Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,4,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2025.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.a (trivial) |
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: | yes |
Analytic conductor: | \(119.478867762\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{12}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(3.08740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.08740 | 1.09156 | 0.545781 | − | 0.837928i | \(-0.316233\pi\) | ||||
0.545781 | + | 0.837928i | \(0.316233\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.53204 | 0.191506 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 31.3204 | 1.69114 | 0.845571 | − | 0.533863i | \(-0.179260\pi\) | ||||
0.845571 | + | 0.533863i | \(0.179260\pi\) | |||||||
\(8\) | −19.9692 | −0.882521 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.1937 | −0.526101 | −0.263051 | − | 0.964782i | \(-0.584729\pi\) | ||||
−0.263051 | + | 0.964782i | \(0.584729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.9909 | 0.447833 | 0.223917 | − | 0.974608i | \(-0.428116\pi\) | ||||
0.223917 | + | 0.974608i | \(0.428116\pi\) | |||||||
\(14\) | 96.6986 | 1.84598 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −73.9092 | −1.15483 | ||||||||
\(17\) | 6.19137 | 0.0883311 | 0.0441656 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441656 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −96.6654 | −1.16719 | −0.583594 | − | 0.812046i | \(-0.698354\pi\) | ||||
−0.583594 | + | 0.812046i | \(0.698354\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −59.2586 | −0.574271 | ||||||||
\(23\) | −162.986 | −1.47760 | −0.738801 | − | 0.673923i | \(-0.764608\pi\) | ||||
−0.738801 | + | 0.673923i | \(0.764608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 64.8074 | 0.488837 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 47.9842 | 0.323863 | ||||||||
\(29\) | 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 | \(0.273987\pi\) | |||||||
\(32\) | −68.4339 | −0.378048 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 19.1153 | 0.0964188 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −155.911 | −0.692748 | −0.346374 | − | 0.938097i | \(-0.612587\pi\) | ||||
−0.346374 | + | 0.938097i | \(0.612587\pi\) | |||||||
\(38\) | −298.445 | −1.27406 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −315.221 | −1.20071 | −0.600357 | − | 0.799732i | \(-0.704975\pi\) | ||||
−0.600357 | + | 0.799732i | \(0.704975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 192.759 | 0.683614 | 0.341807 | − | 0.939770i | \(-0.388961\pi\) | ||||
0.341807 | + | 0.939770i | \(0.388961\pi\) | |||||||
\(44\) | −29.4056 | −0.100751 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −503.202 | −1.61289 | ||||||||
\(47\) | −318.312 | −0.987885 | −0.493942 | − | 0.869495i | \(-0.664445\pi\) | ||||
−0.493942 | + | 0.869495i | \(0.664445\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 637.967 | 1.85996 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 32.1590 | 0.0857625 | ||||||||
\(53\) | −277.459 | −0.719093 | −0.359547 | − | 0.933127i | \(-0.617069\pi\) | ||||
−0.359547 | + | 0.933127i | \(0.617069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −625.442 | −1.49247 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 23.6162 | 0.0534648 | ||||||||
\(59\) | −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 | \(0.530088\pi\) | |||||||
\(62\) | 694.741 | 1.42310 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 379.991 | 0.742169 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −583.304 | −1.06361 | −0.531805 | − | 0.846867i | \(-0.678486\pi\) | ||||
−0.531805 | + | 0.846867i | \(0.678486\pi\) | |||||||
\(68\) | 9.48546 | 0.0169159 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 132.605 | 0.221653 | 0.110826 | − | 0.993840i | \(-0.464650\pi\) | ||||
0.110826 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −259.933 | −0.416752 | −0.208376 | − | 0.978049i | \(-0.566818\pi\) | ||||
−0.208376 | + | 0.978049i | \(0.566818\pi\) | |||||||
\(74\) | −481.361 | −0.756176 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −148.096 | −0.223523 | ||||||||
\(77\) | −601.153 | −0.889712 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 124.649 | 0.177520 | 0.0887601 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887601 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −973.214 | −1.31065 | ||||||||
\(83\) | −36.7198 | −0.0485605 | −0.0242802 | − | 0.999705i | \(-0.507729\pi\) | ||||
−0.0242802 | + | 0.999705i | \(0.507729\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 595.123 | 0.746207 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 383.282 | 0.464295 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | −249.701 | −0.282969 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −982.757 | −1.07834 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1029.25 | 1.07736 | 0.538681 | − | 0.842510i | \(-0.318923\pi\) | ||||
0.538681 | + | 0.842510i | \(0.318923\pi\) | |||||||
\(98\) | 1969.66 | 2.03026 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 926.962 | 0.913230 | 0.456615 | − | 0.889664i | \(-0.349062\pi\) | ||||
0.456615 | + | 0.889664i | \(0.349062\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1687.60 | −1.61441 | −0.807205 | − | 0.590271i | \(-0.799021\pi\) | ||||
−0.807205 | + | 0.590271i | \(0.799021\pi\) | |||||||
\(104\) | −419.171 | −0.395222 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −856.627 | −0.784934 | ||||||||
\(107\) | 750.833 | 0.678372 | 0.339186 | − | 0.940719i | \(-0.389848\pi\) | ||||
0.339186 | + | 0.940719i | \(0.389848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 401.243 | 0.352589 | 0.176294 | − | 0.984338i | \(-0.443589\pi\) | ||||
0.176294 | + | 0.984338i | \(0.443589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2314.86 | −1.95298 | ||||||||
\(113\) | 220.450 | 0.183524 | 0.0917620 | − | 0.995781i | \(-0.470750\pi\) | ||||
0.0917620 | + | 0.995781i | \(0.470750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.7189 | 0.00937997 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1325.40 | −1.03401 | ||||||||
\(119\) | 193.916 | 0.149380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −962.603 | −0.723218 | ||||||||
\(122\) | −277.665 | −0.206054 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 344.748 | 0.249671 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1185.99 | −0.828659 | −0.414329 | − | 0.910127i | \(-0.635984\pi\) | ||||
−0.414329 | + | 0.910127i | \(0.635984\pi\) | |||||||
\(128\) | 1720.65 | 1.18817 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2770.80 | −1.84799 | −0.923993 | − | 0.382408i | \(-0.875095\pi\) | ||||
−0.923993 | + | 0.382408i | \(0.875095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3027.60 | −1.97388 | ||||||||
\(134\) | −1800.89 | −1.16100 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −123.637 | −0.0779541 | ||||||||
\(137\) | −1321.94 | −0.824384 | −0.412192 | − | 0.911097i | \(-0.635237\pi\) | ||||
−0.412192 | + | 0.911097i | \(0.635237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1810.45 | −1.10475 | −0.552374 | − | 0.833596i | \(-0.686278\pi\) | ||||
−0.552374 | + | 0.833596i | \(0.686278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 409.405 | 0.241947 | ||||||||
\(143\) | −402.893 | −0.235606 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −802.518 | −0.454910 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −238.863 | −0.132665 | ||||||||
\(149\) | −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 | \(0.221966\pi\) | |||||||
\(152\) | 1930.33 | 1.03007 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1856.00 | −0.971175 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1745.14 | 0.887115 | 0.443558 | − | 0.896246i | \(-0.353716\pi\) | ||||
0.443558 | + | 0.896246i | \(0.353716\pi\) | |||||||
\(158\) | 384.841 | 0.193774 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5104.77 | −2.49884 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2607.78 | −1.25311 | −0.626554 | − | 0.779378i | \(-0.715535\pi\) | ||||
−0.626554 | + | 0.779378i | \(0.715535\pi\) | |||||||
\(164\) | −482.933 | −0.229943 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −113.369 | −0.0530067 | ||||||||
\(167\) | 1223.32 | 0.566847 | 0.283423 | − | 0.958995i | \(-0.408530\pi\) | ||||
0.283423 | + | 0.958995i | \(0.408530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1756.38 | −0.799445 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 295.315 | 0.130916 | ||||||||
\(173\) | −2789.93 | −1.22610 | −0.613048 | − | 0.790045i | \(-0.710057\pi\) | ||||
−0.613048 | + | 0.790045i | \(0.710057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1418.59 | 0.607558 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1029.41 | 0.433471 | ||||||||
\(179\) | 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 | \(0.343262\pi\) | |||||||
\(182\) | 2029.79 | 0.826693 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3254.69 | 1.30402 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −118.835 | −0.0464711 | ||||||||
\(188\) | −487.668 | −0.189185 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4228.96 | −1.60208 | −0.801039 | − | 0.598612i | \(-0.795719\pi\) | ||||
−0.801039 | + | 0.598612i | \(0.795719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4364.09 | −1.62764 | −0.813818 | − | 0.581119i | \(-0.802615\pi\) | ||||
−0.813818 | + | 0.581119i | \(0.802615\pi\) | |||||||
\(194\) | 3177.69 | 1.17601 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 977.393 | 0.356193 | ||||||||
\(197\) | −1031.50 | −0.373052 | −0.186526 | − | 0.982450i | \(-0.559723\pi\) | ||||
−0.186526 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1271.59 | 0.452966 | 0.226483 | − | 0.974015i | \(-0.427277\pi\) | ||||
0.226483 | + | 0.974015i | \(0.427277\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2861.90 | 0.996846 | ||||||||
\(203\) | 239.577 | 0.0828324 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5210.30 | −1.76223 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1551.42 | −0.517172 | ||||||||
\(209\) | 1855.36 | 0.614059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 346.295 | 0.112986 | 0.0564928 | − | 0.998403i | \(-0.482008\pi\) | ||||
0.0564928 | + | 0.998403i | \(0.482008\pi\) | |||||||
\(212\) | −425.080 | −0.137710 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2318.12 | 0.740484 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7047.86 | 2.20479 | ||||||||
\(218\) | 1238.80 | 0.384872 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.963 | 0.0395576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4039.33 | −1.21297 | −0.606487 | − | 0.795093i | \(-0.707422\pi\) | ||||
−0.606487 | + | 0.795093i | \(0.707422\pi\) | |||||||
\(224\) | −2143.38 | −0.639332 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 680.618 | 0.200328 | ||||||||
\(227\) | 862.451 | 0.252171 | 0.126086 | − | 0.992019i | \(-0.459759\pi\) | ||||
0.126086 | + | 0.992019i | \(0.459759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 958.217 | 0.276510 | 0.138255 | − | 0.990397i | \(-0.455851\pi\) | ||||
0.138255 | + | 0.990397i | \(0.455851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −152.749 | −0.0432260 | ||||||||
\(233\) | −1159.05 | −0.325887 | −0.162944 | − | 0.986635i | \(-0.552099\pi\) | ||||
−0.162944 | + | 0.986635i | \(0.552099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −657.694 | −0.181408 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 598.697 | 0.163058 | ||||||||
\(239\) | −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 | \(0.605078\pi\) | |||||||
\(242\) | −2971.94 | −0.789436 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −137.784 | −0.0361505 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2029.09 | −0.522705 | ||||||||
\(248\) | −4493.55 | −1.15057 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7272.75 | 1.82889 | 0.914445 | − | 0.404709i | \(-0.132627\pi\) | ||||
0.914445 | + | 0.404709i | \(0.132627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3128.29 | 0.777368 | ||||||||
\(254\) | −3661.63 | −0.904532 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2272.43 | 0.554792 | ||||||||
\(257\) | −3234.18 | −0.784990 | −0.392495 | − | 0.919754i | \(-0.628388\pi\) | ||||
−0.392495 | + | 0.919754i | \(0.628388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4883.20 | −1.17153 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8554.58 | −2.01719 | ||||||||
\(263\) | −1056.62 | −0.247733 | −0.123866 | − | 0.992299i | \(-0.539529\pi\) | ||||
−0.123866 | + | 0.992299i | \(0.539529\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9347.41 | −2.15461 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −893.647 | −0.203687 | ||||||||
\(269\) | −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 | \(0.809315\pi\) | |||||||
\(272\) | −457.599 | −0.102008 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4081.35 | −0.899865 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1854.32 | −0.402221 | −0.201111 | − | 0.979569i | \(-0.564455\pi\) | ||||
−0.201111 | + | 0.979569i | \(0.564455\pi\) | |||||||
\(278\) | −5589.57 | −1.20590 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 415.132 | 0.0881306 | 0.0440653 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440653 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4116.22 | 0.864607 | 0.432303 | − | 0.901728i | \(-0.357701\pi\) | ||||
0.432303 | + | 0.901728i | \(0.357701\pi\) | |||||||
\(284\) | 203.157 | 0.0424477 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1243.89 | −0.257178 | ||||||||
\(287\) | −9872.84 | −2.03058 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4874.67 | −0.992198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −398.229 | −0.0798103 | ||||||||
\(293\) | 4906.20 | 0.978236 | 0.489118 | − | 0.872218i | \(-0.337319\pi\) | ||||
0.489118 | + | 0.872218i | \(0.337319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3113.42 | 0.611364 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −786.570 | −0.152902 | ||||||||
\(299\) | −3421.22 | −0.661720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6037.28 | 1.15609 | ||||||||
\(302\) | 8782.86 | 1.67350 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7144.46 | 1.34790 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6909.30 | 1.28448 | 0.642239 | − | 0.766504i | \(-0.278006\pi\) | ||||
0.642239 | + | 0.766504i | \(0.278006\pi\) | |||||||
\(308\) | −920.994 | −0.170385 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5373.87 | −0.979820 | −0.489910 | − | 0.871773i | \(-0.662970\pi\) | ||||
−0.489910 | + | 0.871773i | \(0.662970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2392.60 | 0.432070 | 0.216035 | − | 0.976386i | \(-0.430687\pi\) | ||||
0.216035 | + | 0.976386i | \(0.430687\pi\) | |||||||
\(314\) | 5387.94 | 0.968340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 190.968 | 0.0339961 | ||||||||
\(317\) | −1183.68 | −0.209723 | −0.104861 | − | 0.994487i | \(-0.533440\pi\) | ||||
−0.104861 | + | 0.994487i | \(0.533440\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −146.817 | −0.0257685 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15760.5 | −2.72763 | ||||||||
\(323\) | −598.492 | −0.103099 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8051.25 | −1.36784 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6294.70 | 1.05965 | ||||||||
\(329\) | −9969.66 | −1.67065 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9386.43 | −1.55868 | −0.779342 | − | 0.626598i | \(-0.784447\pi\) | ||||
−0.779342 | + | 0.626598i | \(0.784447\pi\) | |||||||
\(332\) | −56.2563 | −0.00929960 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3776.88 | 0.618748 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12171.6 | 1.96745 | 0.983724 | − | 0.179685i | \(-0.0575078\pi\) | ||||
0.983724 | + | 0.179685i | \(0.0575078\pi\) | |||||||
\(338\) | −5422.65 | −0.872644 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4319.05 | −0.685893 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9238.47 | 1.45432 | ||||||||
\(344\) | −3849.23 | −0.603304 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8613.64 | −1.33836 | ||||||||
\(347\) | 2785.57 | 0.430943 | 0.215471 | − | 0.976510i | \(-0.430871\pi\) | ||||
0.215471 | + | 0.976510i | \(0.430871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3359.76 | −0.515311 | −0.257656 | − | 0.966237i | \(-0.582950\pi\) | ||||
−0.257656 | + | 0.966237i | \(0.582950\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1313.50 | 0.198891 | ||||||||
\(353\) | 5427.68 | 0.818375 | 0.409188 | − | 0.912450i | \(-0.365812\pi\) | ||||
0.409188 | + | 0.912450i | \(0.365812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 510.820 | 0.0760489 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2376.01 | 0.350772 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 7108.37 | 1.03207 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1007.23 | 0.145037 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1677.21 | 0.238554 | 0.119277 | − | 0.992861i | \(-0.461942\pi\) | ||||
0.119277 | + | 0.992861i | \(0.461942\pi\) | |||||||
\(368\) | 12046.1 | 1.70638 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8690.13 | −1.21609 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 956.336 | 0.132754 | 0.0663769 | − | 0.997795i | \(-0.478856\pi\) | ||||
0.0663769 | + | 0.997795i | \(0.478856\pi\) | |||||||
\(374\) | −366.892 | −0.0507260 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6356.43 | 0.871829 | ||||||||
\(377\) | 160.564 | 0.0219349 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10019.0 | 1.35789 | 0.678943 | − | 0.734191i | \(-0.262438\pi\) | ||||
0.678943 | + | 0.734191i | \(0.262438\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13056.5 | −1.74877 | ||||||||
\(383\) | 12886.2 | 1.71920 | 0.859600 | − | 0.510967i | \(-0.170713\pi\) | ||||
0.859600 | + | 0.510967i | \(0.170713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13473.7 | −1.77667 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1576.85 | 0.206321 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | −12739.7 | −1.64145 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3184.65 | −0.407209 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7893.06 | −0.997837 | −0.498918 | − | 0.866649i | \(-0.666269\pi\) | ||||
−0.498918 | + | 0.866649i | \(0.666269\pi\) | |||||||
\(398\) | 3925.90 | 0.494441 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4192.82 | 0.522144 | 0.261072 | − | 0.965319i | \(-0.415924\pi\) | ||||
0.261072 | + | 0.965319i | \(0.415924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4723.47 | 0.583853 | ||||||||
\(404\) | 1420.15 | 0.174889 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 739.669 | 0.0904166 | ||||||||
\(407\) | 2992.51 | 0.364455 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9010.03 | 1.08928 | 0.544642 | − | 0.838668i | \(-0.316665\pi\) | ||||
0.544642 | + | 0.838668i | \(0.316665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2585.48 | −0.309169 | ||||||||
\(413\) | −13445.6 | −1.60197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1436.49 | −0.169302 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5728.25 | 0.670283 | ||||||||
\(419\) | 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 | \(0.239982\pi\) | |||||||
\(422\) | 1069.15 | 0.123331 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5540.63 | 0.634615 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2816.79 | −0.319237 | ||||||||
\(428\) | 1150.31 | 0.129912 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8470.15 | −0.946619 | −0.473310 | − | 0.880896i | \(-0.656941\pi\) | ||||
−0.473310 | + | 0.880896i | \(0.656941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8182.86 | 0.908183 | 0.454092 | − | 0.890955i | \(-0.349964\pi\) | ||||
0.454092 | + | 0.890955i | \(0.349964\pi\) | |||||||
\(434\) | 21759.6 | 2.40666 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 614.723 | 0.0675227 | ||||||||
\(437\) | 15755.1 | 1.72464 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8353.58 | 0.908189 | 0.454094 | − | 0.890954i | \(-0.349963\pi\) | ||||
0.454094 | + | 0.890954i | \(0.349963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 401.247 | 0.0431795 | ||||||||
\(443\) | −2222.59 | −0.238371 | −0.119186 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119186 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12471.0 | −1.32404 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11901.5 | 1.25511 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 337.739 | 0.0351459 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2662.73 | 0.275260 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6974.13 | 0.713865 | 0.356932 | − | 0.934130i | \(-0.383823\pi\) | ||||
0.356932 | + | 0.934130i | \(0.383823\pi\) | |||||||
\(458\) | 2958.40 | 0.301827 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5623.10 | 0.568099 | 0.284050 | − | 0.958810i | \(-0.408322\pi\) | ||||
0.284050 | + | 0.958810i | \(0.408322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2881.60 | 0.289242 | 0.144621 | − | 0.989487i | \(-0.453804\pi\) | ||||
0.144621 | + | 0.989487i | \(0.453804\pi\) | |||||||
\(464\) | −565.348 | −0.0565638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3578.45 | −0.355726 | ||||||||
\(467\) | 16877.2 | 1.67234 | 0.836172 | − | 0.548468i | \(-0.184789\pi\) | ||||
0.836172 | + | 0.548468i | \(0.184789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18269.3 | −1.79872 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8572.61 | 0.835988 | ||||||||
\(473\) | −3699.75 | −0.359650 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 297.088 | 0.0286072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12492.9 | −1.19542 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | −7488.45 | −0.707655 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1474.75 | −0.138500 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12553.6 | 1.16809 | 0.584044 | − | 0.811722i | \(-0.301470\pi\) | ||||
0.584044 | + | 0.811722i | \(0.301470\pi\) | |||||||
\(488\) | 1795.92 | 0.166593 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1569.32 | 0.144241 | 0.0721205 | − | 0.997396i | \(-0.477023\pi\) | ||||
0.0721205 | + | 0.997396i | \(0.477023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.3592 | 0.00432647 | ||||||||
\(494\) | −6264.63 | −0.570565 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16631.4 | −1.50559 | ||||||||
\(497\) | 4153.25 | 0.374846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10714.7 | −0.961232 | −0.480616 | − | 0.876931i | \(-0.659587\pi\) | ||||
−0.480616 | + | 0.876931i | \(0.659587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22453.9 | 1.99635 | ||||||||
\(503\) | 19016.8 | 1.68572 | 0.842862 | − | 0.538130i | \(-0.180869\pi\) | ||||
0.842862 | + | 0.538130i | \(0.180869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9658.30 | 0.848545 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1816.99 | −0.158693 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | −6749.35 | −0.582582 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9985.20 | −0.856865 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6109.58 | 0.519727 | ||||||||
\(518\) | −15076.4 | −1.27880 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9319.21 | −0.783651 | −0.391826 | − | 0.920040i | \(-0.628156\pi\) | ||||
−0.391826 | + | 0.920040i | \(0.628156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19719.6 | 1.64871 | 0.824357 | − | 0.566071i | \(-0.191537\pi\) | ||||
0.824357 | + | 0.566071i | \(0.191537\pi\) | |||||||
\(524\) | −4244.99 | −0.353900 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3262.19 | −0.270415 | ||||||||
\(527\) | 1393.21 | 0.115160 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14397.3 | 1.18331 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4638.41 | −0.378009 | ||||||||
\(533\) | −6616.78 | −0.537719 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11648.1 | 0.938658 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4717.95 | −0.378077 | ||||||||
\(539\) | −12244.9 | −0.978527 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16592.1 | 1.31857 | 0.659287 | − | 0.751891i | \(-0.270858\pi\) | ||||
0.659287 | + | 0.751891i | \(0.270858\pi\) | |||||||
\(542\) | −22750.4 | −1.80297 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −423.700 | −0.0333934 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12264.5 | 0.958667 | 0.479333 | − | 0.877633i | \(-0.340878\pi\) | ||||
0.479333 | + | 0.877633i | \(0.340878\pi\) | |||||||
\(548\) | −2025.26 | −0.157874 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −739.415 | −0.0571690 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3904.05 | 0.300212 | ||||||||
\(554\) | −5725.03 | −0.439049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2773.68 | −0.211565 | ||||||||
\(557\) | 1623.54 | 0.123504 | 0.0617518 | − | 0.998092i | \(-0.480331\pi\) | ||||
0.0617518 | + | 0.998092i | \(0.480331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4046.18 | 0.306145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1281.68 | 0.0961999 | ||||||||
\(563\) | 6842.29 | 0.512199 | 0.256100 | − | 0.966650i | \(-0.417562\pi\) | ||||
0.256100 | + | 0.966650i | \(0.417562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12708.4 | 0.943771 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2648.02 | −0.195613 | ||||||||
\(569\) | −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 | \(0.564616\pi\) | |||||||
\(572\) | −617.250 | −0.0451198 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −30481.4 | −2.21650 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13600.1 | 0.981245 | 0.490622 | − | 0.871372i | \(-0.336769\pi\) | ||||
0.490622 | + | 0.871372i | \(0.336769\pi\) | |||||||
\(578\) | −15050.1 | −1.08304 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1150.08 | −0.0821226 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5325.46 | 0.378316 | ||||||||
\(584\) | 5190.65 | 0.367792 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15147.4 | 1.06780 | ||||||||
\(587\) | −21216.1 | −1.49179 | −0.745896 | − | 0.666062i | \(-0.767979\pi\) | ||||
−0.745896 | + | 0.666062i | \(0.767979\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21752.1 | −1.52170 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11523.3 | 0.800007 | ||||||||
\(593\) | −14973.6 | −1.03692 | −0.518458 | − | 0.855103i | \(-0.673494\pi\) | ||||
−0.518458 | + | 0.855103i | \(0.673494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −390.315 | −0.0268254 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10562.7 | −0.722307 | ||||||||
\(599\) | −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 | \(0.311410\pi\) | |||||||
\(602\) | 18639.5 | 1.26194 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4358.27 | 0.293602 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5457.49 | −0.364930 | −0.182465 | − | 0.983212i | \(-0.558408\pi\) | ||||
−0.182465 | + | 0.983212i | \(0.558408\pi\) | |||||||
\(608\) | 6615.19 | 0.441253 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6681.66 | −0.442408 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10945.3 | −0.721167 | −0.360584 | − | 0.932727i | \(-0.617422\pi\) | ||||
−0.360584 | + | 0.932727i | \(0.617422\pi\) | |||||||
\(614\) | 21331.8 | 1.40209 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12004.5 | 0.785189 | ||||||||
\(617\) | −25534.0 | −1.66606 | −0.833032 | − | 0.553225i | \(-0.813397\pi\) | ||||
−0.833032 | + | 0.553225i | \(0.813397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7895.81 | −0.512697 | −0.256349 | − | 0.966584i | \(-0.582520\pi\) | ||||
−0.256349 | + | 0.966584i | \(0.582520\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16591.3 | −1.06953 | ||||||||
\(623\) | 10443.0 | 0.671570 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7386.93 | 0.471631 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2673.63 | 0.169887 | ||||||||
\(629\) | −965.305 | −0.0611912 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5659.61 | −0.357061 | −0.178531 | − | 0.983934i | \(-0.557134\pi\) | ||||
−0.178531 | + | 0.983934i | \(0.557134\pi\) | |||||||
\(632\) | −2489.14 | −0.156665 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3654.50 | −0.228925 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13391.5 | 0.832952 | ||||||||
\(638\) | −453.282 | −0.0281279 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16082.9 | −0.991010 | −0.495505 | − | 0.868605i | \(-0.665017\pi\) | ||||
−0.495505 | + | 0.868605i | \(0.665017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −66.7491 | −0.00409382 | −0.00204691 | − | 0.999998i | \(-0.500652\pi\) | ||||
−0.00204691 | + | 0.999998i | \(0.500652\pi\) | |||||||
\(644\) | −7820.74 | −0.478541 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1847.78 | −0.112539 | ||||||||
\(647\) | 1263.42 | 0.0767697 | 0.0383849 | − | 0.999263i | \(-0.487779\pi\) | ||||
0.0383849 | + | 0.999263i | \(0.487779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8239.69 | 0.498361 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3995.23 | −0.239977 | ||||||||
\(653\) | −21867.4 | −1.31047 | −0.655235 | − | 0.755425i | \(-0.727430\pi\) | ||||
−0.655235 | + | 0.755425i | \(0.727430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 23297.7 | 1.38662 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30780.3 | −1.82362 | ||||||||
\(659\) | 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 | \(0.503734\pi\) | |||||||
\(662\) | −28979.7 | −1.70140 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 733.263 | 0.0428556 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1246.71 | −0.0723732 | ||||||||
\(668\) | 1874.18 | 0.108554 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1726.18 | 0.0993121 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3104.18 | 0.177797 | 0.0888986 | − | 0.996041i | \(-0.471665\pi\) | ||||
0.0888986 | + | 0.996041i | \(0.471665\pi\) | |||||||
\(674\) | 37578.7 | 2.14759 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2690.85 | −0.153098 | ||||||||
\(677\) | 24565.4 | 1.39457 | 0.697285 | − | 0.716794i | \(-0.254391\pi\) | ||||
0.697285 | + | 0.716794i | \(0.254391\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32236.4 | 1.82197 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13334.6 | −0.748694 | ||||||||
\(683\) | 8921.93 | 0.499836 | 0.249918 | − | 0.968267i | \(-0.419596\pi\) | ||||
0.249918 | + | 0.968267i | \(0.419596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 28522.9 | 1.58747 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14246.6 | −0.789459 | ||||||||
\(689\) | −5824.12 | −0.322034 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6688.21 | −0.368207 | −0.184104 | − | 0.982907i | \(-0.558938\pi\) | ||||
−0.184104 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(692\) | −4274.30 | −0.234804 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8600.17 | 0.470400 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1951.65 | −0.106060 | ||||||||
\(698\) | −10372.9 | −0.562494 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33422.0 | 1.80076 | 0.900380 | − | 0.435105i | \(-0.143289\pi\) | ||||
0.900380 | + | 0.435105i | \(0.143289\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15071.2 | 0.808567 | ||||||||
\(704\) | −7293.42 | −0.390456 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16757.4 | 0.893306 | ||||||||
\(707\) | 29032.8 | 1.54440 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29293.5 | 1.55168 | 0.775840 | − | 0.630929i | \(-0.217326\pi\) | ||||
0.775840 | + | 0.630929i | \(0.217326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6658.20 | −0.350459 | ||||||||
\(713\) | −36675.8 | −1.92639 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1179.04 | 0.0615401 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12104.9 | −0.629180 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 7672.81 | 0.395502 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3527.35 | 0.181067 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4931.68 | −0.251590 | −0.125795 | − | 0.992056i | \(-0.540148\pi\) | ||||
−0.125795 | + | 0.992056i | \(0.540148\pi\) | |||||||
\(728\) | −13128.6 | −0.668377 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1193.44 | 0.0603844 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8225.55 | −0.414485 | −0.207243 | − | 0.978290i | \(-0.566449\pi\) | ||||
−0.207243 | + | 0.978290i | \(0.566449\pi\) | |||||||
\(734\) | 5178.21 | 0.260397 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11153.8 | 0.558604 | ||||||||
\(737\) | 11195.7 | 0.559566 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17847.1 | 0.888382 | 0.444191 | − | 0.895932i | \(-0.353491\pi\) | ||||
0.444191 | + | 0.895932i | \(0.353491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26829.9 | −1.32743 | ||||||||
\(743\) | 23810.6 | 1.17568 | 0.587838 | − | 0.808979i | \(-0.299979\pi\) | ||||
0.587838 | + | 0.808979i | \(0.299979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2952.59 | 0.144909 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −182.061 | −0.00889947 | ||||||||
\(749\) | 23516.4 | 1.14722 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21295.8 | 1.03475 | 0.517374 | − | 0.855759i | \(-0.326909\pi\) | ||||
0.517374 | + | 0.855759i | \(0.326909\pi\) | |||||||
\(752\) | 23526.2 | 1.14084 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 495.726 | 0.0239433 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13423.0 | −0.644472 | −0.322236 | − | 0.946659i | \(-0.604435\pi\) | ||||
−0.322236 | + | 0.946659i | \(0.604435\pi\) | |||||||
\(758\) | 30932.5 | 1.48222 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24100.2 | −1.14801 | −0.574003 | − | 0.818853i | \(-0.694610\pi\) | ||||
−0.574003 | + | 0.818853i | \(0.694610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12567.1 | 0.596277 | ||||||||
\(764\) | −6478.96 | −0.306807 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39784.8 | 1.87661 | ||||||||
\(767\) | −9011.23 | −0.424220 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −986.759 | −0.0462724 | −0.0231362 | − | 0.999732i | \(-0.507365\pi\) | ||||
−0.0231362 | + | 0.999732i | \(0.507365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6685.98 | −0.311701 | ||||||||
\(773\) | 7277.05 | 0.338599 | 0.169300 | − | 0.985565i | \(-0.445849\pi\) | ||||
0.169300 | + | 0.985565i | \(0.445849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20553.2 | −0.950794 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2125.63 | −0.0979533 | ||||||||
\(779\) | 30471.0 | 1.40146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2545.18 | −0.116612 | ||||||||
\(782\) | −3115.51 | −0.142469 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −47151.6 | −2.14794 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4939.44 | −0.223726 | −0.111863 | − | 0.993724i | \(-0.535682\pi\) | ||||
−0.111863 | + | 0.993724i | \(0.535682\pi\) | |||||||
\(788\) | −1580.30 | −0.0714415 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6904.59 | 0.310365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1887.81 | −0.0845375 | ||||||||
\(794\) | −24369.0 | −1.08920 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1948.13 | 0.0867456 | ||||||||
\(797\) | −12447.6 | −0.553219 | −0.276610 | − | 0.960982i | \(-0.589211\pi\) | ||||
−0.276610 | + | 0.960982i | \(0.589211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1970.79 | −0.0872610 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12944.9 | 0.569952 | ||||||||
\(803\) | 4989.07 | 0.219254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14583.2 | 0.637311 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18510.7 | −0.805944 | ||||||||
\(809\) | −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 | \(0.450168\pi\) | |||||||
\(812\) | 367.042 | 0.0158629 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9239.08 | 0.397825 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18633.1 | −0.797906 | ||||||||
\(818\) | 27817.6 | 1.18902 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10824.6 | 0.460147 | 0.230074 | − | 0.973173i | \(-0.426103\pi\) | ||||
0.230074 | + | 0.973173i | \(0.426103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18031.3 | 0.763710 | 0.381855 | − | 0.924222i | \(-0.375285\pi\) | ||||
0.381855 | + | 0.924222i | \(0.375285\pi\) | |||||||
\(824\) | 33700.0 | 1.42475 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41511.9 | −1.74865 | ||||||||
\(827\) | 13172.5 | 0.553873 | 0.276937 | − | 0.960888i | \(-0.410681\pi\) | ||||
0.276937 | + | 0.960888i | \(0.410681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11929.1 | −0.499776 | −0.249888 | − | 0.968275i | \(-0.580394\pi\) | ||||
−0.249888 | + | 0.968275i | \(0.580394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7976.35 | 0.332368 | ||||||||
\(833\) | 3949.89 | 0.164292 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2842.50 | 0.117596 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21179.0 | 0.873049 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 38884.6 | 1.59151 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 530.540 | 0.0216373 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30149.1 | −1.22306 | ||||||||
\(848\) | 20506.8 | 0.830431 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25411.3 | 1.02361 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39373.6 | −1.58045 | −0.790225 | − | 0.612816i | \(-0.790037\pi\) | ||||
−0.790225 | + | 0.612816i | \(0.790037\pi\) | |||||||
\(854\) | −8696.57 | −0.348466 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14993.5 | −0.598677 | ||||||||
\(857\) | −5240.83 | −0.208895 | −0.104448 | − | 0.994530i | \(-0.533307\pi\) | ||||
−0.104448 | + | 0.994530i | \(0.533307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8308.93 | −0.330032 | −0.165016 | − | 0.986291i | \(-0.552768\pi\) | ||||
−0.165016 | + | 0.986291i | \(0.552768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26150.8 | −1.03329 | ||||||||
\(863\) | −5719.30 | −0.225593 | −0.112797 | − | 0.993618i | \(-0.535981\pi\) | ||||
−0.112797 | + | 0.993618i | \(0.535981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25263.8 | 0.991338 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10797.6 | 0.422230 | ||||||||
\(869\) | −2392.47 | −0.0933936 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12244.1 | −0.476320 | ||||||||
\(872\) | −8012.50 | −0.311167 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 48642.2 | 1.88255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12317.6 | 0.474272 | 0.237136 | − | 0.971476i | \(-0.423791\pi\) | ||||
0.237136 | + | 0.971476i | \(0.423791\pi\) | |||||||
\(878\) | 25790.9 | 0.991343 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4540.33 | −0.173630 | −0.0868148 | − | 0.996224i | \(-0.527669\pi\) | ||||
−0.0868148 | + | 0.996224i | \(0.527669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19437.5 | −0.740796 | −0.370398 | − | 0.928873i | \(-0.620779\pi\) | ||||
−0.370398 | + | 0.928873i | \(0.620779\pi\) | |||||||
\(884\) | 199.108 | 0.00757550 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6862.03 | −0.260197 | ||||||||
\(887\) | −2625.66 | −0.0993925 | −0.0496962 | − | 0.998764i | \(-0.515825\pi\) | ||||
−0.0496962 | + | 0.998764i | \(0.515825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37145.7 | −1.40138 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6188.43 | −0.232291 | ||||||||
\(893\) | 30769.8 | 1.15305 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 53891.6 | 2.00936 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16841.8 | −0.625857 | ||||||||
\(899\) | 1721.26 | 0.0638569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1717.85 | −0.0635183 | ||||||||
\(902\) | 18679.5 | 0.689535 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4402.21 | −0.161964 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44880.6 | −1.64304 | −0.821519 | − | 0.570182i | \(-0.806873\pi\) | ||||
−0.821519 | + | 0.570182i | \(0.806873\pi\) | |||||||
\(908\) | 1321.31 | 0.0482922 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52766.0 | 1.91901 | 0.959503 | − | 0.281698i | \(-0.0908976\pi\) | ||||
0.959503 | + | 0.281698i | \(0.0908976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 704.788 | 0.0255477 | ||||||||
\(914\) | 21531.9 | 0.779227 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1468.03 | 0.0529531 | ||||||||
\(917\) | −86782.7 | −3.12521 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33853.3 | −1.21514 | −0.607571 | − | 0.794265i | \(-0.707856\pi\) | ||||
−0.607571 | + | 0.794265i | \(0.707856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17360.8 | 0.620115 | ||||||||
\(923\) | 2783.50 | 0.0992634 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8896.65 | 0.315726 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −523.466 | −0.0185168 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | −1775.71 | −0.0624093 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 52106.7 | 1.82546 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37756.4 | 1.31638 | 0.658190 | − | 0.752852i | \(-0.271323\pi\) | ||||
0.658190 | + | 0.752852i | \(0.271323\pi\) | |||||||
\(938\) | −56404.6 | −1.96341 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3170.18 | 0.109825 | 0.0549123 | − | 0.998491i | \(-0.482512\pi\) | ||||
0.0549123 | + | 0.998491i | \(0.482512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51376.5 | 1.77418 | ||||||||
\(944\) | 31728.6 | 1.09394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11422.6 | −0.392580 | ||||||||
\(947\) | 41521.2 | 1.42477 | 0.712385 | − | 0.701789i | \(-0.247615\pi\) | ||||
0.712385 | + | 0.701789i | \(0.247615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5456.23 | −0.186635 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3872.35 | −0.131831 | ||||||||
\(953\) | −18886.5 | −0.641965 | −0.320982 | − | 0.947085i | \(-0.604013\pi\) | ||||
−0.320982 | + | 0.947085i | \(0.604013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6199.27 | −0.209727 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −58932.8 | −1.98751 | ||||||||
\(959\) | −41403.5 | −1.39415 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20845.1 | 0.699710 | ||||||||
\(962\) | −10104.2 | −0.338641 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3715.96 | −0.124152 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39799.9 | −1.32355 | −0.661777 | − | 0.749700i | \(-0.730198\pi\) | ||||
−0.661777 | + | 0.749700i | \(0.730198\pi\) | |||||||
\(968\) | 19222.4 | 0.638255 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39063.6 | −1.29105 | −0.645525 | − | 0.763739i | \(-0.723361\pi\) | ||||
−0.645525 | + | 0.763739i | \(0.723361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −56703.8 | −1.86829 | ||||||||
\(974\) | 38758.1 | 1.27504 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6647.01 | 0.217997 | ||||||||
\(977\) | −5087.15 | −0.166584 | −0.0832918 | − | 0.996525i | \(-0.526543\pi\) | ||||
−0.0832918 | + | 0.996525i | \(0.526543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6399.63 | −0.208920 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4845.12 | 0.157448 | ||||||||
\(983\) | 32012.1 | 1.03869 | 0.519343 | − | 0.854566i | \(-0.326177\pi\) | ||||
0.519343 | + | 0.854566i | \(0.326177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 146.217 | 0.00472261 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3108.66 | −0.100101 | ||||||||
\(989\) | −31416.9 | −1.01011 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3717.85 | 0.119174 | 0.0595870 | − | 0.998223i | \(-0.481022\pi\) | ||||
0.0595870 | + | 0.998223i | \(0.481022\pi\) | |||||||
\(992\) | −15399.3 | −0.492872 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12822.7 | 0.409168 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5517.11 | 0.175254 | 0.0876272 | − | 0.996153i | \(-0.472072\pi\) | ||||
0.0876272 | + | 0.996153i | \(0.472072\pi\) | |||||||
\(998\) | −33080.5 | −1.04924 | ||||||||
\(999\) | 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 | 2025.4.a.bk.1.13 | 16 | ||
3.2 | odd | 2 | 2025.4.a.bl.1.4 | 16 | |||
5.2 | odd | 4 | 405.4.b.e.244.13 | 16 | |||
5.3 | odd | 4 | 405.4.b.e.244.4 | 16 | |||
5.4 | even | 2 | inner | 2025.4.a.bk.1.4 | 16 | ||
9.4 | even | 3 | 225.4.e.g.151.4 | 32 | |||
9.7 | even | 3 | 225.4.e.g.76.4 | 32 | |||
15.2 | even | 4 | 405.4.b.f.244.4 | 16 | |||
15.8 | even | 4 | 405.4.b.f.244.13 | 16 | |||
15.14 | odd | 2 | 2025.4.a.bl.1.13 | 16 | |||
45.2 | even | 12 | 135.4.j.a.64.4 | 32 | |||
45.4 | even | 6 | 225.4.e.g.151.13 | 32 | |||
45.7 | odd | 12 | 45.4.j.a.4.13 | yes | 32 | ||
45.13 | odd | 12 | 45.4.j.a.34.13 | yes | 32 | ||
45.22 | odd | 12 | 45.4.j.a.34.4 | yes | 32 | ||
45.23 | even | 12 | 135.4.j.a.19.4 | 32 | |||
45.32 | even | 12 | 135.4.j.a.19.13 | 32 | |||
45.34 | even | 6 | 225.4.e.g.76.13 | 32 | |||
45.38 | even | 12 | 135.4.j.a.64.13 | 32 | |||
45.43 | odd | 12 | 45.4.j.a.4.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.4 | ✓ | 32 | 45.43 | odd | 12 | ||
45.4.j.a.4.13 | yes | 32 | 45.7 | odd | 12 | ||
45.4.j.a.34.4 | yes | 32 | 45.22 | odd | 12 | ||
45.4.j.a.34.13 | yes | 32 | 45.13 | odd | 12 | ||
135.4.j.a.19.4 | 32 | 45.23 | even | 12 | |||
135.4.j.a.19.13 | 32 | 45.32 | even | 12 | |||
135.4.j.a.64.4 | 32 | 45.2 | even | 12 | |||
135.4.j.a.64.13 | 32 | 45.38 | even | 12 | |||
225.4.e.g.76.4 | 32 | 9.7 | even | 3 | |||
225.4.e.g.76.13 | 32 | 45.34 | even | 6 | |||
225.4.e.g.151.4 | 32 | 9.4 | even | 3 | |||
225.4.e.g.151.13 | 32 | 45.4 | even | 6 | |||
405.4.b.e.244.4 | 16 | 5.3 | odd | 4 | |||
405.4.b.e.244.13 | 16 | 5.2 | odd | 4 | |||
405.4.b.f.244.4 | 16 | 15.2 | even | 4 | |||
405.4.b.f.244.13 | 16 | 15.8 | even | 4 | |||
2025.4.a.bk.1.4 | 16 | 5.4 | even | 2 | inner | ||
2025.4.a.bk.1.13 | 16 | 1.1 | even | 1 | trivial | ||
2025.4.a.bl.1.4 | 16 | 3.2 | odd | 2 | |||
2025.4.a.bl.1.13 | 16 | 15.14 | odd | 2 |