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 | 167.14 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.a.83.14 |
$q$-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 | ||||
\(3\) | 2.35150 | + | 1.86291i | 0.783835 | + | 0.620970i | ||||
\(4\) | − | 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 | \(0.00169879\pi\) | ||||
−0.999986 | + | 0.00533688i | \(0.998301\pi\) | |||||||
\(12\) | 3.72582 | − | 4.70301i | 0.310485 | − | 0.391917i | ||||
\(13\) | 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 | ||||
\(15\) | 13.1093 | − | 7.29006i | 0.873957 | − | 0.486004i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 13.8691 | + | 13.8691i | 0.815828 | + | 0.815828i | 0.985500 | − | 0.169673i | \(-0.0542710\pi\) |
−0.169673 | + | 0.985500i | \(0.554271\pi\) | |||||||
\(18\) | −10.8204 | − | 6.70213i | −0.601134 | − | 0.372341i | ||||
\(19\) | 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 | ||||
\(21\) | −19.0210 | + | 8.89961i | −0.905760 | + | 0.423791i | ||||
\(22\) | −0.117411 | − | 0.117411i | −0.00533688 | − | 0.00533688i | ||||
\(23\) | 2.25150 | + | 2.25150i | 0.0978912 | + | 0.0978912i | 0.754356 | − | 0.656465i | \(-0.227949\pi\) |
−0.656465 | + | 0.754356i | \(0.727949\pi\) | |||||||
\(24\) | 0.977191 | + | 8.42883i | 0.0407163 | + | 0.351201i | ||||
\(25\) | −17.6562 | − | 17.6991i | −0.706248 | − | 0.707964i | ||||
\(26\) | −19.4452 | −0.747890 | ||||||||
\(27\) | −11.4794 | + | 24.4382i | −0.425162 | + | 0.905117i | ||||
\(28\) | 12.5248 | + | 6.25527i | 0.447316 | + | 0.223402i | ||||
\(29\) | −46.0711 | −1.58866 | −0.794329 | − | 0.607488i | \(-0.792177\pi\) | ||||
−0.794329 | + | 0.607488i | \(0.792177\pi\) | |||||||
\(30\) | −5.81929 | + | 20.3994i | −0.193976 | + | 0.679980i | ||||
\(31\) | − | 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 | ||||
\(33\) | −0.218727 | + | 0.276093i | −0.00662808 | + | 0.00836646i | ||||
\(34\) | −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 | \(-0.552627\pi\) | ||||
−0.164580 | + | 0.986364i | \(0.552627\pi\) | |||||||
\(42\) | 10.1213 | − | 27.9206i | 0.240984 | − | 0.664776i | ||||
\(43\) | 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 | ||||||||
\(45\) | 44.4074 | + | 7.27891i | 0.986831 | + | 0.161754i | ||||
\(46\) | −4.50300 | −0.0978912 | ||||||||
\(47\) | 29.7803 | + | 29.7803i | 0.633624 | + | 0.633624i | 0.948975 | − | 0.315351i | \(-0.102122\pi\) |
−0.315351 | + | 0.948975i | \(0.602122\pi\) | |||||||
\(48\) | −9.40602 | − | 7.45163i | −0.195959 | − | 0.155242i | ||||
\(49\) | −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 | \(-0.955867\pi\) |
−0.138204 | − | 0.990404i | \(-0.544133\pi\) | |||||||
\(54\) | −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 | ||||
\(57\) | 69.8910 | + | 55.3690i | 1.22616 | + | 0.971387i | ||||
\(58\) | 46.0711 | − | 46.0711i | 0.794329 | − | 0.794329i | ||||
\(59\) | − | 84.9209i | − | 1.43934i | −0.694317 | − | 0.719669i | \(-0.744294\pi\) | ||
0.694317 | − | 0.719669i | \(-0.255706\pi\) | |||||||
\(60\) | −14.5801 | − | 26.2187i | −0.243002 | − | 0.436978i | ||||
\(61\) | − | 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 | ||||
\(63\) | −61.3070 | − | 14.5068i | −0.973127 | − | 0.230267i | ||||
\(64\) | 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 | \(0.184165\pi\) | ||||
−0.837244 | + | 0.546829i | \(0.815835\pi\) | |||||||
\(72\) | −13.4043 | + | 21.6408i | −0.186170 | + | 0.300567i | ||||
\(73\) | −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 | ||||||||
\(75\) | −8.54683 | − | 74.5114i | −0.113958 | − | 0.993486i | ||||
\(76\) | − | 59.4436i | − | 0.782153i | ||||||
\(77\) | −0.735279 | − | 0.367220i | −0.00954908 | − | 0.00476909i | ||||
\(78\) | −45.7254 | − | 36.2245i | −0.586223 | − | 0.464417i | ||||
\(79\) | − | 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 | \(-0.430222\pi\) |
0.976069 | − | 0.217461i | \(-0.0697776\pi\) | |||||||
\(84\) | 17.7992 | + | 38.0419i | 0.211896 | + | 0.452880i | ||||
\(85\) | 90.6268 | − | 37.4745i | 1.06620 | − | 0.440876i | ||||
\(86\) | 73.7509i | 0.857568i | ||||||||
\(87\) | −108.336 | − | 85.8262i | −1.24525 | − | 0.986508i | ||||
\(88\) | −0.234823 | + | 0.234823i | −0.00266844 | + | 0.00266844i | ||||
\(89\) | 129.599i | 1.45616i | 0.685490 | + | 0.728082i | \(0.259588\pi\) | ||||
−0.685490 | + | 0.728082i | \(0.740412\pi\) | |||||||
\(90\) | −51.6863 | + | 37.1285i | −0.574292 | + | 0.412539i | ||||
\(91\) | −91.2955 | + | 30.4782i | −1.00325 | + | 0.334925i | ||||
\(92\) | 4.50300 | − | 4.50300i | 0.0489456 | − | 0.0489456i | ||||
\(93\) | 2.81198 | − | 3.54949i | 0.0302363 | − | 0.0381666i | ||||
\(94\) | −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 | \(-0.522794\pi\) | ||||
−0.0715470 | + | 0.997437i | \(0.522794\pi\) | |||||||
\(102\) | −65.2264 | − | 51.6736i | −0.639474 | − | 0.506604i | ||||
\(103\) | 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 | ||||||||
\(105\) | 4.65218 | + | 104.897i | 0.0443065 | + | 0.999018i | ||||
\(106\) | 119.632 | 1.12861 | ||||||||
\(107\) | 105.856 | − | 105.856i | 0.989310 | − | 0.989310i | −0.0106339 | − | 0.999943i | \(-0.503385\pi\) |
0.999943 | + | 0.0106339i | \(0.00338493\pi\) | |||||||
\(108\) | 48.8763 | + | 22.9587i | 0.452559 | + | 0.212581i | ||||
\(109\) | − | 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 | 0.389104 | − | 0.921194i | \(-0.372785\pi\) |
−0.921194 | + | 0.389104i | \(0.872785\pi\) | |||||||
\(114\) | −125.260 | + | 14.5219i | −1.09877 | + | 0.127386i | ||||
\(115\) | 14.7123 | − | 6.08359i | 0.127933 | − | 0.0529007i | ||||
\(116\) | 92.1422i | 0.794329i | ||||||||
\(117\) | −65.1620 | + | 105.202i | −0.556940 | + | 0.899165i | ||||
\(118\) | 84.9209 | + | 84.9209i | 0.719669 | + | 0.719669i | ||||
\(119\) | −130.231 | + | 43.4766i | −1.09438 | + | 0.365350i | ||||
\(120\) | 40.7988 | + | 11.6386i | 0.339990 | + | 0.0969882i | ||||
\(121\) | 120.986 | 0.999886 | ||||||||
\(122\) | 34.8141 | + | 34.8141i | 0.285361 | + | 0.285361i | ||||
\(123\) | −31.7349 | − | 25.1410i | −0.258007 | − | 0.204398i | ||||
\(124\) | −3.01891 | −0.0243461 | ||||||||
\(125\) | −115.572 | + | 47.6252i | −0.924575 | + | 0.381001i | ||||
\(126\) | 75.8139 | − | 46.8002i | 0.601697 | − | 0.371430i | ||||
\(127\) | 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 | \(-0.687838\pi\) | ||||
−0.556453 | + | 0.830879i | \(0.687838\pi\) | |||||||
\(132\) | 0.552187 | + | 0.437453i | 0.00418323 | + | 0.00331404i | ||||
\(133\) | −92.9590 | + | 186.131i | −0.698940 | + | 1.39948i | ||||
\(134\) | 68.9784 | 0.514764 | ||||||||
\(135\) | 90.8642 | + | 99.8433i | 0.673068 | + | 0.739580i | ||||
\(136\) | 55.4763i | 0.407914i | ||||||||
\(137\) | −37.8019 | + | 37.8019i | −0.275926 | + | 0.275926i | −0.831480 | − | 0.555554i | \(-0.812506\pi\) |
0.555554 | + | 0.831480i | \(0.312506\pi\) | |||||||
\(138\) | −10.5888 | − | 8.38867i | −0.0767305 | − | 0.0607875i | ||||
\(139\) | 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 | ||||||||
\(147\) | 3.75748 | − | 146.952i | 0.0255611 | − | 0.999673i | ||||
\(148\) | 10.6522 | − | 10.6522i | 0.0719745 | − | 0.0719745i | ||||
\(149\) | −109.296 | −0.733529 | −0.366765 | − | 0.930314i | \(-0.619535\pi\) | ||||
−0.366765 | + | 0.930314i | \(0.619535\pi\) | |||||||
\(150\) | 83.0582 | + | 65.9646i | 0.553722 | + | 0.439764i | ||||
\(151\) | −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 | ||||
\(153\) | −92.9524 | + | 150.069i | −0.607532 | + | 0.980844i | ||||
\(154\) | 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 | ||||
\(162\) | 36.4384 | − | 108.601i | 0.224929 | − | 0.670378i | ||||
\(163\) | −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 | ||||||||
\(165\) | 0.855936 | + | 1.53919i | 0.00518749 | + | 0.00932840i | ||||
\(166\) | 198.126i | 1.19353i | ||||||||
\(167\) | −122.479 | − | 122.479i | −0.733409 | − | 0.733409i | 0.237884 | − | 0.971293i | \(-0.423546\pi\) |
−0.971293 | + | 0.237884i | \(0.923546\pi\) | |||||||
\(168\) | −55.8411 | − | 20.2427i | −0.332388 | − | 0.120492i | ||||
\(169\) | 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 | −0.738516 | − | 0.674236i | \(-0.764473\pi\) |
0.674236 | + | 0.738516i | \(0.264473\pi\) | |||||||
\(174\) | 194.163 | − | 22.5101i | 1.11588 | − | 0.129369i | ||||
\(175\) | 166.061 | − | 55.2143i | 0.948922 | − | 0.315510i | ||||
\(176\) | − | 0.469645i | − | 0.00266844i | ||||||
\(177\) | 158.200 | − | 199.692i | 0.893785 | − | 1.12820i | ||||
\(178\) | −129.599 | − | 129.599i | −0.728082 | − | 0.728082i | ||||
\(179\) | 167.194 | 0.934042 | 0.467021 | − | 0.884246i | \(-0.345327\pi\) | ||||
0.467021 | + | 0.884246i | \(0.345327\pi\) | |||||||
\(180\) | 14.5578 | − | 88.8148i | 0.0808768 | − | 0.493416i | ||||
\(181\) | − | 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 | ||||
\(183\) | 64.8555 | − | 81.8655i | 0.354402 | − | 0.447352i | ||||
\(184\) | 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 | ||||
\(189\) | −117.139 | − | 148.322i | −0.619782 | − | 0.784774i | ||||
\(190\) | 80.3089 | + | 194.216i | 0.422678 | + | 1.02219i | ||||
\(191\) | − | 274.726i | − | 1.43835i | −0.694827 | − | 0.719177i | \(-0.744519\pi\) | ||
0.694827 | − | 0.719177i | \(-0.255481\pi\) | |||||||
\(192\) | −14.9033 | + | 18.8120i | −0.0776212 | + | 0.0979793i | ||||
\(193\) | −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 | ||||||||
\(195\) | 198.335 | + | 56.5785i | 1.01710 | + | 0.290146i | ||||
\(196\) | −78.3462 | + | 58.8716i | −0.399726 | + | 0.300365i | ||||
\(197\) | −182.638 | + | 182.638i | −0.927095 | + | 0.927095i | −0.997517 | − | 0.0704222i | \(-0.977565\pi\) |
0.0704222 | + | 0.997517i | \(0.477565\pi\) | |||||||
\(198\) | 0.786906 | − | 1.27044i | 0.00397427 | − | 0.00641636i | ||||
\(199\) | −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 | ||||||||
\(207\) | −15.0898 | + | 24.3622i | −0.0728978 | + | 0.117692i | ||||
\(208\) | −38.8903 | − | 38.8903i | −0.186973 | − | 0.186973i | ||||
\(209\) | 3.48968i | 0.0166970i | ||||||||
\(210\) | −109.549 | − | 100.245i | −0.521662 | − | 0.477356i | ||||
\(211\) | 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 | ||||
\(213\) | −144.654 | + | 182.594i | −0.679129 | + | 0.857248i | ||||
\(214\) | 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 | ||||||||
\(222\) | −25.0487 | − | 19.8441i | −0.112832 | − | 0.0893879i | ||||
\(223\) | −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 | ||||
\(225\) | 118.710 | − | 191.136i | 0.527600 | − | 0.849493i | ||||
\(226\) | 120.252 | 0.532089 | ||||||||
\(227\) | 211.845 | + | 211.845i | 0.933238 | + | 0.933238i | 0.997907 | − | 0.0646692i | \(-0.0205992\pi\) |
−0.0646692 | + | 0.997907i | \(0.520599\pi\) | |||||||
\(228\) | 110.738 | − | 139.782i | 0.485693 | − | 0.613079i | ||||
\(229\) | 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 | ||||
\(231\) | −1.04492 | − | 2.23328i | −0.00452344 | − | 0.00966787i | ||||
\(232\) | −92.1422 | − | 92.1422i | −0.397165 | − | 0.397165i | ||||
\(233\) | 135.649 | + | 135.649i | 0.582186 | + | 0.582186i | 0.935504 | − | 0.353317i | \(-0.114946\pi\) |
−0.353317 | + | 0.935504i | \(0.614946\pi\) | |||||||
\(234\) | −40.0404 | − | 170.364i | −0.171113 | − | 0.728053i | ||||
\(235\) | 194.598 | − | 80.4669i | 0.828077 | − | 0.342413i | ||||
\(236\) | −169.842 | −0.719669 | ||||||||
\(237\) | 1.61271 | − | 2.03568i | 0.00680468 | − | 0.00858938i | ||||
\(238\) | 86.7548 | − | 173.708i | 0.364516 | − | 0.729865i | ||||
\(239\) | 25.1069 | 0.105050 | 0.0525250 | − | 0.998620i | \(-0.483273\pi\) | ||||
0.0525250 | + | 0.998620i | \(0.483273\pi\) | |||||||
\(240\) | −52.4374 | + | 29.1602i | −0.218489 | + | 0.121501i | ||||
\(241\) | − | 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 | ||||
\(243\) | −237.747 | − | 50.2522i | −0.978383 | − | 0.206799i | ||||
\(244\) | −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 | \(-0.361744\pi\) | ||||
0.420817 | + | 0.907146i | \(0.361744\pi\) | |||||||
\(252\) | −29.0137 | + | 122.614i | −0.115134 | + | 0.486564i | ||||
\(253\) | −0.264351 | + | 0.264351i | −0.00104487 | + | 0.00104487i | ||||
\(254\) | −343.720 | −1.35323 | ||||||||
\(255\) | 282.921 | + | 80.7082i | 1.10949 | + | 0.316503i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 330.432 | + | 330.432i | 1.28573 | + | 1.28573i | 0.937357 | + | 0.348371i | \(0.113265\pi\) |
0.348371 | + | 0.937357i | \(0.386735\pi\) | |||||||
\(258\) | −137.391 | + | 173.425i | −0.532524 | + | 0.672192i | ||||
\(259\) | −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 | 0.834170 | − | 0.551508i | \(-0.185947\pi\) |
−0.551508 | + | 0.834170i | \(0.685947\pi\) | |||||||
\(264\) | −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 | ||||
\(267\) | −241.430 | + | 304.751i | −0.904233 | + | 1.14139i | ||||
\(268\) | −68.9784 | + | 68.9784i | −0.257382 | + | 0.257382i | ||||
\(269\) | 250.571i | 0.931490i | 0.884919 | + | 0.465745i | \(0.154214\pi\) | ||||
−0.884919 | + | 0.465745i | \(0.845786\pi\) | |||||||
\(270\) | −190.708 | − | 8.97908i | −0.706324 | − | 0.0332559i | ||||
\(271\) | − | 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 | ||||
\(273\) | −271.460 | − | 98.4056i | −0.994359 | − | 0.360460i | ||||
\(274\) | − | 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 | \(-0.783626\pi\) | ||
0.777723 | − | 0.628607i | \(-0.216374\pi\) | |||||||
\(282\) | −140.057 | − | 110.956i | −0.496656 | − | 0.393461i | ||||
\(283\) | −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 | ||||||||
\(285\) | 389.634 | − | 216.674i | 1.36714 | − | 0.760259i | ||||
\(286\) | − | 2.28308i | − | 0.00798280i | ||||||
\(287\) | 42.2092 | − | 84.5149i | 0.147070 | − | 0.294477i | ||||
\(288\) | 43.2817 | + | 26.8085i | 0.150284 | + | 0.0930852i | ||||
\(289\) | 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 | −0.572712 | − | 0.819757i | \(-0.694108\pi\) |
0.819757 | + | 0.572712i | \(0.194108\pi\) | |||||||
\(294\) | 143.194 | + | 150.709i | 0.487056 | + | 0.512617i | ||||
\(295\) | −392.185 | − | 162.727i | −1.32944 | − | 0.551617i | ||||
\(296\) | 21.3044i | 0.0719745i | ||||||||
\(297\) | −2.86932 | − | 1.34781i | −0.00966101 | − | 0.00453808i | ||||
\(298\) | 109.296 | − | 109.296i | 0.366765 | − | 0.366765i | ||||
\(299\) | 43.7807i | 0.146424i | ||||||||
\(300\) | −149.023 | + | 17.0937i | −0.496743 | + | 0.0569789i | ||||
\(301\) | 115.597 | + | 346.262i | 0.384042 | + | 1.15037i | ||||
\(302\) | 223.334 | − | 223.334i | 0.739516 | − | 0.739516i | ||||
\(303\) | −33.9851 | − | 26.9237i | −0.112162 | − | 0.0888571i | ||||
\(304\) | −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 | \(-0.642487\pi\) | ||||
−0.432835 | + | 0.901473i | \(0.642487\pi\) | |||||||
\(312\) | −72.4491 | + | 91.4507i | −0.232209 | + | 0.293111i | ||||
\(313\) | 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 | ||||||||
\(315\) | −184.474 | + | 255.332i | −0.585631 | + | 0.810578i | ||||
\(316\) | −1.73139 | −0.00547908 | ||||||||
\(317\) | −74.8122 | + | 74.8122i | −0.236001 | + | 0.236001i | −0.815192 | − | 0.579191i | \(-0.803368\pi\) |
0.579191 | + | 0.815192i | \(0.303368\pi\) | |||||||
\(318\) | 281.316 | + | 222.864i | 0.884642 | + | 0.700831i | ||||
\(319\) | − | 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 | ||||||
\(327\) | 177.859 | − | 224.507i | 0.543912 | − | 0.686567i | ||||
\(328\) | −26.9911 | − | 26.9911i | −0.0822900 | − | 0.0822900i | ||||
\(329\) | −279.639 | + | 93.3550i | −0.849966 | + | 0.283754i | ||||
\(330\) | −2.39512 | − | 0.683251i | −0.00725795 | − | 0.00207046i | ||||
\(331\) | −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 | ||||
\(333\) | −35.6963 | + | 57.6307i | −0.107196 | + | 0.173065i | ||||
\(334\) | 244.959 | 0.733409 | ||||||||
\(335\) | −225.368 | + | 93.1904i | −0.672741 | + | 0.278180i | ||||
\(336\) | 76.0838 | − | 35.5984i | 0.226440 | − | 0.105948i | ||||
\(337\) | −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 | ||||||||
\(342\) | −321.603 | − | 199.200i | −0.940358 | − | 0.582455i | ||||
\(343\) | 337.383 | − | 61.8203i | 0.983624 | − | 0.180234i | ||||
\(344\) | 147.502 | 0.428784 | ||||||||
\(345\) | 45.9292 | + | 13.1021i | 0.133128 | + | 0.0379772i | ||||
\(346\) | − | 22.2409i | − | 0.0642800i | ||||||
\(347\) | −152.796 | + | 152.796i | −0.440334 | + | 0.440334i | −0.892124 | − | 0.451790i | \(-0.850786\pi\) |
0.451790 | + | 0.892124i | \(0.350786\pi\) | |||||||
\(348\) | −171.652 | + | 216.673i | −0.493254 | + | 0.622623i | ||||
\(349\) | 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 | −0.269695 | − | 0.962946i | \(-0.586923\pi\) |
0.962946 | + | 0.269695i | \(0.0869228\pi\) | |||||||
\(354\) | 41.4920 | + | 357.892i | 0.117209 | + | 1.01099i | ||||
\(355\) | 358.605 | + | 148.794i | 1.01015 | + | 0.419138i | ||||
\(356\) | 259.197 | 0.728082 | ||||||||
\(357\) | −387.232 | − | 140.374i | −1.08468 | − | 0.393204i | ||||
\(358\) | −167.194 | + | 167.194i | −0.467021 | + | 0.467021i | ||||
\(359\) | 599.498 | 1.66991 | 0.834956 | − | 0.550317i | \(-0.185493\pi\) | ||||
0.834956 | + | 0.550317i | \(0.185493\pi\) | |||||||
\(360\) | 74.2570 | + | 103.373i | 0.206269 | + | 0.287146i | ||||
\(361\) | 522.387 | 1.44705 | ||||||||
\(362\) | 271.099 | + | 271.099i | 0.748892 | + | 0.748892i | ||||
\(363\) | 284.500 | + | 225.386i | 0.783745 | + | 0.620899i | ||||
\(364\) | 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 | ||||
\(372\) | −7.09898 | − | 5.62396i | −0.0190833 | − | 0.0151182i | ||||
\(373\) | 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 | ||||||
\(375\) | −360.489 | − | 103.309i | −0.961304 | − | 0.275491i | ||||
\(376\) | 119.121i | 0.316812i | ||||||||
\(377\) | −447.930 | − | 447.930i | −1.18814 | − | 1.18814i | ||||
\(378\) | 265.461 | + | 31.1834i | 0.702278 | + | 0.0824959i | ||||
\(379\) | 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 | −0.980828 | − | 0.194875i | \(-0.937570\pi\) |
0.194875 | + | 0.980828i | \(0.437570\pi\) | |||||||
\(384\) | −3.90876 | − | 33.7153i | −0.0101791 | − | 0.0878003i | ||||
\(385\) | −3.10486 | + | 2.69202i | −0.00806458 | + | 0.00699226i | ||||
\(386\) | − | 404.822i | − | 1.04876i | ||||||
\(387\) | 399.008 | + | 247.144i | 1.03103 | + | 0.638615i | ||||
\(388\) | −31.5856 | − | 31.5856i | −0.0814062 | − | 0.0814062i | ||||
\(389\) | 369.112 | 0.948875 | 0.474438 | − | 0.880289i | \(-0.342651\pi\) | ||||
0.474438 | + | 0.880289i | \(0.342651\pi\) | |||||||
\(390\) | −254.913 | + | 141.756i | −0.653624 | + | 0.363478i | ||||
\(391\) | 62.4524i | 0.159725i | ||||||||
\(392\) | 19.4746 | − | 137.218i | 0.0496801 | − | 0.350046i | ||||
\(393\) | −342.828 | − | 271.595i | −0.872335 | − | 0.691081i | ||||
\(394\) | − | 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 | ||||
\(399\) | −565.338 | + | 264.513i | −1.41689 | + | 0.662939i | ||||
\(400\) | 70.6248 | + | 70.7964i | 0.176562 | + | 0.176991i | ||||
\(401\) | − | 17.1182i | − | 0.0426889i | −0.999772 | − | 0.0213444i | \(-0.993205\pi\) | ||
0.999772 | − | 0.0213444i | \(-0.00679466\pi\) | |||||||
\(402\) | 162.203 | + | 128.500i | 0.403490 | + | 0.319653i | ||||
\(403\) | 14.6758 | − | 14.6758i | 0.0364164 | − | 0.0364164i | ||||
\(404\) | 28.9050i | 0.0715470i | ||||||||
\(405\) | 27.6687 | + | 404.054i | 0.0683177 | + | 0.997664i | ||||
\(406\) | 144.423 | + | 432.610i | 0.355722 | + | 1.06554i | ||||
\(407\) | −0.625346 | + | 0.625346i | −0.00153648 | + | 0.00153648i | ||||
\(408\) | −103.347 | + | 130.453i | −0.253302 | + | 0.319737i | ||||
\(409\) | 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 | ||||||||
\(417\) | 153.905 | + | 121.927i | 0.369077 | + | 0.292390i | ||||
\(418\) | −3.48968 | − | 3.48968i | −0.00834852 | − | 0.00834852i | ||||
\(419\) | 606.909i | 1.44847i | 0.689553 | + | 0.724235i | \(0.257807\pi\) | ||||
−0.689553 | + | 0.724235i | \(0.742193\pi\) | |||||||
\(420\) | 209.794 | − | 9.30436i | 0.499509 | − | 0.0221532i | ||||
\(421\) | −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 | ||||
\(423\) | −199.592 | + | 322.236i | −0.471848 | + | 0.761786i | ||||
\(424\) | − | 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 | \(-0.822700\pi\) | ||
0.848843 | − | 0.528645i | \(-0.177300\pi\) | |||||||
\(432\) | 45.9175 | − | 97.7527i | 0.106290 | − | 0.226279i | ||||
\(433\) | 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 | ||||
\(435\) | −603.962 | + | 335.861i | −1.38842 | + | 0.772094i | ||||
\(436\) | −190.948 | −0.437954 | ||||||||
\(437\) | 66.9186 | + | 66.9186i | 0.153132 | + | 0.153132i | ||||
\(438\) | 194.356 | + | 153.973i | 0.443735 | + | 0.351536i | ||||
\(439\) | 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 | ||||
\(441\) | 282.594 | − | 338.558i | 0.640802 | − | 0.767706i | ||||
\(442\) | −269.686 | − | 269.686i | −0.610150 | − | 0.610150i | ||||
\(443\) | 125.233 | + | 125.233i | 0.282693 | + | 0.282693i | 0.834182 | − | 0.551489i | \(-0.185940\pi\) |
−0.551489 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(444\) | 44.8929 | − | 5.20463i | 0.101110 | − | 0.0117221i | ||||
\(445\) | 598.517 | + | 248.339i | 1.34498 | + | 0.558066i | ||||
\(446\) | 89.7899 | 0.201323 | ||||||||
\(447\) | −257.010 | − | 203.608i | −0.574966 | − | 0.455499i | ||||
\(448\) | −50.0994 | − | 25.0211i | −0.111829 | − | 0.0558506i | ||||
\(449\) | −324.260 | −0.722184 | −0.361092 | − | 0.932530i | \(-0.617596\pi\) | ||||
−0.361092 | + | 0.932530i | \(0.617596\pi\) | |||||||
\(450\) | 72.4258 | + | 309.846i | 0.160946 | + | 0.688547i | ||||
\(451\) | − | 1.58453i | − | 0.00351337i | ||||||
\(452\) | −120.252 | + | 120.252i | −0.266045 | + | 0.266045i | ||||
\(453\) | −525.170 | − | 416.050i | −1.15932 | − | 0.918434i | ||||
\(454\) | −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 | \(-0.675948\pi\) | ||||
−0.525037 | + | 0.851080i | \(0.675948\pi\) | |||||||
\(462\) | 3.27819 | + | 1.18836i | 0.00709565 | + | 0.00257221i | ||||
\(463\) | 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 | ||||||||
\(465\) | −11.0040 | − | 19.7880i | −0.0236646 | − | 0.0425548i | ||||
\(466\) | −271.299 | −0.582186 | ||||||||
\(467\) | 302.621 | + | 302.621i | 0.648011 | + | 0.648011i | 0.952512 | − | 0.304501i | \(-0.0984897\pi\) |
−0.304501 | + | 0.952512i | \(0.598490\pi\) | |||||||
\(468\) | 210.405 | + | 130.324i | 0.449583 | + | 0.278470i | ||||
\(469\) | 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 | ||||
\(477\) | 400.896 | − | 647.236i | 0.840453 | − | 1.35689i | ||||
\(478\) | −25.1069 | + | 25.1069i | −0.0525250 | + | 0.0525250i | ||||
\(479\) | 444.701i | 0.928395i | 0.885732 | + | 0.464198i | \(0.153657\pi\) | ||||
−0.885732 | + | 0.464198i | \(0.846343\pi\) | |||||||
\(480\) | 23.2772 | − | 81.5976i | 0.0484941 | − | 0.169995i | ||||
\(481\) | 103.567i | 0.215316i | ||||||||
\(482\) | 278.949 | + | 278.949i | 0.578733 | + | 0.578733i | ||||
\(483\) | −62.8631 | − | 22.7882i | −0.130151 | − | 0.0471805i | ||||
\(484\) | − | 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 | \(0.0276457\pi\) | ||||
−0.996231 | + | 0.0867425i | \(0.972354\pi\) | |||||||
\(492\) | −50.2820 | + | 63.4697i | −0.102199 | + | 0.129004i | ||||
\(493\) | −638.963 | − | 638.963i | −1.29607 | − | 1.29607i | ||||
\(494\) | −577.945 | −1.16993 | ||||||||
\(495\) | −0.854627 | + | 5.21393i | −0.00172652 | + | 0.0105332i | ||||
\(496\) | 6.03782i | 0.0121730i | ||||||||
\(497\) | −486.275 | − | 242.860i | −0.978421 | − | 0.488652i | ||||
\(498\) | −369.091 | + | 465.894i | −0.741146 | + | 0.935530i | ||||
\(499\) | 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 | −0.589308 | − | 0.807908i | \(-0.700600\pi\) |
0.807908 | + | 0.589308i | \(0.200600\pi\) | |||||||
\(504\) | −93.6004 | − | 151.628i | −0.185715 | − | 0.300849i | ||||
\(505\) | −27.6942 | + | 66.7451i | −0.0548399 | + | 0.132168i | ||||
\(506\) | − | 0.528703i | − | 0.00104487i | ||||||
\(507\) | −37.3643 | + | 47.1641i | −0.0736969 | + | 0.0930257i | ||||
\(508\) | 343.720 | − | 343.720i | 0.676615 | − | 0.676615i | ||||
\(509\) | − | 930.732i | − | 1.82855i | −0.405094 | − | 0.914275i | \(-0.632761\pi\) | ||
0.405094 | − | 0.914275i | \(-0.367239\pi\) | |||||||
\(510\) | −363.629 | + | 202.213i | −0.712998 | + | 0.396496i | ||||
\(511\) | 388.053 | − | 129.548i | 0.759398 | − | 0.253518i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −341.188 | + | 726.347i | −0.665083 | + | 1.41588i | ||||
\(514\) | −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 | \(-0.493193\pi\) | ||||
0.0213821 | + | 0.999771i | \(0.493193\pi\) | |||||||
\(522\) | 498.508 | + | 308.774i | 0.954997 | + | 0.591522i | ||||
\(523\) | 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 | ||||||||
\(525\) | 493.353 | + | 179.521i | 0.939720 | + | 0.341944i | ||||
\(526\) | −148.680 | −0.282662 | ||||||||
\(527\) | 20.9348 | − | 20.9348i | 0.0397244 | − | 0.0397244i | ||||
\(528\) | 0.874907 | − | 1.10437i | 0.00165702 | − | 0.00209162i | ||||
\(529\) | − | 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 | ||||||
\(537\) | 393.156 | + | 311.466i | 0.732134 | + | 0.580012i | ||||
\(538\) | −250.571 | − | 250.571i | −0.465745 | − | 0.465745i | ||||
\(539\) | 4.59937 | − | 3.45610i | 0.00853315 | − | 0.00641206i | ||||
\(540\) | 199.687 | − | 181.728i | 0.369790 | − | 0.336534i | ||||
\(541\) | 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 | ||||
\(543\) | 505.032 | − | 637.490i | 0.930078 | − | 1.17401i | ||||
\(544\) | 110.953 | 0.203957 | ||||||||
\(545\) | −440.921 | − | 182.949i | −0.809030 | − | 0.335686i | ||||
\(546\) | 369.865 | − | 173.054i | 0.677409 | − | 0.316949i | ||||
\(547\) | −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 | ||||||||
\(552\) | −16.7773 | + | 21.1776i | −0.0303937 | + | 0.0383653i | ||||
\(553\) | 5.42134 | + | 2.70757i | 0.00980351 | + | 0.00489616i | ||||
\(554\) | 129.447 | 0.233658 | ||||||||
\(555\) | 108.650 | + | 30.9942i | 0.195765 | + | 0.0558454i | ||||
\(556\) | − | 130.899i | − | 0.235430i | ||||||
\(557\) | 242.020 | − | 242.020i | 0.434506 | − | 0.434506i | −0.455652 | − | 0.890158i | \(-0.650594\pi\) |
0.890158 | + | 0.455652i | \(0.150594\pi\) | |||||||
\(558\) | −10.1166 | + | 16.3329i | −0.0181301 | + | 0.0292705i | ||||
\(559\) | 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 | −0.689223 | − | 0.724549i | \(-0.742048\pi\) |
0.724549 | + | 0.689223i | \(0.242048\pi\) | |||||||
\(564\) | 251.013 | − | 29.1011i | 0.445059 | − | 0.0515976i | ||||
\(565\) | −392.891 | + | 162.462i | −0.695383 | + | 0.287543i | ||||
\(566\) | 362.180 | 0.639894 | ||||||||
\(567\) | 0.858397 | − | 566.999i | 0.00151393 | − | 0.999999i | ||||
\(568\) | −155.300 | + | 155.300i | −0.273415 | + | 0.273415i | ||||
\(569\) | 147.022 | 0.258387 | 0.129194 | − | 0.991619i | \(-0.458761\pi\) | ||||
0.129194 | + | 0.991619i | \(0.458761\pi\) | |||||||
\(570\) | −172.960 | + | 606.308i | −0.303438 | + | 1.06370i | ||||
\(571\) | 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 | ||||
\(573\) | 511.789 | − | 646.018i | 0.893174 | − | 1.12743i | ||||
\(574\) | 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 | ||||
\(582\) | −58.8411 | + | 74.2737i | −0.101102 | + | 0.127618i | ||||
\(583\) | 7.02310 | − | 7.02310i | 0.0120465 | − | 0.0120465i | ||||
\(584\) | − | 165.304i | − | 0.283054i | ||||||
\(585\) | 360.985 | + | 502.524i | 0.617068 | + | 0.859016i | ||||
\(586\) | 144.769i | 0.247045i | ||||||||
\(587\) | 216.371 | + | 216.371i | 0.368605 | + | 0.368605i | 0.866968 | − | 0.498363i | \(-0.166065\pi\) |
−0.498363 | + | 0.866968i | \(0.666065\pi\) | |||||||
\(588\) | −293.904 | − | 7.51496i | −0.499837 | − | 0.0127805i | ||||
\(589\) | − | 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 | −0.929508 | − | 0.368802i | \(-0.879768\pi\) |
0.368802 | + | 0.929508i | \(0.379768\pi\) | |||||||
\(594\) | 4.21713 | − | 1.52151i | 0.00709954 | − | 0.00256147i | ||||
\(595\) | −48.7667 | + | 684.750i | −0.0819608 | + | 1.15084i | ||||
\(596\) | 218.592i | 0.366765i | ||||||||
\(597\) | −579.534 | − | 459.119i | −0.970744 | − | 0.769043i | ||||
\(598\) | −43.7807 | − | 43.7807i | −0.0732119 | − | 0.0732119i | ||||
\(599\) | −735.946 | −1.22862 | −0.614312 | − | 0.789063i | \(-0.710567\pi\) | ||||
−0.614312 | + | 0.789063i | \(0.710567\pi\) | |||||||
\(600\) | 131.929 | − | 166.116i | 0.219882 | − | 0.276861i | ||||
\(601\) | − | 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 | ||||
\(603\) | 231.151 | − | 373.188i | 0.383335 | − | 0.618885i | ||||
\(604\) | 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 | ||||
\(609\) | 876.316 | − | 410.015i | 1.43894 | − | 0.673259i | ||||
\(610\) | 227.491 | − | 94.0683i | 0.372936 | − | 0.154210i | ||||
\(611\) | 579.083i | 0.947763i | ||||||||
\(612\) | 300.138 | + | 185.905i | 0.490422 | + | 0.303766i | ||||
\(613\) | −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 | ||||||
\(615\) | −176.918 | + | 98.3834i | −0.287672 | + | 0.159973i | ||||
\(616\) | −0.736119 | − | 2.20500i | −0.00119500 | − | 0.00357954i | ||||
\(617\) | −238.684 | + | 238.684i | −0.386845 | + | 0.386845i | −0.873561 | − | 0.486715i | \(-0.838195\pi\) |
0.486715 | + | 0.873561i | \(0.338195\pi\) | |||||||
\(618\) | −147.531 | − | 116.877i | −0.238723 | − | 0.189121i | ||||
\(619\) | 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 | ||||||||
\(627\) | −6.50095 | + | 8.20600i | −0.0103683 | + | 0.0130877i | ||||
\(628\) | −3.34288 | − | 3.34288i | −0.00532305 | − | 0.00532305i | ||||
\(629\) | 147.736i | 0.234875i | ||||||||
\(630\) | −70.8584 | − | 439.806i | −0.112474 | − | 0.698104i | ||||
\(631\) | −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 | ||||
\(633\) | 390.069 | + | 309.021i | 0.616223 | + | 0.488185i | ||||
\(634\) | − | 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 | \(0.275548\pi\) | ||||
−0.648137 | + | 0.761524i | \(0.724452\pi\) | |||||||
\(642\) | −394.401 | + | 497.842i | −0.614331 | + | 0.775455i | ||||
\(643\) | 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 | ||||
\(645\) | 214.589 | − | 752.237i | 0.332696 | − | 1.16626i | ||||
\(646\) | −824.428 | −1.27620 | ||||||||
\(647\) | 122.968 | + | 122.968i | 0.190059 | + | 0.190059i | 0.795722 | − | 0.605663i | \(-0.207092\pi\) |
−0.605663 | + | 0.795722i | \(0.707092\pi\) | |||||||
\(648\) | −217.203 | − | 72.8768i | −0.335189 | − | 0.112464i | ||||
\(649\) | 9.97068 | 0.0153631 | ||||||||
\(650\) | 343.328 | + | 344.162i | 0.528196 | + | 0.529480i | ||||
\(651\) | 13.4336 | + | 28.7113i | 0.0206353 | + | 0.0441034i | ||||
\(652\) | 68.3743 | + | 68.3743i | 0.104869 | + | 0.104869i | ||||
\(653\) | −621.793 | − | 621.793i | −0.952209 | − | 0.952209i | 0.0466996 | − | 0.998909i | \(-0.485130\pi\) |
−0.998909 | + | 0.0466996i | \(0.985130\pi\) | |||||||
\(654\) | 46.6482 | + | 402.367i | 0.0713275 | + | 0.615240i | ||||
\(655\) | −279.367 | + | 673.296i | −0.426515 | + | 1.02793i | ||||
\(656\) | 53.9822 | 0.0822900 | ||||||||
\(657\) | 276.972 | − | 447.164i | 0.421570 | − | 0.680614i | ||||
\(658\) | 186.284 | − | 372.994i | 0.283106 | − | 0.566860i | ||||
\(659\) | 307.522 | 0.466650 | 0.233325 | − | 0.972399i | \(-0.425039\pi\) | ||||
0.233325 | + | 0.972399i | \(0.425039\pi\) | |||||||
\(660\) | 3.07837 | − | 1.71187i | 0.00466420 | − | 0.00259375i | ||||
\(661\) | 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 | ||||
\(663\) | −502.401 | + | 634.168i | −0.757769 | + | 0.956513i | ||||
\(664\) | 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 | ||||||||
\(672\) | −40.4854 | + | 111.682i | −0.0602461 | + | 0.166194i | ||||
\(673\) | −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 | ||||||||
\(675\) | 635.216 | − | 228.311i | 0.941061 | − | 0.338238i | ||||
\(676\) | 40.1139 | 0.0593402 | ||||||||
\(677\) | 679.334 | + | 679.334i | 1.00345 | + | 1.00345i | 0.999994 | + | 0.00345318i | \(0.00109918\pi\) |
0.00345318 | + | 0.999994i | \(0.498901\pi\) | |||||||
\(678\) | 282.773 | + | 224.019i | 0.417070 | + | 0.330411i | ||||
\(679\) | 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 | \(-0.935028\pi\) |
−0.202700 | − | 0.979241i | \(-0.564972\pi\) | |||||||
\(684\) | 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 | ||||
\(687\) | 24.0862 | + | 19.0815i | 0.0350599 | + | 0.0277752i | ||||
\(688\) | −147.502 | + | 147.502i | −0.214392 | + | 0.214392i | ||||
\(689\) | − | 1163.14i | − | 1.68815i | ||||||
\(690\) | −59.0314 | + | 32.8271i | −0.0855527 | + | 0.0475755i | ||||
\(691\) | 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 | ||||
\(693\) | 1.70327 | − | 7.19814i | 0.00245782 | − | 0.0103869i | ||||
\(694\) | − | 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 | \(-0.809063\pi\) | ||
0.825422 | − | 0.564516i | \(-0.190937\pi\) | |||||||
\(702\) | 223.218 | − | 475.204i | 0.317974 | − | 0.676929i | ||||
\(703\) | 158.302 | + | 158.302i | 0.225180 | + | 0.225180i | ||||
\(704\) | −0.939291 | −0.00133422 | ||||||||
\(705\) | 607.501 | + | 173.300i | 0.861704 | + | 0.245816i | ||||
\(706\) | 489.435i | 0.693251i | ||||||||
\(707\) | 45.2021 | − | 90.5076i | 0.0639351 | − | 0.128016i | ||||
\(708\) | −399.384 | − | 316.400i | −0.564102 | − | 0.446893i | ||||
\(709\) | − | 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 | ||||
\(714\) | 527.606 | − | 246.859i | 0.738944 | − | 0.345741i | ||||
\(715\) | 3.08446 | + | 7.45935i | 0.00431393 | + | 0.0104327i | ||||
\(716\) | − | 334.387i | − | 0.467021i | ||||||
\(717\) | 59.0391 | + | 46.7719i | 0.0823418 | + | 0.0652328i | ||||
\(718\) | −599.498 | + | 599.498i | −0.834956 | + | 0.834956i | ||||
\(719\) | − | 364.303i | − | 0.506680i | −0.967377 | − | 0.253340i | \(-0.918471\pi\) | ||
0.967377 | − | 0.253340i | \(-0.0815291\pi\) | |||||||
\(720\) | −177.630 | − | 29.1157i | −0.246708 | − | 0.0404384i | ||||
\(721\) | −294.560 | + | 98.3364i | −0.408544 | + | 0.136389i | ||||
\(722\) | −522.387 | + | 522.387i | −0.723527 | + | 0.723527i | ||||
\(723\) | 519.657 | − | 655.950i | 0.718751 | − | 0.907261i | ||||
\(724\) | −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 | ||||||||
\(732\) | −163.731 | − | 129.711i | −0.223676 | − | 0.177201i | ||||
\(733\) | 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 | ||||||
\(735\) | −671.459 | − | 298.945i | −0.913549 | − | 0.406728i | ||||
\(736\) | 18.0120 | 0.0244728 | ||||||||
\(737\) | 4.04942 | − | 4.04942i | 0.00549447 | − | 0.00549447i | ||||
\(738\) | 146.028 | + | 90.4490i | 0.197869 | + | 0.122560i | ||||
\(739\) | 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 | \(0.0167871\pi\) |
0.0527138 | + | 0.998610i | \(0.483213\pi\) | |||||||
\(744\) | 12.7229 | − | 1.47503i | 0.0171007 | − | 0.00198256i | ||||
\(745\) | −209.435 | + | 504.754i | −0.281121 | + | 0.677522i | ||||
\(746\) | 456.732i | 0.612241i | ||||||||
\(747\) | 1071.90 | + | 663.933i | 1.43494 | + | 0.888800i | ||||
\(748\) | 3.25677 | + | 3.25677i | 0.00435398 | + | 0.00435398i | ||||
\(749\) | 331.836 | + | 993.995i | 0.443039 | + | 1.32710i | ||||
\(750\) | 463.798 | − | 257.180i | 0.618397 | − | 0.342907i | ||||
\(751\) | −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 | ||||
\(753\) | 496.755 | + | 393.539i | 0.659701 | + | 0.522629i | ||||
\(754\) | 895.859 | 1.18814 | ||||||||
\(755\) | −427.957 | + | 1031.41i | −0.566830 | + | 1.36610i | ||||
\(756\) | −296.645 | + | 234.278i | −0.392387 | + | 0.309891i | ||||
\(757\) | 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 | \(-0.567158\pi\) | ||||
−0.209420 | + | 0.977826i | \(0.567158\pi\) | |||||||
\(762\) | −808.260 | − | 640.320i | −1.06071 | − | 0.840314i | ||||
\(763\) | 597.898 | + | 298.608i | 0.783615 | + | 0.391360i | ||||
\(764\) | −549.451 | −0.719177 | ||||||||
\(765\) | 514.938 | + | 716.841i | 0.673121 | + | 0.937048i | ||||
\(766\) | − | 602.040i | − | 0.785953i | ||||||
\(767\) | 825.650 | − | 825.650i | 1.07647 | − | 1.07647i | ||||
\(768\) | 37.6241 | + | 29.8065i | 0.0489897 | + | 0.0388106i | ||||
\(769\) | −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 | −0.509729 | − | 0.860335i | \(-0.670254\pi\) |
0.860335 | + | 0.509729i | \(0.170254\pi\) | |||||||
\(774\) | −646.151 | + | 151.864i | −0.834821 | + | 0.196206i | ||||
\(775\) | −26.7160 | + | 26.6513i | −0.0344723 | + | 0.0343887i | ||||
\(776\) | 63.1712 | 0.0814062 | ||||||||
\(777\) | −148.708 | − | 53.9074i | −0.191387 | − | 0.0693789i | ||||
\(778\) | −369.112 | + | 369.112i | −0.474438 | + | 0.474438i | ||||
\(779\) | −401.113 | −0.514907 | ||||||||
\(780\) | 113.157 | − | 396.670i | 0.145073 | − | 0.508551i | ||||
\(781\) | −9.11696 | −0.0116734 | ||||||||
\(782\) | −62.4524 | − | 62.4524i | −0.0798624 | − | 0.0798624i | ||||
\(783\) | 528.867 | − | 1125.89i | 0.675437 | − | 1.43792i | ||||
\(784\) | 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 | ||||
\(792\) | −2.54088 | − | 1.57381i | −0.00320818 | − | 0.00198714i | ||||
\(793\) | 338.483 | − | 338.483i | 0.426838 | − | 0.426838i | ||||
\(794\) | − | 26.0485i | − | 0.0328066i | ||||||
\(795\) | −1220.22 | − | 348.088i | −1.53486 | − | 0.437846i | ||||
\(796\) | 492.905i | 0.619228i | ||||||||
\(797\) | −887.082 | − | 887.082i | −1.11303 | − | 1.11303i | −0.992739 | − | 0.120287i | \(-0.961619\pi\) |
−0.120287 | − | 0.992739i | \(-0.538381\pi\) | |||||||
\(798\) | 300.825 | − | 829.850i | 0.376974 | − | 1.03991i | ||||
\(799\) | 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 | ||||||||
\(807\) | −466.791 | + | 589.218i | −0.578427 | + | 0.730134i | ||||
\(808\) | −28.9050 | − | 28.9050i | −0.0357735 | − | 0.0357735i | ||||
\(809\) | −1442.13 | −1.78261 | −0.891304 | − | 0.453406i | \(-0.850209\pi\) | ||||
−0.891304 | + | 0.453406i | \(0.850209\pi\) | |||||||
\(810\) | −431.722 | − | 376.385i | −0.532991 | − | 0.464673i | ||||
\(811\) | 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 | ||||
\(813\) | 386.531 | − | 487.908i | 0.475438 | − | 0.600133i | ||||
\(814\) | − | 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 | ||||
\(819\) | −455.018 | − | 737.106i | −0.555578 | − | 0.900007i | ||||
\(820\) | 124.651 | + | 51.7209i | 0.152014 | + | 0.0630743i | ||||
\(821\) | 219.050i | 0.266808i | 0.991062 | + | 0.133404i | \(0.0425908\pi\) | ||||
−0.991062 | + | 0.133404i | \(0.957409\pi\) | |||||||
\(822\) | 140.843 | − | 177.783i | 0.171342 | − | 0.216281i | ||||
\(823\) | 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 | ||||||||
\(825\) | 8.74849 | − | 1.00349i | 0.0106042 | − | 0.00121636i | ||||
\(826\) | −797.412 | + | 266.209i | −0.965390 | + | 0.322287i | ||||
\(827\) | 803.540 | − | 803.540i | 0.971633 | − | 0.971633i | −0.0279759 | − | 0.999609i | \(-0.508906\pi\) |
0.999609 | + | 0.0279759i | \(0.00890618\pi\) | |||||||
\(828\) | 48.7243 | + | 30.1797i | 0.0588458 | + | 0.0364489i | ||||
\(829\) | 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 | ||||||||
\(837\) | 36.8883 | + | 17.3276i | 0.0440721 | + | 0.0207020i | ||||
\(838\) | −606.909 | − | 606.909i | −0.724235 | − | 0.724235i | ||||
\(839\) | − | 933.638i | − | 1.11280i | −0.830915 | − | 0.556399i | \(-0.812183\pi\) | ||
0.830915 | − | 0.556399i | \(-0.187817\pi\) | |||||||
\(840\) | −200.489 | + | 219.098i | −0.238678 | + | 0.260831i | ||||
\(841\) | 1281.55 | 1.52383 | ||||||||
\(842\) | 642.340 | − | 642.340i | 0.762874 | − | 0.762874i | ||||
\(843\) | 658.123 | − | 830.732i | 0.780691 | − | 0.985447i | ||||
\(844\) | − | 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 | ||||||||
\(852\) | 365.187 | + | 289.309i | 0.428624 | + | 0.339564i | ||||
\(853\) | 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 | ||||
\(855\) | 1319.87 | + | 216.343i | 1.54371 | + | 0.253032i | ||||
\(856\) | 423.425 | 0.494655 | ||||||||
\(857\) | 399.948 | + | 399.948i | 0.466683 | + | 0.466683i | 0.900838 | − | 0.434155i | \(-0.142953\pi\) |
−0.434155 | + | 0.900838i | \(0.642953\pi\) | |||||||
\(858\) | 4.25317 | − | 5.36868i | 0.00495708 | − | 0.00625720i | ||||
\(859\) | −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 | ||||
\(861\) | 256.698 | − | 120.105i | 0.298140 | − | 0.139495i | ||||
\(862\) | 455.692 | + | 455.692i | 0.528645 | + | 0.528645i | ||||
\(863\) | −31.1106 | − | 31.1106i | −0.0360493 | − | 0.0360493i | 0.688852 | − | 0.724902i | \(-0.258115\pi\) |
−0.724902 | + | 0.688852i | \(0.758115\pi\) | |||||||
\(864\) | 51.8352 | + | 143.670i | 0.0599944 | + | 0.166285i | ||||
\(865\) | 30.0476 | + | 72.6661i | 0.0347372 | + | 0.0840070i | ||||
\(866\) | −403.272 | −0.465672 | ||||||||
\(867\) | −178.285 | + | 225.045i | −0.205634 | + | 0.259567i | ||||
\(868\) | 9.44205 | − | 18.9057i | 0.0108779 | − | 0.0217808i | ||||
\(869\) | 0.101642 | 0.000116965 | ||||||||
\(870\) | 268.101 | − | 939.823i | 0.308162 | − | 1.08026i | ||||
\(871\) | − | 670.648i | − | 0.769974i | ||||||
\(872\) | 190.948 | − | 190.948i | 0.218977 | − | 0.218977i | ||||
\(873\) | 170.885 | + | 105.845i | 0.195744 | + | 0.121243i | ||||
\(874\) | −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 | \(-0.288012\pi\) | ||||
0.617830 | + | 0.786311i | \(0.288012\pi\) | |||||||
\(882\) | 55.9645 | + | 621.152i | 0.0634518 | + | 0.704254i | ||||
\(883\) | 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 | ||||||||
\(885\) | −619.079 | − | 1113.26i | −0.699524 | − | 1.25792i | ||||
\(886\) | −250.466 | −0.282693 | ||||||||
\(887\) | −296.458 | − | 296.458i | −0.334225 | − | 0.334225i | 0.519963 | − | 0.854189i | \(-0.325946\pi\) |
−0.854189 | + | 0.519963i | \(0.825946\pi\) | |||||||
\(888\) | −39.6882 | + | 50.0975i | −0.0446940 | + | 0.0564161i | ||||
\(889\) | −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 | ||||
\(897\) | −81.5595 | + | 102.951i | −0.0909247 | + | 0.114772i | ||||
\(898\) | 324.260 | − | 324.260i | 0.361092 | − | 0.361092i | ||||
\(899\) | 69.5423i | 0.0773551i | ||||||||
\(900\) | −382.272 | − | 237.420i | −0.424746 | − | 0.263800i | ||||
\(901\) | − | 1659.19i | − | 1.84150i | ||||||
\(902\) | 1.58453 | + | 1.58453i | 0.00175669 | + | 0.00175669i | ||||
\(903\) | −373.229 | + | 1029.58i | −0.413321 | + | 1.14018i | ||||
\(904\) | − | 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 | \(-0.965139\pi\) | ||
0.994009 | − | 0.109299i | \(-0.0348607\pi\) | |||||||
\(912\) | −279.564 | − | 221.476i | −0.306539 | − | 0.242847i | ||||
\(913\) | 11.6311 | + | 11.6311i | 0.0127395 | + | 0.0127395i | ||||
\(914\) | 823.513 | 0.900999 | ||||||||
\(915\) | −253.797 | − | 456.390i | −0.277374 | − | 0.498787i | ||||
\(916\) | − | 20.4858i | − | 0.0223644i | ||||||
\(917\) | 455.980 | − | 913.003i | 0.497252 | − | 0.995641i | ||||
\(918\) | 318.416 | − | 677.870i | 0.346859 | − | 0.738420i | ||||
\(919\) | 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 | ||||
\(924\) | −4.46655 | + | 2.08983i | −0.00483393 | + | 0.00226172i | ||||
\(925\) | 0.228483 | − | 188.306i | 0.000247009 | − | 0.203574i | ||||
\(926\) | 479.544i | 0.517866i | ||||||||
\(927\) | −210.242 | + | 339.430i | −0.226798 | + | 0.366160i | ||||
\(928\) | −184.284 | + | 184.284i | −0.198582 | + | 0.198582i | ||||
\(929\) | − | 883.375i | − | 0.950888i | −0.879746 | − | 0.475444i | \(-0.842287\pi\) | ||
0.879746 | − | 0.475444i | \(-0.157713\pi\) | |||||||
\(930\) | 30.7920 | + | 8.78396i | 0.0331097 | + | 0.00944512i | ||||
\(931\) | −874.886 | − | 1164.30i | −0.939727 | − | 1.25059i | ||||
\(932\) | 271.299 | − | 271.299i | 0.291093 | − | 0.291093i | ||||
\(933\) | −633.080 | − | 501.539i | −0.678542 | − | 0.537555i | ||||
\(934\) | −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 | \(-0.522984\pi\) | ||||
−0.0721449 | + | 0.997394i | \(0.522984\pi\) | |||||||
\(942\) | −6.22748 | + | 7.86079i | −0.00661091 | + | 0.00834479i | ||||
\(943\) | −30.3852 | − | 30.3852i | −0.0322219 | − | 0.0322219i | ||||
\(944\) | 339.684i | 0.359835i | ||||||||
\(945\) | −909.451 | + | 256.757i | −0.962382 | + | 0.271700i | ||||
\(946\) | −8.65919 | −0.00915348 | ||||||||
\(947\) | −1262.03 | + | 1262.03i | −1.33266 | + | 1.33266i | −0.429679 | + | 0.902982i | \(0.641373\pi\) |
−0.902982 | + | 0.429679i | \(0.858627\pi\) | |||||||
\(948\) | −4.07137 | − | 3.22542i | −0.00429469 | − | 0.00340234i | ||||
\(949\) | − | 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 | \(-0.967796\pi\) |
−0.101000 | − | 0.994886i | \(-0.532204\pi\) | |||||||
\(954\) | 246.340 | + | 1048.13i | 0.258218 | + | 1.09867i | ||||
\(955\) | −1268.75 | − | 526.435i | −1.32853 | − | 0.551240i | ||||
\(956\) | − | 50.2139i | − | 0.0525250i | ||||||
\(957\) | 10.0770 | − | 12.7199i | 0.0105298 | − | 0.0132915i | ||||
\(958\) | −444.701 | − | 444.701i | −0.464198 | − | 0.464198i | ||||
\(959\) | −118.501 | − | 354.962i | −0.123567 | − | 0.370138i | ||||
\(960\) | 58.3205 | + | 104.875i | 0.0607505 | + | 0.109245i | ||||
\(961\) | 958.722 | 0.997629 | ||||||||
\(962\) | −103.567 | − | 103.567i | −0.107658 | − | 0.107658i | ||||
\(963\) | 1145.41 | + | 709.462i | 1.18942 | + | 0.736720i | ||||
\(964\) | −557.898 | −0.578733 | ||||||||
\(965\) | 546.918 | + | 1322.65i | 0.566754 | + | 1.37062i | ||||
\(966\) | 85.6513 | − | 40.0749i | 0.0886660 | − | 0.0414854i | ||||
\(967\) | 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 | \(-0.380075\pi\) | ||||
0.367906 | + | 0.929863i | \(0.380075\pi\) | |||||||
\(972\) | −100.504 | + | 475.494i | −0.103400 | + | 0.489192i | ||||
\(973\) | −204.702 | + | 409.873i | −0.210383 | + | 0.421247i | ||||
\(974\) | 8.61669 | 0.00884670 | ||||||||
\(975\) | 641.346 | − | 807.540i | 0.657791 | − | 0.828246i | ||||
\(976\) | 139.256i | 0.142681i | ||||||||
\(977\) | −382.167 | + | 382.167i | −0.391164 | + | 0.391164i | −0.875102 | − | 0.483938i | \(-0.839206\pi\) |
0.483938 | + | 0.875102i | \(0.339206\pi\) | |||||||
\(978\) | 127.375 | − | 160.782i | 0.130240 | − | 0.164399i | ||||
\(979\) | −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 | −0.977250 | − | 0.212089i | \(-0.931973\pi\) |
0.212089 | + | 0.977250i | \(0.431973\pi\) | |||||||
\(984\) | −13.1877 | − | 113.752i | −0.0134022 | − | 0.115601i | ||||
\(985\) | 493.490 | + | 1193.44i | 0.501005 | + | 1.21161i | ||||
\(986\) | 1277.93 | 1.29607 | ||||||||
\(987\) | −831.484 | − | 301.417i | −0.842435 | − | 0.305387i | ||||
\(988\) | 577.945 | − | 577.945i | 0.584965 | − | 0.584965i | ||||
\(989\) | 166.050 | 0.167897 | ||||||||
\(990\) | −4.35931 | − | 6.06856i | −0.00440334 | − | 0.00612986i | ||||
\(991\) | −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 | ||||
\(993\) | −1192.00 | − | 944.327i | −1.20040 | − | 0.950984i | ||||
\(994\) | 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.a.167.14 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.b.167.11 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.b.83.6 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.167.3 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.a.83.3 | ✓ | 32 | |
21.20 | even | 2 | 210.3.k.b.167.6 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.b.83.11 | yes | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.a.83.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.3 | ✓ | 32 | 15.8 | even | 4 | inner | |
210.3.k.a.83.14 | yes | 32 | 105.83 | odd | 4 | inner | |
210.3.k.a.167.3 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.14 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.k.b.83.6 | yes | 32 | 5.3 | odd | 4 | ||
210.3.k.b.83.11 | yes | 32 | 35.13 | even | 4 | ||
210.3.k.b.167.6 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.b.167.11 | yes | 32 | 3.2 | odd | 2 |