Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.4 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.l.721.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.27492 | 1.25498 | 0.627492 | − | 0.778623i | \(-0.284082\pi\) | ||||
0.627492 | + | 0.778623i | \(0.284082\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.2749 | −1.75356 | −0.876780 | − | 0.480892i | \(-0.840313\pi\) | ||||
−0.876780 | + | 0.480892i | \(0.840313\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.274917 | 0.0249925 | 0.0124962 | − | 0.999922i | \(-0.496022\pi\) | ||||
0.0124962 | + | 0.999922i | \(0.496022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0192i | 1.00147i | 0.865600 | + | 0.500737i | \(0.166937\pi\) | ||||
−0.865600 | + | 0.500737i | \(0.833063\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.3746 | −1.02203 | −0.511017 | − | 0.859570i | \(-0.670731\pi\) | ||||
−0.511017 | + | 0.859570i | \(0.670731\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.54983 | + | 17.4356i | −0.397360 | + | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.5498 | 0.893471 | 0.446736 | − | 0.894666i | \(-0.352586\pi\) | ||||
0.446736 | + | 0.894666i | \(0.352586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.3746 | 0.574983 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.0383i | 0.897873i | 0.893564 | + | 0.448936i | \(0.148197\pi\) | ||||
−0.893564 | + | 0.448936i | \(0.851803\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 23.5265i | − | 0.758921i | −0.925208 | − | 0.379460i | \(-0.876110\pi\) | ||
0.925208 | − | 0.379460i | \(-0.123890\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −77.0241 | −2.20069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 66.7703i | − | 1.80460i | −0.431107 | − | 0.902301i | \(-0.641877\pi\) | ||
0.431107 | − | 0.902301i | \(-0.358123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57919i | 0.0872973i | 0.999047 | + | 0.0436487i | \(0.0138982\pi\) | ||||
−0.999047 | + | 0.0436487i | \(0.986102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.1238 | 1.11916 | 0.559579 | − | 0.828777i | \(-0.310963\pi\) | ||||
0.559579 | + | 0.828777i | \(0.310963\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.4743 | −0.265410 | −0.132705 | − | 0.991156i | \(-0.542366\pi\) | ||||
−0.132705 | + | 0.991156i | \(0.542366\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 101.674 | 2.07497 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 25.8081i | − | 0.486946i | −0.969908 | − | 0.243473i | \(-0.921713\pi\) | ||
0.969908 | − | 0.243473i | \(-0.0782867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.72508 | 0.0313651 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.230175i | − | 0.00390128i | −0.999998 | − | 0.00195064i | \(-0.999379\pi\) | ||
0.999998 | − | 0.00195064i | \(-0.000620908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.8248 | −0.472537 | −0.236268 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236268 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 81.6941i | 1.25683i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 102.939i | − | 1.53640i | −0.640208 | − | 0.768202i | \(-0.721152\pi\) | ||
0.640208 | − | 0.768202i | \(-0.278848\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 107.732i | − | 1.51736i | −0.651465 | − | 0.758679i | \(-0.725845\pi\) | ||
0.651465 | − | 0.758679i | \(-0.274155\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1752 | 0.153086 | 0.0765428 | − | 0.997066i | \(-0.475612\pi\) | ||||
0.0765428 | + | 0.997066i | \(0.475612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.37459 | −0.0438258 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 26.6454i | − | 0.337283i | −0.985677 | − | 0.168642i | \(-0.946062\pi\) | ||
0.985677 | − | 0.168642i | \(-0.0539381\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −89.6977 | −1.08069 | −0.540347 | − | 0.841442i | \(-0.681707\pi\) | ||||
−0.540347 | + | 0.841442i | \(0.681707\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −109.024 | −1.28264 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 139.255i | − | 1.56466i | −0.622865 | − | 0.782329i | \(-0.714032\pi\) | ||
0.622865 | − | 0.782329i | \(-0.285968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 159.809i | − | 1.75614i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −47.3746 | + | 109.407i | −0.498680 | + | 1.15165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41.3390i | 0.426176i | 0.977033 | + | 0.213088i | \(0.0683521\pi\) | ||||
−0.977033 | + | 0.213088i | \(0.931648\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −150.749 | −1.49257 | −0.746283 | − | 0.665629i | \(-0.768163\pi\) | ||||
−0.746283 | + | 0.665629i | \(0.768163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 22.8360i | 0.221709i | 0.993837 | + | 0.110854i | \(0.0353587\pi\) | ||||
−0.993837 | + | 0.110854i | \(0.964641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 165.063i | − | 1.54264i | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||
0.636446 | − | 0.771321i | \(-0.280404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 46.4460i | − | 0.426110i | −0.977040 | − | 0.213055i | \(-0.931659\pi\) | ||
0.977040 | − | 0.213055i | \(-0.0683414\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.56317i | 0.0403820i | 0.999796 | + | 0.0201910i | \(0.00642744\pi\) | ||||
−0.999796 | + | 0.0201910i | \(0.993573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 128.949 | 1.12129 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 213.272 | 1.79220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.924 | −0.999375 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −66.6736 | −0.533389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 146.790i | 1.15583i | 0.816098 | + | 0.577913i | \(0.196133\pi\) | ||||
−0.816098 | + | 0.577913i | \(0.803867\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −188.921 | −1.44215 | −0.721073 | − | 0.692859i | \(-0.756351\pi\) | ||||
−0.721073 | + | 0.692859i | \(0.756351\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 92.6736 | − | 214.020i | 0.696794 | − | 1.60918i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 71.3264 | 0.520631 | 0.260315 | − | 0.965524i | \(-0.416173\pi\) | ||||
0.260315 | + | 0.965524i | \(0.416173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −43.5739 | −0.313481 | −0.156741 | − | 0.987640i | \(-0.550099\pi\) | ||||
−0.156741 | + | 0.987640i | \(0.550099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.57919i | 0.0250293i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 163.388i | 1.12682i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 71.6769 | 0.481053 | 0.240527 | − | 0.970643i | \(-0.422680\pi\) | ||||
0.240527 | + | 0.970643i | \(0.422680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 68.9051i | 0.456325i | 0.973623 | + | 0.228163i | \(0.0732718\pi\) | ||||
−0.973623 | + | 0.228163i | \(0.926728\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 147.627i | − | 0.952433i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 157.698 | 1.00444 | 0.502222 | − | 0.864739i | \(-0.332516\pi\) | ||||
0.502222 | + | 0.864739i | \(0.332516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −252.248 | −1.56675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 42.3987 | 0.260115 | 0.130057 | − | 0.991506i | \(-0.458484\pi\) | ||||
0.130057 | + | 0.991506i | \(0.458484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 101.558i | 0.608132i | 0.952651 | + | 0.304066i | \(0.0983443\pi\) | ||||
−0.952651 | + | 0.304066i | \(0.901656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.498344 | −0.00294878 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 24.3638i | − | 0.140831i | −0.997518 | − | 0.0704156i | \(-0.977567\pi\) | ||
0.997518 | − | 0.0704156i | \(-0.0224325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −176.447 | −1.00827 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 74.7659i | − | 0.417687i | −0.977949 | − | 0.208843i | \(-0.933030\pi\) | ||
0.977949 | − | 0.208843i | \(-0.0669699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 28.3199i | − | 0.156463i | −0.996935 | − | 0.0782317i | \(-0.975073\pi\) | ||
0.996935 | − | 0.0782317i | \(-0.0249274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 418.978i | − | 2.26475i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.77657 | −0.0255432 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −237.973 | −1.24593 | −0.622965 | − | 0.782250i | \(-0.714072\pi\) | ||||
−0.622965 | + | 0.782250i | \(0.714072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 249.876i | − | 1.29469i | −0.762196 | − | 0.647346i | \(-0.775879\pi\) | ||
0.762196 | − | 0.647346i | \(-0.224121\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −253.251 | −1.28554 | −0.642769 | − | 0.766060i | \(-0.722214\pi\) | ||||
−0.642769 | + | 0.766060i | \(0.722214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 48.0274 | 0.241344 | 0.120672 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120672 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 319.618i | − | 1.57447i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.4591i | 0.109557i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.07558 | + | 4.79335i | −0.00993100 | + | 0.0229347i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 278.279i | − | 1.31886i | −0.751767 | − | 0.659429i | \(-0.770798\pi\) | ||
0.751767 | − | 0.659429i | \(-0.229202\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 301.973 | 1.40452 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 288.786i | 1.33081i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 226.202i | − | 1.02354i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 67.6910i | 0.303547i | 0.988415 | + | 0.151773i | \(0.0484984\pi\) | ||||
−0.988415 | + | 0.151773i | \(0.951502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 409.224i | 1.80275i | 0.433039 | + | 0.901375i | \(0.357441\pi\) | ||||
−0.433039 | + | 0.901375i | \(0.642559\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −246.419 | −1.07607 | −0.538034 | − | 0.842923i | \(-0.680833\pi\) | ||||
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 226.323 | 0.971344 | 0.485672 | − | 0.874141i | \(-0.338575\pi\) | ||||
0.485672 | + | 0.874141i | \(0.338575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −78.2749 | −0.333085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 69.1204 | 0.289207 | 0.144603 | − | 0.989490i | \(-0.453809\pi\) | ||||
0.144603 | + | 0.989490i | \(0.453809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 108.486i | 0.450150i | 0.974341 | + | 0.225075i | \(0.0722628\pi\) | ||||
−0.974341 | + | 0.225075i | \(0.927737\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 637.993 | 2.60405 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −226.997 | − | 98.2924i | −0.919015 | − | 0.397945i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 46.7766 | 0.186361 | 0.0931804 | − | 0.995649i | \(-0.470297\pi\) | ||||
0.0931804 | + | 0.995649i | \(0.470297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.64950 | 0.0223301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 217.139i | 0.844900i | 0.906386 | + | 0.422450i | \(0.138830\pi\) | ||||
−0.906386 | + | 0.422450i | \(0.861170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 819.600i | 3.16448i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −34.8796 | −0.132622 | −0.0663109 | − | 0.997799i | \(-0.521123\pi\) | ||||
−0.0663109 | + | 0.997799i | \(0.521123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 161.944i | − | 0.611109i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 90.2335i | − | 0.335441i | −0.985835 | − | 0.167720i | \(-0.946359\pi\) | ||
0.985835 | − | 0.167720i | \(-0.0536406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 144.997 | 0.535043 | 0.267522 | − | 0.963552i | \(-0.413795\pi\) | ||||
0.267522 | + | 0.963552i | \(0.413795\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.95182 | 0.0143703 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 496.371 | 1.79195 | 0.895977 | − | 0.444100i | \(-0.146477\pi\) | ||||
0.895977 | + | 0.444100i | \(0.146477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 187.459i | − | 0.667112i | −0.942730 | − | 0.333556i | \(-0.891751\pi\) | ||
0.942730 | − | 0.333556i | \(-0.108249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −51.5739 | −0.182240 | −0.0911200 | − | 0.995840i | \(-0.529045\pi\) | ||||
−0.0911200 | + | 0.995840i | \(0.529045\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 43.9343i | − | 0.153081i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8762 | 0.0445545 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 82.6781i | 0.282178i | 0.989997 | + | 0.141089i | \(0.0450603\pi\) | ||||
−0.989997 | + | 0.141089i | \(0.954940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.44433i | − | 0.00489604i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 267.541i | 0.894787i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −590.715 | −1.96251 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −180.873 | −0.593026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 83.3053i | − | 0.271353i | −0.990753 | − | 0.135676i | \(-0.956679\pi\) | ||
0.990753 | − | 0.135676i | \(-0.0433208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.22674 | 0.0135908 | 0.00679540 | − | 0.999977i | \(-0.497837\pi\) | ||||
0.00679540 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.894 | −0.507648 | −0.253824 | − | 0.967250i | \(-0.581688\pi\) | ||||
−0.253824 | + | 0.967250i | \(0.581688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 278.572i | − | 0.878777i | −0.898297 | − | 0.439389i | \(-0.855195\pi\) | ||
0.898297 | − | 0.439389i | \(-0.144805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.15838i | 0.0224401i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 131.175 | − | 302.936i | 0.406115 | − | 0.937883i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 187.145i | 0.575831i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 153.120 | 0.465412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 133.080i | − | 0.402055i | −0.979586 | − | 0.201027i | \(-0.935572\pi\) | ||
0.979586 | − | 0.201027i | \(-0.0644281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 645.934i | − | 1.92816i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 351.831i | − | 1.04401i | −0.852943 | − | 0.522004i | \(-0.825185\pi\) | ||
0.852943 | − | 0.522004i | \(-0.174815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.46785i | − | 0.0189673i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −646.564 | −1.88503 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −348.124 | −1.00324 | −0.501619 | − | 0.865089i | \(-0.667262\pi\) | ||||
−0.501619 | + | 0.865089i | \(0.667262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −614.323 | −1.76024 | −0.880119 | − | 0.474753i | \(-0.842537\pi\) | ||||
−0.880119 | + | 0.474753i | \(0.842537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −151.292 | −0.428590 | −0.214295 | − | 0.976769i | \(-0.568745\pi\) | ||||
−0.214295 | + | 0.976769i | \(0.568745\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 676.012i | − | 1.90426i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 497.519 | 1.38585 | 0.692924 | − | 0.721011i | \(-0.256322\pi\) | ||||
0.692924 | + | 0.721011i | \(0.256322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −247.000 | − | 263.272i | −0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 70.1238 | 0.192120 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 267.003 | 0.727529 | 0.363765 | − | 0.931491i | \(-0.381491\pi\) | ||||
0.363765 | + | 0.931491i | \(0.381491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 316.793i | 0.853889i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 51.4695i | − | 0.137988i | −0.997617 | − | 0.0689940i | \(-0.978021\pi\) | ||
0.997617 | − | 0.0689940i | \(-0.0219789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −338.997 | −0.899195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 447.214i | − | 1.17999i | −0.807409 | − | 0.589993i | \(-0.799131\pi\) | ||
0.807409 | − | 0.589993i | \(-0.200869\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 201.839i | − | 0.526994i | −0.964660 | − | 0.263497i | \(-0.915124\pi\) | ||
0.964660 | − | 0.263497i | \(-0.0848759\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.1752 | −0.0550006 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.7700 | 0.0688174 | 0.0344087 | − | 0.999408i | \(-0.489045\pi\) | ||||
0.0344087 | + | 0.999408i | \(0.489045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −357.045 | −0.913158 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 167.198i | − | 0.423285i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 268.069 | 0.675237 | 0.337618 | − | 0.941283i | \(-0.390379\pi\) | ||||
0.337618 | + | 0.941283i | \(0.390379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 445.540i | − | 1.11107i | −0.831492 | − | 0.555536i | \(-0.812513\pi\) | ||
0.831492 | − | 0.555536i | \(-0.187487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 306.296 | 0.760039 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.3563i | − | 0.0451015i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 325.039i | − | 0.794716i | −0.917664 | − | 0.397358i | \(-0.869927\pi\) | ||
0.917664 | − | 0.397358i | \(-0.130073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.82538i | 0.00684112i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −562.846 | −1.35625 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −51.0033 | −0.121726 | −0.0608631 | − | 0.998146i | \(-0.519385\pi\) | ||||
−0.0608631 | + | 0.998146i | \(0.519385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 214.794i | 0.510201i | 0.966915 | + | 0.255100i | \(0.0821085\pi\) | ||||
−0.966915 | + | 0.255100i | \(0.917892\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −249.752 | −0.587653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 353.821 | 0.828622 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 469.547i | − | 1.08944i | −0.838619 | − | 0.544718i | \(-0.816637\pi\) | ||
0.838619 | − | 0.544718i | \(-0.183363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 175.110i | 0.404411i | 0.979343 | + | 0.202205i | \(0.0648108\pi\) | ||||
−0.979343 | + | 0.202205i | \(0.935189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −155.148 | + | 358.299i | −0.355029 | + | 0.819905i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 542.848i | − | 1.23656i | −0.785959 | − | 0.618278i | \(-0.787830\pi\) | ||
0.785959 | − | 0.618278i | \(-0.212170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 134.680 | 0.304019 | 0.152009 | − | 0.988379i | \(-0.451426\pi\) | ||||
0.152009 | + | 0.988379i | \(0.451426\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 873.811i | − | 1.96362i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 722.541i | − | 1.60922i | −0.593801 | − | 0.804612i | \(-0.702373\pi\) | ||
0.593801 | − | 0.804612i | \(-0.297627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.983981i | 0.00218178i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1002.79i | − | 2.20393i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.7218 | −0.0934831 | −0.0467415 | − | 0.998907i | \(-0.514884\pi\) | ||||
−0.0467415 | + | 0.998907i | \(0.514884\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.6221 | −0.0859482 | −0.0429741 | − | 0.999076i | \(-0.513683\pi\) | ||||
−0.0429741 | + | 0.999076i | \(0.513683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 158.625 | 0.342603 | 0.171302 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171302 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −672.619 | −1.44030 | −0.720149 | − | 0.693820i | \(-0.755926\pi\) | ||||
−0.720149 | + | 0.693820i | \(0.755926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1263.57i | 2.69418i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.2300 | 0.0279705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −108.526 | + | 250.629i | −0.228475 | + | 0.527641i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 870.846 | 1.81805 | 0.909025 | − | 0.416743i | \(-0.136828\pi\) | ||||
0.909025 | + | 0.416743i | \(0.136828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 869.292 | 1.80726 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 259.399i | 0.534843i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 274.616i | 0.563894i | 0.959430 | + | 0.281947i | \(0.0909802\pi\) | ||||
−0.959430 | + | 0.281947i | \(0.909020\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −781.588 | −1.59183 | −0.795915 | − | 0.605409i | \(-0.793010\pi\) | ||||
−0.795915 | + | 0.605409i | \(0.793010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 452.405i | − | 0.917657i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1322.41i | 2.66078i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 387.918 | 0.777390 | 0.388695 | − | 0.921366i | \(-0.372926\pi\) | ||||
0.388695 | + | 0.921366i | \(0.372926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −914.846 | −1.81878 | −0.909389 | − | 0.415946i | \(-0.863450\pi\) | ||||
−0.909389 | + | 0.415946i | \(0.863450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −945.939 | −1.87315 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 185.554i | 0.364546i | 0.983248 | + | 0.182273i | \(0.0583455\pi\) | ||||
−0.983248 | + | 0.182273i | \(0.941655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −137.175 | −0.268445 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 143.294i | 0.278241i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.42939 | −0.00663324 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 212.283i | − | 0.407452i | −0.979028 | − | 0.203726i | \(-0.934695\pi\) | ||
0.979028 | − | 0.203726i | \(-0.0653052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 209.227i | − | 0.400052i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) | ||
0.979791 | − | 0.200026i | \(-0.0641026\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 408.764i | 0.775643i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −106.704 | −0.201709 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.5980 | −0.0874259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1035.75i | − | 1.93599i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.9518 | 0.0518587 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 989.664 | 1.82932 | 0.914661 | − | 0.404221i | \(-0.132457\pi\) | ||||
0.914661 | + | 0.404221i | \(0.132457\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 291.445i | − | 0.534761i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 851.749i | 1.55713i | 0.627565 | + | 0.778564i | \(0.284052\pi\) | ||||
−0.627565 | + | 0.778564i | \(0.715948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −453.993 | − | 196.585i | −0.823944 | − | 0.356778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 327.070i | 0.591446i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −125.423 | −0.225176 | −0.112588 | − | 0.993642i | \(-0.535914\pi\) | ||||
−0.112588 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 626.531i | 1.12081i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 762.666i | 1.35465i | 0.735685 | + | 0.677324i | \(0.236860\pi\) | ||||
−0.735685 | + | 0.677324i | \(0.763140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.6335i | 0.0506788i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 598.818i | − | 1.05240i | −0.850360 | − | 0.526202i | \(-0.823616\pi\) | ||
0.850360 | − | 0.526202i | \(-0.176384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 165.492 | 0.289828 | 0.144914 | − | 0.989444i | \(-0.453709\pi\) | ||||
0.144914 | + | 0.989444i | \(0.453709\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 295.395 | 0.513731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 852.262 | 1.47706 | 0.738528 | − | 0.674222i | \(-0.235521\pi\) | ||||
0.738528 | + | 0.674222i | \(0.235521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1101.03 | 1.89506 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.09510i | − | 0.0121700i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 429.375 | 0.731473 | 0.365736 | − | 0.930718i | \(-0.380817\pi\) | ||||
0.365736 | + | 0.930718i | \(0.380817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 410.199 | + | 177.622i | 0.696434 | + | 0.301565i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 243.100 | 0.409949 | 0.204974 | − | 0.978767i | \(-0.434289\pi\) | ||||
0.204974 | + | 0.978767i | \(0.434289\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1338.26 | 2.24918 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 725.096i | − | 1.21051i | −0.796031 | − | 0.605256i | \(-0.793071\pi\) | ||
0.796031 | − | 0.605256i | \(-0.206929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 595.929i | − | 0.991563i | −0.868447 | − | 0.495781i | \(-0.834882\pi\) | ||
0.868447 | − | 0.495781i | \(-0.165118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −758.791 | −1.25420 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 724.886i | 1.19421i | 0.802163 | + | 0.597106i | \(0.203683\pi\) | ||||
−0.802163 | + | 0.597106i | \(0.796317\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 162.404i | − | 0.265801i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 499.368 | 0.814630 | 0.407315 | − | 0.913288i | \(-0.366465\pi\) | ||||
0.407315 | + | 0.913288i | \(0.366465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 87.2300 | 0.141378 | 0.0706889 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706889 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 846.482 | 1.36750 | 0.683749 | − | 0.729717i | \(-0.260348\pi\) | ||||
0.683749 | + | 0.729717i | \(0.260348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1709.34i | 2.74372i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −777.736 | −1.24438 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1160.11i | 1.84437i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 800.509 | 1.26864 | 0.634318 | − | 0.773072i | \(-0.281281\pi\) | ||||
0.634318 | + | 0.773072i | \(0.281281\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 921.094i | 1.45054i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1323.70i | 2.07803i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 492.363i | 0.768117i | 0.923309 | + | 0.384058i | \(0.125474\pi\) | ||||
−0.923309 | + | 0.384058i | \(0.874526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1212.76 | −1.88609 | −0.943046 | − | 0.332663i | \(-0.892053\pi\) | ||||
−0.943046 | + | 0.332663i | \(0.892053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −157.368 | −0.243227 | −0.121614 | − | 0.992578i | \(-0.538807\pi\) | ||||
−0.121614 | + | 0.992578i | \(0.538807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.0632792i | − | 9.75026e-5i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −726.220 | −1.11213 | −0.556064 | − | 0.831139i | \(-0.687689\pi\) | ||||
−0.556064 | + | 0.831139i | \(0.687689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1185.46 | −1.80987 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 259.756i | − | 0.394167i | −0.980387 | − | 0.197083i | \(-0.936853\pi\) | ||
0.980387 | − | 0.197083i | \(-0.0631469\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 874.021i | 1.32227i | 0.750267 | + | 0.661135i | \(0.229925\pi\) | ||||
−0.750267 | + | 0.661135i | \(0.770075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 581.519 | − | 1342.96i | 0.874465 | − | 2.01949i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 535.083i | 0.802223i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.92442 | −0.0118099 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1035.99i | − | 1.53935i | −0.638434 | − | 0.769677i | \(-0.720417\pi\) | ||
0.638434 | − | 0.769677i | \(-0.279583\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 973.505i | 1.43797i | 0.695026 | + | 0.718984i | \(0.255393\pi\) | ||||
−0.695026 | + | 0.718984i | \(0.744607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 507.433i | − | 0.747325i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1186.44i | 1.73710i | 0.495604 | + | 0.868549i | \(0.334947\pi\) | ||||
−0.495604 | + | 0.868549i | \(0.665053\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 447.567 | 0.653383 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 336.000 | 0.487663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −563.670 | −0.815731 | −0.407866 | − | 0.913042i | \(-0.633727\pi\) | ||||
−0.407866 | + | 0.913042i | \(0.633727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −273.423 | −0.393414 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 62.1869i | − | 0.0892209i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 163.958 | 0.233892 | 0.116946 | − | 0.993138i | \(-0.462690\pi\) | ||||
0.116946 | + | 0.993138i | \(0.462690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1164.18 | + | 504.104i | 1.65602 | + | 0.717076i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1850.43 | 2.61730 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −315.993 | −0.445689 | −0.222844 | − | 0.974854i | \(-0.571534\pi\) | ||||
−0.222844 | + | 0.974854i | \(0.571534\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 483.467i | − | 0.678074i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.4591i | 0.0314114i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −171.072 | −0.237931 | −0.118965 | − | 0.992898i | \(-0.537958\pi\) | ||||
−0.118965 | + | 0.992898i | \(0.537958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 280.310i | − | 0.388780i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 374.290i | 0.516262i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −261.169 | −0.359242 | −0.179621 | − | 0.983736i | \(-0.557487\pi\) | ||||
−0.179621 | + | 0.983736i | \(0.557487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −836.130 | −1.14382 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1185.78 | 1.61771 | 0.808855 | − | 0.588009i | \(-0.200088\pi\) | ||||
0.808855 | + | 0.588009i | \(0.200088\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 28.2997i | − | 0.0383985i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −738.557 | −0.999401 | −0.499701 | − | 0.866198i | \(-0.666557\pi\) | ||||
−0.499701 | + | 0.866198i | \(0.666557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 809.783i | 1.08988i | 0.838474 | + | 0.544941i | \(0.183448\pi\) | ||||
−0.838474 | + | 0.544941i | \(0.816552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 449.767 | 0.603714 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2026.13i | 2.70512i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1167.89i | 1.55512i | 0.628809 | + | 0.777559i | \(0.283543\pi\) | ||||
−0.628809 | + | 0.777559i | \(0.716457\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 432.374i | 0.572681i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −161.828 | −0.213776 | −0.106888 | − | 0.994271i | \(-0.534089\pi\) | ||||
−0.106888 | + | 0.994271i | \(0.534089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1148.47 | −1.50916 | −0.754578 | − | 0.656210i | \(-0.772158\pi\) | ||||
−0.754578 | + | 0.656210i | \(0.772158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 570.121i | 0.747210i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.99669 | 0.00390703 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 77.5673 | 0.100868 | 0.0504339 | − | 0.998727i | \(-0.483940\pi\) | ||||
0.0504339 | + | 0.998727i | \(0.483940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1165.42i | 1.50766i | 0.657068 | + | 0.753831i | \(0.271796\pi\) | ||||
−0.657068 | + | 0.753831i | \(0.728204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 338.184i | − | 0.436367i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −62.4053 | − | 27.0223i | −0.0801095 | − | 0.0346884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.6175i | − | 0.0379225i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 989.540 | 1.26056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1141.88i | − | 1.45092i | −0.688263 | − | 0.725461i | \(-0.741626\pi\) | ||
0.688263 | − | 0.725461i | \(-0.258374\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 56.0125i | − | 0.0708123i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 375.274i | − | 0.473233i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 798.061i | 1.00133i | 0.865641 | + | 0.500666i | \(0.166911\pi\) | ||||
−0.865641 | + | 0.500666i | \(0.833089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 216.735 | 0.271258 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.07227 | 0.00382599 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1582.83 | −1.96625 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −879.175 | −1.08674 | −0.543372 | − | 0.839492i | \(-0.682853\pi\) | ||||
−0.543372 | + | 0.839492i | \(0.682853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 654.537i | − | 0.807074i | −0.914963 | − | 0.403537i | \(-0.867781\pi\) | ||
0.914963 | − | 0.403537i | \(-0.132219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 266.048 | 0.326439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −363.326 | + | 839.066i | −0.444708 | + | 1.02701i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1419.35 | 1.72880 | 0.864402 | − | 0.502801i | \(-0.167697\pi\) | ||||
0.864402 | + | 0.502801i | \(0.167697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 671.107 | 0.815440 | 0.407720 | − | 0.913107i | \(-0.366324\pi\) | ||||
0.407720 | + | 0.913107i | \(0.366324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 186.204i | − | 0.225156i | −0.993643 | − | 0.112578i | \(-0.964089\pi\) | ||
0.993643 | − | 0.112578i | \(-0.0359108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 924.130i | 1.11475i | 0.830260 | + | 0.557376i | \(0.188192\pi\) | ||||
−0.830260 | + | 0.557376i | \(0.811808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1766.54 | −2.12069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 637.268i | 0.763195i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 934.157i | 1.11342i | 0.830708 | + | 0.556708i | \(0.187936\pi\) | ||||
−0.830708 | + | 0.556708i | \(0.812064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 163.007 | 0.193825 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.12707 | −0.00370067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1484.34 | 1.75246 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1372.12i | − | 1.61236i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 344.405 | 0.403758 | 0.201879 | − | 0.979411i | \(-0.435295\pi\) | ||||
0.201879 | + | 0.979411i | \(0.435295\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 931.245i | − | 1.08663i | −0.839528 | − | 0.543317i | \(-0.817168\pi\) | ||
0.839528 | − | 0.543317i | \(-0.182832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1072.73 | 1.24881 | 0.624405 | − | 0.781100i | \(-0.285341\pi\) | ||||
0.624405 | + | 0.781100i | \(0.285341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1240.65i | 1.43760i | 0.695217 | + | 0.718800i | \(0.255308\pi\) | ||||
−0.695217 | + | 0.718800i | \(0.744692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 152.881i | − | 0.176741i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.32527i | − | 0.00842955i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1340.18 | 1.53867 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 818.413 | 0.935329 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 526.564i | 0.600415i | 0.953874 | + | 0.300207i | \(0.0970559\pi\) | ||||
−0.953874 | + | 0.300207i | \(0.902944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1444.25 | −1.63933 | −0.819664 | − | 0.572844i | \(-0.805840\pi\) | ||||
−0.819664 | + | 0.572844i | \(0.805840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −593.086 | −0.671671 | −0.335836 | − | 0.941921i | \(-0.609019\pi\) | ||||
−0.335836 | + | 0.941921i | \(0.609019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 589.691i | 0.664816i | 0.943136 | + | 0.332408i | \(0.107861\pi\) | ||||
−0.943136 | + | 0.332408i | \(0.892139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1801.83i | − | 2.02681i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 94.1786 | − | 217.496i | 0.105463 | − | 0.243557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 469.150i | − | 0.524190i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 612.591 | 0.681414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 448.406i | 0.497675i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 177.705i | − | 0.196359i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 164.499i | − | 0.181366i | −0.995880 | − | 0.0906829i | \(-0.971095\pi\) | ||
0.995880 | − | 0.0906829i | \(-0.0289050\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 474.507i | 0.520864i | 0.965492 | + | 0.260432i | \(0.0838650\pi\) | ||||
−0.965492 | + | 0.260432i | \(0.916135\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.6594 | −0.0270092 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2318.99 | 2.52889 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −708.488 | −0.770934 | −0.385467 | − | 0.922722i | \(-0.625960\pi\) | ||||
−0.385467 | + | 0.922722i | \(0.625960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1402.58 | 1.51959 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 959.795i | − | 1.03762i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −154.482 | −0.166288 | −0.0831441 | − | 0.996538i | \(-0.526496\pi\) | ||||
−0.0831441 | + | 0.996538i | \(0.526496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −767.619 | + | 1772.74i | −0.824510 | + | 1.90412i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.9726 | −0.0320563 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −289.223 | −0.308670 | −0.154335 | − | 0.988019i | \(-0.549323\pi\) | ||||
−0.154335 | + | 0.988019i | \(0.549323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1484.31i | − | 1.57738i | −0.614794 | − | 0.788688i | \(-0.710761\pi\) | ||
0.614794 | − | 0.788688i | \(-0.289239\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 73.5517i | 0.0779976i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 222.206 | 0.234642 | 0.117321 | − | 0.993094i | \(-0.462569\pi\) | ||||
0.117321 | + | 0.993094i | \(0.462569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 145.492i | 0.153311i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1149.54i | − | 1.20623i | −0.797655 | − | 0.603114i | \(-0.793926\pi\) | ||
0.797655 | − | 0.603114i | \(-0.206074\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1493.26 | −1.56362 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −875.526 | −0.912957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 407.502 | 0.424039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1567.95i | − | 1.62482i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −980.296 | −1.01375 | −0.506875 | − | 0.862020i | \(-0.669199\pi\) | ||||
−0.506875 | + | 0.862020i | \(0.669199\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1699.98i | − | 1.75075i | −0.483441 | − | 0.875377i | \(-0.660613\pi\) | ||
0.483441 | − | 0.875377i | \(-0.339387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 534.866 | 0.549708 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 73.3216i | − | 0.0750477i | −0.999296 | − | 0.0375238i | \(-0.988053\pi\) | ||
0.999296 | − | 0.0375238i | \(-0.0119470\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 38.2835i | − | 0.0391047i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 541.654i | 0.551022i | 0.961298 | + | 0.275511i | \(0.0888470\pi\) | ||||
−0.961298 | + | 0.275511i | \(0.911153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1589.13 | −1.61333 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 988.935 | 0.999935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1546.81i | − | 1.56086i | −0.625244 | − | 0.780429i | \(-0.715001\pi\) | ||
0.625244 | − | 0.780429i | \(-0.284999\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 301.368 | 0.302882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1366.20 | −1.37031 | −0.685156 | − | 0.728397i | \(-0.740266\pi\) | ||||
−0.685156 | + | 0.728397i | \(0.740266\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2736.3.o.l.721.4 | 4 | ||
3.2 | odd | 2 | 912.3.o.b.721.1 | 4 | |||
4.3 | odd | 2 | 171.3.c.f.37.1 | 4 | |||
12.11 | even | 2 | 57.3.c.b.37.4 | yes | 4 | ||
19.18 | odd | 2 | inner | 2736.3.o.l.721.3 | 4 | ||
57.56 | even | 2 | 912.3.o.b.721.3 | 4 | |||
76.75 | even | 2 | 171.3.c.f.37.4 | 4 | |||
228.227 | odd | 2 | 57.3.c.b.37.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.c.b.37.1 | ✓ | 4 | 228.227 | odd | 2 | ||
57.3.c.b.37.4 | yes | 4 | 12.11 | even | 2 | ||
171.3.c.f.37.1 | 4 | 4.3 | odd | 2 | |||
171.3.c.f.37.4 | 4 | 76.75 | even | 2 | |||
912.3.o.b.721.1 | 4 | 3.2 | odd | 2 | |||
912.3.o.b.721.3 | 4 | 57.56 | even | 2 | |||
2736.3.o.l.721.3 | 4 | 19.18 | odd | 2 | inner | ||
2736.3.o.l.721.4 | 4 | 1.1 | even | 1 | trivial |