Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,6,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.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: | \(115.797117905\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} + \cdots - 34\!\cdots\!72 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 19^{6} \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-27.8974\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −26.3653 | −1.69134 | −0.845669 | − | 0.533708i | \(-0.820798\pi\) | ||||
−0.845669 | + | 0.533708i | \(0.820798\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 84.5221 | 1.51198 | 0.755989 | − | 0.654584i | \(-0.227156\pi\) | ||||
0.755989 | + | 0.654584i | \(0.227156\pi\) | |||||||
\(6\) | 105.461 | 1.19596 | ||||||||
\(7\) | 15.2607 | 0.117715 | 0.0588573 | − | 0.998266i | \(-0.481254\pi\) | ||||
0.0588573 | + | 0.998266i | \(0.481254\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 452.132 | 1.86062 | ||||||||
\(10\) | −338.089 | −1.06913 | ||||||||
\(11\) | −450.397 | −1.12231 | −0.561156 | − | 0.827710i | \(-0.689643\pi\) | ||||
−0.561156 | + | 0.827710i | \(0.689643\pi\) | |||||||
\(12\) | −421.846 | −0.845669 | ||||||||
\(13\) | −802.449 | −1.31692 | −0.658459 | − | 0.752616i | \(-0.728791\pi\) | ||||
−0.658459 | + | 0.752616i | \(0.728791\pi\) | |||||||
\(14\) | −61.0429 | −0.0832368 | ||||||||
\(15\) | −2228.46 | −2.55727 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1330.28 | −1.11640 | −0.558200 | − | 0.829706i | \(-0.688508\pi\) | ||||
−0.558200 | + | 0.829706i | \(0.688508\pi\) | |||||||
\(18\) | −1808.53 | −1.31566 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1352.35 | 0.755989 | ||||||||
\(21\) | −402.354 | −0.199095 | ||||||||
\(22\) | 1801.59 | 0.793595 | ||||||||
\(23\) | 379.765 | 0.149691 | 0.0748455 | − | 0.997195i | \(-0.476154\pi\) | ||||
0.0748455 | + | 0.997195i | \(0.476154\pi\) | |||||||
\(24\) | 1687.38 | 0.597978 | ||||||||
\(25\) | 4018.99 | 1.28608 | ||||||||
\(26\) | 3209.79 | 0.931202 | ||||||||
\(27\) | −5513.83 | −1.45561 | ||||||||
\(28\) | 244.172 | 0.0588573 | ||||||||
\(29\) | −8332.67 | −1.83988 | −0.919939 | − | 0.392061i | \(-0.871762\pi\) | ||||
−0.919939 | + | 0.392061i | \(0.871762\pi\) | |||||||
\(30\) | 8913.82 | 1.80826 | ||||||||
\(31\) | 6687.09 | 1.24978 | 0.624889 | − | 0.780714i | \(-0.285144\pi\) | ||||
0.624889 | + | 0.780714i | \(0.285144\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 11874.9 | 1.89821 | ||||||||
\(34\) | 5321.11 | 0.789414 | ||||||||
\(35\) | 1289.87 | 0.177982 | ||||||||
\(36\) | 7234.11 | 0.930312 | ||||||||
\(37\) | 4855.55 | 0.583088 | 0.291544 | − | 0.956557i | \(-0.405831\pi\) | ||||
0.291544 | + | 0.956557i | \(0.405831\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 21156.8 | 2.22735 | ||||||||
\(40\) | −5409.42 | −0.534565 | ||||||||
\(41\) | −12578.2 | −1.16858 | −0.584292 | − | 0.811544i | \(-0.698628\pi\) | ||||
−0.584292 | + | 0.811544i | \(0.698628\pi\) | |||||||
\(42\) | 1609.42 | 0.140781 | ||||||||
\(43\) | 14725.8 | 1.21453 | 0.607264 | − | 0.794500i | \(-0.292267\pi\) | ||||
0.607264 | + | 0.794500i | \(0.292267\pi\) | |||||||
\(44\) | −7206.36 | −0.561156 | ||||||||
\(45\) | 38215.1 | 2.81322 | ||||||||
\(46\) | −1519.06 | −0.105847 | ||||||||
\(47\) | −12336.3 | −0.814591 | −0.407296 | − | 0.913296i | \(-0.633528\pi\) | ||||
−0.407296 | + | 0.913296i | \(0.633528\pi\) | |||||||
\(48\) | −6749.53 | −0.422834 | ||||||||
\(49\) | −16574.1 | −0.986143 | ||||||||
\(50\) | −16076.0 | −0.909394 | ||||||||
\(51\) | 35073.2 | 1.88821 | ||||||||
\(52\) | −12839.2 | −0.658459 | ||||||||
\(53\) | −1648.83 | −0.0806283 | −0.0403141 | − | 0.999187i | \(-0.512836\pi\) | ||||
−0.0403141 | + | 0.999187i | \(0.512836\pi\) | |||||||
\(54\) | 22055.3 | 1.02927 | ||||||||
\(55\) | −38068.5 | −1.69691 | ||||||||
\(56\) | −976.687 | −0.0416184 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 33330.7 | 1.30099 | ||||||||
\(59\) | −5537.16 | −0.207089 | −0.103544 | − | 0.994625i | \(-0.533018\pi\) | ||||
−0.103544 | + | 0.994625i | \(0.533018\pi\) | |||||||
\(60\) | −35655.3 | −1.27863 | ||||||||
\(61\) | 33618.4 | 1.15678 | 0.578392 | − | 0.815759i | \(-0.303681\pi\) | ||||
0.578392 | + | 0.815759i | \(0.303681\pi\) | |||||||
\(62\) | −26748.3 | −0.883726 | ||||||||
\(63\) | 6899.86 | 0.219023 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −67824.7 | −1.99115 | ||||||||
\(66\) | −47499.5 | −1.34224 | ||||||||
\(67\) | −1075.80 | −0.0292783 | −0.0146391 | − | 0.999893i | \(-0.504660\pi\) | ||||
−0.0146391 | + | 0.999893i | \(0.504660\pi\) | |||||||
\(68\) | −21284.4 | −0.558200 | ||||||||
\(69\) | −10012.6 | −0.253178 | ||||||||
\(70\) | −5159.48 | −0.125852 | ||||||||
\(71\) | −24655.4 | −0.580452 | −0.290226 | − | 0.956958i | \(-0.593730\pi\) | ||||
−0.290226 | + | 0.956958i | \(0.593730\pi\) | |||||||
\(72\) | −28936.4 | −0.657830 | ||||||||
\(73\) | −49796.7 | −1.09369 | −0.546844 | − | 0.837235i | \(-0.684171\pi\) | ||||
−0.546844 | + | 0.837235i | \(0.684171\pi\) | |||||||
\(74\) | −19422.2 | −0.412306 | ||||||||
\(75\) | −105962. | −2.17519 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6873.39 | −0.132113 | ||||||||
\(78\) | −84627.3 | −1.57498 | ||||||||
\(79\) | −30767.8 | −0.554663 | −0.277331 | − | 0.960774i | \(-0.589450\pi\) | ||||
−0.277331 | + | 0.960774i | \(0.589450\pi\) | |||||||
\(80\) | 21637.7 | 0.377994 | ||||||||
\(81\) | 35506.0 | 0.601297 | ||||||||
\(82\) | 50312.9 | 0.826313 | ||||||||
\(83\) | 37614.0 | 0.599314 | 0.299657 | − | 0.954047i | \(-0.403128\pi\) | ||||
0.299657 | + | 0.954047i | \(0.403128\pi\) | |||||||
\(84\) | −6437.67 | −0.0995476 | ||||||||
\(85\) | −112438. | −1.68797 | ||||||||
\(86\) | −58903.1 | −0.858800 | ||||||||
\(87\) | 219694. | 3.11186 | ||||||||
\(88\) | 28825.4 | 0.396798 | ||||||||
\(89\) | 92745.1 | 1.24113 | 0.620563 | − | 0.784156i | \(-0.286904\pi\) | ||||
0.620563 | + | 0.784156i | \(0.286904\pi\) | |||||||
\(90\) | −152861. | −1.98925 | ||||||||
\(91\) | −12246.0 | −0.155020 | ||||||||
\(92\) | 6076.24 | 0.0748455 | ||||||||
\(93\) | −176307. | −2.11380 | ||||||||
\(94\) | 49345.1 | 0.576003 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 26998.1 | 0.298989 | ||||||||
\(97\) | 114665. | 1.23738 | 0.618689 | − | 0.785636i | \(-0.287664\pi\) | ||||
0.618689 | + | 0.785636i | \(0.287664\pi\) | |||||||
\(98\) | 66296.4 | 0.697309 | ||||||||
\(99\) | −203639. | −2.08820 | ||||||||
\(100\) | 64303.9 | 0.643039 | ||||||||
\(101\) | −45228.4 | −0.441171 | −0.220586 | − | 0.975368i | \(-0.570797\pi\) | ||||
−0.220586 | + | 0.975368i | \(0.570797\pi\) | |||||||
\(102\) | −140293. | −1.33517 | ||||||||
\(103\) | 47420.8 | 0.440428 | 0.220214 | − | 0.975452i | \(-0.429324\pi\) | ||||
0.220214 | + | 0.975452i | \(0.429324\pi\) | |||||||
\(104\) | 51356.7 | 0.465601 | ||||||||
\(105\) | −34007.9 | −0.301027 | ||||||||
\(106\) | 6595.34 | 0.0570128 | ||||||||
\(107\) | 214213. | 1.80878 | 0.904390 | − | 0.426707i | \(-0.140327\pi\) | ||||
0.904390 | + | 0.426707i | \(0.140327\pi\) | |||||||
\(108\) | −88221.2 | −0.727803 | ||||||||
\(109\) | −226865. | −1.82895 | −0.914473 | − | 0.404648i | \(-0.867394\pi\) | ||||
−0.914473 | + | 0.404648i | \(0.867394\pi\) | |||||||
\(110\) | 152274. | 1.19990 | ||||||||
\(111\) | −128018. | −0.986200 | ||||||||
\(112\) | 3906.75 | 0.0294286 | ||||||||
\(113\) | −16431.9 | −0.121058 | −0.0605288 | − | 0.998166i | \(-0.519279\pi\) | ||||
−0.0605288 | + | 0.998166i | \(0.519279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32098.6 | 0.226329 | ||||||||
\(116\) | −133323. | −0.919939 | ||||||||
\(117\) | −362812. | −2.45029 | ||||||||
\(118\) | 22148.6 | 0.146434 | ||||||||
\(119\) | −20301.0 | −0.131417 | ||||||||
\(120\) | 142621. | 0.904130 | ||||||||
\(121\) | 41806.6 | 0.259586 | ||||||||
\(122\) | −134473. | −0.817969 | ||||||||
\(123\) | 331629. | 1.97647 | ||||||||
\(124\) | 106993. | 0.624889 | ||||||||
\(125\) | 75562.1 | 0.432543 | ||||||||
\(126\) | −27599.4 | −0.154872 | ||||||||
\(127\) | −46148.7 | −0.253893 | −0.126946 | − | 0.991910i | \(-0.540518\pi\) | ||||
−0.126946 | + | 0.991910i | \(0.540518\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −388250. | −2.05418 | ||||||||
\(130\) | 271299. | 1.40796 | ||||||||
\(131\) | −299435. | −1.52449 | −0.762245 | − | 0.647289i | \(-0.775903\pi\) | ||||
−0.762245 | + | 0.647289i | \(0.775903\pi\) | |||||||
\(132\) | 189998. | 0.949105 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4303.21 | 0.0207029 | ||||||||
\(135\) | −466040. | −2.20084 | ||||||||
\(136\) | 85137.8 | 0.394707 | ||||||||
\(137\) | 136949. | 0.623387 | 0.311693 | − | 0.950183i | \(-0.399104\pi\) | ||||
0.311693 | + | 0.950183i | \(0.399104\pi\) | |||||||
\(138\) | 40050.6 | 0.179024 | ||||||||
\(139\) | −294957. | −1.29486 | −0.647429 | − | 0.762126i | \(-0.724156\pi\) | ||||
−0.647429 | + | 0.762126i | \(0.724156\pi\) | |||||||
\(140\) | 20637.9 | 0.0889909 | ||||||||
\(141\) | 325250. | 1.37775 | ||||||||
\(142\) | 98621.6 | 0.410441 | ||||||||
\(143\) | 361421. | 1.47799 | ||||||||
\(144\) | 115746. | 0.465156 | ||||||||
\(145\) | −704295. | −2.78186 | ||||||||
\(146\) | 199187. | 0.773354 | ||||||||
\(147\) | 436982. | 1.66790 | ||||||||
\(148\) | 77688.9 | 0.291544 | ||||||||
\(149\) | −183853. | −0.678428 | −0.339214 | − | 0.940709i | \(-0.610161\pi\) | ||||
−0.339214 | + | 0.940709i | \(0.610161\pi\) | |||||||
\(150\) | 423848. | 1.53809 | ||||||||
\(151\) | 444021. | 1.58475 | 0.792376 | − | 0.610033i | \(-0.208844\pi\) | ||||
0.792376 | + | 0.610033i | \(0.208844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −601460. | −2.07720 | ||||||||
\(154\) | 27493.6 | 0.0934177 | ||||||||
\(155\) | 565207. | 1.88964 | ||||||||
\(156\) | 338509. | 1.11368 | ||||||||
\(157\) | 463273. | 1.49999 | 0.749994 | − | 0.661444i | \(-0.230056\pi\) | ||||
0.749994 | + | 0.661444i | \(0.230056\pi\) | |||||||
\(158\) | 123071. | 0.392206 | ||||||||
\(159\) | 43472.1 | 0.136370 | ||||||||
\(160\) | −86550.7 | −0.267282 | ||||||||
\(161\) | 5795.49 | 0.0176208 | ||||||||
\(162\) | −142024. | −0.425181 | ||||||||
\(163\) | −109972. | −0.324199 | −0.162099 | − | 0.986774i | \(-0.551827\pi\) | ||||
−0.162099 | + | 0.986774i | \(0.551827\pi\) | |||||||
\(164\) | −201252. | −0.584292 | ||||||||
\(165\) | 1.00369e6 | 2.87005 | ||||||||
\(166\) | −150456. | −0.423779 | ||||||||
\(167\) | −56327.2 | −0.156288 | −0.0781442 | − | 0.996942i | \(-0.524899\pi\) | ||||
−0.0781442 | + | 0.996942i | \(0.524899\pi\) | |||||||
\(168\) | 25750.7 | 0.0703907 | ||||||||
\(169\) | 272631. | 0.734274 | ||||||||
\(170\) | 449752. | 1.19358 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 235613. | 0.607264 | ||||||||
\(173\) | 51544.8 | 0.130939 | 0.0654696 | − | 0.997855i | \(-0.479145\pi\) | ||||
0.0654696 | + | 0.997855i | \(0.479145\pi\) | |||||||
\(174\) | −878775. | −2.20041 | ||||||||
\(175\) | 61332.7 | 0.151390 | ||||||||
\(176\) | −115302. | −0.280578 | ||||||||
\(177\) | 145989. | 0.350257 | ||||||||
\(178\) | −370981. | −0.877609 | ||||||||
\(179\) | 648104. | 1.51186 | 0.755930 | − | 0.654652i | \(-0.227185\pi\) | ||||
0.755930 | + | 0.654652i | \(0.227185\pi\) | |||||||
\(180\) | 611442. | 1.40661 | ||||||||
\(181\) | −492363. | −1.11709 | −0.558546 | − | 0.829474i | \(-0.688640\pi\) | ||||
−0.558546 | + | 0.829474i | \(0.688640\pi\) | |||||||
\(182\) | 48983.8 | 0.109616 | ||||||||
\(183\) | −886360. | −1.95651 | ||||||||
\(184\) | −24305.0 | −0.0529237 | ||||||||
\(185\) | 410402. | 0.881617 | ||||||||
\(186\) | 705229. | 1.49468 | ||||||||
\(187\) | 599153. | 1.25295 | ||||||||
\(188\) | −197381. | −0.407296 | ||||||||
\(189\) | −84145.0 | −0.171346 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 67382.2 | 0.133648 | 0.0668239 | − | 0.997765i | \(-0.478713\pi\) | ||||
0.0668239 | + | 0.997765i | \(0.478713\pi\) | |||||||
\(192\) | −107992. | −0.211417 | ||||||||
\(193\) | 201463. | 0.389315 | 0.194658 | − | 0.980871i | \(-0.437640\pi\) | ||||
0.194658 | + | 0.980871i | \(0.437640\pi\) | |||||||
\(194\) | −458661. | −0.874959 | ||||||||
\(195\) | 1.78822e6 | 3.36771 | ||||||||
\(196\) | −265186. | −0.493072 | ||||||||
\(197\) | −95170.4 | −0.174717 | −0.0873587 | − | 0.996177i | \(-0.527843\pi\) | ||||
−0.0873587 | + | 0.996177i | \(0.527843\pi\) | |||||||
\(198\) | 814555. | 1.47658 | ||||||||
\(199\) | −120711. | −0.216080 | −0.108040 | − | 0.994147i | \(-0.534457\pi\) | ||||
−0.108040 | + | 0.994147i | \(0.534457\pi\) | |||||||
\(200\) | −257215. | −0.454697 | ||||||||
\(201\) | 28363.9 | 0.0495194 | ||||||||
\(202\) | 180913. | 0.311955 | ||||||||
\(203\) | −127163. | −0.216581 | ||||||||
\(204\) | 561172. | 0.944105 | ||||||||
\(205\) | −1.06314e6 | −1.76687 | ||||||||
\(206\) | −189683. | −0.311430 | ||||||||
\(207\) | 171704. | 0.278518 | ||||||||
\(208\) | −205427. | −0.329230 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 136031. | 0.212859 | ||||||||
\(211\) | 386464. | 0.597589 | 0.298794 | − | 0.954318i | \(-0.403416\pi\) | ||||
0.298794 | + | 0.954318i | \(0.403416\pi\) | |||||||
\(212\) | −26381.4 | −0.0403141 | ||||||||
\(213\) | 650048. | 0.981740 | ||||||||
\(214\) | −856851. | −1.27900 | ||||||||
\(215\) | 1.24465e6 | 1.83634 | ||||||||
\(216\) | 352885. | 0.514634 | ||||||||
\(217\) | 102050. | 0.147117 | ||||||||
\(218\) | 907459. | 1.29326 | ||||||||
\(219\) | 1.31291e6 | 1.84979 | ||||||||
\(220\) | −609097. | −0.848456 | ||||||||
\(221\) | 1.06748e6 | 1.47021 | ||||||||
\(222\) | 512073. | 0.697348 | ||||||||
\(223\) | 452658. | 0.609548 | 0.304774 | − | 0.952425i | \(-0.401419\pi\) | ||||
0.304774 | + | 0.952425i | \(0.401419\pi\) | |||||||
\(224\) | −15627.0 | −0.0208092 | ||||||||
\(225\) | 1.81711e6 | 2.39291 | ||||||||
\(226\) | 65727.6 | 0.0856006 | ||||||||
\(227\) | −23094.4 | −0.0297469 | −0.0148734 | − | 0.999889i | \(-0.504735\pi\) | ||||
−0.0148734 | + | 0.999889i | \(0.504735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 311552. | 0.392593 | 0.196296 | − | 0.980545i | \(-0.437109\pi\) | ||||
0.196296 | + | 0.980545i | \(0.437109\pi\) | |||||||
\(230\) | −128394. | −0.160039 | ||||||||
\(231\) | 181219. | 0.223447 | ||||||||
\(232\) | 533291. | 0.650495 | ||||||||
\(233\) | −838769. | −1.01217 | −0.506084 | − | 0.862484i | \(-0.668907\pi\) | ||||
−0.506084 | + | 0.862484i | \(0.668907\pi\) | |||||||
\(234\) | 1.45125e6 | 1.73262 | ||||||||
\(235\) | −1.04269e6 | −1.23164 | ||||||||
\(236\) | −88594.5 | −0.103544 | ||||||||
\(237\) | 811204. | 0.938122 | ||||||||
\(238\) | 81204.0 | 0.0929256 | ||||||||
\(239\) | 278361. | 0.315220 | 0.157610 | − | 0.987501i | \(-0.449621\pi\) | ||||
0.157610 | + | 0.987501i | \(0.449621\pi\) | |||||||
\(240\) | −570485. | −0.639316 | ||||||||
\(241\) | 962658. | 1.06765 | 0.533826 | − | 0.845595i | \(-0.320754\pi\) | ||||
0.533826 | + | 0.845595i | \(0.320754\pi\) | |||||||
\(242\) | −167227. | −0.183555 | ||||||||
\(243\) | 403732. | 0.438609 | ||||||||
\(244\) | 537894. | 0.578392 | ||||||||
\(245\) | −1.40088e6 | −1.49103 | ||||||||
\(246\) | −1.32652e6 | −1.39758 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −427974. | −0.441863 | ||||||||
\(249\) | −991706. | −1.01364 | ||||||||
\(250\) | −302248. | −0.305854 | ||||||||
\(251\) | −352423. | −0.353085 | −0.176543 | − | 0.984293i | \(-0.556491\pi\) | ||||
−0.176543 | + | 0.984293i | \(0.556491\pi\) | |||||||
\(252\) | 110398. | 0.109511 | ||||||||
\(253\) | −171045. | −0.168000 | ||||||||
\(254\) | 184595. | 0.179529 | ||||||||
\(255\) | 2.96446e6 | 2.85493 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.59171e6 | −1.50325 | −0.751625 | − | 0.659591i | \(-0.770730\pi\) | ||||
−0.751625 | + | 0.659591i | \(0.770730\pi\) | |||||||
\(258\) | 1.55300e6 | 1.45252 | ||||||||
\(259\) | 74099.3 | 0.0686380 | ||||||||
\(260\) | −1.08519e6 | −0.995576 | ||||||||
\(261\) | −3.76746e6 | −3.42332 | ||||||||
\(262\) | 1.19774e6 | 1.07798 | ||||||||
\(263\) | 1.57606e6 | 1.40503 | 0.702514 | − | 0.711670i | \(-0.252061\pi\) | ||||
0.702514 | + | 0.711670i | \(0.252061\pi\) | |||||||
\(264\) | −759992. | −0.671119 | ||||||||
\(265\) | −139363. | −0.121908 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.44526e6 | −2.09916 | ||||||||
\(268\) | −17212.8 | −0.0146391 | ||||||||
\(269\) | −1.07411e6 | −0.905038 | −0.452519 | − | 0.891755i | \(-0.649475\pi\) | ||||
−0.452519 | + | 0.891755i | \(0.649475\pi\) | |||||||
\(270\) | 1.86416e6 | 1.55623 | ||||||||
\(271\) | 829674. | 0.686253 | 0.343126 | − | 0.939289i | \(-0.388514\pi\) | ||||
0.343126 | + | 0.939289i | \(0.388514\pi\) | |||||||
\(272\) | −340551. | −0.279100 | ||||||||
\(273\) | 322869. | 0.262192 | ||||||||
\(274\) | −547796. | −0.440801 | ||||||||
\(275\) | −1.81014e6 | −1.44338 | ||||||||
\(276\) | −160202. | −0.126589 | ||||||||
\(277\) | 546621. | 0.428043 | 0.214021 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214021 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(278\) | 1.17983e6 | 0.915603 | ||||||||
\(279\) | 3.02344e6 | 2.32537 | ||||||||
\(280\) | −82551.6 | −0.0629261 | ||||||||
\(281\) | −774356. | −0.585026 | −0.292513 | − | 0.956262i | \(-0.594491\pi\) | ||||
−0.292513 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(282\) | −1.30100e6 | −0.974216 | ||||||||
\(283\) | 636942. | 0.472753 | 0.236376 | − | 0.971662i | \(-0.424040\pi\) | ||||
0.236376 | + | 0.971662i | \(0.424040\pi\) | |||||||
\(284\) | −394486. | −0.290226 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.44568e6 | −1.04510 | ||||||||
\(287\) | −191953. | −0.137559 | ||||||||
\(288\) | −462983. | −0.328915 | ||||||||
\(289\) | 349781. | 0.246350 | ||||||||
\(290\) | 2.81718e6 | 1.96707 | ||||||||
\(291\) | −3.02319e6 | −2.09283 | ||||||||
\(292\) | −796747. | −0.546844 | ||||||||
\(293\) | 1.15173e6 | 0.783759 | 0.391880 | − | 0.920017i | \(-0.371825\pi\) | ||||
0.391880 | + | 0.920017i | \(0.371825\pi\) | |||||||
\(294\) | −1.74793e6 | −1.17938 | ||||||||
\(295\) | −468012. | −0.313114 | ||||||||
\(296\) | −310755. | −0.206153 | ||||||||
\(297\) | 2.48341e6 | 1.63364 | ||||||||
\(298\) | 735410. | 0.479721 | ||||||||
\(299\) | −304742. | −0.197131 | ||||||||
\(300\) | −1.69539e6 | −1.08760 | ||||||||
\(301\) | 224726. | 0.142968 | ||||||||
\(302\) | −1.77608e6 | −1.12059 | ||||||||
\(303\) | 1.19246e6 | 0.746170 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.84150e6 | 1.74903 | ||||||||
\(306\) | 2.40584e6 | 1.46880 | ||||||||
\(307\) | −2.16078e6 | −1.30847 | −0.654235 | − | 0.756291i | \(-0.727009\pi\) | ||||
−0.654235 | + | 0.756291i | \(0.727009\pi\) | |||||||
\(308\) | −109974. | −0.0660563 | ||||||||
\(309\) | −1.25026e6 | −0.744913 | ||||||||
\(310\) | −2.26083e6 | −1.33617 | ||||||||
\(311\) | 1.97202e6 | 1.15614 | 0.578069 | − | 0.815988i | \(-0.303806\pi\) | ||||
0.578069 | + | 0.815988i | \(0.303806\pi\) | |||||||
\(312\) | −1.35404e6 | −0.787488 | ||||||||
\(313\) | −527176. | −0.304155 | −0.152077 | − | 0.988369i | \(-0.548596\pi\) | ||||
−0.152077 | + | 0.988369i | \(0.548596\pi\) | |||||||
\(314\) | −1.85309e6 | −1.06065 | ||||||||
\(315\) | 583191. | 0.331157 | ||||||||
\(316\) | −492285. | −0.277331 | ||||||||
\(317\) | −1.73044e6 | −0.967185 | −0.483592 | − | 0.875293i | \(-0.660668\pi\) | ||||
−0.483592 | + | 0.875293i | \(0.660668\pi\) | |||||||
\(318\) | −173888. | −0.0964279 | ||||||||
\(319\) | 3.75301e6 | 2.06492 | ||||||||
\(320\) | 346203. | 0.188997 | ||||||||
\(321\) | −5.64779e6 | −3.05926 | ||||||||
\(322\) | −23182.0 | −0.0124598 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 568096. | 0.300648 | ||||||||
\(325\) | −3.22503e6 | −1.69366 | ||||||||
\(326\) | 439886. | 0.229243 | ||||||||
\(327\) | 5.98137e6 | 3.09336 | ||||||||
\(328\) | 805007. | 0.413157 | ||||||||
\(329\) | −188261. | −0.0958893 | ||||||||
\(330\) | −4.01476e6 | −2.02943 | ||||||||
\(331\) | −1.08497e6 | −0.544310 | −0.272155 | − | 0.962253i | \(-0.587736\pi\) | ||||
−0.272155 | + | 0.962253i | \(0.587736\pi\) | |||||||
\(332\) | 601824. | 0.299657 | ||||||||
\(333\) | 2.19535e6 | 1.08491 | ||||||||
\(334\) | 225309. | 0.110513 | ||||||||
\(335\) | −90929.1 | −0.0442681 | ||||||||
\(336\) | −103003. | −0.0497738 | ||||||||
\(337\) | 1.92081e6 | 0.921320 | 0.460660 | − | 0.887577i | \(-0.347613\pi\) | ||||
0.460660 | + | 0.887577i | \(0.347613\pi\) | |||||||
\(338\) | −1.09052e6 | −0.519210 | ||||||||
\(339\) | 433233. | 0.204749 | ||||||||
\(340\) | −1.79901e6 | −0.843986 | ||||||||
\(341\) | −3.01185e6 | −1.40264 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −509420. | −0.233798 | ||||||||
\(344\) | −942450. | −0.429400 | ||||||||
\(345\) | −846290. | −0.382799 | ||||||||
\(346\) | −206179. | −0.0925881 | ||||||||
\(347\) | −1.71545e6 | −0.764812 | −0.382406 | − | 0.923994i | \(-0.624904\pi\) | ||||
−0.382406 | + | 0.923994i | \(0.624904\pi\) | |||||||
\(348\) | 3.51510e6 | 1.55593 | ||||||||
\(349\) | 3.35326e6 | 1.47368 | 0.736842 | − | 0.676066i | \(-0.236316\pi\) | ||||
0.736842 | + | 0.676066i | \(0.236316\pi\) | |||||||
\(350\) | −245331. | −0.107049 | ||||||||
\(351\) | 4.42456e6 | 1.91691 | ||||||||
\(352\) | 461207. | 0.198399 | ||||||||
\(353\) | 2.01176e6 | 0.859289 | 0.429644 | − | 0.902998i | \(-0.358639\pi\) | ||||
0.429644 | + | 0.902998i | \(0.358639\pi\) | |||||||
\(354\) | −583956. | −0.247669 | ||||||||
\(355\) | −2.08393e6 | −0.877630 | ||||||||
\(356\) | 1.48392e6 | 0.620563 | ||||||||
\(357\) | 535243. | 0.222270 | ||||||||
\(358\) | −2.59241e6 | −1.06905 | ||||||||
\(359\) | 2.03110e6 | 0.831756 | 0.415878 | − | 0.909420i | \(-0.363474\pi\) | ||||
0.415878 | + | 0.909420i | \(0.363474\pi\) | |||||||
\(360\) | −2.44577e6 | −0.994624 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 1.96945e6 | 0.789903 | ||||||||
\(363\) | −1.10225e6 | −0.439048 | ||||||||
\(364\) | −195935. | −0.0775102 | ||||||||
\(365\) | −4.20892e6 | −1.65363 | ||||||||
\(366\) | 3.54544e6 | 1.38346 | ||||||||
\(367\) | 353495. | 0.136999 | 0.0684997 | − | 0.997651i | \(-0.478179\pi\) | ||||
0.0684997 | + | 0.997651i | \(0.478179\pi\) | |||||||
\(368\) | 97219.9 | 0.0374227 | ||||||||
\(369\) | −5.68701e6 | −2.17429 | ||||||||
\(370\) | −1.64161e6 | −0.623397 | ||||||||
\(371\) | −25162.4 | −0.00949112 | ||||||||
\(372\) | −2.82092e6 | −1.05690 | ||||||||
\(373\) | 2.76160e6 | 1.02775 | 0.513876 | − | 0.857864i | \(-0.328209\pi\) | ||||
0.513876 | + | 0.857864i | \(0.328209\pi\) | |||||||
\(374\) | −2.39661e6 | −0.885970 | ||||||||
\(375\) | −1.99222e6 | −0.731576 | ||||||||
\(376\) | 789522. | 0.288002 | ||||||||
\(377\) | 6.68654e6 | 2.42297 | ||||||||
\(378\) | 336580. | 0.121160 | ||||||||
\(379\) | 2.01627e6 | 0.721025 | 0.360513 | − | 0.932754i | \(-0.382602\pi\) | ||||
0.360513 | + | 0.932754i | \(0.382602\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.21673e6 | 0.429418 | ||||||||
\(382\) | −269529. | −0.0945033 | ||||||||
\(383\) | 5.64860e6 | 1.96763 | 0.983815 | − | 0.179185i | \(-0.0573460\pi\) | ||||
0.983815 | + | 0.179185i | \(0.0573460\pi\) | |||||||
\(384\) | 431970. | 0.149495 | ||||||||
\(385\) | −580954. | −0.199751 | ||||||||
\(386\) | −805850. | −0.275287 | ||||||||
\(387\) | 6.65799e6 | 2.25978 | ||||||||
\(388\) | 1.83464e6 | 0.618689 | ||||||||
\(389\) | 3.09188e6 | 1.03597 | 0.517986 | − | 0.855389i | \(-0.326682\pi\) | ||||
0.517986 | + | 0.855389i | \(0.326682\pi\) | |||||||
\(390\) | −7.15288e6 | −2.38133 | ||||||||
\(391\) | −505193. | −0.167115 | ||||||||
\(392\) | 1.06074e6 | 0.348654 | ||||||||
\(393\) | 7.89471e6 | 2.57843 | ||||||||
\(394\) | 380681. | 0.123544 | ||||||||
\(395\) | −2.60056e6 | −0.838638 | ||||||||
\(396\) | −3.25822e6 | −1.04410 | ||||||||
\(397\) | 1.60838e6 | 0.512168 | 0.256084 | − | 0.966655i | \(-0.417568\pi\) | ||||
0.256084 | + | 0.966655i | \(0.417568\pi\) | |||||||
\(398\) | 482844. | 0.152791 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.02886e6 | 0.321519 | ||||||||
\(401\) | 2.60056e6 | 0.807616 | 0.403808 | − | 0.914844i | \(-0.367686\pi\) | ||||
0.403808 | + | 0.914844i | \(0.367686\pi\) | |||||||
\(402\) | −113456. | −0.0350155 | ||||||||
\(403\) | −5.36604e6 | −1.64585 | ||||||||
\(404\) | −723654. | −0.220586 | ||||||||
\(405\) | 3.00104e6 | 0.909148 | ||||||||
\(406\) | 508651. | 0.153146 | ||||||||
\(407\) | −2.18693e6 | −0.654408 | ||||||||
\(408\) | −2.24469e6 | −0.667583 | ||||||||
\(409\) | 1.24018e6 | 0.366587 | 0.183293 | − | 0.983058i | \(-0.441324\pi\) | ||||
0.183293 | + | 0.983058i | \(0.441324\pi\) | |||||||
\(410\) | 4.25256e6 | 1.24937 | ||||||||
\(411\) | −3.61071e6 | −1.05436 | ||||||||
\(412\) | 758732. | 0.220214 | ||||||||
\(413\) | −84501.1 | −0.0243774 | ||||||||
\(414\) | −686815. | −0.196942 | ||||||||
\(415\) | 3.17922e6 | 0.906149 | ||||||||
\(416\) | 821707. | 0.232800 | ||||||||
\(417\) | 7.77665e6 | 2.19004 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.66141e6 | 0.462318 | 0.231159 | − | 0.972916i | \(-0.425748\pi\) | ||||
0.231159 | + | 0.972916i | \(0.425748\pi\) | |||||||
\(420\) | −544126. | −0.150514 | ||||||||
\(421\) | −5.13402e6 | −1.41173 | −0.705866 | − | 0.708346i | \(-0.749442\pi\) | ||||
−0.705866 | + | 0.708346i | \(0.749442\pi\) | |||||||
\(422\) | −1.54585e6 | −0.422559 | ||||||||
\(423\) | −5.57762e6 | −1.51565 | ||||||||
\(424\) | 105525. | 0.0285064 | ||||||||
\(425\) | −5.34637e6 | −1.43578 | ||||||||
\(426\) | −2.60019e6 | −0.694195 | ||||||||
\(427\) | 513041. | 0.136170 | ||||||||
\(428\) | 3.42740e6 | 0.904390 | ||||||||
\(429\) | −9.52898e6 | −2.49979 | ||||||||
\(430\) | −4.97862e6 | −1.29849 | ||||||||
\(431\) | 1.17229e6 | 0.303978 | 0.151989 | − | 0.988382i | \(-0.451432\pi\) | ||||
0.151989 | + | 0.988382i | \(0.451432\pi\) | |||||||
\(432\) | −1.41154e6 | −0.363901 | ||||||||
\(433\) | 3.50979e6 | 0.899626 | 0.449813 | − | 0.893123i | \(-0.351491\pi\) | ||||
0.449813 | + | 0.893123i | \(0.351491\pi\) | |||||||
\(434\) | −408199. | −0.104027 | ||||||||
\(435\) | 1.85690e7 | 4.70506 | ||||||||
\(436\) | −3.62984e6 | −0.914473 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.25163e6 | −1.30800 | ||||||||
\(439\) | 3.37606e6 | 0.836082 | 0.418041 | − | 0.908428i | \(-0.362717\pi\) | ||||
0.418041 | + | 0.908428i | \(0.362717\pi\) | |||||||
\(440\) | 2.43639e6 | 0.599949 | ||||||||
\(441\) | −7.49368e6 | −1.83484 | ||||||||
\(442\) | −4.26992e6 | −1.03959 | ||||||||
\(443\) | 1.50788e6 | 0.365053 | 0.182527 | − | 0.983201i | \(-0.441572\pi\) | ||||
0.182527 | + | 0.983201i | \(0.441572\pi\) | |||||||
\(444\) | −2.04829e6 | −0.493100 | ||||||||
\(445\) | 7.83902e6 | 1.87656 | ||||||||
\(446\) | −1.81063e6 | −0.431015 | ||||||||
\(447\) | 4.84734e6 | 1.14745 | ||||||||
\(448\) | 62507.9 | 0.0147143 | ||||||||
\(449\) | 183807. | 0.0430275 | 0.0215137 | − | 0.999769i | \(-0.493151\pi\) | ||||
0.0215137 | + | 0.999769i | \(0.493151\pi\) | |||||||
\(450\) | −7.26845e6 | −1.69204 | ||||||||
\(451\) | 5.66520e6 | 1.31152 | ||||||||
\(452\) | −262910. | −0.0605288 | ||||||||
\(453\) | −1.17068e7 | −2.68035 | ||||||||
\(454\) | 92377.5 | 0.0210342 | ||||||||
\(455\) | −1.03505e6 | −0.234388 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.18883e6 | 1.16219 | 0.581097 | − | 0.813834i | \(-0.302624\pi\) | ||||
0.581097 | + | 0.813834i | \(0.302624\pi\) | |||||||
\(458\) | −1.24621e6 | −0.277605 | ||||||||
\(459\) | 7.33492e6 | 1.62504 | ||||||||
\(460\) | 513577. | 0.113165 | ||||||||
\(461\) | 3.46218e6 | 0.758748 | 0.379374 | − | 0.925243i | \(-0.376139\pi\) | ||||
0.379374 | + | 0.925243i | \(0.376139\pi\) | |||||||
\(462\) | −724877. | −0.158001 | ||||||||
\(463\) | −2.78786e6 | −0.604392 | −0.302196 | − | 0.953246i | \(-0.597720\pi\) | ||||
−0.302196 | + | 0.953246i | \(0.597720\pi\) | |||||||
\(464\) | −2.13316e6 | −0.459970 | ||||||||
\(465\) | −1.49019e7 | −3.19601 | ||||||||
\(466\) | 3.35508e6 | 0.715711 | ||||||||
\(467\) | 179812. | 0.0381528 | 0.0190764 | − | 0.999818i | \(-0.493927\pi\) | ||||
0.0190764 | + | 0.999818i | \(0.493927\pi\) | |||||||
\(468\) | −5.80500e6 | −1.22514 | ||||||||
\(469\) | −16417.5 | −0.00344648 | ||||||||
\(470\) | 4.17076e6 | 0.870904 | ||||||||
\(471\) | −1.22144e7 | −2.53699 | ||||||||
\(472\) | 354378. | 0.0732170 | ||||||||
\(473\) | −6.63245e6 | −1.36308 | ||||||||
\(474\) | −3.24482e6 | −0.663353 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −324816. | −0.0657083 | ||||||||
\(477\) | −745490. | −0.150019 | ||||||||
\(478\) | −1.11344e6 | −0.222894 | ||||||||
\(479\) | −3.24343e6 | −0.645900 | −0.322950 | − | 0.946416i | \(-0.604675\pi\) | ||||
−0.322950 | + | 0.946416i | \(0.604675\pi\) | |||||||
\(480\) | 2.28194e6 | 0.452065 | ||||||||
\(481\) | −3.89633e6 | −0.767880 | ||||||||
\(482\) | −3.85063e6 | −0.754943 | ||||||||
\(483\) | −152800. | −0.0298027 | ||||||||
\(484\) | 668906. | 0.129793 | ||||||||
\(485\) | 9.69176e6 | 1.87089 | ||||||||
\(486\) | −1.61493e6 | −0.310144 | ||||||||
\(487\) | −5.47967e6 | −1.04696 | −0.523482 | − | 0.852037i | \(-0.675367\pi\) | ||||
−0.523482 | + | 0.852037i | \(0.675367\pi\) | |||||||
\(488\) | −2.15158e6 | −0.408985 | ||||||||
\(489\) | 2.89944e6 | 0.548330 | ||||||||
\(490\) | 5.60352e6 | 1.05432 | ||||||||
\(491\) | −6.46147e6 | −1.20956 | −0.604780 | − | 0.796393i | \(-0.706739\pi\) | ||||
−0.604780 | + | 0.796393i | \(0.706739\pi\) | |||||||
\(492\) | 5.30607e6 | 0.988235 | ||||||||
\(493\) | 1.10848e7 | 2.05404 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.72120e7 | −3.15732 | ||||||||
\(496\) | 1.71189e6 | 0.312444 | ||||||||
\(497\) | −376259. | −0.0683276 | ||||||||
\(498\) | 3.96683e6 | 0.716753 | ||||||||
\(499\) | 215507. | 0.0387445 | 0.0193722 | − | 0.999812i | \(-0.493833\pi\) | ||||
0.0193722 | + | 0.999812i | \(0.493833\pi\) | |||||||
\(500\) | 1.20899e6 | 0.216271 | ||||||||
\(501\) | 1.48509e6 | 0.264337 | ||||||||
\(502\) | 1.40969e6 | 0.249669 | ||||||||
\(503\) | 9.57985e6 | 1.68826 | 0.844128 | − | 0.536141i | \(-0.180118\pi\) | ||||
0.844128 | + | 0.536141i | \(0.180118\pi\) | |||||||
\(504\) | −441591. | −0.0774362 | ||||||||
\(505\) | −3.82280e6 | −0.667041 | ||||||||
\(506\) | 684181. | 0.118794 | ||||||||
\(507\) | −7.18800e6 | −1.24190 | ||||||||
\(508\) | −738379. | −0.126946 | ||||||||
\(509\) | −1.53458e6 | −0.262540 | −0.131270 | − | 0.991347i | \(-0.541906\pi\) | ||||
−0.131270 | + | 0.991347i | \(0.541906\pi\) | |||||||
\(510\) | −1.18579e7 | −2.01874 | ||||||||
\(511\) | −759934. | −0.128743 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.36684e6 | 1.06296 | ||||||||
\(515\) | 4.00810e6 | 0.665918 | ||||||||
\(516\) | −6.21201e6 | −1.02709 | ||||||||
\(517\) | 5.55623e6 | 0.914226 | ||||||||
\(518\) | −296397. | −0.0485344 | ||||||||
\(519\) | −1.35900e6 | −0.221463 | ||||||||
\(520\) | 4.34078e6 | 0.703978 | ||||||||
\(521\) | 6.24839e6 | 1.00850 | 0.504248 | − | 0.863559i | \(-0.331770\pi\) | ||||
0.504248 | + | 0.863559i | \(0.331770\pi\) | |||||||
\(522\) | 1.50699e7 | 2.42065 | ||||||||
\(523\) | 1.46135e6 | 0.233615 | 0.116807 | − | 0.993155i | \(-0.462734\pi\) | ||||
0.116807 | + | 0.993155i | \(0.462734\pi\) | |||||||
\(524\) | −4.79096e6 | −0.762245 | ||||||||
\(525\) | −1.61706e6 | −0.256052 | ||||||||
\(526\) | −6.30426e6 | −0.993504 | ||||||||
\(527\) | −8.89568e6 | −1.39525 | ||||||||
\(528\) | 3.03997e6 | 0.474553 | ||||||||
\(529\) | −6.29212e6 | −0.977593 | ||||||||
\(530\) | 557452. | 0.0862021 | ||||||||
\(531\) | −2.50352e6 | −0.385315 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.00934e7 | 1.53893 | ||||||||
\(534\) | 9.78103e6 | 1.48433 | ||||||||
\(535\) | 1.81057e7 | 2.73483 | ||||||||
\(536\) | 68851.3 | 0.0103514 | ||||||||
\(537\) | −1.70875e7 | −2.55707 | ||||||||
\(538\) | 4.29643e6 | 0.639959 | ||||||||
\(539\) | 7.46493e6 | 1.10676 | ||||||||
\(540\) | −7.45665e6 | −1.10042 | ||||||||
\(541\) | −9.78327e6 | −1.43711 | −0.718556 | − | 0.695469i | \(-0.755197\pi\) | ||||
−0.718556 | + | 0.695469i | \(0.755197\pi\) | |||||||
\(542\) | −3.31869e6 | −0.485254 | ||||||||
\(543\) | 1.29813e7 | 1.88938 | ||||||||
\(544\) | 1.36220e6 | 0.197354 | ||||||||
\(545\) | −1.91751e7 | −2.76532 | ||||||||
\(546\) | −1.29148e6 | −0.185398 | ||||||||
\(547\) | 1.17209e7 | 1.67492 | 0.837460 | − | 0.546498i | \(-0.184040\pi\) | ||||
0.837460 | + | 0.546498i | \(0.184040\pi\) | |||||||
\(548\) | 2.19118e6 | 0.311693 | ||||||||
\(549\) | 1.51999e7 | 2.15234 | ||||||||
\(550\) | 7.24057e6 | 1.02062 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 640809. | 0.0895119 | ||||||||
\(553\) | −469539. | −0.0652919 | ||||||||
\(554\) | −2.18648e6 | −0.302672 | ||||||||
\(555\) | −1.08204e7 | −1.49111 | ||||||||
\(556\) | −4.71932e6 | −0.647429 | ||||||||
\(557\) | −1.08382e7 | −1.48019 | −0.740095 | − | 0.672502i | \(-0.765220\pi\) | ||||
−0.740095 | + | 0.672502i | \(0.765220\pi\) | |||||||
\(558\) | −1.20938e7 | −1.64428 | ||||||||
\(559\) | −1.18167e7 | −1.59943 | ||||||||
\(560\) | 330207. | 0.0444955 | ||||||||
\(561\) | −1.57969e7 | −2.11916 | ||||||||
\(562\) | 3.09742e6 | 0.413676 | ||||||||
\(563\) | 7.80000e6 | 1.03711 | 0.518554 | − | 0.855045i | \(-0.326471\pi\) | ||||
0.518554 | + | 0.855045i | \(0.326471\pi\) | |||||||
\(564\) | 5.20401e6 | 0.688875 | ||||||||
\(565\) | −1.38886e6 | −0.183036 | ||||||||
\(566\) | −2.54777e6 | −0.334287 | ||||||||
\(567\) | 541847. | 0.0707814 | ||||||||
\(568\) | 1.57795e6 | 0.205221 | ||||||||
\(569\) | 5.60370e6 | 0.725594 | 0.362797 | − | 0.931868i | \(-0.381822\pi\) | ||||
0.362797 | + | 0.931868i | \(0.381822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.49811e6 | −1.09077 | −0.545383 | − | 0.838187i | \(-0.683616\pi\) | ||||
−0.545383 | + | 0.838187i | \(0.683616\pi\) | |||||||
\(572\) | 5.78273e6 | 0.738997 | ||||||||
\(573\) | −1.77656e6 | −0.226044 | ||||||||
\(574\) | 767812. | 0.0972691 | ||||||||
\(575\) | 1.52627e6 | 0.192514 | ||||||||
\(576\) | 1.85193e6 | 0.232578 | ||||||||
\(577\) | −9.65726e6 | −1.20758 | −0.603788 | − | 0.797145i | \(-0.706343\pi\) | ||||
−0.603788 | + | 0.797145i | \(0.706343\pi\) | |||||||
\(578\) | −1.39913e6 | −0.174196 | ||||||||
\(579\) | −5.31163e6 | −0.658463 | ||||||||
\(580\) | −1.12687e7 | −1.39093 | ||||||||
\(581\) | 574017. | 0.0705480 | ||||||||
\(582\) | 1.20928e7 | 1.47985 | ||||||||
\(583\) | 742631. | 0.0904902 | ||||||||
\(584\) | 3.18699e6 | 0.386677 | ||||||||
\(585\) | −3.06657e7 | −3.70478 | ||||||||
\(586\) | −4.60693e6 | −0.554201 | ||||||||
\(587\) | −1.64588e6 | −0.197153 | −0.0985767 | − | 0.995129i | \(-0.531429\pi\) | ||||
−0.0985767 | + | 0.995129i | \(0.531429\pi\) | |||||||
\(588\) | 6.99171e6 | 0.833951 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.87205e6 | 0.221405 | ||||||||
\(591\) | 2.50920e6 | 0.295506 | ||||||||
\(592\) | 1.24302e6 | 0.145772 | ||||||||
\(593\) | −6.15870e6 | −0.719205 | −0.359602 | − | 0.933106i | \(-0.617088\pi\) | ||||
−0.359602 | + | 0.933106i | \(0.617088\pi\) | |||||||
\(594\) | −9.93365e6 | −1.15516 | ||||||||
\(595\) | −1.71588e6 | −0.198699 | ||||||||
\(596\) | −2.94164e6 | −0.339214 | ||||||||
\(597\) | 3.18259e6 | 0.365464 | ||||||||
\(598\) | 1.21897e6 | 0.139392 | ||||||||
\(599\) | 1.19969e7 | 1.36616 | 0.683078 | − | 0.730346i | \(-0.260641\pi\) | ||||
0.683078 | + | 0.730346i | \(0.260641\pi\) | |||||||
\(600\) | 6.78158e6 | 0.769046 | ||||||||
\(601\) | 8.53734e6 | 0.964132 | 0.482066 | − | 0.876135i | \(-0.339887\pi\) | ||||
0.482066 | + | 0.876135i | \(0.339887\pi\) | |||||||
\(602\) | −898905. | −0.101093 | ||||||||
\(603\) | −486404. | −0.0544758 | ||||||||
\(604\) | 7.10434e6 | 0.792376 | ||||||||
\(605\) | 3.53359e6 | 0.392489 | ||||||||
\(606\) | −4.76984e6 | −0.527622 | ||||||||
\(607\) | −6.86609e6 | −0.756376 | −0.378188 | − | 0.925729i | \(-0.623453\pi\) | ||||
−0.378188 | + | 0.925729i | \(0.623453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.35269e6 | 0.366311 | ||||||||
\(610\) | −1.13660e7 | −1.23675 | ||||||||
\(611\) | 9.89923e6 | 1.07275 | ||||||||
\(612\) | −9.62337e6 | −1.03860 | ||||||||
\(613\) | 1.19450e7 | 1.28391 | 0.641956 | − | 0.766742i | \(-0.278123\pi\) | ||||
0.641956 | + | 0.766742i | \(0.278123\pi\) | |||||||
\(614\) | 8.64310e6 | 0.925228 | ||||||||
\(615\) | 2.80300e7 | 2.98838 | ||||||||
\(616\) | 439897. | 0.0467089 | ||||||||
\(617\) | 1.28809e6 | 0.136218 | 0.0681089 | − | 0.997678i | \(-0.478303\pi\) | ||||
0.0681089 | + | 0.997678i | \(0.478303\pi\) | |||||||
\(618\) | 5.00106e6 | 0.526733 | ||||||||
\(619\) | 5.27313e6 | 0.553149 | 0.276574 | − | 0.960993i | \(-0.410801\pi\) | ||||
0.276574 | + | 0.960993i | \(0.410801\pi\) | |||||||
\(620\) | 9.04331e6 | 0.944818 | ||||||||
\(621\) | −2.09396e6 | −0.217891 | ||||||||
\(622\) | −7.88807e6 | −0.817513 | ||||||||
\(623\) | 1.41536e6 | 0.146099 | ||||||||
\(624\) | 5.41615e6 | 0.556838 | ||||||||
\(625\) | −6.17268e6 | −0.632082 | ||||||||
\(626\) | 2.10870e6 | 0.215070 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.41237e6 | 0.749994 | ||||||||
\(629\) | −6.45923e6 | −0.650960 | ||||||||
\(630\) | −2.33276e6 | −0.234164 | ||||||||
\(631\) | 1.16692e7 | 1.16672 | 0.583360 | − | 0.812214i | \(-0.301738\pi\) | ||||
0.583360 | + | 0.812214i | \(0.301738\pi\) | |||||||
\(632\) | 1.96914e6 | 0.196103 | ||||||||
\(633\) | −1.01892e7 | −1.01072 | ||||||||
\(634\) | 6.92178e6 | 0.683903 | ||||||||
\(635\) | −3.90058e6 | −0.383880 | ||||||||
\(636\) | 695554. | 0.0681848 | ||||||||
\(637\) | 1.32999e7 | 1.29867 | ||||||||
\(638\) | −1.50120e7 | −1.46012 | ||||||||
\(639\) | −1.11475e7 | −1.08000 | ||||||||
\(640\) | −1.38481e6 | −0.133641 | ||||||||
\(641\) | 1.22438e7 | 1.17699 | 0.588494 | − | 0.808502i | \(-0.299721\pi\) | ||||
0.588494 | + | 0.808502i | \(0.299721\pi\) | |||||||
\(642\) | 2.25912e7 | 2.16322 | ||||||||
\(643\) | 1.03196e7 | 0.984320 | 0.492160 | − | 0.870505i | \(-0.336207\pi\) | ||||
0.492160 | + | 0.870505i | \(0.336207\pi\) | |||||||
\(644\) | 92727.9 | 0.00881040 | ||||||||
\(645\) | −3.28158e7 | −3.10587 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.41105e7 | 1.32520 | 0.662601 | − | 0.748972i | \(-0.269452\pi\) | ||||
0.662601 | + | 0.748972i | \(0.269452\pi\) | |||||||
\(648\) | −2.27238e6 | −0.212591 | ||||||||
\(649\) | 2.49392e6 | 0.232419 | ||||||||
\(650\) | 1.29001e7 | 1.19760 | ||||||||
\(651\) | −2.69058e6 | −0.248825 | ||||||||
\(652\) | −1.75955e6 | −0.162099 | ||||||||
\(653\) | 8.05111e6 | 0.738878 | 0.369439 | − | 0.929255i | \(-0.379550\pi\) | ||||
0.369439 | + | 0.929255i | \(0.379550\pi\) | |||||||
\(654\) | −2.39255e7 | −2.18734 | ||||||||
\(655\) | −2.53089e7 | −2.30499 | ||||||||
\(656\) | −3.22003e6 | −0.292146 | ||||||||
\(657\) | −2.25146e7 | −2.03494 | ||||||||
\(658\) | 753043. | 0.0678039 | ||||||||
\(659\) | −3.50112e6 | −0.314046 | −0.157023 | − | 0.987595i | \(-0.550190\pi\) | ||||
−0.157023 | + | 0.987595i | \(0.550190\pi\) | |||||||
\(660\) | 1.60590e7 | 1.43503 | ||||||||
\(661\) | −8.08972e6 | −0.720161 | −0.360081 | − | 0.932921i | \(-0.617251\pi\) | ||||
−0.360081 | + | 0.932921i | \(0.617251\pi\) | |||||||
\(662\) | 4.33987e6 | 0.384885 | ||||||||
\(663\) | −2.81445e7 | −2.48662 | ||||||||
\(664\) | −2.40730e6 | −0.211889 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.78140e6 | −0.767146 | ||||||||
\(667\) | −3.16446e6 | −0.275413 | ||||||||
\(668\) | −901235. | −0.0781442 | ||||||||
\(669\) | −1.19345e7 | −1.03095 | ||||||||
\(670\) | 363716. | 0.0313023 | ||||||||
\(671\) | −1.51416e7 | −1.29827 | ||||||||
\(672\) | 412011. | 0.0351954 | ||||||||
\(673\) | −5.66480e6 | −0.482111 | −0.241055 | − | 0.970511i | \(-0.577494\pi\) | ||||
−0.241055 | + | 0.970511i | \(0.577494\pi\) | |||||||
\(674\) | −7.68326e6 | −0.651472 | ||||||||
\(675\) | −2.21600e7 | −1.87202 | ||||||||
\(676\) | 4.36209e6 | 0.367137 | ||||||||
\(677\) | −4.24946e6 | −0.356338 | −0.178169 | − | 0.984000i | \(-0.557017\pi\) | ||||
−0.178169 | + | 0.984000i | \(0.557017\pi\) | |||||||
\(678\) | −1.73293e6 | −0.144780 | ||||||||
\(679\) | 1.74988e6 | 0.145658 | ||||||||
\(680\) | 7.19603e6 | 0.596788 | ||||||||
\(681\) | 608891. | 0.0503121 | ||||||||
\(682\) | 1.20474e7 | 0.991817 | ||||||||
\(683\) | −2.09008e7 | −1.71440 | −0.857200 | − | 0.514984i | \(-0.827798\pi\) | ||||
−0.857200 | + | 0.514984i | \(0.827798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.15752e7 | 0.942547 | ||||||||
\(686\) | 2.03768e6 | 0.165320 | ||||||||
\(687\) | −8.21418e6 | −0.664007 | ||||||||
\(688\) | 3.76980e6 | 0.303632 | ||||||||
\(689\) | 1.32311e6 | 0.106181 | ||||||||
\(690\) | 3.38516e6 | 0.270680 | ||||||||
\(691\) | −8.97377e6 | −0.714957 | −0.357479 | − | 0.933921i | \(-0.616363\pi\) | ||||
−0.357479 | + | 0.933921i | \(0.616363\pi\) | |||||||
\(692\) | 824718. | 0.0654696 | ||||||||
\(693\) | −3.10768e6 | −0.245812 | ||||||||
\(694\) | 6.86181e6 | 0.540804 | ||||||||
\(695\) | −2.49304e7 | −1.95780 | ||||||||
\(696\) | −1.40604e7 | −1.10021 | ||||||||
\(697\) | 1.67325e7 | 1.30461 | ||||||||
\(698\) | −1.34131e7 | −1.04205 | ||||||||
\(699\) | 2.21144e7 | 1.71192 | ||||||||
\(700\) | 981324. | 0.0756950 | ||||||||
\(701\) | −1.55796e7 | −1.19746 | −0.598730 | − | 0.800951i | \(-0.704328\pi\) | ||||
−0.598730 | + | 0.800951i | \(0.704328\pi\) | |||||||
\(702\) | −1.76982e7 | −1.35546 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.84483e6 | −0.140289 | ||||||||
\(705\) | 2.74909e7 | 2.08313 | ||||||||
\(706\) | −8.04704e6 | −0.607609 | ||||||||
\(707\) | −690218. | −0.0519323 | ||||||||
\(708\) | 2.33583e6 | 0.175129 | ||||||||
\(709\) | 4.54607e6 | 0.339641 | 0.169821 | − | 0.985475i | \(-0.445681\pi\) | ||||
0.169821 | + | 0.985475i | \(0.445681\pi\) | |||||||
\(710\) | 8.33571e6 | 0.620578 | ||||||||
\(711\) | −1.39111e7 | −1.03202 | ||||||||
\(712\) | −5.93569e6 | −0.438805 | ||||||||
\(713\) | 2.53952e6 | 0.187080 | ||||||||
\(714\) | −2.14097e6 | −0.157169 | ||||||||
\(715\) | 3.05480e7 | 2.23469 | ||||||||
\(716\) | 1.03697e7 | 0.755930 | ||||||||
\(717\) | −7.33908e6 | −0.533143 | ||||||||
\(718\) | −8.12442e6 | −0.588140 | ||||||||
\(719\) | −1.78079e7 | −1.28467 | −0.642335 | − | 0.766424i | \(-0.722034\pi\) | ||||
−0.642335 | + | 0.766424i | \(0.722034\pi\) | |||||||
\(720\) | 9.78307e6 | 0.703306 | ||||||||
\(721\) | 723675. | 0.0518448 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.53808e7 | −1.80576 | ||||||||
\(724\) | −7.87780e6 | −0.558546 | ||||||||
\(725\) | −3.34889e7 | −2.36623 | ||||||||
\(726\) | 4.40899e6 | 0.310454 | ||||||||
\(727\) | 2.21888e7 | 1.55703 | 0.778516 | − | 0.627625i | \(-0.215973\pi\) | ||||
0.778516 | + | 0.627625i | \(0.215973\pi\) | |||||||
\(728\) | 783741. | 0.0548080 | ||||||||
\(729\) | −1.92725e7 | −1.34313 | ||||||||
\(730\) | 1.68357e7 | 1.16929 | ||||||||
\(731\) | −1.95894e7 | −1.35590 | ||||||||
\(732\) | −1.41818e7 | −0.978256 | ||||||||
\(733\) | −1.39640e6 | −0.0959951 | −0.0479976 | − | 0.998847i | \(-0.515284\pi\) | ||||
−0.0479976 | + | 0.998847i | \(0.515284\pi\) | |||||||
\(734\) | −1.41398e6 | −0.0968731 | ||||||||
\(735\) | 3.69347e7 | 2.52183 | ||||||||
\(736\) | −388879. | −0.0264619 | ||||||||
\(737\) | 484538. | 0.0328594 | ||||||||
\(738\) | 2.27481e7 | 1.53746 | ||||||||
\(739\) | 2.46795e7 | 1.66236 | 0.831179 | − | 0.556005i | \(-0.187667\pi\) | ||||
0.831179 | + | 0.556005i | \(0.187667\pi\) | |||||||
\(740\) | 6.56643e6 | 0.440808 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 100650. | 0.00671124 | ||||||||
\(743\) | −3.60757e6 | −0.239741 | −0.119871 | − | 0.992790i | \(-0.538248\pi\) | ||||
−0.119871 | + | 0.992790i | \(0.538248\pi\) | |||||||
\(744\) | 1.12837e7 | 0.747340 | ||||||||
\(745\) | −1.55396e7 | −1.02577 | ||||||||
\(746\) | −1.10464e7 | −0.726731 | ||||||||
\(747\) | 1.70065e7 | 1.11510 | ||||||||
\(748\) | 9.58645e6 | 0.626475 | ||||||||
\(749\) | 3.26904e6 | 0.212920 | ||||||||
\(750\) | 7.96888e6 | 0.517302 | ||||||||
\(751\) | 1.49951e7 | 0.970176 | 0.485088 | − | 0.874465i | \(-0.338788\pi\) | ||||
0.485088 | + | 0.874465i | \(0.338788\pi\) | |||||||
\(752\) | −3.15809e6 | −0.203648 | ||||||||
\(753\) | 9.29175e6 | 0.597186 | ||||||||
\(754\) | −2.67462e7 | −1.71330 | ||||||||
\(755\) | 3.75296e7 | 2.39611 | ||||||||
\(756\) | −1.34632e6 | −0.0856730 | ||||||||
\(757\) | 1.17051e7 | 0.742395 | 0.371198 | − | 0.928554i | \(-0.378947\pi\) | ||||
0.371198 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(758\) | −8.06507e6 | −0.509842 | ||||||||
\(759\) | 4.50966e6 | 0.284145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.09596e7 | −0.686016 | −0.343008 | − | 0.939333i | \(-0.611446\pi\) | ||||
−0.343008 | + | 0.939333i | \(0.611446\pi\) | |||||||
\(762\) | −4.86690e6 | −0.303644 | ||||||||
\(763\) | −3.46212e6 | −0.215293 | ||||||||
\(764\) | 1.07812e6 | 0.0668239 | ||||||||
\(765\) | −5.08367e7 | −3.14068 | ||||||||
\(766\) | −2.25944e7 | −1.39133 | ||||||||
\(767\) | 4.44328e6 | 0.272719 | ||||||||
\(768\) | −1.72788e6 | −0.105709 | ||||||||
\(769\) | 2.92163e7 | 1.78160 | 0.890798 | − | 0.454399i | \(-0.150146\pi\) | ||||
0.890798 | + | 0.454399i | \(0.150146\pi\) | |||||||
\(770\) | 2.32381e6 | 0.141246 | ||||||||
\(771\) | 4.19660e7 | 2.54250 | ||||||||
\(772\) | 3.22340e6 | 0.194658 | ||||||||
\(773\) | 9.03923e6 | 0.544105 | 0.272052 | − | 0.962282i | \(-0.412298\pi\) | ||||
0.272052 | + | 0.962282i | \(0.412298\pi\) | |||||||
\(774\) | −2.66320e7 | −1.59790 | ||||||||
\(775\) | 2.68753e7 | 1.60731 | ||||||||
\(776\) | −7.33858e6 | −0.437479 | ||||||||
\(777\) | −1.95365e6 | −0.116090 | ||||||||
\(778\) | −1.23675e7 | −0.732543 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 2.86115e7 | 1.68385 | ||||||||
\(781\) | 1.11047e7 | 0.651448 | ||||||||
\(782\) | 2.02077e6 | 0.118168 | ||||||||
\(783\) | 4.59449e7 | 2.67814 | ||||||||
\(784\) | −4.24297e6 | −0.246536 | ||||||||
\(785\) | 3.91568e7 | 2.26795 | ||||||||
\(786\) | −3.15788e7 | −1.82322 | ||||||||
\(787\) | −1.05569e7 | −0.607572 | −0.303786 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303786 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(788\) | −1.52273e6 | −0.0873587 | ||||||||
\(789\) | −4.15535e7 | −2.37638 | ||||||||
\(790\) | 1.04022e7 | 0.593007 | ||||||||
\(791\) | −250763. | −0.0142502 | ||||||||
\(792\) | 1.30329e7 | 0.738291 | ||||||||
\(793\) | −2.69770e7 | −1.52339 | ||||||||
\(794\) | −6.43352e6 | −0.362157 | ||||||||
\(795\) | 3.67435e6 | 0.206188 | ||||||||
\(796\) | −1.93138e6 | −0.108040 | ||||||||
\(797\) | 3.23295e7 | 1.80282 | 0.901411 | − | 0.432964i | \(-0.142532\pi\) | ||||
0.901411 | + | 0.432964i | \(0.142532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.64107e7 | 0.909410 | ||||||||
\(800\) | −4.11545e6 | −0.227349 | ||||||||
\(801\) | 4.19330e7 | 2.30927 | ||||||||
\(802\) | −1.04022e7 | −0.571071 | ||||||||
\(803\) | 2.24283e7 | 1.22746 | ||||||||
\(804\) | 453822. | 0.0247597 | ||||||||
\(805\) | 489847. | 0.0266423 | ||||||||
\(806\) | 2.14642e7 | 1.16380 | ||||||||
\(807\) | 2.83192e7 | 1.53073 | ||||||||
\(808\) | 2.89461e6 | 0.155978 | ||||||||
\(809\) | 420464. | 0.0225869 | 0.0112935 | − | 0.999936i | \(-0.496405\pi\) | ||||
0.0112935 | + | 0.999936i | \(0.496405\pi\) | |||||||
\(810\) | −1.20042e7 | −0.642865 | ||||||||
\(811\) | −2.57746e7 | −1.37607 | −0.688034 | − | 0.725679i | \(-0.741526\pi\) | ||||
−0.688034 | + | 0.725679i | \(0.741526\pi\) | |||||||
\(812\) | −2.03460e6 | −0.108290 | ||||||||
\(813\) | −2.18746e7 | −1.16068 | ||||||||
\(814\) | 8.74771e6 | 0.462736 | ||||||||
\(815\) | −9.29504e6 | −0.490182 | ||||||||
\(816\) | 8.97875e6 | 0.472053 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −4.96072e6 | −0.259216 | ||||||||
\(819\) | −5.53678e6 | −0.288435 | ||||||||
\(820\) | −1.70102e7 | −0.883436 | ||||||||
\(821\) | 1.69701e7 | 0.878672 | 0.439336 | − | 0.898323i | \(-0.355214\pi\) | ||||
0.439336 | + | 0.898323i | \(0.355214\pi\) | |||||||
\(822\) | 1.44428e7 | 0.745543 | ||||||||
\(823\) | −1.66003e7 | −0.854313 | −0.427157 | − | 0.904178i | \(-0.640485\pi\) | ||||
−0.427157 | + | 0.904178i | \(0.640485\pi\) | |||||||
\(824\) | −3.03493e6 | −0.155715 | ||||||||
\(825\) | 4.77250e7 | 2.44125 | ||||||||
\(826\) | 338004. | 0.0172374 | ||||||||
\(827\) | 2.11542e7 | 1.07556 | 0.537779 | − | 0.843086i | \(-0.319264\pi\) | ||||
0.537779 | + | 0.843086i | \(0.319264\pi\) | |||||||
\(828\) | 2.74726e6 | 0.139259 | ||||||||
\(829\) | 6.12637e6 | 0.309611 | 0.154806 | − | 0.987945i | \(-0.450525\pi\) | ||||
0.154806 | + | 0.987945i | \(0.450525\pi\) | |||||||
\(830\) | −1.27169e7 | −0.640744 | ||||||||
\(831\) | −1.44119e7 | −0.723965 | ||||||||
\(832\) | −3.28683e6 | −0.164615 | ||||||||
\(833\) | 2.20482e7 | 1.10093 | ||||||||
\(834\) | −3.11066e7 | −1.54859 | ||||||||
\(835\) | −4.76089e6 | −0.236305 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.68714e7 | −1.81918 | ||||||||
\(838\) | −6.64562e6 | −0.326908 | ||||||||
\(839\) | 6.14792e6 | 0.301525 | 0.150762 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150762 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(840\) | 2.17650e6 | 0.106429 | ||||||||
\(841\) | 4.89222e7 | 2.38515 | ||||||||
\(842\) | 2.05361e7 | 0.998245 | ||||||||
\(843\) | 2.04162e7 | 0.989476 | ||||||||
\(844\) | 6.18342e6 | 0.298794 | ||||||||
\(845\) | 2.30433e7 | 1.11021 | ||||||||
\(846\) | 2.23105e7 | 1.07172 | ||||||||
\(847\) | 638000. | 0.0305571 | ||||||||
\(848\) | −422102. | −0.0201571 | ||||||||
\(849\) | −1.67932e7 | −0.799584 | ||||||||
\(850\) | 2.13855e7 | 1.01525 | ||||||||
\(851\) | 1.84397e6 | 0.0872830 | ||||||||
\(852\) | 1.04008e7 | 0.490870 | ||||||||
\(853\) | 1.43957e7 | 0.677423 | 0.338711 | − | 0.940890i | \(-0.390009\pi\) | ||||
0.338711 | + | 0.940890i | \(0.390009\pi\) | |||||||
\(854\) | −2.05216e6 | −0.0962869 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.37096e7 | −0.639500 | ||||||||
\(857\) | −3.25050e7 | −1.51181 | −0.755907 | − | 0.654679i | \(-0.772804\pi\) | ||||
−0.755907 | + | 0.654679i | \(0.772804\pi\) | |||||||
\(858\) | 3.81159e7 | 1.76762 | ||||||||
\(859\) | −1.57754e7 | −0.729453 | −0.364726 | − | 0.931115i | \(-0.618838\pi\) | ||||
−0.364726 | + | 0.931115i | \(0.618838\pi\) | |||||||
\(860\) | 1.99145e7 | 0.918169 | ||||||||
\(861\) | 5.06091e6 | 0.232659 | ||||||||
\(862\) | −4.68916e6 | −0.214945 | ||||||||
\(863\) | 3.79160e7 | 1.73299 | 0.866493 | − | 0.499189i | \(-0.166369\pi\) | ||||
0.866493 | + | 0.499189i | \(0.166369\pi\) | |||||||
\(864\) | 5.64616e6 | 0.257317 | ||||||||
\(865\) | 4.35668e6 | 0.197977 | ||||||||
\(866\) | −1.40392e7 | −0.636132 | ||||||||
\(867\) | −9.22211e6 | −0.416661 | ||||||||
\(868\) | 1.63280e6 | 0.0735585 | ||||||||
\(869\) | 1.38577e7 | 0.622505 | ||||||||
\(870\) | −7.42759e7 | −3.32698 | ||||||||
\(871\) | 863276. | 0.0385571 | ||||||||
\(872\) | 1.45193e7 | 0.646630 | ||||||||
\(873\) | 5.18438e7 | 2.30230 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.15313e6 | 0.0509166 | ||||||||
\(876\) | 2.10065e7 | 0.924897 | ||||||||
\(877\) | 5.67995e6 | 0.249371 | 0.124685 | − | 0.992196i | \(-0.460208\pi\) | ||||
0.124685 | + | 0.992196i | \(0.460208\pi\) | |||||||
\(878\) | −1.35042e7 | −0.591199 | ||||||||
\(879\) | −3.03658e7 | −1.32560 | ||||||||
\(880\) | −9.74554e6 | −0.424228 | ||||||||
\(881\) | −3.32419e7 | −1.44293 | −0.721467 | − | 0.692449i | \(-0.756532\pi\) | ||||
−0.721467 | + | 0.692449i | \(0.756532\pi\) | |||||||
\(882\) | 2.99747e7 | 1.29743 | ||||||||
\(883\) | 2.00103e7 | 0.863678 | 0.431839 | − | 0.901951i | \(-0.357865\pi\) | ||||
0.431839 | + | 0.901951i | \(0.357865\pi\) | |||||||
\(884\) | 1.70797e7 | 0.735104 | ||||||||
\(885\) | 1.23393e7 | 0.529581 | ||||||||
\(886\) | −6.03150e6 | −0.258132 | ||||||||
\(887\) | −4.04408e7 | −1.72588 | −0.862941 | − | 0.505304i | \(-0.831380\pi\) | ||||
−0.862941 | + | 0.505304i | \(0.831380\pi\) | |||||||
\(888\) | 8.19317e6 | 0.348674 | ||||||||
\(889\) | −704262. | −0.0298868 | ||||||||
\(890\) | −3.13561e7 | −1.32693 | ||||||||
\(891\) | −1.59918e7 | −0.674843 | ||||||||
\(892\) | 7.24252e6 | 0.304774 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.93893e7 | −0.811371 | ||||||||
\(895\) | 5.47791e7 | 2.28590 | ||||||||
\(896\) | −250032. | −0.0104046 | ||||||||
\(897\) | 8.03463e6 | 0.333415 | ||||||||
\(898\) | −735227. | −0.0304250 | ||||||||
\(899\) | −5.57213e7 | −2.29944 | ||||||||
\(900\) | 2.90738e7 | 1.19645 | ||||||||
\(901\) | 2.19341e6 | 0.0900134 | ||||||||
\(902\) | −2.26608e7 | −0.927382 | ||||||||
\(903\) | −5.92498e6 | −0.241806 | ||||||||
\(904\) | 1.05164e6 | 0.0428003 | ||||||||
\(905\) | −4.16155e7 | −1.68902 | ||||||||
\(906\) | 4.68271e7 | 1.89529 | ||||||||
\(907\) | −2.90090e6 | −0.117088 | −0.0585442 | − | 0.998285i | \(-0.518646\pi\) | ||||
−0.0585442 | + | 0.998285i | \(0.518646\pi\) | |||||||
\(908\) | −369510. | −0.0148734 | ||||||||
\(909\) | −2.04492e7 | −0.820854 | ||||||||
\(910\) | 4.14022e6 | 0.165737 | ||||||||
\(911\) | −2.43185e7 | −0.970824 | −0.485412 | − | 0.874286i | \(-0.661330\pi\) | ||||
−0.485412 | + | 0.874286i | \(0.661330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.69412e7 | −0.672618 | ||||||||
\(914\) | −2.07553e7 | −0.821795 | ||||||||
\(915\) | −7.49170e7 | −2.95820 | ||||||||
\(916\) | 4.98483e6 | 0.196296 | ||||||||
\(917\) | −4.56960e6 | −0.179455 | ||||||||
\(918\) | −2.93397e7 | −1.14908 | ||||||||
\(919\) | 8.22526e6 | 0.321263 | 0.160631 | − | 0.987014i | \(-0.448647\pi\) | ||||
0.160631 | + | 0.987014i | \(0.448647\pi\) | |||||||
\(920\) | −2.05431e6 | −0.0800195 | ||||||||
\(921\) | 5.69696e7 | 2.21307 | ||||||||
\(922\) | −1.38487e7 | −0.536516 | ||||||||
\(923\) | 1.97847e7 | 0.764407 | ||||||||
\(924\) | 2.89951e6 | 0.111724 | ||||||||
\(925\) | 1.95144e7 | 0.749897 | ||||||||
\(926\) | 1.11514e7 | 0.427369 | ||||||||
\(927\) | 2.14404e7 | 0.819472 | ||||||||
\(928\) | 8.53265e6 | 0.325248 | ||||||||
\(929\) | 4.19040e7 | 1.59300 | 0.796501 | − | 0.604638i | \(-0.206682\pi\) | ||||
0.796501 | + | 0.604638i | \(0.206682\pi\) | |||||||
\(930\) | 5.96075e7 | 2.25992 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.34203e7 | −0.506084 | ||||||||
\(933\) | −5.19929e7 | −1.95542 | ||||||||
\(934\) | −719248. | −0.0269781 | ||||||||
\(935\) | 5.06417e7 | 1.89443 | ||||||||
\(936\) | 2.32200e7 | 0.866308 | ||||||||
\(937\) | 2.78186e7 | 1.03511 | 0.517554 | − | 0.855650i | \(-0.326843\pi\) | ||||
0.517554 | + | 0.855650i | \(0.326843\pi\) | |||||||
\(938\) | 65670.1 | 0.00243703 | ||||||||
\(939\) | 1.38992e7 | 0.514429 | ||||||||
\(940\) | −1.66830e7 | −0.615822 | ||||||||
\(941\) | 1.92168e7 | 0.707468 | 0.353734 | − | 0.935346i | \(-0.384912\pi\) | ||||
0.353734 | + | 0.935346i | \(0.384912\pi\) | |||||||
\(942\) | 4.88574e7 | 1.79392 | ||||||||
\(943\) | −4.77677e6 | −0.174926 | ||||||||
\(944\) | −1.41751e6 | −0.0517722 | ||||||||
\(945\) | −7.11212e6 | −0.259071 | ||||||||
\(946\) | 2.65298e7 | 0.963843 | ||||||||
\(947\) | −1.85612e7 | −0.672559 | −0.336280 | − | 0.941762i | \(-0.609169\pi\) | ||||
−0.336280 | + | 0.941762i | \(0.609169\pi\) | |||||||
\(948\) | 1.29793e7 | 0.469061 | ||||||||
\(949\) | 3.99593e7 | 1.44030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.56238e7 | 1.63584 | ||||||||
\(952\) | 1.29926e6 | 0.0464628 | ||||||||
\(953\) | −4.84999e7 | −1.72985 | −0.864926 | − | 0.501900i | \(-0.832635\pi\) | ||||
−0.864926 | + | 0.501900i | \(0.832635\pi\) | |||||||
\(954\) | 2.98196e6 | 0.106079 | ||||||||
\(955\) | 5.69529e6 | 0.202073 | ||||||||
\(956\) | 4.45377e6 | 0.157610 | ||||||||
\(957\) | −9.89495e7 | −3.49248 | ||||||||
\(958\) | 1.29737e7 | 0.456720 | ||||||||
\(959\) | 2.08994e6 | 0.0733817 | ||||||||
\(960\) | −9.12775e6 | −0.319658 | ||||||||
\(961\) | 1.60880e7 | 0.561944 | ||||||||
\(962\) | 1.55853e7 | 0.542973 | ||||||||
\(963\) | 9.68523e7 | 3.36546 | ||||||||
\(964\) | 1.54025e7 | 0.533826 | ||||||||
\(965\) | 1.70280e7 | 0.588636 | ||||||||
\(966\) | 611201. | 0.0210737 | ||||||||
\(967\) | −1.02262e7 | −0.351680 | −0.175840 | − | 0.984419i | \(-0.556264\pi\) | ||||
−0.175840 | + | 0.984419i | \(0.556264\pi\) | |||||||
\(968\) | −2.67562e6 | −0.0917776 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.87670e7 | −1.32292 | ||||||||
\(971\) | −4.50010e7 | −1.53170 | −0.765851 | − | 0.643018i | \(-0.777682\pi\) | ||||
−0.765851 | + | 0.643018i | \(0.777682\pi\) | |||||||
\(972\) | 6.45972e6 | 0.219305 | ||||||||
\(973\) | −4.50126e6 | −0.152424 | ||||||||
\(974\) | 2.19187e7 | 0.740315 | ||||||||
\(975\) | 8.50292e7 | 2.86455 | ||||||||
\(976\) | 8.60630e6 | 0.289196 | ||||||||
\(977\) | −1.34958e7 | −0.452336 | −0.226168 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226168 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(978\) | −1.15978e7 | −0.387728 | ||||||||
\(979\) | −4.17721e7 | −1.39293 | ||||||||
\(980\) | −2.24141e7 | −0.745513 | ||||||||
\(981\) | −1.02573e8 | −3.40298 | ||||||||
\(982\) | 2.58459e7 | 0.855288 | ||||||||
\(983\) | −1.59856e7 | −0.527650 | −0.263825 | − | 0.964571i | \(-0.584984\pi\) | ||||
−0.263825 | + | 0.964571i | \(0.584984\pi\) | |||||||
\(984\) | −2.12243e7 | −0.698788 | ||||||||
\(985\) | −8.04400e6 | −0.264169 | ||||||||
\(986\) | −4.43391e7 | −1.45243 | ||||||||
\(987\) | 4.96356e6 | 0.162181 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.59234e6 | 0.181804 | ||||||||
\(990\) | 6.88479e7 | 2.23256 | ||||||||
\(991\) | −5.93854e6 | −0.192086 | −0.0960430 | − | 0.995377i | \(-0.530619\pi\) | ||||
−0.0960430 | + | 0.995377i | \(0.530619\pi\) | |||||||
\(992\) | −6.84758e6 | −0.220932 | ||||||||
\(993\) | 2.86055e7 | 0.920612 | ||||||||
\(994\) | 1.50504e6 | 0.0483149 | ||||||||
\(995\) | −1.02028e7 | −0.326708 | ||||||||
\(996\) | −1.58673e7 | −0.506821 | ||||||||
\(997\) | −1.69917e7 | −0.541377 | −0.270689 | − | 0.962667i | \(-0.587251\pi\) | ||||
−0.270689 | + | 0.962667i | \(0.587251\pi\) | |||||||
\(998\) | −862028. | −0.0273965 | ||||||||
\(999\) | −2.67727e7 | −0.848747 |
(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 | 722.6.a.q.1.1 | 15 | ||
19.14 | odd | 18 | 38.6.e.b.25.1 | ✓ | 30 | ||
19.15 | odd | 18 | 38.6.e.b.35.1 | yes | 30 | ||
19.18 | odd | 2 | 722.6.a.r.1.15 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.e.b.25.1 | ✓ | 30 | 19.14 | odd | 18 | ||
38.6.e.b.35.1 | yes | 30 | 19.15 | odd | 18 | ||
722.6.a.q.1.1 | 15 | 1.1 | even | 1 | trivial | ||
722.6.a.r.1.15 | 15 | 19.18 | odd | 2 |