Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(721,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, 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("912.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.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: | \(24.8502001097\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.3 | ||
Root | \(2.13746 - 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.721 |
Dual form | 912.3.o.b.721.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.27492 | −1.25498 | −0.627492 | − | 0.778623i | \(-0.715918\pi\) | ||||
−0.627492 | + | 0.778623i | \(0.715918\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.2749 | −1.75356 | −0.876780 | − | 0.480892i | \(-0.840313\pi\) | ||||
−0.876780 | + | 0.480892i | \(0.840313\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.274917 | −0.0249925 | −0.0124962 | − | 0.999922i | \(-0.503978\pi\) | ||||
−0.0124962 | + | 0.999922i | \(0.503978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 13.0192i | − | 1.00147i | −0.865600 | − | 0.500737i | \(-0.833063\pi\) | ||
0.865600 | − | 0.500737i | \(-0.166937\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 10.8685i | − | 0.724565i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.3746 | 1.02203 | 0.511017 | − | 0.859570i | \(-0.329269\pi\) | ||||
0.511017 | + | 0.859570i | \(0.329269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.54983 | − | 17.4356i | −0.397360 | − | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 21.2608i | − | 1.01242i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −20.5498 | −0.893471 | −0.446736 | − | 0.894666i | \(-0.647414\pi\) | ||||
−0.446736 | + | 0.894666i | \(0.647414\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.3746 | 0.574983 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 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 | \(0.123890\pi\) | ||||
−0.925208 | + | 0.379460i | \(0.876110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.476171i | − | 0.0144294i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 77.0241 | 2.20069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.7703i | 1.80460i | 0.431107 | + | 0.902301i | \(0.358123\pi\) | ||||
−0.431107 | + | 0.902301i | \(0.641877\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 22.5498 | 0.578201 | ||||||||
\(40\) | 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 | ||||||||
\(45\) | 18.8248 | 0.418328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4743 | 0.265410 | 0.132705 | − | 0.991156i | \(-0.457634\pi\) | ||||
0.132705 | + | 0.991156i | \(0.457634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 101.674 | 2.07497 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.0937i | 0.590072i | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 30.1993 | − | 13.0767i | 0.529813 | − | 0.229416i | ||||
\(58\) | 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 | ||||||||
\(63\) | 36.8248 | 0.584520 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 81.6941i | 1.25683i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 102.939i | 1.53640i | 0.640208 | + | 0.768202i | \(0.278848\pi\) | ||||
−0.640208 | + | 0.768202i | \(0.721152\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 35.5934i | − | 0.515846i | ||||||
\(70\) | 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 | ||||||||
\(75\) | 24.8975i | 0.331967i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.37459 | 0.0438258 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26.6454i | 0.337283i | 0.985677 | + | 0.168642i | \(0.0539381\pi\) | ||||
−0.985677 | + | 0.168642i | \(0.946062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 89.6977 | 1.08069 | 0.540347 | − | 0.841442i | \(-0.318293\pi\) | ||||
0.540347 | + | 0.841442i | \(0.318293\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −109.024 | −1.28264 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −45.0997 | −0.518387 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | −40.7492 | −0.438163 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 47.3746 | + | 109.407i | 0.498680 | + | 1.15165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 41.3390i | − | 0.426176i | −0.977033 | − | 0.213088i | \(-0.931648\pi\) | ||
0.977033 | − | 0.213088i | \(-0.0683521\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.824752 | 0.00833082 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 150.749 | 1.49257 | 0.746283 | − | 0.665629i | \(-0.231837\pi\) | ||||
0.746283 | + | 0.665629i | \(0.231837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 22.8360i | − | 0.221709i | −0.993837 | − | 0.110854i | \(-0.964641\pi\) | ||
0.993837 | − | 0.110854i | \(-0.0353587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 133.410i | 1.27057i | ||||||||
\(106\) | 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 | \(0.0683414\pi\) | ||||
−0.977040 | + | 0.213055i | \(0.931659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −115.650 | −1.04189 | ||||||||
\(112\) | 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 | ||||||||
\(117\) | 39.0575i | 0.333824i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −213.272 | −1.79220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.924 | −0.999375 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.19934 | −0.0504011 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 66.6736 | 0.533389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 146.790i | − | 1.15583i | −0.816098 | − | 0.577913i | \(-0.803867\pi\) | ||
0.816098 | − | 0.577913i | \(-0.196133\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 83.3528i | 0.646146i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 188.921 | 1.44215 | 0.721073 | − | 0.692859i | \(-0.243649\pi\) | ||||
0.721073 | + | 0.692859i | \(0.243649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 92.6736 | + | 214.020i | 0.696794 | + | 1.60918i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 32.6054i | 0.241522i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −71.3264 | −0.520631 | −0.260315 | − | 0.965524i | \(-0.583827\pi\) | ||||
−0.260315 | + | 0.965524i | \(0.583827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −43.5739 | −0.313481 | −0.156741 | − | 0.987640i | \(-0.550099\pi\) | ||||
−0.156741 | + | 0.987640i | \(0.550099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.6060i | 0.153234i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.57919i | 0.0250293i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 163.388i | − | 1.12682i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 176.104i | 1.19799i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −71.6769 | −0.481053 | −0.240527 | − | 0.970643i | \(-0.577320\pi\) | ||||
−0.240527 | + | 0.970643i | \(0.577320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 68.9051i | − | 0.456325i | −0.973623 | − | 0.228163i | \(-0.926728\pi\) | ||
0.973623 | − | 0.228163i | \(-0.0732718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −52.1238 | −0.340678 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 44.7010 | 0.281138 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 2.98793i | 0.0181087i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 22.6495 | + | 52.3068i | 0.132453 | + | 0.305888i | ||||
\(172\) | 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 | ||||||||
\(177\) | 0.398675 | 0.00225240 | ||||||||
\(178\) | 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 | \(0.0249274\pi\) | ||||
−0.996935 | + | 0.0782317i | \(0.975073\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 49.9259i | − | 0.272819i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 418.978i | − | 2.26475i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.77657 | −0.0255432 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 63.7823i | 0.337473i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 237.973 | 1.24593 | 0.622965 | − | 0.782250i | \(-0.285928\pi\) | ||||
0.622965 | + | 0.782250i | \(0.285928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 249.876i | 1.29469i | 0.762196 | + | 0.647346i | \(0.224121\pi\) | ||||
−0.762196 | + | 0.647346i | \(0.775879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −141.498 | −0.725633 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 253.251 | 1.28554 | 0.642769 | − | 0.766060i | \(-0.277786\pi\) | ||||
0.642769 | + | 0.766060i | \(0.277786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 48.0274 | 0.241344 | 0.120672 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120672 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −178.296 | −0.887043 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 319.618i | − | 1.57447i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 22.4591i | − | 0.109557i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 61.6495 | 0.297824 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.07558 | + | 4.79335i | 0.00993100 | + | 0.0229347i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 278.279i | 1.31886i | 0.751767 | + | 0.659429i | \(0.229202\pi\) | ||||
−0.751767 | + | 0.659429i | \(0.770798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 186.598 | 0.876047 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −301.973 | −1.40452 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 288.786i | − | 1.33081i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.3561i | 0.0883840i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 226.202i | − | 1.02354i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 67.6910i | − | 0.303547i | −0.988415 | − | 0.151773i | \(-0.951502\pi\) | ||
0.988415 | − | 0.151773i | \(-0.0484984\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −43.1238 | −0.191661 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | 5.84495i | 0.0253028i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −226.323 | −0.971344 | −0.485672 | − | 0.874141i | \(-0.661425\pi\) | ||||
−0.485672 | + | 0.874141i | \(0.661425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −78.2749 | −0.333085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −46.1512 | −0.194731 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −69.1204 | −0.289207 | −0.144603 | − | 0.989490i | \(-0.546191\pi\) | ||||
−0.144603 | + | 0.989490i | \(0.546191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 108.486i | − | 0.450150i | −0.974341 | − | 0.225075i | \(-0.927737\pi\) | ||
0.974341 | − | 0.225075i | \(-0.0722628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −637.993 | −2.60405 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −226.997 | + | 98.2924i | −0.919015 | + | 0.397945i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 155.361i | 0.623940i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −46.7766 | −0.186361 | −0.0931804 | − | 0.995649i | \(-0.529703\pi\) | ||||
−0.0931804 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.64950 | 0.0223301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 188.835i | − | 0.740530i | ||||||
\(256\) | 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 | ||||||||
\(261\) | − | 78.1149i | − | 0.299291i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 34.8796 | 0.132622 | 0.0663109 | − | 0.997799i | \(-0.478877\pi\) | ||||
0.0663109 | + | 0.997799i | \(0.478877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 161.944i | 0.611109i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 241.196 | 0.903356 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | −276.797 | −1.01391 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | − | 70.5796i | − | 0.252974i | ||||||
\(280\) | 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 | ||||||||
\(285\) | −189.498 | + | 82.0552i | −0.664906 | + | 0.287913i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 43.9343i | − | 0.153081i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8762 | 0.0445545 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 71.6013 | 0.246053 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 1.42851i | 0.00480980i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 267.541i | 0.894787i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −590.715 | −1.96251 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 261.105i | 0.861733i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 180.873 | 0.593026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 83.3053i | 0.271353i | 0.990753 | + | 0.135676i | \(0.0433208\pi\) | ||||
−0.990753 | + | 0.135676i | \(0.956679\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.5531 | 0.128004 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.22674 | −0.0135908 | −0.00679540 | − | 0.999977i | \(-0.502163\pi\) | ||||
−0.00679540 | + | 0.999977i | \(0.502163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.894 | −0.507648 | −0.253824 | − | 0.967250i | \(-0.581688\pi\) | ||||
−0.253824 | + | 0.967250i | \(0.581688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −231.072 | −0.733563 | ||||||||
\(316\) | 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 | ||||||||
\(321\) | 285.897 | 0.890645 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −131.175 | − | 302.936i | −0.406115 | − | 0.937883i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 187.145i | − | 0.575831i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −80.4469 | −0.246015 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −153.120 | −0.465412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 133.080i | 0.402055i | 0.979586 | + | 0.201027i | \(0.0644281\pi\) | ||||
−0.979586 | + | 0.201027i | \(0.935572\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 200.311i | − | 0.601534i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 645.934i | − | 1.92816i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 351.831i | 1.04401i | 0.852943 | + | 0.522004i | \(0.174815\pi\) | ||||
−0.852943 | + | 0.522004i | \(0.825185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.90364 | −0.0233146 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.46785i | − | 0.0189673i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −646.564 | −1.88503 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 223.345i | 0.647378i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 348.124 | 1.00324 | 0.501619 | − | 0.865089i | \(-0.332738\pi\) | ||||
0.501619 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −614.323 | −1.76024 | −0.880119 | − | 0.474753i | \(-0.842537\pi\) | ||||
−0.880119 | + | 0.474753i | \(0.842537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −67.6495 | −0.192734 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 151.292 | 0.428590 | 0.214295 | − | 0.976769i | \(-0.431255\pi\) | ||||
0.214295 | + | 0.976769i | \(0.431255\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 676.012i | 1.90426i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 369.397i | − | 1.03473i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −497.519 | −1.38585 | −0.692924 | − | 0.721011i | \(-0.743678\pi\) | ||||
−0.692924 | + | 0.721011i | \(0.743678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −247.000 | + | 263.272i | −0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 209.447i | − | 0.576990i | ||||||
\(364\) | 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 | ||||||||
\(369\) | − | 10.7376i | − | 0.0290991i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 316.793i | 0.853889i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 51.4695i | 0.137988i | 0.997617 | + | 0.0689940i | \(0.0219789\pi\) | ||||
−0.997617 | + | 0.0689940i | \(0.978021\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 115.482i | 0.307952i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 338.997 | 0.899195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 447.214i | 1.17999i | 0.807409 | + | 0.589993i | \(0.200869\pi\) | ||||
−0.807409 | + | 0.589993i | \(0.799131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 254.248 | 0.667316 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | −144.371 | −0.373052 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.7700 | −0.0688174 | −0.0344087 | − | 0.999408i | \(-0.510955\pi\) | ||||
−0.0344087 | + | 0.999408i | \(0.510955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −357.045 | −0.913158 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 327.221i | 0.832623i | ||||||||
\(394\) | 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 | ||||||||
\(399\) | −370.694 | + | 160.515i | −0.929059 | + | 0.402294i | ||||
\(400\) | 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 | ||||||||
\(405\) | −56.4743 | −0.139443 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.3563i | − | 0.0451015i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 325.039i | 0.794716i | 0.917664 | + | 0.397358i | \(0.130073\pi\) | ||||
−0.917664 | + | 0.397358i | \(0.869927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 123.541i | − | 0.300586i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.82538i | 0.00684112i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −562.846 | −1.35625 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 75.4722i | − | 0.180989i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 51.0033 | 0.121726 | 0.0608631 | − | 0.998146i | \(-0.480615\pi\) | ||||
0.0608631 | + | 0.998146i | \(0.480615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 214.794i | − | 0.510201i | −0.966915 | − | 0.255100i | \(-0.917892\pi\) | ||
0.966915 | − | 0.255100i | \(-0.0821085\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37.4228 | −0.0884699 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 249.752 | 0.587653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 353.821 | 0.828622 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.19934 | −0.0144507 | ||||||||
\(430\) | 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 | \(-0.935189\pi\) | ||
0.979343 | − | 0.202205i | \(-0.0648108\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 282.997 | 0.650567 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 155.148 | + | 358.299i | 0.355029 | + | 0.819905i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 542.848i | 1.23656i | 0.785959 | + | 0.618278i | \(0.212170\pi\) | ||||
−0.785959 | + | 0.618278i | \(0.787830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −305.021 | −0.691657 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −134.680 | −0.304019 | −0.152009 | − | 0.988379i | \(-0.548574\pi\) | ||||
−0.152009 | + | 0.988379i | \(0.548574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 873.811i | 1.96362i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 124.148i | − | 0.277736i | ||||||
\(448\) | 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 | ||||||||
\(453\) | 119.347 | 0.263460 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | − | 90.2810i | − | 0.196691i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.6221 | 0.0859482 | 0.0429741 | − | 0.999076i | \(-0.486317\pi\) | ||||
0.0429741 | + | 0.999076i | \(0.486317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 158.625 | 0.342603 | 0.171302 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171302 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 255.698 | 0.549887 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 672.619 | 1.44030 | 0.720149 | − | 0.693820i | \(-0.244074\pi\) | ||||
0.720149 | + | 0.693820i | \(0.244074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1263.57i | − | 2.69418i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 273.140i | 0.579916i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.2300 | −0.0279705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −108.526 | − | 250.629i | −0.228475 | − | 0.527641i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 77.4244i | 0.162315i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −870.846 | −1.81805 | −0.909025 | − | 0.416743i | \(-0.863172\pi\) | ||||
−0.909025 | + | 0.416743i | \(0.863172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 869.292 | 1.80726 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 436.906i | 0.904566i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 259.399i | 0.534843i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 274.616i | − | 0.563894i | −0.959430 | − | 0.281947i | \(-0.909020\pi\) | ||
0.959430 | − | 0.281947i | \(-0.0909802\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 73.4367i | 0.150177i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 781.588 | 1.59183 | 0.795915 | − | 0.605409i | \(-0.206990\pi\) | ||||
0.795915 | + | 0.605409i | \(0.206990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 452.405i | 0.917657i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.17525 | −0.0104550 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | −175.904 | −0.351105 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 914.846 | 1.81878 | 0.909389 | − | 0.415946i | \(-0.136550\pi\) | ||||
0.909389 | + | 0.415946i | \(0.136550\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −945.939 | −1.87315 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 0.863158i | − | 0.00170248i | ||||||
\(508\) | 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 | ||||||||
\(513\) | −90.5980 | + | 39.2301i | −0.176604 | + | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 143.294i | 0.278241i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.42939 | −0.00663324 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.1993 | 0.0813089 | ||||||||
\(520\) | 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 | \(0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 305.615i | − | 0.582124i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 408.764i | 0.775643i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −106.704 | −0.201709 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.690526i | 0.00130043i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.5980 | 0.0874259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1035.75i | 1.93599i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 129.498 | 0.241151 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | −49.0515 | −0.0903342 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 291.445i | − | 0.534761i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 851.749i | − | 1.55713i | −0.627565 | − | 0.778564i | \(-0.715948\pi\) | ||
0.627565 | − | 0.778564i | \(-0.284052\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 86.4743 | 0.157512 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 453.993 | − | 196.585i | 0.823944 | − | 0.356778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 327.070i | − | 0.591446i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 725.691 | 1.30755 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 125.423 | 0.225176 | 0.112588 | − | 0.993642i | \(-0.464086\pi\) | ||||
0.112588 | + | 0.993642i | \(0.464086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 626.531i | − | 1.12081i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 8.27327i | − | 0.0147474i | ||||||
\(562\) | 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 | ||||||||
\(567\) | −110.474 | −0.194840 | ||||||||
\(568\) | 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 | ||||||||
\(573\) | 412.181i | 0.719338i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −432.797 | −0.747491 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1101.03 | −1.89506 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.09510i | 0.0121700i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 245.082i | − | 0.418944i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −429.375 | −0.731473 | −0.365736 | − | 0.930718i | \(-0.619183\pi\) | ||||
−0.365736 | + | 0.930718i | \(0.619183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 410.199 | − | 177.622i | 0.696434 | − | 0.301565i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 438.643i | 0.742205i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −243.100 | −0.409949 | −0.204974 | − | 0.978767i | \(-0.565711\pi\) | ||||
−0.204974 | + | 0.978767i | \(0.565711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1338.26 | 2.24918 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 83.1859i | 0.139340i | ||||||||
\(598\) | 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 | \(0.165118\pi\) | ||||
−0.868447 | + | 0.495781i | \(0.834882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 308.817i | − | 0.512135i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 758.791 | 1.25420 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 724.886i | − | 1.19421i | −0.802163 | − | 0.597106i | \(-0.796317\pi\) | ||
0.802163 | − | 0.597106i | \(-0.203683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 553.595 | 0.909022 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 38.9003 | 0.0632526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −87.2300 | −0.141378 | −0.0706889 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706889 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 846.482 | 1.36750 | 0.683749 | − | 0.729717i | \(-0.260348\pi\) | ||||
0.683749 | + | 0.729717i | \(0.260348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 106.780i | 0.171949i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1709.34i | 2.74372i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −777.736 | −1.24438 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.30232 | + | 3.59501i | −0.0132413 | + | 0.00573367i | ||||
\(628\) | 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 | ||||||||
\(633\) | −481.993 | −0.761443 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 921.094i | 1.45054i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1323.70i | − | 2.07803i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 323.197i | 0.505786i | ||||||||
\(640\) | 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 | ||||||||
\(645\) | − | 523.032i | − | 0.810902i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 157.368 | 0.243227 | 0.121614 | − | 0.992578i | \(-0.461193\pi\) | ||||
0.121614 | + | 0.992578i | \(0.461193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0632792i | 9.75026e-5i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 500.193 | 0.768345 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 726.220 | 1.11213 | 0.556064 | − | 0.831139i | \(-0.312311\pi\) | ||||
0.556064 | + | 0.831139i | \(0.312311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1185.46 | −1.80987 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.5257 | −0.0510285 | ||||||||
\(658\) | 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 | \(-0.770075\pi\) | ||
0.750267 | − | 0.661135i | \(-0.229925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 391.794 | 0.590941 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −581.519 | − | 1342.96i | −0.874465 | − | 2.01949i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 535.083i | − | 0.802223i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 117.244 | 0.175253 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.92442 | 0.0118099 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1035.99i | 1.53935i | 0.638434 | + | 0.769677i | \(0.279583\pi\) | ||||
−0.638434 | + | 0.769677i | \(0.720417\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 74.6925i | − | 0.110656i | ||||||
\(676\) | 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 | ||||||||
\(681\) | −708.797 | −1.04082 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | − | 426.811i | − | 0.621268i | ||||||
\(688\) | 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 | ||||||||
\(693\) | −10.1238 | −0.0146086 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 273.423 | 0.393414 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 62.1869i | 0.0892209i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 392.003i | − | 0.560806i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −163.958 | −0.233892 | −0.116946 | − | 0.993138i | \(-0.537310\pi\) | ||||
−0.116946 | + | 0.993138i | \(0.537310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1164.18 | − | 504.104i | 1.65602 | − | 0.717076i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 135.576i | − | 0.192307i | ||||||
\(706\) | 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 | ||||||||
\(711\) | − | 79.9362i | − | 0.112428i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 483.467i | − | 0.678074i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 22.4591i | − | 0.0314114i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 119.720i | − | 0.166974i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 171.072 | 0.237931 | 0.118965 | − | 0.992898i | \(-0.462042\pi\) | ||||
0.118965 | + | 0.992898i | \(0.462042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 280.310i | 0.388780i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 187.904 | 0.259894 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | − | 1105.04i | − | 1.50345i | ||||||
\(736\) | 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 | ||||||||
\(741\) | −170.248 | − | 393.170i | −0.229754 | − | 0.530594i | ||||
\(742\) | 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 | ||||||||
\(747\) | −269.093 | −0.360232 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2026.13i | 2.70512i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1167.89i | − | 1.55512i | −0.628809 | − | 0.777559i | \(-0.716457\pi\) | ||
0.628809 | − | 0.777559i | \(-0.283543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 81.0194i | − | 0.107595i | ||||||
\(754\) | 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 | ||||||||
\(759\) | 9.78523i | 0.0128923i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1148.47 | 1.50916 | 0.754578 | − | 0.656210i | \(-0.227842\pi\) | ||||
0.754578 | + | 0.656210i | \(0.227842\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 570.121i | − | 0.747210i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 327.072 | 0.427545 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −376.096 | −0.487803 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 1419.59 | 1.82701 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 62.4053 | − | 27.0223i | 0.0801095 | − | 0.0346884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.6175i | 0.0379225i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 135.299 | 0.172796 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −989.540 | −1.26056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1141.88i | 1.45092i | 0.688263 | + | 0.725461i | \(0.258374\pi\) | ||||
−0.688263 | + | 0.725461i | \(0.741626\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 60.4132i | 0.0765693i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 56.0125i | − | 0.0708123i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 375.274i | 0.473233i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −280.495 | −0.352824 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 417.764i | 0.521553i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.07227 | −0.00382599 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1582.83 | −1.96625 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 156.289 | 0.193667 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 879.175 | 1.08674 | 0.543372 | − | 0.839492i | \(-0.317147\pi\) | ||||
0.543372 | + | 0.839492i | \(0.317147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 654.537i | 0.807074i | 0.914963 | + | 0.403537i | \(0.132219\pi\) | ||||
−0.914963 | + | 0.403537i | \(0.867781\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 251.142i | 0.308907i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −266.048 | −0.326439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −363.326 | − | 839.066i | −0.444708 | − | 1.02701i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 479.427i | − | 0.585381i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1419.35 | −1.72880 | −0.864402 | − | 0.502801i | \(-0.832303\pi\) | ||||
−0.864402 | + | 0.502801i | \(0.832303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 671.107 | 0.815440 | 0.407720 | − | 0.913107i | \(-0.366324\pi\) | ||||
0.407720 | + | 0.913107i | \(0.366324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.84476i | − | 0.00829667i | ||||||
\(826\) | 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 | \(-0.811808\pi\) | ||
0.830260 | − | 0.557376i | \(-0.188192\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 859.740i | 1.03459i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1766.54 | 2.12069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 637.268i | − | 0.763195i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 122.248 | 0.146054 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 324.688 | 0.385157 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.12707 | 0.00370067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1484.34 | 1.75246 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 89.3287i | − | 0.105216i | ||||||
\(850\) | 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 | ||||||||
\(855\) | −142.124 | − | 328.221i | −0.166227 | − | 0.383884i | ||||
\(856\) | 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 | ||||||||
\(861\) | 76.0964 | 0.0883814 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 22.3023i | 0.0257235i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.32527i | − | 0.00842955i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1340.18 | 1.53867 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 124.017i | 0.142059i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −818.413 | −0.935329 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 526.564i | − | 0.600415i | −0.953874 | − | 0.300207i | \(-0.902944\pi\) | ||
0.953874 | − | 0.300207i | \(-0.0970559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −143.203 | −0.162915 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1444.25 | 1.63933 | 0.819664 | − | 0.572844i | \(-0.194160\pi\) | ||||
0.819664 | + | 0.572844i | \(0.194160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −593.086 | −0.671671 | −0.335836 | − | 0.941921i | \(-0.609019\pi\) | ||||
−0.335836 | + | 0.941921i | \(0.609019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.50166 | −0.00282673 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | −2.47425 | −0.00277694 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −94.1786 | − | 217.496i | −0.105463 | − | 0.243557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 469.150i | 0.524190i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −463.395 | −0.516606 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −612.591 | −0.681414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 448.406i | − | 0.497675i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1023.15i | − | 1.13305i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 177.705i | − | 0.196359i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 164.499i | 0.181366i | 0.995880 | + | 0.0906829i | \(0.0289050\pi\) | ||||
−0.995880 | + | 0.0906829i | \(0.971095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −452.248 | −0.497522 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 313.281i | 0.342384i | ||||||||
\(916\) | 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 | ||||||||
\(921\) | −144.289 | −0.156666 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1402.58 | −1.51959 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 959.795i | 1.03762i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 68.5081i | 0.0739030i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 154.482 | 0.166288 | 0.0831441 | − | 0.996538i | \(-0.473504\pi\) | ||||
0.0831441 | + | 0.996538i | \(0.473504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −767.619 | − | 1772.74i | −0.824510 | − | 1.90412i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 7.32093i | − | 0.00784665i | ||||||
\(934\) | 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 | ||||||||
\(939\) | − | 275.212i | − | 0.293090i | ||||||
\(940\) | 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 | ||||||||
\(945\) | − | 400.229i | − | 0.423523i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −222.206 | −0.234642 | −0.117321 | − | 0.993094i | \(-0.537431\pi\) | ||||
−0.117321 | + | 0.993094i | \(0.537431\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 145.492i | − | 0.153311i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 482.502 | 0.507362 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 12.3987 | 0.0129558 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 875.526 | 0.912957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 407.502 | 0.424039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 495.188i | 0.514214i | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 524.701 | − | 227.202i | 0.541487 | − | 0.234471i | ||||
\(970\) | 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 | ||||||||
\(975\) | 324.145 | 0.332456 | ||||||||
\(976\) | 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 | ||||||||
\(981\) | − | 139.338i | − | 0.142037i | ||||||
\(982\) | 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 | ||||||||
\(987\) | − | 265.212i | − | 0.268706i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −988.935 | −0.999935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1546.81i | 1.56086i | 0.625244 | + | 0.780429i | \(0.284999\pi\) | ||||
−0.625244 | + | 0.780429i | \(0.715001\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −230.502 | −0.232127 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 346.949 | 0.347296 |
(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 | 912.3.o.b.721.3 | 4 | ||
3.2 | odd | 2 | 2736.3.o.l.721.3 | 4 | |||
4.3 | odd | 2 | 57.3.c.b.37.1 | ✓ | 4 | ||
12.11 | even | 2 | 171.3.c.f.37.4 | 4 | |||
19.18 | odd | 2 | inner | 912.3.o.b.721.1 | 4 | ||
57.56 | even | 2 | 2736.3.o.l.721.4 | 4 | |||
76.75 | even | 2 | 57.3.c.b.37.4 | yes | 4 | ||
228.227 | odd | 2 | 171.3.c.f.37.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.c.b.37.1 | ✓ | 4 | 4.3 | odd | 2 | ||
57.3.c.b.37.4 | yes | 4 | 76.75 | even | 2 | ||
171.3.c.f.37.1 | 4 | 228.227 | odd | 2 | |||
171.3.c.f.37.4 | 4 | 12.11 | even | 2 | |||
912.3.o.b.721.1 | 4 | 19.18 | odd | 2 | inner | ||
912.3.o.b.721.3 | 4 | 1.1 | even | 1 | trivial | ||
2736.3.o.l.721.3 | 4 | 3.2 | odd | 2 | |||
2736.3.o.l.721.4 | 4 | 57.56 | even | 2 |