Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(47,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.l (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.3 | ||
Character | \(\chi\) | \(=\) | 966.47 |
Dual form | 966.2.l.c.185.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −1.43165 | + | 0.974877i | −0.826562 | + | 0.562845i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.723421 | + | 1.25300i | −0.323524 | + | 0.560359i | −0.981212 | − | 0.192930i | \(-0.938201\pi\) |
0.657689 | + | 0.753290i | \(0.271534\pi\) | |||||||
\(6\) | 1.72728 | − | 0.128444i | 0.705160 | − | 0.0524372i | ||||
\(7\) | −1.91613 | − | 1.82440i | −0.724229 | − | 0.689560i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.09923 | − | 2.79136i | 0.366410 | − | 0.930453i | ||||
\(10\) | 1.25300 | − | 0.723421i | 0.396234 | − | 0.228766i | ||||
\(11\) | 2.11952 | − | 1.22371i | 0.639061 | − | 0.368962i | −0.145192 | − | 0.989403i | \(-0.546380\pi\) |
0.784253 | + | 0.620442i | \(0.213047\pi\) | |||||||
\(12\) | −1.56009 | − | 0.752405i | −0.450360 | − | 0.217201i | ||||
\(13\) | 3.42072i | 0.948738i | 0.880326 | + | 0.474369i | \(0.157324\pi\) | ||||
−0.880326 | + | 0.474369i | \(0.842676\pi\) | |||||||
\(14\) | 0.747214 | + | 2.53804i | 0.199701 | + | 0.678321i | ||||
\(15\) | −0.185839 | − | 2.49910i | −0.0479833 | − | 0.645265i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.94087 | − | 3.36168i | −0.470729 | − | 0.815327i | 0.528710 | − | 0.848802i | \(-0.322676\pi\) |
−0.999440 | + | 0.0334756i | \(0.989342\pi\) | |||||||
\(18\) | −2.34764 | + | 1.86777i | −0.553344 | + | 0.440239i | ||||
\(19\) | 6.23947 | + | 3.60236i | 1.43143 | + | 0.826437i | 0.997230 | − | 0.0743785i | \(-0.0236973\pi\) |
0.434201 | + | 0.900816i | \(0.357031\pi\) | |||||||
\(20\) | −1.44684 | −0.323524 | ||||||||
\(21\) | 4.52179 | + | 0.743914i | 0.986736 | + | 0.162335i | ||||
\(22\) | −2.44742 | −0.521791 | ||||||||
\(23\) | 0.866025 | + | 0.500000i | 0.180579 | + | 0.104257i | ||||
\(24\) | 0.974877 | + | 1.43165i | 0.198996 | + | 0.292234i | ||||
\(25\) | 1.45333 | + | 2.51723i | 0.290665 | + | 0.503447i | ||||
\(26\) | 1.71036 | − | 2.96243i | 0.335430 | − | 0.580981i | ||||
\(27\) | 1.14752 | + | 5.06786i | 0.220841 | + | 0.975310i | ||||
\(28\) | 0.621916 | − | 2.57162i | 0.117531 | − | 0.485990i | ||||
\(29\) | − | 6.88037i | − | 1.27765i | −0.769351 | − | 0.638826i | \(-0.779420\pi\) | ||
0.769351 | − | 0.638826i | \(-0.220580\pi\) | |||||||
\(30\) | −1.08861 | + | 2.25721i | −0.198752 | + | 0.412107i | ||||
\(31\) | 2.91493 | − | 1.68294i | 0.523537 | − | 0.302264i | −0.214843 | − | 0.976649i | \(-0.568924\pi\) |
0.738381 | + | 0.674384i | \(0.235591\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −1.84145 | + | 3.81819i | −0.320555 | + | 0.664662i | ||||
\(34\) | 3.88173i | 0.665711i | ||||||||
\(35\) | 3.67215 | − | 1.08110i | 0.620706 | − | 0.182739i | ||||
\(36\) | 2.96700 | − | 0.443719i | 0.494501 | − | 0.0739532i | ||||
\(37\) | −3.58636 | + | 6.21176i | −0.589594 | + | 1.02121i | 0.404691 | + | 0.914453i | \(0.367379\pi\) |
−0.994285 | + | 0.106754i | \(0.965954\pi\) | |||||||
\(38\) | −3.60236 | − | 6.23947i | −0.584379 | − | 1.01217i | ||||
\(39\) | −3.33478 | − | 4.89727i | −0.533993 | − | 0.784191i | ||||
\(40\) | 1.25300 | + | 0.723421i | 0.198117 | + | 0.114383i | ||||
\(41\) | −9.80512 | −1.53130 | −0.765652 | − | 0.643255i | \(-0.777583\pi\) | ||||
−0.765652 | + | 0.643255i | \(0.777583\pi\) | |||||||
\(42\) | −3.54403 | − | 2.90514i | −0.546856 | − | 0.448273i | ||||
\(43\) | −8.24338 | −1.25710 | −0.628552 | − | 0.777768i | \(-0.716352\pi\) | ||||
−0.628552 | + | 0.777768i | \(0.716352\pi\) | |||||||
\(44\) | 2.11952 | + | 1.22371i | 0.319530 | + | 0.184481i | ||||
\(45\) | 2.70237 | + | 3.39666i | 0.402846 | + | 0.506345i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | −5.75052 | + | 9.96019i | −0.838799 | + | 1.45284i | 0.0521006 | + | 0.998642i | \(0.483408\pi\) |
−0.890900 | + | 0.454200i | \(0.849925\pi\) | |||||||
\(48\) | −0.128444 | − | 1.72728i | −0.0185393 | − | 0.249312i | ||||
\(49\) | 0.343100 | + | 6.99159i | 0.0490143 | + | 0.998798i | ||||
\(50\) | − | 2.90665i | − | 0.411062i | ||||||
\(51\) | 6.05586 | + | 2.92063i | 0.847990 | + | 0.408970i | ||||
\(52\) | −2.96243 | + | 1.71036i | −0.410816 | + | 0.237185i | ||||
\(53\) | −3.27867 | + | 1.89294i | −0.450360 | + | 0.260015i | −0.707982 | − | 0.706230i | \(-0.750394\pi\) |
0.257622 | + | 0.966246i | \(0.417061\pi\) | |||||||
\(54\) | 1.54015 | − | 4.96266i | 0.209587 | − | 0.675332i | ||||
\(55\) | 3.54102i | 0.477471i | ||||||||
\(56\) | −1.82440 | + | 1.91613i | −0.243796 | + | 0.256053i | ||||
\(57\) | −12.4446 | + | 0.925404i | −1.64832 | + | 0.122573i | ||||
\(58\) | −3.44018 | + | 5.95857i | −0.451718 | + | 0.782399i | ||||
\(59\) | 5.49526 | + | 9.51808i | 0.715422 | + | 1.23915i | 0.962796 | + | 0.270228i | \(0.0870990\pi\) |
−0.247374 | + | 0.968920i | \(0.579568\pi\) | |||||||
\(60\) | 2.07137 | − | 1.41049i | 0.267412 | − | 0.182094i | ||||
\(61\) | 1.89515 | + | 1.09417i | 0.242649 | + | 0.140093i | 0.616394 | − | 0.787438i | \(-0.288593\pi\) |
−0.373745 | + | 0.927532i | \(0.621926\pi\) | |||||||
\(62\) | −3.36587 | −0.427467 | ||||||||
\(63\) | −7.19884 | + | 3.34317i | −0.906968 | + | 0.421199i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.28617 | − | 2.47462i | −0.531634 | − | 0.306939i | ||||
\(66\) | 3.50384 | − | 2.38593i | 0.431293 | − | 0.293688i | ||||
\(67\) | 1.28247 | + | 2.22130i | 0.156679 | + | 0.271375i | 0.933669 | − | 0.358137i | \(-0.116588\pi\) |
−0.776990 | + | 0.629512i | \(0.783255\pi\) | |||||||
\(68\) | 1.94087 | − | 3.36168i | 0.235365 | − | 0.407663i | ||||
\(69\) | −1.72728 | + | 0.128444i | −0.207940 | + | 0.0154629i | ||||
\(70\) | −3.72072 | − | 0.899813i | −0.444712 | − | 0.107548i | ||||
\(71\) | − | 12.4084i | − | 1.47260i | −0.676654 | − | 0.736301i | \(-0.736571\pi\) | ||
0.676654 | − | 0.736301i | \(-0.263429\pi\) | |||||||
\(72\) | −2.79136 | − | 1.09923i | −0.328965 | − | 0.129546i | ||||
\(73\) | −2.08792 | + | 1.20546i | −0.244372 | + | 0.141088i | −0.617185 | − | 0.786818i | \(-0.711727\pi\) |
0.372812 | + | 0.927907i | \(0.378393\pi\) | |||||||
\(74\) | 6.21176 | − | 3.58636i | 0.722102 | − | 0.416906i | ||||
\(75\) | −4.53464 | − | 2.18698i | −0.523615 | − | 0.252530i | ||||
\(76\) | 7.20471i | 0.826437i | ||||||||
\(77\) | −6.29382 | − | 1.52209i | −0.717247 | − | 0.173458i | ||||
\(78\) | 0.439373 | + | 5.90855i | 0.0497491 | + | 0.669012i | ||||
\(79\) | −5.93001 | + | 10.2711i | −0.667179 | + | 1.15559i | 0.311511 | + | 0.950242i | \(0.399165\pi\) |
−0.978690 | + | 0.205345i | \(0.934168\pi\) | |||||||
\(80\) | −0.723421 | − | 1.25300i | −0.0808809 | − | 0.140090i | ||||
\(81\) | −6.58339 | − | 6.13669i | −0.731487 | − | 0.681855i | ||||
\(82\) | 8.49149 | + | 4.90256i | 0.937728 | + | 0.541397i | ||||
\(83\) | 13.5344 | 1.48560 | 0.742798 | − | 0.669516i | \(-0.233498\pi\) | ||||
0.742798 | + | 0.669516i | \(0.233498\pi\) | |||||||
\(84\) | 1.61665 | + | 4.28794i | 0.176391 | + | 0.467853i | ||||
\(85\) | 5.61625 | 0.609168 | ||||||||
\(86\) | 7.13898 | + | 4.12169i | 0.769816 | + | 0.444453i | ||||
\(87\) | 6.70751 | + | 9.85026i | 0.719120 | + | 1.05606i | ||||
\(88\) | −1.22371 | − | 2.11952i | −0.130448 | − | 0.225942i | ||||
\(89\) | −4.34273 | + | 7.52183i | −0.460329 | + | 0.797313i | −0.998977 | − | 0.0452180i | \(-0.985602\pi\) |
0.538648 | + | 0.842531i | \(0.318935\pi\) | |||||||
\(90\) | −0.641991 | − | 4.29278i | −0.0676718 | − | 0.452499i | ||||
\(91\) | 6.24078 | − | 6.55455i | 0.654212 | − | 0.687103i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | −2.53250 | + | 5.25107i | −0.262608 | + | 0.544511i | ||||
\(94\) | 9.96019 | − | 5.75052i | 1.02731 | − | 0.593120i | ||||
\(95\) | −9.02752 | + | 5.21204i | −0.926204 | + | 0.534744i | ||||
\(96\) | −0.752405 | + | 1.56009i | −0.0767920 | + | 0.159226i | ||||
\(97\) | 3.37559i | 0.342739i | 0.985207 | + | 0.171370i | \(0.0548193\pi\) | ||||
−0.985207 | + | 0.171370i | \(0.945181\pi\) | |||||||
\(98\) | 3.19866 | − | 6.22644i | 0.323113 | − | 0.628966i | ||||
\(99\) | −1.08596 | − | 7.26149i | −0.109144 | − | 0.729807i | ||||
\(100\) | −1.45333 | + | 2.51723i | −0.145333 | + | 0.251723i | ||||
\(101\) | −2.74710 | − | 4.75812i | −0.273347 | − | 0.473451i | 0.696370 | − | 0.717683i | \(-0.254797\pi\) |
−0.969717 | + | 0.244232i | \(0.921464\pi\) | |||||||
\(102\) | −3.78421 | − | 5.55727i | −0.374693 | − | 0.550252i | ||||
\(103\) | 6.75677 | + | 3.90102i | 0.665765 | + | 0.384379i | 0.794470 | − | 0.607304i | \(-0.207749\pi\) |
−0.128705 | + | 0.991683i | \(0.541082\pi\) | |||||||
\(104\) | 3.42072 | 0.335430 | ||||||||
\(105\) | −4.20328 | + | 5.12765i | −0.410198 | + | 0.500407i | ||||
\(106\) | 3.78588 | 0.367717 | ||||||||
\(107\) | 5.72784 | + | 3.30697i | 0.553731 | + | 0.319697i | 0.750625 | − | 0.660728i | \(-0.229752\pi\) |
−0.196895 | + | 0.980425i | \(0.563086\pi\) | |||||||
\(108\) | −3.81513 | + | 3.52771i | −0.367111 | + | 0.339454i | ||||
\(109\) | −1.46428 | − | 2.53621i | −0.140253 | − | 0.242925i | 0.787339 | − | 0.616520i | \(-0.211458\pi\) |
−0.927592 | + | 0.373595i | \(0.878125\pi\) | |||||||
\(110\) | 1.77051 | − | 3.06661i | 0.168812 | − | 0.292390i | ||||
\(111\) | −0.921295 | − | 12.3893i | −0.0874455 | − | 1.17594i | ||||
\(112\) | 2.53804 | − | 0.747214i | 0.239823 | − | 0.0706051i | ||||
\(113\) | 17.2501i | 1.62275i | 0.584527 | + | 0.811374i | \(0.301280\pi\) | ||||
−0.584527 | + | 0.811374i | \(0.698720\pi\) | |||||||
\(114\) | 11.2400 | + | 5.42086i | 1.05272 | + | 0.507710i | ||||
\(115\) | −1.25300 | + | 0.723421i | −0.116843 | + | 0.0674593i | ||||
\(116\) | 5.95857 | − | 3.44018i | 0.553239 | − | 0.319413i | ||||
\(117\) | 9.54847 | + | 3.76016i | 0.882757 | + | 0.347627i | ||||
\(118\) | − | 10.9905i | − | 1.01176i | ||||||
\(119\) | −2.41411 | + | 9.98233i | −0.221301 | + | 0.915079i | ||||
\(120\) | −2.49910 | + | 0.185839i | −0.228136 | + | 0.0169647i | ||||
\(121\) | −2.50508 | + | 4.33892i | −0.227734 | + | 0.394448i | ||||
\(122\) | −1.09417 | − | 1.89515i | −0.0990611 | − | 0.171579i | ||||
\(123\) | 14.0375 | − | 9.55879i | 1.26572 | − | 0.861887i | ||||
\(124\) | 2.91493 | + | 1.68294i | 0.261769 | + | 0.151132i | ||||
\(125\) | −11.4397 | −1.02320 | ||||||||
\(126\) | 7.90596 | + | 0.704151i | 0.704319 | + | 0.0627307i | ||||
\(127\) | 15.6980 | 1.39297 | 0.696484 | − | 0.717572i | \(-0.254747\pi\) | ||||
0.696484 | + | 0.717572i | \(0.254747\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 11.8016 | − | 8.03628i | 1.03907 | − | 0.707555i | ||||
\(130\) | 2.47462 | + | 4.28617i | 0.217039 | + | 0.375922i | ||||
\(131\) | −6.69869 | + | 11.6025i | −0.585267 | + | 1.01371i | 0.409575 | + | 0.912276i | \(0.365677\pi\) |
−0.994842 | + | 0.101436i | \(0.967656\pi\) | |||||||
\(132\) | −4.22738 | + | 0.314357i | −0.367946 | + | 0.0273612i | ||||
\(133\) | −5.38347 | − | 18.2859i | −0.466806 | − | 1.58559i | ||||
\(134\) | − | 2.56494i | − | 0.221577i | ||||||
\(135\) | −7.18017 | − | 2.22835i | −0.617971 | − | 0.191786i | ||||
\(136\) | −3.36168 | + | 1.94087i | −0.288261 | + | 0.166428i | ||||
\(137\) | −2.73228 | + | 1.57748i | −0.233434 | + | 0.134773i | −0.612155 | − | 0.790737i | \(-0.709697\pi\) |
0.378721 | + | 0.925511i | \(0.376364\pi\) | |||||||
\(138\) | 1.56009 | + | 0.752405i | 0.132804 | + | 0.0640490i | ||||
\(139\) | 21.1498i | 1.79391i | 0.442127 | + | 0.896953i | \(0.354224\pi\) | ||||
−0.442127 | + | 0.896953i | \(0.645776\pi\) | |||||||
\(140\) | 2.77233 | + | 2.63962i | 0.234305 | + | 0.223089i | ||||
\(141\) | −1.47724 | − | 19.8655i | −0.124406 | − | 1.67298i | ||||
\(142\) | −6.20418 | + | 10.7460i | −0.520643 | + | 0.901781i | ||||
\(143\) | 4.18597 | + | 7.25031i | 0.350048 | + | 0.606301i | ||||
\(144\) | 1.86777 | + | 2.34764i | 0.155648 | + | 0.195637i | ||||
\(145\) | 8.62111 | + | 4.97740i | 0.715944 | + | 0.413350i | ||||
\(146\) | 2.41092 | 0.199529 | ||||||||
\(147\) | −7.30713 | − | 9.67501i | −0.602682 | − | 0.797981i | ||||
\(148\) | −7.17272 | −0.589594 | ||||||||
\(149\) | 2.37873 | + | 1.37336i | 0.194873 | + | 0.112510i | 0.594262 | − | 0.804272i | \(-0.297444\pi\) |
−0.399389 | + | 0.916782i | \(0.630778\pi\) | |||||||
\(150\) | 2.83363 | + | 4.16130i | 0.231365 | + | 0.339769i | ||||
\(151\) | −4.71729 | − | 8.17059i | −0.383888 | − | 0.664914i | 0.607726 | − | 0.794147i | \(-0.292082\pi\) |
−0.991614 | + | 0.129233i | \(0.958748\pi\) | |||||||
\(152\) | 3.60236 | − | 6.23947i | 0.292190 | − | 0.506087i | ||||
\(153\) | −11.5171 | + | 1.72240i | −0.931103 | + | 0.139248i | ||||
\(154\) | 4.68956 | + | 4.46507i | 0.377896 | + | 0.359806i | ||||
\(155\) | 4.86989i | 0.391159i | ||||||||
\(156\) | 2.57377 | − | 5.33664i | 0.206066 | − | 0.427273i | ||||
\(157\) | −2.66109 | + | 1.53638i | −0.212378 | + | 0.122617i | −0.602416 | − | 0.798182i | \(-0.705795\pi\) |
0.390038 | + | 0.920799i | \(0.372462\pi\) | |||||||
\(158\) | 10.2711 | − | 5.93001i | 0.817123 | − | 0.471766i | ||||
\(159\) | 2.84851 | − | 5.90632i | 0.225902 | − | 0.468402i | ||||
\(160\) | 1.44684i | 0.114383i | ||||||||
\(161\) | −0.747214 | − | 2.53804i | −0.0588887 | − | 0.200026i | ||||
\(162\) | 2.63303 | + | 8.60623i | 0.206871 | + | 0.676169i | ||||
\(163\) | −0.601674 | + | 1.04213i | −0.0471268 | + | 0.0816259i | −0.888627 | − | 0.458631i | \(-0.848340\pi\) |
0.841500 | + | 0.540257i | \(0.181673\pi\) | |||||||
\(164\) | −4.90256 | − | 8.49149i | −0.382826 | − | 0.663074i | ||||
\(165\) | −3.45206 | − | 5.06950i | −0.268743 | − | 0.394660i | ||||
\(166\) | −11.7212 | − | 6.76721i | −0.909738 | − | 0.525237i | ||||
\(167\) | −9.17724 | −0.710156 | −0.355078 | − | 0.934837i | \(-0.615546\pi\) | ||||
−0.355078 | + | 0.934837i | \(0.615546\pi\) | |||||||
\(168\) | 0.743914 | − | 4.52179i | 0.0573942 | − | 0.348864i | ||||
\(169\) | 1.29865 | 0.0998959 | ||||||||
\(170\) | −4.86381 | − | 2.80812i | −0.373038 | − | 0.215373i | ||||
\(171\) | 16.9141 | − | 13.4568i | 1.29345 | − | 1.02907i | ||||
\(172\) | −4.12169 | − | 7.13898i | −0.314276 | − | 0.544342i | ||||
\(173\) | 9.50912 | − | 16.4703i | 0.722965 | − | 1.25221i | −0.236841 | − | 0.971548i | \(-0.576112\pi\) |
0.959806 | − | 0.280664i | \(-0.0905546\pi\) | |||||||
\(174\) | −0.883744 | − | 11.8843i | −0.0669964 | − | 0.900949i | ||||
\(175\) | 1.80769 | − | 7.47480i | 0.136649 | − | 0.565041i | ||||
\(176\) | 2.44742i | 0.184481i | ||||||||
\(177\) | −17.1462 | − | 8.26933i | −1.28879 | − | 0.621561i | ||||
\(178\) | 7.52183 | − | 4.34273i | 0.563785 | − | 0.325502i | ||||
\(179\) | −13.3216 | + | 7.69121i | −0.995701 | + | 0.574868i | −0.906973 | − | 0.421188i | \(-0.861613\pi\) |
−0.0887274 | + | 0.996056i | \(0.528280\pi\) | |||||||
\(180\) | −1.59041 | + | 4.03866i | −0.118542 | + | 0.301024i | ||||
\(181\) | − | 19.2438i | − | 1.43038i | −0.698929 | − | 0.715191i | \(-0.746339\pi\) | ||
0.698929 | − | 0.715191i | \(-0.253661\pi\) | |||||||
\(182\) | −8.68195 | + | 2.55601i | −0.643549 | + | 0.189464i | ||||
\(183\) | −3.77986 | + | 0.281079i | −0.279415 | + | 0.0207779i | ||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −5.18890 | − | 8.98743i | −0.381495 | − | 0.660769i | ||||
\(186\) | 4.81875 | − | 3.28131i | 0.353328 | − | 0.240598i | ||||
\(187\) | −8.22742 | − | 4.75010i | −0.601649 | − | 0.347362i | ||||
\(188\) | −11.5010 | −0.838799 | ||||||||
\(189\) | 7.04702 | − | 11.8042i | 0.512595 | − | 0.858630i | ||||
\(190\) | 10.4241 | 0.756242 | ||||||||
\(191\) | 17.0429 | + | 9.83973i | 1.23318 | + | 0.711978i | 0.967692 | − | 0.252136i | \(-0.0811331\pi\) |
0.265490 | + | 0.964114i | \(0.414466\pi\) | |||||||
\(192\) | 1.43165 | − | 0.974877i | 0.103320 | − | 0.0703557i | ||||
\(193\) | −11.6616 | − | 20.1985i | −0.839422 | − | 1.45392i | −0.890378 | − | 0.455221i | \(-0.849560\pi\) |
0.0509560 | − | 0.998701i | \(-0.483773\pi\) | |||||||
\(194\) | 1.68780 | − | 2.92335i | 0.121177 | − | 0.209884i | ||||
\(195\) | 8.54874 | − | 0.635702i | 0.612188 | − | 0.0455236i | ||||
\(196\) | −5.88334 | + | 3.79293i | −0.420239 | + | 0.270923i | ||||
\(197\) | 12.5022i | 0.890747i | 0.895345 | + | 0.445373i | \(0.146929\pi\) | ||||
−0.895345 | + | 0.445373i | \(0.853071\pi\) | |||||||
\(198\) | −2.69027 | + | 6.83162i | −0.191189 | + | 0.485502i | ||||
\(199\) | 3.95601 | − | 2.28400i | 0.280434 | − | 0.161909i | −0.353186 | − | 0.935553i | \(-0.614902\pi\) |
0.633620 | + | 0.773644i | \(0.281568\pi\) | |||||||
\(200\) | 2.51723 | − | 1.45333i | 0.177995 | − | 0.102766i | ||||
\(201\) | −4.00154 | − | 1.92987i | −0.282247 | − | 0.136123i | ||||
\(202\) | 5.49421i | 0.386571i | ||||||||
\(203\) | −12.5526 | + | 13.1837i | −0.881017 | + | 0.925312i | ||||
\(204\) | 0.498586 | + | 6.70484i | 0.0349080 | + | 0.469433i | ||||
\(205\) | 7.09323 | − | 12.2858i | 0.495413 | − | 0.858080i | ||||
\(206\) | −3.90102 | − | 6.75677i | −0.271797 | − | 0.470767i | ||||
\(207\) | 2.34764 | − | 1.86777i | 0.163172 | − | 0.129819i | ||||
\(208\) | −2.96243 | − | 1.71036i | −0.205408 | − | 0.118592i | ||||
\(209\) | 17.6329 | 1.21970 | ||||||||
\(210\) | 6.20397 | − | 2.33903i | 0.428115 | − | 0.161409i | ||||
\(211\) | 12.4221 | 0.855174 | 0.427587 | − | 0.903974i | \(-0.359364\pi\) | ||||
0.427587 | + | 0.903974i | \(0.359364\pi\) | |||||||
\(212\) | −3.27867 | − | 1.89294i | −0.225180 | − | 0.130008i | ||||
\(213\) | 12.0966 | + | 17.7644i | 0.828847 | + | 1.21720i | ||||
\(214\) | −3.30697 | − | 5.72784i | −0.226060 | − | 0.391547i | ||||
\(215\) | 5.96343 | − | 10.3290i | 0.406703 | − | 0.704430i | ||||
\(216\) | 5.06786 | − | 1.14752i | 0.344824 | − | 0.0780790i | ||||
\(217\) | −8.65574 | − | 2.09329i | −0.587590 | − | 0.142102i | ||||
\(218\) | 2.92857i | 0.198348i | ||||||||
\(219\) | 1.81399 | − | 3.76126i | 0.122578 | − | 0.254162i | ||||
\(220\) | −3.06661 | + | 1.77051i | −0.206751 | + | 0.119368i | ||||
\(221\) | 11.4994 | − | 6.63917i | 0.773531 | − | 0.446599i | ||||
\(222\) | −5.39679 | + | 11.1901i | −0.362209 | + | 0.751031i | ||||
\(223\) | − | 4.65691i | − | 0.311850i | −0.987769 | − | 0.155925i | \(-0.950164\pi\) | ||
0.987769 | − | 0.155925i | \(-0.0498358\pi\) | |||||||
\(224\) | −2.57162 | − | 0.621916i | −0.171823 | − | 0.0415535i | ||||
\(225\) | 8.62404 | − | 1.28974i | 0.574936 | − | 0.0859824i | ||||
\(226\) | 8.62503 | − | 14.9390i | 0.573728 | − | 0.993727i | ||||
\(227\) | 0.120944 | + | 0.209482i | 0.00802737 | + | 0.0139038i | 0.870011 | − | 0.493032i | \(-0.164111\pi\) |
−0.861984 | + | 0.506936i | \(0.830778\pi\) | |||||||
\(228\) | −7.02371 | − | 10.3146i | −0.465156 | − | 0.683102i | ||||
\(229\) | 15.8613 | + | 9.15753i | 1.04814 | + | 0.605147i | 0.922129 | − | 0.386882i | \(-0.126448\pi\) |
0.126015 | + | 0.992028i | \(0.459781\pi\) | |||||||
\(230\) | 1.44684 | 0.0954019 | ||||||||
\(231\) | 10.4944 | − | 3.95661i | 0.690479 | − | 0.260326i | ||||
\(232\) | −6.88037 | −0.451718 | ||||||||
\(233\) | 7.97801 | + | 4.60611i | 0.522657 | + | 0.301756i | 0.738021 | − | 0.674778i | \(-0.235760\pi\) |
−0.215364 | + | 0.976534i | \(0.569094\pi\) | |||||||
\(234\) | −6.38914 | − | 8.03063i | −0.417671 | − | 0.524979i | ||||
\(235\) | −8.32008 | − | 14.4108i | −0.542742 | − | 0.940057i | ||||
\(236\) | −5.49526 | + | 9.51808i | −0.357711 | + | 0.619574i | ||||
\(237\) | −1.52335 | − | 20.4856i | −0.0989524 | − | 1.33068i | ||||
\(238\) | 7.08185 | − | 7.43790i | 0.459048 | − | 0.482127i | ||||
\(239\) | − | 22.4033i | − | 1.44915i | −0.689196 | − | 0.724575i | \(-0.742036\pi\) | ||
0.689196 | − | 0.724575i | \(-0.257964\pi\) | |||||||
\(240\) | 2.25721 | + | 1.08861i | 0.145702 | + | 0.0702695i | ||||
\(241\) | −25.7428 | + | 14.8626i | −1.65824 | + | 0.957385i | −0.684713 | + | 0.728813i | \(0.740072\pi\) |
−0.973527 | + | 0.228572i | \(0.926594\pi\) | |||||||
\(242\) | 4.33892 | − | 2.50508i | 0.278917 | − | 0.161033i | ||||
\(243\) | 15.4076 | + | 2.36759i | 0.988399 | + | 0.151881i | ||||
\(244\) | 2.18833i | 0.140093i | ||||||||
\(245\) | −9.00867 | − | 4.62795i | −0.575543 | − | 0.295669i | ||||
\(246\) | −16.9362 | + | 1.25941i | −1.07981 | + | 0.0802972i | ||||
\(247\) | −12.3227 | + | 21.3435i | −0.784073 | + | 1.35805i | ||||
\(248\) | −1.68294 | − | 2.91493i | −0.106867 | − | 0.185098i | ||||
\(249\) | −19.3765 | + | 13.1944i | −1.22794 | + | 0.836161i | ||||
\(250\) | 9.90704 | + | 5.71983i | 0.626576 | + | 0.361754i | ||||
\(251\) | 13.2669 | 0.837396 | 0.418698 | − | 0.908125i | \(-0.362487\pi\) | ||||
0.418698 | + | 0.908125i | \(0.362487\pi\) | |||||||
\(252\) | −6.49469 | − | 4.56279i | −0.409127 | − | 0.287429i | ||||
\(253\) | 2.44742 | 0.153868 | ||||||||
\(254\) | −13.5948 | − | 7.84898i | −0.853015 | − | 0.492489i | ||||
\(255\) | −8.04049 | + | 5.47515i | −0.503515 | + | 0.342867i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.09084 | − | 7.08554i | 0.255180 | − | 0.441984i | −0.709765 | − | 0.704439i | \(-0.751199\pi\) |
0.964944 | + | 0.262455i | \(0.0845321\pi\) | |||||||
\(258\) | −14.2386 | + | 1.05882i | −0.886459 | + | 0.0659190i | ||||
\(259\) | 18.2047 | − | 5.35956i | 1.13118 | − | 0.333027i | ||||
\(260\) | − | 4.94924i | − | 0.306939i | ||||||
\(261\) | −19.2056 | − | 7.56310i | −1.18880 | − | 0.468144i | ||||
\(262\) | 11.6025 | − | 6.69869i | 0.716803 | − | 0.413846i | ||||
\(263\) | −15.0577 | + | 8.69357i | −0.928498 | + | 0.536069i | −0.886336 | − | 0.463042i | \(-0.846758\pi\) |
−0.0421620 | + | 0.999111i | \(0.513425\pi\) | |||||||
\(264\) | 3.81819 | + | 1.84145i | 0.234994 | + | 0.113333i | ||||
\(265\) | − | 5.47757i | − | 0.336484i | ||||||
\(266\) | −4.48073 | + | 18.5278i | −0.274731 | + | 1.13601i | ||||
\(267\) | −1.11560 | − | 15.0022i | −0.0682735 | − | 0.918122i | ||||
\(268\) | −1.28247 | + | 2.22130i | −0.0783393 | + | 0.135688i | ||||
\(269\) | 5.25247 | + | 9.09754i | 0.320249 | + | 0.554687i | 0.980539 | − | 0.196323i | \(-0.0629002\pi\) |
−0.660291 | + | 0.751010i | \(0.729567\pi\) | |||||||
\(270\) | 5.10404 | + | 5.51989i | 0.310622 | + | 0.335930i | ||||
\(271\) | 13.5483 | + | 7.82211i | 0.823000 | + | 0.475159i | 0.851450 | − | 0.524436i | \(-0.175724\pi\) |
−0.0284501 | + | 0.999595i | \(0.509057\pi\) | |||||||
\(272\) | 3.88173 | 0.235365 | ||||||||
\(273\) | −2.54472 | + | 15.4678i | −0.154014 | + | 0.936154i | ||||
\(274\) | 3.15496 | 0.190598 | ||||||||
\(275\) | 6.16072 | + | 3.55689i | 0.371505 | + | 0.214489i | ||||
\(276\) | −0.974877 | − | 1.43165i | −0.0586807 | − | 0.0861751i | ||||
\(277\) | 2.08719 | + | 3.61511i | 0.125407 | + | 0.217211i | 0.921892 | − | 0.387447i | \(-0.126643\pi\) |
−0.796485 | + | 0.604658i | \(0.793310\pi\) | |||||||
\(278\) | 10.5749 | − | 18.3163i | 0.634241 | − | 1.09854i | ||||
\(279\) | −1.49350 | − | 9.98656i | −0.0894137 | − | 0.597880i | ||||
\(280\) | −1.08110 | − | 3.67215i | −0.0646081 | − | 0.219453i | ||||
\(281\) | − | 3.31167i | − | 0.197558i | −0.995109 | − | 0.0987788i | \(-0.968506\pi\) | ||
0.995109 | − | 0.0987788i | \(-0.0314936\pi\) | |||||||
\(282\) | −8.65343 | + | 17.9427i | −0.515304 | + | 1.06847i | ||||
\(283\) | −25.2731 | + | 14.5915i | −1.50233 | + | 0.867372i | −0.502336 | + | 0.864673i | \(0.667526\pi\) |
−0.999996 | + | 0.00269944i | \(0.999141\pi\) | |||||||
\(284\) | 10.7460 | − | 6.20418i | 0.637655 | − | 0.368150i | ||||
\(285\) | 7.84313 | − | 16.2625i | 0.464587 | − | 0.963308i | ||||
\(286\) | − | 8.37193i | − | 0.495043i | ||||||
\(287\) | 18.7879 | + | 17.8885i | 1.10901 | + | 1.05593i | ||||
\(288\) | −0.443719 | − | 2.96700i | −0.0261464 | − | 0.174832i | ||||
\(289\) | 0.966081 | − | 1.67330i | 0.0568283 | − | 0.0984295i | ||||
\(290\) | −4.97740 | − | 8.62111i | −0.292283 | − | 0.506249i | ||||
\(291\) | −3.29079 | − | 4.83266i | −0.192909 | − | 0.283295i | ||||
\(292\) | −2.08792 | − | 1.20546i | −0.122186 | − | 0.0705442i | ||||
\(293\) | −10.5616 | −0.617016 | −0.308508 | − | 0.951222i | \(-0.599830\pi\) | ||||
−0.308508 | + | 0.951222i | \(0.599830\pi\) | |||||||
\(294\) | 1.49066 | + | 12.0324i | 0.0869370 | + | 0.701742i | ||||
\(295\) | −15.9015 | −0.925824 | ||||||||
\(296\) | 6.21176 | + | 3.58636i | 0.361051 | + | 0.208453i | ||||
\(297\) | 8.63378 | + | 9.33722i | 0.500983 | + | 0.541800i | ||||
\(298\) | −1.37336 | − | 2.37873i | −0.0795566 | − | 0.137796i | ||||
\(299\) | −1.71036 | + | 2.96243i | −0.0989128 | + | 0.171322i | ||||
\(300\) | −0.373343 | − | 5.02060i | −0.0215550 | − | 0.289865i | ||||
\(301\) | 15.7954 | + | 15.0393i | 0.910430 | + | 0.866848i | ||||
\(302\) | 9.43459i | 0.542900i | ||||||||
\(303\) | 8.57147 | + | 4.13387i | 0.492418 | + | 0.237484i | ||||
\(304\) | −6.23947 | + | 3.60236i | −0.357858 | + | 0.206609i | ||||
\(305\) | −2.74198 | + | 1.58308i | −0.157005 | + | 0.0906471i | ||||
\(306\) | 10.8353 | + | 4.26692i | 0.619413 | + | 0.243923i | ||||
\(307\) | 4.53097i | 0.258596i | 0.991606 | + | 0.129298i | \(0.0412724\pi\) | ||||
−0.991606 | + | 0.129298i | \(0.958728\pi\) | |||||||
\(308\) | −1.82874 | − | 6.21165i | −0.104202 | − | 0.353942i | ||||
\(309\) | −13.4763 | + | 1.00213i | −0.766642 | + | 0.0570091i | ||||
\(310\) | 2.43494 | − | 4.21745i | 0.138295 | − | 0.239535i | ||||
\(311\) | −0.131501 | − | 0.227766i | −0.00745672 | − | 0.0129154i | 0.862273 | − | 0.506444i | \(-0.169040\pi\) |
−0.869730 | + | 0.493528i | \(0.835707\pi\) | |||||||
\(312\) | −4.89727 | + | 3.33478i | −0.277253 | + | 0.188795i | ||||
\(313\) | 6.49269 | + | 3.74855i | 0.366988 | + | 0.211881i | 0.672142 | − | 0.740422i | \(-0.265374\pi\) |
−0.305154 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(314\) | 3.07277 | 0.173406 | ||||||||
\(315\) | 1.01879 | − | 11.4387i | 0.0574026 | − | 0.644496i | ||||
\(316\) | −11.8600 | −0.667179 | ||||||||
\(317\) | −25.8522 | − | 14.9258i | −1.45201 | − | 0.838316i | −0.453411 | − | 0.891302i | \(-0.649793\pi\) |
−0.998595 | + | 0.0529853i | \(0.983126\pi\) | |||||||
\(318\) | −5.42004 | + | 3.69077i | −0.303941 | + | 0.206968i | ||||
\(319\) | −8.41956 | − | 14.5831i | −0.471405 | − | 0.816497i | ||||
\(320\) | 0.723421 | − | 1.25300i | 0.0404404 | − | 0.0700449i | ||||
\(321\) | −11.4241 | + | 0.849522i | −0.637633 | + | 0.0474157i | ||||
\(322\) | −0.621916 | + | 2.57162i | −0.0346580 | + | 0.143311i | ||||
\(323\) | − | 27.9668i | − | 1.55611i | ||||||
\(324\) | 2.02284 | − | 8.76973i | 0.112380 | − | 0.487207i | ||||
\(325\) | −8.61076 | + | 4.97142i | −0.477639 | + | 0.275765i | ||||
\(326\) | 1.04213 | − | 0.601674i | 0.0577183 | − | 0.0333237i | ||||
\(327\) | 4.56883 | + | 2.20347i | 0.252657 | + | 0.121852i | ||||
\(328\) | 9.80512i | 0.541397i | ||||||||
\(329\) | 29.1901 | − | 8.59373i | 1.60930 | − | 0.473788i | ||||
\(330\) | 0.454824 | + | 6.11634i | 0.0250372 | + | 0.336694i | ||||
\(331\) | −5.72774 | + | 9.92074i | −0.314825 | + | 0.545293i | −0.979400 | − | 0.201928i | \(-0.935279\pi\) |
0.664575 | + | 0.747221i | \(0.268613\pi\) | |||||||
\(332\) | 6.76721 | + | 11.7212i | 0.371399 | + | 0.643282i | ||||
\(333\) | 13.3970 | + | 16.8390i | 0.734152 | + | 0.922770i | ||||
\(334\) | 7.94772 | + | 4.58862i | 0.434880 | + | 0.251078i | ||||
\(335\) | −3.71106 | −0.202757 | ||||||||
\(336\) | −2.90514 | + | 3.54403i | −0.158489 | + | 0.193343i | ||||
\(337\) | −27.3588 | −1.49033 | −0.745164 | − | 0.666882i | \(-0.767629\pi\) | ||||
−0.745164 | + | 0.666882i | \(0.767629\pi\) | |||||||
\(338\) | −1.12466 | − | 0.649323i | −0.0611735 | − | 0.0353185i | ||||
\(339\) | −16.8167 | − | 24.6960i | −0.913357 | − | 1.34130i | ||||
\(340\) | 2.80812 | + | 4.86381i | 0.152292 | + | 0.263777i | ||||
\(341\) | 4.11885 | − | 7.13405i | 0.223048 | − | 0.386331i | ||||
\(342\) | −21.3764 | + | 3.19687i | −1.15590 | + | 0.172867i | ||||
\(343\) | 12.0981 | − | 14.0227i | 0.653234 | − | 0.757156i | ||||
\(344\) | 8.24338i | 0.444453i | ||||||||
\(345\) | 1.08861 | − | 2.25721i | 0.0586088 | − | 0.121524i | ||||
\(346\) | −16.4703 | + | 9.50912i | −0.885448 | + | 0.511214i | ||||
\(347\) | 31.3790 | − | 18.1167i | 1.68451 | − | 0.972554i | 0.725918 | − | 0.687781i | \(-0.241415\pi\) |
0.958595 | − | 0.284773i | \(-0.0919181\pi\) | |||||||
\(348\) | −5.17682 | + | 10.7340i | −0.277507 | + | 0.575403i | ||||
\(349\) | − | 12.0514i | − | 0.645098i | −0.946553 | − | 0.322549i | \(-0.895460\pi\) | ||
0.946553 | − | 0.322549i | \(-0.104540\pi\) | |||||||
\(350\) | −5.30290 | + | 5.56952i | −0.283452 | + | 0.297703i | ||||
\(351\) | −17.3357 | + | 3.92536i | −0.925314 | + | 0.209520i | ||||
\(352\) | 1.22371 | − | 2.11952i | 0.0652238 | − | 0.112971i | ||||
\(353\) | 6.98889 | + | 12.1051i | 0.371981 | + | 0.644290i | 0.989870 | − | 0.141975i | \(-0.0453454\pi\) |
−0.617889 | + | 0.786265i | \(0.712012\pi\) | |||||||
\(354\) | 10.7144 | + | 15.7346i | 0.569465 | + | 0.836283i | ||||
\(355\) | 15.5477 | + | 8.97646i | 0.825186 | + | 0.476421i | ||||
\(356\) | −8.68546 | −0.460329 | ||||||||
\(357\) | −6.27539 | − | 16.6446i | −0.332129 | − | 0.880928i | ||||
\(358\) | 15.3824 | 0.812986 | ||||||||
\(359\) | 3.84620 | + | 2.22060i | 0.202995 | + | 0.117199i | 0.598052 | − | 0.801458i | \(-0.295942\pi\) |
−0.395057 | + | 0.918657i | \(0.629275\pi\) | |||||||
\(360\) | 3.39666 | − | 2.70237i | 0.179020 | − | 0.142428i | ||||
\(361\) | 16.4539 | + | 28.4991i | 0.865997 | + | 1.49995i | ||||
\(362\) | −9.62192 | + | 16.6656i | −0.505717 | + | 0.875927i | ||||
\(363\) | −0.643526 | − | 8.65395i | −0.0337764 | − | 0.454215i | ||||
\(364\) | 8.79680 | + | 2.12740i | 0.461077 | + | 0.111506i | ||||
\(365\) | − | 3.48822i | − | 0.182582i | ||||||
\(366\) | 3.41400 | + | 1.64651i | 0.178452 | + | 0.0860645i | ||||
\(367\) | 11.2829 | − | 6.51420i | 0.588963 | − | 0.340038i | −0.175724 | − | 0.984439i | \(-0.556227\pi\) |
0.764688 | + | 0.644401i | \(0.222893\pi\) | |||||||
\(368\) | −0.866025 | + | 0.500000i | −0.0451447 | + | 0.0260643i | ||||
\(369\) | −10.7781 | + | 27.3696i | −0.561085 | + | 1.42481i | ||||
\(370\) | 10.3778i | 0.539516i | ||||||||
\(371\) | 9.73583 | + | 2.35450i | 0.505459 | + | 0.122239i | ||||
\(372\) | −5.81381 | + | 0.432327i | −0.301432 | + | 0.0224151i | ||||
\(373\) | 10.0316 | − | 17.3753i | 0.519417 | − | 0.899657i | −0.480328 | − | 0.877089i | \(-0.659482\pi\) |
0.999745 | − | 0.0225681i | \(-0.00718425\pi\) | |||||||
\(374\) | 4.75010 | + | 8.22742i | 0.245622 | + | 0.425430i | ||||
\(375\) | 16.3776 | − | 11.1523i | 0.845734 | − | 0.575901i | ||||
\(376\) | 9.96019 | + | 5.75052i | 0.513657 | + | 0.296560i | ||||
\(377\) | 23.5358 | 1.21216 | ||||||||
\(378\) | −12.0050 | + | 6.69924i | −0.617471 | + | 0.344572i | ||||
\(379\) | 12.5836 | 0.646378 | 0.323189 | − | 0.946334i | \(-0.395245\pi\) | ||||
0.323189 | + | 0.946334i | \(0.395245\pi\) | |||||||
\(380\) | −9.02752 | − | 5.21204i | −0.463102 | − | 0.267372i | ||||
\(381\) | −22.4739 | + | 15.3036i | −1.15137 | + | 0.784026i | ||||
\(382\) | −9.83973 | − | 17.0429i | −0.503444 | − | 0.871991i | ||||
\(383\) | −3.35063 | + | 5.80345i | −0.171209 | + | 0.296543i | −0.938843 | − | 0.344346i | \(-0.888101\pi\) |
0.767634 | + | 0.640889i | \(0.221434\pi\) | |||||||
\(384\) | −1.72728 | + | 0.128444i | −0.0881450 | + | 0.00655465i | ||||
\(385\) | 6.46025 | − | 6.78505i | 0.329245 | − | 0.345798i | ||||
\(386\) | 23.3233i | 1.18712i | ||||||||
\(387\) | −9.06137 | + | 23.0102i | −0.460615 | + | 1.16968i | ||||
\(388\) | −2.92335 | + | 1.68780i | −0.148411 | + | 0.0856849i | ||||
\(389\) | −20.5683 | + | 11.8751i | −1.04285 | + | 0.602092i | −0.920641 | − | 0.390411i | \(-0.872333\pi\) |
−0.122214 | + | 0.992504i | \(0.538999\pi\) | |||||||
\(390\) | −7.72128 | − | 3.72384i | −0.390982 | − | 0.188564i | ||||
\(391\) | − | 3.88173i | − | 0.196308i | ||||||
\(392\) | 6.99159 | − | 0.343100i | 0.353128 | − | 0.0173292i | ||||
\(393\) | −1.72082 | − | 23.1410i | −0.0868037 | − | 1.16731i | ||||
\(394\) | 6.25111 | − | 10.8272i | 0.314926 | − | 0.545469i | ||||
\(395\) | −8.57979 | − | 14.8606i | −0.431696 | − | 0.747719i | ||||
\(396\) | 5.74565 | − | 4.57122i | 0.288730 | − | 0.229712i | ||||
\(397\) | −2.05223 | − | 1.18485i | −0.102998 | − | 0.0594661i | 0.447616 | − | 0.894226i | \(-0.352273\pi\) |
−0.550614 | + | 0.834760i | \(0.685606\pi\) | |||||||
\(398\) | −4.56801 | −0.228974 | ||||||||
\(399\) | 25.5337 | + | 20.9307i | 1.27828 | + | 1.04785i | ||||
\(400\) | −2.90665 | −0.145333 | ||||||||
\(401\) | 16.0596 | + | 9.27203i | 0.801980 | + | 0.463023i | 0.844163 | − | 0.536087i | \(-0.180098\pi\) |
−0.0421831 | + | 0.999110i | \(0.513431\pi\) | |||||||
\(402\) | 2.50050 | + | 3.67209i | 0.124714 | + | 0.183147i | ||||
\(403\) | 5.75686 | + | 9.97118i | 0.286770 | + | 0.496700i | ||||
\(404\) | 2.74710 | − | 4.75812i | 0.136673 | − | 0.236725i | ||||
\(405\) | 12.4518 | − | 3.80958i | 0.618737 | − | 0.189300i | ||||
\(406\) | 17.4627 | − | 5.14111i | 0.866658 | − | 0.255149i | ||||
\(407\) | 17.5546i | 0.870151i | ||||||||
\(408\) | 2.92063 | − | 6.05586i | 0.144593 | − | 0.299810i | ||||
\(409\) | 29.3001 | − | 16.9164i | 1.44879 | − | 0.836462i | 0.450385 | − | 0.892835i | \(-0.351287\pi\) |
0.998410 | + | 0.0563727i | \(0.0179535\pi\) | |||||||
\(410\) | −12.2858 | + | 7.09323i | −0.606754 | + | 0.350310i | ||||
\(411\) | 2.37381 | − | 4.92203i | 0.117091 | − | 0.242786i | ||||
\(412\) | 7.80205i | 0.384379i | ||||||||
\(413\) | 6.83518 | − | 28.2634i | 0.336337 | − | 1.39075i | ||||
\(414\) | −2.96700 | + | 0.443719i | −0.145820 | + | 0.0218076i | ||||
\(415\) | −9.79108 | + | 16.9586i | −0.480625 | + | 0.832467i | ||||
\(416\) | 1.71036 | + | 2.96243i | 0.0838574 | + | 0.145245i | ||||
\(417\) | −20.6185 | − | 30.2791i | −1.00969 | − | 1.48277i | ||||
\(418\) | −15.2706 | − | 8.81646i | −0.746908 | − | 0.431227i | ||||
\(419\) | −17.9477 | −0.876803 | −0.438402 | − | 0.898779i | \(-0.644455\pi\) | ||||
−0.438402 | + | 0.898779i | \(0.644455\pi\) | |||||||
\(420\) | −6.54231 | − | 1.07633i | −0.319232 | − | 0.0525193i | ||||
\(421\) | −7.19559 | −0.350691 | −0.175346 | − | 0.984507i | \(-0.556104\pi\) | ||||
−0.175346 | + | 0.984507i | \(0.556104\pi\) | |||||||
\(422\) | −10.7579 | − | 6.21106i | −0.523685 | − | 0.302350i | ||||
\(423\) | 21.4813 | + | 27.0003i | 1.04446 | + | 1.31280i | ||||
\(424\) | 1.89294 | + | 3.27867i | 0.0919293 | + | 0.159226i | ||||
\(425\) | 5.64142 | − | 9.77122i | 0.273649 | − | 0.473974i | ||||
\(426\) | −1.59378 | − | 21.4327i | −0.0772191 | − | 1.03842i | ||||
\(427\) | −1.63515 | − | 5.55408i | −0.0791305 | − | 0.268781i | ||||
\(428\) | 6.61393i | 0.319697i | ||||||||
\(429\) | −13.0610 | − | 6.29908i | −0.630590 | − | 0.304123i | ||||
\(430\) | −10.3290 | + | 5.96343i | −0.498107 | + | 0.287582i | ||||
\(431\) | −23.9684 | + | 13.8382i | −1.15452 | + | 0.666561i | −0.949984 | − | 0.312299i | \(-0.898901\pi\) |
−0.204533 | + | 0.978860i | \(0.565568\pi\) | |||||||
\(432\) | −4.96266 | − | 1.54015i | −0.238766 | − | 0.0741003i | ||||
\(433\) | 14.2435i | 0.684500i | 0.939609 | + | 0.342250i | \(0.111189\pi\) | ||||
−0.939609 | + | 0.342250i | \(0.888811\pi\) | |||||||
\(434\) | 6.44945 | + | 6.14072i | 0.309583 | + | 0.294764i | ||||
\(435\) | −17.1947 | + | 1.27864i | −0.824425 | + | 0.0613059i | ||||
\(436\) | 1.46428 | − | 2.53621i | 0.0701265 | − | 0.121463i | ||||
\(437\) | 3.60236 | + | 6.23947i | 0.172324 | + | 0.298474i | ||||
\(438\) | −3.45159 | + | 2.35035i | −0.164923 | + | 0.112304i | ||||
\(439\) | −18.6271 | − | 10.7544i | −0.889025 | − | 0.513279i | −0.0154017 | − | 0.999881i | \(-0.504903\pi\) |
−0.873624 | + | 0.486602i | \(0.838236\pi\) | |||||||
\(440\) | 3.54102 | 0.168812 | ||||||||
\(441\) | 19.8932 | + | 6.72765i | 0.947294 | + | 0.320364i | ||||
\(442\) | −13.2783 | −0.631586 | ||||||||
\(443\) | 18.2078 | + | 10.5123i | 0.865079 | + | 0.499454i | 0.865710 | − | 0.500546i | \(-0.166867\pi\) |
−0.000630757 | 1.00000i | \(0.500201\pi\) | ||||||||
\(444\) | 10.2688 | − | 6.99252i | 0.487336 | − | 0.331850i | ||||
\(445\) | −6.28324 | − | 10.8829i | −0.297854 | − | 0.515899i | ||||
\(446\) | −2.32846 | + | 4.03300i | −0.110256 | + | 0.190968i | ||||
\(447\) | −4.74436 | + | 0.352801i | −0.224401 | + | 0.0166869i | ||||
\(448\) | 1.91613 | + | 1.82440i | 0.0905286 | + | 0.0861950i | ||||
\(449\) | 16.6184i | 0.784269i | 0.919908 | + | 0.392134i | \(0.128263\pi\) | ||||
−0.919908 | + | 0.392134i | \(0.871737\pi\) | |||||||
\(450\) | −8.11351 | − | 3.19508i | −0.382474 | − | 0.150617i | ||||
\(451\) | −20.7822 | + | 11.9986i | −0.978595 | + | 0.564992i | ||||
\(452\) | −14.9390 | + | 8.62503i | −0.702671 | + | 0.405687i | ||||
\(453\) | 14.7188 | + | 7.09863i | 0.691551 | + | 0.333523i | ||||
\(454\) | − | 0.241889i | − | 0.0113524i | ||||||
\(455\) | 3.69815 | + | 12.5614i | 0.173372 | + | 0.588888i | ||||
\(456\) | 0.925404 | + | 12.4446i | 0.0433360 | + | 0.582770i | ||||
\(457\) | 2.74544 | − | 4.75524i | 0.128426 | − | 0.222441i | −0.794641 | − | 0.607080i | \(-0.792341\pi\) |
0.923067 | + | 0.384639i | \(0.125674\pi\) | |||||||
\(458\) | −9.15753 | − | 15.8613i | −0.427903 | − | 0.741150i | ||||
\(459\) | 14.8093 | − | 13.6936i | 0.691240 | − | 0.639164i | ||||
\(460\) | −1.25300 | − | 0.723421i | −0.0584215 | − | 0.0337297i | ||||
\(461\) | −19.7605 | −0.920339 | −0.460170 | − | 0.887831i | \(-0.652211\pi\) | ||||
−0.460170 | + | 0.887831i | \(0.652211\pi\) | |||||||
\(462\) | −11.0667 | − | 1.82067i | −0.514870 | − | 0.0847051i | ||||
\(463\) | 26.2725 | 1.22098 | 0.610492 | − | 0.792022i | \(-0.290972\pi\) | ||||
0.610492 | + | 0.792022i | \(0.290972\pi\) | |||||||
\(464\) | 5.95857 | + | 3.44018i | 0.276620 | + | 0.159706i | ||||
\(465\) | −4.74754 | − | 6.97196i | −0.220162 | − | 0.323317i | ||||
\(466\) | −4.60611 | − | 7.97801i | −0.213374 | − | 0.369574i | ||||
\(467\) | 5.19590 | − | 8.99957i | 0.240438 | − | 0.416450i | −0.720401 | − | 0.693557i | \(-0.756042\pi\) |
0.960839 | + | 0.277107i | \(0.0893757\pi\) | |||||||
\(468\) | 1.51784 | + | 10.1493i | 0.0701622 | + | 0.469152i | ||||
\(469\) | 1.59518 | − | 6.59604i | 0.0736584 | − | 0.304577i | ||||
\(470\) | 16.6402i | 0.767554i | ||||||||
\(471\) | 2.31196 | − | 4.79380i | 0.106530 | − | 0.220887i | ||||
\(472\) | 9.51808 | − | 5.49526i | 0.438105 | − | 0.252940i | ||||
\(473\) | −17.4720 | + | 10.0875i | −0.803365 | + | 0.463823i | ||||
\(474\) | −8.92354 | + | 18.5027i | −0.409872 | + | 0.849859i | ||||
\(475\) | 20.9416i | 0.960866i | ||||||||
\(476\) | −9.85201 | + | 2.90049i | −0.451566 | + | 0.132944i | ||||
\(477\) | 1.67987 | + | 11.2327i | 0.0769158 | + | 0.514311i | ||||
\(478\) | −11.2017 | + | 19.4018i | −0.512352 | + | 0.887420i | ||||
\(479\) | 8.56433 | + | 14.8339i | 0.391314 | + | 0.677776i | 0.992623 | − | 0.121240i | \(-0.0386872\pi\) |
−0.601309 | + | 0.799017i | \(0.705354\pi\) | |||||||
\(480\) | −1.41049 | − | 2.07137i | −0.0643799 | − | 0.0945445i | ||||
\(481\) | −21.2487 | − | 12.2680i | −0.968858 | − | 0.559370i | ||||
\(482\) | 29.7252 | 1.35395 | ||||||||
\(483\) | 3.54403 | + | 2.90514i | 0.161259 | + | 0.132189i | ||||
\(484\) | −5.01016 | −0.227734 | ||||||||
\(485\) | −4.22962 | − | 2.44197i | −0.192057 | − | 0.110884i | ||||
\(486\) | −12.1596 | − | 9.75420i | −0.551570 | − | 0.442460i | ||||
\(487\) | 8.16266 | + | 14.1381i | 0.369885 | + | 0.640660i | 0.989547 | − | 0.144209i | \(-0.0460637\pi\) |
−0.619662 | + | 0.784869i | \(0.712730\pi\) | |||||||
\(488\) | 1.09417 | − | 1.89515i | 0.0495305 | − | 0.0857894i | ||||
\(489\) | −0.154563 | − | 2.07852i | −0.00698959 | − | 0.0939940i | ||||
\(490\) | 5.48776 | + | 8.51226i | 0.247912 | + | 0.384545i | ||||
\(491\) | − | 18.5093i | − | 0.835313i | −0.908605 | − | 0.417657i | \(-0.862852\pi\) | ||
0.908605 | − | 0.417657i | \(-0.137148\pi\) | |||||||
\(492\) | 15.2969 | + | 7.37742i | 0.689637 | + | 0.332600i | ||||
\(493\) | −23.1296 | + | 13.3539i | −1.04170 | + | 0.601428i | ||||
\(494\) | 21.3435 | − | 12.3227i | 0.960289 | − | 0.554423i | ||||
\(495\) | 9.88427 | + | 3.89240i | 0.444265 | + | 0.174950i | ||||
\(496\) | 3.36587i | 0.151132i | ||||||||
\(497\) | −22.6379 | + | 23.7760i | −1.01545 | + | 1.06650i | ||||
\(498\) | 23.3778 | − | 1.73842i | 1.04758 | − | 0.0779004i | ||||
\(499\) | 5.20048 | − | 9.00749i | 0.232805 | − | 0.403231i | −0.725827 | − | 0.687877i | \(-0.758543\pi\) |
0.958633 | + | 0.284646i | \(0.0918762\pi\) | |||||||
\(500\) | −5.71983 | − | 9.90704i | −0.255799 | − | 0.443056i | ||||
\(501\) | 13.1386 | − | 8.94668i | 0.586988 | − | 0.399708i | ||||
\(502\) | −11.4894 | − | 6.63343i | −0.512798 | − | 0.296064i | ||||
\(503\) | 30.4653 | 1.35838 | 0.679191 | − | 0.733961i | \(-0.262331\pi\) | ||||
0.679191 | + | 0.733961i | \(0.262331\pi\) | |||||||
\(504\) | 3.34317 | + | 7.19884i | 0.148916 | + | 0.320662i | ||||
\(505\) | 7.94924 | 0.353737 | ||||||||
\(506\) | −2.11952 | − | 1.22371i | −0.0942243 | − | 0.0544004i | ||||
\(507\) | −1.85920 | + | 1.26602i | −0.0825702 | + | 0.0562260i | ||||
\(508\) | 7.84898 | + | 13.5948i | 0.348242 | + | 0.603173i | ||||
\(509\) | −14.2418 | + | 24.6675i | −0.631257 | + | 1.09337i | 0.356038 | + | 0.934471i | \(0.384127\pi\) |
−0.987295 | + | 0.158897i | \(0.949206\pi\) | |||||||
\(510\) | 9.70084 | − | 0.721375i | 0.429561 | − | 0.0319430i | ||||
\(511\) | 6.19996 | + | 1.49939i | 0.274270 | + | 0.0663290i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −11.0963 | + | 35.7545i | −0.489914 | + | 1.57860i | ||||
\(514\) | −7.08554 | + | 4.09084i | −0.312530 | + | 0.180439i | ||||
\(515\) | −9.77598 | + | 5.64416i | −0.430781 | + | 0.248712i | ||||
\(516\) | 12.8604 | + | 6.20236i | 0.566149 | + | 0.273044i | ||||
\(517\) | 28.1478i | 1.23794i | ||||||||
\(518\) | −18.4455 | − | 4.46083i | −0.810449 | − | 0.195998i | ||||
\(519\) | 2.44278 | + | 32.8499i | 0.107226 | + | 1.44195i | ||||
\(520\) | −2.47462 | + | 4.28617i | −0.108519 | + | 0.187961i | ||||
\(521\) | 9.07394 | + | 15.7165i | 0.397537 | + | 0.688554i | 0.993421 | − | 0.114516i | \(-0.0365318\pi\) |
−0.595885 | + | 0.803070i | \(0.703198\pi\) | |||||||
\(522\) | 12.8510 | + | 16.1526i | 0.562472 | + | 0.706981i | ||||
\(523\) | −10.1577 | − | 5.86458i | −0.444167 | − | 0.256440i | 0.261196 | − | 0.965286i | \(-0.415883\pi\) |
−0.705364 | + | 0.708846i | \(0.749216\pi\) | |||||||
\(524\) | −13.3974 | −0.585267 | ||||||||
\(525\) | 4.69903 | + | 12.4636i | 0.205082 | + | 0.543954i | ||||
\(526\) | 17.3871 | 0.758116 | ||||||||
\(527\) | −11.3150 | − | 6.53271i | −0.492889 | − | 0.284569i | ||||
\(528\) | −2.38593 | − | 3.50384i | −0.103834 | − | 0.152485i | ||||
\(529\) | 0.500000 | + | 0.866025i | 0.0217391 | + | 0.0376533i | ||||
\(530\) | −2.73878 | + | 4.74371i | −0.118965 | + | 0.206054i | ||||
\(531\) | 32.6089 | − | 4.87671i | 1.41511 | − | 0.211631i | ||||
\(532\) | 13.1443 | − | 13.8052i | 0.569878 | − | 0.598530i | ||||
\(533\) | − | 33.5406i | − | 1.45281i | ||||||
\(534\) | −6.53498 | + | 13.5501i | −0.282796 | + | 0.586371i | ||||
\(535\) | −8.28727 | + | 4.78466i | −0.358290 | + | 0.206859i | ||||
\(536\) | 2.22130 | − | 1.28247i | 0.0959456 | − | 0.0553942i | ||||
\(537\) | 11.5738 | − | 23.9980i | 0.499447 | − | 1.03559i | ||||
\(538\) | − | 10.5049i | − | 0.452900i | ||||||
\(539\) | 9.28287 | + | 14.3990i | 0.399841 | + | 0.620208i | ||||
\(540\) | −1.66028 | − | 7.33239i | −0.0714472 | − | 0.315536i | ||||
\(541\) | −11.4735 | + | 19.8727i | −0.493286 | + | 0.854396i | −0.999970 | − | 0.00773560i | \(-0.997538\pi\) |
0.506684 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(542\) | −7.82211 | − | 13.5483i | −0.335988 | − | 0.581949i | ||||
\(543\) | 18.7604 | + | 27.5504i | 0.805084 | + | 1.18230i | ||||
\(544\) | −3.36168 | − | 1.94087i | −0.144131 | − | 0.0832139i | ||||
\(545\) | 4.23717 | 0.181501 | ||||||||
\(546\) | 9.93770 | − | 12.1231i | 0.425294 | − | 0.518823i | ||||
\(547\) | −10.5205 | −0.449824 | −0.224912 | − | 0.974379i | \(-0.572209\pi\) | ||||
−0.224912 | + | 0.974379i | \(0.572209\pi\) | |||||||
\(548\) | −2.73228 | − | 1.57748i | −0.116717 | − | 0.0673867i | ||||
\(549\) | 5.13741 | − | 4.08731i | 0.219260 | − | 0.174442i | ||||
\(550\) | −3.55689 | − | 6.16072i | −0.151666 | − | 0.262694i | ||||
\(551\) | 24.7855 | − | 42.9298i | 1.05590 | − | 1.82887i | ||||
\(552\) | 0.128444 | + | 1.72728i | 0.00546695 | + | 0.0735180i | ||||
\(553\) | 30.1013 | − | 8.86198i | 1.28004 | − | 0.376850i | ||||
\(554\) | − | 4.17437i | − | 0.177352i | ||||||
\(555\) | 16.1903 | + | 7.80830i | 0.687240 | + | 0.331444i | ||||
\(556\) | −18.3163 | + | 10.5749i | −0.776784 | + | 0.448476i | ||||
\(557\) | 4.62535 | − | 2.67044i | 0.195982 | − | 0.113150i | −0.398798 | − | 0.917039i | \(-0.630572\pi\) |
0.594780 | + | 0.803888i | \(0.297239\pi\) | |||||||
\(558\) | −3.69987 | + | 9.39537i | −0.156628 | + | 0.397738i | ||||
\(559\) | − | 28.1983i | − | 1.19266i | ||||||
\(560\) | −0.899813 | + | 3.72072i | −0.0380241 | + | 0.157229i | ||||
\(561\) | 16.4095 | − | 1.22025i | 0.692811 | − | 0.0515189i | ||||
\(562\) | −1.65583 | + | 2.86799i | −0.0698471 | + | 0.120979i | ||||
\(563\) | −12.2178 | − | 21.1619i | −0.514919 | − | 0.891867i | −0.999850 | − | 0.0173140i | \(-0.994489\pi\) |
0.484931 | − | 0.874553i | \(-0.338845\pi\) | |||||||
\(564\) | 16.4654 | − | 11.2121i | 0.693319 | − | 0.472114i | ||||
\(565\) | −21.6143 | − | 12.4790i | −0.909322 | − | 0.524997i | ||||
\(566\) | 29.1829 | 1.22665 | ||||||||
\(567\) | 1.41881 | + | 23.7695i | 0.0595842 | + | 0.998223i | ||||
\(568\) | −12.4084 | −0.520643 | ||||||||
\(569\) | 19.7524 | + | 11.4040i | 0.828063 | + | 0.478082i | 0.853189 | − | 0.521602i | \(-0.174665\pi\) |
−0.0251263 | + | 0.999684i | \(0.507999\pi\) | |||||||
\(570\) | −14.9236 | + | 10.1622i | −0.625081 | + | 0.425647i | ||||
\(571\) | −5.56651 | − | 9.64147i | −0.232951 | − | 0.403483i | 0.725724 | − | 0.687986i | \(-0.241505\pi\) |
−0.958675 | + | 0.284503i | \(0.908172\pi\) | |||||||
\(572\) | −4.18597 | + | 7.25031i | −0.175024 | + | 0.303151i | ||||
\(573\) | −33.9920 | + | 2.52771i | −1.42003 | + | 0.105597i | ||||
\(574\) | −7.32653 | − | 24.8858i | −0.305803 | − | 1.03872i | ||||
\(575\) | 2.90665i | 0.121216i | ||||||||
\(576\) | −1.09923 | + | 2.79136i | −0.0458013 | + | 0.116307i | ||||
\(577\) | −3.46746 | + | 2.00194i | −0.144352 | + | 0.0833419i | −0.570437 | − | 0.821342i | \(-0.693226\pi\) |
0.426084 | + | 0.904683i | \(0.359893\pi\) | |||||||
\(578\) | −1.67330 | + | 0.966081i | −0.0696002 | + | 0.0401837i | ||||
\(579\) | 36.3864 | + | 17.5485i | 1.51217 | + | 0.729292i | ||||
\(580\) | 9.95480i | 0.413350i | ||||||||
\(581\) | −25.9337 | − | 24.6922i | −1.07591 | − | 1.02441i | ||||
\(582\) | 0.433576 | + | 5.83060i | 0.0179723 | + | 0.241686i | ||||
\(583\) | −4.63281 | + | 8.02426i | −0.191871 | + | 0.332331i | ||||
\(584\) | 1.20546 | + | 2.08792i | 0.0498823 | + | 0.0863986i | ||||
\(585\) | −11.6191 | + | 9.24407i | −0.480389 | + | 0.382195i | ||||
\(586\) | 9.14662 | + | 5.28080i | 0.377843 | + | 0.218148i | ||||
\(587\) | −3.59374 | −0.148330 | −0.0741648 | − | 0.997246i | \(-0.523629\pi\) | ||||
−0.0741648 | + | 0.997246i | \(0.523629\pi\) | |||||||
\(588\) | 4.72524 | − | 11.1657i | 0.194865 | − | 0.460464i | ||||
\(589\) | 24.2502 | 0.999211 | ||||||||
\(590\) | 13.7711 | + | 7.95077i | 0.566949 | + | 0.327328i | ||||
\(591\) | −12.1881 | − | 17.8988i | −0.501353 | − | 0.736257i | ||||
\(592\) | −3.58636 | − | 6.21176i | −0.147399 | − | 0.255302i | ||||
\(593\) | −16.3362 | + | 28.2952i | −0.670849 | + | 1.16194i | 0.306815 | + | 0.951769i | \(0.400737\pi\) |
−0.977664 | + | 0.210175i | \(0.932596\pi\) | |||||||
\(594\) | −2.80846 | − | 12.4032i | −0.115233 | − | 0.508908i | ||||
\(595\) | −10.7615 | − | 10.2463i | −0.441177 | − | 0.420058i | ||||
\(596\) | 2.74672i | 0.112510i | ||||||||
\(597\) | −3.43699 | + | 7.12652i | −0.140667 | + | 0.291669i | ||||
\(598\) | 2.96243 | − | 1.71036i | 0.121143 | − | 0.0699419i | ||||
\(599\) | −32.9491 | + | 19.0232i | −1.34627 | + | 0.777266i | −0.987718 | − | 0.156245i | \(-0.950061\pi\) |
−0.358547 | + | 0.933512i | \(0.616728\pi\) | |||||||
\(600\) | −2.18698 | + | 4.53464i | −0.0892830 | + | 0.185126i | ||||
\(601\) | − | 15.3195i | − | 0.624895i | −0.949935 | − | 0.312447i | \(-0.898851\pi\) | ||
0.949935 | − | 0.312447i | \(-0.101149\pi\) | |||||||
\(602\) | −6.15957 | − | 20.9221i | −0.251045 | − | 0.852720i | ||||
\(603\) | 7.61018 | − | 1.13811i | 0.309911 | − | 0.0463475i | ||||
\(604\) | 4.71729 | − | 8.17059i | 0.191944 | − | 0.332457i | ||||
\(605\) | −3.62445 | − | 6.27773i | −0.147355 | − | 0.255226i | ||||
\(606\) | −5.35617 | − | 7.86577i | −0.217580 | − | 0.319525i | ||||
\(607\) | −33.0295 | − | 19.0696i | −1.34062 | − | 0.774010i | −0.353726 | − | 0.935349i | \(-0.615085\pi\) |
−0.986899 | + | 0.161339i | \(0.948419\pi\) | |||||||
\(608\) | 7.20471 | 0.292190 | ||||||||
\(609\) | 5.11840 | − | 31.1116i | 0.207408 | − | 1.26070i | ||||
\(610\) | 3.16617 | 0.128194 | ||||||||
\(611\) | −34.0710 | − | 19.6709i | −1.37837 | − | 0.795801i | ||||
\(612\) | −7.25020 | − | 9.11291i | −0.293072 | − | 0.368368i | ||||
\(613\) | −18.9794 | − | 32.8733i | −0.766571 | − | 1.32774i | −0.939412 | − | 0.342790i | \(-0.888628\pi\) |
0.172841 | − | 0.984950i | \(-0.444705\pi\) | |||||||
\(614\) | 2.26548 | − | 3.92393i | 0.0914275 | − | 0.158357i | ||||
\(615\) | 1.82217 | + | 24.5040i | 0.0734770 | + | 0.988097i | ||||
\(616\) | −1.52209 | + | 6.29382i | −0.0613266 | + | 0.253585i | ||||
\(617\) | 8.17554i | 0.329135i | 0.986366 | + | 0.164567i | \(0.0526228\pi\) | ||||
−0.986366 | + | 0.164567i | \(0.947377\pi\) | |||||||
\(618\) | 12.1719 | + | 5.87030i | 0.489626 | + | 0.236138i | ||||
\(619\) | 29.7243 | − | 17.1613i | 1.19472 | − | 0.689772i | 0.235347 | − | 0.971911i | \(-0.424377\pi\) |
0.959374 | + | 0.282139i | \(0.0910440\pi\) | |||||||
\(620\) | −4.21745 | + | 2.43494i | −0.169377 | + | 0.0977897i | ||||
\(621\) | −1.54015 | + | 4.96266i | −0.0618039 | + | 0.199145i | ||||
\(622\) | 0.263002i | 0.0105454i | ||||||||
\(623\) | 22.0441 | − | 6.48990i | 0.883178 | − | 0.260012i | ||||
\(624\) | 5.90855 | − | 0.439373i | 0.236531 | − | 0.0175890i | ||||
\(625\) | 1.00907 | − | 1.74775i | 0.0403626 | − | 0.0699101i | ||||
\(626\) | −3.74855 | − | 6.49269i | −0.149822 | − | 0.259500i | ||||
\(627\) | −25.2441 | + | 17.1899i | −1.00815 | + | 0.686500i | ||||
\(628\) | −2.66109 | − | 1.53638i | −0.106189 | − | 0.0613084i | ||||
\(629\) | 27.8426 | 1.11016 | ||||||||
\(630\) | −6.60163 | + | 9.39678i | −0.263015 | + | 0.374377i | ||||
\(631\) | 8.25964 | 0.328811 | 0.164406 | − | 0.986393i | \(-0.447429\pi\) | ||||
0.164406 | + | 0.986393i | \(0.447429\pi\) | |||||||
\(632\) | 10.2711 | + | 5.93001i | 0.408562 | + | 0.235883i | ||||
\(633\) | −17.7841 | + | 12.1100i | −0.706855 | + | 0.481331i | ||||
\(634\) | 14.9258 | + | 25.8522i | 0.592779 | + | 1.02672i | ||||
\(635\) | −11.3562 | + | 19.6696i | −0.450658 | + | 0.780563i | ||||
\(636\) | 6.53928 | − | 0.486275i | 0.259299 | − | 0.0192820i | ||||
\(637\) | −23.9163 | + | 1.17365i | −0.947598 | + | 0.0465017i | ||||
\(638\) | 16.8391i | 0.666667i | ||||||||
\(639\) | −34.6362 | − | 13.6396i | −1.37019 | − | 0.539576i | ||||
\(640\) | −1.25300 | + | 0.723421i | −0.0495292 | + | 0.0285957i | ||||
\(641\) | 18.7316 | − | 10.8147i | 0.739852 | − | 0.427154i | −0.0821634 | − | 0.996619i | \(-0.526183\pi\) |
0.822016 | + | 0.569465i | \(0.192850\pi\) | |||||||
\(642\) | 10.3183 | + | 4.97636i | 0.407233 | + | 0.196401i | ||||
\(643\) | − | 12.7991i | − | 0.504746i | −0.967630 | − | 0.252373i | \(-0.918789\pi\) | ||
0.967630 | − | 0.252373i | \(-0.0812109\pi\) | |||||||
\(644\) | 1.82440 | − | 1.91613i | 0.0718916 | − | 0.0755061i | ||||
\(645\) | 1.53194 | + | 20.6010i | 0.0603200 | + | 0.811165i | ||||
\(646\) | −13.9834 | + | 24.2199i | −0.550169 | + | 0.952920i | ||||
\(647\) | −22.7515 | − | 39.4067i | −0.894453 | − | 1.54924i | −0.834480 | − | 0.551039i | \(-0.814232\pi\) |
−0.0599736 | − | 0.998200i | \(-0.519102\pi\) | |||||||
\(648\) | −6.13669 | + | 6.58339i | −0.241072 | + | 0.258620i | ||||
\(649\) | 23.2947 | + | 13.4492i | 0.914396 | + | 0.527927i | ||||
\(650\) | 9.94285 | 0.389991 | ||||||||
\(651\) | 14.4327 | − | 5.44143i | 0.565661 | − | 0.213266i | ||||
\(652\) | −1.20335 | −0.0471268 | ||||||||
\(653\) | −16.4102 | − | 9.47445i | −0.642182 | − | 0.370764i | 0.143273 | − | 0.989683i | \(-0.454237\pi\) |
−0.785455 | + | 0.618919i | \(0.787571\pi\) | |||||||
\(654\) | −2.85499 | − | 4.19268i | −0.111639 | − | 0.163947i | ||||
\(655\) | −9.69194 | − | 16.7869i | −0.378695 | − | 0.655920i | ||||
\(656\) | 4.90256 | − | 8.49149i | 0.191413 | − | 0.331537i | ||||
\(657\) | 1.06977 | + | 7.15321i | 0.0417357 | + | 0.279073i | ||||
\(658\) | −29.5763 | − | 7.15267i | −1.15300 | − | 0.278840i | ||||
\(659\) | − | 36.9553i | − | 1.43958i | −0.694194 | − | 0.719788i | \(-0.744239\pi\) | ||
0.694194 | − | 0.719788i | \(-0.255761\pi\) | |||||||
\(660\) | 2.66428 | − | 5.52432i | 0.103707 | − | 0.215034i | ||||
\(661\) | 22.4021 | − | 12.9339i | 0.871341 | − | 0.503069i | 0.00354723 | − | 0.999994i | \(-0.498871\pi\) |
0.867794 | + | 0.496925i | \(0.165538\pi\) | |||||||
\(662\) | 9.92074 | − | 5.72774i | 0.385580 | − | 0.222615i | ||||
\(663\) | −9.99068 | + | 20.7154i | −0.388006 | + | 0.804520i | ||||
\(664\) | − | 13.5344i | − | 0.525237i | ||||||
\(665\) | 26.8067 | + | 6.48290i | 1.03952 | + | 0.251396i | ||||
\(666\) | −3.18267 | − | 21.2815i | −0.123326 | − | 0.824641i | ||||
\(667\) | 3.44018 | − | 5.95857i | 0.133204 | − | 0.230717i | ||||
\(668\) | −4.58862 | − | 7.94772i | −0.177539 | − | 0.307507i | ||||
\(669\) | 4.53992 | + | 6.66706i | 0.175523 | + | 0.257763i | ||||
\(670\) | 3.21387 | + | 1.85553i | 0.124163 | + | 0.0716853i | ||||
\(671\) | 5.35575 | 0.206757 | ||||||||
\(672\) | 4.28794 | − | 1.61665i | 0.165411 | − | 0.0623635i | ||||
\(673\) | −0.993438 | −0.0382942 | −0.0191471 | − | 0.999817i | \(-0.506095\pi\) | ||||
−0.0191471 | + | 0.999817i | \(0.506095\pi\) | |||||||
\(674\) | 23.6934 | + | 13.6794i | 0.912635 | + | 0.526910i | ||||
\(675\) | −11.0893 | + | 10.2538i | −0.426826 | + | 0.394670i | ||||
\(676\) | 0.649323 | + | 1.12466i | 0.0249740 | + | 0.0432562i | ||||
\(677\) | −23.4253 | + | 40.5738i | −0.900307 | + | 1.55938i | −0.0732114 | + | 0.997316i | \(0.523325\pi\) |
−0.827096 | + | 0.562061i | \(0.810009\pi\) | |||||||
\(678\) | 2.21567 | + | 29.7957i | 0.0850924 | + | 1.14430i | ||||
\(679\) | 6.15844 | − | 6.46807i | 0.236339 | − | 0.248222i | ||||
\(680\) | − | 5.61625i | − | 0.215373i | ||||||
\(681\) | −0.377369 | − | 0.181998i | −0.0144608 | − | 0.00697420i | ||||
\(682\) | −7.13405 | + | 4.11885i | −0.273177 | + | 0.157719i | ||||
\(683\) | 28.9057 | − | 16.6887i | 1.10605 | − | 0.638576i | 0.168244 | − | 0.985745i | \(-0.446190\pi\) |
0.937803 | + | 0.347169i | \(0.112857\pi\) | |||||||
\(684\) | 20.1110 | + | 7.91964i | 0.768962 | + | 0.302815i | ||||
\(685\) | − | 4.56473i | − | 0.174409i | ||||||
\(686\) | −17.4886 | + | 6.09502i | −0.667717 | + | 0.232709i | ||||
\(687\) | −31.6353 | + | 2.35247i | −1.20696 | + | 0.0897522i | ||||
\(688\) | 4.12169 | − | 7.13898i | 0.157138 | − | 0.272171i | ||||
\(689\) | −6.47522 | − | 11.2154i | −0.246686 | − | 0.427273i | ||||
\(690\) | −2.07137 | + | 1.41049i | −0.0788556 | + | 0.0536965i | ||||
\(691\) | −25.2447 | − | 14.5750i | −0.960354 | − | 0.554461i | −0.0640721 | − | 0.997945i | \(-0.520409\pi\) |
−0.896282 | + | 0.443485i | \(0.853742\pi\) | |||||||
\(692\) | 19.0182 | 0.722965 | ||||||||
\(693\) | −11.1670 | + | 15.8952i | −0.424201 | + | 0.603808i | ||||
\(694\) | −36.2333 | −1.37540 | ||||||||
\(695\) | −26.5008 | − | 15.3002i | −1.00523 | − | 0.580371i | ||||
\(696\) | 9.85026 | − | 6.70751i | 0.373373 | − | 0.254247i | ||||
\(697\) | 19.0304 | + | 32.9617i | 0.720829 | + | 1.24851i | ||||
\(698\) | −6.02571 | + | 10.4368i | −0.228076 | + | 0.395040i | ||||
\(699\) | −15.9121 | + | 1.18326i | −0.601851 | + | 0.0447549i | ||||
\(700\) | 7.37721 | − | 2.17189i | 0.278832 | − | 0.0820898i | ||||
\(701\) | − | 13.3764i | − | 0.505220i | −0.967568 | − | 0.252610i | \(-0.918711\pi\) | ||
0.967568 | − | 0.252610i | \(-0.0812889\pi\) | |||||||
\(702\) | 16.9759 | + | 5.26841i | 0.640713 | + | 0.198843i | ||||
\(703\) | −44.7540 | + | 25.8387i | −1.68793 | + | 0.974525i | ||||
\(704\) | −2.11952 | + | 1.22371i | −0.0798826 | + | 0.0461202i | ||||
\(705\) | 25.9602 | + | 12.5201i | 0.977717 | + | 0.471536i | ||||
\(706\) | − | 13.9778i | − | 0.526060i | ||||||
\(707\) | −3.41693 | + | 14.1290i | −0.128507 | + | 0.531376i | ||||
\(708\) | −1.41167 | − | 18.9837i | −0.0530538 | − | 0.713452i | ||||
\(709\) | −17.9255 | + | 31.0479i | −0.673206 | + | 1.16603i | 0.303784 | + | 0.952741i | \(0.401750\pi\) |
−0.976990 | + | 0.213286i | \(0.931583\pi\) | |||||||
\(710\) | −8.97646 | − | 15.5477i | −0.336881 | − | 0.583495i | ||||
\(711\) | 22.1518 | + | 27.8431i | 0.830759 | + | 1.04420i | ||||
\(712\) | 7.52183 | + | 4.34273i | 0.281893 | + | 0.162751i | ||||
\(713\) | 3.36587 | 0.126053 | ||||||||
\(714\) | −2.88767 | + | 17.5524i | −0.108068 | + | 0.656881i | ||||
\(715\) | −12.1129 | −0.452995 | ||||||||
\(716\) | −13.3216 | − | 7.69121i | −0.497850 | − | 0.287434i | ||||
\(717\) | 21.8405 | + | 32.0737i | 0.815648 | + | 1.19781i | ||||
\(718\) | −2.22060 | − | 3.84620i | −0.0828722 | − | 0.143539i | ||||
\(719\) | −25.3910 | + | 43.9785i | −0.946923 | + | 1.64012i | −0.195070 | + | 0.980789i | \(0.562493\pi\) |
−0.751854 | + | 0.659330i | \(0.770840\pi\) | |||||||
\(720\) | −4.29278 | + | 0.641991i | −0.159983 | + | 0.0239256i | ||||
\(721\) | −5.82980 | − | 19.8019i | −0.217113 | − | 0.737463i | ||||
\(722\) | − | 32.9079i | − | 1.22471i | ||||||
\(723\) | 22.3654 | − | 46.3741i | 0.831778 | − | 1.72467i | ||||
\(724\) | 16.6656 | − | 9.62192i | 0.619374 | − | 0.357596i | ||||
\(725\) | 17.3195 | − | 9.99941i | 0.643229 | − | 0.371369i | ||||
\(726\) | −3.76967 | + | 7.81631i | −0.139905 | + | 0.290090i | ||||
\(727\) | 1.26742i | 0.0470062i | 0.999724 | + | 0.0235031i | \(0.00748195\pi\) | ||||
−0.999724 | + | 0.0235031i | \(0.992518\pi\) | |||||||
\(728\) | −6.55455 | − | 6.24078i | −0.242928 | − | 0.231299i | ||||
\(729\) | −24.3664 | + | 11.6310i | −0.902459 | + | 0.430776i | ||||
\(730\) | −1.74411 | + | 3.02088i | −0.0645524 | + | 0.111808i | ||||
\(731\) | 15.9993 | + | 27.7116i | 0.591755 | + | 1.02495i | ||||
\(732\) | −2.13335 | − | 3.13292i | −0.0788510 | − | 0.115796i | ||||
\(733\) | 15.8708 | + | 9.16302i | 0.586202 | + | 0.338444i | 0.763594 | − | 0.645696i | \(-0.223433\pi\) |
−0.177392 | + | 0.984140i | \(0.556766\pi\) | |||||||
\(734\) | −13.0284 | −0.480887 | ||||||||
\(735\) | 17.4089 | − | 2.15675i | 0.642138 | − | 0.0795529i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 5.43645 | + | 3.13873i | 0.200254 | + | 0.115617i | ||||
\(738\) | 23.0189 | − | 18.3138i | 0.847338 | − | 0.674139i | ||||
\(739\) | 17.3186 | + | 29.9968i | 0.637076 | + | 1.10345i | 0.986071 | + | 0.166324i | \(0.0531898\pi\) |
−0.348995 | + | 0.937125i | \(0.613477\pi\) | |||||||
\(740\) | 5.18890 | − | 8.98743i | 0.190748 | − | 0.330385i | ||||
\(741\) | −3.16555 | − | 42.5694i | −0.116290 | − | 1.56383i | ||||
\(742\) | −7.25423 | − | 6.90697i | −0.266311 | − | 0.253563i | ||||
\(743\) | 4.55621i | 0.167151i | 0.996501 | + | 0.0835756i | \(0.0266340\pi\) | ||||
−0.996501 | + | 0.0835756i | \(0.973366\pi\) | |||||||
\(744\) | 5.25107 | + | 2.53250i | 0.192514 | + | 0.0928460i | ||||
\(745\) | −3.44165 | + | 1.98703i | −0.126092 | + | 0.0727993i | ||||
\(746\) | −17.3753 | + | 10.0316i | −0.636154 | + | 0.367283i | ||||
\(747\) | 14.8774 | − | 37.7794i | 0.544337 | − | 1.38228i | ||||
\(748\) | − | 9.50021i | − | 0.347362i | ||||||
\(749\) | −4.94203 | − | 16.7865i | −0.180578 | − | 0.613364i | ||||
\(750\) | −19.7595 | + | 1.46936i | −0.721516 | + | 0.0536535i | ||||
\(751\) | 2.28060 | − | 3.95011i | 0.0832202 | − | 0.144142i | −0.821411 | − | 0.570336i | \(-0.806813\pi\) |
0.904631 | + | 0.426195i | \(0.140146\pi\) | |||||||
\(752\) | −5.75052 | − | 9.96019i | −0.209700 | − | 0.363211i | ||||
\(753\) | −18.9935 | + | 12.9335i | −0.692160 | + | 0.471325i | ||||
\(754\) | −20.3826 | − | 11.7679i | −0.742292 | − | 0.428562i | ||||
\(755\) | 13.6504 | 0.496787 | ||||||||
\(756\) | 13.7463 | + | 0.200791i | 0.499947 | + | 0.00730271i | ||||
\(757\) | −7.75387 | −0.281819 | −0.140910 | − | 0.990022i | \(-0.545003\pi\) | ||||
−0.140910 | + | 0.990022i | \(0.545003\pi\) | |||||||
\(758\) | −10.8977 | − | 6.29182i | −0.395824 | − | 0.228529i | ||||
\(759\) | −3.50384 | + | 2.38593i | −0.127181 | + | 0.0866037i | ||||
\(760\) | 5.21204 | + | 9.02752i | 0.189061 | + | 0.327462i | ||||
\(761\) | 17.4653 | − | 30.2507i | 0.633115 | − | 1.09659i | −0.353796 | − | 0.935323i | \(-0.615109\pi\) |
0.986911 | − | 0.161265i | \(-0.0515575\pi\) | |||||||
\(762\) | 27.1148 | − | 2.01631i | 0.982265 | − | 0.0730433i | ||||
\(763\) | −1.82132 | + | 7.53116i | −0.0659363 | + | 0.272646i | ||||
\(764\) | 19.6795i | 0.711978i | ||||||||
\(765\) | 6.17355 | − | 15.6770i | 0.223205 | − | 0.566802i | ||||
\(766\) | 5.80345 | − | 3.35063i | 0.209687 | − | 0.121063i | ||||
\(767\) | −32.5587 | + | 18.7978i | −1.17563 | + | 0.678748i | ||||
\(768\) | 1.56009 | + | 0.752405i | 0.0562950 | + | 0.0271501i | ||||
\(769\) | 19.8213i | 0.714774i | 0.933956 | + | 0.357387i | \(0.116332\pi\) | ||||
−0.933956 | + | 0.357387i | \(0.883668\pi\) | |||||||
\(770\) | −8.98727 | + | 2.64590i | −0.323879 | + | 0.0953517i | ||||
\(771\) | 1.05089 | + | 14.1321i | 0.0378469 | + | 0.508954i | ||||
\(772\) | 11.6616 | − | 20.1985i | 0.419711 | − | 0.726961i | ||||
\(773\) | 11.5793 | + | 20.0559i | 0.416477 | + | 0.721359i | 0.995582 | − | 0.0938937i | \(-0.0299314\pi\) |
−0.579105 | + | 0.815253i | \(0.696598\pi\) | |||||||
\(774\) | 19.3525 | − | 15.3968i | 0.695611 | − | 0.553425i | ||||
\(775\) | 8.47269 | + | 4.89171i | 0.304348 | + | 0.175715i | ||||
\(776\) | 3.37559 | 0.121177 | ||||||||
\(777\) | −20.8378 | + | 25.4203i | −0.747552 | + | 0.911949i | ||||
\(778\) | 23.7502 | 0.851487 | ||||||||
\(779\) | −61.1787 | − | 35.3216i | −2.19196 | − | 1.26553i | ||||
\(780\) | 4.82490 | + | 7.08557i | 0.172759 | + | 0.253704i | ||||
\(781\) | −15.1842 | − | 26.2998i | −0.543334 | − | 0.941082i | ||||
\(782\) | −1.94087 | + | 3.36168i | −0.0694052 | + | 0.120213i | ||||
\(783\) | 34.8687 | − | 7.89537i | 1.24611 | − | 0.282158i | ||||
\(784\) | −6.22644 | − | 3.19866i | −0.222373 | − | 0.114238i | ||||
\(785\) | − | 4.44580i | − | 0.158678i | ||||||
\(786\) | −10.0803 | + | 20.9011i | −0.359551 | + | 0.745519i | ||||
\(787\) | 22.6414 | − | 13.0720i | 0.807080 | − | 0.465968i | −0.0388610 | − | 0.999245i | \(-0.512373\pi\) |
0.845941 | + | 0.533277i | \(0.179040\pi\) | |||||||
\(788\) | −10.8272 | + | 6.25111i | −0.385705 | + | 0.222687i | ||||
\(789\) | 13.0822 | − | 27.1256i | 0.465738 | − | 0.965695i | ||||
\(790\) | 17.1596i | 0.610510i | ||||||||
\(791\) | 31.4711 | − | 33.0533i | 1.11898 | − | 1.17524i | ||||
\(792\) | −7.26149 | + | 1.08596i | −0.258026 | + | 0.0385881i | ||||
\(793\) | −3.74284 | + | 6.48278i | −0.132912 | + | 0.230210i | ||||
\(794\) | 1.18485 | + | 2.05223i | 0.0420489 | + | 0.0728308i | ||||
\(795\) | 5.33995 | + | 7.84194i | 0.189389 | + | 0.278125i | ||||
\(796\) | 3.95601 | + | 2.28400i | 0.140217 | + | 0.0809544i | ||||
\(797\) | −28.3000 | −1.00244 | −0.501218 | − | 0.865321i | \(-0.667115\pi\) | ||||
−0.501218 | + | 0.865321i | \(0.667115\pi\) | |||||||
\(798\) | −11.6475 | − | 30.8934i | −0.412316 | − | 1.09361i | ||||
\(799\) | 44.6439 | 1.57939 | ||||||||
\(800\) | 2.51723 | + | 1.45333i | 0.0889976 | + | 0.0513828i | ||||
\(801\) | 16.2225 | + | 20.3904i | 0.573193 | + | 0.720458i | ||||
\(802\) | −9.27203 | − | 16.0596i | −0.327407 | − | 0.567085i | ||||
\(803\) | −2.95026 | + | 5.11000i | −0.104112 | + | 0.180328i | ||||
\(804\) | −0.329452 | − | 4.43037i | −0.0116189 | − | 0.156247i | ||||
\(805\) | 3.72072 | + | 0.899813i | 0.131138 | + | 0.0317143i | ||||
\(806\) | − | 11.5137i | − | 0.405554i | ||||||
\(807\) | −16.3887 | − | 7.90397i | −0.576909 | − | 0.278233i | ||||
\(808\) | −4.75812 | + | 2.74710i | −0.167390 | + | 0.0966428i | ||||
\(809\) | −0.830641 | + | 0.479571i | −0.0292038 | + | 0.0168608i | −0.514531 | − | 0.857472i | \(-0.672034\pi\) |
0.485327 | + | 0.874333i | \(0.338701\pi\) | |||||||
\(810\) | −12.6884 | − | 2.92673i | −0.445825 | − | 0.102835i | ||||
\(811\) | − | 2.35197i | − | 0.0825889i | −0.999147 | − | 0.0412944i | \(-0.986852\pi\) | ||
0.999147 | − | 0.0412944i | \(-0.0131482\pi\) | |||||||
\(812\) | −17.6937 | − | 4.27901i | −0.620926 | − | 0.150164i | ||||
\(813\) | −27.0220 | + | 2.00941i | −0.947701 | + | 0.0704731i | ||||
\(814\) | 8.77732 | − | 15.2028i | 0.307645 | − | 0.532856i | ||||
\(815\) | −0.870527 | − | 1.50780i | −0.0304932 | − | 0.0528158i | ||||
\(816\) | −5.55727 | + | 3.78421i | −0.194543 | + | 0.132474i | ||||
\(817\) | −51.4343 | − | 29.6956i | −1.79946 | − | 1.03892i | ||||
\(818\) | −33.8328 | −1.18294 | ||||||||
\(819\) | −11.4361 | − | 24.6252i | −0.399608 | − | 0.860475i | ||||
\(820\) | 14.1865 | 0.495413 | ||||||||
\(821\) | 24.6815 | + | 14.2499i | 0.861391 | + | 0.497324i | 0.864478 | − | 0.502671i | \(-0.167649\pi\) |
−0.00308670 | + | 0.999995i | \(0.500983\pi\) | |||||||
\(822\) | −4.51680 | + | 3.07570i | −0.157541 | + | 0.107277i | ||||
\(823\) | −16.6608 | − | 28.8574i | −0.580760 | − | 1.00591i | −0.995389 | − | 0.0959155i | \(-0.969422\pi\) |
0.414629 | − | 0.909990i | \(-0.363911\pi\) | |||||||
\(824\) | 3.90102 | − | 6.75677i | 0.135899 | − | 0.235383i | ||||
\(825\) | −12.2875 | + | 0.913725i | −0.427796 | + | 0.0318118i | ||||
\(826\) | −20.0512 | + | 21.0593i | −0.697669 | + | 0.732746i | ||||
\(827\) | 1.02702i | 0.0357129i | 0.999841 | + | 0.0178564i | \(0.00568418\pi\) | ||||
−0.999841 | + | 0.0178564i | \(0.994316\pi\) | |||||||
\(828\) | 2.79136 | + | 1.09923i | 0.0970065 | + | 0.0382009i | ||||
\(829\) | 35.9104 | − | 20.7329i | 1.24722 | − | 0.720083i | 0.276666 | − | 0.960966i | \(-0.410770\pi\) |
0.970554 | + | 0.240883i | \(0.0774371\pi\) | |||||||
\(830\) | 16.9586 | − | 9.79108i | 0.588643 | − | 0.339853i | ||||
\(831\) | −6.51240 | − | 3.14082i | −0.225913 | − | 0.108954i | ||||
\(832\) | − | 3.42072i | − | 0.118592i | ||||||
\(833\) | 22.8376 | − | 14.7231i | 0.791274 | − | 0.510126i | ||||
\(834\) | 2.71658 | + | 36.5317i | 0.0940673 | + | 1.26499i | ||||
\(835\) | 6.63900 | − | 11.4991i | 0.229752 | − | 0.397942i | ||||
\(836\) | 8.81646 | + | 15.2706i | 0.304924 | + | 0.528144i | ||||
\(837\) | 11.8738 | + | 12.8413i | 0.410420 | + | 0.443859i | ||||
\(838\) | 15.5432 | + | 8.97386i | 0.536930 | + | 0.309997i | ||||
\(839\) | −35.2868 | −1.21823 | −0.609117 | − | 0.793080i | \(-0.708476\pi\) | ||||
−0.609117 | + | 0.793080i | \(0.708476\pi\) | |||||||
\(840\) | 5.12765 | + | 4.20328i | 0.176921 | + | 0.145027i | ||||
\(841\) | −18.3394 | −0.632394 | ||||||||
\(842\) | 6.23156 | + | 3.59779i | 0.214754 | + | 0.123988i | ||||
\(843\) | 3.22847 | + | 4.74114i | 0.111194 | + | 0.163294i | ||||
\(844\) | 6.21106 | + | 10.7579i | 0.213794 | + | 0.370301i | ||||
\(845\) | −0.939468 | + | 1.62721i | −0.0323187 | + | 0.0559776i | ||||
\(846\) | −5.10323 | − | 34.1236i | −0.175453 | − | 1.17319i | ||||
\(847\) | 12.7160 | − | 3.74366i | 0.436927 | − | 0.128634i | ||||
\(848\) | − | 3.78588i | − | 0.130008i | ||||||
\(849\) | 21.9574 | − | 45.5280i | 0.753575 | − | 1.56252i | ||||
\(850\) | −9.77122 | + | 5.64142i | −0.335150 | + | 0.193499i | ||||
\(851\) | −6.21176 | + | 3.58636i | −0.212936 | + | 0.122939i | ||||
\(852\) | −9.33611 | + | 19.3582i | −0.319850 | + | 0.663200i | ||||
\(853\) | 8.56089i | 0.293119i | 0.989202 | + | 0.146560i | \(0.0468200\pi\) | ||||
−0.989202 | + | 0.146560i | \(0.953180\pi\) | |||||||
\(854\) | −1.36096 | + | 5.62755i | −0.0465710 | + | 0.192571i | ||||
\(855\) | 4.62536 | + | 30.9283i | 0.158184 | + | 1.05772i | ||||
\(856\) | 3.30697 | − | 5.72784i | 0.113030 | − | 0.195773i | ||||
\(857\) | −0.873753 | − | 1.51338i | −0.0298468 | − | 0.0516962i | 0.850716 | − | 0.525625i | \(-0.176169\pi\) |
−0.880563 | + | 0.473929i | \(0.842835\pi\) | |||||||
\(858\) | 8.16160 | + | 11.9857i | 0.278633 | + | 0.409184i | ||||
\(859\) | 3.44538 | + | 1.98919i | 0.117555 | + | 0.0678704i | 0.557625 | − | 0.830093i | \(-0.311713\pi\) |
−0.440070 | + | 0.897964i | \(0.645046\pi\) | |||||||
\(860\) | 11.9269 | 0.406703 | ||||||||
\(861\) | −44.3367 | − | 7.29417i | −1.51099 | − | 0.248585i | ||||
\(862\) | 27.6763 | 0.942660 | ||||||||
\(863\) | 8.66323 | + | 5.00172i | 0.294900 | + | 0.170261i | 0.640150 | − | 0.768250i | \(-0.278872\pi\) |
−0.345250 | + | 0.938511i | \(0.612206\pi\) | |||||||
\(864\) | 3.52771 | + | 3.81513i | 0.120015 | + | 0.129793i | ||||
\(865\) | 13.7582 | + | 23.8299i | 0.467792 | + | 0.810240i | ||||
\(866\) | 7.12176 | − | 12.3353i | 0.242007 | − | 0.419169i | ||||
\(867\) | 0.248175 | + | 3.33739i | 0.00842848 | + | 0.113344i | ||||
\(868\) | −2.51503 | − | 8.54274i | −0.0853657 | − | 0.289959i | ||||
\(869\) | 29.0264i | 0.984654i | ||||||||
\(870\) | 15.5304 | + | 7.49004i | 0.526530 | + | 0.253936i | ||||
\(871\) | −7.59846 | + | 4.38697i | −0.257464 | + | 0.148647i | ||||
\(872\) | −2.53621 | + | 1.46428i | −0.0858870 | + | 0.0495869i | ||||
\(873\) | 9.42249 | + | 3.71055i | 0.318903 | + | 0.125583i | ||||
\(874\) | − | 7.20471i | − | 0.243703i | ||||||
\(875\) | 21.9199 | + | 20.8706i | 0.741027 | + | 0.705554i | ||||
\(876\) | 4.16434 | − | 0.309669i | 0.140700 | − | 0.0104627i | ||||
\(877\) | −9.85284 | + | 17.0656i | −0.332707 | + | 0.576265i | −0.983042 | − | 0.183383i | \(-0.941295\pi\) |
0.650335 | + | 0.759648i | \(0.274629\pi\) | |||||||
\(878\) | 10.7544 | + | 18.6271i | 0.362943 | + | 0.628636i | ||||
\(879\) | 15.1205 | − | 10.2963i | 0.510002 | − | 0.347285i | ||||
\(880\) | −3.06661 | − | 1.77051i | −0.103376 | − | 0.0596839i | ||||
\(881\) | −17.8121 | −0.600105 | −0.300053 | − | 0.953923i | \(-0.597004\pi\) | ||||
−0.300053 | + | 0.953923i | \(0.597004\pi\) | |||||||
\(882\) | −13.8642 | − | 15.7729i | −0.466831 | − | 0.531101i | ||||
\(883\) | 24.2005 | 0.814410 | 0.407205 | − | 0.913337i | \(-0.366503\pi\) | ||||
0.407205 | + | 0.913337i | \(0.366503\pi\) | |||||||
\(884\) | 11.4994 | + | 6.63917i | 0.386766 | + | 0.223299i | ||||
\(885\) | 22.7654 | − | 15.5021i | 0.765251 | − | 0.521096i | ||||
\(886\) | −10.5123 | − | 18.2078i | −0.353167 | − | 0.611703i | ||||
\(887\) | 21.0312 | − | 36.4271i | 0.706158 | − | 1.22310i | −0.260114 | − | 0.965578i | \(-0.583760\pi\) |
0.966272 | − | 0.257524i | \(-0.0829066\pi\) | |||||||
\(888\) | −12.3893 | + | 0.921295i | −0.415758 | + | 0.0309167i | ||||
\(889\) | −30.0793 | − | 28.6394i | −1.00883 | − | 0.960535i | ||||
\(890\) | 12.5665i | 0.421230i | ||||||||
\(891\) | −21.4632 | − | 4.95073i | −0.719043 | − | 0.165856i | ||||
\(892\) | 4.03300 | − | 2.32846i | 0.135035 | − | 0.0779625i | ||||
\(893\) | −71.7603 | + | 41.4308i | −2.40137 | + | 1.38643i | ||||
\(894\) | 4.28514 | + | 2.06665i | 0.143316 | + | 0.0691190i | ||||
\(895\) | − | 22.2559i | − | 0.743934i | ||||||
\(896\) | −0.747214 | − | 2.53804i | −0.0249627 | − | 0.0847901i | ||||
\(897\) | −0.439373 | − | 5.90855i | −0.0146702 | − | 0.197281i | ||||
\(898\) | 8.30918 | − | 14.3919i | 0.277281 | − | 0.480265i | ||||
\(899\) | −11.5792 | − | 20.0558i | −0.386189 | − | 0.668898i | ||||
\(900\) | 5.42897 | + | 6.82377i | 0.180966 | + | 0.227459i | ||||
\(901\) | 12.7269 | + | 7.34788i | 0.423995 | + | 0.244793i | ||||
\(902\) | 23.9972 | 0.799020 | ||||||||
\(903\) | −37.2748 | − | 6.13236i | −1.24043 | − | 0.204072i | ||||
\(904\) | 17.2501 | 0.573728 | ||||||||
\(905\) | 24.1125 | + | 13.9214i | 0.801528 | + | 0.462763i | ||||
\(906\) | −9.19756 | − | 13.5070i | −0.305569 | − | 0.448740i | ||||
\(907\) | −29.2429 | − | 50.6502i | −0.970995 | − | 1.68181i | −0.692565 | − | 0.721356i | \(-0.743519\pi\) |
−0.278430 | − | 0.960456i | \(-0.589814\pi\) | |||||||
\(908\) | −0.120944 | + | 0.209482i | −0.00401368 | + | 0.00695190i | ||||
\(909\) | −16.3013 | + | 2.43788i | −0.540681 | + | 0.0808595i | ||||
\(910\) | 3.07801 | − | 12.7276i | 0.102035 | − | 0.421915i | ||||
\(911\) | − | 33.2372i | − | 1.10120i | −0.834770 | − | 0.550599i | \(-0.814399\pi\) | ||
0.834770 | − | 0.550599i | \(-0.185601\pi\) | |||||||
\(912\) | 5.42086 | − | 11.2400i | 0.179503 | − | 0.372194i | ||||
\(913\) | 28.6865 | − | 16.5622i | 0.949385 | − | 0.548128i | ||||
\(914\) | −4.75524 | + | 2.74544i | −0.157289 | + | 0.0908110i | ||||
\(915\) | 2.38224 | − | 4.93951i | 0.0787544 | − | 0.163295i | ||||
\(916\) | 18.3151i | 0.605147i | ||||||||
\(917\) | 34.0031 | − | 10.0107i | 1.12288 | − | 0.330583i | ||||
\(918\) | −19.6721 | + | 4.45437i | −0.649275 | + | 0.147016i | ||||
\(919\) | 23.6889 | − | 41.0305i | 0.781426 | − | 1.35347i | −0.149685 | − | 0.988734i | \(-0.547826\pi\) |
0.931111 | − | 0.364736i | \(-0.118841\pi\) | |||||||
\(920\) | 0.723421 | + | 1.25300i | 0.0238505 | + | 0.0413102i | ||||
\(921\) | −4.41714 | − | 6.48675i | −0.145550 | − | 0.213746i | ||||
\(922\) | 17.1131 | + | 9.88026i | 0.563590 | + | 0.325389i | ||||
\(923\) | 42.4456 | 1.39711 | ||||||||
\(924\) | 8.67371 | + | 7.11009i | 0.285344 | + | 0.233905i | ||||
\(925\) | −20.8486 | −0.685498 | ||||||||
\(926\) | −22.7526 | − | 13.1362i | −0.747697 | − | 0.431683i | ||||
\(927\) | 18.3164 | − | 14.5725i | 0.601590 | − | 0.478623i | ||||
\(928\) | −3.44018 | − | 5.95857i | −0.112930 | − | 0.195600i | ||||
\(929\) | 10.9618 | − | 18.9864i | 0.359646 | − | 0.622925i | −0.628256 | − | 0.778007i | \(-0.716231\pi\) |
0.987902 | + | 0.155082i | \(0.0495642\pi\) | |||||||
\(930\) | 0.625509 | + | 8.41167i | 0.0205113 | + | 0.275829i | ||||
\(931\) | −23.0454 | + | 44.8597i | −0.755283 | + | 1.47022i | ||||
\(932\) | 9.21222i | 0.301756i | ||||||||
\(933\) | 0.410307 | + | 0.197884i | 0.0134328 | + | 0.00647842i | ||||
\(934\) | −8.99957 | + | 5.19590i | −0.294475 | + | 0.170015i | ||||
\(935\) | 11.9038 | − | 6.87265i | 0.389295 | − | 0.224760i | ||||
\(936\) | 3.76016 | − | 9.54847i | 0.122905 | − | 0.312102i | ||||
\(937\) | − | 30.2316i | − | 0.987625i | −0.869568 | − | 0.493812i | \(-0.835603\pi\) | ||
0.869568 | − | 0.493812i | \(-0.164397\pi\) | |||||||
\(938\) | −4.67948 | + | 4.91475i | −0.152791 | + | 0.160472i | ||||
\(939\) | −12.9496 | + | 0.962961i | −0.422595 | + | 0.0314250i | ||||
\(940\) | 8.32008 | − | 14.4108i | 0.271371 | − | 0.470029i | ||||
\(941\) | −1.14371 | − | 1.98096i | −0.0372839 | − | 0.0645776i | 0.846781 | − | 0.531941i | \(-0.178537\pi\) |
−0.884065 | + | 0.467364i | \(0.845204\pi\) | |||||||
\(942\) | −4.39912 | + | 2.99557i | −0.143331 | + | 0.0976009i | ||||
\(943\) | −8.49149 | − | 4.90256i | −0.276521 | − | 0.159649i | ||||
\(944\) | −10.9905 | −0.357711 | ||||||||
\(945\) | 9.69274 | + | 17.3693i | 0.315305 | + | 0.565025i | ||||
\(946\) | 20.1750 | 0.655945 | ||||||||
\(947\) | 18.1446 | + | 10.4758i | 0.589622 | + | 0.340418i | 0.764948 | − | 0.644092i | \(-0.222765\pi\) |
−0.175326 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(948\) | 16.9794 | − | 11.5621i | 0.551465 | − | 0.375518i | ||||
\(949\) | −4.12354 | − | 7.14219i | −0.133856 | − | 0.231845i | ||||
\(950\) | 10.4708 | − | 18.1359i | 0.339717 | − | 0.588408i | ||||
\(951\) | 51.5621 | − | 3.83427i | 1.67202 | − | 0.124335i | ||||
\(952\) | 9.98233 | + | 2.41411i | 0.323529 | + | 0.0782417i | ||||
\(953\) | 0.303311i | 0.00982520i | 0.999988 | + | 0.00491260i | \(0.00156374\pi\) | ||||
−0.999988 | + | 0.00491260i | \(0.998436\pi\) | |||||||
\(954\) | 4.16155 | − | 10.5678i | 0.134735 | − | 0.342144i | ||||
\(955\) | −24.6584 | + | 14.2365i | −0.797926 | + | 0.460683i | ||||
\(956\) | 19.4018 | − | 11.2017i | 0.627501 | − | 0.362288i | ||||
\(957\) | 26.2706 | + | 12.6698i | 0.849207 | + | 0.409557i | ||||
\(958\) | − | 17.1287i | − | 0.553402i | ||||||
\(959\) | 8.11336 | + | 1.96212i | 0.261994 | + | 0.0633602i | ||||
\(960\) | 0.185839 | + | 2.49910i | 0.00599791 | + | 0.0806582i | ||||
\(961\) | −9.83544 | + | 17.0355i | −0.317272 | + | 0.549532i | ||||
\(962\) | 12.2680 | + | 21.2487i | 0.395535 | + | 0.685086i | ||||
\(963\) | 15.5271 | − | 12.3533i | 0.500355 | − | 0.398081i | ||||
\(964\) | −25.7428 | − | 14.8626i | −0.829120 | − | 0.478693i | ||||
\(965\) | 33.7450 | 1.08629 | ||||||||
\(966\) | −1.61665 | − | 4.28794i | −0.0520148 | − | 0.137962i | ||||
\(967\) | 17.1539 | 0.551633 | 0.275817 | − | 0.961210i | \(-0.411052\pi\) | ||||
0.275817 | + | 0.961210i | \(0.411052\pi\) | |||||||
\(968\) | 4.33892 | + | 2.50508i | 0.139458 | + | 0.0805163i | ||||
\(969\) | 27.2641 | + | 40.0385i | 0.875851 | + | 1.28622i | ||||
\(970\) | 2.44197 | + | 4.22962i | 0.0784070 | + | 0.135805i | ||||
\(971\) | −21.3853 | + | 37.0404i | −0.686287 | + | 1.18868i | 0.286743 | + | 0.958007i | \(0.407427\pi\) |
−0.973030 | + | 0.230677i | \(0.925906\pi\) | |||||||
\(972\) | 5.65341 | + | 14.5272i | 0.181333 | + | 0.465960i | ||||
\(973\) | 38.5858 | − | 40.5258i | 1.23700 | − | 1.29920i | ||||
\(974\) | − | 16.3253i | − | 0.523097i | ||||||
\(975\) | 7.48105 | − | 15.5118i | 0.239585 | − | 0.496774i | ||||
\(976\) | −1.89515 | + | 1.09417i | −0.0606623 | + | 0.0350234i | ||||
\(977\) | −27.8828 | + | 16.0981i | −0.892050 | + | 0.515025i | −0.874613 | − | 0.484823i | \(-0.838884\pi\) |
−0.0174376 | + | 0.999848i | \(0.505551\pi\) | |||||||
\(978\) | −0.905405 | + | 1.87733i | −0.0289517 | + | 0.0600305i | ||||
\(979\) | 21.2569i | 0.679375i | ||||||||
\(980\) | −0.496411 | − | 10.1157i | −0.0158573 | − | 0.323135i | ||||
\(981\) | −8.68907 | + | 1.29946i | −0.277421 | + | 0.0414886i | ||||
\(982\) | −9.25465 | + | 16.0295i | −0.295328 | + | 0.511523i | ||||
\(983\) | 16.8936 | + | 29.2606i | 0.538822 | + | 0.933268i | 0.998968 | + | 0.0454241i | \(0.0144639\pi\) |
−0.460145 | + | 0.887844i | \(0.652203\pi\) | |||||||
\(984\) | −9.55879 | − | 14.0375i | −0.304723 | − | 0.447499i | ||||
\(985\) | −15.6653 | − | 9.04437i | −0.499138 | − | 0.288177i | ||||
\(986\) | 26.7077 | 0.850547 | ||||||||
\(987\) | −33.4121 | + | 40.7600i | −1.06352 | + | 1.29740i | ||||
\(988\) | −24.6453 | −0.784073 | ||||||||
\(989\) | −7.13898 | − | 4.12169i | −0.227006 | − | 0.131062i | ||||
\(990\) | −6.61383 | − | 8.31305i | −0.210201 | − | 0.264206i | ||||
\(991\) | −6.50216 | − | 11.2621i | −0.206548 | − | 0.357752i | 0.744077 | − | 0.668094i | \(-0.232890\pi\) |
−0.950625 | + | 0.310342i | \(0.899556\pi\) | |||||||
\(992\) | 1.68294 | − | 2.91493i | 0.0534333 | − | 0.0925492i | ||||
\(993\) | −1.47139 | − | 19.7868i | −0.0466932 | − | 0.627916i | ||||
\(994\) | 31.4930 | − | 9.27171i | 0.998897 | − | 0.294081i | ||||
\(995\) | 6.60918i | 0.209525i | ||||||||
\(996\) | −21.1149 | − | 10.1834i | −0.669052 | − | 0.322672i | ||||
\(997\) | 19.0599 | − | 11.0042i | 0.603633 | − | 0.348508i | −0.166836 | − | 0.985985i | \(-0.553355\pi\) |
0.770470 | + | 0.637477i | \(0.220022\pi\) | |||||||
\(998\) | −9.00749 | + | 5.20048i | −0.285127 | + | 0.164618i | ||||
\(999\) | −35.5958 | − | 11.0470i | −1.12620 | − | 0.349513i |
(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 | 966.2.l.c.47.3 | ✓ | 56 | |
3.2 | odd | 2 | inner | 966.2.l.c.47.17 | yes | 56 | |
7.3 | odd | 6 | inner | 966.2.l.c.185.17 | yes | 56 | |
21.17 | even | 6 | inner | 966.2.l.c.185.3 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.l.c.47.3 | ✓ | 56 | 1.1 | even | 1 | trivial | |
966.2.l.c.47.17 | yes | 56 | 3.2 | odd | 2 | inner | |
966.2.l.c.185.3 | yes | 56 | 21.17 | even | 6 | inner | |
966.2.l.c.185.17 | yes | 56 | 7.3 | odd | 6 | inner |