Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(17,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.t (of order \(6\), degree \(2\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + \cdots + 7375227456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.1 | ||
Root | \(4.65022 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.89 |
Dual form | 252.4.t.a.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.1259 | + | 17.5386i | −0.905689 | + | 1.56870i | −0.0856984 | + | 0.996321i | \(0.527312\pi\) |
−0.819990 | + | 0.572378i | \(0.806021\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0269 | + | 14.0838i | 0.649390 | + | 0.760455i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.4532 | + | 8.92191i | −0.423574 | + | 0.244551i | −0.696605 | − | 0.717455i | \(-0.745307\pi\) |
0.273031 | + | 0.962005i | \(0.411974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 33.1829i | − | 0.707945i | −0.935256 | − | 0.353973i | \(-0.884831\pi\) | ||
0.935256 | − | 0.353973i | \(-0.115169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.9077 | − | 39.6772i | −0.326819 | − | 0.566067i | 0.655060 | − | 0.755577i | \(-0.272643\pi\) |
−0.981879 | + | 0.189510i | \(0.939310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.0091 | − | 20.2125i | −0.422718 | − | 0.244056i | 0.273522 | − | 0.961866i | \(-0.411811\pi\) |
−0.696239 | + | 0.717810i | \(0.745145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −69.7804 | − | 40.2877i | −0.632618 | − | 0.365242i | 0.149147 | − | 0.988815i | \(-0.452347\pi\) |
−0.781765 | + | 0.623573i | \(0.785680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −142.568 | − | 246.935i | −1.14054 | − | 1.97548i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 233.844i | 1.49737i | 0.662926 | + | 0.748685i | \(0.269314\pi\) | ||||
−0.662926 | + | 0.748685i | \(0.730686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −195.398 | + | 112.813i | −1.13208 | + | 0.653607i | −0.944457 | − | 0.328635i | \(-0.893412\pi\) |
−0.187623 | + | 0.982241i | \(0.560078\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −368.793 | + | 68.3228i | −1.78107 | + | 0.329962i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 135.456 | − | 234.617i | 0.601860 | − | 1.04245i | −0.390679 | − | 0.920527i | \(-0.627760\pi\) |
0.992539 | − | 0.121925i | \(-0.0389069\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −154.432 | −0.588248 | −0.294124 | − | 0.955767i | \(-0.595028\pi\) | ||||
−0.294124 | + | 0.955767i | \(0.595028\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 367.102 | 1.30192 | 0.650960 | − | 0.759112i | \(-0.274366\pi\) | ||||
0.650960 | + | 0.759112i | \(0.274366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −263.852 | + | 457.006i | −0.818869 | + | 1.41832i | 0.0876480 | + | 0.996152i | \(0.472065\pi\) |
−0.906517 | + | 0.422170i | \(0.861268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −53.7086 | + | 338.769i | −0.156585 | + | 0.987665i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 78.8892 | − | 45.5467i | 0.204458 | − | 0.118044i | −0.394275 | − | 0.918992i | \(-0.629004\pi\) |
0.598733 | + | 0.800949i | \(0.295671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 361.370i | − | 0.885947i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −312.768 | − | 541.729i | −0.690150 | − | 1.19538i | −0.971788 | − | 0.235855i | \(-0.924211\pi\) |
0.281638 | − | 0.959521i | \(-0.409122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −78.8343 | − | 45.5150i | −0.165470 | − | 0.0955344i | 0.414978 | − | 0.909832i | \(-0.363789\pi\) |
−0.580448 | + | 0.814297i | \(0.697123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 581.982 | + | 336.007i | 1.11055 | + | 0.641178i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −431.509 | − | 747.395i | −0.786823 | − | 1.36282i | −0.927904 | − | 0.372820i | \(-0.878391\pi\) |
0.141080 | − | 0.989998i | \(-0.454942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 303.596i | − | 0.507468i | −0.967274 | − | 0.253734i | \(-0.918341\pi\) | ||
0.967274 | − | 0.253734i | \(-0.0816587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −999.127 | + | 576.846i | −1.60190 | + | 0.924859i | −0.610797 | + | 0.791787i | \(0.709151\pi\) |
−0.991106 | + | 0.133072i | \(0.957516\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −311.508 | − | 110.338i | −0.461035 | − | 0.163300i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.48120 | − | 6.02961i | 0.00495779 | − | 0.00858715i | −0.863536 | − | 0.504287i | \(-0.831755\pi\) |
0.868494 | + | 0.495700i | \(0.165089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 815.694 | 1.07872 | 0.539362 | − | 0.842074i | \(-0.318666\pi\) | ||||
0.539362 | + | 0.842074i | \(0.318666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 927.844 | 1.18399 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 155.494 | − | 269.323i | 0.185194 | − | 0.320766i | −0.758448 | − | 0.651734i | \(-0.774042\pi\) |
0.943642 | + | 0.330968i | \(0.107375\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 467.343 | − | 399.087i | 0.538361 | − | 0.459733i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 708.998 | − | 409.340i | 0.765701 | − | 0.442078i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1832.92i | 1.91861i | 0.282370 | + | 0.959305i | \(0.408879\pi\) | ||||
−0.282370 | + | 0.959305i | \(0.591121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 721.053 | + | 1248.90i | 0.710371 | + | 1.23040i | 0.964718 | + | 0.263285i | \(0.0848060\pi\) |
−0.254347 | + | 0.967113i | \(0.581861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 928.361 | + | 535.989i | 0.888098 | + | 0.512744i | 0.873320 | − | 0.487147i | \(-0.161962\pi\) |
0.0147781 | + | 0.999891i | \(0.495296\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −722.125 | − | 416.919i | −0.652434 | − | 0.376683i | 0.136954 | − | 0.990577i | \(-0.456269\pi\) |
−0.789388 | + | 0.613894i | \(0.789602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 922.514 | + | 1597.84i | 0.810650 | + | 1.40409i | 0.912410 | + | 0.409278i | \(0.134219\pi\) |
−0.101760 | + | 0.994809i | \(0.532447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1388.90i | − | 1.15626i | −0.815946 | − | 0.578128i | \(-0.803784\pi\) | ||
0.815946 | − | 0.578128i | \(-0.196216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1413.18 | − | 815.899i | 1.14591 | − | 0.661591i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 283.300 | − | 799.821i | 0.218236 | − | 0.616130i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −506.299 | + | 876.936i | −0.380390 | + | 0.658855i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3243.04 | 2.32053 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −838.992 | −0.586208 | −0.293104 | − | 0.956080i | \(-0.594688\pi\) | ||||
−0.293104 | + | 0.956080i | \(0.594688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −195.038 | + | 337.815i | −0.130080 | + | 0.225306i | −0.923707 | − | 0.383099i | \(-0.874857\pi\) |
0.793627 | + | 0.608405i | \(0.208190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −136.380 | − | 736.155i | −0.0889149 | − | 0.479946i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1191.72 | + | 688.039i | −0.743178 | + | 0.429074i | −0.823224 | − | 0.567717i | \(-0.807827\pi\) |
0.0800456 | + | 0.996791i | \(0.474493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 953.705i | 0.581958i | 0.956729 | + | 0.290979i | \(0.0939810\pi\) | ||||
−0.956729 | + | 0.290979i | \(0.906019\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 296.055 | + | 512.782i | 0.173128 | + | 0.299867i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4101.29 | − | 2367.88i | −2.34892 | − | 1.35615i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2198.94 | + | 1269.56i | 1.20902 | + | 0.698029i | 0.962546 | − | 0.271120i | \(-0.0873939\pi\) |
0.246476 | + | 0.969149i | \(0.420727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 515.001 | + | 892.008i | 0.277551 | + | 0.480733i | 0.970776 | − | 0.239989i | \(-0.0771439\pi\) |
−0.693225 | + | 0.720722i | \(0.743811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4569.33i | − | 2.36786i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1558.78 | − | 899.959i | 0.792381 | − | 0.457481i | −0.0484190 | − | 0.998827i | \(-0.515418\pi\) |
0.840800 | + | 0.541346i | \(0.182085\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −271.834 | − | 1467.31i | −0.133065 | − | 0.718262i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1312.03 | + | 2272.50i | −0.630466 | + | 1.09200i | 0.356991 | + | 0.934108i | \(0.383803\pi\) |
−0.987457 | + | 0.157891i | \(0.949531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −714.138 | −0.330908 | −0.165454 | − | 0.986217i | \(-0.552909\pi\) | ||||
−0.165454 | + | 0.986217i | \(0.552909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1095.89 | 0.498813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −373.785 | + | 647.415i | −0.164268 | + | 0.284520i | −0.936395 | − | 0.350948i | \(-0.885859\pi\) |
0.772127 | + | 0.635468i | \(0.219193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1763.14 | − | 4977.76i | 0.761606 | − | 2.15019i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3797.55 | + | 2192.52i | −1.58571 | + | 0.915511i | −0.591710 | + | 0.806151i | \(0.701547\pi\) |
−0.994002 | + | 0.109360i | \(0.965120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2143.42i | 0.880215i | 0.897945 | + | 0.440107i | \(0.145060\pi\) | ||||
−0.897945 | + | 0.440107i | \(0.854940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2743.23 | + | 4751.41i | 1.09020 | + | 1.88827i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 707.993 | + | 408.760i | 0.276864 | + | 0.159848i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4030.20 | − | 2326.84i | −1.52678 | − | 0.881486i | −0.999494 | − | 0.0317981i | \(-0.989877\pi\) |
−0.527285 | − | 0.849688i | \(-0.676790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1052.69 | + | 1823.32i | 0.392614 | + | 0.680028i | 0.992793 | − | 0.119838i | \(-0.0382374\pi\) |
−0.600179 | + | 0.799866i | \(0.704904\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 707.475i | − | 0.255866i | −0.991783 | − | 0.127933i | \(-0.959166\pi\) | ||
0.991783 | − | 0.127933i | \(-0.0408342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1115.28 | + | 643.907i | −0.397287 | + | 0.229374i | −0.685313 | − | 0.728249i | \(-0.740334\pi\) |
0.288026 | + | 0.957623i | \(0.407001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3293.42 | + | 2812.41i | −1.13868 | + | 0.972377i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1563.76 | − | 2708.51i | 0.532770 | − | 0.922785i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 721.336 | 0.238736 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1193.83 | 0.389509 | 0.194755 | − | 0.980852i | \(-0.437609\pi\) | ||||
0.194755 | + | 0.980852i | \(0.437609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3717.24 | + | 6438.46i | −1.17913 | + | 2.04232i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3938.86 | − | 1395.16i | −1.23220 | − | 0.436451i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1316.61 | + | 760.144i | −0.400745 | + | 0.231370i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 420.089i | − | 0.126149i | −0.998009 | − | 0.0630745i | \(-0.979909\pi\) | ||
0.998009 | − | 0.0630745i | \(-0.0200906\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −483.829 | − | 838.016i | −0.141466 | − | 0.245027i | 0.786583 | − | 0.617485i | \(-0.211848\pi\) |
−0.928049 | + | 0.372458i | \(0.878515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3018.69 | − | 1742.84i | −0.871096 | − | 0.502927i | −0.00338359 | − | 0.999994i | \(-0.501077\pi\) |
−0.867712 | + | 0.497067i | \(0.834410\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1814.94 | + | 1047.86i | 0.510305 | + | 0.294625i | 0.732959 | − | 0.680273i | \(-0.238139\pi\) |
−0.222654 | + | 0.974897i | \(0.571472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5343.49 | − | 9255.19i | −1.48328 | − | 2.56912i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6892.95i | − | 1.86555i | −0.360453 | − | 0.932777i | \(-0.617378\pi\) | ||
0.360453 | − | 0.932777i | \(-0.382622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2348.99 | + | 1356.19i | −0.627850 | + | 0.362489i | −0.779919 | − | 0.625881i | \(-0.784740\pi\) |
0.152069 | + | 0.988370i | \(0.451406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5397.68 | − | 4372.32i | −1.40753 | − | 1.14015i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −670.710 | + | 1161.70i | −0.172778 | + | 0.299261i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6334.19 | 1.59287 | 0.796435 | − | 0.604724i | \(-0.206716\pi\) | ||||
0.796435 | + | 0.604724i | \(0.206716\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1437.77 | 0.357281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2395.68 | + | 4149.44i | −0.581472 | + | 1.00714i | 0.413833 | + | 0.910353i | \(0.364190\pi\) |
−0.995305 | + | 0.0967867i | \(0.969144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4933.41 | − | 913.966i | 1.18358 | − | 0.219270i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −200.111 | + | 115.534i | −0.0469177 | + | 0.0270879i | −0.523275 | − | 0.852164i | \(-0.675290\pi\) |
0.476358 | + | 0.879252i | \(0.341957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1844.81i | 0.427644i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2356.86 | − | 4082.21i | −0.534203 | − | 0.925266i | −0.999201 | − | 0.0399551i | \(-0.987279\pi\) |
0.464999 | − | 0.885311i | \(-0.346055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3251.50 | − | 1877.26i | −0.728836 | − | 0.420794i | 0.0891599 | − | 0.996017i | \(-0.471582\pi\) |
−0.817996 | + | 0.575223i | \(0.804915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4406.26 | + | 2543.96i | 0.966209 | + | 0.557841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 757.120 | + | 1311.37i | 0.164227 | + | 0.284450i | 0.936381 | − | 0.350986i | \(-0.114154\pi\) |
−0.772153 | + | 0.635436i | \(0.780820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4418.40i | 0.938005i | 0.883197 | + | 0.469003i | \(0.155387\pi\) | ||||
−0.883197 | + | 0.469003i | \(0.844613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4219.93 | + | 2436.38i | −0.886391 | + | 0.511758i | −0.872760 | − | 0.488149i | \(-0.837672\pi\) |
−0.0136304 | + | 0.999907i | \(0.504339\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1857.33 | − | 2174.99i | −0.382003 | − | 0.447337i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1406.98 | − | 2436.96i | 0.286378 | − | 0.496022i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 340.271 | 0.0678458 | 0.0339229 | − | 0.999424i | \(-0.489200\pi\) | ||||
0.0339229 | + | 0.999424i | \(0.489200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12668.2 | 2.50025 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1336.86 | + | 2315.52i | −0.258571 | + | 0.447859i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4415.09 | + | 5170.21i | 0.845454 | + | 0.990053i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1596.54 | − | 921.761i | 0.299729 | − | 0.173049i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7302.13i | 1.35751i | 0.734366 | + | 0.678754i | \(0.237480\pi\) | ||||
−0.734366 | + | 0.678754i | \(0.762520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 372.538 | + | 645.255i | 0.0679251 | + | 0.117650i | 0.897988 | − | 0.440020i | \(-0.145029\pi\) |
−0.830063 | + | 0.557670i | \(0.811695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 689.742 | + | 398.223i | 0.124558 | + | 0.0719133i | 0.560984 | − | 0.827827i | \(-0.310423\pi\) |
−0.436427 | + | 0.899740i | \(0.643756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 974.487 | + | 562.621i | 0.172658 | + | 0.0996843i | 0.583839 | − | 0.811870i | \(-0.301550\pi\) |
−0.411180 | + | 0.911554i | \(0.634883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2086.33 | − | 3613.64i | −0.366183 | − | 0.634247i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1852.09i | 0.319049i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8194.03 | + | 4730.82i | −1.39853 | + | 0.807443i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9609.71 | + | 1780.30i | −1.61034 | + | 0.298331i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1216 | + | 19.2632i | −0.00184683 | + | 0.00319880i | −0.866947 | − | 0.498400i | \(-0.833921\pi\) |
0.865101 | + | 0.501599i | \(0.167255\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17477.7 | 2.85047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9570.35 | 1.54697 | 0.773487 | − | 0.633812i | \(-0.218511\pi\) | ||||
0.773487 | + | 0.633812i | \(0.218511\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2013.01 | − | 3486.64i | 0.319680 | − | 0.553702i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5417.11 | + | 3317.91i | −0.852759 | + | 0.522304i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9927.17 | − | 5731.45i | 1.53579 | − | 0.886688i | 0.536709 | − | 0.843767i | \(-0.319667\pi\) |
0.999078 | − | 0.0429203i | \(-0.0136662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1575.13i | 0.241590i | 0.992677 | + | 0.120795i | \(0.0385443\pi\) | ||||
−0.992677 | + | 0.120795i | \(0.961456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2316.74 | + | 4012.71i | 0.349313 | + | 0.605028i | 0.986128 | − | 0.165989i | \(-0.0530816\pi\) |
−0.636814 | + | 0.771017i | \(0.719748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5324.64 | + | 3074.18i | 0.796064 | + | 0.459608i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2062.64 | − | 1190.86i | −0.303236 | − | 0.175073i | 0.340660 | − | 0.940187i | \(-0.389350\pi\) |
−0.643896 | + | 0.765113i | \(0.722683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2612.41 | − | 4524.83i | −0.380873 | − | 0.659692i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 23364.4i | − | 3.35054i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −990.766 | + | 572.019i | −0.140920 | + | 0.0813601i | −0.568802 | − | 0.822474i | \(-0.692593\pi\) |
0.427882 | + | 0.903834i | \(0.359260\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1590.26 | + | 563.278i | 0.222540 | + | 0.0788246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 205.226 | − | 355.461i | 0.0284884 | − | 0.0493434i | −0.851430 | − | 0.524469i | \(-0.824264\pi\) |
0.879918 | + | 0.475125i | \(0.157597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7759.63 | 1.06006 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6400.00 | −0.867403 | −0.433702 | − | 0.901057i | \(-0.642793\pi\) | ||||
−0.433702 | + | 0.901057i | \(0.642793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1742.19 | − | 3017.57i | 0.232433 | − | 0.402586i | −0.726090 | − | 0.687599i | \(-0.758665\pi\) |
0.958524 | + | 0.285013i | \(0.0919980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5089.47 | − | 4346.15i | 0.673723 | − | 0.575325i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3641.68 | − | 2102.53i | 0.474654 | − | 0.274042i | −0.243532 | − | 0.969893i | \(-0.578306\pi\) |
0.718186 | + | 0.695851i | \(0.244973\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3691.59i | 0.477472i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 70.5006 | + | 122.111i | 0.00898043 | + | 0.0155546i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4699.38 | − | 2713.19i | −0.594093 | − | 0.343000i | 0.172621 | − | 0.984988i | \(-0.444776\pi\) |
−0.766714 | + | 0.641989i | \(0.778110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7357.88 | + | 4248.07i | 0.916297 | + | 0.529024i | 0.882452 | − | 0.470403i | \(-0.155891\pi\) |
0.0338449 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3743.47 | + | 6483.87i | 0.462718 | + | 0.801451i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4834.10i | 0.588741i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5581.42 | − | 3222.44i | 0.674776 | − | 0.389582i | −0.123108 | − | 0.992393i | \(-0.539286\pi\) |
0.797884 | + | 0.602811i | \(0.205953\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3868.01 | − | 10920.3i | 0.460853 | − | 1.30109i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8259.64 | + | 14306.1i | −0.976987 | + | 1.69219i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14198.4 | −1.65546 | −0.827728 | − | 0.561130i | \(-0.810367\pi\) | ||||
−0.827728 | + | 0.561130i | \(0.810367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6986.18 | 0.808754 | 0.404377 | − | 0.914592i | \(-0.367488\pi\) | ||||
0.404377 | + | 0.914592i | \(0.367488\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6531.80 | + | 11313.4i | −0.745503 | + | 1.29125i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −307.104 | − | 1657.69i | −0.0348052 | − | 0.187872i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12104.1 | + | 6988.29i | −1.35274 | + | 0.781007i | −0.988633 | − | 0.150349i | \(-0.951960\pi\) |
−0.364111 | + | 0.931356i | \(0.618627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4418.70i | − | 0.490414i | −0.969471 | − | 0.245207i | \(-0.921144\pi\) | ||
0.969471 | − | 0.245207i | \(-0.0788559\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1628.63 | + | 2820.87i | 0.178279 | + | 0.308789i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2497.13 | + | 1441.72i | 0.271484 | + | 0.156742i | 0.629562 | − | 0.776950i | \(-0.283234\pi\) |
−0.358078 | + | 0.933692i | \(0.616568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11013.8 | + | 6358.80i | 1.18122 | + | 0.681976i | 0.956296 | − | 0.292400i | \(-0.0944540\pi\) |
0.224922 | + | 0.974377i | \(0.427787\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3149.03 | + | 5454.28i | 0.335457 | + | 0.581029i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5375.10i | 0.564959i | 0.959273 | + | 0.282479i | \(0.0911569\pi\) | ||||
−0.959273 | + | 0.282479i | \(0.908843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2386.46 | − | 1377.83i | 0.249167 | − | 0.143856i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2267.15 | + | 12237.7i | 0.233595 | + | 1.26090i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2060.59 | − | 3569.05i | 0.210920 | − | 0.365324i | −0.741083 | − | 0.671414i | \(-0.765687\pi\) |
0.952003 | + | 0.306090i | \(0.0990208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6019.06 | −0.608103 | −0.304052 | − | 0.952656i | \(-0.598340\pi\) | ||||
−0.304052 | + | 0.952656i | \(0.598340\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3263.90 | −0.327616 | −0.163808 | − | 0.986492i | \(-0.552378\pi\) | ||||
−0.163808 | + | 0.986492i | \(0.552378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 660.961 | − | 1144.82i | 0.0654938 | − | 0.113439i | −0.831419 | − | 0.555646i | \(-0.812471\pi\) |
0.896913 | + | 0.442207i | \(0.145804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5336.48 | − | 15066.1i | 0.525407 | − | 1.48334i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5672.90 | + | 3275.25i | −0.551460 | + | 0.318385i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11526.6i | 1.11343i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1887.69 | − | 3269.58i | −0.180064 | − | 0.311881i | 0.761838 | − | 0.647768i | \(-0.224297\pi\) |
−0.941902 | + | 0.335887i | \(0.890964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7785.27 | − | 4494.83i | −0.737999 | − | 0.426084i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32146.9 | − | 18560.0i | −3.00972 | − | 1.73766i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6119.80 | + | 10599.8i | 0.569434 | + | 0.986289i | 0.996622 | + | 0.0821263i | \(0.0261711\pi\) |
−0.427187 | + | 0.904163i | \(0.640496\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13018.0i | − | 1.19652i | −0.801301 | − | 0.598261i | \(-0.795858\pi\) | ||
0.801301 | − | 0.598261i | \(-0.204142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9278.28 | − | 5356.82i | 0.847612 | − | 0.489369i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4275.79 | − | 3651.31i | 0.385906 | − | 0.329544i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8603.67 | − | 14902.0i | 0.771850 | − | 1.33688i | −0.164697 | − | 0.986344i | \(-0.552665\pi\) |
0.936548 | − | 0.350540i | \(-0.114002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19760.5 | 1.75164 | 0.875821 | − | 0.482635i | \(-0.160320\pi\) | ||||
0.875821 | + | 0.482635i | \(0.160320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29205.3 | −2.57350 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2351.82 | − | 4073.48i | 0.204799 | − | 0.354722i | −0.745270 | − | 0.666763i | \(-0.767679\pi\) |
0.950069 | + | 0.312041i | \(0.101013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20140.6 | − | 7133.88i | −1.74357 | − | 0.617582i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18801.0 | + | 10854.8i | −1.60868 | + | 0.928772i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9416.26i | − | 0.801019i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7971.12 | + | 13806.4i | 0.670290 | + | 1.16098i | 0.977822 | + | 0.209438i | \(0.0671635\pi\) |
−0.307532 | + | 0.951538i | \(0.599503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17362.2 | − | 10024.0i | −1.45161 | − | 0.838090i | −0.453041 | − | 0.891490i | \(-0.649661\pi\) |
−0.998573 | + | 0.0533995i | \(0.982994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8952.22 | + | 5168.56i | 0.739971 | + | 0.427222i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2837.30 | − | 4914.35i | −0.233196 | − | 0.403908i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5124.50i | 0.416448i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14624.3 | − | 8443.37i | 1.18180 | − | 0.682315i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2192.50 | − | 5714.25i | −0.175209 | − | 0.456642i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1931.85 | + | 3346.06i | −0.153524 | + | 0.265912i | −0.932521 | − | 0.361117i | \(-0.882396\pi\) |
0.778997 | + | 0.627028i | \(0.215729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37365.2 | −2.93678 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18674.5 | −1.45972 | −0.729859 | − | 0.683598i | \(-0.760414\pi\) | ||||
−0.729859 | + | 0.683598i | \(0.760414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4726.57 | − | 8186.66i | 0.365442 | − | 0.632965i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 126.788 | − | 23.4888i | 0.00974968 | − | 0.00180623i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1489.14 | − | 859.753i | 0.113280 | − | 0.0654020i | −0.442290 | − | 0.896872i | \(-0.645834\pi\) |
0.555569 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12181.5i | − | 0.921689i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6596.37 | + | 11425.3i | 0.493790 | + | 0.855270i | 0.999974 | − | 0.00715535i | \(-0.00227764\pi\) |
−0.506184 | + | 0.862426i | \(0.668944\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24359.4 | + | 14063.9i | 1.81382 | + | 1.04721i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21405.5 | − | 12358.4i | −1.57709 | − | 0.910533i | −0.995263 | − | 0.0972193i | \(-0.969005\pi\) |
−0.581826 | − | 0.813313i | \(-0.697661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1032.73 | − | 1788.73i | −0.0756887 | − | 0.131097i | 0.825697 | − | 0.564114i | \(-0.190782\pi\) |
−0.901386 | + | 0.433017i | \(0.857449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22974.9i | 1.66630i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6759.61 | + | 3902.66i | −0.487706 | + | 0.281577i | −0.723622 | − | 0.690196i | \(-0.757524\pi\) |
0.235916 | + | 0.971773i | \(0.424191\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9810.25 | + | 11488.1i | 0.700512 | + | 0.820321i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −812.727 | + | 1407.68i | −0.0577353 | + | 0.100001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6297.78 | −0.442823 | −0.221412 | − | 0.975180i | \(-0.571066\pi\) | ||||
−0.221412 | + | 0.975180i | \(0.571066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9120.93 | 0.638067 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9115.60 | + | 15788.7i | −0.631253 | + | 1.09336i | 0.356043 | + | 0.934470i | \(0.384126\pi\) |
−0.987296 | + | 0.158893i | \(0.949208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11159.1 | + | 13067.6i | 0.768869 | + | 0.900368i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7161.55 | + | 4134.72i | −0.488503 | + | 0.282037i | −0.723953 | − | 0.689849i | \(-0.757677\pi\) |
0.235450 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11106.1i | − | 0.753788i | −0.926256 | − | 0.376894i | \(-0.876992\pi\) | ||
0.926256 | − | 0.376894i | \(-0.123008\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10253.5 | − | 17759.5i | −0.689030 | − | 1.19343i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10414.3 | − | 6012.71i | −0.696382 | − | 0.402056i | 0.109616 | − | 0.993974i | \(-0.465038\pi\) |
−0.805999 | + | 0.591917i | \(0.798371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15164.8 | + | 8755.40i | 1.00409 | + | 0.579714i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2027.75 | + | 3512.16i | 0.133605 | + | 0.231411i | 0.925064 | − | 0.379812i | \(-0.124011\pi\) |
−0.791459 | + | 0.611223i | \(0.790678\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7236.59i | 0.472178i | 0.971731 | + | 0.236089i | \(0.0758658\pi\) | ||||
−0.971731 | + | 0.236089i | \(0.924134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13803.6 | − | 7969.54i | 0.896309 | − | 0.517484i | 0.0203081 | − | 0.999794i | \(-0.493535\pi\) |
0.876001 | + | 0.482310i | \(0.160202\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5663.20 | − | 1049.17i | 0.364192 | − | 0.0674703i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15017.8 | + | 26011.5i | −0.961136 | + | 1.66474i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12411.9 | −0.786798 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25310.1 | 1.59680 | 0.798399 | − | 0.602129i | \(-0.205681\pi\) | ||||
0.798399 | + | 0.602129i | \(0.205681\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8495.55 | − | 14714.7i | 0.530922 | − | 0.919584i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11241.3 | + | 1782.21i | 0.699213 | + | 0.110854i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21593.9 | − | 12467.2i | 1.33059 | − | 0.768216i | 0.345199 | − | 0.938530i | \(-0.387812\pi\) |
0.985390 | + | 0.170314i | \(0.0544782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12466.1i | 0.764563i | 0.924046 | + | 0.382282i | \(0.124862\pi\) | ||||
−0.924046 | + | 0.382282i | \(0.875138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12339.6 | − | 21372.8i | −0.749799 | − | 1.29869i | −0.947919 | − | 0.318513i | \(-0.896817\pi\) |
0.198119 | − | 0.980178i | \(-0.436517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9666.52 | + | 5580.97i | 0.584659 | + | 0.337553i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16498.1 | + | 9525.16i | 0.988697 | + | 0.570825i | 0.904885 | − | 0.425657i | \(-0.139957\pi\) |
0.0838127 | + | 0.996482i | \(0.473290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3949.87 | − | 6841.37i | −0.235625 | − | 0.408114i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5983.49i | − | 0.353693i | −0.984238 | − | 0.176847i | \(-0.943410\pi\) | ||
0.984238 | − | 0.176847i | \(-0.0565897\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12000.7 | + | 6928.61i | −0.706162 | + | 0.407703i | −0.809638 | − | 0.586929i | \(-0.800337\pi\) |
0.103476 | + | 0.994632i | \(0.467003\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14292.1 | + | 5062.32i | 0.833419 | + | 0.295201i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9421.03 | − | 16317.7i | 0.546902 | − | 0.947263i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1624.32 | 0.0934519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21469.4 | −1.22970 | −0.614849 | − | 0.788645i | \(-0.710783\pi\) | ||||
−0.614849 | + | 0.788645i | \(0.710783\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10221.4 | − | 17703.9i | 0.580265 | − | 1.00505i | −0.415183 | − | 0.909738i | \(-0.636282\pi\) |
0.995448 | − | 0.0953099i | \(-0.0303842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25814.6 | + | 22044.3i | −1.45902 | + | 1.24593i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16958.6 | − | 9791.08i | 0.950080 | − | 0.548529i | 0.0569740 | − | 0.998376i | \(-0.481855\pi\) |
0.893106 | + | 0.449847i | \(0.148521\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27868.1i | − | 1.55443i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1511.37 | − | 2617.77i | −0.0835685 | − | 0.144745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10137.3 | + | 5852.75i | 0.558089 | + | 0.322213i | 0.752378 | − | 0.658731i | \(-0.228907\pi\) |
−0.194289 | + | 0.980944i | \(0.562240\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16726.6 | − | 9657.13i | −0.912917 | − | 0.527073i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3537.67 | + | 6127.43i | 0.192251 | + | 0.332988i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17998.6i | 0.969752i | 0.874583 | + | 0.484876i | \(0.161135\pi\) | ||||
−0.874583 | + | 0.484876i | \(0.838865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9484.38 | + | 5475.81i | −0.508834 | + | 0.293775i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8917.29 | + | 25175.5i | −0.474355 | + | 1.33921i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11891.5 | − | 20596.7i | 0.629895 | − | 1.09101i | −0.357677 | − | 0.933845i | \(-0.616431\pi\) |
0.987572 | − | 0.157166i | \(-0.0502356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18179.9 | 0.954899 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11991.3 | −0.627202 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16513.5 | − | 28602.2i | 0.856536 | − | 1.48356i | −0.0186774 | − | 0.999826i | \(-0.505946\pi\) |
0.875213 | − | 0.483738i | \(-0.160721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3616.49 | + | 19521.2i | 0.186803 | + | 1.00833i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 57744.2 | − | 33338.6i | 2.95802 | − | 1.70782i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6816.11i | − | 0.347724i | −0.984770 | − | 0.173862i | \(-0.944375\pi\) | ||
0.984770 | − | 0.173862i | \(-0.0556247\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8409.46 | − | 14565.6i | −0.425493 | − | 0.736975i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20701.4 | + | 11951.9i | 1.04314 | + | 0.602258i | 0.920722 | − | 0.390220i | \(-0.127601\pi\) |
0.122420 | + | 0.992478i | \(0.460934\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13336.4 | + | 7699.76i | 0.666556 | + | 0.384836i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4558.07 | − | 7894.81i | −0.226889 | − | 0.392984i | 0.729995 | − | 0.683452i | \(-0.239522\pi\) |
−0.956885 | + | 0.290468i | \(0.906189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32818.5i | 1.62045i | 0.586121 | + | 0.810224i | \(0.300654\pi\) | ||||
−0.586121 | + | 0.810224i | \(0.699346\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44532.5 | + | 25710.9i | −2.18999 | + | 1.26439i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2813.09 | − | 15184.5i | −0.137234 | − | 0.740762i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4620.07 | − | 8002.20i | 0.224486 | − | 0.388821i | −0.731679 | − | 0.681649i | \(-0.761263\pi\) |
0.956165 | + | 0.292828i | \(0.0945964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20859.4 | −1.00550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16610.7 | 0.797523 | 0.398761 | − | 0.917055i | \(-0.369440\pi\) | ||||
0.398761 | + | 0.917055i | \(0.369440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1121.42 | − | 1942.35i | 0.0534184 | − | 0.0925234i | −0.838080 | − | 0.545548i | \(-0.816322\pi\) |
0.891498 | + | 0.453024i | \(0.149655\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11408.8 | + | 32209.6i | −0.541317 | + | 1.52826i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17976.2 | + | 10378.5i | −0.846261 | + | 0.488589i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9182.73i | − | 0.430608i | −0.976547 | − | 0.215304i | \(-0.930926\pi\) | ||
0.976547 | − | 0.215304i | \(-0.0690743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4272.40 | + | 7400.02i | 0.198794 | + | 0.344321i | 0.948138 | − | 0.317860i | \(-0.102964\pi\) |
−0.749344 | + | 0.662181i | \(0.769631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55714.9 | + | 32167.0i | 2.58237 | + | 1.49093i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5406.51 | + | 3121.45i | 0.248663 | + | 0.143566i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2708.65 | + | 4691.53i | 0.124101 | + | 0.214950i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36451.6i | 1.65734i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20236.4 | − | 11683.5i | 0.916583 | − | 0.529190i | 0.0340400 | − | 0.999420i | \(-0.489163\pi\) |
0.882544 | + | 0.470231i | \(0.155829\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19561.1 | − | 16704.1i | 0.879281 | − | 0.750861i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1510.32 | + | 2615.95i | −0.0676331 | + | 0.117144i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8319.18 | −0.369737 | −0.184869 | − | 0.982763i | \(-0.559186\pi\) | ||||
−0.184869 | + | 0.982763i | \(0.559186\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24177.0 | 1.07049 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10293.1 | − | 17828.2i | 0.452350 | − | 0.783493i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28487.1 | + | 10090.3i | 1.24725 | + | 0.441782i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7769.07 | − | 4485.47i | 0.337634 | − | 0.194933i | −0.321591 | − | 0.946879i | \(-0.604218\pi\) |
0.659225 | + | 0.751946i | \(0.270884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29055.1i | 1.25803i | 0.777393 | + | 0.629015i | \(0.216542\pi\) | ||||
−0.777393 | + | 0.629015i | \(0.783458\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26570.9 | − | 46022.2i | −1.14201 | − | 1.97802i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12851.9 | − | 7420.06i | −0.550345 | − | 0.317742i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13864.8 | + | 8004.83i | 0.589384 | + | 0.340281i | 0.764854 | − | 0.644204i | \(-0.222811\pi\) |
−0.175470 | + | 0.984485i | \(0.556144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3875.80 | − | 6713.08i | −0.164158 | − | 0.284330i | 0.772198 | − | 0.635382i | \(-0.219157\pi\) |
−0.936356 | + | 0.351052i | \(0.885824\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4705.84i | 0.197870i | 0.995094 | + | 0.0989348i | \(0.0315435\pi\) | ||||
−0.995094 | + | 0.0989348i | \(0.968456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33842.3 | − | 19538.9i | 1.41784 | − | 0.818593i | 0.421735 | − | 0.906719i | \(-0.361421\pi\) |
0.996109 | + | 0.0881261i | \(0.0280878\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14671.8 | − | 5629.40i | 0.610260 | − | 0.234150i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7231.29 | − | 12525.0i | 0.299700 | − | 0.519095i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24699.3 | −1.01634 | −0.508172 | − | 0.861255i | \(-0.669679\pi\) | ||||
−0.508172 | + | 0.861255i | \(0.669679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30294.0 | −1.24212 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11096.9 | + | 19220.4i | −0.451769 | + | 0.782488i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18439.8 | + | 3416.17i | −0.748051 | + | 0.138584i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18904.3 | + | 10914.4i | −0.761495 | + | 0.439649i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4313.27i | 0.173134i | 0.996246 | + | 0.0865671i | \(0.0275897\pi\) | ||||
−0.996246 | + | 0.0865671i | \(0.972410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13238.5 | + | 22929.8i | 0.527678 | + | 0.913965i | 0.999479 | + | 0.0322604i | \(0.0102706\pi\) |
−0.471801 | + | 0.881705i | \(0.656396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33468.0 | − | 19322.8i | −1.32935 | − | 0.767502i | −0.344154 | − | 0.938913i | \(-0.611834\pi\) |
−0.985200 | + | 0.171411i | \(0.945167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10813.1 | − | 6242.96i | −0.426516 | − | 0.246249i | 0.271345 | − | 0.962482i | \(-0.412531\pi\) |
−0.697861 | + | 0.716233i | \(0.745865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7569.82 | − | 13111.3i | −0.297551 | − | 0.515374i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 124.236i | 0.00484972i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24800.8 | + | 14318.7i | −0.964801 | + | 0.557028i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39003.7 | + | 45674.5i | 1.50693 | + | 1.76466i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11426.5 | + | 19791.2i | −0.439959 | + | 0.762032i | −0.997686 | − | 0.0679931i | \(-0.978340\pi\) |
0.557727 | + | 0.830025i | \(0.311674\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20304.1 | −0.776463 | −0.388231 | − | 0.921562i | \(-0.626914\pi\) | ||||
−0.388231 | + | 0.921562i | \(0.626914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12868.9 | −0.490456 | −0.245228 | − | 0.969465i | \(-0.578863\pi\) | ||||
−0.245228 | + | 0.969465i | \(0.578863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5090.81 | − | 8817.55i | 0.192709 | − | 0.333782i | −0.753438 | − | 0.657519i | \(-0.771606\pi\) |
0.946147 | + | 0.323737i | \(0.104939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10090.4 | − | 11816.2i | −0.380678 | − | 0.445785i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18474.5 | − | 10666.2i | 0.692300 | − | 0.399700i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 88805.0i | − | 3.31667i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26380.6 | − | 45692.6i | −0.978691 | − | 1.69514i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3614.33 | − | 2086.74i | −0.133641 | − | 0.0771579i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37592.5 | − | 21704.0i | −1.38079 | − | 0.797200i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4590.66 | − | 7951.26i | −0.168060 | − | 0.291088i | 0.769678 | − | 0.638433i | \(-0.220417\pi\) |
−0.937738 | + | 0.347344i | \(0.887084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18656.7i | 0.678511i | 0.940694 | + | 0.339255i | \(0.110175\pi\) | ||||
−0.940694 | + | 0.339255i | \(0.889825\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12605.1 | + | 7277.54i | −0.456919 | + | 0.263802i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7103.43 | + | 1315.98i | −0.255808 | + | 0.0473910i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2394.27 | − | 4147.00i | 0.0859410 | − | 0.148854i | −0.819851 | − | 0.572577i | \(-0.805944\pi\) |
0.905792 | + | 0.423723i | \(0.139277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10074.2 | −0.359259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −77246.7 | −2.74579 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −698.963 | + | 1210.64i | −0.0246848 | + | 0.0427554i | −0.878104 | − | 0.478470i | \(-0.841192\pi\) |
0.853419 | + | 0.521225i | \(0.174525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8727.66 | − | 10774.4i | 0.307237 | − | 0.379288i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14338.2 | + | 8278.13i | −0.501506 | + | 0.289544i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13520.0i | − | 0.471376i | −0.971829 | − | 0.235688i | \(-0.924266\pi\) | ||
0.971829 | − | 0.235688i | \(-0.0757343\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20604.4 | + | 35687.9i | 0.713800 | + | 1.23634i | 0.963421 | + | 0.267994i | \(0.0863607\pi\) |
−0.249621 | + | 0.968344i | \(0.580306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10776.3 | + | 6221.70i | 0.372136 | + | 0.214853i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6629.68 | − | 3827.65i | −0.227493 | − | 0.131343i | 0.381922 | − | 0.924194i | \(-0.375262\pi\) |
−0.609415 | + | 0.792852i | \(0.708596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19141.4 | + | 33154.0i | 0.654750 | + | 1.13406i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22854.9i | 0.776854i | 0.921479 | + | 0.388427i | \(0.126981\pi\) | ||||
−0.921479 | + | 0.388427i | \(0.873019\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81618.8 | − | 47122.6i | 2.76557 | − | 1.59670i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24022.9 | − | 8509.01i | −0.808904 | − | 0.286517i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10558.0 | − | 18287.0i | 0.354403 | − | 0.613845i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42637.9 | −1.42234 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11432.2 | −0.380180 | −0.190090 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190090 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9403.48 | − | 16287.3i | 0.310785 | − | 0.538295i | −0.667748 | − | 0.744388i | \(-0.732741\pi\) |
0.978533 | + | 0.206093i | \(0.0660748\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13431.8 | + | 11470.1i | −0.442553 | + | 0.377918i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32098.8 | + | 18532.3i | −1.05111 | + | 0.606857i | −0.922959 | − | 0.384898i | \(-0.874237\pi\) |
−0.128148 | + | 0.991755i | \(0.540903\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5549.20i | 0.181158i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23541.5 | + | 40775.0i | 0.763841 | + | 1.32301i | 0.940857 | + | 0.338804i | \(0.110022\pi\) |
−0.177016 | + | 0.984208i | \(0.556644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12408.1 | + | 7163.83i | 0.401376 | + | 0.231735i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25616.5 | − | 14789.7i | −0.823618 | − | 0.475516i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17117.9 | + | 29649.0i | 0.548705 | + | 0.950386i | 0.998364 | + | 0.0571849i | \(0.0182124\pi\) |
−0.449658 | + | 0.893201i | \(0.648454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 26080.6i | − | 0.830964i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7484.38 | + | 4321.11i | −0.237746 | + | 0.137263i | −0.614140 | − | 0.789197i | \(-0.710497\pi\) |
0.376394 | + | 0.926460i | \(0.377164\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.4.t.a.89.1 | yes | 16 | |
3.2 | odd | 2 | inner | 252.4.t.a.89.8 | yes | 16 | |
4.3 | odd | 2 | 1008.4.bt.b.593.1 | 16 | |||
7.2 | even | 3 | 1764.4.f.a.881.15 | 16 | |||
7.3 | odd | 6 | inner | 252.4.t.a.17.8 | yes | 16 | |
7.4 | even | 3 | 1764.4.t.b.521.1 | 16 | |||
7.5 | odd | 6 | 1764.4.f.a.881.1 | 16 | |||
7.6 | odd | 2 | 1764.4.t.b.1097.8 | 16 | |||
12.11 | even | 2 | 1008.4.bt.b.593.8 | 16 | |||
21.2 | odd | 6 | 1764.4.f.a.881.2 | 16 | |||
21.5 | even | 6 | 1764.4.f.a.881.16 | 16 | |||
21.11 | odd | 6 | 1764.4.t.b.521.8 | 16 | |||
21.17 | even | 6 | inner | 252.4.t.a.17.1 | ✓ | 16 | |
21.20 | even | 2 | 1764.4.t.b.1097.1 | 16 | |||
28.3 | even | 6 | 1008.4.bt.b.17.8 | 16 | |||
84.59 | odd | 6 | 1008.4.bt.b.17.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.t.a.17.1 | ✓ | 16 | 21.17 | even | 6 | inner | |
252.4.t.a.17.8 | yes | 16 | 7.3 | odd | 6 | inner | |
252.4.t.a.89.1 | yes | 16 | 1.1 | even | 1 | trivial | |
252.4.t.a.89.8 | yes | 16 | 3.2 | odd | 2 | inner | |
1008.4.bt.b.17.1 | 16 | 84.59 | odd | 6 | |||
1008.4.bt.b.17.8 | 16 | 28.3 | even | 6 | |||
1008.4.bt.b.593.1 | 16 | 4.3 | odd | 2 | |||
1008.4.bt.b.593.8 | 16 | 12.11 | even | 2 | |||
1764.4.f.a.881.1 | 16 | 7.5 | odd | 6 | |||
1764.4.f.a.881.2 | 16 | 21.2 | odd | 6 | |||
1764.4.f.a.881.15 | 16 | 7.2 | even | 3 | |||
1764.4.f.a.881.16 | 16 | 21.5 | even | 6 | |||
1764.4.t.b.521.1 | 16 | 7.4 | even | 3 | |||
1764.4.t.b.521.8 | 16 | 21.11 | odd | 6 | |||
1764.4.t.b.1097.1 | 16 | 21.20 | even | 2 | |||
1764.4.t.b.1097.8 | 16 | 7.6 | odd | 2 |