Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,3,Mod(67,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.g (of order \(6\), degree \(2\), not 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: | \(5.34061318146\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.1728283481971641.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 4 x^{10} - 6 x^{9} + 6 x^{8} - 8 x^{7} + 9 x^{6} - 16 x^{5} + 24 x^{4} - 48 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.0455406 - 1.41348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.67 |
Dual form | 196.3.g.k.79.1 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84709 | − | 0.766985i | −0.923544 | − | 0.383492i | ||||
\(3\) | −2.58484 | − | 1.49236i | −0.861614 | − | 0.497453i | 0.00293865 | − | 0.999996i | \(-0.499065\pi\) |
−0.864552 | + | 0.502543i | \(0.832398\pi\) | |||||||
\(4\) | 2.82347 | + | 2.83338i | 0.705867 | + | 0.708344i | ||||
\(5\) | 3.40268 | + | 5.89361i | 0.680536 | + | 1.17872i | 0.974818 | + | 0.223004i | \(0.0715862\pi\) |
−0.294282 | + | 0.955719i | \(0.595080\pi\) | |||||||
\(6\) | 3.62981 | + | 4.73905i | 0.604969 | + | 0.789842i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.04204 | − | 7.39905i | −0.380255 | − | 0.924882i | ||||
\(9\) | −0.0457311 | − | 0.0792086i | −0.00508124 | − | 0.00880096i | ||||
\(10\) | −1.76474 | − | 13.4958i | −0.176474 | − | 1.34958i | ||||
\(11\) | −12.4211 | − | 7.17132i | −1.12919 | − | 0.651938i | −0.185459 | − | 0.982652i | \(-0.559377\pi\) |
−0.943731 | + | 0.330714i | \(0.892710\pi\) | |||||||
\(12\) | −3.06981 | − | 11.5375i | −0.255817 | − | 0.961455i | ||||
\(13\) | 4.62243 | 0.355572 | 0.177786 | − | 0.984069i | \(-0.443107\pi\) | ||||
0.177786 | + | 0.984069i | \(0.443107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 20.3121i | − | 1.35414i | ||||||
\(16\) | −0.0560414 | + | 15.9999i | −0.00350259 | + | 0.999994i | ||||
\(17\) | −5.80536 | + | 10.0552i | −0.341492 | + | 0.591481i | −0.984710 | − | 0.174202i | \(-0.944265\pi\) |
0.643218 | + | 0.765683i | \(0.277599\pi\) | |||||||
\(18\) | 0.0237176 | + | 0.181380i | 0.00131765 | + | 0.0100767i | ||||
\(19\) | −19.4361 | + | 11.2214i | −1.02295 | + | 0.590601i | −0.914957 | − | 0.403550i | \(-0.867776\pi\) |
−0.107994 | + | 0.994152i | \(0.534443\pi\) | |||||||
\(20\) | −7.09146 | + | 26.2815i | −0.354573 | + | 1.31408i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 17.4426 | + | 22.7728i | 0.792843 | + | 1.03513i | ||||
\(23\) | −0.739535 | + | 0.426971i | −0.0321537 | + | 0.0185639i | −0.515991 | − | 0.856594i | \(-0.672576\pi\) |
0.483837 | + | 0.875158i | \(0.339243\pi\) | |||||||
\(24\) | −3.17885 | + | 23.6652i | −0.132452 | + | 0.986050i | ||||
\(25\) | −10.6564 | + | 18.4575i | −0.426258 | + | 0.738300i | ||||
\(26\) | −8.53804 | − | 3.54533i | −0.328386 | − | 0.136359i | ||||
\(27\) | 27.1354i | 1.00502i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.8321 | −1.47697 | −0.738485 | − | 0.674270i | \(-0.764459\pi\) | ||||
−0.738485 | + | 0.674270i | \(0.764459\pi\) | |||||||
\(30\) | −15.5790 | + | 37.5182i | −0.519301 | + | 1.25061i | ||||
\(31\) | −1.34219 | − | 0.774912i | −0.0432963 | − | 0.0249972i | 0.478196 | − | 0.878253i | \(-0.341291\pi\) |
−0.521492 | + | 0.853256i | \(0.674624\pi\) | |||||||
\(32\) | 12.3752 | − | 29.5102i | 0.386725 | − | 0.922195i | ||||
\(33\) | 21.4044 | + | 37.0734i | 0.648617 | + | 1.12344i | ||||
\(34\) | 18.4352 | − | 14.1202i | 0.542211 | − | 0.415299i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0953074 | − | 0.353217i | 0.00264743 | − | 0.00981157i | ||||
\(37\) | −22.5075 | − | 38.9842i | −0.608312 | − | 1.05363i | −0.991519 | − | 0.129964i | \(-0.958514\pi\) |
0.383207 | − | 0.923663i | \(-0.374820\pi\) | |||||||
\(38\) | 44.5068 | − | 5.81979i | 1.17123 | − | 0.153152i | ||||
\(39\) | −11.9483 | − | 6.89833i | −0.306366 | − | 0.176880i | ||||
\(40\) | 33.2561 | − | 43.1052i | 0.831402 | − | 1.07763i | ||||
\(41\) | −36.6492 | −0.893883 | −0.446942 | − | 0.894563i | \(-0.647487\pi\) | ||||
−0.446942 | + | 0.894563i | \(0.647487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.9894i | 0.650916i | 0.945557 | + | 0.325458i | \(0.105518\pi\) | ||||
−0.945557 | + | 0.325458i | \(0.894482\pi\) | |||||||
\(44\) | −14.7515 | − | 55.4416i | −0.335262 | − | 1.26004i | ||||
\(45\) | 0.311217 | − | 0.539043i | 0.00691592 | − | 0.0119787i | ||||
\(46\) | 1.69347 | − | 0.221441i | 0.0368145 | − | 0.00481393i | ||||
\(47\) | −36.5237 | + | 21.0870i | −0.777100 | + | 0.448659i | −0.835402 | − | 0.549640i | \(-0.814765\pi\) |
0.0583012 | + | 0.998299i | \(0.481432\pi\) | |||||||
\(48\) | 24.0225 | − | 41.2736i | 0.500468 | − | 0.859866i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 33.8400 | − | 25.9193i | 0.676800 | − | 0.518386i | ||||
\(51\) | 30.0119 | − | 17.3274i | 0.588468 | − | 0.339752i | ||||
\(52\) | 13.0513 | + | 13.0971i | 0.250987 | + | 0.251867i | ||||
\(53\) | −21.7022 | + | 37.5893i | −0.409475 | + | 0.709232i | −0.994831 | − | 0.101545i | \(-0.967621\pi\) |
0.585356 | + | 0.810776i | \(0.300955\pi\) | |||||||
\(54\) | 20.8125 | − | 50.1216i | 0.385416 | − | 0.928177i | ||||
\(55\) | − | 97.6068i | − | 1.77467i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 66.9856 | 1.17519 | ||||||||
\(58\) | 79.1147 | + | 32.8516i | 1.36405 | + | 0.566407i | ||||
\(59\) | −46.7636 | − | 26.9990i | −0.792603 | − | 0.457609i | 0.0482754 | − | 0.998834i | \(-0.484627\pi\) |
−0.840878 | + | 0.541225i | \(0.817961\pi\) | |||||||
\(60\) | 57.5517 | − | 57.3505i | 0.959196 | − | 0.955842i | ||||
\(61\) | 7.97489 | + | 13.8129i | 0.130736 | + | 0.226441i | 0.923960 | − | 0.382488i | \(-0.124933\pi\) |
−0.793225 | + | 0.608929i | \(0.791599\pi\) | |||||||
\(62\) | 1.88479 | + | 2.46077i | 0.0303999 | + | 0.0396898i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −45.4920 | + | 45.0164i | −0.710812 | + | 0.703382i | ||||
\(65\) | 15.7287 | + | 27.2428i | 0.241979 | + | 0.419120i | ||||
\(66\) | −11.1010 | − | 84.8947i | −0.168197 | − | 1.28628i | ||||
\(67\) | 79.6270 | + | 45.9726i | 1.18846 | + | 0.686159i | 0.957957 | − | 0.286912i | \(-0.0926288\pi\) |
0.230505 | + | 0.973071i | \(0.425962\pi\) | |||||||
\(68\) | −44.8813 | + | 11.9417i | −0.660020 | + | 0.175613i | ||||
\(69\) | 2.54877 | 0.0369387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.3585i | − | 0.230401i | −0.993342 | − | 0.115201i | \(-0.963249\pi\) | ||
0.993342 | − | 0.115201i | \(-0.0367511\pi\) | |||||||
\(72\) | −0.446953 | + | 0.579323i | −0.00620768 | + | 0.00804615i | ||||
\(73\) | −4.79364 | + | 8.30283i | −0.0656663 | + | 0.113737i | −0.896989 | − | 0.442052i | \(-0.854251\pi\) |
0.831323 | + | 0.555790i | \(0.187584\pi\) | |||||||
\(74\) | 11.6731 | + | 89.2702i | 0.157745 | + | 1.20635i | ||||
\(75\) | 55.0904 | − | 31.8065i | 0.734539 | − | 0.424086i | ||||
\(76\) | −86.6717 | − | 23.3864i | −1.14042 | − | 0.307715i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.7786 | + | 21.9059i | 0.215110 | + | 0.280845i | ||||
\(79\) | 49.3484 | − | 28.4913i | 0.624663 | − | 0.360649i | −0.154019 | − | 0.988068i | \(-0.549222\pi\) |
0.778682 | + | 0.627418i | \(0.215888\pi\) | |||||||
\(80\) | −94.4879 | + | 54.1122i | −1.18110 | + | 0.676403i | ||||
\(81\) | 40.0842 | − | 69.4279i | 0.494867 | − | 0.857135i | ||||
\(82\) | 67.6943 | + | 28.1094i | 0.825541 | + | 0.342797i | ||||
\(83\) | − | 14.3077i | − | 0.172381i | −0.996279 | − | 0.0861907i | \(-0.972531\pi\) | ||
0.996279 | − | 0.0861907i | \(-0.0274694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −79.0151 | −0.929589 | ||||||||
\(86\) | 21.4674 | − | 51.6989i | 0.249621 | − | 0.601150i | ||||
\(87\) | 110.714 | + | 63.9209i | 1.27258 | + | 0.734723i | ||||
\(88\) | −15.2755 | + | 113.720i | −0.173585 | + | 1.29227i | ||||
\(89\) | −50.0680 | − | 86.7204i | −0.562562 | − | 0.974386i | −0.997272 | − | 0.0738155i | \(-0.976482\pi\) |
0.434710 | − | 0.900571i | \(-0.356851\pi\) | |||||||
\(90\) | −0.988282 | + | 0.756962i | −0.0109809 | + | 0.00841068i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.29782 | − | 0.889842i | −0.0358459 | − | 0.00967219i | ||||
\(93\) | 2.31289 | + | 4.00605i | 0.0248698 | + | 0.0430758i | ||||
\(94\) | 83.6359 | − | 10.9364i | 0.889744 | − | 0.116344i | ||||
\(95\) | −132.269 | − | 76.3658i | −1.39231 | − | 0.803850i | ||||
\(96\) | −76.0278 | + | 57.8111i | −0.791956 | + | 0.602199i | ||||
\(97\) | 68.2834 | 0.703952 | 0.351976 | − | 0.936009i | \(-0.385510\pi\) | ||||
0.351976 | + | 0.936009i | \(0.385510\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.31181i | 0.0132506i | ||||||||
\(100\) | −82.3852 | + | 21.9205i | −0.823852 | + | 0.219205i | ||||
\(101\) | 14.0814 | − | 24.3897i | 0.139420 | − | 0.241483i | −0.787857 | − | 0.615858i | \(-0.788810\pi\) |
0.927277 | + | 0.374375i | \(0.122143\pi\) | |||||||
\(102\) | −68.7244 | + | 8.98652i | −0.673768 | + | 0.0881031i | ||||
\(103\) | 138.774 | − | 80.1213i | 1.34732 | − | 0.777877i | 0.359453 | − | 0.933163i | \(-0.382963\pi\) |
0.987870 | + | 0.155286i | \(0.0496299\pi\) | |||||||
\(104\) | −14.0616 | − | 34.2016i | −0.135208 | − | 0.328862i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 68.9162 | − | 52.7855i | 0.650153 | − | 0.497976i | ||||
\(107\) | −102.990 | + | 59.4613i | −0.962524 | + | 0.555713i | −0.896949 | − | 0.442134i | \(-0.854221\pi\) |
−0.0655750 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(108\) | −76.8849 | + | 76.6161i | −0.711897 | + | 0.709408i | ||||
\(109\) | 49.1333 | − | 85.1014i | 0.450764 | − | 0.780747i | −0.547669 | − | 0.836695i | \(-0.684485\pi\) |
0.998434 | + | 0.0559480i | \(0.0178181\pi\) | |||||||
\(110\) | −74.8629 | + | 180.288i | −0.680572 | + | 1.63898i | ||||
\(111\) | 134.357i | 1.21043i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 96.9977 | 0.858387 | 0.429193 | − | 0.903213i | \(-0.358798\pi\) | ||||
0.429193 | + | 0.903213i | \(0.358798\pi\) | |||||||
\(114\) | −123.728 | − | 51.3769i | −1.08534 | − | 0.450674i | ||||
\(115\) | −5.03280 | − | 2.90569i | −0.0437635 | − | 0.0252669i | ||||
\(116\) | −120.935 | − | 121.360i | −1.04255 | − | 1.04620i | ||||
\(117\) | −0.211389 | − | 0.366137i | −0.00180674 | − | 0.00312937i | ||||
\(118\) | 65.6686 | + | 85.7364i | 0.556514 | + | 0.726579i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −150.290 | + | 61.7901i | −1.25242 | + | 0.514918i | ||||
\(121\) | 42.3556 | + | 73.3620i | 0.350046 | + | 0.606298i | ||||
\(122\) | −4.13603 | − | 31.6303i | −0.0339019 | − | 0.259265i | ||||
\(123\) | 94.7324 | + | 54.6938i | 0.770182 | + | 0.444665i | ||||
\(124\) | −1.59401 | − | 5.99086i | −0.0128549 | − | 0.0483134i | ||||
\(125\) | 25.0921 | 0.200737 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 71.8712i | 0.565915i | 0.959132 | + | 0.282958i | \(0.0913156\pi\) | ||||
−0.959132 | + | 0.282958i | \(0.908684\pi\) | |||||||
\(128\) | 118.555 | − | 48.2577i | 0.926208 | − | 0.377013i | ||||
\(129\) | 41.7702 | − | 72.3481i | 0.323800 | − | 0.560838i | ||||
\(130\) | −8.15738 | − | 62.3835i | −0.0627491 | − | 0.479873i | ||||
\(131\) | −181.724 | + | 104.919i | −1.38721 | + | 0.800906i | −0.993000 | − | 0.118115i | \(-0.962315\pi\) |
−0.394209 | + | 0.919021i | \(0.628982\pi\) | |||||||
\(132\) | −44.6084 | + | 165.322i | −0.337943 | + | 1.25244i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −111.818 | − | 145.988i | −0.834460 | − | 1.08946i | ||||
\(135\) | −159.926 | + | 92.3332i | −1.18464 | + | 0.683950i | ||||
\(136\) | 92.0589 | + | 12.3659i | 0.676904 | + | 0.0909257i | ||||
\(137\) | 9.08248 | − | 15.7313i | 0.0662954 | − | 0.114827i | −0.830972 | − | 0.556314i | \(-0.812215\pi\) |
0.897268 | + | 0.441486i | \(0.145549\pi\) | |||||||
\(138\) | −4.70781 | − | 1.95487i | −0.0341146 | − | 0.0141657i | ||||
\(139\) | 134.084i | 0.964635i | 0.875996 | + | 0.482318i | \(0.160205\pi\) | ||||
−0.875996 | + | 0.482318i | \(0.839795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 125.877 | 0.892747 | ||||||||
\(142\) | −12.5467 | + | 30.2156i | −0.0883571 | + | 0.212786i | ||||
\(143\) | −57.4156 | − | 33.1489i | −0.401508 | − | 0.231811i | ||||
\(144\) | 1.26989 | − | 0.727254i | 0.00881870 | − | 0.00505038i | ||||
\(145\) | −145.744 | − | 252.436i | −1.00513 | − | 1.74094i | ||||
\(146\) | 15.2224 | − | 11.6594i | 0.104263 | − | 0.0798590i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 46.9076 | − | 173.843i | 0.316943 | − | 1.17461i | ||||
\(149\) | 10.3809 | + | 17.9803i | 0.0696706 | + | 0.120673i | 0.898756 | − | 0.438449i | \(-0.144472\pi\) |
−0.829086 | + | 0.559122i | \(0.811139\pi\) | |||||||
\(150\) | −126.152 | + | 16.4959i | −0.841013 | + | 0.109972i | ||||
\(151\) | 80.6348 | + | 46.5545i | 0.534005 | + | 0.308308i | 0.742646 | − | 0.669684i | \(-0.233571\pi\) |
−0.208641 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(152\) | 142.153 | + | 109.673i | 0.935219 | + | 0.721530i | ||||
\(153\) | 1.06194 | 0.00694080 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 10.5471i | − | 0.0680458i | ||||||
\(156\) | −14.1900 | − | 53.3311i | −0.0909614 | − | 0.341866i | ||||
\(157\) | −79.6687 | + | 137.990i | −0.507444 | + | 0.878919i | 0.492519 | + | 0.870302i | \(0.336076\pi\) |
−0.999963 | + | 0.00861697i | \(0.997257\pi\) | |||||||
\(158\) | −113.003 | + | 14.7765i | −0.715210 | + | 0.0935222i | ||||
\(159\) | 112.193 | − | 64.7749i | 0.705619 | − | 0.407389i | ||||
\(160\) | 216.031 | − | 27.4793i | 1.35019 | − | 0.171746i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −127.289 | + | 97.4955i | −0.785736 | + | 0.601824i | ||||
\(163\) | −39.6880 | + | 22.9139i | −0.243485 | + | 0.140576i | −0.616777 | − | 0.787138i | \(-0.711562\pi\) |
0.373293 | + | 0.927714i | \(0.378229\pi\) | |||||||
\(164\) | −103.478 | − | 103.841i | −0.630963 | − | 0.633177i | ||||
\(165\) | −145.664 | + | 252.298i | −0.882814 | + | 1.52908i | ||||
\(166\) | −10.9738 | + | 26.4275i | −0.0661070 | + | 0.159202i | ||||
\(167\) | 15.5845i | 0.0933203i | 0.998911 | + | 0.0466602i | \(0.0148578\pi\) | ||||
−0.998911 | + | 0.0466602i | \(0.985142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −147.633 | −0.873569 | ||||||||
\(170\) | 145.948 | + | 60.6033i | 0.858516 | + | 0.356490i | ||||
\(171\) | 1.77767 | + | 1.02634i | 0.0103957 | + | 0.00600197i | ||||
\(172\) | −79.3045 | + | 79.0272i | −0.461072 | + | 0.459460i | ||||
\(173\) | 133.011 | + | 230.381i | 0.768848 | + | 1.33168i | 0.938188 | + | 0.346126i | \(0.112503\pi\) |
−0.169340 | + | 0.985558i | \(0.554164\pi\) | |||||||
\(174\) | −155.473 | − | 202.984i | −0.893521 | − | 1.16657i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 115.436 | − | 198.334i | 0.655889 | − | 1.12690i | ||||
\(177\) | 80.5842 | + | 139.576i | 0.455278 | + | 0.788565i | ||||
\(178\) | 25.9669 | + | 198.582i | 0.145881 | + | 1.11563i | ||||
\(179\) | 38.5433 | + | 22.2530i | 0.215325 | + | 0.124318i | 0.603784 | − | 0.797148i | \(-0.293659\pi\) |
−0.388458 | + | 0.921466i | \(0.626992\pi\) | |||||||
\(180\) | 2.40602 | − | 0.640178i | 0.0133668 | − | 0.00355654i | ||||
\(181\) | −168.111 | −0.928787 | −0.464394 | − | 0.885629i | \(-0.653728\pi\) | ||||
−0.464394 | + | 0.885629i | \(0.653728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 47.6056i | − | 0.260140i | ||||||
\(184\) | 5.40887 | + | 4.17300i | 0.0293961 | + | 0.0226793i | ||||
\(185\) | 153.172 | − | 265.301i | 0.827956 | − | 1.43406i | ||||
\(186\) | −1.19954 | − | 9.17348i | −0.00644914 | − | 0.0493198i | ||||
\(187\) | 144.218 | − | 83.2641i | 0.771218 | − | 0.445263i | ||||
\(188\) | −162.871 | − | 43.9470i | −0.866335 | − | 0.233761i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 185.742 | + | 242.503i | 0.977589 | + | 1.27633i | ||||
\(191\) | 306.232 | − | 176.803i | 1.60331 | − | 0.925672i | 0.612491 | − | 0.790477i | \(-0.290167\pi\) |
0.990819 | − | 0.135194i | \(-0.0431659\pi\) | |||||||
\(192\) | 184.770 | − | 48.4700i | 0.962345 | − | 0.252448i | ||||
\(193\) | 174.287 | − | 301.874i | 0.903042 | − | 1.56411i | 0.0795170 | − | 0.996834i | \(-0.474662\pi\) |
0.823525 | − | 0.567280i | \(-0.192004\pi\) | |||||||
\(194\) | −126.125 | − | 52.3723i | −0.650131 | − | 0.269960i | ||||
\(195\) | − | 93.8912i | − | 0.481493i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.9314 | −0.136707 | −0.0683537 | − | 0.997661i | \(-0.521775\pi\) | ||||
−0.0683537 | + | 0.997661i | \(0.521775\pi\) | |||||||
\(198\) | 1.00614 | − | 2.42303i | 0.00508150 | − | 0.0122375i | ||||
\(199\) | −200.537 | − | 115.780i | −1.00772 | − | 0.581809i | −0.0971981 | − | 0.995265i | \(-0.530988\pi\) |
−0.910524 | + | 0.413457i | \(0.864321\pi\) | |||||||
\(200\) | 168.985 | + | 22.6991i | 0.844927 | + | 0.113496i | ||||
\(201\) | −137.215 | − | 237.664i | −0.682663 | − | 1.18241i | ||||
\(202\) | −44.7162 | + | 34.2498i | −0.221367 | + | 0.169553i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 133.832 | + | 36.1116i | 0.656041 | + | 0.177018i | ||||
\(205\) | −124.706 | − | 215.996i | −0.608320 | − | 1.05364i | ||||
\(206\) | −317.780 | + | 41.5535i | −1.54262 | + | 0.201716i | ||||
\(207\) | 0.0676395 | + | 0.0390517i | 0.000326761 | + | 0.000188655i | ||||
\(208\) | −0.259047 | + | 73.9585i | −0.00124542 | + | 0.355570i | ||||
\(209\) | 321.890 | 1.54014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 79.6903i | − | 0.377679i | −0.982008 | − | 0.188840i | \(-0.939527\pi\) | ||
0.982008 | − | 0.188840i | \(-0.0604726\pi\) | |||||||
\(212\) | −167.780 | + | 44.6417i | −0.791415 | + | 0.210574i | ||||
\(213\) | −24.4127 | + | 42.2841i | −0.114614 | + | 0.198517i | ||||
\(214\) | 235.838 | − | 30.8385i | 1.10205 | − | 0.144105i | ||||
\(215\) | −164.959 | + | 95.2389i | −0.767249 | + | 0.442972i | ||||
\(216\) | 200.777 | − | 82.5471i | 0.929521 | − | 0.382163i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −156.025 | + | 119.505i | −0.715711 | + | 0.548189i | ||||
\(219\) | 24.7816 | − | 14.3077i | 0.113158 | − | 0.0653318i | ||||
\(220\) | 276.557 | − | 275.590i | 1.25708 | − | 1.25268i | ||||
\(221\) | −26.8349 | + | 46.4794i | −0.121425 | + | 0.210314i | ||||
\(222\) | 103.050 | − | 248.170i | 0.464189 | − | 1.11788i | ||||
\(223\) | − | 264.367i | − | 1.18550i | −0.805386 | − | 0.592750i | \(-0.798042\pi\) | ||
0.805386 | − | 0.592750i | \(-0.201958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.94932 | 0.00866367 | ||||||||
\(226\) | −179.163 | − | 74.3958i | −0.792758 | − | 0.329185i | ||||
\(227\) | 373.538 | + | 215.662i | 1.64554 | + | 0.950053i | 0.978814 | + | 0.204750i | \(0.0656383\pi\) |
0.666726 | + | 0.745303i | \(0.267695\pi\) | |||||||
\(228\) | 189.132 | + | 189.795i | 0.829525 | + | 0.832435i | ||||
\(229\) | 212.451 | + | 367.975i | 0.927732 | + | 1.60688i | 0.787107 | + | 0.616816i | \(0.211578\pi\) |
0.140625 | + | 0.990063i | \(0.455089\pi\) | |||||||
\(230\) | 7.06741 | + | 9.22714i | 0.0307279 | + | 0.0401180i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 130.297 | + | 316.917i | 0.561626 | + | 1.36602i | ||||
\(233\) | −109.414 | − | 189.511i | −0.469588 | − | 0.813350i | 0.529808 | − | 0.848118i | \(-0.322264\pi\) |
−0.999395 | + | 0.0347679i | \(0.988931\pi\) | |||||||
\(234\) | 0.109633 | + | 0.838419i | 0.000468518 | + | 0.00358299i | ||||
\(235\) | −248.557 | − | 143.504i | −1.05769 | − | 0.610657i | ||||
\(236\) | −55.5373 | − | 208.729i | −0.235327 | − | 0.884447i | ||||
\(237\) | −170.077 | −0.717625 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 90.1656i | 0.377262i | 0.982048 | + | 0.188631i | \(0.0604050\pi\) | ||||
−0.982048 | + | 0.188631i | \(0.939595\pi\) | |||||||
\(240\) | 324.991 | + | 1.13832i | 1.35413 | + | 0.00474298i | ||||
\(241\) | −187.972 | + | 325.577i | −0.779968 | + | 1.35094i | 0.151992 | + | 0.988382i | \(0.451431\pi\) |
−0.931960 | + | 0.362562i | \(0.881902\pi\) | |||||||
\(242\) | −21.9670 | − | 167.992i | −0.0907726 | − | 0.694183i | ||||
\(243\) | 4.27710 | − | 2.46938i | 0.0176012 | − | 0.0101621i | ||||
\(244\) | −16.6203 | + | 61.5962i | −0.0681161 | + | 0.252443i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −133.030 | − | 173.683i | −0.540772 | − | 0.706027i | ||||
\(247\) | −89.8420 | + | 51.8703i | −0.363733 | + | 0.210001i | ||||
\(248\) | −1.65063 | + | 12.2882i | −0.00665575 | + | 0.0495493i | ||||
\(249\) | −21.3522 | + | 36.9830i | −0.0857516 | + | 0.148526i | ||||
\(250\) | −46.3473 | − | 19.2452i | −0.185389 | − | 0.0769810i | ||||
\(251\) | − | 319.525i | − | 1.27301i | −0.771274 | − | 0.636503i | \(-0.780380\pi\) | ||
0.771274 | − | 0.636503i | \(-0.219620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2478 | 0.0484101 | ||||||||
\(254\) | 55.1241 | − | 132.753i | 0.217024 | − | 0.522648i | ||||
\(255\) | 204.241 | + | 117.919i | 0.800947 | + | 0.462427i | ||||
\(256\) | −255.994 | − | 1.79331i | −0.999975 | − | 0.00700513i | ||||
\(257\) | 83.7329 | + | 145.030i | 0.325809 | + | 0.564318i | 0.981676 | − | 0.190559i | \(-0.0610300\pi\) |
−0.655867 | + | 0.754877i | \(0.727697\pi\) | |||||||
\(258\) | −132.643 | + | 101.596i | −0.514121 | + | 0.393784i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −32.7798 | + | 121.484i | −0.126076 | + | 0.467248i | ||||
\(261\) | 1.95876 | + | 3.39267i | 0.00750483 | + | 0.0129988i | ||||
\(262\) | 416.132 | − | 54.4142i | 1.58829 | − | 0.207688i | ||||
\(263\) | −74.5887 | − | 43.0638i | −0.283607 | − | 0.163741i | 0.351448 | − | 0.936207i | \(-0.385689\pi\) |
−0.635055 | + | 0.772467i | \(0.719023\pi\) | |||||||
\(264\) | 209.195 | − | 271.151i | 0.792407 | − | 1.02709i | ||||
\(265\) | −295.382 | −1.11465 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 298.878i | 1.11939i | ||||||||
\(268\) | 94.5665 | + | 355.415i | 0.352860 | + | 1.32618i | ||||
\(269\) | −134.672 | + | 233.258i | −0.500638 | + | 0.867130i | 0.499362 | + | 0.866394i | \(0.333568\pi\) |
−1.00000 | 0.000736768i | \(0.999765\pi\) | ||||||||
\(270\) | 366.215 | − | 47.8869i | 1.35635 | − | 0.177359i | ||||
\(271\) | −275.671 | + | 159.159i | −1.01724 | + | 0.587302i | −0.913302 | − | 0.407282i | \(-0.866477\pi\) |
−0.103935 | + | 0.994584i | \(0.533143\pi\) | |||||||
\(272\) | −160.556 | − | 93.4487i | −0.590281 | − | 0.343561i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.8418 | + | 22.0910i | −0.105262 | + | 0.0806241i | ||||
\(275\) | 264.729 | − | 152.842i | 0.962652 | − | 0.555787i | ||||
\(276\) | 7.19638 | + | 7.22163i | 0.0260739 | + | 0.0261653i | ||||
\(277\) | −178.298 | + | 308.822i | −0.643677 | + | 1.11488i | 0.340929 | + | 0.940089i | \(0.389259\pi\) |
−0.984605 | + | 0.174792i | \(0.944075\pi\) | |||||||
\(278\) | 102.841 | − | 247.665i | 0.369930 | − | 0.890883i | ||||
\(279\) | 0.141750i | 0.000508066i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 109.846 | 0.390911 | 0.195455 | − | 0.980713i | \(-0.437381\pi\) | ||||
0.195455 | + | 0.980713i | \(0.437381\pi\) | |||||||
\(282\) | −232.507 | − | 96.5460i | −0.824491 | − | 0.342362i | ||||
\(283\) | −445.641 | − | 257.291i | −1.57470 | − | 0.909155i | −0.995580 | − | 0.0939154i | \(-0.970062\pi\) |
−0.579123 | − | 0.815240i | \(-0.696605\pi\) | |||||||
\(284\) | 46.3497 | − | 46.1877i | 0.163203 | − | 0.162633i | ||||
\(285\) | 227.930 | + | 394.787i | 0.799755 | + | 1.38522i | ||||
\(286\) | 80.6270 | + | 105.266i | 0.281913 | + | 0.368063i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.90340 | + | 0.369315i | −0.0100812 | + | 0.00128234i | ||||
\(289\) | 77.0956 | + | 133.534i | 0.266767 | + | 0.462054i | ||||
\(290\) | 75.5875 | + | 578.055i | 0.260647 | + | 1.99329i | ||||
\(291\) | −176.502 | − | 101.903i | −0.606535 | − | 0.350183i | ||||
\(292\) | −37.0597 | + | 9.86059i | −0.126917 | + | 0.0337692i | ||||
\(293\) | −133.002 | −0.453931 | −0.226965 | − | 0.973903i | \(-0.572880\pi\) | ||||
−0.226965 | + | 0.973903i | \(0.572880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 367.475i | − | 1.24568i | ||||||
\(296\) | −219.977 | + | 285.126i | −0.743166 | + | 0.963263i | ||||
\(297\) | 194.597 | − | 337.052i | 0.655208 | − | 1.13485i | ||||
\(298\) | −5.38388 | − | 41.1732i | −0.0180667 | − | 0.138165i | ||||
\(299\) | −3.41845 | + | 1.97364i | −0.0114329 | + | 0.00660081i | ||||
\(300\) | 245.666 | + | 66.2873i | 0.818886 | + | 0.220958i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −113.233 | − | 147.836i | −0.374944 | − | 0.489523i | ||||
\(303\) | −72.7965 | + | 42.0291i | −0.240252 | + | 0.138710i | ||||
\(304\) | −178.452 | − | 311.604i | −0.587015 | − | 1.02501i | ||||
\(305\) | −54.2720 | + | 94.0018i | −0.177941 | + | 0.308203i | ||||
\(306\) | −1.96150 | − | 0.814493i | −0.00641013 | − | 0.00266174i | ||||
\(307\) | 382.811i | 1.24694i | 0.781847 | + | 0.623471i | \(0.214278\pi\) | ||||
−0.781847 | + | 0.623471i | \(0.785722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −478.279 | −1.54783 | ||||||||
\(310\) | −8.08947 | + | 19.4814i | −0.0260951 | + | 0.0628433i | ||||
\(311\) | −170.064 | − | 98.1868i | −0.546831 | − | 0.315713i | 0.201012 | − | 0.979589i | \(-0.435577\pi\) |
−0.747843 | + | 0.663876i | \(0.768910\pi\) | |||||||
\(312\) | −14.6940 | + | 109.391i | −0.0470962 | + | 0.350611i | ||||
\(313\) | −213.523 | − | 369.832i | −0.682181 | − | 1.18157i | −0.974314 | − | 0.225194i | \(-0.927698\pi\) |
0.292133 | − | 0.956378i | \(-0.405635\pi\) | |||||||
\(314\) | 252.991 | − | 193.775i | 0.805705 | − | 0.617119i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 220.060 | + | 59.3782i | 0.696393 | + | 0.187906i | ||||
\(317\) | −55.5247 | − | 96.1716i | −0.175157 | − | 0.303381i | 0.765059 | − | 0.643961i | \(-0.222710\pi\) |
−0.940216 | + | 0.340580i | \(0.889377\pi\) | |||||||
\(318\) | −256.912 | + | 33.5943i | −0.807900 | + | 0.105642i | ||||
\(319\) | 532.022 | + | 307.163i | 1.66778 | + | 0.962893i | ||||
\(320\) | −420.104 | − | 114.936i | −1.31283 | − | 0.359174i | ||||
\(321\) | 354.951 | 1.10577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 260.577i | − | 0.806741i | ||||||
\(324\) | 309.892 | − | 82.4539i | 0.956457 | − | 0.254487i | ||||
\(325\) | −49.2587 | + | 85.3186i | −0.151565 | + | 0.262519i | ||||
\(326\) | 90.8818 | − | 11.8839i | 0.278779 | − | 0.0364536i | ||||
\(327\) | −254.004 | + | 146.649i | −0.776770 | + | 0.448468i | ||||
\(328\) | 111.488 | + | 271.170i | 0.339904 | + | 0.826736i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 462.563 | − | 354.294i | 1.40171 | − | 1.07362i | ||||
\(331\) | 103.601 | − | 59.8143i | 0.312995 | − | 0.180708i | −0.335271 | − | 0.942122i | \(-0.608828\pi\) |
0.648266 | + | 0.761414i | \(0.275495\pi\) | |||||||
\(332\) | 40.5390 | − | 40.3972i | 0.122105 | − | 0.121678i | ||||
\(333\) | −2.05859 | + | 3.56558i | −0.00618195 | + | 0.0107075i | ||||
\(334\) | 11.9531 | − | 28.7859i | 0.0357876 | − | 0.0861854i | ||||
\(335\) | 625.721i | 1.86782i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −57.3636 | −0.170218 | −0.0851092 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851092 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(338\) | 272.691 | + | 113.232i | 0.806779 | + | 0.335007i | ||||
\(339\) | −250.724 | − | 144.755i | −0.739598 | − | 0.427007i | ||||
\(340\) | −223.097 | − | 223.879i | −0.656167 | − | 0.658469i | ||||
\(341\) | 11.1143 | + | 19.2505i | 0.0325932 | + | 0.0564531i | ||||
\(342\) | −2.49632 | − | 3.25918i | −0.00729919 | − | 0.00952976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 207.095 | − | 85.1449i | 0.602020 | − | 0.247514i | ||||
\(345\) | 8.67266 | + | 15.0215i | 0.0251381 | + | 0.0435405i | ||||
\(346\) | −68.9836 | − | 527.552i | −0.199375 | − | 1.52472i | ||||
\(347\) | −232.766 | − | 134.387i | −0.670794 | − | 0.387283i | 0.125583 | − | 0.992083i | \(-0.459920\pi\) |
−0.796377 | + | 0.604800i | \(0.793253\pi\) | |||||||
\(348\) | 131.486 | + | 494.174i | 0.377834 | + | 1.42004i | ||||
\(349\) | 97.0498 | 0.278080 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 125.432i | 0.357356i | ||||||||
\(352\) | −365.341 | + | 277.803i | −1.03790 | + | 0.789213i | ||||
\(353\) | 158.464 | − | 274.468i | 0.448907 | − | 0.777529i | −0.549409 | − | 0.835554i | \(-0.685147\pi\) |
0.998315 | + | 0.0580249i | \(0.0184803\pi\) | |||||||
\(354\) | −41.7936 | − | 319.616i | −0.118061 | − | 0.902870i | ||||
\(355\) | 96.4105 | − | 55.6627i | 0.271579 | − | 0.156796i | ||||
\(356\) | 104.346 | − | 386.714i | 0.293106 | − | 1.08627i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −54.1251 | − | 70.6653i | −0.151187 | − | 0.197389i | ||||
\(359\) | −511.123 | + | 295.097i | −1.42374 | + | 0.821997i | −0.996616 | − | 0.0821961i | \(-0.973807\pi\) |
−0.427124 | + | 0.904193i | \(0.640473\pi\) | |||||||
\(360\) | −4.93514 | − | 0.662917i | −0.0137087 | − | 0.00184144i | ||||
\(361\) | 71.3407 | − | 123.566i | 0.197620 | − | 0.342287i | ||||
\(362\) | 310.515 | + | 128.938i | 0.857776 | + | 0.356183i | ||||
\(363\) | − | 252.839i | − | 0.696526i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −65.2449 | −0.178753 | ||||||||
\(366\) | −36.5127 | + | 87.9317i | −0.0997616 | + | 0.240251i | ||||
\(367\) | 152.025 | + | 87.7718i | 0.414238 | + | 0.239160i | 0.692609 | − | 0.721313i | \(-0.256461\pi\) |
−0.278371 | + | 0.960474i | \(0.589795\pi\) | |||||||
\(368\) | −6.79004 | − | 11.8564i | −0.0184512 | − | 0.0322185i | ||||
\(369\) | 1.67601 | + | 2.90293i | 0.00454203 | + | 0.00786703i | ||||
\(370\) | −486.404 | + | 372.555i | −1.31461 | + | 1.00690i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.82026 | + | 17.8642i | −0.0129577 | + | 0.0480222i | ||||
\(373\) | −277.008 | − | 479.792i | −0.742649 | − | 1.28631i | −0.951285 | − | 0.308312i | \(-0.900236\pi\) |
0.208637 | − | 0.977993i | \(-0.433097\pi\) | |||||||
\(374\) | −330.245 | + | 43.1834i | −0.883008 | + | 0.115464i | ||||
\(375\) | −64.8590 | − | 37.4464i | −0.172957 | − | 0.0998570i | ||||
\(376\) | 267.130 | + | 206.093i | 0.710453 | + | 0.548121i | ||||
\(377\) | −197.989 | −0.525169 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 749.909i | − | 1.97865i | −0.145723 | − | 0.989325i | \(-0.546551\pi\) | ||
0.145723 | − | 0.989325i | \(-0.453449\pi\) | |||||||
\(380\) | −157.086 | − | 590.386i | −0.413383 | − | 1.55365i | ||||
\(381\) | 107.258 | − | 185.776i | 0.281516 | − | 0.487600i | ||||
\(382\) | −701.243 | + | 91.6958i | −1.83572 | + | 0.240041i | ||||
\(383\) | 213.242 | − | 123.115i | 0.556767 | − | 0.321450i | −0.195080 | − | 0.980787i | \(-0.562497\pi\) |
0.751847 | + | 0.659338i | \(0.229163\pi\) | |||||||
\(384\) | −378.463 | − | 52.1875i | −0.985580 | − | 0.135905i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −553.456 | + | 423.912i | −1.43382 | + | 1.09822i | ||||
\(387\) | 2.21700 | − | 1.27999i | 0.00572868 | − | 0.00330746i | ||||
\(388\) | 192.796 | + | 193.472i | 0.496897 | + | 0.498640i | ||||
\(389\) | −149.009 | + | 258.092i | −0.383058 | + | 0.663475i | −0.991498 | − | 0.130125i | \(-0.958462\pi\) |
0.608440 | + | 0.793600i | \(0.291796\pi\) | |||||||
\(390\) | −72.0131 | + | 173.425i | −0.184649 | + | 0.444680i | ||||
\(391\) | − | 9.91487i | − | 0.0253577i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 626.305 | 1.59365 | ||||||||
\(394\) | 49.7446 | + | 20.6559i | 0.126255 | + | 0.0524262i | ||||
\(395\) | 335.833 | + | 193.894i | 0.850211 | + | 0.490870i | ||||
\(396\) | −3.71685 | + | 3.70385i | −0.00938598 | + | 0.00935317i | ||||
\(397\) | −63.9113 | − | 110.698i | −0.160986 | − | 0.278835i | 0.774237 | − | 0.632896i | \(-0.218134\pi\) |
−0.935222 | + | 0.354061i | \(0.884801\pi\) | |||||||
\(398\) | 281.608 | + | 367.664i | 0.707557 | + | 0.923779i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −294.721 | − | 171.536i | −0.736803 | − | 0.428841i | ||||
\(401\) | 387.143 | + | 670.552i | 0.965444 | + | 1.67220i | 0.708416 | + | 0.705795i | \(0.249410\pi\) |
0.257028 | + | 0.966404i | \(0.417257\pi\) | |||||||
\(402\) | 71.1643 | + | 544.228i | 0.177026 | + | 1.35380i | ||||
\(403\) | −6.20417 | − | 3.58198i | −0.0153950 | − | 0.00888828i | ||||
\(404\) | 108.864 | − | 28.9657i | 0.269465 | − | 0.0716973i | ||||
\(405\) | 545.575 | 1.34710 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 645.635i | 1.58633i | ||||||||
\(408\) | −219.503 | − | 169.349i | −0.537998 | − | 0.415071i | ||||
\(409\) | −333.442 | + | 577.538i | −0.815262 | + | 1.41207i | 0.0938783 | + | 0.995584i | \(0.470074\pi\) |
−0.909140 | + | 0.416491i | \(0.863260\pi\) | |||||||
\(410\) | 64.6763 | + | 494.611i | 0.157747 | + | 1.20637i | ||||
\(411\) | −46.9535 | + | 27.1086i | −0.114242 | + | 0.0659577i | ||||
\(412\) | 618.839 | + | 166.979i | 1.50204 | + | 0.405290i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0949841 | − | 0.124010i | −0.000229430 | − | 0.000299542i | ||||
\(415\) | 84.3238 | − | 48.6844i | 0.203190 | − | 0.117312i | ||||
\(416\) | 57.2035 | − | 136.409i | 0.137508 | − | 0.327907i | ||||
\(417\) | 200.102 | − | 346.587i | 0.479861 | − | 0.831143i | ||||
\(418\) | −594.558 | − | 246.884i | −1.42239 | − | 0.590632i | ||||
\(419\) | 95.3634i | 0.227598i | 0.993504 | + | 0.113799i | \(0.0363019\pi\) | ||||
−0.993504 | + | 0.113799i | \(0.963698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −279.158 | −0.663083 | −0.331541 | − | 0.943441i | \(-0.607569\pi\) | ||||
−0.331541 | + | 0.943441i | \(0.607569\pi\) | |||||||
\(422\) | −61.1212 | + | 147.195i | −0.144837 | + | 0.348803i | ||||
\(423\) | 3.34054 | + | 1.92866i | 0.00789726 | + | 0.00455949i | ||||
\(424\) | 344.144 | + | 46.2274i | 0.811660 | + | 0.109027i | ||||
\(425\) | −123.729 | − | 214.305i | −0.291127 | − | 0.504247i | ||||
\(426\) | 77.5237 | − | 59.3782i | 0.181980 | − | 0.139386i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −459.266 | − | 123.922i | −1.07305 | − | 0.289538i | ||||
\(429\) | 98.9402 | + | 171.369i | 0.230630 | + | 0.399463i | ||||
\(430\) | 377.740 | − | 49.3939i | 0.878465 | − | 0.114870i | ||||
\(431\) | 146.682 | + | 84.6868i | 0.340329 | + | 0.196489i | 0.660418 | − | 0.750899i | \(-0.270379\pi\) |
−0.320088 | + | 0.947388i | \(0.603713\pi\) | |||||||
\(432\) | −434.164 | − | 1.52071i | −1.00501 | − | 0.00352016i | ||||
\(433\) | −295.214 | −0.681787 | −0.340894 | − | 0.940102i | \(-0.610730\pi\) | ||||
−0.340894 | + | 0.940102i | \(0.610730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 870.010i | 2.00002i | ||||||||
\(436\) | 379.851 | − | 101.068i | 0.871217 | − | 0.231807i | ||||
\(437\) | 9.58244 | − | 16.5973i | 0.0219278 | − | 0.0379800i | ||||
\(438\) | −56.7475 | + | 7.42041i | −0.129561 | + | 0.0169416i | ||||
\(439\) | 282.994 | − | 163.386i | 0.644632 | − | 0.372179i | −0.141764 | − | 0.989900i | \(-0.545278\pi\) |
0.786397 | + | 0.617722i | \(0.211944\pi\) | |||||||
\(440\) | −722.198 | + | 296.924i | −1.64136 | + | 0.674827i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 85.2153 | − | 65.2696i | 0.192795 | − | 0.147669i | ||||
\(443\) | −445.821 | + | 257.395i | −1.00637 | + | 0.581026i | −0.910126 | − | 0.414332i | \(-0.864015\pi\) |
−0.0962414 | + | 0.995358i | \(0.530682\pi\) | |||||||
\(444\) | −380.685 | + | 379.354i | −0.857398 | + | 0.854400i | ||||
\(445\) | 340.731 | − | 590.163i | 0.765687 | − | 1.32621i | ||||
\(446\) | −202.765 | + | 488.309i | −0.454630 | + | 1.09486i | ||||
\(447\) | − | 61.9682i | − | 0.138631i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 602.217 | 1.34124 | 0.670620 | − | 0.741801i | \(-0.266028\pi\) | ||||
0.670620 | + | 0.741801i | \(0.266028\pi\) | |||||||
\(450\) | −3.60057 | − | 1.49510i | −0.00800128 | − | 0.00332245i | ||||
\(451\) | 455.223 | + | 262.823i | 1.00936 | + | 0.582757i | ||||
\(452\) | 273.870 | + | 274.831i | 0.605907 | + | 0.608033i | ||||
\(453\) | −138.952 | − | 240.672i | −0.306738 | − | 0.531285i | ||||
\(454\) | −524.548 | − | 684.845i | −1.15539 | − | 1.50847i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −203.773 | − | 495.630i | −0.446870 | − | 1.08691i | ||||
\(457\) | 132.317 | + | 229.180i | 0.289534 | + | 0.501488i | 0.973699 | − | 0.227840i | \(-0.0731662\pi\) |
−0.684164 | + | 0.729328i | \(0.739833\pi\) | |||||||
\(458\) | −110.184 | − | 842.629i | −0.240576 | − | 1.83980i | ||||
\(459\) | −272.852 | − | 157.531i | −0.594448 | − | 0.343205i | ||||
\(460\) | −5.97705 | − | 22.4639i | −0.0129936 | − | 0.0488346i | ||||
\(461\) | −434.788 | −0.943140 | −0.471570 | − | 0.881829i | \(-0.656313\pi\) | ||||
−0.471570 | + | 0.881829i | \(0.656313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 193.258i | 0.417403i | 0.977979 | + | 0.208702i | \(0.0669237\pi\) | ||||
−0.977979 | + | 0.208702i | \(0.933076\pi\) | |||||||
\(464\) | 2.40037 | − | 685.310i | 0.00517322 | − | 1.47696i | ||||
\(465\) | −15.7401 | + | 27.2626i | −0.0338496 | + | 0.0586292i | ||||
\(466\) | 56.7456 | + | 433.961i | 0.121772 | + | 0.931248i | ||||
\(467\) | 567.503 | − | 327.648i | 1.21521 | − | 0.701602i | 0.251321 | − | 0.967904i | \(-0.419135\pi\) |
0.963890 | + | 0.266301i | \(0.0858017\pi\) | |||||||
\(468\) | 0.440552 | − | 1.63272i | 0.000941351 | − | 0.00348872i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 349.041 | + | 455.705i | 0.742640 | + | 0.969585i | ||||
\(471\) | 411.862 | − | 237.789i | 0.874441 | − | 0.504859i | ||||
\(472\) | −57.5100 | + | 428.138i | −0.121843 | + | 0.907072i | ||||
\(473\) | 200.721 | − | 347.659i | 0.424357 | − | 0.735008i | ||||
\(474\) | 314.147 | + | 130.446i | 0.662758 | + | 0.275203i | ||||
\(475\) | − | 478.322i | − | 1.00699i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.96986 | 0.00832256 | ||||||||
\(478\) | 69.1556 | − | 166.544i | 0.144677 | − | 0.348418i | ||||
\(479\) | −88.9066 | − | 51.3302i | −0.185609 | − | 0.107161i | 0.404316 | − | 0.914619i | \(-0.367509\pi\) |
−0.589925 | + | 0.807458i | \(0.700843\pi\) | |||||||
\(480\) | −599.414 | − | 251.366i | −1.24878 | − | 0.523679i | ||||
\(481\) | −104.040 | − | 180.202i | −0.216298 | − | 0.374640i | ||||
\(482\) | 596.914 | − | 457.198i | 1.23841 | − | 0.948544i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −88.2725 | + | 327.145i | −0.182381 | + | 0.675919i | ||||
\(485\) | 232.346 | + | 402.436i | 0.479065 | + | 0.829764i | ||||
\(486\) | −9.79416 | + | 1.28070i | −0.0201526 | + | 0.00263519i | ||||
\(487\) | −130.469 | − | 75.3260i | −0.267903 | − | 0.154674i | 0.360032 | − | 0.932940i | \(-0.382766\pi\) |
−0.627934 | + | 0.778267i | \(0.716099\pi\) | |||||||
\(488\) | 77.9425 | − | 101.026i | 0.159718 | − | 0.207021i | ||||
\(489\) | 136.783 | 0.279720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 118.795i | − | 0.241946i | −0.992656 | − | 0.120973i | \(-0.961399\pi\) | ||
0.992656 | − | 0.120973i | \(-0.0386014\pi\) | |||||||
\(492\) | 112.506 | + | 422.839i | 0.228671 | + | 0.859428i | ||||
\(493\) | 248.656 | − | 430.685i | 0.504373 | − | 0.873600i | ||||
\(494\) | 205.730 | − | 26.9016i | 0.416457 | − | 0.0544566i | ||||
\(495\) | −7.73130 | + | 4.46367i | −0.0156188 | + | 0.00901751i | ||||
\(496\) | 12.4737 | − | 21.4314i | 0.0251487 | − | 0.0432085i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 67.8047 | − | 51.9341i | 0.136154 | − | 0.104285i | ||||
\(499\) | 473.223 | − | 273.215i | 0.948343 | − | 0.547526i | 0.0557769 | − | 0.998443i | \(-0.482236\pi\) |
0.892566 | + | 0.450917i | \(0.148903\pi\) | |||||||
\(500\) | 70.8467 | + | 71.0953i | 0.141693 | + | 0.142191i | ||||
\(501\) | 23.2577 | − | 40.2834i | 0.0464225 | − | 0.0804061i | ||||
\(502\) | −245.070 | + | 590.190i | −0.488188 | + | 1.17568i | ||||
\(503\) | − | 520.718i | − | 1.03522i | −0.855615 | − | 0.517612i | \(-0.826821\pi\) | ||
0.855615 | − | 0.517612i | \(-0.173179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 191.658 | 0.379521 | ||||||||
\(506\) | −22.6227 | − | 9.39385i | −0.0447089 | − | 0.0185649i | ||||
\(507\) | 381.608 | + | 220.322i | 0.752679 | + | 0.434559i | ||||
\(508\) | −203.638 | + | 202.926i | −0.400863 | + | 0.399461i | ||||
\(509\) | −300.714 | − | 520.851i | −0.590793 | − | 1.02328i | −0.994126 | − | 0.108230i | \(-0.965482\pi\) |
0.403333 | − | 0.915053i | \(-0.367852\pi\) | |||||||
\(510\) | −286.810 | − | 374.456i | −0.562372 | − | 0.734228i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 471.468 | + | 199.656i | 0.920835 | + | 0.389952i | ||||
\(513\) | −304.498 | − | 527.407i | −0.593564 | − | 1.02808i | ||||
\(514\) | −43.4266 | − | 332.105i | −0.0844875 | − | 0.646118i | ||||
\(515\) | 944.408 | + | 545.254i | 1.83380 | + | 1.05875i | ||||
\(516\) | 322.926 | − | 85.9220i | 0.625826 | − | 0.166515i | ||||
\(517\) | 604.886 | 1.16999 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 793.998i | − | 1.52986i | ||||||
\(520\) | 153.724 | − | 199.251i | 0.295623 | − | 0.383175i | ||||
\(521\) | 291.134 | − | 504.259i | 0.558798 | − | 0.967867i | −0.438799 | − | 0.898585i | \(-0.644596\pi\) |
0.997597 | − | 0.0692818i | \(-0.0220708\pi\) | |||||||
\(522\) | −1.01588 | − | 7.76891i | −0.00194612 | − | 0.0148830i | ||||
\(523\) | 124.355 | − | 71.7965i | 0.237773 | − | 0.137278i | −0.376380 | − | 0.926465i | \(-0.622831\pi\) |
0.614153 | + | 0.789187i | \(0.289498\pi\) | |||||||
\(524\) | −810.367 | − | 218.659i | −1.54650 | − | 0.417288i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 104.743 | + | 136.751i | 0.199130 | + | 0.259983i | ||||
\(527\) | 15.5837 | − | 8.99728i | 0.0295707 | − | 0.0170726i | ||||
\(528\) | −594.371 | + | 340.390i | −1.12570 | + | 0.644678i | ||||
\(529\) | −264.135 | + | 457.496i | −0.499311 | + | 0.864832i | ||||
\(530\) | 545.597 | + | 226.554i | 1.02943 | + | 0.427460i | ||||
\(531\) | 4.93877i | 0.00930088i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −169.409 | −0.317840 | ||||||||
\(534\) | 229.235 | − | 552.054i | 0.429278 | − | 1.03381i | ||||
\(535\) | −700.884 | − | 404.656i | −1.31006 | − | 0.756366i | ||||
\(536\) | 97.9256 | − | 729.015i | 0.182697 | − | 1.36010i | ||||
\(537\) | −66.4188 | − | 115.041i | −0.123685 | − | 0.214229i | ||||
\(538\) | 427.656 | − | 327.557i | 0.794899 | − | 0.608842i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −713.160 | − | 192.430i | −1.32067 | − | 0.356352i | ||||
\(541\) | −416.548 | − | 721.483i | −0.769960 | − | 1.33361i | −0.937584 | − | 0.347759i | \(-0.886943\pi\) |
0.167624 | − | 0.985851i | \(-0.446391\pi\) | |||||||
\(542\) | 631.262 | − | 82.5449i | 1.16469 | − | 0.152297i | ||||
\(543\) | 434.539 | + | 250.881i | 0.800256 | + | 0.462028i | ||||
\(544\) | 224.888 | + | 295.752i | 0.413398 | + | 0.543662i | ||||
\(545\) | 668.740 | 1.22705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 356.858i | 0.652391i | 0.945302 | + | 0.326196i | \(0.105767\pi\) | ||||
−0.945302 | + | 0.326196i | \(0.894233\pi\) | |||||||
\(548\) | 70.2168 | − | 18.6828i | 0.128133 | − | 0.0340927i | ||||
\(549\) | 0.729401 | − | 1.26336i | 0.00132860 | − | 0.00230120i | ||||
\(550\) | −606.205 | + | 79.2685i | −1.10219 | + | 0.144125i | ||||
\(551\) | 832.489 | − | 480.638i | 1.51087 | − | 0.872301i | ||||
\(552\) | −7.75347 | − | 18.8585i | −0.0140461 | − | 0.0341640i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 566.195 | − | 433.669i | 1.02201 | − | 0.782796i | ||||
\(555\) | −791.850 | + | 457.175i | −1.42676 | + | 0.823738i | ||||
\(556\) | −379.911 | + | 378.583i | −0.683294 | + | 0.680904i | ||||
\(557\) | −162.430 | + | 281.336i | −0.291615 | + | 0.505092i | −0.974192 | − | 0.225722i | \(-0.927526\pi\) |
0.682577 | + | 0.730814i | \(0.260859\pi\) | |||||||
\(558\) | 0.108720 | − | 0.261825i | 0.000194839 | − | 0.000469221i | ||||
\(559\) | 129.379i | 0.231447i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −497.040 | −0.885989 | ||||||||
\(562\) | −202.895 | − | 84.2502i | −0.361023 | − | 0.149911i | ||||
\(563\) | −73.8314 | − | 42.6266i | −0.131139 | − | 0.0757133i | 0.432995 | − | 0.901396i | \(-0.357457\pi\) |
−0.564134 | + | 0.825683i | \(0.690790\pi\) | |||||||
\(564\) | 355.411 | + | 356.658i | 0.630161 | + | 0.632372i | ||||
\(565\) | 330.052 | + | 571.667i | 0.584163 | + | 1.01180i | ||||
\(566\) | 625.800 | + | 817.039i | 1.10565 | + | 1.44353i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −121.037 | + | 49.7632i | −0.213094 | + | 0.0876112i | ||||
\(569\) | 14.3756 | + | 24.8993i | 0.0252647 | + | 0.0437597i | 0.878381 | − | 0.477961i | \(-0.158624\pi\) |
−0.853117 | + | 0.521720i | \(0.825290\pi\) | |||||||
\(570\) | −118.212 | − | 904.025i | −0.207389 | − | 1.58601i | ||||
\(571\) | 586.760 | + | 338.766i | 1.02760 | + | 0.593286i | 0.916296 | − | 0.400501i | \(-0.131164\pi\) |
0.111304 | + | 0.993786i | \(0.464497\pi\) | |||||||
\(572\) | −68.1879 | − | 256.275i | −0.119210 | − | 0.448033i | ||||
\(573\) | −1055.42 | −1.84191 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.2000i | − | 0.0316521i | ||||||
\(576\) | 5.64609 | + | 1.54470i | 0.00980224 | + | 0.00268178i | ||||
\(577\) | 10.3338 | − | 17.8986i | 0.0179095 | − | 0.0310201i | −0.856932 | − | 0.515430i | \(-0.827632\pi\) |
0.874841 | + | 0.484410i | \(0.160966\pi\) | |||||||
\(578\) | −39.9843 | − | 305.779i | −0.0691769 | − | 0.529030i | ||||
\(579\) | −901.009 | + | 520.198i | −1.55615 | + | 0.898441i | ||||
\(580\) | 303.743 | − | 1125.69i | 0.523694 | − | 1.94085i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 247.856 | + | 323.598i | 0.425869 | + | 0.556011i | ||||
\(583\) | 539.129 | − | 311.266i | 0.924750 | − | 0.533905i | ||||
\(584\) | 76.0155 | + | 10.2109i | 0.130164 | + | 0.0174843i | ||||
\(585\) | 1.43858 | − | 2.49169i | 0.00245911 | − | 0.00425930i | ||||
\(586\) | 245.666 | + | 102.010i | 0.419225 | + | 0.174079i | ||||
\(587\) | 551.489i | 0.939504i | 0.882798 | + | 0.469752i | \(0.155657\pi\) | ||||
−0.882798 | + | 0.469752i | \(0.844343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.7825 | 0.0590534 | ||||||||
\(590\) | −281.848 | + | 678.759i | −0.477708 | + | 1.15044i | ||||
\(591\) | 69.6133 | + | 40.1912i | 0.117789 | + | 0.0680055i | ||||
\(592\) | 625.005 | − | 357.934i | 1.05575 | − | 0.604618i | ||||
\(593\) | −22.9656 | − | 39.7776i | −0.0387279 | − | 0.0670787i | 0.846012 | − | 0.533164i | \(-0.178997\pi\) |
−0.884740 | + | 0.466086i | \(0.845664\pi\) | |||||||
\(594\) | −617.951 | + | 473.311i | −1.04032 | + | 0.796821i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.6347 | + | 80.1798i | −0.0362998 | + | 0.134530i | ||||
\(597\) | 345.570 | + | 598.545i | 0.578845 | + | 1.00259i | ||||
\(598\) | 7.82793 | − | 1.02359i | 0.0130902 | − | 0.00171170i | ||||
\(599\) | −573.698 | − | 331.225i | −0.957759 | − | 0.552963i | −0.0622766 | − | 0.998059i | \(-0.519836\pi\) |
−0.895483 | + | 0.445096i | \(0.853169\pi\) | |||||||
\(600\) | −402.925 | − | 310.860i | −0.671542 | − | 0.518101i | ||||
\(601\) | −840.257 | −1.39810 | −0.699049 | − | 0.715074i | \(-0.746393\pi\) | ||||
−0.699049 | + | 0.715074i | \(0.746393\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 8.40952i | − | 0.0139461i | ||||||
\(604\) | 95.7634 | + | 359.914i | 0.158549 | + | 0.595884i | ||||
\(605\) | −288.245 | + | 499.255i | −0.476438 | + | 0.825215i | ||||
\(606\) | 166.697 | − | 21.7976i | 0.275078 | − | 0.0359697i | ||||
\(607\) | −887.606 | + | 512.459i | −1.46228 | + | 0.844249i | −0.999117 | − | 0.0420222i | \(-0.986620\pi\) |
−0.463166 | + | 0.886272i | \(0.653287\pi\) | |||||||
\(608\) | 90.6218 | + | 712.431i | 0.149049 | + | 1.17176i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 172.343 | − | 132.004i | 0.282530 | − | 0.216400i | ||||
\(611\) | −168.828 | + | 97.4732i | −0.276315 | + | 0.159531i | ||||
\(612\) | 2.99836 | + | 3.00888i | 0.00489928 | + | 0.00491647i | ||||
\(613\) | 54.5739 | − | 94.5248i | 0.0890276 | − | 0.154200i | −0.818073 | − | 0.575115i | \(-0.804957\pi\) |
0.907100 | + | 0.420914i | \(0.138291\pi\) | |||||||
\(614\) | 293.610 | − | 707.086i | 0.478192 | − | 1.15161i | ||||
\(615\) | 744.422i | 1.21044i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 78.9177 | 0.127905 | 0.0639527 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639527 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(618\) | 883.424 | + | 366.833i | 1.42949 | + | 0.593580i | ||||
\(619\) | −620.070 | − | 357.997i | −1.00173 | − | 0.578348i | −0.0929689 | − | 0.995669i | \(-0.529636\pi\) |
−0.908759 | + | 0.417321i | \(0.862969\pi\) | |||||||
\(620\) | 29.8839 | − | 29.7794i | 0.0481999 | − | 0.0480313i | ||||
\(621\) | −11.5860 | − | 20.0676i | −0.0186571 | − | 0.0323150i | ||||
\(622\) | 238.816 | + | 311.796i | 0.383949 | + | 0.501281i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 111.042 | − | 190.784i | 0.177952 | − | 0.305744i | ||||
\(625\) | 351.791 | + | 609.321i | 0.562866 | + | 0.974913i | ||||
\(626\) | 110.740 | + | 846.881i | 0.176900 | + | 1.35284i | ||||
\(627\) | −832.033 | − | 480.375i | −1.32701 | − | 0.766148i | ||||
\(628\) | −615.920 | + | 163.880i | −0.980765 | + | 0.260955i | ||||
\(629\) | 522.657 | 0.830933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 849.316i | 1.34598i | 0.739650 | + | 0.672992i | \(0.234991\pi\) | ||||
−0.739650 | + | 0.672992i | \(0.765009\pi\) | |||||||
\(632\) | −360.929 | − | 278.460i | −0.571089 | − | 0.440601i | ||||
\(633\) | −118.927 | + | 205.987i | −0.187878 | + | 0.325414i | ||||
\(634\) | 28.7969 | + | 220.224i | 0.0454210 | + | 0.347357i | ||||
\(635\) | −423.581 | + | 244.555i | −0.667057 | + | 0.385126i | ||||
\(636\) | 500.306 | + | 134.996i | 0.786645 | + | 0.212258i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −747.102 | − | 975.409i | −1.17101 | − | 1.52885i | ||||
\(639\) | −1.29573 | + | 0.748092i | −0.00202775 | + | 0.00117072i | ||||
\(640\) | 687.815 | + | 534.509i | 1.07471 | + | 0.835171i | ||||
\(641\) | −244.045 | + | 422.698i | −0.380725 | + | 0.659435i | −0.991166 | − | 0.132627i | \(-0.957659\pi\) |
0.610441 | + | 0.792062i | \(0.290992\pi\) | |||||||
\(642\) | −655.625 | − | 272.242i | −1.02122 | − | 0.424052i | ||||
\(643\) | − | 257.106i | − | 0.399854i | −0.979811 | − | 0.199927i | \(-0.935930\pi\) | ||
0.979811 | − | 0.199927i | \(-0.0640705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 568.522 | 0.881430 | ||||||||
\(646\) | −199.859 | + | 481.310i | −0.309379 | + | 0.745061i | ||||
\(647\) | 605.816 | + | 349.768i | 0.936346 | + | 0.540600i | 0.888813 | − | 0.458270i | \(-0.151531\pi\) |
0.0475329 | + | 0.998870i | \(0.484864\pi\) | |||||||
\(648\) | −635.639 | − | 85.3828i | −0.980924 | − | 0.131764i | ||||
\(649\) | 387.236 | + | 670.713i | 0.596666 | + | 1.03346i | ||||
\(650\) | 156.423 | − | 119.810i | 0.240651 | − | 0.184324i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −176.981 | − | 47.7544i | −0.271444 | − | 0.0732429i | ||||
\(653\) | −138.815 | − | 240.434i | −0.212580 | − | 0.368199i | 0.739941 | − | 0.672671i | \(-0.234853\pi\) |
−0.952521 | + | 0.304472i | \(0.901520\pi\) | |||||||
\(654\) | 581.645 | − | 76.0569i | 0.889365 | − | 0.116295i | ||||
\(655\) | −1236.70 | − | 714.009i | −1.88809 | − | 1.09009i | ||||
\(656\) | 2.05387 | − | 586.384i | 0.00313090 | − | 0.893878i | ||||
\(657\) | 0.876874 | 0.00133466 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 522.721i | − | 0.793204i | −0.917991 | − | 0.396602i | \(-0.870189\pi\) | ||
0.917991 | − | 0.396602i | \(-0.129811\pi\) | |||||||
\(660\) | −1126.13 | + | 299.634i | −1.70626 | + | 0.453991i | ||||
\(661\) | −257.961 | + | 446.802i | −0.390259 | + | 0.675948i | −0.992484 | − | 0.122378i | \(-0.960948\pi\) |
0.602224 | + | 0.798327i | \(0.294281\pi\) | |||||||
\(662\) | −237.237 | + | 31.0216i | −0.358365 | + | 0.0468604i | ||||
\(663\) | 138.728 | − | 80.0945i | 0.209243 | − | 0.120806i | ||||
\(664\) | −105.863 | + | 43.5245i | −0.159432 | + | 0.0655489i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.53714 | − | 5.00704i | 0.00981553 | − | 0.00751807i | ||||
\(667\) | 31.6759 | − | 18.2881i | 0.0474901 | − | 0.0274184i | ||||
\(668\) | −44.1567 | + | 44.0023i | −0.0661029 | + | 0.0658718i | ||||
\(669\) | −394.530 | + | 683.346i | −0.589731 | + | 1.02144i | ||||
\(670\) | 479.918 | − | 1155.76i | 0.716296 | − | 1.72502i | ||||
\(671\) | − | 228.762i | − | 0.340927i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1231.64 | −1.83008 | −0.915041 | − | 0.403361i | \(-0.867842\pi\) | ||||
−0.915041 | + | 0.403361i | \(0.867842\pi\) | |||||||
\(674\) | 105.956 | + | 43.9970i | 0.157204 | + | 0.0652774i | ||||
\(675\) | −500.853 | − | 289.167i | −0.742004 | − | 0.428396i | ||||
\(676\) | −416.838 | − | 418.300i | −0.616624 | − | 0.618787i | ||||
\(677\) | 288.282 | + | 499.319i | 0.425822 | + | 0.737546i | 0.996497 | − | 0.0836304i | \(-0.0266515\pi\) |
−0.570674 | + | 0.821176i | \(0.693318\pi\) | |||||||
\(678\) | 352.084 | + | 459.677i | 0.519297 | + | 0.677990i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 240.367 | + | 584.637i | 0.353481 | + | 0.859760i | ||||
\(681\) | −643.690 | − | 1114.90i | −0.945213 | − | 1.63716i | ||||
\(682\) | −5.76422 | − | 44.0818i | −0.00845193 | − | 0.0646361i | ||||
\(683\) | 139.772 | + | 80.6973i | 0.204644 | + | 0.118151i | 0.598820 | − | 0.800884i | \(-0.295637\pi\) |
−0.394176 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(684\) | 2.11119 | + | 7.93463i | 0.00308654 | + | 0.0116003i | ||||
\(685\) | 123.619 | 0.180466 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1268.21i | − | 1.84601i | ||||||
\(688\) | −447.827 | − | 1.56856i | −0.650912 | − | 0.00227989i | ||||
\(689\) | −100.317 | + | 173.754i | −0.145598 | + | 0.252183i | ||||
\(690\) | −4.49792 | − | 34.3978i | −0.00651872 | − | 0.0498519i | ||||
\(691\) | −98.4337 | + | 56.8307i | −0.142451 | + | 0.0822442i | −0.569532 | − | 0.821969i | \(-0.692875\pi\) |
0.427081 | + | 0.904214i | \(0.359542\pi\) | |||||||
\(692\) | −277.205 | + | 1027.34i | −0.400585 | + | 1.48460i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 326.865 | + | 426.753i | 0.470988 | + | 0.614917i | ||||
\(695\) | −790.241 | + | 456.246i | −1.13704 | + | 0.656469i | ||||
\(696\) | 136.157 | − | 1013.63i | 0.195628 | − | 1.45637i | ||||
\(697\) | 212.762 | − | 368.514i | 0.305254 | − | 0.528715i | ||||
\(698\) | −179.260 | − | 74.4357i | −0.256819 | − | 0.106641i | ||||
\(699\) | 653.140i | 0.934391i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 331.011 | 0.472198 | 0.236099 | − | 0.971729i | \(-0.424131\pi\) | ||||
0.236099 | + | 0.971729i | \(0.424131\pi\) | |||||||
\(702\) | 96.2042 | − | 231.684i | 0.137043 | − | 0.330034i | ||||
\(703\) | 874.916 | + | 505.133i | 1.24455 | + | 0.718539i | ||||
\(704\) | 887.887 | − | 232.916i | 1.26120 | − | 0.330846i | ||||
\(705\) | 428.320 | + | 741.872i | 0.607546 | + | 1.05230i | ||||
\(706\) | −503.210 | + | 385.427i | −0.712761 | + | 0.545930i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −167.944 | + | 622.414i | −0.237209 | + | 0.879116i | ||||
\(709\) | 295.675 | + | 512.125i | 0.417032 | + | 0.722320i | 0.995639 | − | 0.0932861i | \(-0.0297371\pi\) |
−0.578608 | + | 0.815606i | \(0.696404\pi\) | |||||||
\(710\) | −220.771 | + | 28.8684i | −0.310945 | + | 0.0406598i | ||||
\(711\) | −4.51351 | − | 2.60588i | −0.00634812 | − | 0.00366509i | ||||
\(712\) | −489.340 | + | 634.263i | −0.687275 | + | 0.890819i | ||||
\(713\) | 1.32346 | 0.00185618 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 451.181i | − | 0.631022i | ||||||
\(716\) | 45.7747 | + | 172.038i | 0.0639312 | + | 0.240277i | ||||
\(717\) | 134.559 | − | 233.064i | 0.187670 | − | 0.325054i | ||||
\(718\) | 1170.42 | − | 153.047i | 1.63012 | − | 0.213157i | ||||
\(719\) | −418.810 | + | 241.800i | −0.582489 | + | 0.336300i | −0.762122 | − | 0.647433i | \(-0.775842\pi\) |
0.179633 | + | 0.983734i | \(0.442509\pi\) | |||||||
\(720\) | 8.60719 | + | 5.00964i | 0.0119544 | + | 0.00695784i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −226.545 | + | 173.519i | −0.313775 | + | 0.240332i | ||||
\(723\) | 971.756 | − | 561.044i | 1.34406 | − | 0.775994i | ||||
\(724\) | −474.655 | − | 476.320i | −0.655601 | − | 0.657901i | ||||
\(725\) | 456.438 | − | 790.575i | 0.629570 | − | 1.09045i | ||||
\(726\) | −193.924 | + | 467.016i | −0.267112 | + | 0.643272i | ||||
\(727\) | − | 659.508i | − | 0.907163i | −0.891215 | − | 0.453582i | \(-0.850146\pi\) | ||
0.891215 | − | 0.453582i | \(-0.149854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −736.257 | −1.00995 | ||||||||
\(730\) | 120.513 | + | 50.0418i | 0.165086 | + | 0.0685504i | ||||
\(731\) | −281.438 | − | 162.488i | −0.385004 | − | 0.222282i | ||||
\(732\) | 134.884 | − | 134.413i | 0.184268 | − | 0.183624i | ||||
\(733\) | −105.888 | − | 183.403i | −0.144458 | − | 0.250209i | 0.784713 | − | 0.619860i | \(-0.212811\pi\) |
−0.929171 | + | 0.369651i | \(0.879477\pi\) | |||||||
\(734\) | −213.484 | − | 278.723i | −0.290851 | − | 0.379732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.44812 | + | 27.1077i | 0.00468495 | + | 0.0368311i | ||||
\(737\) | −659.369 | − | 1142.06i | −0.894666 | − | 1.54961i | ||||
\(738\) | −0.869232 | − | 6.64745i | −0.00117782 | − | 0.00900738i | ||||
\(739\) | −213.832 | − | 123.456i | −0.289353 | − | 0.167058i | 0.348297 | − | 0.937384i | \(-0.386760\pi\) |
−0.637650 | + | 0.770326i | \(0.720093\pi\) | |||||||
\(740\) | 1184.17 | − | 315.077i | 1.60024 | − | 0.425780i | ||||
\(741\) | 309.636 | 0.417863 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 333.126i | 0.448352i | 0.974549 | + | 0.224176i | \(0.0719691\pi\) | ||||
−0.974549 | + | 0.224176i | \(0.928031\pi\) | |||||||
\(744\) | 22.6050 | − | 29.2998i | 0.0303831 | − | 0.0393814i | ||||
\(745\) | −70.6459 | + | 122.362i | −0.0948267 | + | 0.164245i | ||||
\(746\) | 143.665 | + | 1098.68i | 0.192581 | + | 1.47276i | ||||
\(747\) | −1.13329 | + | 0.654305i | −0.00151712 | + | 0.000875911i | ||||
\(748\) | 643.113 | + | 173.529i | 0.859776 | + | 0.231991i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 91.0796 | + | 118.913i | 0.121439 | + | 0.158550i | ||||
\(751\) | −528.203 | + | 304.958i | −0.703333 | + | 0.406069i | −0.808588 | − | 0.588376i | \(-0.799768\pi\) |
0.105255 | + | 0.994445i | \(0.466434\pi\) | |||||||
\(752\) | −335.343 | − | 585.558i | −0.445935 | − | 0.778667i | ||||
\(753\) | −476.845 | + | 825.920i | −0.633261 | + | 1.09684i | ||||
\(754\) | 365.703 | + | 151.854i | 0.485017 | + | 0.201398i | ||||
\(755\) | 633.640i | 0.839259i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 439.344 | 0.580375 | 0.290187 | − | 0.956970i | \(-0.406282\pi\) | ||||
0.290187 | + | 0.956970i | \(0.406282\pi\) | |||||||
\(758\) | −575.168 | + | 1385.15i | −0.758797 | + | 1.82737i | ||||
\(759\) | −31.6585 | − | 18.2781i | −0.0417108 | − | 0.0240818i | ||||
\(760\) | −162.666 | + | 1210.98i | −0.214034 | + | 1.59339i | ||||
\(761\) | 230.484 | + | 399.210i | 0.302870 | + | 0.524586i | 0.976785 | − | 0.214223i | \(-0.0687219\pi\) |
−0.673915 | + | 0.738809i | \(0.735389\pi\) | |||||||
\(762\) | −340.601 | + | 260.879i | −0.446984 | + | 0.342361i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1365.59 | + | 368.473i | 1.78742 | + | 0.482294i | ||||
\(765\) | 3.61345 | + | 6.25867i | 0.00472346 | + | 0.00818127i | ||||
\(766\) | −488.304 | + | 63.8515i | −0.637472 | + | 0.0833570i | ||||
\(767\) | −216.161 | − | 124.801i | −0.281827 | − | 0.162713i | ||||
\(768\) | 659.027 | + | 386.670i | 0.858108 | + | 0.503476i | ||||
\(769\) | 1431.37 | 1.86134 | 0.930670 | − | 0.365859i | \(-0.119225\pi\) | ||||
0.930670 | + | 0.365859i | \(0.119225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 499.838i | − | 0.648299i | ||||||
\(772\) | 1347.42 | − | 358.511i | 1.74536 | − | 0.464393i | ||||
\(773\) | −122.740 | + | 212.592i | −0.158784 | + | 0.275022i | −0.934430 | − | 0.356146i | \(-0.884091\pi\) |
0.775646 | + | 0.631168i | \(0.217424\pi\) | |||||||
\(774\) | −5.07672 | + | 0.663842i | −0.00655908 | + | 0.000857676i | ||||
\(775\) | 28.6059 | − | 16.5156i | 0.0369108 | − | 0.0213105i | ||||
\(776\) | −207.721 | − | 505.232i | −0.267681 | − | 0.651073i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 473.186 | − | 362.431i | 0.608208 | − | 0.465849i | ||||
\(779\) | 712.317 | − | 411.256i | 0.914399 | − | 0.527929i | ||||
\(780\) | 266.029 | − | 265.099i | 0.341063 | − | 0.339870i | ||||
\(781\) | −117.312 | + | 203.190i | −0.150207 | + | 0.260167i | ||||
\(782\) | −7.60455 | + | 18.3136i | −0.00972449 | + | 0.0234190i | ||||
\(783\) | − | 1162.27i | − | 1.48438i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1084.35 | −1.38134 | ||||||||
\(786\) | −1156.84 | − | 480.366i | −1.47181 | − | 0.611153i | ||||
\(787\) | −502.289 | − | 289.997i | −0.638232 | − | 0.368483i | 0.145701 | − | 0.989329i | \(-0.453456\pi\) |
−0.783933 | + | 0.620845i | \(0.786790\pi\) | |||||||
\(788\) | −76.0399 | − | 76.3067i | −0.0964973 | − | 0.0968359i | ||||
\(789\) | 128.533 | + | 222.626i | 0.162907 | + | 0.282162i | ||||
\(790\) | −471.601 | − | 615.718i | −0.596963 | − | 0.779389i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.70615 | − | 3.99058i | 0.0122552 | − | 0.00503861i | ||||
\(793\) | 36.8634 | + | 63.8493i | 0.0464860 | + | 0.0805161i | ||||
\(794\) | 33.1464 | + | 253.487i | 0.0417461 | + | 0.319253i | ||||
\(795\) | 763.516 | + | 440.816i | 0.960397 | + | 0.554486i | ||||
\(796\) | −238.161 | − | 895.097i | −0.299197 | − | 1.12449i | ||||
\(797\) | −1348.22 | −1.69162 | −0.845810 | − | 0.533484i | \(-0.820882\pi\) | ||||
−0.845810 | + | 0.533484i | \(0.820882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 489.670i | − | 0.612853i | ||||||
\(800\) | 412.810 | + | 542.890i | 0.516013 | + | 0.678612i | ||||
\(801\) | −4.57933 | + | 7.93164i | −0.00571702 | + | 0.00990217i | ||||
\(802\) | −200.785 | − | 1535.50i | −0.250355 | − | 1.91459i | ||||
\(803\) | 119.084 | − | 68.7534i | 0.148299 | − | 0.0856207i | ||||
\(804\) | 285.968 | − | 1059.82i | 0.355682 | − | 1.31818i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.71232 | + | 11.3747i | 0.0108093 | + | 0.0141126i | ||||
\(807\) | 696.209 | − | 401.957i | 0.862713 | − | 0.498088i | ||||
\(808\) | −223.297 | − | 29.9946i | −0.276358 | − | 0.0371220i | ||||
\(809\) | 348.732 | − | 604.022i | 0.431066 | − | 0.746628i | −0.565899 | − | 0.824474i | \(-0.691471\pi\) |
0.996965 | + | 0.0778461i | \(0.0248043\pi\) | |||||||
\(810\) | −1007.73 | − | 418.448i | −1.24411 | − | 0.516602i | ||||
\(811\) | − | 482.271i | − | 0.594662i | −0.954774 | − | 0.297331i | \(-0.903903\pi\) | ||
0.954774 | − | 0.297331i | \(-0.0960965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 950.089 | 1.16862 | ||||||||
\(814\) | 495.192 | − | 1192.54i | 0.608344 | − | 1.46504i | ||||
\(815\) | −270.091 | − | 155.937i | −0.331400 | − | 0.191334i | ||||
\(816\) | 275.554 | + | 481.158i | 0.337689 | + | 0.589654i | ||||
\(817\) | −314.081 | − | 544.004i | −0.384432 | − | 0.665855i | ||||
\(818\) | 1058.86 | − | 811.020i | 1.29445 | − | 0.991467i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 259.897 | − | 963.197i | 0.316947 | − | 1.17463i | ||||
\(821\) | 193.173 | + | 334.585i | 0.235289 | + | 0.407533i | 0.959357 | − | 0.282196i | \(-0.0910629\pi\) |
−0.724067 | + | 0.689729i | \(0.757730\pi\) | |||||||
\(822\) | 107.519 | − | 14.0594i | 0.130802 | − | 0.0171039i | ||||
\(823\) | 306.907 | + | 177.193i | 0.372913 | + | 0.215301i | 0.674730 | − | 0.738064i | \(-0.264260\pi\) |
−0.301817 | + | 0.953366i | \(0.597593\pi\) | |||||||
\(824\) | −1014.98 | − | 783.066i | −1.23177 | − | 0.950322i | ||||
\(825\) | −912.377 | −1.10591 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1260.47i | 1.52414i | 0.647493 | + | 0.762072i | \(0.275818\pi\) | ||||
−0.647493 | + | 0.762072i | \(0.724182\pi\) | |||||||
\(828\) | 0.0803300 | + | 0.301909i | 9.70169e−5 | + | 0.000364625i | ||||
\(829\) | 721.843 | − | 1250.27i | 0.870739 | − | 1.50816i | 0.00950526 | − | 0.999955i | \(-0.496974\pi\) |
0.861234 | − | 0.508209i | \(-0.169692\pi\) | |||||||
\(830\) | −193.094 | + | 25.2493i | −0.232643 | + | 0.0304208i | ||||
\(831\) | 921.746 | − | 532.170i | 1.10920 | − | 0.640398i | ||||
\(832\) | −210.284 | + | 208.086i | −0.252745 | + | 0.250103i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −635.432 | + | 486.701i | −0.761909 | + | 0.583574i | ||||
\(835\) | −91.8490 | + | 53.0290i | −0.109999 | + | 0.0635078i | ||||
\(836\) | 908.845 | + | 912.034i | 1.08714 | + | 1.09095i | ||||
\(837\) | 21.0276 | − | 36.4208i | 0.0251226 | − | 0.0435135i | ||||
\(838\) | 73.1423 | − | 176.145i | 0.0872819 | − | 0.210196i | ||||
\(839\) | − | 44.6511i | − | 0.0532194i | −0.999646 | − | 0.0266097i | \(-0.991529\pi\) | ||
0.999646 | − | 0.0266097i | \(-0.00847114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 993.593 | 1.18144 | ||||||||
\(842\) | 515.629 | + | 214.110i | 0.612386 | + | 0.254287i | ||||
\(843\) | −283.934 | − | 163.930i | −0.336814 | − | 0.194460i | ||||
\(844\) | 225.793 | − | 225.003i | 0.267527 | − | 0.266591i | ||||
\(845\) | −502.348 | − | 870.092i | −0.594495 | − | 1.02970i | ||||
\(846\) | −4.69102 | − | 6.12455i | −0.00554494 | − | 0.00723942i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −600.208 | − | 349.339i | −0.707793 | − | 0.411957i | ||||
\(849\) | 767.941 | + | 1330.11i | 0.904524 | + | 1.56668i | ||||
\(850\) | 64.1698 | + | 490.738i | 0.0754939 | + | 0.577339i | ||||
\(851\) | 33.2902 | + | 19.2201i | 0.0391189 | + | 0.0225853i | ||||
\(852\) | −188.735 | + | 50.2174i | −0.221520 | + | 0.0589406i | ||||
\(853\) | −118.167 | −0.138531 | −0.0692655 | − | 0.997598i | \(-0.522066\pi\) | ||||
−0.0692655 | + | 0.997598i | \(0.522066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.9692i | 0.0163382i | ||||||||
\(856\) | 753.258 | + | 581.145i | 0.879974 | + | 0.678908i | ||||
\(857\) | 76.5651 | − | 132.615i | 0.0893408 | − | 0.154743i | −0.817892 | − | 0.575372i | \(-0.804857\pi\) |
0.907233 | + | 0.420629i | \(0.138191\pi\) | |||||||
\(858\) | −51.3135 | − | 392.420i | −0.0598060 | − | 0.457366i | ||||
\(859\) | 118.348 | − | 68.3281i | 0.137774 | − | 0.0795437i | −0.429529 | − | 0.903053i | \(-0.641320\pi\) |
0.567303 | + | 0.823509i | \(0.307987\pi\) | |||||||
\(860\) | −735.603 | − | 198.486i | −0.855353 | − | 0.230797i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −205.981 | − | 268.927i | −0.238957 | − | 0.311980i | ||||
\(863\) | 1266.58 | − | 731.262i | 1.46765 | − | 0.847349i | 0.468308 | − | 0.883565i | \(-0.344864\pi\) |
0.999344 | + | 0.0362164i | \(0.0115306\pi\) | |||||||
\(864\) | 800.774 | + | 335.806i | 0.926821 | + | 0.388665i | ||||
\(865\) | −905.185 | + | 1567.83i | −1.04646 | + | 1.81252i | ||||
\(866\) | 545.286 | + | 226.424i | 0.629661 | + | 0.261460i | ||||
\(867\) | − | 460.217i | − | 0.530816i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −817.281 | −0.940484 | ||||||||
\(870\) | 667.284 | − | 1606.98i | 0.766993 | − | 1.84711i | ||||
\(871\) | 368.070 | + | 212.505i | 0.422584 | + | 0.243979i | ||||
\(872\) | −779.135 | − | 104.658i | −0.893504 | − | 0.120021i | ||||
\(873\) | −3.12267 | − | 5.40863i | −0.00357695 | − | 0.00619545i | ||||
\(874\) | −30.4295 | + | 23.3070i | −0.0348163 | + | 0.0266671i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 110.509 | + | 29.8183i | 0.126152 | + | 0.0340392i | ||||
\(877\) | −14.9440 | − | 25.8838i | −0.0170399 | − | 0.0295140i | 0.857380 | − | 0.514684i | \(-0.172091\pi\) |
−0.874420 | + | 0.485170i | \(0.838758\pi\) | |||||||
\(878\) | −648.029 | + | 84.7374i | −0.738074 | + | 0.0965118i | ||||
\(879\) | 343.788 | + | 198.486i | 0.391113 | + | 0.225809i | ||||
\(880\) | 1561.70 | + | 5.47002i | 1.77466 | + | 0.00621593i | ||||
\(881\) | −497.832 | −0.565076 | −0.282538 | − | 0.959256i | \(-0.591176\pi\) | ||||
−0.282538 | + | 0.959256i | \(0.591176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1430.98i | 1.62059i | 0.586022 | + | 0.810295i | \(0.300693\pi\) | ||||
−0.586022 | + | 0.810295i | \(0.699307\pi\) | |||||||
\(884\) | −207.461 | + | 55.1998i | −0.234684 | + | 0.0624432i | ||||
\(885\) | −548.405 | + | 949.865i | −0.619666 | + | 1.07329i | ||||
\(886\) | 1020.89 | − | 133.493i | 1.15224 | − | 0.150669i | ||||
\(887\) | −1028.15 | + | 593.605i | −1.15914 | + | 0.669228i | −0.951097 | − | 0.308892i | \(-0.900042\pi\) |
−0.208040 | + | 0.978120i | \(0.566708\pi\) | |||||||
\(888\) | 994.117 | − | 408.720i | 1.11950 | − | 0.460271i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1082.01 | + | 828.748i | −1.21574 | + | 0.931178i | ||||
\(891\) | −995.780 | + | 574.914i | −1.11760 | + | 0.645245i | ||||
\(892\) | 749.050 | − | 746.431i | 0.839743 | − | 0.836806i | ||||
\(893\) | 473.252 | − | 819.696i | 0.529957 | − | 0.917913i | ||||
\(894\) | −47.5287 | + | 114.461i | −0.0531641 | + | 0.128032i | ||||
\(895\) | 302.879i | 0.338412i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.7815 | 0.0131344 | ||||||||
\(898\) | −1112.35 | − | 461.891i | −1.23869 | − | 0.514355i | ||||
\(899\) | 57.4887 | + | 33.1911i | 0.0639474 | + | 0.0369201i | ||||
\(900\) | 5.50386 | + | 5.52317i | 0.00611540 | + | 0.00613686i | ||||
\(901\) | −251.978 | − | 436.438i | −0.279665 | − | 0.484393i | ||||
\(902\) | −639.256 | − | 834.607i | −0.708709 | − | 0.925285i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −295.071 | − | 717.691i | −0.326406 | − | 0.793906i | ||||
\(905\) | −572.026 | − | 990.778i | −0.632073 | − | 1.09478i | ||||
\(906\) | 72.0650 | + | 551.117i | 0.0795419 | + | 0.608297i | ||||
\(907\) | 708.980 | + | 409.330i | 0.781676 | + | 0.451301i | 0.837024 | − | 0.547166i | \(-0.184294\pi\) |
−0.0553481 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(908\) | 443.620 | + | 1667.29i | 0.488569 | + | 1.83622i | ||||
\(909\) | −2.57584 | −0.00283370 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 774.905i | 0.850610i | 0.905050 | + | 0.425305i | \(0.139833\pi\) | ||||
−0.905050 | + | 0.425305i | \(0.860167\pi\) | |||||||
\(912\) | −3.75396 | + | 1071.76i | −0.00411619 | + | 1.17518i | ||||
\(913\) | −102.605 | + | 177.717i | −0.112382 | + | 0.194651i | ||||
\(914\) | −68.6239 | − | 524.801i | −0.0750809 | − | 0.574181i | ||||
\(915\) | 280.569 | − | 161.986i | 0.306633 | − | 0.177034i | ||||
\(916\) | −442.765 | + | 1640.92i | −0.483367 | + | 1.79140i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 383.157 | + | 500.247i | 0.417383 | + | 0.544931i | ||||
\(919\) | −1468.77 | + | 847.993i | −1.59822 | + | 0.922734i | −0.606393 | + | 0.795165i | \(0.707384\pi\) |
−0.991830 | + | 0.127569i | \(0.959282\pi\) | |||||||
\(920\) | −6.18936 | + | 46.0772i | −0.00672756 | + | 0.0500839i | ||||
\(921\) | 571.291 | − | 989.506i | 0.620295 | − | 1.07438i | ||||
\(922\) | 803.091 | + | 333.475i | 0.871032 | + | 0.361687i | ||||
\(923\) | − | 75.6160i | − | 0.0819241i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 959.401 | 1.03719 | ||||||||
\(926\) | 148.226 | − | 356.964i | 0.160071 | − | 0.385490i | ||||
\(927\) | −12.6926 | − | 7.32808i | −0.0136921 | − | 0.00790515i | ||||
\(928\) | −530.056 | + | 1263.99i | −0.571181 | + | 1.36206i | ||||
\(929\) | 586.655 | + | 1016.12i | 0.631491 | + | 1.09378i | 0.987247 | + | 0.159196i | \(0.0508902\pi\) |
−0.355756 | + | 0.934579i | \(0.615776\pi\) | |||||||
\(930\) | 49.9833 | − | 38.2840i | 0.0537455 | − | 0.0411656i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 228.028 | − | 845.088i | 0.244665 | − | 0.906747i | ||||
\(933\) | 293.060 | + | 507.594i | 0.314105 | + | 0.544046i | ||||
\(934\) | −1299.53 | + | 169.929i | −1.39136 | + | 0.181937i | ||||
\(935\) | 981.453 | + | 566.642i | 1.04968 | + | 0.606034i | ||||
\(936\) | −2.06601 | + | 2.67788i | −0.00220728 | + | 0.00286098i | ||||
\(937\) | −315.505 | −0.336719 | −0.168359 | − | 0.985726i | \(-0.553847\pi\) | ||||
−0.168359 | + | 0.985726i | \(0.553847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1274.61i | 1.35741i | ||||||||
\(940\) | −295.191 | − | 1109.44i | −0.314033 | − | 1.18025i | ||||
\(941\) | 211.752 | − | 366.766i | 0.225029 | − | 0.389762i | −0.731299 | − | 0.682057i | \(-0.761086\pi\) |
0.956328 | + | 0.292295i | \(0.0944189\pi\) | |||||||
\(942\) | −943.125 | + | 123.325i | −1.00119 | + | 0.130918i | ||||
\(943\) | 27.1034 | − | 15.6481i | 0.0287417 | − | 0.0165940i | ||||
\(944\) | 434.601 | − | 746.699i | 0.460383 | − | 0.790995i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −637.398 | + | 488.206i | −0.673782 | + | 0.516074i | ||||
\(947\) | −993.572 | + | 573.639i | −1.04918 | + | 0.605743i | −0.922419 | − | 0.386190i | \(-0.873791\pi\) |
−0.126759 | + | 0.991934i | \(0.540458\pi\) | |||||||
\(948\) | −480.207 | − | 481.892i | −0.506548 | − | 0.508325i | ||||
\(949\) | −22.1583 | + | 38.3793i | −0.0233491 | + | 0.0404418i | ||||
\(950\) | −366.866 | + | 883.503i | −0.386174 | + | 0.930003i | ||||
\(951\) | 331.451i | 0.348529i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 736.494 | 0.772816 | 0.386408 | − | 0.922328i | \(-0.373716\pi\) | ||||
0.386408 | + | 0.922328i | \(0.373716\pi\) | |||||||
\(954\) | −7.33268 | − | 3.04482i | −0.00768625 | − | 0.00319164i | ||||
\(955\) | 2084.02 | + | 1203.21i | 2.18222 | + | 1.25991i | ||||
\(956\) | −255.473 | + | 254.580i | −0.267231 | + | 0.266297i | ||||
\(957\) | −916.794 | − | 1587.93i | −0.957988 | − | 1.65928i | ||||
\(958\) | 124.849 | + | 163.001i | 0.130322 | + | 0.170148i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 914.377 | + | 924.036i | 0.952476 | + | 0.962538i | ||||
\(961\) | −479.299 | − | 830.170i | −0.498750 | − | 0.863861i | ||||
\(962\) | 53.9582 | + | 412.645i | 0.0560897 | + | 0.428945i | ||||
\(963\) | 9.41970 | + | 5.43847i | 0.00978162 | + | 0.00564742i | ||||
\(964\) | −1453.22 | + | 386.662i | −1.50749 | + | 0.401101i | ||||
\(965\) | 2372.17 | 2.45821 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1147.66i | − | 1.18682i | −0.804899 | − | 0.593411i | \(-0.797781\pi\) | ||
0.804899 | − | 0.593411i | \(-0.202219\pi\) | |||||||
\(968\) | 413.962 | − | 536.561i | 0.427647 | − | 0.554299i | ||||
\(969\) | −388.875 | + | 673.551i | −0.401316 | + | 0.695099i | ||||
\(970\) | −120.502 | − | 921.540i | −0.124229 | − | 0.950042i | ||||
\(971\) | 960.111 | − | 554.321i | 0.988786 | − | 0.570876i | 0.0838750 | − | 0.996476i | \(-0.473270\pi\) |
0.904911 | + | 0.425600i | \(0.139937\pi\) | |||||||
\(972\) | 19.0730 | + | 5.14640i | 0.0196224 | + | 0.00529465i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 183.213 | + | 239.201i | 0.188104 | + | 0.245586i | ||||
\(975\) | 254.652 | − | 147.023i | 0.261181 | − | 0.150793i | ||||
\(976\) | −221.452 | + | 126.823i | −0.226898 | + | 0.129942i | ||||
\(977\) | −389.513 | + | 674.657i | −0.398683 | + | 0.690539i | −0.993564 | − | 0.113275i | \(-0.963866\pi\) |
0.594881 | + | 0.803814i | \(0.297199\pi\) | |||||||
\(978\) | −252.650 | − | 104.910i | −0.258333 | − | 0.107270i | ||||
\(979\) | 1436.21i | 1.46702i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.98769 | −0.00916176 | ||||||||
\(982\) | −91.1142 | + | 219.426i | −0.0927843 | + | 0.223448i | ||||
\(983\) | −68.9305 | − | 39.7970i | −0.0701225 | − | 0.0404853i | 0.464529 | − | 0.885558i | \(-0.346224\pi\) |
−0.534651 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(984\) | 116.502 | − | 867.311i | 0.118397 | − | 0.881414i | ||||
\(985\) | −91.6387 | − | 158.723i | −0.0930343 | − | 0.161140i | ||||
\(986\) | −789.618 | + | 604.797i | −0.800830 | + | 0.613385i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −400.634 | − | 108.102i | −0.405500 | − | 0.109415i | ||||
\(989\) | −11.9506 | − | 20.6991i | −0.0120836 | − | 0.0209293i | ||||
\(990\) | 17.7039 | − | 2.31500i | 0.0178828 | − | 0.00233838i | ||||
\(991\) | −557.931 | − | 322.122i | −0.562998 | − | 0.325047i | 0.191350 | − | 0.981522i | \(-0.438714\pi\) |
−0.754348 | + | 0.656475i | \(0.772047\pi\) | |||||||
\(992\) | −39.4777 | + | 30.0186i | −0.0397960 | + | 0.0302607i | ||||
\(993\) | −357.057 | −0.359574 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1575.85i | − | 1.58377i | ||||||
\(996\) | −165.074 | + | 43.9217i | −0.165737 | + | 0.0440981i | ||||
\(997\) | 869.997 | − | 1506.88i | 0.872615 | − | 1.51141i | 0.0133331 | − | 0.999911i | \(-0.495756\pi\) |
0.859282 | − | 0.511502i | \(-0.170911\pi\) | |||||||
\(998\) | −1083.64 | + | 141.698i | −1.08581 | + | 0.141982i | ||||
\(999\) | 1057.85 | − | 610.752i | 1.05891 | − | 0.611363i |
(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 | 196.3.g.k.67.1 | 12 | ||
4.3 | odd | 2 | inner | 196.3.g.k.67.3 | 12 | ||
7.2 | even | 3 | inner | 196.3.g.k.79.3 | 12 | ||
7.3 | odd | 6 | 196.3.c.g.99.5 | 6 | |||
7.4 | even | 3 | 28.3.c.a.15.5 | ✓ | 6 | ||
7.5 | odd | 6 | 196.3.g.j.79.3 | 12 | |||
7.6 | odd | 2 | 196.3.g.j.67.1 | 12 | |||
21.11 | odd | 6 | 252.3.g.a.127.2 | 6 | |||
28.3 | even | 6 | 196.3.c.g.99.6 | 6 | |||
28.11 | odd | 6 | 28.3.c.a.15.6 | yes | 6 | ||
28.19 | even | 6 | 196.3.g.j.79.1 | 12 | |||
28.23 | odd | 6 | inner | 196.3.g.k.79.1 | 12 | ||
28.27 | even | 2 | 196.3.g.j.67.3 | 12 | |||
56.11 | odd | 6 | 448.3.d.d.127.5 | 6 | |||
56.53 | even | 6 | 448.3.d.d.127.2 | 6 | |||
84.11 | even | 6 | 252.3.g.a.127.1 | 6 | |||
112.11 | odd | 12 | 1792.3.g.g.127.3 | 12 | |||
112.53 | even | 12 | 1792.3.g.g.127.9 | 12 | |||
112.67 | odd | 12 | 1792.3.g.g.127.10 | 12 | |||
112.109 | even | 12 | 1792.3.g.g.127.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.3.c.a.15.5 | ✓ | 6 | 7.4 | even | 3 | ||
28.3.c.a.15.6 | yes | 6 | 28.11 | odd | 6 | ||
196.3.c.g.99.5 | 6 | 7.3 | odd | 6 | |||
196.3.c.g.99.6 | 6 | 28.3 | even | 6 | |||
196.3.g.j.67.1 | 12 | 7.6 | odd | 2 | |||
196.3.g.j.67.3 | 12 | 28.27 | even | 2 | |||
196.3.g.j.79.1 | 12 | 28.19 | even | 6 | |||
196.3.g.j.79.3 | 12 | 7.5 | odd | 6 | |||
196.3.g.k.67.1 | 12 | 1.1 | even | 1 | trivial | ||
196.3.g.k.67.3 | 12 | 4.3 | odd | 2 | inner | ||
196.3.g.k.79.1 | 12 | 28.23 | odd | 6 | inner | ||
196.3.g.k.79.3 | 12 | 7.2 | even | 3 | inner | ||
252.3.g.a.127.1 | 6 | 84.11 | even | 6 | |||
252.3.g.a.127.2 | 6 | 21.11 | odd | 6 | |||
448.3.d.d.127.2 | 6 | 56.53 | even | 6 | |||
448.3.d.d.127.5 | 6 | 56.11 | odd | 6 | |||
1792.3.g.g.127.3 | 12 | 112.11 | odd | 12 | |||
1792.3.g.g.127.4 | 12 | 112.109 | even | 12 | |||
1792.3.g.g.127.9 | 12 | 112.53 | even | 12 | |||
1792.3.g.g.127.10 | 12 | 112.67 | odd | 12 |