Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(47,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.17 | ||
Character | \(\chi\) | \(=\) | 63.47 |
Dual form | 63.4.s.a.59.17 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52419 | − | 1.45734i | 0.892435 | − | 0.515248i | 0.0176967 | − | 0.999843i | \(-0.494367\pi\) |
0.874738 | + | 0.484596i | \(0.161033\pi\) | |||||||
\(3\) | −4.29460 | + | 2.92513i | −0.826497 | + | 0.562941i | ||||
\(4\) | 0.247680 | − | 0.428994i | 0.0309600 | − | 0.0536243i | ||||
\(5\) | 17.2113 | 1.53943 | 0.769715 | − | 0.638388i | \(-0.220398\pi\) | ||||
0.769715 | + | 0.638388i | \(0.220398\pi\) | |||||||
\(6\) | −6.57748 | + | 13.6423i | −0.447541 | + | 0.928239i | ||||
\(7\) | 17.7231 | − | 5.37495i | 0.956960 | − | 0.290220i | ||||
\(8\) | 21.8736i | 0.966687i | ||||||||
\(9\) | 9.88725 | − | 25.1245i | 0.366194 | − | 0.930538i | ||||
\(10\) | 43.4446 | − | 25.0828i | 1.37384 | − | 0.793187i | ||||
\(11\) | 35.6923i | 0.978331i | 0.872191 | + | 0.489165i | \(0.162699\pi\) | ||||
−0.872191 | + | 0.489165i | \(0.837301\pi\) | |||||||
\(12\) | 0.191176 | + | 2.56686i | 0.00459898 | + | 0.0617489i | ||||
\(13\) | −8.99430 | + | 5.19286i | −0.191890 | + | 0.110788i | −0.592867 | − | 0.805300i | \(-0.702004\pi\) |
0.400977 | + | 0.916088i | \(0.368671\pi\) | |||||||
\(14\) | 36.9034 | − | 39.3960i | 0.704489 | − | 0.752074i | ||||
\(15\) | −73.9159 | + | 50.3454i | −1.27233 | + | 0.866608i | ||||
\(16\) | 33.8587 | + | 58.6451i | 0.529043 | + | 0.916329i | ||||
\(17\) | −64.1402 | − | 111.094i | −0.915075 | − | 1.58496i | −0.806791 | − | 0.590837i | \(-0.798798\pi\) |
−0.108285 | − | 0.994120i | \(-0.534536\pi\) | |||||||
\(18\) | −11.6577 | − | 77.8281i | −0.152653 | − | 1.01913i | ||||
\(19\) | −84.7576 | − | 48.9348i | −1.02341 | − | 0.590864i | −0.108317 | − | 0.994116i | \(-0.534546\pi\) |
−0.915089 | + | 0.403253i | \(0.867880\pi\) | |||||||
\(20\) | 4.26290 | − | 7.38356i | 0.0476607 | − | 0.0825508i | ||||
\(21\) | −60.3915 | + | 74.9258i | −0.627548 | + | 0.778578i | ||||
\(22\) | 52.0158 | + | 90.0941i | 0.504082 | + | 0.873096i | ||||
\(23\) | − | 25.5640i | − | 0.231759i | −0.993263 | − | 0.115880i | \(-0.963031\pi\) | ||
0.993263 | − | 0.115880i | \(-0.0369687\pi\) | |||||||
\(24\) | −63.9832 | − | 93.9386i | −0.544188 | − | 0.798964i | ||||
\(25\) | 171.230 | 1.36984 | ||||||||
\(26\) | −15.1355 | + | 26.2155i | −0.114166 | + | 0.197742i | ||||
\(27\) | 31.0307 | + | 136.821i | 0.221180 | + | 0.975233i | ||||
\(28\) | 2.08385 | − | 8.93439i | 0.0140646 | − | 0.0603015i | ||||
\(29\) | −14.1366 | − | 8.16176i | −0.0905206 | − | 0.0522621i | 0.454056 | − | 0.890973i | \(-0.349976\pi\) |
−0.544577 | + | 0.838711i | \(0.683310\pi\) | |||||||
\(30\) | −113.207 | + | 234.802i | −0.688957 | + | 1.42896i | ||||
\(31\) | 160.589 | + | 92.7160i | 0.930406 | + | 0.537170i | 0.886940 | − | 0.461884i | \(-0.152827\pi\) |
0.0434664 | + | 0.999055i | \(0.486160\pi\) | |||||||
\(32\) | 19.3867 | + | 11.1929i | 0.107097 | + | 0.0618327i | ||||
\(33\) | −104.405 | − | 153.284i | −0.550743 | − | 0.808587i | ||||
\(34\) | −323.804 | − | 186.948i | −1.63329 | − | 0.942981i | ||||
\(35\) | 305.039 | − | 92.5101i | 1.47317 | − | 0.446773i | ||||
\(36\) | −8.32941 | − | 10.4644i | −0.0385621 | − | 0.0484464i | ||||
\(37\) | −0.462855 | + | 0.801688i | −0.00205656 | + | 0.00356207i | −0.867052 | − | 0.498218i | \(-0.833988\pi\) |
0.864995 | + | 0.501780i | \(0.167321\pi\) | |||||||
\(38\) | −285.259 | −1.21776 | ||||||||
\(39\) | 23.4372 | − | 48.6108i | 0.0962295 | − | 0.199589i | ||||
\(40\) | 376.474i | 1.48815i | ||||||||
\(41\) | −231.546 | − | 401.049i | −0.881984 | − | 1.52764i | −0.849132 | − | 0.528181i | \(-0.822874\pi\) |
−0.0328523 | − | 0.999460i | \(-0.510459\pi\) | |||||||
\(42\) | −43.2471 | + | 277.138i | −0.158885 | + | 1.01817i | ||||
\(43\) | −43.2469 | + | 74.9058i | −0.153374 | + | 0.265652i | −0.932466 | − | 0.361258i | \(-0.882347\pi\) |
0.779092 | + | 0.626910i | \(0.215681\pi\) | |||||||
\(44\) | 15.3118 | + | 8.84027i | 0.0524623 | + | 0.0302891i | ||||
\(45\) | 170.173 | − | 432.427i | 0.563730 | − | 1.43250i | ||||
\(46\) | −37.2555 | − | 64.5283i | −0.119413 | − | 0.206830i | ||||
\(47\) | −143.746 | − | 248.976i | −0.446118 | − | 0.772698i | 0.552012 | − | 0.833836i | \(-0.313860\pi\) |
−0.998129 | + | 0.0611380i | \(0.980527\pi\) | |||||||
\(48\) | −316.954 | − | 152.816i | −0.953092 | − | 0.459523i | ||||
\(49\) | 285.220 | − | 190.522i | 0.831545 | − | 0.555458i | ||||
\(50\) | 432.217 | − | 249.541i | 1.22250 | − | 0.705808i | ||||
\(51\) | 600.421 | + | 289.487i | 1.64854 | + | 0.794828i | ||||
\(52\) | 5.14467i | 0.0137200i | ||||||||
\(53\) | −334.811 | + | 193.303i | −0.867732 | + | 0.500985i | −0.866594 | − | 0.499014i | \(-0.833696\pi\) |
−0.00113806 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(54\) | 277.723 | + | 300.141i | 0.699875 | + | 0.756369i | ||||
\(55\) | 614.313i | 1.50607i | ||||||||
\(56\) | 117.570 | + | 387.669i | 0.280552 | + | 0.925081i | ||||
\(57\) | 507.141 | − | 37.7712i | 1.17846 | − | 0.0877704i | ||||
\(58\) | −47.5778 | −0.107712 | ||||||||
\(59\) | −45.2274 | + | 78.3362i | −0.0997985 | + | 0.172856i | −0.911601 | − | 0.411076i | \(-0.865153\pi\) |
0.811803 | + | 0.583932i | \(0.198486\pi\) | |||||||
\(60\) | 3.29040 | + | 44.1790i | 0.00707980 | + | 0.0950581i | ||||
\(61\) | 120.761 | − | 69.7214i | 0.253473 | − | 0.146343i | −0.367880 | − | 0.929873i | \(-0.619916\pi\) |
0.621354 | + | 0.783530i | \(0.286583\pi\) | |||||||
\(62\) | 540.475 | 1.10710 | ||||||||
\(63\) | 40.1900 | − | 498.429i | 0.0803725 | − | 0.996765i | ||||
\(64\) | −476.492 | −0.930649 | ||||||||
\(65\) | −154.804 | + | 89.3761i | −0.295401 | + | 0.170550i | ||||
\(66\) | −486.924 | − | 234.765i | −0.908124 | − | 0.437843i | ||||
\(67\) | −151.612 | + | 262.599i | −0.276452 | + | 0.478830i | −0.970501 | − | 0.241099i | \(-0.922492\pi\) |
0.694048 | + | 0.719929i | \(0.255826\pi\) | |||||||
\(68\) | −63.5449 | −0.113323 | ||||||||
\(69\) | 74.7780 | + | 109.787i | 0.130467 | + | 0.191548i | ||||
\(70\) | 635.157 | − | 678.059i | 1.08451 | − | 1.15776i | ||||
\(71\) | 351.969i | 0.588325i | 0.955755 | + | 0.294163i | \(0.0950407\pi\) | ||||
−0.955755 | + | 0.294163i | \(0.904959\pi\) | |||||||
\(72\) | 549.565 | + | 216.270i | 0.899539 | + | 0.353995i | ||||
\(73\) | 761.691 | − | 439.763i | 1.22122 | − | 0.705073i | 0.256044 | − | 0.966665i | \(-0.417581\pi\) |
0.965179 | + | 0.261592i | \(0.0842475\pi\) | |||||||
\(74\) | 2.69815i | 0.00423856i | ||||||||
\(75\) | −735.367 | + | 500.871i | −1.13217 | + | 0.771141i | ||||
\(76\) | −41.9855 | + | 24.2403i | −0.0633693 | + | 0.0365863i | ||||
\(77\) | 191.844 | + | 632.580i | 0.283931 | + | 0.936223i | ||||
\(78\) | −11.6826 | − | 156.859i | −0.0169589 | − | 0.227702i | ||||
\(79\) | 7.12361 | + | 12.3385i | 0.0101452 | + | 0.0175720i | 0.871053 | − | 0.491188i | \(-0.163437\pi\) |
−0.860908 | + | 0.508760i | \(0.830104\pi\) | |||||||
\(80\) | 582.755 | + | 1009.36i | 0.814424 | + | 1.41062i | ||||
\(81\) | −533.485 | − | 496.825i | −0.731803 | − | 0.681516i | ||||
\(82\) | −1168.93 | − | 674.881i | −1.57423 | − | 0.908880i | ||||
\(83\) | −125.688 | + | 217.699i | −0.166218 | + | 0.287898i | −0.937087 | − | 0.349095i | \(-0.886489\pi\) |
0.770869 | + | 0.636994i | \(0.219822\pi\) | |||||||
\(84\) | 17.1850 | + | 44.4652i | 0.0223218 | + | 0.0577565i | ||||
\(85\) | −1103.94 | − | 1912.08i | −1.40869 | − | 2.43993i | ||||
\(86\) | 252.102i | 0.316102i | ||||||||
\(87\) | 84.5852 | − | 6.29979i | 0.104235 | − | 0.00776332i | ||||
\(88\) | −780.720 | −0.945739 | ||||||||
\(89\) | −505.658 | + | 875.825i | −0.602243 | + | 1.04312i | 0.390238 | + | 0.920714i | \(0.372393\pi\) |
−0.992481 | + | 0.122401i | \(0.960940\pi\) | |||||||
\(90\) | −200.645 | − | 1339.53i | −0.234999 | − | 1.56887i | ||||
\(91\) | −131.496 | + | 140.378i | −0.151478 | + | 0.161710i | ||||
\(92\) | −10.9668 | − | 6.33169i | −0.0124279 | − | 0.00717527i | ||||
\(93\) | −960.871 | + | 71.5644i | −1.07137 | + | 0.0797945i | ||||
\(94\) | −725.684 | − | 418.974i | −0.796262 | − | 0.459722i | ||||
\(95\) | −1458.79 | − | 842.234i | −1.57546 | − | 0.909593i | ||||
\(96\) | −115.999 | + | 8.63945i | −0.123324 | + | 0.00918500i | ||||
\(97\) | 1125.76 | + | 649.959i | 1.17839 | + | 0.680344i | 0.955642 | − | 0.294532i | \(-0.0951638\pi\) |
0.222748 | + | 0.974876i | \(0.428497\pi\) | |||||||
\(98\) | 442.293 | − | 896.575i | 0.455901 | − | 0.924161i | ||||
\(99\) | 896.753 | + | 352.899i | 0.910374 | + | 0.358259i | ||||
\(100\) | 42.4103 | − | 73.4568i | 0.0424103 | − | 0.0734568i | ||||
\(101\) | −852.814 | −0.840180 | −0.420090 | − | 0.907482i | \(-0.638002\pi\) | ||||
−0.420090 | + | 0.907482i | \(0.638002\pi\) | |||||||
\(102\) | 1937.46 | − | 144.299i | 1.88075 | − | 0.140076i | ||||
\(103\) | 42.6846i | 0.0408334i | 0.999792 | + | 0.0204167i | \(0.00649929\pi\) | ||||
−0.999792 | + | 0.0204167i | \(0.993501\pi\) | |||||||
\(104\) | −113.587 | − | 196.738i | −0.107097 | − | 0.185498i | ||||
\(105\) | −1039.42 | + | 1289.57i | −0.966065 | + | 1.19857i | ||||
\(106\) | −563.417 | + | 975.866i | −0.516263 | + | 0.894193i | ||||
\(107\) | 718.939 | + | 415.080i | 0.649556 | + | 0.375021i | 0.788286 | − | 0.615309i | \(-0.210969\pi\) |
−0.138730 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(108\) | 66.3813 | + | 20.5759i | 0.0591439 | + | 0.0183326i | ||||
\(109\) | 689.418 | + | 1194.11i | 0.605819 | + | 1.04931i | 0.991921 | + | 0.126853i | \(0.0404877\pi\) |
−0.386103 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(110\) | 895.262 | + | 1550.64i | 0.775999 | + | 1.34407i | ||||
\(111\) | −0.357262 | − | 4.79684i | −0.000305494 | − | 0.00410177i | ||||
\(112\) | 915.298 | + | 857.386i | 0.772210 | + | 0.723352i | ||||
\(113\) | 1325.63 | − | 765.354i | 1.10358 | − | 0.637155i | 0.166424 | − | 0.986054i | \(-0.446778\pi\) |
0.937160 | + | 0.348900i | \(0.113445\pi\) | |||||||
\(114\) | 1225.07 | − | 834.418i | 1.00648 | − | 0.685530i | ||||
\(115\) | − | 439.991i | − | 0.356777i | ||||||
\(116\) | −7.00269 | + | 4.04301i | −0.00560503 | + | 0.00323607i | ||||
\(117\) | 41.5394 | + | 277.321i | 0.0328232 | + | 0.219131i | ||||
\(118\) | 263.647i | 0.205684i | ||||||||
\(119\) | −1733.89 | − | 1624.19i | −1.33568 | − | 1.25117i | ||||
\(120\) | −1101.24 | − | 1616.81i | −0.837739 | − | 1.22995i | ||||
\(121\) | 57.0592 | 0.0428694 | ||||||||
\(122\) | 203.216 | − | 351.980i | 0.150806 | − | 0.261203i | ||||
\(123\) | 2167.52 | + | 1045.04i | 1.58893 | + | 0.766086i | ||||
\(124\) | 79.5492 | − | 45.9278i | 0.0576107 | − | 0.0332616i | ||||
\(125\) | 795.686 | 0.569347 | ||||||||
\(126\) | −624.934 | − | 1316.70i | −0.441853 | − | 0.930959i | ||||
\(127\) | 106.298 | 0.0742710 | 0.0371355 | − | 0.999310i | \(-0.488177\pi\) | ||||
0.0371355 | + | 0.999310i | \(0.488177\pi\) | |||||||
\(128\) | −1357.85 | + | 783.955i | −0.937641 | + | 0.541347i | ||||
\(129\) | −33.3808 | − | 448.193i | −0.0227831 | − | 0.305901i | ||||
\(130\) | −260.503 | + | 451.204i | −0.175751 | + | 0.304409i | ||||
\(131\) | −27.2836 | −0.0181968 | −0.00909841 | − | 0.999959i | \(-0.502896\pi\) | ||||
−0.00909841 | + | 0.999959i | \(0.502896\pi\) | |||||||
\(132\) | −91.6170 | + | 6.82351i | −0.0604109 | + | 0.00449932i | ||||
\(133\) | −1765.19 | − | 411.711i | −1.15084 | − | 0.268420i | ||||
\(134\) | 883.799i | 0.569766i | ||||||||
\(135\) | 534.080 | + | 2354.88i | 0.340491 | + | 1.50130i | ||||
\(136\) | 2430.03 | − | 1402.98i | 1.53216 | − | 0.884591i | ||||
\(137\) | − | 86.9719i | − | 0.0542373i | −0.999632 | − | 0.0271186i | \(-0.991367\pi\) | ||
0.999632 | − | 0.0271186i | \(-0.00863319\pi\) | |||||||
\(138\) | 348.751 | + | 168.147i | 0.215128 | + | 0.103722i | ||||
\(139\) | −248.393 | + | 143.410i | −0.151572 | + | 0.0875099i | −0.573868 | − | 0.818948i | \(-0.694558\pi\) |
0.422296 | + | 0.906458i | \(0.361224\pi\) | |||||||
\(140\) | 35.8658 | − | 153.773i | 0.0216515 | − | 0.0928299i | ||||
\(141\) | 1345.62 | + | 648.776i | 0.803699 | + | 0.387495i | ||||
\(142\) | 512.939 | + | 888.437i | 0.303133 | + | 0.525042i | ||||
\(143\) | −185.345 | − | 321.027i | −0.108387 | − | 0.187732i | ||||
\(144\) | 1808.20 | − | 270.847i | 1.04641 | − | 0.156740i | ||||
\(145\) | −243.310 | − | 140.475i | −0.139350 | − | 0.0804538i | ||||
\(146\) | 1281.77 | − | 2220.09i | 0.726574 | − | 1.25846i | ||||
\(147\) | −667.605 | + | 1652.52i | −0.374579 | + | 0.927195i | ||||
\(148\) | 0.229280 | + | 0.397124i | 0.000127342 | + | 0.000220563i | ||||
\(149\) | − | 2020.90i | − | 1.11113i | −0.831473 | − | 0.555566i | \(-0.812502\pi\) | ||
0.831473 | − | 0.555566i | \(-0.187498\pi\) | |||||||
\(150\) | −1126.26 | + | 2335.97i | −0.613060 | + | 1.27154i | ||||
\(151\) | −1919.05 | −1.03424 | −0.517120 | − | 0.855913i | \(-0.672996\pi\) | ||||
−0.517120 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(152\) | 1070.38 | − | 1853.95i | 0.571180 | − | 0.989313i | ||||
\(153\) | −3425.36 | + | 513.078i | −1.80996 | + | 0.271111i | ||||
\(154\) | 1406.14 | + | 1317.17i | 0.735777 | + | 0.689223i | ||||
\(155\) | 2763.95 | + | 1595.77i | 1.43230 | + | 0.826936i | ||||
\(156\) | −15.0488 | − | 22.0943i | −0.00772353 | − | 0.0113395i | ||||
\(157\) | 784.058 | + | 452.676i | 0.398565 | + | 0.230111i | 0.685864 | − | 0.727729i | \(-0.259424\pi\) |
−0.287300 | + | 0.957841i | \(0.592758\pi\) | |||||||
\(158\) | 35.9626 | + | 20.7630i | 0.0181078 | + | 0.0104545i | ||||
\(159\) | 872.443 | − | 1809.52i | 0.435152 | − | 0.902545i | ||||
\(160\) | 333.671 | + | 192.645i | 0.164869 | + | 0.0951871i | ||||
\(161\) | −137.405 | − | 453.075i | −0.0672612 | − | 0.221784i | ||||
\(162\) | −2070.66 | − | 476.610i | −1.00424 | − | 0.231148i | ||||
\(163\) | 1124.59 | − | 1947.85i | 0.540397 | − | 0.935995i | −0.458484 | − | 0.888703i | \(-0.651607\pi\) |
0.998881 | − | 0.0472926i | \(-0.0150593\pi\) | |||||||
\(164\) | −229.397 | −0.109225 | ||||||||
\(165\) | −1796.94 | − | 2638.23i | −0.847829 | − | 1.24476i | ||||
\(166\) | 732.683i | 0.342574i | ||||||||
\(167\) | 1097.47 | + | 1900.88i | 0.508534 | + | 0.880807i | 0.999951 | + | 0.00988229i | \(0.00314568\pi\) |
−0.491417 | + | 0.870924i | \(0.663521\pi\) | |||||||
\(168\) | −1638.90 | − | 1320.98i | −0.752641 | − | 0.606642i | ||||
\(169\) | −1044.57 | + | 1809.25i | −0.475452 | + | 0.823507i | ||||
\(170\) | −5573.10 | − | 3217.63i | −2.51434 | − | 1.45165i | ||||
\(171\) | −2067.48 | + | 1645.66i | −0.924587 | + | 0.735948i | ||||
\(172\) | 21.4228 | + | 37.1053i | 0.00949692 | + | 0.0164491i | ||||
\(173\) | −1351.18 | − | 2340.32i | −0.593807 | − | 1.02850i | −0.993714 | − | 0.111948i | \(-0.964291\pi\) |
0.399908 | − | 0.916555i | \(-0.369042\pi\) | |||||||
\(174\) | 204.328 | − | 139.171i | 0.0890233 | − | 0.0606353i | ||||
\(175\) | 3034.74 | − | 920.354i | 1.31088 | − | 0.397556i | ||||
\(176\) | −2093.18 | + | 1208.50i | −0.896473 | + | 0.517579i | ||||
\(177\) | −34.9096 | − | 468.719i | −0.0148247 | − | 0.199046i | ||||
\(178\) | 2947.66i | 1.24122i | ||||||||
\(179\) | 351.098 | − | 202.707i | 0.146605 | − | 0.0846425i | −0.424903 | − | 0.905239i | \(-0.639692\pi\) |
0.571508 | + | 0.820596i | \(0.306359\pi\) | |||||||
\(180\) | −143.360 | − | 180.107i | −0.0593636 | − | 0.0745797i | ||||
\(181\) | 3023.81i | 1.24176i | 0.783907 | + | 0.620878i | \(0.213224\pi\) | ||||
−0.783907 | + | 0.620878i | \(0.786776\pi\) | |||||||
\(182\) | −127.342 | + | 545.974i | −0.0518639 | + | 0.222364i | ||||
\(183\) | −314.677 | + | 652.667i | −0.127112 | + | 0.263642i | ||||
\(184\) | 559.178 | 0.224039 | ||||||||
\(185\) | −7.96635 | + | 13.7981i | −0.00316593 | + | 0.00548356i | ||||
\(186\) | −2321.13 | + | 1580.96i | −0.915017 | + | 0.623234i | ||||
\(187\) | 3965.20 | − | 2289.31i | 1.55061 | − | 0.895246i | ||||
\(188\) | −142.412 | −0.0552472 | ||||||||
\(189\) | 1285.37 | + | 2258.12i | 0.494692 | + | 0.869068i | ||||
\(190\) | −4909.68 | −1.87466 | ||||||||
\(191\) | −890.669 | + | 514.228i | −0.337416 | + | 0.194807i | −0.659129 | − | 0.752030i | \(-0.729075\pi\) |
0.321713 | + | 0.946837i | \(0.395742\pi\) | |||||||
\(192\) | 2046.35 | − | 1393.80i | 0.769179 | − | 0.523901i | ||||
\(193\) | 2051.01 | − | 3552.46i | 0.764948 | − | 1.32493i | −0.175326 | − | 0.984510i | \(-0.556098\pi\) |
0.940274 | − | 0.340419i | \(-0.110569\pi\) | |||||||
\(194\) | 3788.85 | 1.40218 | ||||||||
\(195\) | 403.385 | − | 836.657i | 0.148139 | − | 0.307253i | ||||
\(196\) | −11.0896 | − | 169.546i | −0.00404140 | − | 0.0617879i | ||||
\(197\) | 805.333i | 0.291257i | 0.989339 | + | 0.145628i | \(0.0465204\pi\) | ||||
−0.989339 | + | 0.145628i | \(0.953480\pi\) | |||||||
\(198\) | 2777.86 | − | 416.092i | 0.997042 | − | 0.149345i | ||||
\(199\) | −1923.11 | + | 1110.31i | −0.685054 | + | 0.395516i | −0.801757 | − | 0.597651i | \(-0.796101\pi\) |
0.116702 | + | 0.993167i | \(0.462768\pi\) | |||||||
\(200\) | 3745.43i | 1.32421i | ||||||||
\(201\) | −117.024 | − | 1571.24i | −0.0410659 | − | 0.551378i | ||||
\(202\) | −2152.66 | + | 1242.84i | −0.749806 | + | 0.432901i | ||||
\(203\) | −294.414 | − | 68.6687i | −0.101792 | − | 0.0237418i | ||||
\(204\) | 272.900 | − | 185.877i | 0.0936610 | − | 0.0637941i | ||||
\(205\) | −3985.21 | − | 6902.59i | −1.35775 | − | 2.35170i | ||||
\(206\) | 62.2060 | + | 107.744i | 0.0210393 | + | 0.0364411i | ||||
\(207\) | −642.284 | − | 252.758i | −0.215661 | − | 0.0848690i | ||||
\(208\) | −609.072 | − | 351.648i | −0.203036 | − | 0.117223i | ||||
\(209\) | 1746.60 | − | 3025.19i | 0.578060 | − | 1.00123i | ||||
\(210\) | −744.340 | + | 4769.91i | −0.244592 | + | 1.56740i | ||||
\(211\) | 1123.34 | + | 1945.68i | 0.366511 | + | 0.634816i | 0.989017 | − | 0.147799i | \(-0.0472188\pi\) |
−0.622506 | + | 0.782615i | \(0.713885\pi\) | |||||||
\(212\) | 191.509i | 0.0620420i | ||||||||
\(213\) | −1029.56 | − | 1511.57i | −0.331193 | − | 0.486249i | ||||
\(214\) | 2419.65 | 0.772915 | ||||||||
\(215\) | −744.337 | + | 1289.23i | −0.236109 | + | 0.408952i | ||||
\(216\) | −2992.78 | + | 678.754i | −0.942745 | + | 0.213812i | ||||
\(217\) | 3344.48 | + | 780.062i | 1.04626 | + | 0.244028i | ||||
\(218\) | 3480.44 | + | 2009.43i | 1.08131 | + | 0.624293i | ||||
\(219\) | −1984.80 | + | 4116.65i | −0.612422 | + | 1.27022i | ||||
\(220\) | 263.536 | + | 152.153i | 0.0807619 | + | 0.0466279i | ||||
\(221\) | 1153.79 | + | 666.142i | 0.351188 | + | 0.202758i | ||||
\(222\) | −7.89242 | − | 11.5875i | −0.00238606 | − | 0.00350315i | ||||
\(223\) | 3632.93 | + | 2097.48i | 1.09094 | + | 0.629854i | 0.933826 | − | 0.357727i | \(-0.116448\pi\) |
0.157112 | + | 0.987581i | \(0.449782\pi\) | |||||||
\(224\) | 403.755 | + | 94.1712i | 0.120433 | + | 0.0280896i | ||||
\(225\) | 1693.00 | − | 4302.08i | 0.501629 | − | 1.27469i | ||||
\(226\) | 2230.76 | − | 3863.79i | 0.656585 | − | 1.13724i | ||||
\(227\) | −2341.01 | −0.684487 | −0.342243 | − | 0.939611i | \(-0.611187\pi\) | ||||
−0.342243 | + | 0.939611i | \(0.611187\pi\) | |||||||
\(228\) | 109.405 | − | 226.916i | 0.0317786 | − | 0.0659116i | ||||
\(229\) | 3060.73i | 0.883225i | 0.897206 | + | 0.441613i | \(0.145593\pi\) | ||||
−0.897206 | + | 0.441613i | \(0.854407\pi\) | |||||||
\(230\) | −641.217 | − | 1110.62i | −0.183829 | − | 0.318400i | ||||
\(231\) | −2674.27 | − | 2155.51i | −0.761707 | − | 0.613949i | ||||
\(232\) | 178.527 | − | 309.218i | 0.0505211 | − | 0.0875051i | ||||
\(233\) | 2201.24 | + | 1270.89i | 0.618920 | + | 0.357333i | 0.776448 | − | 0.630181i | \(-0.217019\pi\) |
−0.157529 | + | 0.987514i | \(0.550353\pi\) | |||||||
\(234\) | 509.004 | + | 639.473i | 0.142199 | + | 0.178648i | ||||
\(235\) | −2474.06 | − | 4285.20i | −0.686766 | − | 1.18951i | ||||
\(236\) | 22.4039 | + | 38.8046i | 0.00617952 | + | 0.0107032i | ||||
\(237\) | −66.6846 | − | 32.1513i | −0.0182769 | − | 0.00881203i | ||||
\(238\) | −6743.66 | − | 1572.88i | −1.83667 | − | 0.428381i | ||||
\(239\) | −1543.33 | + | 891.040i | −0.417697 | + | 0.241157i | −0.694091 | − | 0.719887i | \(-0.744194\pi\) |
0.276395 | + | 0.961044i | \(0.410860\pi\) | |||||||
\(240\) | −5455.21 | − | 2630.17i | −1.46722 | − | 0.707404i | ||||
\(241\) | 1610.36i | 0.430426i | 0.976567 | + | 0.215213i | \(0.0690445\pi\) | ||||
−0.976567 | + | 0.215213i | \(0.930955\pi\) | |||||||
\(242\) | 144.028 | − | 83.1547i | 0.0382582 | − | 0.0220884i | ||||
\(243\) | 3744.38 | + | 573.155i | 0.988487 | + | 0.151308i | ||||
\(244\) | − | 69.0743i | − | 0.0181231i | ||||||
\(245\) | 4909.02 | − | 3279.14i | 1.28010 | − | 0.855088i | ||||
\(246\) | 6994.20 | − | 520.919i | 1.81274 | − | 0.135010i | ||||
\(247\) | 1016.45 | 0.261842 | ||||||||
\(248\) | −2028.03 | + | 3512.66i | −0.519276 | + | 0.899412i | ||||
\(249\) | −97.0148 | − | 1302.58i | −0.0246910 | − | 0.331518i | ||||
\(250\) | 2008.46 | − | 1159.59i | 0.508105 | − | 0.293355i | ||||
\(251\) | −603.105 | −0.151664 | −0.0758320 | − | 0.997121i | \(-0.524161\pi\) | ||||
−0.0758320 | + | 0.997121i | \(0.524161\pi\) | |||||||
\(252\) | −203.869 | − | 140.692i | −0.0509625 | − | 0.0351697i | ||||
\(253\) | 912.439 | 0.226737 | ||||||||
\(254\) | 268.316 | − | 154.912i | 0.0662820 | − | 0.0382679i | ||||
\(255\) | 10334.1 | + | 4982.46i | 2.53782 | + | 1.22358i | ||||
\(256\) | −379.008 | + | 656.461i | −0.0925312 | + | 0.160269i | ||||
\(257\) | −1336.18 | −0.324313 | −0.162157 | − | 0.986765i | \(-0.551845\pi\) | ||||
−0.162157 | + | 0.986765i | \(0.551845\pi\) | |||||||
\(258\) | −737.429 | − | 1082.68i | −0.177947 | − | 0.261258i | ||||
\(259\) | −3.89421 | + | 16.6962i | −0.000934264 | + | 0.00400562i | ||||
\(260\) | 88.5467i | 0.0211209i | ||||||||
\(261\) | −344.832 | + | 274.478i | −0.0817800 | + | 0.0650948i | ||||
\(262\) | −68.8690 | + | 39.7615i | −0.0162395 | + | 0.00937587i | ||||
\(263\) | 5754.61i | 1.34922i | 0.738175 | + | 0.674609i | \(0.235688\pi\) | ||||
−0.738175 | + | 0.674609i | \(0.764312\pi\) | |||||||
\(264\) | 3352.88 | − | 2283.71i | 0.781651 | − | 0.532396i | ||||
\(265\) | −5762.54 | + | 3327.01i | −1.33581 | + | 0.771231i | ||||
\(266\) | −5055.68 | + | 1533.25i | −1.16535 | + | 0.353420i | ||||
\(267\) | −390.301 | − | 5240.44i | −0.0894608 | − | 1.20116i | ||||
\(268\) | 75.1023 | + | 130.081i | 0.0171179 | + | 0.0296491i | ||||
\(269\) | −926.438 | − | 1604.64i | −0.209985 | − | 0.363704i | 0.741725 | − | 0.670705i | \(-0.234008\pi\) |
−0.951709 | + | 0.307000i | \(0.900675\pi\) | |||||||
\(270\) | 4779.98 | + | 5165.82i | 1.07741 | + | 1.16438i | ||||
\(271\) | −6459.12 | − | 3729.17i | −1.44784 | − | 0.835908i | −0.449483 | − | 0.893289i | \(-0.648392\pi\) |
−0.998352 | + | 0.0573809i | \(0.981725\pi\) | |||||||
\(272\) | 4343.41 | − | 7523.01i | 0.968228 | − | 1.67702i | ||||
\(273\) | 154.100 | − | 987.510i | 0.0341632 | − | 0.218926i | ||||
\(274\) | −126.748 | − | 219.533i | −0.0279456 | − | 0.0484032i | ||||
\(275\) | 6111.61i | 1.34016i | ||||||||
\(276\) | 65.6191 | − | 4.88723i | 0.0143109 | − | 0.00106586i | ||||
\(277\) | 1370.01 | 0.297169 | 0.148585 | − | 0.988900i | \(-0.452528\pi\) | ||||
0.148585 | + | 0.988900i | \(0.452528\pi\) | |||||||
\(278\) | −417.994 | + | 723.987i | −0.0901785 | + | 0.156194i | ||||
\(279\) | 3917.23 | − | 3118.01i | 0.840567 | − | 0.669070i | ||||
\(280\) | 2023.53 | + | 6672.31i | 0.431890 | + | 1.42410i | ||||
\(281\) | −3574.32 | − | 2063.63i | −0.758811 | − | 0.438100i | 0.0700574 | − | 0.997543i | \(-0.477682\pi\) |
−0.828869 | + | 0.559443i | \(0.811015\pi\) | |||||||
\(282\) | 4342.08 | − | 323.392i | 0.916904 | − | 0.0682898i | ||||
\(283\) | −1647.02 | − | 950.906i | −0.345954 | − | 0.199737i | 0.316948 | − | 0.948443i | \(-0.397342\pi\) |
−0.662902 | + | 0.748706i | \(0.730675\pi\) | |||||||
\(284\) | 150.993 | + | 87.1758i | 0.0315485 | + | 0.0182145i | ||||
\(285\) | 8728.57 | − | 650.093i | 1.81416 | − | 0.135116i | ||||
\(286\) | −935.692 | − | 540.222i | −0.193457 | − | 0.111692i | ||||
\(287\) | −6259.33 | − | 5863.30i | −1.28738 | − | 1.20592i | ||||
\(288\) | 472.898 | − | 376.415i | 0.0967562 | − | 0.0770155i | ||||
\(289\) | −5771.43 | + | 9996.41i | −1.17473 | + | 2.03469i | ||||
\(290\) | −818.878 | −0.165814 | ||||||||
\(291\) | −6735.92 | + | 501.682i | −1.35693 | + | 0.101062i | ||||
\(292\) | − | 435.681i | − | 0.0873162i | ||||||
\(293\) | 3959.77 | + | 6858.52i | 0.789530 | + | 1.36751i | 0.926255 | + | 0.376896i | \(0.123009\pi\) |
−0.136726 | + | 0.990609i | \(0.543658\pi\) | |||||||
\(294\) | 723.126 | + | 5144.20i | 0.143447 | + | 1.02046i | ||||
\(295\) | −778.425 | + | 1348.27i | −0.153633 | + | 0.266100i | ||||
\(296\) | −17.5358 | − | 10.1243i | −0.00344341 | − | 0.00198805i | ||||
\(297\) | −4883.47 | + | 1107.56i | −0.954100 | + | 0.216387i | ||||
\(298\) | −2945.14 | − | 5101.13i | −0.572508 | − | 0.991612i | ||||
\(299\) | 132.750 | + | 229.930i | 0.0256761 | + | 0.0444723i | ||||
\(300\) | 32.7351 | + | 439.523i | 0.00629988 | + | 0.0845863i | ||||
\(301\) | −363.856 | + | 1560.02i | −0.0696754 | + | 0.298730i | ||||
\(302\) | −4844.05 | + | 2796.71i | −0.922993 | + | 0.532890i | ||||
\(303\) | 3662.50 | − | 2494.59i | 0.694406 | − | 0.472972i | ||||
\(304\) | − | 6627.48i | − | 1.25037i | ||||||
\(305\) | 2078.46 | − | 1200.00i | 0.390204 | − | 0.225284i | ||||
\(306\) | −7898.51 | + | 6287.02i | −1.47558 | + | 1.17453i | ||||
\(307\) | − | 1709.99i | − | 0.317896i | −0.987287 | − | 0.158948i | \(-0.949190\pi\) | ||
0.987287 | − | 0.158948i | \(-0.0508102\pi\) | |||||||
\(308\) | 318.889 | + | 74.3772i | 0.0589948 | + | 0.0137599i | ||||
\(309\) | −124.858 | − | 183.313i | −0.0229868 | − | 0.0337487i | ||||
\(310\) | 9302.30 | 1.70431 | ||||||||
\(311\) | 5182.89 | − | 8977.03i | 0.944999 | − | 1.63679i | 0.189245 | − | 0.981930i | \(-0.439396\pi\) |
0.755753 | − | 0.654856i | \(-0.227271\pi\) | |||||||
\(312\) | 1063.29 | + | 512.656i | 0.192940 | + | 0.0930238i | ||||
\(313\) | −7088.96 | + | 4092.81i | −1.28016 | + | 0.739103i | −0.976878 | − | 0.213796i | \(-0.931417\pi\) |
−0.303286 | + | 0.952899i | \(0.598084\pi\) | |||||||
\(314\) | 2638.81 | 0.474257 | ||||||||
\(315\) | 691.724 | − | 8578.64i | 0.123728 | − | 1.53445i | ||||
\(316\) | 7.05750 | 0.00125638 | ||||||||
\(317\) | 3116.43 | − | 1799.27i | 0.552165 | − | 0.318792i | −0.197830 | − | 0.980236i | \(-0.563389\pi\) |
0.749995 | + | 0.661444i | \(0.230056\pi\) | |||||||
\(318\) | −434.883 | − | 5839.02i | −0.0766887 | − | 1.02967i | ||||
\(319\) | 291.312 | − | 504.567i | 0.0511296 | − | 0.0885591i | ||||
\(320\) | −8201.07 | −1.43267 | ||||||||
\(321\) | −4301.72 | + | 320.386i | −0.747971 | + | 0.0557079i | ||||
\(322\) | −1007.12 | − | 943.399i | −0.174300 | − | 0.163272i | ||||
\(323\) | 12554.7i | 2.16274i | ||||||||
\(324\) | −345.268 | + | 105.808i | −0.0592024 | + | 0.0181427i | ||||
\(325\) | −1540.10 | + | 889.176i | −0.262859 | + | 0.151762i | ||||
\(326\) | − | 6555.64i | − | 1.11375i | ||||||
\(327\) | −6453.69 | − | 3111.58i | −1.09141 | − | 0.526210i | ||||
\(328\) | 8772.39 | − | 5064.74i | 1.47675 | − | 0.852602i | ||||
\(329\) | −3885.86 | − | 3640.00i | −0.651169 | − | 0.609969i | ||||
\(330\) | −8380.62 | − | 4040.63i | −1.39799 | − | 0.674028i | ||||
\(331\) | −3992.83 | − | 6915.79i | −0.663039 | − | 1.14842i | −0.979813 | − | 0.199917i | \(-0.935933\pi\) |
0.316773 | − | 0.948501i | \(-0.397401\pi\) | |||||||
\(332\) | 62.2610 | + | 107.839i | 0.0102922 | + | 0.0178266i | ||||
\(333\) | 15.5657 | + | 19.5555i | 0.00256154 | + | 0.00321812i | ||||
\(334\) | 5540.46 | + | 3198.79i | 0.907667 | + | 0.524042i | ||||
\(335\) | −2609.44 | + | 4519.68i | −0.425579 | + | 0.737125i | ||||
\(336\) | −6438.81 | − | 1004.77i | −1.04543 | − | 0.163139i | ||||
\(337\) | −4758.03 | − | 8241.15i | −0.769100 | − | 1.33212i | −0.938052 | − | 0.346495i | \(-0.887372\pi\) |
0.168952 | − | 0.985624i | \(-0.445962\pi\) | |||||||
\(338\) | 6089.17i | 0.979902i | ||||||||
\(339\) | −3454.31 | + | 7164.54i | −0.553428 | + | 1.14786i | ||||
\(340\) | −1093.69 | −0.174453 | ||||||||
\(341\) | −3309.25 | + | 5731.78i | −0.525530 | + | 0.910245i | ||||
\(342\) | −2820.42 | + | 7166.99i | −0.445938 | + | 1.13318i | ||||
\(343\) | 4030.95 | − | 4909.69i | 0.634550 | − | 0.772882i | ||||
\(344\) | −1638.46 | − | 945.966i | −0.256802 | − | 0.148265i | ||||
\(345\) | 1287.03 | + | 1889.59i | 0.200845 | + | 0.294875i | ||||
\(346\) | −6821.28 | − | 3938.27i | −1.05987 | − | 0.611915i | ||||
\(347\) | 6785.01 | + | 3917.33i | 1.04968 | + | 0.606032i | 0.922559 | − | 0.385855i | \(-0.126094\pi\) |
0.127119 | + | 0.991887i | \(0.459427\pi\) | |||||||
\(348\) | 18.2475 | − | 37.8469i | 0.00281083 | − | 0.00582990i | ||||
\(349\) | 5127.39 | + | 2960.30i | 0.786427 | + | 0.454044i | 0.838703 | − | 0.544589i | \(-0.183314\pi\) |
−0.0522759 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(350\) | 6318.98 | − | 6745.80i | 0.965040 | − | 1.03022i | ||||
\(351\) | −989.594 | − | 1069.47i | −0.150486 | − | 0.162633i | ||||
\(352\) | −399.501 | + | 691.956i | −0.0604928 | + | 0.104777i | ||||
\(353\) | 4592.76 | 0.692487 | 0.346244 | − | 0.938145i | \(-0.387457\pi\) | ||||
0.346244 | + | 0.938145i | \(0.387457\pi\) | |||||||
\(354\) | −771.201 | − | 1132.26i | −0.115788 | − | 0.169997i | ||||
\(355\) | 6057.87i | 0.905685i | ||||||||
\(356\) | 250.483 | + | 433.849i | 0.0372909 | + | 0.0645897i | ||||
\(357\) | 12197.3 | + | 1903.38i | 1.80827 | + | 0.282178i | ||||
\(358\) | 590.825 | − | 1023.34i | 0.0872237 | − | 0.151076i | ||||
\(359\) | −10030.3 | − | 5790.97i | −1.47459 | − | 0.851353i | −0.474997 | − | 0.879987i | \(-0.657551\pi\) |
−0.999590 | + | 0.0286338i | \(0.990884\pi\) | |||||||
\(360\) | 9458.75 | + | 3722.30i | 1.38478 | + | 0.544951i | ||||
\(361\) | 1359.73 | + | 2355.12i | 0.198240 | + | 0.343362i | ||||
\(362\) | 4406.72 | + | 7632.66i | 0.639812 | + | 1.10819i | ||||
\(363\) | −245.047 | + | 166.905i | −0.0354314 | + | 0.0241330i | ||||
\(364\) | 27.6523 | + | 91.1797i | 0.00398180 | + | 0.0131294i | ||||
\(365\) | 13109.7 | − | 7568.91i | 1.87999 | − | 1.08541i | ||||
\(366\) | 156.855 | + | 2106.04i | 0.0224015 | + | 0.300778i | ||||
\(367\) | 4647.15i | 0.660979i | 0.943810 | + | 0.330490i | \(0.107214\pi\) | ||||
−0.943810 | + | 0.330490i | \(0.892786\pi\) | |||||||
\(368\) | 1499.20 | − | 865.565i | 0.212368 | − | 0.122611i | ||||
\(369\) | −12365.5 | + | 1852.21i | −1.74451 | + | 0.261307i | ||||
\(370\) | 46.4387i | 0.00652496i | ||||||||
\(371\) | −4894.91 | + | 5225.53i | −0.684989 | + | 0.731256i | ||||
\(372\) | −207.288 | + | 429.933i | −0.0288908 | + | 0.0599220i | ||||
\(373\) | 13272.9 | 1.84247 | 0.921237 | − | 0.389001i | \(-0.127180\pi\) | ||||
0.921237 | + | 0.389001i | \(0.127180\pi\) | |||||||
\(374\) | 6672.61 | − | 11557.3i | 0.922547 | − | 1.59790i | ||||
\(375\) | −3417.16 | + | 2327.48i | −0.470563 | + | 0.320509i | ||||
\(376\) | 5446.00 | − | 3144.25i | 0.746957 | − | 0.431256i | ||||
\(377\) | 169.532 | 0.0231600 | ||||||||
\(378\) | 6535.36 | + | 3826.69i | 0.889266 | + | 0.520698i | ||||
\(379\) | 11820.6 | 1.60207 | 0.801033 | − | 0.598620i | \(-0.204284\pi\) | ||||
0.801033 | + | 0.598620i | \(0.204284\pi\) | |||||||
\(380\) | −722.626 | + | 417.209i | −0.0975525 | + | 0.0563220i | ||||
\(381\) | −456.507 | + | 310.935i | −0.0613847 | + | 0.0418102i | ||||
\(382\) | −1498.81 | + | 2596.02i | −0.200748 | + | 0.347706i | ||||
\(383\) | 4630.60 | 0.617787 | 0.308894 | − | 0.951097i | \(-0.400041\pi\) | ||||
0.308894 | + | 0.951097i | \(0.400041\pi\) | |||||||
\(384\) | 3538.26 | − | 7338.66i | 0.470211 | − | 0.975259i | ||||
\(385\) | 3301.90 | + | 10887.6i | 0.437092 | + | 1.44125i | ||||
\(386\) | − | 11956.1i | − | 1.57655i | ||||||
\(387\) | 1454.38 | + | 1827.17i | 0.191034 | + | 0.240001i | ||||
\(388\) | 557.657 | − | 321.964i | 0.0729659 | − | 0.0421269i | ||||
\(389\) | 8332.61i | 1.08607i | 0.839711 | + | 0.543034i | \(0.182724\pi\) | ||||
−0.839711 | + | 0.543034i | \(0.817276\pi\) | |||||||
\(390\) | −201.074 | − | 2699.75i | −0.0261071 | − | 0.350531i | ||||
\(391\) | −2840.01 | + | 1639.68i | −0.367329 | + | 0.212077i | ||||
\(392\) | 4167.41 | + | 6238.79i | 0.536954 | + | 0.803843i | ||||
\(393\) | 117.172 | − | 79.8082i | 0.0150396 | − | 0.0102437i | ||||
\(394\) | 1173.64 | + | 2032.81i | 0.150069 | + | 0.259928i | ||||
\(395\) | 122.607 | + | 212.361i | 0.0156178 | + | 0.0270508i | ||||
\(396\) | 373.499 | − | 297.296i | 0.0473965 | − | 0.0377264i | ||||
\(397\) | 5613.15 | + | 3240.75i | 0.709611 | + | 0.409694i | 0.810917 | − | 0.585161i | \(-0.198969\pi\) |
−0.101306 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(398\) | −3236.20 | + | 5605.26i | −0.407577 | + | 0.705945i | ||||
\(399\) | 8785.11 | − | 3395.28i | 1.10227 | − | 0.426006i | ||||
\(400\) | 5797.65 | + | 10041.8i | 0.724706 | + | 1.25523i | ||||
\(401\) | 1709.94i | 0.212944i | 0.994316 | + | 0.106472i | \(0.0339554\pi\) | ||||
−0.994316 | + | 0.106472i | \(0.966045\pi\) | |||||||
\(402\) | −2585.23 | − | 3795.57i | −0.320745 | − | 0.470910i | ||||
\(403\) | −1925.85 | −0.238048 | ||||||||
\(404\) | −211.225 | + | 365.852i | −0.0260120 | + | 0.0450540i | ||||
\(405\) | −9181.99 | − | 8551.02i | −1.12656 | − | 1.04915i | ||||
\(406\) | −843.229 | + | 255.728i | −0.103076 | + | 0.0312601i | ||||
\(407\) | −28.6141 | − | 16.5203i | −0.00348488 | − | 0.00201200i | ||||
\(408\) | −6332.12 | + | 13133.4i | −0.768350 | + | 1.59363i | ||||
\(409\) | −5376.61 | − | 3104.19i | −0.650016 | − | 0.375287i | 0.138447 | − | 0.990370i | \(-0.455789\pi\) |
−0.788462 | + | 0.615083i | \(0.789122\pi\) | |||||||
\(410\) | −20118.8 | − | 11615.6i | −2.42341 | − | 1.39916i | ||||
\(411\) | 254.404 | + | 373.510i | 0.0305324 | + | 0.0448269i | ||||
\(412\) | 18.3114 | + | 10.5721i | 0.00218966 | + | 0.00126420i | ||||
\(413\) | −380.519 | + | 1631.46i | −0.0453369 | + | 0.194380i | ||||
\(414\) | −1989.60 | + | 298.019i | −0.236192 | + | 0.0353788i | ||||
\(415\) | −2163.27 | + | 3746.89i | −0.255881 | + | 0.443199i | ||||
\(416\) | −232.493 | −0.0274012 | ||||||||
\(417\) | 647.259 | − | 1342.47i | 0.0760105 | − | 0.157653i | ||||
\(418\) | − | 10181.5i | − | 1.19138i | ||||||
\(419\) | −5926.05 | − | 10264.2i | −0.690946 | − | 1.19675i | −0.971528 | − | 0.236924i | \(-0.923861\pi\) |
0.280582 | − | 0.959830i | \(-0.409473\pi\) | |||||||
\(420\) | 295.776 | + | 765.306i | 0.0343629 | + | 0.0889121i | ||||
\(421\) | −218.101 | + | 377.763i | −0.0252485 | + | 0.0437317i | −0.878374 | − | 0.477975i | \(-0.841371\pi\) |
0.853125 | + | 0.521706i | \(0.174704\pi\) | |||||||
\(422\) | 5671.04 | + | 3274.17i | 0.654175 | + | 0.377688i | ||||
\(423\) | −7676.65 | + | 1149.87i | −0.882391 | + | 0.132172i | ||||
\(424\) | −4228.24 | − | 7323.52i | −0.484296 | − | 0.838825i | ||||
\(425\) | −10982.7 | − | 19022.7i | −1.25351 | − | 2.17114i | ||||
\(426\) | −4801.66 | − | 2315.07i | −0.546106 | − | 0.263299i | ||||
\(427\) | 1765.52 | − | 1884.77i | 0.200092 | − | 0.213607i | ||||
\(428\) | 356.133 | − | 205.614i | 0.0402205 | − | 0.0232213i | ||||
\(429\) | 1735.03 | + | 836.527i | 0.195264 | + | 0.0941443i | ||||
\(430\) | 4339.01i | 0.486617i | ||||||||
\(431\) | 10890.9 | − | 6287.86i | 1.21716 | − | 0.702728i | 0.252850 | − | 0.967505i | \(-0.418632\pi\) |
0.964309 | + | 0.264778i | \(0.0852986\pi\) | |||||||
\(432\) | −6973.24 | + | 6452.40i | −0.776621 | + | 0.718614i | ||||
\(433\) | − | 15488.3i | − | 1.71898i | −0.511149 | − | 0.859492i | \(-0.670780\pi\) | ||
0.511149 | − | 0.859492i | \(-0.329220\pi\) | |||||||
\(434\) | 9578.92 | − | 2905.02i | 1.05945 | − | 0.321303i | ||||
\(435\) | 1455.83 | − | 108.428i | 0.160463 | − | 0.0119511i | ||||
\(436\) | 683.020 | 0.0750246 | ||||||||
\(437\) | −1250.97 | + | 2166.74i | −0.136938 | + | 0.237184i | ||||
\(438\) | 989.355 | + | 13283.7i | 0.107930 | + | 1.44913i | ||||
\(439\) | −10844.1 | + | 6260.84i | −1.17895 | + | 0.680669i | −0.955772 | − | 0.294108i | \(-0.904977\pi\) |
−0.223181 | + | 0.974777i | \(0.571644\pi\) | |||||||
\(440\) | −13437.2 | −1.45590 | ||||||||
\(441\) | −1966.74 | − | 9049.75i | −0.212368 | − | 0.977190i | ||||
\(442\) | 3883.18 | 0.417883 | ||||||||
\(443\) | 705.907 | − | 407.556i | 0.0757080 | − | 0.0437100i | −0.461668 | − | 0.887053i | \(-0.652749\pi\) |
0.537376 | + | 0.843343i | \(0.319416\pi\) | |||||||
\(444\) | −2.14630 | − | 1.03482i | −0.000229412 | − | 0.000110609i | ||||
\(445\) | −8703.05 | + | 15074.1i | −0.927111 | + | 1.60580i | ||||
\(446\) | 12226.9 | 1.29812 | ||||||||
\(447\) | 5911.39 | + | 8678.96i | 0.625502 | + | 0.918347i | ||||
\(448\) | −8444.95 | + | 2561.12i | −0.890594 | + | 0.270093i | ||||
\(449\) | 5276.20i | 0.554565i | 0.960788 | + | 0.277282i | \(0.0894337\pi\) | ||||
−0.960788 | + | 0.277282i | \(0.910566\pi\) | |||||||
\(450\) | −1996.16 | − | 13326.5i | −0.209111 | − | 1.39604i | ||||
\(451\) | 14314.4 | − | 8264.40i | 1.49454 | − | 0.862872i | ||||
\(452\) | − | 758.251i | − | 0.0789052i | ||||||
\(453\) | 8241.58 | − | 5613.48i | 0.854797 | − | 0.582217i | ||||
\(454\) | −5909.15 | + | 3411.65i | −0.610860 | + | 0.352680i | ||||
\(455\) | −2263.22 | + | 2416.09i | −0.233190 | + | 0.248941i | ||||
\(456\) | 826.192 | + | 11093.0i | 0.0848465 | + | 1.13921i | ||||
\(457\) | 4560.82 | + | 7899.58i | 0.466841 | + | 0.808592i | 0.999283 | − | 0.0378745i | \(-0.0120587\pi\) |
−0.532442 | + | 0.846467i | \(0.678725\pi\) | |||||||
\(458\) | 4460.52 | + | 7725.85i | 0.455080 | + | 0.788221i | ||||
\(459\) | 13209.7 | − | 12223.1i | 1.34331 | − | 1.24297i | ||||
\(460\) | −188.754 | − | 108.977i | −0.0191319 | − | 0.0110458i | ||||
\(461\) | −420.112 | + | 727.655i | −0.0424437 | + | 0.0735147i | −0.886467 | − | 0.462792i | \(-0.846848\pi\) |
0.844023 | + | 0.536307i | \(0.180181\pi\) | |||||||
\(462\) | −9891.68 | − | 1543.59i | −0.996109 | − | 0.155442i | ||||
\(463\) | −1889.21 | − | 3272.21i | −0.189631 | − | 0.328450i | 0.755496 | − | 0.655153i | \(-0.227396\pi\) |
−0.945127 | + | 0.326703i | \(0.894062\pi\) | |||||||
\(464\) | − | 1105.39i | − | 0.110596i | ||||||
\(465\) | −16537.9 | + | 1231.72i | −1.64930 | + | 0.122838i | ||||
\(466\) | 7408.47 | 0.736461 | ||||||||
\(467\) | 3197.40 | − | 5538.05i | 0.316826 | − | 0.548759i | −0.662998 | − | 0.748621i | \(-0.730716\pi\) |
0.979824 | + | 0.199862i | \(0.0640495\pi\) | |||||||
\(468\) | 129.257 | + | 50.8666i | 0.0127669 | + | 0.00502417i | ||||
\(469\) | −1275.58 | + | 5468.99i | −0.125588 | + | 0.538453i | ||||
\(470\) | −12490.0 | − | 7211.10i | −1.22579 | − | 0.707709i | ||||
\(471\) | −4691.36 | + | 349.406i | −0.458952 | + | 0.0341821i | ||||
\(472\) | −1713.50 | − | 989.288i | −0.167098 | − | 0.0964739i | ||||
\(473\) | −2673.56 | − | 1543.58i | −0.259895 | − | 0.150051i | ||||
\(474\) | −215.180 | + | 16.0263i | −0.0208513 | + | 0.00155298i | ||||
\(475\) | −14513.1 | − | 8379.12i | −1.40191 | − | 0.809390i | ||||
\(476\) | −1126.22 | + | 341.551i | −0.108445 | + | 0.0328886i | ||||
\(477\) | 1546.29 | + | 10323.2i | 0.148428 | + | 0.990916i | ||||
\(478\) | −2597.10 | + | 4498.30i | −0.248511 | + | 0.430434i | ||||
\(479\) | −17221.8 | −1.64276 | −0.821382 | − | 0.570379i | \(-0.806797\pi\) | ||||
−0.821382 | + | 0.570379i | \(0.806797\pi\) | |||||||
\(480\) | −1996.50 | + | 148.696i | −0.189848 | + | 0.0141397i | ||||
\(481\) | − | 9.61416i | − | 0.000911368i | ||||||
\(482\) | 2346.85 | + | 4064.86i | 0.221776 | + | 0.384127i | ||||
\(483\) | 1915.40 | + | 1543.85i | 0.180443 | + | 0.145440i | ||||
\(484\) | 14.1324 | − | 24.4781i | 0.00132724 | − | 0.00229884i | ||||
\(485\) | 19375.9 | + | 11186.7i | 1.81405 | + | 1.04734i | ||||
\(486\) | 10286.8 | − | 4010.09i | 0.960121 | − | 0.374282i | ||||
\(487\) | 1435.74 | + | 2486.77i | 0.133592 | + | 0.231389i | 0.925059 | − | 0.379824i | \(-0.124015\pi\) |
−0.791466 | + | 0.611213i | \(0.790682\pi\) | |||||||
\(488\) | 1525.06 | + | 2641.48i | 0.141468 | + | 0.245029i | ||||
\(489\) | 868.035 | + | 11654.8i | 0.0802738 | + | 1.07781i | ||||
\(490\) | 7612.45 | − | 15431.3i | 0.701828 | − | 1.42268i | ||||
\(491\) | −4900.34 | + | 2829.21i | −0.450406 | + | 0.260042i | −0.708002 | − | 0.706211i | \(-0.750403\pi\) |
0.257596 | + | 0.966253i | \(0.417070\pi\) | |||||||
\(492\) | 985.168 | − | 671.015i | 0.0902740 | − | 0.0614872i | ||||
\(493\) | 2093.99i | 0.191295i | ||||||||
\(494\) | 2565.70 | − | 1481.31i | 0.233677 | − | 0.134913i | ||||
\(495\) | 15434.3 | + | 6073.86i | 1.40146 | + | 0.551514i | ||||
\(496\) | 12557.0i | 1.13674i | ||||||||
\(497\) | 1891.82 | + | 6238.01i | 0.170744 | + | 0.563004i | ||||
\(498\) | −2143.19 | − | 3146.58i | −0.192849 | − | 0.283136i | ||||
\(499\) | −18601.4 | −1.66876 | −0.834380 | − | 0.551190i | \(-0.814174\pi\) | ||||
−0.834380 | + | 0.551190i | \(0.814174\pi\) | |||||||
\(500\) | 197.075 | − | 341.345i | 0.0176270 | − | 0.0305308i | ||||
\(501\) | −10273.5 | − | 4953.28i | −0.916144 | − | 0.441709i | ||||
\(502\) | −1522.35 | + | 878.930i | −0.135350 | + | 0.0781445i | ||||
\(503\) | −14649.8 | −1.29862 | −0.649308 | − | 0.760526i | \(-0.724941\pi\) | ||||
−0.649308 | + | 0.760526i | \(0.724941\pi\) | |||||||
\(504\) | 10902.5 | + | 879.101i | 0.963559 | + | 0.0776950i | ||||
\(505\) | −14678.1 | −1.29340 | ||||||||
\(506\) | 2303.17 | − | 1329.73i | 0.202348 | − | 0.116826i | ||||
\(507\) | −806.268 | − | 10825.5i | −0.0706265 | − | 0.948278i | ||||
\(508\) | 26.3279 | − | 45.6012i | 0.00229943 | − | 0.00398273i | ||||
\(509\) | −2629.20 | −0.228953 | −0.114477 | − | 0.993426i | \(-0.536519\pi\) | ||||
−0.114477 | + | 0.993426i | \(0.536519\pi\) | |||||||
\(510\) | 33346.2 | − | 2483.58i | 2.89529 | − | 0.215637i | ||||
\(511\) | 11135.9 | − | 11888.0i | 0.964035 | − | 1.02915i | ||||
\(512\) | − | 10333.9i | − | 0.891989i | ||||||
\(513\) | 4065.24 | − | 13115.1i | 0.349873 | − | 1.12875i | ||||
\(514\) | −3372.76 | + | 1947.27i | −0.289428 | + | 0.167102i | ||||
\(515\) | 734.659i | 0.0628601i | ||||||||
\(516\) | −200.540 | − | 96.6882i | −0.0171091 | − | 0.00824896i | ||||
\(517\) | 8886.51 | − | 5130.63i | 0.755954 | − | 0.436450i | ||||
\(518\) | 14.5024 | + | 47.8196i | 0.00123011 | + | 0.00405613i | ||||
\(519\) | 12648.5 | + | 6098.35i | 1.06977 | + | 0.515776i | ||||
\(520\) | −1954.98 | − | 3386.13i | −0.164868 | − | 0.285560i | ||||
\(521\) | 8915.56 | + | 15442.2i | 0.749708 | + | 1.29853i | 0.947963 | + | 0.318382i | \(0.103139\pi\) |
−0.198255 | + | 0.980151i | \(0.563527\pi\) | |||||||
\(522\) | −470.414 | + | 1195.37i | −0.0394434 | + | 0.100230i | ||||
\(523\) | −18929.9 | − | 10929.2i | −1.58269 | − | 0.913766i | −0.994465 | − | 0.105068i | \(-0.966494\pi\) |
−0.588224 | − | 0.808698i | \(-0.700173\pi\) | |||||||
\(524\) | −6.75761 | + | 11.7045i | −0.000563373 | + | 0.000975791i | ||||
\(525\) | −10340.9 | + | 12829.6i | −0.859642 | + | 1.06653i | ||||
\(526\) | 8386.42 | + | 14525.7i | 0.695181 | + | 1.20409i | ||||
\(527\) | − | 23787.3i | − | 1.96621i | ||||||
\(528\) | 5454.36 | − | 11312.8i | 0.449566 | − | 0.932439i | ||||
\(529\) | 11513.5 | 0.946288 | ||||||||
\(530\) | −9697.16 | + | 16796.0i | −0.794750 | + | 1.37655i | ||||
\(531\) | 1520.99 | + | 1910.85i | 0.124304 | + | 0.156165i | ||||
\(532\) | −613.824 | + | 655.285i | −0.0500238 | + | 0.0534026i | ||||
\(533\) | 4165.18 | + | 2404.77i | 0.338488 | + | 0.195426i | ||||
\(534\) | −8622.29 | − | 12659.0i | −0.698732 | − | 1.02586i | ||||
\(535\) | 12373.9 | + | 7144.08i | 0.999945 | + | 0.577319i | ||||
\(536\) | −5744.00 | − | 3316.30i | −0.462878 | − | 0.267243i | ||||
\(537\) | −914.885 | + | 1897.55i | −0.0735199 | + | 0.152487i | ||||
\(538\) | −4677.01 | − | 2700.27i | −0.374796 | − | 0.216388i | ||||
\(539\) | 6800.17 | + | 10180.2i | 0.543421 | + | 0.813526i | ||||
\(540\) | 1142.51 | + | 354.139i | 0.0910478 | + | 0.0282217i | ||||
\(541\) | −5561.14 | + | 9632.17i | −0.441944 | + | 0.765470i | −0.997834 | − | 0.0657862i | \(-0.979044\pi\) |
0.555889 | + | 0.831256i | \(0.312378\pi\) | |||||||
\(542\) | −21738.7 | −1.72280 | ||||||||
\(543\) | −8845.03 | − | 12986.1i | −0.699036 | − | 1.02631i | ||||
\(544\) | − | 2871.66i | − | 0.226326i | ||||||
\(545\) | 11865.8 | + | 20552.2i | 0.932615 | + | 1.61534i | ||||
\(546\) | −1050.16 | − | 2717.24i | −0.0823126 | − | 0.212980i | ||||
\(547\) | 7533.25 | − | 13048.0i | 0.588845 | − | 1.01991i | −0.405539 | − | 0.914078i | \(-0.632916\pi\) |
0.994384 | − | 0.105832i | \(-0.0337506\pi\) | |||||||
\(548\) | −37.3104 | − | 21.5412i | −0.00290843 | − | 0.00167919i | ||||
\(549\) | −557.724 | − | 3723.42i | −0.0433572 | − | 0.289456i | ||||
\(550\) | 8906.69 | + | 15426.8i | 0.690514 | + | 1.19600i | ||||
\(551\) | 798.788 | + | 1383.54i | 0.0617596 | + | 0.106971i | ||||
\(552\) | −2401.45 | + | 1635.67i | −0.185167 | + | 0.126121i | ||||
\(553\) | 192.571 | + | 180.387i | 0.0148083 | + | 0.0138713i | ||||
\(554\) | 3458.16 | − | 1996.57i | 0.265204 | − | 0.153116i | ||||
\(555\) | −6.14896 | − | 82.5601i | −0.000470287 | − | 0.00631438i | ||||
\(556\) | 142.079i | 0.0108372i | ||||||||
\(557\) | 6994.00 | − | 4037.99i | 0.532038 | − | 0.307172i | −0.209808 | − | 0.977743i | \(-0.567284\pi\) |
0.741846 | + | 0.670570i | \(0.233951\pi\) | |||||||
\(558\) | 5343.81 | − | 13579.2i | 0.405415 | − | 1.03020i | ||||
\(559\) | − | 898.300i | − | 0.0679679i | ||||||
\(560\) | 15753.5 | + | 14756.8i | 1.18876 | + | 1.11355i | ||||
\(561\) | −10332.4 | + | 21430.4i | −0.777605 | + | 1.61282i | ||||
\(562\) | −12029.7 | −0.902920 | ||||||||
\(563\) | 4491.15 | − | 7778.89i | 0.336198 | − | 0.582311i | −0.647517 | − | 0.762051i | \(-0.724192\pi\) |
0.983714 | + | 0.179740i | \(0.0575257\pi\) | |||||||
\(564\) | 611.603 | − | 416.574i | 0.0456616 | − | 0.0311009i | ||||
\(565\) | 22815.9 | − | 13172.8i | 1.69889 | − | 0.980855i | ||||
\(566\) | −5543.18 | −0.411656 | ||||||||
\(567\) | −12125.4 | − | 5937.85i | −0.898096 | − | 0.439799i | ||||
\(568\) | −7698.85 | −0.568726 | ||||||||
\(569\) | 9591.95 | − | 5537.92i | 0.706706 | − | 0.408017i | −0.103134 | − | 0.994667i | \(-0.532887\pi\) |
0.809840 | + | 0.586651i | \(0.199554\pi\) | |||||||
\(570\) | 21085.1 | − | 14361.5i | 1.54940 | − | 1.05532i | ||||
\(571\) | 11164.3 | − | 19337.1i | 0.818233 | − | 1.41722i | −0.0887498 | − | 0.996054i | \(-0.528287\pi\) |
0.906983 | − | 0.421167i | \(-0.138380\pi\) | |||||||
\(572\) | −183.625 | −0.0134226 | ||||||||
\(573\) | 2320.89 | − | 4813.73i | 0.169209 | − | 0.350953i | ||||
\(574\) | −24344.5 | − | 5678.09i | −1.77025 | − | 0.412890i | ||||
\(575\) | − | 4377.33i | − | 0.317474i | ||||||
\(576\) | −4711.20 | + | 11971.7i | −0.340798 | + | 0.866005i | ||||
\(577\) | 2753.56 | − | 1589.77i | 0.198669 | − | 0.114702i | −0.397365 | − | 0.917660i | \(-0.630075\pi\) |
0.596035 | + | 0.802959i | \(0.296742\pi\) | |||||||
\(578\) | 33643.7i | 2.42110i | ||||||||
\(579\) | 1583.11 | + | 21255.9i | 0.113630 | + | 1.52567i | ||||
\(580\) | −120.526 | + | 69.5856i | −0.00862855 | + | 0.00498170i | ||||
\(581\) | −1057.47 | + | 4533.87i | −0.0755102 | + | 0.323747i | ||||
\(582\) | −16271.6 | + | 11082.9i | −1.15890 | + | 0.789346i | ||||
\(583\) | −6899.43 | − | 11950.2i | −0.490129 | − | 0.848929i | ||||
\(584\) | 9619.21 | + | 16661.0i | 0.681585 | + | 1.18054i | ||||
\(585\) | 714.949 | + | 4773.06i | 0.0505291 | + | 0.337337i | ||||
\(586\) | 19990.4 | + | 11541.5i | 1.40921 | + | 0.813606i | ||||
\(587\) | 9230.28 | − | 15987.3i | 0.649019 | − | 1.12413i | −0.334338 | − | 0.942453i | \(-0.608513\pi\) |
0.983357 | − | 0.181681i | \(-0.0581540\pi\) | |||||||
\(588\) | 543.570 | + | 695.695i | 0.0381232 | + | 0.0487925i | ||||
\(589\) | −9074.08 | − | 15716.8i | −0.634789 | − | 1.09949i | ||||
\(590\) | 4537.72i | 0.316636i | ||||||||
\(591\) | −2355.70 | − | 3458.58i | −0.163960 | − | 0.240723i | ||||
\(592\) | −62.6867 | −0.00435204 | ||||||||
\(593\) | 4842.31 | − | 8387.12i | 0.335328 | − | 0.580806i | −0.648220 | − | 0.761453i | \(-0.724486\pi\) |
0.983548 | + | 0.180648i | \(0.0578194\pi\) | |||||||
\(594\) | −10712.7 | + | 9912.56i | −0.739979 | + | 0.684709i | ||||
\(595\) | −29842.6 | − | 27954.4i | −2.05618 | − | 1.92608i | ||||
\(596\) | −866.954 | − | 500.536i | −0.0595836 | − | 0.0344006i | ||||
\(597\) | 5011.21 | − | 10393.7i | 0.343543 | − | 0.712538i | ||||
\(598\) | 670.174 | + | 386.925i | 0.0458285 | + | 0.0264591i | ||||
\(599\) | −3303.93 | − | 1907.53i | −0.225367 | − | 0.130116i | 0.383066 | − | 0.923721i | \(-0.374868\pi\) |
−0.608433 | + | 0.793605i | \(0.708202\pi\) | |||||||
\(600\) | −10955.9 | − | 16085.1i | −0.745452 | − | 1.09445i | ||||
\(601\) | 7609.28 | + | 4393.22i | 0.516454 | + | 0.298175i | 0.735483 | − | 0.677544i | \(-0.236955\pi\) |
−0.219029 | + | 0.975718i | \(0.570289\pi\) | |||||||
\(602\) | 1355.03 | + | 4468.03i | 0.0917392 | + | 0.302497i | ||||
\(603\) | 5098.66 | + | 6405.56i | 0.344334 | + | 0.432594i | ||||
\(604\) | −475.311 | + | 823.263i | −0.0320201 | + | 0.0554604i | ||||
\(605\) | 982.066 | 0.0659944 | ||||||||
\(606\) | 5609.37 | − | 11634.3i | 0.376015 | − | 0.779888i | ||||
\(607\) | 11742.5i | 0.785194i | 0.919711 | + | 0.392597i | \(0.128423\pi\) | ||||
−0.919711 | + | 0.392597i | \(0.871577\pi\) | |||||||
\(608\) | −1095.45 | − | 1897.37i | −0.0730694 | − | 0.126560i | ||||
\(609\) | 1465.26 | − | 566.293i | 0.0974961 | − | 0.0376804i | ||||
\(610\) | 3497.61 | − | 6058.04i | 0.232154 | − | 0.402103i | ||||
\(611\) | 2585.79 | + | 1492.91i | 0.171211 | + | 0.0988487i | ||||
\(612\) | −628.284 | + | 1596.54i | −0.0414982 | + | 0.105451i | ||||
\(613\) | 9443.86 | + | 16357.2i | 0.622241 | + | 1.07775i | 0.989067 | + | 0.147464i | \(0.0471110\pi\) |
−0.366826 | + | 0.930289i | \(0.619556\pi\) | |||||||
\(614\) | −2492.03 | − | 4316.33i | −0.163795 | − | 0.283702i | ||||
\(615\) | 37305.9 | + | 17986.6i | 2.44604 | + | 1.17933i | ||||
\(616\) | −13836.8 | + | 4196.33i | −0.905035 | + | 0.274472i | ||||
\(617\) | −10726.8 | + | 6193.11i | −0.699909 | + | 0.404093i | −0.807314 | − | 0.590123i | \(-0.799079\pi\) |
0.107404 | + | 0.994215i | \(0.465746\pi\) | |||||||
\(618\) | −582.315 | − | 280.757i | −0.0379031 | − | 0.0182746i | ||||
\(619\) | 2663.48i | 0.172947i | 0.996254 | + | 0.0864735i | \(0.0275598\pi\) | ||||
−0.996254 | + | 0.0864735i | \(0.972440\pi\) | |||||||
\(620\) | 1369.15 | − | 790.479i | 0.0886877 | − | 0.0512038i | ||||
\(621\) | 3497.70 | − | 793.269i | 0.226019 | − | 0.0512605i | ||||
\(622\) | − | 30212.9i | − | 1.94763i | ||||||
\(623\) | −4254.33 | + | 18240.3i | −0.273590 | + | 1.17300i | ||||
\(624\) | 3644.34 | − | 271.425i | 0.233798 | − | 0.0174130i | ||||
\(625\) | −7708.96 | −0.493374 | ||||||||
\(626\) | −11929.2 | + | 20662.0i | −0.761642 | + | 1.31920i | ||||
\(627\) | 1348.14 | + | 18101.0i | 0.0858685 | + | 1.15293i | ||||
\(628\) | 388.391 | − | 224.238i | 0.0246791 | − | 0.0142485i | ||||
\(629\) | 118.750 | 0.00752764 | ||||||||
\(630\) | −10756.0 | − | 22662.2i | −0.680202 | − | 1.43315i | ||||
\(631\) | 20380.6 | 1.28580 | 0.642898 | − | 0.765952i | \(-0.277732\pi\) | ||||
0.642898 | + | 0.765952i | \(0.277732\pi\) | |||||||
\(632\) | −269.887 | + | 155.819i | −0.0169866 | + | 0.00980720i | ||||
\(633\) | −10515.7 | − | 5070.02i | −0.660284 | − | 0.318349i | ||||
\(634\) | 5244.30 | − | 9083.40i | 0.328514 | − | 0.569003i | ||||
\(635\) | 1829.53 | 0.114335 | ||||||||
\(636\) | −560.189 | − | 822.456i | −0.0349260 | − | 0.0512775i | ||||
\(637\) | −1576.00 | + | 3194.72i | −0.0980272 | + | 0.198712i | ||||
\(638\) | − | 1698.16i | − | 0.105378i | ||||||
\(639\) | 8843.07 | + | 3480.01i | 0.547459 | + | 0.215441i | ||||
\(640\) | −23370.4 | + | 13492.9i | −1.44343 | + | 0.833366i | ||||
\(641\) | − | 20778.8i | − | 1.28036i | −0.768224 | − | 0.640181i | \(-0.778859\pi\) | ||
0.768224 | − | 0.640181i | \(-0.221141\pi\) | |||||||
\(642\) | −10391.4 | + | 7077.78i | −0.638812 | + | 0.435106i | ||||
\(643\) | −6344.01 | + | 3662.72i | −0.389088 | + | 0.224640i | −0.681765 | − | 0.731572i | \(-0.738787\pi\) |
0.292677 | + | 0.956211i | \(0.405454\pi\) | |||||||
\(644\) | −228.399 | − | 53.2714i | −0.0139754 | − | 0.00325961i | ||||
\(645\) | −574.529 | − | 7714.01i | −0.0350730 | − | 0.470913i | ||||
\(646\) | 18296.5 | + | 31690.5i | 1.11435 | + | 1.93010i | ||||
\(647\) | 5424.13 | + | 9394.87i | 0.329590 | + | 0.570866i | 0.982430 | − | 0.186629i | \(-0.0597562\pi\) |
−0.652841 | + | 0.757495i | \(0.726423\pi\) | |||||||
\(648\) | 10867.4 | − | 11669.2i | 0.658812 | − | 0.707425i | ||||
\(649\) | −2796.00 | − | 1614.27i | −0.169110 | − | 0.0976359i | ||||
\(650\) | −2591.66 | + | 4488.89i | −0.156390 | + | 0.270875i | ||||
\(651\) | −16645.0 | + | 6432.98i | −1.00210 | + | 0.387294i | ||||
\(652\) | −557.077 | − | 964.885i | −0.0334614 | − | 0.0579568i | ||||
\(653\) | − | 11896.6i | − | 0.712941i | −0.934307 | − | 0.356470i | \(-0.883980\pi\) | ||
0.934307 | − | 0.356470i | \(-0.116020\pi\) | |||||||
\(654\) | −20825.0 | + | 1551.02i | −1.24514 | + | 0.0927362i | ||||
\(655\) | −469.588 | −0.0280127 | ||||||||
\(656\) | 15679.7 | − | 27158.0i | 0.933215 | − | 1.61638i | ||||
\(657\) | −3517.80 | − | 23485.2i | −0.208893 | − | 1.39459i | ||||
\(658\) | −15113.4 | − | 3525.02i | −0.895411 | − | 0.208844i | ||||
\(659\) | −24001.0 | − | 13857.0i | −1.41874 | − | 0.819108i | −0.422549 | − | 0.906340i | \(-0.638865\pi\) |
−0.996188 | + | 0.0872319i | \(0.972198\pi\) | |||||||
\(660\) | −1576.85 | + | 117.442i | −0.0929983 | + | 0.00692639i | ||||
\(661\) | 24782.6 | + | 14308.3i | 1.45829 | + | 0.841947i | 0.998928 | − | 0.0462996i | \(-0.0147429\pi\) |
0.459367 | + | 0.888246i | \(0.348076\pi\) | |||||||
\(662\) | −20157.3 | − | 11637.8i | −1.18344 | − | 0.683259i | ||||
\(663\) | −6903.63 | + | 514.174i | −0.404397 | + | 0.0301189i | ||||
\(664\) | −4761.86 | − | 2749.26i | −0.278307 | − | 0.160681i | ||||
\(665\) | −30381.3 | − | 7086.10i | −1.77164 | − | 0.413214i | ||||
\(666\) | 67.7897 | + | 26.6772i | 0.00394414 | + | 0.00155213i | ||||
\(667\) | −208.647 | + | 361.388i | −0.0121122 | + | 0.0209790i | ||||
\(668\) | 1087.29 | 0.0629768 | ||||||||
\(669\) | −21737.4 | + | 1618.97i | −1.25623 | + | 0.0935622i | ||||
\(670\) | 15211.4i | 0.877114i | ||||||||
\(671\) | 2488.52 | + | 4310.24i | 0.143172 | + | 0.247981i | ||||
\(672\) | −2009.43 | + | 776.606i | −0.115350 | + | 0.0445807i | ||||
\(673\) | −3408.12 | + | 5903.03i | −0.195205 | + | 0.338106i | −0.946968 | − | 0.321328i | \(-0.895871\pi\) |
0.751762 | + | 0.659434i | \(0.229204\pi\) | |||||||
\(674\) | −24020.3 | − | 13868.1i | −1.37274 | − | 0.792553i | ||||
\(675\) | 5313.40 | + | 23428.0i | 0.302982 | + | 1.33592i | ||||
\(676\) | 517.437 | + | 896.227i | 0.0294400 | + | 0.0509915i | ||||
\(677\) | −2806.77 | − | 4861.47i | −0.159340 | − | 0.275984i | 0.775291 | − | 0.631604i | \(-0.217603\pi\) |
−0.934631 | + | 0.355620i | \(0.884270\pi\) | |||||||
\(678\) | 1721.85 | + | 23118.7i | 0.0975330 | + | 1.30954i | ||||
\(679\) | 23445.5 | + | 5468.41i | 1.32512 | + | 0.309069i | ||||
\(680\) | 41824.1 | − | 24147.1i | 2.35865 | − | 1.36177i | ||||
\(681\) | 10053.7 | − | 6847.76i | 0.565726 | − | 0.385326i | ||||
\(682\) | 19290.8i | 1.08311i | ||||||||
\(683\) | −8374.35 | + | 4834.94i | −0.469159 | + | 0.270869i | −0.715888 | − | 0.698215i | \(-0.753978\pi\) |
0.246728 | + | 0.969085i | \(0.420644\pi\) | |||||||
\(684\) | 193.906 | + | 1294.54i | 0.0108395 | + | 0.0723652i | ||||
\(685\) | − | 1496.90i | − | 0.0834945i | ||||||
\(686\) | 3019.77 | − | 18267.4i | 0.168069 | − | 1.01670i | ||||
\(687\) | −8953.02 | − | 13144.6i | −0.497204 | − | 0.729983i | ||||
\(688\) | −5857.14 | −0.324566 | ||||||||
\(689\) | 2007.59 | − | 3477.25i | 0.111006 | − | 0.192268i | ||||
\(690\) | 6002.48 | + | 2894.03i | 0.331174 | + | 0.159672i | ||||
\(691\) | 3737.34 | − | 2157.76i | 0.205753 | − | 0.118792i | −0.393583 | − | 0.919289i | \(-0.628765\pi\) |
0.599336 | + | 0.800497i | \(0.295431\pi\) | |||||||
\(692\) | −1338.64 | −0.0735370 | ||||||||
\(693\) | 17790.1 | + | 1434.47i | 0.975166 | + | 0.0786308i | ||||
\(694\) | 22835.5 | 1.24903 | ||||||||
\(695\) | −4275.18 | + | 2468.28i | −0.233334 | + | 0.134715i | ||||
\(696\) | 137.799 | + | 1850.19i | 0.00750470 | + | 0.100763i | ||||
\(697\) | −29702.8 | + | 51446.7i | −1.61416 | + | 2.79581i | ||||
\(698\) | 17256.7 | 0.935780 | ||||||||
\(699\) | −13171.0 | + | 980.957i | −0.712693 | + | 0.0530804i | ||||
\(700\) | 356.818 | − | 1529.84i | 0.0192663 | − | 0.0826035i | ||||
\(701\) | − | 22520.8i | − | 1.21341i | −0.794929 | − | 0.606703i | \(-0.792492\pi\) | ||
0.794929 | − | 0.606703i | \(-0.207508\pi\) | |||||||
\(702\) | −4056.51 | − | 1257.38i | −0.218096 | − | 0.0676022i | ||||
\(703\) | 78.4608 | − | 45.2994i | 0.00420940 | − | 0.00243030i | ||||
\(704\) | − | 17007.1i | − | 0.910483i | ||||||
\(705\) | 23159.9 | + | 11166.3i | 1.23724 | + | 0.596521i | ||||
\(706\) | 11593.0 | − | 6693.21i | 0.618000 | − | 0.356802i | ||||
\(707\) | −15114.6 | + | 4583.83i | −0.804019 | + | 0.243837i | ||||
\(708\) | −209.724 | − | 101.116i | −0.0111327 | − | 0.00536749i | ||||
\(709\) | 1407.50 | + | 2437.87i | 0.0745556 | + | 0.129134i | 0.900893 | − | 0.434041i | \(-0.142913\pi\) |
−0.826337 | + | 0.563175i | \(0.809579\pi\) | |||||||
\(710\) | 8828.37 | + | 15291.2i | 0.466652 | + | 0.808265i | ||||
\(711\) | 380.431 | − | 56.9841i | 0.0200665 | − | 0.00300572i | ||||
\(712\) | −19157.5 | − | 11060.6i | −1.00837 | − | 0.582180i | ||||
\(713\) | 2370.19 | − | 4105.29i | 0.124494 | − | 0.215630i | ||||
\(714\) | 33562.2 | − | 12971.2i | 1.75915 | − | 0.679879i | ||||
\(715\) | −3190.04 | − | 5525.31i | −0.166854 | − | 0.289000i | ||||
\(716\) | − | 200.826i | − | 0.0104821i | ||||||
\(717\) | 4021.57 | − | 8341.09i | 0.209468 | − | 0.434455i | ||||
\(718\) | −33757.7 | −1.75463 | ||||||||
\(719\) | −5377.34 | + | 9313.82i | −0.278916 | + | 0.483097i | −0.971116 | − | 0.238609i | \(-0.923309\pi\) |
0.692199 | + | 0.721706i | \(0.256642\pi\) | |||||||
\(720\) | 31121.6 | − | 4661.64i | 1.61088 | − | 0.241291i | ||||
\(721\) | 229.428 | + | 756.505i | 0.0118507 | + | 0.0390759i | ||||
\(722\) | 6864.42 | + | 3963.17i | 0.353833 | + | 0.204285i | ||||
\(723\) | −4710.52 | − | 6915.87i | −0.242304 | − | 0.355745i | ||||
\(724\) | 1297.20 | + | 748.936i | 0.0665883 | + | 0.0384447i | ||||
\(725\) | −2420.61 | − | 1397.54i | −0.123999 | − | 0.0715908i | ||||
\(726\) | −375.306 | + | 778.417i | −0.0191858 | + | 0.0397931i | ||||
\(727\) | 5477.81 | + | 3162.62i | 0.279451 | + | 0.161341i | 0.633175 | − | 0.774009i | \(-0.281751\pi\) |
−0.353724 | + | 0.935350i | \(0.615085\pi\) | |||||||
\(728\) | −3070.57 | − | 2876.29i | −0.156323 | − | 0.146432i | ||||
\(729\) | −17757.2 | + | 8491.33i | −0.902159 | + | 0.431404i | ||||
\(730\) | 22060.9 | − | 38210.7i | 1.11851 | − | 1.93732i | ||||
\(731\) | 11095.4 | 0.561395 | ||||||||
\(732\) | 202.051 | + | 296.647i | 0.0102022 | + | 0.0149787i | ||||
\(733\) | − | 14798.7i | − | 0.745706i | −0.927890 | − | 0.372853i | \(-0.878380\pi\) | ||
0.927890 | − | 0.372853i | \(-0.121620\pi\) | |||||||
\(734\) | 6772.48 | + | 11730.3i | 0.340568 | + | 0.589881i | ||||
\(735\) | −11490.4 | + | 28442.1i | −0.576638 | + | 1.42735i | ||||
\(736\) | 286.136 | − | 495.602i | 0.0143303 | − | 0.0248208i | ||||
\(737\) | −9372.77 | − | 5411.37i | −0.468454 | − | 0.270462i | ||||
\(738\) | −28513.6 | + | 22696.1i | −1.42222 | + | 1.13205i | ||||
\(739\) | 12825.4 | + | 22214.3i | 0.638418 | + | 1.10577i | 0.985780 | + | 0.168041i | \(0.0537441\pi\) |
−0.347362 | + | 0.937731i | \(0.612923\pi\) | |||||||
\(740\) | 3.94621 | + | 6.83503i | 0.000196034 | + | 0.000339542i | ||||
\(741\) | −4365.24 | + | 2973.24i | −0.216412 | + | 0.147402i | ||||
\(742\) | −4740.28 | + | 20323.8i | −0.234530 | + | 1.00554i | ||||
\(743\) | −30440.0 | + | 17574.5i | −1.50301 | + | 0.867761i | −0.503012 | + | 0.864279i | \(0.667775\pi\) |
−0.999994 | + | 0.00348188i | \(0.998892\pi\) | |||||||
\(744\) | −1565.37 | − | 21017.7i | −0.0771363 | − | 1.03568i | ||||
\(745\) | − | 34782.4i | − | 1.71051i | ||||||
\(746\) | 33503.2 | − | 19343.1i | 1.64429 | − | 0.949331i | ||||
\(747\) | 4226.87 | + | 5310.30i | 0.207032 | + | 0.260099i | ||||
\(748\) | − | 2268.07i | − | 0.110867i | ||||||
\(749\) | 14972.9 | + | 3492.26i | 0.730438 | + | 0.170366i | ||||
\(750\) | −5233.61 | + | 10855.0i | −0.254806 | + | 0.528490i | ||||
\(751\) | −15906.4 | −0.772881 | −0.386440 | − | 0.922314i | \(-0.626295\pi\) | ||||
−0.386440 | + | 0.922314i | \(0.626295\pi\) | |||||||
\(752\) | 9734.13 | − | 16860.0i | 0.472031 | − | 0.817581i | ||||
\(753\) | 2590.10 | − | 1764.16i | 0.125350 | − | 0.0853780i | ||||
\(754\) | 427.929 | − | 247.065i | 0.0206688 | − | 0.0119331i | ||||
\(755\) | −33029.5 | −1.59214 | ||||||||
\(756\) | 1287.08 | + | 7.87423i | 0.0619188 | + | 0.000378814i | ||||
\(757\) | 8886.22 | 0.426651 | 0.213326 | − | 0.976981i | \(-0.431570\pi\) | ||||
0.213326 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(758\) | 29837.4 | − | 17226.6i | 1.42974 | − | 0.825461i | ||||
\(759\) | −3918.56 | + | 2669.00i | −0.187398 | + | 0.127640i | ||||
\(760\) | 18422.7 | − | 31909.1i | 0.879292 | − | 1.52298i | ||||
\(761\) | 6896.64 | 0.328519 | 0.164259 | − | 0.986417i | \(-0.447477\pi\) | ||||
0.164259 | + | 0.986417i | \(0.447477\pi\) | |||||||
\(762\) | −699.172 | + | 1450.14i | −0.0332393 | + | 0.0689412i | ||||
\(763\) | 18636.9 | + | 17457.7i | 0.884275 | + | 0.828326i | ||||
\(764\) | 509.456i | 0.0241249i | ||||||||
\(765\) | −58955.0 | + | 8830.77i | −2.78630 | + | 0.417356i | ||||
\(766\) | 11688.5 | − | 6748.35i | 0.551335 | − | 0.318313i | ||||
\(767\) | − | 939.440i | − | 0.0442258i | ||||||
\(768\) | −292.544 | − | 3927.88i | −0.0137451 | − | 0.184551i | ||||
\(769\) | 23996.6 | − | 13854.4i | 1.12528 | − | 0.649680i | 0.182536 | − | 0.983199i | \(-0.441569\pi\) |
0.942743 | + | 0.333519i | \(0.108236\pi\) | |||||||
\(770\) | 24201.5 | + | 22670.2i | 1.13268 | + | 1.06101i | ||||
\(771\) | 5738.36 | − | 3908.49i | 0.268044 | − | 0.182569i | ||||
\(772\) | −1015.99 | − | 1759.74i | −0.0473656 | − | 0.0820396i | ||||
\(773\) | −17922.3 | − | 31042.4i | −0.833921 | − | 1.44439i | −0.894906 | − | 0.446255i | \(-0.852757\pi\) |
0.0609846 | − | 0.998139i | \(-0.480576\pi\) | |||||||
\(774\) | 6333.93 | + | 2492.59i | 0.294145 | + | 0.115755i | ||||
\(775\) | 27497.7 | + | 15875.8i | 1.27451 | + | 0.735839i | ||||
\(776\) | −14217.0 | + | 24624.5i | −0.657679 | + | 1.13913i | ||||
\(777\) | −32.1146 | − | 83.0948i | −0.00148276 | − | 0.00383656i | ||||
\(778\) | 12143.5 | + | 21033.1i | 0.559594 | + | 0.969245i | ||||
\(779\) | 45322.5i | 2.08453i | ||||||||
\(780\) | −259.010 | − | 380.273i | −0.0118898 | − | 0.0174564i | ||||
\(781\) | −12562.6 | −0.575577 | ||||||||
\(782\) | −4779.14 | + | 8277.72i | −0.218545 | + | 0.378530i | ||||
\(783\) | 678.035 | − | 2187.45i | 0.0309464 | − | 0.0998380i | ||||
\(784\) | 20830.4 | + | 10275.9i | 0.948905 | + | 0.468108i | ||||
\(785\) | 13494.7 | + | 7791.17i | 0.613562 | + | 0.354240i | ||||
\(786\) | 179.458 | − | 372.211i | 0.00814381 | − | 0.0168910i | ||||
\(787\) | 7049.71 | + | 4070.15i | 0.319307 | + | 0.184352i | 0.651084 | − | 0.759006i | \(-0.274315\pi\) |
−0.331776 | + | 0.943358i | \(0.607648\pi\) | |||||||
\(788\) | 345.483 | + | 199.465i | 0.0156184 | + | 0.00901730i | ||||
\(789\) | −16833.0 | − | 24713.8i | −0.759530 | − | 1.11512i | ||||
\(790\) | 618.965 | + | 357.360i | 0.0278757 | + | 0.0160940i | ||||
\(791\) | 19380.6 | − | 20689.7i | 0.871171 | − | 0.930014i | ||||
\(792\) | −7719.17 | + | 19615.2i | −0.346324 | + | 0.880047i | ||||
\(793\) | −724.107 | + | 1254.19i | −0.0324260 | + | 0.0561635i | ||||
\(794\) | 18891.5 | 0.844376 | ||||||||
\(795\) | 15015.9 | − | 31144.3i | 0.669887 | − | 1.38940i | ||||
\(796\) | 1100.00i | 0.0489807i | ||||||||
\(797\) | −2028.87 | − | 3514.10i | −0.0901708 | − | 0.156180i | 0.817412 | − | 0.576053i | \(-0.195408\pi\) |
−0.907583 | + | 0.419873i | \(0.862075\pi\) | |||||||
\(798\) | 17227.2 | − | 21373.2i | 0.764205 | − | 0.948125i | ||||
\(799\) | −18439.8 | + | 31938.7i | −0.816462 | + | 1.41415i | ||||
\(800\) | 3319.59 | + | 1916.57i | 0.146707 | + | 0.0847011i | ||||
\(801\) | 17005.1 | + | 21363.9i | 0.750121 | + | 0.942393i | ||||
\(802\) | 2491.97 | + | 4316.21i | 0.109719 | + | 0.190038i | ||||
\(803\) | 15696.1 | + | 27186.5i | 0.689794 | + | 1.19476i | ||||
\(804\) | −703.039 | − | 338.963i | −0.0308386 | − | 0.0148685i | ||||
\(805\) | −2364.93 | − | 7798.03i | −0.103544 | − | 0.341421i | ||||
\(806\) | −4861.19 | + | 2806.61i | −0.212442 | + | 0.122653i | ||||
\(807\) | 8672.46 | + | 4181.33i | 0.378296 | + | 0.182391i | ||||
\(808\) | − | 18654.1i | − | 0.812191i | ||||||
\(809\) | 1680.09 | − | 970.002i | 0.0730148 | − | 0.0421551i | −0.463048 | − | 0.886333i | \(-0.653244\pi\) |
0.536063 | + | 0.844178i | \(0.319911\pi\) | |||||||
\(810\) | −35638.8 | − | 8203.11i | −1.54595 | − | 0.355837i | ||||
\(811\) | 35635.2i | 1.54294i | 0.636268 | + | 0.771468i | \(0.280477\pi\) | ||||
−0.636268 | + | 0.771468i | \(0.719523\pi\) | |||||||
\(812\) | −102.379 | + | 109.294i | −0.00442462 | + | 0.00472348i | ||||
\(813\) | 38647.7 | − | 2878.43i | 1.66720 | − | 0.124171i | ||||
\(814\) | −96.3031 | −0.00414671 | ||||||||
\(815\) | 19355.7 | − | 33525.1i | 0.831903 | − | 1.44090i | ||||
\(816\) | 3352.54 | + | 45013.4i | 0.143826 | + | 1.93111i | ||||
\(817\) | 7331.00 | − | 4232.55i | 0.313928 | − | 0.181246i | ||||
\(818\) | −18095.4 | −0.773462 | ||||||||
\(819\) | 2226.79 | + | 4691.73i | 0.0950067 | + | 0.200174i | ||||
\(820\) | −3948.23 | −0.168144 | ||||||||
\(821\) | 22330.0 | − | 12892.2i | 0.949234 | − | 0.548040i | 0.0563908 | − | 0.998409i | \(-0.482041\pi\) |
0.892843 | + | 0.450368i | \(0.148707\pi\) | |||||||
\(822\) | 1186.49 | + | 572.055i | 0.0503452 | + | 0.0242734i | ||||
\(823\) | 18894.9 | − | 32726.9i | 0.800284 | − | 1.38613i | −0.119146 | − | 0.992877i | \(-0.538016\pi\) |
0.919429 | − | 0.393255i | \(-0.128651\pi\) | |||||||
\(824\) | −933.667 | −0.0394731 | ||||||||
\(825\) | −17877.2 | − | 26246.9i | −0.754431 | − | 1.10764i | ||||
\(826\) | 1417.09 | + | 4672.66i | 0.0596935 | + | 0.196831i | ||||
\(827\) | − | 9246.54i | − | 0.388795i | −0.980923 | − | 0.194398i | \(-0.937725\pi\) | ||
0.980923 | − | 0.194398i | \(-0.0622752\pi\) | |||||||
\(828\) | −267.512 | + | 212.933i | −0.0112279 | + | 0.00893712i | ||||
\(829\) | −22476.1 | + | 12976.6i | −0.941649 | + | 0.543661i | −0.890477 | − | 0.455029i | \(-0.849629\pi\) |
−0.0511721 | + | 0.998690i | \(0.516296\pi\) | |||||||
\(830\) | 12610.5i | 0.527368i | ||||||||
\(831\) | −5883.65 | + | 4007.45i | −0.245609 | + | 0.167289i | ||||
\(832\) | 4285.72 | − | 2474.36i | 0.178582 | − | 0.103105i | ||||
\(833\) | −39459.9 | − | 19466.1i | −1.64130 | − | 0.809677i | ||||
\(834\) | −322.636 | − | 4331.93i | −0.0133957 | − | 0.179859i | ||||
\(835\) | 18889.0 | + | 32716.7i | 0.782852 | + | 1.35594i | ||||
\(836\) | −865.193 | − | 1498.56i | −0.0357935 | − | 0.0619961i | ||||
\(837\) | −7702.35 | + | 24849.0i | −0.318079 | + | 1.02617i | ||||
\(838\) | −29916.9 | − | 17272.5i | −1.23325 | − | 0.712017i | ||||
\(839\) | −16562.3 | + | 28686.7i | −0.681518 | + | 1.18042i | 0.292999 | + | 0.956113i | \(0.405347\pi\) |
−0.974517 | + | 0.224312i | \(0.927987\pi\) | |||||||
\(840\) | −28207.6 | − | 22735.9i | −1.15864 | − | 0.933883i | ||||
\(841\) | −12061.3 | − | 20890.7i | −0.494537 | − | 0.856564i | ||||
\(842\) | 1271.39i | 0.0520369i | ||||||||
\(843\) | 21386.7 | − | 1592.85i | 0.873780 | − | 0.0650780i | ||||
\(844\) | 1112.91 | 0.0453887 | ||||||||
\(845\) | −17978.4 | + | 31139.5i | −0.731925 | + | 1.26773i | ||||
\(846\) | −17701.5 | + | 14090.0i | −0.719375 | + | 0.572605i | ||||
\(847\) | 1011.27 | − | 306.690i | 0.0410243 | − | 0.0124416i | ||||
\(848\) | −22672.5 | − | 13090.0i | −0.918135 | − | 0.530085i | ||||
\(849\) | 9854.81 | − | 733.973i | 0.398370 | − | 0.0296701i | ||||
\(850\) | −55445.0 | − | 32011.2i | −2.23735 | − | 1.29174i | ||||
\(851\) | 20.4944 | + | 11.8324i | 0.000825543 | + | 0.000476628i | ||||
\(852\) | −903.455 | + | 67.2881i | −0.0363285 | + | 0.00270570i | ||||
\(853\) | −33036.5 | − | 19073.6i | −1.32608 | − | 0.765614i | −0.341392 | − | 0.939921i | \(-0.610898\pi\) |
−0.984691 | + | 0.174307i | \(0.944232\pi\) | |||||||
\(854\) | 1709.75 | − | 7330.46i | 0.0685086 | − | 0.293727i | ||||
\(855\) | −35584.2 | + | 28324.1i | −1.42334 | + | 1.13294i | ||||
\(856\) | −9079.30 | + | 15725.8i | −0.362528 | + | 0.627917i | ||||
\(857\) | −29314.0 | −1.16843 | −0.584217 | − | 0.811598i | \(-0.698598\pi\) | ||||
−0.584217 | + | 0.811598i | \(0.698598\pi\) | |||||||
\(858\) | 5598.65 | − | 416.980i | 0.222768 | − | 0.0165914i | ||||
\(859\) | − | 30802.0i | − | 1.22346i | −0.791067 | − | 0.611729i | \(-0.790474\pi\) | ||
0.791067 | − | 0.611729i | \(-0.209526\pi\) | |||||||
\(860\) | 368.714 | + | 638.632i | 0.0146198 | + | 0.0253223i | ||||
\(861\) | 44032.3 | + | 6871.20i | 1.74288 | + | 0.271974i | ||||
\(862\) | 18327.1 | − | 31743.5i | 0.724157 | − | 1.25428i | ||||
\(863\) | 10009.9 | + | 5779.21i | 0.394832 | + | 0.227957i | 0.684252 | − | 0.729246i | \(-0.260129\pi\) |
−0.289419 | + | 0.957202i | \(0.593462\pi\) | |||||||
\(864\) | −929.848 | + | 2999.84i | −0.0366135 | + | 0.118121i | ||||
\(865\) | −23255.7 | − | 40280.0i | −0.914123 | − | 1.58331i | ||||
\(866\) | −22571.7 | − | 39095.4i | −0.885702 | − | 1.53408i | ||||
\(867\) | −4454.78 | − | 59812.8i | −0.174501 | − | 2.34296i | ||||
\(868\) | 1163.00 | − | 1241.56i | 0.0454780 | − | 0.0485498i | ||||
\(869\) | −440.388 | + | 254.258i | −0.0171912 | + | 0.00992533i | ||||
\(870\) | 3516.76 | − | 2395.32i | 0.137045 | − | 0.0933438i | ||||
\(871\) | − | 3149.19i | − | 0.122510i | ||||||
\(872\) | −26119.4 | + | 15080.1i | −1.01435 | + | 0.585637i | ||||
\(873\) | 27460.6 | − | 21857.9i | 1.06461 | − | 0.847399i | ||||
\(874\) | 7292.35i | 0.282228i | ||||||||
\(875\) | 14102.1 | − | 4276.77i | 0.544842 | − | 0.165236i | ||||
\(876\) | 1274.42 | + | 1871.08i | 0.0491539 | + | 0.0721666i | ||||
\(877\) | −8118.17 | −0.312578 | −0.156289 | − | 0.987711i | \(-0.549953\pi\) | ||||
−0.156289 | + | 0.987711i | \(0.549953\pi\) | |||||||
\(878\) | −18248.3 | + | 31607.1i | −0.701426 | + | 1.21490i | ||||
\(879\) | −37067.7 | − | 17871.8i | −1.42237 | − | 0.685780i | ||||
\(880\) | −36026.4 | + | 20799.9i | −1.38006 | + | 0.796776i | ||||
\(881\) | 20509.9 | 0.784331 | 0.392165 | − | 0.919895i | \(-0.371726\pi\) | ||||
0.392165 | + | 0.919895i | \(0.371726\pi\) | |||||||
\(882\) | −18153.0 | − | 19977.1i | −0.693019 | − | 0.762656i | ||||
\(883\) | −12792.6 | −0.487549 | −0.243774 | − | 0.969832i | \(-0.578386\pi\) | ||||
−0.243774 | + | 0.969832i | \(0.578386\pi\) | |||||||
\(884\) | 571.542 | − | 329.980i | 0.0217455 | − | 0.0125548i | ||||
\(885\) | −600.841 | − | 8067.29i | −0.0228215 | − | 0.306417i | ||||
\(886\) | 1187.89 | − | 2057.49i | 0.0450430 | − | 0.0780167i | ||||
\(887\) | 1469.19 | 0.0556150 | 0.0278075 | − | 0.999613i | \(-0.491147\pi\) | ||||
0.0278075 | + | 0.999613i | \(0.491147\pi\) | |||||||
\(888\) | 104.924 | − | 7.81462i | 0.00396512 | − | 0.000295317i | ||||
\(889\) | 1883.93 | − | 571.346i | 0.0710743 | − | 0.0215549i | ||||
\(890\) | 50733.2i | 1.91077i | ||||||||
\(891\) | 17732.8 | − | 19041.3i | 0.666748 | − | 0.715946i | ||||
\(892\) | 1799.61 | − | 1039.00i | 0.0675509 | − | 0.0390005i | ||||
\(893\) | 28136.7i | 1.05438i | ||||||||
\(894\) | 27569.7 | + | 13292.4i | 1.03140 | + | 0.497276i | ||||
\(895\) | 6042.87 | − | 3488.86i | 0.225688 | − | 0.130301i | ||||
\(896\) | −19851.7 | + | 21192.5i | −0.740175 | + | 0.790170i | ||||
\(897\) | −1242.69 | − | 599.148i | −0.0462565 | − | 0.0223021i | ||||
\(898\) | 7689.22 | + | 13318.1i | 0.285738 | + | 0.494913i | ||||
\(899\) | −1513.45 | − | 2621.37i | −0.0561473 | − | 0.0972500i | ||||
\(900\) | −1426.25 | − | 1791.82i | −0.0528240 | − | 0.0663639i | ||||
\(901\) | 42949.7 | + | 24797.0i | 1.58808 | + | 0.916879i | ||||
\(902\) | 24088.1 | − | 41721.8i | 0.889185 | − | 1.54011i | ||||
\(903\) | −3000.63 | − | 7763.97i | −0.110581 | − | 0.286123i | ||||
\(904\) | 16741.1 | + | 28996.4i | 0.615929 | + | 1.06682i | ||||
\(905\) | 52043.8i | 1.91160i | ||||||||
\(906\) | 12622.5 | − | 26180.3i | 0.462865 | − | 0.960023i | ||||
\(907\) | −9286.67 | −0.339977 | −0.169988 | − | 0.985446i | \(-0.554373\pi\) | ||||
−0.169988 | + | 0.985446i | \(0.554373\pi\) | |||||||
\(908\) | −579.822 | + | 1004.28i | −0.0211917 | + | 0.0367051i | ||||
\(909\) | −8431.98 | + | 21426.6i | −0.307669 | + | 0.781820i | ||||
\(910\) | −2191.73 | + | 9396.95i | −0.0798409 | + | 0.342314i | ||||
\(911\) | 17555.0 | + | 10135.4i | 0.638444 | + | 0.368606i | 0.784015 | − | 0.620742i | \(-0.213169\pi\) |
−0.145571 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(912\) | 19386.2 | + | 28462.4i | 0.703884 | + | 1.03343i | ||||
\(913\) | −7770.17 | − | 4486.11i | −0.281659 | − | 0.162616i | ||||
\(914\) | 23024.7 | + | 13293.3i | 0.833250 | + | 0.481077i | ||||
\(915\) | −5416.01 | + | 11233.3i | −0.195681 | + | 0.405859i | ||||
\(916\) | 1313.03 | + | 758.081i | 0.0473623 | + | 0.0273446i | ||||
\(917\) | −483.552 | + | 146.648i | −0.0174136 | + | 0.00528108i | ||||
\(918\) | 15530.7 | − | 50104.4i | 0.558375 | − | 1.80141i | ||||
\(919\) | 18209.8 | − | 31540.4i | 0.653632 | − | 1.13212i | −0.328603 | − | 0.944468i | \(-0.606578\pi\) |
0.982235 | − | 0.187655i | \(-0.0600887\pi\) | |||||||
\(920\) | 9624.20 | 0.344892 | ||||||||
\(921\) | 5001.93 | + | 7343.72i | 0.178957 | + | 0.262740i | ||||
\(922\) | 2448.98i | 0.0874761i | ||||||||
\(923\) | −1827.73 | − | 3165.72i | −0.0651792 | − | 0.112894i | ||||
\(924\) | −1587.07 | + | 613.371i | −0.0565050 | + | 0.0218381i | ||||
\(925\) | −79.2547 | + | 137.273i | −0.00281717 | + | 0.00487948i | ||||
\(926\) | −9537.45 | − | 5506.45i | −0.338467 | − | 0.195414i | ||||
\(927\) | 1072.43 | + | 422.033i | 0.0379970 | + | 0.0149530i | ||||
\(928\) | −182.708 | − | 316.459i | −0.00646301 | − | 0.0111943i | ||||
\(929\) | −10201.3 | − | 17669.2i | −0.360275 | − | 0.624014i | 0.627731 | − | 0.778430i | \(-0.283984\pi\) |
−0.988006 | + | 0.154416i | \(0.950650\pi\) | |||||||
\(930\) | −39949.7 | + | 27210.4i | −1.40860 | + | 0.959425i | ||||
\(931\) | −33497.7 | + | 2191.00i | −1.17921 | + | 0.0771291i | ||||
\(932\) | 1090.41 | − | 629.547i | 0.0383235 | − | 0.0221261i | ||||
\(933\) | 4000.50 | + | 53713.4i | 0.140376 | + | 1.88478i | ||||
\(934\) | − | 18638.8i | − | 0.652976i | ||||||
\(935\) | 68246.5 | − | 39402.1i | 2.38706 | − | 1.37817i | ||||
\(936\) | −6066.01 | + | 908.617i | −0.211831 | + | 0.0317298i | ||||
\(937\) | − | 18280.7i | − | 0.637357i | −0.947863 | − | 0.318679i | \(-0.896761\pi\) | ||
0.947863 | − | 0.318679i | \(-0.103239\pi\) | |||||||
\(938\) | 4750.37 | + | 15663.7i | 0.165357 | + | 0.545243i | ||||
\(939\) | 18472.3 | − | 38313.1i | 0.641980 | − | 1.33152i | ||||
\(940\) | −2451.10 | −0.0850491 | ||||||||
\(941\) | 20474.1 | − | 35462.2i | 0.709286 | − | 1.22852i | −0.255837 | − | 0.966720i | \(-0.582351\pi\) |
0.965122 | − | 0.261799i | \(-0.0843157\pi\) | |||||||
\(942\) | −11332.7 | + | 7718.87i | −0.391972 | + | 0.266979i | ||||
\(943\) | −10252.4 | + | 5919.23i | −0.354045 | + | 0.204408i | ||||
\(944\) | −6125.38 | −0.211191 | ||||||||
\(945\) | 22122.9 | + | 38865.2i | 0.761544 | + | 1.33787i | ||||
\(946\) | −8998.08 | −0.309253 | ||||||||
\(947\) | −29968.9 | + | 17302.6i | −1.02836 | + | 0.593725i | −0.916515 | − | 0.400001i | \(-0.869010\pi\) |
−0.111847 | + | 0.993725i | \(0.535677\pi\) | |||||||
\(948\) | −30.3092 | + | 20.6441i | −0.00103839 | + | 0.000707267i | ||||
\(949\) | −4567.26 | + | 7910.72i | −0.156227 | + | 0.270593i | ||||
\(950\) | −48844.9 | −1.66815 | ||||||||
\(951\) | −8120.74 | + | 16843.1i | −0.276901 | + | 0.574317i | ||||
\(952\) | 35526.8 | − | 37926.5i | 1.20949 | − | 1.29118i | ||||
\(953\) | 35792.0i | 1.21660i | 0.793709 | + | 0.608298i | \(0.208147\pi\) | ||||
−0.793709 | + | 0.608298i | \(0.791853\pi\) | |||||||
\(954\) | 18947.5 | + | 23804.2i | 0.643029 | + | 0.807851i | ||||
\(955\) | −15329.6 | + | 8850.55i | −0.519429 | + | 0.299892i | ||||
\(956\) | 882.771i | 0.0298649i | ||||||||
\(957\) | 224.854 | + | 3019.04i | 0.00759509 | + | 0.101977i | ||||
\(958\) | −43471.0 | + | 25098.0i | −1.46606 | + | 0.846430i | ||||
\(959\) | −467.469 | − | 1541.42i | −0.0157407 | − | 0.0519029i | ||||
\(960\) | 35220.4 | − | 23989.2i | 1.18410 | − | 0.806508i | ||||
\(961\) | 2297.01 | + | 3978.54i | 0.0771041 | + | 0.133548i | ||||
\(962\) | −14.0111 | − | 24.2679i | −0.000469580 | − | 0.000813337i | ||||
\(963\) | 17537.0 | − | 13959.0i | 0.586835 | − | 0.467106i | ||||
\(964\) | 690.836 | + | 398.854i | 0.0230813 | + | 0.0133260i | ||||
\(965\) | 35300.7 | − | 61142.5i | 1.17758 | − | 2.03963i | ||||
\(966\) | 7084.75 | + | 1105.57i | 0.235971 | + | 0.0368231i | ||||
\(967\) | −2517.30 | − | 4360.10i | −0.0837135 | − | 0.144996i | 0.821129 | − | 0.570743i | \(-0.193345\pi\) |
−0.904842 | + | 0.425747i | \(0.860011\pi\) | |||||||
\(968\) | 1248.09i | 0.0414413i | ||||||||
\(969\) | −36724.3 | − | 53917.7i | −1.21750 | − | 1.78750i | ||||
\(970\) | 65211.1 | 2.15856 | ||||||||
\(971\) | −5636.92 | + | 9763.43i | −0.186300 | + | 0.322681i | −0.944014 | − | 0.329906i | \(-0.892983\pi\) |
0.757714 | + | 0.652587i | \(0.226316\pi\) | |||||||
\(972\) | 1173.29 | − | 1464.36i | 0.0387173 | − | 0.0483224i | ||||
\(973\) | −3631.49 | + | 3876.78i | −0.119651 | + | 0.127733i | ||||
\(974\) | 7248.14 | + | 4184.72i | 0.238445 | + | 0.137666i | ||||
\(975\) | 4013.16 | − | 8323.64i | 0.131819 | − | 0.273405i | ||||
\(976\) | 8177.63 | + | 4721.36i | 0.268196 | + | 0.154843i | ||||
\(977\) | 28739.0 | + | 16592.5i | 0.941087 | + | 0.543337i | 0.890301 | − | 0.455373i | \(-0.150494\pi\) |
0.0507863 | + | 0.998710i | \(0.483827\pi\) | |||||||
\(978\) | 19176.1 | + | 28153.9i | 0.626978 | + | 0.920514i | ||||
\(979\) | −31260.2 | − | 18048.1i | −1.02051 | − | 0.589193i | ||||
\(980\) | −190.867 | − | 2918.12i | −0.00622145 | − | 0.0951182i | ||||
\(981\) | 36817.8 | − | 5514.88i | 1.19827 | − | 0.179487i | ||||
\(982\) | −8246.25 | + | 14282.9i | −0.267972 | + | 0.464141i | ||||
\(983\) | 46854.4 | 1.52027 | 0.760134 | − | 0.649767i | \(-0.225133\pi\) | ||||
0.760134 | + | 0.649767i | \(0.225133\pi\) | |||||||
\(984\) | −22858.9 | + | 47411.4i | −0.740565 | + | 1.53600i | ||||
\(985\) | 13860.9i | 0.448369i | ||||||||
\(986\) | 3051.65 | + | 5285.62i | 0.0985643 | + | 0.170718i | ||||
\(987\) | 27335.7 | + | 4265.72i | 0.881566 | + | 0.137568i | ||||
\(988\) | 251.753 | − | 436.050i | 0.00810662 | − | 0.0140411i | ||||
\(989\) | 1914.89 | + | 1105.56i | 0.0615673 | + | 0.0355459i | ||||
\(990\) | 47810.8 | − | 7161.49i | 1.53488 | − | 0.229906i | ||||
\(991\) | −3756.98 | − | 6507.28i | −0.120428 | − | 0.208588i | 0.799508 | − | 0.600655i | \(-0.205093\pi\) |
−0.919937 | + | 0.392067i | \(0.871760\pi\) | |||||||
\(992\) | 2075.52 | + | 3594.91i | 0.0664294 | + | 0.115059i | ||||
\(993\) | 37377.2 | + | 18021.0i | 1.19449 | + | 0.575912i | ||||
\(994\) | 13866.2 | + | 12988.9i | 0.442464 | + | 0.414469i | ||||
\(995\) | −33099.3 | + | 19109.9i | −1.05459 | + | 0.608869i | ||||
\(996\) | −582.830 | − | 281.005i | −0.0185418 | − | 0.00893975i | ||||
\(997\) | 33471.9i | 1.06325i | 0.846978 | + | 0.531627i | \(0.178419\pi\) | ||||
−0.846978 | + | 0.531627i | \(0.821581\pi\) | |||||||
\(998\) | −46953.3 | + | 27108.5i | −1.48926 | + | 0.859824i | ||||
\(999\) | −124.051 | − | 38.4515i | −0.00392872 | − | 0.00121777i |
(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 | 63.4.s.a.47.17 | yes | 44 | |
3.2 | odd | 2 | 189.4.s.a.89.6 | 44 | |||
7.3 | odd | 6 | 63.4.i.a.38.17 | yes | 44 | ||
9.4 | even | 3 | 189.4.i.a.152.17 | 44 | |||
9.5 | odd | 6 | 63.4.i.a.5.6 | ✓ | 44 | ||
21.17 | even | 6 | 189.4.i.a.143.6 | 44 | |||
63.31 | odd | 6 | 189.4.s.a.17.6 | 44 | |||
63.59 | even | 6 | inner | 63.4.s.a.59.17 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.6 | ✓ | 44 | 9.5 | odd | 6 | ||
63.4.i.a.38.17 | yes | 44 | 7.3 | odd | 6 | ||
63.4.s.a.47.17 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.s.a.59.17 | yes | 44 | 63.59 | even | 6 | inner | |
189.4.i.a.143.6 | 44 | 21.17 | even | 6 | |||
189.4.i.a.152.17 | 44 | 9.4 | even | 3 | |||
189.4.s.a.17.6 | 44 | 63.31 | odd | 6 | |||
189.4.s.a.89.6 | 44 | 3.2 | odd | 2 |