Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(599,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.599");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.5 | ||
Character | \(\chi\) | \(=\) | 690.599 |
Dual form | 690.3.b.a.599.6 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −2.79936 | − | 1.07869i | −0.933121 | − | 0.359564i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 4.72534 | + | 1.63438i | 0.945067 | + | 0.326875i | ||||
\(6\) | 3.95890 | + | 1.52550i | 0.659816 | + | 0.254250i | ||||
\(7\) | 7.69411i | 1.09916i | 0.835441 | + | 0.549580i | \(0.185212\pi\) | ||||
−0.835441 | + | 0.549580i | \(0.814788\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 6.67285 | + | 6.03929i | 0.741428 | + | 0.671032i | ||||
\(10\) | −6.68264 | − | 2.31136i | −0.668264 | − | 0.231136i | ||||
\(11\) | − | 16.6679i | − | 1.51527i | −0.652680 | − | 0.757633i | \(-0.726356\pi\) | ||
0.652680 | − | 0.757633i | \(-0.273644\pi\) | |||||||
\(12\) | −5.59872 | − | 2.15738i | −0.466560 | − | 0.179782i | ||||
\(13\) | − | 13.7877i | − | 1.06059i | −0.847813 | − | 0.530295i | \(-0.822081\pi\) | ||
0.847813 | − | 0.530295i | \(-0.177919\pi\) | |||||||
\(14\) | − | 10.8811i | − | 0.777223i | ||||||
\(15\) | −11.4649 | − | 9.67239i | −0.764329 | − | 0.644826i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −26.8740 | −1.58082 | −0.790411 | − | 0.612578i | \(-0.790133\pi\) | ||||
−0.790411 | + | 0.612578i | \(0.790133\pi\) | |||||||
\(18\) | −9.43684 | − | 8.54085i | −0.524269 | − | 0.474492i | ||||
\(19\) | 31.7201 | 1.66948 | 0.834740 | − | 0.550644i | \(-0.185618\pi\) | ||||
0.834740 | + | 0.550644i | \(0.185618\pi\) | |||||||
\(20\) | 9.45067 | + | 3.26875i | 0.472534 | + | 0.163438i | ||||
\(21\) | 8.29957 | − | 21.5386i | 0.395218 | − | 1.02565i | ||||
\(22\) | 23.5720i | 1.07146i | ||||||||
\(23\) | −4.79583 | −0.208514 | ||||||||
\(24\) | 7.91779 | + | 3.05100i | 0.329908 | + | 0.127125i | ||||
\(25\) | 19.6576 | + | 15.4460i | 0.786305 | + | 0.617839i | ||||
\(26\) | 19.4987i | 0.749950i | ||||||||
\(27\) | −12.1652 | − | 24.1041i | −0.450563 | − | 0.892745i | ||||
\(28\) | 15.3882i | 0.549580i | ||||||||
\(29\) | 26.0495i | 0.898259i | 0.893467 | + | 0.449129i | \(0.148266\pi\) | ||||
−0.893467 | + | 0.449129i | \(0.851734\pi\) | |||||||
\(30\) | 16.2139 | + | 13.6788i | 0.540462 | + | 0.455961i | ||||
\(31\) | −7.68297 | −0.247838 | −0.123919 | − | 0.992292i | \(-0.539546\pi\) | ||||
−0.123919 | + | 0.992292i | \(0.539546\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | −17.9795 | + | 46.6596i | −0.544835 | + | 1.41393i | ||||
\(34\) | 38.0055 | 1.11781 | ||||||||
\(35\) | −12.5751 | + | 36.3573i | −0.359288 | + | 1.03878i | ||||
\(36\) | 13.3457 | + | 12.0786i | 0.370714 | + | 0.335516i | ||||
\(37\) | 39.6223i | 1.07087i | 0.844575 | + | 0.535437i | \(0.179853\pi\) | ||||
−0.844575 | + | 0.535437i | \(0.820147\pi\) | |||||||
\(38\) | −44.8590 | −1.18050 | ||||||||
\(39\) | −14.8726 | + | 38.5967i | −0.381349 | + | 0.989658i | ||||
\(40\) | −13.3653 | − | 4.62272i | −0.334132 | − | 0.115568i | ||||
\(41\) | − | 64.5050i | − | 1.57329i | −0.617404 | − | 0.786646i | \(-0.711816\pi\) | ||
0.617404 | − | 0.786646i | \(-0.288184\pi\) | |||||||
\(42\) | −11.7374 | + | 30.4602i | −0.279461 | + | 0.725243i | ||||
\(43\) | − | 58.0405i | − | 1.34978i | −0.737919 | − | 0.674890i | \(-0.764191\pi\) | ||
0.737919 | − | 0.674890i | \(-0.235809\pi\) | |||||||
\(44\) | − | 33.3359i | − | 0.757633i | ||||||
\(45\) | 21.6610 | + | 39.4436i | 0.481355 | + | 0.876526i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 72.2219 | 1.53664 | 0.768318 | − | 0.640068i | \(-0.221094\pi\) | ||||
0.768318 | + | 0.640068i | \(0.221094\pi\) | |||||||
\(48\) | −11.1974 | − | 4.31476i | −0.233280 | − | 0.0898909i | ||||
\(49\) | −10.1994 | −0.208151 | ||||||||
\(50\) | −27.8001 | − | 21.8439i | −0.556001 | − | 0.436878i | ||||
\(51\) | 75.2299 | + | 28.9887i | 1.47510 | + | 0.568406i | ||||
\(52\) | − | 27.5753i | − | 0.530295i | ||||||
\(53\) | 20.7097 | 0.390749 | 0.195375 | − | 0.980729i | \(-0.437408\pi\) | ||||
0.195375 | + | 0.980729i | \(0.437408\pi\) | |||||||
\(54\) | 17.2042 | + | 34.0884i | 0.318596 | + | 0.631266i | ||||
\(55\) | 27.2417 | − | 78.7616i | 0.495303 | − | 1.43203i | ||||
\(56\) | − | 21.7622i | − | 0.388611i | ||||||
\(57\) | −88.7961 | − | 34.2162i | −1.55783 | − | 0.600284i | ||||
\(58\) | − | 36.8396i | − | 0.635165i | ||||||
\(59\) | 30.3283i | 0.514039i | 0.966406 | + | 0.257019i | \(0.0827405\pi\) | ||||
−0.966406 | + | 0.257019i | \(0.917260\pi\) | |||||||
\(60\) | −22.9299 | − | 19.3448i | −0.382165 | − | 0.322413i | ||||
\(61\) | −7.15931 | −0.117366 | −0.0586829 | − | 0.998277i | \(-0.518690\pi\) | ||||
−0.0586829 | + | 0.998277i | \(0.518690\pi\) | |||||||
\(62\) | 10.8654 | 0.175248 | ||||||||
\(63\) | −46.4670 | + | 51.3417i | −0.737571 | + | 0.814947i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 22.5342 | − | 65.1514i | 0.346681 | − | 1.00233i | ||||
\(66\) | 25.4269 | − | 65.9866i | 0.385256 | − | 0.999797i | ||||
\(67\) | − | 88.3837i | − | 1.31916i | −0.751635 | − | 0.659580i | \(-0.770734\pi\) | ||
0.751635 | − | 0.659580i | \(-0.229266\pi\) | |||||||
\(68\) | −53.7479 | −0.790411 | ||||||||
\(69\) | 13.4253 | + | 5.17322i | 0.194569 | + | 0.0749742i | ||||
\(70\) | 17.7839 | − | 51.4170i | 0.254055 | − | 0.734528i | ||||
\(71\) | − | 71.2117i | − | 1.00298i | −0.865163 | − | 0.501491i | \(-0.832785\pi\) | ||
0.865163 | − | 0.501491i | \(-0.167215\pi\) | |||||||
\(72\) | −18.8737 | − | 17.0817i | −0.262134 | − | 0.237246i | ||||
\(73\) | 28.2401i | 0.386850i | 0.981115 | + | 0.193425i | \(0.0619596\pi\) | ||||
−0.981115 | + | 0.193425i | \(0.938040\pi\) | |||||||
\(74\) | − | 56.0344i | − | 0.757222i | ||||||
\(75\) | −38.3674 | − | 64.4433i | −0.511565 | − | 0.859245i | ||||
\(76\) | 63.4402 | 0.834740 | ||||||||
\(77\) | 128.245 | 1.66552 | ||||||||
\(78\) | 21.0331 | − | 54.5839i | 0.269655 | − | 0.699794i | ||||
\(79\) | −23.1310 | −0.292798 | −0.146399 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146399 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(80\) | 18.9013 | + | 6.53751i | 0.236267 | + | 0.0817189i | ||||
\(81\) | 8.05390 | + | 80.5986i | 0.0994309 | + | 0.995044i | ||||
\(82\) | 91.2238i | 1.11249i | ||||||||
\(83\) | 139.074 | 1.67559 | 0.837793 | − | 0.545988i | \(-0.183845\pi\) | ||||
0.837793 | + | 0.545988i | \(0.183845\pi\) | |||||||
\(84\) | 16.5991 | − | 43.0772i | 0.197609 | − | 0.512824i | ||||
\(85\) | −126.989 | − | 43.9222i | −1.49398 | − | 0.516732i | ||||
\(86\) | 82.0817i | 0.954438i | ||||||||
\(87\) | 28.0994 | − | 72.9220i | 0.322981 | − | 0.838184i | ||||
\(88\) | 47.1440i | 0.535728i | ||||||||
\(89\) | − | 44.9943i | − | 0.505554i | −0.967525 | − | 0.252777i | \(-0.918656\pi\) | ||
0.967525 | − | 0.252777i | \(-0.0813440\pi\) | |||||||
\(90\) | −30.6333 | − | 55.7817i | −0.340370 | − | 0.619797i | ||||
\(91\) | 106.084 | 1.16576 | ||||||||
\(92\) | −9.59166 | −0.104257 | ||||||||
\(93\) | 21.5074 | + | 8.28755i | 0.231262 | + | 0.0891134i | ||||
\(94\) | −102.137 | −1.08657 | ||||||||
\(95\) | 149.888 | + | 51.8426i | 1.57777 | + | 0.545712i | ||||
\(96\) | 15.8356 | + | 6.10200i | 0.164954 | + | 0.0635625i | ||||
\(97\) | 59.4001i | 0.612372i | 0.951972 | + | 0.306186i | \(0.0990530\pi\) | ||||
−0.951972 | + | 0.306186i | \(0.900947\pi\) | |||||||
\(98\) | 14.4241 | 0.147185 | ||||||||
\(99\) | 100.663 | − | 111.223i | 1.01679 | − | 1.12346i | ||||
\(100\) | 39.3152 | + | 30.8919i | 0.393152 | + | 0.308919i | ||||
\(101\) | − | 36.3941i | − | 0.360338i | −0.983636 | − | 0.180169i | \(-0.942336\pi\) | ||
0.983636 | − | 0.180169i | \(-0.0576644\pi\) | |||||||
\(102\) | −106.391 | − | 40.9962i | −1.04305 | − | 0.401924i | ||||
\(103\) | 4.70396i | 0.0456696i | 0.999739 | + | 0.0228348i | \(0.00726917\pi\) | ||||
−0.999739 | + | 0.0228348i | \(0.992731\pi\) | |||||||
\(104\) | 38.9974i | 0.374975i | ||||||||
\(105\) | 74.4205 | − | 88.2126i | 0.708767 | − | 0.840120i | ||||
\(106\) | −29.2879 | −0.276301 | ||||||||
\(107\) | 143.867 | 1.34455 | 0.672276 | − | 0.740301i | \(-0.265317\pi\) | ||||
0.672276 | + | 0.740301i | \(0.265317\pi\) | |||||||
\(108\) | −24.3304 | − | 48.2082i | −0.225281 | − | 0.446372i | ||||
\(109\) | 101.340 | 0.929721 | 0.464860 | − | 0.885384i | \(-0.346105\pi\) | ||||
0.464860 | + | 0.885384i | \(0.346105\pi\) | |||||||
\(110\) | −38.5256 | + | 111.386i | −0.350232 | + | 1.01260i | ||||
\(111\) | 42.7402 | − | 110.917i | 0.385047 | − | 0.999254i | ||||
\(112\) | 30.7765i | 0.274790i | ||||||||
\(113\) | 44.1938 | 0.391096 | 0.195548 | − | 0.980694i | \(-0.437351\pi\) | ||||
0.195548 | + | 0.980694i | \(0.437351\pi\) | |||||||
\(114\) | 125.577 | + | 48.3890i | 1.10155 | + | 0.424465i | ||||
\(115\) | −22.6619 | − | 7.83820i | −0.197060 | − | 0.0681582i | ||||
\(116\) | 52.0990i | 0.449129i | ||||||||
\(117\) | 83.2677 | − | 92.0030i | 0.711690 | − | 0.786351i | ||||
\(118\) | − | 42.8907i | − | 0.363480i | ||||||
\(119\) | − | 206.771i | − | 1.73757i | ||||||
\(120\) | 32.4277 | + | 27.3577i | 0.270231 | + | 0.227980i | ||||
\(121\) | −156.820 | −1.29603 | ||||||||
\(122\) | 10.1248 | 0.0829902 | ||||||||
\(123\) | −69.5810 | + | 180.573i | −0.565699 | + | 1.46807i | ||||
\(124\) | −15.3659 | −0.123919 | ||||||||
\(125\) | 67.6443 | + | 105.115i | 0.541155 | + | 0.840923i | ||||
\(126\) | 65.7143 | − | 72.6081i | 0.521542 | − | 0.576255i | ||||
\(127\) | − | 221.597i | − | 1.74486i | −0.488739 | − | 0.872430i | \(-0.662543\pi\) | ||
0.488739 | − | 0.872430i | \(-0.337457\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | −62.6078 | + | 162.476i | −0.485332 | + | 1.25951i | ||||
\(130\) | −31.8682 | + | 92.1379i | −0.245140 | + | 0.708753i | ||||
\(131\) | − | 100.251i | − | 0.765273i | −0.923899 | − | 0.382637i | \(-0.875016\pi\) | ||
0.923899 | − | 0.382637i | \(-0.124984\pi\) | |||||||
\(132\) | −35.9591 | + | 93.3191i | −0.272417 | + | 0.706963i | ||||
\(133\) | 244.058i | 1.83502i | ||||||||
\(134\) | 124.993i | 0.932787i | ||||||||
\(135\) | −18.0894 | − | 133.783i | −0.133996 | − | 0.990982i | ||||
\(136\) | 76.0110 | 0.558905 | ||||||||
\(137\) | −154.818 | −1.13006 | −0.565030 | − | 0.825070i | \(-0.691136\pi\) | ||||
−0.565030 | + | 0.825070i | \(0.691136\pi\) | |||||||
\(138\) | −18.9862 | − | 7.31604i | −0.137581 | − | 0.0530148i | ||||
\(139\) | 188.794 | 1.35823 | 0.679114 | − | 0.734033i | \(-0.262364\pi\) | ||||
0.679114 | + | 0.734033i | \(0.262364\pi\) | |||||||
\(140\) | −25.1502 | + | 72.7146i | −0.179644 | + | 0.519390i | ||||
\(141\) | −202.175 | − | 77.9051i | −1.43387 | − | 0.552519i | ||||
\(142\) | 100.709i | 0.709215i | ||||||||
\(143\) | −229.812 | −1.60708 | ||||||||
\(144\) | 26.6914 | + | 24.1572i | 0.185357 | + | 0.167758i | ||||
\(145\) | −42.5747 | + | 123.093i | −0.293619 | + | 0.848915i | ||||
\(146\) | − | 39.9375i | − | 0.273544i | ||||||
\(147\) | 28.5518 | + | 11.0020i | 0.194230 | + | 0.0748435i | ||||
\(148\) | 79.2446i | 0.535437i | ||||||||
\(149\) | − | 47.2917i | − | 0.317394i | −0.987327 | − | 0.158697i | \(-0.949271\pi\) | ||
0.987327 | − | 0.158697i | \(-0.0507293\pi\) | |||||||
\(150\) | 54.2596 | + | 91.1367i | 0.361731 | + | 0.607578i | ||||
\(151\) | 31.0861 | 0.205868 | 0.102934 | − | 0.994688i | \(-0.467177\pi\) | ||||
0.102934 | + | 0.994688i | \(0.467177\pi\) | |||||||
\(152\) | −89.7180 | −0.590250 | ||||||||
\(153\) | −179.326 | − | 162.300i | −1.17206 | − | 1.06078i | ||||
\(154\) | −181.366 | −1.17770 | ||||||||
\(155\) | −36.3046 | − | 12.5569i | −0.234223 | − | 0.0810120i | ||||
\(156\) | −29.7453 | + | 77.1933i | −0.190675 | + | 0.494829i | ||||
\(157\) | 47.1835i | 0.300532i | 0.988646 | + | 0.150266i | \(0.0480130\pi\) | ||||
−0.988646 | + | 0.150266i | \(0.951987\pi\) | |||||||
\(158\) | 32.7122 | 0.207039 | ||||||||
\(159\) | −57.9739 | − | 22.3394i | −0.364616 | − | 0.140499i | ||||
\(160\) | −26.7305 | − | 9.24543i | −0.167066 | − | 0.0577840i | ||||
\(161\) | − | 36.8997i | − | 0.229191i | ||||||
\(162\) | −11.3899 | − | 113.984i | −0.0703083 | − | 0.703603i | ||||
\(163\) | − | 240.131i | − | 1.47320i | −0.676331 | − | 0.736598i | \(-0.736431\pi\) | ||
0.676331 | − | 0.736598i | \(-0.263569\pi\) | |||||||
\(164\) | − | 129.010i | − | 0.786646i | ||||||
\(165\) | −161.219 | + | 191.097i | −0.977083 | + | 1.15816i | ||||
\(166\) | −196.680 | −1.18482 | ||||||||
\(167\) | 81.2198 | 0.486346 | 0.243173 | − | 0.969983i | \(-0.421812\pi\) | ||||
0.243173 | + | 0.969983i | \(0.421812\pi\) | |||||||
\(168\) | −23.4747 | + | 60.9204i | −0.139731 | + | 0.362621i | ||||
\(169\) | −21.0997 | −0.124850 | ||||||||
\(170\) | 179.589 | + | 62.1154i | 1.05641 | + | 0.365384i | ||||
\(171\) | 211.664 | + | 191.567i | 1.23780 | + | 1.12028i | ||||
\(172\) | − | 116.081i | − | 0.674890i | ||||||
\(173\) | −31.4683 | −0.181898 | −0.0909488 | − | 0.995856i | \(-0.528990\pi\) | ||||
−0.0909488 | + | 0.995856i | \(0.528990\pi\) | |||||||
\(174\) | −39.7385 | + | 103.127i | −0.228382 | + | 0.592685i | ||||
\(175\) | −118.843 | + | 151.248i | −0.679103 | + | 0.864274i | ||||
\(176\) | − | 66.6717i | − | 0.378817i | ||||||
\(177\) | 32.7149 | − | 84.8999i | 0.184830 | − | 0.479660i | ||||
\(178\) | 63.6316i | 0.357481i | ||||||||
\(179\) | 100.597i | 0.561996i | 0.959708 | + | 0.280998i | \(0.0906653\pi\) | ||||
−0.959708 | + | 0.280998i | \(0.909335\pi\) | |||||||
\(180\) | 43.3220 | + | 78.8873i | 0.240678 | + | 0.438263i | ||||
\(181\) | 79.4785 | 0.439108 | 0.219554 | − | 0.975600i | \(-0.429540\pi\) | ||||
0.219554 | + | 0.975600i | \(0.429540\pi\) | |||||||
\(182\) | −150.025 | −0.824315 | ||||||||
\(183\) | 20.0415 | + | 7.72269i | 0.109516 | + | 0.0422005i | ||||
\(184\) | 13.5647 | 0.0737210 | ||||||||
\(185\) | −64.7578 | + | 187.229i | −0.350042 | + | 1.01205i | ||||
\(186\) | −30.4161 | − | 11.7204i | −0.163527 | − | 0.0630127i | ||||
\(187\) | 447.933i | 2.39537i | ||||||||
\(188\) | 144.444 | 0.768318 | ||||||||
\(189\) | 185.460 | − | 93.6004i | 0.981269 | − | 0.495240i | ||||
\(190\) | −211.974 | − | 73.3166i | −1.11565 | − | 0.385877i | ||||
\(191\) | 181.244i | 0.948921i | 0.880277 | + | 0.474461i | \(0.157357\pi\) | ||||
−0.880277 | + | 0.474461i | \(0.842643\pi\) | |||||||
\(192\) | −22.3949 | − | 8.62953i | −0.116640 | − | 0.0449455i | ||||
\(193\) | − | 180.172i | − | 0.933532i | −0.884381 | − | 0.466766i | \(-0.845419\pi\) | ||
0.884381 | − | 0.466766i | \(-0.154581\pi\) | |||||||
\(194\) | − | 84.0044i | − | 0.433013i | ||||||
\(195\) | −133.360 | + | 158.075i | −0.683896 | + | 0.810640i | ||||
\(196\) | −20.3988 | −0.104075 | ||||||||
\(197\) | 273.165 | 1.38663 | 0.693313 | − | 0.720637i | \(-0.256150\pi\) | ||||
0.693313 | + | 0.720637i | \(0.256150\pi\) | |||||||
\(198\) | −142.358 | + | 157.293i | −0.718981 | + | 0.794407i | ||||
\(199\) | −1.98578 | −0.00997879 | −0.00498939 | − | 0.999988i | \(-0.501588\pi\) | ||||
−0.00498939 | + | 0.999988i | \(0.501588\pi\) | |||||||
\(200\) | −55.6001 | − | 43.6878i | −0.278001 | − | 0.218439i | ||||
\(201\) | −95.3387 | + | 247.418i | −0.474322 | + | 1.23093i | ||||
\(202\) | 51.4691i | 0.254797i | ||||||||
\(203\) | −200.428 | −0.987329 | ||||||||
\(204\) | 150.460 | + | 57.9774i | 0.737548 | + | 0.284203i | ||||
\(205\) | 105.426 | − | 304.808i | 0.514271 | − | 1.48687i | ||||
\(206\) | − | 6.65241i | − | 0.0322933i | ||||||
\(207\) | −32.0019 | − | 28.9634i | −0.154598 | − | 0.139920i | ||||
\(208\) | − | 55.1507i | − | 0.265147i | ||||||
\(209\) | − | 528.709i | − | 2.52971i | ||||||
\(210\) | −105.246 | + | 124.751i | −0.501174 | + | 0.594054i | ||||
\(211\) | −216.942 | −1.02816 | −0.514081 | − | 0.857741i | \(-0.671867\pi\) | ||||
−0.514081 | + | 0.857741i | \(0.671867\pi\) | |||||||
\(212\) | 41.4194 | 0.195375 | ||||||||
\(213\) | −76.8154 | + | 199.347i | −0.360636 | + | 0.935903i | ||||
\(214\) | −203.459 | −0.950742 | ||||||||
\(215\) | 94.8601 | − | 274.261i | 0.441210 | − | 1.27563i | ||||
\(216\) | 34.4084 | + | 68.1767i | 0.159298 | + | 0.315633i | ||||
\(217\) | − | 59.1136i | − | 0.272413i | ||||||
\(218\) | −143.316 | −0.657412 | ||||||||
\(219\) | 30.4623 | − | 79.0541i | 0.139097 | − | 0.360978i | ||||
\(220\) | 54.4834 | − | 157.523i | 0.247652 | − | 0.716015i | ||||
\(221\) | 370.529i | 1.67660i | ||||||||
\(222\) | −60.4438 | + | 156.861i | −0.272269 | + | 0.706579i | ||||
\(223\) | 256.080i | 1.14834i | 0.818736 | + | 0.574171i | \(0.194675\pi\) | ||||
−0.818736 | + | 0.574171i | \(0.805325\pi\) | |||||||
\(224\) | − | 43.5245i | − | 0.194306i | ||||||
\(225\) | 37.8897 | + | 221.787i | 0.168399 | + | 0.985719i | ||||
\(226\) | −62.4995 | −0.276547 | ||||||||
\(227\) | 215.303 | 0.948473 | 0.474237 | − | 0.880397i | \(-0.342724\pi\) | ||||
0.474237 | + | 0.880397i | \(0.342724\pi\) | |||||||
\(228\) | −177.592 | − | 68.4324i | −0.778913 | − | 0.300142i | ||||
\(229\) | −182.701 | −0.797823 | −0.398911 | − | 0.916989i | \(-0.630612\pi\) | ||||
−0.398911 | + | 0.916989i | \(0.630612\pi\) | |||||||
\(230\) | 32.0488 | + | 11.0849i | 0.139343 | + | 0.0481952i | ||||
\(231\) | −359.004 | − | 138.337i | −1.55413 | − | 0.598860i | ||||
\(232\) | − | 73.6791i | − | 0.317582i | ||||||
\(233\) | 135.492 | 0.581512 | 0.290756 | − | 0.956797i | \(-0.406093\pi\) | ||||
0.290756 | + | 0.956797i | \(0.406093\pi\) | |||||||
\(234\) | −117.758 | + | 130.112i | −0.503241 | + | 0.556034i | ||||
\(235\) | 341.273 | + | 118.038i | 1.45222 | + | 0.502289i | ||||
\(236\) | 60.6566i | 0.257019i | ||||||||
\(237\) | 64.7521 | + | 24.9512i | 0.273216 | + | 0.105279i | ||||
\(238\) | 292.419i | 1.22865i | ||||||||
\(239\) | 301.405i | 1.26111i | 0.776145 | + | 0.630555i | \(0.217173\pi\) | ||||
−0.776145 | + | 0.630555i | \(0.782827\pi\) | |||||||
\(240\) | −45.8598 | − | 38.6896i | −0.191082 | − | 0.161207i | ||||
\(241\) | −88.1708 | −0.365854 | −0.182927 | − | 0.983127i | \(-0.558557\pi\) | ||||
−0.182927 | + | 0.983127i | \(0.558557\pi\) | |||||||
\(242\) | 221.777 | 0.916434 | ||||||||
\(243\) | 64.3952 | − | 234.312i | 0.265001 | − | 0.964248i | ||||
\(244\) | −14.3186 | −0.0586829 | ||||||||
\(245\) | −48.1956 | − | 16.6697i | −0.196717 | − | 0.0680394i | ||||
\(246\) | 98.4023 | − | 255.369i | 0.400009 | − | 1.03808i | ||||
\(247\) | − | 437.346i | − | 1.77063i | ||||||
\(248\) | 21.7307 | 0.0876238 | ||||||||
\(249\) | −389.318 | − | 150.018i | −1.56352 | − | 0.602480i | ||||
\(250\) | −95.6636 | − | 148.656i | −0.382654 | − | 0.594622i | ||||
\(251\) | − | 176.705i | − | 0.704003i | −0.936000 | − | 0.352001i | \(-0.885501\pi\) | ||
0.936000 | − | 0.352001i | \(-0.114499\pi\) | |||||||
\(252\) | −92.9340 | + | 102.683i | −0.368786 | + | 0.407474i | ||||
\(253\) | 79.9366i | 0.315955i | ||||||||
\(254\) | 313.386i | 1.23380i | ||||||||
\(255\) | 308.108 | + | 259.935i | 1.20827 | + | 1.01935i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 257.023 | 1.00009 | 0.500044 | − | 0.866000i | \(-0.333317\pi\) | ||||
0.500044 | + | 0.866000i | \(0.333317\pi\) | |||||||
\(258\) | 88.5408 | − | 229.776i | 0.343181 | − | 0.890606i | ||||
\(259\) | −304.859 | −1.17706 | ||||||||
\(260\) | 45.0685 | − | 130.303i | 0.173340 | − | 0.501164i | ||||
\(261\) | −157.321 | + | 173.824i | −0.602761 | + | 0.665994i | ||||
\(262\) | 141.776i | 0.541130i | ||||||||
\(263\) | 64.1622 | 0.243963 | 0.121981 | − | 0.992532i | \(-0.461075\pi\) | ||||
0.121981 | + | 0.992532i | \(0.461075\pi\) | |||||||
\(264\) | 50.8538 | − | 131.973i | 0.192628 | − | 0.499898i | ||||
\(265\) | 97.8603 | + | 33.8475i | 0.369284 | + | 0.127726i | ||||
\(266\) | − | 345.150i | − | 1.29756i | ||||||
\(267\) | −48.5350 | + | 125.955i | −0.181779 | + | 0.471743i | ||||
\(268\) | − | 176.767i | − | 0.659580i | ||||||
\(269\) | 417.123i | 1.55064i | 0.631568 | + | 0.775321i | \(0.282412\pi\) | ||||
−0.631568 | + | 0.775321i | \(0.717588\pi\) | |||||||
\(270\) | 25.5823 | + | 189.197i | 0.0947494 | + | 0.700730i | ||||
\(271\) | −375.668 | −1.38623 | −0.693115 | − | 0.720827i | \(-0.743762\pi\) | ||||
−0.693115 | + | 0.720827i | \(0.743762\pi\) | |||||||
\(272\) | −107.496 | −0.395205 | ||||||||
\(273\) | −296.967 | − | 114.432i | −1.08779 | − | 0.419164i | ||||
\(274\) | 218.946 | 0.799074 | ||||||||
\(275\) | 257.452 | − | 327.652i | 0.936190 | − | 1.19146i | ||||
\(276\) | 26.8505 | + | 10.3464i | 0.0972845 | + | 0.0374871i | ||||
\(277\) | 361.975i | 1.30677i | 0.757027 | + | 0.653384i | \(0.226651\pi\) | ||||
−0.757027 | + | 0.653384i | \(0.773349\pi\) | |||||||
\(278\) | −266.995 | −0.960412 | ||||||||
\(279\) | −51.2673 | − | 46.3997i | −0.183754 | − | 0.166307i | ||||
\(280\) | 35.5677 | − | 102.834i | 0.127028 | − | 0.367264i | ||||
\(281\) | − | 53.2019i | − | 0.189330i | −0.995509 | − | 0.0946652i | \(-0.969822\pi\) | ||
0.995509 | − | 0.0946652i | \(-0.0301781\pi\) | |||||||
\(282\) | 285.919 | + | 110.174i | 1.01390 | + | 0.390690i | ||||
\(283\) | − | 262.727i | − | 0.928363i | −0.885740 | − | 0.464182i | \(-0.846349\pi\) | ||
0.885740 | − | 0.464182i | \(-0.153651\pi\) | |||||||
\(284\) | − | 142.423i | − | 0.501491i | ||||||
\(285\) | −363.669 | − | 306.809i | −1.27603 | − | 1.07652i | ||||
\(286\) | 325.003 | 1.13637 | ||||||||
\(287\) | 496.309 | 1.72930 | ||||||||
\(288\) | −37.7473 | − | 34.1634i | −0.131067 | − | 0.118623i | ||||
\(289\) | 433.210 | 1.49900 | ||||||||
\(290\) | 60.2097 | − | 174.079i | 0.207620 | − | 0.600274i | ||||
\(291\) | 64.0744 | − | 166.282i | 0.220187 | − | 0.571417i | ||||
\(292\) | 56.4801i | 0.193425i | ||||||||
\(293\) | −249.475 | −0.851452 | −0.425726 | − | 0.904852i | \(-0.639981\pi\) | ||||
−0.425726 | + | 0.904852i | \(0.639981\pi\) | |||||||
\(294\) | −40.3783 | − | 15.5592i | −0.137341 | − | 0.0529223i | ||||
\(295\) | −49.5679 | + | 143.311i | −0.168027 | + | 0.485801i | ||||
\(296\) | − | 112.069i | − | 0.378611i | ||||||
\(297\) | −401.766 | + | 202.769i | −1.35275 | + | 0.682723i | ||||
\(298\) | 66.8806i | 0.224432i | ||||||||
\(299\) | 66.1233i | 0.221148i | ||||||||
\(300\) | −76.7347 | − | 128.887i | −0.255782 | − | 0.429622i | ||||
\(301\) | 446.570 | 1.48362 | ||||||||
\(302\) | −43.9624 | −0.145571 | ||||||||
\(303\) | −39.2580 | + | 101.880i | −0.129564 | + | 0.336239i | ||||
\(304\) | 126.880 | 0.417370 | ||||||||
\(305\) | −33.8302 | − | 11.7010i | −0.110919 | − | 0.0383640i | ||||
\(306\) | 253.605 | + | 229.526i | 0.828775 | + | 0.750086i | ||||
\(307\) | − | 368.547i | − | 1.20048i | −0.799820 | − | 0.600240i | \(-0.795072\pi\) | ||
0.799820 | − | 0.600240i | \(-0.204928\pi\) | |||||||
\(308\) | 256.490 | 0.832760 | ||||||||
\(309\) | 5.07412 | − | 13.1681i | 0.0164211 | − | 0.0426152i | ||||
\(310\) | 51.3425 | + | 17.7581i | 0.165621 | + | 0.0572842i | ||||
\(311\) | 446.781i | 1.43660i | 0.695735 | + | 0.718298i | \(0.255079\pi\) | ||||
−0.695735 | + | 0.718298i | \(0.744921\pi\) | |||||||
\(312\) | 42.0661 | − | 109.168i | 0.134827 | − | 0.349897i | ||||
\(313\) | 55.1749i | 0.176278i | 0.996108 | + | 0.0881388i | \(0.0280919\pi\) | ||||
−0.996108 | + | 0.0881388i | \(0.971908\pi\) | |||||||
\(314\) | − | 66.7276i | − | 0.212508i | ||||||
\(315\) | −303.484 | + | 166.662i | −0.963441 | + | 0.529086i | ||||
\(316\) | −46.2621 | −0.146399 | ||||||||
\(317\) | −296.868 | −0.936492 | −0.468246 | − | 0.883598i | \(-0.655114\pi\) | ||||
−0.468246 | + | 0.883598i | \(0.655114\pi\) | |||||||
\(318\) | 81.9875 | + | 31.5926i | 0.257822 | + | 0.0993479i | ||||
\(319\) | 434.191 | 1.36110 | ||||||||
\(320\) | 37.8027 | + | 13.0750i | 0.118133 | + | 0.0408594i | ||||
\(321\) | −402.736 | − | 155.188i | −1.25463 | − | 0.483452i | ||||
\(322\) | 52.1840i | 0.162062i | ||||||||
\(323\) | −852.445 | −2.63915 | ||||||||
\(324\) | 16.1078 | + | 161.197i | 0.0497154 | + | 0.497522i | ||||
\(325\) | 212.964 | − | 271.033i | 0.655273 | − | 0.833947i | ||||
\(326\) | 339.596i | 1.04171i | ||||||||
\(327\) | −283.686 | − | 109.314i | −0.867542 | − | 0.334294i | ||||
\(328\) | 182.448i | 0.556243i | ||||||||
\(329\) | 555.684i | 1.68901i | ||||||||
\(330\) | 227.998 | − | 270.252i | 0.690902 | − | 0.818945i | ||||
\(331\) | −589.940 | −1.78230 | −0.891148 | − | 0.453712i | \(-0.850100\pi\) | ||||
−0.891148 | + | 0.453712i | \(0.850100\pi\) | |||||||
\(332\) | 278.147 | 0.837793 | ||||||||
\(333\) | −239.291 | + | 264.394i | −0.718591 | + | 0.793975i | ||||
\(334\) | −114.862 | −0.343899 | ||||||||
\(335\) | 144.452 | − | 417.643i | 0.431201 | − | 1.24669i | ||||
\(336\) | 33.1983 | − | 86.1544i | 0.0988044 | − | 0.256412i | ||||
\(337\) | − | 58.6794i | − | 0.174123i | −0.996203 | − | 0.0870614i | \(-0.972252\pi\) | ||
0.996203 | − | 0.0870614i | \(-0.0277476\pi\) | |||||||
\(338\) | 29.8395 | 0.0882825 | ||||||||
\(339\) | −123.715 | − | 47.6715i | −0.364940 | − | 0.140624i | ||||
\(340\) | −253.977 | − | 87.8444i | −0.746991 | − | 0.258366i | ||||
\(341\) | 128.059i | 0.375540i | ||||||||
\(342\) | −299.338 | − | 270.917i | −0.875256 | − | 0.792154i | ||||
\(343\) | 298.536i | 0.870368i | ||||||||
\(344\) | 164.163i | 0.477219i | ||||||||
\(345\) | 54.9839 | + | 46.3872i | 0.159374 | + | 0.134456i | ||||
\(346\) | 44.5029 | 0.128621 | ||||||||
\(347\) | 202.744 | 0.584277 | 0.292138 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292138 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(348\) | 56.1987 | − | 145.844i | 0.161491 | − | 0.419092i | ||||
\(349\) | −201.859 | −0.578391 | −0.289196 | − | 0.957270i | \(-0.593388\pi\) | ||||
−0.289196 | + | 0.957270i | \(0.593388\pi\) | |||||||
\(350\) | 168.069 | − | 213.897i | 0.480198 | − | 0.611134i | ||||
\(351\) | −332.339 | + | 167.730i | −0.946836 | + | 0.477862i | ||||
\(352\) | 94.2881i | 0.267864i | ||||||||
\(353\) | 212.494 | 0.601965 | 0.300982 | − | 0.953630i | \(-0.402685\pi\) | ||||
0.300982 | + | 0.953630i | \(0.402685\pi\) | |||||||
\(354\) | −46.2658 | + | 120.067i | −0.130694 | + | 0.339171i | ||||
\(355\) | 116.387 | − | 336.499i | 0.327850 | − | 0.947885i | ||||
\(356\) | − | 89.9887i | − | 0.252777i | ||||||
\(357\) | −223.042 | + | 578.828i | −0.624768 | + | 1.62137i | ||||
\(358\) | − | 142.266i | − | 0.397391i | ||||||
\(359\) | 663.928i | 1.84938i | 0.380720 | + | 0.924690i | \(0.375676\pi\) | ||||
−0.380720 | + | 0.924690i | \(0.624324\pi\) | |||||||
\(360\) | −61.2665 | − | 111.563i | −0.170185 | − | 0.309899i | ||||
\(361\) | 645.166 | 1.78716 | ||||||||
\(362\) | −112.400 | −0.310496 | ||||||||
\(363\) | 438.996 | + | 169.160i | 1.20935 | + | 0.466006i | ||||
\(364\) | 212.168 | 0.582878 | ||||||||
\(365\) | −46.1549 | + | 133.444i | −0.126452 | + | 0.365599i | ||||
\(366\) | −28.3430 | − | 10.9215i | −0.0774398 | − | 0.0298402i | ||||
\(367\) | − | 630.396i | − | 1.71770i | −0.512227 | − | 0.858850i | \(-0.671179\pi\) | ||
0.512227 | − | 0.858850i | \(-0.328821\pi\) | |||||||
\(368\) | −19.1833 | −0.0521286 | ||||||||
\(369\) | 389.565 | − | 430.432i | 1.05573 | − | 1.16648i | ||||
\(370\) | 91.5814 | − | 264.781i | 0.247517 | − | 0.715626i | ||||
\(371\) | 159.343i | 0.429495i | ||||||||
\(372\) | 43.0148 | + | 16.5751i | 0.115631 | + | 0.0445567i | ||||
\(373\) | 383.897i | 1.02921i | 0.857426 | + | 0.514607i | \(0.172062\pi\) | ||||
−0.857426 | + | 0.514607i | \(0.827938\pi\) | |||||||
\(374\) | − | 633.473i | − | 1.69378i | ||||||
\(375\) | −75.9740 | − | 367.223i | −0.202597 | − | 0.979262i | ||||
\(376\) | −204.274 | −0.543283 | ||||||||
\(377\) | 359.162 | 0.952684 | ||||||||
\(378\) | −262.280 | + | 132.371i | −0.693862 | + | 0.350188i | ||||
\(379\) | 210.581 | 0.555621 | 0.277811 | − | 0.960636i | \(-0.410391\pi\) | ||||
0.277811 | + | 0.960636i | \(0.410391\pi\) | |||||||
\(380\) | 299.777 | + | 103.685i | 0.788886 | + | 0.272856i | ||||
\(381\) | −239.035 | + | 620.331i | −0.627388 | + | 1.62816i | ||||
\(382\) | − | 256.318i | − | 0.670989i | ||||||
\(383\) | −566.239 | −1.47843 | −0.739216 | − | 0.673469i | \(-0.764804\pi\) | ||||
−0.739216 | + | 0.673469i | \(0.764804\pi\) | |||||||
\(384\) | 31.6712 | + | 12.2040i | 0.0824770 | + | 0.0317812i | ||||
\(385\) | 606.001 | + | 209.601i | 1.57403 | + | 0.544417i | ||||
\(386\) | 254.801i | 0.660107i | ||||||||
\(387\) | 350.524 | − | 387.296i | 0.905746 | − | 1.00076i | ||||
\(388\) | 118.800i | 0.306186i | ||||||||
\(389\) | − | 120.478i | − | 0.309713i | −0.987937 | − | 0.154856i | \(-0.950509\pi\) | ||
0.987937 | − | 0.154856i | \(-0.0494915\pi\) | |||||||
\(390\) | 188.599 | − | 223.551i | 0.483587 | − | 0.573209i | ||||
\(391\) | 128.883 | 0.329624 | ||||||||
\(392\) | 28.8482 | 0.0735924 | ||||||||
\(393\) | −108.140 | + | 280.638i | −0.275164 | + | 0.714092i | ||||
\(394\) | −386.314 | −0.980492 | ||||||||
\(395\) | −109.302 | − | 37.8048i | −0.276714 | − | 0.0957085i | ||||
\(396\) | 201.325 | − | 222.445i | 0.508397 | − | 0.561731i | ||||
\(397\) | 214.516i | 0.540342i | 0.962812 | + | 0.270171i | \(0.0870802\pi\) | ||||
−0.962812 | + | 0.270171i | \(0.912920\pi\) | |||||||
\(398\) | 2.80831 | 0.00705607 | ||||||||
\(399\) | 263.263 | − | 683.207i | 0.659808 | − | 1.71230i | ||||
\(400\) | 78.6305 | + | 61.7839i | 0.196576 | + | 0.154460i | ||||
\(401\) | − | 630.643i | − | 1.57268i | −0.617796 | − | 0.786338i | \(-0.711974\pi\) | ||
0.617796 | − | 0.786338i | \(-0.288026\pi\) | |||||||
\(402\) | 134.829 | − | 349.902i | 0.335396 | − | 0.870402i | ||||
\(403\) | 105.930i | 0.262854i | ||||||||
\(404\) | − | 72.7883i | − | 0.180169i | ||||||
\(405\) | −93.6711 | + | 394.019i | −0.231287 | + | 0.972886i | ||||
\(406\) | 283.448 | 0.698147 | ||||||||
\(407\) | 660.422 | 1.62266 | ||||||||
\(408\) | −212.782 | − | 81.9924i | −0.521525 | − | 0.200962i | ||||
\(409\) | −464.370 | −1.13538 | −0.567689 | − | 0.823243i | \(-0.692163\pi\) | ||||
−0.567689 | + | 0.823243i | \(0.692163\pi\) | |||||||
\(410\) | −149.094 | + | 431.063i | −0.363644 | + | 1.05137i | ||||
\(411\) | 433.393 | + | 167.001i | 1.05448 | + | 0.406329i | ||||
\(412\) | 9.40793i | 0.0228348i | ||||||||
\(413\) | −233.349 | −0.565011 | ||||||||
\(414\) | 45.2575 | + | 40.9605i | 0.109318 | + | 0.0989383i | ||||
\(415\) | 657.170 | + | 227.299i | 1.58354 | + | 0.547708i | ||||
\(416\) | 77.9948i | 0.187488i | ||||||||
\(417\) | −528.502 | − | 203.650i | −1.26739 | − | 0.488369i | ||||
\(418\) | 747.707i | 1.78877i | ||||||||
\(419\) | − | 586.065i | − | 1.39872i | −0.714769 | − | 0.699361i | \(-0.753468\pi\) | ||
0.714769 | − | 0.699361i | \(-0.246532\pi\) | |||||||
\(420\) | 148.841 | − | 176.425i | 0.354383 | − | 0.420060i | ||||
\(421\) | −228.330 | −0.542353 | −0.271176 | − | 0.962530i | \(-0.587413\pi\) | ||||
−0.271176 | + | 0.962530i | \(0.587413\pi\) | |||||||
\(422\) | 306.803 | 0.727021 | ||||||||
\(423\) | 481.926 | + | 436.169i | 1.13931 | + | 1.03113i | ||||
\(424\) | −58.5759 | −0.138151 | ||||||||
\(425\) | −528.278 | − | 415.094i | −1.24301 | − | 0.976692i | ||||
\(426\) | 108.633 | − | 281.920i | 0.255008 | − | 0.661783i | ||||
\(427\) | − | 55.0846i | − | 0.129004i | ||||||
\(428\) | 287.734 | 0.672276 | ||||||||
\(429\) | 643.327 | + | 247.896i | 1.49960 | + | 0.577846i | ||||
\(430\) | −134.152 | + | 387.864i | −0.311982 | + | 0.902009i | ||||
\(431\) | − | 562.763i | − | 1.30571i | −0.757481 | − | 0.652857i | \(-0.773570\pi\) | ||
0.757481 | − | 0.652857i | \(-0.226430\pi\) | |||||||
\(432\) | −48.6608 | − | 96.4164i | −0.112641 | − | 0.223186i | ||||
\(433\) | − | 402.222i | − | 0.928919i | −0.885594 | − | 0.464459i | \(-0.846249\pi\) | ||
0.885594 | − | 0.464459i | \(-0.153751\pi\) | |||||||
\(434\) | 83.5993i | 0.192625i | ||||||||
\(435\) | 251.961 | − | 298.656i | 0.579221 | − | 0.686566i | ||||
\(436\) | 202.679 | 0.464860 | ||||||||
\(437\) | −152.124 | −0.348111 | ||||||||
\(438\) | −43.0802 | + | 111.799i | −0.0983566 | + | 0.255250i | ||||
\(439\) | −146.580 | −0.333896 | −0.166948 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166948 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(440\) | −77.0511 | + | 222.771i | −0.175116 | + | 0.506299i | ||||
\(441\) | −68.0590 | − | 61.5971i | −0.154329 | − | 0.139676i | ||||
\(442\) | − | 524.007i | − | 1.18554i | ||||||
\(443\) | −784.192 | −1.77019 | −0.885093 | − | 0.465414i | \(-0.845905\pi\) | ||||
−0.885093 | + | 0.465414i | \(0.845905\pi\) | |||||||
\(444\) | 85.4805 | − | 221.834i | 0.192524 | − | 0.499627i | ||||
\(445\) | 73.5377 | − | 212.613i | 0.165253 | − | 0.477783i | ||||
\(446\) | − | 362.152i | − | 0.812000i | ||||||
\(447\) | −51.0131 | + | 132.387i | −0.114123 | + | 0.296167i | ||||
\(448\) | 61.5529i | 0.137395i | ||||||||
\(449\) | − | 579.670i | − | 1.29103i | −0.763750 | − | 0.645513i | \(-0.776644\pi\) | ||
0.763750 | − | 0.645513i | \(-0.223356\pi\) | |||||||
\(450\) | −53.5841 | − | 313.654i | −0.119076 | − | 0.697009i | ||||
\(451\) | −1075.16 | −2.38396 | ||||||||
\(452\) | 88.3877 | 0.195548 | ||||||||
\(453\) | −87.0212 | − | 33.5323i | −0.192100 | − | 0.0740227i | ||||
\(454\) | −304.485 | −0.670672 | ||||||||
\(455\) | 501.282 | + | 173.381i | 1.10172 | + | 0.381057i | ||||
\(456\) | 251.153 | + | 96.7780i | 0.550775 | + | 0.212233i | ||||
\(457\) | 72.8841i | 0.159484i | 0.996816 | + | 0.0797419i | \(0.0254096\pi\) | ||||
−0.996816 | + | 0.0797419i | \(0.974590\pi\) | |||||||
\(458\) | 258.379 | 0.564146 | ||||||||
\(459\) | 326.927 | + | 647.773i | 0.712259 | + | 1.41127i | ||||
\(460\) | −45.3238 | − | 15.6764i | −0.0985301 | − | 0.0340791i | ||||
\(461\) | 188.695i | 0.409316i | 0.978834 | + | 0.204658i | \(0.0656082\pi\) | ||||
−0.978834 | + | 0.204658i | \(0.934392\pi\) | |||||||
\(462\) | 507.708 | + | 195.638i | 1.09894 | + | 0.423458i | ||||
\(463\) | 553.814i | 1.19614i | 0.801443 | + | 0.598072i | \(0.204066\pi\) | ||||
−0.801443 | + | 0.598072i | \(0.795934\pi\) | |||||||
\(464\) | 104.198i | 0.224565i | ||||||||
\(465\) | 88.0847 | + | 74.3127i | 0.189430 | + | 0.159812i | ||||
\(466\) | −191.615 | −0.411191 | ||||||||
\(467\) | −425.497 | −0.911129 | −0.455565 | − | 0.890203i | \(-0.650563\pi\) | ||||
−0.455565 | + | 0.890203i | \(0.650563\pi\) | |||||||
\(468\) | 166.535 | − | 184.006i | 0.355845 | − | 0.393175i | ||||
\(469\) | 680.034 | 1.44997 | ||||||||
\(470\) | −482.633 | − | 166.931i | −1.02688 | − | 0.355172i | ||||
\(471\) | 50.8964 | − | 132.084i | 0.108060 | − | 0.280432i | ||||
\(472\) | − | 85.7814i | − | 0.181740i | ||||||
\(473\) | −967.416 | −2.04528 | ||||||||
\(474\) | −91.5734 | − | 35.2864i | −0.193193 | − | 0.0744438i | ||||
\(475\) | 623.542 | + | 489.948i | 1.31272 | + | 1.03147i | ||||
\(476\) | − | 413.543i | − | 0.868787i | ||||||
\(477\) | 138.193 | + | 125.072i | 0.289712 | + | 0.262205i | ||||
\(478\) | − | 426.251i | − | 0.891739i | ||||||
\(479\) | − | 166.558i | − | 0.347720i | −0.984770 | − | 0.173860i | \(-0.944376\pi\) | ||
0.984770 | − | 0.173860i | \(-0.0556240\pi\) | |||||||
\(480\) | 64.8555 | + | 54.7153i | 0.135116 | + | 0.113990i | ||||
\(481\) | 546.299 | 1.13576 | ||||||||
\(482\) | 124.692 | 0.258698 | ||||||||
\(483\) | −39.8033 | + | 103.296i | −0.0824086 | + | 0.213862i | ||||
\(484\) | −313.640 | −0.648016 | ||||||||
\(485\) | −97.0822 | + | 280.686i | −0.200169 | + | 0.578733i | ||||
\(486\) | −91.0686 | + | 331.368i | −0.187384 | + | 0.681826i | ||||
\(487\) | − | 332.759i | − | 0.683284i | −0.939830 | − | 0.341642i | \(-0.889017\pi\) | ||
0.939830 | − | 0.341642i | \(-0.110983\pi\) | |||||||
\(488\) | 20.2496 | 0.0414951 | ||||||||
\(489\) | −259.027 | + | 672.213i | −0.529708 | + | 1.37467i | ||||
\(490\) | 68.1588 | + | 23.5745i | 0.139100 | + | 0.0481111i | ||||
\(491\) | 499.918i | 1.01816i | 0.860719 | + | 0.509081i | \(0.170015\pi\) | ||||
−0.860719 | + | 0.509081i | \(0.829985\pi\) | |||||||
\(492\) | −139.162 | + | 361.146i | −0.282849 | + | 0.734036i | ||||
\(493\) | − | 700.053i | − | 1.41999i | ||||||
\(494\) | 618.501i | 1.25203i | ||||||||
\(495\) | 657.444 | − | 361.044i | 1.32817 | − | 0.729382i | ||||
\(496\) | −30.7319 | −0.0619594 | ||||||||
\(497\) | 547.911 | 1.10244 | ||||||||
\(498\) | 550.578 | + | 212.157i | 1.10558 | + | 0.426018i | ||||
\(499\) | −29.1297 | −0.0583761 | −0.0291881 | − | 0.999574i | \(-0.509292\pi\) | ||||
−0.0291881 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(500\) | 135.289 | + | 210.231i | 0.270577 | + | 0.420462i | ||||
\(501\) | −227.364 | − | 87.6111i | −0.453820 | − | 0.174872i | ||||
\(502\) | 249.898i | 0.497805i | ||||||||
\(503\) | 445.761 | 0.886204 | 0.443102 | − | 0.896471i | \(-0.353878\pi\) | ||||
0.443102 | + | 0.896471i | \(0.353878\pi\) | |||||||
\(504\) | 131.429 | − | 145.216i | 0.260771 | − | 0.288127i | ||||
\(505\) | 59.4817 | − | 171.975i | 0.117786 | − | 0.340544i | ||||
\(506\) | − | 113.047i | − | 0.223414i | ||||||
\(507\) | 59.0657 | + | 22.7601i | 0.116500 | + | 0.0448916i | ||||
\(508\) | − | 443.194i | − | 0.872430i | ||||||
\(509\) | 208.350i | 0.409333i | 0.978832 | + | 0.204666i | \(0.0656110\pi\) | ||||
−0.978832 | + | 0.204666i | \(0.934389\pi\) | |||||||
\(510\) | −435.731 | − | 367.604i | −0.854374 | − | 0.720793i | ||||
\(511\) | −217.282 | −0.425210 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −385.881 | − | 764.585i | −0.752206 | − | 1.49042i | ||||
\(514\) | −363.485 | −0.707169 | ||||||||
\(515\) | −7.68805 | + | 22.2278i | −0.0149283 | + | 0.0431608i | ||||
\(516\) | −125.216 | + | 324.953i | −0.242666 | + | 0.629754i | ||||
\(517\) | − | 1203.79i | − | 2.32841i | ||||||
\(518\) | 431.135 | 0.832307 | ||||||||
\(519\) | 88.0912 | + | 33.9446i | 0.169732 | + | 0.0654038i | ||||
\(520\) | −63.7365 | + | 184.276i | −0.122570 | + | 0.354377i | ||||
\(521\) | − | 823.005i | − | 1.57966i | −0.613324 | − | 0.789832i | \(-0.710168\pi\) | ||
0.613324 | − | 0.789832i | \(-0.289832\pi\) | |||||||
\(522\) | 222.485 | − | 245.825i | 0.426216 | − | 0.470929i | ||||
\(523\) | 293.166i | 0.560546i | 0.959920 | + | 0.280273i | \(0.0904250\pi\) | ||||
−0.959920 | + | 0.280273i | \(0.909575\pi\) | |||||||
\(524\) | − | 200.502i | − | 0.382637i | ||||||
\(525\) | 495.834 | − | 295.203i | 0.944447 | − | 0.562291i | ||||
\(526\) | −90.7391 | −0.172508 | ||||||||
\(527\) | 206.472 | 0.391787 | ||||||||
\(528\) | −71.9182 | + | 186.638i | −0.136209 | + | 0.353482i | ||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | −138.395 | − | 47.8676i | −0.261123 | − | 0.0903161i | ||||
\(531\) | −183.161 | + | 202.376i | −0.344937 | + | 0.381123i | ||||
\(532\) | 488.116i | 0.917512i | ||||||||
\(533\) | −889.373 | −1.66862 | ||||||||
\(534\) | 68.6388 | − | 178.128i | 0.128537 | − | 0.333573i | ||||
\(535\) | 679.820 | + | 235.133i | 1.27069 | + | 0.439501i | ||||
\(536\) | 249.987i | 0.466393i | ||||||||
\(537\) | 108.513 | − | 281.608i | 0.202073 | − | 0.524410i | ||||
\(538\) | − | 589.900i | − | 1.09647i | ||||||
\(539\) | 170.003i | 0.315404i | ||||||||
\(540\) | −36.1789 | − | 267.565i | −0.0669979 | − | 0.495491i | ||||
\(541\) | 572.496 | 1.05822 | 0.529109 | − | 0.848554i | \(-0.322526\pi\) | ||||
0.529109 | + | 0.848554i | \(0.322526\pi\) | |||||||
\(542\) | 531.275 | 0.980212 | ||||||||
\(543\) | −222.489 | − | 85.7327i | −0.409740 | − | 0.157887i | ||||
\(544\) | 152.022 | 0.279452 | ||||||||
\(545\) | 478.864 | + | 165.627i | 0.878649 | + | 0.303903i | ||||
\(546\) | 419.975 | + | 161.831i | 0.769185 | + | 0.296394i | ||||
\(547\) | − | 168.725i | − | 0.308456i | −0.988035 | − | 0.154228i | \(-0.950711\pi\) | ||
0.988035 | − | 0.154228i | \(-0.0492890\pi\) | |||||||
\(548\) | −309.637 | −0.565030 | ||||||||
\(549\) | −47.7730 | − | 43.2372i | −0.0870183 | − | 0.0787563i | ||||
\(550\) | −364.093 | + | 463.370i | −0.661987 | + | 0.842490i | ||||
\(551\) | 826.293i | 1.49962i | ||||||||
\(552\) | −37.9724 | − | 14.6321i | −0.0687906 | − | 0.0265074i | ||||
\(553\) | − | 177.973i | − | 0.321832i | ||||||
\(554\) | − | 511.909i | − | 0.924024i | ||||||
\(555\) | 383.243 | − | 454.267i | 0.690527 | − | 0.818500i | ||||
\(556\) | 377.587 | 0.679114 | ||||||||
\(557\) | −990.965 | −1.77911 | −0.889555 | − | 0.456828i | \(-0.848986\pi\) | ||||
−0.889555 | + | 0.456828i | \(0.848986\pi\) | |||||||
\(558\) | 72.5029 | + | 65.6190i | 0.129934 | + | 0.117597i | ||||
\(559\) | −800.243 | −1.43156 | ||||||||
\(560\) | −50.3003 | + | 145.429i | −0.0898220 | + | 0.259695i | ||||
\(561\) | 483.182 | − | 1253.93i | 0.861286 | − | 2.23516i | ||||
\(562\) | 75.2388i | 0.133877i | ||||||||
\(563\) | 790.012 | 1.40322 | 0.701609 | − | 0.712562i | \(-0.252465\pi\) | ||||
0.701609 | + | 0.712562i | \(0.252465\pi\) | |||||||
\(564\) | −404.350 | − | 155.810i | −0.716933 | − | 0.276259i | ||||
\(565\) | 208.831 | + | 72.2294i | 0.369612 | + | 0.127840i | ||||
\(566\) | 371.552i | 0.656452i | ||||||||
\(567\) | −620.135 | + | 61.9676i | −1.09371 | + | 0.109290i | ||||
\(568\) | 201.417i | 0.354608i | ||||||||
\(569\) | − | 133.372i | − | 0.234398i | −0.993108 | − | 0.117199i | \(-0.962609\pi\) | ||
0.993108 | − | 0.117199i | \(-0.0373915\pi\) | |||||||
\(570\) | 514.306 | + | 433.894i | 0.902291 | + | 0.761218i | ||||
\(571\) | 1030.36 | 1.80449 | 0.902244 | − | 0.431227i | \(-0.141919\pi\) | ||||
0.902244 | + | 0.431227i | \(0.141919\pi\) | |||||||
\(572\) | −459.624 | −0.803538 | ||||||||
\(573\) | 195.506 | − | 507.367i | 0.341198 | − | 0.885458i | ||||
\(574\) | −701.887 | −1.22280 | ||||||||
\(575\) | −94.2746 | − | 74.0763i | −0.163956 | − | 0.128828i | ||||
\(576\) | 53.3828 | + | 48.3143i | 0.0926785 | + | 0.0838791i | ||||
\(577\) | 967.625i | 1.67699i | 0.544907 | + | 0.838497i | \(0.316565\pi\) | ||||
−0.544907 | + | 0.838497i | \(0.683435\pi\) | |||||||
\(578\) | −612.651 | −1.05995 | ||||||||
\(579\) | −194.349 | + | 504.365i | −0.335664 | + | 0.871098i | ||||
\(580\) | −85.1494 | + | 246.185i | −0.146809 | + | 0.424458i | ||||
\(581\) | 1070.05i | 1.84174i | ||||||||
\(582\) | −90.6148 | + | 235.159i | −0.155696 | + | 0.404053i | ||||
\(583\) | − | 345.188i | − | 0.592089i | ||||||
\(584\) | − | 79.8750i | − | 0.136772i | ||||||
\(585\) | 543.836 | − | 298.654i | 0.929634 | − | 0.510520i | ||||
\(586\) | 352.811 | 0.602067 | ||||||||
\(587\) | −947.013 | −1.61331 | −0.806655 | − | 0.591023i | \(-0.798724\pi\) | ||||
−0.806655 | + | 0.591023i | \(0.798724\pi\) | |||||||
\(588\) | 57.1036 | + | 22.0040i | 0.0971149 | + | 0.0374217i | ||||
\(589\) | −243.705 | −0.413760 | ||||||||
\(590\) | 70.0996 | − | 202.673i | 0.118813 | − | 0.343514i | ||||
\(591\) | −764.688 | − | 294.661i | −1.29389 | − | 0.498580i | ||||
\(592\) | 158.489i | 0.267718i | ||||||||
\(593\) | −579.653 | −0.977492 | −0.488746 | − | 0.872426i | \(-0.662546\pi\) | ||||
−0.488746 | + | 0.872426i | \(0.662546\pi\) | |||||||
\(594\) | 568.182 | − | 286.758i | 0.956536 | − | 0.482758i | ||||
\(595\) | 337.942 | − | 977.064i | 0.567970 | − | 1.64212i | ||||
\(596\) | − | 94.5834i | − | 0.158697i | ||||||
\(597\) | 5.55891 | + | 2.14204i | 0.00931141 | + | 0.00358801i | ||||
\(598\) | − | 93.5125i | − | 0.156375i | ||||||
\(599\) | − | 537.808i | − | 0.897843i | −0.893571 | − | 0.448922i | \(-0.851808\pi\) | ||
0.893571 | − | 0.448922i | \(-0.148192\pi\) | |||||||
\(600\) | 108.519 | + | 182.273i | 0.180865 | + | 0.303789i | ||||
\(601\) | 29.8675 | 0.0496964 | 0.0248482 | − | 0.999691i | \(-0.492090\pi\) | ||||
0.0248482 | + | 0.999691i | \(0.492090\pi\) | |||||||
\(602\) | −631.546 | −1.04908 | ||||||||
\(603\) | 533.775 | − | 589.771i | 0.885199 | − | 0.978062i | ||||
\(604\) | 62.1722 | 0.102934 | ||||||||
\(605\) | −741.027 | − | 256.303i | −1.22484 | − | 0.423641i | ||||
\(606\) | 55.5192 | − | 144.081i | 0.0916159 | − | 0.237757i | ||||
\(607\) | 828.617i | 1.36510i | 0.730838 | + | 0.682551i | \(0.239130\pi\) | ||||
−0.730838 | + | 0.682551i | \(0.760870\pi\) | |||||||
\(608\) | −179.436 | −0.295125 | ||||||||
\(609\) | 561.070 | + | 216.200i | 0.921297 | + | 0.355008i | ||||
\(610\) | 47.8431 | + | 16.5477i | 0.0784313 | + | 0.0271274i | ||||
\(611\) | − | 995.771i | − | 1.62974i | ||||||
\(612\) | −358.652 | − | 324.599i | −0.586032 | − | 0.530391i | ||||
\(613\) | − | 255.509i | − | 0.416817i | −0.978042 | − | 0.208409i | \(-0.933172\pi\) | ||
0.978042 | − | 0.208409i | \(-0.0668284\pi\) | |||||||
\(614\) | 521.204i | 0.848867i | ||||||||
\(615\) | −623.918 | + | 739.546i | −1.01450 | + | 1.20251i | ||||
\(616\) | −362.732 | −0.588850 | ||||||||
\(617\) | 591.174 | 0.958142 | 0.479071 | − | 0.877776i | \(-0.340974\pi\) | ||||
0.479071 | + | 0.877776i | \(0.340974\pi\) | |||||||
\(618\) | −7.17589 | + | 18.6225i | −0.0116115 | + | 0.0301335i | ||||
\(619\) | −1201.44 | −1.94094 | −0.970472 | − | 0.241215i | \(-0.922454\pi\) | ||||
−0.970472 | + | 0.241215i | \(0.922454\pi\) | |||||||
\(620\) | −72.6092 | − | 25.1137i | −0.117112 | − | 0.0405060i | ||||
\(621\) | 58.3422 | + | 115.599i | 0.0939488 | + | 0.186150i | ||||
\(622\) | − | 631.844i | − | 1.01583i | ||||||
\(623\) | 346.192 | 0.555685 | ||||||||
\(624\) | −59.4905 | + | 154.387i | −0.0953374 | + | 0.247414i | ||||
\(625\) | 147.844 | + | 607.262i | 0.236551 | + | 0.971619i | ||||
\(626\) | − | 78.0291i | − | 0.124647i | ||||||
\(627\) | −570.313 | + | 1480.05i | −0.909591 | + | 2.36052i | ||||
\(628\) | 94.3670i | 0.150266i | ||||||||
\(629\) | − | 1064.81i | − | 1.69286i | ||||||
\(630\) | 429.191 | − | 235.696i | 0.681256 | − | 0.374120i | ||||
\(631\) | 129.923 | 0.205900 | 0.102950 | − | 0.994687i | \(-0.467172\pi\) | ||||
0.102950 | + | 0.994687i | \(0.467172\pi\) | |||||||
\(632\) | 65.4245 | 0.103520 | ||||||||
\(633\) | 607.300 | + | 234.014i | 0.959400 | + | 0.369690i | ||||
\(634\) | 419.835 | 0.662200 | ||||||||
\(635\) | 362.174 | − | 1047.12i | 0.570352 | − | 1.64901i | ||||
\(636\) | −115.948 | − | 44.6787i | −0.182308 | − | 0.0702496i | ||||
\(637\) | 140.626i | 0.220763i | ||||||||
\(638\) | −614.039 | −0.962444 | ||||||||
\(639\) | 430.068 | − | 475.185i | 0.673033 | − | 0.743639i | ||||
\(640\) | −53.4611 | − | 18.4909i | −0.0835329 | − | 0.0288920i | ||||
\(641\) | 395.927i | 0.617670i | 0.951116 | + | 0.308835i | \(0.0999391\pi\) | ||||
−0.951116 | + | 0.308835i | \(0.900061\pi\) | |||||||
\(642\) | 569.555 | + | 219.469i | 0.887157 | + | 0.341852i | ||||
\(643\) | 787.933i | 1.22540i | 0.790315 | + | 0.612701i | \(0.209917\pi\) | ||||
−0.790315 | + | 0.612701i | \(0.790083\pi\) | |||||||
\(644\) | − | 73.7993i | − | 0.114595i | ||||||
\(645\) | −561.391 | + | 665.431i | −0.870373 | + | 1.03168i | ||||
\(646\) | 1205.54 | 1.86616 | ||||||||
\(647\) | −752.984 | −1.16381 | −0.581904 | − | 0.813257i | \(-0.697692\pi\) | ||||
−0.581904 | + | 0.813257i | \(0.697692\pi\) | |||||||
\(648\) | −22.7799 | − | 227.967i | −0.0351541 | − | 0.351801i | ||||
\(649\) | 505.510 | 0.778906 | ||||||||
\(650\) | −301.176 | + | 383.298i | −0.463348 | + | 0.589689i | ||||
\(651\) | −63.7653 | + | 165.480i | −0.0979498 | + | 0.254194i | ||||
\(652\) | − | 480.262i | − | 0.736598i | ||||||
\(653\) | 36.4462 | 0.0558135 | 0.0279067 | − | 0.999611i | \(-0.491116\pi\) | ||||
0.0279067 | + | 0.999611i | \(0.491116\pi\) | |||||||
\(654\) | 401.193 | + | 154.593i | 0.613445 | + | 0.236381i | ||||
\(655\) | 163.848 | − | 473.719i | 0.250149 | − | 0.723235i | ||||
\(656\) | − | 258.020i | − | 0.393323i | ||||||
\(657\) | −170.550 | + | 188.442i | −0.259589 | + | 0.286822i | ||||
\(658\) | − | 785.855i | − | 1.19431i | ||||||
\(659\) | 683.468i | 1.03713i | 0.855038 | + | 0.518565i | \(0.173533\pi\) | ||||
−0.855038 | + | 0.518565i | \(0.826467\pi\) | |||||||
\(660\) | −322.438 | + | 382.194i | −0.488542 | + | 0.579081i | ||||
\(661\) | −499.832 | −0.756176 | −0.378088 | − | 0.925770i | \(-0.623418\pi\) | ||||
−0.378088 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(662\) | 834.302 | 1.26027 | ||||||||
\(663\) | 399.686 | − | 1037.25i | 0.602845 | − | 1.56447i | ||||
\(664\) | −393.360 | −0.592409 | ||||||||
\(665\) | −398.883 | + | 1153.26i | −0.599824 | + | 1.73422i | ||||
\(666\) | 338.408 | − | 373.909i | 0.508120 | − | 0.561425i | ||||
\(667\) | − | 124.929i | − | 0.187300i | ||||||
\(668\) | 162.440 | 0.243173 | ||||||||
\(669\) | 276.231 | − | 716.861i | 0.412902 | − | 1.07154i | ||||
\(670\) | −204.286 | + | 590.636i | −0.304905 | + | 0.881546i | ||||
\(671\) | 119.331i | 0.177840i | ||||||||
\(672\) | −46.9495 | + | 121.841i | −0.0698653 | + | 0.181311i | ||||
\(673\) | − | 61.0956i | − | 0.0907810i | −0.998969 | − | 0.0453905i | \(-0.985547\pi\) | ||
0.998969 | − | 0.0453905i | \(-0.0144532\pi\) | |||||||
\(674\) | 82.9852i | 0.123123i | ||||||||
\(675\) | 133.172 | − | 661.733i | 0.197293 | − | 0.980345i | ||||
\(676\) | −42.1994 | −0.0624252 | ||||||||
\(677\) | −905.990 | −1.33824 | −0.669121 | − | 0.743153i | \(-0.733329\pi\) | ||||
−0.669121 | + | 0.743153i | \(0.733329\pi\) | |||||||
\(678\) | 174.959 | + | 67.4177i | 0.258051 | + | 0.0994361i | ||||
\(679\) | −457.031 | −0.673095 | ||||||||
\(680\) | 359.178 | + | 124.231i | 0.528203 | + | 0.182692i | ||||
\(681\) | −602.712 | − | 232.246i | −0.885040 | − | 0.341036i | ||||
\(682\) | − | 181.103i | − | 0.265547i | ||||||
\(683\) | 244.248 | 0.357611 | 0.178806 | − | 0.983884i | \(-0.442777\pi\) | ||||
0.178806 | + | 0.983884i | \(0.442777\pi\) | |||||||
\(684\) | 423.327 | + | 383.134i | 0.618900 | + | 0.560138i | ||||
\(685\) | −731.569 | − | 253.032i | −1.06798 | − | 0.369389i | ||||
\(686\) | − | 422.194i | − | 0.615443i | ||||||
\(687\) | 511.447 | + | 197.078i | 0.744465 | + | 0.286868i | ||||
\(688\) | − | 232.162i | − | 0.337445i | ||||||
\(689\) | − | 285.538i | − | 0.414424i | ||||||
\(690\) | −77.7590 | − | 65.6014i | −0.112694 | − | 0.0950744i | ||||
\(691\) | 919.272 | 1.33035 | 0.665175 | − | 0.746688i | \(-0.268357\pi\) | ||||
0.665175 | + | 0.746688i | \(0.268357\pi\) | |||||||
\(692\) | −62.9366 | −0.0909488 | ||||||||
\(693\) | 855.760 | + | 774.509i | 1.23486 | + | 1.11762i | ||||
\(694\) | −286.723 | −0.413146 | ||||||||
\(695\) | 892.114 | + | 308.560i | 1.28362 | + | 0.443971i | ||||
\(696\) | −79.4770 | + | 206.255i | −0.114191 | + | 0.296343i | ||||
\(697\) | 1733.50i | 2.48709i | ||||||||
\(698\) | 285.471 | 0.408984 | ||||||||
\(699\) | −379.292 | − | 146.154i | −0.542621 | − | 0.209091i | ||||
\(700\) | −237.686 | + | 302.496i | −0.339552 | + | 0.432137i | ||||
\(701\) | 310.828i | 0.443407i | 0.975114 | + | 0.221703i | \(0.0711617\pi\) | ||||
−0.975114 | + | 0.221703i | \(0.928838\pi\) | |||||||
\(702\) | 469.999 | − | 237.206i | 0.669514 | − | 0.337900i | ||||
\(703\) | 1256.82i | 1.78780i | ||||||||
\(704\) | − | 133.343i | − | 0.189408i | ||||||
\(705\) | −828.020 | − | 698.559i | −1.17450 | − | 0.990863i | ||||
\(706\) | −300.511 | −0.425653 | ||||||||
\(707\) | 280.021 | 0.396069 | ||||||||
\(708\) | 65.4297 | − | 169.800i | 0.0924149 | − | 0.239830i | ||||
\(709\) | −479.118 | −0.675766 | −0.337883 | − | 0.941188i | \(-0.609711\pi\) | ||||
−0.337883 | + | 0.941188i | \(0.609711\pi\) | |||||||
\(710\) | −164.596 | + | 475.882i | −0.231825 | + | 0.670256i | ||||
\(711\) | −154.350 | − | 139.695i | −0.217089 | − | 0.196477i | ||||
\(712\) | 127.263i | 0.178740i | ||||||||
\(713\) | 36.8462 | 0.0516777 | ||||||||
\(714\) | 315.429 | − | 818.586i | 0.441778 | − | 1.14648i | ||||
\(715\) | −1085.94 | − | 375.599i | −1.51880 | − | 0.525314i | ||||
\(716\) | 201.194i | 0.280998i | ||||||||
\(717\) | 325.123 | − | 843.742i | 0.453449 | − | 1.17677i | ||||
\(718\) | − | 938.935i | − | 1.30771i | ||||||
\(719\) | 1121.51i | 1.55982i | 0.625895 | + | 0.779908i | \(0.284734\pi\) | ||||
−0.625895 | + | 0.779908i | \(0.715266\pi\) | |||||||
\(720\) | 86.6440 | + | 157.775i | 0.120339 | + | 0.219131i | ||||
\(721\) | −36.1928 | −0.0501981 | ||||||||
\(722\) | −912.402 | −1.26372 | ||||||||
\(723\) | 246.822 | + | 95.1090i | 0.341386 | + | 0.131548i | ||||
\(724\) | 158.957 | 0.219554 | ||||||||
\(725\) | −402.360 | + | 512.071i | −0.554979 | + | 0.706305i | ||||
\(726\) | −620.834 | − | 239.229i | −0.855143 | − | 0.329516i | ||||
\(727\) | 552.754i | 0.760322i | 0.924920 | + | 0.380161i | \(0.124131\pi\) | ||||
−0.924920 | + | 0.380161i | \(0.875869\pi\) | |||||||
\(728\) | −300.050 | −0.412157 | ||||||||
\(729\) | −433.016 | + | 586.462i | −0.593986 | + | 0.804475i | ||||
\(730\) | 65.2729 | − | 188.718i | 0.0894150 | − | 0.258518i | ||||
\(731\) | 1559.78i | 2.13376i | ||||||||
\(732\) | 40.0830 | + | 15.4454i | 0.0547582 | + | 0.0211002i | ||||
\(733\) | − | 73.2361i | − | 0.0999128i | −0.998751 | − | 0.0499564i | \(-0.984092\pi\) | ||
0.998751 | − | 0.0499564i | \(-0.0159082\pi\) | |||||||
\(734\) | 891.514i | 1.21460i | ||||||||
\(735\) | 116.935 | + | 98.6525i | 0.159096 | + | 0.134221i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −1473.17 | −1.99888 | ||||||||
\(738\) | −550.927 | + | 608.723i | −0.746514 | + | 0.824828i | ||||
\(739\) | −503.948 | −0.681933 | −0.340966 | − | 0.940075i | \(-0.610754\pi\) | ||||
−0.340966 | + | 0.940075i | \(0.610754\pi\) | |||||||
\(740\) | −129.516 | + | 374.458i | −0.175021 | + | 0.506024i | ||||
\(741\) | −471.762 | + | 1224.29i | −0.636655 | + | 1.65221i | ||||
\(742\) | − | 225.345i | − | 0.303699i | ||||||
\(743\) | −310.256 | −0.417572 | −0.208786 | − | 0.977961i | \(-0.566951\pi\) | ||||
−0.208786 | + | 0.977961i | \(0.566951\pi\) | |||||||
\(744\) | −60.8321 | − | 23.4407i | −0.0817636 | − | 0.0315063i | ||||
\(745\) | 77.2925 | − | 223.469i | 0.103748 | − | 0.299959i | ||||
\(746\) | − | 542.912i | − | 0.727764i | ||||||
\(747\) | 928.018 | + | 839.907i | 1.24233 | + | 1.12437i | ||||
\(748\) | 895.867i | 1.19768i | ||||||||
\(749\) | 1106.93i | 1.47788i | ||||||||
\(750\) | 107.443 | + | 519.332i | 0.143258 | + | 0.692443i | ||||
\(751\) | 413.103 | 0.550070 | 0.275035 | − | 0.961434i | \(-0.411311\pi\) | ||||
0.275035 | + | 0.961434i | \(0.411311\pi\) | |||||||
\(752\) | 288.888 | 0.384159 | ||||||||
\(753\) | −190.610 | + | 494.660i | −0.253134 | + | 0.656919i | ||||
\(754\) | −507.932 | −0.673649 | ||||||||
\(755\) | 146.892 | + | 50.8064i | 0.194559 | + | 0.0672933i | ||||
\(756\) | 370.920 | − | 187.201i | 0.490634 | − | 0.247620i | ||||
\(757\) | 941.341i | 1.24351i | 0.783210 | + | 0.621757i | \(0.213581\pi\) | ||||
−0.783210 | + | 0.621757i | \(0.786419\pi\) | |||||||
\(758\) | −297.806 | −0.392884 | ||||||||
\(759\) | 86.2269 | − | 223.771i | 0.113606 | − | 0.294824i | ||||
\(760\) | −423.948 | − | 146.633i | −0.557826 | − | 0.192938i | ||||
\(761\) | 27.9347i | 0.0367079i | 0.999832 | + | 0.0183539i | \(0.00584256\pi\) | ||||
−0.999832 | + | 0.0183539i | \(0.994157\pi\) | |||||||
\(762\) | 338.046 | − | 877.280i | 0.443631 | − | 1.15129i | ||||
\(763\) | 779.718i | 1.02191i | ||||||||
\(764\) | 362.488i | 0.474461i | ||||||||
\(765\) | −582.117 | − | 1060.01i | −0.760937 | − | 1.38563i | ||||
\(766\) | 800.783 | 1.04541 | ||||||||
\(767\) | 418.156 | 0.545184 | ||||||||
\(768\) | −44.7898 | − | 17.2591i | −0.0583200 | − | 0.0224727i | ||||
\(769\) | −699.658 | −0.909829 | −0.454914 | − | 0.890535i | \(-0.650330\pi\) | ||||
−0.454914 | + | 0.890535i | \(0.650330\pi\) | |||||||
\(770\) | −857.014 | − | 296.420i | −1.11301 | − | 0.384961i | ||||
\(771\) | −719.499 | − | 277.248i | −0.933203 | − | 0.359595i | ||||
\(772\) | − | 360.343i | − | 0.466766i | ||||||
\(773\) | 1255.17 | 1.62376 | 0.811881 | − | 0.583823i | \(-0.198444\pi\) | ||||
0.811881 | + | 0.583823i | \(0.198444\pi\) | |||||||
\(774\) | −495.715 | + | 547.719i | −0.640459 | + | 0.707647i | ||||
\(775\) | −151.029 | − | 118.671i | −0.194876 | − | 0.153124i | ||||
\(776\) | − | 168.009i | − | 0.216506i | ||||||
\(777\) | 853.409 | + | 328.848i | 1.09834 | + | 0.423228i | ||||
\(778\) | 170.382i | 0.219000i | ||||||||
\(779\) | − | 2046.11i | − | 2.62658i | ||||||
\(780\) | −266.719 | + | 316.149i | −0.341948 | + | 0.405320i | ||||
\(781\) | −1186.95 | −1.51978 | ||||||||
\(782\) | −182.268 | −0.233079 | ||||||||
\(783\) | 627.900 | − | 316.897i | 0.801916 | − | 0.404722i | ||||
\(784\) | −40.7976 | −0.0520377 | ||||||||
\(785\) | −77.1157 | + | 222.958i | −0.0982365 | + | 0.284023i | ||||
\(786\) | 152.933 | − | 396.882i | 0.194571 | − | 0.504939i | ||||
\(787\) | − | 1188.27i | − | 1.50987i | −0.655800 | − | 0.754935i | \(-0.727669\pi\) | ||
0.655800 | − | 0.754935i | \(-0.272331\pi\) | |||||||
\(788\) | 546.330 | 0.693313 | ||||||||
\(789\) | −179.613 | − | 69.2112i | −0.227647 | − | 0.0877202i | ||||
\(790\) | 154.576 | + | 53.4641i | 0.195666 | + | 0.0676761i | ||||
\(791\) | 340.032i | 0.429877i | ||||||||
\(792\) | −284.717 | + | 314.585i | −0.359491 | + | 0.397203i | ||||
\(793\) | 98.7102i | 0.124477i | ||||||||
\(794\) | − | 303.371i | − | 0.382079i | ||||||
\(795\) | −237.435 | − | 200.312i | −0.298661 | − | 0.251965i | ||||
\(796\) | −3.97156 | −0.00498939 | ||||||||
\(797\) | −383.572 | −0.481270 | −0.240635 | − | 0.970616i | \(-0.577356\pi\) | ||||
−0.240635 | + | 0.970616i | \(0.577356\pi\) | |||||||
\(798\) | −372.311 | + | 966.201i | −0.466555 | + | 1.21078i | ||||
\(799\) | −1940.89 | −2.42915 | ||||||||
\(800\) | −111.200 | − | 87.3756i | −0.139000 | − | 0.109219i | ||||
\(801\) | 271.734 | − | 300.241i | 0.339243 | − | 0.374832i | ||||
\(802\) | 891.864i | 1.11205i | ||||||||
\(803\) | 470.703 | 0.586181 | ||||||||
\(804\) | −190.677 | + | 494.836i | −0.237161 | + | 0.615467i | ||||
\(805\) | 60.3080 | − | 174.363i | 0.0749168 | − | 0.216600i | ||||
\(806\) | − | 149.808i | − | 0.185866i | ||||||
\(807\) | 449.946 | − | 1167.68i | 0.557554 | − | 1.44694i | ||||
\(808\) | 102.938i | 0.127399i | ||||||||
\(809\) | 748.595i | 0.925334i | 0.886532 | + | 0.462667i | \(0.153107\pi\) | ||||
−0.886532 | + | 0.462667i | \(0.846893\pi\) | |||||||
\(810\) | 132.471 | − | 557.227i | 0.163544 | − | 0.687934i | ||||
\(811\) | 790.431 | 0.974638 | 0.487319 | − | 0.873224i | \(-0.337975\pi\) | ||||
0.487319 | + | 0.873224i | \(0.337975\pi\) | |||||||
\(812\) | −400.856 | −0.493665 | ||||||||
\(813\) | 1051.63 | + | 405.230i | 1.29352 | + | 0.498438i | ||||
\(814\) | −933.978 | −1.14739 | ||||||||
\(815\) | 392.464 | − | 1134.70i | 0.481551 | − | 1.39227i | ||||
\(816\) | 300.920 | + | 115.955i | 0.368774 | + | 0.142101i | ||||
\(817\) | − | 1841.05i | − | 2.25343i | ||||||
\(818\) | 656.718 | 0.802834 | ||||||||
\(819\) | 707.882 | + | 640.671i | 0.864325 | + | 0.782261i | ||||
\(820\) | 210.851 | − | 609.616i | 0.257135 | − | 0.743434i | ||||
\(821\) | − | 1076.43i | − | 1.31113i | −0.755140 | − | 0.655563i | \(-0.772431\pi\) | ||
0.755140 | − | 0.655563i | \(-0.227569\pi\) | |||||||
\(822\) | −612.910 | − | 236.175i | −0.745632 | − | 0.287318i | ||||
\(823\) | − | 156.761i | − | 0.190475i | −0.995455 | − | 0.0952377i | \(-0.969639\pi\) | ||
0.995455 | − | 0.0952377i | \(-0.0303611\pi\) | |||||||
\(824\) | − | 13.3048i | − | 0.0161466i | ||||||
\(825\) | −1074.14 | + | 639.505i | −1.30198 | + | 0.775157i | ||||
\(826\) | 330.006 | 0.399523 | ||||||||
\(827\) | −731.147 | −0.884095 | −0.442048 | − | 0.896992i | \(-0.645748\pi\) | ||||
−0.442048 | + | 0.896992i | \(0.645748\pi\) | |||||||
\(828\) | −64.0037 | − | 57.9269i | −0.0772992 | − | 0.0699600i | ||||
\(829\) | −147.303 | −0.177688 | −0.0888439 | − | 0.996046i | \(-0.528317\pi\) | ||||
−0.0888439 | + | 0.996046i | \(0.528317\pi\) | |||||||
\(830\) | −929.379 | − | 321.449i | −1.11973 | − | 0.387288i | ||||
\(831\) | 390.459 | − | 1013.30i | 0.469866 | − | 1.21937i | ||||
\(832\) | − | 110.301i | − | 0.132574i | ||||||
\(833\) | 274.098 | 0.329049 | ||||||||
\(834\) | 747.414 | + | 288.005i | 0.896180 | + | 0.345329i | ||||
\(835\) | 383.791 | + | 132.744i | 0.459630 | + | 0.158975i | ||||
\(836\) | − | 1057.42i | − | 1.26485i | ||||||
\(837\) | 93.4648 | + | 185.191i | 0.111666 | + | 0.221256i | ||||
\(838\) | 828.821i | 0.989046i | ||||||||
\(839\) | 932.751i | 1.11174i | 0.831269 | + | 0.555871i | \(0.187615\pi\) | ||||
−0.831269 | + | 0.555871i | \(0.812385\pi\) | |||||||
\(840\) | −210.493 | + | 249.503i | −0.250587 | + | 0.297027i | ||||
\(841\) | 162.423 | 0.193131 | ||||||||
\(842\) | 322.908 | 0.383501 | ||||||||
\(843\) | −57.3884 | + | 148.931i | −0.0680764 | + | 0.176668i | ||||
\(844\) | −433.885 | −0.514081 | ||||||||
\(845\) | −99.7032 | − | 34.4849i | −0.117992 | − | 0.0408105i | ||||
\(846\) | −681.546 | − | 616.836i | −0.805610 | − | 0.729121i | ||||
\(847\) | − | 1206.59i | − | 1.42455i | ||||||
\(848\) | 82.8388 | 0.0976873 | ||||||||
\(849\) | −283.401 | + | 735.467i | −0.333806 | + | 0.866275i | ||||
\(850\) | 747.098 | + | 587.032i | 0.878939 | + | 0.690626i | ||||
\(851\) | − | 190.022i | − | 0.223293i | ||||||
\(852\) | −153.631 | + | 398.695i | −0.180318 | + | 0.467952i | ||||
\(853\) | − | 592.947i | − | 0.695131i | −0.937656 | − | 0.347566i | \(-0.887008\pi\) | ||
0.937656 | − | 0.347566i | \(-0.112992\pi\) | |||||||
\(854\) | 77.9014i | 0.0912194i | ||||||||
\(855\) | 687.089 | + | 1251.16i | 0.803613 | + | 1.46334i | ||||
\(856\) | −406.918 | −0.475371 | ||||||||
\(857\) | −127.840 | −0.149171 | −0.0745855 | − | 0.997215i | \(-0.523763\pi\) | ||||
−0.0745855 | + | 0.997215i | \(0.523763\pi\) | |||||||
\(858\) | −909.801 | − | 350.578i | −1.06037 | − | 0.408599i | ||||
\(859\) | −171.883 | −0.200097 | −0.100049 | − | 0.994983i | \(-0.531900\pi\) | ||||
−0.100049 | + | 0.994983i | \(0.531900\pi\) | |||||||
\(860\) | 189.720 | − | 548.522i | 0.220605 | − | 0.637816i | ||||
\(861\) | −1389.35 | − | 535.364i | −1.61364 | − | 0.621793i | ||||
\(862\) | 795.867i | 0.923279i | ||||||||
\(863\) | 60.4223 | 0.0700143 | 0.0350071 | − | 0.999387i | \(-0.488855\pi\) | ||||
0.0350071 | + | 0.999387i | \(0.488855\pi\) | |||||||
\(864\) | 68.8167 | + | 136.353i | 0.0796490 | + | 0.157816i | ||||
\(865\) | −148.698 | − | 51.4311i | −0.171906 | − | 0.0594579i | ||||
\(866\) | 568.828i | 0.656845i | ||||||||
\(867\) | −1212.71 | − | 467.299i | −1.39874 | − | 0.538984i | ||||
\(868\) | − | 118.227i | − | 0.136206i | ||||||
\(869\) | 385.547i | 0.443667i | ||||||||
\(870\) | −356.327 | + | 422.363i | −0.409571 | + | 0.485475i | ||||
\(871\) | −1218.60 | −1.39909 | ||||||||
\(872\) | −286.632 | −0.328706 | ||||||||
\(873\) | −358.735 | + | 396.368i | −0.410922 | + | 0.454030i | ||||
\(874\) | 215.136 | 0.246151 | ||||||||
\(875\) | −808.770 | + | 520.463i | −0.924308 | + | 0.594815i | ||||
\(876\) | 60.9246 | − | 158.108i | 0.0695486 | − | 0.180489i | ||||
\(877\) | − | 295.791i | − | 0.337275i | −0.985678 | − | 0.168638i | \(-0.946063\pi\) | ||
0.985678 | − | 0.168638i | \(-0.0539368\pi\) | |||||||
\(878\) | 207.296 | 0.236100 | ||||||||
\(879\) | 698.372 | + | 269.107i | 0.794507 | + | 0.306151i | ||||
\(880\) | 108.967 | − | 315.046i | 0.123826 | − | 0.358007i | ||||
\(881\) | 1056.63i | 1.19935i | 0.800243 | + | 0.599676i | \(0.204704\pi\) | ||||
−0.800243 | + | 0.599676i | \(0.795296\pi\) | |||||||
\(882\) | 96.2500 | + | 87.1115i | 0.109127 | + | 0.0987658i | ||||
\(883\) | − | 1207.51i | − | 1.36751i | −0.729712 | − | 0.683755i | \(-0.760346\pi\) | ||
0.729712 | − | 0.683755i | \(-0.239654\pi\) | |||||||
\(884\) | 741.058i | 0.838301i | ||||||||
\(885\) | 293.347 | − | 347.712i | 0.331466 | − | 0.392895i | ||||
\(886\) | 1109.02 | 1.25171 | ||||||||
\(887\) | 1677.87 | 1.89163 | 0.945813 | − | 0.324712i | \(-0.105267\pi\) | ||||
0.945813 | + | 0.324712i | \(0.105267\pi\) | |||||||
\(888\) | −120.888 | + | 313.721i | −0.136135 | + | 0.353290i | ||||
\(889\) | 1704.99 | 1.91788 | ||||||||
\(890\) | −103.998 | + | 300.681i | −0.116852 | + | 0.337844i | ||||
\(891\) | 1343.41 | − | 134.242i | 1.50776 | − | 0.150664i | ||||
\(892\) | 512.160i | 0.574171i | ||||||||
\(893\) | 2290.89 | 2.56538 | ||||||||
\(894\) | 72.1435 | − | 187.223i | 0.0806974 | − | 0.209422i | ||||
\(895\) | −164.414 | + | 475.356i | −0.183703 | + | 0.531124i | ||||
\(896\) | − | 87.0490i | − | 0.0971529i | ||||||
\(897\) | 71.3266 | − | 185.103i | 0.0795169 | − | 0.206358i | ||||
\(898\) | 819.778i | 0.912893i | ||||||||
\(899\) | − | 200.137i | − | 0.222622i | ||||||
\(900\) | 75.7794 | + | 443.574i | 0.0841993 | + | 0.492859i | ||||
\(901\) | −556.552 | −0.617704 | ||||||||
\(902\) | 1520.51 | 1.68571 | ||||||||
\(903\) | −1250.11 | − | 481.711i | −1.38440 | − | 0.533457i | ||||
\(904\) | −124.999 | −0.138273 | ||||||||
\(905\) | 375.563 | + | 129.898i | 0.414986 | + | 0.143534i | ||||
\(906\) | 123.067 | + | 47.4218i | 0.135835 | + | 0.0523420i | ||||
\(907\) | 844.746i | 0.931363i | 0.884952 | + | 0.465682i | \(0.154191\pi\) | ||||
−0.884952 | + | 0.465682i | \(0.845809\pi\) | |||||||
\(908\) | 430.607 | 0.474237 | ||||||||
\(909\) | 219.795 | − | 242.853i | 0.241798 | − | 0.267165i | ||||
\(910\) | −708.920 | − | 245.198i | −0.779033 | − | 0.269448i | ||||
\(911\) | − | 536.985i | − | 0.589446i | −0.955583 | − | 0.294723i | \(-0.904773\pi\) | ||
0.955583 | − | 0.294723i | \(-0.0952273\pi\) | |||||||
\(912\) | −355.184 | − | 136.865i | −0.389457 | − | 0.150071i | ||||
\(913\) | − | 2318.07i | − | 2.53896i | ||||||
\(914\) | − | 103.074i | − | 0.112772i | ||||||
\(915\) | 82.0811 | + | 69.2477i | 0.0897061 | + | 0.0756805i | ||||
\(916\) | −365.403 | −0.398911 | ||||||||
\(917\) | 771.341 | 0.841157 | ||||||||
\(918\) | −462.345 | − | 916.089i | −0.503643 | − | 0.997918i | ||||
\(919\) | −210.848 | −0.229432 | −0.114716 | − | 0.993398i | \(-0.536596\pi\) | ||||
−0.114716 | + | 0.993398i | \(0.536596\pi\) | |||||||
\(920\) | 64.0976 | + | 22.1698i | 0.0696713 | + | 0.0240976i | ||||
\(921\) | −397.548 | + | 1031.70i | −0.431649 | + | 1.12019i | ||||
\(922\) | − | 266.855i | − | 0.289430i | ||||||
\(923\) | −981.843 | −1.06375 | ||||||||
\(924\) | −718.008 | − | 276.673i | −0.777065 | − | 0.299430i | ||||
\(925\) | −612.005 | + | 778.880i | −0.661627 | + | 0.842033i | ||||
\(926\) | − | 783.212i | − | 0.845801i | ||||||
\(927\) | −28.4086 | + | 31.3889i | −0.0306458 | + | 0.0338607i | ||||
\(928\) | − | 147.358i | − | 0.158791i | ||||||
\(929\) | 522.829i | 0.562787i | 0.959593 | + | 0.281393i | \(0.0907965\pi\) | ||||
−0.959593 | + | 0.281393i | \(0.909203\pi\) | |||||||
\(930\) | −124.571 | − | 105.094i | −0.133947 | − | 0.113004i | ||||
\(931\) | −323.526 | −0.347504 | ||||||||
\(932\) | 270.985 | 0.290756 | ||||||||
\(933\) | 481.939 | − | 1250.70i | 0.516548 | − | 1.34052i | ||||
\(934\) | 601.744 | 0.644266 | ||||||||
\(935\) | −732.092 | + | 2116.64i | −0.782986 | + | 2.26378i | ||||
\(936\) | −235.517 | + | 260.224i | −0.251620 | + | 0.278017i | ||||
\(937\) | 1249.72i | 1.33374i | 0.745172 | + | 0.666872i | \(0.232367\pi\) | ||||
−0.745172 | + | 0.666872i | \(0.767633\pi\) | |||||||
\(938\) | −961.714 | −1.02528 | ||||||||
\(939\) | 59.5167 | − | 154.454i | 0.0633830 | − | 0.164488i | ||||
\(940\) | 682.546 | + | 236.076i | 0.726112 | + | 0.251144i | ||||
\(941\) | − | 541.307i | − | 0.575247i | −0.957744 | − | 0.287623i | \(-0.907135\pi\) | ||
0.957744 | − | 0.287623i | \(-0.0928651\pi\) | |||||||
\(942\) | −71.9784 | + | 186.795i | −0.0764102 | + | 0.198296i | ||||
\(943\) | 309.355i | 0.328054i | ||||||||
\(944\) | 121.313i | 0.128510i | ||||||||
\(945\) | 1029.34 | − | 139.182i | 1.08925 | − | 0.147283i | ||||
\(946\) | 1368.13 | 1.44623 | ||||||||
\(947\) | 1102.89 | 1.16462 | 0.582310 | − | 0.812967i | \(-0.302149\pi\) | ||||
0.582310 | + | 0.812967i | \(0.302149\pi\) | |||||||
\(948\) | 129.504 | + | 49.9025i | 0.136608 | + | 0.0526397i | ||||
\(949\) | 389.365 | 0.410289 | ||||||||
\(950\) | −881.822 | − | 692.891i | −0.928233 | − | 0.729359i | ||||
\(951\) | 831.041 | + | 320.229i | 0.873860 | + | 0.336729i | ||||
\(952\) | 584.838i | 0.614325i | ||||||||
\(953\) | 955.559 | 1.00269 | 0.501343 | − | 0.865249i | \(-0.332840\pi\) | ||||
0.501343 | + | 0.865249i | \(0.332840\pi\) | |||||||
\(954\) | −195.434 | − | 176.878i | −0.204858 | − | 0.185407i | ||||
\(955\) | −296.221 | + | 856.439i | −0.310179 | + | 0.896794i | ||||
\(956\) | 602.811i | 0.630555i | ||||||||
\(957\) | −1215.46 | − | 468.358i | −1.27007 | − | 0.489403i | ||||
\(958\) | 235.549i | 0.245875i | ||||||||
\(959\) | − | 1191.19i | − | 1.24212i | ||||||
\(960\) | −91.7195 | − | 77.3791i | −0.0955412 | − | 0.0806033i | ||||
\(961\) | −901.972 | −0.938577 | ||||||||
\(962\) | −772.584 | −0.803102 | ||||||||
\(963\) | 960.004 | + | 868.855i | 0.996889 | + | 0.902238i | ||||
\(964\) | −176.342 | −0.182927 | ||||||||
\(965\) | 294.468 | − | 851.372i | 0.305149 | − | 0.882250i | ||||
\(966\) | 56.2904 | − | 146.082i | 0.0582717 | − | 0.151224i | ||||
\(967\) | − | 295.569i | − | 0.305656i | −0.988253 | − | 0.152828i | \(-0.951162\pi\) | ||
0.988253 | − | 0.152828i | \(-0.0488381\pi\) | |||||||
\(968\) | 443.554 | 0.458217 | ||||||||
\(969\) | 2386.30 | + | 919.525i | 2.46264 | + | 0.948942i | ||||
\(970\) | 137.295 | − | 396.949i | 0.141541 | − | 0.409226i | ||||
\(971\) | − | 667.702i | − | 0.687644i | −0.939035 | − | 0.343822i | \(-0.888278\pi\) | ||
0.939035 | − | 0.343822i | \(-0.111722\pi\) | |||||||
\(972\) | 128.790 | − | 468.625i | 0.132500 | − | 0.482124i | ||||
\(973\) | 1452.60i | 1.49291i | ||||||||
\(974\) | 470.593i | 0.483155i | ||||||||
\(975\) | −888.523 | + | 528.996i | −0.911306 | + | 0.542560i | ||||
\(976\) | −28.6373 | −0.0293415 | ||||||||
\(977\) | −1296.04 | −1.32655 | −0.663277 | − | 0.748374i | \(-0.730835\pi\) | ||||
−0.663277 | + | 0.748374i | \(0.730835\pi\) | |||||||
\(978\) | 366.319 | − | 950.653i | 0.374560 | − | 0.972038i | ||||
\(979\) | −749.963 | −0.766050 | ||||||||
\(980\) | −96.3911 | − | 33.3393i | −0.0983583 | − | 0.0340197i | ||||
\(981\) | 676.224 | + | 612.019i | 0.689321 | + | 0.623873i | ||||
\(982\) | − | 706.990i | − | 0.719949i | ||||||
\(983\) | −1094.14 | −1.11306 | −0.556532 | − | 0.830826i | \(-0.687868\pi\) | ||||
−0.556532 | + | 0.830826i | \(0.687868\pi\) | |||||||
\(984\) | 196.805 | − | 510.737i | 0.200005 | − | 0.519042i | ||||
\(985\) | 1290.80 | + | 446.455i | 1.31045 | + | 0.453254i | ||||
\(986\) | 990.025i | 1.00408i | ||||||||
\(987\) | 599.411 | − | 1555.56i | 0.607306 | − | 1.57605i | ||||
\(988\) | − | 874.693i | − | 0.885317i | ||||||
\(989\) | 278.353i | 0.281449i | ||||||||
\(990\) | −929.766 | + | 510.593i | −0.939158 | + | 0.515751i | ||||
\(991\) | −326.015 | −0.328976 | −0.164488 | − | 0.986379i | \(-0.552597\pi\) | ||||
−0.164488 | + | 0.986379i | \(0.552597\pi\) | |||||||
\(992\) | 43.4614 | 0.0438119 | ||||||||
\(993\) | 1651.46 | + | 636.363i | 1.66310 | + | 0.640849i | ||||
\(994\) | −774.863 | −0.779540 | ||||||||
\(995\) | −9.38347 | − | 3.24551i | −0.00943063 | − | 0.00326182i | ||||
\(996\) | −778.635 | − | 300.035i | −0.781762 | − | 0.301240i | ||||
\(997\) | 1813.34i | 1.81880i | 0.415922 | + | 0.909400i | \(0.363459\pi\) | ||||
−0.415922 | + | 0.909400i | \(0.636541\pi\) | |||||||
\(998\) | 41.1956 | 0.0412781 | ||||||||
\(999\) | 955.060 | − | 482.013i | 0.956016 | − | 0.482496i |
(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 | 690.3.b.a.599.5 | ✓ | 88 | |
3.2 | odd | 2 | inner | 690.3.b.a.599.83 | yes | 88 | |
5.4 | even | 2 | inner | 690.3.b.a.599.84 | yes | 88 | |
15.14 | odd | 2 | inner | 690.3.b.a.599.6 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.b.a.599.5 | ✓ | 88 | 1.1 | even | 1 | trivial | |
690.3.b.a.599.6 | yes | 88 | 15.14 | odd | 2 | inner | |
690.3.b.a.599.83 | yes | 88 | 3.2 | odd | 2 | inner | |
690.3.b.a.599.84 | yes | 88 | 5.4 | even | 2 | inner |