Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.19 | ||
Root | \(2.51841i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.e.694.2 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.51841i | 1.78078i | 0.455195 | + | 0.890392i | \(0.349569\pi\) | ||||
−0.455195 | + | 0.890392i | \(0.650431\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −4.34238 | −2.17119 | ||||||||
\(5\) | −2.17741 | + | 0.508790i | −0.973769 | + | 0.227538i | ||||
\(6\) | 2.51841 | 1.02814 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 5.89907i | − | 2.08563i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.28134 | − | 5.48362i | −0.405195 | − | 1.73407i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.34238i | 1.25354i | ||||||||
\(13\) | 1.93158i | 0.535725i | 0.963457 | + | 0.267863i | \(0.0863173\pi\) | ||||
−0.963457 | + | 0.267863i | \(0.913683\pi\) | |||||||
\(14\) | −2.51841 | −0.673073 | ||||||||
\(15\) | 0.508790 | + | 2.17741i | 0.131369 | + | 0.562206i | ||||
\(16\) | 6.17150 | 1.54287 | ||||||||
\(17\) | − | 2.73533i | − | 0.663415i | −0.943382 | − | 0.331708i | \(-0.892375\pi\) | ||
0.943382 | − | 0.331708i | \(-0.107625\pi\) | |||||||
\(18\) | − | 2.51841i | − | 0.593594i | ||||||
\(19\) | −5.74934 | −1.31899 | −0.659495 | − | 0.751709i | \(-0.729230\pi\) | ||||
−0.659495 | + | 0.751709i | \(0.729230\pi\) | |||||||
\(20\) | 9.45516 | − | 2.20936i | 2.11424 | − | 0.494028i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | − | 2.51841i | − | 0.536926i | ||||||
\(23\) | − | 3.98220i | − | 0.830346i | −0.909742 | − | 0.415173i | \(-0.863721\pi\) | ||
0.909742 | − | 0.415173i | \(-0.136279\pi\) | |||||||
\(24\) | −5.89907 | −1.20414 | ||||||||
\(25\) | 4.48227 | − | 2.21569i | 0.896453 | − | 0.443139i | ||||
\(26\) | −4.86452 | −0.954010 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 4.34238i | − | 0.820632i | ||||||
\(29\) | 0.897314 | 0.166627 | 0.0833135 | − | 0.996523i | \(-0.473450\pi\) | ||||
0.0833135 | + | 0.996523i | \(0.473450\pi\) | |||||||
\(30\) | −5.48362 | + | 1.28134i | −1.00117 | + | 0.233940i | ||||
\(31\) | 10.2982 | 1.84961 | 0.924803 | − | 0.380447i | \(-0.124230\pi\) | ||||
0.924803 | + | 0.380447i | \(0.124230\pi\) | |||||||
\(32\) | 3.74421i | 0.661890i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 6.88868 | 1.18140 | ||||||||
\(35\) | −0.508790 | − | 2.17741i | −0.0860012 | − | 0.368050i | ||||
\(36\) | 4.34238 | 0.723730 | ||||||||
\(37\) | − | 3.09664i | − | 0.509085i | −0.967062 | − | 0.254542i | \(-0.918075\pi\) | ||
0.967062 | − | 0.254542i | \(-0.0819248\pi\) | |||||||
\(38\) | − | 14.4792i | − | 2.34883i | ||||||
\(39\) | 1.93158 | 0.309301 | ||||||||
\(40\) | 3.00139 | + | 12.8447i | 0.474561 | + | 2.03093i | ||||
\(41\) | 7.83869 | 1.22420 | 0.612099 | − | 0.790781i | \(-0.290326\pi\) | ||||
0.612099 | + | 0.790781i | \(0.290326\pi\) | |||||||
\(42\) | 2.51841i | 0.388599i | ||||||||
\(43\) | − | 4.01145i | − | 0.611740i | −0.952073 | − | 0.305870i | \(-0.901053\pi\) | ||
0.952073 | − | 0.305870i | \(-0.0989473\pi\) | |||||||
\(44\) | 4.34238 | 0.654638 | ||||||||
\(45\) | 2.17741 | − | 0.508790i | 0.324590 | − | 0.0758459i | ||||
\(46\) | 10.0288 | 1.47867 | ||||||||
\(47\) | − | 3.41906i | − | 0.498721i | −0.968411 | − | 0.249360i | \(-0.919780\pi\) | ||
0.968411 | − | 0.249360i | \(-0.0802204\pi\) | |||||||
\(48\) | − | 6.17150i | − | 0.890779i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 5.58002 | + | 11.2882i | 0.789134 | + | 1.59639i | ||||
\(51\) | −2.73533 | −0.383023 | ||||||||
\(52\) | − | 8.38767i | − | 1.16316i | ||||||
\(53\) | − | 9.17420i | − | 1.26017i | −0.776525 | − | 0.630087i | \(-0.783019\pi\) | ||
0.776525 | − | 0.630087i | \(-0.216981\pi\) | |||||||
\(54\) | −2.51841 | −0.342712 | ||||||||
\(55\) | 2.17741 | − | 0.508790i | 0.293602 | − | 0.0686052i | ||||
\(56\) | 5.89907 | 0.788296 | ||||||||
\(57\) | 5.74934i | 0.761519i | ||||||||
\(58\) | 2.25980i | 0.296727i | ||||||||
\(59\) | −9.82410 | −1.27899 | −0.639494 | − | 0.768796i | \(-0.720856\pi\) | ||||
−0.639494 | + | 0.768796i | \(0.720856\pi\) | |||||||
\(60\) | −2.20936 | − | 9.45516i | −0.285227 | − | 1.22066i | ||||
\(61\) | 1.57645 | 0.201843 | 0.100922 | − | 0.994894i | \(-0.467821\pi\) | ||||
0.100922 | + | 0.994894i | \(0.467821\pi\) | |||||||
\(62\) | 25.9350i | 3.29375i | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 2.91353 | 0.364192 | ||||||||
\(65\) | −0.982771 | − | 4.20586i | −0.121898 | − | 0.521673i | ||||
\(66\) | −2.51841 | −0.309995 | ||||||||
\(67\) | 5.66006i | 0.691486i | 0.938329 | + | 0.345743i | \(0.112373\pi\) | ||||
−0.938329 | + | 0.345743i | \(0.887627\pi\) | |||||||
\(68\) | 11.8778i | 1.44040i | ||||||||
\(69\) | −3.98220 | −0.479401 | ||||||||
\(70\) | 5.48362 | − | 1.28134i | 0.655418 | − | 0.153149i | ||||
\(71\) | −5.57815 | −0.662005 | −0.331002 | − | 0.943630i | \(-0.607387\pi\) | ||||
−0.331002 | + | 0.943630i | \(0.607387\pi\) | |||||||
\(72\) | 5.89907i | 0.695212i | ||||||||
\(73\) | 9.45961i | 1.10716i | 0.832795 | + | 0.553582i | \(0.186739\pi\) | ||||
−0.832795 | + | 0.553582i | \(0.813261\pi\) | |||||||
\(74\) | 7.79861 | 0.906570 | ||||||||
\(75\) | −2.21569 | − | 4.48227i | −0.255846 | − | 0.517567i | ||||
\(76\) | 24.9658 | 2.86378 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | 4.86452i | 0.550798i | ||||||||
\(79\) | 13.4115 | 1.50892 | 0.754458 | − | 0.656348i | \(-0.227900\pi\) | ||||
0.754458 | + | 0.656348i | \(0.227900\pi\) | |||||||
\(80\) | −13.4379 | + | 3.13999i | −1.50240 | + | 0.351062i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 19.7410i | 2.18003i | ||||||||
\(83\) | − | 8.24025i | − | 0.904485i | −0.891895 | − | 0.452243i | \(-0.850624\pi\) | ||
0.891895 | − | 0.452243i | \(-0.149376\pi\) | |||||||
\(84\) | −4.34238 | −0.473792 | ||||||||
\(85\) | 1.39171 | + | 5.95595i | 0.150952 | + | 0.646014i | ||||
\(86\) | 10.1025 | 1.08938 | ||||||||
\(87\) | − | 0.897314i | − | 0.0962021i | ||||||
\(88\) | 5.89907i | 0.628842i | ||||||||
\(89\) | −9.21337 | −0.976615 | −0.488307 | − | 0.872672i | \(-0.662386\pi\) | ||||
−0.488307 | + | 0.872672i | \(0.662386\pi\) | |||||||
\(90\) | 1.28134 | + | 5.48362i | 0.135065 | + | 0.578024i | ||||
\(91\) | −1.93158 | −0.202485 | ||||||||
\(92\) | 17.2922i | 1.80284i | ||||||||
\(93\) | − | 10.2982i | − | 1.06787i | ||||||
\(94\) | 8.61058 | 0.888114 | ||||||||
\(95\) | 12.5187 | − | 2.92521i | 1.28439 | − | 0.300120i | ||||
\(96\) | 3.74421 | 0.382142 | ||||||||
\(97\) | − | 15.8647i | − | 1.61081i | −0.592723 | − | 0.805406i | \(-0.701947\pi\) | ||
0.592723 | − | 0.805406i | \(-0.298053\pi\) | |||||||
\(98\) | − | 2.51841i | − | 0.254398i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −19.4637 | + | 9.62138i | −1.94637 | + | 0.962138i | ||||
\(101\) | −17.6934 | −1.76056 | −0.880281 | − | 0.474453i | \(-0.842646\pi\) | ||||
−0.880281 | + | 0.474453i | \(0.842646\pi\) | |||||||
\(102\) | − | 6.88868i | − | 0.682081i | ||||||
\(103\) | 10.6962i | 1.05393i | 0.849888 | + | 0.526964i | \(0.176670\pi\) | ||||
−0.849888 | + | 0.526964i | \(0.823330\pi\) | |||||||
\(104\) | 11.3945 | 1.11733 | ||||||||
\(105\) | −2.17741 | + | 0.508790i | −0.212494 | + | 0.0496528i | ||||
\(106\) | 23.1044 | 2.24410 | ||||||||
\(107\) | − | 5.79452i | − | 0.560177i | −0.959974 | − | 0.280089i | \(-0.909636\pi\) | ||
0.959974 | − | 0.280089i | \(-0.0903638\pi\) | |||||||
\(108\) | − | 4.34238i | − | 0.417846i | ||||||
\(109\) | 9.96757 | 0.954721 | 0.477360 | − | 0.878708i | \(-0.341594\pi\) | ||||
0.477360 | + | 0.878708i | \(0.341594\pi\) | |||||||
\(110\) | 1.28134 | + | 5.48362i | 0.122171 | + | 0.522842i | ||||
\(111\) | −3.09664 | −0.293920 | ||||||||
\(112\) | 6.17150i | 0.583152i | ||||||||
\(113\) | − | 8.06070i | − | 0.758287i | −0.925338 | − | 0.379144i | \(-0.876219\pi\) | ||
0.925338 | − | 0.379144i | \(-0.123781\pi\) | |||||||
\(114\) | −14.4792 | −1.35610 | ||||||||
\(115\) | 2.02610 | + | 8.67090i | 0.188935 | + | 0.808566i | ||||
\(116\) | −3.89648 | −0.361779 | ||||||||
\(117\) | − | 1.93158i | − | 0.178575i | ||||||
\(118\) | − | 24.7411i | − | 2.27760i | ||||||
\(119\) | 2.73533 | 0.250747 | ||||||||
\(120\) | 12.8447 | − | 3.00139i | 1.17256 | − | 0.273988i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.97014i | 0.359440i | ||||||||
\(123\) | − | 7.83869i | − | 0.706791i | ||||||
\(124\) | −44.7185 | −4.01584 | ||||||||
\(125\) | −8.63243 | + | 7.10501i | −0.772108 | + | 0.635492i | ||||
\(126\) | 2.51841 | 0.224358 | ||||||||
\(127\) | − | 18.2960i | − | 1.62351i | −0.583998 | − | 0.811755i | \(-0.698512\pi\) | ||
0.583998 | − | 0.811755i | \(-0.301488\pi\) | |||||||
\(128\) | 14.8259i | 1.31044i | ||||||||
\(129\) | −4.01145 | −0.353188 | ||||||||
\(130\) | 10.5921 | − | 2.47502i | 0.928986 | − | 0.217073i | ||||
\(131\) | 2.32349 | 0.203004 | 0.101502 | − | 0.994835i | \(-0.467635\pi\) | ||||
0.101502 | + | 0.994835i | \(0.467635\pi\) | |||||||
\(132\) | − | 4.34238i | − | 0.377956i | ||||||
\(133\) | − | 5.74934i | − | 0.498531i | ||||||
\(134\) | −14.2543 | −1.23139 | ||||||||
\(135\) | −0.508790 | − | 2.17741i | −0.0437897 | − | 0.187402i | ||||
\(136\) | −16.1359 | −1.38364 | ||||||||
\(137\) | − | 18.6392i | − | 1.59245i | −0.605000 | − | 0.796226i | \(-0.706827\pi\) | ||
0.605000 | − | 0.796226i | \(-0.293173\pi\) | |||||||
\(138\) | − | 10.0288i | − | 0.853709i | ||||||
\(139\) | −7.27340 | −0.616922 | −0.308461 | − | 0.951237i | \(-0.599814\pi\) | ||||
−0.308461 | + | 0.951237i | \(0.599814\pi\) | |||||||
\(140\) | 2.20936 | + | 9.45516i | 0.186725 | + | 0.799107i | ||||
\(141\) | −3.41906 | −0.287937 | ||||||||
\(142\) | − | 14.0481i | − | 1.17889i | ||||||
\(143\) | − | 1.93158i | − | 0.161527i | ||||||
\(144\) | −6.17150 | −0.514291 | ||||||||
\(145\) | −1.95382 | + | 0.456544i | −0.162256 | + | 0.0379139i | ||||
\(146\) | −23.8232 | −1.97162 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 13.4468i | 1.10532i | ||||||||
\(149\) | 5.55113 | 0.454767 | 0.227383 | − | 0.973805i | \(-0.426983\pi\) | ||||
0.227383 | + | 0.973805i | \(0.426983\pi\) | |||||||
\(150\) | 11.2882 | − | 5.58002i | 0.921676 | − | 0.455607i | ||||
\(151\) | −4.91722 | −0.400158 | −0.200079 | − | 0.979780i | \(-0.564120\pi\) | ||||
−0.200079 | + | 0.979780i | \(0.564120\pi\) | |||||||
\(152\) | 33.9157i | 2.75093i | ||||||||
\(153\) | 2.73533i | 0.221138i | ||||||||
\(154\) | 2.51841 | 0.202939 | ||||||||
\(155\) | −22.4234 | + | 5.23960i | −1.80109 | + | 0.420855i | ||||
\(156\) | −8.38767 | −0.671551 | ||||||||
\(157\) | − | 10.7928i | − | 0.861360i | −0.902505 | − | 0.430680i | \(-0.858274\pi\) | ||
0.902505 | − | 0.430680i | \(-0.141726\pi\) | |||||||
\(158\) | 33.7757i | 2.68705i | ||||||||
\(159\) | −9.17420 | −0.727561 | ||||||||
\(160\) | −1.90502 | − | 8.15270i | −0.150605 | − | 0.644528i | ||||
\(161\) | 3.98220 | 0.313841 | ||||||||
\(162\) | 2.51841i | 0.197865i | ||||||||
\(163\) | − | 5.23865i | − | 0.410322i | −0.978728 | − | 0.205161i | \(-0.934228\pi\) | ||
0.978728 | − | 0.205161i | \(-0.0657719\pi\) | |||||||
\(164\) | −34.0386 | −2.65796 | ||||||||
\(165\) | −0.508790 | − | 2.17741i | −0.0396092 | − | 0.169511i | ||||
\(166\) | 20.7523 | 1.61069 | ||||||||
\(167\) | 16.7794i | 1.29843i | 0.760604 | + | 0.649216i | \(0.224903\pi\) | ||||
−0.760604 | + | 0.649216i | \(0.775097\pi\) | |||||||
\(168\) | − | 5.89907i | − | 0.455123i | ||||||
\(169\) | 9.26898 | 0.712999 | ||||||||
\(170\) | −14.9995 | + | 3.50489i | −1.15041 | + | 0.268813i | ||||
\(171\) | 5.74934 | 0.439663 | ||||||||
\(172\) | 17.4192i | 1.32820i | ||||||||
\(173\) | − | 1.79619i | − | 0.136562i | −0.997666 | − | 0.0682808i | \(-0.978249\pi\) | ||
0.997666 | − | 0.0682808i | \(-0.0217514\pi\) | |||||||
\(174\) | 2.25980 | 0.171315 | ||||||||
\(175\) | 2.21569 | + | 4.48227i | 0.167491 | + | 0.338827i | ||||
\(176\) | −6.17150 | −0.465194 | ||||||||
\(177\) | 9.82410i | 0.738424i | ||||||||
\(178\) | − | 23.2030i | − | 1.73914i | ||||||
\(179\) | −8.35101 | −0.624184 | −0.312092 | − | 0.950052i | \(-0.601030\pi\) | ||||
−0.312092 | + | 0.950052i | \(0.601030\pi\) | |||||||
\(180\) | −9.45516 | + | 2.20936i | −0.704746 | + | 0.164676i | ||||
\(181\) | −13.7909 | −1.02507 | −0.512536 | − | 0.858666i | \(-0.671294\pi\) | ||||
−0.512536 | + | 0.858666i | \(0.671294\pi\) | |||||||
\(182\) | − | 4.86452i | − | 0.360582i | ||||||
\(183\) | − | 1.57645i | − | 0.116534i | ||||||
\(184\) | −23.4913 | −1.73180 | ||||||||
\(185\) | 1.57554 | + | 6.74267i | 0.115836 | + | 0.495731i | ||||
\(186\) | 25.9350 | 1.90165 | ||||||||
\(187\) | 2.73533i | 0.200027i | ||||||||
\(188\) | 14.8468i | 1.08282i | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 7.36686 | + | 31.5272i | 0.534449 | + | 2.28722i | ||||
\(191\) | −17.3693 | −1.25680 | −0.628399 | − | 0.777891i | \(-0.716290\pi\) | ||||
−0.628399 | + | 0.777891i | \(0.716290\pi\) | |||||||
\(192\) | − | 2.91353i | − | 0.210266i | ||||||
\(193\) | 19.1698i | 1.37987i | 0.723869 | + | 0.689937i | \(0.242362\pi\) | ||||
−0.723869 | + | 0.689937i | \(0.757638\pi\) | |||||||
\(194\) | 39.9537 | 2.86851 | ||||||||
\(195\) | −4.20586 | + | 0.982771i | −0.301188 | + | 0.0703777i | ||||
\(196\) | 4.34238 | 0.310170 | ||||||||
\(197\) | − | 13.2602i | − | 0.944752i | −0.881397 | − | 0.472376i | \(-0.843396\pi\) | ||
0.881397 | − | 0.472376i | \(-0.156604\pi\) | |||||||
\(198\) | 2.51841i | 0.178975i | ||||||||
\(199\) | −11.6731 | −0.827486 | −0.413743 | − | 0.910394i | \(-0.635779\pi\) | ||||
−0.413743 | + | 0.910394i | \(0.635779\pi\) | |||||||
\(200\) | −13.0705 | − | 26.4412i | −0.924225 | − | 1.86967i | ||||
\(201\) | 5.66006 | 0.399230 | ||||||||
\(202\) | − | 44.5593i | − | 3.13518i | ||||||
\(203\) | 0.897314i | 0.0629791i | ||||||||
\(204\) | 11.8778 | 0.831616 | ||||||||
\(205\) | −17.0681 | + | 3.98825i | −1.19209 | + | 0.278551i | ||||
\(206\) | −26.9374 | −1.87682 | ||||||||
\(207\) | 3.98220i | 0.276782i | ||||||||
\(208\) | 11.9208i | 0.826556i | ||||||||
\(209\) | 5.74934 | 0.397690 | ||||||||
\(210\) | −1.28134 | − | 5.48362i | −0.0884209 | − | 0.378406i | ||||
\(211\) | −6.24626 | −0.430010 | −0.215005 | − | 0.976613i | \(-0.568977\pi\) | ||||
−0.215005 | + | 0.976613i | \(0.568977\pi\) | |||||||
\(212\) | 39.8378i | 2.73607i | ||||||||
\(213\) | 5.57815i | 0.382209i | ||||||||
\(214\) | 14.5930 | 0.997554 | ||||||||
\(215\) | 2.04098 | + | 8.73458i | 0.139194 | + | 0.595693i | ||||
\(216\) | 5.89907 | 0.401381 | ||||||||
\(217\) | 10.2982i | 0.699085i | ||||||||
\(218\) | 25.1024i | 1.70015i | ||||||||
\(219\) | 9.45961 | 0.639221 | ||||||||
\(220\) | −9.45516 | + | 2.20936i | −0.637467 | + | 0.148955i | ||||
\(221\) | 5.28352 | 0.355408 | ||||||||
\(222\) | − | 7.79861i | − | 0.523408i | ||||||
\(223\) | − | 15.6620i | − | 1.04880i | −0.851471 | − | 0.524402i | \(-0.824289\pi\) | ||
0.851471 | − | 0.524402i | \(-0.175711\pi\) | |||||||
\(224\) | −3.74421 | −0.250171 | ||||||||
\(225\) | −4.48227 | + | 2.21569i | −0.298818 | + | 0.147713i | ||||
\(226\) | 20.3001 | 1.35035 | ||||||||
\(227\) | 12.5488i | 0.832895i | 0.909160 | + | 0.416448i | \(0.136725\pi\) | ||||
−0.909160 | + | 0.416448i | \(0.863275\pi\) | |||||||
\(228\) | − | 24.9658i | − | 1.65340i | ||||||
\(229\) | −27.4136 | −1.81154 | −0.905772 | − | 0.423765i | \(-0.860708\pi\) | ||||
−0.905772 | + | 0.423765i | \(0.860708\pi\) | |||||||
\(230\) | −21.8369 | + | 5.10256i | −1.43988 | + | 0.336453i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | − | 5.29331i | − | 0.347523i | ||||||
\(233\) | − | 13.8607i | − | 0.908047i | −0.890990 | − | 0.454023i | \(-0.849988\pi\) | ||
0.890990 | − | 0.454023i | \(-0.150012\pi\) | |||||||
\(234\) | 4.86452 | 0.318003 | ||||||||
\(235\) | 1.73958 | + | 7.44470i | 0.113478 | + | 0.485639i | ||||
\(236\) | 42.6600 | 2.77693 | ||||||||
\(237\) | − | 13.4115i | − | 0.871173i | ||||||
\(238\) | 6.88868i | 0.446527i | ||||||||
\(239\) | 20.8546 | 1.34897 | 0.674486 | − | 0.738288i | \(-0.264365\pi\) | ||||
0.674486 | + | 0.738288i | \(0.264365\pi\) | |||||||
\(240\) | 3.13999 | + | 13.4379i | 0.202686 | + | 0.867413i | ||||
\(241\) | −16.6597 | −1.07315 | −0.536574 | − | 0.843853i | \(-0.680282\pi\) | ||||
−0.536574 | + | 0.843853i | \(0.680282\pi\) | |||||||
\(242\) | 2.51841i | 0.161889i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −6.84553 | −0.438240 | ||||||||
\(245\) | 2.17741 | − | 0.508790i | 0.139110 | − | 0.0325054i | ||||
\(246\) | 19.7410 | 1.25864 | ||||||||
\(247\) | − | 11.1053i | − | 0.706616i | ||||||
\(248\) | − | 60.7496i | − | 3.85760i | ||||||
\(249\) | −8.24025 | −0.522205 | ||||||||
\(250\) | −17.8933 | − | 21.7400i | −1.13167 | − | 1.37496i | ||||
\(251\) | 5.04024 | 0.318137 | 0.159068 | − | 0.987268i | \(-0.449151\pi\) | ||||
0.159068 | + | 0.987268i | \(0.449151\pi\) | |||||||
\(252\) | 4.34238i | 0.273544i | ||||||||
\(253\) | 3.98220i | 0.250359i | ||||||||
\(254\) | 46.0769 | 2.89112 | ||||||||
\(255\) | 5.95595 | − | 1.39171i | 0.372976 | − | 0.0871522i | ||||
\(256\) | −31.5106 | −1.96941 | ||||||||
\(257\) | − | 22.8836i | − | 1.42744i | −0.700430 | − | 0.713721i | \(-0.747009\pi\) | ||
0.700430 | − | 0.713721i | \(-0.252991\pi\) | |||||||
\(258\) | − | 10.1025i | − | 0.628952i | ||||||
\(259\) | 3.09664 | 0.192416 | ||||||||
\(260\) | 4.26756 | + | 18.2634i | 0.264663 | + | 1.13265i | ||||
\(261\) | −0.897314 | −0.0555423 | ||||||||
\(262\) | 5.85150i | 0.361507i | ||||||||
\(263\) | − | 1.94233i | − | 0.119769i | −0.998205 | − | 0.0598845i | \(-0.980927\pi\) | ||
0.998205 | − | 0.0598845i | \(-0.0190733\pi\) | |||||||
\(264\) | 5.89907 | 0.363062 | ||||||||
\(265\) | 4.66774 | + | 19.9760i | 0.286737 | + | 1.22712i | ||||
\(266\) | 14.4792 | 0.887776 | ||||||||
\(267\) | 9.21337i | 0.563849i | ||||||||
\(268\) | − | 24.5781i | − | 1.50135i | ||||||
\(269\) | 18.0770 | 1.10217 | 0.551086 | − | 0.834448i | \(-0.314214\pi\) | ||||
0.551086 | + | 0.834448i | \(0.314214\pi\) | |||||||
\(270\) | 5.48362 | − | 1.28134i | 0.333722 | − | 0.0779799i | ||||
\(271\) | −0.990072 | −0.0601426 | −0.0300713 | − | 0.999548i | \(-0.509573\pi\) | ||||
−0.0300713 | + | 0.999548i | \(0.509573\pi\) | |||||||
\(272\) | − | 16.8811i | − | 1.02357i | ||||||
\(273\) | 1.93158i | 0.116905i | ||||||||
\(274\) | 46.9410 | 2.83581 | ||||||||
\(275\) | −4.48227 | + | 2.21569i | −0.270291 | + | 0.133611i | ||||
\(276\) | 17.2922 | 1.04087 | ||||||||
\(277\) | − | 21.6115i | − | 1.29851i | −0.760571 | − | 0.649255i | \(-0.775081\pi\) | ||
0.760571 | − | 0.649255i | \(-0.224919\pi\) | |||||||
\(278\) | − | 18.3174i | − | 1.09860i | ||||||
\(279\) | −10.2982 | −0.616535 | ||||||||
\(280\) | −12.8447 | + | 3.00139i | −0.767618 | + | 0.179367i | ||||
\(281\) | −1.05458 | −0.0629112 | −0.0314556 | − | 0.999505i | \(-0.510014\pi\) | ||||
−0.0314556 | + | 0.999505i | \(0.510014\pi\) | |||||||
\(282\) | − | 8.61058i | − | 0.512753i | ||||||
\(283\) | − | 15.5919i | − | 0.926844i | −0.886138 | − | 0.463422i | \(-0.846621\pi\) | ||
0.886138 | − | 0.463422i | \(-0.153379\pi\) | |||||||
\(284\) | 24.2224 | 1.43734 | ||||||||
\(285\) | −2.92521 | − | 12.5187i | −0.173274 | − | 0.741544i | ||||
\(286\) | 4.86452 | 0.287645 | ||||||||
\(287\) | 7.83869i | 0.462703i | ||||||||
\(288\) | − | 3.74421i | − | 0.220630i | ||||||
\(289\) | 9.51796 | 0.559880 | ||||||||
\(290\) | −1.14976 | − | 4.92053i | −0.0675165 | − | 0.288943i | ||||
\(291\) | −15.8647 | −0.930003 | ||||||||
\(292\) | − | 41.0772i | − | 2.40386i | ||||||
\(293\) | − | 28.2397i | − | 1.64978i | −0.565292 | − | 0.824891i | \(-0.691236\pi\) | ||
0.565292 | − | 0.824891i | \(-0.308764\pi\) | |||||||
\(294\) | −2.51841 | −0.146877 | ||||||||
\(295\) | 21.3911 | − | 4.99840i | 1.24544 | − | 0.291018i | ||||
\(296\) | −18.2673 | −1.06176 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | 13.9800i | 0.809841i | ||||||||
\(299\) | 7.69196 | 0.444837 | ||||||||
\(300\) | 9.62138 | + | 19.4637i | 0.555490 | + | 1.12374i | ||||
\(301\) | 4.01145 | 0.231216 | ||||||||
\(302\) | − | 12.3836i | − | 0.712595i | ||||||
\(303\) | 17.6934i | 1.01646i | ||||||||
\(304\) | −35.4820 | −2.03503 | ||||||||
\(305\) | −3.43258 | + | 0.802081i | −0.196549 | + | 0.0459270i | ||||
\(306\) | −6.88868 | −0.393800 | ||||||||
\(307\) | 7.96272i | 0.454456i | 0.973842 | + | 0.227228i | \(0.0729663\pi\) | ||||
−0.973842 | + | 0.227228i | \(0.927034\pi\) | |||||||
\(308\) | 4.34238i | 0.247430i | ||||||||
\(309\) | 10.6962 | 0.608486 | ||||||||
\(310\) | −13.1955 | − | 56.4712i | −0.749452 | − | 3.20735i | ||||
\(311\) | −7.18130 | −0.407214 | −0.203607 | − | 0.979053i | \(-0.565266\pi\) | ||||
−0.203607 | + | 0.979053i | \(0.565266\pi\) | |||||||
\(312\) | − | 11.3945i | − | 0.645089i | ||||||
\(313\) | 22.5430i | 1.27421i | 0.770779 | + | 0.637103i | \(0.219867\pi\) | ||||
−0.770779 | + | 0.637103i | \(0.780133\pi\) | |||||||
\(314\) | 27.1807 | 1.53389 | ||||||||
\(315\) | 0.508790 | + | 2.17741i | 0.0286671 | + | 0.122683i | ||||
\(316\) | −58.2380 | −3.27614 | ||||||||
\(317\) | 19.7730i | 1.11056i | 0.831663 | + | 0.555281i | \(0.187389\pi\) | ||||
−0.831663 | + | 0.555281i | \(0.812611\pi\) | |||||||
\(318\) | − | 23.1044i | − | 1.29563i | ||||||
\(319\) | −0.897314 | −0.0502399 | ||||||||
\(320\) | −6.34397 | + | 1.48238i | −0.354639 | + | 0.0828674i | ||||
\(321\) | −5.79452 | −0.323418 | ||||||||
\(322\) | 10.0288i | 0.558884i | ||||||||
\(323\) | 15.7264i | 0.875038i | ||||||||
\(324\) | −4.34238 | −0.241243 | ||||||||
\(325\) | 4.27980 | + | 8.65787i | 0.237400 | + | 0.480252i | ||||
\(326\) | 13.1930 | 0.730695 | ||||||||
\(327\) | − | 9.96757i | − | 0.551208i | ||||||
\(328\) | − | 46.2409i | − | 2.55323i | ||||||
\(329\) | 3.41906 | 0.188499 | ||||||||
\(330\) | 5.48362 | − | 1.28134i | 0.301863 | − | 0.0705355i | ||||
\(331\) | 29.2958 | 1.61024 | 0.805121 | − | 0.593110i | \(-0.202100\pi\) | ||||
0.805121 | + | 0.593110i | \(0.202100\pi\) | |||||||
\(332\) | 35.7823i | 1.96381i | ||||||||
\(333\) | 3.09664i | 0.169695i | ||||||||
\(334\) | −42.2575 | −2.31223 | ||||||||
\(335\) | −2.87978 | − | 12.3243i | −0.157339 | − | 0.673348i | ||||
\(336\) | 6.17150 | 0.336683 | ||||||||
\(337\) | 14.7637i | 0.804230i | 0.915589 | + | 0.402115i | \(0.131725\pi\) | ||||
−0.915589 | + | 0.402115i | \(0.868275\pi\) | |||||||
\(338\) | 23.3431i | 1.26970i | ||||||||
\(339\) | −8.06070 | −0.437797 | ||||||||
\(340\) | −6.04333 | − | 25.8630i | −0.327746 | − | 1.40262i | ||||
\(341\) | −10.2982 | −0.557677 | ||||||||
\(342\) | 14.4792i | 0.782945i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −23.6638 | −1.27587 | ||||||||
\(345\) | 8.67090 | − | 2.02610i | 0.466826 | − | 0.109082i | ||||
\(346\) | 4.52353 | 0.243187 | ||||||||
\(347\) | 8.14373i | 0.437179i | 0.975817 | + | 0.218589i | \(0.0701455\pi\) | ||||
−0.975817 | + | 0.218589i | \(0.929855\pi\) | |||||||
\(348\) | 3.89648i | 0.208873i | ||||||||
\(349\) | 31.6394 | 1.69362 | 0.846809 | − | 0.531897i | \(-0.178521\pi\) | ||||
0.846809 | + | 0.531897i | \(0.178521\pi\) | |||||||
\(350\) | −11.2882 | + | 5.58002i | −0.603378 | + | 0.298265i | ||||
\(351\) | −1.93158 | −0.103100 | ||||||||
\(352\) | − | 3.74421i | − | 0.199567i | ||||||
\(353\) | 17.5983i | 0.936665i | 0.883552 | + | 0.468332i | \(0.155145\pi\) | ||||
−0.883552 | + | 0.468332i | \(0.844855\pi\) | |||||||
\(354\) | −24.7411 | −1.31497 | ||||||||
\(355\) | 12.1459 | − | 2.83811i | 0.644640 | − | 0.150631i | ||||
\(356\) | 40.0079 | 2.12042 | ||||||||
\(357\) | − | 2.73533i | − | 0.144769i | ||||||
\(358\) | − | 21.0312i | − | 1.11154i | ||||||
\(359\) | −21.7549 | −1.14818 | −0.574091 | − | 0.818791i | \(-0.694644\pi\) | ||||
−0.574091 | + | 0.818791i | \(0.694644\pi\) | |||||||
\(360\) | −3.00139 | − | 12.8447i | −0.158187 | − | 0.676976i | ||||
\(361\) | 14.0549 | 0.739733 | ||||||||
\(362\) | − | 34.7312i | − | 1.82543i | ||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | 8.38767 | 0.439633 | ||||||||
\(365\) | −4.81296 | − | 20.5975i | −0.251922 | − | 1.07812i | ||||
\(366\) | 3.97014 | 0.207522 | ||||||||
\(367\) | 4.67786i | 0.244182i | 0.992519 | + | 0.122091i | \(0.0389600\pi\) | ||||
−0.992519 | + | 0.122091i | \(0.961040\pi\) | |||||||
\(368\) | − | 24.5761i | − | 1.28112i | ||||||
\(369\) | −7.83869 | −0.408066 | ||||||||
\(370\) | −16.9808 | + | 3.96785i | −0.882790 | + | 0.206279i | ||||
\(371\) | 9.17420 | 0.476301 | ||||||||
\(372\) | 44.7185i | 2.31855i | ||||||||
\(373\) | 3.00329i | 0.155504i | 0.996973 | + | 0.0777522i | \(0.0247743\pi\) | ||||
−0.996973 | + | 0.0777522i | \(0.975226\pi\) | |||||||
\(374\) | −6.88868 | −0.356205 | ||||||||
\(375\) | 7.10501 | + | 8.63243i | 0.366901 | + | 0.445777i | ||||
\(376\) | −20.1692 | −1.04015 | ||||||||
\(377\) | 1.73324i | 0.0892663i | ||||||||
\(378\) | − | 2.51841i | − | 0.129533i | ||||||
\(379\) | −14.0793 | −0.723204 | −0.361602 | − | 0.932333i | \(-0.617770\pi\) | ||||
−0.361602 | + | 0.932333i | \(0.617770\pi\) | |||||||
\(380\) | −54.3609 | + | 12.7024i | −2.78866 | + | 0.651617i | ||||
\(381\) | −18.2960 | −0.937334 | ||||||||
\(382\) | − | 43.7430i | − | 2.23809i | ||||||
\(383\) | − | 3.12889i | − | 0.159879i | −0.996800 | − | 0.0799395i | \(-0.974527\pi\) | ||
0.996800 | − | 0.0799395i | \(-0.0254727\pi\) | |||||||
\(384\) | 14.8259 | 0.756581 | ||||||||
\(385\) | 0.508790 | + | 2.17741i | 0.0259303 | + | 0.110971i | ||||
\(386\) | −48.2774 | −2.45726 | ||||||||
\(387\) | 4.01145i | 0.203913i | ||||||||
\(388\) | 68.8904i | 3.49738i | ||||||||
\(389\) | 6.46694 | 0.327887 | 0.163943 | − | 0.986470i | \(-0.447579\pi\) | ||||
0.163943 | + | 0.986470i | \(0.447579\pi\) | |||||||
\(390\) | −2.47502 | − | 10.5921i | −0.125327 | − | 0.536350i | ||||
\(391\) | −10.8926 | −0.550865 | ||||||||
\(392\) | 5.89907i | 0.297948i | ||||||||
\(393\) | − | 2.32349i | − | 0.117205i | ||||||
\(394\) | 33.3947 | 1.68240 | ||||||||
\(395\) | −29.2025 | + | 6.82366i | −1.46934 | + | 0.343335i | ||||
\(396\) | −4.34238 | −0.218213 | ||||||||
\(397\) | − | 14.6224i | − | 0.733877i | −0.930245 | − | 0.366938i | \(-0.880406\pi\) | ||
0.930245 | − | 0.366938i | \(-0.119594\pi\) | |||||||
\(398\) | − | 29.3977i | − | 1.47357i | ||||||
\(399\) | −5.74934 | −0.287827 | ||||||||
\(400\) | 27.6623 | − | 13.6741i | 1.38311 | − | 0.683707i | ||||
\(401\) | 25.7387 | 1.28533 | 0.642665 | − | 0.766147i | \(-0.277829\pi\) | ||||
0.642665 | + | 0.766147i | \(0.277829\pi\) | |||||||
\(402\) | 14.2543i | 0.710942i | ||||||||
\(403\) | 19.8918i | 0.990880i | ||||||||
\(404\) | 76.8316 | 3.82251 | ||||||||
\(405\) | −2.17741 | + | 0.508790i | −0.108197 | + | 0.0252820i | ||||
\(406\) | −2.25980 | −0.112152 | ||||||||
\(407\) | 3.09664i | 0.153495i | ||||||||
\(408\) | 16.1359i | 0.798846i | ||||||||
\(409\) | 10.0472 | 0.496803 | 0.248401 | − | 0.968657i | \(-0.420095\pi\) | ||||
0.248401 | + | 0.968657i | \(0.420095\pi\) | |||||||
\(410\) | −10.0440 | − | 42.9844i | −0.496039 | − | 2.12285i | ||||
\(411\) | −18.6392 | −0.919402 | ||||||||
\(412\) | − | 46.4470i | − | 2.28828i | ||||||
\(413\) | − | 9.82410i | − | 0.483412i | ||||||
\(414\) | −10.0288 | −0.492889 | ||||||||
\(415\) | 4.19256 | + | 17.9424i | 0.205805 | + | 0.880760i | ||||
\(416\) | −7.23226 | −0.354591 | ||||||||
\(417\) | 7.27340i | 0.356180i | ||||||||
\(418\) | 14.4792i | 0.708200i | ||||||||
\(419\) | 6.75857 | 0.330178 | 0.165089 | − | 0.986279i | \(-0.447209\pi\) | ||||
0.165089 | + | 0.986279i | \(0.447209\pi\) | |||||||
\(420\) | 9.45516 | − | 2.20936i | 0.461364 | − | 0.107806i | ||||
\(421\) | 2.33958 | 0.114024 | 0.0570121 | − | 0.998373i | \(-0.481843\pi\) | ||||
0.0570121 | + | 0.998373i | \(0.481843\pi\) | |||||||
\(422\) | − | 15.7306i | − | 0.765755i | ||||||
\(423\) | 3.41906i | 0.166240i | ||||||||
\(424\) | −54.1192 | −2.62826 | ||||||||
\(425\) | −6.06066 | − | 12.2605i | −0.293985 | − | 0.594721i | ||||
\(426\) | −14.0481 | −0.680631 | ||||||||
\(427\) | 1.57645i | 0.0762897i | ||||||||
\(428\) | 25.1620i | 1.21625i | ||||||||
\(429\) | −1.93158 | −0.0932578 | ||||||||
\(430\) | −21.9972 | + | 5.14003i | −1.06080 | + | 0.247874i | ||||
\(431\) | 13.1471 | 0.633273 | 0.316636 | − | 0.948547i | \(-0.397447\pi\) | ||||
0.316636 | + | 0.948547i | \(0.397447\pi\) | |||||||
\(432\) | 6.17150i | 0.296926i | ||||||||
\(433\) | 27.4941i | 1.32128i | 0.750702 | + | 0.660641i | \(0.229715\pi\) | ||||
−0.750702 | + | 0.660641i | \(0.770285\pi\) | |||||||
\(434\) | −25.9350 | −1.24492 | ||||||||
\(435\) | 0.456544 | + | 1.95382i | 0.0218896 | + | 0.0936787i | ||||
\(436\) | −43.2830 | −2.07288 | ||||||||
\(437\) | 22.8950i | 1.09522i | ||||||||
\(438\) | 23.8232i | 1.13831i | ||||||||
\(439\) | −32.6151 | −1.55663 | −0.778317 | − | 0.627872i | \(-0.783926\pi\) | ||||
−0.778317 | + | 0.627872i | \(0.783926\pi\) | |||||||
\(440\) | −3.00139 | − | 12.8447i | −0.143085 | − | 0.612347i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 13.3061i | 0.632905i | ||||||||
\(443\) | 21.4514i | 1.01919i | 0.860415 | + | 0.509595i | \(0.170205\pi\) | ||||
−0.860415 | + | 0.509595i | \(0.829795\pi\) | |||||||
\(444\) | 13.4468 | 0.638156 | ||||||||
\(445\) | 20.0613 | − | 4.68767i | 0.950998 | − | 0.222217i | ||||
\(446\) | 39.4432 | 1.86769 | ||||||||
\(447\) | − | 5.55113i | − | 0.262560i | ||||||
\(448\) | 2.91353i | 0.137652i | ||||||||
\(449\) | −36.2417 | −1.71035 | −0.855176 | − | 0.518338i | \(-0.826551\pi\) | ||||
−0.855176 | + | 0.518338i | \(0.826551\pi\) | |||||||
\(450\) | −5.58002 | − | 11.2882i | −0.263045 | − | 0.532130i | ||||
\(451\) | −7.83869 | −0.369109 | ||||||||
\(452\) | 35.0026i | 1.64639i | ||||||||
\(453\) | 4.91722i | 0.231031i | ||||||||
\(454\) | −31.6031 | −1.48321 | ||||||||
\(455\) | 4.20586 | − | 0.982771i | 0.197174 | − | 0.0460730i | ||||
\(456\) | 33.9157 | 1.58825 | ||||||||
\(457\) | − | 15.9313i | − | 0.745233i | −0.927986 | − | 0.372616i | \(-0.878461\pi\) | ||
0.927986 | − | 0.372616i | \(-0.121539\pi\) | |||||||
\(458\) | − | 69.0387i | − | 3.22597i | ||||||
\(459\) | 2.73533 | 0.127674 | ||||||||
\(460\) | −8.79811 | − | 37.6523i | −0.410214 | − | 1.75555i | ||||
\(461\) | 35.7258 | 1.66391 | 0.831957 | − | 0.554839i | \(-0.187220\pi\) | ||||
0.831957 | + | 0.554839i | \(0.187220\pi\) | |||||||
\(462\) | − | 2.51841i | − | 0.117167i | ||||||
\(463\) | − | 29.5009i | − | 1.37102i | −0.728061 | − | 0.685512i | \(-0.759578\pi\) | ||
0.728061 | − | 0.685512i | \(-0.240422\pi\) | |||||||
\(464\) | 5.53777 | 0.257084 | ||||||||
\(465\) | 5.23960 | + | 22.4234i | 0.242981 | + | 1.03986i | ||||
\(466\) | 34.9070 | 1.61703 | ||||||||
\(467\) | − | 18.9759i | − | 0.878099i | −0.898463 | − | 0.439050i | \(-0.855315\pi\) | ||
0.898463 | − | 0.439050i | \(-0.144685\pi\) | |||||||
\(468\) | 8.38767i | 0.387720i | ||||||||
\(469\) | −5.66006 | −0.261357 | ||||||||
\(470\) | −18.7488 | + | 4.38098i | −0.864818 | + | 0.202079i | ||||
\(471\) | −10.7928 | −0.497306 | ||||||||
\(472\) | 57.9530i | 2.66750i | ||||||||
\(473\) | 4.01145i | 0.184447i | ||||||||
\(474\) | 33.7757 | 1.55137 | ||||||||
\(475\) | −25.7701 | + | 12.7388i | −1.18241 | + | 0.584495i | ||||
\(476\) | −11.8778 | −0.544420 | ||||||||
\(477\) | 9.17420i | 0.420058i | ||||||||
\(478\) | 52.5204i | 2.40223i | ||||||||
\(479\) | −11.2070 | −0.512061 | −0.256031 | − | 0.966669i | \(-0.582415\pi\) | ||||
−0.256031 | + | 0.966669i | \(0.582415\pi\) | |||||||
\(480\) | −8.15270 | + | 1.90502i | −0.372118 | + | 0.0869518i | ||||
\(481\) | 5.98142 | 0.272729 | ||||||||
\(482\) | − | 41.9560i | − | 1.91104i | ||||||
\(483\) | − | 3.98220i | − | 0.181196i | ||||||
\(484\) | −4.34238 | −0.197381 | ||||||||
\(485\) | 8.07178 | + | 34.5439i | 0.366521 | + | 1.56856i | ||||
\(486\) | 2.51841 | 0.114237 | ||||||||
\(487\) | 12.8184i | 0.580859i | 0.956896 | + | 0.290429i | \(0.0937981\pi\) | ||||
−0.956896 | + | 0.290429i | \(0.906202\pi\) | |||||||
\(488\) | − | 9.29957i | − | 0.420972i | ||||||
\(489\) | −5.23865 | −0.236900 | ||||||||
\(490\) | 1.28134 | + | 5.48362i | 0.0578851 | + | 0.247725i | ||||
\(491\) | −17.5676 | −0.792817 | −0.396408 | − | 0.918074i | \(-0.629744\pi\) | ||||
−0.396408 | + | 0.918074i | \(0.629744\pi\) | |||||||
\(492\) | 34.0386i | 1.53458i | ||||||||
\(493\) | − | 2.45445i | − | 0.110543i | ||||||
\(494\) | 27.9678 | 1.25833 | ||||||||
\(495\) | −2.17741 | + | 0.508790i | −0.0978675 | + | 0.0228684i | ||||
\(496\) | 63.5551 | 2.85371 | ||||||||
\(497\) | − | 5.57815i | − | 0.250214i | ||||||
\(498\) | − | 20.7523i | − | 0.929933i | ||||||
\(499\) | −29.7751 | −1.33292 | −0.666458 | − | 0.745543i | \(-0.732190\pi\) | ||||
−0.666458 | + | 0.745543i | \(0.732190\pi\) | |||||||
\(500\) | 37.4853 | − | 30.8527i | 1.67639 | − | 1.37977i | ||||
\(501\) | 16.7794 | 0.749650 | ||||||||
\(502\) | 12.6934i | 0.566533i | ||||||||
\(503\) | − | 23.6396i | − | 1.05404i | −0.849853 | − | 0.527019i | \(-0.823310\pi\) | ||
0.849853 | − | 0.527019i | \(-0.176690\pi\) | |||||||
\(504\) | −5.89907 | −0.262765 | ||||||||
\(505\) | 38.5259 | − | 9.00224i | 1.71438 | − | 0.400594i | ||||
\(506\) | −10.0288 | −0.445835 | ||||||||
\(507\) | − | 9.26898i | − | 0.411650i | ||||||
\(508\) | 79.4483i | 3.52495i | ||||||||
\(509\) | −26.7267 | −1.18464 | −0.592321 | − | 0.805702i | \(-0.701788\pi\) | ||||
−0.592321 | + | 0.805702i | \(0.701788\pi\) | |||||||
\(510\) | 3.50489 | + | 14.9995i | 0.155199 | + | 0.664190i | ||||
\(511\) | −9.45961 | −0.418469 | ||||||||
\(512\) | − | 49.7047i | − | 2.19666i | ||||||
\(513\) | − | 5.74934i | − | 0.253840i | ||||||
\(514\) | 57.6303 | 2.54196 | ||||||||
\(515\) | −5.44212 | − | 23.2901i | −0.239808 | − | 1.02628i | ||||
\(516\) | 17.4192 | 0.766838 | ||||||||
\(517\) | 3.41906i | 0.150370i | ||||||||
\(518\) | 7.79861i | 0.342651i | ||||||||
\(519\) | −1.79619 | −0.0788439 | ||||||||
\(520\) | −24.8106 | + | 5.79743i | −1.08802 | + | 0.254234i | ||||
\(521\) | 40.2358 | 1.76276 | 0.881381 | − | 0.472407i | \(-0.156615\pi\) | ||||
0.881381 | + | 0.472407i | \(0.156615\pi\) | |||||||
\(522\) | − | 2.25980i | − | 0.0989089i | ||||||
\(523\) | − | 1.59645i | − | 0.0698079i | −0.999391 | − | 0.0349040i | \(-0.988887\pi\) | ||
0.999391 | − | 0.0349040i | \(-0.0111125\pi\) | |||||||
\(524\) | −10.0895 | −0.440761 | ||||||||
\(525\) | 4.48227 | − | 2.21569i | 0.195622 | − | 0.0967008i | ||||
\(526\) | 4.89157 | 0.213283 | ||||||||
\(527\) | − | 28.1689i | − | 1.22706i | ||||||
\(528\) | 6.17150i | 0.268580i | ||||||||
\(529\) | 7.14207 | 0.310525 | ||||||||
\(530\) | −50.3078 | + | 11.7553i | −2.18523 | + | 0.510616i | ||||
\(531\) | 9.82410 | 0.426330 | ||||||||
\(532\) | 24.9658i | 1.08241i | ||||||||
\(533\) | 15.1411i | 0.655833i | ||||||||
\(534\) | −23.2030 | −1.00409 | ||||||||
\(535\) | 2.94819 | + | 12.6171i | 0.127461 | + | 0.545483i | ||||
\(536\) | 33.3891 | 1.44219 | ||||||||
\(537\) | 8.35101i | 0.360373i | ||||||||
\(538\) | 45.5252i | 1.96273i | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 2.20936 | + | 9.45516i | 0.0950757 | + | 0.406885i | ||||
\(541\) | −9.91477 | −0.426269 | −0.213135 | − | 0.977023i | \(-0.568367\pi\) | ||||
−0.213135 | + | 0.977023i | \(0.568367\pi\) | |||||||
\(542\) | − | 2.49341i | − | 0.107101i | ||||||
\(543\) | 13.7909i | 0.591826i | ||||||||
\(544\) | 10.2417 | 0.439108 | ||||||||
\(545\) | −21.7035 | + | 5.07140i | −0.929677 | + | 0.217235i | ||||
\(546\) | −4.86452 | −0.208182 | ||||||||
\(547\) | 11.1725i | 0.477704i | 0.971056 | + | 0.238852i | \(0.0767710\pi\) | ||||
−0.971056 | + | 0.238852i | \(0.923229\pi\) | |||||||
\(548\) | 80.9383i | 3.45751i | ||||||||
\(549\) | −1.57645 | −0.0672812 | ||||||||
\(550\) | −5.58002 | − | 11.2882i | −0.237933 | − | 0.481329i | ||||
\(551\) | −5.15896 | −0.219779 | ||||||||
\(552\) | 23.4913i | 0.999855i | ||||||||
\(553\) | 13.4115i | 0.570317i | ||||||||
\(554\) | 54.4266 | 2.31236 | ||||||||
\(555\) | 6.74267 | − | 1.57554i | 0.286210 | − | 0.0668780i | ||||
\(556\) | 31.5839 | 1.33945 | ||||||||
\(557\) | − | 25.0884i | − | 1.06303i | −0.847048 | − | 0.531516i | \(-0.821623\pi\) | ||
0.847048 | − | 0.531516i | \(-0.178377\pi\) | |||||||
\(558\) | − | 25.9350i | − | 1.09792i | ||||||
\(559\) | 7.74845 | 0.327724 | ||||||||
\(560\) | −3.13999 | − | 13.4379i | −0.132689 | − | 0.567855i | ||||
\(561\) | 2.73533 | 0.115486 | ||||||||
\(562\) | − | 2.65587i | − | 0.112031i | ||||||
\(563\) | 26.3424i | 1.11020i | 0.831784 | + | 0.555099i | \(0.187320\pi\) | ||||
−0.831784 | + | 0.555099i | \(0.812680\pi\) | |||||||
\(564\) | 14.8468 | 0.625165 | ||||||||
\(565\) | 4.10121 | + | 17.5515i | 0.172539 | + | 0.738397i | ||||
\(566\) | 39.2668 | 1.65051 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 32.9059i | 1.38070i | ||||||||
\(569\) | 26.1376 | 1.09574 | 0.547872 | − | 0.836562i | \(-0.315438\pi\) | ||||
0.547872 | + | 0.836562i | \(0.315438\pi\) | |||||||
\(570\) | 31.5272 | − | 7.36686i | 1.32053 | − | 0.308564i | ||||
\(571\) | −5.02585 | −0.210325 | −0.105163 | − | 0.994455i | \(-0.533536\pi\) | ||||
−0.105163 | + | 0.994455i | \(0.533536\pi\) | |||||||
\(572\) | 8.38767i | 0.350706i | ||||||||
\(573\) | 17.3693i | 0.725613i | ||||||||
\(574\) | −19.7410 | −0.823974 | ||||||||
\(575\) | −8.82333 | − | 17.8493i | −0.367959 | − | 0.744367i | ||||
\(576\) | −2.91353 | −0.121397 | ||||||||
\(577\) | 30.4481i | 1.26757i | 0.773508 | + | 0.633786i | \(0.218500\pi\) | ||||
−0.773508 | + | 0.633786i | \(0.781500\pi\) | |||||||
\(578\) | 23.9701i | 0.997025i | ||||||||
\(579\) | 19.1698 | 0.796671 | ||||||||
\(580\) | 8.48424 | − | 1.98249i | 0.352289 | − | 0.0823183i | ||||
\(581\) | 8.24025 | 0.341863 | ||||||||
\(582\) | − | 39.9537i | − | 1.65613i | ||||||
\(583\) | 9.17420i | 0.379957i | ||||||||
\(584\) | 55.8029 | 2.30914 | ||||||||
\(585\) | 0.982771 | + | 4.20586i | 0.0406326 | + | 0.173891i | ||||
\(586\) | 71.1192 | 2.93791 | ||||||||
\(587\) | 30.4031i | 1.25487i | 0.778669 | + | 0.627435i | \(0.215895\pi\) | ||||
−0.778669 | + | 0.627435i | \(0.784105\pi\) | |||||||
\(588\) | − | 4.34238i | − | 0.179077i | ||||||
\(589\) | −59.2077 | −2.43961 | ||||||||
\(590\) | 12.5880 | + | 53.8716i | 0.518240 | + | 2.21786i | ||||
\(591\) | −13.2602 | −0.545453 | ||||||||
\(592\) | − | 19.1109i | − | 0.785454i | ||||||
\(593\) | 10.7140i | 0.439972i | 0.975503 | + | 0.219986i | \(0.0706012\pi\) | ||||
−0.975503 | + | 0.219986i | \(0.929399\pi\) | |||||||
\(594\) | 2.51841 | 0.103332 | ||||||||
\(595\) | −5.95595 | + | 1.39171i | −0.244170 | + | 0.0570545i | ||||
\(596\) | −24.1051 | −0.987384 | ||||||||
\(597\) | 11.6731i | 0.477749i | ||||||||
\(598\) | 19.3715i | 0.792159i | ||||||||
\(599\) | −27.1016 | −1.10734 | −0.553670 | − | 0.832736i | \(-0.686773\pi\) | ||||
−0.553670 | + | 0.832736i | \(0.686773\pi\) | |||||||
\(600\) | −26.4412 | + | 13.0705i | −1.07946 | + | 0.533602i | ||||
\(601\) | 38.3834 | 1.56569 | 0.782845 | − | 0.622217i | \(-0.213768\pi\) | ||||
0.782845 | + | 0.622217i | \(0.213768\pi\) | |||||||
\(602\) | 10.1025i | 0.411745i | ||||||||
\(603\) | − | 5.66006i | − | 0.230495i | ||||||
\(604\) | 21.3524 | 0.868819 | ||||||||
\(605\) | −2.17741 | + | 0.508790i | −0.0885245 | + | 0.0206853i | ||||
\(606\) | −44.5593 | −1.81010 | ||||||||
\(607\) | − | 31.6429i | − | 1.28435i | −0.766560 | − | 0.642173i | \(-0.778033\pi\) | ||
0.766560 | − | 0.642173i | \(-0.221967\pi\) | |||||||
\(608\) | − | 21.5268i | − | 0.873025i | ||||||
\(609\) | 0.897314 | 0.0363610 | ||||||||
\(610\) | −2.01997 | − | 8.64464i | −0.0817861 | − | 0.350011i | ||||
\(611\) | 6.60420 | 0.267177 | ||||||||
\(612\) | − | 11.8778i | − | 0.480134i | ||||||
\(613\) | 16.1066i | 0.650538i | 0.945622 | + | 0.325269i | \(0.105455\pi\) | ||||
−0.945622 | + | 0.325269i | \(0.894545\pi\) | |||||||
\(614\) | −20.0534 | −0.809288 | ||||||||
\(615\) | 3.98825 | + | 17.0681i | 0.160822 | + | 0.688251i | ||||
\(616\) | −5.89907 | −0.237680 | ||||||||
\(617\) | − | 35.3185i | − | 1.42187i | −0.703258 | − | 0.710935i | \(-0.748272\pi\) | ||
0.703258 | − | 0.710935i | \(-0.251728\pi\) | |||||||
\(618\) | 26.9374i | 1.08358i | ||||||||
\(619\) | 37.8224 | 1.52021 | 0.760105 | − | 0.649800i | \(-0.225147\pi\) | ||||
0.760105 | + | 0.649800i | \(0.225147\pi\) | |||||||
\(620\) | 97.3708 | − | 22.7523i | 3.91051 | − | 0.913756i | ||||
\(621\) | 3.98220 | 0.159800 | ||||||||
\(622\) | − | 18.0854i | − | 0.725160i | ||||||
\(623\) | − | 9.21337i | − | 0.369126i | ||||||
\(624\) | 11.9208 | 0.477212 | ||||||||
\(625\) | 15.1814 | − | 19.8626i | 0.607256 | − | 0.794506i | ||||
\(626\) | −56.7725 | −2.26908 | ||||||||
\(627\) | − | 5.74934i | − | 0.229607i | ||||||
\(628\) | 46.8664i | 1.87017i | ||||||||
\(629\) | −8.47034 | −0.337735 | ||||||||
\(630\) | −5.48362 | + | 1.28134i | −0.218473 | + | 0.0510498i | ||||
\(631\) | −37.3162 | −1.48554 | −0.742768 | − | 0.669549i | \(-0.766487\pi\) | ||||
−0.742768 | + | 0.669549i | \(0.766487\pi\) | |||||||
\(632\) | − | 79.1156i | − | 3.14705i | ||||||
\(633\) | 6.24626i | 0.248267i | ||||||||
\(634\) | −49.7965 | −1.97767 | ||||||||
\(635\) | 9.30884 | + | 39.8380i | 0.369410 | + | 1.58092i | ||||
\(636\) | 39.8378 | 1.57967 | ||||||||
\(637\) | − | 1.93158i | − | 0.0765322i | ||||||
\(638\) | − | 2.25980i | − | 0.0894664i | ||||||
\(639\) | 5.57815 | 0.220668 | ||||||||
\(640\) | −7.54327 | − | 32.2821i | −0.298174 | − | 1.27606i | ||||
\(641\) | 33.5681 | 1.32586 | 0.662930 | − | 0.748682i | \(-0.269313\pi\) | ||||
0.662930 | + | 0.748682i | \(0.269313\pi\) | |||||||
\(642\) | − | 14.5930i | − | 0.575938i | ||||||
\(643\) | − | 19.3063i | − | 0.761366i | −0.924706 | − | 0.380683i | \(-0.875689\pi\) | ||
0.924706 | − | 0.380683i | \(-0.124311\pi\) | |||||||
\(644\) | −17.2922 | −0.681409 | ||||||||
\(645\) | 8.73458 | − | 2.04098i | 0.343924 | − | 0.0803636i | ||||
\(646\) | −39.6054 | −1.55825 | ||||||||
\(647\) | − | 6.02907i | − | 0.237027i | −0.992952 | − | 0.118514i | \(-0.962187\pi\) | ||
0.992952 | − | 0.118514i | \(-0.0378129\pi\) | |||||||
\(648\) | − | 5.89907i | − | 0.231737i | ||||||
\(649\) | 9.82410 | 0.385630 | ||||||||
\(650\) | −21.8041 | + | 10.7783i | −0.855226 | + | 0.422759i | ||||
\(651\) | 10.2982 | 0.403617 | ||||||||
\(652\) | 22.7482i | 0.890888i | ||||||||
\(653\) | 37.2726i | 1.45859i | 0.684199 | + | 0.729295i | \(0.260152\pi\) | ||||
−0.684199 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(654\) | 25.1024 | 0.981582 | ||||||||
\(655\) | −5.05920 | + | 1.18217i | −0.197679 | + | 0.0461911i | ||||
\(656\) | 48.3764 | 1.88878 | ||||||||
\(657\) | − | 9.45961i | − | 0.369055i | ||||||
\(658\) | 8.61058i | 0.335675i | ||||||||
\(659\) | −5.54093 | −0.215844 | −0.107922 | − | 0.994159i | \(-0.534420\pi\) | ||||
−0.107922 | + | 0.994159i | \(0.534420\pi\) | |||||||
\(660\) | 2.20936 | + | 9.45516i | 0.0859992 | + | 0.368042i | ||||
\(661\) | 34.7511 | 1.35166 | 0.675831 | − | 0.737057i | \(-0.263785\pi\) | ||||
0.675831 | + | 0.737057i | \(0.263785\pi\) | |||||||
\(662\) | 73.7788i | 2.86749i | ||||||||
\(663\) | − | 5.28352i | − | 0.205195i | ||||||
\(664\) | −48.6098 | −1.88643 | ||||||||
\(665\) | 2.92521 | + | 12.5187i | 0.113435 | + | 0.485454i | ||||
\(666\) | −7.79861 | −0.302190 | ||||||||
\(667\) | − | 3.57328i | − | 0.138358i | ||||||
\(668\) | − | 72.8627i | − | 2.81914i | ||||||
\(669\) | −15.6620 | −0.605527 | ||||||||
\(670\) | 31.0376 | − | 7.25246i | 1.19909 | − | 0.280187i | ||||
\(671\) | −1.57645 | −0.0608581 | ||||||||
\(672\) | 3.74421i | 0.144436i | ||||||||
\(673\) | − | 23.0302i | − | 0.887751i | −0.896089 | − | 0.443875i | \(-0.853603\pi\) | ||
0.896089 | − | 0.443875i | \(-0.146397\pi\) | |||||||
\(674\) | −37.1810 | −1.43216 | ||||||||
\(675\) | 2.21569 | + | 4.48227i | 0.0852821 | + | 0.172522i | ||||
\(676\) | −40.2494 | −1.54806 | ||||||||
\(677\) | 13.6076i | 0.522982i | 0.965206 | + | 0.261491i | \(0.0842141\pi\) | ||||
−0.965206 | + | 0.261491i | \(0.915786\pi\) | |||||||
\(678\) | − | 20.3001i | − | 0.779622i | ||||||
\(679\) | 15.8647 | 0.608830 | ||||||||
\(680\) | 35.1345 | − | 8.20978i | 1.34735 | − | 0.314831i | ||||
\(681\) | 12.5488 | 0.480872 | ||||||||
\(682\) | − | 25.9350i | − | 0.993102i | ||||||
\(683\) | 26.8635i | 1.02790i | 0.857819 | + | 0.513951i | \(0.171819\pi\) | ||||
−0.857819 | + | 0.513951i | \(0.828181\pi\) | |||||||
\(684\) | −24.9658 | −0.954592 | ||||||||
\(685\) | 9.48342 | + | 40.5852i | 0.362343 | + | 1.55068i | ||||
\(686\) | 2.51841 | 0.0961533 | ||||||||
\(687\) | 27.4136i | 1.04590i | ||||||||
\(688\) | − | 24.7566i | − | 0.943837i | ||||||
\(689\) | 17.7207 | 0.675106 | ||||||||
\(690\) | 5.10256 | + | 21.8369i | 0.194251 | + | 0.831315i | ||||
\(691\) | −40.9306 | −1.55707 | −0.778537 | − | 0.627598i | \(-0.784038\pi\) | ||||
−0.778537 | + | 0.627598i | \(0.784038\pi\) | |||||||
\(692\) | 7.79973i | 0.296501i | ||||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | −20.5092 | −0.778520 | ||||||||
\(695\) | 15.8372 | − | 3.70063i | 0.600740 | − | 0.140373i | ||||
\(696\) | −5.29331 | −0.200643 | ||||||||
\(697\) | − | 21.4414i | − | 0.812151i | ||||||
\(698\) | 79.6809i | 3.01597i | ||||||||
\(699\) | −13.8607 | −0.524261 | ||||||||
\(700\) | −9.62138 | − | 19.4637i | −0.363654 | − | 0.735659i | ||||
\(701\) | −16.4709 | −0.622096 | −0.311048 | − | 0.950394i | \(-0.600680\pi\) | ||||
−0.311048 | + | 0.950394i | \(0.600680\pi\) | |||||||
\(702\) | − | 4.86452i | − | 0.183599i | ||||||
\(703\) | 17.8037i | 0.671477i | ||||||||
\(704\) | −2.91353 | −0.109808 | ||||||||
\(705\) | 7.44470 | − | 1.73958i | 0.280384 | − | 0.0655164i | ||||
\(706\) | −44.3198 | −1.66800 | ||||||||
\(707\) | − | 17.6934i | − | 0.665430i | ||||||
\(708\) | − | 42.6600i | − | 1.60326i | ||||||
\(709\) | 26.5439 | 0.996878 | 0.498439 | − | 0.866925i | \(-0.333907\pi\) | ||||
0.498439 | + | 0.866925i | \(0.333907\pi\) | |||||||
\(710\) | 7.14751 | + | 30.5884i | 0.268241 | + | 1.14796i | ||||
\(711\) | −13.4115 | −0.502972 | ||||||||
\(712\) | 54.3502i | 2.03686i | ||||||||
\(713\) | − | 41.0094i | − | 1.53581i | ||||||
\(714\) | 6.88868 | 0.257802 | ||||||||
\(715\) | 0.982771 | + | 4.20586i | 0.0367535 | + | 0.157290i | ||||
\(716\) | 36.2632 | 1.35522 | ||||||||
\(717\) | − | 20.8546i | − | 0.778829i | ||||||
\(718\) | − | 54.7878i | − | 2.04466i | ||||||
\(719\) | −29.5195 | −1.10089 | −0.550446 | − | 0.834871i | \(-0.685542\pi\) | ||||
−0.550446 | + | 0.834871i | \(0.685542\pi\) | |||||||
\(720\) | 13.4379 | − | 3.13999i | 0.500801 | − | 0.117021i | ||||
\(721\) | −10.6962 | −0.398347 | ||||||||
\(722\) | 35.3960i | 1.31730i | ||||||||
\(723\) | 16.6597i | 0.619582i | ||||||||
\(724\) | 59.8855 | 2.22563 | ||||||||
\(725\) | 4.02200 | − | 1.98817i | 0.149373 | − | 0.0738389i | ||||
\(726\) | 2.51841 | 0.0934669 | ||||||||
\(727\) | 15.4557i | 0.573222i | 0.958047 | + | 0.286611i | \(0.0925287\pi\) | ||||
−0.958047 | + | 0.286611i | \(0.907471\pi\) | |||||||
\(728\) | 11.3945i | 0.422310i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 51.8729 | − | 12.1210i | 1.91990 | − | 0.448618i | ||||
\(731\) | −10.9726 | −0.405838 | ||||||||
\(732\) | 6.84553i | 0.253018i | ||||||||
\(733\) | 27.1612i | 1.00322i | 0.865093 | + | 0.501611i | \(0.167259\pi\) | ||||
−0.865093 | + | 0.501611i | \(0.832741\pi\) | |||||||
\(734\) | −11.7808 | −0.434836 | ||||||||
\(735\) | −0.508790 | − | 2.17741i | −0.0187670 | − | 0.0803151i | ||||
\(736\) | 14.9102 | 0.549598 | ||||||||
\(737\) | − | 5.66006i | − | 0.208491i | ||||||
\(738\) | − | 19.7410i | − | 0.726677i | ||||||
\(739\) | 28.6245 | 1.05297 | 0.526485 | − | 0.850185i | \(-0.323510\pi\) | ||||
0.526485 | + | 0.850185i | \(0.323510\pi\) | |||||||
\(740\) | −6.84159 | − | 29.2792i | −0.251502 | − | 1.07633i | ||||
\(741\) | −11.1053 | −0.407965 | ||||||||
\(742\) | 23.1044i | 0.848188i | ||||||||
\(743\) | − | 0.730764i | − | 0.0268091i | −0.999910 | − | 0.0134046i | \(-0.995733\pi\) | ||
0.999910 | − | 0.0134046i | \(-0.00426693\pi\) | |||||||
\(744\) | −60.7496 | −2.22719 | ||||||||
\(745\) | −12.0871 | + | 2.82436i | −0.442838 | + | 0.103477i | ||||
\(746\) | −7.56351 | −0.276920 | ||||||||
\(747\) | 8.24025i | 0.301495i | ||||||||
\(748\) | − | 11.8778i | − | 0.434297i | ||||||
\(749\) | 5.79452 | 0.211727 | ||||||||
\(750\) | −21.7400 | + | 17.8933i | −0.793832 | + | 0.653372i | ||||
\(751\) | 29.3236 | 1.07003 | 0.535016 | − | 0.844842i | \(-0.320306\pi\) | ||||
0.535016 | + | 0.844842i | \(0.320306\pi\) | |||||||
\(752\) | − | 21.1007i | − | 0.769463i | ||||||
\(753\) | − | 5.04024i | − | 0.183676i | ||||||
\(754\) | −4.36500 | −0.158964 | ||||||||
\(755\) | 10.7068 | − | 2.50183i | 0.389661 | − | 0.0910510i | ||||
\(756\) | 4.34238 | 0.157931 | ||||||||
\(757\) | − | 40.9665i | − | 1.48895i | −0.667649 | − | 0.744476i | \(-0.732699\pi\) | ||
0.667649 | − | 0.744476i | \(-0.267301\pi\) | |||||||
\(758\) | − | 35.4574i | − | 1.28787i | ||||||
\(759\) | 3.98220 | 0.144545 | ||||||||
\(760\) | −17.2560 | − | 73.8486i | −0.625940 | − | 2.67877i | ||||
\(761\) | 19.2534 | 0.697935 | 0.348967 | − | 0.937135i | \(-0.386532\pi\) | ||||
0.348967 | + | 0.937135i | \(0.386532\pi\) | |||||||
\(762\) | − | 46.0769i | − | 1.66919i | ||||||
\(763\) | 9.96757i | 0.360850i | ||||||||
\(764\) | 75.4241 | 2.72875 | ||||||||
\(765\) | −1.39171 | − | 5.95595i | −0.0503174 | − | 0.215338i | ||||
\(766\) | 7.87983 | 0.284710 | ||||||||
\(767\) | − | 18.9761i | − | 0.685186i | ||||||
\(768\) | 31.5106i | 1.13704i | ||||||||
\(769\) | −18.8886 | −0.681140 | −0.340570 | − | 0.940219i | \(-0.610620\pi\) | ||||
−0.340570 | + | 0.940219i | \(0.610620\pi\) | |||||||
\(770\) | −5.48362 | + | 1.28134i | −0.197616 | + | 0.0461763i | ||||
\(771\) | −22.8836 | −0.824134 | ||||||||
\(772\) | − | 83.2426i | − | 2.99597i | ||||||
\(773\) | − | 39.2200i | − | 1.41065i | −0.708886 | − | 0.705323i | \(-0.750802\pi\) | ||
0.708886 | − | 0.705323i | \(-0.249198\pi\) | |||||||
\(774\) | −10.1025 | −0.363125 | ||||||||
\(775\) | 46.1591 | − | 22.8176i | 1.65808 | − | 0.819632i | ||||
\(776\) | −93.5867 | −3.35957 | ||||||||
\(777\) | − | 3.09664i | − | 0.111091i | ||||||
\(778\) | 16.2864i | 0.583895i | ||||||||
\(779\) | −45.0673 | −1.61470 | ||||||||
\(780\) | 18.2634 | − | 4.26756i | 0.653936 | − | 0.152803i | ||||
\(781\) | 5.57815 | 0.199602 | ||||||||
\(782\) | − | 27.4321i | − | 0.980970i | ||||||
\(783\) | 0.897314i | 0.0320674i | ||||||||
\(784\) | −6.17150 | −0.220411 | ||||||||
\(785\) | 5.49127 | + | 23.5004i | 0.195992 | + | 0.838766i | ||||
\(786\) | 5.85150 | 0.208716 | ||||||||
\(787\) | 6.02795i | 0.214873i | 0.994212 | + | 0.107437i | \(0.0342643\pi\) | ||||
−0.994212 | + | 0.107437i | \(0.965736\pi\) | |||||||
\(788\) | 57.5809i | 2.05124i | ||||||||
\(789\) | −1.94233 | −0.0691487 | ||||||||
\(790\) | −17.1848 | − | 73.5438i | −0.611406 | − | 2.61657i | ||||
\(791\) | 8.06070 | 0.286606 | ||||||||
\(792\) | − | 5.89907i | − | 0.209614i | ||||||
\(793\) | 3.04504i | 0.108133i | ||||||||
\(794\) | 36.8252 | 1.30688 | ||||||||
\(795\) | 19.9760 | − | 4.66774i | 0.708477 | − | 0.165548i | ||||
\(796\) | 50.6891 | 1.79663 | ||||||||
\(797\) | − | 39.3052i | − | 1.39226i | −0.717916 | − | 0.696130i | \(-0.754904\pi\) | ||
0.717916 | − | 0.696130i | \(-0.245096\pi\) | |||||||
\(798\) | − | 14.4792i | − | 0.512558i | ||||||
\(799\) | −9.35226 | −0.330859 | ||||||||
\(800\) | 8.29603 | + | 16.7826i | 0.293309 | + | 0.593353i | ||||
\(801\) | 9.21337 | 0.325538 | ||||||||
\(802\) | 64.8206i | 2.28889i | ||||||||
\(803\) | − | 9.45961i | − | 0.333822i | ||||||
\(804\) | −24.5781 | −0.866803 | ||||||||
\(805\) | −8.67090 | + | 2.02610i | −0.305609 | + | 0.0714108i | ||||
\(806\) | −50.0956 | −1.76454 | ||||||||
\(807\) | − | 18.0770i | − | 0.636340i | ||||||
\(808\) | 104.375i | 3.67189i | ||||||||
\(809\) | −3.75113 | −0.131883 | −0.0659414 | − | 0.997823i | \(-0.521005\pi\) | ||||
−0.0659414 | + | 0.997823i | \(0.521005\pi\) | |||||||
\(810\) | −1.28134 | − | 5.48362i | −0.0450217 | − | 0.192675i | ||||
\(811\) | 19.3790 | 0.680490 | 0.340245 | − | 0.940337i | \(-0.389490\pi\) | ||||
0.340245 | + | 0.940337i | \(0.389490\pi\) | |||||||
\(812\) | − | 3.89648i | − | 0.136740i | ||||||
\(813\) | 0.990072i | 0.0347234i | ||||||||
\(814\) | −7.79861 | −0.273341 | ||||||||
\(815\) | 2.66537 | + | 11.4067i | 0.0933639 | + | 0.399559i | ||||
\(816\) | −16.8811 | −0.590956 | ||||||||
\(817\) | 23.0632i | 0.806878i | ||||||||
\(818\) | 25.3030i | 0.884698i | ||||||||
\(819\) | 1.93158 | 0.0674950 | ||||||||
\(820\) | 74.1160 | − | 17.3185i | 2.58824 | − | 0.604787i | ||||
\(821\) | 36.8702 | 1.28678 | 0.643390 | − | 0.765539i | \(-0.277528\pi\) | ||||
0.643390 | + | 0.765539i | \(0.277528\pi\) | |||||||
\(822\) | − | 46.9410i | − | 1.63726i | ||||||
\(823\) | − | 44.2773i | − | 1.54341i | −0.635981 | − | 0.771705i | \(-0.719404\pi\) | ||
0.635981 | − | 0.771705i | \(-0.280596\pi\) | |||||||
\(824\) | 63.0976 | 2.19811 | ||||||||
\(825\) | 2.21569 | + | 4.48227i | 0.0771405 | + | 0.156052i | ||||
\(826\) | 24.7411 | 0.860852 | ||||||||
\(827\) | − | 44.5865i | − | 1.55042i | −0.631701 | − | 0.775212i | \(-0.717643\pi\) | ||
0.631701 | − | 0.775212i | \(-0.282357\pi\) | |||||||
\(828\) | − | 17.2922i | − | 0.600946i | ||||||
\(829\) | −45.3494 | −1.57505 | −0.787525 | − | 0.616283i | \(-0.788638\pi\) | ||||
−0.787525 | + | 0.616283i | \(0.788638\pi\) | |||||||
\(830\) | −45.1864 | + | 10.5586i | −1.56844 | + | 0.366493i | ||||
\(831\) | −21.6115 | −0.749695 | ||||||||
\(832\) | 5.62774i | 0.195107i | ||||||||
\(833\) | 2.73533i | 0.0947736i | ||||||||
\(834\) | −18.3174 | −0.634280 | ||||||||
\(835\) | −8.53721 | − | 36.5358i | −0.295442 | − | 1.26437i | ||||
\(836\) | −24.9658 | −0.863461 | ||||||||
\(837\) | 10.2982i | 0.355957i | ||||||||
\(838\) | 17.0208i | 0.587975i | ||||||||
\(839\) | −45.3592 | −1.56597 | −0.782987 | − | 0.622038i | \(-0.786305\pi\) | ||||
−0.782987 | + | 0.622038i | \(0.786305\pi\) | |||||||
\(840\) | 3.00139 | + | 12.8447i | 0.103558 | + | 0.443185i | ||||
\(841\) | −28.1948 | −0.972235 | ||||||||
\(842\) | 5.89202i | 0.203052i | ||||||||
\(843\) | 1.05458i | 0.0363218i | ||||||||
\(844\) | 27.1236 | 0.933634 | ||||||||
\(845\) | −20.1824 | + | 4.71596i | −0.694296 | + | 0.162234i | ||||
\(846\) | −8.61058 | −0.296038 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | − | 56.6185i | − | 1.94429i | ||||||
\(849\) | −15.5919 | −0.535113 | ||||||||
\(850\) | 30.8769 | − | 15.2632i | 1.05907 | − | 0.523524i | ||||
\(851\) | −12.3315 | −0.422717 | ||||||||
\(852\) | − | 24.2224i | − | 0.829847i | ||||||
\(853\) | 29.1110i | 0.996740i | 0.866964 | + | 0.498370i | \(0.166068\pi\) | ||||
−0.866964 | + | 0.498370i | \(0.833932\pi\) | |||||||
\(854\) | −3.97014 | −0.135855 | ||||||||
\(855\) | −12.5187 | + | 2.92521i | −0.428130 | + | 0.100040i | ||||
\(856\) | −34.1822 | −1.16832 | ||||||||
\(857\) | 0.199601i | 0.00681824i | 0.999994 | + | 0.00340912i | \(0.00108516\pi\) | ||||
−0.999994 | + | 0.00340912i | \(0.998915\pi\) | |||||||
\(858\) | − | 4.86452i | − | 0.166072i | ||||||
\(859\) | −4.79202 | −0.163502 | −0.0817509 | − | 0.996653i | \(-0.526051\pi\) | ||||
−0.0817509 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(860\) | −8.86272 | − | 37.9289i | −0.302216 | − | 1.29336i | ||||
\(861\) | 7.83869 | 0.267142 | ||||||||
\(862\) | 33.1097i | 1.12772i | ||||||||
\(863\) | 34.8190i | 1.18525i | 0.805478 | + | 0.592626i | \(0.201909\pi\) | ||||
−0.805478 | + | 0.592626i | \(0.798091\pi\) | |||||||
\(864\) | −3.74421 | −0.127381 | ||||||||
\(865\) | 0.913882 | + | 3.91104i | 0.0310729 | + | 0.132979i | ||||
\(866\) | −69.2413 | −2.35292 | ||||||||
\(867\) | − | 9.51796i | − | 0.323247i | ||||||
\(868\) | − | 44.7185i | − | 1.51785i | ||||||
\(869\) | −13.4115 | −0.454955 | ||||||||
\(870\) | −4.92053 | + | 1.14976i | −0.166821 | + | 0.0389807i | ||||
\(871\) | −10.9329 | −0.370446 | ||||||||
\(872\) | − | 58.7994i | − | 1.99120i | ||||||
\(873\) | 15.8647i | 0.536937i | ||||||||
\(874\) | −57.6590 | −1.95035 | ||||||||
\(875\) | −7.10501 | − | 8.63243i | −0.240193 | − | 0.291829i | ||||
\(876\) | −41.0772 | −1.38787 | ||||||||
\(877\) | 21.1956i | 0.715725i | 0.933774 | + | 0.357863i | \(0.116494\pi\) | ||||
−0.933774 | + | 0.357863i | \(0.883506\pi\) | |||||||
\(878\) | − | 82.1381i | − | 2.77203i | ||||||
\(879\) | −28.2397 | −0.952502 | ||||||||
\(880\) | 13.4379 | − | 3.13999i | 0.452992 | − | 0.105849i | ||||
\(881\) | −46.8565 | −1.57864 | −0.789318 | − | 0.613984i | \(-0.789566\pi\) | ||||
−0.789318 | + | 0.613984i | \(0.789566\pi\) | |||||||
\(882\) | 2.51841i | 0.0847992i | ||||||||
\(883\) | 5.15615i | 0.173518i | 0.996229 | + | 0.0867591i | \(0.0276511\pi\) | ||||
−0.996229 | + | 0.0867591i | \(0.972349\pi\) | |||||||
\(884\) | −22.9431 | −0.771659 | ||||||||
\(885\) | −4.99840 | − | 21.3911i | −0.168019 | − | 0.719055i | ||||
\(886\) | −54.0235 | −1.81495 | ||||||||
\(887\) | − | 32.1671i | − | 1.08007i | −0.841644 | − | 0.540033i | \(-0.818412\pi\) | ||
0.841644 | − | 0.540033i | \(-0.181588\pi\) | |||||||
\(888\) | 18.2673i | 0.613010i | ||||||||
\(889\) | 18.2960 | 0.613629 | ||||||||
\(890\) | 11.8055 | + | 50.5226i | 0.395720 | + | 1.69352i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 68.0102i | 2.27715i | ||||||||
\(893\) | 19.6573i | 0.657807i | ||||||||
\(894\) | 13.9800 | 0.467562 | ||||||||
\(895\) | 18.1836 | − | 4.24891i | 0.607811 | − | 0.142025i | ||||
\(896\) | −14.8259 | −0.495298 | ||||||||
\(897\) | − | 7.69196i | − | 0.256827i | ||||||
\(898\) | − | 91.2714i | − | 3.04577i | ||||||
\(899\) | 9.24069 | 0.308194 | ||||||||
\(900\) | 19.4637 | − | 9.62138i | 0.648790 | − | 0.320713i | ||||
\(901\) | −25.0945 | −0.836018 | ||||||||
\(902\) | − | 19.7410i | − | 0.657304i | ||||||
\(903\) | − | 4.01145i | − | 0.133493i | ||||||
\(904\) | −47.5506 | −1.58151 | ||||||||
\(905\) | 30.0286 | − | 7.01669i | 0.998184 | − | 0.233243i | ||||
\(906\) | −12.3836 | −0.411417 | ||||||||
\(907\) | − | 1.43291i | − | 0.0475791i | −0.999717 | − | 0.0237896i | \(-0.992427\pi\) | ||
0.999717 | − | 0.0237896i | \(-0.00757317\pi\) | |||||||
\(908\) | − | 54.4918i | − | 1.80837i | ||||||
\(909\) | 17.6934 | 0.586854 | ||||||||
\(910\) | 2.47502 | + | 10.5921i | 0.0820460 | + | 0.351124i | ||||
\(911\) | −32.8612 | −1.08874 | −0.544371 | − | 0.838845i | \(-0.683231\pi\) | ||||
−0.544371 | + | 0.838845i | \(0.683231\pi\) | |||||||
\(912\) | 35.4820i | 1.17493i | ||||||||
\(913\) | 8.24025i | 0.272713i | ||||||||
\(914\) | 40.1214 | 1.32710 | ||||||||
\(915\) | 0.802081 | + | 3.43258i | 0.0265160 | + | 0.113478i | ||||
\(916\) | 119.040 | 3.93321 | ||||||||
\(917\) | 2.32349i | 0.0767284i | ||||||||
\(918\) | 6.88868i | 0.227360i | ||||||||
\(919\) | 8.11060 | 0.267544 | 0.133772 | − | 0.991012i | \(-0.457291\pi\) | ||||
0.133772 | + | 0.991012i | \(0.457291\pi\) | |||||||
\(920\) | 51.1502 | − | 11.9521i | 1.68637 | − | 0.394050i | ||||
\(921\) | 7.96272 | 0.262380 | ||||||||
\(922\) | 89.9721i | 2.96307i | ||||||||
\(923\) | − | 10.7747i | − | 0.354653i | ||||||
\(924\) | 4.34238 | 0.142854 | ||||||||
\(925\) | −6.86121 | − | 13.8800i | −0.225595 | − | 0.456371i | ||||
\(926\) | 74.2954 | 2.44150 | ||||||||
\(927\) | − | 10.6962i | − | 0.351309i | ||||||
\(928\) | 3.35973i | 0.110289i | ||||||||
\(929\) | 32.0625 | 1.05194 | 0.525968 | − | 0.850505i | \(-0.323703\pi\) | ||||
0.525968 | + | 0.850505i | \(0.323703\pi\) | |||||||
\(930\) | −56.4712 | + | 13.1955i | −1.85176 | + | 0.432696i | ||||
\(931\) | 5.74934 | 0.188427 | ||||||||
\(932\) | 60.1885i | 1.97154i | ||||||||
\(933\) | 7.18130i | 0.235105i | ||||||||
\(934\) | 47.7890 | 1.56370 | ||||||||
\(935\) | −1.39171 | − | 5.95595i | −0.0455138 | − | 0.194780i | ||||
\(936\) | −11.3945 | −0.372442 | ||||||||
\(937\) | − | 10.5934i | − | 0.346072i | −0.984915 | − | 0.173036i | \(-0.944642\pi\) | ||
0.984915 | − | 0.173036i | \(-0.0553578\pi\) | |||||||
\(938\) | − | 14.2543i | − | 0.465421i | ||||||
\(939\) | 22.5430 | 0.735663 | ||||||||
\(940\) | −7.55392 | − | 32.3277i | −0.246382 | − | 1.05441i | ||||
\(941\) | 30.9354 | 1.00846 | 0.504232 | − | 0.863568i | \(-0.331776\pi\) | ||||
0.504232 | + | 0.863568i | \(0.331776\pi\) | |||||||
\(942\) | − | 27.1807i | − | 0.885595i | ||||||
\(943\) | − | 31.2152i | − | 1.01651i | ||||||
\(944\) | −60.6294 | −1.97332 | ||||||||
\(945\) | 2.17741 | − | 0.508790i | 0.0708313 | − | 0.0165509i | ||||
\(946\) | −10.1025 | −0.328459 | ||||||||
\(947\) | − | 57.8119i | − | 1.87863i | −0.343051 | − | 0.939317i | \(-0.611460\pi\) | ||
0.343051 | − | 0.939317i | \(-0.388540\pi\) | |||||||
\(948\) | 58.2380i | 1.89148i | ||||||||
\(949\) | −18.2720 | −0.593135 | ||||||||
\(950\) | −32.0814 | − | 64.8996i | −1.04086 | − | 2.10562i | ||||
\(951\) | 19.7730 | 0.641184 | ||||||||
\(952\) | − | 16.1359i | − | 0.522968i | ||||||
\(953\) | − | 8.67683i | − | 0.281070i | −0.990076 | − | 0.140535i | \(-0.955118\pi\) | ||
0.990076 | − | 0.140535i | \(-0.0448823\pi\) | |||||||
\(954\) | −23.1044 | −0.748032 | ||||||||
\(955\) | 37.8202 | − | 8.83732i | 1.22383 | − | 0.285969i | ||||
\(956\) | −90.5585 | −2.92887 | ||||||||
\(957\) | 0.897314i | 0.0290060i | ||||||||
\(958\) | − | 28.2238i | − | 0.911870i | ||||||
\(959\) | 18.6392 | 0.601890 | ||||||||
\(960\) | 1.48238 | + | 6.34397i | 0.0478435 | + | 0.204751i | ||||
\(961\) | 75.0522 | 2.42104 | ||||||||
\(962\) | 15.0637i | 0.485672i | ||||||||
\(963\) | 5.79452i | 0.186726i | ||||||||
\(964\) | 72.3429 | 2.33001 | ||||||||
\(965\) | −9.75341 | − | 41.7407i | −0.313974 | − | 1.34368i | ||||
\(966\) | 10.0288 | 0.322672 | ||||||||
\(967\) | − | 45.1612i | − | 1.45229i | −0.687544 | − | 0.726143i | \(-0.741311\pi\) | ||
0.687544 | − | 0.726143i | \(-0.258689\pi\) | |||||||
\(968\) | − | 5.89907i | − | 0.189603i | ||||||
\(969\) | 15.7264 | 0.505203 | ||||||||
\(970\) | −86.9957 | + | 20.3280i | −2.79326 | + | 0.652694i | ||||
\(971\) | −2.33588 | −0.0749619 | −0.0374809 | − | 0.999297i | \(-0.511933\pi\) | ||||
−0.0374809 | + | 0.999297i | \(0.511933\pi\) | |||||||
\(972\) | 4.34238i | 0.139282i | ||||||||
\(973\) | − | 7.27340i | − | 0.233175i | ||||||
\(974\) | −32.2821 | −1.03438 | ||||||||
\(975\) | 8.65787 | − | 4.27980i | 0.277274 | − | 0.137063i | ||||
\(976\) | 9.72904 | 0.311419 | ||||||||
\(977\) | 17.7364i | 0.567437i | 0.958908 | + | 0.283719i | \(0.0915681\pi\) | ||||
−0.958908 | + | 0.283719i | \(0.908432\pi\) | |||||||
\(978\) | − | 13.1930i | − | 0.421867i | ||||||
\(979\) | 9.21337 | 0.294460 | ||||||||
\(980\) | −9.45516 | + | 2.20936i | −0.302034 | + | 0.0705754i | ||||
\(981\) | −9.96757 | −0.318240 | ||||||||
\(982\) | − | 44.2425i | − | 1.41183i | ||||||
\(983\) | 23.0645i | 0.735642i | 0.929897 | + | 0.367821i | \(0.119896\pi\) | ||||
−0.929897 | + | 0.367821i | \(0.880104\pi\) | |||||||
\(984\) | −46.2409 | −1.47411 | ||||||||
\(985\) | 6.74667 | + | 28.8730i | 0.214967 | + | 0.919971i | ||||
\(986\) | 6.18131 | 0.196853 | ||||||||
\(987\) | − | 3.41906i | − | 0.108830i | ||||||
\(988\) | 48.2236i | 1.53420i | ||||||||
\(989\) | −15.9744 | −0.507956 | ||||||||
\(990\) | −1.28134 | − | 5.48362i | −0.0407237 | − | 0.174281i | ||||
\(991\) | 0.575473 | 0.0182805 | 0.00914025 | − | 0.999958i | \(-0.497091\pi\) | ||||
0.00914025 | + | 0.999958i | \(0.497091\pi\) | |||||||
\(992\) | 38.5585i | 1.22423i | ||||||||
\(993\) | − | 29.2958i | − | 0.929674i | ||||||
\(994\) | 14.0481 | 0.445577 | ||||||||
\(995\) | 25.4172 | − | 5.93917i | 0.805780 | − | 0.188284i | ||||
\(996\) | 35.7823 | 1.13381 | ||||||||
\(997\) | − | 52.5486i | − | 1.66423i | −0.554602 | − | 0.832116i | \(-0.687129\pi\) | ||
0.554602 | − | 0.832116i | \(-0.312871\pi\) | |||||||
\(998\) | − | 74.9858i | − | 2.37363i | ||||||
\(999\) | 3.09664 | 0.0979734 |
(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 | 1155.2.c.e.694.19 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.cm.1.2 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cp.1.9 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.e.694.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.e.694.2 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.e.694.19 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cm.1.2 | 10 | 5.2 | odd | 4 | |||
5775.2.a.cp.1.9 | 10 | 5.3 | odd | 4 |