Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(244,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.244");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.b (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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + \cdots + 614656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{12}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.4 | ||
Root | \(-3.08740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.244 |
Dual form | 405.4.b.f.244.13 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.08740i | − | 1.09156i | −0.837928 | − | 0.545781i | \(-0.816233\pi\) | ||
0.837928 | − | 0.545781i | \(-0.183767\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.53204 | −0.191506 | ||||||||
\(5\) | 5.83763 | − | 9.53531i | 0.522133 | − | 0.852864i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 31.3204i | 1.69114i | 0.533863 | + | 0.845571i | \(0.320740\pi\) | ||||
−0.533863 | + | 0.845571i | \(0.679260\pi\) | |||||||
\(8\) | − | 19.9692i | − | 0.882521i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −29.4393 | − | 18.0231i | −0.930953 | − | 0.569940i | ||||
\(11\) | 19.1937 | 0.526101 | 0.263051 | − | 0.964782i | \(-0.415271\pi\) | ||||
0.263051 | + | 0.964782i | \(0.415271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 20.9909i | − | 0.447833i | −0.974608 | − | 0.223917i | \(-0.928116\pi\) | ||
0.974608 | − | 0.223917i | \(-0.0718843\pi\) | |||||||
\(14\) | 96.6986 | 1.84598 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −73.9092 | −1.15483 | ||||||||
\(17\) | − | 6.19137i | − | 0.0883311i | −0.999024 | − | 0.0441656i | \(-0.985937\pi\) | ||
0.999024 | − | 0.0441656i | \(-0.0140629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 96.6654 | 1.16719 | 0.583594 | − | 0.812046i | \(-0.301646\pi\) | ||||
0.583594 | + | 0.812046i | \(0.301646\pi\) | |||||||
\(20\) | −8.94350 | + | 14.6085i | −0.0999914 | + | 0.163328i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 59.2586i | − | 0.574271i | ||||||
\(23\) | − | 162.986i | − | 1.47760i | −0.673923 | − | 0.738801i | \(-0.735392\pi\) | ||
0.673923 | − | 0.738801i | \(-0.264608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −56.8442 | − | 111.327i | −0.454754 | − | 0.890617i | ||||
\(26\) | −64.8074 | −0.488837 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 47.9842i | − | 0.323863i | ||||||
\(29\) | 7.64922 | 0.0489802 | 0.0244901 | − | 0.999700i | \(-0.492204\pi\) | ||||
0.0244901 | + | 0.999700i | \(0.492204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 225.025 | 1.30373 | 0.651865 | − | 0.758335i | \(-0.273987\pi\) | ||||
0.651865 | + | 0.758335i | \(0.273987\pi\) | |||||||
\(32\) | 68.4339i | 0.378048i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −19.1153 | −0.0964188 | ||||||||
\(35\) | 298.650 | + | 182.837i | 1.44231 | + | 0.883001i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 155.911i | − | 0.692748i | −0.938097 | − | 0.346374i | \(-0.887413\pi\) | ||
0.938097 | − | 0.346374i | \(-0.112587\pi\) | |||||||
\(38\) | − | 298.445i | − | 1.27406i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −190.412 | − | 116.573i | −0.752670 | − | 0.460793i | ||||
\(41\) | 315.221 | 1.20071 | 0.600357 | − | 0.799732i | \(-0.295025\pi\) | ||||
0.600357 | + | 0.799732i | \(0.295025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 192.759i | − | 0.683614i | −0.939770 | − | 0.341807i | \(-0.888961\pi\) | ||
0.939770 | − | 0.341807i | \(-0.111039\pi\) | |||||||
\(44\) | −29.4056 | −0.100751 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −503.202 | −1.61289 | ||||||||
\(47\) | 318.312i | 0.987885i | 0.869495 | + | 0.493942i | \(0.164445\pi\) | ||||
−0.869495 | + | 0.493942i | \(0.835555\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −637.967 | −1.85996 | ||||||||
\(50\) | −343.711 | + | 175.501i | −0.972163 | + | 0.496392i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 32.1590i | 0.0857625i | ||||||||
\(53\) | − | 277.459i | − | 0.719093i | −0.933127 | − | 0.359547i | \(-0.882931\pi\) | ||
0.933127 | − | 0.359547i | \(-0.117069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 112.046 | − | 183.018i | 0.274695 | − | 0.448693i | ||||
\(56\) | 625.442 | 1.49247 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 23.6162i | − | 0.0534648i | ||||||
\(59\) | −429.292 | −0.947272 | −0.473636 | − | 0.880721i | \(-0.657059\pi\) | ||||
−0.473636 | + | 0.880721i | \(0.657059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −89.9348 | −0.188770 | −0.0943850 | − | 0.995536i | \(-0.530088\pi\) | ||||
−0.0943850 | + | 0.995536i | \(0.530088\pi\) | |||||||
\(62\) | − | 694.741i | − | 1.42310i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −379.991 | −0.742169 | ||||||||
\(65\) | −200.155 | − | 122.537i | −0.381941 | − | 0.233829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 583.304i | − | 1.06361i | −0.846867 | − | 0.531805i | \(-0.821514\pi\) | ||
0.846867 | − | 0.531805i | \(-0.178486\pi\) | |||||||
\(68\) | 9.48546i | 0.0169159i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 564.490 | − | 922.051i | 0.963850 | − | 1.57437i | ||||
\(71\) | −132.605 | −0.221653 | −0.110826 | − | 0.993840i | \(-0.535350\pi\) | ||||
−0.110826 | + | 0.993840i | \(0.535350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 259.933i | 0.416752i | 0.978049 | + | 0.208376i | \(0.0668177\pi\) | ||||
−0.978049 | + | 0.208376i | \(0.933182\pi\) | |||||||
\(74\) | −481.361 | −0.756176 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −148.096 | −0.223523 | ||||||||
\(77\) | 601.153i | 0.889712i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −124.649 | −0.177520 | −0.0887601 | − | 0.996053i | \(-0.528290\pi\) | ||||
−0.0887601 | + | 0.996053i | \(0.528290\pi\) | |||||||
\(80\) | −431.454 | + | 704.747i | −0.602976 | + | 0.984914i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 973.214i | − | 1.31065i | ||||||
\(83\) | − | 36.7198i | − | 0.0485605i | −0.999705 | − | 0.0242802i | \(-0.992271\pi\) | ||
0.999705 | − | 0.0242802i | \(-0.00772940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −59.0367 | − | 36.1429i | −0.0753344 | − | 0.0461206i | ||||
\(86\) | −595.123 | −0.746207 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 383.282i | − | 0.464295i | ||||||
\(89\) | 333.424 | 0.397111 | 0.198555 | − | 0.980090i | \(-0.436375\pi\) | ||||
0.198555 | + | 0.980090i | \(0.436375\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 657.443 | 0.757349 | ||||||||
\(92\) | 249.701i | 0.282969i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 982.757 | 1.07834 | ||||||||
\(95\) | 564.296 | − | 921.735i | 0.609427 | − | 0.995452i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1029.25i | 1.07736i | 0.842510 | + | 0.538681i | \(0.181077\pi\) | ||||
−0.842510 | + | 0.538681i | \(0.818923\pi\) | |||||||
\(98\) | 1969.66i | 2.03026i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 87.0879 | + | 170.558i | 0.0870879 | + | 0.170558i | ||||
\(101\) | −926.962 | −0.913230 | −0.456615 | − | 0.889664i | \(-0.650938\pi\) | ||||
−0.456615 | + | 0.889664i | \(0.650938\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1687.60i | 1.61441i | 0.590271 | + | 0.807205i | \(0.299021\pi\) | ||||
−0.590271 | + | 0.807205i | \(0.700979\pi\) | |||||||
\(104\) | −419.171 | −0.395222 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −856.627 | −0.784934 | ||||||||
\(107\) | − | 750.833i | − | 0.678372i | −0.940719 | − | 0.339186i | \(-0.889848\pi\) | ||
0.940719 | − | 0.339186i | \(-0.110152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −401.243 | −0.352589 | −0.176294 | − | 0.984338i | \(-0.556411\pi\) | ||||
−0.176294 | + | 0.984338i | \(0.556411\pi\) | |||||||
\(110\) | −565.049 | − | 345.929i | −0.489775 | − | 0.299846i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 2314.86i | − | 1.95298i | ||||||
\(113\) | 220.450i | 0.183524i | 0.995781 | + | 0.0917620i | \(0.0292499\pi\) | ||||
−0.995781 | + | 0.0917620i | \(0.970750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1554.12 | − | 951.449i | −1.26019 | − | 0.771505i | ||||
\(116\) | −11.7189 | −0.00937997 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1325.40i | 1.03401i | ||||||||
\(119\) | 193.916 | 0.149380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −962.603 | −0.723218 | ||||||||
\(122\) | 277.665i | 0.206054i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −344.748 | −0.249671 | ||||||||
\(125\) | −1393.37 | − | 107.859i | −0.997017 | − | 0.0771774i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1185.99i | − | 0.828659i | −0.910127 | − | 0.414329i | \(-0.864016\pi\) | ||
0.910127 | − | 0.414329i | \(-0.135984\pi\) | |||||||
\(128\) | 1720.65i | 1.18817i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −378.321 | + | 617.958i | −0.255238 | + | 0.416912i | ||||
\(131\) | 2770.80 | 1.84799 | 0.923993 | − | 0.382408i | \(-0.124905\pi\) | ||||
0.923993 | + | 0.382408i | \(0.124905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3027.60i | 1.97388i | ||||||||
\(134\) | −1800.89 | −1.16100 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −123.637 | −0.0779541 | ||||||||
\(137\) | 1321.94i | 0.824384i | 0.911097 | + | 0.412192i | \(0.135237\pi\) | ||||
−0.911097 | + | 0.412192i | \(0.864763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1810.45 | 1.10475 | 0.552374 | − | 0.833596i | \(-0.313722\pi\) | ||||
0.552374 | + | 0.833596i | \(0.313722\pi\) | |||||||
\(140\) | −457.544 | − | 280.114i | −0.276211 | − | 0.169100i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 409.405i | 0.241947i | ||||||||
\(143\) | − | 402.893i | − | 0.235606i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 44.6533 | − | 72.9377i | 0.0255742 | − | 0.0417734i | ||||
\(146\) | 802.518 | 0.454910 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 238.863i | 0.132665i | ||||||||
\(149\) | −254.768 | −0.140076 | −0.0700382 | − | 0.997544i | \(-0.522312\pi\) | ||||
−0.0700382 | + | 0.997544i | \(0.522312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2844.74 | 1.53313 | 0.766563 | − | 0.642170i | \(-0.221966\pi\) | ||||
0.766563 | + | 0.642170i | \(0.221966\pi\) | |||||||
\(152\) | − | 1930.33i | − | 1.03007i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1856.00 | 0.971175 | ||||||||
\(155\) | 1313.61 | − | 2145.68i | 0.680720 | − | 1.11190i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1745.14i | 0.887115i | 0.896246 | + | 0.443558i | \(0.146284\pi\) | ||||
−0.896246 | + | 0.443558i | \(0.853716\pi\) | |||||||
\(158\) | 384.841i | 0.193774i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 652.539 | + | 399.492i | 0.322423 | + | 0.197391i | ||||
\(161\) | 5104.77 | 2.49884 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2607.78i | 1.25311i | 0.779378 | + | 0.626554i | \(0.215535\pi\) | ||||
−0.779378 | + | 0.626554i | \(0.784465\pi\) | |||||||
\(164\) | −482.933 | −0.229943 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −113.369 | −0.0530067 | ||||||||
\(167\) | − | 1223.32i | − | 0.566847i | −0.958995 | − | 0.283423i | \(-0.908530\pi\) | ||
0.958995 | − | 0.283423i | \(-0.0914701\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1756.38 | 0.799445 | ||||||||
\(170\) | −111.588 | + | 182.270i | −0.0503434 | + | 0.0822321i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 295.315i | 0.130916i | ||||||||
\(173\) | − | 2789.93i | − | 1.22610i | −0.790045 | − | 0.613048i | \(-0.789943\pi\) | ||
0.790045 | − | 0.613048i | \(-0.210057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3486.81 | − | 1780.38i | 1.50616 | − | 0.769054i | ||||
\(176\) | −1418.59 | −0.607558 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 1029.41i | − | 0.433471i | ||||||
\(179\) | 769.584 | 0.321349 | 0.160674 | − | 0.987007i | \(-0.448633\pi\) | ||||
0.160674 | + | 0.987007i | \(0.448633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2302.38 | 0.945495 | 0.472747 | − | 0.881198i | \(-0.343262\pi\) | ||||
0.472747 | + | 0.881198i | \(0.343262\pi\) | |||||||
\(182\) | − | 2029.79i | − | 0.826693i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3254.69 | −1.30402 | ||||||||
\(185\) | −1486.66 | − | 910.152i | −0.590820 | − | 0.361707i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 118.835i | − | 0.0464711i | ||||||
\(188\) | − | 487.668i | − | 0.189185i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2845.76 | − | 1742.21i | −1.08660 | − | 0.665227i | ||||
\(191\) | 4228.96 | 1.60208 | 0.801039 | − | 0.598612i | \(-0.204281\pi\) | ||||
0.801039 | + | 0.598612i | \(0.204281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4364.09i | 1.62764i | 0.581119 | + | 0.813818i | \(0.302615\pi\) | ||||
−0.581119 | + | 0.813818i | \(0.697385\pi\) | |||||||
\(194\) | 3177.69 | 1.17601 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 977.393 | 0.356193 | ||||||||
\(197\) | 1031.50i | 0.373052i | 0.982450 | + | 0.186526i | \(0.0597228\pi\) | ||||
−0.982450 | + | 0.186526i | \(0.940277\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1271.59 | −0.452966 | −0.226483 | − | 0.974015i | \(-0.572723\pi\) | ||||
−0.226483 | + | 0.974015i | \(0.572723\pi\) | |||||||
\(200\) | −2223.11 | + | 1135.13i | −0.785988 | + | 0.401330i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2861.90i | 0.996846i | ||||||||
\(203\) | 239.577i | 0.0828324i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1840.14 | − | 3005.73i | 0.626932 | − | 1.02405i | ||||
\(206\) | 5210.30 | 1.76223 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1551.42i | 0.517172i | ||||||||
\(209\) | 1855.36 | 0.614059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 346.295 | 0.112986 | 0.0564928 | − | 0.998403i | \(-0.482008\pi\) | ||||
0.0564928 | + | 0.998403i | \(0.482008\pi\) | |||||||
\(212\) | 425.080i | 0.137710i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2318.12 | −0.740484 | ||||||||
\(215\) | −1838.01 | − | 1125.25i | −0.583030 | − | 0.356938i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7047.86i | 2.20479i | ||||||||
\(218\) | 1238.80i | 0.384872i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −171.659 | + | 280.391i | −0.0526056 | + | 0.0859271i | ||||
\(221\) | −129.963 | −0.0395576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4039.33i | 1.21297i | 0.795093 | + | 0.606487i | \(0.207422\pi\) | ||||
−0.795093 | + | 0.606487i | \(0.792578\pi\) | |||||||
\(224\) | −2143.38 | −0.639332 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 680.618 | 0.200328 | ||||||||
\(227\) | − | 862.451i | − | 0.252171i | −0.992019 | − | 0.126086i | \(-0.959759\pi\) | ||
0.992019 | − | 0.126086i | \(-0.0402414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −958.217 | −0.276510 | −0.138255 | − | 0.990397i | \(-0.544149\pi\) | ||||
−0.138255 | + | 0.990397i | \(0.544149\pi\) | |||||||
\(230\) | −2937.51 | + | 4798.19i | −0.842145 | + | 1.37558i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 152.749i | − | 0.0432260i | ||||||
\(233\) | − | 1159.05i | − | 0.325887i | −0.986635 | − | 0.162944i | \(-0.947901\pi\) | ||
0.986635 | − | 0.162944i | \(-0.0520989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3035.20 | + | 1858.19i | 0.842531 | + | 0.515807i | ||||
\(236\) | 657.694 | 0.181408 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 598.697i | − | 0.163058i | ||||||
\(239\) | −4046.40 | −1.09515 | −0.547573 | − | 0.836758i | \(-0.684448\pi\) | ||||
−0.547573 | + | 0.836758i | \(0.684448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2425.49 | −0.648296 | −0.324148 | − | 0.946006i | \(-0.605078\pi\) | ||||
−0.324148 | + | 0.946006i | \(0.605078\pi\) | |||||||
\(242\) | 2971.94i | 0.789436i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 137.784 | 0.0361505 | ||||||||
\(245\) | −3724.21 | + | 6083.21i | −0.971147 | + | 1.58629i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2029.09i | − | 0.522705i | ||||||
\(248\) | − | 4493.55i | − | 1.15057i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −333.003 | + | 4301.90i | −0.0842438 | + | 1.08831i | ||||
\(251\) | −7272.75 | −1.82889 | −0.914445 | − | 0.404709i | \(-0.867373\pi\) | ||||
−0.914445 | + | 0.404709i | \(0.867373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3128.29i | − | 0.777368i | ||||||
\(254\) | −3661.63 | −0.904532 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2272.43 | 0.554792 | ||||||||
\(257\) | 3234.18i | 0.784990i | 0.919754 | + | 0.392495i | \(0.128388\pi\) | ||||
−0.919754 | + | 0.392495i | \(0.871612\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4883.20 | 1.17153 | ||||||||
\(260\) | 306.646 | + | 187.732i | 0.0731438 | + | 0.0447795i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 8554.58i | − | 2.01719i | ||||||
\(263\) | − | 1056.62i | − | 0.247733i | −0.992299 | − | 0.123866i | \(-0.960471\pi\) | ||
0.992299 | − | 0.123866i | \(-0.0395294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2645.66 | − | 1619.70i | −0.613289 | − | 0.375462i | ||||
\(266\) | 9347.41 | 2.15461 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 893.647i | 0.203687i | ||||||||
\(269\) | −1528.13 | −0.346363 | −0.173182 | − | 0.984890i | \(-0.555405\pi\) | ||||
−0.173182 | + | 0.984890i | \(0.555405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7368.77 | −1.65174 | −0.825869 | − | 0.563862i | \(-0.809315\pi\) | ||||
−0.825869 | + | 0.563862i | \(0.809315\pi\) | |||||||
\(272\) | 457.599i | 0.102008i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4081.35 | 0.899865 | ||||||||
\(275\) | −1091.05 | − | 2136.78i | −0.239247 | − | 0.468555i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1854.32i | − | 0.402221i | −0.979569 | − | 0.201111i | \(-0.935545\pi\) | ||
0.979569 | − | 0.201111i | \(-0.0644551\pi\) | |||||||
\(278\) | − | 5589.57i | − | 1.20590i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3651.10 | − | 5963.78i | 0.779267 | − | 1.27287i | ||||
\(281\) | −415.132 | −0.0881306 | −0.0440653 | − | 0.999029i | \(-0.514031\pi\) | ||||
−0.0440653 | + | 0.999029i | \(0.514031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4116.22i | − | 0.864607i | −0.901728 | − | 0.432303i | \(-0.857701\pi\) | ||
0.901728 | − | 0.432303i | \(-0.142299\pi\) | |||||||
\(284\) | 203.157 | 0.0424477 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1243.89 | −0.257178 | ||||||||
\(287\) | 9872.84i | 2.03058i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4874.67 | 0.992198 | ||||||||
\(290\) | −225.188 | − | 137.863i | −0.0455982 | − | 0.0279158i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 398.229i | − | 0.0798103i | ||||||
\(293\) | 4906.20i | 0.978236i | 0.872218 | + | 0.489118i | \(0.162681\pi\) | ||||
−0.872218 | + | 0.489118i | \(0.837319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2506.05 | + | 4093.43i | −0.494602 | + | 0.807894i | ||||
\(296\) | −3113.42 | −0.611364 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 786.570i | 0.152902i | ||||||||
\(299\) | −3421.22 | −0.661720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6037.28 | 1.15609 | ||||||||
\(302\) | − | 8782.86i | − | 1.67350i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7144.46 | −1.34790 | ||||||||
\(305\) | −525.006 | + | 857.556i | −0.0985631 | + | 0.160995i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6909.30i | 1.28448i | 0.766504 | + | 0.642239i | \(0.221994\pi\) | ||||
−0.766504 | + | 0.642239i | \(0.778006\pi\) | |||||||
\(308\) | − | 920.994i | − | 0.170385i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6624.57 | − | 4055.64i | −1.21371 | − | 0.743048i | ||||
\(311\) | 5373.87 | 0.979820 | 0.489910 | − | 0.871773i | \(-0.337030\pi\) | ||||
0.489910 | + | 0.871773i | \(0.337030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2392.60i | − | 0.432070i | −0.976386 | − | 0.216035i | \(-0.930687\pi\) | ||
0.976386 | − | 0.216035i | \(-0.0693125\pi\) | |||||||
\(314\) | 5387.94 | 0.968340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 190.968 | 0.0339961 | ||||||||
\(317\) | 1183.68i | 0.209723i | 0.994487 | + | 0.104861i | \(0.0334399\pi\) | ||||
−0.994487 | + | 0.104861i | \(0.966560\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 146.817 | 0.0257685 | ||||||||
\(320\) | −2218.24 | + | 3623.33i | −0.387511 | + | 0.632969i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 15760.5i | − | 2.72763i | ||||||
\(323\) | − | 598.492i | − | 0.103099i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2336.86 | + | 1193.21i | −0.398848 | + | 0.203654i | ||||
\(326\) | 8051.25 | 1.36784 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6294.70i | − | 1.05965i | ||||||
\(329\) | −9969.66 | −1.67065 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9386.43 | −1.55868 | −0.779342 | − | 0.626598i | \(-0.784447\pi\) | ||||
−0.779342 | + | 0.626598i | \(0.784447\pi\) | |||||||
\(332\) | 56.2563i | 0.00929960i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3776.88 | −0.618748 | ||||||||
\(335\) | −5561.98 | − | 3405.11i | −0.907115 | − | 0.555346i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12171.6i | 1.96745i | 0.179685 | + | 0.983724i | \(0.442492\pi\) | ||||
−0.179685 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(338\) | − | 5422.65i | − | 0.872644i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 90.4468 | + | 55.3726i | 0.0144270 | + | 0.00883235i | ||||
\(341\) | 4319.05 | 0.685893 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9238.47i | − | 1.45432i | ||||||
\(344\) | −3849.23 | −0.603304 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8613.64 | −1.33836 | ||||||||
\(347\) | − | 2785.57i | − | 0.430943i | −0.976510 | − | 0.215471i | \(-0.930871\pi\) | ||
0.976510 | − | 0.215471i | \(-0.0691288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3359.76 | 0.515311 | 0.257656 | − | 0.966237i | \(-0.417050\pi\) | ||||
0.257656 | + | 0.966237i | \(0.417050\pi\) | |||||||
\(350\) | −5496.76 | − | 10765.2i | −0.839469 | − | 1.64407i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1313.50i | 0.198891i | ||||||||
\(353\) | 5427.68i | 0.818375i | 0.912450 | + | 0.409188i | \(0.134188\pi\) | ||||
−0.912450 | + | 0.409188i | \(0.865812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −774.100 | + | 1264.43i | −0.115732 | + | 0.189040i | ||||
\(356\) | −510.820 | −0.0760489 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2376.01i | − | 0.350772i | ||||||
\(359\) | −3920.74 | −0.576404 | −0.288202 | − | 0.957570i | \(-0.593057\pi\) | ||||
−0.288202 | + | 0.957570i | \(0.593057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2485.20 | 0.362327 | ||||||||
\(362\) | − | 7108.37i | − | 1.03207i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1007.23 | −0.145037 | ||||||||
\(365\) | 2478.54 | + | 1517.39i | 0.355433 | + | 0.217600i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1677.21i | 0.238554i | 0.992861 | + | 0.119277i | \(0.0380577\pi\) | ||||
−0.992861 | + | 0.119277i | \(0.961942\pi\) | |||||||
\(368\) | 12046.1i | 1.70638i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2810.00 | + | 4589.92i | −0.394825 | + | 0.644916i | ||||
\(371\) | 8690.13 | 1.21609 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 956.336i | − | 0.132754i | −0.997795 | − | 0.0663769i | \(-0.978856\pi\) | ||
0.997795 | − | 0.0663769i | \(-0.0211440\pi\) | |||||||
\(374\) | −366.892 | −0.0507260 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6356.43 | 0.871829 | ||||||||
\(377\) | − | 160.564i | − | 0.0219349i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10019.0 | −1.35789 | −0.678943 | − | 0.734191i | \(-0.737562\pi\) | ||||
−0.678943 | + | 0.734191i | \(0.737562\pi\) | |||||||
\(380\) | −864.527 | + | 1412.14i | −0.116709 | + | 0.190635i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 13056.5i | − | 1.74877i | ||||||
\(383\) | 12886.2i | 1.71920i | 0.510967 | + | 0.859600i | \(0.329287\pi\) | ||||
−0.510967 | + | 0.859600i | \(0.670713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5732.18 | + | 3509.31i | 0.758803 | + | 0.464548i | ||||
\(386\) | 13473.7 | 1.77667 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1576.85i | − | 0.206321i | ||||||
\(389\) | −688.486 | −0.0897369 | −0.0448684 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448684 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1009.11 | −0.130518 | ||||||||
\(392\) | 12739.7i | 1.64145i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3184.65 | 0.407209 | ||||||||
\(395\) | −727.654 | + | 1188.57i | −0.0926892 | + | 0.151401i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7893.06i | − | 0.997837i | −0.866649 | − | 0.498918i | \(-0.833731\pi\) | ||
0.866649 | − | 0.498918i | \(-0.166269\pi\) | |||||||
\(398\) | 3925.90i | 0.494441i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4201.31 | + | 8228.10i | 0.525164 | + | 1.02851i | ||||
\(401\) | −4192.82 | −0.522144 | −0.261072 | − | 0.965319i | \(-0.584076\pi\) | ||||
−0.261072 | + | 0.965319i | \(0.584076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4723.47i | − | 0.583853i | ||||||
\(404\) | 1420.15 | 0.174889 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 739.669 | 0.0904166 | ||||||||
\(407\) | − | 2992.51i | − | 0.364455i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9010.03 | −1.08928 | −0.544642 | − | 0.838668i | \(-0.683335\pi\) | ||||
−0.544642 | + | 0.838668i | \(0.683335\pi\) | |||||||
\(410\) | −9279.89 | − | 5681.26i | −1.11781 | − | 0.684335i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2585.48i | − | 0.309169i | ||||||
\(413\) | − | 13445.6i | − | 1.60197i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −350.134 | − | 214.356i | −0.0414155 | − | 0.0253550i | ||||
\(416\) | 1436.49 | 0.169302 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 5728.25i | − | 0.670283i | ||||||
\(419\) | 6859.80 | 0.799817 | 0.399908 | − | 0.916555i | \(-0.369042\pi\) | ||||
0.399908 | + | 0.916555i | \(0.369042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12594.6 | 1.45801 | 0.729007 | − | 0.684507i | \(-0.239982\pi\) | ||||
0.729007 | + | 0.684507i | \(0.239982\pi\) | |||||||
\(422\) | − | 1069.15i | − | 0.123331i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5540.63 | −0.634615 | ||||||||
\(425\) | −689.268 | + | 351.944i | −0.0786692 | + | 0.0401689i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2816.79i | − | 0.319237i | ||||||
\(428\) | 1150.31i | 0.129912i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3474.11 | + | 5674.68i | −0.389619 | + | 0.636413i | ||||
\(431\) | 8470.15 | 0.946619 | 0.473310 | − | 0.880896i | \(-0.343059\pi\) | ||||
0.473310 | + | 0.880896i | \(0.343059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8182.86i | − | 0.908183i | −0.890955 | − | 0.454092i | \(-0.849964\pi\) | ||
0.890955 | − | 0.454092i | \(-0.150036\pi\) | |||||||
\(434\) | 21759.6 | 2.40666 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 614.723 | 0.0675227 | ||||||||
\(437\) | − | 15755.1i | − | 1.72464i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8353.58 | −0.908189 | −0.454094 | − | 0.890954i | \(-0.650037\pi\) | ||||
−0.454094 | + | 0.890954i | \(0.650037\pi\) | |||||||
\(440\) | −3654.71 | − | 2237.46i | −0.395981 | − | 0.242424i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 401.247i | 0.0431795i | ||||||||
\(443\) | − | 2222.59i | − | 0.238371i | −0.992872 | − | 0.119186i | \(-0.961972\pi\) | ||
0.992872 | − | 0.119186i | \(-0.0380284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1946.40 | − | 3179.30i | 0.207345 | − | 0.338681i | ||||
\(446\) | 12471.0 | 1.32404 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 11901.5i | − | 1.25511i | ||||||
\(449\) | −5455.02 | −0.573360 | −0.286680 | − | 0.958026i | \(-0.592552\pi\) | ||||
−0.286680 | + | 0.958026i | \(0.592552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6050.25 | 0.631697 | ||||||||
\(452\) | − | 337.739i | − | 0.0351459i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2662.73 | −0.275260 | ||||||||
\(455\) | 3837.91 | − | 6268.93i | 0.395437 | − | 0.645916i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6974.13i | 0.713865i | 0.934130 | + | 0.356932i | \(0.116177\pi\) | ||||
−0.934130 | + | 0.356932i | \(0.883823\pi\) | |||||||
\(458\) | 2958.40i | 0.301827i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2380.98 | + | 1457.66i | 0.241334 | + | 0.147748i | ||||
\(461\) | −5623.10 | −0.568099 | −0.284050 | − | 0.958810i | \(-0.591678\pi\) | ||||
−0.284050 | + | 0.958810i | \(0.591678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2881.60i | − | 0.289242i | −0.989487 | − | 0.144621i | \(-0.953804\pi\) | ||
0.989487 | − | 0.144621i | \(-0.0461963\pi\) | |||||||
\(464\) | −565.348 | −0.0565638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3578.45 | −0.355726 | ||||||||
\(467\) | − | 16877.2i | − | 1.67234i | −0.548468 | − | 0.836172i | \(-0.684789\pi\) | ||
0.548468 | − | 0.836172i | \(-0.315211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18269.3 | 1.79872 | ||||||||
\(470\) | 5736.97 | − | 9370.89i | 0.563035 | − | 0.919675i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8572.61i | 0.835988i | ||||||||
\(473\) | − | 3699.75i | − | 0.359650i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5494.87 | − | 10761.5i | −0.530783 | − | 1.03952i | ||||
\(476\) | −297.088 | −0.0286072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12492.9i | 1.19542i | ||||||||
\(479\) | −19088.2 | −1.82079 | −0.910397 | − | 0.413736i | \(-0.864224\pi\) | ||||
−0.910397 | + | 0.413736i | \(0.864224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3272.72 | −0.310235 | ||||||||
\(482\) | 7488.45i | 0.707655i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1474.75 | 0.138500 | ||||||||
\(485\) | 9814.18 | + | 6008.35i | 0.918843 | + | 0.562526i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12553.6i | 1.16809i | 0.811722 | + | 0.584044i | \(0.198530\pi\) | ||||
−0.811722 | + | 0.584044i | \(0.801470\pi\) | |||||||
\(488\) | 1795.92i | 0.166593i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18781.3 | + | 11498.1i | 1.73154 | + | 1.06007i | ||||
\(491\) | −1569.32 | −0.144241 | −0.0721205 | − | 0.997396i | \(-0.522977\pi\) | ||||
−0.0721205 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 47.3592i | − | 0.00432647i | ||||||
\(494\) | −6264.63 | −0.570565 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16631.4 | −1.50559 | ||||||||
\(497\) | − | 4153.25i | − | 0.374846i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10714.7 | 0.961232 | 0.480616 | − | 0.876931i | \(-0.340413\pi\) | ||||
0.480616 | + | 0.876931i | \(0.340413\pi\) | |||||||
\(500\) | 2134.71 | + | 165.244i | 0.190934 | + | 0.0147799i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22453.9i | 1.99635i | ||||||||
\(503\) | 19016.8i | 1.68572i | 0.538130 | + | 0.842862i | \(0.319131\pi\) | ||||
−0.538130 | + | 0.842862i | \(0.680869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5411.26 | + | 8838.87i | −0.476827 | + | 0.778861i | ||||
\(506\) | −9658.30 | −0.848545 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1816.99i | 0.158693i | ||||||||
\(509\) | 16411.5 | 1.42913 | 0.714563 | − | 0.699571i | \(-0.246625\pi\) | ||||
0.714563 | + | 0.699571i | \(0.246625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8141.21 | −0.704786 | ||||||||
\(512\) | 6749.35i | 0.582582i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9985.20 | 0.856865 | ||||||||
\(515\) | 16091.8 | + | 9851.58i | 1.37687 | + | 0.842937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6109.58i | 0.519727i | ||||||||
\(518\) | − | 15076.4i | − | 1.27880i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2446.96 | + | 3996.93i | −0.206359 | + | 0.337071i | ||||
\(521\) | 9319.21 | 0.783651 | 0.391826 | − | 0.920040i | \(-0.371844\pi\) | ||||
0.391826 | + | 0.920040i | \(0.371844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 19719.6i | − | 1.64871i | −0.566071 | − | 0.824357i | \(-0.691537\pi\) | ||
0.566071 | − | 0.824357i | \(-0.308463\pi\) | |||||||
\(524\) | −4244.99 | −0.353900 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3262.19 | −0.270415 | ||||||||
\(527\) | − | 1393.21i | − | 0.115160i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14397.3 | −1.18331 | ||||||||
\(530\) | −5000.67 | + | 8168.21i | −0.409840 | + | 0.669442i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 4638.41i | − | 0.378009i | ||||||
\(533\) | − | 6616.78i | − | 0.537719i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7159.42 | − | 4383.08i | −0.578559 | − | 0.354200i | ||||
\(536\) | −11648.1 | −0.938658 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4717.95i | 0.378077i | ||||||||
\(539\) | −12244.9 | −0.978527 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16592.1 | 1.31857 | 0.659287 | − | 0.751891i | \(-0.270858\pi\) | ||||
0.659287 | + | 0.751891i | \(0.270858\pi\) | |||||||
\(542\) | 22750.4i | 1.80297i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 423.700 | 0.0333934 | ||||||||
\(545\) | −2342.31 | + | 3825.98i | −0.184098 | + | 0.300710i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12264.5i | 0.958667i | 0.877633 | + | 0.479333i | \(0.159122\pi\) | ||||
−0.877633 | + | 0.479333i | \(0.840878\pi\) | |||||||
\(548\) | − | 2025.26i | − | 0.157874i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6597.09 | + | 3368.51i | −0.511456 | + | 0.261152i | ||||
\(551\) | 739.415 | 0.0571690 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3904.05i | − | 0.300212i | ||||||
\(554\) | −5725.03 | −0.439049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2773.68 | −0.211565 | ||||||||
\(557\) | − | 1623.54i | − | 0.123504i | −0.998092 | − | 0.0617518i | \(-0.980331\pi\) | ||
0.998092 | − | 0.0617518i | \(-0.0196687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4046.18 | −0.306145 | ||||||||
\(560\) | −22072.9 | − | 13513.3i | −1.66563 | − | 1.01972i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1281.68i | 0.0961999i | ||||||||
\(563\) | 6842.29i | 0.512199i | 0.966650 | + | 0.256100i | \(0.0824375\pi\) | ||||
−0.966650 | + | 0.256100i | \(0.917562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2102.06 | + | 1286.91i | 0.156521 | + | 0.0958240i | ||||
\(566\) | −12708.4 | −0.943771 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2648.02i | 0.195613i | ||||||||
\(569\) | −9076.58 | −0.668735 | −0.334367 | − | 0.942443i | \(-0.608523\pi\) | ||||
−0.334367 | + | 0.942443i | \(0.608523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5501.59 | −0.403213 | −0.201606 | − | 0.979467i | \(-0.564616\pi\) | ||||
−0.201606 | + | 0.979467i | \(0.564616\pi\) | |||||||
\(572\) | 617.250i | 0.0451198i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 30481.4 | 2.21650 | ||||||||
\(575\) | −18144.7 | + | 9264.80i | −1.31598 | + | 0.671946i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13600.1i | 0.981245i | 0.871372 | + | 0.490622i | \(0.163231\pi\) | ||||
−0.871372 | + | 0.490622i | \(0.836769\pi\) | |||||||
\(578\) | − | 15050.1i | − | 1.08304i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −68.4108 | + | 111.744i | −0.00489759 | + | 0.00799984i | ||||
\(581\) | 1150.08 | 0.0821226 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5325.46i | − | 0.378316i | ||||||
\(584\) | 5190.65 | 0.367792 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15147.4 | 1.06780 | ||||||||
\(587\) | 21216.1i | 1.49179i | 0.666062 | + | 0.745896i | \(0.267979\pi\) | ||||
−0.666062 | + | 0.745896i | \(0.732021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21752.1 | 1.52170 | ||||||||
\(590\) | 12638.1 | + | 7737.17i | 0.881866 | + | 0.539889i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11523.3i | 0.800007i | ||||||||
\(593\) | − | 14973.6i | − | 1.03692i | −0.855103 | − | 0.518458i | \(-0.826506\pi\) | ||
0.855103 | − | 0.518458i | \(-0.173494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1132.01 | − | 1849.05i | 0.0779965 | − | 0.127401i | ||||
\(596\) | 390.315 | 0.0268254 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10562.7i | 0.722307i | ||||||||
\(599\) | −17904.8 | −1.22132 | −0.610659 | − | 0.791894i | \(-0.709095\pi\) | ||||
−0.610659 | + | 0.791894i | \(0.709095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16455.0 | 1.11683 | 0.558414 | − | 0.829562i | \(-0.311410\pi\) | ||||
0.558414 | + | 0.829562i | \(0.311410\pi\) | |||||||
\(602\) | − | 18639.5i | − | 1.26194i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4358.27 | −0.293602 | ||||||||
\(605\) | −5619.31 | + | 9178.71i | −0.377616 | + | 0.616806i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5457.49i | − | 0.364930i | −0.983212 | − | 0.182465i | \(-0.941592\pi\) | ||
0.983212 | − | 0.182465i | \(-0.0584077\pi\) | |||||||
\(608\) | 6615.19i | 0.441253i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2647.62 | + | 1620.90i | 0.175736 | + | 0.107588i | ||||
\(611\) | 6681.66 | 0.442408 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10945.3i | 0.721167i | 0.932727 | + | 0.360584i | \(0.117422\pi\) | ||||
−0.932727 | + | 0.360584i | \(0.882578\pi\) | |||||||
\(614\) | 21331.8 | 1.40209 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12004.5 | 0.785189 | ||||||||
\(617\) | 25534.0i | 1.66606i | 0.553225 | + | 0.833032i | \(0.313397\pi\) | ||||
−0.553225 | + | 0.833032i | \(0.686603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7895.81 | 0.512697 | 0.256349 | − | 0.966584i | \(-0.417480\pi\) | ||||
0.256349 | + | 0.966584i | \(0.417480\pi\) | |||||||
\(620\) | −2012.51 | + | 3287.27i | −0.130362 | + | 0.212936i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 16591.3i | − | 1.06953i | ||||||
\(623\) | 10443.0i | 0.671570i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9162.46 | + | 12656.6i | −0.586398 | + | 0.810023i | ||||
\(626\) | −7386.93 | −0.471631 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 2673.63i | − | 0.169887i | ||||||
\(629\) | −965.305 | −0.0611912 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5659.61 | −0.357061 | −0.178531 | − | 0.983934i | \(-0.557134\pi\) | ||||
−0.178531 | + | 0.983934i | \(0.557134\pi\) | |||||||
\(632\) | 2489.14i | 0.156665i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3654.50 | 0.228925 | ||||||||
\(635\) | −11308.8 | − | 6923.37i | −0.706733 | − | 0.432670i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13391.5i | 0.832952i | ||||||||
\(638\) | − | 453.282i | − | 0.0281279i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16407.0 | + | 10044.5i | 1.01335 | + | 0.620383i | ||||
\(641\) | 16082.9 | 0.991010 | 0.495505 | − | 0.868605i | \(-0.334983\pi\) | ||||
0.495505 | + | 0.868605i | \(0.334983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 66.7491i | 0.00409382i | 0.999998 | + | 0.00204691i | \(0.000651552\pi\) | ||||
−0.999998 | + | 0.00204691i | \(0.999348\pi\) | |||||||
\(644\) | −7820.74 | −0.478541 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1847.78 | −0.112539 | ||||||||
\(647\) | − | 1263.42i | − | 0.0767697i | −0.999263 | − | 0.0383849i | \(-0.987779\pi\) | ||
0.999263 | − | 0.0383849i | \(-0.0122213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8239.69 | −0.498361 | ||||||||
\(650\) | 3683.93 | + | 7214.82i | 0.222301 | + | 0.435367i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3995.23i | − | 0.239977i | ||||||
\(653\) | − | 21867.4i | − | 1.31047i | −0.755425 | − | 0.655235i | \(-0.772570\pi\) | ||
0.755425 | − | 0.655235i | \(-0.227430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16174.9 | − | 26420.5i | 0.964895 | − | 1.57608i | ||||
\(656\) | −23297.7 | −1.38662 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30780.3i | 1.82362i | ||||||||
\(659\) | 362.493 | 0.0214275 | 0.0107138 | − | 0.999943i | \(-0.496590\pi\) | ||||
0.0107138 | + | 0.999943i | \(0.496590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −398.741 | −0.0234633 | −0.0117316 | − | 0.999931i | \(-0.503734\pi\) | ||||
−0.0117316 | + | 0.999931i | \(0.503734\pi\) | |||||||
\(662\) | 28979.7i | 1.70140i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −733.263 | −0.0428556 | ||||||||
\(665\) | 28869.1 | + | 17674.0i | 1.68345 | + | 1.03063i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1246.71i | − | 0.0723732i | ||||||
\(668\) | 1874.18i | 0.108554i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10512.9 | + | 17172.1i | −0.606194 | + | 0.990171i | ||||
\(671\) | −1726.18 | −0.0993121 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3104.18i | − | 0.177797i | −0.996041 | − | 0.0888986i | \(-0.971665\pi\) | ||
0.996041 | − | 0.0888986i | \(-0.0283347\pi\) | |||||||
\(674\) | 37578.7 | 2.14759 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2690.85 | −0.153098 | ||||||||
\(677\) | − | 24565.4i | − | 1.39457i | −0.716794 | − | 0.697285i | \(-0.754391\pi\) | ||
0.716794 | − | 0.697285i | \(-0.245609\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32236.4 | −1.82197 | ||||||||
\(680\) | −721.744 | + | 1178.91i | −0.0407024 | + | 0.0664842i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 13334.6i | − | 0.748694i | ||||||
\(683\) | 8921.93i | 0.499836i | 0.968267 | + | 0.249918i | \(0.0804037\pi\) | ||||
−0.968267 | + | 0.249918i | \(0.919596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12605.1 | + | 7716.97i | 0.703087 | + | 0.430438i | ||||
\(686\) | −28522.9 | −1.58747 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14246.6i | 0.789459i | ||||||||
\(689\) | −5824.12 | −0.322034 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6688.21 | −0.368207 | −0.184104 | − | 0.982907i | \(-0.558938\pi\) | ||||
−0.184104 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(692\) | 4274.30i | 0.234804i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8600.17 | −0.470400 | ||||||||
\(695\) | 10568.7 | − | 17263.2i | 0.576825 | − | 0.942200i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1951.65i | − | 0.106060i | ||||||
\(698\) | − | 10372.9i | − | 0.562494i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5341.95 | + | 2727.63i | −0.288438 | + | 0.147278i | ||||
\(701\) | −33422.0 | −1.80076 | −0.900380 | − | 0.435105i | \(-0.856711\pi\) | ||||
−0.900380 | + | 0.435105i | \(0.856711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 15071.2i | − | 0.808567i | ||||||
\(704\) | −7293.42 | −0.390456 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16757.4 | 0.893306 | ||||||||
\(707\) | − | 29032.8i | − | 1.54440i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29293.5 | −1.55168 | −0.775840 | − | 0.630929i | \(-0.782674\pi\) | ||||
−0.775840 | + | 0.630929i | \(0.782674\pi\) | |||||||
\(710\) | 3903.81 | + | 2389.96i | 0.206348 | + | 0.126329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 6658.20i | − | 0.350459i | ||||||
\(713\) | − | 36675.8i | − | 1.92639i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3841.71 | − | 2351.94i | −0.200939 | − | 0.123017i | ||||
\(716\) | −1179.04 | −0.0615401 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12104.9i | 0.629180i | ||||||||
\(719\) | 29311.2 | 1.52034 | 0.760169 | − | 0.649725i | \(-0.225116\pi\) | ||||
0.760169 | + | 0.649725i | \(0.225116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52856.3 | −2.73020 | ||||||||
\(722\) | − | 7672.81i | − | 0.395502i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3527.35 | −0.181067 | ||||||||
\(725\) | −434.814 | − | 851.566i | −0.0222739 | − | 0.0436226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4931.68i | − | 0.251590i | −0.992056 | − | 0.125795i | \(-0.959852\pi\) | ||
0.992056 | − | 0.125795i | \(-0.0401481\pi\) | |||||||
\(728\) | − | 13128.6i | − | 0.668377i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4684.80 | − | 7652.26i | 0.237524 | − | 0.387976i | ||||
\(731\) | −1193.44 | −0.0603844 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8225.55i | 0.414485i | 0.978290 | + | 0.207243i | \(0.0664489\pi\) | ||||
−0.978290 | + | 0.207243i | \(0.933551\pi\) | |||||||
\(734\) | 5178.21 | 0.260397 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11153.8 | 0.558604 | ||||||||
\(737\) | − | 11195.7i | − | 0.559566i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17847.1 | −0.888382 | −0.444191 | − | 0.895932i | \(-0.646509\pi\) | ||||
−0.444191 | + | 0.895932i | \(0.646509\pi\) | |||||||
\(740\) | 2277.63 | + | 1394.39i | 0.113145 | + | 0.0692688i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 26829.9i | − | 1.32743i | ||||||
\(743\) | 23810.6i | 1.17568i | 0.808979 | + | 0.587838i | \(0.200021\pi\) | ||||
−0.808979 | + | 0.587838i | \(0.799979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1487.24 | + | 2429.29i | −0.0731385 | + | 0.119466i | ||||
\(746\) | −2952.59 | −0.144909 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 182.061i | 0.00889947i | ||||||||
\(749\) | 23516.4 | 1.14722 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21295.8 | 1.03475 | 0.517374 | − | 0.855759i | \(-0.326909\pi\) | ||||
0.517374 | + | 0.855759i | \(0.326909\pi\) | |||||||
\(752\) | − | 23526.2i | − | 1.14084i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −495.726 | −0.0239433 | ||||||||
\(755\) | 16606.5 | − | 27125.5i | 0.800495 | − | 1.30755i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13423.0i | − | 0.644472i | −0.946659 | − | 0.322236i | \(-0.895565\pi\) | ||
0.946659 | − | 0.322236i | \(-0.104435\pi\) | |||||||
\(758\) | 30932.5i | 1.48222i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18406.3 | − | 11268.5i | −0.878508 | − | 0.537832i | ||||
\(761\) | 24100.2 | 1.14801 | 0.574003 | − | 0.818853i | \(-0.305390\pi\) | ||||
0.574003 | + | 0.818853i | \(0.305390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12567.1i | − | 0.596277i | ||||||
\(764\) | −6478.96 | −0.306807 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39784.8 | 1.87661 | ||||||||
\(767\) | 9011.23i | 0.424220i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 986.759 | 0.0462724 | 0.0231362 | − | 0.999732i | \(-0.492635\pi\) | ||||
0.0231362 | + | 0.999732i | \(0.492635\pi\) | |||||||
\(770\) | 10834.6 | − | 17697.6i | 0.507082 | − | 0.828280i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 6685.98i | − | 0.311701i | ||||||
\(773\) | 7277.05i | 0.338599i | 0.985565 | + | 0.169300i | \(0.0541505\pi\) | ||||
−0.985565 | + | 0.169300i | \(0.945849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12791.4 | − | 25051.3i | −0.592876 | − | 1.16112i | ||||
\(776\) | 20553.2 | 0.950794 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2125.63i | 0.0979533i | ||||||||
\(779\) | 30471.0 | 1.40146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2545.18 | −0.116612 | ||||||||
\(782\) | 3115.51i | 0.142469i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 47151.6 | 2.14794 | ||||||||
\(785\) | 16640.4 | + | 10187.5i | 0.756588 | + | 0.463192i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4939.44i | − | 0.223726i | −0.993724 | − | 0.111863i | \(-0.964318\pi\) | ||
0.993724 | − | 0.111863i | \(-0.0356817\pi\) | |||||||
\(788\) | − | 1580.30i | − | 0.0714415i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3669.58 | + | 2246.56i | 0.165263 | + | 0.101176i | ||||
\(791\) | −6904.59 | −0.310365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1887.81i | 0.0845375i | ||||||||
\(794\) | −24369.0 | −1.08920 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1948.13 | 0.0867456 | ||||||||
\(797\) | 12447.6i | 0.553219i | 0.960982 | + | 0.276610i | \(0.0892109\pi\) | ||||
−0.960982 | + | 0.276610i | \(0.910789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1970.79 | 0.0872610 | ||||||||
\(800\) | 7618.55 | − | 3890.08i | 0.336696 | − | 0.171919i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12944.9i | 0.569952i | ||||||||
\(803\) | 4989.07i | 0.219254i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29799.8 | − | 48675.6i | 1.30472 | − | 2.13117i | ||||
\(806\) | −14583.2 | −0.637311 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18510.7i | 0.805944i | ||||||||
\(809\) | −37250.9 | −1.61888 | −0.809438 | − | 0.587205i | \(-0.800228\pi\) | ||||
−0.809438 | + | 0.587205i | \(0.800228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7201.80 | 0.311824 | 0.155912 | − | 0.987771i | \(-0.450168\pi\) | ||||
0.155912 | + | 0.987771i | \(0.450168\pi\) | |||||||
\(812\) | − | 367.042i | − | 0.0158629i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9239.08 | −0.397825 | ||||||||
\(815\) | 24865.9 | + | 15223.2i | 1.06873 | + | 0.654290i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 18633.1i | − | 0.797906i | ||||||
\(818\) | 27817.6i | 1.18902i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2819.18 | + | 4604.91i | −0.120061 | + | 0.196110i | ||||
\(821\) | −10824.6 | −0.460147 | −0.230074 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230074 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18031.3i | − | 0.763710i | −0.924222 | − | 0.381855i | \(-0.875285\pi\) | ||
0.924222 | − | 0.381855i | \(-0.124715\pi\) | |||||||
\(824\) | 33700.0 | 1.42475 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41511.9 | −1.74865 | ||||||||
\(827\) | − | 13172.5i | − | 0.553873i | −0.960888 | − | 0.276937i | \(-0.910681\pi\) | ||
0.960888 | − | 0.276937i | \(-0.0893192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11929.1 | 0.499776 | 0.249888 | − | 0.968275i | \(-0.419606\pi\) | ||||
0.249888 | + | 0.968275i | \(0.419606\pi\) | |||||||
\(830\) | −661.804 | + | 1081.01i | −0.0276766 | + | 0.0452075i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7976.35i | 0.332368i | ||||||||
\(833\) | 3949.89i | 0.164292i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11664.7 | − | 7141.29i | −0.483443 | − | 0.295969i | ||||
\(836\) | −2842.50 | −0.117596 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 21179.0i | − | 0.873049i | ||||||
\(839\) | 25393.4 | 1.04491 | 0.522453 | − | 0.852668i | \(-0.325017\pi\) | ||||
0.522453 | + | 0.852668i | \(0.325017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24330.5 | −0.997601 | ||||||||
\(842\) | − | 38884.6i | − | 1.59151i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −530.540 | −0.0216373 | ||||||||
\(845\) | 10253.1 | − | 16747.6i | 0.417417 | − | 0.681818i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30149.1i | − | 1.22306i | ||||||
\(848\) | 20506.8i | 0.830431i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1086.59 | + | 2128.05i | 0.0438468 | + | 0.0858722i | ||||
\(851\) | −25411.3 | −1.02361 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39373.6i | 1.58045i | 0.612816 | + | 0.790225i | \(0.290037\pi\) | ||||
−0.612816 | + | 0.790225i | \(0.709963\pi\) | |||||||
\(854\) | −8696.57 | −0.348466 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14993.5 | −0.598677 | ||||||||
\(857\) | 5240.83i | 0.208895i | 0.994530 | + | 0.104448i | \(0.0333075\pi\) | ||||
−0.994530 | + | 0.104448i | \(0.966693\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8308.93 | 0.330032 | 0.165016 | − | 0.986291i | \(-0.447232\pi\) | ||||
0.165016 | + | 0.986291i | \(0.447232\pi\) | |||||||
\(860\) | 2815.92 | + | 1723.94i | 0.111653 | + | 0.0683556i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 26150.8i | − | 1.03329i | ||||||
\(863\) | − | 5719.30i | − | 0.225593i | −0.993618 | − | 0.112797i | \(-0.964019\pi\) | ||
0.993618 | − | 0.112797i | \(-0.0359809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26602.9 | − | 16286.6i | −1.04569 | − | 0.640186i | ||||
\(866\) | −25263.8 | −0.991338 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 10797.6i | − | 0.422230i | ||||||
\(869\) | −2392.47 | −0.0933936 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12244.1 | −0.476320 | ||||||||
\(872\) | 8012.50i | 0.311167i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −48642.2 | −1.88255 | ||||||||
\(875\) | 3378.17 | − | 43641.0i | 0.130518 | − | 1.68610i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12317.6i | 0.474272i | 0.971476 | + | 0.237136i | \(0.0762087\pi\) | ||||
−0.971476 | + | 0.237136i | \(0.923791\pi\) | |||||||
\(878\) | 25790.9i | 0.991343i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8281.19 | + | 13526.7i | −0.317226 | + | 0.518164i | ||||
\(881\) | 4540.33 | 0.173630 | 0.0868148 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868148 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19437.5i | 0.740796i | 0.928873 | + | 0.370398i | \(0.120779\pi\) | ||||
−0.928873 | + | 0.370398i | \(0.879221\pi\) | |||||||
\(884\) | 199.108 | 0.00757550 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6862.03 | −0.260197 | ||||||||
\(887\) | 2625.66i | 0.0993925i | 0.998764 | + | 0.0496962i | \(0.0158253\pi\) | ||||
−0.998764 | + | 0.0496962i | \(0.984175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37145.7 | 1.40138 | ||||||||
\(890\) | −9815.77 | − | 6009.33i | −0.369691 | − | 0.226329i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 6188.43i | − | 0.232291i | ||||||
\(893\) | 30769.8i | 1.15305i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4492.54 | − | 7338.22i | 0.167787 | − | 0.274067i | ||||
\(896\) | −53891.6 | −2.00936 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16841.8i | 0.625857i | ||||||||
\(899\) | 1721.26 | 0.0638569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1717.85 | −0.0635183 | ||||||||
\(902\) | − | 18679.5i | − | 0.689535i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4402.21 | 0.161964 | ||||||||
\(905\) | 13440.4 | − | 21953.9i | 0.493674 | − | 0.806378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44880.6i | − | 1.64304i | −0.570182 | − | 0.821519i | \(-0.693127\pi\) | ||
0.570182 | − | 0.821519i | \(-0.306873\pi\) | |||||||
\(908\) | 1321.31i | 0.0482922i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19354.7 | − | 11849.2i | −0.705057 | − | 0.431644i | ||||
\(911\) | −52766.0 | −1.91901 | −0.959503 | − | 0.281698i | \(-0.909102\pi\) | ||||
−0.959503 | + | 0.281698i | \(0.909102\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 704.788i | − | 0.0255477i | ||||||
\(914\) | 21531.9 | 0.779227 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1468.03 | 0.0529531 | ||||||||
\(917\) | 86782.7i | 3.12521i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33853.3 | 1.21514 | 0.607571 | − | 0.794265i | \(-0.292144\pi\) | ||||
0.607571 | + | 0.794265i | \(0.292144\pi\) | |||||||
\(920\) | −18999.7 | + | 31034.5i | −0.680870 | + | 1.11215i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17360.8i | 0.620115i | ||||||||
\(923\) | 2783.50i | 0.0992634i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17357.2 | + | 8862.66i | −0.616973 | + | 0.315030i | ||||
\(926\) | −8896.65 | −0.315726 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 523.466i | 0.0185168i | ||||||||
\(929\) | −5402.22 | −0.190787 | −0.0953935 | − | 0.995440i | \(-0.530411\pi\) | ||||
−0.0953935 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −61669.3 | −2.17092 | ||||||||
\(932\) | 1775.71i | 0.0624093i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −52106.7 | −1.82546 | ||||||||
\(935\) | −1133.13 | − | 693.716i | −0.0396335 | − | 0.0242641i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37756.4i | 1.31638i | 0.752852 | + | 0.658190i | \(0.228677\pi\) | ||||
−0.752852 | + | 0.658190i | \(0.771323\pi\) | |||||||
\(938\) | − | 56404.6i | − | 1.96341i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4650.07 | − | 2846.82i | −0.161349 | − | 0.0987800i | ||||
\(941\) | −3170.18 | −0.109825 | −0.0549123 | − | 0.998491i | \(-0.517488\pi\) | ||||
−0.0549123 | + | 0.998491i | \(0.517488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 51376.5i | − | 1.77418i | ||||||
\(944\) | 31728.6 | 1.09394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11422.6 | −0.392580 | ||||||||
\(947\) | − | 41521.2i | − | 1.42477i | −0.701789 | − | 0.712385i | \(-0.747615\pi\) | ||
0.701789 | − | 0.712385i | \(-0.252385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5456.23 | 0.186635 | ||||||||
\(950\) | −33225.0 | + | 16964.9i | −1.13470 | + | 0.579382i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 3872.35i | − | 0.131831i | ||||||
\(953\) | − | 18886.5i | − | 0.641965i | −0.947085 | − | 0.320982i | \(-0.895987\pi\) | ||
0.947085 | − | 0.320982i | \(-0.104013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24687.1 | − | 40324.5i | 0.836498 | − | 1.36636i | ||||
\(956\) | 6199.27 | 0.209727 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 58932.8i | 1.98751i | ||||||||
\(959\) | −41403.5 | −1.39415 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20845.1 | 0.699710 | ||||||||
\(962\) | 10104.2i | 0.338641i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3715.96 | 0.124152 | ||||||||
\(965\) | 41612.9 | + | 25475.9i | 1.38815 | + | 0.849843i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39799.9i | − | 1.32355i | −0.749700 | − | 0.661777i | \(-0.769802\pi\) | ||
0.749700 | − | 0.661777i | \(-0.230198\pi\) | |||||||
\(968\) | 19222.4i | 0.638255i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18550.2 | − | 30300.3i | 0.614032 | − | 1.00297i | ||||
\(971\) | 39063.6 | 1.29105 | 0.645525 | − | 0.763739i | \(-0.276639\pi\) | ||||
0.645525 | + | 0.763739i | \(0.276639\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56703.8i | 1.86829i | ||||||||
\(974\) | 38758.1 | 1.27504 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6647.01 | 0.217997 | ||||||||
\(977\) | 5087.15i | 0.166584i | 0.996525 | + | 0.0832918i | \(0.0265434\pi\) | ||||
−0.996525 | + | 0.0832918i | \(0.973457\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6399.63 | 0.208920 | ||||||||
\(980\) | 5705.65 | − | 9319.74i | 0.185980 | − | 0.303784i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4845.12i | 0.157448i | ||||||||
\(983\) | 32012.1i | 1.03869i | 0.854566 | + | 0.519343i | \(0.173823\pi\) | ||||
−0.854566 | + | 0.519343i | \(0.826177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9835.65 | + | 6021.50i | 0.318162 | + | 0.194783i | ||||
\(986\) | −146.217 | −0.00472261 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3108.66i | 0.100101i | ||||||||
\(989\) | −31416.9 | −1.01011 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3717.85 | 0.119174 | 0.0595870 | − | 0.998223i | \(-0.481022\pi\) | ||||
0.0595870 | + | 0.998223i | \(0.481022\pi\) | |||||||
\(992\) | 15399.3i | 0.492872i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12822.7 | −0.409168 | ||||||||
\(995\) | −7423.04 | + | 12125.0i | −0.236509 | + | 0.386319i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5517.11i | 0.175254i | 0.996153 | + | 0.0876272i | \(0.0279284\pi\) | ||||
−0.996153 | + | 0.0876272i | \(0.972072\pi\) | |||||||
\(998\) | − | 33080.5i | − | 1.04924i | ||||||
\(999\) | 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 | 405.4.b.f.244.4 | 16 | ||
3.2 | odd | 2 | 405.4.b.e.244.13 | 16 | |||
5.2 | odd | 4 | 2025.4.a.bl.1.13 | 16 | |||
5.3 | odd | 4 | 2025.4.a.bl.1.4 | 16 | |||
5.4 | even | 2 | inner | 405.4.b.f.244.13 | 16 | ||
9.2 | odd | 6 | 45.4.j.a.4.13 | yes | 32 | ||
9.4 | even | 3 | 135.4.j.a.19.13 | 32 | |||
9.5 | odd | 6 | 45.4.j.a.34.4 | yes | 32 | ||
9.7 | even | 3 | 135.4.j.a.64.4 | 32 | |||
15.2 | even | 4 | 2025.4.a.bk.1.4 | 16 | |||
15.8 | even | 4 | 2025.4.a.bk.1.13 | 16 | |||
15.14 | odd | 2 | 405.4.b.e.244.4 | 16 | |||
45.2 | even | 12 | 225.4.e.g.76.13 | 32 | |||
45.4 | even | 6 | 135.4.j.a.19.4 | 32 | |||
45.14 | odd | 6 | 45.4.j.a.34.13 | yes | 32 | ||
45.23 | even | 12 | 225.4.e.g.151.4 | 32 | |||
45.29 | odd | 6 | 45.4.j.a.4.4 | ✓ | 32 | ||
45.32 | even | 12 | 225.4.e.g.151.13 | 32 | |||
45.34 | even | 6 | 135.4.j.a.64.13 | 32 | |||
45.38 | even | 12 | 225.4.e.g.76.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.4 | ✓ | 32 | 45.29 | odd | 6 | ||
45.4.j.a.4.13 | yes | 32 | 9.2 | odd | 6 | ||
45.4.j.a.34.4 | yes | 32 | 9.5 | odd | 6 | ||
45.4.j.a.34.13 | yes | 32 | 45.14 | odd | 6 | ||
135.4.j.a.19.4 | 32 | 45.4 | even | 6 | |||
135.4.j.a.19.13 | 32 | 9.4 | even | 3 | |||
135.4.j.a.64.4 | 32 | 9.7 | even | 3 | |||
135.4.j.a.64.13 | 32 | 45.34 | even | 6 | |||
225.4.e.g.76.4 | 32 | 45.38 | even | 12 | |||
225.4.e.g.76.13 | 32 | 45.2 | even | 12 | |||
225.4.e.g.151.4 | 32 | 45.23 | even | 12 | |||
225.4.e.g.151.13 | 32 | 45.32 | even | 12 | |||
405.4.b.e.244.4 | 16 | 15.14 | odd | 2 | |||
405.4.b.e.244.13 | 16 | 3.2 | odd | 2 | |||
405.4.b.f.244.4 | 16 | 1.1 | even | 1 | trivial | ||
405.4.b.f.244.13 | 16 | 5.4 | even | 2 | inner | ||
2025.4.a.bk.1.4 | 16 | 15.2 | even | 4 | |||
2025.4.a.bk.1.13 | 16 | 15.8 | even | 4 | |||
2025.4.a.bl.1.4 | 16 | 5.3 | odd | 4 | |||
2025.4.a.bl.1.13 | 16 | 5.2 | odd | 4 |