Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(319,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.703 |
Dual form | 768.3.l.b.319.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.73205 | + | 2.73205i | −0.546410 | + | 0.546410i | −0.925401 | − | 0.378990i | \(-0.876271\pi\) |
0.378990 | + | 0.925401i | \(0.376271\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.17209 | −0.310298 | −0.155149 | − | 0.987891i | \(-0.549586\pi\) | ||||
−0.155149 | + | 0.987891i | \(0.549586\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.277401 | − | 0.277401i | −0.0252183 | − | 0.0252183i | 0.694385 | − | 0.719604i | \(-0.255676\pi\) |
−0.719604 | + | 0.694385i | \(0.755676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.3923 | + | 13.3923i | 1.03018 | + | 1.03018i | 0.999530 | + | 0.0306470i | \(0.00975678\pi\) |
0.0306470 | + | 0.999530i | \(0.490243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.69213i | − | 0.446142i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −26.3923 | −1.55249 | −0.776244 | − | 0.630432i | \(-0.782878\pi\) | ||||
−0.776244 | + | 0.630432i | \(0.782878\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.17209 | + | 2.17209i | −0.114320 | + | 0.114320i | −0.761953 | − | 0.647632i | \(-0.775759\pi\) |
0.647632 | + | 0.761953i | \(0.275759\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.66025 | − | 2.66025i | 0.126679 | − | 0.126679i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.52433 | −0.327145 | −0.163572 | − | 0.986531i | \(-0.552302\pi\) | ||||
−0.163572 | + | 0.986531i | \(0.552302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0718i | 0.402872i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.19615 | + | 6.19615i | 0.213660 | + | 0.213660i | 0.805820 | − | 0.592160i | \(-0.201725\pi\) |
−0.592160 | + | 0.805820i | \(0.701725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 28.7375i | − | 0.927017i | −0.886092 | − | 0.463509i | \(-0.846590\pi\) | ||
0.886092 | − | 0.463509i | \(-0.153410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.679492 | 0.0205907 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.93426 | − | 5.93426i | 0.169550 | − | 0.169550i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.07180 | + | 4.07180i | −0.110049 | + | 0.110049i | −0.759987 | − | 0.649938i | \(-0.774795\pi\) |
0.649938 | + | 0.759987i | \(0.274795\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.8043 | −0.841136 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 23.1769i | − | 0.565291i | −0.959224 | − | 0.282645i | \(-0.908788\pi\) | ||
0.959224 | − | 0.282645i | \(-0.0912119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −49.0913 | − | 49.0913i | −1.14166 | − | 1.14166i | −0.988147 | − | 0.153512i | \(-0.950942\pi\) |
−0.153512 | − | 0.988147i | \(-0.549058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.19615 | + | 8.19615i | 0.182137 | + | 0.182137i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 90.4553i | − | 1.92458i | −0.272026 | − | 0.962290i | \(-0.587694\pi\) | ||
0.272026 | − | 0.962290i | \(-0.412306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.2820 | −0.903715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 32.3238 | − | 32.3238i | 0.633801 | − | 0.633801i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.5167 | − | 37.5167i | 0.707862 | − | 0.707862i | −0.258224 | − | 0.966085i | \(-0.583137\pi\) |
0.966085 | + | 0.258224i | \(0.0831371\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.51575 | 0.0275591 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.32051i | − | 0.0933422i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44.8487 | − | 44.8487i | −0.760147 | − | 0.760147i | 0.216201 | − | 0.976349i | \(-0.430633\pi\) |
−0.976349 | + | 0.216201i | \(0.930633\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.4974 | + | 57.4974i | 0.942581 | + | 0.942581i | 0.998439 | − | 0.0558580i | \(-0.0177894\pi\) |
−0.0558580 | + | 0.998439i | \(0.517789\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.51626i | 0.103433i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −73.1769 | −1.12580 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 57.8812 | − | 57.8812i | 0.863899 | − | 0.863899i | −0.127890 | − | 0.991788i | \(-0.540820\pi\) |
0.991788 | + | 0.127890i | \(0.0408203\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.21539 | − | 9.21539i | 0.133556 | − | 0.133556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46.5675 | 0.655880 | 0.327940 | − | 0.944698i | \(-0.393646\pi\) | ||||
0.327940 | + | 0.944698i | \(0.393646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.43078i | − | 0.0332984i | −0.999861 | − | 0.0166492i | \(-0.994700\pi\) | ||
0.999861 | − | 0.0166492i | \(-0.00529984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.3354 | − | 12.3354i | −0.164472 | − | 0.164472i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.602540 | + | 0.602540i | 0.00782520 | + | 0.00782520i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.76594i | − | 0.0223537i | −0.999938 | − | 0.0111769i | \(-0.996442\pi\) | ||
0.999938 | − | 0.0111769i | \(-0.00355778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −58.5648 | + | 58.5648i | −0.705600 | + | 0.705600i | −0.965607 | − | 0.260007i | \(-0.916275\pi\) |
0.260007 | + | 0.965607i | \(0.416275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.1051 | − | 72.1051i | 0.848296 | − | 0.848296i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.1774 | −0.174453 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 126.785i | − | 1.42455i | −0.701902 | − | 0.712273i | \(-0.747666\pi\) | ||
0.701902 | − | 0.712273i | \(-0.252334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.0893 | − | 29.0893i | −0.319662 | − | 0.319662i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 35.1962 | + | 35.1962i | 0.378453 | + | 0.378453i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 11.8685i | − | 0.124932i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 46.9282 | 0.483796 | 0.241898 | − | 0.970302i | \(-0.422230\pi\) | ||||
0.241898 | + | 0.970302i | \(0.422230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.832204 | + | 0.832204i | −0.00840610 | + | 0.00840610i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −66.8756 | + | 66.8756i | −0.662135 | + | 0.662135i | −0.955883 | − | 0.293748i | \(-0.905097\pi\) |
0.293748 | + | 0.955883i | \(0.405097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −166.518 | −1.61668 | −0.808341 | − | 0.588715i | \(-0.799634\pi\) | ||||
−0.808341 | + | 0.588715i | \(0.799634\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.5359i | 0.138437i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −129.350 | − | 129.350i | −1.20888 | − | 1.20888i | −0.971391 | − | 0.237485i | \(-0.923677\pi\) |
−0.237485 | − | 0.971391i | \(-0.576323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 98.3205 | + | 98.3205i | 0.902023 | + | 0.902023i | 0.995611 | − | 0.0935880i | \(-0.0298336\pi\) |
−0.0935880 | + | 0.995611i | \(0.529834\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.97382i | − | 0.0898543i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −211.990 | −1.87601 | −0.938007 | − | 0.346615i | \(-0.887331\pi\) | ||||
−0.938007 | + | 0.346615i | \(0.887331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.5569 | − | 20.5569i | 0.178755 | − | 0.178755i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40.1769 | − | 40.1769i | 0.343392 | − | 0.343392i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 57.3264 | 0.481735 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 120.846i | − | 0.998728i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.3858 | + | 28.3858i | 0.230779 | + | 0.230779i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −95.8179 | − | 95.8179i | −0.766543 | − | 0.766543i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 32.0664i | − | 0.252491i | −0.991999 | − | 0.126245i | \(-0.959707\pi\) | ||
0.991999 | − | 0.126245i | \(-0.0402927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 120.249 | 0.932161 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −30.0031 | + | 30.0031i | −0.229031 | + | 0.229031i | −0.812288 | − | 0.583257i | \(-0.801778\pi\) |
0.583257 | + | 0.812288i | \(0.301778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.71797 | − | 4.71797i | 0.0354734 | − | 0.0354734i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20.0764 | −0.148714 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 97.5307i | 0.711903i | 0.934504 | + | 0.355952i | \(0.115843\pi\) | ||||
−0.934504 | + | 0.355952i | \(0.884157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 151.720 | + | 151.720i | 1.09151 | + | 1.09151i | 0.995368 | + | 0.0961409i | \(0.0306500\pi\) |
0.0961409 | + | 0.995368i | \(0.469350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 110.785 | + | 110.785i | 0.785706 | + | 0.785706i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7.43009i | − | 0.0519587i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8564 | −0.233492 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.2342 | − | 54.2342i | 0.368940 | − | 0.368940i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −61.9474 | + | 61.9474i | −0.415755 | + | 0.415755i | −0.883738 | − | 0.467983i | \(-0.844981\pi\) |
0.467983 | + | 0.883738i | \(0.344981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 47.7242 | 0.316055 | 0.158027 | − | 0.987435i | \(-0.449487\pi\) | ||||
0.158027 | + | 0.987435i | \(0.449487\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 79.1769i | 0.517496i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 78.5124 | + | 78.5124i | 0.506532 | + | 0.506532i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −167.851 | − | 167.851i | −1.06912 | − | 1.06912i | −0.997427 | − | 0.0716892i | \(-0.977161\pi\) |
−0.0716892 | − | 0.997427i | \(-0.522839\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 91.8967i | 0.577967i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3435 | 0.101513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 38.8872 | − | 38.8872i | 0.238572 | − | 0.238572i | −0.577687 | − | 0.816259i | \(-0.696044\pi\) |
0.816259 | + | 0.577687i | \(0.196044\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.85641 | + | 1.85641i | −0.0112509 | + | 0.0112509i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 239.658 | 1.43508 | 0.717540 | − | 0.696517i | \(-0.245268\pi\) | ||||
0.717540 | + | 0.696517i | \(0.245268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 189.708i | 1.12253i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.51626 | + | 6.51626i | 0.0381068 | + | 0.0381068i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −55.3064 | − | 55.3064i | −0.319690 | − | 0.319690i | 0.528958 | − | 0.848648i | \(-0.322583\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 21.8768i | − | 0.125010i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 109.856 | 0.620658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −183.793 | + | 183.793i | −1.02678 | + | 1.02678i | −0.0271470 | + | 0.999631i | \(0.508642\pi\) |
−0.999631 | + | 0.0271470i | \(0.991358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1821 | + | 15.1821i | −0.0838788 | + | 0.0838788i | −0.747801 | − | 0.663923i | \(-0.768890\pi\) |
0.663923 | + | 0.747801i | \(0.268890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −140.839 | −0.769614 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 22.2487i | − | 0.120263i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.32126 | + | 7.32126i | 0.0391511 | + | 0.0391511i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.98076 | − | 7.98076i | −0.0422263 | − | 0.0422263i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 198.545i | − | 1.03950i | −0.854318 | − | 0.519751i | \(-0.826025\pi\) | ||
0.854318 | − | 0.519751i | \(-0.173975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 244.851 | 1.26866 | 0.634330 | − | 0.773063i | \(-0.281276\pi\) | ||||
0.634330 | + | 0.773063i | \(0.281276\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 89.6231 | − | 89.6231i | 0.459605 | − | 0.459605i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −91.5833 | + | 91.5833i | −0.464890 | + | 0.464890i | −0.900254 | − | 0.435364i | \(-0.856620\pi\) |
0.435364 | + | 0.900254i | \(0.356620\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −196.630 | −0.988091 | −0.494045 | − | 0.869436i | \(-0.664482\pi\) | ||||
−0.494045 | + | 0.869436i | \(0.664482\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 141.779i | 0.705370i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.4586 | − | 13.4586i | −0.0662985 | − | 0.0662985i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 63.3205 | + | 63.3205i | 0.308881 | + | 0.308881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.5730i | 0.109048i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.20508 | 0.00576594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 80.2113 | − | 80.2113i | 0.380148 | − | 0.380148i | −0.491007 | − | 0.871156i | \(-0.663371\pi\) |
0.871156 | + | 0.491007i | \(0.163371\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −57.0333 | + | 57.0333i | −0.267762 | + | 0.267762i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 268.240 | 1.24763 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 62.4205i | 0.287652i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.97709 | + | 2.97709i | 0.0135940 | + | 0.0135940i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −353.454 | − | 353.454i | −1.59934 | − | 1.59934i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 344.194i | 1.54347i | 0.635943 | + | 0.771736i | \(0.280611\pi\) | ||||
−0.635943 | + | 0.771736i | \(0.719389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 30.2154 | 0.134291 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −286.395 | + | 286.395i | −1.26165 | + | 1.26165i | −0.311357 | + | 0.950293i | \(0.600783\pi\) |
−0.950293 | + | 0.311357i | \(0.899217\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −122.244 | + | 122.244i | −0.533815 | + | 0.533815i | −0.921705 | − | 0.387891i | \(-0.873204\pi\) |
0.387891 | + | 0.921705i | \(0.373204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.47592 | −0.00638925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 67.7795i | 0.290899i | 0.989366 | + | 0.145449i | \(0.0464628\pi\) | ||||
−0.989366 | + | 0.145449i | \(0.953537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 247.128 | + | 247.128i | 1.05161 | + | 1.05161i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.16283 | + | 2.16283i | 0.00912587 | + | 0.00912587i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 309.760i | 1.29607i | 0.761612 | + | 0.648033i | \(0.224408\pi\) | ||||
−0.761612 | + | 0.648033i | \(0.775592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 262.497 | 1.08920 | 0.544600 | − | 0.838696i | \(-0.316681\pi\) | ||||
0.544600 | + | 0.838696i | \(0.316681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 120.981 | − | 120.981i | 0.493799 | − | 0.493799i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −58.1785 | −0.235541 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 143.454i | − | 0.576120i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 222.044 | + | 222.044i | 0.884638 | + | 0.884638i | 0.994002 | − | 0.109364i | \(-0.0348813\pi\) |
−0.109364 | + | 0.994002i | \(0.534881\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.08726 | + | 2.08726i | 0.00825004 | + | 0.00825004i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 176.621i | 0.692630i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −73.0821 | −0.284366 | −0.142183 | − | 0.989840i | \(-0.545412\pi\) | ||||
−0.142183 | + | 0.989840i | \(0.545412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.84430 | − | 8.84430i | 0.0341479 | − | 0.0341479i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.5885 | − | 18.5885i | 0.0712201 | − | 0.0712201i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 362.039 | 1.37657 | 0.688286 | − | 0.725439i | \(-0.258363\pi\) | ||||
0.688286 | + | 0.725439i | \(0.258363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 204.995i | 0.773565i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 155.279 | + | 155.279i | 0.581569 | + | 0.581569i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −118.119 | − | 118.119i | −0.439105 | − | 0.439105i | 0.452606 | − | 0.891711i | \(-0.350494\pi\) |
−0.891711 | + | 0.452606i | \(0.850494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 333.598i | 1.23099i | 0.788141 | + | 0.615495i | \(0.211044\pi\) | ||||
−0.788141 | + | 0.615495i | \(0.788956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 71.2539 | 0.261003 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.79393 | − | 2.79393i | 0.0101597 | − | 0.0101597i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 161.172 | − | 161.172i | 0.581848 | − | 0.581848i | −0.353563 | − | 0.935411i | \(-0.615030\pi\) |
0.935411 | + | 0.353563i | \(0.115030\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −86.2126 | −0.309006 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 453.482i | − | 1.61381i | −0.590678 | − | 0.806907i | \(-0.701140\pi\) | ||
0.590678 | − | 0.806907i | \(-0.298860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −72.4839 | − | 72.4839i | −0.256127 | − | 0.256127i | 0.567350 | − | 0.823477i | \(-0.307969\pi\) |
−0.823477 | + | 0.567350i | \(0.807969\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.5359 | + | 14.5359i | 0.0510032 | + | 0.0510032i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 50.3423i | 0.175409i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 407.554 | 1.41022 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −57.4751 | + | 57.4751i | −0.197509 | + | 0.197509i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −328.291 | + | 328.291i | −1.12045 | + | 1.12045i | −0.128773 | + | 0.991674i | \(0.541104\pi\) |
−0.991674 | + | 0.128773i | \(0.958896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 245.058 | 0.830704 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.03848i | − | 0.00686355i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −100.768 | − | 100.768i | −0.337017 | − | 0.337017i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 106.631 | + | 106.631i | 0.354255 | + | 0.354255i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 163.811i | − | 0.540631i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −314.172 | −1.03007 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −138.593 | + | 138.593i | −0.451443 | + | 0.451443i | −0.895833 | − | 0.444390i | \(-0.853420\pi\) |
0.444390 | + | 0.895833i | \(0.353420\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 203.942 | − | 203.942i | 0.660007 | − | 0.660007i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −312.534 | −1.00493 | −0.502466 | − | 0.864597i | \(-0.667574\pi\) | ||||
−0.502466 | + | 0.864597i | \(0.667574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 275.282i | − | 0.879495i | −0.898121 | − | 0.439748i | \(-0.855068\pi\) | ||
0.898121 | − | 0.439748i | \(-0.144932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.8028 | − | 17.8028i | −0.0565167 | − | 0.0565167i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −260.263 | − | 260.263i | −0.821018 | − | 0.821018i | 0.165236 | − | 0.986254i | \(-0.447161\pi\) |
−0.986254 | + | 0.165236i | \(0.947161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.43764i | − | 0.0107763i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 316.841 | 0.987043 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 57.3264 | − | 57.3264i | 0.177481 | − | 0.177481i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −134.885 | + | 134.885i | −0.415029 | + | 0.415029i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −240.835 | −0.736499 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 196.477i | 0.597194i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −105.761 | − | 105.761i | −0.319521 | − | 0.319521i | 0.529062 | − | 0.848583i | \(-0.322544\pi\) |
−0.848583 | + | 0.529062i | \(0.822544\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.2154 | + | 12.2154i | 0.0366829 | + | 0.0366829i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 316.269i | 0.944086i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −138.851 | −0.412022 | −0.206011 | − | 0.978550i | \(-0.566048\pi\) | ||||
−0.206011 | + | 0.978550i | \(0.566048\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 259.633 | − | 259.633i | 0.765880 | − | 0.765880i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.97183 | + | 7.97183i | −0.0233778 | + | 0.0233778i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 202.617 | 0.590720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 50.3538i | 0.145953i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −83.0052 | − | 83.0052i | −0.239208 | − | 0.239208i | 0.577314 | − | 0.816522i | \(-0.304101\pi\) |
−0.816522 | + | 0.577314i | \(0.804101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −176.138 | − | 176.138i | −0.504695 | − | 0.504695i | 0.408199 | − | 0.912893i | \(-0.366157\pi\) |
−0.912893 | + | 0.408199i | \(0.866157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 98.4129i | 0.280379i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 378.785 | 1.07304 | 0.536522 | − | 0.843886i | \(-0.319738\pi\) | ||||
0.536522 | + | 0.843886i | \(0.319738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −127.225 | + | 127.225i | −0.358380 | + | 0.358380i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −70.2102 | + | 70.2102i | −0.196667 | + | 0.196667i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 70.3045 | 0.195834 | 0.0979172 | − | 0.995195i | \(-0.468782\pi\) | ||||
0.0979172 | + | 0.995195i | \(0.468782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 351.564i | 0.973862i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 148.006 | + | 148.006i | 0.407729 | + | 0.407729i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.64102 | + | 6.64102i | 0.0181946 | + | 0.0181946i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 83.8846i | − | 0.228568i | −0.993448 | − | 0.114284i | \(-0.963543\pi\) | ||
0.993448 | − | 0.114284i | \(-0.0364574\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −69.5307 | −0.188430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −81.4895 | + | 81.4895i | −0.219648 | + | 0.219648i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 144.646 | − | 144.646i | 0.387791 | − | 0.387791i | −0.486108 | − | 0.873899i | \(-0.661584\pi\) |
0.873899 | + | 0.486108i | \(0.161584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 234.705 | 0.625880 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 165.962i | 0.440216i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.8768 | + | 21.8768i | 0.0577225 | + | 0.0577225i | 0.735379 | − | 0.677656i | \(-0.237004\pi\) |
−0.677656 | + | 0.735379i | \(0.737004\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.2731 | + | 39.2731i | 0.103079 | + | 0.103079i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 344.107i | − | 0.898452i | −0.893418 | − | 0.449226i | \(-0.851700\pi\) | ||
0.893418 | − | 0.449226i | \(-0.148300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.29234 | −0.00855154 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −147.274 | + | 147.274i | −0.380553 | + | 0.380553i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 245.401 | − | 245.401i | 0.630851 | − | 0.630851i | −0.317430 | − | 0.948282i | \(-0.602820\pi\) |
0.948282 | + | 0.317430i | \(0.102820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 198.585 | 0.507889 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 73.4923i | − | 0.187003i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.82465 | + | 4.82465i | 0.0122143 | + | 0.0122143i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 160.138 | + | 160.138i | 0.403371 | + | 0.403371i | 0.879419 | − | 0.476048i | \(-0.157931\pi\) |
−0.476048 | + | 0.879419i | \(0.657931\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.5566i | 0.0289639i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −344.018 | −0.857900 | −0.428950 | − | 0.903328i | \(-0.641116\pi\) | ||||
−0.428950 | + | 0.903328i | \(0.641116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 384.862 | − | 384.862i | 0.954992 | − | 0.954992i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.5885 | − | 24.5885i | 0.0607122 | − | 0.0607122i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.25904 | 0.00555048 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 336.651i | 0.823108i | 0.911385 | + | 0.411554i | \(0.135014\pi\) | ||||
−0.911385 | + | 0.411554i | \(0.864986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −119.450 | − | 119.450i | −0.290633 | − | 0.290633i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 97.4153 | + | 97.4153i | 0.235872 | + | 0.235872i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 320.004i | − | 0.771094i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −371.636 | −0.891213 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 269.830 | − | 269.830i | 0.643986 | − | 0.643986i | −0.307547 | − | 0.951533i | \(-0.599508\pi\) |
0.951533 | + | 0.307547i | \(0.0995081\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.2436 | + | 30.2436i | −0.0718374 | + | 0.0718374i | −0.742113 | − | 0.670275i | \(-0.766176\pi\) |
0.670275 | + | 0.742113i | \(0.266176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −271.366 | −0.641527 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 265.818i | − | 0.625454i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −124.889 | − | 124.889i | −0.292481 | − | 0.292481i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.09996 | + | 9.09996i | 0.0212120 | + | 0.0212120i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 699.038i | − | 1.62190i | −0.585116 | − | 0.810949i | \(-0.698951\pi\) | ||
0.585116 | − | 0.810949i | \(-0.301049\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −493.703 | −1.14019 | −0.570095 | − | 0.821579i | \(-0.693094\pi\) | ||||
−0.570095 | + | 0.821579i | \(0.693094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41.4655 | − | 41.4655i | 0.0953229 | − | 0.0953229i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3435 | − | 16.3435i | 0.0373994 | − | 0.0373994i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −653.276 | −1.48810 | −0.744050 | − | 0.668124i | \(-0.767098\pi\) | ||||
−0.744050 | + | 0.668124i | \(0.767098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 132.846i | 0.301238i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −92.3971 | − | 92.3971i | −0.208571 | − | 0.208571i | 0.595089 | − | 0.803660i | \(-0.297117\pi\) |
−0.803660 | + | 0.595089i | \(0.797117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 346.382 | + | 346.382i | 0.778387 | + | 0.778387i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 151.740i | − | 0.339462i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 197.474 | 0.439809 | 0.219905 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219905 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.42931 | + | 6.42931i | −0.0142557 | + | 0.0142557i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −58.4500 | + | 58.4500i | −0.129029 | + | 0.129029i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 158.947 | 0.349333 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 576.344i | − | 1.26115i | −0.776130 | − | 0.630573i | \(-0.782820\pi\) | ||
0.776130 | − | 0.630573i | \(-0.217180\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −96.9715 | − | 96.9715i | −0.211267 | − | 0.211267i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 386.578 | + | 386.578i | 0.838564 | + | 0.838564i | 0.988670 | − | 0.150106i | \(-0.0479614\pi\) |
−0.150106 | + | 0.988670i | \(0.547961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 165.924i | − | 0.358366i | −0.983816 | − | 0.179183i | \(-0.942655\pi\) | ||
0.983816 | − | 0.179183i | \(-0.0573454\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −192.315 | −0.413581 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −528.381 | + | 528.381i | −1.13144 | + | 1.13144i | −0.141498 | + | 0.989938i | \(0.545192\pi\) |
−0.989938 | + | 0.141498i | \(0.954808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −125.723 | + | 125.723i | −0.268066 | + | 0.268066i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 411.150 | 0.872930 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.2360i | 0.0575814i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.8768 | − | 21.8768i | −0.0460565 | − | 0.0460565i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −112.550 | − | 112.550i | −0.235954 | − | 0.235954i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 439.298i | − | 0.917115i | −0.888665 | − | 0.458558i | \(-0.848366\pi\) | ||
0.888665 | − | 0.458558i | \(-0.151634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −109.061 | −0.226739 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.0166 | + | 20.0166i | −0.0414423 | + | 0.0414423i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −128.210 | + | 128.210i | −0.264351 | + | 0.264351i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −722.173 | −1.48290 | −0.741451 | − | 0.671007i | \(-0.765862\pi\) | ||||
−0.741451 | + | 0.671007i | \(0.765862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 95.2539i | 0.194793i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −104.558 | − | 104.558i | −0.212948 | − | 0.212948i | 0.592570 | − | 0.805519i | \(-0.298113\pi\) |
−0.805519 | + | 0.592570i | \(0.798113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −163.531 | − | 163.531i | −0.331705 | − | 0.331705i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.54725i | − | 0.00918636i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −101.149 | −0.203519 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 202.483 | − | 202.483i | 0.405777 | − | 0.405777i | −0.474486 | − | 0.880263i | \(-0.657366\pi\) |
0.880263 | + | 0.474486i | \(0.157366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −293.520 | + | 293.520i | −0.585869 | + | 0.585869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −874.361 | −1.73829 | −0.869146 | − | 0.494555i | \(-0.835331\pi\) | ||||
−0.869146 | + | 0.494555i | \(0.835331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 365.415i | − | 0.723595i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −232.343 | − | 232.343i | −0.458271 | − | 0.458271i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 542.014 | + | 542.014i | 1.06486 | + | 1.06486i | 0.997745 | + | 0.0671155i | \(0.0213796\pi\) |
0.0671155 | + | 0.997745i | \(0.478620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.27987i | 0.0103324i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.9615 | −0.0311141 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 454.936 | − | 454.936i | 0.883371 | − | 0.883371i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.0924 | + | 25.0924i | −0.0485347 | + | 0.0485347i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 135.473 | 0.261026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 41.2999i | − | 0.0792704i | −0.999214 | − | 0.0396352i | \(-0.987380\pi\) | ||
0.999214 | − | 0.0396352i | \(-0.0126196\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 93.2910 | + | 93.2910i | 0.178377 | + | 0.178377i | 0.790648 | − | 0.612271i | \(-0.209744\pi\) |
−0.612271 | + | 0.790648i | \(0.709744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.7935 | + | 26.7935i | 0.0510353 | + | 0.0510353i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 758.450i | 1.43918i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −472.384 | −0.892976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −134.546 | + | 134.546i | −0.253382 | + | 0.253382i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 310.392 | − | 310.392i | 0.582350 | − | 0.582350i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 706.780 | 1.32108 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 450.200i | − | 0.838361i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.2839 | + | 12.2839i | 0.0227902 | + | 0.0227902i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 46.6640 | + | 46.6640i | 0.0862551 | + | 0.0862551i | 0.748918 | − | 0.662663i | \(-0.230574\pi\) |
−0.662663 | + | 0.748918i | \(0.730574\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 37.1883i | − | 0.0684868i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −537.233 | −0.985749 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −371.423 | + | 371.423i | −0.679019 | + | 0.679019i | −0.959778 | − | 0.280760i | \(-0.909414\pi\) |
0.280760 | + | 0.959778i | \(0.409414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 172.492 | − | 172.492i | 0.314194 | − | 0.314194i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.9172 | −0.0488515 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.83579i | 0.00693632i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.2490 | + | 27.2490i | 0.0490973 | + | 0.0490973i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 537.717 | + | 537.717i | 0.965380 | + | 0.965380i | 0.999420 | − | 0.0340406i | \(-0.0108375\pi\) |
−0.0340406 | + | 0.999420i | \(0.510838\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1314.89i | − | 2.35222i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.9334 | −0.0319668 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 272.321 | − | 272.321i | 0.483697 | − | 0.483697i | −0.422613 | − | 0.906310i | \(-0.638887\pi\) |
0.906310 | + | 0.422613i | \(0.138887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 579.167 | − | 579.167i | 1.02507 | − | 1.02507i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.5488 | 0.0344776 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 304.018i | 0.534302i | 0.963655 | + | 0.267151i | \(0.0860823\pi\) | ||||
−0.963655 | + | 0.267151i | \(0.913918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −326.012 | − | 326.012i | −0.570950 | − | 0.570950i | 0.361444 | − | 0.932394i | \(-0.382284\pi\) |
−0.932394 | + | 0.361444i | \(0.882284\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 243.167 | + | 243.167i | 0.424375 | + | 0.424375i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 75.7836i | − | 0.131798i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1074.26 | −1.86180 | −0.930898 | − | 0.365279i | \(-0.880973\pi\) | ||||
−0.930898 | + | 0.365279i | \(0.880973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −299.880 | + | 299.880i | −0.517928 | + | 0.517928i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 127.208 | − | 127.208i | 0.218946 | − | 0.218946i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.8143 | −0.0357021 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 219.531i | 0.375266i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −413.585 | − | 413.585i | −0.704574 | − | 0.704574i | 0.260815 | − | 0.965389i | \(-0.416009\pi\) |
−0.965389 | + | 0.260815i | \(0.916009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.4205 | + | 62.4205i | 0.105977 | + | 0.105977i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 224.332i | − | 0.379581i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 312.297 | 0.526640 | 0.263320 | − | 0.964709i | \(-0.415183\pi\) | ||||
0.263320 | + | 0.964709i | \(0.415183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −156.619 | + | 156.619i | −0.263225 | + | 0.263225i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 240.822 | − | 240.822i | 0.403386 | − | 0.403386i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −466.651 | −0.779049 | −0.389525 | − | 0.921016i | \(-0.627361\pi\) | ||||
−0.389525 | + | 0.921016i | \(0.627361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 991.272i | − | 1.64937i | −0.565592 | − | 0.824685i | \(-0.691352\pi\) | ||
0.565592 | − | 0.824685i | \(-0.308648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −173.644 | − | 173.644i | −0.287966 | − | 0.287966i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 330.158 | + | 330.158i | 0.545715 | + | 0.545715i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 458.347i | 0.755101i | 0.925989 | + | 0.377551i | \(0.123234\pi\) | ||||
−0.925989 | + | 0.377551i | \(0.876766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.9667 | 0.0541325 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1211.40 | − | 1211.40i | 1.98266 | − | 1.98266i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.7283 | + | 43.7283i | −0.0713349 | + | 0.0713349i | −0.741874 | − | 0.670539i | \(-0.766063\pi\) |
0.670539 | + | 0.741874i | \(0.266063\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −155.103 | −0.252200 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 281.559i | 0.456335i | 0.973622 | + | 0.228168i | \(0.0732734\pi\) | ||||
−0.973622 | + | 0.228168i | \(0.926727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −418.959 | − | 418.959i | −0.676832 | − | 0.676832i | 0.282450 | − | 0.959282i | \(-0.408853\pi\) |
−0.959282 | + | 0.282450i | \(0.908853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.6462 | − | 27.6462i | −0.0445188 | − | 0.0445188i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 275.387i | 0.442034i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 271.764 | 0.434822 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.47592 | + | 1.47592i | −0.00235393 | + | 0.00235393i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 107.464 | − | 107.464i | 0.170849 | − | 0.170849i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 279.670 | 0.443217 | 0.221608 | − | 0.975136i | \(-0.428869\pi\) | ||||
0.221608 | + | 0.975136i | \(0.428869\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 196.477i | 0.310390i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 87.6069 | + | 87.6069i | 0.137964 | + | 0.137964i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −593.038 | − | 593.038i | −0.930987 | − | 0.930987i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 139.703i | − | 0.218627i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 428.823 | 0.668991 | 0.334495 | − | 0.942397i | \(-0.391434\pi\) | ||||
0.334495 | + | 0.942397i | \(0.391434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −439.414 | + | 439.414i | −0.683381 | + | 0.683381i | −0.960761 | − | 0.277379i | \(-0.910534\pi\) |
0.277379 | + | 0.960761i | \(0.410534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −328.526 | + | 328.526i | −0.509342 | + | 0.509342i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.2598 | 0.0452238 | 0.0226119 | − | 0.999744i | \(-0.492802\pi\) | ||||
0.0226119 | + | 0.999744i | \(0.492802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.8822i | 0.0383393i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −76.4492 | − | 76.4492i | −0.117433 | − | 0.117433i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −160.694 | − | 160.694i | −0.246085 | − | 0.246085i | 0.573277 | − | 0.819362i | \(-0.305672\pi\) |
−0.819362 | + | 0.573277i | \(0.805672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 163.940i | − | 0.250290i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.29234 | −0.0110995 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −101.932 | + | 101.932i | −0.154677 | + | 0.154677i | −0.780203 | − | 0.625526i | \(-0.784884\pi\) |
0.625526 | + | 0.780203i | \(0.284884\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −610.251 | + | 610.251i | −0.923224 | + | 0.923224i | −0.997256 | − | 0.0740318i | \(-0.976413\pi\) |
0.0740318 | + | 0.997256i | \(0.476413\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 865.781 | 1.30585 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.7795i | 0.0387661i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.6219 | − | 46.6219i | −0.0698979 | − | 0.0698979i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −421.550 | − | 421.550i | −0.630120 | − | 0.630120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.8997i | − | 0.0475406i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 241.261 | 0.358486 | 0.179243 | − | 0.983805i | \(-0.442635\pi\) | ||||
0.179243 | + | 0.983805i | \(0.442635\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −37.0061 | + | 37.0061i | −0.0548239 | + | 0.0548239i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 270.922 | − | 270.922i | 0.400180 | − | 0.400180i | −0.478117 | − | 0.878296i | \(-0.658680\pi\) |
0.878296 | + | 0.478117i | \(0.158680\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −101.932 | −0.150121 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 701.520i | − | 1.03013i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −363.629 | − | 363.629i | −0.532399 | − | 0.532399i | 0.388886 | − | 0.921286i | \(-0.372860\pi\) |
−0.921286 | + | 0.388886i | \(0.872860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −266.459 | − | 266.459i | −0.388991 | − | 0.388991i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 299.434i | − | 0.435858i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1004.87 | 1.45845 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 709.086 | − | 709.086i | 1.02617 | − | 1.02617i | 0.0265262 | − | 0.999648i | \(-0.491555\pi\) |
0.999648 | − | 0.0265262i | \(-0.00844455\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.80762 | − | 1.80762i | 0.00260840 | − | 0.00260840i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −829.012 | −1.19282 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 611.692i | 0.877607i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −83.0125 | − | 83.0125i | −0.118759 | − | 0.118759i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 116.263 | + | 116.263i | 0.165853 | + | 0.165853i | 0.785154 | − | 0.619301i | \(-0.212584\pi\) |
−0.619301 | + | 0.785154i | \(0.712584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17.6886i | − | 0.0251616i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −605.338 | −0.858636 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 145.260 | − | 145.260i | 0.205459 | − | 0.205459i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 692.751 | − | 692.751i | 0.977082 | − | 0.977082i | −0.0226610 | − | 0.999743i | \(-0.507214\pi\) |
0.999743 | + | 0.0226610i | \(0.00721384\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.29783 | −0.00745124 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 216.231i | 0.303269i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.2994 | + | 20.2994i | 0.0283907 | + | 0.0283907i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −379.377 | − | 379.377i | −0.529117 | − | 0.529117i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1036.41i | 1.44146i | 0.693217 | + | 0.720729i | \(0.256193\pi\) | ||||
−0.693217 | + | 0.720729i | \(0.743807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 361.692 | 0.501654 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −321.492 | + | 321.492i | −0.444664 | + | 0.444664i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −62.4064 | + | 62.4064i | −0.0860778 | + | 0.0860778i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 868.875 | 1.19515 | 0.597575 | − | 0.801813i | \(-0.296131\pi\) | ||||
0.597575 | + | 0.801813i | \(0.296131\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1295.63 | + | 1295.63i | 1.77241 | + | 1.77241i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 240.685 | + | 240.685i | 0.328356 | + | 0.328356i | 0.851961 | − | 0.523605i | \(-0.175413\pi\) |
−0.523605 | + | 0.851961i | \(0.675413\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 296.341i | 0.403185i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.1127 | −0.0435721 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.9489 | − | 38.9489i | 0.0527049 | − | 0.0527049i | −0.680263 | − | 0.732968i | \(-0.738134\pi\) |
0.732968 | + | 0.680263i | \(0.238134\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 71.2539 | − | 71.2539i | 0.0961591 | − | 0.0961591i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −312.791 | −0.420984 | −0.210492 | − | 0.977596i | \(-0.567507\pi\) | ||||
−0.210492 | + | 0.977596i | \(0.567507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 338.487i | − | 0.454345i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 175.694 | + | 175.694i | 0.235200 | + | 0.235200i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 280.959 | + | 280.959i | 0.375112 | + | 0.375112i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 495.790i | − | 0.660174i | −0.943951 | − | 0.330087i | \(-0.892922\pi\) | ||
0.943951 | − | 0.330087i | \(-0.107078\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −543.895 | −0.722304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −130.385 | + | 130.385i | −0.172695 | + | 0.172695i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −610.664 | + | 610.664i | −0.806690 | + | 0.806690i | −0.984131 | − | 0.177442i | \(-0.943218\pi\) |
0.177442 | + | 0.984131i | \(0.443218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.11272 | −0.00673613 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 336.879i | − | 0.442680i | −0.975197 | − | 0.221340i | \(-0.928957\pi\) | ||
0.975197 | − | 0.221340i | \(-0.0710430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −213.561 | − | 213.561i | −0.279896 | − | 0.279896i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −216.315 | − | 216.315i | −0.282765 | − | 0.282765i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1201.25i | − | 1.56617i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −633.979 | −0.824421 | −0.412210 | − | 0.911089i | \(-0.635243\pi\) | ||||
−0.412210 | + | 0.911089i | \(0.635243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 89.5069 | − | 89.5069i | 0.116092 | − | 0.116092i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 902.729 | − | 902.729i | 1.16783 | − | 1.16783i | 0.185107 | − | 0.982718i | \(-0.440737\pi\) |
0.982718 | − | 0.185107i | \(-0.0592633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 289.439 | 0.373469 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.6640i | 0.0278816i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.3423 | + | 50.3423i | 0.0646243 | + | 0.0646243i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9179 | − | 12.9179i | −0.0165402 | − | 0.0165402i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.5322i | 0.0581510i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 917.156 | 1.16835 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −587.548 | + | 587.548i | −0.746566 | + | 0.746566i | −0.973833 | − | 0.227266i | \(-0.927021\pi\) |
0.227266 | + | 0.973833i | \(0.427021\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −443.405 | + | 443.405i | −0.561984 | + | 0.561984i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 460.460 | 0.582124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1540.05i | 1.94205i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −251.066 | − | 251.066i | −0.315807 | − | 0.315807i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 236.322 | + | 236.322i | 0.296514 | + | 0.296514i | 0.839647 | − | 0.543133i | \(-0.182762\pi\) |
−0.543133 | + | 0.839647i | \(0.682762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2387.32i | 2.98789i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −380.354 | −0.474849 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.674302 | + | 0.674302i | −0.000839729 | + | 0.000839729i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −44.6513 | + | 44.6513i | −0.0554675 | + | 0.0554675i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 289.332 | 0.358528 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 196.382i | − | 0.242747i | −0.992607 | − | 0.121373i | \(-0.961270\pi\) | ||
0.992607 | − | 0.121373i | \(-0.0387298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 910.895 | + | 910.895i | 1.12317 | + | 1.12317i | 0.991261 | + | 0.131914i | \(0.0421122\pi\) |
0.131914 | + | 0.991261i | \(0.457888\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −408.573 | − | 408.573i | −0.502550 | − | 0.502550i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 212.484i | 0.260716i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 213.261 | 0.261030 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −87.2678 | + | 87.2678i | −0.106554 | + | 0.106554i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1003.54 | + | 1003.54i | −1.22234 | + | 1.22234i | −0.255544 | + | 0.966798i | \(0.582254\pi\) |
−0.966798 | + | 0.255544i | \(0.917746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −554.187 | −0.673374 | −0.336687 | − | 0.941617i | \(-0.609306\pi\) | ||||
−0.336687 | + | 0.941617i | \(0.609306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.84370i | 0.00829540i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 647.789 | + | 647.789i | 0.783300 | + | 0.783300i | 0.980386 | − | 0.197086i | \(-0.0631478\pi\) |
−0.197086 | + | 0.980386i | \(0.563148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.2384 | + | 33.2384i | 0.0400946 | + | 0.0400946i | 0.726870 | − | 0.686775i | \(-0.240974\pi\) |
−0.686775 | + | 0.726870i | \(0.740974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 394.789i | 0.475077i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1168.70 | 1.40301 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −654.759 | + | 654.759i | −0.784143 | + | 0.784143i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 105.588 | − | 105.588i | 0.126151 | − | 0.126151i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −904.408 | −1.07796 | −0.538980 | − | 0.842319i | \(-0.681190\pi\) | ||||
−0.538980 | + | 0.842319i | \(0.681190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 764.215i | − | 0.908698i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 555.400 | + | 555.400i | 0.658837 | + | 0.658837i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −518.291 | − | 518.291i | −0.613362 | − | 0.613362i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 262.488i | 0.309904i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 177.549 | 0.209127 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.6376 | − | 30.6376i | 0.0360018 | − | 0.0360018i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −576.846 | + | 576.846i | −0.676256 | + | 0.676256i | −0.959151 | − | 0.282895i | \(-0.908705\pi\) |
0.282895 | + | 0.959151i | \(0.408705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −35.6055 | −0.0416439 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1425.60i | 1.66348i | 0.555166 | + | 0.831740i | \(0.312655\pi\) | ||||
−0.555166 | + | 0.831740i | \(0.687345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 193.044 | + | 193.044i | 0.224731 | + | 0.224731i | 0.810487 | − | 0.585756i | \(-0.199202\pi\) |
−0.585756 | + | 0.810487i | \(0.699202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −61.6565 | − | 61.6565i | −0.0716103 | − | 0.0716103i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1139.04i | 1.31986i | 0.751327 | + | 0.659930i | \(0.229414\pi\) | ||||
−0.751327 | + | 0.659930i | \(0.770586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 302.200 | 0.349364 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −499.149 | + | 499.149i | −0.575720 | + | 0.575720i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.489875 | + | 0.489875i | −0.000563723 | + | 0.000563723i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1550.33 | 1.77994 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 140.785i | − | 0.161265i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 208.125 | + | 208.125i | 0.237857 | + | 0.237857i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1012.96 | − | 1012.96i | −1.15503 | − | 1.15503i | −0.985531 | − | 0.169496i | \(-0.945786\pi\) |
−0.169496 | − | 0.985531i | \(-0.554214\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 804.145i | − | 0.914841i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1437.75 | 1.63195 | 0.815975 | − | 0.578087i | \(-0.196200\pi\) | ||||
0.815975 | + | 0.578087i | \(0.196200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −902.217 | + | 902.217i | −1.02176 | + | 1.02176i | −0.0220057 | + | 0.999758i | \(0.507005\pi\) |
−0.999758 | + | 0.0220057i | \(0.992995\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −300.133 | + | 300.133i | −0.339134 | + | 0.339134i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1389.64 | −1.56667 | −0.783334 | − | 0.621601i | \(-0.786483\pi\) | ||||
−0.783334 | + | 0.621601i | \(0.786483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 69.6510i | 0.0783475i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.49661 | + | 2.49661i | 0.00280203 | + | 0.00280203i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 196.477 | + | 196.477i | 0.220019 | + | 0.220019i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1004.27i | − | 1.12208i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 246.831 | 0.275174 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 178.062 | − | 178.062i | 0.198067 | − | 0.198067i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −990.151 | + | 990.151i | −1.09895 | + | 1.09895i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −261.191 | −0.289248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 82.9564i | − | 0.0916645i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −767.091 | − | 767.091i | −0.845745 | − | 0.845745i | 0.143854 | − | 0.989599i | \(-0.454051\pi\) |
−0.989599 | + | 0.143854i | \(0.954051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 200.627 | + | 200.627i | 0.220712 | + | 0.220712i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1531.36i | 1.68097i | 0.541834 | + | 0.840485i | \(0.317730\pi\) | ||||
−0.541834 | + | 0.840485i | \(0.682270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.4919 | 0.0355881 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 384.780 | − | 384.780i | 0.420525 | − | 0.420525i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 65.1694 | − | 65.1694i | 0.0710680 | − | 0.0710680i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1083.73 | 1.17925 | 0.589623 | − | 0.807679i | \(-0.299277\pi\) | ||||
0.589623 | + | 0.807679i | \(0.299277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 339.482i | − | 0.368601i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 623.646 | + | 623.646i | 0.675673 | + | 0.675673i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.0103 | − | 41.0103i | −0.0443355 | − | 0.0443355i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 499.555i | 0.538894i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −878.008 | −0.945110 | −0.472555 | − | 0.881301i | \(-0.656668\pi\) | ||||
−0.472555 | + | 0.881301i | \(0.656668\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 96.1845 | − | 96.1845i | 0.103313 | − | 0.103313i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 382.774 | − | 382.774i | 0.410262 | − | 0.410262i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.0041 | −0.0427852 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1216.28i | 1.29805i | 0.760765 | + | 0.649027i | \(0.224824\pi\) | ||||
−0.760765 | + | 0.649027i | \(0.775176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 337.150 | + | 337.150i | 0.359052 | + | 0.359052i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 92.7424 | + | 92.7424i | 0.0985572 | + | 0.0985572i | 0.754666 | − | 0.656109i | \(-0.227799\pi\) |
−0.656109 | + | 0.754666i | \(0.727799\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 174.391i | 0.184932i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 43.6077 | 0.0461457 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 325.918 | − | 325.918i | 0.344159 | − | 0.344159i | −0.513770 | − | 0.857928i | \(-0.671751\pi\) |
0.857928 | + | 0.513770i | \(0.171751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.5538 | − | 32.5538i | 0.0343032 | − | 0.0343032i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 637.511 | 0.670359 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 172.172i | 0.180663i | 0.995912 | + | 0.0903315i | \(0.0287926\pi\) | ||||
−0.995912 | + | 0.0903315i | \(0.971207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 542.434 | + | 542.434i | 0.567994 | + | 0.567994i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.21024 | + | 4.21024i | 0.00439941 | + | 0.00439941i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 211.845i | − | 0.220902i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 135.154 | 0.140639 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −388.049 | + | 388.049i | −0.402959 | + | 0.402959i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −668.946 | + | 668.946i | −0.693208 | + | 0.693208i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −124.969 | −0.129234 | −0.0646169 | − | 0.997910i | \(-0.520583\pi\) | ||||
−0.0646169 | + | 0.997910i | \(0.520583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 140.420i | 0.144913i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −63.3695 | − | 63.3695i | −0.0652621 | − | 0.0652621i | 0.673722 | − | 0.738985i | \(-0.264694\pi\) |
−0.738985 | + | 0.673722i | \(0.764694\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −329.549 | − | 329.549i | −0.338693 | − | 0.338693i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 330.398i | − | 0.338870i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 192.192 | 0.196717 | 0.0983584 | − | 0.995151i | \(-0.468641\pi\) | ||||
0.0983584 | + | 0.995151i | \(0.468641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.1702 | + | 35.1702i | −0.0359246 | + | 0.0359246i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 294.962 | − | 294.962i | 0.300674 | − | 0.300674i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 613.021 | 0.623623 | 0.311812 | − | 0.950144i | \(-0.399064\pi\) | ||||
0.311812 | + | 0.950144i | \(0.399064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 500.420i | − | 0.508041i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −240.634 | − | 240.634i | −0.243803 | − | 0.243803i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 369.380 | + | 369.380i | 0.373488 | + | 0.373488i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 954.148i | − | 0.962813i | −0.876497 | − | 0.481407i | \(-0.840126\pi\) | ||
0.876497 | − | 0.481407i | \(-0.159874\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 259.061 | 0.260888 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 537.203 | − | 537.203i | 0.539903 | − | 0.539903i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1384.92 | − | 1384.92i | 1.38909 | − | 1.38909i | 0.561854 | − | 0.827237i | \(-0.310088\pi\) |
0.827237 | − | 0.561854i | \(-0.189912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.9215 | −0.0299514 |
(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 | 768.3.l.b.703.1 | yes | 8 | |
4.3 | odd | 2 | inner | 768.3.l.b.703.3 | yes | 8 | |
8.3 | odd | 2 | 768.3.l.c.703.2 | yes | 8 | ||
8.5 | even | 2 | 768.3.l.c.703.4 | yes | 8 | ||
16.3 | odd | 4 | 768.3.l.c.319.4 | yes | 8 | ||
16.5 | even | 4 | inner | 768.3.l.b.319.3 | yes | 8 | |
16.11 | odd | 4 | inner | 768.3.l.b.319.1 | ✓ | 8 | |
16.13 | even | 4 | 768.3.l.c.319.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.3.l.b.319.1 | ✓ | 8 | 16.11 | odd | 4 | inner | |
768.3.l.b.319.3 | yes | 8 | 16.5 | even | 4 | inner | |
768.3.l.b.703.1 | yes | 8 | 1.1 | even | 1 | trivial | |
768.3.l.b.703.3 | yes | 8 | 4.3 | odd | 2 | inner | |
768.3.l.c.319.2 | yes | 8 | 16.13 | even | 4 | ||
768.3.l.c.319.4 | yes | 8 | 16.3 | odd | 4 | ||
768.3.l.c.703.2 | yes | 8 | 8.3 | odd | 2 | ||
768.3.l.c.703.4 | yes | 8 | 8.5 | even | 2 |