Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 176x^{6} + 272x^{5} + 9055x^{4} - 15851x^{3} - 118840x^{2} + 149572x - 33248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.894159\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89416 | −0.334843 | −0.167422 | − | 0.985885i | \(-0.553544\pi\) | ||||
−0.167422 | + | 0.985885i | \(0.553544\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −28.4122 | −0.887880 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −17.0474 | −0.193322 | ||||||||
\(7\) | 191.987 | 1.48090 | 0.740452 | − | 0.672109i | \(-0.234612\pi\) | ||||
0.740452 | + | 0.672109i | \(0.234612\pi\) | |||||||
\(8\) | 114.430 | 0.632144 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −255.709 | −0.512618 | ||||||||
\(13\) | 536.985 | 0.881259 | 0.440630 | − | 0.897689i | \(-0.354755\pi\) | ||||
0.440630 | + | 0.897689i | \(0.354755\pi\) | |||||||
\(14\) | −363.654 | −0.495871 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 692.440 | 0.676211 | ||||||||
\(17\) | −1324.89 | −1.11188 | −0.555940 | − | 0.831223i | \(-0.687641\pi\) | ||||
−0.555940 | + | 0.831223i | \(0.687641\pi\) | |||||||
\(18\) | −153.427 | −0.111614 | ||||||||
\(19\) | −912.564 | −0.579935 | −0.289968 | − | 0.957036i | \(-0.593645\pi\) | ||||
−0.289968 | + | 0.957036i | \(0.593645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1727.88 | 0.855000 | ||||||||
\(22\) | 229.193 | 0.100959 | ||||||||
\(23\) | −4124.56 | −1.62577 | −0.812883 | − | 0.582427i | \(-0.802103\pi\) | ||||
−0.812883 | + | 0.582427i | \(0.802103\pi\) | |||||||
\(24\) | 1029.87 | 0.364968 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1017.14 | −0.295084 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −5454.77 | −1.31486 | ||||||||
\(29\) | 340.490 | 0.0751811 | 0.0375906 | − | 0.999293i | \(-0.488032\pi\) | ||||
0.0375906 | + | 0.999293i | \(0.488032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4697.47 | 0.877930 | 0.438965 | − | 0.898504i | \(-0.355345\pi\) | ||||
0.438965 | + | 0.898504i | \(0.355345\pi\) | |||||||
\(32\) | −4973.36 | −0.858568 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 2509.55 | 0.372305 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2301.38 | −0.295960 | ||||||||
\(37\) | −8279.99 | −0.994318 | −0.497159 | − | 0.867659i | \(-0.665623\pi\) | ||||
−0.497159 | + | 0.867659i | \(0.665623\pi\) | |||||||
\(38\) | 1728.54 | 0.194187 | ||||||||
\(39\) | 4832.86 | 0.508795 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17495.0 | −1.62537 | −0.812687 | − | 0.582701i | \(-0.801996\pi\) | ||||
−0.812687 | + | 0.582701i | \(0.801996\pi\) | |||||||
\(42\) | −3272.89 | −0.286291 | ||||||||
\(43\) | 5947.60 | 0.490535 | 0.245268 | − | 0.969455i | \(-0.421124\pi\) | ||||
0.245268 | + | 0.969455i | \(0.421124\pi\) | |||||||
\(44\) | 3437.87 | 0.267706 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7812.57 | 0.544377 | ||||||||
\(47\) | 628.580 | 0.0415065 | 0.0207532 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207532 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(48\) | 6231.96 | 0.390411 | ||||||||
\(49\) | 20052.0 | 1.19308 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11924.0 | −0.641944 | ||||||||
\(52\) | −15256.9 | −0.782453 | ||||||||
\(53\) | −16952.3 | −0.828969 | −0.414485 | − | 0.910056i | \(-0.636038\pi\) | ||||
−0.414485 | + | 0.910056i | \(0.636038\pi\) | |||||||
\(54\) | −1380.84 | −0.0644406 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21969.1 | 0.936144 | ||||||||
\(57\) | −8213.08 | −0.334826 | ||||||||
\(58\) | −644.942 | −0.0251739 | ||||||||
\(59\) | −28406.8 | −1.06241 | −0.531204 | − | 0.847244i | \(-0.678260\pi\) | ||||
−0.531204 | + | 0.847244i | \(0.678260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51510.2 | 1.77243 | 0.886215 | − | 0.463275i | \(-0.153326\pi\) | ||||
0.886215 | + | 0.463275i | \(0.153326\pi\) | |||||||
\(62\) | −8897.76 | −0.293969 | ||||||||
\(63\) | 15550.9 | 0.493635 | ||||||||
\(64\) | −12737.7 | −0.388725 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2062.74 | 0.0582887 | ||||||||
\(67\) | 15258.0 | 0.415251 | 0.207625 | − | 0.978208i | \(-0.433427\pi\) | ||||
0.207625 | + | 0.978208i | \(0.433427\pi\) | |||||||
\(68\) | 37643.0 | 0.987215 | ||||||||
\(69\) | −37121.0 | −0.938636 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38398.8 | 0.904007 | 0.452004 | − | 0.892016i | \(-0.350709\pi\) | ||||
0.452004 | + | 0.892016i | \(0.350709\pi\) | |||||||
\(72\) | 9268.85 | 0.210715 | ||||||||
\(73\) | 40463.3 | 0.888699 | 0.444349 | − | 0.895854i | \(-0.353435\pi\) | ||||
0.444349 | + | 0.895854i | \(0.353435\pi\) | |||||||
\(74\) | 15683.6 | 0.332941 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 25927.9 | 0.514913 | ||||||||
\(77\) | −23230.4 | −0.446509 | ||||||||
\(78\) | −9154.22 | −0.170367 | ||||||||
\(79\) | −27358.8 | −0.493207 | −0.246604 | − | 0.969116i | \(-0.579315\pi\) | ||||
−0.246604 | + | 0.969116i | \(0.579315\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 33138.2 | 0.544245 | ||||||||
\(83\) | −51818.0 | −0.825631 | −0.412815 | − | 0.910815i | \(-0.635455\pi\) | ||||
−0.412815 | + | 0.910815i | \(0.635455\pi\) | |||||||
\(84\) | −49092.9 | −0.759138 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11265.7 | −0.164252 | ||||||||
\(87\) | 3064.41 | 0.0434058 | ||||||||
\(88\) | −13846.1 | −0.190599 | ||||||||
\(89\) | 20215.2 | 0.270523 | 0.135261 | − | 0.990810i | \(-0.456813\pi\) | ||||
0.135261 | + | 0.990810i | \(0.456813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 103094. | 1.30506 | ||||||||
\(92\) | 117188. | 1.44348 | ||||||||
\(93\) | 42277.2 | 0.506873 | ||||||||
\(94\) | −1190.63 | −0.0138982 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −44760.2 | −0.495695 | ||||||||
\(97\) | −166901. | −1.80106 | −0.900531 | − | 0.434791i | \(-0.856822\pi\) | ||||
−0.900531 | + | 0.434791i | \(0.856822\pi\) | |||||||
\(98\) | −37981.7 | −0.399493 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18494.4 | 0.180400 | 0.0901999 | − | 0.995924i | \(-0.471249\pi\) | ||||
0.0901999 | + | 0.995924i | \(0.471249\pi\) | |||||||
\(102\) | 22586.0 | 0.214951 | ||||||||
\(103\) | 88991.8 | 0.826527 | 0.413263 | − | 0.910612i | \(-0.364389\pi\) | ||||
0.413263 | + | 0.910612i | \(0.364389\pi\) | |||||||
\(104\) | 61447.3 | 0.557083 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 32110.3 | 0.277575 | ||||||||
\(107\) | 112300. | 0.948248 | 0.474124 | − | 0.880458i | \(-0.342765\pi\) | ||||
0.474124 | + | 0.880458i | \(0.342765\pi\) | |||||||
\(108\) | −20712.5 | −0.170873 | ||||||||
\(109\) | −194142. | −1.56514 | −0.782569 | − | 0.622564i | \(-0.786091\pi\) | ||||
−0.782569 | + | 0.622564i | \(0.786091\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74519.9 | −0.574070 | ||||||||
\(112\) | 132940. | 1.00140 | ||||||||
\(113\) | −4270.92 | −0.0314648 | −0.0157324 | − | 0.999876i | \(-0.505008\pi\) | ||||
−0.0157324 | + | 0.999876i | \(0.505008\pi\) | |||||||
\(114\) | 15556.9 | 0.112114 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9674.05 | −0.0667518 | ||||||||
\(117\) | 43495.8 | 0.293753 | ||||||||
\(118\) | 53806.9 | 0.355740 | ||||||||
\(119\) | −254362. | −1.64659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −97568.6 | −0.593486 | ||||||||
\(123\) | −157455. | −0.938410 | ||||||||
\(124\) | −133465. | −0.779496 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −29456.0 | −0.165290 | ||||||||
\(127\) | −338246. | −1.86090 | −0.930452 | − | 0.366414i | \(-0.880585\pi\) | ||||
−0.930452 | + | 0.366414i | \(0.880585\pi\) | |||||||
\(128\) | 183275. | 0.988730 | ||||||||
\(129\) | 53528.4 | 0.283211 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −113323. | −0.576950 | −0.288475 | − | 0.957487i | \(-0.593148\pi\) | ||||
−0.288475 | + | 0.957487i | \(0.593148\pi\) | |||||||
\(132\) | 30940.8 | 0.154560 | ||||||||
\(133\) | −175201. | −0.858828 | ||||||||
\(134\) | −28901.1 | −0.139044 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −151608. | −0.702868 | ||||||||
\(137\) | 28035.0 | 0.127614 | 0.0638072 | − | 0.997962i | \(-0.479676\pi\) | ||||
0.0638072 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(138\) | 70313.1 | 0.314296 | ||||||||
\(139\) | −59383.8 | −0.260694 | −0.130347 | − | 0.991468i | \(-0.541609\pi\) | ||||
−0.130347 | + | 0.991468i | \(0.541609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5657.22 | 0.0239638 | ||||||||
\(142\) | −72733.5 | −0.302701 | ||||||||
\(143\) | −64975.2 | −0.265710 | ||||||||
\(144\) | 56087.6 | 0.225404 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −76644.0 | −0.297575 | ||||||||
\(147\) | 180468. | 0.688823 | ||||||||
\(148\) | 235252. | 0.882835 | ||||||||
\(149\) | −226515. | −0.835855 | −0.417928 | − | 0.908480i | \(-0.637243\pi\) | ||||
−0.417928 | + | 0.908480i | \(0.637243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 231802. | 0.827323 | 0.413661 | − | 0.910431i | \(-0.364250\pi\) | ||||
0.413661 | + | 0.910431i | \(0.364250\pi\) | |||||||
\(152\) | −104425. | −0.366602 | ||||||||
\(153\) | −107316. | −0.370626 | ||||||||
\(154\) | 44002.1 | 0.149511 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −137312. | −0.451749 | ||||||||
\(157\) | −196398. | −0.635897 | −0.317949 | − | 0.948108i | \(-0.602994\pi\) | ||||
−0.317949 | + | 0.948108i | \(0.602994\pi\) | |||||||
\(158\) | 51822.0 | 0.165147 | ||||||||
\(159\) | −152570. | −0.478606 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −791862. | −2.40760 | ||||||||
\(162\) | −12427.6 | −0.0372048 | ||||||||
\(163\) | −604868. | −1.78317 | −0.891583 | − | 0.452857i | \(-0.850405\pi\) | ||||
−0.891583 | + | 0.452857i | \(0.850405\pi\) | |||||||
\(164\) | 497069. | 1.44314 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 98151.6 | 0.276457 | ||||||||
\(167\) | 140409. | 0.389587 | 0.194793 | − | 0.980844i | \(-0.437596\pi\) | ||||
0.194793 | + | 0.980844i | \(0.437596\pi\) | |||||||
\(168\) | 197722. | 0.540483 | ||||||||
\(169\) | −82940.2 | −0.223382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −73917.7 | −0.193312 | ||||||||
\(172\) | −168984. | −0.435537 | ||||||||
\(173\) | 352914. | 0.896506 | 0.448253 | − | 0.893907i | \(-0.352046\pi\) | ||||
0.448253 | + | 0.893907i | \(0.352046\pi\) | |||||||
\(174\) | −5804.47 | −0.0145342 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −83785.2 | −0.203885 | ||||||||
\(177\) | −255661. | −0.613382 | ||||||||
\(178\) | −38290.9 | −0.0905827 | ||||||||
\(179\) | −784162. | −1.82925 | −0.914625 | − | 0.404303i | \(-0.867514\pi\) | ||||
−0.914625 | + | 0.404303i | \(0.867514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2532.32 | −0.00574542 | −0.00287271 | − | 0.999996i | \(-0.500914\pi\) | ||||
−0.00287271 | + | 0.999996i | \(0.500914\pi\) | |||||||
\(182\) | −195277. | −0.436991 | ||||||||
\(183\) | 463592. | 1.02331 | ||||||||
\(184\) | −471974. | −1.02772 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −80079.8 | −0.169723 | ||||||||
\(187\) | 160312. | 0.335244 | ||||||||
\(188\) | −17859.3 | −0.0368527 | ||||||||
\(189\) | 139959. | 0.285000 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 185241. | 0.367411 | 0.183706 | − | 0.982981i | \(-0.441191\pi\) | ||||
0.183706 | + | 0.982981i | \(0.441191\pi\) | |||||||
\(192\) | −114640. | −0.224431 | ||||||||
\(193\) | 523822. | 1.01226 | 0.506128 | − | 0.862458i | \(-0.331076\pi\) | ||||
0.506128 | + | 0.862458i | \(0.331076\pi\) | |||||||
\(194\) | 316136. | 0.603074 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −569721. | −1.05931 | ||||||||
\(197\) | −166997. | −0.306580 | −0.153290 | − | 0.988181i | \(-0.548987\pi\) | ||||
−0.153290 | + | 0.988181i | \(0.548987\pi\) | |||||||
\(198\) | 18564.7 | 0.0336530 | ||||||||
\(199\) | −715314. | −1.28045 | −0.640227 | − | 0.768186i | \(-0.721160\pi\) | ||||
−0.640227 | + | 0.768186i | \(0.721160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 137322. | 0.239745 | ||||||||
\(202\) | −35031.3 | −0.0604056 | ||||||||
\(203\) | 65369.6 | 0.111336 | ||||||||
\(204\) | 338787. | 0.569969 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −168565. | −0.276757 | ||||||||
\(207\) | −334089. | −0.541922 | ||||||||
\(208\) | 371830. | 0.595917 | ||||||||
\(209\) | 110420. | 0.174857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 917870. | 1.41930 | 0.709651 | − | 0.704553i | \(-0.248852\pi\) | ||||
0.709651 | + | 0.704553i | \(0.248852\pi\) | |||||||
\(212\) | 481651. | 0.736025 | ||||||||
\(213\) | 345589. | 0.521929 | ||||||||
\(214\) | −212715. | −0.317515 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 83419.7 | 0.121656 | ||||||||
\(217\) | 901854. | 1.30013 | ||||||||
\(218\) | 367735. | 0.524076 | ||||||||
\(219\) | 364170. | 0.513090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −711446. | −0.979854 | ||||||||
\(222\) | 141153. | 0.192223 | ||||||||
\(223\) | −65289.2 | −0.0879182 | −0.0439591 | − | 0.999033i | \(-0.513997\pi\) | ||||
−0.0439591 | + | 0.999033i | \(0.513997\pi\) | |||||||
\(224\) | −954821. | −1.27146 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8089.80 | 0.0105358 | ||||||||
\(227\) | 558110. | 0.718879 | 0.359439 | − | 0.933168i | \(-0.382968\pi\) | ||||
0.359439 | + | 0.933168i | \(0.382968\pi\) | |||||||
\(228\) | 233351. | 0.297285 | ||||||||
\(229\) | 980050. | 1.23498 | 0.617490 | − | 0.786579i | \(-0.288150\pi\) | ||||
0.617490 | + | 0.786579i | \(0.288150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −209074. | −0.257792 | ||||||||
\(232\) | 38962.3 | 0.0475253 | ||||||||
\(233\) | 798554. | 0.963640 | 0.481820 | − | 0.876270i | \(-0.339976\pi\) | ||||
0.481820 | + | 0.876270i | \(0.339976\pi\) | |||||||
\(234\) | −82387.9 | −0.0983612 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 807097. | 0.943292 | ||||||||
\(237\) | −246229. | −0.284753 | ||||||||
\(238\) | 481802. | 0.551348 | ||||||||
\(239\) | −1.31819e6 | −1.49274 | −0.746369 | − | 0.665532i | \(-0.768205\pi\) | ||||
−0.746369 | + | 0.665532i | \(0.768205\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.07597e6 | −1.19332 | −0.596660 | − | 0.802494i | \(-0.703506\pi\) | ||||
−0.596660 | + | 0.802494i | \(0.703506\pi\) | |||||||
\(242\) | −27732.4 | −0.0304403 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.46352e6 | −1.57370 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 298244. | 0.314220 | ||||||||
\(247\) | −490033. | −0.511073 | ||||||||
\(248\) | 537533. | 0.554978 | ||||||||
\(249\) | −466362. | −0.476678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −814105. | −0.815635 | −0.407818 | − | 0.913063i | \(-0.633710\pi\) | ||||
−0.407818 | + | 0.913063i | \(0.633710\pi\) | |||||||
\(252\) | −441836. | −0.438288 | ||||||||
\(253\) | 499072. | 0.490187 | ||||||||
\(254\) | 640693. | 0.623111 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 60456.1 | 0.0576554 | ||||||||
\(257\) | −1.89491e6 | −1.78960 | −0.894801 | − | 0.446466i | \(-0.852682\pi\) | ||||
−0.894801 | + | 0.446466i | \(0.852682\pi\) | |||||||
\(258\) | −101391. | −0.0948312 | ||||||||
\(259\) | −1.58965e6 | −1.47249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27579.7 | 0.0250604 | ||||||||
\(262\) | 214651. | 0.193188 | ||||||||
\(263\) | 1.39679e6 | 1.24521 | 0.622603 | − | 0.782538i | \(-0.286075\pi\) | ||||
0.622603 | + | 0.782538i | \(0.286075\pi\) | |||||||
\(264\) | −124615. | −0.110042 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 331858. | 0.287573 | ||||||||
\(267\) | 181937. | 0.156186 | ||||||||
\(268\) | −433513. | −0.368693 | ||||||||
\(269\) | 1.06051e6 | 0.893585 | 0.446793 | − | 0.894638i | \(-0.352566\pi\) | ||||
0.446793 | + | 0.894638i | \(0.352566\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −710526. | −0.587702 | −0.293851 | − | 0.955851i | \(-0.594937\pi\) | ||||
−0.293851 | + | 0.955851i | \(0.594937\pi\) | |||||||
\(272\) | −917407. | −0.751865 | ||||||||
\(273\) | 927847. | 0.753477 | ||||||||
\(274\) | −53102.8 | −0.0427308 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.05469e6 | 0.833396 | ||||||||
\(277\) | 678042. | 0.530955 | 0.265477 | − | 0.964117i | \(-0.414470\pi\) | ||||
0.265477 | + | 0.964117i | \(0.414470\pi\) | |||||||
\(278\) | 112482. | 0.0872917 | ||||||||
\(279\) | 380495. | 0.292643 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 527403. | 0.398453 | 0.199226 | − | 0.979953i | \(-0.436157\pi\) | ||||
0.199226 | + | 0.979953i | \(0.436157\pi\) | |||||||
\(282\) | −10715.7 | −0.00802410 | ||||||||
\(283\) | −563399. | −0.418167 | −0.209084 | − | 0.977898i | \(-0.567048\pi\) | ||||
−0.209084 | + | 0.977898i | \(0.567048\pi\) | |||||||
\(284\) | −1.09099e6 | −0.802650 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 123073. | 0.0889711 | ||||||||
\(287\) | −3.35880e6 | −2.40702 | ||||||||
\(288\) | −402842. | −0.286189 | ||||||||
\(289\) | 335478. | 0.236276 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50211e6 | −1.03984 | ||||||||
\(292\) | −1.14965e6 | −0.789058 | ||||||||
\(293\) | −1.31300e6 | −0.893505 | −0.446753 | − | 0.894657i | \(-0.647420\pi\) | ||||
−0.446753 | + | 0.894657i | \(0.647420\pi\) | |||||||
\(294\) | −341836. | −0.230648 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −947481. | −0.628552 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 429055. | 0.279880 | ||||||||
\(299\) | −2.21483e6 | −1.43272 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14186e6 | 0.726436 | ||||||||
\(302\) | −439070. | −0.277023 | ||||||||
\(303\) | 166449. | 0.104154 | ||||||||
\(304\) | −631896. | −0.392159 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 203274. | 0.124102 | ||||||||
\(307\) | −2.59454e6 | −1.57114 | −0.785570 | − | 0.618773i | \(-0.787630\pi\) | ||||
−0.785570 | + | 0.618773i | \(0.787630\pi\) | |||||||
\(308\) | 660027. | 0.396447 | ||||||||
\(309\) | 800926. | 0.477196 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −68979.7 | −0.0404408 | −0.0202204 | − | 0.999796i | \(-0.506437\pi\) | ||||
−0.0202204 | + | 0.999796i | \(0.506437\pi\) | |||||||
\(312\) | 553026. | 0.321632 | ||||||||
\(313\) | −2.10415e6 | −1.21399 | −0.606996 | − | 0.794705i | \(-0.707626\pi\) | ||||
−0.606996 | + | 0.794705i | \(0.707626\pi\) | |||||||
\(314\) | 372008. | 0.212926 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 777323. | 0.437909 | ||||||||
\(317\) | −3.32293e6 | −1.85726 | −0.928632 | − | 0.371003i | \(-0.879014\pi\) | ||||
−0.928632 | + | 0.371003i | \(0.879014\pi\) | |||||||
\(318\) | 288993. | 0.160258 | ||||||||
\(319\) | −41199.2 | −0.0226680 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.01070e6 | 0.547472 | ||||||||
\(322\) | 1.49991e6 | 0.806169 | ||||||||
\(323\) | 1.20905e6 | 0.644818 | ||||||||
\(324\) | −186412. | −0.0986533 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.14572e6 | 0.597081 | ||||||||
\(327\) | −1.74728e6 | −0.903633 | ||||||||
\(328\) | −2.00195e6 | −1.02747 | ||||||||
\(329\) | 120679. | 0.0614671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.65460e6 | −1.33177 | −0.665886 | − | 0.746054i | \(-0.731946\pi\) | ||||
−0.665886 | + | 0.746054i | \(0.731946\pi\) | |||||||
\(332\) | 1.47226e6 | 0.733061 | ||||||||
\(333\) | −670679. | −0.331439 | ||||||||
\(334\) | −265957. | −0.130451 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.19646e6 | 0.578160 | ||||||||
\(337\) | −1.56818e6 | −0.752179 | −0.376089 | − | 0.926583i | \(-0.622731\pi\) | ||||
−0.376089 | + | 0.926583i | \(0.622731\pi\) | |||||||
\(338\) | 157102. | 0.0747980 | ||||||||
\(339\) | −38438.3 | −0.0181662 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −568394. | −0.264706 | ||||||||
\(342\) | 140012. | 0.0647291 | ||||||||
\(343\) | 623002. | 0.285926 | ||||||||
\(344\) | 680585. | 0.310089 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −668475. | −0.300189 | ||||||||
\(347\) | 3.47302e6 | 1.54840 | 0.774202 | − | 0.632939i | \(-0.218152\pi\) | ||||
0.774202 | + | 0.632939i | \(0.218152\pi\) | |||||||
\(348\) | −87066.4 | −0.0385392 | ||||||||
\(349\) | 1.54641e6 | 0.679611 | 0.339805 | − | 0.940496i | \(-0.389639\pi\) | ||||
0.339805 | + | 0.940496i | \(0.389639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 391462. | 0.169598 | ||||||||
\(352\) | 601777. | 0.258868 | ||||||||
\(353\) | −1.08681e6 | −0.464214 | −0.232107 | − | 0.972690i | \(-0.574562\pi\) | ||||
−0.232107 | + | 0.972690i | \(0.574562\pi\) | |||||||
\(354\) | 484262. | 0.205387 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −574358. | −0.240192 | ||||||||
\(357\) | −2.28926e6 | −0.950657 | ||||||||
\(358\) | 1.48533e6 | 0.612512 | ||||||||
\(359\) | −1.38446e6 | −0.566948 | −0.283474 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283474 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.64333e6 | −0.663675 | ||||||||
\(362\) | 4796.62 | 0.00192382 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −2.92913e6 | −1.15874 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −878117. | −0.342649 | ||||||||
\(367\) | 3.09462e6 | 1.19934 | 0.599669 | − | 0.800248i | \(-0.295299\pi\) | ||||
0.599669 | + | 0.800248i | \(0.295299\pi\) | |||||||
\(368\) | −2.85601e6 | −1.09936 | ||||||||
\(369\) | −1.41709e6 | −0.541791 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.25462e6 | −1.22762 | ||||||||
\(372\) | −1.20119e6 | −0.450043 | ||||||||
\(373\) | 3.81239e6 | 1.41881 | 0.709407 | − | 0.704799i | \(-0.248963\pi\) | ||||
0.709407 | + | 0.704799i | \(0.248963\pi\) | |||||||
\(374\) | −303656. | −0.112254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 71928.5 | 0.0262380 | ||||||||
\(377\) | 182838. | 0.0662541 | ||||||||
\(378\) | −265104. | −0.0954303 | ||||||||
\(379\) | −1.79432e6 | −0.641656 | −0.320828 | − | 0.947138i | \(-0.603961\pi\) | ||||
−0.320828 | + | 0.947138i | \(0.603961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.04422e6 | −1.07439 | ||||||||
\(382\) | −350875. | −0.123025 | ||||||||
\(383\) | −1.79578e6 | −0.625541 | −0.312771 | − | 0.949829i | \(-0.601257\pi\) | ||||
−0.312771 | + | 0.949829i | \(0.601257\pi\) | |||||||
\(384\) | 1.64947e6 | 0.570844 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −992202. | −0.338947 | ||||||||
\(387\) | 481755. | 0.163512 | ||||||||
\(388\) | 4.74201e6 | 1.59913 | ||||||||
\(389\) | 3.20505e6 | 1.07389 | 0.536946 | − | 0.843617i | \(-0.319578\pi\) | ||||
0.536946 | + | 0.843617i | \(0.319578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.46459e6 | 1.80765 | ||||||||
\(392\) | 2.29456e6 | 0.754195 | ||||||||
\(393\) | −1.01990e6 | −0.333102 | ||||||||
\(394\) | 316319. | 0.102656 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 278468. | 0.0892353 | ||||||||
\(397\) | −5.06822e6 | −1.61391 | −0.806954 | − | 0.590614i | \(-0.798886\pi\) | ||||
−0.806954 | + | 0.590614i | \(0.798886\pi\) | |||||||
\(398\) | 1.35492e6 | 0.428751 | ||||||||
\(399\) | −1.57680e6 | −0.495845 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.04243e6 | −1.56595 | −0.782977 | − | 0.622051i | \(-0.786300\pi\) | ||||
−0.782977 | + | 0.622051i | \(0.786300\pi\) | |||||||
\(402\) | −260110. | −0.0802770 | ||||||||
\(403\) | 2.52247e6 | 0.773684 | ||||||||
\(404\) | −525465. | −0.160173 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −123820. | −0.0372801 | ||||||||
\(407\) | 1.00188e6 | 0.299798 | ||||||||
\(408\) | −1.36447e6 | −0.405801 | ||||||||
\(409\) | −6.11825e6 | −1.80850 | −0.904252 | − | 0.427000i | \(-0.859570\pi\) | ||||
−0.904252 | + | 0.427000i | \(0.859570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 252315. | 0.0736782 | ||||||||
\(412\) | −2.52845e6 | −0.733857 | ||||||||
\(413\) | −5.45373e6 | −1.57333 | ||||||||
\(414\) | 632818. | 0.181459 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.67062e6 | −0.756621 | ||||||||
\(417\) | −534454. | −0.150512 | ||||||||
\(418\) | −209154. | −0.0585497 | ||||||||
\(419\) | 6.32243e6 | 1.75934 | 0.879669 | − | 0.475586i | \(-0.157764\pi\) | ||||
0.879669 | + | 0.475586i | \(0.157764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.04093e6 | 0.286232 | 0.143116 | − | 0.989706i | \(-0.454288\pi\) | ||||
0.143116 | + | 0.989706i | \(0.454288\pi\) | |||||||
\(422\) | −1.73859e6 | −0.475244 | ||||||||
\(423\) | 50914.9 | 0.0138355 | ||||||||
\(424\) | −1.93985e6 | −0.524028 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −654601. | −0.174764 | ||||||||
\(427\) | 9.88930e6 | 2.62480 | ||||||||
\(428\) | −3.19070e6 | −0.841931 | ||||||||
\(429\) | −584777. | −0.153408 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.82045e6 | 0.731349 | 0.365674 | − | 0.930743i | \(-0.380838\pi\) | ||||
0.365674 | + | 0.930743i | \(0.380838\pi\) | |||||||
\(432\) | 504789. | 0.130137 | ||||||||
\(433\) | 2.15739e6 | 0.552980 | 0.276490 | − | 0.961017i | \(-0.410829\pi\) | ||||
0.276490 | + | 0.961017i | \(0.410829\pi\) | |||||||
\(434\) | −1.70825e6 | −0.435340 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.51599e6 | 1.38966 | ||||||||
\(437\) | 3.76392e6 | 0.942839 | ||||||||
\(438\) | −689796. | −0.171805 | ||||||||
\(439\) | 4.60164e6 | 1.13960 | 0.569798 | − | 0.821785i | \(-0.307021\pi\) | ||||
0.569798 | + | 0.821785i | \(0.307021\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.62421e6 | 0.397692 | ||||||||
\(442\) | 1.34759e6 | 0.328097 | ||||||||
\(443\) | −5.03529e6 | −1.21903 | −0.609516 | − | 0.792774i | \(-0.708636\pi\) | ||||
−0.609516 | + | 0.792774i | \(0.708636\pi\) | |||||||
\(444\) | 2.11727e6 | 0.509705 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 123668. | 0.0294388 | ||||||||
\(447\) | −2.03863e6 | −0.482581 | ||||||||
\(448\) | −2.44548e6 | −0.575664 | ||||||||
\(449\) | −6.46043e6 | −1.51233 | −0.756163 | − | 0.654383i | \(-0.772928\pi\) | ||||
−0.756163 | + | 0.654383i | \(0.772928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.11689e6 | 0.490068 | ||||||||
\(452\) | 121346. | 0.0279370 | ||||||||
\(453\) | 2.08622e6 | 0.477655 | ||||||||
\(454\) | −1.05715e6 | −0.240712 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −939825. | −0.211658 | ||||||||
\(457\) | 4.15028e6 | 0.929580 | 0.464790 | − | 0.885421i | \(-0.346130\pi\) | ||||
0.464790 | + | 0.885421i | \(0.346130\pi\) | |||||||
\(458\) | −1.85637e6 | −0.413524 | ||||||||
\(459\) | −965845. | −0.213981 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.82145e6 | 0.618330 | 0.309165 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309165 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(462\) | 396019. | 0.0863200 | ||||||||
\(463\) | 2.16321e6 | 0.468971 | 0.234486 | − | 0.972120i | \(-0.424659\pi\) | ||||
0.234486 | + | 0.972120i | \(0.424659\pi\) | |||||||
\(464\) | 235769. | 0.0508383 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.51259e6 | −0.322668 | ||||||||
\(467\) | −1.87682e6 | −0.398226 | −0.199113 | − | 0.979977i | \(-0.563806\pi\) | ||||
−0.199113 | + | 0.979977i | \(0.563806\pi\) | |||||||
\(468\) | −1.23581e6 | −0.260818 | ||||||||
\(469\) | 2.92934e6 | 0.614946 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.76758e6 | −0.367135 | ||||||||
\(472\) | −3.25059e6 | −0.671595 | ||||||||
\(473\) | −719659. | −0.147902 | ||||||||
\(474\) | 466398. | 0.0953478 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.22697e6 | 1.46197 | ||||||||
\(477\) | −1.37313e6 | −0.276323 | ||||||||
\(478\) | 2.49686e6 | 0.499833 | ||||||||
\(479\) | −4.84619e6 | −0.965076 | −0.482538 | − | 0.875875i | \(-0.660285\pi\) | ||||
−0.482538 | + | 0.875875i | \(0.660285\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.44623e6 | −0.876252 | ||||||||
\(482\) | 2.03806e6 | 0.399575 | ||||||||
\(483\) | −7.12676e6 | −1.39003 | ||||||||
\(484\) | −415982. | −0.0807164 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −111848. | −0.0214802 | ||||||||
\(487\) | 9.13800e6 | 1.74594 | 0.872969 | − | 0.487776i | \(-0.162192\pi\) | ||||
0.872969 | + | 0.487776i | \(0.162192\pi\) | |||||||
\(488\) | 5.89433e6 | 1.12043 | ||||||||
\(489\) | −5.44382e6 | −1.02951 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.14270e6 | −0.962692 | −0.481346 | − | 0.876531i | \(-0.659852\pi\) | ||||
−0.481346 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(492\) | 4.47362e6 | 0.833195 | ||||||||
\(493\) | −451111. | −0.0835923 | ||||||||
\(494\) | 928201. | 0.171129 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.25272e6 | 0.593666 | ||||||||
\(497\) | 7.37207e6 | 1.33875 | ||||||||
\(498\) | 883365. | 0.159612 | ||||||||
\(499\) | 2.18975e6 | 0.393679 | 0.196840 | − | 0.980436i | \(-0.436932\pi\) | ||||
0.196840 | + | 0.980436i | \(0.436932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.26368e6 | 0.224928 | ||||||||
\(502\) | 1.54204e6 | 0.273110 | ||||||||
\(503\) | 2.77987e6 | 0.489897 | 0.244948 | − | 0.969536i | \(-0.421229\pi\) | ||||
0.244948 | + | 0.969536i | \(0.421229\pi\) | |||||||
\(504\) | 1.77950e6 | 0.312048 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −945321. | −0.164136 | ||||||||
\(507\) | −746462. | −0.128970 | ||||||||
\(508\) | 9.61031e6 | 1.65226 | ||||||||
\(509\) | 885490. | 0.151492 | 0.0757459 | − | 0.997127i | \(-0.475866\pi\) | ||||
0.0757459 | + | 0.997127i | \(0.475866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.76843e6 | 1.31608 | ||||||||
\(512\) | −5.97931e6 | −1.00804 | ||||||||
\(513\) | −665259. | −0.111609 | ||||||||
\(514\) | 3.58927e6 | 0.599236 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.52086e6 | −0.251457 | ||||||||
\(517\) | −76058.1 | −0.0125147 | ||||||||
\(518\) | 3.01105e6 | 0.493053 | ||||||||
\(519\) | 3.17622e6 | 0.517598 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.25668e6 | −0.525631 | −0.262816 | − | 0.964846i | \(-0.584651\pi\) | ||||
−0.262816 | + | 0.964846i | \(0.584651\pi\) | |||||||
\(522\) | −52240.3 | −0.00839130 | ||||||||
\(523\) | 2.14727e6 | 0.343268 | 0.171634 | − | 0.985161i | \(-0.445095\pi\) | ||||
0.171634 | + | 0.985161i | \(0.445095\pi\) | |||||||
\(524\) | 3.21974e6 | 0.512263 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.64574e6 | −0.416949 | ||||||||
\(527\) | −6.22363e6 | −0.976152 | ||||||||
\(528\) | −754067. | −0.117713 | ||||||||
\(529\) | 1.05756e7 | 1.64311 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.30095e6 | −0.354136 | ||||||||
\(532\) | 4.97783e6 | 0.762536 | ||||||||
\(533\) | −9.39453e6 | −1.43238 | ||||||||
\(534\) | −344618. | −0.0522979 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.74598e6 | 0.262498 | ||||||||
\(537\) | −7.05746e6 | −1.05612 | ||||||||
\(538\) | −2.00878e6 | −0.299211 | ||||||||
\(539\) | −2.42629e6 | −0.359726 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.92326e6 | 0.429412 | 0.214706 | − | 0.976679i | \(-0.431121\pi\) | ||||
0.214706 | + | 0.976679i | \(0.431121\pi\) | |||||||
\(542\) | 1.34585e6 | 0.196788 | ||||||||
\(543\) | −22790.9 | −0.00331712 | ||||||||
\(544\) | 6.58916e6 | 0.954625 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.75749e6 | −0.252297 | ||||||||
\(547\) | 9.05734e6 | 1.29429 | 0.647146 | − | 0.762366i | \(-0.275962\pi\) | ||||
0.647146 | + | 0.762366i | \(0.275962\pi\) | |||||||
\(548\) | −796535. | −0.113306 | ||||||||
\(549\) | 4.17233e6 | 0.590810 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −310719. | −0.0436002 | ||||||||
\(552\) | −4.24777e6 | −0.593353 | ||||||||
\(553\) | −5.25254e6 | −0.730393 | ||||||||
\(554\) | −1.28432e6 | −0.177787 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.68722e6 | 0.231465 | ||||||||
\(557\) | −9.32565e6 | −1.27362 | −0.636812 | − | 0.771019i | \(-0.719747\pi\) | ||||
−0.636812 | + | 0.771019i | \(0.719747\pi\) | |||||||
\(558\) | −720718. | −0.0979896 | ||||||||
\(559\) | 3.19377e6 | 0.432289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.44281e6 | 0.193553 | ||||||||
\(562\) | −998985. | −0.133419 | ||||||||
\(563\) | 1.27073e6 | 0.168960 | 0.0844798 | − | 0.996425i | \(-0.473077\pi\) | ||||
0.0844798 | + | 0.996425i | \(0.473077\pi\) | |||||||
\(564\) | −160734. | −0.0212769 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.06717e6 | 0.140020 | ||||||||
\(567\) | 1.25963e6 | 0.164545 | ||||||||
\(568\) | 4.39399e6 | 0.571463 | ||||||||
\(569\) | 7.32601e6 | 0.948608 | 0.474304 | − | 0.880361i | \(-0.342700\pi\) | ||||
0.474304 | + | 0.880361i | \(0.342700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.10876e7 | 1.42314 | 0.711569 | − | 0.702617i | \(-0.247985\pi\) | ||||
0.711569 | + | 0.702617i | \(0.247985\pi\) | |||||||
\(572\) | 1.84609e6 | 0.235918 | ||||||||
\(573\) | 1.66717e6 | 0.212125 | ||||||||
\(574\) | 6.36211e6 | 0.805975 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.03176e6 | −0.129575 | ||||||||
\(577\) | 3.23610e6 | 0.404653 | 0.202327 | − | 0.979318i | \(-0.435150\pi\) | ||||
0.202327 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(578\) | −635448. | −0.0791153 | ||||||||
\(579\) | 4.71440e6 | 0.584426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.94839e6 | −1.22268 | ||||||||
\(582\) | 2.84523e6 | 0.348185 | ||||||||
\(583\) | 2.05123e6 | 0.249944 | ||||||||
\(584\) | 4.63023e6 | 0.561785 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.48704e6 | 0.299184 | ||||||||
\(587\) | −9.64747e6 | −1.15563 | −0.577814 | − | 0.816168i | \(-0.696094\pi\) | ||||
−0.577814 | + | 0.816168i | \(0.696094\pi\) | |||||||
\(588\) | −5.12749e6 | −0.611592 | ||||||||
\(589\) | −4.28674e6 | −0.509142 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50298e6 | −0.177004 | ||||||||
\(592\) | −5.73339e6 | −0.672369 | ||||||||
\(593\) | −120468. | −0.0140681 | −0.00703406 | − | 0.999975i | \(-0.502239\pi\) | ||||
−0.00703406 | + | 0.999975i | \(0.502239\pi\) | |||||||
\(594\) | 167082. | 0.0194296 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.43578e6 | 0.742139 | ||||||||
\(597\) | −6.43783e6 | −0.739270 | ||||||||
\(598\) | 4.19523e6 | 0.479737 | ||||||||
\(599\) | 1.39130e7 | 1.58436 | 0.792178 | − | 0.610290i | \(-0.208947\pi\) | ||||
0.792178 | + | 0.610290i | \(0.208947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.27530e6 | 0.708677 | 0.354339 | − | 0.935117i | \(-0.384706\pi\) | ||||
0.354339 | + | 0.935117i | \(0.384706\pi\) | |||||||
\(602\) | −2.16287e6 | −0.243242 | ||||||||
\(603\) | 1.23590e6 | 0.138417 | ||||||||
\(604\) | −6.58600e6 | −0.734563 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −315281. | −0.0348752 | ||||||||
\(607\) | 7.85752e6 | 0.865593 | 0.432796 | − | 0.901492i | \(-0.357527\pi\) | ||||
0.432796 | + | 0.901492i | \(0.357527\pi\) | |||||||
\(608\) | 4.53851e6 | 0.497914 | ||||||||
\(609\) | 588326. | 0.0642799 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 337538. | 0.0365779 | ||||||||
\(612\) | 3.04908e6 | 0.329072 | ||||||||
\(613\) | −1.19554e7 | −1.28503 | −0.642514 | − | 0.766274i | \(-0.722109\pi\) | ||||
−0.642514 | + | 0.766274i | \(0.722109\pi\) | |||||||
\(614\) | 4.91447e6 | 0.526085 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.65826e6 | −0.282258 | ||||||||
\(617\) | 8.19632e6 | 0.866774 | 0.433387 | − | 0.901208i | \(-0.357318\pi\) | ||||
0.433387 | + | 0.901208i | \(0.357318\pi\) | |||||||
\(618\) | −1.51708e6 | −0.159786 | ||||||||
\(619\) | −3.47785e6 | −0.364824 | −0.182412 | − | 0.983222i | \(-0.558390\pi\) | ||||
−0.182412 | + | 0.983222i | \(0.558390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00680e6 | −0.312879 | ||||||||
\(622\) | 130658. | 0.0135413 | ||||||||
\(623\) | 3.88106e6 | 0.400618 | ||||||||
\(624\) | 3.34647e6 | 0.344053 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.98560e6 | 0.406497 | ||||||||
\(627\) | 993783. | 0.100954 | ||||||||
\(628\) | 5.58008e6 | 0.564601 | ||||||||
\(629\) | 1.09701e7 | 1.10556 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.07592e6 | 0.107574 | 0.0537868 | − | 0.998552i | \(-0.482871\pi\) | ||||
0.0537868 | + | 0.998552i | \(0.482871\pi\) | |||||||
\(632\) | −3.13068e6 | −0.311778 | ||||||||
\(633\) | 8.26083e6 | 0.819435 | ||||||||
\(634\) | 6.29416e6 | 0.621892 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.33486e6 | 0.424944 | ||||||||
\(637\) | 1.07676e7 | 1.05141 | ||||||||
\(638\) | 78037.9 | 0.00759021 | ||||||||
\(639\) | 3.11030e6 | 0.301336 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.30837e7 | 1.25772 | 0.628862 | − | 0.777517i | \(-0.283521\pi\) | ||||
0.628862 | + | 0.777517i | \(0.283521\pi\) | |||||||
\(642\) | −1.91443e6 | −0.183317 | ||||||||
\(643\) | −7.84966e6 | −0.748727 | −0.374363 | − | 0.927282i | \(-0.622139\pi\) | ||||
−0.374363 | + | 0.927282i | \(0.622139\pi\) | |||||||
\(644\) | 2.24985e7 | 2.13766 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.29013e6 | −0.215913 | ||||||||
\(647\) | 2.02801e7 | 1.90463 | 0.952313 | − | 0.305123i | \(-0.0986976\pi\) | ||||
0.952313 | + | 0.305123i | \(0.0986976\pi\) | |||||||
\(648\) | 750777. | 0.0702382 | ||||||||
\(649\) | 3.43722e6 | 0.320328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.11668e6 | 0.750630 | ||||||||
\(652\) | 1.71856e7 | 1.58324 | ||||||||
\(653\) | −1.04023e7 | −0.954655 | −0.477328 | − | 0.878725i | \(-0.658394\pi\) | ||||
−0.477328 | + | 0.878725i | \(0.658394\pi\) | |||||||
\(654\) | 3.30962e6 | 0.302575 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.21142e7 | −1.09910 | ||||||||
\(657\) | 3.27753e6 | 0.296233 | ||||||||
\(658\) | −228585. | −0.0205818 | ||||||||
\(659\) | −1.05552e7 | −0.946785 | −0.473392 | − | 0.880852i | \(-0.656971\pi\) | ||||
−0.473392 | + | 0.880852i | \(0.656971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.20388e6 | −0.374237 | −0.187119 | − | 0.982337i | \(-0.559915\pi\) | ||||
−0.187119 | + | 0.982337i | \(0.559915\pi\) | |||||||
\(662\) | 5.02824e6 | 0.445935 | ||||||||
\(663\) | −6.40302e6 | −0.565719 | ||||||||
\(664\) | −5.92955e6 | −0.521917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.27037e6 | 0.110980 | ||||||||
\(667\) | −1.40437e6 | −0.122227 | ||||||||
\(668\) | −3.98933e6 | −0.345906 | ||||||||
\(669\) | −587602. | −0.0507596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.23274e6 | −0.534407 | ||||||||
\(672\) | −8.59339e6 | −0.734076 | ||||||||
\(673\) | −1.41220e7 | −1.20187 | −0.600935 | − | 0.799298i | \(-0.705205\pi\) | ||||
−0.600935 | + | 0.799298i | \(0.705205\pi\) | |||||||
\(674\) | 2.97038e6 | 0.251862 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.35651e6 | 0.198336 | ||||||||
\(677\) | −6.70088e6 | −0.561901 | −0.280951 | − | 0.959722i | \(-0.590650\pi\) | ||||
−0.280951 | + | 0.959722i | \(0.590650\pi\) | |||||||
\(678\) | 72808.2 | 0.00608283 | ||||||||
\(679\) | −3.20428e7 | −2.66720 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.02299e6 | 0.415045 | ||||||||
\(682\) | 1.07663e6 | 0.0886350 | ||||||||
\(683\) | 7.21441e6 | 0.591765 | 0.295882 | − | 0.955224i | \(-0.404386\pi\) | ||||
0.295882 | + | 0.955224i | \(0.404386\pi\) | |||||||
\(684\) | 2.10016e6 | 0.171638 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.18007e6 | −0.0957405 | ||||||||
\(687\) | 8.82045e6 | 0.713016 | ||||||||
\(688\) | 4.11835e6 | 0.331705 | ||||||||
\(689\) | −9.10312e6 | −0.730537 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.64521e6 | −0.609108 | −0.304554 | − | 0.952495i | \(-0.598507\pi\) | ||||
−0.304554 | + | 0.952495i | \(0.598507\pi\) | |||||||
\(692\) | −1.00270e7 | −0.795990 | ||||||||
\(693\) | −1.88166e6 | −0.148836 | ||||||||
\(694\) | −6.57846e6 | −0.518472 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 350661. | 0.0274387 | ||||||||
\(697\) | 2.31789e7 | 1.80722 | ||||||||
\(698\) | −2.92914e6 | −0.227563 | ||||||||
\(699\) | 7.18699e6 | 0.556358 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.16637e6 | 0.473952 | 0.236976 | − | 0.971515i | \(-0.423844\pi\) | ||||
0.236976 | + | 0.971515i | \(0.423844\pi\) | |||||||
\(702\) | −741491. | −0.0567889 | ||||||||
\(703\) | 7.55602e6 | 0.576640 | ||||||||
\(704\) | 1.54127e6 | 0.117205 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.05860e6 | 0.155439 | ||||||||
\(707\) | 3.55068e6 | 0.267155 | ||||||||
\(708\) | 7.26388e6 | 0.544610 | ||||||||
\(709\) | −1.96108e7 | −1.46514 | −0.732571 | − | 0.680691i | \(-0.761680\pi\) | ||||
−0.732571 | + | 0.680691i | \(0.761680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.21606e6 | −0.164402 | ||||||||
\(712\) | 2.31323e6 | 0.171009 | ||||||||
\(713\) | −1.93750e7 | −1.42731 | ||||||||
\(714\) | 4.33622e6 | 0.318321 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.22797e7 | 1.62415 | ||||||||
\(717\) | −1.18637e7 | −0.861833 | ||||||||
\(718\) | 2.62238e6 | 0.189839 | ||||||||
\(719\) | −8.44447e6 | −0.609187 | −0.304593 | − | 0.952483i | \(-0.598521\pi\) | ||||
−0.304593 | + | 0.952483i | \(0.598521\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.70853e7 | 1.22401 | ||||||||
\(722\) | 3.11272e6 | 0.222227 | ||||||||
\(723\) | −9.68372e6 | −0.688964 | ||||||||
\(724\) | 71948.7 | 0.00510125 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −249591. | −0.0175747 | ||||||||
\(727\) | 2.39210e7 | 1.67858 | 0.839291 | − | 0.543682i | \(-0.182970\pi\) | ||||
0.839291 | + | 0.543682i | \(0.182970\pi\) | |||||||
\(728\) | 1.17971e7 | 0.824986 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.87991e6 | −0.545416 | ||||||||
\(732\) | −1.31717e7 | −0.908579 | ||||||||
\(733\) | −1.40807e7 | −0.967973 | −0.483986 | − | 0.875076i | \(-0.660812\pi\) | ||||
−0.483986 | + | 0.875076i | \(0.660812\pi\) | |||||||
\(734\) | −5.86170e6 | −0.401590 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.05129e7 | 1.39583 | ||||||||
\(737\) | −1.84622e6 | −0.125203 | ||||||||
\(738\) | 2.68420e6 | 0.181415 | ||||||||
\(739\) | −1.14610e7 | −0.771987 | −0.385993 | − | 0.922502i | \(-0.626141\pi\) | ||||
−0.385993 | + | 0.922502i | \(0.626141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.41030e6 | −0.295068 | ||||||||
\(742\) | 6.16476e6 | 0.411061 | ||||||||
\(743\) | −2.82841e7 | −1.87962 | −0.939810 | − | 0.341698i | \(-0.888998\pi\) | ||||
−0.939810 | + | 0.341698i | \(0.888998\pi\) | |||||||
\(744\) | 4.83780e6 | 0.320417 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.22128e6 | −0.475081 | ||||||||
\(747\) | −4.19726e6 | −0.275210 | ||||||||
\(748\) | −4.55480e6 | −0.297657 | ||||||||
\(749\) | 2.15602e7 | 1.40426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.65142e7 | −1.06846 | −0.534228 | − | 0.845340i | \(-0.679398\pi\) | ||||
−0.534228 | + | 0.845340i | \(0.679398\pi\) | |||||||
\(752\) | 435254. | 0.0280671 | ||||||||
\(753\) | −7.32694e6 | −0.470907 | ||||||||
\(754\) | −346324. | −0.0221847 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.97652e6 | −0.253046 | ||||||||
\(757\) | 1.68113e7 | 1.06626 | 0.533128 | − | 0.846034i | \(-0.321016\pi\) | ||||
0.533128 | + | 0.846034i | \(0.321016\pi\) | |||||||
\(758\) | 3.39873e6 | 0.214854 | ||||||||
\(759\) | 4.49164e6 | 0.283009 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 391721. | 0.0245197 | 0.0122598 | − | 0.999925i | \(-0.496097\pi\) | ||||
0.0122598 | + | 0.999925i | \(0.496097\pi\) | |||||||
\(762\) | 5.76623e6 | 0.359753 | ||||||||
\(763\) | −3.72727e7 | −2.31782 | ||||||||
\(764\) | −5.26308e6 | −0.326217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.40149e6 | 0.209458 | ||||||||
\(767\) | −1.52540e7 | −0.936258 | ||||||||
\(768\) | 544105. | 0.0332874 | ||||||||
\(769\) | 2.68596e7 | 1.63789 | 0.818944 | − | 0.573874i | \(-0.194560\pi\) | ||||
0.818944 | + | 0.573874i | \(0.194560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.70542e7 | −1.03323 | ||||||||
\(772\) | −1.48829e7 | −0.898762 | ||||||||
\(773\) | 1.65258e7 | 0.994748 | 0.497374 | − | 0.867536i | \(-0.334298\pi\) | ||||
0.497374 | + | 0.867536i | \(0.334298\pi\) | |||||||
\(774\) | −912521. | −0.0547508 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.90985e7 | −1.13853 | ||||||||
\(777\) | −1.43069e7 | −0.850142 | ||||||||
\(778\) | −6.07087e6 | −0.359585 | ||||||||
\(779\) | 1.59653e7 | 0.942611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.64626e6 | −0.272568 | ||||||||
\(782\) | −1.03508e7 | −0.605281 | ||||||||
\(783\) | 248217. | 0.0144686 | ||||||||
\(784\) | 1.38848e7 | 0.806771 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.93186e6 | 0.111537 | ||||||||
\(787\) | −368901. | −0.0212311 | −0.0106155 | − | 0.999944i | \(-0.503379\pi\) | ||||
−0.0106155 | + | 0.999944i | \(0.503379\pi\) | |||||||
\(788\) | 4.74475e6 | 0.272206 | ||||||||
\(789\) | 1.25711e7 | 0.718921 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −819961. | −0.0465963 | ||||||||
\(792\) | −1.12153e6 | −0.0635328 | ||||||||
\(793\) | 2.76602e7 | 1.56197 | ||||||||
\(794\) | 9.60001e6 | 0.540406 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.03236e7 | 1.13689 | ||||||||
\(797\) | 1.03717e7 | 0.578370 | 0.289185 | − | 0.957273i | \(-0.406616\pi\) | ||||
0.289185 | + | 0.957273i | \(0.406616\pi\) | |||||||
\(798\) | 2.98672e6 | 0.166030 | ||||||||
\(799\) | −832799. | −0.0461502 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.63743e6 | 0.0901742 | ||||||||
\(802\) | 9.55117e6 | 0.524349 | ||||||||
\(803\) | −4.89606e6 | −0.267953 | ||||||||
\(804\) | −3.90161e6 | −0.212865 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.77796e6 | −0.259063 | ||||||||
\(807\) | 9.54463e6 | 0.515912 | ||||||||
\(808\) | 2.11631e6 | 0.114039 | ||||||||
\(809\) | −2.51123e7 | −1.34901 | −0.674505 | − | 0.738271i | \(-0.735643\pi\) | ||||
−0.674505 | + | 0.738271i | \(0.735643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14510e7 | −0.611350 | −0.305675 | − | 0.952136i | \(-0.598882\pi\) | ||||
−0.305675 | + | 0.952136i | \(0.598882\pi\) | |||||||
\(812\) | −1.85729e6 | −0.0988530 | ||||||||
\(813\) | −6.39474e6 | −0.339310 | ||||||||
\(814\) | −1.89772e6 | −0.100385 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.25666e6 | −0.434089 | ||||||||
\(817\) | −5.42756e6 | −0.284479 | ||||||||
\(818\) | 1.15889e7 | 0.605565 | ||||||||
\(819\) | 8.35063e6 | 0.435020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.48065e7 | −0.766646 | −0.383323 | − | 0.923614i | \(-0.625220\pi\) | ||||
−0.383323 | + | 0.923614i | \(0.625220\pi\) | |||||||
\(822\) | −477925. | −0.0246706 | ||||||||
\(823\) | −2.56659e6 | −0.132086 | −0.0660430 | − | 0.997817i | \(-0.521037\pi\) | ||||
−0.0660430 | + | 0.997817i | \(0.521037\pi\) | |||||||
\(824\) | 1.01834e7 | 0.522484 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.03302e7 | 0.526817 | ||||||||
\(827\) | −3.42288e7 | −1.74032 | −0.870159 | − | 0.492772i | \(-0.835984\pi\) | ||||
−0.870159 | + | 0.492772i | \(0.835984\pi\) | |||||||
\(828\) | 9.49220e6 | 0.481162 | ||||||||
\(829\) | 7.49591e6 | 0.378824 | 0.189412 | − | 0.981898i | \(-0.439342\pi\) | ||||
0.189412 | + | 0.981898i | \(0.439342\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.10238e6 | 0.306547 | ||||||||
\(832\) | −6.83998e6 | −0.342568 | ||||||||
\(833\) | −2.65667e7 | −1.32656 | ||||||||
\(834\) | 1.01234e6 | 0.0503979 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.13728e6 | −0.155252 | ||||||||
\(837\) | 3.42446e6 | 0.168958 | ||||||||
\(838\) | −1.19757e7 | −0.589102 | ||||||||
\(839\) | 2.91814e7 | 1.43120 | 0.715601 | − | 0.698509i | \(-0.246153\pi\) | ||||
0.715601 | + | 0.698509i | \(0.246153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03952e7 | −0.994348 | ||||||||
\(842\) | −1.97169e6 | −0.0958427 | ||||||||
\(843\) | 4.74663e6 | 0.230047 | ||||||||
\(844\) | −2.60787e7 | −1.26017 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −96441.0 | −0.00463272 | ||||||||
\(847\) | 2.81088e6 | 0.134628 | ||||||||
\(848\) | −1.17384e7 | −0.560558 | ||||||||
\(849\) | −5.07059e6 | −0.241429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.41513e7 | 1.61653 | ||||||||
\(852\) | −9.81894e6 | −0.463410 | ||||||||
\(853\) | 265247. | 0.0124818 | 0.00624091 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624091 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(854\) | −1.87319e7 | −0.878895 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.28506e7 | 0.599429 | ||||||||
\(857\) | −2.09223e7 | −0.973102 | −0.486551 | − | 0.873652i | \(-0.661745\pi\) | ||||
−0.486551 | + | 0.873652i | \(0.661745\pi\) | |||||||
\(858\) | 1.10766e6 | 0.0513675 | ||||||||
\(859\) | −3.16166e7 | −1.46195 | −0.730976 | − | 0.682404i | \(-0.760935\pi\) | ||||
−0.730976 | + | 0.682404i | \(0.760935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.02292e7 | −1.38969 | ||||||||
\(862\) | −5.34237e6 | −0.244887 | ||||||||
\(863\) | 3.04614e7 | 1.39227 | 0.696133 | − | 0.717913i | \(-0.254902\pi\) | ||||
0.696133 | + | 0.717913i | \(0.254902\pi\) | |||||||
\(864\) | −3.62558e6 | −0.165232 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.08645e6 | −0.185162 | ||||||||
\(867\) | 3.01930e6 | 0.136414 | ||||||||
\(868\) | −2.56236e7 | −1.15436 | ||||||||
\(869\) | 3.31042e6 | 0.148708 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.19331e6 | 0.365944 | ||||||||
\(872\) | −2.22157e7 | −0.989393 | ||||||||
\(873\) | −1.35190e7 | −0.600354 | ||||||||
\(874\) | −7.12947e6 | −0.315703 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.03469e7 | −0.455563 | ||||||||
\(877\) | 3.21784e6 | 0.141275 | 0.0706376 | − | 0.997502i | \(-0.477497\pi\) | ||||
0.0706376 | + | 0.997502i | \(0.477497\pi\) | |||||||
\(878\) | −8.71623e6 | −0.381586 | ||||||||
\(879\) | −1.18170e7 | −0.515866 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.71105e7 | −1.17679 | −0.588394 | − | 0.808574i | \(-0.700240\pi\) | ||||
−0.588394 | + | 0.808574i | \(0.700240\pi\) | |||||||
\(882\) | −3.07652e6 | −0.133164 | ||||||||
\(883\) | 7.92568e6 | 0.342086 | 0.171043 | − | 0.985264i | \(-0.445286\pi\) | ||||
0.171043 | + | 0.985264i | \(0.445286\pi\) | |||||||
\(884\) | 2.02137e7 | 0.869993 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.53764e6 | 0.408185 | ||||||||
\(887\) | 2.02221e7 | 0.863011 | 0.431506 | − | 0.902110i | \(-0.357983\pi\) | ||||
0.431506 | + | 0.902110i | \(0.357983\pi\) | |||||||
\(888\) | −8.52733e6 | −0.362895 | ||||||||
\(889\) | −6.49389e7 | −2.75582 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 1.85501e6 | 0.0780608 | ||||||||
\(893\) | −573619. | −0.0240711 | ||||||||
\(894\) | 3.86150e6 | 0.161589 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.51864e7 | 1.46421 | ||||||||
\(897\) | −1.99334e7 | −0.827182 | ||||||||
\(898\) | 1.22371e7 | 0.506392 | ||||||||
\(899\) | 1.59944e6 | 0.0660038 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.24599e7 | 0.921714 | ||||||||
\(902\) | −4.00973e6 | −0.164096 | ||||||||
\(903\) | 1.02768e7 | 0.419408 | ||||||||
\(904\) | −488722. | −0.0198903 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.95163e6 | −0.159940 | ||||||||
\(907\) | 7.88692e6 | 0.318338 | 0.159169 | − | 0.987251i | \(-0.449118\pi\) | ||||
0.159169 | + | 0.987251i | \(0.449118\pi\) | |||||||
\(908\) | −1.58571e7 | −0.638278 | ||||||||
\(909\) | 1.49804e6 | 0.0601332 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.12818e6 | −0.244644 | −0.122322 | − | 0.992490i | \(-0.539034\pi\) | ||||
−0.122322 | + | 0.992490i | \(0.539034\pi\) | |||||||
\(912\) | −5.68706e6 | −0.226413 | ||||||||
\(913\) | 6.26998e6 | 0.248937 | ||||||||
\(914\) | −7.86129e6 | −0.311264 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.78453e7 | −1.09651 | ||||||||
\(917\) | −2.17565e7 | −0.854408 | ||||||||
\(918\) | 1.82946e6 | 0.0716502 | ||||||||
\(919\) | 2.38050e7 | 0.929779 | 0.464890 | − | 0.885369i | \(-0.346094\pi\) | ||||
0.464890 | + | 0.885369i | \(0.346094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.33509e7 | −0.907098 | ||||||||
\(922\) | −5.34428e6 | −0.207044 | ||||||||
\(923\) | 2.06196e7 | 0.796665 | ||||||||
\(924\) | 5.94024e6 | 0.228889 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.09746e6 | −0.157032 | ||||||||
\(927\) | 7.20834e6 | 0.275509 | ||||||||
\(928\) | −1.69338e6 | −0.0645481 | ||||||||
\(929\) | 3.89856e7 | 1.48206 | 0.741028 | − | 0.671474i | \(-0.234339\pi\) | ||||
0.741028 | + | 0.671474i | \(0.234339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.82988e7 | −0.691907 | ||||||||
\(932\) | −2.26887e7 | −0.855596 | ||||||||
\(933\) | −620817. | −0.0233485 | ||||||||
\(934\) | 3.55499e6 | 0.133343 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.97723e6 | 0.185694 | ||||||||
\(937\) | −1.66079e7 | −0.617967 | −0.308983 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308983 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(938\) | −5.54863e6 | −0.205911 | ||||||||
\(939\) | −1.89374e7 | −0.700899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.15988e7 | −0.795161 | −0.397581 | − | 0.917567i | \(-0.630150\pi\) | ||||
−0.397581 | + | 0.917567i | \(0.630150\pi\) | |||||||
\(942\) | 3.34807e6 | 0.122933 | ||||||||
\(943\) | 7.21589e7 | 2.64248 | ||||||||
\(944\) | −1.96700e7 | −0.718412 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.36315e6 | 0.0495240 | ||||||||
\(947\) | 4.65688e7 | 1.68741 | 0.843705 | − | 0.536808i | \(-0.180370\pi\) | ||||
0.843705 | + | 0.536808i | \(0.180370\pi\) | |||||||
\(948\) | 6.99591e6 | 0.252827 | ||||||||
\(949\) | 2.17282e7 | 0.783174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.99064e7 | −1.07229 | ||||||||
\(952\) | −2.91067e7 | −1.04088 | ||||||||
\(953\) | 2.71746e7 | 0.969240 | 0.484620 | − | 0.874725i | \(-0.338958\pi\) | ||||
0.484620 | + | 0.874725i | \(0.338958\pi\) | |||||||
\(954\) | 2.60094e6 | 0.0925249 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.74527e7 | 1.32537 | ||||||||
\(957\) | −370793. | −0.0130874 | ||||||||
\(958\) | 9.17946e6 | 0.323149 | ||||||||
\(959\) | 5.38236e6 | 0.188985 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.56292e6 | −0.229239 | ||||||||
\(962\) | 8.42186e6 | 0.293407 | ||||||||
\(963\) | 9.09634e6 | 0.316083 | ||||||||
\(964\) | 3.05706e7 | 1.05953 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.34992e7 | 0.465442 | ||||||||
\(967\) | −2.23871e6 | −0.0769897 | −0.0384948 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384948 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(968\) | 1.67537e6 | 0.0574676 | ||||||||
\(969\) | 1.08814e7 | 0.372286 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.25051e7 | −0.425638 | −0.212819 | − | 0.977092i | \(-0.568264\pi\) | ||||
−0.212819 | + | 0.977092i | \(0.568264\pi\) | |||||||
\(972\) | −1.67771e6 | −0.0569575 | ||||||||
\(973\) | −1.14009e7 | −0.386063 | ||||||||
\(974\) | −1.73088e7 | −0.584616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.56677e7 | 1.19854 | ||||||||
\(977\) | 5.79995e7 | 1.94396 | 0.971982 | − | 0.235056i | \(-0.0755275\pi\) | ||||
0.971982 | + | 0.235056i | \(0.0755275\pi\) | |||||||
\(978\) | 1.03115e7 | 0.344725 | ||||||||
\(979\) | −2.44604e6 | −0.0815656 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.57255e7 | −0.521713 | ||||||||
\(982\) | 9.74109e6 | 0.322351 | ||||||||
\(983\) | 3.40518e7 | 1.12397 | 0.561987 | − | 0.827146i | \(-0.310037\pi\) | ||||
0.561987 | + | 0.827146i | \(0.310037\pi\) | |||||||
\(984\) | −1.80176e7 | −0.593210 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 854477. | 0.0279903 | ||||||||
\(987\) | 1.08611e6 | 0.0354880 | ||||||||
\(988\) | 1.39229e7 | 0.453772 | ||||||||
\(989\) | −2.45312e7 | −0.797495 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.08858e7 | 0.675565 | 0.337782 | − | 0.941224i | \(-0.390323\pi\) | ||||
0.337782 | + | 0.941224i | \(0.390323\pi\) | |||||||
\(992\) | −2.33622e7 | −0.753763 | ||||||||
\(993\) | −2.38914e7 | −0.768899 | ||||||||
\(994\) | −1.39639e7 | −0.448271 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.32504e7 | 0.423233 | ||||||||
\(997\) | 3.35610e7 | 1.06929 | 0.534646 | − | 0.845076i | \(-0.320445\pi\) | ||||
0.534646 | + | 0.845076i | \(0.320445\pi\) | |||||||
\(998\) | −4.14773e6 | −0.131821 | ||||||||
\(999\) | −6.03611e6 | −0.191357 |
(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 | 825.6.a.p.1.4 | ✓ | 8 | |
5.4 | even | 2 | 825.6.a.q.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.p.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
825.6.a.q.1.5 | yes | 8 | 5.4 | even | 2 |