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 | 167.3 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.a.83.3 |
$q$-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 | ||||
\(7\) | 6.26242 | − | 3.12763i | 0.894631 | − | 0.446805i | ||||
\(8\) | 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 | 0.226192 | − | 0.974083i | \(-0.427372\pi\) |
−0.974083 | + | 0.226192i | \(0.927372\pi\) | |||||||
\(14\) | −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 | 0.169673 | − | 0.985500i | \(-0.445729\pi\) |
−0.985500 | + | 0.169673i | \(0.945729\pi\) | |||||||
\(18\) | −10.8204 | − | 6.70213i | −0.601134 | − | 0.372341i | ||||
\(19\) | −29.7218 | −1.56431 | −0.782153 | − | 0.623086i | \(-0.785879\pi\) | ||||
−0.782153 | + | 0.623086i | \(0.785879\pi\) | |||||||
\(20\) | 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 | 0.754356 | − | 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 | ||||
\(28\) | −6.25527 | − | 12.5248i | −0.223402 | − | 0.447316i | ||||
\(29\) | −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 | \(0.00775036\pi\) | ||||
−0.999704 | + | 0.0243461i | \(0.992250\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.218727 | − | 0.276093i | 0.00662808 | − | 0.00836646i | ||||
\(34\) | 27.7381 | 0.815828 | ||||||||
\(35\) | 2.44398 | + | 34.9146i | 0.0698280 | + | 0.997559i | ||||
\(36\) | 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 | \(0.447373\pi\) | |||||||
\(42\) | 24.8643 | − | 16.2409i | 0.592007 | − | 0.386689i | ||||
\(43\) | 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 | 0.315351 | − | 0.948975i | \(-0.397878\pi\) |
−0.948975 | + | 0.315351i | \(0.897878\pi\) | |||||||
\(48\) | 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 | \(0.255706\pi\) | ||||
−0.694317 | + | 0.719669i | \(0.744294\pi\) | |||||||
\(60\) | −14.5801 | − | 26.2187i | −0.243002 | − | 0.436978i | ||||
\(61\) | 34.8141i | 0.570723i | 0.958420 | + | 0.285361i | \(0.0921137\pi\) | ||||
−0.958420 | + | 0.285361i | \(0.907886\pi\) | |||||||
\(62\) | −1.50946 | − | 1.50946i | −0.0243461 | − | 0.0243461i | ||||
\(63\) | 40.2973 | + | 48.4265i | 0.639639 | + | 0.768675i | ||||
\(64\) | 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 | ||||
\(70\) | −37.3585 | − | 32.4706i | −0.533694 | − | 0.463866i | ||||
\(71\) | 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 | 0.931036 | − | 0.364928i | \(-0.118906\pi\) |
−0.364928 | + | 0.931036i | \(0.618906\pi\) | |||||||
\(74\) | −10.6522 | −0.143949 | ||||||||
\(75\) | 8.54683 | + | 74.5114i | 0.113958 | + | 0.993486i | ||||
\(76\) | 59.4436i | 0.782153i | ||||||||
\(77\) | 0.367220 | + | 0.735279i | 0.00476909 | + | 0.00954908i | ||||
\(78\) | −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 | \(0.569778\pi\) |
−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 | ||||||||
\(87\) | 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 | \(-0.740412\pi\) | ||
0.685490 | − | 0.728082i | \(-0.259588\pi\) | |||||||
\(90\) | 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 | −0.783811 | − | 0.620999i | \(-0.786727\pi\) |
0.620999 | + | 0.783811i | \(0.286727\pi\) | |||||||
\(98\) | 9.73729 | + | 68.6089i | 0.0993602 | + | 0.700091i | ||||
\(99\) | −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 | \(0.477206\pi\) | |||||||
\(102\) | −65.2264 | − | 51.6736i | −0.639474 | − | 0.506604i | ||||
\(103\) | −31.3694 | − | 31.3694i | −0.304557 | − | 0.304557i | 0.538237 | − | 0.842794i | \(-0.319091\pi\) |
−0.842794 | + | 0.538237i | \(0.819091\pi\) | |||||||
\(104\) | − | 38.8903i | − | 0.373945i | ||||||
\(105\) | 59.2956 | − | 86.6547i | 0.564720 | − | 0.825282i | ||||
\(106\) | 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 | ||||
\(112\) | −25.0497 | + | 12.5105i | −0.223658 | + | 0.111701i | ||||
\(113\) | −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 | ||||
\(126\) | −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 | \(0.312162\pi\) | |||||||
\(132\) | −0.552187 | − | 0.437453i | −0.00418323 | − | 0.00331404i | ||||
\(133\) | −186.131 | + | 92.9590i | −1.39948 | + | 0.698940i | ||||
\(134\) | 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 | \(-0.575650\pi\) | ||||
−0.235430 | + | 0.971891i | \(0.575650\pi\) | |||||||
\(140\) | 69.8291 | − | 4.88796i | 0.498780 | − | 0.0349140i | ||||
\(141\) | 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 | ||||||||
\(147\) | −142.194 | + | 37.2795i | −0.967309 | + | 0.253602i | ||||
\(148\) | 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 | −0.712410 | − | 0.701764i | \(-0.752396\pi\) |
0.701764 | + | 0.712410i | \(0.252396\pi\) | |||||||
\(158\) | 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 | 0.971293 | − | 0.237884i | \(-0.0764539\pi\) |
−0.237884 | + | 0.971293i | \(0.576454\pi\) | |||||||
\(168\) | −32.4819 | − | 49.7286i | −0.193344 | − | 0.296003i | ||||
\(169\) | 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 | ||||
\(175\) | −165.927 | − | 55.6171i | −0.948154 | − | 0.317812i | ||||
\(176\) | − | 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 | \(0.269414\pi\) | ||||
−0.662692 | + | 0.748892i | \(0.730586\pi\) | |||||||
\(182\) | 121.774 | − | 60.8173i | 0.669086 | − | 0.334161i | ||||
\(183\) | 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 | ||||
\(189\) | −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 | \(-0.744519\pi\) | ||
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 | \(-0.287446\pi\) | ||||
0.619228 | + | 0.785211i | \(0.287446\pi\) | |||||||
\(200\) | 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 | ||||
\(203\) | −288.517 | + | 144.093i | −1.42126 | + | 0.709820i | ||||
\(204\) | 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 | ||||||
\(210\) | 27.3590 | + | 145.950i | 0.130281 | + | 0.695001i | ||||
\(211\) | 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 | ||||
\(217\) | 4.72102 | + | 9.45285i | 0.0217559 | + | 0.0435615i | ||||
\(218\) | 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 | 0.800567 | − | 0.599244i | \(-0.204532\pi\) |
−0.599244 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(224\) | 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 | 0.0646692 | − | 0.997907i | \(-0.479401\pi\) |
−0.997907 | + | 0.0646692i | \(0.979401\pi\) | |||||||
\(228\) | 110.738 | − | 139.782i | 0.485693 | − | 0.613079i | ||||
\(229\) | −10.2429 | −0.0447287 | −0.0223644 | − | 0.999750i | \(-0.507119\pi\) | ||||
−0.0223644 | + | 0.999750i | \(0.507119\pi\) | |||||||
\(230\) | 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 | 0.935504 | − | 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 | ||||
\(238\) | 173.708 | − | 86.7548i | 0.729865 | − | 0.364516i | ||||
\(239\) | 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 | \(0.196452\pi\) | ||||
−0.815517 | + | 0.578733i | \(0.803548\pi\) | |||||||
\(242\) | −120.986 | + | 120.986i | −0.499943 | + | 0.499943i | ||||
\(243\) | 237.747 | + | 50.2522i | 0.978383 | + | 0.206799i | ||||
\(244\) | 69.6282 | 0.285361 | ||||||||
\(245\) | 124.505 | + | 211.006i | 0.508184 | + | 0.861248i | ||||
\(246\) | 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 | \(0.638256\pi\) | |||||||
\(252\) | 96.8531 | − | 80.5946i | 0.384338 | − | 0.319820i | ||||
\(253\) | −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 | \(-0.886735\pi\) |
−0.348371 | − | 0.937357i | \(-0.613265\pi\) | |||||||
\(258\) | 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 | \(-0.845786\pi\) | ||
0.884919 | − | 0.465745i | \(-0.154214\pi\) | |||||||
\(270\) | −190.708 | − | 8.97908i | −0.706324 | − | 0.0332559i | ||||
\(271\) | 207.488i | 0.765638i | 0.923823 | + | 0.382819i | \(0.125047\pi\) | ||||
−0.923823 | + | 0.382819i | \(0.874953\pi\) | |||||||
\(272\) | 55.4763 | + | 55.4763i | 0.203957 | + | 0.203957i | ||||
\(273\) | 157.904 | + | 241.745i | 0.578402 | + | 0.885512i | ||||
\(274\) | − | 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 | ||||
\(280\) | −64.9412 | + | 74.7171i | −0.231933 | + | 0.266847i | ||||
\(281\) | − | 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 | 0.950529 | − | 0.310635i | \(-0.100542\pi\) |
−0.310635 | + | 0.950529i | \(0.600542\pi\) | |||||||
\(284\) | 155.300 | 0.546829 | ||||||||
\(285\) | −389.634 | + | 216.674i | −1.36714 | + | 0.760259i | ||||
\(286\) | 2.28308i | 0.00798280i | ||||||||
\(287\) | 84.5149 | − | 42.2092i | 0.294477 | − | 0.147070i | ||||
\(288\) | 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 | −0.819757 | − | 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 | ||||||||
\(297\) | 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 | −0.228532 | − | 0.973536i | \(-0.573392\pi\) |
0.973536 | + | 0.228532i | \(0.0733925\pi\) | |||||||
\(308\) | 1.47056 | − | 0.734439i | 0.00477454 | − | 0.00238454i | ||||
\(309\) | 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 | \(0.357513\pi\) | |||||||
\(312\) | −72.4491 | + | 91.4507i | −0.232209 | + | 0.293111i | ||||
\(313\) | −421.023 | − | 421.023i | −1.34512 | − | 1.34512i | −0.890877 | − | 0.454244i | \(-0.849909\pi\) |
−0.454244 | − | 0.890877i | \(-0.650091\pi\) | |||||||
\(314\) | − | 3.34288i | − | 0.0106461i | ||||||
\(315\) | −300.864 | + | 93.3065i | −0.955123 | + | 0.296211i | ||||
\(316\) | −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 | ||||
\(322\) | −28.1997 | + | 14.0837i | −0.0875766 | + | 0.0437383i | ||||
\(323\) | 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 | ||||
\(336\) | 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 | ||||||||
\(342\) | 321.603 | + | 199.200i | 0.940358 | + | 0.582455i | ||||
\(343\) | 61.8203 | − | 337.383i | 0.180234 | − | 0.983624i | ||||
\(344\) | 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 | \(-0.676960\pi\) | ||||
−0.527740 | + | 0.849406i | \(0.676960\pi\) | |||||||
\(350\) | 221.544 | − | 110.310i | 0.632983 | − | 0.315171i | ||||
\(351\) | −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 | ||||||||
\(357\) | 225.247 | + | 344.844i | 0.630943 | + | 0.965951i | ||||
\(358\) | −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 | −0.652168 | − | 0.758075i | \(-0.726140\pi\) |
0.758075 | + | 0.652168i | \(0.226140\pi\) | |||||||
\(368\) | −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 | ||||
\(378\) | 193.490 | + | 184.400i | 0.511879 | + | 0.487832i | ||||
\(379\) | 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 | ||||
\(385\) | −4.09937 | + | 0.286951i | −0.0106477 | + | 0.000745327i | ||||
\(386\) | − | 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 | ||||||
\(392\) | 137.218 | − | 19.4746i | 0.350046 | − | 0.0496801i | ||||
\(393\) | −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 | −0.690513 | − | 0.723320i | \(-0.742615\pi\) |
0.723320 | + | 0.690513i | \(0.242615\pi\) | |||||||
\(398\) | −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 | \(-0.993205\pi\) | ||
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 | \(-0.573038\pi\) | ||||
−0.227447 | + | 0.973790i | \(0.573038\pi\) | |||||||
\(410\) | −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 | ||||
\(413\) | 265.602 | + | 531.811i | 0.643103 | + | 1.28768i | ||||
\(414\) | −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 | \(-0.742193\pi\) | ||
0.689553 | − | 0.724235i | \(-0.257807\pi\) | |||||||
\(420\) | −173.309 | − | 118.591i | −0.412641 | − | 0.282360i | ||||
\(421\) | −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 | ||||
\(427\) | 108.886 | + | 218.021i | 0.255002 | + | 0.510587i | ||||
\(428\) | −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 | 0.434837 | − | 0.900509i | \(-0.356806\pi\) |
−0.900509 | + | 0.434837i | \(0.856806\pi\) | |||||||
\(434\) | −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 | \(-0.534161\pi\) | ||||
−0.107113 | + | 0.994247i | \(0.534161\pi\) | |||||||
\(440\) | −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 | 0.834182 | − | 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 | ||||
\(448\) | 25.0211 | + | 50.0994i | 0.0558506 | + | 0.111829i | ||||
\(449\) | −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 | ||||||||
\(455\) | 315.698 | − | 363.221i | 0.693841 | − | 0.798289i | ||||
\(456\) | 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 | \(0.324052\pi\) | |||||||
\(462\) | 1.90687 | + | 2.91935i | 0.00412742 | + | 0.00631894i | ||||
\(463\) | 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 | 0.304501 | − | 0.952512i | \(-0.401510\pi\) |
−0.952512 | + | 0.304501i | \(0.901510\pi\) | |||||||
\(468\) | −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 | \(-0.846343\pi\) | ||
0.885732 | − | 0.464198i | \(-0.153657\pi\) | |||||||
\(480\) | 23.2772 | − | 81.5976i | 0.0484941 | − | 0.169995i | ||||
\(481\) | − | 103.567i | − | 0.215316i | ||||||
\(482\) | −278.949 | − | 278.949i | −0.578733 | − | 0.578733i | ||||
\(483\) | −36.5664 | − | 55.9819i | −0.0757069 | − | 0.115904i | ||||
\(484\) | − | 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 | ||||
\(490\) | −335.511 | − | 86.5006i | −0.684716 | − | 0.176532i | ||||
\(491\) | 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 | ||||||
\(497\) | 242.860 | + | 486.275i | 0.488652 | + | 0.978421i | ||||
\(498\) | −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 | −0.807908 | − | 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 | ||||||
\(507\) | 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 | \(0.367239\pi\) | ||||
−0.405094 | + | 0.914275i | \(0.632761\pi\) | |||||||
\(510\) | 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 | ||||
\(518\) | −66.7087 | + | 33.3162i | −0.128781 | + | 0.0643171i | ||||
\(519\) | −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 | \(0.506807\pi\) | |||||||
\(522\) | 498.508 | + | 308.774i | 0.954997 | + | 0.591522i | ||||
\(523\) | −110.356 | − | 110.356i | −0.211006 | − | 0.211006i | 0.593689 | − | 0.804695i | \(-0.297671\pi\) |
−0.804695 | + | 0.593689i | \(0.797671\pi\) | |||||||
\(524\) | − | 291.582i | − | 0.556453i | ||||||
\(525\) | 286.568 | + | 439.890i | 0.545844 | + | 0.837887i | ||||
\(526\) | −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 | ||||
\(532\) | 185.918 | + | 372.261i | 0.349470 | + | 0.699739i | ||||
\(533\) | −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 | ||||
\(546\) | −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 | ||||||||
\(552\) | 16.7773 | − | 21.1776i | 0.0303937 | − | 0.0383653i | ||||
\(553\) | −2.70757 | − | 5.42134i | −0.00489616 | − | 0.00980351i | ||||
\(554\) | 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 | ||||||||
\(560\) | −9.77592 | − | 139.658i | −0.0174570 | − | 0.249390i | ||||
\(561\) | −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 | ||||||||
\(567\) | −341.300 | + | 452.773i | −0.601941 | + | 0.798541i | ||||
\(568\) | −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 | −0.358723 | − | 0.933444i | \(-0.616788\pi\) |
0.933444 | + | 0.358723i | \(0.116788\pi\) | |||||||
\(578\) | −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 | 0.498363 | − | 0.866968i | \(-0.333935\pi\) |
−0.866968 | + | 0.498363i | \(0.833935\pi\) | |||||||
\(588\) | 74.5590 | + | 284.389i | 0.126801 | + | 0.483654i | ||||
\(589\) | − | 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 | ||||
\(595\) | 450.337 | − | 518.128i | 0.756869 | − | 0.870804i | ||||
\(596\) | 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 | \(0.250677\pi\) | ||||
−0.705600 | + | 0.708610i | \(0.749323\pi\) | |||||||
\(602\) | 230.666 | + | 461.859i | 0.383166 | + | 0.767207i | ||||
\(603\) | 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 | −0.206621 | − | 0.978421i | \(-0.566247\pi\) |
0.978421 | + | 0.206621i | \(0.0662466\pi\) | |||||||
\(608\) | −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 | ||||||||
\(612\) | −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 | \(-0.604746\pi\) | ||||
−0.323161 | + | 0.946344i | \(0.604746\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | −405.337 | − | 811.600i | −0.650621 | − | 1.30273i | ||||
\(624\) | −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 | ||||||
\(630\) | 207.557 | − | 394.170i | 0.329456 | − | 0.625667i | ||||
\(631\) | −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 | ||||
\(637\) | −667.056 | + | 94.6716i | −1.04718 | + | 0.148621i | ||||
\(638\) | 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 | 0.576078 | − | 0.817395i | \(-0.304583\pi\) |
−0.817395 | + | 0.576078i | \(0.804583\pi\) | |||||||
\(644\) | 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 | 0.605663 | − | 0.795722i | \(-0.292908\pi\) |
−0.795722 | + | 0.605663i | \(0.792908\pi\) | |||||||
\(648\) | −217.203 | − | 72.8768i | −0.335189 | − | 0.112464i | ||||
\(649\) | −9.97068 | −0.0153631 | ||||||||
\(650\) | −343.328 | − | 344.162i | −0.528196 | − | 0.529480i | ||||
\(651\) | 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 | 0.0466996 | − | 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 | ||||
\(658\) | 372.994 | − | 186.284i | 0.566860 | − | 0.283106i | ||||
\(659\) | 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 | \(-0.844201\pi\) | ||
0.882589 | − | 0.470146i | \(-0.155799\pi\) | |||||||
\(662\) | 506.910 | − | 506.910i | 0.765725 | − | 0.765725i | ||||
\(663\) | 502.401 | − | 634.168i | 0.757769 | − | 0.956513i | ||||
\(664\) | −396.252 | −0.596765 | ||||||||
\(665\) | −72.6395 | − | 1037.72i | −0.109232 | − | 1.56049i | ||||
\(666\) | −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 | ||||||||
\(672\) | −99.4571 | + | 64.9637i | −0.148002 | + | 0.0966722i | ||||
\(673\) | −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 | \(-0.998901\pi\) |
−0.00345318 | − | 0.999994i | \(-0.501099\pi\) | |||||||
\(678\) | −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 | \(-0.933365\pi\) | ||
0.978169 | − | 0.207813i | \(-0.0666346\pi\) | |||||||
\(692\) | −22.2409 | − | 22.2409i | −0.0321400 | − | 0.0321400i | ||||
\(693\) | −5.68583 | + | 4.73136i | −0.00820465 | + | 0.00682736i | ||||
\(694\) | − | 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 | ||||
\(700\) | −111.234 | + | 331.854i | −0.158906 | + | 0.474077i | ||||
\(701\) | − | 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 | ||||||
\(707\) | 90.5076 | − | 45.2021i | 0.128016 | − | 0.0639351i | ||||
\(708\) | −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 | ||||
\(714\) | −570.091 | − | 119.598i | −0.798447 | − | 0.167504i | ||||
\(715\) | 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 | \(0.0815291\pi\) | ||||
−0.967377 | + | 0.253340i | \(0.918471\pi\) | |||||||
\(720\) | 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 | −0.565468 | − | 0.824771i | \(-0.691304\pi\) |
0.824771 | + | 0.565468i | \(0.191304\pi\) | |||||||
\(728\) | −121.635 | − | 243.547i | −0.167081 | − | 0.334543i | ||||
\(729\) | −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 | 0.706110 | − | 0.708102i | \(-0.250449\pi\) |
−0.708102 | + | 0.706110i | \(0.750449\pi\) | |||||||
\(734\) | 77.7356i | 0.105907i | ||||||||
\(735\) | 100.310 | − | 728.123i | 0.136476 | − | 0.990643i | ||||
\(736\) | 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 | ||||
\(742\) | 749.188 | − | 374.166i | 1.00969 | − | 0.504267i | ||||
\(743\) | 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 | ||||
\(756\) | −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 | \(0.432842\pi\) | |||||||
\(762\) | 808.260 | + | 640.320i | 1.06071 | + | 0.840314i | ||||
\(763\) | −298.608 | − | 597.898i | −0.391360 | − | 0.783615i | ||||
\(764\) | −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 | \(-0.0975773\pi\) | ||||
0.953381 | + | 0.301769i | \(0.0975773\pi\) | |||||||
\(770\) | 3.81242 | − | 4.38632i | 0.00495119 | − | 0.00569652i | ||||
\(771\) | 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 | ||||||||
\(777\) | −86.5010 | − | 132.430i | −0.111327 | − | 0.170437i | ||||
\(778\) | −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 | −0.864097 | − | 0.503325i | \(-0.832110\pi\) |
0.503325 | + | 0.864097i | \(0.332110\pi\) | |||||||
\(788\) | 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 | \(0.0383813\pi\) |
0.120287 | + | 0.992739i | \(0.461619\pi\) | |||||||
\(798\) | −739.012 | + | 482.710i | −0.926080 | + | 0.604900i | ||||
\(799\) | 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 | ||||
\(805\) | −73.1075 | + | 84.1127i | −0.0908167 | + | 0.104488i | ||||
\(806\) | 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 | \(-0.976703\pi\) | ||
0.997323 | − | 0.0731248i | \(-0.0232971\pi\) | |||||||
\(812\) | 288.187 | + | 577.033i | 0.354910 | + | 0.710632i | ||||
\(813\) | 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 | ||||
\(819\) | 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 | \(0.0425908\pi\) | ||||
−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 | \(-0.636452\pi\) | ||||
−0.415668 | + | 0.909516i | \(0.636452\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | −951.542 | + | 135.047i | −1.14231 | + | 0.162122i | ||||
\(834\) | −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 | \(0.187817\pi\) | ||||
−0.830915 | + | 0.556399i | \(0.812183\pi\) | |||||||
\(840\) | 291.901 | − | 54.7181i | 0.347501 | − | 0.0651406i | ||||
\(841\) | 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 | ||||
\(847\) | 757.667 | − | 378.401i | 0.894530 | − | 0.446754i | ||||
\(848\) | 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 | 0.626892 | − | 0.779106i | \(-0.284327\pi\) |
−0.779106 | + | 0.626892i | \(0.784327\pi\) | |||||||
\(854\) | −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 | 0.434155 | − | 0.900838i | \(-0.357047\pi\) |
−0.900838 | + | 0.434155i | \(0.857047\pi\) | |||||||
\(858\) | 4.25317 | − | 5.36868i | 0.00495708 | − | 0.00625720i | ||||
\(859\) | 191.398 | 0.222815 | 0.111407 | − | 0.993775i | \(-0.464464\pi\) | ||||
0.111407 | + | 0.993775i | \(0.464464\pi\) | |||||||
\(860\) | 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 | 0.688852 | − | 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 | ||||
\(868\) | 18.9057 | − | 9.44205i | 0.0217808 | − | 0.0108779i | ||||
\(869\) | 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 | ||||||||
\(875\) | 574.805 | − | 659.715i | 0.656920 | − | 0.753960i | ||||
\(876\) | −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 | \(0.711988\pi\) | |||||||
\(882\) | −581.051 | + | 226.587i | −0.658788 | + | 0.256901i | ||||
\(883\) | 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 | 0.854189 | − | 0.519963i | \(-0.174054\pi\) |
−0.519963 | + | 0.854189i | \(0.674054\pi\) | |||||||
\(888\) | 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 | ||||
\(903\) | −916.881 | + | 598.891i | −1.01537 | + | 0.663224i | ||||
\(904\) | − | 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 | ||||
\(910\) | 47.5235 | + | 678.919i | 0.0522237 | + | 0.746065i | ||||
\(911\) | − | 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 | ||||||||
\(917\) | 913.003 | − | 455.980i | 0.995641 | − | 0.497252i | ||||
\(918\) | 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 | ||||
\(924\) | −4.82622 | − | 1.01248i | −0.00522318 | − | 0.00109576i | ||||
\(925\) | 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 | \(0.157713\pi\) | ||||
−0.879746 | + | 0.475444i | \(0.842287\pi\) | |||||||
\(930\) | −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 | −0.924945 | − | 0.380102i | \(-0.875889\pi\) |
0.380102 | + | 0.924945i | \(0.375889\pi\) | |||||||
\(938\) | 431.972 | − | 215.739i | 0.460524 | − | 0.229999i | ||||
\(939\) | 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 | \(0.477016\pi\) | |||||||
\(942\) | −6.22748 | + | 7.86079i | −0.00661091 | + | 0.00834479i | ||||
\(943\) | 30.3852 | + | 30.3852i | 0.0322219 | + | 0.0322219i | ||||
\(944\) | − | 339.684i | − | 0.359835i | ||||||
\(945\) | 881.303 | + | 341.071i | 0.932596 | + | 0.360922i | ||||
\(946\) | −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 | ||||
\(952\) | −173.510 | − | 347.416i | −0.182258 | − | 0.364933i | ||||
\(953\) | −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 | ||||
\(966\) | 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 | \(0.619925\pi\) | |||||||
\(972\) | 100.504 | − | 475.494i | 0.103400 | − | 0.489192i | ||||
\(973\) | −409.873 | + | 204.702i | −0.421247 | + | 0.210383i | ||||
\(974\) | 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 | ||||||||
\(980\) | 422.012 | − | 249.010i | 0.430624 | − | 0.254092i | ||||
\(981\) | 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 | ||||||||
\(987\) | 483.660 | + | 740.466i | 0.490031 | + | 0.750219i | ||||
\(988\) | 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 | \(-0.483946\pi\) |
0.998728 | − | 0.0504122i | \(-0.0160535\pi\) | |||||||
\(998\) | −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.167.3 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.b.167.6 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.b.83.11 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.167.14 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.a.83.14 | yes | 32 | |
21.20 | even | 2 | 210.3.k.b.167.11 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.b.83.6 | yes | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.a.83.3 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.3 | ✓ | 32 | 105.83 | odd | 4 | inner | |
210.3.k.a.83.14 | yes | 32 | 15.8 | even | 4 | inner | |
210.3.k.a.167.3 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.k.a.167.14 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.b.83.6 | yes | 32 | 35.13 | even | 4 | ||
210.3.k.b.83.11 | yes | 32 | 5.3 | odd | 4 | ||
210.3.k.b.167.6 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.167.11 | yes | 32 | 21.20 | even | 2 |