Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.16928550682624.32 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 62x^{6} - 152x^{5} + 1187x^{4} - 1424x^{3} + 7038x^{2} + 1452x + 5287 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.1 | ||
Root | \(-0.207107 + 0.854139i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.i.783.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.98491 | −1.92160 | −0.960799 | − | 0.277247i | \(-0.910578\pi\) | ||||
−0.960799 | + | 0.277247i | \(0.910578\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 9.37011i | − 0.838088i | −0.907966 | − | 0.419044i | \(-0.862365\pi\) | ||||
0.907966 | − | 0.419044i | \(-0.137635\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 72.6985 | 2.69254 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 44.5415i | − 1.22089i | −0.792059 | − | 0.610445i | \(-0.790991\pi\) | ||||
0.792059 | − | 0.610445i | \(-0.209009\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.8225i | 1.53231i | 0.642658 | + | 0.766153i | \(0.277832\pi\) | ||||
−0.642658 | + | 0.766153i | \(0.722168\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 93.5597i | 1.61047i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 52.6114i | 0.750596i | 0.926904 | + | 0.375298i | \(0.122460\pi\) | ||||
−0.926904 | + | 0.375298i | \(0.877540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −68.8909 | −0.831823 | −0.415912 | − | 0.909405i | \(-0.636537\pi\) | ||||
−0.415912 | + | 0.909405i | \(0.636537\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 155.783i | − 1.41230i | −0.708060 | − | 0.706152i | \(-0.750430\pi\) | ||||
0.708060 | − | 0.706152i | \(-0.249570\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37.2010 | 0.297608 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −456.295 | −3.25237 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −131.799 | −0.843947 | −0.421973 | − | 0.906608i | \(-0.638662\pi\) | ||||
−0.421973 | + | 0.906608i | \(0.638662\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00707 | −0.0116284 | −0.00581420 | − | 0.999983i | \(-0.501851\pi\) | ||||
−0.00581420 | + | 0.999983i | \(0.501851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 444.743i | 2.34606i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −277.186 | −1.23160 | −0.615798 | − | 0.787904i | \(-0.711166\pi\) | ||||
−0.615798 | + | 0.787904i | \(0.711166\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 717.141i | − 2.94448i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 272.652i | − 1.03856i | −0.854603 | − | 0.519282i | \(-0.826199\pi\) | ||||
0.854603 | − | 0.519282i | \(-0.173801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 445.640i | 1.58045i | 0.612814 | + | 0.790227i | \(0.290037\pi\) | ||||
−0.612814 | + | 0.790227i | \(0.709963\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 681.193i | − 2.25658i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −135.775 | −0.421378 | −0.210689 | − | 0.977553i | \(-0.567571\pi\) | ||||
−0.210689 | + | 0.977553i | \(0.567571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 525.320i | − 1.44234i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 362.583 | 0.939709 | 0.469855 | − | 0.882744i | \(-0.344306\pi\) | ||||
0.469855 | + | 0.882744i | \(0.344306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −417.359 | −1.02321 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 687.869 | 1.59843 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −488.257 | −1.07738 | −0.538692 | − | 0.842503i | \(-0.681081\pi\) | ||||
−0.538692 | + | 0.842503i | \(0.681081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 113.696i | − 0.238644i | −0.992856 | − | 0.119322i | \(-0.961928\pi\) | ||||
0.992856 | − | 0.119322i | \(-0.0380722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 672.985 | 1.28421 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 463.322i | 0.844833i | 0.906402 | + | 0.422416i | \(0.138818\pi\) | ||||
−0.906402 | + | 0.422416i | \(0.861182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1555.48i | 2.71388i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 480.779i | 0.803633i | 0.915720 | + | 0.401816i | \(0.131621\pi\) | ||||
−0.915720 | + | 0.401816i | \(0.868379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 146.445i | 0.234796i | 0.993085 | + | 0.117398i | \(0.0374554\pi\) | ||||
−0.993085 | + | 0.117398i | \(0.962545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −371.449 | −0.571883 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1104.36i | 1.57279i | 0.617725 | + | 0.786394i | \(0.288054\pi\) | ||||
−0.617725 | + | 0.786394i | \(0.711946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2593.21 | 3.55722 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 727.895 | 0.962613 | 0.481306 | − | 0.876552i | \(-0.340162\pi\) | ||||
0.481306 | + | 0.876552i | \(0.340162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 492.975 | 0.629066 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1316.00 | 1.62173 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 51.3114i | 0.0611124i | 0.999533 | + | 0.0305562i | \(0.00972785\pi\) | ||||
−0.999533 | + | 0.0305562i | \(0.990272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.0404 | 0.0223451 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 645.515i | 0.697141i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 556.128i | 0.582126i | 0.956704 | + | 0.291063i | \(0.0940090\pi\) | ||||
−0.956704 | + | 0.291063i | \(0.905991\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3238.10i | − 3.28729i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1286.22i | − 1.26716i | −0.773677 | − | 0.633580i | \(-0.781585\pi\) | ||||
0.773677 | − | 0.633580i | \(-0.218415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1785.24 | 1.70782 | 0.853908 | − | 0.520423i | \(-0.174226\pi\) | ||||
0.853908 | + | 0.520423i | \(0.174226\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 566.735i | − 0.512041i | −0.966671 | − | 0.256020i | \(-0.917589\pi\) | ||||
0.966671 | − | 0.256020i | \(-0.0824114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 189.206 | 0.166263 | 0.0831314 | − | 0.996539i | \(-0.473508\pi\) | ||||
0.0831314 | + | 0.996539i | \(0.473508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2767.68 | 2.36663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −396.935 | −0.330447 | −0.165223 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165223 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1459.70 | −1.18364 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5221.39i | 4.12579i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −652.949 | −0.490571 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2722.41i | 1.99570i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1519.84i | − 1.08751i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 163.386i | 0.114159i | 0.998370 | + | 0.0570795i | \(0.0181789\pi\) | ||||
−0.998370 | + | 0.0570795i | \(0.981821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 4449.68i | − 3.03700i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 726.791 | 0.484733 | 0.242366 | − | 0.970185i | \(-0.422076\pi\) | ||||
0.242366 | + | 0.970185i | \(0.422076\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4275.54i | 2.72578i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 133.497 | 0.0832515 | 0.0416258 | − | 0.999133i | \(-0.486746\pi\) | ||||
0.0416258 | + | 0.999133i | \(0.486746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1431.86 | 0.873730 | 0.436865 | − | 0.899527i | \(-0.356089\pi\) | ||||
0.436865 | + | 0.899527i | \(0.356089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1355.70 | 0.809719 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3199.09 | 1.87078 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1234.97i | 0.707302i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 485.839 | 0.267124 | 0.133562 | − | 0.991040i | \(-0.457358\pi\) | ||||
0.133562 | + | 0.991040i | \(0.457358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 386.319i | 0.208200i | 0.994567 | + | 0.104100i | \(0.0331962\pi\) | ||||
−0.994567 | + | 0.104100i | \(0.966804\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3824.77i | 2.02101i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.8065i | 0.00974562i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2533.11i | 1.28767i | 0.765165 | + | 0.643835i | \(0.222658\pi\) | ||||
−0.765165 | + | 0.643835i | \(0.777342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3620.36 | −1.80574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2993.24i | − 1.43833i | −0.694837 | − | 0.719167i | \(-0.744524\pi\) | ||||
0.694837 | − | 0.719167i | \(-0.255476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4167.30 | 1.96620 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 375.413 | 0.173954 | 0.0869769 | − | 0.996210i | \(-0.472279\pi\) | ||||
0.0869769 | + | 0.996210i | \(0.472279\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2961.47 | −1.34796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5008.26 | −2.23972 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 453.129i | − 0.199137i | −0.995031 | − | 0.0995687i | \(-0.968254\pi\) | ||||
0.995031 | − | 0.0995687i | \(-0.0317463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4875.21 | 2.07030 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 218.456i | 0.0912188i | 0.998959 | + | 0.0456094i | \(0.0145230\pi\) | ||||
−0.998959 | + | 0.0456094i | \(0.985477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1634.88i | 0.671378i | 0.941973 | + | 0.335689i | \(0.108969\pi\) | ||||
−0.941973 | + | 0.335689i | \(0.891031\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1135.25i | 0.458579i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2597.26i | 1.03219i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2343.39 | 0.916395 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1887.30i | − 0.714976i | −0.933918 | − | 0.357488i | \(-0.883633\pi\) | ||||
0.933918 | − | 0.357488i | \(-0.116367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3167.95 | 1.18152 | 0.590762 | − | 0.806846i | \(-0.298827\pi\) | ||||
0.590762 | + | 0.806846i | \(0.298827\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6719.70 | −2.46773 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4767.83 | 1.72433 | 0.862167 | − | 0.506625i | \(-0.169107\pi\) | ||||
0.862167 | + | 0.506625i | \(0.169107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3977.71 | 1.41695 | 0.708473 | − | 0.705738i | \(-0.249384\pi\) | ||||
0.708473 | + | 0.705738i | \(0.249384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 4626.23i | − 1.62343i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2554.78 | −0.870409 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 11325.2i | − 3.80268i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3068.51i | 1.01556i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1882.40i | 0.614169i | 0.951682 | + | 0.307084i | \(0.0993534\pi\) | ||||
−0.951682 | + | 0.307084i | \(0.900647\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4800.53i | − 1.54426i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4175.70 | 1.32456 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1462.24i | − 0.451184i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3778.68 | −1.15014 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4664.81 | −1.40080 | −0.700401 | − | 0.713750i | \(-0.746995\pi\) | ||||
−0.700401 | + | 0.713750i | \(0.746995\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2704.46 | 0.801321 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1008.58 | −0.294897 | −0.147448 | − | 0.989070i | \(-0.547106\pi\) | ||||
−0.147448 | + | 0.989070i | \(0.547106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 152.488i | 0.0440030i | 0.999758 | + | 0.0220015i | \(0.00700386\pi\) | ||||
−0.999758 | + | 0.0220015i | \(0.992996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2329.92 | −0.655099 | −0.327550 | − | 0.944834i | \(-0.606223\pi\) | ||||
−0.327550 | + | 0.944834i | \(0.606223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1272.22i | 0.353152i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 11026.9i | − 3.02227i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6739.43i | 1.82401i | 0.410184 | + | 0.912003i | \(0.365465\pi\) | ||||
−0.410184 | + | 0.912003i | \(0.634535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 473.861i | − 0.126656i | −0.997993 | − | 0.0633279i | \(-0.979829\pi\) | ||||
0.997993 | − | 0.0633279i | \(-0.0201714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13573.0 | −3.58316 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4947.91i | − 1.27461i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7267.97 | −1.84975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4796.42 | −1.20616 | −0.603082 | − | 0.797679i | \(-0.706061\pi\) | ||||
−0.603082 | + | 0.797679i | \(0.706061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6938.81 | −1.72427 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4922.31 | −1.20881 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3956.97i | 0.960425i | 0.877152 | + | 0.480212i | \(0.159440\pi\) | ||||
−0.877152 | + | 0.480212i | \(0.840560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9581.59 | −2.27236 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1449.04i | 0.339740i | 0.985466 | + | 0.169870i | \(0.0543348\pi\) | ||||
−0.985466 | + | 0.169870i | \(0.945665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 3397.44i | − 0.787559i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 512.340i | − 0.117433i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3513.91i | − 0.796457i | −0.917286 | − | 0.398228i | \(-0.869625\pi\) | ||||
0.917286 | − | 0.398228i | \(-0.130375\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 375.413 | 0.0841501 | 0.0420751 | − | 0.999114i | \(-0.486603\pi\) | ||||
0.0420751 | + | 0.999114i | \(0.486603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1656.99i | − 0.363347i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1183.53 | 0.256720 | 0.128360 | − | 0.991728i | \(-0.459029\pi\) | ||||
0.128360 | + | 0.991728i | \(0.459029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −145.911 | −0.0313099 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5391.53 | 1.14460 | 0.572298 | − | 0.820046i | \(-0.306052\pi\) | ||||
0.572298 | + | 0.820046i | \(0.306052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4112.53 | 0.863832 | 0.431916 | − | 0.901914i | \(-0.357838\pi\) | ||||
0.431916 | + | 0.901914i | \(0.357838\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 6445.41i | − 1.33963i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2145.04 | 0.436605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 5552.89i | − 1.11861i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 321.668i | − 0.0641367i | −0.999486 | − | 0.0320683i | \(-0.989791\pi\) | ||||
0.999486 | − | 0.0320683i | \(-0.0102094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4575.02i | 0.902943i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20324.1i | 3.97079i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11188.7 | 2.16408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12842.7i | 2.43497i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1065.35 | −0.200005 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9844.77 | 1.83020 | 0.915099 | − | 0.403229i | \(-0.132112\pi\) | ||||
0.915099 | + | 0.403229i | \(0.132112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17825.5 | −3.28174 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3862.10 | −0.704179 | −0.352090 | − | 0.935966i | \(-0.614529\pi\) | ||||
−0.352090 | + | 0.935966i | \(0.614529\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 7799.27i | − 1.40844i | −0.709983 | − | 0.704218i | \(-0.751298\pi\) | ||||
0.709983 | − | 0.704218i | \(-0.248702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8229.84 | 1.45815 | 0.729075 | − | 0.684434i | \(-0.239950\pi\) | ||||
0.729075 | + | 0.684434i | \(0.239950\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5870.53i | 1.03037i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5658.80i | 0.983936i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3624.44i | − 0.624364i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2671.87i | 0.456027i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1889.21 | −0.319490 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5778.57i | − 0.959574i | −0.877385 | − | 0.479787i | \(-0.840714\pi\) | ||||
0.877385 | − | 0.479787i | \(-0.159286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20151.0 | −3.31612 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4341.38 | 0.708044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8187.84 | 1.32350 | 0.661751 | − | 0.749724i | \(-0.269814\pi\) | ||||
0.661751 | + | 0.749724i | \(0.269814\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3963.36 | 0.634986 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 89.3979i | 0.0141970i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14575.0 | 2.27447 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7716.85i | 1.19384i | 0.802301 | + | 0.596919i | \(0.203609\pi\) | ||||
−0.802301 | + | 0.596919i | \(0.796391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3609.62i | 0.553634i | 0.960923 | + | 0.276817i | \(0.0892796\pi\) | ||||
−0.960923 | + | 0.276817i | \(0.910720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 32772.3i | − 4.98363i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6932.46i | 1.04526i | 0.852559 | + | 0.522631i | \(0.175049\pi\) | ||||
−0.852559 | + | 0.522631i | \(0.824951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4504.95 | 0.673515 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 6166.91i | − 0.906622i | −0.891352 | − | 0.453311i | \(-0.850243\pi\) | ||||
0.891352 | − | 0.453311i | \(-0.149757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2113.05 | −0.308070 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6519.64 | 0.942679 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1372.21 | 0.196780 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4113.88 | 0.585131 | 0.292565 | − | 0.956245i | \(-0.405491\pi\) | ||||
0.292565 | + | 0.956245i | \(0.405491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 19821.4i | − 2.79637i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7657.56 | −1.06298 | −0.531492 | − | 0.847063i | \(-0.678369\pi\) | ||||
−0.531492 | + | 0.847063i | \(0.678369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15175.5i | 2.08976i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 9466.13i | − 1.29318i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9044.59i | 1.22583i | 0.790149 | + | 0.612915i | \(0.210003\pi\) | ||||
−0.790149 | + | 0.612915i | \(0.789997\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1631.40i | − 0.219368i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2346.71 | −0.313084 | −0.156542 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156542 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32397.4i | 4.25543i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1944.72 | −0.253474 | −0.126737 | − | 0.991936i | \(-0.540450\pi\) | ||||
−0.126737 | + | 0.991936i | \(0.540450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8195.96 | 1.06007 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7256.94 | −0.931461 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10348.0 | 1.31814 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10331.6i | 1.30612i | 0.757306 | + | 0.653060i | \(0.226515\pi\) | ||||
−0.757306 | + | 0.653060i | \(0.773485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4176.29 | −0.520085 | −0.260042 | − | 0.965597i | \(-0.583737\pi\) | ||||
−0.260042 | + | 0.965597i | \(0.583737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 144.153i | − 0.0178183i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 24298.7i | − 2.98126i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12346.3i | 1.50364i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 6370.70i | − 0.770198i | −0.922875 | − | 0.385099i | \(-0.874167\pi\) | ||||
0.922875 | − | 0.385099i | \(-0.125833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1332.96 | −0.159976 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 6820.46i | − 0.806755i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14297.0 | −1.67896 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12152.0 | 1.41686 | 0.708432 | − | 0.705779i | \(-0.249403\pi\) | ||||
0.708432 | + | 0.705779i | \(0.249403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3412.11 | −0.395003 | −0.197501 | − | 0.980303i | \(-0.563283\pi\) | ||||
−0.197501 | + | 0.980303i | \(0.563283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9870.61 | −1.13458 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1957.20i | 0.223384i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31942.6 | −3.59488 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12838.3i | 1.43480i | 0.696662 | + | 0.717400i | \(0.254668\pi\) | ||||
−0.696662 | + | 0.717400i | \(0.745332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7230.12i | 0.802442i | 0.915981 | + | 0.401221i | \(0.131414\pi\) | ||||
−0.915981 | + | 0.401221i | \(0.868586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 12331.1i | − 1.35915i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10732.0i | 1.17479i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10429.8 | 1.13391 | 0.566954 | − | 0.823749i | \(-0.308122\pi\) | ||||
0.566954 | + | 0.823749i | \(0.308122\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2284.40i | − 0.245000i | −0.992469 | − | 0.122500i | \(-0.960909\pi\) | ||||
0.992469 | − | 0.122500i | \(-0.0390911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 480.794 | 0.0512176 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4851.06 | −0.513305 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6250.59 | −0.656979 | −0.328490 | − | 0.944508i | \(-0.606540\pi\) | ||||
−0.328490 | + | 0.944508i | \(0.606540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12144.4 | −1.26797 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3857.36i | − 0.400077i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4529.34 | −0.463618 | −0.231809 | − | 0.972761i | \(-0.574464\pi\) | ||||
−0.231809 | + | 0.972761i | \(0.574464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 24006.3i | − 2.44122i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 17621.4i | − 1.78028i | −0.455687 | − | 0.890140i | \(-0.650607\pi\) | ||||
0.455687 | − | 0.890140i | \(-0.349393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1856.39i | − 0.186337i | −0.995650 | − | 0.0931683i | \(-0.970301\pi\) | ||||
0.995650 | − | 0.0931683i | \(-0.0296995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 187.781i | − 0.0187272i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1862.77 | 0.184579 | 0.0922897 | − | 0.995732i | \(-0.470581\pi\) | ||||
0.0922897 | + | 0.995732i | \(0.470581\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 25292.9i | − 2.47438i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19849.5 | 1.92956 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2562.81 | −0.247557 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26359.2 | 2.53020 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9006.29 | −0.859098 | −0.429549 | − | 0.903044i | \(-0.641327\pi\) | ||||
−0.429549 | + | 0.903044i | \(0.641327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 19908.2i | − 1.88718i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5210.98 | 0.487873 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2416.92i | − 0.224889i | −0.993658 | − | 0.112445i | \(-0.964132\pi\) | ||||
0.993658 | − | 0.112445i | \(-0.0358681\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29887.2i | 2.76390i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17100.0i | 1.57171i | 0.618410 | + | 0.785855i | \(0.287777\pi\) | ||||
−0.618410 | + | 0.785855i | \(0.712223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6934.13i | − 0.633464i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30341.4 | −2.75504 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16112.4i | 1.44547i | 0.691123 | + | 0.722737i | \(0.257116\pi\) | ||||
−0.691123 | + | 0.722737i | \(0.742884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3748.46 | −0.334269 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15531.4 | −1.37676 | −0.688381 | − | 0.725350i | \(-0.741678\pi\) | ||||
−0.688381 | + | 0.725350i | \(0.741678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12052.0 | −1.06199 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29570.0 | 2.59024 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6159.53i | 0.536378i | 0.963366 | + | 0.268189i | \(0.0864252\pi\) | ||||
−0.963366 | + | 0.268189i | \(0.913575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31434.6 | 2.70540 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 16727.9i | − 1.43130i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6047.61i | 0.514456i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4524.45i | 0.382662i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9860.29i | 0.829150i | 0.910015 | + | 0.414575i | \(0.136070\pi\) | ||||
−0.910015 | + | 0.414575i | \(0.863930\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15816.1 | 1.32235 | 0.661174 | − | 0.750233i | \(-0.270059\pi\) | ||||
0.661174 | + | 0.750233i | \(0.270059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 105.595i | − 0.00872823i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12101.3 | −0.994602 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35495.6 | −2.90090 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19582.6 | 1.59140 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5310.37 | −0.429135 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2181.26i | − 0.175286i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21732.0 | 1.72704 | 0.863522 | − | 0.504312i | \(-0.168254\pi\) | ||||
0.863522 | + | 0.504312i | \(0.168254\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 16324.1i | − 1.29012i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1772.88i | − 0.139343i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14469.3i | 1.13101i | 0.824746 | + | 0.565503i | \(0.191318\pi\) | ||||
−0.824746 | + | 0.565503i | \(0.808682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8265.54i | − 0.642559i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9079.75 | 0.702015 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 25933.4i | − 1.98345i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11976.7 | 0.911074 | 0.455537 | − | 0.890217i | \(-0.349447\pi\) | ||||
0.455537 | + | 0.890217i | \(0.349447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32007.0 | −2.42174 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23398.6 | −1.76094 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11099.0 | 0.830844 | 0.415422 | − | 0.909629i | \(-0.363634\pi\) | ||||
0.415422 | + | 0.909629i | \(0.363634\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3719.32i | 0.276944i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15503.4 | 1.14224 | 0.571121 | − | 0.820866i | \(-0.306509\pi\) | ||||
0.571121 | + | 0.820866i | \(0.306509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17956.0i | 1.31600i | 0.753017 | + | 0.658001i | \(0.228598\pi\) | ||||
−0.753017 | + | 0.658001i | \(0.771402\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18844.5i | 1.37390i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 5795.28i | − 0.420313i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 12632.1i | − 0.911403i | −0.890133 | − | 0.455701i | \(-0.849389\pi\) | ||||
0.890133 | − | 0.455701i | \(-0.150611\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31631.7 | −2.27041 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 16150.0i | − 1.14728i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 48925.0 | 3.45778 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12331.1 | 0.867049 | 0.433524 | − | 0.901142i | \(-0.357270\pi\) | ||||
0.433524 | + | 0.901142i | \(0.357270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 138.269 | 0.00967277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47606.3 | −3.31347 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13057.5i | 0.904226i | 0.891961 | + | 0.452113i | \(0.149330\pi\) | ||||
−0.891961 | + | 0.452113i | \(0.850670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −39717.1 | −2.72280 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 12969.9i | − 0.884702i | −0.896842 | − | 0.442351i | \(-0.854145\pi\) | ||||
0.896842 | − | 0.442351i | \(-0.145855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 602.499i | − 0.0408926i | −0.999791 | − | 0.0204463i | \(-0.993491\pi\) | ||||
0.999791 | − | 0.0204463i | \(-0.00650871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33682.8i | 2.27474i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6118.21i | 0.411141i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 80.6862 | 0.00539531 | 0.00269765 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269765 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 9751.67i | − 0.645680i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26381.5 | −1.73824 | −0.869120 | − | 0.494602i | \(-0.835314\pi\) | ||||
−0.869120 | + | 0.494602i | \(0.835314\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 25509.3 | 1.67258 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21916.5 | 1.43003 | 0.715013 | − | 0.699111i | \(-0.246421\pi\) | ||||
0.715013 | + | 0.699111i | \(0.246421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6523.46 | 0.423586 | 0.211793 | − | 0.977315i | \(-0.432070\pi\) | ||||
0.211793 | + | 0.977315i | \(0.432070\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 71083.0i | 4.59334i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9590.96 | −0.613821 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 30638.8i | − 1.95151i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 14583.1i | − 0.924432i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 254.337i | 0.0160460i | 0.999968 | + | 0.00802298i | \(0.00255382\pi\) | ||||
−0.999968 | + | 0.00802298i | \(0.997446\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 18795.6i | − 1.18019i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1530.95 | 0.0956754 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34951.9i | 2.16381i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9171.59 | −0.565142 | −0.282571 | − | 0.959246i | \(-0.591187\pi\) | ||||
−0.282571 | + | 0.959246i | \(0.591187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 566.427 | 0.0347398 | 0.0173699 | − | 0.999849i | \(-0.494471\pi\) | ||||
0.0173699 | + | 0.999849i | \(0.494471\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41694.0 | −2.54527 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22582.8 | 1.37221 | 0.686105 | − | 0.727503i | \(-0.259319\pi\) | ||||
0.686105 | + | 0.727503i | \(0.259319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21747.7i | 1.31537i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21180.9 | −1.26933 | −0.634666 | − | 0.772787i | \(-0.718862\pi\) | ||||
−0.634666 | + | 0.772787i | \(0.718862\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 6810.11i | − 0.406249i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10646.4i | 0.632198i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 26581.0i | − 1.57125i | −0.618706 | − | 0.785623i | \(-0.712343\pi\) | ||||
0.618706 | − | 0.785623i | \(-0.287657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 33622.0i | − 1.97843i | −0.146468 | − | 0.989215i | \(-0.546791\pi\) | ||||
0.146468 | − | 0.989215i | \(-0.453209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37729.8 | 2.21011 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20532.0i | 1.19191i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46577.7 | 2.69178 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5064.21 | −0.291358 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15410.3 | 0.882650 | 0.441325 | − | 0.897347i | \(-0.354509\pi\) | ||||
0.441325 | + | 0.897347i | \(0.354509\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16974.6 | −0.967933 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 235.019i | − 0.0133420i | −0.999978 | − | 0.00667098i | \(-0.997877\pi\) | ||||
0.999978 | − | 0.00667098i | \(-0.00212345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10070.6 | 0.566673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28591.2i | 1.60177i | 0.598816 | + | 0.800886i | \(0.295638\pi\) | ||||
−0.598816 | + | 0.800886i | \(0.704362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1250.89i | − 0.0697721i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1522.58i | − 0.0845561i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26041.6i | 1.43992i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25202.6 | −1.38748 | −0.693742 | − | 0.720224i | \(-0.744039\pi\) | ||||
−0.693742 | + | 0.720224i | \(0.744039\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 13416.7i | − 0.732263i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14344.6 | 0.779543 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23264.0 | 1.25884 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15570.3 | 0.838919 | 0.419460 | − | 0.907774i | \(-0.362220\pi\) | ||||
0.419460 | + | 0.907774i | \(0.362220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19095.6 | 1.02447 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 12703.0i | − 0.678616i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20099.0 | 1.06465 | 0.532323 | − | 0.846541i | \(-0.321319\pi\) | ||||
0.532323 | + | 0.846541i | \(0.321319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 80285.3i | 4.23479i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 312.667i | 0.0164228i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 29975.8i | − 1.56788i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 67292.6i | − 3.50500i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17029.4 | −0.883298 | −0.441649 | − | 0.897188i | \(-0.645606\pi\) | ||||
−0.441649 | + | 0.897188i | \(0.645606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4731.46i | 0.243382i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4903.06 | −0.251165 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14129.5 | 0.720817 | 0.360409 | − | 0.932795i | \(-0.382637\pi\) | ||||
0.360409 | + | 0.932795i | \(0.382637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 65508.6 | 3.32818 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23445.8 | −1.18628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32735.0i | − 1.64951i | −0.565487 | − | 0.824757i | \(-0.691312\pi\) | ||||
0.565487 | − | 0.824757i | \(-0.308688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20637.1 | 1.03145 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13549.9i | 0.674478i | 0.941419 | + | 0.337239i | \(0.109493\pi\) | ||||
−0.941419 | + | 0.337239i | \(0.890507\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49404.5i | 2.44928i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 12007.9i | − 0.592905i | −0.955048 | − | 0.296452i | \(-0.904196\pi\) | ||||
0.955048 | − | 0.296452i | \(-0.0958036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 4552.37i | − 0.223874i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 52916.9 | 2.59187 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1831.36i | 0.0889841i | 0.999010 | + | 0.0444921i | \(0.0141669\pi\) | ||||
−0.999010 | + | 0.0444921i | \(0.985833\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 47891.8 | 2.31776 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3619.85 | 0.174490 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40198.4 | −1.93003 | −0.965016 | − | 0.262190i | \(-0.915555\pi\) | ||||
−0.965016 | + | 0.262190i | \(0.915555\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 69283.4 | 3.31335 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24225.4i | 1.15397i | 0.816756 | + | 0.576984i | \(0.195770\pi\) | ||||
−0.816756 | + | 0.576984i | \(0.804230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 35838.5 | 1.69378 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 35067.9i | − 1.65088i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5497.35i | 0.257789i | 0.991658 | + | 0.128894i | \(0.0411428\pi\) | ||||
−0.991658 | + | 0.128894i | \(0.958857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 39510.0i | − 1.84555i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41568.2i | 1.93416i | 0.254475 | + | 0.967079i | \(0.418097\pi\) | ||||
−0.254475 | + | 0.967079i | \(0.581903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −74.6650 | −0.00346070 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18783.3i | 0.863903i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21414.6 | 0.981147 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 60139.3 | 2.74483 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23735.5 | 1.07918 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9169.82 | 0.415335 | 0.207668 | − | 0.978199i | \(-0.433413\pi\) | ||||
0.207668 | + | 0.978199i | \(0.433413\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 14468.5i | − 0.652844i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8165.95 | 0.365676 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33923.2i | 1.51337i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14252.4i | 0.633435i | 0.948520 | + | 0.316717i | \(0.102581\pi\) | ||||
−0.948520 | + | 0.316717i | \(0.897419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 7143.29i | − 0.316285i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3730.26i | 0.164547i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6522.91 | 0.286660 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35086.1i | 1.53047i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3169.13 | −0.137727 | −0.0688633 | − | 0.997626i | \(-0.521937\pi\) | ||||
−0.0688633 | + | 0.997626i | \(0.521937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18422.1 | 0.797640 | 0.398820 | − | 0.917029i | \(-0.369420\pi\) | ||||
0.398820 | + | 0.917029i | \(0.369420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3748.46 | −0.161703 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28047.0 | −1.20545 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 30700.6i | − 1.31466i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38927.2 | −1.65477 | −0.827386 | − | 0.561633i | \(-0.810173\pi\) | ||||
−0.827386 | + | 0.561633i | \(0.810173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 39291.9i | − 1.66419i | −0.554631 | − | 0.832097i | \(-0.687140\pi\) | ||||
0.554631 | − | 0.832097i | \(-0.312860\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16544.9i | 0.698206i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7699.59i | 0.323750i | 0.986811 | + | 0.161875i | \(0.0517541\pi\) | ||||
−0.986811 | + | 0.161875i | \(0.948246\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4971.23i | 0.208273i | 0.994563 | + | 0.104136i | \(0.0332078\pi\) | ||||
−0.994563 | + | 0.104136i | \(0.966792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11817.4 | −0.493312 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3517.66i | − 0.145789i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 915.816 | 0.0378199 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −326.749 | −0.0134453 | −0.00672266 | − | 0.999977i | \(-0.502140\pi\) | ||||
−0.00672266 | + | 0.999977i | \(0.502140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7018.03 | −0.287754 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −53833.9 | −2.19945 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27749.3i | 1.12971i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41063.2 | −1.65994 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43180.8i | 1.73939i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7306.34i | − 0.293276i | −0.989190 | − | 0.146638i | \(-0.953155\pi\) | ||||
0.989190 | − | 0.146638i | \(-0.0468452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 46928.0i | 1.87708i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3886.28i | 0.154904i | 0.996996 | + | 0.0774521i | \(0.0246785\pi\) | ||||
−0.996996 | + | 0.0774521i | \(0.975322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8254.71 | 0.327878 | 0.163939 | − | 0.986470i | \(-0.447580\pi\) | ||||
0.163939 | + | 0.986470i | \(0.447580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42051.3i | 1.65868i | 0.558742 | + | 0.829342i | \(0.311284\pi\) | ||||
−0.558742 | + | 0.829342i | \(0.688716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4245.87 | −0.166895 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21418.0 | −0.838979 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49189.9 | 1.92020 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33277.0 | −1.29454 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 40429.7i | 1.56740i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33485.8 | −1.28932 | −0.644661 | − | 0.764469i | \(-0.723001\pi\) | ||||
−0.644661 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3211.83i | 0.123245i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 31744.2i | − 1.21395i | −0.794721 | − | 0.606975i | \(-0.792383\pi\) | ||||
0.794721 | − | 0.606975i | \(-0.207617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 30695.6i | − 1.16986i | −0.811083 | − | 0.584931i | \(-0.801121\pi\) | ||||
0.811083 | − | 0.584931i | \(-0.198879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 45681.2i | − 1.73509i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20840.2 | −0.788888 | −0.394444 | − | 0.918920i | \(-0.629063\pi\) | ||||
−0.394444 | + | 0.918920i | \(0.629063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 115506.i | − 4.34297i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9353.63 | 0.350512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2046.96 | 0.0764494 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −111718. | −4.15849 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 264.530 | 0.00981374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19076.0i | 0.705342i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15319.0 | 0.562674 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22901.1i | − 0.838388i | −0.907897 | − | 0.419194i | \(-0.862313\pi\) | ||||
0.907897 | − | 0.419194i | \(-0.137687\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 93505.9i | − 3.41188i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 4526.12i | − 0.164607i | −0.996607 | − | 0.0823035i | \(-0.973772\pi\) | ||||
0.996607 | − | 0.0823035i | \(-0.0262277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 32421.6i | − 1.17524i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10637.4 | 0.384329 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8790.70i | 0.315537i | 0.987476 | + | 0.157769i | \(0.0504300\pi\) | ||||
−0.987476 | + | 0.157769i | \(0.949570\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −98299.2 | −3.51690 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34530.7 | −1.23141 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10311.6 | −0.366533 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 129784. | 4.59836 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51590.8i | 1.82200i | 0.412405 | + | 0.911001i | \(0.364689\pi\) | ||||
−0.412405 | + | 0.911001i | \(0.635311\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38562.8 | 1.35315 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 21957.9i | − 0.768020i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25622.6i | 0.893335i | 0.894700 | + | 0.446668i | \(0.147389\pi\) | ||||
−0.894700 | + | 0.446668i | \(0.852611\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 77875.0i | 2.70645i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48959.9i | 1.69612i | 0.529902 | + | 0.848059i | \(0.322229\pi\) | ||||
−0.529902 | + | 0.848059i | \(0.677771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42474.6 | −1.46677 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29422.8i | 1.00962i | 0.863230 | + | 0.504811i | \(0.168438\pi\) | ||||
−0.863230 | + | 0.504811i | \(0.831562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10518.1 | −0.359780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −82174.2 | −2.80198 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34930.5 | 1.18731 | 0.593657 | − | 0.804718i | \(-0.297683\pi\) | ||||
0.593657 | + | 0.804718i | \(0.297683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17684.2 | −0.599213 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 58616.7i | − 1.97995i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29787.0 | −0.999865 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 41200.8i | − 1.37869i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 29684.0i | − 0.990221i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49631.3i | 1.65050i | 0.564767 | + | 0.825250i | \(0.308966\pi\) | ||||
−0.564767 | + | 0.825250i | \(0.691034\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36189.8i | 1.19978i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56603.7 | −1.87075 | −0.935375 | − | 0.353658i | \(-0.884938\pi\) | ||||
−0.935375 | + | 0.353658i | \(0.884938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 26678.4i | − 0.876300i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11175.4 | −0.365950 | −0.182975 | − | 0.983118i | \(-0.558573\pi\) | ||||
−0.182975 | + | 0.983118i | \(0.558573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2285.49 | 0.0746115 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13755.0 | 0.447669 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9444.83 | −0.306453 | −0.153226 | − | 0.988191i | \(-0.548966\pi\) | ||||
−0.153226 | + | 0.988191i | \(0.548966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 44675.1i | − 1.44514i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 69423.2 | 2.23208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 30310.1i | − 0.971575i | −0.874077 | − | 0.485788i | \(-0.838533\pi\) | ||||
0.874077 | − | 0.485788i | \(-0.161467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 57698.5i | 1.84391i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 37271.6i | − 1.18753i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 19773.8i | − 0.628126i | −0.949402 | − | 0.314063i | \(-0.898310\pi\) | ||||
0.949402 | − | 0.314063i | \(-0.101690\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 126479. | 4.00561 |
(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 | 784.4.f.i.783.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 784.4.f.i.783.7 | yes | 8 | |
7.6 | odd | 2 | inner | 784.4.f.i.783.8 | yes | 8 | |
28.27 | even | 2 | inner | 784.4.f.i.783.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.4.f.i.783.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
784.4.f.i.783.2 | yes | 8 | 28.27 | even | 2 | inner | |
784.4.f.i.783.7 | yes | 8 | 4.3 | odd | 2 | inner | |
784.4.f.i.783.8 | yes | 8 | 7.6 | odd | 2 | inner |