Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 167.11 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.b.83.11 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.86291 | + | 2.35150i | 0.620970 | + | 0.783835i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −1.91622 | + | 4.61824i | −0.383244 | + | 0.923647i | ||||
\(6\) | 4.21441 | + | 0.488596i | 0.702402 | + | 0.0814326i | ||||
\(7\) | −3.12763 | + | 6.26242i | −0.446805 | + | 0.894631i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.05914 | + | 8.76127i | −0.228794 | + | 0.973475i | ||||
\(10\) | 2.70202 | + | 6.53446i | 0.270202 | + | 0.653446i | ||||
\(11\) | − | 0.117411i | − | 0.0106738i | −0.999986 | − | 0.00533688i | \(-0.998301\pi\) | ||
0.999986 | − | 0.00533688i | \(-0.00169879\pi\) | |||||||
\(12\) | 4.70301 | − | 3.72582i | 0.391917 | − | 0.310485i | ||||
\(13\) | 9.72258 | + | 9.72258i | 0.747890 | + | 0.747890i | 0.974083 | − | 0.226192i | \(-0.0726277\pi\) |
−0.226192 | + | 0.974083i | \(0.572628\pi\) | |||||||
\(14\) | 3.13479 | + | 9.39005i | 0.223913 | + | 0.670718i | ||||
\(15\) | −14.4295 | + | 4.09735i | −0.961969 | + | 0.273157i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −13.8691 | − | 13.8691i | −0.815828 | − | 0.815828i | 0.169673 | − | 0.985500i | \(-0.445729\pi\) |
−0.985500 | + | 0.169673i | \(0.945729\pi\) | |||||||
\(18\) | 6.70213 | + | 10.8204i | 0.372341 | + | 0.601134i | ||||
\(19\) | 29.7218 | 1.56431 | 0.782153 | − | 0.623086i | \(-0.214121\pi\) | ||||
0.782153 | + | 0.623086i | \(0.214121\pi\) | |||||||
\(20\) | 9.23647 | + | 3.83244i | 0.461824 | + | 0.191622i | ||||
\(21\) | −20.5526 | + | 4.31167i | −0.978695 | + | 0.205318i | ||||
\(22\) | −0.117411 | − | 0.117411i | −0.00533688 | − | 0.00533688i | ||||
\(23\) | −2.25150 | − | 2.25150i | −0.0978912 | − | 0.0978912i | 0.656465 | − | 0.754356i | \(-0.272051\pi\) |
−0.754356 | + | 0.656465i | \(0.772051\pi\) | |||||||
\(24\) | 0.977191 | − | 8.42883i | 0.0407163 | − | 0.351201i | ||||
\(25\) | −17.6562 | − | 17.6991i | −0.706248 | − | 0.707964i | ||||
\(26\) | 19.4452 | 0.747890 | ||||||||
\(27\) | −24.4382 | + | 11.4794i | −0.905117 | + | 0.425162i | ||||
\(28\) | 12.5248 | + | 6.25527i | 0.447316 | + | 0.223402i | ||||
\(29\) | 46.0711 | 1.58866 | 0.794329 | − | 0.607488i | \(-0.207823\pi\) | ||||
0.794329 | + | 0.607488i | \(0.207823\pi\) | |||||||
\(30\) | −10.3322 | + | 18.5269i | −0.344406 | + | 0.617563i | ||||
\(31\) | − | 1.50946i | − | 0.0486921i | −0.999704 | − | 0.0243461i | \(-0.992250\pi\) | ||
0.999704 | − | 0.0243461i | \(-0.00775036\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0.276093 | − | 0.218727i | 0.00836646 | − | 0.00662808i | ||||
\(34\) | −27.7381 | −0.815828 | ||||||||
\(35\) | −22.9281 | − | 26.4443i | −0.655089 | − | 0.755552i | ||||
\(36\) | 17.5225 | + | 4.11829i | 0.486737 | + | 0.114397i | ||||
\(37\) | 5.32611 | + | 5.32611i | 0.143949 | + | 0.143949i | 0.775409 | − | 0.631460i | \(-0.217544\pi\) |
−0.631460 | + | 0.775409i | \(0.717544\pi\) | |||||||
\(38\) | 29.7218 | − | 29.7218i | 0.782153 | − | 0.782153i | ||||
\(39\) | −4.75041 | + | 40.9749i | −0.121805 | + | 1.05064i | ||||
\(40\) | 13.0689 | − | 5.40403i | 0.326723 | − | 0.135101i | ||||
\(41\) | 13.4956 | 0.329160 | 0.164580 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164580 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(42\) | −16.2409 | + | 24.8643i | −0.386689 | + | 0.592007i | ||||
\(43\) | 36.8754 | − | 36.8754i | 0.857568 | − | 0.857568i | −0.133483 | − | 0.991051i | \(-0.542616\pi\) |
0.991051 | + | 0.133483i | \(0.0426162\pi\) | |||||||
\(44\) | −0.234823 | −0.00533688 | ||||||||
\(45\) | −36.5159 | − | 26.2981i | −0.811464 | − | 0.584403i | ||||
\(46\) | −4.50300 | −0.0978912 | ||||||||
\(47\) | −29.7803 | − | 29.7803i | −0.633624 | − | 0.633624i | 0.315351 | − | 0.948975i | \(-0.397878\pi\) |
−0.948975 | + | 0.315351i | \(0.897878\pi\) | |||||||
\(48\) | −7.45163 | − | 9.40602i | −0.155242 | − | 0.195959i | ||||
\(49\) | −29.4358 | − | 39.1731i | −0.600731 | − | 0.799451i | ||||
\(50\) | −35.3553 | − | 0.0428987i | −0.707106 | − | 0.000857974i | ||||
\(51\) | 6.77637 | − | 58.4500i | 0.132870 | − | 1.14608i | ||||
\(52\) | 19.4452 | − | 19.4452i | 0.373945 | − | 0.373945i | ||||
\(53\) | 59.8162 | + | 59.8162i | 1.12861 | + | 1.12861i | 0.990404 | + | 0.138204i | \(0.0441329\pi\) |
0.138204 | + | 0.990404i | \(0.455867\pi\) | |||||||
\(54\) | −12.9588 | + | 35.9175i | −0.239978 | + | 0.665140i | ||||
\(55\) | 0.542233 | + | 0.224986i | 0.00985879 | + | 0.00409065i | ||||
\(56\) | 18.7801 | − | 6.26957i | 0.335359 | − | 0.111957i | ||||
\(57\) | 55.3690 | + | 69.8910i | 0.971387 | + | 1.22616i | ||||
\(58\) | 46.0711 | − | 46.0711i | 0.794329 | − | 0.794329i | ||||
\(59\) | 84.9209i | 1.43934i | 0.694317 | + | 0.719669i | \(0.255706\pi\) | ||||
−0.694317 | + | 0.719669i | \(0.744294\pi\) | |||||||
\(60\) | 8.19471 | + | 28.8591i | 0.136578 | + | 0.480985i | ||||
\(61\) | − | 34.8141i | − | 0.570723i | −0.958420 | − | 0.285361i | \(-0.907886\pi\) | ||
0.958420 | − | 0.285361i | \(-0.0921137\pi\) | |||||||
\(62\) | −1.50946 | − | 1.50946i | −0.0243461 | − | 0.0243461i | ||||
\(63\) | −48.4265 | − | 40.2973i | −0.768675 | − | 0.639639i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −63.5317 | + | 26.2706i | −0.977411 | + | 0.404163i | ||||
\(66\) | 0.0573667 | − | 0.494820i | 0.000869192 | − | 0.00749727i | ||||
\(67\) | −34.4892 | − | 34.4892i | −0.514764 | − | 0.514764i | 0.401218 | − | 0.915982i | \(-0.368587\pi\) |
−0.915982 | + | 0.401218i | \(0.868587\pi\) | |||||||
\(68\) | −27.7381 | + | 27.7381i | −0.407914 | + | 0.407914i | ||||
\(69\) | 1.10007 | − | 9.48874i | 0.0159431 | − | 0.137518i | ||||
\(70\) | −49.3724 | − | 3.51622i | −0.705320 | − | 0.0502317i | ||||
\(71\) | − | 77.6498i | − | 1.09366i | −0.837244 | − | 0.546829i | \(-0.815835\pi\) | ||
0.837244 | − | 0.546829i | \(-0.184165\pi\) | |||||||
\(72\) | 21.6408 | − | 13.4043i | 0.300567 | − | 0.186170i | ||||
\(73\) | −41.3259 | − | 41.3259i | −0.566108 | − | 0.566108i | 0.364928 | − | 0.931036i | \(-0.381094\pi\) |
−0.931036 | + | 0.364928i | \(0.881094\pi\) | |||||||
\(74\) | 10.6522 | 0.143949 | ||||||||
\(75\) | 8.72762 | − | 74.4905i | 0.116368 | − | 0.993206i | ||||
\(76\) | − | 59.4436i | − | 0.782153i | ||||||
\(77\) | 0.735279 | + | 0.367220i | 0.00954908 | + | 0.00476909i | ||||
\(78\) | 36.2245 | + | 45.7254i | 0.464417 | + | 0.586223i | ||||
\(79\) | − | 0.865694i | − | 0.0109582i | −0.999985 | − | 0.00547908i | \(-0.998256\pi\) | ||
0.999985 | − | 0.00547908i | \(-0.00174405\pi\) | |||||||
\(80\) | 7.66488 | − | 18.4729i | 0.0958110 | − | 0.230912i | ||||
\(81\) | −72.5199 | − | 36.0814i | −0.895307 | − | 0.445450i | ||||
\(82\) | 13.4956 | − | 13.4956i | 0.164580 | − | 0.164580i | ||||
\(83\) | −99.0630 | + | 99.0630i | −1.19353 | + | 1.19353i | −0.217461 | + | 0.976069i | \(0.569778\pi\) |
−0.976069 | + | 0.217461i | \(0.930222\pi\) | |||||||
\(84\) | 8.62335 | + | 41.1052i | 0.102659 | + | 0.489348i | ||||
\(85\) | 90.6268 | − | 37.4745i | 1.06620 | − | 0.440876i | ||||
\(86\) | − | 73.7509i | − | 0.857568i | ||||||
\(87\) | 85.8262 | + | 108.336i | 0.986508 | + | 1.24525i | ||||
\(88\) | −0.234823 | + | 0.234823i | −0.00266844 | + | 0.00266844i | ||||
\(89\) | − | 129.599i | − | 1.45616i | −0.685490 | − | 0.728082i | \(-0.740412\pi\) | ||
0.685490 | − | 0.728082i | \(-0.259588\pi\) | |||||||
\(90\) | −62.8140 | + | 10.2177i | −0.697933 | + | 0.113530i | ||||
\(91\) | −91.2955 | + | 30.4782i | −1.00325 | + | 0.334925i | ||||
\(92\) | −4.50300 | + | 4.50300i | −0.0489456 | + | 0.0489456i | ||||
\(93\) | 3.54949 | − | 2.81198i | 0.0381666 | − | 0.0302363i | ||||
\(94\) | −59.5607 | −0.633624 | ||||||||
\(95\) | −56.9535 | + | 137.262i | −0.599511 | + | 1.44487i | ||||
\(96\) | −16.8577 | − | 1.95438i | −0.175601 | − | 0.0203581i | ||||
\(97\) | 15.7928 | − | 15.7928i | 0.162812 | − | 0.162812i | −0.620999 | − | 0.783811i | \(-0.713273\pi\) |
0.783811 | + | 0.620999i | \(0.213273\pi\) | |||||||
\(98\) | −68.6089 | − | 9.73729i | −0.700091 | − | 0.0993602i | ||||
\(99\) | 1.02867 | + | 0.241767i | 0.0103906 | + | 0.00244209i | ||||
\(100\) | −35.3982 | + | 35.3124i | −0.353982 | + | 0.353124i | ||||
\(101\) | 14.4525 | 0.143094 | 0.0715470 | − | 0.997437i | \(-0.477206\pi\) | ||||
0.0715470 | + | 0.997437i | \(0.477206\pi\) | |||||||
\(102\) | −51.6736 | − | 65.2264i | −0.506604 | − | 0.639474i | ||||
\(103\) | 31.3694 | + | 31.3694i | 0.304557 | + | 0.304557i | 0.842794 | − | 0.538237i | \(-0.180909\pi\) |
−0.538237 | + | 0.842794i | \(0.680909\pi\) | |||||||
\(104\) | − | 38.8903i | − | 0.373945i | ||||||
\(105\) | 19.4710 | − | 103.179i | 0.185438 | − | 0.982656i | ||||
\(106\) | 119.632 | 1.12861 | ||||||||
\(107\) | −105.856 | + | 105.856i | −0.989310 | + | 0.989310i | −0.999943 | − | 0.0106339i | \(-0.996615\pi\) |
0.0106339 | + | 0.999943i | \(0.496615\pi\) | |||||||
\(108\) | 22.9587 | + | 48.8763i | 0.212581 | + | 0.452559i | ||||
\(109\) | − | 95.4740i | − | 0.875908i | −0.898997 | − | 0.437954i | \(-0.855703\pi\) | ||
0.898997 | − | 0.437954i | \(-0.144297\pi\) | |||||||
\(110\) | 0.767219 | − | 0.317247i | 0.00697472 | − | 0.00288407i | ||||
\(111\) | −2.60231 | + | 22.4464i | −0.0234443 | + | 0.202220i | ||||
\(112\) | 12.5105 | − | 25.0497i | 0.111701 | − | 0.223658i | ||||
\(113\) | 60.1261 | + | 60.1261i | 0.532089 | + | 0.532089i | 0.921194 | − | 0.389104i | \(-0.127215\pi\) |
−0.389104 | + | 0.921194i | \(0.627215\pi\) | |||||||
\(114\) | 125.260 | + | 14.5219i | 1.09877 | + | 0.127386i | ||||
\(115\) | 14.7123 | − | 6.08359i | 0.127933 | − | 0.0529007i | ||||
\(116\) | − | 92.1422i | − | 0.794329i | ||||||
\(117\) | −105.202 | + | 65.1620i | −0.899165 | + | 0.556940i | ||||
\(118\) | 84.9209 | + | 84.9209i | 0.719669 | + | 0.719669i | ||||
\(119\) | 130.231 | − | 43.4766i | 1.09438 | − | 0.365350i | ||||
\(120\) | 37.0538 | + | 20.6644i | 0.308782 | + | 0.172203i | ||||
\(121\) | 120.986 | 0.999886 | ||||||||
\(122\) | −34.8141 | − | 34.8141i | −0.285361 | − | 0.285361i | ||||
\(123\) | 25.1410 | + | 31.7349i | 0.204398 | + | 0.258007i | ||||
\(124\) | −3.01891 | −0.0243461 | ||||||||
\(125\) | 115.572 | − | 47.6252i | 0.924575 | − | 0.381001i | ||||
\(126\) | −88.7238 | + | 8.12926i | −0.704157 | + | 0.0645179i | ||||
\(127\) | 171.860 | + | 171.860i | 1.35323 | + | 1.35323i | 0.882022 | + | 0.471207i | \(0.156182\pi\) |
0.471207 | + | 0.882022i | \(0.343818\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 155.408 | + | 18.0172i | 1.20472 | + | 0.139668i | ||||
\(130\) | −37.2612 | + | 89.8023i | −0.286624 | + | 0.690787i | ||||
\(131\) | 145.791 | 1.11291 | 0.556453 | − | 0.830879i | \(-0.312162\pi\) | ||||
0.556453 | + | 0.830879i | \(0.312162\pi\) | |||||||
\(132\) | −0.437453 | − | 0.552187i | −0.00331404 | − | 0.00418323i | ||||
\(133\) | −92.9590 | + | 186.131i | −0.698940 | + | 1.39948i | ||||
\(134\) | −68.9784 | −0.514764 | ||||||||
\(135\) | −6.18554 | − | 134.858i | −0.0458188 | − | 0.998950i | ||||
\(136\) | 55.4763i | 0.407914i | ||||||||
\(137\) | 37.8019 | − | 37.8019i | 0.275926 | − | 0.275926i | −0.555554 | − | 0.831480i | \(-0.687494\pi\) |
0.831480 | + | 0.555554i | \(0.187494\pi\) | |||||||
\(138\) | −8.38867 | − | 10.5888i | −0.0607875 | − | 0.0767305i | ||||
\(139\) | 65.4496 | 0.470861 | 0.235430 | − | 0.971891i | \(-0.424350\pi\) | ||||
0.235430 | + | 0.971891i | \(0.424350\pi\) | |||||||
\(140\) | −52.8886 | + | 45.8562i | −0.377776 | + | 0.327544i | ||||
\(141\) | 14.5505 | − | 125.507i | 0.103195 | − | 0.890118i | ||||
\(142\) | −77.6498 | − | 77.6498i | −0.546829 | − | 0.546829i | ||||
\(143\) | 1.14154 | − | 1.14154i | 0.00798280 | − | 0.00798280i | ||||
\(144\) | 8.23657 | − | 35.0451i | 0.0571984 | − | 0.243369i | ||||
\(145\) | −88.2823 | + | 212.767i | −0.608844 | + | 1.46736i | ||||
\(146\) | −82.6518 | −0.566108 | ||||||||
\(147\) | 37.2795 | − | 142.194i | 0.253602 | − | 0.967309i | ||||
\(148\) | 10.6522 | − | 10.6522i | 0.0719745 | − | 0.0719745i | ||||
\(149\) | 109.296 | 0.733529 | 0.366765 | − | 0.930314i | \(-0.380465\pi\) | ||||
0.366765 | + | 0.930314i | \(0.380465\pi\) | |||||||
\(150\) | −65.7628 | − | 83.2181i | −0.438419 | − | 0.554787i | ||||
\(151\) | −223.334 | −1.47903 | −0.739516 | − | 0.673139i | \(-0.764946\pi\) | ||||
−0.739516 | + | 0.673139i | \(0.764946\pi\) | |||||||
\(152\) | −59.4436 | − | 59.4436i | −0.391077 | − | 0.391077i | ||||
\(153\) | 150.069 | − | 92.9524i | 0.980844 | − | 0.607532i | ||||
\(154\) | 1.10250 | − | 0.368060i | 0.00715908 | − | 0.00239000i | ||||
\(155\) | 6.97102 | + | 2.89245i | 0.0449743 | + | 0.0186610i | ||||
\(156\) | 81.9499 | + | 9.50082i | 0.525320 | + | 0.0609027i | ||||
\(157\) | 1.67144 | − | 1.67144i | 0.0106461 | − | 0.0106461i | −0.701764 | − | 0.712410i | \(-0.747604\pi\) |
0.712410 | + | 0.701764i | \(0.247604\pi\) | |||||||
\(158\) | −0.865694 | − | 0.865694i | −0.00547908 | − | 0.00547908i | ||||
\(159\) | −29.2259 | + | 252.090i | −0.183811 | + | 1.58547i | ||||
\(160\) | −10.8081 | − | 26.1378i | −0.0675504 | − | 0.163361i | ||||
\(161\) | 21.1417 | − | 7.05797i | 0.131315 | − | 0.0438383i | ||||
\(162\) | −108.601 | + | 36.4384i | −0.670378 | + | 0.224929i | ||||
\(163\) | −34.1872 | + | 34.1872i | −0.209737 | + | 0.209737i | −0.804156 | − | 0.594419i | \(-0.797382\pi\) |
0.594419 | + | 0.804156i | \(0.297382\pi\) | |||||||
\(164\) | − | 26.9911i | − | 0.164580i | ||||||
\(165\) | 0.481076 | + | 1.69419i | 0.00291561 | + | 0.0102678i | ||||
\(166\) | 198.126i | 1.19353i | ||||||||
\(167\) | 122.479 | + | 122.479i | 0.733409 | + | 0.733409i | 0.971293 | − | 0.237884i | \(-0.0764539\pi\) |
−0.237884 | + | 0.971293i | \(0.576454\pi\) | |||||||
\(168\) | 49.7286 | + | 32.4819i | 0.296003 | + | 0.193344i | ||||
\(169\) | 20.0570i | 0.118680i | ||||||||
\(170\) | 53.1524 | − | 128.101i | 0.312661 | − | 0.753537i | ||||
\(171\) | −61.2015 | + | 260.401i | −0.357903 | + | 1.52281i | ||||
\(172\) | −73.7509 | − | 73.7509i | −0.428784 | − | 0.428784i | ||||
\(173\) | 11.1204 | − | 11.1204i | 0.0642800 | − | 0.0642800i | −0.674236 | − | 0.738516i | \(-0.735527\pi\) |
0.738516 | + | 0.674236i | \(0.235527\pi\) | |||||||
\(174\) | 194.163 | + | 22.5101i | 1.11588 | + | 0.129369i | ||||
\(175\) | 166.061 | − | 55.2143i | 0.948922 | − | 0.315510i | ||||
\(176\) | 0.469645i | 0.00266844i | ||||||||
\(177\) | −199.692 | + | 158.200i | −1.12820 | + | 0.893785i | ||||
\(178\) | −129.599 | − | 129.599i | −0.728082 | − | 0.728082i | ||||
\(179\) | −167.194 | −0.934042 | −0.467021 | − | 0.884246i | \(-0.654673\pi\) | ||||
−0.467021 | + | 0.884246i | \(0.654673\pi\) | |||||||
\(180\) | −52.5963 | + | 73.0317i | −0.292201 | + | 0.405732i | ||||
\(181\) | − | 271.099i | − | 1.49778i | −0.662692 | − | 0.748892i | \(-0.730586\pi\) | ||
0.662692 | − | 0.748892i | \(-0.269414\pi\) | |||||||
\(182\) | −60.8173 | + | 121.774i | −0.334161 | + | 0.669086i | ||||
\(183\) | 81.8655 | − | 64.8555i | 0.447352 | − | 0.354402i | ||||
\(184\) | 9.00599i | 0.0489456i | ||||||||
\(185\) | −34.8032 | + | 14.3912i | −0.188126 | + | 0.0777905i | ||||
\(186\) | 0.737513 | − | 6.36147i | 0.00396513 | − | 0.0342015i | ||||
\(187\) | −1.62839 | + | 1.62839i | −0.00870795 | + | 0.00870795i | ||||
\(188\) | −59.5607 | + | 59.5607i | −0.316812 | + | 0.316812i | ||||
\(189\) | 4.54500 | − | 188.945i | 0.0240476 | − | 0.999711i | ||||
\(190\) | 80.3089 | + | 194.216i | 0.422678 | + | 1.02219i | ||||
\(191\) | 274.726i | 1.43835i | 0.694827 | + | 0.719177i | \(0.255481\pi\) | ||||
−0.694827 | + | 0.719177i | \(0.744519\pi\) | |||||||
\(192\) | −18.8120 | + | 14.9033i | −0.0979793 | + | 0.0776212i | ||||
\(193\) | −202.411 | + | 202.411i | −1.04876 | + | 1.04876i | −0.0500128 | + | 0.998749i | \(0.515926\pi\) |
−0.998749 | + | 0.0500128i | \(0.984074\pi\) | |||||||
\(194\) | − | 31.5856i | − | 0.162812i | ||||||
\(195\) | −180.129 | − | 100.455i | −0.923739 | − | 0.515156i | ||||
\(196\) | −78.3462 | + | 58.8716i | −0.399726 | + | 0.300365i | ||||
\(197\) | 182.638 | − | 182.638i | 0.927095 | − | 0.927095i | −0.0704222 | − | 0.997517i | \(-0.522435\pi\) |
0.997517 | + | 0.0704222i | \(0.0224347\pi\) | |||||||
\(198\) | 1.27044 | − | 0.786906i | 0.00641636 | − | 0.00397427i | ||||
\(199\) | −246.453 | −1.23846 | −0.619228 | − | 0.785211i | \(-0.712554\pi\) | ||||
−0.619228 | + | 0.785211i | \(0.712554\pi\) | |||||||
\(200\) | −0.0857974 | + | 70.7106i | −0.000428987 | + | 0.353553i | ||||
\(201\) | 16.8513 | − | 145.352i | 0.0838372 | − | 0.723143i | ||||
\(202\) | 14.4525 | − | 14.4525i | 0.0715470 | − | 0.0715470i | ||||
\(203\) | −144.093 | + | 288.517i | −0.709820 | + | 1.42126i | ||||
\(204\) | −116.900 | − | 13.5527i | −0.573039 | − | 0.0664350i | ||||
\(205\) | −25.8605 | + | 62.3257i | −0.126149 | + | 0.304028i | ||||
\(206\) | 62.7388 | 0.304557 | ||||||||
\(207\) | 24.3622 | − | 15.0898i | 0.117692 | − | 0.0728978i | ||||
\(208\) | −38.8903 | − | 38.8903i | −0.186973 | − | 0.186973i | ||||
\(209\) | − | 3.48968i | − | 0.0166970i | ||||||
\(210\) | −83.7079 | − | 122.650i | −0.398609 | − | 0.584047i | ||||
\(211\) | 165.881 | 0.786165 | 0.393083 | − | 0.919503i | \(-0.371409\pi\) | ||||
0.393083 | + | 0.919503i | \(0.371409\pi\) | |||||||
\(212\) | 119.632 | − | 119.632i | 0.564304 | − | 0.564304i | ||||
\(213\) | 182.594 | − | 144.654i | 0.857248 | − | 0.679129i | ||||
\(214\) | 211.712i | 0.989310i | ||||||||
\(215\) | 99.6380 | + | 240.961i | 0.463433 | + | 1.12075i | ||||
\(216\) | 71.8351 | + | 25.9176i | 0.332570 | + | 0.119989i | ||||
\(217\) | 9.45285 | + | 4.72102i | 0.0435615 | + | 0.0217559i | ||||
\(218\) | −95.4740 | − | 95.4740i | −0.437954 | − | 0.437954i | ||||
\(219\) | 20.1917 | − | 174.164i | 0.0921994 | − | 0.795271i | ||||
\(220\) | 0.449972 | − | 1.08447i | 0.00204533 | − | 0.00492939i | ||||
\(221\) | − | 269.686i | − | 1.22030i | ||||||
\(222\) | 19.8441 | + | 25.0487i | 0.0893879 | + | 0.112832i | ||||
\(223\) | −44.8950 | − | 44.8950i | −0.201323 | − | 0.201323i | 0.599244 | − | 0.800567i | \(-0.295468\pi\) |
−0.800567 | + | 0.599244i | \(0.795468\pi\) | |||||||
\(224\) | −12.5391 | − | 37.5602i | −0.0559783 | − | 0.167680i | ||||
\(225\) | 191.423 | − | 118.246i | 0.850771 | − | 0.525537i | ||||
\(226\) | 120.252 | 0.532089 | ||||||||
\(227\) | −211.845 | − | 211.845i | −0.933238 | − | 0.933238i | 0.0646692 | − | 0.997907i | \(-0.479401\pi\) |
−0.997907 | + | 0.0646692i | \(0.979401\pi\) | |||||||
\(228\) | 139.782 | − | 110.738i | 0.613079 | − | 0.485693i | ||||
\(229\) | 10.2429 | 0.0447287 | 0.0223644 | − | 0.999750i | \(-0.492881\pi\) | ||||
0.0223644 | + | 0.999750i | \(0.492881\pi\) | |||||||
\(230\) | 8.62873 | − | 20.7959i | 0.0375162 | − | 0.0904170i | ||||
\(231\) | 0.506239 | + | 2.41311i | 0.00219151 | + | 0.0104464i | ||||
\(232\) | −92.1422 | − | 92.1422i | −0.397165 | − | 0.397165i | ||||
\(233\) | −135.649 | − | 135.649i | −0.582186 | − | 0.582186i | 0.353317 | − | 0.935504i | \(-0.385054\pi\) |
−0.935504 | + | 0.353317i | \(0.885054\pi\) | |||||||
\(234\) | −40.0404 | + | 170.364i | −0.171113 | + | 0.728053i | ||||
\(235\) | 194.598 | − | 80.4669i | 0.828077 | − | 0.342413i | ||||
\(236\) | 169.842 | 0.719669 | ||||||||
\(237\) | 2.03568 | − | 1.61271i | 0.00858938 | − | 0.00680468i | ||||
\(238\) | 86.7548 | − | 173.708i | 0.364516 | − | 0.729865i | ||||
\(239\) | −25.1069 | −0.105050 | −0.0525250 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525250 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(240\) | 57.7182 | − | 16.3894i | 0.240492 | − | 0.0682892i | ||||
\(241\) | − | 278.949i | − | 1.15747i | −0.815517 | − | 0.578733i | \(-0.803548\pi\) | ||
0.815517 | − | 0.578733i | \(-0.196452\pi\) | |||||||
\(242\) | 120.986 | − | 120.986i | 0.499943 | − | 0.499943i | ||||
\(243\) | −50.2522 | − | 237.747i | −0.206799 | − | 0.978383i | ||||
\(244\) | −69.6282 | −0.285361 | ||||||||
\(245\) | 237.316 | − | 60.8773i | 0.968637 | − | 0.248479i | ||||
\(246\) | 56.8759 | + | 6.59387i | 0.231203 | + | 0.0268044i | ||||
\(247\) | 288.973 | + | 288.973i | 1.16993 | + | 1.16993i | ||||
\(248\) | −3.01891 | + | 3.01891i | −0.0121730 | + | 0.0121730i | ||||
\(249\) | −417.492 | − | 48.4017i | −1.67668 | − | 0.194385i | ||||
\(250\) | 67.9466 | − | 163.197i | 0.271787 | − | 0.652788i | ||||
\(251\) | −211.250 | −0.841633 | −0.420817 | − | 0.907146i | \(-0.638256\pi\) | ||||
−0.420817 | + | 0.907146i | \(0.638256\pi\) | |||||||
\(252\) | −80.5946 | + | 96.8531i | −0.319820 | + | 0.384338i | ||||
\(253\) | −0.264351 | + | 0.264351i | −0.00104487 | + | 0.00104487i | ||||
\(254\) | 343.720 | 1.35323 | ||||||||
\(255\) | 256.951 | + | 143.298i | 1.00765 | + | 0.561953i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −330.432 | − | 330.432i | −1.28573 | − | 1.28573i | −0.937357 | − | 0.348371i | \(-0.886735\pi\) |
−0.348371 | − | 0.937357i | \(-0.613265\pi\) | |||||||
\(258\) | 173.425 | − | 137.391i | 0.672192 | − | 0.532524i | ||||
\(259\) | −50.0125 | + | 16.6962i | −0.193098 | + | 0.0644642i | ||||
\(260\) | 52.5411 | + | 127.063i | 0.202081 | + | 0.488706i | ||||
\(261\) | −94.8670 | + | 403.641i | −0.363475 | + | 1.54652i | ||||
\(262\) | 145.791 | − | 145.791i | 0.556453 | − | 0.556453i | ||||
\(263\) | −74.3401 | − | 74.3401i | −0.282662 | − | 0.282662i | 0.551508 | − | 0.834170i | \(-0.314053\pi\) |
−0.834170 | + | 0.551508i | \(0.814053\pi\) | |||||||
\(264\) | −0.989640 | − | 0.114733i | −0.00374864 | − | 0.000434596i | ||||
\(265\) | −390.866 | + | 161.624i | −1.47497 | + | 0.609903i | ||||
\(266\) | 93.1716 | + | 279.089i | 0.350269 | + | 1.04921i | ||||
\(267\) | 304.751 | − | 241.430i | 1.14139 | − | 0.904233i | ||||
\(268\) | −68.9784 | + | 68.9784i | −0.257382 | + | 0.257382i | ||||
\(269\) | − | 250.571i | − | 0.931490i | −0.884919 | − | 0.465745i | \(-0.845786\pi\) | ||
0.884919 | − | 0.465745i | \(-0.154214\pi\) | |||||||
\(270\) | −141.044 | − | 128.673i | −0.522384 | − | 0.476565i | ||||
\(271\) | − | 207.488i | − | 0.765638i | −0.923823 | − | 0.382819i | \(-0.874953\pi\) | ||
0.923823 | − | 0.382819i | \(-0.125047\pi\) | |||||||
\(272\) | 55.4763 | + | 55.4763i | 0.203957 | + | 0.203957i | ||||
\(273\) | −241.745 | − | 157.904i | −0.885512 | − | 0.578402i | ||||
\(274\) | − | 75.6039i | − | 0.275926i | ||||||
\(275\) | −2.07808 | + | 2.07304i | −0.00755664 | + | 0.00753833i | ||||
\(276\) | −18.9775 | − | 2.20014i | −0.0687590 | − | 0.00797154i | ||||
\(277\) | −64.7233 | − | 64.7233i | −0.233658 | − | 0.233658i | 0.580560 | − | 0.814218i | \(-0.302834\pi\) |
−0.814218 | + | 0.580560i | \(0.802834\pi\) | |||||||
\(278\) | 65.4496 | − | 65.4496i | 0.235430 | − | 0.235430i | ||||
\(279\) | 13.2248 | + | 3.10819i | 0.0474006 | + | 0.0111405i | ||||
\(280\) | −7.03243 | + | 98.7448i | −0.0251158 | + | 0.352660i | ||||
\(281\) | 353.277i | 1.25721i | 0.777723 | + | 0.628607i | \(0.216374\pi\) | ||||
−0.777723 | + | 0.628607i | \(0.783626\pi\) | |||||||
\(282\) | −110.956 | − | 140.057i | −0.393461 | − | 0.496656i | ||||
\(283\) | −181.090 | − | 181.090i | −0.639894 | − | 0.639894i | 0.310635 | − | 0.950529i | \(-0.399458\pi\) |
−0.950529 | + | 0.310635i | \(0.899458\pi\) | |||||||
\(284\) | −155.300 | −0.546829 | ||||||||
\(285\) | −428.872 | + | 121.781i | −1.50481 | + | 0.427301i | ||||
\(286\) | − | 2.28308i | − | 0.00798280i | ||||||
\(287\) | −42.2092 | + | 84.5149i | −0.147070 | + | 0.294477i | ||||
\(288\) | −26.8085 | − | 43.2817i | −0.0930852 | − | 0.150284i | ||||
\(289\) | 95.7024i | 0.331150i | ||||||||
\(290\) | 124.485 | + | 301.049i | 0.429258 | + | 1.03810i | ||||
\(291\) | 66.5574 | + | 7.71630i | 0.228720 | + | 0.0265165i | ||||
\(292\) | −82.6518 | + | 82.6518i | −0.283054 | + | 0.283054i | ||||
\(293\) | −72.3843 | + | 72.3843i | −0.247045 | + | 0.247045i | −0.819757 | − | 0.572712i | \(-0.805892\pi\) |
0.572712 | + | 0.819757i | \(0.305892\pi\) | |||||||
\(294\) | −104.915 | − | 179.474i | −0.356853 | − | 0.610455i | ||||
\(295\) | −392.185 | − | 162.727i | −1.32944 | − | 0.551617i | ||||
\(296\) | − | 21.3044i | − | 0.0719745i | ||||||
\(297\) | 1.34781 | + | 2.86932i | 0.00453808 | + | 0.00966101i | ||||
\(298\) | 109.296 | − | 109.296i | 0.366765 | − | 0.366765i | ||||
\(299\) | − | 43.7807i | − | 0.146424i | ||||||
\(300\) | −148.981 | − | 17.4552i | −0.496603 | − | 0.0581841i | ||||
\(301\) | 115.597 | + | 346.262i | 0.384042 | + | 1.15037i | ||||
\(302\) | −223.334 | + | 223.334i | −0.739516 | + | 0.739516i | ||||
\(303\) | 26.9237 | + | 33.9851i | 0.0888571 | + | 0.112162i | ||||
\(304\) | −118.887 | −0.391077 | ||||||||
\(305\) | 160.780 | + | 66.7115i | 0.527147 | + | 0.218726i | ||||
\(306\) | 57.1168 | − | 243.022i | 0.186656 | − | 0.794188i | ||||
\(307\) | −228.716 | + | 228.716i | −0.745005 | + | 0.745005i | −0.973536 | − | 0.228532i | \(-0.926608\pi\) |
0.228532 | + | 0.973536i | \(0.426608\pi\) | |||||||
\(308\) | 0.734439 | − | 1.47056i | 0.00238454 | − | 0.00477454i | ||||
\(309\) | −15.3269 | + | 132.204i | −0.0496018 | + | 0.427843i | ||||
\(310\) | 9.86347 | − | 4.07857i | 0.0318177 | − | 0.0131567i | ||||
\(311\) | 269.223 | 0.865670 | 0.432835 | − | 0.901473i | \(-0.357513\pi\) | ||||
0.432835 | + | 0.901473i | \(0.357513\pi\) | |||||||
\(312\) | 91.4507 | − | 72.4491i | 0.293111 | − | 0.232209i | ||||
\(313\) | 421.023 | + | 421.023i | 1.34512 | + | 1.34512i | 0.890877 | + | 0.454244i | \(0.150091\pi\) |
0.454244 | + | 0.890877i | \(0.349909\pi\) | |||||||
\(314\) | − | 3.34288i | − | 0.0106461i | ||||||
\(315\) | 278.898 | − | 146.427i | 0.885391 | − | 0.464847i | ||||
\(316\) | −1.73139 | −0.00547908 | ||||||||
\(317\) | 74.8122 | − | 74.8122i | 0.236001 | − | 0.236001i | −0.579191 | − | 0.815192i | \(-0.696632\pi\) |
0.815192 | + | 0.579191i | \(0.196632\pi\) | |||||||
\(318\) | 222.864 | + | 281.316i | 0.700831 | + | 0.884642i | ||||
\(319\) | − | 5.40927i | − | 0.0169570i | ||||||
\(320\) | −36.9459 | − | 15.3298i | −0.115456 | − | 0.0479055i | ||||
\(321\) | −446.121 | − | 51.7208i | −1.38979 | − | 0.161124i | ||||
\(322\) | 14.0837 | − | 28.1997i | 0.0437383 | − | 0.0875766i | ||||
\(323\) | −412.214 | − | 412.214i | −1.27620 | − | 1.27620i | ||||
\(324\) | −72.1629 | + | 145.040i | −0.222725 | + | 0.447653i | ||||
\(325\) | 0.417086 | − | 343.745i | 0.00128334 | − | 1.05768i | ||||
\(326\) | 68.3743i | 0.209737i | ||||||||
\(327\) | 224.507 | − | 177.859i | 0.686567 | − | 0.543912i | ||||
\(328\) | −26.9911 | − | 26.9911i | −0.0822900 | − | 0.0822900i | ||||
\(329\) | 279.639 | − | 93.3550i | 0.849966 | − | 0.283754i | ||||
\(330\) | 2.17527 | + | 1.21312i | 0.00659172 | + | 0.00367611i | ||||
\(331\) | −506.910 | −1.53145 | −0.765725 | − | 0.643168i | \(-0.777620\pi\) | ||||
−0.765725 | + | 0.643168i | \(0.777620\pi\) | |||||||
\(332\) | 198.126 | + | 198.126i | 0.596765 | + | 0.596765i | ||||
\(333\) | −57.6307 | + | 35.6963i | −0.173065 | + | 0.107196i | ||||
\(334\) | 244.959 | 0.733409 | ||||||||
\(335\) | 225.368 | − | 93.1904i | 0.672741 | − | 0.278180i | ||||
\(336\) | 82.2104 | − | 17.2467i | 0.244674 | − | 0.0513294i | ||||
\(337\) | −187.948 | − | 187.948i | −0.557709 | − | 0.557709i | 0.370945 | − | 0.928655i | \(-0.379034\pi\) |
−0.928655 | + | 0.370945i | \(0.879034\pi\) | |||||||
\(338\) | 20.0570 | + | 20.0570i | 0.0593402 | + | 0.0593402i | ||||
\(339\) | −29.3773 | + | 253.396i | −0.0866588 | + | 0.747481i | ||||
\(340\) | −74.9489 | − | 181.254i | −0.220438 | − | 0.533099i | ||||
\(341\) | −0.177227 | −0.000519728 | ||||||||
\(342\) | 199.200 | + | 321.603i | 0.582455 | + | 0.940358i | ||||
\(343\) | 337.383 | − | 61.8203i | 0.983624 | − | 0.180234i | ||||
\(344\) | −147.502 | −0.428784 | ||||||||
\(345\) | 41.7133 | + | 23.2629i | 0.120908 | + | 0.0674287i | ||||
\(346\) | − | 22.2409i | − | 0.0642800i | ||||||
\(347\) | 152.796 | − | 152.796i | 0.440334 | − | 0.440334i | −0.451790 | − | 0.892124i | \(-0.649214\pi\) |
0.892124 | + | 0.451790i | \(0.149214\pi\) | |||||||
\(348\) | 216.673 | − | 171.652i | 0.622623 | − | 0.493254i | ||||
\(349\) | 368.362 | 1.05548 | 0.527740 | − | 0.849406i | \(-0.323040\pi\) | ||||
0.527740 | + | 0.849406i | \(0.323040\pi\) | |||||||
\(350\) | 110.847 | − | 221.276i | 0.316706 | − | 0.632216i | ||||
\(351\) | −349.211 | − | 125.993i | −0.994903 | − | 0.358954i | ||||
\(352\) | 0.469645 | + | 0.469645i | 0.00133422 | + | 0.00133422i | ||||
\(353\) | −244.718 | + | 244.718i | −0.693251 | + | 0.693251i | −0.962946 | − | 0.269695i | \(-0.913077\pi\) |
0.269695 | + | 0.962946i | \(0.413077\pi\) | |||||||
\(354\) | −41.4920 | + | 357.892i | −0.117209 | + | 1.01099i | ||||
\(355\) | 358.605 | + | 148.794i | 1.01015 | + | 0.419138i | ||||
\(356\) | −259.197 | −0.728082 | ||||||||
\(357\) | 344.844 | + | 225.247i | 0.965951 | + | 0.630943i | ||||
\(358\) | −167.194 | + | 167.194i | −0.467021 | + | 0.467021i | ||||
\(359\) | −599.498 | −1.66991 | −0.834956 | − | 0.550317i | \(-0.814507\pi\) | ||||
−0.834956 | + | 0.550317i | \(0.814507\pi\) | |||||||
\(360\) | 20.4355 | + | 125.628i | 0.0567652 | + | 0.348967i | ||||
\(361\) | 522.387 | 1.44705 | ||||||||
\(362\) | −271.099 | − | 271.099i | −0.748892 | − | 0.748892i | ||||
\(363\) | 225.386 | + | 284.500i | 0.620899 | + | 0.783745i | ||||
\(364\) | 60.9564 | + | 182.591i | 0.167463 | + | 0.501624i | ||||
\(365\) | 270.042 | − | 111.663i | 0.739842 | − | 0.305927i | ||||
\(366\) | 17.0100 | − | 146.721i | 0.0464755 | − | 0.400877i | ||||
\(367\) | −38.8678 | + | 38.8678i | −0.105907 | + | 0.105907i | −0.758075 | − | 0.652168i | \(-0.773860\pi\) |
0.652168 | + | 0.758075i | \(0.273860\pi\) | |||||||
\(368\) | 9.00599 | + | 9.00599i | 0.0244728 | + | 0.0244728i | ||||
\(369\) | −27.7893 | + | 118.238i | −0.0753097 | + | 0.320429i | ||||
\(370\) | −20.4120 | + | 49.1945i | −0.0551676 | + | 0.132958i | ||||
\(371\) | −561.677 | + | 187.511i | −1.51396 | + | 0.505421i | ||||
\(372\) | −5.62396 | − | 7.09898i | −0.0151182 | − | 0.0190833i | ||||
\(373\) | 228.366 | − | 228.366i | 0.612241 | − | 0.612241i | −0.331289 | − | 0.943529i | \(-0.607483\pi\) |
0.943529 | + | 0.331289i | \(0.107483\pi\) | |||||||
\(374\) | 3.25677i | 0.00870795i | ||||||||
\(375\) | 327.290 | + | 183.046i | 0.872775 | + | 0.488123i | ||||
\(376\) | 119.121i | 0.316812i | ||||||||
\(377\) | 447.930 | + | 447.930i | 1.18814 | + | 1.18814i | ||||
\(378\) | −184.400 | − | 193.490i | −0.487832 | − | 0.511879i | ||||
\(379\) | 217.075i | 0.572757i | 0.958117 | + | 0.286378i | \(0.0924515\pi\) | ||||
−0.958117 | + | 0.286378i | \(0.907549\pi\) | |||||||
\(380\) | 274.525 | + | 113.907i | 0.722434 | + | 0.299755i | ||||
\(381\) | −83.9701 | + | 724.290i | −0.220394 | + | 1.90102i | ||||
\(382\) | 274.726 | + | 274.726i | 0.719177 | + | 0.719177i | ||||
\(383\) | 301.020 | − | 301.020i | 0.785953 | − | 0.785953i | −0.194875 | − | 0.980828i | \(-0.562430\pi\) |
0.980828 | + | 0.194875i | \(0.0624303\pi\) | |||||||
\(384\) | −3.90876 | + | 33.7153i | −0.0101791 | + | 0.0878003i | ||||
\(385\) | −3.10486 | + | 2.69202i | −0.00806458 | + | 0.00699226i | ||||
\(386\) | 404.822i | 1.04876i | ||||||||
\(387\) | 247.144 | + | 399.008i | 0.638615 | + | 1.03103i | ||||
\(388\) | −31.5856 | − | 31.5856i | −0.0814062 | − | 0.0814062i | ||||
\(389\) | −369.112 | −0.948875 | −0.474438 | − | 0.880289i | \(-0.657349\pi\) | ||||
−0.474438 | + | 0.880289i | \(0.657349\pi\) | |||||||
\(390\) | −280.585 | + | 79.6737i | −0.719448 | + | 0.204291i | ||||
\(391\) | 62.4524i | 0.159725i | ||||||||
\(392\) | −19.4746 | + | 137.218i | −0.0496801 | + | 0.350046i | ||||
\(393\) | 271.595 | + | 342.828i | 0.691081 | + | 0.872335i | ||||
\(394\) | − | 365.275i | − | 0.927095i | ||||||
\(395\) | 3.99798 | + | 1.65886i | 0.0101215 | + | 0.00419965i | ||||
\(396\) | 0.483534 | − | 2.05735i | 0.00122104 | − | 0.00519532i | ||||
\(397\) | −13.0242 | + | 13.0242i | −0.0328066 | + | 0.0328066i | −0.723320 | − | 0.690513i | \(-0.757385\pi\) |
0.690513 | + | 0.723320i | \(0.257385\pi\) | |||||||
\(398\) | −246.453 | + | 246.453i | −0.619228 | + | 0.619228i | ||||
\(399\) | −610.861 | + | 128.151i | −1.53098 | + | 0.321180i | ||||
\(400\) | 70.6248 | + | 70.7964i | 0.176562 | + | 0.176991i | ||||
\(401\) | 17.1182i | 0.0426889i | 0.999772 | + | 0.0213444i | \(0.00679466\pi\) | ||||
−0.999772 | + | 0.0213444i | \(0.993205\pi\) | |||||||
\(402\) | −128.500 | − | 162.203i | −0.319653 | − | 0.403490i | ||||
\(403\) | 14.6758 | − | 14.6758i | 0.0364164 | − | 0.0364164i | ||||
\(404\) | − | 28.9050i | − | 0.0715470i | ||||||
\(405\) | 305.597 | − | 265.774i | 0.754559 | − | 0.656232i | ||||
\(406\) | 144.423 | + | 432.610i | 0.355722 | + | 1.06554i | ||||
\(407\) | 0.625346 | − | 0.625346i | 0.00153648 | − | 0.00153648i | ||||
\(408\) | −130.453 | + | 103.347i | −0.319737 | + | 0.253302i | ||||
\(409\) | 186.052 | 0.454895 | 0.227447 | − | 0.973790i | \(-0.426962\pi\) | ||||
0.227447 | + | 0.973790i | \(0.426962\pi\) | |||||||
\(410\) | 36.4652 | + | 88.1861i | 0.0889396 | + | 0.215088i | ||||
\(411\) | 159.313 | + | 18.4699i | 0.387623 | + | 0.0449388i | ||||
\(412\) | 62.7388 | − | 62.7388i | 0.152279 | − | 0.152279i | ||||
\(413\) | −531.811 | − | 265.602i | −1.28768 | − | 0.643103i | ||||
\(414\) | 9.27232 | − | 39.4520i | 0.0223969 | − | 0.0952947i | ||||
\(415\) | −267.670 | − | 647.323i | −0.644988 | − | 1.55981i | ||||
\(416\) | −77.7806 | −0.186973 | ||||||||
\(417\) | 121.927 | + | 153.905i | 0.292390 | + | 0.369077i | ||||
\(418\) | −3.48968 | − | 3.48968i | −0.00834852 | − | 0.00834852i | ||||
\(419\) | − | 606.909i | − | 1.44847i | −0.689553 | − | 0.724235i | \(-0.742193\pi\) | ||
0.689553 | − | 0.724235i | \(-0.257807\pi\) | |||||||
\(420\) | −206.358 | − | 38.9419i | −0.491328 | − | 0.0927189i | ||||
\(421\) | −642.340 | −1.52575 | −0.762874 | − | 0.646547i | \(-0.776212\pi\) | ||||
−0.762874 | + | 0.646547i | \(0.776212\pi\) | |||||||
\(422\) | 165.881 | − | 165.881i | 0.393083 | − | 0.393083i | ||||
\(423\) | 322.236 | − | 199.592i | 0.761786 | − | 0.471848i | ||||
\(424\) | − | 239.265i | − | 0.564304i | ||||||
\(425\) | −0.594965 | + | 490.345i | −0.00139992 | + | 1.15375i | ||||
\(426\) | 37.9393 | − | 327.248i | 0.0890595 | − | 0.768188i | ||||
\(427\) | 218.021 | + | 108.886i | 0.510587 | + | 0.255002i | ||||
\(428\) | 211.712 | + | 211.712i | 0.494655 | + | 0.494655i | ||||
\(429\) | 4.81092 | + | 0.557752i | 0.0112143 | + | 0.00130012i | ||||
\(430\) | 340.599 | + | 141.323i | 0.792090 | + | 0.328658i | ||||
\(431\) | 455.692i | 1.05729i | 0.848843 | + | 0.528645i | \(0.177300\pi\) | ||||
−0.848843 | + | 0.528645i | \(0.822700\pi\) | |||||||
\(432\) | 97.7527 | − | 45.9175i | 0.226279 | − | 0.106290i | ||||
\(433\) | 201.636 | + | 201.636i | 0.465672 | + | 0.465672i | 0.900509 | − | 0.434837i | \(-0.143194\pi\) |
−0.434837 | + | 0.900509i | \(0.643194\pi\) | |||||||
\(434\) | 14.1739 | − | 4.73182i | 0.0326587 | − | 0.0109028i | ||||
\(435\) | −664.785 | + | 188.770i | −1.52824 | + | 0.433953i | ||||
\(436\) | −190.948 | −0.437954 | ||||||||
\(437\) | −66.9186 | − | 66.9186i | −0.153132 | − | 0.153132i | ||||
\(438\) | −153.973 | − | 194.356i | −0.351536 | − | 0.443735i | ||||
\(439\) | 94.0452 | 0.214226 | 0.107113 | − | 0.994247i | \(-0.465839\pi\) | ||||
0.107113 | + | 0.994247i | \(0.465839\pi\) | |||||||
\(440\) | −0.634495 | − | 1.53444i | −0.00144203 | − | 0.00348736i | ||||
\(441\) | 403.819 | − | 177.232i | 0.915689 | − | 0.401887i | ||||
\(442\) | −269.686 | − | 269.686i | −0.610150 | − | 0.610150i | ||||
\(443\) | −125.233 | − | 125.233i | −0.282693 | − | 0.282693i | 0.551489 | − | 0.834182i | \(-0.314060\pi\) |
−0.834182 | + | 0.551489i | \(0.814060\pi\) | |||||||
\(444\) | 44.8929 | + | 5.20463i | 0.101110 | + | 0.0117221i | ||||
\(445\) | 598.517 | + | 248.339i | 1.34498 | + | 0.558066i | ||||
\(446\) | −89.7899 | −0.201323 | ||||||||
\(447\) | 203.608 | + | 257.010i | 0.455499 | + | 0.574966i | ||||
\(448\) | −50.0994 | − | 25.0211i | −0.111829 | − | 0.0558506i | ||||
\(449\) | 324.260 | 0.722184 | 0.361092 | − | 0.932530i | \(-0.382404\pi\) | ||||
0.361092 | + | 0.932530i | \(0.382404\pi\) | |||||||
\(450\) | 73.1775 | − | 309.669i | 0.162617 | − | 0.688154i | ||||
\(451\) | − | 1.58453i | − | 0.00351337i | ||||||
\(452\) | 120.252 | − | 120.252i | 0.266045 | − | 0.266045i | ||||
\(453\) | −416.050 | − | 525.170i | −0.918434 | − | 1.15932i | ||||
\(454\) | −423.690 | −0.933238 | ||||||||
\(455\) | 34.1867 | − | 480.027i | 0.0751356 | − | 1.05500i | ||||
\(456\) | 29.0439 | − | 250.520i | 0.0636928 | − | 0.549386i | ||||
\(457\) | −411.756 | − | 411.756i | −0.900999 | − | 0.900999i | 0.0945240 | − | 0.995523i | \(-0.469867\pi\) |
−0.995523 | + | 0.0945240i | \(0.969867\pi\) | |||||||
\(458\) | 10.2429 | − | 10.2429i | 0.0223644 | − | 0.0223644i | ||||
\(459\) | 498.143 | + | 179.727i | 1.08528 | + | 0.391561i | ||||
\(460\) | −12.1672 | − | 29.4246i | −0.0264504 | − | 0.0639666i | ||||
\(461\) | 484.084 | 1.05007 | 0.525037 | − | 0.851080i | \(-0.324052\pi\) | ||||
0.525037 | + | 0.851080i | \(0.324052\pi\) | |||||||
\(462\) | 2.91935 | + | 1.90687i | 0.00631894 | + | 0.00412742i | ||||
\(463\) | 239.772 | − | 239.772i | 0.517866 | − | 0.517866i | −0.399059 | − | 0.916925i | \(-0.630663\pi\) |
0.916925 | + | 0.399059i | \(0.130663\pi\) | |||||||
\(464\) | −184.284 | −0.397165 | ||||||||
\(465\) | 6.18477 | + | 21.7808i | 0.0133006 | + | 0.0468403i | ||||
\(466\) | −271.299 | −0.582186 | ||||||||
\(467\) | −302.621 | − | 302.621i | −0.648011 | − | 0.648011i | 0.304501 | − | 0.952512i | \(-0.401510\pi\) |
−0.952512 | + | 0.304501i | \(0.901510\pi\) | |||||||
\(468\) | 130.324 | + | 210.405i | 0.278470 | + | 0.449583i | ||||
\(469\) | 323.855 | − | 108.116i | 0.690523 | − | 0.230525i | ||||
\(470\) | 114.131 | − | 275.065i | 0.242832 | − | 0.585245i | ||||
\(471\) | 7.04413 | + | 0.816658i | 0.0149557 | + | 0.00173388i | ||||
\(472\) | 169.842 | − | 169.842i | 0.359835 | − | 0.359835i | ||||
\(473\) | −4.32959 | − | 4.32959i | −0.00915348 | − | 0.00915348i | ||||
\(474\) | 0.422974 | − | 3.64839i | 0.000892351 | − | 0.00769703i | ||||
\(475\) | −524.775 | − | 526.050i | −1.10479 | − | 1.10747i | ||||
\(476\) | −86.9532 | − | 260.463i | −0.182675 | − | 0.547191i | ||||
\(477\) | −647.236 | + | 400.896i | −1.35689 | + | 0.840453i | ||||
\(478\) | −25.1069 | + | 25.1069i | −0.0525250 | + | 0.0525250i | ||||
\(479\) | − | 444.701i | − | 0.928395i | −0.885732 | − | 0.464198i | \(-0.846343\pi\) | ||
0.885732 | − | 0.464198i | \(-0.153657\pi\) | |||||||
\(480\) | 41.3288 | − | 74.1076i | 0.0861016 | − | 0.154391i | ||||
\(481\) | 103.567i | 0.215316i | ||||||||
\(482\) | −278.949 | − | 278.949i | −0.578733 | − | 0.578733i | ||||
\(483\) | 55.9819 | + | 36.5664i | 0.115904 | + | 0.0757069i | ||||
\(484\) | − | 241.972i | − | 0.499943i | ||||||
\(485\) | 42.6724 | + | 103.197i | 0.0879844 | + | 0.212778i | ||||
\(486\) | −287.999 | − | 187.495i | −0.592591 | − | 0.385792i | ||||
\(487\) | −4.30834 | − | 4.30834i | −0.00884670 | − | 0.00884670i | 0.702670 | − | 0.711516i | \(-0.251991\pi\) |
−0.711516 | + | 0.702670i | \(0.751991\pi\) | |||||||
\(488\) | −69.6282 | + | 69.6282i | −0.142681 | + | 0.142681i | ||||
\(489\) | −144.079 | − | 16.7037i | −0.294640 | − | 0.0341589i | ||||
\(490\) | 176.439 | − | 298.193i | 0.360079 | − | 0.608558i | ||||
\(491\) | − | 85.1811i | − | 0.173485i | −0.996231 | − | 0.0867425i | \(-0.972354\pi\) | ||
0.996231 | − | 0.0867425i | \(-0.0276457\pi\) | |||||||
\(492\) | 63.4697 | − | 50.2820i | 0.129004 | − | 0.102199i | ||||
\(493\) | −638.963 | − | 638.963i | −1.29607 | − | 1.29607i | ||||
\(494\) | 577.945 | 1.16993 | ||||||||
\(495\) | −3.08770 | + | 4.28738i | −0.00623778 | + | 0.00866137i | ||||
\(496\) | 6.03782i | 0.0121730i | ||||||||
\(497\) | 486.275 | + | 242.860i | 0.978421 | + | 0.488652i | ||||
\(498\) | −465.894 | + | 369.091i | −0.935530 | + | 0.741146i | ||||
\(499\) | 352.315i | 0.706043i | 0.935615 | + | 0.353021i | \(0.114846\pi\) | ||||
−0.935615 | + | 0.353021i | \(0.885154\pi\) | |||||||
\(500\) | −95.2503 | − | 231.144i | −0.190501 | − | 0.462287i | ||||
\(501\) | −59.8429 | + | 516.178i | −0.119447 | + | 1.03030i | ||||
\(502\) | −211.250 | + | 211.250i | −0.420817 | + | 0.420817i | ||||
\(503\) | −109.956 | + | 109.956i | −0.218600 | + | 0.218600i | −0.807908 | − | 0.589308i | \(-0.799400\pi\) |
0.589308 | + | 0.807908i | \(0.299400\pi\) | |||||||
\(504\) | 16.2585 | + | 177.448i | 0.0322590 | + | 0.352079i | ||||
\(505\) | −27.6942 | + | 66.7451i | −0.0548399 | + | 0.132168i | ||||
\(506\) | 0.528703i | 0.00104487i | ||||||||
\(507\) | −47.1641 | + | 37.3643i | −0.0930257 | + | 0.0736969i | ||||
\(508\) | 343.720 | − | 343.720i | 0.676615 | − | 0.676615i | ||||
\(509\) | 930.732i | 1.82855i | 0.405094 | + | 0.914275i | \(0.367239\pi\) | ||||
−0.405094 | + | 0.914275i | \(0.632761\pi\) | |||||||
\(510\) | 400.249 | − | 113.653i | 0.784802 | − | 0.222849i | ||||
\(511\) | 388.053 | − | 129.548i | 0.759398 | − | 0.253518i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −726.347 | + | 341.188i | −1.41588 | + | 0.665083i | ||||
\(514\) | −660.864 | −1.28573 | ||||||||
\(515\) | −204.982 | + | 84.7606i | −0.398023 | + | 0.164584i | ||||
\(516\) | 36.0343 | − | 310.817i | 0.0698340 | − | 0.602358i | ||||
\(517\) | −3.49655 | + | 3.49655i | −0.00676315 | + | 0.00676315i | ||||
\(518\) | −33.3162 | + | 66.7087i | −0.0643171 | + | 0.128781i | ||||
\(519\) | 46.8662 | + | 5.43340i | 0.0903009 | + | 0.0104690i | ||||
\(520\) | 179.605 | + | 74.5224i | 0.345393 | + | 0.143312i | ||||
\(521\) | −22.2801 | −0.0427641 | −0.0213821 | − | 0.999771i | \(-0.506807\pi\) | ||||
−0.0213821 | + | 0.999771i | \(0.506807\pi\) | |||||||
\(522\) | 308.774 | + | 498.508i | 0.591522 | + | 0.954997i | ||||
\(523\) | 110.356 | + | 110.356i | 0.211006 | + | 0.211006i | 0.804695 | − | 0.593689i | \(-0.202329\pi\) |
−0.593689 | + | 0.804695i | \(0.702329\pi\) | |||||||
\(524\) | − | 291.582i | − | 0.556453i | ||||||
\(525\) | 439.194 | + | 287.635i | 0.836560 | + | 0.547876i | ||||
\(526\) | −148.680 | −0.282662 | ||||||||
\(527\) | −20.9348 | + | 20.9348i | −0.0397244 | + | 0.0397244i | ||||
\(528\) | −1.10437 | + | 0.874907i | −0.00209162 | + | 0.00165702i | ||||
\(529\) | − | 518.862i | − | 0.980835i | ||||||
\(530\) | −229.242 | + | 552.491i | −0.432532 | + | 1.04244i | ||||
\(531\) | −744.016 | − | 174.864i | −1.40116 | − | 0.329311i | ||||
\(532\) | 372.261 | + | 185.918i | 0.699739 | + | 0.349470i | ||||
\(533\) | 131.212 | + | 131.212i | 0.246176 | + | 0.246176i | ||||
\(534\) | 63.3213 | − | 546.182i | 0.118579 | − | 1.02281i | ||||
\(535\) | −286.025 | − | 691.712i | −0.534626 | − | 1.29292i | ||||
\(536\) | 137.957i | 0.257382i | ||||||||
\(537\) | −311.466 | − | 393.156i | −0.580012 | − | 0.732134i | ||||
\(538\) | −250.571 | − | 250.571i | −0.465745 | − | 0.465745i | ||||
\(539\) | −4.59937 | + | 3.45610i | −0.00853315 | + | 0.00641206i | ||||
\(540\) | −269.716 | + | 12.3711i | −0.499475 | + | 0.0229094i | ||||
\(541\) | 693.609 | 1.28209 | 0.641044 | − | 0.767504i | \(-0.278502\pi\) | ||||
0.641044 | + | 0.767504i | \(0.278502\pi\) | |||||||
\(542\) | −207.488 | − | 207.488i | −0.382819 | − | 0.382819i | ||||
\(543\) | 637.490 | − | 505.032i | 1.17401 | − | 0.930078i | ||||
\(544\) | 110.953 | 0.203957 | ||||||||
\(545\) | 440.921 | + | 182.949i | 0.809030 | + | 0.335686i | ||||
\(546\) | −399.648 | + | 83.8411i | −0.731957 | + | 0.153555i | ||||
\(547\) | −529.859 | − | 529.859i | −0.968664 | − | 0.968664i | 0.0308595 | − | 0.999524i | \(-0.490176\pi\) |
−0.999524 | + | 0.0308595i | \(0.990176\pi\) | |||||||
\(548\) | −75.6039 | − | 75.6039i | −0.137963 | − | 0.137963i | ||||
\(549\) | 305.016 | + | 71.6872i | 0.555585 | + | 0.130578i | ||||
\(550\) | −0.00503679 | + | 4.15112i | −9.15781e−6 | + | 0.00754748i | ||||
\(551\) | 1369.32 | 2.48515 | ||||||||
\(552\) | −21.1776 | + | 16.7773i | −0.0383653 | + | 0.0303937i | ||||
\(553\) | 5.42134 | + | 2.70757i | 0.00980351 | + | 0.00489616i | ||||
\(554\) | −129.447 | −0.233658 | ||||||||
\(555\) | −98.6763 | − | 55.0304i | −0.177795 | − | 0.0991538i | ||||
\(556\) | − | 130.899i | − | 0.235430i | ||||||
\(557\) | −242.020 | + | 242.020i | −0.434506 | + | 0.434506i | −0.890158 | − | 0.455652i | \(-0.849406\pi\) |
0.455652 | + | 0.890158i | \(0.349406\pi\) | |||||||
\(558\) | 16.3329 | − | 10.1166i | 0.0292705 | − | 0.0181301i | ||||
\(559\) | 717.048 | 1.28273 | ||||||||
\(560\) | 91.7124 | + | 105.777i | 0.163772 | + | 0.188888i | ||||
\(561\) | −6.86269 | − | 0.795623i | −0.0122330 | − | 0.00141822i | ||||
\(562\) | 353.277 | + | 353.277i | 0.628607 | + | 0.628607i | ||||
\(563\) | −19.8889 | + | 19.8889i | −0.0353266 | + | 0.0353266i | −0.724549 | − | 0.689223i | \(-0.757952\pi\) |
0.689223 | + | 0.724549i | \(0.257952\pi\) | |||||||
\(564\) | −251.013 | − | 29.1011i | −0.445059 | − | 0.0515976i | ||||
\(565\) | −392.891 | + | 162.462i | −0.695383 | + | 0.287543i | ||||
\(566\) | −362.180 | −0.639894 | ||||||||
\(567\) | 452.773 | − | 341.300i | 0.798541 | − | 0.601941i | ||||
\(568\) | −155.300 | + | 155.300i | −0.273415 | + | 0.273415i | ||||
\(569\) | −147.022 | −0.258387 | −0.129194 | − | 0.991619i | \(-0.541239\pi\) | ||||
−0.129194 | + | 0.991619i | \(0.541239\pi\) | |||||||
\(570\) | −307.091 | + | 550.653i | −0.538757 | + | 0.966058i | ||||
\(571\) | 831.318 | 1.45590 | 0.727949 | − | 0.685631i | \(-0.240474\pi\) | ||||
0.727949 | + | 0.685631i | \(0.240474\pi\) | |||||||
\(572\) | −2.28308 | − | 2.28308i | −0.00399140 | − | 0.00399140i | ||||
\(573\) | −646.018 | + | 511.789i | −1.12743 | + | 0.893174i | ||||
\(574\) | 42.3057 | + | 126.724i | 0.0737033 | + | 0.220774i | ||||
\(575\) | −0.0965863 | + | 79.6024i | −0.000167976 | + | 0.138439i | ||||
\(576\) | −70.0902 | − | 16.4731i | −0.121684 | − | 0.0285992i | ||||
\(577\) | −331.614 | + | 331.614i | −0.574721 | + | 0.574721i | −0.933444 | − | 0.358723i | \(-0.883212\pi\) |
0.358723 | + | 0.933444i | \(0.383212\pi\) | |||||||
\(578\) | 95.7024 | + | 95.7024i | 0.165575 | + | 0.165575i | ||||
\(579\) | −853.043 | − | 98.8971i | −1.47330 | − | 0.170807i | ||||
\(580\) | 425.534 | + | 176.565i | 0.733680 | + | 0.304422i | ||||
\(581\) | −310.541 | − | 930.207i | −0.534495 | − | 1.60104i | ||||
\(582\) | 74.2737 | − | 58.8411i | 0.127618 | − | 0.101102i | ||||
\(583\) | 7.02310 | − | 7.02310i | 0.0120465 | − | 0.0120465i | ||||
\(584\) | 165.304i | 0.283054i | ||||||||
\(585\) | −99.3427 | − | 610.714i | −0.169816 | − | 1.04396i | ||||
\(586\) | 144.769i | 0.247045i | ||||||||
\(587\) | −216.371 | − | 216.371i | −0.368605 | − | 0.368605i | 0.498363 | − | 0.866968i | \(-0.333935\pi\) |
−0.866968 | + | 0.498363i | \(0.833935\pi\) | |||||||
\(588\) | −284.389 | − | 74.5590i | −0.483654 | − | 0.126801i | ||||
\(589\) | − | 44.8638i | − | 0.0761694i | ||||||
\(590\) | −554.912 | + | 229.458i | −0.940529 | + | 0.388912i | ||||
\(591\) | 769.711 | + | 89.2360i | 1.30239 | + | 0.150992i | ||||
\(592\) | −21.3044 | − | 21.3044i | −0.0359872 | − | 0.0359872i | ||||
\(593\) | 332.499 | − | 332.499i | 0.560706 | − | 0.560706i | −0.368802 | − | 0.929508i | \(-0.620232\pi\) |
0.929508 | + | 0.368802i | \(0.120232\pi\) | |||||||
\(594\) | 4.21713 | + | 1.52151i | 0.00709954 | + | 0.00256147i | ||||
\(595\) | −48.7667 | + | 684.750i | −0.0819608 | + | 1.15084i | ||||
\(596\) | − | 218.592i | − | 0.366765i | ||||||
\(597\) | −459.119 | − | 579.534i | −0.769043 | − | 0.970744i | ||||
\(598\) | −43.7807 | − | 43.7807i | −0.0732119 | − | 0.0732119i | ||||
\(599\) | 735.946 | 1.22862 | 0.614312 | − | 0.789063i | \(-0.289433\pi\) | ||||
0.614312 | + | 0.789063i | \(0.289433\pi\) | |||||||
\(600\) | −166.436 | + | 131.526i | −0.277394 | + | 0.219209i | ||||
\(601\) | − | 851.749i | − | 1.41722i | −0.705600 | − | 0.708610i | \(-0.749323\pi\) | ||
0.705600 | − | 0.708610i | \(-0.250677\pi\) | |||||||
\(602\) | 461.859 | + | 230.666i | 0.767207 | + | 0.383166i | ||||
\(603\) | 373.188 | − | 231.151i | 0.618885 | − | 0.383335i | ||||
\(604\) | 446.668i | 0.739516i | ||||||||
\(605\) | −231.836 | + | 558.743i | −0.383200 | + | 0.923542i | ||||
\(606\) | 60.9088 | + | 7.06143i | 0.100510 | + | 0.0116525i | ||||
\(607\) | −468.483 | + | 468.483i | −0.771801 | + | 0.771801i | −0.978421 | − | 0.206621i | \(-0.933753\pi\) |
0.206621 | + | 0.978421i | \(0.433753\pi\) | |||||||
\(608\) | −118.887 | + | 118.887i | −0.195538 | + | 0.195538i | ||||
\(609\) | −946.881 | + | 198.643i | −1.55481 | + | 0.326180i | ||||
\(610\) | 227.491 | − | 94.0683i | 0.372936 | − | 0.154210i | ||||
\(611\) | − | 579.083i | − | 0.947763i | ||||||
\(612\) | −185.905 | − | 300.138i | −0.303766 | − | 0.490422i | ||||
\(613\) | −653.475 | + | 653.475i | −1.06603 | + | 1.06603i | −0.0683679 | + | 0.997660i | \(0.521779\pi\) |
−0.997660 | + | 0.0683679i | \(0.978221\pi\) | |||||||
\(614\) | 457.433i | 0.745005i | ||||||||
\(615\) | −194.735 | + | 55.2961i | −0.316642 | + | 0.0899123i | ||||
\(616\) | −0.736119 | − | 2.20500i | −0.00119500 | − | 0.00357954i | ||||
\(617\) | 238.684 | − | 238.684i | 0.386845 | − | 0.386845i | −0.486715 | − | 0.873561i | \(-0.661805\pi\) |
0.873561 | + | 0.486715i | \(0.161805\pi\) | |||||||
\(618\) | 116.877 | + | 147.531i | 0.189121 | + | 0.238723i | ||||
\(619\) | 400.073 | 0.646322 | 0.323161 | − | 0.946344i | \(-0.395254\pi\) | ||||
0.323161 | + | 0.946344i | \(0.395254\pi\) | |||||||
\(620\) | 5.78490 | − | 13.9420i | 0.00933048 | − | 0.0224872i | ||||
\(621\) | 80.8683 | + | 29.1767i | 0.130223 | + | 0.0469834i | ||||
\(622\) | 269.223 | − | 269.223i | 0.432835 | − | 0.432835i | ||||
\(623\) | 811.600 | + | 405.337i | 1.30273 | + | 0.650621i | ||||
\(624\) | 19.0016 | − | 163.900i | 0.0304513 | − | 0.262660i | ||||
\(625\) | −1.51670 | + | 624.998i | −0.00242671 | + | 0.999997i | ||||
\(626\) | 842.046 | 1.34512 | ||||||||
\(627\) | 8.20600 | − | 6.50095i | 0.0130877 | − | 0.0103683i | ||||
\(628\) | −3.34288 | − | 3.34288i | −0.00532305 | − | 0.00532305i | ||||
\(629\) | − | 147.736i | − | 0.234875i | ||||||
\(630\) | 132.471 | − | 425.325i | 0.210272 | − | 0.675119i | ||||
\(631\) | −343.679 | −0.544658 | −0.272329 | − | 0.962204i | \(-0.587794\pi\) | ||||
−0.272329 | + | 0.962204i | \(0.587794\pi\) | |||||||
\(632\) | −1.73139 | + | 1.73139i | −0.00273954 | + | 0.00273954i | ||||
\(633\) | 309.021 | + | 390.069i | 0.488185 | + | 0.616223i | ||||
\(634\) | − | 149.624i | − | 0.236001i | ||||||
\(635\) | −1123.01 | + | 464.369i | −1.76852 | + | 0.731290i | ||||
\(636\) | 504.180 | + | 58.4519i | 0.792736 | + | 0.0919055i | ||||
\(637\) | 94.6716 | − | 667.056i | 0.148621 | − | 1.04718i | ||||
\(638\) | −5.40927 | − | 5.40927i | −0.00847848 | − | 0.00847848i | ||||
\(639\) | 680.311 | + | 159.892i | 1.06465 | + | 0.250222i | ||||
\(640\) | −52.2756 | + | 21.6161i | −0.0816807 | + | 0.0337752i | ||||
\(641\) | − | 976.273i | − | 1.52305i | −0.648137 | − | 0.761524i | \(-0.724452\pi\) | ||
0.648137 | − | 0.761524i | \(-0.275548\pi\) | |||||||
\(642\) | −497.842 | + | 394.401i | −0.775455 | + | 0.614331i | ||||
\(643\) | 155.167 | + | 155.167i | 0.241317 | + | 0.241317i | 0.817395 | − | 0.576078i | \(-0.195417\pi\) |
−0.576078 | + | 0.817395i | \(0.695417\pi\) | |||||||
\(644\) | −14.1159 | − | 42.2834i | −0.0219192 | − | 0.0656574i | ||||
\(645\) | −381.004 | + | 683.187i | −0.590704 | + | 1.05920i | ||||
\(646\) | −824.428 | −1.27620 | ||||||||
\(647\) | −122.968 | − | 122.968i | −0.190059 | − | 0.190059i | 0.605663 | − | 0.795722i | \(-0.292908\pi\) |
−0.795722 | + | 0.605663i | \(0.792908\pi\) | |||||||
\(648\) | 72.8768 | + | 217.203i | 0.112464 | + | 0.335189i | ||||
\(649\) | 9.97068 | 0.0153631 | ||||||||
\(650\) | −343.328 | − | 344.162i | −0.528196 | − | 0.529480i | ||||
\(651\) | 6.50828 | + | 31.0232i | 0.00999736 | + | 0.0476548i | ||||
\(652\) | 68.3743 | + | 68.3743i | 0.104869 | + | 0.104869i | ||||
\(653\) | 621.793 | + | 621.793i | 0.952209 | + | 0.952209i | 0.998909 | − | 0.0466996i | \(-0.0148703\pi\) |
−0.0466996 | + | 0.998909i | \(0.514870\pi\) | |||||||
\(654\) | 46.6482 | − | 402.367i | 0.0713275 | − | 0.615240i | ||||
\(655\) | −279.367 | + | 673.296i | −0.426515 | + | 1.02793i | ||||
\(656\) | −53.9822 | −0.0822900 | ||||||||
\(657\) | 447.164 | − | 276.972i | 0.680614 | − | 0.421570i | ||||
\(658\) | 186.284 | − | 372.994i | 0.283106 | − | 0.566860i | ||||
\(659\) | −307.522 | −0.466650 | −0.233325 | − | 0.972399i | \(-0.574961\pi\) | ||||
−0.233325 | + | 0.972399i | \(0.574961\pi\) | |||||||
\(660\) | 3.38838 | − | 0.962152i | 0.00513392 | − | 0.00145781i | ||||
\(661\) | 621.533i | 0.940292i | 0.882589 | + | 0.470146i | \(0.155799\pi\) | ||||
−0.882589 | + | 0.470146i | \(0.844201\pi\) | |||||||
\(662\) | −506.910 | + | 506.910i | −0.765725 | + | 0.765725i | ||||
\(663\) | 634.168 | − | 502.401i | 0.956513 | − | 0.757769i | ||||
\(664\) | 396.252 | 0.596765 | ||||||||
\(665\) | −681.465 | − | 785.973i | −1.02476 | − | 1.18191i | ||||
\(666\) | −21.9345 | + | 93.3270i | −0.0329346 | + | 0.140131i | ||||
\(667\) | −103.729 | − | 103.729i | −0.155516 | − | 0.155516i | ||||
\(668\) | 244.959 | − | 244.959i | 0.366705 | − | 0.366705i | ||||
\(669\) | 21.9355 | − | 189.206i | 0.0327885 | − | 0.282819i | ||||
\(670\) | 132.178 | − | 318.559i | 0.197280 | − | 0.475461i | ||||
\(671\) | −4.08757 | −0.00609176 | ||||||||
\(672\) | 64.9637 | − | 99.4571i | 0.0966722 | − | 0.148002i | ||||
\(673\) | −571.899 | + | 571.899i | −0.849776 | + | 0.849776i | −0.990105 | − | 0.140329i | \(-0.955184\pi\) |
0.140329 | + | 0.990105i | \(0.455184\pi\) | |||||||
\(674\) | −375.896 | −0.557709 | ||||||||
\(675\) | 634.660 | + | 229.852i | 0.940237 | + | 0.340521i | ||||
\(676\) | 40.1139 | 0.0593402 | ||||||||
\(677\) | −679.334 | − | 679.334i | −1.00345 | − | 1.00345i | −0.999994 | − | 0.00345318i | \(-0.998901\pi\) |
−0.00345318 | − | 0.999994i | \(-0.501099\pi\) | |||||||
\(678\) | 224.019 | + | 282.773i | 0.330411 | + | 0.417070i | ||||
\(679\) | 49.5071 | + | 148.295i | 0.0729118 | + | 0.218403i | ||||
\(680\) | −256.203 | − | 106.305i | −0.376769 | − | 0.156331i | ||||
\(681\) | 103.506 | − | 892.802i | 0.151992 | − | 1.31102i | ||||
\(682\) | −0.177227 | + | 0.177227i | −0.000259864 | + | 0.000259864i | ||||
\(683\) | 807.265 | + | 807.265i | 1.18194 | + | 1.18194i | 0.979241 | + | 0.202700i | \(0.0649715\pi\) |
0.202700 | + | 0.979241i | \(0.435028\pi\) | |||||||
\(684\) | 520.802 | + | 122.403i | 0.761407 | + | 0.178952i | ||||
\(685\) | 102.141 | + | 247.015i | 0.149112 | + | 0.360606i | ||||
\(686\) | 275.563 | − | 399.203i | 0.401695 | − | 0.581929i | ||||
\(687\) | 19.0815 | + | 24.0862i | 0.0277752 | + | 0.0350599i | ||||
\(688\) | −147.502 | + | 147.502i | −0.214392 | + | 0.214392i | ||||
\(689\) | 1163.14i | 1.68815i | ||||||||
\(690\) | 64.9762 | − | 18.4504i | 0.0941684 | − | 0.0267397i | ||||
\(691\) | 287.198i | 0.415626i | 0.978169 | + | 0.207813i | \(0.0666346\pi\) | ||||
−0.978169 | + | 0.207813i | \(0.933365\pi\) | |||||||
\(692\) | −22.2409 | − | 22.2409i | −0.0321400 | − | 0.0321400i | ||||
\(693\) | −4.73136 | + | 5.68583i | −0.00682736 | + | 0.00820465i | ||||
\(694\) | − | 305.592i | − | 0.440334i | ||||||
\(695\) | −125.416 | + | 302.262i | −0.180454 | + | 0.434909i | ||||
\(696\) | 45.0203 | − | 388.325i | 0.0646843 | − | 0.557938i | ||||
\(697\) | −187.171 | − | 187.171i | −0.268538 | − | 0.268538i | ||||
\(698\) | 368.362 | − | 368.362i | 0.527740 | − | 0.527740i | ||||
\(699\) | 66.2777 | − | 571.682i | 0.0948179 | − | 0.817858i | ||||
\(700\) | −110.429 | − | 332.123i | −0.157755 | − | 0.474461i | ||||
\(701\) | 791.451i | 1.12903i | 0.825422 | + | 0.564516i | \(0.190937\pi\) | ||||
−0.825422 | + | 0.564516i | \(0.809063\pi\) | |||||||
\(702\) | −475.204 | + | 223.218i | −0.676929 | + | 0.317974i | ||||
\(703\) | 158.302 | + | 158.302i | 0.225180 | + | 0.225180i | ||||
\(704\) | 0.939291 | 0.00133422 | ||||||||
\(705\) | 551.737 | + | 307.696i | 0.782606 | + | 0.436448i | ||||
\(706\) | 489.435i | 0.693251i | ||||||||
\(707\) | −45.2021 | + | 90.5076i | −0.0639351 | + | 0.128016i | ||||
\(708\) | 316.400 | + | 399.384i | 0.446893 | + | 0.564102i | ||||
\(709\) | − | 56.1623i | − | 0.0792133i | −0.999215 | − | 0.0396067i | \(-0.987390\pi\) | ||
0.999215 | − | 0.0396067i | \(-0.0126105\pi\) | |||||||
\(710\) | 507.399 | − | 209.811i | 0.714646 | − | 0.295508i | ||||
\(711\) | 7.58459 | + | 1.78259i | 0.0106675 | + | 0.00250716i | ||||
\(712\) | −259.197 | + | 259.197i | −0.364041 | + | 0.364041i | ||||
\(713\) | −3.39854 | + | 3.39854i | −0.00476653 | + | 0.00476653i | ||||
\(714\) | 570.091 | − | 119.598i | 0.798447 | − | 0.167504i | ||||
\(715\) | 3.08446 | + | 7.45935i | 0.00431393 | + | 0.0104327i | ||||
\(716\) | 334.387i | 0.467021i | ||||||||
\(717\) | −46.7719 | − | 59.0391i | −0.0652328 | − | 0.0823418i | ||||
\(718\) | −599.498 | + | 599.498i | −0.834956 | + | 0.834956i | ||||
\(719\) | 364.303i | 0.506680i | 0.967377 | + | 0.253340i | \(0.0815291\pi\) | ||||
−0.967377 | + | 0.253340i | \(0.918471\pi\) | |||||||
\(720\) | 146.063 | + | 105.193i | 0.202866 | + | 0.146101i | ||||
\(721\) | −294.560 | + | 98.3364i | −0.408544 | + | 0.136389i | ||||
\(722\) | 522.387 | − | 522.387i | 0.723527 | − | 0.723527i | ||||
\(723\) | 655.950 | − | 519.657i | 0.907261 | − | 0.718751i | ||||
\(724\) | −542.198 | −0.748892 | ||||||||
\(725\) | −813.441 | − | 815.417i | −1.12199 | − | 1.12471i | ||||
\(726\) | 509.886 | + | 59.1133i | 0.702322 | + | 0.0814233i | ||||
\(727\) | −188.513 | + | 188.513i | −0.259303 | + | 0.259303i | −0.824771 | − | 0.565468i | \(-0.808696\pi\) |
0.565468 | + | 0.824771i | \(0.308696\pi\) | |||||||
\(728\) | 243.547 | + | 121.635i | 0.334543 | + | 0.167081i | ||||
\(729\) | 465.448 | − | 561.070i | 0.638475 | − | 0.769643i | ||||
\(730\) | 158.379 | − | 381.706i | 0.216958 | − | 0.522884i | ||||
\(731\) | −1022.86 | −1.39926 | ||||||||
\(732\) | −129.711 | − | 163.731i | −0.177201 | − | 0.223676i | ||||
\(733\) | 1.46070 | + | 1.46070i | 0.00199277 | + | 0.00199277i | 0.708102 | − | 0.706110i | \(-0.249551\pi\) |
−0.706110 | + | 0.708102i | \(0.749551\pi\) | |||||||
\(734\) | 77.7356i | 0.105907i | ||||||||
\(735\) | 585.251 | + | 444.641i | 0.796260 | + | 0.604954i | ||||
\(736\) | 18.0120 | 0.0244728 | ||||||||
\(737\) | −4.04942 | + | 4.04942i | −0.00549447 | + | 0.00549447i | ||||
\(738\) | 90.4490 | + | 146.028i | 0.122560 | + | 0.197869i | ||||
\(739\) | 757.965i | 1.02566i | 0.858489 | + | 0.512832i | \(0.171404\pi\) | ||||
−0.858489 | + | 0.512832i | \(0.828596\pi\) | |||||||
\(740\) | 28.7825 | + | 69.6065i | 0.0388952 | + | 0.0940628i | ||||
\(741\) | −141.191 | + | 1217.85i | −0.190541 | + | 1.64352i | ||||
\(742\) | −374.166 | + | 749.188i | −0.504267 | + | 1.00969i | ||||
\(743\) | −781.133 | − | 781.133i | −1.05132 | − | 1.05132i | −0.998610 | − | 0.0527138i | \(-0.983213\pi\) |
−0.0527138 | − | 0.998610i | \(-0.516787\pi\) | |||||||
\(744\) | −12.7229 | − | 1.47503i | −0.0171007 | − | 0.00198256i | ||||
\(745\) | −209.435 | + | 504.754i | −0.281121 | + | 0.677522i | ||||
\(746\) | − | 456.732i | − | 0.612241i | ||||||
\(747\) | −663.933 | − | 1071.90i | −0.888800 | − | 1.43494i | ||||
\(748\) | 3.25677 | + | 3.25677i | 0.00435398 | + | 0.00435398i | ||||
\(749\) | −331.836 | − | 993.995i | −0.443039 | − | 1.32710i | ||||
\(750\) | 510.337 | − | 144.244i | 0.680449 | − | 0.192326i | ||||
\(751\) | −483.342 | −0.643598 | −0.321799 | − | 0.946808i | \(-0.604287\pi\) | ||||
−0.321799 | + | 0.946808i | \(0.604287\pi\) | |||||||
\(752\) | 119.121 | + | 119.121i | 0.158406 | + | 0.158406i | ||||
\(753\) | −393.539 | − | 496.755i | −0.522629 | − | 0.659701i | ||||
\(754\) | 895.859 | 1.18814 | ||||||||
\(755\) | 427.957 | − | 1031.41i | 0.566830 | − | 1.36610i | ||||
\(756\) | −377.891 | − | 9.09000i | −0.499855 | − | 0.0120238i | ||||
\(757\) | 669.202 | + | 669.202i | 0.884018 | + | 0.884018i | 0.993940 | − | 0.109922i | \(-0.0350601\pi\) |
−0.109922 | + | 0.993940i | \(0.535060\pi\) | |||||||
\(758\) | 217.075 | + | 217.075i | 0.286378 | + | 0.286378i | ||||
\(759\) | −1.11409 | − | 0.129161i | −0.00146783 | − | 0.000170173i | ||||
\(760\) | 388.432 | − | 160.618i | 0.511094 | − | 0.211339i | ||||
\(761\) | 318.737 | 0.418840 | 0.209420 | − | 0.977826i | \(-0.432842\pi\) | ||||
0.209420 | + | 0.977826i | \(0.432842\pi\) | |||||||
\(762\) | 640.320 | + | 808.260i | 0.840314 | + | 1.06071i | ||||
\(763\) | 597.898 | + | 298.608i | 0.783615 | + | 0.391360i | ||||
\(764\) | 549.451 | 0.719177 | ||||||||
\(765\) | 141.710 | + | 871.172i | 0.185242 | + | 1.13879i | ||||
\(766\) | − | 602.040i | − | 0.785953i | ||||||
\(767\) | −825.650 | + | 825.650i | −1.07647 | + | 1.07647i | ||||
\(768\) | 29.8065 | + | 37.6241i | 0.0388106 | + | 0.0489897i | ||||
\(769\) | −1466.30 | −1.90676 | −0.953381 | − | 0.301769i | \(-0.902423\pi\) | ||||
−0.953381 | + | 0.301769i | \(0.902423\pi\) | |||||||
\(770\) | −0.412844 | + | 5.79688i | −0.000536161 | + | 0.00752842i | ||||
\(771\) | 161.448 | − | 1392.58i | 0.209400 | − | 1.80620i | ||||
\(772\) | 404.822 | + | 404.822i | 0.524381 | + | 0.524381i | ||||
\(773\) | −271.019 | + | 271.019i | −0.350606 | + | 0.350606i | −0.860335 | − | 0.509729i | \(-0.829746\pi\) |
0.509729 | + | 0.860335i | \(0.329746\pi\) | |||||||
\(774\) | 646.151 | + | 151.864i | 0.834821 | + | 0.196206i | ||||
\(775\) | −26.7160 | + | 26.6513i | −0.0344723 | + | 0.0343887i | ||||
\(776\) | −63.1712 | −0.0814062 | ||||||||
\(777\) | −132.430 | − | 86.5010i | −0.170437 | − | 0.111327i | ||||
\(778\) | −369.112 | + | 369.112i | −0.474438 | + | 0.474438i | ||||
\(779\) | 401.113 | 0.514907 | ||||||||
\(780\) | −200.911 | + | 360.258i | −0.257578 | + | 0.461870i | ||||
\(781\) | −9.11696 | −0.0116734 | ||||||||
\(782\) | 62.4524 | + | 62.4524i | 0.0798624 | + | 0.0798624i | ||||
\(783\) | −1125.89 | + | 528.867i | −1.43792 | + | 0.675437i | ||||
\(784\) | 117.743 | + | 156.692i | 0.150183 | + | 0.199863i | ||||
\(785\) | 4.51626 | + | 10.9219i | 0.00575319 | + | 0.0139133i | ||||
\(786\) | 614.423 | + | 71.2327i | 0.781708 | + | 0.0906269i | ||||
\(787\) | 283.928 | − | 283.928i | 0.360772 | − | 0.360772i | −0.503325 | − | 0.864097i | \(-0.667890\pi\) |
0.864097 | + | 0.503325i | \(0.167890\pi\) | |||||||
\(788\) | −365.275 | − | 365.275i | −0.463548 | − | 0.463548i | ||||
\(789\) | 36.3222 | − | 313.300i | 0.0460358 | − | 0.397085i | ||||
\(790\) | 5.65684 | − | 2.33912i | 0.00716056 | − | 0.00296091i | ||||
\(791\) | −564.587 | + | 188.482i | −0.713764 | + | 0.238284i | ||||
\(792\) | −1.57381 | − | 2.54088i | −0.00198714 | − | 0.00320818i | ||||
\(793\) | 338.483 | − | 338.483i | 0.426838 | − | 0.426838i | ||||
\(794\) | 26.0485i | 0.0328066i | ||||||||
\(795\) | −1108.21 | − | 618.032i | −1.39397 | − | 0.777399i | ||||
\(796\) | 492.905i | 0.619228i | ||||||||
\(797\) | 887.082 | + | 887.082i | 1.11303 | + | 1.11303i | 0.992739 | + | 0.120287i | \(0.0383813\pi\) |
0.120287 | + | 0.992739i | \(0.461619\pi\) | |||||||
\(798\) | −482.710 | + | 739.012i | −0.604900 | + | 0.926080i | ||||
\(799\) | 826.051i | 1.03386i | ||||||||
\(800\) | 141.421 | + | 0.171595i | 0.176777 | + | 0.000214493i | ||||
\(801\) | 1135.45 | + | 266.862i | 1.41754 | + | 0.333161i | ||||
\(802\) | 17.1182 | + | 17.1182i | 0.0213444 | + | 0.0213444i | ||||
\(803\) | −4.85213 | + | 4.85213i | −0.00604251 | + | 0.00604251i | ||||
\(804\) | −290.703 | − | 33.7025i | −0.361571 | − | 0.0419186i | ||||
\(805\) | −7.91676 | + | 111.162i | −0.00983448 | + | 0.138089i | ||||
\(806\) | − | 29.3516i | − | 0.0364164i | ||||||
\(807\) | 589.218 | − | 466.791i | 0.730134 | − | 0.578427i | ||||
\(808\) | −28.9050 | − | 28.9050i | −0.0357735 | − | 0.0357735i | ||||
\(809\) | 1442.13 | 1.78261 | 0.891304 | − | 0.453406i | \(-0.149791\pi\) | ||||
0.891304 | + | 0.453406i | \(0.149791\pi\) | |||||||
\(810\) | 39.8227 | − | 571.370i | 0.0491638 | − | 0.705396i | ||||
\(811\) | 118.608i | 0.146250i | 0.997323 | + | 0.0731248i | \(0.0232971\pi\) | ||||
−0.997323 | + | 0.0731248i | \(0.976703\pi\) | |||||||
\(812\) | 577.033 | + | 288.187i | 0.710632 | + | 0.354910i | ||||
\(813\) | 487.908 | − | 386.531i | 0.600133 | − | 0.475438i | ||||
\(814\) | − | 1.25069i | − | 0.00153648i | ||||||
\(815\) | −92.3743 | − | 223.394i | −0.113343 | − | 0.274104i | ||||
\(816\) | −27.1055 | + | 233.800i | −0.0332175 | + | 0.286520i | ||||
\(817\) | 1096.00 | − | 1096.00i | 1.34150 | − | 1.34150i | ||||
\(818\) | 186.052 | − | 186.052i | 0.227447 | − | 0.227447i | ||||
\(819\) | −79.0374 | − | 862.624i | −0.0965047 | − | 1.05326i | ||||
\(820\) | 124.651 | + | 51.7209i | 0.152014 | + | 0.0630743i | ||||
\(821\) | − | 219.050i | − | 0.266808i | −0.991062 | − | 0.133404i | \(-0.957409\pi\) | ||
0.991062 | − | 0.133404i | \(-0.0425908\pi\) | |||||||
\(822\) | 177.783 | − | 140.843i | 0.216281 | − | 0.171342i | ||||
\(823\) | 391.907 | − | 391.907i | 0.476194 | − | 0.476194i | −0.427718 | − | 0.903912i | \(-0.640682\pi\) |
0.903912 | + | 0.427718i | \(0.140682\pi\) | |||||||
\(824\) | − | 125.478i | − | 0.152279i | ||||||
\(825\) | −8.74603 | − | 1.02472i | −0.0106012 | − | 0.00124209i | ||||
\(826\) | −797.412 | + | 266.209i | −0.965390 | + | 0.322287i | ||||
\(827\) | −803.540 | + | 803.540i | −0.971633 | + | 0.971633i | −0.999609 | − | 0.0279759i | \(-0.991094\pi\) |
0.0279759 | + | 0.999609i | \(0.491094\pi\) | |||||||
\(828\) | −30.1797 | − | 48.7243i | −0.0364489 | − | 0.0588458i | ||||
\(829\) | 689.177 | 0.831336 | 0.415668 | − | 0.909516i | \(-0.363548\pi\) | ||||
0.415668 | + | 0.909516i | \(0.363548\pi\) | |||||||
\(830\) | −914.993 | − | 379.653i | −1.10240 | − | 0.457413i | ||||
\(831\) | 31.6235 | − | 272.771i | 0.0380548 | − | 0.328244i | ||||
\(832\) | −77.7806 | + | 77.7806i | −0.0934863 | + | 0.0934863i | ||||
\(833\) | −135.047 | + | 951.542i | −0.162122 | + | 1.14231i | ||||
\(834\) | 275.832 | + | 31.9784i | 0.330733 | + | 0.0383434i | ||||
\(835\) | −800.336 | + | 330.941i | −0.958486 | + | 0.396337i | ||||
\(836\) | −6.97936 | −0.00834852 | ||||||||
\(837\) | 17.3276 | + | 36.8883i | 0.0207020 | + | 0.0440721i | ||||
\(838\) | −606.909 | − | 606.909i | −0.724235 | − | 0.724235i | ||||
\(839\) | 933.638i | 1.11280i | 0.830915 | + | 0.556399i | \(0.187817\pi\) | ||||
−0.830915 | + | 0.556399i | \(0.812183\pi\) | |||||||
\(840\) | −245.300 | + | 167.416i | −0.292023 | + | 0.199305i | ||||
\(841\) | 1281.55 | 1.52383 | ||||||||
\(842\) | −642.340 | + | 642.340i | −0.762874 | + | 0.762874i | ||||
\(843\) | −830.732 | + | 658.123i | −0.985447 | + | 0.780691i | ||||
\(844\) | − | 331.762i | − | 0.393083i | ||||||
\(845\) | −92.6278 | − | 38.4336i | −0.109619 | − | 0.0454835i | ||||
\(846\) | 122.644 | − | 521.827i | 0.144969 | − | 0.616817i | ||||
\(847\) | −378.401 | + | 757.667i | −0.446754 | + | 0.894530i | ||||
\(848\) | −239.265 | − | 239.265i | −0.282152 | − | 0.282152i | ||||
\(849\) | 88.4797 | − | 763.188i | 0.104216 | − | 0.898926i | ||||
\(850\) | 489.750 | + | 490.940i | 0.576177 | + | 0.577577i | ||||
\(851\) | − | 23.9835i | − | 0.0281827i | ||||||
\(852\) | −289.309 | − | 365.187i | −0.339564 | − | 0.428624i | ||||
\(853\) | 129.839 | + | 129.839i | 0.152215 | + | 0.152215i | 0.779106 | − | 0.626892i | \(-0.215673\pi\) |
−0.626892 | + | 0.779106i | \(0.715673\pi\) | |||||||
\(854\) | 326.906 | − | 109.135i | 0.382794 | − | 0.127792i | ||||
\(855\) | −1085.32 | − | 781.628i | −1.26938 | − | 0.914185i | ||||
\(856\) | 423.425 | 0.494655 | ||||||||
\(857\) | −399.948 | − | 399.948i | −0.466683 | − | 0.466683i | 0.434155 | − | 0.900838i | \(-0.357047\pi\) |
−0.900838 | + | 0.434155i | \(0.857047\pi\) | |||||||
\(858\) | 5.36868 | − | 4.25317i | 0.00625720 | − | 0.00495708i | ||||
\(859\) | −191.398 | −0.222815 | −0.111407 | − | 0.993775i | \(-0.535536\pi\) | ||||
−0.111407 | + | 0.993775i | \(0.535536\pi\) | |||||||
\(860\) | 481.922 | − | 199.276i | 0.560374 | − | 0.231716i | ||||
\(861\) | −277.369 | + | 58.1884i | −0.322147 | + | 0.0675824i | ||||
\(862\) | 455.692 | + | 455.692i | 0.528645 | + | 0.528645i | ||||
\(863\) | 31.1106 | + | 31.1106i | 0.0360493 | + | 0.0360493i | 0.724902 | − | 0.688852i | \(-0.241885\pi\) |
−0.688852 | + | 0.724902i | \(0.741885\pi\) | |||||||
\(864\) | 51.8352 | − | 143.670i | 0.0599944 | − | 0.166285i | ||||
\(865\) | 30.0476 | + | 72.6661i | 0.0347372 | + | 0.0840070i | ||||
\(866\) | 403.272 | 0.465672 | ||||||||
\(867\) | −225.045 | + | 178.285i | −0.259567 | + | 0.205634i | ||||
\(868\) | 9.44205 | − | 18.9057i | 0.0108779 | − | 0.0217808i | ||||
\(869\) | −0.101642 | −0.000116965 | ||||||||
\(870\) | −476.015 | + | 853.554i | −0.547144 | + | 0.981097i | ||||
\(871\) | − | 670.648i | − | 0.769974i | ||||||
\(872\) | −190.948 | + | 190.948i | −0.218977 | + | 0.218977i | ||||
\(873\) | 105.845 | + | 170.885i | 0.121243 | + | 0.195744i | ||||
\(874\) | −133.837 | −0.153132 | ||||||||
\(875\) | −63.2175 | + | 872.713i | −0.0722486 | + | 0.997387i | ||||
\(876\) | −348.329 | − | 40.3833i | −0.397636 | − | 0.0460997i | ||||
\(877\) | −277.162 | − | 277.162i | −0.316034 | − | 0.316034i | 0.531208 | − | 0.847242i | \(-0.321738\pi\) |
−0.847242 | + | 0.531208i | \(0.821738\pi\) | |||||||
\(878\) | 94.0452 | − | 94.0452i | 0.107113 | − | 0.107113i | ||||
\(879\) | −305.057 | − | 35.3667i | −0.347050 | − | 0.0402351i | ||||
\(880\) | −2.16893 | − | 0.899944i | −0.00246470 | − | 0.00102266i | ||||
\(881\) | −1088.62 | −1.23566 | −0.617830 | − | 0.786311i | \(-0.711988\pi\) | ||||
−0.617830 | + | 0.786311i | \(0.711988\pi\) | |||||||
\(882\) | 226.587 | − | 581.051i | 0.256901 | − | 0.658788i | ||||
\(883\) | 595.876 | − | 595.876i | 0.674831 | − | 0.674831i | −0.283994 | − | 0.958826i | \(-0.591660\pi\) |
0.958826 | + | 0.283994i | \(0.0916597\pi\) | |||||||
\(884\) | −539.373 | −0.610150 | ||||||||
\(885\) | −347.951 | − | 1225.37i | −0.393165 | − | 1.38460i | ||||
\(886\) | −250.466 | −0.282693 | ||||||||
\(887\) | 296.458 | + | 296.458i | 0.334225 | + | 0.334225i | 0.854189 | − | 0.519963i | \(-0.174054\pi\) |
−0.519963 | + | 0.854189i | \(0.674054\pi\) | |||||||
\(888\) | 50.0975 | − | 39.6882i | 0.0564161 | − | 0.0446940i | ||||
\(889\) | −1613.78 | + | 538.745i | −1.81527 | + | 0.606012i | ||||
\(890\) | 846.856 | − | 350.177i | 0.951523 | − | 0.393458i | ||||
\(891\) | −4.23637 | + | 8.51466i | −0.00475463 | + | 0.00955629i | ||||
\(892\) | −89.7899 | + | 89.7899i | −0.100661 | + | 0.100661i | ||||
\(893\) | −885.126 | − | 885.126i | −0.991182 | − | 0.991182i | ||||
\(894\) | 460.618 | + | 53.4015i | 0.515233 | + | 0.0597332i | ||||
\(895\) | 320.379 | − | 772.139i | 0.357966 | − | 0.862725i | ||||
\(896\) | −75.1204 | + | 25.0783i | −0.0838398 | + | 0.0279892i | ||||
\(897\) | 102.951 | − | 81.5595i | 0.114772 | − | 0.0909247i | ||||
\(898\) | 324.260 | − | 324.260i | 0.361092 | − | 0.361092i | ||||
\(899\) | − | 69.5423i | − | 0.0773551i | ||||||
\(900\) | −236.492 | − | 382.847i | −0.262769 | − | 0.425385i | ||||
\(901\) | − | 1659.19i | − | 1.84150i | ||||||
\(902\) | −1.58453 | − | 1.58453i | −0.00175669 | − | 0.00175669i | ||||
\(903\) | −598.891 | + | 916.881i | −0.663224 | + | 1.01537i | ||||
\(904\) | − | 240.504i | − | 0.266045i | ||||||
\(905\) | 1252.00 | + | 519.485i | 1.38342 | + | 0.574016i | ||||
\(906\) | −941.221 | − | 109.120i | −1.03888 | − | 0.120441i | ||||
\(907\) | −909.570 | − | 909.570i | −1.00283 | − | 1.00283i | −0.999996 | − | 0.00283720i | \(-0.999097\pi\) |
−0.00283720 | − | 0.999996i | \(-0.500903\pi\) | |||||||
\(908\) | −423.690 | + | 423.690i | −0.466619 | + | 0.466619i | ||||
\(909\) | −29.7598 | + | 126.622i | −0.0327390 | + | 0.139298i | ||||
\(910\) | −445.840 | − | 514.214i | −0.489935 | − | 0.565070i | ||||
\(911\) | 199.143i | 0.218598i | 0.994009 | + | 0.109299i | \(0.0348607\pi\) | ||||
−0.994009 | + | 0.109299i | \(0.965139\pi\) | |||||||
\(912\) | −221.476 | − | 279.564i | −0.242847 | − | 0.306539i | ||||
\(913\) | 11.6311 | + | 11.6311i | 0.0127395 | + | 0.0127395i | ||||
\(914\) | −823.513 | −0.900999 | ||||||||
\(915\) | 142.646 | + | 502.352i | 0.155897 | + | 0.549018i | ||||
\(916\) | − | 20.4858i | − | 0.0223644i | ||||||
\(917\) | −455.980 | + | 913.003i | −0.497252 | + | 0.995641i | ||||
\(918\) | 677.870 | − | 318.416i | 0.738420 | − | 0.346859i | ||||
\(919\) | 841.677i | 0.915862i | 0.888988 | + | 0.457931i | \(0.151409\pi\) | ||||
−0.888988 | + | 0.457931i | \(0.848591\pi\) | |||||||
\(920\) | −41.5918 | − | 17.2575i | −0.0452085 | − | 0.0187581i | ||||
\(921\) | −963.905 | − | 111.750i | −1.04659 | − | 0.121335i | ||||
\(922\) | 484.084 | − | 484.084i | 0.525037 | − | 0.525037i | ||||
\(923\) | 754.956 | − | 754.956i | 0.817937 | − | 0.817937i | ||||
\(924\) | 4.82622 | − | 1.01248i | 0.00522318 | − | 0.00109576i | ||||
\(925\) | 0.228483 | − | 188.306i | 0.000247009 | − | 0.203574i | ||||
\(926\) | − | 479.544i | − | 0.517866i | ||||||
\(927\) | −339.430 | + | 210.242i | −0.366160 | + | 0.226798i | ||||
\(928\) | −184.284 | + | 184.284i | −0.198582 | + | 0.198582i | ||||
\(929\) | 883.375i | 0.950888i | 0.879746 | + | 0.475444i | \(0.157713\pi\) | ||||
−0.879746 | + | 0.475444i | \(0.842287\pi\) | |||||||
\(930\) | 27.9655 | + | 15.5960i | 0.0300705 | + | 0.0167699i | ||||
\(931\) | −874.886 | − | 1164.30i | −0.939727 | − | 1.25059i | ||||
\(932\) | −271.299 | + | 271.299i | −0.291093 | + | 0.291093i | ||||
\(933\) | 501.539 | + | 633.080i | 0.537555 | + | 0.678542i | ||||
\(934\) | −605.242 | −0.648011 | ||||||||
\(935\) | −4.39993 | − | 10.6406i | −0.00470581 | − | 0.0113803i | ||||
\(936\) | 340.729 | + | 80.0807i | 0.364026 | + | 0.0855563i | ||||
\(937\) | 510.517 | − | 510.517i | 0.544843 | − | 0.544843i | −0.380102 | − | 0.924945i | \(-0.624111\pi\) |
0.924945 | + | 0.380102i | \(0.124111\pi\) | |||||||
\(938\) | 215.739 | − | 431.972i | 0.229999 | − | 0.460524i | ||||
\(939\) | −205.710 | + | 1774.36i | −0.219073 | + | 1.88963i | ||||
\(940\) | −160.934 | − | 389.196i | −0.171206 | − | 0.414039i | ||||
\(941\) | 135.777 | 0.144290 | 0.0721449 | − | 0.997394i | \(-0.477016\pi\) | ||||
0.0721449 | + | 0.997394i | \(0.477016\pi\) | |||||||
\(942\) | 7.86079 | − | 6.22748i | 0.00834479 | − | 0.00661091i | ||||
\(943\) | −30.3852 | − | 30.3852i | −0.0322219 | − | 0.0322219i | ||||
\(944\) | − | 339.684i | − | 0.359835i | ||||||
\(945\) | 863.885 | + | 383.051i | 0.914164 | + | 0.405345i | ||||
\(946\) | −8.65919 | −0.00915348 | ||||||||
\(947\) | 1262.03 | − | 1262.03i | 1.33266 | − | 1.33266i | 0.429679 | − | 0.902982i | \(-0.358627\pi\) |
0.902982 | − | 0.429679i | \(-0.141373\pi\) | |||||||
\(948\) | −3.22542 | − | 4.07137i | −0.00340234 | − | 0.00429469i | ||||
\(949\) | − | 803.589i | − | 0.846774i | ||||||
\(950\) | −1050.82 | − | 1.27503i | −1.10613 | − | 0.00134213i | ||||
\(951\) | 315.290 | + | 36.5529i | 0.331535 | + | 0.0384363i | ||||
\(952\) | −347.416 | − | 173.510i | −0.364933 | − | 0.182258i | ||||
\(953\) | 1044.38 | + | 1044.38i | 1.09589 | + | 1.09589i | 0.994886 | + | 0.101000i | \(0.0322044\pi\) |
0.101000 | + | 0.994886i | \(0.467796\pi\) | |||||||
\(954\) | −246.340 | + | 1048.13i | −0.258218 | + | 1.09867i | ||||
\(955\) | −1268.75 | − | 526.435i | −1.32853 | − | 0.551240i | ||||
\(956\) | 50.2139i | 0.0525250i | ||||||||
\(957\) | 12.7199 | − | 10.0770i | 0.0132915 | − | 0.0105298i | ||||
\(958\) | −444.701 | − | 444.701i | −0.464198 | − | 0.464198i | ||||
\(959\) | 118.501 | + | 354.962i | 0.123567 | + | 0.370138i | ||||
\(960\) | −32.7788 | − | 115.436i | −0.0341446 | − | 0.120246i | ||||
\(961\) | 958.722 | 0.997629 | ||||||||
\(962\) | 103.567 | + | 103.567i | 0.107658 | + | 0.107658i | ||||
\(963\) | −709.462 | − | 1145.41i | −0.736720 | − | 1.18942i | ||||
\(964\) | −557.898 | −0.578733 | ||||||||
\(965\) | −546.918 | − | 1322.65i | −0.566754 | − | 1.37062i | ||||
\(966\) | 92.5483 | − | 19.4154i | 0.0958057 | − | 0.0200988i | ||||
\(967\) | 1190.89 | + | 1190.89i | 1.23153 | + | 1.23153i | 0.963374 | + | 0.268161i | \(0.0864158\pi\) |
0.268161 | + | 0.963374i | \(0.413584\pi\) | |||||||
\(968\) | −241.972 | − | 241.972i | −0.249972 | − | 0.249972i | ||||
\(969\) | 201.406 | − | 1737.24i | 0.207849 | − | 1.79282i | ||||
\(970\) | 145.870 | + | 60.5250i | 0.150381 | + | 0.0623969i | ||||
\(971\) | −714.474 | −0.735812 | −0.367906 | − | 0.929863i | \(-0.619925\pi\) | ||||
−0.367906 | + | 0.929863i | \(0.619925\pi\) | |||||||
\(972\) | −475.494 | + | 100.504i | −0.489192 | + | 0.103400i | ||||
\(973\) | −204.702 | + | 409.873i | −0.210383 | + | 0.421247i | ||||
\(974\) | −8.61669 | −0.00884670 | ||||||||
\(975\) | 809.094 | − | 639.384i | 0.829840 | − | 0.655779i | ||||
\(976\) | 139.256i | 0.142681i | ||||||||
\(977\) | 382.167 | − | 382.167i | 0.391164 | − | 0.391164i | −0.483938 | − | 0.875102i | \(-0.660794\pi\) |
0.875102 | + | 0.483938i | \(0.160794\pi\) | |||||||
\(978\) | −160.782 | + | 127.375i | −0.164399 | + | 0.130240i | ||||
\(979\) | −15.2163 | −0.0155427 | ||||||||
\(980\) | −121.755 | − | 474.632i | −0.124239 | − | 0.484319i | ||||
\(981\) | 836.474 | + | 196.595i | 0.852674 | + | 0.200402i | ||||
\(982\) | −85.1811 | − | 85.1811i | −0.0867425 | − | 0.0867425i | ||||
\(983\) | 752.154 | − | 752.154i | 0.765162 | − | 0.765162i | −0.212089 | − | 0.977250i | \(-0.568027\pi\) |
0.977250 | + | 0.212089i | \(0.0680265\pi\) | |||||||
\(984\) | 13.1877 | − | 113.752i | 0.0134022 | − | 0.115601i | ||||
\(985\) | 493.490 | + | 1193.44i | 0.501005 | + | 1.21161i | ||||
\(986\) | −1277.93 | −1.29607 | ||||||||
\(987\) | 740.466 | + | 483.660i | 0.750219 | + | 0.490031i | ||||
\(988\) | 577.945 | − | 577.945i | 0.584965 | − | 0.584965i | ||||
\(989\) | −166.050 | −0.167897 | ||||||||
\(990\) | 1.19968 | + | 7.37508i | 0.00121180 | + | 0.00744957i | ||||
\(991\) | −438.406 | −0.442387 | −0.221194 | − | 0.975230i | \(-0.570995\pi\) | ||||
−0.221194 | + | 0.975230i | \(0.570995\pi\) | |||||||
\(992\) | 6.03782 | + | 6.03782i | 0.00608652 | + | 0.00608652i | ||||
\(993\) | −944.327 | − | 1192.00i | −0.950984 | − | 1.20040i | ||||
\(994\) | 729.135 | − | 243.415i | 0.733537 | − | 0.244885i | ||||
\(995\) | 472.257 | − | 1138.18i | 0.474630 | − | 1.14390i | ||||
\(996\) | −96.8035 | + | 834.985i | −0.0971923 | + | 0.838338i | ||||
\(997\) | −1045.99 | + | 1045.99i | −1.04914 | + | 1.04914i | −0.0504122 | + | 0.998728i | \(0.516054\pi\) |
−0.998728 | + | 0.0504122i | \(0.983946\pi\) | |||||||
\(998\) | 352.315 | + | 352.315i | 0.353021 | + | 0.353021i | ||||
\(999\) | −191.301 | − | 69.0200i | −0.191492 | − | 0.0690891i |
(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 | 210.3.k.b.167.11 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.a.167.14 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.a.83.3 | ✓ | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.b.167.6 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.b.83.6 | yes | 32 | |
21.20 | even | 2 | 210.3.k.a.167.3 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.a.83.14 | yes | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.b.83.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.3 | ✓ | 32 | 5.3 | odd | 4 | ||
210.3.k.a.83.14 | yes | 32 | 35.13 | even | 4 | ||
210.3.k.a.167.3 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.a.167.14 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.83.6 | yes | 32 | 15.8 | even | 4 | inner | |
210.3.k.b.83.11 | yes | 32 | 105.83 | odd | 4 | inner | |
210.3.k.b.167.6 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.b.167.11 | yes | 32 | 1.1 | even | 1 | trivial |