Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,3,Mod(37,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("171.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.65941252056\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-1.63746 - 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 171.37 |
Dual form | 171.3.c.f.37.4 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.04547i | − | 1.52274i | −0.648319 | − | 0.761369i | \(-0.724528\pi\) | ||
0.648319 | − | 0.761369i | \(-0.275472\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.27492 | −1.31873 | ||||||||
\(5\) | 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 | \(-0.159687\pi\) | ||||
0.876780 | + | 0.480892i | \(0.159687\pi\) | |||||||
\(8\) | 3.88273i | 0.485341i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 19.1101i | − | 1.91101i | ||||||
\(11\) | −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 | \(0.166937\pi\) | ||||
−0.865600 | + | 0.500737i | \(0.833063\pi\) | |||||||
\(14\) | − | 37.3830i | − | 2.67021i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.27492 | −0.579682 | ||||||||
\(17\) | −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 | ||||
\(20\) | −33.0997 | −1.65498 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.837253i | 0.0380570i | ||||||||
\(23\) | −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 | ||||||||
\(26\) | 39.6495 | 1.52498 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −64.7492 | −2.31247 | ||||||||
\(29\) | 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 | \(0.876110\pi\) | |||||||
\(32\) | 43.7774i | 1.36805i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 52.9139i | 1.55629i | ||||||||
\(35\) | 77.0241 | 2.20069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 66.7703i | − | 1.80460i | −0.431107 | − | 0.902301i | \(-0.641877\pi\) | ||
0.431107 | − | 0.902301i | \(-0.358123\pi\) | |||||||
\(38\) | −53.0997 | − | 22.9928i | −1.39736 | − | 0.605075i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.3638i | 0.609095i | ||||||||
\(41\) | 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 | \(-0.689037\pi\) | ||||
−0.559579 | + | 0.828777i | \(0.689037\pi\) | |||||||
\(44\) | 1.45017 | 0.0329583 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 62.5840i | 1.36052i | ||||||||
\(47\) | 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 | ||||||||
\(50\) | − | 43.7774i | − | 0.875549i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 68.6750i | − | 1.32067i | ||||||
\(53\) | − | 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 | ||||||||
\(56\) | 47.6602i | 0.851074i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 79.2990 | 1.36722 | ||||||||
\(59\) | 0.230175i | 0.00390128i | 0.999998 | + | 0.00195064i | \(0.000620908\pi\) | ||||
−0.999998 | + | 0.00195064i | \(0.999379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.8248 | −0.472537 | −0.236268 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236268 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(62\) | 71.6495 | 1.15564 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 96.2234 | 1.50349 | ||||||||
\(65\) | 81.6941i | 1.25683i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 102.939i | 1.53640i | 0.640208 | + | 0.768202i | \(0.278848\pi\) | ||||
−0.640208 | + | 0.768202i | \(0.721152\pi\) | |||||||
\(68\) | 91.6495 | 1.34779 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 234.575i | − | 3.35107i | ||||||
\(71\) | 107.732i | 1.51736i | 0.651465 | + | 0.758679i | \(0.274155\pi\) | ||||
−0.651465 | + | 0.758679i | \(0.725845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1752 | 0.153086 | 0.0765428 | − | 0.997066i | \(-0.475612\pi\) | ||||
0.0765428 | + | 0.997066i | \(0.475612\pi\) | |||||||
\(74\) | −203.347 | −2.74793 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −39.8248 | + | 91.9713i | −0.524010 | + | 1.21015i | ||||
\(77\) | −3.37459 | −0.0438258 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26.6454i | 0.337283i | 0.985677 | + | 0.168642i | \(0.0539381\pi\) | ||||
−0.985677 | + | 0.168642i | \(0.946062\pi\) | |||||||
\(80\) | −58.1993 | −0.727492 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.9003 | 0.132931 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 146.560i | 1.70418i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.06743i | − | 0.0121299i | ||||||
\(89\) | − | 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 | ||||||||
\(92\) | 108.399 | 1.17825 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 37.9900i | − | 0.404149i | ||||||
\(95\) | 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 | \(0.931648\pi\) | |||||||
\(98\) | − | 309.644i | − | 3.15964i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −75.8248 | −0.758248 | ||||||||
\(101\) | −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 | \(-0.964641\pi\) | ||
0.993837 | − | 0.110854i | \(-0.0353587\pi\) | |||||||
\(104\) | −50.5498 | −0.486056 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −78.5980 | −0.741491 | ||||||||
\(107\) | 165.063i | 1.54264i | 0.636446 | + | 0.771321i | \(0.280404\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 46.4460i | − | 0.426110i | −0.977040 | − | 0.213055i | \(-0.931659\pi\) | ||
0.977040 | − | 0.213055i | \(-0.0683414\pi\) | |||||||
\(110\) | 5.25370i | 0.0477609i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −113.849 | −1.01651 | ||||||||
\(113\) | 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 | ||||||||
\(116\) | − | 137.350i | − | 1.18405i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.700993 | 0.00594062 | ||||||||
\(119\) | −213.272 | −1.79220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.924 | −0.999375 | ||||||||
\(122\) | 87.7851i | 0.719550i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 124.101i | − | 1.00081i | ||||||
\(125\) | −66.6736 | −0.533389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 146.790i | − | 1.15583i | −0.816098 | − | 0.577913i | \(-0.803867\pi\) | ||
0.816098 | − | 0.577913i | \(-0.196133\pi\) | |||||||
\(128\) | − | 117.936i | − | 0.921377i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 248.797 | 1.91383 | ||||||||
\(131\) | 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 | ||||
\(134\) | 313.498 | 2.33954 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 67.4608i | − | 0.496035i | ||||||
\(137\) | 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 | \(-0.449901\pi\) | ||||
0.156741 | + | 0.987640i | \(0.449901\pi\) | |||||||
\(140\) | −406.296 | −2.90211 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 328.096 | 2.31054 | ||||||||
\(143\) | − | 3.57919i | − | 0.0250293i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 163.388i | 1.12682i | ||||||||
\(146\) | − | 34.0339i | − | 0.233109i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 352.208i | 2.37978i | ||||||||
\(149\) | 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 | \(-0.926728\pi\) | ||
0.973623 | − | 0.228163i | \(-0.0732718\pi\) | |||||||
\(152\) | 67.6977 | + | 29.3140i | 0.445379 | + | 0.192855i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.2772i | 0.0667352i | ||||||||
\(155\) | 147.627i | 0.952433i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 157.698 | 1.00444 | 0.502222 | − | 0.864739i | \(-0.332516\pi\) | ||||
0.502222 | + | 0.864739i | \(0.332516\pi\) | |||||||
\(158\) | 81.1478 | 0.513594 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 274.700i | 1.71687i | ||||||||
\(161\) | −252.248 | −1.56675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −42.3987 | −0.260115 | −0.130057 | − | 0.991506i | \(-0.541516\pi\) | ||||
−0.130057 | + | 0.991506i | \(0.541516\pi\) | |||||||
\(164\) | − | 18.8799i | − | 0.115122i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 273.172i | − | 1.64561i | ||||||
\(167\) | − | 101.558i | − | 0.608132i | −0.952651 | − | 0.304066i | \(-0.901656\pi\) | ||
0.952651 | − | 0.304066i | \(-0.0983443\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.498344 | −0.00294878 | ||||||||
\(170\) | 332.030i | 1.95312i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 253.849 | 1.47587 | ||||||||
\(173\) | − | 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 | ||||||||
\(176\) | 2.54983 | 0.0144877 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −424.096 | −2.38256 | ||||||||
\(179\) | 74.7659i | 0.417687i | 0.977949 | + | 0.208843i | \(0.0669699\pi\) | ||||
−0.977949 | + | 0.208843i | \(0.933030\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 28.3199i | − | 0.156463i | −0.996935 | − | 0.0782317i | \(-0.975073\pi\) | ||
0.996935 | − | 0.0782317i | \(-0.0249274\pi\) | |||||||
\(182\) | 486.694 | 2.67414 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 79.7894i | − | 0.433638i | ||||||
\(185\) | − | 418.978i | − | 2.26475i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.77657 | 0.0255432 | ||||||||
\(188\) | −65.8007 | −0.350004 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −333.196 | − | 144.278i | −1.75366 | − | 0.759358i | ||||
\(191\) | 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 | \(-0.775879\pi\) | ||
0.762196 | − | 0.647346i | \(-0.224121\pi\) | |||||||
\(194\) | 125.897 | 0.648954 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −536.320 | −2.73633 | ||||||||
\(197\) | −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 | \(-0.538505\pi\) | ||||
−0.120672 | + | 0.992692i | \(0.538505\pi\) | |||||||
\(200\) | 55.8126i | 0.279063i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 459.103i | 2.27279i | ||||||||
\(203\) | 319.618i | 1.57447i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.4591i | 0.109557i | ||||||||
\(206\) | −69.5465 | −0.337604 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 120.752i | − | 0.580536i | ||||||
\(209\) | −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 | \(0.770798\pi\) | |||||||
\(212\) | 136.136i | 0.642150i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 502.694 | 2.34904 | ||||||||
\(215\) | −301.973 | −1.40452 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 288.786i | 1.33081i | ||||||||
\(218\) | −141.450 | −0.648854 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.09967 | 0.0413621 | ||||||||
\(221\) | − | 226.202i | − | 1.02354i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 67.6910i | − | 0.303547i | −0.988415 | − | 0.151773i | \(-0.951502\pi\) | ||
0.988415 | − | 0.151773i | \(-0.0484984\pi\) | |||||||
\(224\) | 537.364i | 2.39895i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8970 | 0.0614912 | ||||||||
\(227\) | − | 409.224i | − | 1.80275i | −0.433039 | − | 0.901375i | \(-0.642559\pi\) | ||
0.433039 | − | 0.901375i | \(-0.357441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −246.419 | −1.07607 | −0.538034 | − | 0.842923i | \(-0.680833\pi\) | ||||
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(230\) | 392.709i | 1.70743i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −101.100 | −0.435774 | ||||||||
\(233\) | 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 | ||||||||
\(236\) | − | 1.21416i | − | 0.00514473i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 649.513i | 2.72905i | ||||||||
\(239\) | −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 | \(0.0722628\pi\) | ||||
−0.974341 | + | 0.225075i | \(0.927737\pi\) | |||||||
\(242\) | 368.272i | 1.52179i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 152.048 | 0.623148 | ||||||||
\(245\) | 637.993 | 2.60405 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 226.997 | + | 98.2924i | 0.919015 | + | 0.397945i | ||||
\(248\) | −91.3472 | −0.368335 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 203.053i | 0.812211i | ||||||||
\(251\) | −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 | ||||||||
\(254\) | −447.045 | −1.76002 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 25.7218 | 0.100476 | ||||||||
\(257\) | 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 | ||||||
\(260\) | − | 430.930i | − | 1.65742i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 575.354i | − | 2.19601i | ||||||
\(263\) | 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 | ||||||
\(266\) | −651.794 | − | 282.235i | −2.45035 | − | 1.06103i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 542.995i | − | 2.02610i | ||||||
\(269\) | − | 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 | \(-0.586205\pi\) | ||||
−0.267522 | + | 0.963552i | \(0.586205\pi\) | |||||||
\(272\) | 161.148 | 0.592455 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 217.223i | − | 0.792784i | ||||||
\(275\) | −3.95182 | −0.0143703 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 496.371 | 1.79195 | 0.895977 | − | 0.444100i | \(-0.146477\pi\) | ||||
0.895977 | + | 0.444100i | \(0.146477\pi\) | |||||||
\(278\) | − | 132.703i | − | 0.477350i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 299.064i | 1.06808i | ||||||||
\(281\) | − | 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 | \(-0.470955\pi\) | ||||
0.0911200 | + | 0.995840i | \(0.470955\pi\) | |||||||
\(284\) | − | 568.280i | − | 2.00098i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.9003 | −0.0381130 | ||||||||
\(287\) | 43.9343i | 0.153081i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8762 | 0.0445545 | ||||||||
\(290\) | 497.595 | 1.71584 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −58.9485 | −0.201878 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | 259.251 | 0.875847 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 218.290i | − | 0.732517i | ||||||
\(299\) | − | 267.541i | − | 0.894787i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −590.715 | −1.96251 | ||||||||
\(302\) | −209.849 | −0.694864 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −70.0241 | + | 161.714i | −0.230342 | + | 0.531953i | ||||
\(305\) | −180.873 | −0.593026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 83.3053i | 0.271353i | 0.990753 | + | 0.135676i | \(0.0433208\pi\) | ||||
−0.990753 | + | 0.135676i | \(0.956679\pi\) | |||||||
\(308\) | 17.8007 | 0.0577944 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 449.595 | 1.45031 | ||||||||
\(311\) | −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 | \(0.581688\pi\) | |||||||
\(314\) | − | 480.264i | − | 1.52950i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 140.552i | − | 0.444785i | ||||||
\(317\) | − | 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 | ||||||
\(320\) | 603.794 | 1.88686 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 768.213i | 2.38576i | ||||||||
\(323\) | −131.175 | + | 302.936i | −0.406115 | + | 0.937883i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 187.145i | 0.575831i | ||||||||
\(326\) | 129.124i | 0.396086i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.8970 | −0.0423690 | ||||||||
\(329\) | 153.120 | 0.465412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 133.080i | 0.402055i | 0.979586 | + | 0.201027i | \(0.0644281\pi\) | ||||
−0.979586 | + | 0.201027i | \(0.935572\pi\) | |||||||
\(332\) | −473.148 | −1.42514 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −309.292 | −0.926025 | ||||||||
\(335\) | 645.934i | 1.92816i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 351.831i | − | 1.04401i | −0.852943 | − | 0.522004i | \(-0.825185\pi\) | ||
0.852943 | − | 0.522004i | \(-0.174815\pi\) | |||||||
\(338\) | 1.51770i | 0.00449022i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 575.093 | 1.69145 | ||||||||
\(341\) | − | 6.46785i | − | 0.0189673i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 646.564 | 1.88503 | ||||||||
\(344\) | − | 186.851i | − | 0.543173i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −74.1993 | −0.214449 | ||||||||
\(347\) | 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 | \(0.842537\pi\) | |||||||
\(350\) | − | 537.364i | − | 1.53533i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 12.0352i | − | 0.0341908i | ||||||
\(353\) | −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 | ||||||||
\(356\) | 734.556i | 2.06336i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 227.698 | 0.636027 | ||||||||
\(359\) | −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 | ||||
\(362\) | −86.2475 | −0.238253 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 842.979i | − | 2.31588i | ||||||
\(365\) | 70.1238 | 0.192120 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −267.003 | −0.727529 | −0.363765 | − | 0.931491i | \(-0.618509\pi\) | ||||
−0.363765 | + | 0.931491i | \(0.618509\pi\) | |||||||
\(368\) | 190.598 | 0.517929 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1275.99 | −3.44861 | ||||||||
\(371\) | − | 316.793i | − | 0.853889i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 51.4695i | − | 0.137988i | −0.997617 | − | 0.0689940i | \(-0.978021\pi\) | ||
0.997617 | − | 0.0689940i | \(-0.0219789\pi\) | |||||||
\(374\) | − | 14.5469i | − | 0.0388955i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.4341i | 0.128814i | ||||||||
\(377\) | −338.997 | −0.899195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 447.214i | 1.17999i | 0.807409 | + | 0.589993i | \(0.200869\pi\) | ||||
−0.807409 | + | 0.589993i | \(0.799131\pi\) | |||||||
\(380\) | −249.897 | + | 577.112i | −0.657624 | + | 1.51872i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 724.740i | − | 1.89722i | ||||||
\(383\) | 201.839i | 0.526994i | 0.964660 | + | 0.263497i | \(0.0848759\pi\) | ||||
−0.964660 | + | 0.263497i | \(0.915124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.1752 | −0.0550006 | ||||||||
\(386\) | −760.990 | −1.97148 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 218.060i | − | 0.562010i | ||||||
\(389\) | 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 | ||||||||
\(392\) | 394.771i | 1.00707i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 771.269i | 1.95754i | ||||||||
\(395\) | 167.198i | 0.423285i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 268.069 | 0.675237 | 0.337618 | − | 0.941283i | \(-0.390379\pi\) | ||||
0.337618 | + | 0.941283i | \(0.390379\pi\) | |||||||
\(398\) | 146.266i | 0.367503i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −133.323 | −0.333308 | ||||||||
\(401\) | − | 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 | ||||||||
\(404\) | 795.189 | 1.96829 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 973.389 | 2.39751 | ||||||||
\(407\) | 18.3563i | 0.0451015i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 325.039i | − | 0.794716i | −0.917664 | − | 0.397358i | \(-0.869927\pi\) | ||
0.917664 | − | 0.397358i | \(-0.130073\pi\) | |||||||
\(410\) | 68.3987 | 0.166826 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 120.458i | 0.292374i | ||||||||
\(413\) | 2.82538i | 0.00684112i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 562.846 | 1.35625 | ||||||||
\(416\) | −569.945 | −1.37006 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.5980 | + | 6.32113i | 0.0349235 | + | 0.0151223i | ||||
\(419\) | 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 | \(0.0821085\pi\) | ||||
−0.966915 | + | 0.255100i | \(0.917892\pi\) | |||||||
\(422\) | 847.492 | 2.00827 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 100.206 | 0.236335 | ||||||||
\(425\) | −249.752 | −0.587653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −353.821 | −0.828622 | ||||||||
\(428\) | − | 870.692i | − | 2.03433i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 919.650i | 2.13872i | ||||||||
\(431\) | 469.547i | 1.08944i | 0.838619 | + | 0.544718i | \(0.183363\pi\) | ||||
−0.838619 | + | 0.544718i | \(0.816637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 175.110i | 0.404411i | 0.979343 | + | 0.202205i | \(0.0648108\pi\) | ||||
−0.979343 | + | 0.202205i | \(0.935189\pi\) | |||||||
\(434\) | 879.492 | 2.02648 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 244.999i | 0.561924i | ||||||||
\(437\) | −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 | \(0.787830\pi\) | |||||||
\(440\) | − | 6.69803i | − | 0.0152228i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −688.894 | −1.55858 | ||||||||
\(443\) | −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 | ||||||
\(446\) | −206.151 | −0.462222 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1181.13 | 2.63646 | ||||||||
\(449\) | − | 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 | ||||||
\(452\) | − | 24.0703i | − | 0.0532530i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1246.28 | −2.74512 | ||||||||
\(455\) | 1002.79i | 2.20393i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.7218 | −0.0934831 | −0.0467415 | − | 0.998907i | \(-0.514884\pi\) | ||||
−0.0467415 | + | 0.998907i | \(0.514884\pi\) | |||||||
\(458\) | 750.464i | 1.63857i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 680.193 | 1.47868 | ||||||||
\(461\) | −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 | \(-0.554797\pi\) | ||||
−0.171302 | + | 0.985219i | \(0.554797\pi\) | |||||||
\(464\) | − | 241.503i | − | 0.520481i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 689.261i | − | 1.47910i | ||||||
\(467\) | 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 | ||||||||
\(470\) | − | 238.384i | − | 0.507201i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.893709 | −0.00189345 | ||||||||
\(473\) | 13.2300 | 0.0279705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 108.526 | − | 250.629i | 0.228475 | − | 0.527641i | ||||
\(476\) | 1124.99 | 2.36342 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 210.505i | 0.440386i | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 330.392 | 0.685461 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 637.866 | 1.31791 | ||||||||
\(485\) | 259.399i | 0.534843i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 274.616i | − | 0.563894i | −0.959430 | − | 0.281947i | \(-0.909020\pi\) | ||
0.959430 | − | 0.281947i | \(-0.0909802\pi\) | |||||||
\(488\) | − | 111.919i | − | 0.229342i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 1942.99i | − | 3.96529i | ||||||
\(491\) | 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 | ||||||
\(494\) | 299.347 | − | 691.313i | 0.605966 | − | 1.39942i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 218.207i | − | 0.439933i | ||||||
\(497\) | 1322.41i | 2.66078i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −387.918 | −0.777390 | −0.388695 | − | 0.921366i | \(-0.627074\pi\) | ||||
−0.388695 | + | 0.921366i | \(0.627074\pi\) | |||||||
\(500\) | 351.698 | 0.703395 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 142.457i | 0.283779i | ||||||||
\(503\) | 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 | ||||||||
\(506\) | − | 17.2054i | − | 0.0340028i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 774.304i | 1.52422i | ||||||||
\(509\) | 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 | ||||||||
\(512\) | − | 550.080i | − | 1.07438i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 661.292 | 1.28656 | ||||||||
\(515\) | − | 143.294i | − | 0.278241i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.42939 | −0.00663324 | ||||||||
\(518\) | −2496.07 | −4.81867 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −317.196 | −0.609992 | ||||||||
\(521\) | − | 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 | \(0.935897\pi\) | |||||||
\(524\) | −996.543 | −1.90180 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 106.225i | − | 0.201948i | ||||||
\(527\) | − | 408.764i | − | 0.775643i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −106.704 | −0.201709 | ||||||||
\(530\) | −493.196 | −0.930559 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −488.846 | + | 1128.94i | −0.918883 | + | 2.12207i | ||||
\(533\) | −46.5980 | −0.0874259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1035.75i | 1.93599i | ||||||||
\(536\) | −399.684 | −0.745680 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −274.804 | −0.510788 | ||||||||
\(539\) | −27.9518 | −0.0518587 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 989.664 | 1.82932 | 0.914661 | − | 0.404221i | \(-0.132457\pi\) | ||||
0.914661 | + | 0.404221i | \(0.132457\pi\) | |||||||
\(542\) | 441.584i | 0.814730i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 760.615i | − | 1.39819i | ||||||
\(545\) | − | 291.445i | − | 0.534761i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 851.749i | − | 1.55713i | −0.627565 | − | 0.778564i | \(-0.715948\pi\) | ||
0.627565 | − | 0.778564i | \(-0.284052\pi\) | |||||||
\(548\) | −376.241 | −0.686571 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.0352i | 0.0218821i | ||||||||
\(551\) | 453.993 | + | 196.585i | 0.823944 | + | 0.356778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 327.070i | 0.591446i | ||||||||
\(554\) | − | 1511.69i | − | 2.72868i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −229.849 | −0.413397 | ||||||||
\(557\) | −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 | ||||||
\(560\) | −714.392 | −1.27570 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −570.900 | −1.01584 | ||||||||
\(563\) | − | 762.666i | − | 1.35465i | −0.735685 | − | 0.677324i | \(-0.763140\pi\) | ||
0.735685 | − | 0.677324i | \(-0.236860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.6335i | 0.0506788i | ||||||||
\(566\) | − | 157.067i | − | 0.277504i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −418.296 | −0.736436 | ||||||||
\(569\) | − | 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 | \(-0.546291\pi\) | ||||
−0.144914 | + | 0.989444i | \(0.546291\pi\) | |||||||
\(572\) | 18.8799i | 0.0330069i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 133.801 | 0.233102 | ||||||||
\(575\) | −295.395 | −0.513731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 852.262 | 1.47706 | 0.738528 | − | 0.674222i | \(-0.235521\pi\) | ||||
0.738528 | + | 0.674222i | \(0.235521\pi\) | |||||||
\(578\) | − | 39.2143i | − | 0.0678448i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 861.859i | − | 1.48596i | ||||||
\(581\) | 1101.03 | 1.89506 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.09510i | 0.0121700i | ||||||||
\(584\) | 43.3905i | 0.0742987i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 251.794 | 0.429683 | ||||||||
\(587\) | −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 | ||||
\(590\) | 4.39868 | 0.00745538 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 619.289i | 1.04610i | ||||||||
\(593\) | 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 | ||||||||
\(596\) | −378.090 | −0.634379 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −814.791 | −1.36253 | ||||||||
\(599\) | 725.096i | 1.21051i | 0.796031 | + | 0.605256i | \(0.206929\pi\) | ||||
−0.796031 | + | 0.605256i | \(0.793071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 595.929i | − | 0.991563i | −0.868447 | − | 0.495781i | \(-0.834882\pi\) | ||
0.868447 | − | 0.495781i | \(-0.165118\pi\) | |||||||
\(602\) | 1799.01i | 2.98839i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 363.469i | 0.601770i | ||||||||
\(605\) | −758.791 | −1.25420 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 724.886i | − | 1.19421i | −0.802163 | − | 0.597106i | \(-0.796317\pi\) | ||
0.802163 | − | 0.597106i | \(-0.203683\pi\) | |||||||
\(608\) | 763.286 | + | 330.512i | 1.25540 | + | 0.543606i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 550.844i | 0.903023i | ||||||||
\(611\) | 162.404i | 0.265801i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 499.368 | 0.814630 | 0.407315 | − | 0.913288i | \(-0.366465\pi\) | ||||
0.407315 | + | 0.913288i | \(0.366465\pi\) | |||||||
\(614\) | 253.704 | 0.413199 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 13.1026i | − | 0.0212705i | ||||||
\(617\) | 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 | \(-0.739652\pi\) | ||||
−0.683749 | + | 0.729717i | \(0.739652\pi\) | |||||||
\(620\) | − | 778.721i | − | 1.25600i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.8724i | 0.0206952i | ||||||||
\(623\) | − | 1709.34i | − | 2.74372i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −777.736 | −1.24438 | ||||||||
\(626\) | 483.907i | 0.773014i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −831.842 | −1.32459 | ||||||||
\(629\) | 1160.11i | 1.84437i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −800.509 | −1.26864 | −0.634318 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634318 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(632\) | −103.457 | −0.163697 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −848.385 | −1.33815 | ||||||||
\(635\) | − | 921.094i | − | 1.45054i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1323.70i | 2.07803i | ||||||||
\(638\) | −21.8007 | −0.0341703 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 740.040i | − | 1.15631i | ||||||
\(641\) | 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 | \(-0.107947\pi\) | ||||
0.943046 | + | 0.332663i | \(0.107947\pi\) | |||||||
\(644\) | 1330.58 | 2.06613 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 922.585 | + | 399.491i | 1.42815 | + | 0.618407i | ||||
\(647\) | 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 | ||||||
\(650\) | 569.945 | 0.876839 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 223.650 | 0.343021 | ||||||||
\(653\) | −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 | ||||||||
\(656\) | − | 33.1967i | − | 0.0506047i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 466.324i | − | 0.708700i | ||||||
\(659\) | 259.756i | 0.394167i | 0.980387 | + | 0.197083i | \(0.0631469\pi\) | ||||
−0.980387 | + | 0.197083i | \(0.936853\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 874.021i | 1.32227i | 0.750267 | + | 0.661135i | \(0.229925\pi\) | ||||
−0.750267 | + | 0.661135i | \(0.770075\pi\) | |||||||
\(662\) | 405.292 | 0.612224 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 348.272i | 0.524506i | ||||||||
\(665\) | 581.519 | − | 1342.96i | 0.874465 | − | 2.01949i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 535.083i | − | 0.802223i | ||||||
\(668\) | 535.710i | 0.801961i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1967.18 | 2.93608 | ||||||||
\(671\) | 7.92442 | 0.0118099 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1035.99i | − | 1.53935i | −0.638434 | − | 0.769677i | \(-0.720417\pi\) | ||
0.638434 | − | 0.769677i | \(-0.279583\pi\) | |||||||
\(674\) | −1071.49 | −1.58975 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.62873 | 0.00388865 | ||||||||
\(677\) | 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 | ||||||||
\(680\) | − | 423.311i | − | 0.622516i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.6977 | −0.0288822 | ||||||||
\(683\) | − | 1186.44i | − | 1.73710i | −0.495604 | − | 0.868549i | \(-0.665053\pi\) | ||
0.495604 | − | 0.868549i | \(-0.334947\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 447.567 | 0.653383 | ||||||||
\(686\) | − | 1969.09i | − | 2.87040i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 446.344 | 0.648756 | ||||||||
\(689\) | 336.000 | 0.487663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 563.670 | 0.815731 | 0.407866 | − | 0.913042i | \(-0.366273\pi\) | ||||
0.407866 | + | 0.913042i | \(0.366273\pi\) | |||||||
\(692\) | 128.517i | 0.185718i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1060.20i | − | 1.52767i | ||||||
\(695\) | 273.423 | 0.393414 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 62.1869i | − | 0.0892209i | ||||||
\(698\) | 1870.91i | 2.68038i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −930.743 | −1.32963 | ||||||||
\(701\) | 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 | ||||
\(704\) | −26.4535 | −0.0375760 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 460.757i | 0.652631i | ||||||||
\(707\) | −1850.43 | −2.61730 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −315.993 | −0.445689 | −0.222844 | − | 0.974854i | \(-0.571534\pi\) | ||||
−0.222844 | + | 0.974854i | \(0.571534\pi\) | |||||||
\(710\) | 2058.78 | 2.89969 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 540.688 | 0.759393 | ||||||||
\(713\) | − | 483.467i | − | 0.678074i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 22.4591i | − | 0.0314114i | ||||||
\(716\) | − | 394.384i | − | 0.550816i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1515.18i | 2.11028i | ||||||||
\(719\) | 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 | ||||||
\(722\) | −801.787 | + | 752.232i | −1.11051 | + | 1.04187i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 149.385i | 0.206333i | ||||||||
\(725\) | 374.290i | 0.516262i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 261.169 | 0.359242 | 0.179621 | − | 0.983736i | \(-0.442513\pi\) | ||||
0.179621 | + | 0.983736i | \(0.442513\pi\) | |||||||
\(728\) | −620.495 | −0.852328 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 213.560i | − | 0.292548i | ||||||
\(731\) | 836.130 | 1.14382 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1185.78 | 1.61771 | 0.808855 | − | 0.588009i | \(-0.200088\pi\) | ||||
0.808855 | + | 0.588009i | \(0.200088\pi\) | |||||||
\(734\) | 813.152i | 1.10784i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 899.619i | − | 1.22231i | ||||||
\(737\) | − | 28.2997i | − | 0.0383985i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 738.557 | 0.999401 | 0.499701 | − | 0.866198i | \(-0.333443\pi\) | ||||
0.499701 | + | 0.866198i | \(0.333443\pi\) | |||||||
\(740\) | 2210.07i | 2.98659i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −964.784 | −1.30025 | ||||||||
\(743\) | − | 809.783i | − | 1.08988i | −0.838474 | − | 0.544941i | \(-0.816552\pi\) | ||
0.838474 | − | 0.544941i | \(-0.183448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 449.767 | 0.603714 | ||||||||
\(746\) | −156.749 | −0.210120 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.1960 | −0.0336845 | ||||||||
\(749\) | 2026.13i | 2.70512i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1167.89i | − | 1.55512i | −0.628809 | − | 0.777559i | \(-0.716457\pi\) | ||
0.628809 | − | 0.777559i | \(-0.283543\pi\) | |||||||
\(752\) | −115.698 | −0.153853 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1032.41i | 1.36924i | ||||||||
\(755\) | − | 432.374i | − | 0.572681i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −161.828 | −0.213776 | −0.106888 | − | 0.994271i | \(-0.534089\pi\) | ||||
−0.106888 | + | 0.994271i | \(0.534089\pi\) | |||||||
\(758\) | 1361.98 | 1.79681 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 424.797 | + | 183.943i | 0.558944 | + | 0.242030i | ||||
\(761\) | −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 | ||||||
\(764\) | −1255.29 | −1.64304 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 614.694 | 0.802473 | ||||||||
\(767\) | −2.99669 | −0.00390703 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 77.5673 | 0.100868 | 0.0504339 | − | 0.998727i | \(-0.483940\pi\) | ||||
0.0504339 | + | 0.998727i | \(0.483940\pi\) | |||||||
\(770\) | 64.4887i | 0.0837515i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1318.07i | 1.70735i | ||||||||
\(773\) | 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 | ||||||||
\(776\) | −160.508 | −0.206841 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 81.5272i | − | 0.104791i | ||||||
\(779\) | 62.4053 | + | 27.0223i | 0.0801095 | + | 0.0346884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.6175i | − | 0.0379225i | ||||||
\(782\) | − | 1087.37i | − | 1.39050i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −943.014 | −1.20282 | ||||||||
\(785\) | 989.540 | 1.26056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1141.88i | 1.45092i | 0.688263 | + | 0.725461i | \(0.258374\pi\) | ||||
−0.688263 | + | 0.725461i | \(0.741626\pi\) | |||||||
\(788\) | 1335.88 | 1.69528 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 509.196 | 0.644552 | ||||||||
\(791\) | 56.0125i | 0.0708123i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 375.274i | − | 0.473233i | ||||||
\(794\) | − | 816.397i | − | 1.02821i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 253.341 | 0.318267 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 629.283i | 0.786603i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1356.88 | −1.69187 | ||||||||
\(803\) | −3.07227 | −0.00382599 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1582.83 | −1.96625 | ||||||||
\(806\) | 932.816i | 1.15734i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 585.318i | − | 0.724404i | ||||||
\(809\) | −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 | \(0.132219\pi\) | ||||
−0.914963 | + | 0.403537i | \(0.867781\pi\) | |||||||
\(812\) | − | 1685.96i | − | 2.07630i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 55.9036 | 0.0686777 | ||||||||
\(815\) | −266.048 | −0.326439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −363.326 | + | 839.066i | −0.444708 | + | 1.02701i | ||||
\(818\) | −989.897 | −1.21014 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 118.470i | − | 0.144476i | ||||||
\(821\) | 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 | \(-0.633676\pi\) | ||||
−0.407720 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(824\) | 88.6661 | 0.107604 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.60464 | 0.0104172 | ||||||||
\(827\) | 186.204i | 0.225156i | 0.993643 | + | 0.112578i | \(0.0359108\pi\) | ||||
−0.993643 | + | 0.112578i | \(0.964089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 924.130i | 1.11475i | 0.830260 | + | 0.557376i | \(0.188192\pi\) | ||||
−0.830260 | + | 0.557376i | \(0.811808\pi\) | |||||||
\(830\) | − | 1714.13i | − | 2.06522i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1252.75i | 1.50571i | ||||||||
\(833\) | −1766.54 | −2.12069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 637.268i | − | 0.763195i | ||||||
\(836\) | 10.9485 | − | 25.2845i | 0.0130963 | − | 0.0302446i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 155.329i | − | 0.185357i | ||||||
\(839\) | − | 934.157i | − | 1.11342i | −0.830708 | − | 0.556708i | \(-0.812064\pi\) | ||
0.830708 | − | 0.556708i | \(-0.187936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 163.007 | 0.193825 | ||||||||
\(842\) | 654.151 | 0.776902 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 1467.90i | − | 1.73922i | ||||||
\(845\) | −3.12707 | −0.00370067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1484.34 | −1.75246 | ||||||||
\(848\) | 239.368i | 0.282274i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 760.615i | 0.894841i | ||||||||
\(851\) | 1372.12i | 1.61236i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 344.405 | 0.403758 | 0.201879 | − | 0.979411i | \(-0.435295\pi\) | ||||
0.201879 | + | 0.979411i | \(0.435295\pi\) | |||||||
\(854\) | 1077.55i | 1.26177i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −640.894 | −0.748708 | ||||||||
\(857\) | − | 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 | \(-0.714659\pi\) | ||||
−0.624405 | + | 0.781100i | \(0.714659\pi\) | |||||||
\(860\) | 1592.88 | 1.85219 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1429.99 | 1.65893 | ||||||||
\(863\) | − | 1240.65i | − | 1.43760i | −0.695217 | − | 0.718800i | \(-0.744692\pi\) | ||
0.695217 | − | 0.718800i | \(-0.255308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 152.881i | − | 0.176741i | ||||||
\(866\) | 533.292 | 0.615811 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 1523.32i | − | 1.75498i | ||||||
\(869\) | − | 7.32527i | − | 0.00842955i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1340.18 | −1.53867 | ||||||||
\(872\) | 180.337 | 0.206809 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1091.19 | + | 472.499i | 1.24850 | + | 0.540617i | ||||
\(875\) | −818.413 | −0.935329 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 526.564i | 0.600415i | 0.953874 | + | 0.300207i | \(0.0970559\pi\) | ||||
−0.953874 | + | 0.300207i | \(0.902944\pi\) | |||||||
\(878\) | 1653.23 | 1.88295 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.0000 | 0.0181818 | ||||||||
\(881\) | −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 | \(-0.390981\pi\) | ||||
0.335836 | + | 0.941921i | \(0.390981\pi\) | |||||||
\(884\) | 1193.20i | 1.34977i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 410.165i | 0.462940i | ||||||||
\(887\) | − | 589.691i | − | 0.664816i | −0.943136 | − | 0.332408i | \(-0.892139\pi\) | ||
0.943136 | − | 0.332408i | \(-0.107861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1801.83i | − | 2.02681i | ||||||
\(890\) | −2661.17 | −2.99008 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 357.064i | 0.400296i | ||||||||
\(893\) | 94.1786 | − | 217.496i | 0.105463 | − | 0.243557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 469.150i | 0.524190i | ||||||||
\(896\) | − | 1447.66i | − | 1.61569i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2200.48 | −2.45043 | ||||||||
\(899\) | −612.591 | −0.681414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 448.406i | 0.497675i | ||||||||
\(902\) | −2.99669 | −0.00332227 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.7175 | −0.0195991 | ||||||||
\(905\) | − | 177.705i | − | 0.196359i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 164.499i | 0.181366i | 0.995880 | + | 0.0906829i | \(0.0289050\pi\) | ||||
−0.995880 | + | 0.0906829i | \(0.971095\pi\) | |||||||
\(908\) | 2158.62i | 2.37734i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3053.97 | 3.35601 | ||||||||
\(911\) | − | 474.507i | − | 0.520864i | −0.965492 | − | 0.260432i | \(-0.916135\pi\) | ||
0.965492 | − | 0.260432i | \(-0.0838650\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.6594 | −0.0270092 | ||||||||
\(914\) | 130.108i | 0.142350i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1299.84 | 1.41904 | ||||||||
\(917\) | 2318.99 | 2.52889 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 708.488 | 0.770934 | 0.385467 | − | 0.922722i | \(-0.374040\pi\) | ||||
0.385467 | + | 0.922722i | \(0.374040\pi\) | |||||||
\(920\) | − | 500.672i | − | 0.544209i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 120.668i | 0.130876i | ||||||||
\(923\) | −1402.58 | −1.51959 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 959.795i | − | 1.03762i | ||||||
\(926\) | 483.090i | 0.521695i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1139.89 | −1.22833 | ||||||||
\(929\) | −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 | ||||
\(932\) | −1193.84 | −1.28094 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 2048.44i | − | 2.19319i | ||||||
\(935\) | 29.9726 | 0.0320563 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −289.223 | −0.308670 | −0.154335 | − | 0.988019i | \(-0.549323\pi\) | ||||
−0.154335 | + | 0.988019i | \(0.549323\pi\) | |||||||
\(938\) | 3848.17 | 4.10252 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −412.894 | −0.439249 | ||||||||
\(941\) | − | 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 | ||||||
\(944\) | − | 2.13486i | − | 0.00226150i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 40.2918i | − | 0.0425917i | ||||||
\(947\) | −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 | ||||||||
\(950\) | −763.286 | − | 330.512i | −0.803459 | − | 0.347908i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 828.076i | − | 0.869827i | ||||||
\(953\) | − | 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 | ||||||||
\(956\) | 364.605 | 0.381386 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2652.14i | 2.76841i | ||||||||
\(959\) | 875.526 | 0.912957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 407.502 | 0.424039 | ||||||||
\(962\) | − | 2647.41i | − | 2.75198i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 572.256i | − | 0.593626i | ||||||
\(965\) | − | 1567.95i | − | 1.62482i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 980.296 | 1.01375 | 0.506875 | − | 0.862020i | \(-0.330801\pi\) | ||||
0.506875 | + | 0.862020i | \(0.330801\pi\) | |||||||
\(968\) | − | 469.517i | − | 0.485038i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 789.993 | 0.814426 | ||||||||
\(971\) | 1699.98i | 1.75075i | 0.483441 | + | 0.875377i | \(0.339387\pi\) | ||||
−0.483441 | + | 0.875377i | \(0.660613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 534.866 | 0.549708 | ||||||||
\(974\) | −836.337 | −0.858662 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 267.347 | 0.273921 | ||||||||
\(977\) | − | 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 | ||||||||
\(980\) | −3365.36 | −3.43404 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 2380.31i | − | 2.42394i | ||||||
\(983\) | − | 541.654i | − | 0.551022i | −0.961298 | − | 0.275511i | \(-0.911153\pi\) | ||
0.961298 | − | 0.275511i | \(-0.0888470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1589.13 | −1.61333 | ||||||||
\(986\) | −1377.79 | −1.39735 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1197.39 | − | 518.485i | −1.21193 | − | 0.524782i | ||||
\(989\) | 988.935 | 0.999935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1546.81i | 1.56086i | 0.625244 | + | 0.780429i | \(0.284999\pi\) | ||||
−0.625244 | + | 0.780429i | \(0.715001\pi\) | |||||||
\(992\) | −1029.93 | −1.03824 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4027.36 | 4.05167 | ||||||||
\(995\) | −301.368 | −0.302882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1366.20 | −1.37031 | −0.685156 | − | 0.728397i | \(-0.740266\pi\) | ||||
−0.685156 | + | 0.728397i | \(0.740266\pi\) | |||||||
\(998\) | 1181.39i | 1.18376i | ||||||||
\(999\) | 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 | 171.3.c.f.37.1 | 4 | ||
3.2 | odd | 2 | 57.3.c.b.37.4 | yes | 4 | ||
4.3 | odd | 2 | 2736.3.o.l.721.4 | 4 | |||
12.11 | even | 2 | 912.3.o.b.721.1 | 4 | |||
19.18 | odd | 2 | inner | 171.3.c.f.37.4 | 4 | ||
57.56 | even | 2 | 57.3.c.b.37.1 | ✓ | 4 | ||
76.75 | even | 2 | 2736.3.o.l.721.3 | 4 | |||
228.227 | odd | 2 | 912.3.o.b.721.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.c.b.37.1 | ✓ | 4 | 57.56 | even | 2 | ||
57.3.c.b.37.4 | yes | 4 | 3.2 | odd | 2 | ||
171.3.c.f.37.1 | 4 | 1.1 | even | 1 | trivial | ||
171.3.c.f.37.4 | 4 | 19.18 | odd | 2 | inner | ||
912.3.o.b.721.1 | 4 | 12.11 | even | 2 | |||
912.3.o.b.721.3 | 4 | 228.227 | odd | 2 | |||
2736.3.o.l.721.3 | 4 | 76.75 | even | 2 | |||
2736.3.o.l.721.4 | 4 | 4.3 | odd | 2 |