Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.b (of order \(2\), degree \(1\), 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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.21 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.3.b.a.119.18 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.201372i | 0.100686i | 0.998732 | + | 0.0503431i | \(0.0160315\pi\) | ||||
−0.998732 | + | 0.0503431i | \(0.983969\pi\) | |||||||
\(3\) | −2.12758 | − | 2.11504i | −0.709193 | − | 0.705014i | ||||
\(4\) | 3.95945 | 0.989862 | ||||||||
\(5\) | 6.21609i | 1.24322i | 0.783328 | + | 0.621609i | \(0.213521\pi\) | ||||
−0.783328 | + | 0.621609i | \(0.786479\pi\) | |||||||
\(6\) | 0.425911 | − | 0.428435i | 0.0709852 | − | 0.0714059i | ||||
\(7\) | −0.661651 | −0.0945215 | −0.0472608 | − | 0.998883i | \(-0.515049\pi\) | ||||
−0.0472608 | + | 0.998883i | \(0.515049\pi\) | |||||||
\(8\) | 1.60281i | 0.200352i | ||||||||
\(9\) | 0.0531837 | + | 8.99984i | 0.00590930 | + | 0.999983i | ||||
\(10\) | −1.25175 | −0.125175 | ||||||||
\(11\) | 5.79475i | 0.526795i | 0.964687 | + | 0.263398i | \(0.0848431\pi\) | ||||
−0.964687 | + | 0.263398i | \(0.915157\pi\) | |||||||
\(12\) | −8.42404 | − | 8.37441i | −0.702003 | − | 0.697867i | ||||
\(13\) | 3.06045 | 0.235419 | 0.117710 | − | 0.993048i | \(-0.462445\pi\) | ||||
0.117710 | + | 0.993048i | \(0.462445\pi\) | |||||||
\(14\) | − | 0.133238i | − | 0.00951701i | ||||||
\(15\) | 13.1473 | − | 13.2252i | 0.876487 | − | 0.881682i | ||||
\(16\) | 15.5150 | 0.969690 | ||||||||
\(17\) | 12.8260i | 0.754470i | 0.926118 | + | 0.377235i | \(0.123125\pi\) | ||||
−0.926118 | + | 0.377235i | \(0.876875\pi\) | |||||||
\(18\) | −1.81232 | + | 0.0107097i | −0.100684 | + | 0.000594984i | ||||
\(19\) | 24.1445 | 1.27076 | 0.635381 | − | 0.772199i | \(-0.280843\pi\) | ||||
0.635381 | + | 0.772199i | \(0.280843\pi\) | |||||||
\(20\) | 24.6123i | 1.23061i | ||||||||
\(21\) | 1.40771 | + | 1.39942i | 0.0670340 | + | 0.0666391i | ||||
\(22\) | −1.16690 | −0.0530410 | ||||||||
\(23\) | 10.5674i | 0.459454i | 0.973255 | + | 0.229727i | \(0.0737833\pi\) | ||||
−0.973255 | + | 0.229727i | \(0.926217\pi\) | |||||||
\(24\) | 3.39002 | − | 3.41011i | 0.141251 | − | 0.142088i | ||||
\(25\) | −13.6398 | −0.545592 | ||||||||
\(26\) | 0.616289i | 0.0237034i | ||||||||
\(27\) | 18.9219 | − | 19.2604i | 0.700811 | − | 0.713347i | ||||
\(28\) | −2.61977 | −0.0935633 | ||||||||
\(29\) | − | 3.55194i | − | 0.122481i | −0.998123 | − | 0.0612403i | \(-0.980494\pi\) | ||
0.998123 | − | 0.0612403i | \(-0.0195056\pi\) | |||||||
\(30\) | 2.66319 | + | 2.64750i | 0.0887731 | + | 0.0882501i | ||||
\(31\) | 23.2167 | 0.748925 | 0.374462 | − | 0.927242i | \(-0.377827\pi\) | ||||
0.374462 | + | 0.927242i | \(0.377827\pi\) | |||||||
\(32\) | 9.53555i | 0.297986i | ||||||||
\(33\) | 12.2561 | − | 12.3288i | 0.371398 | − | 0.373599i | ||||
\(34\) | −2.58280 | −0.0759647 | ||||||||
\(35\) | − | 4.11288i | − | 0.117511i | ||||||
\(36\) | 0.210578 | + | 35.6344i | 0.00584939 | + | 0.989845i | ||||
\(37\) | −63.0720 | −1.70465 | −0.852324 | − | 0.523015i | \(-0.824807\pi\) | ||||
−0.852324 | + | 0.523015i | \(0.824807\pi\) | |||||||
\(38\) | 4.86203i | 0.127948i | ||||||||
\(39\) | −6.51134 | − | 6.47298i | −0.166958 | − | 0.165974i | ||||
\(40\) | −9.96323 | −0.249081 | ||||||||
\(41\) | − | 25.4591i | − | 0.620954i | −0.950581 | − | 0.310477i | \(-0.899511\pi\) | ||
0.950581 | − | 0.310477i | \(-0.100489\pi\) | |||||||
\(42\) | −0.281804 | + | 0.283475i | −0.00670963 | + | 0.00674940i | ||||
\(43\) | −26.9762 | −0.627354 | −0.313677 | − | 0.949530i | \(-0.601561\pi\) | ||||
−0.313677 | + | 0.949530i | \(0.601561\pi\) | |||||||
\(44\) | 22.9440i | 0.521455i | ||||||||
\(45\) | −55.9438 | + | 0.330595i | −1.24320 | + | 0.00734655i | ||||
\(46\) | −2.12799 | −0.0462607 | ||||||||
\(47\) | − | 4.63050i | − | 0.0985213i | −0.998786 | − | 0.0492606i | \(-0.984314\pi\) | ||
0.998786 | − | 0.0492606i | \(-0.0156865\pi\) | |||||||
\(48\) | −33.0095 | − | 32.8150i | −0.687697 | − | 0.683645i | ||||
\(49\) | −48.5622 | −0.991066 | ||||||||
\(50\) | − | 2.74668i | − | 0.0549336i | ||||||
\(51\) | 27.1275 | − | 27.2883i | 0.531912 | − | 0.535065i | ||||
\(52\) | 12.1177 | 0.233032 | ||||||||
\(53\) | − | 39.5277i | − | 0.745805i | −0.927871 | − | 0.372902i | \(-0.878363\pi\) | ||
0.927871 | − | 0.372902i | \(-0.121637\pi\) | |||||||
\(54\) | 3.87850 | + | 3.81035i | 0.0718241 | + | 0.0705620i | ||||
\(55\) | −36.0207 | −0.654921 | ||||||||
\(56\) | − | 1.06050i | − | 0.0189375i | ||||||
\(57\) | −51.3693 | − | 51.0666i | −0.901215 | − | 0.895905i | ||||
\(58\) | 0.715262 | 0.0123321 | ||||||||
\(59\) | − | 7.68115i | − | 0.130189i | ||||||
\(60\) | 52.0561 | − | 52.3646i | 0.867601 | − | 0.872743i | ||||
\(61\) | 48.9008 | 0.801653 | 0.400827 | − | 0.916154i | \(-0.368723\pi\) | ||||
0.400827 | + | 0.916154i | \(0.368723\pi\) | |||||||
\(62\) | 4.67519i | 0.0754064i | ||||||||
\(63\) | −0.0351890 | − | 5.95475i | −0.000558556 | − | 0.0945199i | ||||
\(64\) | 60.1399 | 0.939687 | ||||||||
\(65\) | 19.0240i | 0.292677i | ||||||||
\(66\) | 2.48267 | + | 2.46805i | 0.0376163 | + | 0.0373946i | ||||
\(67\) | 35.5322 | 0.530332 | 0.265166 | − | 0.964203i | \(-0.414573\pi\) | ||||
0.265166 | + | 0.964203i | \(0.414573\pi\) | |||||||
\(68\) | 50.7838i | 0.746821i | ||||||||
\(69\) | 22.3506 | − | 22.4831i | 0.323922 | − | 0.325842i | ||||
\(70\) | 0.828221 | 0.0118317 | ||||||||
\(71\) | − | 103.764i | − | 1.46146i | −0.682665 | − | 0.730732i | \(-0.739179\pi\) | ||
0.682665 | − | 0.730732i | \(-0.260821\pi\) | |||||||
\(72\) | −14.4251 | + | 0.0852435i | −0.200348 | + | 0.00118394i | ||||
\(73\) | −76.1989 | −1.04382 | −0.521911 | − | 0.853000i | \(-0.674781\pi\) | ||||
−0.521911 | + | 0.853000i | \(0.674781\pi\) | |||||||
\(74\) | − | 12.7009i | − | 0.171634i | ||||||
\(75\) | 29.0197 | + | 28.8488i | 0.386930 | + | 0.384650i | ||||
\(76\) | 95.5988 | 1.25788 | ||||||||
\(77\) | − | 3.83410i | − | 0.0497935i | ||||||
\(78\) | 1.30348 | − | 1.31120i | 0.0167113 | − | 0.0168103i | ||||
\(79\) | 26.3243 | 0.333219 | 0.166610 | − | 0.986023i | \(-0.446718\pi\) | ||||
0.166610 | + | 0.986023i | \(0.446718\pi\) | |||||||
\(80\) | 96.4429i | 1.20554i | ||||||||
\(81\) | −80.9943 | + | 0.957289i | −0.999930 | + | 0.0118184i | ||||
\(82\) | 5.12676 | 0.0625215 | ||||||||
\(83\) | 52.3210i | 0.630373i | 0.949030 | + | 0.315187i | \(0.102067\pi\) | ||||
−0.949030 | + | 0.315187i | \(0.897933\pi\) | |||||||
\(84\) | 5.57377 | + | 5.54093i | 0.0663544 | + | 0.0659635i | ||||
\(85\) | −79.7275 | −0.937971 | ||||||||
\(86\) | − | 5.43227i | − | 0.0631659i | ||||||
\(87\) | −7.51250 | + | 7.55703i | −0.0863506 | + | 0.0868624i | ||||
\(88\) | −9.28789 | −0.105544 | ||||||||
\(89\) | − | 7.05059i | − | 0.0792201i | −0.999215 | − | 0.0396100i | \(-0.987388\pi\) | ||
0.999215 | − | 0.0396100i | \(-0.0126116\pi\) | |||||||
\(90\) | −0.0665726 | − | 11.2655i | −0.000739696 | − | 0.125173i | ||||
\(91\) | −2.02495 | −0.0222522 | ||||||||
\(92\) | 41.8413i | 0.454796i | ||||||||
\(93\) | −49.3953 | − | 49.1043i | −0.531132 | − | 0.528003i | ||||
\(94\) | 0.932455 | 0.00991973 | ||||||||
\(95\) | 150.084i | 1.57983i | ||||||||
\(96\) | 20.1681 | − | 20.2876i | 0.210084 | − | 0.211330i | ||||
\(97\) | 106.653 | 1.09951 | 0.549756 | − | 0.835325i | \(-0.314721\pi\) | ||||
0.549756 | + | 0.835325i | \(0.314721\pi\) | |||||||
\(98\) | − | 9.77909i | − | 0.0997866i | ||||||
\(99\) | −52.1518 | + | 0.308186i | −0.526786 | + | 0.00311299i | ||||
\(100\) | −54.0061 | −0.540061 | ||||||||
\(101\) | 173.195i | 1.71480i | 0.514650 | + | 0.857400i | \(0.327922\pi\) | ||||
−0.514650 | + | 0.857400i | \(0.672078\pi\) | |||||||
\(102\) | 5.49511 | + | 5.46273i | 0.0538736 | + | 0.0535562i | ||||
\(103\) | −15.3050 | −0.148592 | −0.0742962 | − | 0.997236i | \(-0.523671\pi\) | ||||
−0.0742962 | + | 0.997236i | \(0.523671\pi\) | |||||||
\(104\) | 4.90532i | 0.0471666i | ||||||||
\(105\) | −8.69892 | + | 8.75048i | −0.0828469 | + | 0.0833379i | ||||
\(106\) | 7.95977 | 0.0750922 | ||||||||
\(107\) | − | 196.423i | − | 1.83573i | −0.396896 | − | 0.917864i | \(-0.629912\pi\) | ||
0.396896 | − | 0.917864i | \(-0.370088\pi\) | |||||||
\(108\) | 74.9203 | − | 76.2604i | 0.693707 | − | 0.706115i | ||||
\(109\) | −130.315 | −1.19555 | −0.597776 | − | 0.801663i | \(-0.703949\pi\) | ||||
−0.597776 | + | 0.801663i | \(0.703949\pi\) | |||||||
\(110\) | − | 7.25357i | − | 0.0659415i | ||||||
\(111\) | 134.191 | + | 133.400i | 1.20892 | + | 1.20180i | ||||
\(112\) | −10.2655 | −0.0916566 | ||||||||
\(113\) | − | 181.249i | − | 1.60397i | −0.597342 | − | 0.801986i | \(-0.703777\pi\) | ||
0.597342 | − | 0.801986i | \(-0.296223\pi\) | |||||||
\(114\) | 10.2834 | − | 10.3443i | 0.0902053 | − | 0.0907399i | ||||
\(115\) | −65.6882 | −0.571202 | ||||||||
\(116\) | − | 14.0637i | − | 0.121239i | ||||||
\(117\) | 0.162766 | + | 27.5435i | 0.00139116 | + | 0.235415i | ||||
\(118\) | 1.54677 | 0.0131082 | ||||||||
\(119\) | − | 8.48633i | − | 0.0713137i | ||||||
\(120\) | 21.1976 | + | 21.0727i | 0.176646 | + | 0.175606i | ||||
\(121\) | 87.4209 | 0.722487 | ||||||||
\(122\) | 9.84727i | 0.0807154i | ||||||||
\(123\) | −53.8471 | + | 54.1663i | −0.437781 | + | 0.440376i | ||||
\(124\) | 91.9252 | 0.741332 | ||||||||
\(125\) | 70.6161i | 0.564928i | ||||||||
\(126\) | 1.19912 | − | 0.00708609i | 0.00951685 | − | 5.62388e-5i | ||||
\(127\) | −5.71681 | −0.0450142 | −0.0225071 | − | 0.999747i | \(-0.507165\pi\) | ||||
−0.0225071 | + | 0.999747i | \(0.507165\pi\) | |||||||
\(128\) | 50.2527i | 0.392599i | ||||||||
\(129\) | 57.3941 | + | 57.0559i | 0.444915 | + | 0.442294i | ||||
\(130\) | −3.83091 | −0.0294685 | ||||||||
\(131\) | − | 40.2469i | − | 0.307228i | −0.988131 | − | 0.153614i | \(-0.950909\pi\) | ||
0.988131 | − | 0.153614i | \(-0.0490913\pi\) | |||||||
\(132\) | 48.5276 | − | 48.8152i | 0.367633 | − | 0.369812i | ||||
\(133\) | −15.9752 | −0.120114 | ||||||||
\(134\) | 7.15521i | 0.0533971i | ||||||||
\(135\) | 119.724 | + | 117.620i | 0.886846 | + | 0.871261i | ||||
\(136\) | −20.5577 | −0.151159 | ||||||||
\(137\) | 26.7603i | 0.195331i | 0.995219 | + | 0.0976653i | \(0.0311375\pi\) | ||||
−0.995219 | + | 0.0976653i | \(0.968863\pi\) | |||||||
\(138\) | 4.52747 | + | 4.50079i | 0.0328077 | + | 0.0326144i | ||||
\(139\) | 199.418 | 1.43466 | 0.717331 | − | 0.696733i | \(-0.245364\pi\) | ||||
0.717331 | + | 0.696733i | \(0.245364\pi\) | |||||||
\(140\) | − | 16.2847i | − | 0.116320i | ||||||
\(141\) | −9.79371 | + | 9.85175i | −0.0694589 | + | 0.0698706i | ||||
\(142\) | 20.8952 | 0.147149 | ||||||||
\(143\) | 17.7345i | 0.124018i | ||||||||
\(144\) | 0.825147 | + | 139.633i | 0.00573018 | + | 0.969673i | ||||
\(145\) | 22.0792 | 0.152270 | ||||||||
\(146\) | − | 15.3444i | − | 0.105098i | ||||||
\(147\) | 103.320 | + | 102.711i | 0.702857 | + | 0.698716i | ||||
\(148\) | −249.730 | −1.68737 | ||||||||
\(149\) | − | 176.143i | − | 1.18217i | −0.806609 | − | 0.591085i | \(-0.798700\pi\) | ||
0.806609 | − | 0.591085i | \(-0.201300\pi\) | |||||||
\(150\) | −5.80934 | + | 5.84377i | −0.0387289 | + | 0.0389585i | ||||
\(151\) | 158.877 | 1.05217 | 0.526084 | − | 0.850433i | \(-0.323660\pi\) | ||||
0.526084 | + | 0.850433i | \(0.323660\pi\) | |||||||
\(152\) | 38.6991i | 0.254599i | ||||||||
\(153\) | −115.432 | + | 0.682133i | −0.754457 | + | 0.00445839i | ||||
\(154\) | 0.772081 | 0.00501351 | ||||||||
\(155\) | 144.317i | 0.931077i | ||||||||
\(156\) | −25.7813 | − | 25.6294i | −0.165265 | − | 0.164291i | ||||
\(157\) | 287.164 | 1.82907 | 0.914535 | − | 0.404506i | \(-0.132556\pi\) | ||||
0.914535 | + | 0.404506i | \(0.132556\pi\) | |||||||
\(158\) | 5.30099i | 0.0335506i | ||||||||
\(159\) | −83.6027 | + | 84.0982i | −0.525803 | + | 0.528919i | ||||
\(160\) | −59.2739 | −0.370462 | ||||||||
\(161\) | − | 6.99196i | − | 0.0434283i | ||||||
\(162\) | −0.192772 | − | 16.3100i | −0.00118995 | − | 0.100679i | ||||
\(163\) | 76.9398 | 0.472023 | 0.236012 | − | 0.971750i | \(-0.424160\pi\) | ||||
0.236012 | + | 0.971750i | \(0.424160\pi\) | |||||||
\(164\) | − | 100.804i | − | 0.614659i | ||||||
\(165\) | 76.6368 | + | 76.1853i | 0.464466 | + | 0.461729i | ||||
\(166\) | −10.5360 | −0.0634699 | ||||||||
\(167\) | − | 294.401i | − | 1.76288i | −0.472296 | − | 0.881440i | \(-0.656575\pi\) | ||
0.472296 | − | 0.881440i | \(-0.343425\pi\) | |||||||
\(168\) | −2.24301 | + | 2.25630i | −0.0133512 | + | 0.0134304i | ||||
\(169\) | −159.634 | −0.944578 | ||||||||
\(170\) | − | 16.0549i | − | 0.0944407i | ||||||
\(171\) | 1.28409 | + | 217.296i | 0.00750931 | + | 1.27074i | ||||
\(172\) | −106.811 | −0.620994 | ||||||||
\(173\) | − | 260.169i | − | 1.50387i | −0.659239 | − | 0.751934i | \(-0.729121\pi\) | ||
0.659239 | − | 0.751934i | \(-0.270879\pi\) | |||||||
\(174\) | −1.52178 | − | 1.51281i | −0.00874584 | − | 0.00869431i | ||||
\(175\) | 9.02478 | 0.0515702 | ||||||||
\(176\) | 89.9057i | 0.510828i | ||||||||
\(177\) | −16.2460 | + | 16.3422i | −0.0917851 | + | 0.0923291i | ||||
\(178\) | 1.41979 | 0.00797637 | ||||||||
\(179\) | 350.468i | 1.95792i | 0.204053 | + | 0.978960i | \(0.434589\pi\) | ||||
−0.204053 | + | 0.978960i | \(0.565411\pi\) | |||||||
\(180\) | −221.507 | + | 1.30897i | −1.23059 | + | 0.00727207i | ||||
\(181\) | 208.790 | 1.15353 | 0.576767 | − | 0.816909i | \(-0.304314\pi\) | ||||
0.576767 | + | 0.816909i | \(0.304314\pi\) | |||||||
\(182\) | − | 0.407768i | − | 0.00224049i | ||||||
\(183\) | −104.040 | − | 103.427i | −0.568527 | − | 0.565177i | ||||
\(184\) | −16.9376 | −0.0920523 | ||||||||
\(185\) | − | 392.061i | − | 2.11925i | ||||||
\(186\) | 9.88824 | − | 9.94684i | 0.0531626 | − | 0.0534777i | ||||
\(187\) | −74.3233 | −0.397451 | ||||||||
\(188\) | − | 18.3342i | − | 0.0975225i | ||||||
\(189\) | −12.5197 | + | 12.7436i | −0.0662418 | + | 0.0674266i | ||||
\(190\) | −30.2228 | −0.159067 | ||||||||
\(191\) | − | 262.744i | − | 1.37562i | −0.725889 | − | 0.687812i | \(-0.758572\pi\) | ||
0.725889 | − | 0.687812i | \(-0.241428\pi\) | |||||||
\(192\) | −127.952 | − | 127.199i | −0.666419 | − | 0.662493i | ||||
\(193\) | −231.780 | −1.20094 | −0.600468 | − | 0.799649i | \(-0.705019\pi\) | ||||
−0.600468 | + | 0.799649i | \(0.705019\pi\) | |||||||
\(194\) | 21.4769i | 0.110706i | ||||||||
\(195\) | 40.2366 | − | 40.4751i | 0.206342 | − | 0.207565i | ||||
\(196\) | −192.280 | −0.981019 | ||||||||
\(197\) | − | 223.225i | − | 1.13312i | −0.824019 | − | 0.566562i | \(-0.808273\pi\) | ||
0.824019 | − | 0.566562i | \(-0.191727\pi\) | |||||||
\(198\) | −0.0620601 | − | 10.5019i | −0.000313435 | − | 0.0530400i | ||||
\(199\) | 40.6294 | 0.204168 | 0.102084 | − | 0.994776i | \(-0.467449\pi\) | ||||
0.102084 | + | 0.994776i | \(0.467449\pi\) | |||||||
\(200\) | − | 21.8620i | − | 0.109310i | ||||||
\(201\) | −75.5976 | − | 75.1522i | −0.376108 | − | 0.373892i | ||||
\(202\) | −34.8766 | −0.172657 | ||||||||
\(203\) | 2.35014i | 0.0115771i | ||||||||
\(204\) | 107.410 | − | 108.047i | 0.526520 | − | 0.529640i | ||||
\(205\) | 158.256 | 0.771981 | ||||||||
\(206\) | − | 3.08201i | − | 0.0149612i | ||||||
\(207\) | −95.1053 | + | 0.562015i | −0.459446 | + | 0.00271505i | ||||
\(208\) | 47.4829 | 0.228283 | ||||||||
\(209\) | 139.911i | 0.669431i | ||||||||
\(210\) | −1.76210 | − | 1.75172i | −0.00839097 | − | 0.00834154i | ||||
\(211\) | −316.346 | −1.49927 | −0.749636 | − | 0.661850i | \(-0.769771\pi\) | ||||
−0.749636 | + | 0.661850i | \(0.769771\pi\) | |||||||
\(212\) | − | 156.508i | − | 0.738244i | ||||||
\(213\) | −219.465 | + | 220.766i | −1.03035 | + | 1.03646i | ||||
\(214\) | 39.5541 | 0.184832 | ||||||||
\(215\) | − | 167.687i | − | 0.779938i | ||||||
\(216\) | 30.8708 | + | 30.3283i | 0.142920 | + | 0.140409i | ||||
\(217\) | −15.3613 | −0.0707895 | ||||||||
\(218\) | − | 26.2419i | − | 0.120376i | ||||||
\(219\) | 162.119 | + | 161.164i | 0.740271 | + | 0.735909i | ||||
\(220\) | −142.622 | −0.648282 | ||||||||
\(221\) | 39.2533i | 0.177617i | ||||||||
\(222\) | −26.8630 | + | 27.0223i | −0.121005 | + | 0.121722i | ||||
\(223\) | −95.5535 | −0.428491 | −0.214245 | − | 0.976780i | \(-0.568729\pi\) | ||||
−0.214245 | + | 0.976780i | \(0.568729\pi\) | |||||||
\(224\) | − | 6.30920i | − | 0.0281661i | ||||||
\(225\) | −0.725415 | − | 122.756i | −0.00322406 | − | 0.545582i | ||||
\(226\) | 36.4985 | 0.161498 | ||||||||
\(227\) | 392.945i | 1.73104i | 0.500878 | + | 0.865518i | \(0.333010\pi\) | ||||
−0.500878 | + | 0.865518i | \(0.666990\pi\) | |||||||
\(228\) | −203.394 | − | 202.196i | −0.892079 | − | 0.886823i | ||||
\(229\) | 213.168 | 0.930863 | 0.465431 | − | 0.885084i | \(-0.345899\pi\) | ||||
0.465431 | + | 0.885084i | \(0.345899\pi\) | |||||||
\(230\) | − | 13.2278i | − | 0.0575121i | ||||||
\(231\) | −8.10928 | + | 8.15735i | −0.0351051 | + | 0.0353132i | ||||
\(232\) | 5.69309 | 0.0245392 | ||||||||
\(233\) | 174.471i | 0.748803i | 0.927267 | + | 0.374401i | \(0.122152\pi\) | ||||
−0.927267 | + | 0.374401i | \(0.877848\pi\) | |||||||
\(234\) | −5.54651 | + | 0.0327765i | −0.0237030 | + | 0.000140071i | ||||
\(235\) | 28.7836 | 0.122483 | ||||||||
\(236\) | − | 30.4131i | − | 0.128869i | ||||||
\(237\) | −56.0071 | − | 55.6771i | −0.236317 | − | 0.234924i | ||||
\(238\) | 1.70891 | 0.00718030 | ||||||||
\(239\) | 208.017i | 0.870365i | 0.900342 | + | 0.435183i | \(0.143316\pi\) | ||||
−0.900342 | + | 0.435183i | \(0.856684\pi\) | |||||||
\(240\) | 203.981 | − | 205.190i | 0.849920 | − | 0.854958i | ||||
\(241\) | −386.692 | −1.60453 | −0.802266 | − | 0.596967i | \(-0.796372\pi\) | ||||
−0.802266 | + | 0.596967i | \(0.796372\pi\) | |||||||
\(242\) | 17.6042i | 0.0727444i | ||||||||
\(243\) | 174.347 | + | 169.270i | 0.717476 | + | 0.696584i | ||||
\(244\) | 193.620 | 0.793526 | ||||||||
\(245\) | − | 301.867i | − | 1.23211i | ||||||
\(246\) | −10.9076 | − | 10.8433i | −0.0443398 | − | 0.0440785i | ||||
\(247\) | 73.8929 | 0.299161 | ||||||||
\(248\) | 37.2120i | 0.150048i | ||||||||
\(249\) | 110.661 | − | 111.317i | 0.444422 | − | 0.447056i | ||||
\(250\) | −14.2201 | −0.0568805 | ||||||||
\(251\) | − | 29.5693i | − | 0.117806i | −0.998264 | − | 0.0589030i | \(-0.981240\pi\) | ||
0.998264 | − | 0.0589030i | \(-0.0187603\pi\) | |||||||
\(252\) | −0.139329 | − | 23.5775i | −0.000552893 | − | 0.0935617i | ||||
\(253\) | −61.2356 | −0.242038 | ||||||||
\(254\) | − | 1.15121i | − | 0.00453231i | ||||||
\(255\) | 169.627 | + | 168.627i | 0.665202 | + | 0.661283i | ||||
\(256\) | 230.440 | 0.900157 | ||||||||
\(257\) | 248.436i | 0.966676i | 0.875434 | + | 0.483338i | \(0.160576\pi\) | ||||
−0.875434 | + | 0.483338i | \(0.839424\pi\) | |||||||
\(258\) | −11.4895 | + | 11.5576i | −0.0445329 | + | 0.0447968i | ||||
\(259\) | 41.7316 | 0.161126 | ||||||||
\(260\) | 75.3246i | 0.289710i | ||||||||
\(261\) | 31.9669 | − | 0.188905i | 0.122478 | − | 0.000723774i | ||||
\(262\) | 8.10461 | 0.0309336 | ||||||||
\(263\) | 9.74268i | 0.0370444i | 0.999828 | + | 0.0185222i | \(0.00589614\pi\) | ||||
−0.999828 | + | 0.0185222i | \(0.994104\pi\) | |||||||
\(264\) | 19.7607 | + | 19.6443i | 0.0748512 | + | 0.0744102i | ||||
\(265\) | 245.708 | 0.927198 | ||||||||
\(266\) | − | 3.21696i | − | 0.0120939i | ||||||
\(267\) | −14.9123 | + | 15.0007i | −0.0558513 | + | 0.0561823i | ||||
\(268\) | 140.688 | 0.524956 | ||||||||
\(269\) | 309.815i | 1.15173i | 0.817545 | + | 0.575865i | \(0.195335\pi\) | ||||
−0.817545 | + | 0.575865i | \(0.804665\pi\) | |||||||
\(270\) | −23.6855 | + | 24.1091i | −0.0877240 | + | 0.0892931i | ||||
\(271\) | −185.506 | −0.684526 | −0.342263 | − | 0.939604i | \(-0.611193\pi\) | ||||
−0.342263 | + | 0.939604i | \(0.611193\pi\) | |||||||
\(272\) | 198.996i | 0.731602i | ||||||||
\(273\) | 4.30824 | + | 4.28285i | 0.0157811 | + | 0.0156881i | ||||
\(274\) | −5.38878 | −0.0196671 | ||||||||
\(275\) | − | 79.0392i | − | 0.287415i | ||||||
\(276\) | 88.4961 | − | 89.0206i | 0.320638 | − | 0.322538i | ||||
\(277\) | −66.4098 | −0.239746 | −0.119873 | − | 0.992789i | \(-0.538249\pi\) | ||||
−0.119873 | + | 0.992789i | \(0.538249\pi\) | |||||||
\(278\) | 40.1573i | 0.144451i | ||||||||
\(279\) | 1.23475 | + | 208.946i | 0.00442562 | + | 0.748912i | ||||
\(280\) | 6.59218 | 0.0235435 | ||||||||
\(281\) | − | 225.137i | − | 0.801201i | −0.916253 | − | 0.400601i | \(-0.868802\pi\) | ||
0.916253 | − | 0.400601i | \(-0.131198\pi\) | |||||||
\(282\) | −1.98387 | − | 1.97218i | −0.00703500 | − | 0.00699355i | ||||
\(283\) | −192.753 | −0.681107 | −0.340553 | − | 0.940225i | \(-0.610614\pi\) | ||||
−0.340553 | + | 0.940225i | \(0.610614\pi\) | |||||||
\(284\) | − | 410.848i | − | 1.44665i | ||||||
\(285\) | 317.435 | − | 319.316i | 1.11381 | − | 1.12041i | ||||
\(286\) | −3.57124 | −0.0124869 | ||||||||
\(287\) | 16.8450i | 0.0586935i | ||||||||
\(288\) | −85.8184 | + | 0.507136i | −0.297981 | + | 0.00176089i | ||||
\(289\) | 124.494 | 0.430775 | ||||||||
\(290\) | 4.44613i | 0.0153315i | ||||||||
\(291\) | −226.912 | − | 225.575i | −0.779766 | − | 0.775172i | ||||
\(292\) | −301.706 | −1.03324 | ||||||||
\(293\) | − | 49.5040i | − | 0.168956i | −0.996425 | − | 0.0844778i | \(-0.973078\pi\) | ||
0.996425 | − | 0.0844778i | \(-0.0269222\pi\) | |||||||
\(294\) | −20.6832 | + | 20.8058i | −0.0703510 | + | 0.0707680i | ||||
\(295\) | 47.7467 | 0.161853 | ||||||||
\(296\) | − | 101.093i | − | 0.341529i | ||||||
\(297\) | 111.609 | + | 109.648i | 0.375788 | + | 0.369184i | ||||
\(298\) | 35.4704 | 0.119028 | ||||||||
\(299\) | 32.3411i | 0.108164i | ||||||||
\(300\) | 114.902 | + | 114.225i | 0.383007 | + | 0.380751i | ||||
\(301\) | 17.8488 | 0.0592985 | ||||||||
\(302\) | 31.9935i | 0.105939i | ||||||||
\(303\) | 366.315 | − | 368.486i | 1.20896 | − | 1.21612i | ||||
\(304\) | 374.602 | 1.23224 | ||||||||
\(305\) | 303.972i | 0.996630i | ||||||||
\(306\) | −0.137363 | − | 23.2448i | −0.000448898 | − | 0.0759633i | ||||
\(307\) | 326.249 | 1.06270 | 0.531350 | − | 0.847153i | \(-0.321685\pi\) | ||||
0.531350 | + | 0.847153i | \(0.321685\pi\) | |||||||
\(308\) | − | 15.1809i | − | 0.0492887i | ||||||
\(309\) | 32.5626 | + | 32.3708i | 0.105381 | + | 0.104760i | ||||
\(310\) | −29.0614 | −0.0937466 | ||||||||
\(311\) | − | 530.351i | − | 1.70531i | −0.522475 | − | 0.852655i | \(-0.674991\pi\) | ||
0.522475 | − | 0.852655i | \(-0.325009\pi\) | |||||||
\(312\) | 10.3750 | − | 10.4365i | 0.0332531 | − | 0.0334502i | ||||
\(313\) | −330.130 | −1.05473 | −0.527364 | − | 0.849639i | \(-0.676820\pi\) | ||||
−0.527364 | + | 0.849639i | \(0.676820\pi\) | |||||||
\(314\) | 57.8269i | 0.184162i | ||||||||
\(315\) | 37.0153 | − | 0.218738i | 0.117509 | − | 0.000694407i | ||||
\(316\) | 104.230 | 0.329841 | ||||||||
\(317\) | 553.376i | 1.74566i | 0.488020 | + | 0.872832i | \(0.337719\pi\) | ||||
−0.488020 | + | 0.872832i | \(0.662281\pi\) | |||||||
\(318\) | −16.9350 | − | 16.8353i | −0.0532549 | − | 0.0529411i | ||||
\(319\) | 20.5826 | 0.0645222 | ||||||||
\(320\) | 373.835i | 1.16824i | ||||||||
\(321\) | −415.443 | + | 417.905i | −1.29421 | + | 1.30189i | ||||
\(322\) | 1.40799 | 0.00437263 | ||||||||
\(323\) | 309.677i | 0.958751i | ||||||||
\(324\) | −320.693 | + | 3.79034i | −0.989793 | + | 0.0116986i | ||||
\(325\) | −41.7439 | −0.128443 | ||||||||
\(326\) | 15.4935i | 0.0475262i | ||||||||
\(327\) | 277.256 | + | 275.622i | 0.847877 | + | 0.842882i | ||||
\(328\) | 40.8062 | 0.124409 | ||||||||
\(329\) | 3.06377i | 0.00931238i | ||||||||
\(330\) | −15.3416 | + | 15.4325i | −0.0464897 | + | 0.0467653i | ||||
\(331\) | −227.087 | −0.686062 | −0.343031 | − | 0.939324i | \(-0.611454\pi\) | ||||
−0.343031 | + | 0.939324i | \(0.611454\pi\) | |||||||
\(332\) | 207.162i | 0.623983i | ||||||||
\(333\) | −3.35440 | − | 567.638i | −0.0100733 | − | 1.70462i | ||||
\(334\) | 59.2842 | 0.177498 | ||||||||
\(335\) | 220.872i | 0.659318i | ||||||||
\(336\) | 21.8407 | + | 21.7121i | 0.0650022 | + | 0.0646192i | ||||
\(337\) | −419.516 | −1.24485 | −0.622427 | − | 0.782678i | \(-0.713853\pi\) | ||||
−0.622427 | + | 0.782678i | \(0.713853\pi\) | |||||||
\(338\) | − | 32.1458i | − | 0.0951059i | ||||||
\(339\) | −383.349 | + | 385.621i | −1.13082 | + | 1.13753i | ||||
\(340\) | −315.677 | −0.928462 | ||||||||
\(341\) | 134.535i | 0.394530i | ||||||||
\(342\) | −43.7575 | + | 0.258581i | −0.127946 | + | 0.000756083i | ||||
\(343\) | 64.5521 | 0.188199 | ||||||||
\(344\) | − | 43.2378i | − | 0.125691i | ||||||
\(345\) | 139.757 | + | 138.933i | 0.405092 | + | 0.402705i | ||||
\(346\) | 52.3909 | 0.151419 | ||||||||
\(347\) | − | 87.7142i | − | 0.252779i | −0.991981 | − | 0.126389i | \(-0.959661\pi\) | ||
0.991981 | − | 0.126389i | \(-0.0403389\pi\) | |||||||
\(348\) | −29.7454 | + | 29.9217i | −0.0854752 | + | 0.0859818i | ||||
\(349\) | 191.406 | 0.548441 | 0.274220 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274220 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(350\) | 1.81734i | 0.00519240i | ||||||||
\(351\) | 57.9095 | − | 58.9453i | 0.164984 | − | 0.167935i | ||||
\(352\) | −55.2561 | −0.156978 | ||||||||
\(353\) | 56.5655i | 0.160242i | 0.996785 | + | 0.0801212i | \(0.0255307\pi\) | ||||
−0.996785 | + | 0.0801212i | \(0.974469\pi\) | |||||||
\(354\) | −3.29088 | − | 3.27149i | −0.00929626 | − | 0.00924149i | ||||
\(355\) | 645.006 | 1.81692 | ||||||||
\(356\) | − | 27.9164i | − | 0.0784170i | ||||||
\(357\) | −17.9489 | + | 18.0553i | −0.0502772 | + | 0.0505751i | ||||
\(358\) | −70.5745 | −0.197135 | ||||||||
\(359\) | 378.385i | 1.05400i | 0.849866 | + | 0.526999i | \(0.176683\pi\) | ||||
−0.849866 | + | 0.526999i | \(0.823317\pi\) | |||||||
\(360\) | −0.529881 | − | 89.6675i | −0.00147189 | − | 0.249076i | ||||
\(361\) | 221.955 | 0.614835 | ||||||||
\(362\) | 42.0445i | 0.116145i | ||||||||
\(363\) | −185.995 | − | 184.899i | −0.512383 | − | 0.509364i | ||||
\(364\) | −8.01768 | −0.0220266 | ||||||||
\(365\) | − | 473.660i | − | 1.29770i | ||||||
\(366\) | 20.8274 | − | 20.9509i | 0.0569055 | − | 0.0572428i | ||||
\(367\) | 203.283 | 0.553905 | 0.276953 | − | 0.960884i | \(-0.410675\pi\) | ||||
0.276953 | + | 0.960884i | \(0.410675\pi\) | |||||||
\(368\) | 163.954i | 0.445528i | ||||||||
\(369\) | 229.128 | − | 1.35401i | 0.620943 | − | 0.00366940i | ||||
\(370\) | 78.9502 | 0.213379 | ||||||||
\(371\) | 26.1535i | 0.0704946i | ||||||||
\(372\) | −195.578 | − | 194.426i | −0.525748 | − | 0.522650i | ||||
\(373\) | 541.295 | 1.45119 | 0.725597 | − | 0.688120i | \(-0.241564\pi\) | ||||
0.725597 | + | 0.688120i | \(0.241564\pi\) | |||||||
\(374\) | − | 14.9667i | − | 0.0400178i | ||||||
\(375\) | 149.356 | − | 150.241i | 0.398283 | − | 0.400643i | ||||
\(376\) | 7.42182 | 0.0197389 | ||||||||
\(377\) | − | 10.8705i | − | 0.0288343i | ||||||
\(378\) | −2.56622 | − | 2.52112i | −0.00678893 | − | 0.00666963i | ||||
\(379\) | 30.9500 | 0.0816623 | 0.0408312 | − | 0.999166i | \(-0.486999\pi\) | ||||
0.0408312 | + | 0.999166i | \(0.486999\pi\) | |||||||
\(380\) | 594.251i | 1.56382i | ||||||||
\(381\) | 12.1630 | + | 12.0913i | 0.0319238 | + | 0.0317357i | ||||
\(382\) | 52.9094 | 0.138506 | ||||||||
\(383\) | − | 335.532i | − | 0.876063i | −0.898960 | − | 0.438031i | \(-0.855676\pi\) | ||
0.898960 | − | 0.438031i | \(-0.144324\pi\) | |||||||
\(384\) | 106.287 | − | 106.917i | 0.276788 | − | 0.278429i | ||||
\(385\) | 23.8331 | 0.0619042 | ||||||||
\(386\) | − | 46.6742i | − | 0.120918i | ||||||
\(387\) | −1.43469 | − | 242.782i | −0.00370722 | − | 0.627343i | ||||
\(388\) | 422.286 | 1.08837 | ||||||||
\(389\) | − | 260.756i | − | 0.670323i | −0.942161 | − | 0.335161i | \(-0.891209\pi\) | ||
0.942161 | − | 0.335161i | \(-0.108791\pi\) | |||||||
\(390\) | 8.15057 | + | 8.10254i | 0.0208989 | + | 0.0207758i | ||||
\(391\) | −135.538 | −0.346644 | ||||||||
\(392\) | − | 77.8361i | − | 0.198562i | ||||||
\(393\) | −85.1239 | + | 85.6284i | −0.216600 | + | 0.217884i | ||||
\(394\) | 44.9514 | 0.114090 | ||||||||
\(395\) | 163.634i | 0.414264i | ||||||||
\(396\) | −206.492 | + | 1.22025i | −0.521445 | + | 0.00308143i | ||||
\(397\) | 14.8867 | 0.0374980 | 0.0187490 | − | 0.999824i | \(-0.494032\pi\) | ||||
0.0187490 | + | 0.999824i | \(0.494032\pi\) | |||||||
\(398\) | 8.18164i | 0.0205569i | ||||||||
\(399\) | 33.9885 | + | 33.7883i | 0.0851842 | + | 0.0846823i | ||||
\(400\) | −211.622 | −0.529055 | ||||||||
\(401\) | − | 122.196i | − | 0.304729i | −0.988324 | − | 0.152364i | \(-0.951311\pi\) | ||
0.988324 | − | 0.152364i | \(-0.0486887\pi\) | |||||||
\(402\) | 15.1336 | − | 15.2233i | 0.0376457 | − | 0.0378688i | ||||
\(403\) | 71.0534 | 0.176311 | ||||||||
\(404\) | 685.756i | 1.69742i | ||||||||
\(405\) | −5.95060 | − | 503.468i | −0.0146928 | − | 1.24313i | ||||
\(406\) | −0.473254 | −0.00116565 | ||||||||
\(407\) | − | 365.486i | − | 0.898000i | ||||||
\(408\) | 43.7380 | + | 43.4803i | 0.107201 | + | 0.106569i | ||||
\(409\) | −51.7725 | −0.126583 | −0.0632916 | − | 0.997995i | \(-0.520160\pi\) | ||||
−0.0632916 | + | 0.997995i | \(0.520160\pi\) | |||||||
\(410\) | 31.8684i | 0.0777278i | ||||||||
\(411\) | 56.5992 | − | 56.9347i | 0.137711 | − | 0.138527i | ||||
\(412\) | −60.5994 | −0.147086 | ||||||||
\(413\) | 5.08224i | 0.0123057i | ||||||||
\(414\) | −0.113174 | − | 19.1516i | −0.000273368 | − | 0.0462599i | ||||
\(415\) | −325.232 | −0.783692 | ||||||||
\(416\) | 29.1830i | 0.0701516i | ||||||||
\(417\) | −424.277 | − | 421.778i | −1.01745 | − | 1.01146i | ||||
\(418\) | −28.1742 | −0.0674024 | ||||||||
\(419\) | − | 259.597i | − | 0.619564i | −0.950808 | − | 0.309782i | \(-0.899744\pi\) | ||
0.950808 | − | 0.309782i | \(-0.100256\pi\) | |||||||
\(420\) | −34.4429 | + | 34.6471i | −0.0820070 | + | 0.0824931i | ||||
\(421\) | −572.956 | −1.36094 | −0.680471 | − | 0.732775i | \(-0.738225\pi\) | ||||
−0.680471 | + | 0.732775i | \(0.738225\pi\) | |||||||
\(422\) | − | 63.7034i | − | 0.150956i | ||||||
\(423\) | 41.6738 | − | 0.246267i | 0.0985196 | − | 0.000582192i | ||||
\(424\) | 63.3554 | 0.149423 | ||||||||
\(425\) | − | 174.944i | − | 0.411633i | ||||||
\(426\) | −44.4561 | − | 44.1942i | −0.104357 | − | 0.103742i | ||||
\(427\) | −32.3553 | −0.0757735 | ||||||||
\(428\) | − | 777.726i | − | 1.81712i | ||||||
\(429\) | 37.5093 | − | 37.7316i | 0.0874342 | − | 0.0879524i | ||||
\(430\) | 33.7675 | 0.0785290 | ||||||||
\(431\) | 67.2883i | 0.156121i | 0.996949 | + | 0.0780607i | \(0.0248728\pi\) | ||||
−0.996949 | + | 0.0780607i | \(0.975127\pi\) | |||||||
\(432\) | 293.574 | − | 298.825i | 0.679569 | − | 0.691725i | ||||
\(433\) | −386.339 | −0.892238 | −0.446119 | − | 0.894974i | \(-0.647194\pi\) | ||||
−0.446119 | + | 0.894974i | \(0.647194\pi\) | |||||||
\(434\) | − | 3.09335i | − | 0.00712753i | ||||||
\(435\) | −46.9752 | − | 46.6984i | −0.107989 | − | 0.107353i | ||||
\(436\) | −515.976 | −1.18343 | ||||||||
\(437\) | 255.145i | 0.583857i | ||||||||
\(438\) | −32.4540 | + | 32.6463i | −0.0740958 | + | 0.0745350i | ||||
\(439\) | −386.344 | −0.880054 | −0.440027 | − | 0.897985i | \(-0.645031\pi\) | ||||
−0.440027 | + | 0.897985i | \(0.645031\pi\) | |||||||
\(440\) | − | 57.7344i | − | 0.131215i | ||||||
\(441\) | −2.58272 | − | 437.052i | −0.00585650 | − | 0.991048i | ||||
\(442\) | −7.90452 | −0.0178835 | ||||||||
\(443\) | 712.881i | 1.60921i | 0.593809 | + | 0.804606i | \(0.297623\pi\) | ||||
−0.593809 | + | 0.804606i | \(0.702377\pi\) | |||||||
\(444\) | 531.321 | + | 528.190i | 1.19667 | + | 1.18962i | ||||
\(445\) | 43.8271 | 0.0984879 | ||||||||
\(446\) | − | 19.2418i | − | 0.0431431i | ||||||
\(447\) | −372.551 | + | 374.759i | −0.833447 | + | 0.838386i | ||||
\(448\) | −39.7916 | −0.0888206 | ||||||||
\(449\) | 667.401i | 1.48642i | 0.669060 | + | 0.743209i | \(0.266697\pi\) | ||||
−0.669060 | + | 0.743209i | \(0.733303\pi\) | |||||||
\(450\) | 24.7197 | − | 0.146078i | 0.0549326 | − | 0.000324619i | ||||
\(451\) | 147.529 | 0.327115 | ||||||||
\(452\) | − | 717.646i | − | 1.58771i | ||||||
\(453\) | −338.024 | − | 336.032i | −0.746190 | − | 0.741793i | ||||
\(454\) | −79.1283 | −0.174291 | ||||||||
\(455\) | − | 12.5873i | − | 0.0276643i | ||||||
\(456\) | 81.8502 | − | 82.3353i | 0.179496 | − | 0.180560i | ||||
\(457\) | −21.3230 | −0.0466587 | −0.0233294 | − | 0.999728i | \(-0.507427\pi\) | ||||
−0.0233294 | + | 0.999728i | \(0.507427\pi\) | |||||||
\(458\) | 42.9260i | 0.0937250i | ||||||||
\(459\) | 247.033 | + | 242.692i | 0.538199 | + | 0.528741i | ||||
\(460\) | −260.089 | −0.565411 | ||||||||
\(461\) | − | 100.149i | − | 0.217242i | −0.994083 | − | 0.108621i | \(-0.965356\pi\) | ||
0.994083 | − | 0.108621i | \(-0.0346435\pi\) | |||||||
\(462\) | −1.64266 | − | 1.63299i | −0.00355555 | − | 0.00353460i | ||||
\(463\) | −647.449 | −1.39838 | −0.699189 | − | 0.714937i | \(-0.746455\pi\) | ||||
−0.699189 | + | 0.714937i | \(0.746455\pi\) | |||||||
\(464\) | − | 55.1084i | − | 0.118768i | ||||||
\(465\) | 305.237 | − | 307.046i | 0.656423 | − | 0.660313i | ||||
\(466\) | −35.1336 | −0.0753941 | ||||||||
\(467\) | 150.407i | 0.322070i | 0.986949 | + | 0.161035i | \(0.0514832\pi\) | ||||
−0.986949 | + | 0.161035i | \(0.948517\pi\) | |||||||
\(468\) | 0.644463 | + | 109.057i | 0.00137706 | + | 0.233028i | ||||
\(469\) | −23.5099 | −0.0501278 | ||||||||
\(470\) | 5.79622i | 0.0123324i | ||||||||
\(471\) | −610.964 | − | 607.365i | −1.29716 | − | 1.28952i | ||||
\(472\) | 12.3114 | 0.0260836 | ||||||||
\(473\) | − | 156.320i | − | 0.330487i | ||||||
\(474\) | 11.2118 | − | 11.2783i | 0.0236536 | − | 0.0237938i | ||||
\(475\) | −329.326 | −0.693317 | ||||||||
\(476\) | − | 33.6012i | − | 0.0705907i | ||||||
\(477\) | 355.743 | − | 2.10223i | 0.745792 | − | 0.00440718i | ||||
\(478\) | −41.8889 | −0.0876337 | ||||||||
\(479\) | − | 162.850i | − | 0.339979i | −0.985446 | − | 0.169989i | \(-0.945627\pi\) | ||
0.985446 | − | 0.169989i | \(-0.0543734\pi\) | |||||||
\(480\) | 126.110 | + | 125.367i | 0.262729 | + | 0.261181i | ||||
\(481\) | −193.028 | −0.401306 | ||||||||
\(482\) | − | 77.8691i | − | 0.161554i | ||||||
\(483\) | −14.7883 | + | 14.8759i | −0.0306176 | + | 0.0307990i | ||||
\(484\) | 346.139 | 0.715163 | ||||||||
\(485\) | 662.963i | 1.36693i | ||||||||
\(486\) | −34.0863 | + | 35.1086i | −0.0701363 | + | 0.0722399i | ||||
\(487\) | 372.472 | 0.764829 | 0.382414 | − | 0.923991i | \(-0.375093\pi\) | ||||
0.382414 | + | 0.923991i | \(0.375093\pi\) | |||||||
\(488\) | 78.3789i | 0.160612i | ||||||||
\(489\) | −163.695 | − | 162.731i | −0.334756 | − | 0.332783i | ||||
\(490\) | 60.7877 | 0.124057 | ||||||||
\(491\) | − | 446.687i | − | 0.909750i | −0.890555 | − | 0.454875i | \(-0.849684\pi\) | ||
0.890555 | − | 0.454875i | \(-0.150316\pi\) | |||||||
\(492\) | −213.205 | + | 214.469i | −0.433343 | + | 0.435912i | ||||
\(493\) | 45.5571 | 0.0924080 | ||||||||
\(494\) | 14.8800i | 0.0301214i | ||||||||
\(495\) | −1.91571 | − | 324.180i | −0.00387012 | − | 0.654910i | ||||
\(496\) | 360.207 | 0.726225 | ||||||||
\(497\) | 68.6555i | 0.138140i | ||||||||
\(498\) | 22.4162 | + | 22.2841i | 0.0450124 | + | 0.0447472i | ||||
\(499\) | 19.3772 | 0.0388321 | 0.0194160 | − | 0.999811i | \(-0.493819\pi\) | ||||
0.0194160 | + | 0.999811i | \(0.493819\pi\) | |||||||
\(500\) | 279.601i | 0.559201i | ||||||||
\(501\) | −622.671 | + | 626.361i | −1.24286 | + | 1.25022i | ||||
\(502\) | 5.95444 | 0.0118614 | ||||||||
\(503\) | − | 706.414i | − | 1.40440i | −0.711979 | − | 0.702200i | \(-0.752201\pi\) | ||
0.711979 | − | 0.702200i | \(-0.247799\pi\) | |||||||
\(504\) | 9.54435 | − | 0.0564014i | 0.0189372 | − | 0.000111908i | ||||
\(505\) | −1076.60 | −2.13187 | ||||||||
\(506\) | − | 12.3312i | − | 0.0243699i | ||||||
\(507\) | 339.633 | + | 337.632i | 0.669888 | + | 0.665941i | ||||
\(508\) | −22.6354 | −0.0445579 | ||||||||
\(509\) | 193.892i | 0.380927i | 0.981694 | + | 0.190463i | \(0.0609990\pi\) | ||||
−0.981694 | + | 0.190463i | \(0.939001\pi\) | |||||||
\(510\) | −33.9568 | + | 34.1581i | −0.0665820 | + | 0.0669767i | ||||
\(511\) | 50.4171 | 0.0986636 | ||||||||
\(512\) | 247.415i | 0.483233i | ||||||||
\(513\) | 456.859 | − | 465.031i | 0.890564 | − | 0.906494i | ||||
\(514\) | −50.0281 | −0.0973309 | ||||||||
\(515\) | − | 95.1373i | − | 0.184733i | ||||||
\(516\) | 227.249 | + | 225.910i | 0.440405 | + | 0.437810i | ||||
\(517\) | 26.8326 | 0.0519005 | ||||||||
\(518\) | 8.40359i | 0.0162231i | ||||||||
\(519\) | −550.269 | + | 553.530i | −1.06025 | + | 1.06653i | ||||
\(520\) | −30.4919 | −0.0586384 | ||||||||
\(521\) | − | 153.395i | − | 0.294424i | −0.989105 | − | 0.147212i | \(-0.952970\pi\) | ||
0.989105 | − | 0.147212i | \(-0.0470299\pi\) | |||||||
\(522\) | 0.0380403 | + | 6.43725i | 7.28741e−5 | + | 0.0123319i | ||||
\(523\) | 701.181 | 1.34069 | 0.670345 | − | 0.742049i | \(-0.266146\pi\) | ||||
0.670345 | + | 0.742049i | \(0.266146\pi\) | |||||||
\(524\) | − | 159.355i | − | 0.304114i | ||||||
\(525\) | −19.2009 | − | 19.0878i | −0.0365732 | − | 0.0363577i | ||||
\(526\) | −1.96191 | −0.00372986 | ||||||||
\(527\) | 297.777i | 0.565041i | ||||||||
\(528\) | 190.154 | − | 191.281i | 0.360141 | − | 0.362275i | ||||
\(529\) | 417.329 | 0.788902 | ||||||||
\(530\) | 49.4787i | 0.0933560i | ||||||||
\(531\) | 69.1291 | − | 0.408512i | 0.130187 | − | 0.000769325i | ||||
\(532\) | −63.2530 | −0.118897 | ||||||||
\(533\) | − | 77.9163i | − | 0.146184i | ||||||
\(534\) | −3.02072 | − | 3.00292i | −0.00565678 | − | 0.00562345i | ||||
\(535\) | 1220.98 | 2.28221 | ||||||||
\(536\) | 56.9515i | 0.106253i | ||||||||
\(537\) | 741.254 | − | 745.648i | 1.38036 | − | 1.38854i | ||||
\(538\) | −62.3882 | −0.115963 | ||||||||
\(539\) | − | 281.406i | − | 0.522088i | ||||||
\(540\) | 474.042 | + | 465.712i | 0.877855 | + | 0.862429i | ||||
\(541\) | −787.414 | −1.45548 | −0.727739 | − | 0.685854i | \(-0.759429\pi\) | ||||
−0.727739 | + | 0.685854i | \(0.759429\pi\) | |||||||
\(542\) | − | 37.3559i | − | 0.0689223i | ||||||
\(543\) | −444.216 | − | 441.599i | −0.818078 | − | 0.813258i | ||||
\(544\) | −122.303 | −0.224821 | ||||||||
\(545\) | − | 810.051i | − | 1.48633i | ||||||
\(546\) | −0.862448 | + | 0.867559i | −0.00157957 | + | 0.00158894i | ||||
\(547\) | 814.439 | 1.48892 | 0.744460 | − | 0.667667i | \(-0.232707\pi\) | ||||
0.744460 | + | 0.667667i | \(0.232707\pi\) | |||||||
\(548\) | 105.956i | 0.193350i | ||||||||
\(549\) | 2.60073 | + | 440.100i | 0.00473721 | + | 0.801639i | ||||
\(550\) | 15.9163 | 0.0289387 | ||||||||
\(551\) | − | 85.7597i | − | 0.155644i | ||||||
\(552\) | 36.0361 | + | 35.8238i | 0.0652829 | + | 0.0648982i | ||||
\(553\) | −17.4175 | −0.0314964 | ||||||||
\(554\) | − | 13.3731i | − | 0.0241392i | ||||||
\(555\) | −829.226 | + | 834.141i | −1.49410 | + | 1.50296i | ||||
\(556\) | 789.585 | 1.42012 | ||||||||
\(557\) | 241.406i | 0.433403i | 0.976238 | + | 0.216702i | \(0.0695299\pi\) | ||||
−0.976238 | + | 0.216702i | \(0.930470\pi\) | |||||||
\(558\) | −42.0760 | + | 0.248644i | −0.0754050 | + | 0.000445599i | ||||
\(559\) | −82.5593 | −0.147691 | ||||||||
\(560\) | − | 63.8115i | − | 0.113949i | ||||||
\(561\) | 158.129 | + | 157.197i | 0.281869 | + | 0.280209i | ||||
\(562\) | 45.3365 | 0.0806699 | ||||||||
\(563\) | − | 1026.75i | − | 1.82371i | −0.410514 | − | 0.911854i | \(-0.634651\pi\) | ||
0.410514 | − | 0.911854i | \(-0.365349\pi\) | |||||||
\(564\) | −38.7777 | + | 39.0075i | −0.0687548 | + | 0.0691623i | ||||
\(565\) | 1126.66 | 1.99409 | ||||||||
\(566\) | − | 38.8152i | − | 0.0685780i | ||||||
\(567\) | 53.5900 | − | 0.633391i | 0.0945149 | − | 0.00111709i | ||||
\(568\) | 166.314 | 0.292807 | ||||||||
\(569\) | 388.817i | 0.683334i | 0.939821 | + | 0.341667i | \(0.110992\pi\) | ||||
−0.939821 | + | 0.341667i | \(0.889008\pi\) | |||||||
\(570\) | 64.3014 | + | 63.9226i | 0.112809 | + | 0.112145i | ||||
\(571\) | −181.869 | −0.318510 | −0.159255 | − | 0.987238i | \(-0.550909\pi\) | ||||
−0.159255 | + | 0.987238i | \(0.550909\pi\) | |||||||
\(572\) | 70.2189i | 0.122760i | ||||||||
\(573\) | −555.715 | + | 559.009i | −0.969834 | + | 0.975582i | ||||
\(574\) | −3.39212 | −0.00590962 | ||||||||
\(575\) | − | 144.138i | − | 0.250674i | ||||||
\(576\) | 3.19846 | + | 541.250i | 0.00555289 | + | 0.939670i | ||||
\(577\) | −670.081 | −1.16132 | −0.580659 | − | 0.814147i | \(-0.697205\pi\) | ||||
−0.580659 | + | 0.814147i | \(0.697205\pi\) | |||||||
\(578\) | 25.0697i | 0.0433731i | ||||||||
\(579\) | 493.131 | + | 490.226i | 0.851695 | + | 0.846677i | ||||
\(580\) | 87.4214 | 0.150727 | ||||||||
\(581\) | − | 34.6182i | − | 0.0595839i | ||||||
\(582\) | 45.4246 | − | 45.6938i | 0.0780491 | − | 0.0785117i | ||||
\(583\) | 229.053 | 0.392886 | ||||||||
\(584\) | − | 122.133i | − | 0.209131i | ||||||
\(585\) | −171.213 | + | 1.01177i | −0.292672 | + | 0.00172952i | ||||
\(586\) | 9.96873 | 0.0170115 | ||||||||
\(587\) | 184.990i | 0.315145i | 0.987507 | + | 0.157572i | \(0.0503668\pi\) | ||||
−0.987507 | + | 0.157572i | \(0.949633\pi\) | |||||||
\(588\) | 409.090 | + | 406.680i | 0.695731 | + | 0.691632i | ||||
\(589\) | 560.554 | 0.951705 | ||||||||
\(590\) | 9.61487i | 0.0162964i | ||||||||
\(591\) | −472.131 | + | 474.929i | −0.798868 | + | 0.803603i | ||||
\(592\) | −978.564 | −1.65298 | ||||||||
\(593\) | 551.382i | 0.929818i | 0.885358 | + | 0.464909i | \(0.153913\pi\) | ||||
−0.885358 | + | 0.464909i | \(0.846087\pi\) | |||||||
\(594\) | −22.0800 | + | 22.4749i | −0.0371717 | + | 0.0378366i | ||||
\(595\) | 52.7518 | 0.0886584 | ||||||||
\(596\) | − | 697.430i | − | 1.17019i | ||||||
\(597\) | −86.4423 | − | 85.9330i | −0.144794 | − | 0.143941i | ||||
\(598\) | −6.51260 | −0.0108906 | ||||||||
\(599\) | − | 1007.58i | − | 1.68211i | −0.540950 | − | 0.841055i | \(-0.681935\pi\) | ||
0.540950 | − | 0.841055i | \(-0.318065\pi\) | |||||||
\(600\) | −46.2392 | + | 46.5132i | −0.0770653 | + | 0.0775220i | ||||
\(601\) | −494.345 | −0.822538 | −0.411269 | − | 0.911514i | \(-0.634914\pi\) | ||||
−0.411269 | + | 0.911514i | \(0.634914\pi\) | |||||||
\(602\) | 3.59426i | 0.00597054i | ||||||||
\(603\) | 1.88974 | + | 319.785i | 0.00313389 | + | 0.530323i | ||||
\(604\) | 629.066 | 1.04150 | ||||||||
\(605\) | 543.417i | 0.898209i | ||||||||
\(606\) | 74.2028 | + | 73.7656i | 0.122447 | + | 0.121725i | ||||
\(607\) | −966.032 | −1.59149 | −0.795743 | − | 0.605635i | \(-0.792919\pi\) | ||||
−0.795743 | + | 0.605635i | \(0.792919\pi\) | |||||||
\(608\) | 230.231i | 0.378669i | ||||||||
\(609\) | 4.97065 | − | 5.00011i | 0.00816199 | − | 0.00821037i | ||||
\(610\) | −61.2116 | −0.100347 | ||||||||
\(611\) | − | 14.1714i | − | 0.0231938i | ||||||
\(612\) | −457.047 | + | 2.70087i | −0.746808 | + | 0.00441319i | ||||
\(613\) | 354.491 | 0.578289 | 0.289144 | − | 0.957285i | \(-0.406629\pi\) | ||||
0.289144 | + | 0.957285i | \(0.406629\pi\) | |||||||
\(614\) | 65.6975i | 0.106999i | ||||||||
\(615\) | −336.702 | − | 334.719i | −0.547484 | − | 0.544258i | ||||
\(616\) | 6.14534 | 0.00997620 | ||||||||
\(617\) | 474.368i | 0.768830i | 0.923160 | + | 0.384415i | \(0.125597\pi\) | ||||
−0.923160 | + | 0.384415i | \(0.874403\pi\) | |||||||
\(618\) | −6.51857 | + | 6.55721i | −0.0105479 | + | 0.0106104i | ||||
\(619\) | 684.540 | 1.10588 | 0.552940 | − | 0.833221i | \(-0.313506\pi\) | ||||
0.552940 | + | 0.833221i | \(0.313506\pi\) | |||||||
\(620\) | 571.416i | 0.921638i | ||||||||
\(621\) | 203.533 | + | 199.956i | 0.327750 | + | 0.321991i | ||||
\(622\) | 106.798 | 0.171701 | ||||||||
\(623\) | 4.66503i | 0.00748801i | ||||||||
\(624\) | −101.024 | − | 100.428i | −0.161897 | − | 0.160943i | ||||
\(625\) | −779.951 | −1.24792 | ||||||||
\(626\) | − | 66.4790i | − | 0.106197i | ||||||
\(627\) | 295.918 | − | 297.672i | 0.471958 | − | 0.474756i | ||||
\(628\) | 1137.01 | 1.81053 | ||||||||
\(629\) | − | 808.960i | − | 1.28611i | ||||||
\(630\) | 0.0440478 | + | 7.45386i | 6.99172e−5 | + | 0.0118315i | ||||
\(631\) | −162.171 | −0.257006 | −0.128503 | − | 0.991709i | \(-0.541017\pi\) | ||||
−0.128503 | + | 0.991709i | \(0.541017\pi\) | |||||||
\(632\) | 42.1930i | 0.0667610i | ||||||||
\(633\) | 673.052 | + | 669.086i | 1.06327 | + | 1.05701i | ||||
\(634\) | −111.435 | −0.175764 | ||||||||
\(635\) | − | 35.5362i | − | 0.0559625i | ||||||
\(636\) | −331.021 | + | 332.983i | −0.520473 | + | 0.523557i | ||||
\(637\) | −148.622 | −0.233316 | ||||||||
\(638\) | 4.14476i | 0.00649649i | ||||||||
\(639\) | 933.859 | − | 5.51855i | 1.46144 | − | 0.00863622i | ||||
\(640\) | −312.376 | −0.488087 | ||||||||
\(641\) | 893.542i | 1.39398i | 0.717080 | + | 0.696991i | \(0.245478\pi\) | ||||
−0.717080 | + | 0.696991i | \(0.754522\pi\) | |||||||
\(642\) | −84.1545 | − | 83.6587i | −0.131082 | − | 0.130309i | ||||
\(643\) | 420.351 | 0.653734 | 0.326867 | − | 0.945070i | \(-0.394007\pi\) | ||||
0.326867 | + | 0.945070i | \(0.394007\pi\) | |||||||
\(644\) | − | 27.6843i | − | 0.0429880i | ||||||
\(645\) | −354.665 | + | 356.767i | −0.549868 | + | 0.553127i | ||||
\(646\) | −62.3603 | −0.0965330 | ||||||||
\(647\) | 618.128i | 0.955375i | 0.878530 | + | 0.477687i | \(0.158525\pi\) | ||||
−0.878530 | + | 0.477687i | \(0.841475\pi\) | |||||||
\(648\) | −1.53436 | − | 129.819i | −0.00236783 | − | 0.200338i | ||||
\(649\) | 44.5103 | 0.0685829 | ||||||||
\(650\) | − | 8.40606i | − | 0.0129324i | ||||||
\(651\) | 32.6824 | + | 32.4899i | 0.0502034 | + | 0.0499076i | ||||
\(652\) | 304.639 | 0.467238 | ||||||||
\(653\) | 54.2816i | 0.0831265i | 0.999136 | + | 0.0415632i | \(0.0132338\pi\) | ||||
−0.999136 | + | 0.0415632i | \(0.986766\pi\) | |||||||
\(654\) | −55.5027 | + | 55.8317i | −0.0848665 | + | 0.0853695i | ||||
\(655\) | 250.178 | 0.381952 | ||||||||
\(656\) | − | 394.999i | − | 0.602132i | ||||||
\(657\) | −4.05254 | − | 685.778i | −0.00616825 | − | 1.04380i | ||||
\(658\) | −0.616959 | −0.000937628 | ||||||||
\(659\) | − | 53.8500i | − | 0.0817147i | −0.999165 | − | 0.0408573i | \(-0.986991\pi\) | ||
0.999165 | − | 0.0408573i | \(-0.0130089\pi\) | |||||||
\(660\) | 303.440 | + | 301.652i | 0.459757 | + | 0.457048i | ||||
\(661\) | 848.128 | 1.28310 | 0.641549 | − | 0.767082i | \(-0.278292\pi\) | ||||
0.641549 | + | 0.767082i | \(0.278292\pi\) | |||||||
\(662\) | − | 45.7290i | − | 0.0690770i | ||||||
\(663\) | 83.0223 | − | 83.5144i | 0.125222 | − | 0.125964i | ||||
\(664\) | −83.8607 | −0.126296 | ||||||||
\(665\) | − | 99.3034i | − | 0.149328i | ||||||
\(666\) | 114.307 | − | 0.675483i | 0.171631 | − | 0.00101424i | ||||
\(667\) | 37.5349 | 0.0562742 | ||||||||
\(668\) | − | 1165.67i | − | 1.74501i | ||||||
\(669\) | 203.298 | + | 202.100i | 0.303883 | + | 0.302092i | ||||
\(670\) | −44.4774 | −0.0663842 | ||||||||
\(671\) | 283.368i | 0.422307i | ||||||||
\(672\) | −13.3442 | + | 13.4233i | −0.0198575 | + | 0.0199752i | ||||
\(673\) | −701.378 | −1.04217 | −0.521083 | − | 0.853506i | \(-0.674472\pi\) | ||||
−0.521083 | + | 0.853506i | \(0.674472\pi\) | |||||||
\(674\) | − | 84.4788i | − | 0.125340i | ||||||
\(675\) | −258.091 | + | 262.707i | −0.382357 | + | 0.389196i | ||||
\(676\) | −632.061 | −0.935002 | ||||||||
\(677\) | − | 153.683i | − | 0.227006i | −0.993538 | − | 0.113503i | \(-0.963793\pi\) | ||
0.993538 | − | 0.113503i | \(-0.0362071\pi\) | |||||||
\(678\) | −77.6535 | − | 77.1959i | −0.114533 | − | 0.113858i | ||||
\(679\) | −70.5668 | −0.103928 | ||||||||
\(680\) | − | 127.788i | − | 0.187924i | ||||||
\(681\) | 831.096 | − | 836.022i | 1.22040 | − | 1.22764i | ||||
\(682\) | −27.0916 | −0.0397237 | ||||||||
\(683\) | − | 623.259i | − | 0.912531i | −0.889844 | − | 0.456266i | \(-0.849187\pi\) | ||
0.889844 | − | 0.456266i | \(-0.150813\pi\) | |||||||
\(684\) | 5.08430 | + | 860.374i | 0.00743318 | + | 1.25786i | ||||
\(685\) | −166.345 | −0.242839 | ||||||||
\(686\) | 12.9990i | 0.0189490i | ||||||||
\(687\) | −453.531 | − | 450.859i | −0.660161 | − | 0.656272i | ||||
\(688\) | −418.537 | −0.608339 | ||||||||
\(689\) | − | 120.972i | − | 0.175577i | ||||||
\(690\) | −27.9773 | + | 28.1432i | −0.0405469 | + | 0.0407872i | ||||
\(691\) | 219.421 | 0.317542 | 0.158771 | − | 0.987315i | \(-0.449247\pi\) | ||||
0.158771 | + | 0.987315i | \(0.449247\pi\) | |||||||
\(692\) | − | 1030.13i | − | 1.48862i | ||||||
\(693\) | 34.5063 | − | 0.203911i | 0.0497926 | − | 0.000294244i | ||||
\(694\) | 17.6632 | 0.0254513 | ||||||||
\(695\) | 1239.60i | 1.78360i | ||||||||
\(696\) | −12.1125 | − | 12.0411i | −0.0174030 | − | 0.0173005i | ||||
\(697\) | 326.538 | 0.468491 | ||||||||
\(698\) | 38.5438i | 0.0552204i | ||||||||
\(699\) | 369.014 | − | 371.201i | 0.527917 | − | 0.531046i | ||||
\(700\) | 35.7332 | 0.0510474 | ||||||||
\(701\) | − | 681.802i | − | 0.972613i | −0.873788 | − | 0.486307i | \(-0.838344\pi\) | ||
0.873788 | − | 0.486307i | \(-0.161656\pi\) | |||||||
\(702\) | 11.8700 | + | 11.6614i | 0.0169088 | + | 0.0166116i | ||||
\(703\) | −1522.84 | −2.16620 | ||||||||
\(704\) | 348.496i | 0.495022i | ||||||||
\(705\) | −61.2394 | − | 60.8786i | −0.0868644 | − | 0.0863526i | ||||
\(706\) | −11.3907 | −0.0161342 | ||||||||
\(707\) | − | 114.595i | − | 0.162086i | ||||||
\(708\) | −64.3250 | + | 64.7063i | −0.0908546 | + | 0.0913931i | ||||
\(709\) | −1188.93 | −1.67692 | −0.838458 | − | 0.544966i | \(-0.816542\pi\) | ||||
−0.838458 | + | 0.544966i | \(0.816542\pi\) | |||||||
\(710\) | 129.886i | 0.182939i | ||||||||
\(711\) | 1.40002 | + | 236.915i | 0.00196909 | + | 0.333214i | ||||
\(712\) | 11.3008 | 0.0158719 | ||||||||
\(713\) | 245.341i | 0.344096i | ||||||||
\(714\) | −3.63584 | − | 3.61442i | −0.00509222 | − | 0.00506221i | ||||
\(715\) | −110.239 | −0.154181 | ||||||||
\(716\) | 1387.66i | 1.93807i | ||||||||
\(717\) | 439.966 | − | 442.573i | 0.613620 | − | 0.617257i | ||||
\(718\) | −76.1964 | −0.106123 | ||||||||
\(719\) | − | 789.054i | − | 1.09743i | −0.836009 | − | 0.548716i | \(-0.815117\pi\) | ||
0.836009 | − | 0.548716i | \(-0.184883\pi\) | |||||||
\(720\) | −867.971 | + | 5.12919i | −1.20551 | + | 0.00712387i | ||||
\(721\) | 10.1266 | 0.0140452 | ||||||||
\(722\) | 44.6957i | 0.0619054i | ||||||||
\(723\) | 822.718 | + | 817.871i | 1.13792 | + | 1.13122i | ||||
\(724\) | 826.692 | 1.14184 | ||||||||
\(725\) | 48.4477i | 0.0668244i | ||||||||
\(726\) | 37.2335 | − | 37.4542i | 0.0512859 | − | 0.0515898i | ||||
\(727\) | −486.812 | −0.669617 | −0.334808 | − | 0.942286i | \(-0.608672\pi\) | ||||
−0.334808 | + | 0.942286i | \(0.608672\pi\) | |||||||
\(728\) | − | 3.24561i | − | 0.00445826i | ||||||
\(729\) | −12.9230 | − | 728.885i | −0.0177271 | − | 0.999843i | ||||
\(730\) | 95.3819 | 0.130660 | ||||||||
\(731\) | − | 345.997i | − | 0.473320i | ||||||
\(732\) | −411.943 | − | 409.515i | −0.562763 | − | 0.559447i | ||||
\(733\) | 53.4071 | 0.0728609 | 0.0364305 | − | 0.999336i | \(-0.488401\pi\) | ||||
0.0364305 | + | 0.999336i | \(0.488401\pi\) | |||||||
\(734\) | 40.9356i | 0.0557706i | ||||||||
\(735\) | −638.462 | + | 642.246i | −0.868656 | + | 0.873804i | ||||
\(736\) | −100.766 | −0.136911 | ||||||||
\(737\) | 205.900i | 0.279376i | ||||||||
\(738\) | 0.272660 | + | 46.1400i | 0.000369458 | + | 0.0625204i | ||||
\(739\) | −985.718 | −1.33385 | −0.666927 | − | 0.745123i | \(-0.732391\pi\) | ||||
−0.666927 | + | 0.745123i | \(0.732391\pi\) | |||||||
\(740\) | − | 1552.35i | − | 2.09776i | ||||||
\(741\) | −157.213 | − | 156.287i | −0.212163 | − | 0.210913i | ||||
\(742\) | −5.26659 | −0.00709783 | ||||||||
\(743\) | 227.475i | 0.306157i | 0.988214 | + | 0.153078i | \(0.0489187\pi\) | ||||
−0.988214 | + | 0.153078i | \(0.951081\pi\) | |||||||
\(744\) | 78.7049 | − | 79.1714i | 0.105786 | − | 0.106413i | ||||
\(745\) | 1094.92 | 1.46969 | ||||||||
\(746\) | 109.002i | 0.146115i | ||||||||
\(747\) | −470.881 | + | 2.78262i | −0.630362 | + | 0.00372506i | ||||
\(748\) | −294.279 | −0.393422 | ||||||||
\(749\) | 129.963i | 0.173516i | ||||||||
\(750\) | 30.2544 | + | 30.0762i | 0.0403392 | + | 0.0401016i | ||||
\(751\) | 828.891 | 1.10372 | 0.551858 | − | 0.833938i | \(-0.313919\pi\) | ||||
0.551858 | + | 0.833938i | \(0.313919\pi\) | |||||||
\(752\) | − | 71.8424i | − | 0.0955351i | ||||||
\(753\) | −62.5404 | + | 62.9111i | −0.0830550 | + | 0.0835472i | ||||
\(754\) | 2.18902 | 0.00290321 | ||||||||
\(755\) | 987.596i | 1.30807i | ||||||||
\(756\) | −49.5711 | + | 50.4578i | −0.0655702 | + | 0.0667431i | ||||
\(757\) | 226.194 | 0.298804 | 0.149402 | − | 0.988777i | \(-0.452265\pi\) | ||||
0.149402 | + | 0.988777i | \(0.452265\pi\) | |||||||
\(758\) | 6.23248i | 0.00822227i | ||||||||
\(759\) | 130.284 | + | 129.516i | 0.171652 | + | 0.170640i | ||||
\(760\) | −240.557 | −0.316522 | ||||||||
\(761\) | − | 900.642i | − | 1.18350i | −0.806122 | − | 0.591749i | \(-0.798438\pi\) | ||
0.806122 | − | 0.591749i | \(-0.201562\pi\) | |||||||
\(762\) | −2.43485 | + | 2.44928i | −0.00319534 | + | 0.00321428i | ||||
\(763\) | 86.2232 | 0.113005 | ||||||||
\(764\) | − | 1040.32i | − | 1.36168i | ||||||
\(765\) | −4.24020 | − | 717.535i | −0.00554275 | − | 0.937954i | ||||
\(766\) | 67.5669 | 0.0882074 | ||||||||
\(767\) | − | 23.5077i | − | 0.0306489i | ||||||
\(768\) | −490.280 | − | 487.391i | −0.638385 | − | 0.634624i | ||||
\(769\) | −4.80971 | −0.00625450 | −0.00312725 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312725 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(770\) | 4.79933i | 0.00623289i | ||||||||
\(771\) | 525.452 | − | 528.567i | 0.681521 | − | 0.685560i | ||||
\(772\) | −917.723 | −1.18876 | ||||||||
\(773\) | 380.638i | 0.492417i | 0.969217 | + | 0.246208i | \(0.0791847\pi\) | ||||
−0.969217 | + | 0.246208i | \(0.920815\pi\) | |||||||
\(774\) | 48.8895 | − | 0.288908i | 0.0631648 | − | 0.000373266i | ||||
\(775\) | −316.671 | −0.408607 | ||||||||
\(776\) | 170.944i | 0.220289i | ||||||||
\(777\) | −88.7873 | − | 88.2642i | −0.114269 | − | 0.113596i | ||||
\(778\) | 52.5090 | 0.0674922 | ||||||||
\(779\) | − | 614.697i | − | 0.789084i | ||||||
\(780\) | 159.315 | − | 160.259i | 0.204250 | − | 0.205460i | ||||
\(781\) | 601.285 | 0.769892 | ||||||||
\(782\) | − | 27.2936i | − | 0.0349023i | ||||||
\(783\) | −68.4116 | − | 67.2094i | −0.0873712 | − | 0.0858358i | ||||
\(784\) | −753.444 | −0.961026 | ||||||||
\(785\) | 1785.04i | 2.27393i | ||||||||
\(786\) | −17.2432 | − | 17.1416i | −0.0219379 | − | 0.0218086i | ||||
\(787\) | 354.777 | 0.450797 | 0.225399 | − | 0.974267i | \(-0.427632\pi\) | ||||
0.225399 | + | 0.974267i | \(0.427632\pi\) | |||||||
\(788\) | − | 883.849i | − | 1.12164i | ||||||
\(789\) | 20.6062 | − | 20.7283i | 0.0261168 | − | 0.0262716i | ||||
\(790\) | −32.9515 | −0.0417107 | ||||||||
\(791\) | 119.923i | 0.151610i | ||||||||
\(792\) | −0.493964 | − | 83.5896i | −0.000623692 | − | 0.105542i | ||||
\(793\) | 149.658 | 0.188724 | ||||||||
\(794\) | 2.99777i | 0.00377553i | ||||||||
\(795\) | −522.762 | − | 519.682i | −0.657562 | − | 0.653688i | ||||
\(796\) | 160.870 | 0.202098 | ||||||||
\(797\) | 289.726i | 0.363521i | 0.983343 | + | 0.181760i | \(0.0581795\pi\) | ||||
−0.983343 | + | 0.181760i | \(0.941820\pi\) | |||||||
\(798\) | −6.80402 | + | 6.84435i | −0.00852634 | + | 0.00857687i | ||||
\(799\) | 59.3907 | 0.0743313 | ||||||||
\(800\) | − | 130.063i | − | 0.162579i | ||||||
\(801\) | 63.4542 | − | 0.374976i | 0.0792187 | − | 0.000468135i | ||||
\(802\) | 24.6069 | 0.0306820 | ||||||||
\(803\) | − | 441.553i | − | 0.549880i | ||||||
\(804\) | −299.325 | − | 297.561i | −0.372295 | − | 0.370101i | ||||
\(805\) | 43.4626 | 0.0539909 | ||||||||
\(806\) | 14.3082i | 0.0177521i | ||||||||
\(807\) | 655.273 | − | 659.157i | 0.811986 | − | 0.816799i | ||||
\(808\) | −277.599 | −0.343563 | ||||||||
\(809\) | − | 273.374i | − | 0.337916i | −0.985623 | − | 0.168958i | \(-0.945960\pi\) | ||
0.985623 | − | 0.168958i | \(-0.0540402\pi\) | |||||||
\(810\) | 101.385 | − | 1.19829i | 0.125166 | − | 0.00147937i | ||||
\(811\) | −187.700 | −0.231442 | −0.115721 | − | 0.993282i | \(-0.536918\pi\) | ||||
−0.115721 | + | 0.993282i | \(0.536918\pi\) | |||||||
\(812\) | 9.30527i | 0.0114597i | ||||||||
\(813\) | 394.680 | + | 392.354i | 0.485461 | + | 0.482600i | ||||
\(814\) | 73.5987 | 0.0904161 | ||||||||
\(815\) | 478.265i | 0.586828i | ||||||||
\(816\) | 420.884 | − | 423.379i | 0.515790 | − | 0.518847i | ||||
\(817\) | −651.327 | −0.797217 | ||||||||
\(818\) | − | 10.4256i | − | 0.0127452i | ||||||
\(819\) | −0.107694 | − | 18.2242i | −0.000131495 | − | 0.0222518i | ||||
\(820\) | 626.607 | 0.764155 | ||||||||
\(821\) | 1212.34i | 1.47666i | 0.674437 | + | 0.738332i | \(0.264386\pi\) | ||||
−0.674437 | + | 0.738332i | \(0.735614\pi\) | |||||||
\(822\) | 11.4651 | + | 11.3975i | 0.0139478 | + | 0.0138656i | ||||
\(823\) | −1052.56 | −1.27893 | −0.639465 | − | 0.768820i | \(-0.720844\pi\) | ||||
−0.639465 | + | 0.768820i | \(0.720844\pi\) | |||||||
\(824\) | − | 24.5311i | − | 0.0297707i | ||||||
\(825\) | −167.171 | + | 168.162i | −0.202632 | + | 0.203833i | ||||
\(826\) | −1.02342 | −0.00123901 | ||||||||
\(827\) | 991.862i | 1.19935i | 0.800244 | + | 0.599675i | \(0.204703\pi\) | ||||
−0.800244 | + | 0.599675i | \(0.795297\pi\) | |||||||
\(828\) | −376.565 | + | 2.22527i | −0.454788 | + | 0.00268753i | ||||
\(829\) | 111.278 | 0.134231 | 0.0671155 | − | 0.997745i | \(-0.478620\pi\) | ||||
0.0671155 | + | 0.997745i | \(0.478620\pi\) | |||||||
\(830\) | − | 65.4927i | − | 0.0789069i | ||||||
\(831\) | 141.292 | + | 140.460i | 0.170027 | + | 0.169025i | ||||
\(832\) | 184.055 | 0.221220 | ||||||||
\(833\) | − | 622.858i | − | 0.747729i | ||||||
\(834\) | 84.9343 | − | 85.4377i | 0.101840 | − | 0.102443i | ||||
\(835\) | 1830.02 | 2.19164 | ||||||||
\(836\) | 553.971i | 0.662644i | ||||||||
\(837\) | 439.304 | − | 447.161i | 0.524855 | − | 0.534243i | ||||
\(838\) | 52.2757 | 0.0623815 | ||||||||
\(839\) | 717.714i | 0.855439i | 0.903911 | + | 0.427720i | \(0.140683\pi\) | ||||
−0.903911 | + | 0.427720i | \(0.859317\pi\) | |||||||
\(840\) | −14.0254 | − | 13.9427i | −0.0166969 | − | 0.0165985i | ||||
\(841\) | 828.384 | 0.984998 | ||||||||
\(842\) | − | 115.378i | − | 0.137028i | ||||||
\(843\) | −476.176 | + | 478.998i | −0.564858 | + | 0.568206i | ||||
\(844\) | −1252.56 | −1.48407 | ||||||||
\(845\) | − | 992.298i | − | 1.17432i | ||||||
\(846\) | 0.0495914 | + | 8.39194i | 5.86186e−5 | + | 0.00991956i | ||||
\(847\) | −57.8421 | −0.0682906 | ||||||||
\(848\) | − | 613.273i | − | 0.723199i | ||||||
\(849\) | 410.098 | + | 407.682i | 0.483036 | + | 0.480190i | ||||
\(850\) | 35.2289 | 0.0414457 | ||||||||
\(851\) | − | 666.509i | − | 0.783207i | ||||||
\(852\) | −868.961 | + | 874.111i | −1.01991 | + | 1.02595i | ||||
\(853\) | −898.614 | −1.05348 | −0.526738 | − | 0.850028i | \(-0.676585\pi\) | ||||
−0.526738 | + | 0.850028i | \(0.676585\pi\) | |||||||
\(854\) | − | 6.51546i | − | 0.00762934i | ||||||
\(855\) | −1350.73 | + | 7.98203i | −1.57981 | + | 0.00933571i | ||||
\(856\) | 314.829 | 0.367791 | ||||||||
\(857\) | 150.552i | 0.175673i | 0.996135 | + | 0.0878367i | \(0.0279954\pi\) | ||||
−0.996135 | + | 0.0878367i | \(0.972005\pi\) | |||||||
\(858\) | 7.59809 | + | 7.55333i | 0.00885559 | + | 0.00880341i | ||||
\(859\) | −859.268 | −1.00031 | −0.500156 | − | 0.865935i | \(-0.666724\pi\) | ||||
−0.500156 | + | 0.865935i | \(0.666724\pi\) | |||||||
\(860\) | − | 663.947i | − | 0.772031i | ||||||
\(861\) | 35.6280 | − | 35.8391i | 0.0413798 | − | 0.0416250i | ||||
\(862\) | −13.5500 | −0.0157193 | ||||||||
\(863\) | − | 1334.75i | − | 1.54664i | −0.634017 | − | 0.773319i | \(-0.718595\pi\) | ||
0.634017 | − | 0.773319i | \(-0.281405\pi\) | |||||||
\(864\) | 183.658 | + | 180.431i | 0.212567 | + | 0.208832i | ||||
\(865\) | 1617.23 | 1.86964 | ||||||||
\(866\) | − | 77.7980i | − | 0.0898360i | ||||||
\(867\) | −264.871 | − | 263.310i | −0.305503 | − | 0.303703i | ||||
\(868\) | −60.8224 | −0.0700719 | ||||||||
\(869\) | 152.543i | 0.175538i | ||||||||
\(870\) | 9.40377 | − | 9.45950i | 0.0108089 | − | 0.0108730i | ||||
\(871\) | 108.745 | 0.124850 | ||||||||
\(872\) | − | 208.871i | − | 0.239531i | ||||||
\(873\) | 5.67218 | + | 959.857i | 0.00649734 | + | 1.09949i | ||||
\(874\) | −51.3792 | −0.0587863 | ||||||||
\(875\) | − | 46.7232i | − | 0.0533979i | ||||||
\(876\) | 641.903 | + | 638.121i | 0.732766 | + | 0.728448i | ||||
\(877\) | 1274.37 | 1.45310 | 0.726548 | − | 0.687116i | \(-0.241124\pi\) | ||||
0.726548 | + | 0.687116i | \(0.241124\pi\) | |||||||
\(878\) | − | 77.7989i | − | 0.0886092i | ||||||
\(879\) | −104.703 | + | 105.324i | −0.119116 | + | 0.119822i | ||||
\(880\) | −558.862 | −0.635070 | ||||||||
\(881\) | 1390.38i | 1.57818i | 0.614275 | + | 0.789092i | \(0.289449\pi\) | ||||
−0.614275 | + | 0.789092i | \(0.710551\pi\) | |||||||
\(882\) | 88.0102 | − | 0.520088i | 0.0997849 | − | 0.000589669i | ||||
\(883\) | 456.278 | 0.516737 | 0.258368 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258368 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(884\) | 155.421i | 0.175816i | ||||||||
\(885\) | −101.585 | − | 100.986i | −0.114785 | − | 0.114109i | ||||
\(886\) | −143.554 | −0.162025 | ||||||||
\(887\) | 431.879i | 0.486899i | 0.969914 | + | 0.243450i | \(0.0782790\pi\) | ||||
−0.969914 | + | 0.243450i | \(0.921721\pi\) | |||||||
\(888\) | −213.815 | + | 215.082i | −0.240783 | + | 0.242210i | ||||
\(889\) | 3.78253 | 0.00425481 | ||||||||
\(890\) | 8.82557i | 0.00991637i | ||||||||
\(891\) | −5.54725 | − | 469.342i | −0.00622587 | − | 0.526758i | ||||
\(892\) | −378.339 | −0.424147 | ||||||||
\(893\) | − | 111.801i | − | 0.125197i | ||||||
\(894\) | −75.4660 | − | 75.0214i | −0.0844139 | − | 0.0839165i | ||||
\(895\) | −2178.54 | −2.43412 | ||||||||
\(896\) | − | 33.2498i | − | 0.0371091i | ||||||
\(897\) | 68.4028 | − | 68.8082i | 0.0762573 | − | 0.0767093i | ||||
\(898\) | −134.396 | −0.149662 | ||||||||
\(899\) | − | 82.4642i | − | 0.0917288i | ||||||
\(900\) | −2.87224 | − | 486.046i | −0.00319138 | − | 0.540051i | ||||
\(901\) | 506.981 | 0.562687 | ||||||||
\(902\) | 29.7083i | 0.0329360i | ||||||||
\(903\) | −37.9748 | − | 37.7511i | −0.0420541 | − | 0.0418063i | ||||
\(904\) | 290.508 | 0.321358 | ||||||||
\(905\) | 1297.86i | 1.43409i | ||||||||
\(906\) | 67.6676 | − | 68.0687i | 0.0746883 | − | 0.0751310i | ||||
\(907\) | 241.763 | 0.266552 | 0.133276 | − | 0.991079i | \(-0.457450\pi\) | ||||
0.133276 | + | 0.991079i | \(0.457450\pi\) | |||||||
\(908\) | 1555.85i | 1.71349i | ||||||||
\(909\) | −1558.73 | + | 9.21114i | −1.71477 | + | 0.0101333i | ||||
\(910\) | 2.53473 | 0.00278541 | ||||||||
\(911\) | − | 1121.30i | − | 1.23084i | −0.788198 | − | 0.615422i | \(-0.788986\pi\) | ||
0.788198 | − | 0.615422i | \(-0.211014\pi\) | |||||||
\(912\) | −796.996 | − | 792.300i | −0.873899 | − | 0.868750i | ||||
\(913\) | −303.187 | −0.332078 | ||||||||
\(914\) | − | 4.29387i | − | 0.00469789i | ||||||
\(915\) | 642.914 | − | 646.725i | 0.702638 | − | 0.706803i | ||||
\(916\) | 844.026 | 0.921426 | ||||||||
\(917\) | 26.6294i | 0.0290397i | ||||||||
\(918\) | −48.8715 | + | 49.7456i | −0.0532369 | + | 0.0541892i | ||||
\(919\) | 516.218 | 0.561717 | 0.280859 | − | 0.959749i | \(-0.409381\pi\) | ||||
0.280859 | + | 0.959749i | \(0.409381\pi\) | |||||||
\(920\) | − | 105.286i | − | 0.114441i | ||||||
\(921\) | −694.120 | − | 690.030i | −0.753659 | − | 0.749218i | ||||
\(922\) | 20.1672 | 0.0218733 | ||||||||
\(923\) | − | 317.564i | − | 0.344056i | ||||||
\(924\) | −32.1083 | + | 32.2986i | −0.0347492 | + | 0.0349552i | ||||
\(925\) | 860.289 | 0.930042 | ||||||||
\(926\) | − | 130.378i | − | 0.140797i | ||||||
\(927\) | −0.813977 | − | 137.743i | −0.000878076 | − | 0.148590i | ||||
\(928\) | 33.8697 | 0.0364975 | ||||||||
\(929\) | 1296.87i | 1.39599i | 0.716105 | + | 0.697993i | \(0.245923\pi\) | ||||
−0.716105 | + | 0.697993i | \(0.754077\pi\) | |||||||
\(930\) | 61.8305 | + | 61.4662i | 0.0664844 | + | 0.0660927i | ||||
\(931\) | −1172.51 | −1.25941 | ||||||||
\(932\) | 690.809i | 0.741212i | ||||||||
\(933\) | −1121.72 | + | 1128.36i | −1.20227 | + | 1.20939i | ||||
\(934\) | −30.2877 | −0.0324280 | ||||||||
\(935\) | − | 462.001i | − | 0.494118i | ||||||
\(936\) | −44.1471 | + | 0.260883i | −0.0471658 | + | 0.000278721i | ||||
\(937\) | 975.307 | 1.04088 | 0.520442 | − | 0.853897i | \(-0.325767\pi\) | ||||
0.520442 | + | 0.853897i | \(0.325767\pi\) | |||||||
\(938\) | − | 4.73425i | − | 0.00504718i | ||||||
\(939\) | 702.377 | + | 698.239i | 0.748006 | + | 0.743599i | ||||
\(940\) | 113.967 | 0.121242 | ||||||||
\(941\) | 1851.87i | 1.96798i | 0.178220 | + | 0.983991i | \(0.442966\pi\) | ||||
−0.178220 | + | 0.983991i | \(0.557034\pi\) | |||||||
\(942\) | 122.306 | − | 123.031i | 0.129837 | − | 0.130606i | ||||
\(943\) | 269.038 | 0.285300 | ||||||||
\(944\) | − | 119.173i | − | 0.126243i | ||||||
\(945\) | −79.2156 | − | 77.8236i | −0.0838260 | − | 0.0823530i | ||||
\(946\) | 31.4786 | 0.0332755 | ||||||||
\(947\) | 1063.50i | 1.12302i | 0.827469 | + | 0.561512i | \(0.189780\pi\) | ||||
−0.827469 | + | 0.561512i | \(0.810220\pi\) | |||||||
\(948\) | −221.757 | − | 220.451i | −0.233921 | − | 0.232543i | ||||
\(949\) | −233.203 | −0.245735 | ||||||||
\(950\) | − | 66.3171i | − | 0.0698074i | ||||||
\(951\) | 1170.41 | − | 1177.35i | 1.23072 | − | 1.23801i | ||||
\(952\) | 13.6020 | 0.0142878 | ||||||||
\(953\) | − | 1230.32i | − | 1.29100i | −0.763762 | − | 0.645498i | \(-0.776650\pi\) | ||
0.763762 | − | 0.645498i | \(-0.223350\pi\) | |||||||
\(954\) | 0.423330 | + | 71.6367i | 0.000443742 | + | 0.0750909i | ||||
\(955\) | 1633.24 | 1.71020 | ||||||||
\(956\) | 823.634i | 0.861542i | ||||||||
\(957\) | −43.7911 | − | 43.5330i | −0.0457587 | − | 0.0454891i | ||||
\(958\) | 32.7935 | 0.0342312 | ||||||||
\(959\) | − | 17.7060i | − | 0.0184630i | ||||||
\(960\) | 790.678 | − | 795.364i | 0.823623 | − | 0.828504i | ||||
\(961\) | −421.986 | −0.439112 | ||||||||
\(962\) | − | 38.8706i | − | 0.0404060i | ||||||
\(963\) | 1767.77 | − | 10.4465i | 1.83570 | − | 0.0108479i | ||||
\(964\) | −1531.09 | −1.58827 | ||||||||
\(965\) | − | 1440.77i | − | 1.49302i | ||||||
\(966\) | −2.99560 | − | 2.97795i | −0.00310104 | − | 0.00308277i | ||||
\(967\) | −506.206 | −0.523481 | −0.261740 | − | 0.965138i | \(-0.584296\pi\) | ||||
−0.261740 | + | 0.965138i | \(0.584296\pi\) | |||||||
\(968\) | 140.119i | 0.144751i | ||||||||
\(969\) | 654.980 | − | 658.862i | 0.675933 | − | 0.679940i | ||||
\(970\) | −133.502 | −0.137631 | ||||||||
\(971\) | 1658.06i | 1.70758i | 0.520620 | + | 0.853788i | \(0.325701\pi\) | ||||
−0.520620 | + | 0.853788i | \(0.674299\pi\) | |||||||
\(972\) | 690.316 | + | 670.215i | 0.710202 | + | 0.689522i | ||||
\(973\) | −131.945 | −0.135606 | ||||||||
\(974\) | 75.0055i | 0.0770077i | ||||||||
\(975\) | 88.8134 | + | 88.2901i | 0.0910907 | + | 0.0905540i | ||||
\(976\) | 758.698 | 0.777355 | ||||||||
\(977\) | 1701.18i | 1.74123i | 0.491968 | + | 0.870613i | \(0.336278\pi\) | ||||
−0.491968 | + | 0.870613i | \(0.663722\pi\) | |||||||
\(978\) | 32.7695 | − | 32.9637i | 0.0335067 | − | 0.0337053i | ||||
\(979\) | 40.8564 | 0.0417328 | ||||||||
\(980\) | − | 1195.23i | − | 1.21962i | ||||||
\(981\) | −6.93064 | − | 1172.82i | −0.00706487 | − | 1.19553i | ||||
\(982\) | 89.9505 | 0.0915993 | ||||||||
\(983\) | 768.733i | 0.782027i | 0.920385 | + | 0.391014i | \(0.127875\pi\) | ||||
−0.920385 | + | 0.391014i | \(0.872125\pi\) | |||||||
\(984\) | −86.8184 | − | 86.3068i | −0.0882300 | − | 0.0877102i | ||||
\(985\) | 1387.59 | 1.40872 | ||||||||
\(986\) | 9.17394i | 0.00930420i | ||||||||
\(987\) | 6.48001 | − | 6.51842i | 0.00656536 | − | 0.00660428i | ||||
\(988\) | 292.575 | 0.296129 | ||||||||
\(989\) | − | 285.070i | − | 0.288240i | ||||||
\(990\) | 65.2810 | − | 0.385771i | 0.0659404 | − | 0.000389668i | ||||
\(991\) | −1439.51 | −1.45258 | −0.726290 | − | 0.687388i | \(-0.758757\pi\) | ||||
−0.726290 | + | 0.687388i | \(0.758757\pi\) | |||||||
\(992\) | 221.384i | 0.223169i | ||||||||
\(993\) | 483.145 | + | 480.298i | 0.486551 | + | 0.483684i | ||||
\(994\) | −13.8253 | −0.0139088 | ||||||||
\(995\) | 252.556i | 0.253825i | ||||||||
\(996\) | 438.157 | − | 440.754i | 0.439917 | − | 0.442524i | ||||
\(997\) | 670.766 | 0.672784 | 0.336392 | − | 0.941722i | \(-0.390793\pi\) | ||||
0.336392 | + | 0.941722i | \(0.390793\pi\) | |||||||
\(998\) | 3.90203i | 0.00390985i | ||||||||
\(999\) | −1193.44 | + | 1214.79i | −1.19464 | + | 1.21600i |
(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 | 177.3.b.a.119.21 | yes | 38 | |
3.2 | odd | 2 | inner | 177.3.b.a.119.18 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.b.a.119.18 | ✓ | 38 | 3.2 | odd | 2 | inner | |
177.3.b.a.119.21 | yes | 38 | 1.1 | even | 1 | trivial |