −0.225982 | ||||||||
\(782\) | 1665.18 | + | 1665.18i | 0.0761465 | + | 0.0761465i | ||||
\(783\) | −15130.8 | + | 9100.79i | −0.690588 | + | 0.415371i | ||||
\(784\) | 58.9485i | 0.00268533i | ||||||||
\(785\) | −10175.6 | − | 16173.6i | −0.462653 | − | 0.735365i | ||||
\(786\) | −9823.43 | + | 14209.0i | −0.445789 | + | 0.644809i | ||||
\(787\) | 14716.0 | − | 14716.0i | 0.666542 | − | 0.666542i | −0.290372 | − | 0.956914i | \(-0.593779\pi\) |
0.956914 | + | 0.290372i | \(0.0937789\pi\) | |||||||
\(788\) | 15511.1 | − | 15511.1i | 0.701217 | − | 0.701217i | ||||
\(789\) | −21968.5 | + | 31776.2i | −0.991253 | + | 1.43379i | ||||
\(790\) | −480.189 | − | 763.238i | −0.0216258 | − | 0.0343731i | ||||
\(791\) | − | 7245.10i | − | 0.325672i | ||||||
\(792\) | 15640.0 | + | 7067.03i | 0.701697 | + | 0.317066i | ||||
\(793\) | 28.3578 | + | 28.3578i | 0.00126988 | + | 0.00126988i | ||||
\(794\) | 3183.22 | 0.142277 | ||||||||
\(795\) | 8908.37 | + | 9715.69i | 0.397418 | + | 0.433434i | ||||
\(796\) | 566.871 | 0.0252415 | ||||||||
\(797\) | 17463.9 | + | 17463.9i | 0.776163 | + | 0.776163i | 0.979176 | − | 0.203013i | \(-0.0650735\pi\) |
−0.203013 | + | 0.979176i | \(0.565073\pi\) | |||||||
\(798\) | −1452.47 | − | 7959.28i | −0.0644321 | − | 0.353077i | ||||
\(799\) | 4623.35i | 0.204709i | ||||||||
\(800\) | −7630.82 | − | 21727.2i | −0.337238 | − | 0.960214i | ||||
\(801\) | −35798.1 | + | 13515.5i | −1.57911 | + | 0.596188i | ||||
\(802\) | −2709.42 | + | 2709.42i | −0.119293 | + | 0.119293i | ||||
\(803\) | −8038.49 | + | 8038.49i | −0.353265 | + | 0.353265i | ||||
\(804\) | 10330.0 | + | 7141.64i | 0.453122 | + | 0.313266i | ||||
\(805\) | −11001.2 | − | 2504.28i | −0.481667 | − | 0.109645i | ||||
\(806\) | − | 8331.22i | − | 0.364088i | ||||||
\(807\) | 9867.40 | − | 1800.68i | 0.430420 | − | 0.0785462i | ||||
\(808\) | −5285.22 | − | 5285.22i | −0.230115 | − | 0.230115i | ||||
\(809\) | −24097.9 | −1.04727 | −0.523633 | − | 0.851944i | \(-0.675424\pi\) | ||||
−0.523633 | + | 0.851944i | \(0.675424\pi\) | |||||||
\(810\) | 3878.04 | − | 13128.8i | 0.168223 | − | 0.569506i | ||||
\(811\) | 25302.7 | 1.09556 | 0.547780 | − | 0.836622i | \(-0.315473\pi\) | ||||
0.547780 | + | 0.836622i | \(0.315473\pi\) | |||||||
\(812\) | −8706.47 | − | 8706.47i | −0.376277 | − | 0.376277i | ||||
\(813\) | −16672.8 | + | 3042.57i | −0.719238 | + | 0.131252i | ||||
\(814\) | − | 8694.39i | − | 0.374371i | ||||||
\(815\) | −8378.61 | + | 5271.38i | −0.360110 | + | 0.226562i | ||||
\(816\) | 477.025 | + | 329.791i | 0.0204647 | + | 0.0141483i | ||||
\(817\) | −1933.46 | + | 1933.46i | −0.0827945 | + | 0.0827945i | ||||
\(818\) | −5480.85 | + | 5480.85i | −0.234271 | + | 0.234271i | ||||
\(819\) | −9568.33 | + | 3612.50i | −0.408235 | + | 0.154128i | ||||
\(820\) | −5016.42 | + | 22037.0i | −0.213635 | + | 0.938494i | ||||
\(821\) | − | 27925.3i | − | 1.18709i | −0.804802 | − | 0.593544i | \(-0.797728\pi\) | ||
0.804802 | − | 0.593544i | \(-0.202272\pi\) | |||||||
\(822\) | 1124.39 | + | 6161.50i | 0.0477102 | + | 0.261444i | ||||
\(823\) | 997.907 | + | 997.907i | 0.0422659 | + | 0.0422659i | 0.727924 | − | 0.685658i | \(-0.240485\pi\) |
−0.685658 | + | 0.727924i | \(0.740485\pi\) | |||||||
\(824\) | 29222.6 | 1.23546 | ||||||||
\(825\) | −4923.67 | + | 17990.3i | −0.207782 | + | 0.759200i | ||||
\(826\) | 23144.0 | 0.974918 | ||||||||
\(827\) | −18683.3 | − | 18683.3i | −0.785590 | − | 0.785590i | 0.195178 | − | 0.980768i | \(-0.437471\pi\) |
−0.980768 | + | 0.195178i | \(0.937471\pi\) | |||||||
\(828\) | −6807.11 | − | 3075.83i | −0.285705 | − | 0.129097i | ||||
\(829\) | 21146.9i | 0.885962i | 0.896531 | + | 0.442981i | \(0.146079\pi\) | ||||
−0.896531 | + | 0.442981i | \(0.853921\pi\) | |||||||
\(830\) | −851.473 | + | 3740.49i | −0.0356085 | + | 0.156427i | ||||
\(831\) | 20332.8 | − | 29410.2i | 0.848780 | − | 1.22771i | ||||
\(832\) | 3904.99 | − | 3904.99i | 0.162718 | − | 0.162718i | ||||
\(833\) | −257.270 | + | 257.270i | −0.0107009 | + | 0.0107009i | ||||
\(834\) | −339.644 | + | 491.276i | −0.0141018 | + | 0.0203975i | ||||
\(835\) | 40278.2 | − | 25340.9i | 1.66932 | − | 1.05025i | ||||
\(836\) | 7298.19i | 0.301930i | ||||||||
\(837\) | 29739.6 | − | 17887.6i | 1.22814 | − | 0.738695i | ||||
\(838\) | 2544.31 | + | 2544.31i | 0.104883 | + | 0.104883i | ||||
\(839\) | 30903.4 | 1.27164 | 0.635820 | − | 0.771838i | \(-0.280662\pi\) | ||||
0.635820 | + | 0.771838i | \(0.280662\pi\) | |||||||
\(840\) | 24269.9 | + | 1052.06i | 0.996894 | + | 0.0432138i | ||||
\(841\) | −8549.68 | −0.350555 | ||||||||
\(842\) | 10557.5 | + | 10557.5i | 0.432109 | + | 0.432109i | ||||
\(843\) | 3714.48 | + | 20354.7i | 0.151760 | + | 0.831618i | ||||
\(844\) | − | 14060.4i | − | 0.573435i | ||||||
\(845\) | 19567.2 | + | 4454.21i | 0.796607 | + | 0.181337i | ||||
\(846\) | 2821.65 | + | 7473.63i | 0.114669 | + | 0.303722i | ||||
\(847\) | −6763.96 | + | 6763.96i | −0.274395 | + | 0.274395i | ||||
\(848\) | −682.252 | + | 682.252i | −0.0276281 | + | 0.0276281i | ||||
\(849\) | −24738.3 | − | 17102.8i | −1.00002 | − | 0.691364i | ||||
\(850\) | 2385.12 | − | 4967.42i | 0.0962460 | − | 0.200448i | ||||
\(851\) | 9629.53i | 0.387892i | ||||||||
\(852\) | −4547.02 | + | 829.774i | −0.182839 | + | 0.0333657i | ||||
\(853\) | 181.224 | + | 181.224i | 0.00727432 | + | 0.00727432i | 0.710735 | − | 0.703460i | \(-0.248363\pi\) |
−0.703460 | + | 0.710735i | \(0.748363\pi\) | |||||||
\(854\) | 63.4584 | 0.00254274 | ||||||||
\(855\) | 14674.6 | − | 2025.78i | 0.586971 | − | 0.0810295i | ||||
\(856\) | −18663.2 | −0.745205 | ||||||||
\(857\) | −13852.9 | − | 13852.9i | −0.552167 | − | 0.552167i | 0.374899 | − | 0.927066i | \(-0.377677\pi\) |
−0.927066 | + | 0.374899i | \(0.877677\pi\) | |||||||
\(858\) | −4943.85 | + | 902.189i | −0.196713 | + | 0.0358977i | ||||
\(859\) | − | 8910.47i | − | 0.353925i | −0.984218 | − | 0.176962i | \(-0.943373\pi\) | ||
0.984218 | − | 0.176962i | \(-0.0566271\pi\) | |||||||
\(860\) | −1718.04 | − | 2730.74i | −0.0681216 | − | 0.108276i | ||||
\(861\) | −31515.9 | − | 21788.5i | −1.24746 | − | 0.862428i | ||||
\(862\) | −18655.0 | + | 18655.0i | −0.737112 | + | 0.737112i | ||||
\(863\) | −6487.75 | + | 6487.75i | −0.255905 | + | 0.255905i | −0.823386 | − | 0.567481i | \(-0.807918\pi\) |
0.567481 | + | 0.823386i | \(0.307918\pi\) | |||||||
\(864\) | 25081.2 | + | 6241.43i | 0.987594 | + | 0.245761i | ||||
\(865\) | −15486.1 | − | 24614.4i | −0.608720 | − | 0.967533i | ||||
\(866\) | − | 12900.0i | − | 0.506187i | ||||||
\(867\) | −3940.40 | − | 21592.8i | −0.154352 | − | 0.845823i | ||||
\(868\) | 17112.6 | + | 17112.6i | 0.669170 | + | 0.669170i | ||||
\(869\) | −1378.93 | −0.0538285 | ||||||||
\(870\) | −9051.50 | + | 8299.37i | −0.352729 | + | 0.323419i | ||||
\(871\) | −9357.71 | −0.364034 | ||||||||
\(872\) | −32471.9 | − | 32471.9i | −1.26105 | − | 1.26105i | ||||
\(873\) | 14278.2 | − | 31599.0i | 0.553543 | − | 1.22504i | ||||
\(874\) | 4403.12i | 0.170409i | ||||||||
\(875\) | 3001.35 | + | 26229.5i | 0.115959 | + | 1.01339i | ||||
\(876\) | −6058.22 | + | 8762.89i | −0.233662 | + | 0.337980i | ||||
\(877\) | −20231.6 | + | 20231.6i | −0.778987 | + | 0.778987i | −0.979659 | − | 0.200672i | \(-0.935688\pi\) |
0.200672 | + | 0.979659i | \(0.435688\pi\) | |||||||
\(878\) | −9764.88 | + | 9764.88i | −0.375340 | + | 0.375340i | ||||
\(879\) | 18869.2 | − | 27293.3i | 0.724054 | − | 1.04730i | ||||
\(880\) | −1331.20 | − | 303.031i | −0.0509942 | − | 0.0116081i | ||||
\(881\) | 33209.0i | 1.26996i | 0.772527 | + | 0.634982i | \(0.218993\pi\) | ||||
−0.772527 | + | 0.634982i | \(0.781007\pi\) | |||||||
\(882\) | −258.863 | + | 572.889i | −0.00988251 | + | 0.0218709i | ||||
\(883\) | 26984.3 | + | 26984.3i | 1.02842 | + | 1.02842i | 0.999584 | + | 0.0288331i | \(0.00917914\pi\) |
0.0288331 | + | 0.999584i | \(0.490821\pi\) | |||||||
\(884\) | −2725.57 | −0.103700 | ||||||||
\(885\) | −1835.19 | + | 42335.9i | −0.0697055 | + | 1.60803i | ||||
\(886\) | 4656.90 | 0.176582 | ||||||||
\(887\) | 24008.9 | + | 24008.9i | 0.908838 | + | 0.908838i | 0.996179 | − | 0.0873406i | \(-0.0278369\pi\) |
−0.0873406 | + | 0.996179i | \(0.527837\pi\) | |||||||
\(888\) | −3722.11 | − | 20396.5i | −0.140660 | − | 0.770792i | ||||
\(889\) | 2820.84i | 0.106421i | ||||||||
\(890\) | −22525.8 | + | 14172.1i | −0.848390 | + | 0.533762i | ||||
\(891\) | −13835.3 | − | 15710.8i | −0.520200 | − | 0.590720i | ||||
\(892\) | 14658.8 | − | 14658.8i | 0.550240 | − | 0.550240i | ||||
\(893\) | −6112.61 | + | 6112.61i | −0.229060 | + | 0.229060i | ||||
\(894\) | 2608.50 | + | 1803.39i | 0.0975853 | + | 0.0674656i | ||||
\(895\) | −2038.81 | + | 8956.44i | −0.0761452 | + | 0.334504i | ||||
\(896\) | 19102.9i | 0.712258i | ||||||||
\(897\) | 5475.59 | − | 999.226i | 0.203818 | − | 0.0371942i | ||||
\(898\) | −21198.9 | − | 21198.9i | −0.787768 | − | 0.787768i | ||||
\(899\) | −31132.2 | −1.15497 | ||||||||
\(900\) | −1512.52 | + | 17413.3i | −0.0560191 | + | 0.644935i | ||||
\(901\) | −5955.13 | −0.220193 | ||||||||
\(902\) | −13312.3 | − | 13312.3i | −0.491409 | − | 0.491409i | ||||
\(903\) | 5380.49 | − | 981.871i | 0.198285 | − | 0.0361845i | ||||
\(904\) | − | 8489.50i | − | 0.312341i | ||||||
\(905\) | −5742.86 | + | 25228.2i | −0.210938 | + | 0.926645i | ||||
\(906\) | 14954.7 | + | 10338.9i | 0.548384 | + | 0.379125i | ||||
\(907\) | −23026.7 | + | 23026.7i | −0.842989 | + | 0.842989i | −0.989246 | − | 0.146258i | \(-0.953277\pi\) |
0.146258 | + | 0.989246i | \(0.453277\pi\) | |||||||
\(908\) | 7245.11 | − | 7245.11i | 0.264799 | − | 0.264799i | ||||
\(909\) | 3220.25 | + | 8529.38i | 0.117501 | + | 0.311223i | ||||
\(910\) | −6020.83 | + | 3787.99i | −0.219328 | + | 0.137990i | ||||
\(911\) | − | 33422.1i | − | 1.21550i | −0.794127 | − | 0.607752i | \(-0.792071\pi\) | ||
0.794127 | − | 0.607752i | \(-0.207929\pi\) | |||||||
\(912\) | 194.660 | + | 1066.71i | 0.00706781 | + | 0.0387304i | ||||
\(913\) | 4148.12 | + | 4148.12i | 0.150364 | + | 0.150364i | ||||
\(914\) | 15075.7 | 0.545581 | ||||||||
\(915\) | −5.03191 | + | 116.080i | −0.000181803 | + | 0.00419399i | ||||
\(916\) | 20355.1 | 0.734226 | ||||||||
\(917\) | 26438.8 | + | 26438.8i | 0.952112 | + | 0.952112i | ||||
\(918\) | 3187.73 | + | 5299.85i | 0.114609 | + | 0.190546i | ||||
\(919\) | − | 42542.2i | − | 1.52703i | −0.645792 | − | 0.763513i | \(-0.723473\pi\) | ||
0.645792 | − | 0.763513i | \(-0.276527\pi\) | |||||||
\(920\) | −12890.7 | − | 2934.40i | −0.461951 | − | 0.105157i | ||||
\(921\) | 7651.86 | − | 11068.0i | 0.273765 | − | 0.395986i | ||||
\(922\) | −10508.7 | + | 10508.7i | −0.375363 | + | 0.375363i | ||||
\(923\) | 2435.36 | − | 2435.36i | 0.0868482 | − | 0.0868482i | ||||
\(924\) | 8301.70 | − | 12007.9i | 0.295569 | − | 0.427524i | ||||
\(925\) | 21259.5 | − | 7466.56i | 0.755684 | − | 0.265404i | ||||
\(926\) | − | 3157.84i | − | 0.112066i | ||||||
\(927\) | −32482.6 | − | 14677.4i | −1.15088 | − | 0.520033i | ||||
\(928\) | −16394.7 | − | 16394.7i | −0.579938 | − | 0.579938i | ||||
\(929\) | 5721.21 | 0.202053 | 0.101026 | − | 0.994884i | \(-0.467787\pi\) | ||||
0.101026 | + | 0.994884i | \(0.467787\pi\) | |||||||
\(930\) | 17790.8 | − | 16312.4i | 0.627292 | − | 0.575168i | ||||
\(931\) | −680.282 | −0.0239477 | ||||||||
\(932\) | −10257.9 | − | 10257.9i | −0.360524 | − | 0.360524i | ||||
\(933\) | 3740.83 | + | 20499.1i | 0.131264 | + | 0.719305i | ||||
\(934\) | 3515.38i | 0.123155i | ||||||||
\(935\) | −4487.28 | − | 7132.32i | −0.156952 | − | 0.249467i | ||||
\(936\) | −11211.8 | + | 4232.97i | −0.391525 | + | 0.147819i | ||||
\(937\) | 1344.01 | − | 1344.01i | 0.0468589 | − | 0.0468589i | −0.683289 | − | 0.730148i | \(-0.739451\pi\) |
0.730148 | + | 0.683289i | \(0.239451\pi\) | |||||||
\(938\) | −10470.2 | + | 10470.2i | −0.364461 | + | 0.364461i | ||||
\(939\) | 36706.8 | + | 25377.2i | 1.27570 | + | 0.881953i | ||||
\(940\) | −5431.56 | − | 8633.22i | −0.188466 | − | 0.299558i | ||||
\(941\) | − | 9625.77i | − | 0.333466i | −0.986002 | − | 0.166733i | \(-0.946678\pi\) | ||
0.986002 | − | 0.166733i | \(-0.0533217\pi\) | |||||||
\(942\) | 14673.9 | − | 2677.80i | 0.507538 | − | 0.0926192i | ||||
\(943\) | 14744.1 | + | 14744.1i | 0.509157 | + | 0.509157i | ||||
\(944\) | −3101.77 | −0.106943 | ||||||||
\(945\) | −26448.9 | − | 13359.3i | −0.910459 | − | 0.459870i | ||||
\(946\) | 2687.46 | 0.0923645 | ||||||||
\(947\) | −2234.24 | − | 2234.24i | −0.0766664 | − | 0.0766664i | 0.667734 | − | 0.744400i | \(-0.267264\pi\) |
−0.744400 | + | 0.667734i | \(0.767264\pi\) | |||||||
\(948\) | −1271.21 | + | 231.980i | −0.0435518 | + | 0.00794765i | ||||
\(949\) | − | 7938.11i | − | 0.271530i | ||||||
\(950\) | 9720.93 | − | 3414.10i | 0.331988 | − | 0.116598i | ||||
\(951\) | −18811.3 | − | 13005.2i | −0.641427 | − | 0.443451i | ||||
\(952\) | −7760.41 | + | 7760.41i | −0.264198 | + | 0.264198i | ||||
\(953\) | 6457.14 | − | 6457.14i | 0.219483 | − | 0.219483i | −0.588798 | − | 0.808281i | \(-0.700398\pi\) |
0.808281 | + | 0.588798i | \(0.200398\pi\) | |||||||
\(954\) | −9626.45 | + | 3634.44i | −0.326696 | + | 0.123343i | ||||
\(955\) | 10151.1 | + | 2310.75i | 0.343959 | + | 0.0782977i | ||||
\(956\) | − | 15413.5i | − | 0.521451i | ||||||
\(957\) | 3371.32 | + | 18474.3i | 0.113876 | + | 0.624021i | ||||
\(958\) | 5985.35 | + | 5985.35i | 0.201856 | + | 0.201856i | ||||
\(959\) | 13556.9 | 0.456491 | ||||||||
\(960\) | 15984.8 | + | 692.916i | 0.537403 | + | 0.0232956i | ||||
\(961\) | 31399.6 | 1.05399 | ||||||||
\(962\) | 4292.91 | + | 4292.91i | 0.143876 | + | 0.143876i | ||||
\(963\) | 20745.2 | + | 9373.84i | 0.694190 | + | 0.313674i | ||||
\(964\) | − | 9505.61i | − | 0.317588i | ||||||
\(965\) | 35107.4 | − | 22087.7i | 1.17114 | − | 0.736817i | ||||
\(966\) | 5008.55 | − | 7244.59i | 0.166819 | − | 0.241295i | ||||
\(967\) | 13166.9 | − | 13166.9i | 0.437869 | − | 0.437869i | −0.453425 | − | 0.891294i | \(-0.649798\pi\) |
0.891294 | + | 0.453425i | \(0.149798\pi\) | |||||||
\(968\) | −7925.72 | + | 7925.72i | −0.263163 | + | 0.263163i | ||||
\(969\) | −3805.89 | + | 5505.01i | −0.126174 | + | 0.182504i | ||||
\(970\) | 5352.90 | − | 23515.1i | 0.177187 | − | 0.778376i | ||||
\(971\) | − | 21504.3i | − | 0.710716i | −0.934730 | − | 0.355358i | \(-0.884359\pi\) | ||
0.934730 | − | 0.355358i | \(-0.115641\pi\) | |||||||
\(972\) | −15397.6 | − | 12156.0i | −0.508104 | − | 0.401136i | ||||
\(973\) | 914.119 | + | 914.119i | 0.0301185 | + | 0.0301185i | ||||
\(974\) | −3071.14 | −0.101032 | ||||||||
\(975\) | −6451.71 | − | 11313.9i | −0.211918 | − | 0.371625i | ||||
\(976\) | −8.50472 | −0.000278924 | ||||||||
\(977\) | −8996.19 | − | 8996.19i | −0.294589 | − | 0.294589i | 0.544301 | − | 0.838890i | \(-0.316795\pi\) |
−0.838890 | + | 0.544301i | \(0.816795\pi\) | |||||||
\(978\) | −1387.21 | − | 7601.68i | −0.0453559 | − | 0.248543i | ||||
\(979\) | 40697.1i | 1.32858i | ||||||||
\(980\) | 178.159 | − | 782.646i | 0.00580722 | − | 0.0255109i | ||||
\(981\) | 19784.9 | + | 52403.7i | 0.643917 | + | 1.70553i | ||||
\(982\) | 16467.8 | − | 16467.8i | 0.535142 | − | 0.535142i | ||||
\(983\) | −16337.3 | + | 16337.3i | −0.530090 | + | 0.530090i | −0.920599 | − | 0.390509i | \(-0.872299\pi\) |
0.390509 | + | 0.920599i | \(0.372299\pi\) | |||||||
\(984\) | −36929.0 | − | 25530.8i | −1.19639 | − | 0.827128i | ||||
\(985\) | −40082.8 | + | 25218.0i | −1.29659 | + | 0.815748i | ||||
\(986\) | − | 5548.02i | − | 0.179194i | ||||||
\(987\) | 17010.4 | − | 3104.18i | 0.548578 | − | 0.100108i | ||||
\(988\) | −3603.53 | − | 3603.53i | −0.116036 | − | 0.116036i | ||||
\(989\) | −2976.52 | −0.0957004 | ||||||||
\(990\) | −11606.6 | − | 8790.77i | −0.372607 | − | 0.282211i | ||||
\(991\) | −18296.9 | −0.586500 | −0.293250 | − | 0.956036i | \(-0.594737\pi\) | ||||
−0.293250 | + | 0.956036i | \(0.594737\pi\) | |||||||
\(992\) | 32223.9 | + | 32223.9i | 1.03136 | + | 1.03136i | ||||
\(993\) | −49018.8 | + | 8945.31i | −1.56653 | + | 0.285872i | ||||
\(994\) | − | 5449.79i | − | 0.173900i | ||||||
\(995\) | −1193.25 | − | 271.627i | −0.0380186 | − | 0.00865441i | ||||
\(996\) | 4521.93 | + | 3126.24i | 0.143858 | + | 0.0994564i | ||||
\(997\) | 20406.0 | − | 20406.0i | 0.648210 | − | 0.648210i | −0.304350 | − | 0.952560i | \(-0.598439\pi\) |
0.952560 | + | 0.304350i | \(0.0984393\pi\) | |||||||
\(998\) | 12926.9 | − | 12926.9i | 0.410015 | − | 0.410015i | ||||
\(999\) | −6107.09 | + | 24541.4i | −0.193413 | + | 0.777232i |
(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 | 15.4.e.a.8.2 | yes | 8 | |
3.2 | odd | 2 | inner | 15.4.e.a.8.3 | yes | 8 | |
4.3 | odd | 2 | 240.4.v.c.113.1 | 8 | |||
5.2 | odd | 4 | inner | 15.4.e.a.2.3 | yes | 8 | |
5.3 | odd | 4 | 75.4.e.c.32.2 | 8 | |||
5.4 | even | 2 | 75.4.e.c.68.3 | 8 | |||
12.11 | even | 2 | 240.4.v.c.113.2 | 8 | |||
15.2 | even | 4 | inner | 15.4.e.a.2.2 | ✓ | 8 | |
15.8 | even | 4 | 75.4.e.c.32.3 | 8 | |||
15.14 | odd | 2 | 75.4.e.c.68.2 | 8 | |||
20.7 | even | 4 | 240.4.v.c.17.2 | 8 | |||
60.47 | odd | 4 | 240.4.v.c.17.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.e.a.2.2 | ✓ | 8 | 15.2 | even | 4 | inner | |
15.4.e.a.2.3 | yes | 8 | 5.2 | odd | 4 | inner | |
15.4.e.a.8.2 | yes | 8 | 1.1 | even | 1 | trivial | |
15.4.e.a.8.3 | yes | 8 | 3.2 | odd | 2 | inner | |
75.4.e.c.32.2 | 8 | 5.3 | odd | 4 | |||
75.4.e.c.32.3 | 8 | 15.8 | even | 4 | |||
75.4.e.c.68.2 | 8 | 15.14 | odd | 2 | |||
75.4.e.c.68.3 | 8 | 5.4 | even | 2 | |||
240.4.v.c.17.1 | 8 | 60.47 | odd | 4 | |||
240.4.v.c.17.2 | 8 | 20.7 | even | 4 | |||
240.4.v.c.113.1 | 8 | 4.3 | odd | 2 | |||
240.4.v.c.113.2 | 8 | 12.11 | even | 2 |