Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,6,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, 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("495.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(79.3899908074\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 246 x^{8} + 640 x^{7} + 20433 x^{6} - 44595 x^{5} - 667026 x^{4} + 1173648 x^{3} + 7949136 x^{2} - 8226800 x - 30445728 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.29463\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.29463 | −0.582414 | −0.291207 | − | 0.956660i | \(-0.594057\pi\) | ||||
−0.291207 | + | 0.956660i | \(0.594057\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −21.1454 | −0.660794 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −180.725 | −1.39403 | −0.697017 | − | 0.717054i | \(-0.745490\pi\) | ||||
−0.697017 | + | 0.717054i | \(0.745490\pi\) | |||||||
\(8\) | 175.095 | 0.967270 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −82.3658 | −0.260464 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −945.350 | −1.55144 | −0.775718 | − | 0.631079i | \(-0.782612\pi\) | ||||
−0.775718 | + | 0.631079i | \(0.782612\pi\) | |||||||
\(14\) | 595.423 | 0.811906 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 99.7806 | 0.0974420 | ||||||||
\(17\) | 844.526 | 0.708746 | 0.354373 | − | 0.935104i | \(-0.384694\pi\) | ||||
0.354373 | + | 0.935104i | \(0.384694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2418.74 | −1.53711 | −0.768554 | − | 0.639785i | \(-0.779024\pi\) | ||||
−0.768554 | + | 0.639785i | \(0.779024\pi\) | |||||||
\(20\) | −528.635 | −0.295516 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 398.651 | 0.175604 | ||||||||
\(23\) | −1493.94 | −0.588860 | −0.294430 | − | 0.955673i | \(-0.595130\pi\) | ||||
−0.294430 | + | 0.955673i | \(0.595130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 3114.58 | 0.903579 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3821.51 | 0.921169 | ||||||||
\(29\) | 3410.10 | 0.752961 | 0.376480 | − | 0.926425i | \(-0.377134\pi\) | ||||
0.376480 | + | 0.926425i | \(0.377134\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7071.07 | −1.32154 | −0.660771 | − | 0.750587i | \(-0.729771\pi\) | ||||
−0.660771 | + | 0.750587i | \(0.729771\pi\) | |||||||
\(32\) | −5931.77 | −1.02402 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2782.40 | −0.412784 | ||||||||
\(35\) | −4518.13 | −0.623431 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −270.574 | −0.0324925 | −0.0162462 | − | 0.999868i | \(-0.505172\pi\) | ||||
−0.0162462 | + | 0.999868i | \(0.505172\pi\) | |||||||
\(38\) | 7968.85 | 0.895234 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4377.36 | 0.432576 | ||||||||
\(41\) | −5475.08 | −0.508664 | −0.254332 | − | 0.967117i | \(-0.581856\pi\) | ||||
−0.254332 | + | 0.967117i | \(0.581856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14747.4 | −1.21631 | −0.608154 | − | 0.793819i | \(-0.708090\pi\) | ||||
−0.608154 | + | 0.793819i | \(0.708090\pi\) | |||||||
\(44\) | 2558.59 | 0.199237 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4921.97 | 0.342961 | ||||||||
\(47\) | −6997.75 | −0.462077 | −0.231038 | − | 0.972945i | \(-0.574212\pi\) | ||||
−0.231038 | + | 0.972945i | \(0.574212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15854.6 | 0.943333 | ||||||||
\(50\) | −2059.15 | −0.116483 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19989.8 | 1.02518 | ||||||||
\(53\) | 11572.5 | 0.565900 | 0.282950 | − | 0.959135i | \(-0.408687\pi\) | ||||
0.282950 | + | 0.959135i | \(0.408687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −31644.0 | −1.34841 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11235.0 | −0.438535 | ||||||||
\(59\) | −25557.7 | −0.955855 | −0.477928 | − | 0.878399i | \(-0.658612\pi\) | ||||
−0.477928 | + | 0.878399i | \(0.658612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30403.1 | 1.04615 | 0.523075 | − | 0.852287i | \(-0.324785\pi\) | ||||
0.523075 | + | 0.852287i | \(0.324785\pi\) | |||||||
\(62\) | 23296.6 | 0.769685 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16350.0 | 0.498963 | ||||||||
\(65\) | −23633.7 | −0.693824 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29343.2 | −0.798583 | −0.399291 | − | 0.916824i | \(-0.630744\pi\) | ||||
−0.399291 | + | 0.916824i | \(0.630744\pi\) | |||||||
\(68\) | −17857.8 | −0.468335 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 14885.6 | 0.363095 | ||||||||
\(71\) | −82066.9 | −1.93207 | −0.966033 | − | 0.258418i | \(-0.916799\pi\) | ||||
−0.966033 | + | 0.258418i | \(0.916799\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26184.8 | 0.575097 | 0.287549 | − | 0.957766i | \(-0.407160\pi\) | ||||
0.287549 | + | 0.957766i | \(0.407160\pi\) | |||||||
\(74\) | 891.443 | 0.0189241 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 51145.1 | 1.01571 | ||||||||
\(77\) | 21867.7 | 0.420317 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −61005.4 | −1.09977 | −0.549883 | − | 0.835242i | \(-0.685328\pi\) | ||||
−0.549883 | + | 0.835242i | \(0.685328\pi\) | |||||||
\(80\) | 2494.51 | 0.0435774 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18038.4 | 0.296253 | ||||||||
\(83\) | 109129. | 1.73879 | 0.869394 | − | 0.494120i | \(-0.164510\pi\) | ||||
0.869394 | + | 0.494120i | \(0.164510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21113.2 | 0.316961 | ||||||||
\(86\) | 48587.2 | 0.708395 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −21186.4 | −0.291643 | ||||||||
\(89\) | −63238.7 | −0.846268 | −0.423134 | − | 0.906067i | \(-0.639070\pi\) | ||||
−0.423134 | + | 0.906067i | \(0.639070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 170848. | 2.16276 | ||||||||
\(92\) | 31589.9 | 0.389115 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 23055.0 | 0.269120 | ||||||||
\(95\) | −60468.4 | −0.687416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14447.4 | 0.155905 | 0.0779525 | − | 0.996957i | \(-0.475162\pi\) | ||||
0.0779525 | + | 0.996957i | \(0.475162\pi\) | |||||||
\(98\) | −52235.1 | −0.549410 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13215.9 | −0.132159 | ||||||||
\(101\) | 200117. | 1.95201 | 0.976004 | − | 0.217752i | \(-0.0698725\pi\) | ||||
0.976004 | + | 0.217752i | \(0.0698725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 91402.9 | 0.848920 | 0.424460 | − | 0.905447i | \(-0.360464\pi\) | ||||
0.424460 | + | 0.905447i | \(0.360464\pi\) | |||||||
\(104\) | −165526. | −1.50066 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −38127.3 | −0.329588 | ||||||||
\(107\) | −103550. | −0.874358 | −0.437179 | − | 0.899375i | \(-0.644022\pi\) | ||||
−0.437179 | + | 0.899375i | \(0.644022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −70943.0 | −0.571931 | −0.285965 | − | 0.958240i | \(-0.592314\pi\) | ||||
−0.285965 | + | 0.958240i | \(0.592314\pi\) | |||||||
\(110\) | 9966.26 | 0.0785327 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18032.9 | −0.135838 | ||||||||
\(113\) | −26564.6 | −0.195707 | −0.0978537 | − | 0.995201i | \(-0.531198\pi\) | ||||
−0.0978537 | + | 0.995201i | \(0.531198\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37348.4 | −0.263346 | ||||||||
\(116\) | −72107.9 | −0.497552 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 84203.3 | 0.556704 | ||||||||
\(119\) | −152627. | −0.988017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −100167. | −0.609292 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 149521. | 0.873267 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −56632.1 | −0.311568 | −0.155784 | − | 0.987791i | \(-0.549790\pi\) | ||||
−0.155784 | + | 0.987791i | \(0.549790\pi\) | |||||||
\(128\) | 135949. | 0.733419 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 77864.5 | 0.404093 | ||||||||
\(131\) | 267308. | 1.36092 | 0.680462 | − | 0.732783i | \(-0.261779\pi\) | ||||
0.680462 | + | 0.732783i | \(0.261779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 437127. | 2.14278 | ||||||||
\(134\) | 96674.9 | 0.465106 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 147872. | 0.685549 | ||||||||
\(137\) | −31486.0 | −0.143323 | −0.0716615 | − | 0.997429i | \(-0.522830\pi\) | ||||
−0.0716615 | + | 0.997429i | \(0.522830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 204257. | 0.896686 | 0.448343 | − | 0.893862i | \(-0.352014\pi\) | ||||
0.448343 | + | 0.893862i | \(0.352014\pi\) | |||||||
\(140\) | 95537.7 | 0.411959 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 270380. | 1.12526 | ||||||||
\(143\) | 114387. | 0.467776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 85252.5 | 0.336734 | ||||||||
\(146\) | −86269.2 | −0.334945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5721.40 | 0.0214708 | ||||||||
\(149\) | 73706.2 | 0.271981 | 0.135990 | − | 0.990710i | \(-0.456578\pi\) | ||||
0.135990 | + | 0.990710i | \(0.456578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 394152. | 1.40677 | 0.703383 | − | 0.710811i | \(-0.251672\pi\) | ||||
0.703383 | + | 0.710811i | \(0.251672\pi\) | |||||||
\(152\) | −423508. | −1.48680 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −72046.2 | −0.244799 | ||||||||
\(155\) | −176777. | −0.591012 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −103881. | −0.336345 | −0.168173 | − | 0.985758i | \(-0.553787\pi\) | ||||
−0.168173 | + | 0.985758i | \(0.553787\pi\) | |||||||
\(158\) | 200990. | 0.640519 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −148294. | −0.457956 | ||||||||
\(161\) | 269992. | 0.820892 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −128673. | −0.379330 | −0.189665 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189665 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(164\) | 115773. | 0.336122 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −359541. | −1.01269 | ||||||||
\(167\) | 172447. | 0.478481 | 0.239240 | − | 0.970960i | \(-0.423102\pi\) | ||||
0.239240 | + | 0.970960i | \(0.423102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 522393. | 1.40696 | ||||||||
\(170\) | −69560.1 | −0.184603 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 311839. | 0.803729 | ||||||||
\(173\) | 729257. | 1.85253 | 0.926265 | − | 0.376872i | \(-0.123000\pi\) | ||||
0.926265 | + | 0.376872i | \(0.123000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −112953. | −0.278807 | ||||||||
\(176\) | −12073.5 | −0.0293799 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 208348. | 0.492879 | ||||||||
\(179\) | 569405. | 1.32828 | 0.664138 | − | 0.747610i | \(-0.268799\pi\) | ||||
0.664138 | + | 0.747610i | \(0.268799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −57038.7 | −0.129412 | −0.0647058 | − | 0.997904i | \(-0.520611\pi\) | ||||
−0.0647058 | + | 0.997904i | \(0.520611\pi\) | |||||||
\(182\) | −562883. | −1.25962 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −261580. | −0.569587 | ||||||||
\(185\) | −6764.36 | −0.0145311 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −102188. | −0.213695 | ||||||||
\(188\) | 147970. | 0.305337 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 199221. | 0.400361 | ||||||||
\(191\) | 8693.32 | 0.0172426 | 0.00862129 | − | 0.999963i | \(-0.497256\pi\) | ||||
0.00862129 | + | 0.999963i | \(0.497256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −373496. | −0.721760 | −0.360880 | − | 0.932612i | \(-0.617524\pi\) | ||||
−0.360880 | + | 0.932612i | \(0.617524\pi\) | |||||||
\(194\) | −47598.8 | −0.0908013 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −335252. | −0.623348 | ||||||||
\(197\) | 197958. | 0.363418 | 0.181709 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181709 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −220261. | −0.394281 | −0.197140 | − | 0.980375i | \(-0.563166\pi\) | ||||
−0.197140 | + | 0.980375i | \(0.563166\pi\) | |||||||
\(200\) | 109434. | 0.193454 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −659314. | −1.13688 | ||||||||
\(203\) | −616291. | −1.04965 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −136877. | −0.227481 | ||||||||
\(206\) | −301139. | −0.494423 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −94327.5 | −0.151175 | ||||||||
\(209\) | 292667. | 0.463456 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 917849. | 1.41927 | 0.709635 | − | 0.704569i | \(-0.248860\pi\) | ||||
0.709635 | + | 0.704569i | \(0.248860\pi\) | |||||||
\(212\) | −244706. | −0.373943 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 341158. | 0.509238 | ||||||||
\(215\) | −368684. | −0.543950 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.27792e6 | 1.84228 | ||||||||
\(218\) | 233731. | 0.333101 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 63964.8 | 0.0891014 | ||||||||
\(221\) | −798372. | −1.09958 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19384e6 | 1.60763 | 0.803813 | − | 0.594882i | \(-0.202801\pi\) | ||||
0.803813 | + | 0.594882i | \(0.202801\pi\) | |||||||
\(224\) | 1.07202e6 | 1.42752 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 87520.6 | 0.113983 | ||||||||
\(227\) | −397814. | −0.512407 | −0.256204 | − | 0.966623i | \(-0.582472\pi\) | ||||
−0.256204 | + | 0.966623i | \(0.582472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −543516. | −0.684895 | −0.342447 | − | 0.939537i | \(-0.611256\pi\) | ||||
−0.342447 | + | 0.939537i | \(0.611256\pi\) | |||||||
\(230\) | 123049. | 0.153377 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 597090. | 0.728316 | ||||||||
\(233\) | −1.07137e6 | −1.29285 | −0.646426 | − | 0.762977i | \(-0.723737\pi\) | ||||
−0.646426 | + | 0.762977i | \(0.723737\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −174944. | −0.206647 | ||||||||
\(236\) | 540428. | 0.631623 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 502850. | 0.575435 | ||||||||
\(239\) | 127756. | 0.144673 | 0.0723365 | − | 0.997380i | \(-0.476954\pi\) | ||||
0.0723365 | + | 0.997380i | \(0.476954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 209989. | 0.232892 | 0.116446 | − | 0.993197i | \(-0.462850\pi\) | ||||
0.116446 | + | 0.993197i | \(0.462850\pi\) | |||||||
\(242\) | −48236.7 | −0.0529467 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −642886. | −0.691289 | ||||||||
\(245\) | 396365. | 0.421871 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.28655e6 | 2.38473 | ||||||||
\(248\) | −1.23811e6 | −1.27829 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −51478.6 | −0.0520927 | ||||||||
\(251\) | 109061. | 0.109266 | 0.0546329 | − | 0.998507i | \(-0.482601\pi\) | ||||
0.0546329 | + | 0.998507i | \(0.482601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 180766. | 0.177548 | ||||||||
\(254\) | 186582. | 0.181462 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −971103. | −0.926116 | ||||||||
\(257\) | 1.90416e6 | 1.79834 | 0.899168 | − | 0.437603i | \(-0.144173\pi\) | ||||
0.899168 | + | 0.437603i | \(0.144173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48899.6 | 0.0452956 | ||||||||
\(260\) | 499745. | 0.458474 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −880683. | −0.792622 | ||||||||
\(263\) | 1.97795e6 | 1.76330 | 0.881651 | − | 0.471903i | \(-0.156433\pi\) | ||||
0.881651 | + | 0.471903i | \(0.156433\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 289314. | 0.253078 | ||||||||
\(266\) | −1.44017e6 | −1.24799 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 620473. | 0.527699 | ||||||||
\(269\) | −1.41432e6 | −1.19170 | −0.595849 | − | 0.803096i | \(-0.703184\pi\) | ||||
−0.595849 | + | 0.803096i | \(0.703184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.62919e6 | −1.34756 | −0.673780 | − | 0.738932i | \(-0.735331\pi\) | ||||
−0.673780 | + | 0.738932i | \(0.735331\pi\) | |||||||
\(272\) | 84267.3 | 0.0690616 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 103735. | 0.0834734 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 320454. | 0.250938 | 0.125469 | − | 0.992098i | \(-0.459956\pi\) | ||||
0.125469 | + | 0.992098i | \(0.459956\pi\) | |||||||
\(278\) | −672953. | −0.522243 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −791100. | −0.603026 | ||||||||
\(281\) | −2.38129e6 | −1.79906 | −0.899530 | − | 0.436858i | \(-0.856091\pi\) | ||||
−0.899530 | + | 0.436858i | \(0.856091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −493913. | −0.366593 | −0.183297 | − | 0.983058i | \(-0.558677\pi\) | ||||
−0.183297 | + | 0.983058i | \(0.558677\pi\) | |||||||
\(284\) | 1.73534e6 | 1.27670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −376864. | −0.272439 | ||||||||
\(287\) | 989485. | 0.709095 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −706633. | −0.497679 | ||||||||
\(290\) | −280876. | −0.196119 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −553687. | −0.380021 | ||||||||
\(293\) | 2.24861e6 | 1.53019 | 0.765094 | − | 0.643919i | \(-0.222693\pi\) | ||||
0.765094 | + | 0.643919i | \(0.222693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −638943. | −0.427472 | ||||||||
\(296\) | −47376.1 | −0.0314290 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −242835. | −0.158405 | ||||||||
\(299\) | 1.41229e6 | 0.913579 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.66522e6 | 1.69558 | ||||||||
\(302\) | −1.29859e6 | −0.819320 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −241343. | −0.149779 | ||||||||
\(305\) | 760078. | 0.467852 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.86642e6 | −1.13022 | −0.565111 | − | 0.825015i | \(-0.691167\pi\) | ||||
−0.565111 | + | 0.825015i | \(0.691167\pi\) | |||||||
\(308\) | −462402. | −0.277743 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 582415. | 0.344214 | ||||||||
\(311\) | −1.35283e6 | −0.793128 | −0.396564 | − | 0.918007i | \(-0.629797\pi\) | ||||
−0.396564 | + | 0.918007i | \(0.629797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 528408. | 0.304866 | 0.152433 | − | 0.988314i | \(-0.451289\pi\) | ||||
0.152433 | + | 0.988314i | \(0.451289\pi\) | |||||||
\(314\) | 342248. | 0.195892 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.28998e6 | 0.726718 | ||||||||
\(317\) | −1.64065e6 | −0.916996 | −0.458498 | − | 0.888695i | \(-0.651612\pi\) | ||||
−0.458498 | + | 0.888695i | \(0.651612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −412622. | −0.227026 | ||||||||
\(320\) | 408750. | 0.223143 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −889524. | −0.478099 | ||||||||
\(323\) | −2.04269e6 | −1.08942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −590844. | −0.310287 | ||||||||
\(326\) | 423929. | 0.220927 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −958657. | −0.492015 | ||||||||
\(329\) | 1.26467e6 | 0.644151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.07626e6 | −1.04163 | −0.520814 | − | 0.853670i | \(-0.674371\pi\) | ||||
−0.520814 | + | 0.853670i | \(0.674371\pi\) | |||||||
\(332\) | −2.30758e6 | −1.14898 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −568150. | −0.278674 | ||||||||
\(335\) | −733579. | −0.357137 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.66930e6 | −1.28033 | −0.640165 | − | 0.768237i | \(-0.721134\pi\) | ||||
−0.640165 | + | 0.768237i | \(0.721134\pi\) | |||||||
\(338\) | −1.72109e6 | −0.819431 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −446446. | −0.209446 | ||||||||
\(341\) | 855600. | 0.398460 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 172124. | 0.0789960 | ||||||||
\(344\) | −2.58219e6 | −1.17650 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.40263e6 | −1.07894 | ||||||||
\(347\) | −1.83737e6 | −0.819169 | −0.409585 | − | 0.912272i | \(-0.634326\pi\) | ||||
−0.409585 | + | 0.912272i | \(0.634326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.67575e6 | −1.61541 | −0.807705 | − | 0.589587i | \(-0.799291\pi\) | ||||
−0.807705 | + | 0.589587i | \(0.799291\pi\) | |||||||
\(350\) | 372139. | 0.162381 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 717744. | 0.308754 | ||||||||
\(353\) | 3.11656e6 | 1.33118 | 0.665592 | − | 0.746316i | \(-0.268179\pi\) | ||||
0.665592 | + | 0.746316i | \(0.268179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.05167e6 | −0.864046 | ||||||||
\(356\) | 1.33721e6 | 0.559209 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.87598e6 | −0.773607 | ||||||||
\(359\) | −1.30402e6 | −0.534008 | −0.267004 | − | 0.963695i | \(-0.586034\pi\) | ||||
−0.267004 | + | 0.963695i | \(0.586034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.37419e6 | 1.36270 | ||||||||
\(362\) | 187922. | 0.0753712 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.61266e6 | −1.42914 | ||||||||
\(365\) | 654619. | 0.257191 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.47448e6 | −1.34656 | −0.673279 | − | 0.739388i | \(-0.735115\pi\) | ||||
−0.673279 | + | 0.739388i | \(0.735115\pi\) | |||||||
\(368\) | −149066. | −0.0573797 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22286.1 | 0.00846310 | ||||||||
\(371\) | −2.09145e6 | −0.788884 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.49852e6 | −0.929846 | −0.464923 | − | 0.885351i | \(-0.653918\pi\) | ||||
−0.464923 | + | 0.885351i | \(0.653918\pi\) | |||||||
\(374\) | 336671. | 0.124459 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.22527e6 | −0.446953 | ||||||||
\(377\) | −3.22374e6 | −1.16817 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.45997e6 | −0.522091 | −0.261045 | − | 0.965327i | \(-0.584067\pi\) | ||||
−0.261045 | + | 0.965327i | \(0.584067\pi\) | |||||||
\(380\) | 1.27863e6 | 0.454240 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −28641.3 | −0.0100423 | ||||||||
\(383\) | −286578. | −0.0998267 | −0.0499133 | − | 0.998754i | \(-0.515895\pi\) | ||||
−0.0499133 | + | 0.998754i | \(0.515895\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 546694. | 0.187972 | ||||||||
\(386\) | 1.23053e6 | 0.420363 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −305496. | −0.103021 | ||||||||
\(389\) | −3.29651e6 | −1.10454 | −0.552269 | − | 0.833666i | \(-0.686238\pi\) | ||||
−0.552269 | + | 0.833666i | \(0.686238\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.26167e6 | −0.417353 | ||||||||
\(392\) | 2.77605e6 | 0.912457 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −652197. | −0.211660 | ||||||||
\(395\) | −1.52513e6 | −0.491830 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.23453e6 | 0.393119 | 0.196559 | − | 0.980492i | \(-0.437023\pi\) | ||||
0.196559 | + | 0.980492i | \(0.437023\pi\) | |||||||
\(398\) | 725680. | 0.229635 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 62362.9 | 0.0194884 | ||||||||
\(401\) | −1.22869e6 | −0.381575 | −0.190788 | − | 0.981631i | \(-0.561104\pi\) | ||||
−0.190788 | + | 0.981631i | \(0.561104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.68464e6 | 2.05029 | ||||||||
\(404\) | −4.23156e6 | −1.28987 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.03045e6 | 0.611333 | ||||||||
\(407\) | 32739.5 | 0.00979684 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.55858e6 | 0.460703 | 0.230351 | − | 0.973107i | \(-0.426012\pi\) | ||||
0.230351 | + | 0.973107i | \(0.426012\pi\) | |||||||
\(410\) | 450960. | 0.132488 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.93275e6 | −0.560961 | ||||||||
\(413\) | 4.61893e6 | 1.33250 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.72823e6 | 0.777609 | ||||||||
\(416\) | 5.60759e6 | 1.58870 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −964230. | −0.269923 | ||||||||
\(419\) | 2.29946e6 | 0.639868 | 0.319934 | − | 0.947440i | \(-0.396339\pi\) | ||||
0.319934 | + | 0.947440i | \(0.396339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 145656. | 0.0400520 | 0.0200260 | − | 0.999799i | \(-0.493625\pi\) | ||||
0.0200260 | + | 0.999799i | \(0.493625\pi\) | |||||||
\(422\) | −3.02398e6 | −0.826603 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.02629e6 | 0.547378 | ||||||||
\(425\) | 527829. | 0.141749 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.49461e6 | −1.45837 | ||||||||
\(428\) | 2.18960e6 | 0.577770 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.21468e6 | 0.316804 | ||||||||
\(431\) | −2069.36 | −0.000536589 0 | −0.000268295 | − | 1.00000i | \(-0.500085\pi\) | ||||
−0.000268295 | 1.00000i | \(0.500085\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.66773e6 | 0.940108 | 0.470054 | − | 0.882638i | \(-0.344235\pi\) | ||||
0.470054 | + | 0.882638i | \(0.344235\pi\) | |||||||
\(434\) | −4.21028e6 | −1.07297 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.50012e6 | 0.377928 | ||||||||
\(437\) | 3.61344e6 | 0.905142 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.46332e6 | −1.84829 | −0.924147 | − | 0.382038i | \(-0.875222\pi\) | ||||
−0.924147 | + | 0.382038i | \(0.875222\pi\) | |||||||
\(440\) | −529661. | −0.130427 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.63034e6 | 0.640408 | ||||||||
\(443\) | 6.66093e6 | 1.61260 | 0.806298 | − | 0.591509i | \(-0.201468\pi\) | ||||
0.806298 | + | 0.591509i | \(0.201468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.58097e6 | −0.378463 | ||||||||
\(446\) | −3.93327e6 | −0.936304 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.95486e6 | −0.695571 | ||||||||
\(449\) | −1.48930e6 | −0.348631 | −0.174316 | − | 0.984690i | \(-0.555771\pi\) | ||||
−0.174316 | + | 0.984690i | \(0.555771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 662485. | 0.153368 | ||||||||
\(452\) | 561719. | 0.129322 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.31065e6 | 0.298433 | ||||||||
\(455\) | 4.27121e6 | 0.967214 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.53066e6 | 1.68672 | 0.843359 | − | 0.537351i | \(-0.180575\pi\) | ||||
0.843359 | + | 0.537351i | \(0.180575\pi\) | |||||||
\(458\) | 1.79069e6 | 0.398892 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 789746. | 0.174018 | ||||||||
\(461\) | −7.53965e6 | −1.65234 | −0.826169 | − | 0.563422i | \(-0.809484\pi\) | ||||
−0.826169 | + | 0.563422i | \(0.809484\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.38293e6 | −0.950193 | −0.475096 | − | 0.879934i | \(-0.657587\pi\) | ||||
−0.475096 | + | 0.879934i | \(0.657587\pi\) | |||||||
\(464\) | 340262. | 0.0733700 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.52976e6 | 0.752975 | ||||||||
\(467\) | 5.28954e6 | 1.12234 | 0.561172 | − | 0.827699i | \(-0.310351\pi\) | ||||
0.561172 | + | 0.827699i | \(0.310351\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.30305e6 | 1.11325 | ||||||||
\(470\) | 576376. | 0.120354 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.47502e6 | −0.924570 | ||||||||
\(473\) | 1.78443e6 | 0.366731 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.51171e6 | −0.307422 | ||||||||
\(476\) | 3.22736e6 | 0.652875 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −420910. | −0.0842596 | ||||||||
\(479\) | −5.14928e6 | −1.02543 | −0.512717 | − | 0.858558i | \(-0.671361\pi\) | ||||
−0.512717 | + | 0.858558i | \(0.671361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 255787. | 0.0504100 | ||||||||
\(482\) | −691838. | −0.135640 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −309590. | −0.0600722 | ||||||||
\(485\) | 361185. | 0.0697228 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.47941e6 | 0.282661 | 0.141331 | − | 0.989962i | \(-0.454862\pi\) | ||||
0.141331 | + | 0.989962i | \(0.454862\pi\) | |||||||
\(488\) | 5.32342e6 | 1.01191 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.30588e6 | −0.245704 | ||||||||
\(491\) | 324127. | 0.0606753 | 0.0303376 | − | 0.999540i | \(-0.490342\pi\) | ||||
0.0303376 | + | 0.999540i | \(0.490342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.87992e6 | 0.533658 | ||||||||
\(494\) | −7.53335e6 | −1.38890 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −705556. | −0.128774 | ||||||||
\(497\) | 1.48316e7 | 2.69337 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.12721e6 | −1.46113 | −0.730567 | − | 0.682841i | \(-0.760744\pi\) | ||||
−0.730567 | + | 0.682841i | \(0.760744\pi\) | |||||||
\(500\) | −330397. | −0.0591032 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −359315. | −0.0636379 | ||||||||
\(503\) | 4.32339e6 | 0.761911 | 0.380956 | − | 0.924593i | \(-0.375595\pi\) | ||||
0.380956 | + | 0.924593i | \(0.375595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00294e6 | 0.872965 | ||||||||
\(506\) | −595558. | −0.103407 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.19751e6 | 0.205882 | ||||||||
\(509\) | 8.17724e6 | 1.39898 | 0.699491 | − | 0.714641i | \(-0.253410\pi\) | ||||
0.699491 | + | 0.714641i | \(0.253410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.73225e6 | −0.801706 | ||||||||
\(512\) | −1.15095e6 | −0.194035 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.27351e6 | −1.04738 | ||||||||
\(515\) | 2.28507e6 | 0.379649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 846728. | 0.139321 | ||||||||
\(518\) | −161106. | −0.0263808 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.13814e6 | −0.671115 | ||||||||
\(521\) | −7.40849e6 | −1.19574 | −0.597868 | − | 0.801595i | \(-0.703985\pi\) | ||||
−0.597868 | + | 0.801595i | \(0.703985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.52332e6 | 1.04283 | 0.521416 | − | 0.853303i | \(-0.325404\pi\) | ||||
0.521416 | + | 0.853303i | \(0.325404\pi\) | |||||||
\(524\) | −5.65234e6 | −0.899291 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.51663e6 | −1.02697 | ||||||||
\(527\) | −5.97171e6 | −0.936638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.20450e6 | −0.653244 | ||||||||
\(530\) | −953182. | −0.147396 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.24321e6 | −1.41594 | ||||||||
\(533\) | 5.17587e6 | 0.789160 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.58874e6 | −0.391025 | ||||||||
\(536\) | −5.13783e6 | −0.772445 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.65966e6 | 0.694062 | ||||||||
\(539\) | −1.91841e6 | −0.284426 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.91809e6 | 0.281758 | 0.140879 | − | 0.990027i | \(-0.455007\pi\) | ||||
0.140879 | + | 0.990027i | \(0.455007\pi\) | |||||||
\(542\) | 5.36758e6 | 0.784839 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.00953e6 | −0.725771 | ||||||||
\(545\) | −1.77358e6 | −0.255775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.18882e6 | 1.02728 | 0.513640 | − | 0.858006i | \(-0.328297\pi\) | ||||
0.513640 | + | 0.858006i | \(0.328297\pi\) | |||||||
\(548\) | 665784. | 0.0947069 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 249157. | 0.0351209 | ||||||||
\(551\) | −8.24813e6 | −1.15738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.10252e7 | 1.53311 | ||||||||
\(554\) | −1.05578e6 | −0.146150 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.31910e6 | −0.592525 | ||||||||
\(557\) | 5.90963e6 | 0.807091 | 0.403546 | − | 0.914960i | \(-0.367778\pi\) | ||||
0.403546 | + | 0.914960i | \(0.367778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.39414e7 | 1.88703 | ||||||||
\(560\) | −450822. | −0.0607484 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.84546e6 | 1.04780 | ||||||||
\(563\) | 1.11686e6 | 0.148501 | 0.0742504 | − | 0.997240i | \(-0.476344\pi\) | ||||
0.0742504 | + | 0.997240i | \(0.476344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −664115. | −0.0875230 | ||||||||
\(566\) | 1.62726e6 | 0.213509 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.43695e7 | −1.86883 | ||||||||
\(569\) | 2.10146e6 | 0.272107 | 0.136054 | − | 0.990701i | \(-0.456558\pi\) | ||||
0.136054 | + | 0.990701i | \(0.456558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.14330e7 | 1.46747 | 0.733736 | − | 0.679435i | \(-0.237775\pi\) | ||||
0.733736 | + | 0.679435i | \(0.237775\pi\) | |||||||
\(572\) | −2.41877e6 | −0.309103 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.25999e6 | −0.412987 | ||||||||
\(575\) | −933710. | −0.117772 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.77121e6 | 1.22182 | 0.610912 | − | 0.791698i | \(-0.290803\pi\) | ||||
0.610912 | + | 0.791698i | \(0.290803\pi\) | |||||||
\(578\) | 2.32809e6 | 0.289855 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.80270e6 | −0.222512 | ||||||||
\(581\) | −1.97224e7 | −2.42393 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.40028e6 | −0.170625 | ||||||||
\(584\) | 4.58481e6 | 0.556274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.40833e6 | −0.891203 | ||||||||
\(587\) | −1.31926e7 | −1.58028 | −0.790140 | − | 0.612927i | \(-0.789992\pi\) | ||||
−0.790140 | + | 0.612927i | \(0.789992\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.71031e7 | 2.03135 | ||||||||
\(590\) | 2.10508e6 | 0.248965 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26998.1 | −0.00316613 | ||||||||
\(593\) | −5.13585e6 | −0.599757 | −0.299879 | − | 0.953977i | \(-0.596946\pi\) | ||||
−0.299879 | + | 0.953977i | \(0.596946\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.81568e6 | −0.441855 | ||||||||
\(596\) | −1.55855e6 | −0.179723 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.65298e6 | −0.532082 | ||||||||
\(599\) | 4.57610e6 | 0.521109 | 0.260554 | − | 0.965459i | \(-0.416095\pi\) | ||||
0.260554 | + | 0.965459i | \(0.416095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.10948e7 | 1.25295 | 0.626477 | − | 0.779440i | \(-0.284496\pi\) | ||||
0.626477 | + | 0.779440i | \(0.284496\pi\) | |||||||
\(602\) | −8.78093e6 | −0.987527 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.33451e6 | −0.929582 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.73172e7 | 1.90768 | 0.953838 | − | 0.300320i | \(-0.0970935\pi\) | ||||
0.953838 | + | 0.300320i | \(0.0970935\pi\) | |||||||
\(608\) | 1.43474e7 | 1.57403 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.50418e6 | −0.272484 | ||||||||
\(611\) | 6.61532e6 | 0.716883 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.17134e7 | 1.25902 | 0.629509 | − | 0.776993i | \(-0.283256\pi\) | ||||
0.629509 | + | 0.776993i | \(0.283256\pi\) | |||||||
\(614\) | 6.14917e6 | 0.658258 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.82892e6 | 0.406560 | ||||||||
\(617\) | 4.37822e6 | 0.463003 | 0.231502 | − | 0.972834i | \(-0.425636\pi\) | ||||
0.231502 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.72030e6 | 0.285358 | 0.142679 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142679 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(620\) | 3.73802e6 | 0.390537 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.45709e6 | 0.461929 | ||||||||
\(623\) | 1.14288e7 | 1.17973 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.74091e6 | −0.177558 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.19660e6 | 0.222255 | ||||||||
\(629\) | −228507. | −0.0230289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.12758e7 | 1.12739 | 0.563696 | − | 0.825982i | \(-0.309379\pi\) | ||||
0.563696 | + | 0.825982i | \(0.309379\pi\) | |||||||
\(632\) | −1.06817e7 | −1.06377 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.40533e6 | 0.534071 | ||||||||
\(635\) | −1.41580e6 | −0.139338 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.49881e7 | −1.46352 | ||||||||
\(638\) | 1.35944e6 | 0.132223 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.39873e6 | 0.327995 | ||||||||
\(641\) | 9.52986e6 | 0.916097 | 0.458049 | − | 0.888927i | \(-0.348549\pi\) | ||||
0.458049 | + | 0.888927i | \(0.348549\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 74782.1 | 0.00713297 | 0.00356648 | − | 0.999994i | \(-0.498865\pi\) | ||||
0.00356648 | + | 0.999994i | \(0.498865\pi\) | |||||||
\(644\) | −5.70908e6 | −0.542440 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.72990e6 | 0.634494 | ||||||||
\(647\) | −1.16024e7 | −1.08965 | −0.544827 | − | 0.838549i | \(-0.683405\pi\) | ||||
−0.544827 | + | 0.838549i | \(0.683405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.09248e6 | 0.288201 | ||||||||
\(650\) | 1.94661e6 | 0.180716 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.72084e6 | 0.250659 | ||||||||
\(653\) | −1.51711e7 | −1.39231 | −0.696154 | − | 0.717892i | \(-0.745107\pi\) | ||||
−0.696154 | + | 0.717892i | \(0.745107\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.68271e6 | 0.608624 | ||||||||
\(656\) | −546307. | −0.0495652 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.16662e6 | −0.375163 | ||||||||
\(659\) | 1.44146e7 | 1.29298 | 0.646488 | − | 0.762924i | \(-0.276237\pi\) | ||||
0.646488 | + | 0.762924i | \(0.276237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.51827e6 | −0.758312 | −0.379156 | − | 0.925333i | \(-0.623786\pi\) | ||||
−0.379156 | + | 0.925333i | \(0.623786\pi\) | |||||||
\(662\) | 6.84053e6 | 0.606659 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.91080e7 | 1.68188 | ||||||||
\(665\) | 1.09282e7 | 0.958281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.09447e6 | −0.443389 | ||||||||
\(668\) | −3.64646e6 | −0.316177 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.41687e6 | 0.208002 | ||||||||
\(671\) | −3.67878e6 | −0.315426 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.99938e6 | 0.851012 | 0.425506 | − | 0.904956i | \(-0.360096\pi\) | ||||
0.425506 | + | 0.904956i | \(0.360096\pi\) | |||||||
\(674\) | 8.79435e6 | 0.745683 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.10462e7 | −0.929708 | ||||||||
\(677\) | −3.47845e6 | −0.291685 | −0.145842 | − | 0.989308i | \(-0.546589\pi\) | ||||
−0.145842 | + | 0.989308i | \(0.546589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.61101e6 | −0.217337 | ||||||||
\(680\) | 3.69680e6 | 0.306587 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.81889e6 | −0.232069 | ||||||||
\(683\) | 156171. | 0.0128099 | 0.00640497 | − | 0.999979i | \(-0.497961\pi\) | ||||
0.00640497 | + | 0.999979i | \(0.497961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −787150. | −0.0640960 | ||||||||
\(686\) | −567084. | −0.0460084 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.47150e6 | −0.118519 | ||||||||
\(689\) | −1.09401e7 | −0.877957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.30184e6 | −0.422407 | −0.211204 | − | 0.977442i | \(-0.567738\pi\) | ||||
−0.211204 | + | 0.977442i | \(0.567738\pi\) | |||||||
\(692\) | −1.54204e7 | −1.22414 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.05347e6 | 0.477096 | ||||||||
\(695\) | 5.10643e6 | 0.401010 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.62385e6 | −0.360514 | ||||||||
\(698\) | 1.21103e7 | 0.940838 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.38844e6 | 0.184234 | ||||||||
\(701\) | −2.17241e7 | −1.66973 | −0.834865 | − | 0.550455i | \(-0.814454\pi\) | ||||
−0.834865 | + | 0.550455i | \(0.814454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 654448. | 0.0499444 | ||||||||
\(704\) | −1.97835e6 | −0.150443 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.02679e7 | −0.775301 | ||||||||
\(707\) | −3.61663e7 | −2.72117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −138290. | −0.0103318 | −0.00516589 | − | 0.999987i | \(-0.501644\pi\) | ||||
−0.00516589 | + | 0.999987i | \(0.501644\pi\) | |||||||
\(710\) | 6.75950e6 | 0.503233 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.10728e7 | −0.818570 | ||||||||
\(713\) | 1.05637e7 | 0.778204 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.85968e6 | 0.209196 | ||||||||
\(716\) | −1.20403e7 | −0.877717 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.29626e6 | 0.311014 | ||||||||
\(719\) | −2.45634e7 | −1.77201 | −0.886007 | − | 0.463672i | \(-0.846532\pi\) | ||||
−0.886007 | + | 0.463672i | \(0.846532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.65188e7 | −1.18342 | ||||||||
\(722\) | −1.11167e7 | −0.793657 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.20611e6 | 0.0855144 | ||||||||
\(725\) | 2.13131e6 | 0.150592 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.75381e7 | 1.23068 | 0.615342 | − | 0.788260i | \(-0.289018\pi\) | ||||
0.615342 | + | 0.788260i | \(0.289018\pi\) | |||||||
\(728\) | 2.99146e7 | 2.09197 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.15673e6 | −0.149792 | ||||||||
\(731\) | −1.24545e7 | −0.862054 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.22300e7 | −0.840750 | −0.420375 | − | 0.907350i | \(-0.638101\pi\) | ||||
−0.420375 | + | 0.907350i | \(0.638101\pi\) | |||||||
\(734\) | 1.14471e7 | 0.784255 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.86168e6 | 0.603006 | ||||||||
\(737\) | 3.55052e6 | 0.240782 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.41581e7 | 0.953664 | 0.476832 | − | 0.878995i | \(-0.341785\pi\) | ||||
0.476832 | + | 0.878995i | \(0.341785\pi\) | |||||||
\(740\) | 143035. | 0.00960204 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.89056e6 | 0.459457 | ||||||||
\(743\) | −1.13314e7 | −0.753029 | −0.376515 | − | 0.926411i | \(-0.622878\pi\) | ||||
−0.376515 | + | 0.926411i | \(0.622878\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.84265e6 | 0.121634 | ||||||||
\(746\) | 8.23171e6 | 0.541556 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.16080e6 | 0.141208 | ||||||||
\(749\) | 1.87140e7 | 1.21889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.62110e7 | 1.69584 | 0.847919 | − | 0.530125i | \(-0.177855\pi\) | ||||
0.847919 | + | 0.530125i | \(0.177855\pi\) | |||||||
\(752\) | −698240. | −0.0450257 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.06210e7 | 0.680359 | ||||||||
\(755\) | 9.85381e6 | 0.629125 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −83559.5 | −0.00529976 | −0.00264988 | − | 0.999996i | \(-0.500843\pi\) | ||||
−0.00264988 | + | 0.999996i | \(0.500843\pi\) | |||||||
\(758\) | 4.81007e6 | 0.304073 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.05877e7 | −0.664917 | ||||||||
\(761\) | −2.52607e7 | −1.58119 | −0.790596 | − | 0.612339i | \(-0.790229\pi\) | ||||
−0.790596 | + | 0.612339i | \(0.790229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.28212e7 | 0.797291 | ||||||||
\(764\) | −183824. | −0.0113938 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 944171. | 0.0581405 | ||||||||
\(767\) | 2.41610e7 | 1.48295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.97858e6 | 0.303592 | 0.151796 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151796 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(770\) | −1.80115e6 | −0.109477 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.89773e6 | 0.476935 | ||||||||
\(773\) | −500595. | −0.0301327 | −0.0150664 | − | 0.999886i | \(-0.504796\pi\) | ||||
−0.0150664 | + | 0.999886i | \(0.504796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.41942e6 | −0.264308 | ||||||||
\(776\) | 2.52966e6 | 0.150802 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.08608e7 | 0.643298 | ||||||||
\(779\) | 1.32428e7 | 0.781872 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.93009e6 | 0.582540 | ||||||||
\(782\) | 4.15673e6 | 0.243072 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.58198e6 | 0.0919202 | ||||||||
\(785\) | −2.59701e6 | −0.150418 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.50797e7 | −0.867873 | −0.433936 | − | 0.900944i | \(-0.642876\pi\) | ||||
−0.433936 | + | 0.900944i | \(0.642876\pi\) | |||||||
\(788\) | −4.18589e6 | −0.240144 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.02476e6 | 0.286449 | ||||||||
\(791\) | 4.80089e6 | 0.272823 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.87416e7 | −1.62303 | ||||||||
\(794\) | −4.06731e6 | −0.228958 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.65752e6 | 0.260538 | ||||||||
\(797\) | −1.57167e6 | −0.0876426 | −0.0438213 | − | 0.999039i | \(-0.513953\pi\) | ||||
−0.0438213 | + | 0.999039i | \(0.513953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.90979e6 | −0.327495 | ||||||||
\(800\) | −3.70735e6 | −0.204804 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.04807e6 | 0.222235 | ||||||||
\(803\) | −3.16836e6 | −0.173398 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.74979e6 | 0.367114 | ||||||||
\(806\) | −2.20234e7 | −1.19412 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.50395e7 | 1.88812 | ||||||||
\(809\) | −5.11766e6 | −0.274916 | −0.137458 | − | 0.990508i | \(-0.543893\pi\) | ||||
−0.137458 | + | 0.990508i | \(0.543893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.33210e7 | 0.711189 | 0.355594 | − | 0.934640i | \(-0.384278\pi\) | ||||
0.355594 | + | 0.934640i | \(0.384278\pi\) | |||||||
\(812\) | 1.30317e7 | 0.693604 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −107865. | −0.00570582 | ||||||||
\(815\) | −3.21682e6 | −0.169642 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.56700e7 | 1.86960 | ||||||||
\(818\) | −5.13495e6 | −0.268320 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.89432e6 | 0.150318 | ||||||||
\(821\) | 1.78379e7 | 0.923603 | 0.461802 | − | 0.886983i | \(-0.347203\pi\) | ||||
0.461802 | + | 0.886983i | \(0.347203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.28197e7 | −1.68902 | −0.844510 | − | 0.535540i | \(-0.820108\pi\) | ||||
−0.844510 | + | 0.535540i | \(0.820108\pi\) | |||||||
\(824\) | 1.60041e7 | 0.821135 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.52177e7 | −0.776064 | ||||||||
\(827\) | −3.90869e7 | −1.98732 | −0.993658 | − | 0.112440i | \(-0.964133\pi\) | ||||
−0.993658 | + | 0.112440i | \(0.964133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.52155e7 | −1.77970 | −0.889851 | − | 0.456252i | \(-0.849192\pi\) | ||||
−0.889851 | + | 0.456252i | \(0.849192\pi\) | |||||||
\(830\) | −8.98853e6 | −0.452891 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.54565e7 | −0.774109 | ||||||||
\(833\) | 1.33896e7 | 0.668584 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.31118e6 | 0.213983 | ||||||||
\(836\) | −6.18856e6 | −0.306249 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.57587e6 | −0.372668 | ||||||||
\(839\) | −1.90083e7 | −0.932265 | −0.466132 | − | 0.884715i | \(-0.654353\pi\) | ||||
−0.466132 | + | 0.884715i | \(0.654353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.88236e6 | −0.433050 | ||||||||
\(842\) | −479884. | −0.0233269 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.94083e7 | −0.937845 | ||||||||
\(845\) | 1.30598e7 | 0.629210 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.64600e6 | −0.126730 | ||||||||
\(848\) | 1.15472e6 | 0.0551424 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.73900e6 | −0.0825568 | ||||||||
\(851\) | 404221. | 0.0191335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.07361e7 | −1.44636 | −0.723179 | − | 0.690660i | \(-0.757320\pi\) | ||||
−0.723179 | + | 0.690660i | \(0.757320\pi\) | |||||||
\(854\) | 1.81027e7 | 0.849374 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.81310e7 | −0.845740 | ||||||||
\(857\) | 1.34454e7 | 0.625349 | 0.312675 | − | 0.949860i | \(-0.398775\pi\) | ||||
0.312675 | + | 0.949860i | \(0.398775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.39306e6 | 0.203135 | 0.101567 | − | 0.994829i | \(-0.467614\pi\) | ||||
0.101567 | + | 0.994829i | \(0.467614\pi\) | |||||||
\(860\) | 7.79598e6 | 0.359438 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6817.77 | 0.000312517 0 | ||||||||
\(863\) | 3.82863e7 | 1.74991 | 0.874956 | − | 0.484203i | \(-0.160890\pi\) | ||||
0.874956 | + | 0.484203i | \(0.160890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.82314e7 | 0.828477 | ||||||||
\(866\) | −1.20838e7 | −0.547532 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.70221e7 | −1.21736 | ||||||||
\(869\) | 7.38165e6 | 0.331592 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.77396e7 | 1.23895 | ||||||||
\(872\) | −1.24217e7 | −0.553211 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.19049e7 | −0.527168 | ||||||||
\(875\) | −2.82383e6 | −0.124686 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.33306e7 | −1.90237 | −0.951186 | − | 0.308617i | \(-0.900134\pi\) | ||||
−0.951186 | + | 0.308617i | \(0.900134\pi\) | |||||||
\(878\) | 2.45889e7 | 1.07647 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −301836. | −0.0131391 | ||||||||
\(881\) | −3.08399e7 | −1.33867 | −0.669335 | − | 0.742961i | \(-0.733421\pi\) | ||||
−0.669335 | + | 0.742961i | \(0.733421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.89082e7 | 1.24772 | 0.623862 | − | 0.781534i | \(-0.285563\pi\) | ||||
0.623862 | + | 0.781534i | \(0.285563\pi\) | |||||||
\(884\) | 1.68819e7 | 0.726592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.19453e7 | −0.939199 | ||||||||
\(887\) | 2.37686e7 | 1.01436 | 0.507182 | − | 0.861839i | \(-0.330687\pi\) | ||||
0.507182 | + | 0.861839i | \(0.330687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.02348e7 | 0.434337 | ||||||||
\(890\) | 5.20871e6 | 0.220422 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.52443e7 | −1.06231 | ||||||||
\(893\) | 1.69257e7 | 0.710262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.42351e7 | 0.594023 | ||||||||
\(896\) | −2.45695e7 | −1.02241 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.90670e6 | 0.203048 | ||||||||
\(899\) | −2.41131e7 | −0.995069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.77332e6 | 0.401079 | ||||||||
\(902\) | −2.18264e6 | −0.0893237 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.65132e6 | −0.189302 | ||||||||
\(905\) | −1.42597e6 | −0.0578746 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.36759e6 | 0.378102 | 0.189051 | − | 0.981967i | \(-0.439459\pi\) | ||||
0.189051 | + | 0.981967i | \(0.439459\pi\) | |||||||
\(908\) | 8.41193e6 | 0.338595 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.40721e7 | −0.563319 | ||||||||
\(911\) | 2.58520e7 | 1.03205 | 0.516023 | − | 0.856575i | \(-0.327412\pi\) | ||||
0.516023 | + | 0.856575i | \(0.327412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.32047e7 | −0.524264 | ||||||||
\(914\) | −2.48107e7 | −0.982368 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.14929e7 | 0.452574 | ||||||||
\(917\) | −4.83093e7 | −1.89718 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.61821e7 | 1.80378 | 0.901892 | − | 0.431961i | \(-0.142178\pi\) | ||||
0.901892 | + | 0.431961i | \(0.142178\pi\) | |||||||
\(920\) | −6.53950e6 | −0.254727 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.48404e7 | 0.962345 | ||||||||
\(923\) | 7.75819e7 | 2.99748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −169109. | −0.00649849 | ||||||||
\(926\) | 1.44401e7 | 0.553406 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.02279e7 | −0.771048 | ||||||||
\(929\) | 1.95110e6 | 0.0741721 | 0.0370860 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370860 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.83481e7 | −1.45000 | ||||||||
\(932\) | 2.26545e7 | 0.854308 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.74271e7 | −0.653669 | ||||||||
\(935\) | −2.55469e6 | −0.0955673 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.45128e7 | −1.28420 | −0.642098 | − | 0.766623i | \(-0.721936\pi\) | ||||
−0.642098 | + | 0.766623i | \(0.721936\pi\) | |||||||
\(938\) | −1.74716e7 | −0.648374 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.69926e6 | 0.136551 | ||||||||
\(941\) | −4.64180e7 | −1.70888 | −0.854442 | − | 0.519547i | \(-0.826101\pi\) | ||||
−0.854442 | + | 0.519547i | \(0.826101\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.17942e6 | 0.299532 | ||||||||
\(944\) | −2.55017e6 | −0.0931404 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.87905e6 | −0.213589 | ||||||||
\(947\) | −4.57523e7 | −1.65782 | −0.828911 | − | 0.559381i | \(-0.811039\pi\) | ||||
−0.828911 | + | 0.559381i | \(0.811039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.47538e7 | −0.892227 | ||||||||
\(950\) | 4.98053e6 | 0.179047 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.67242e7 | −0.955679 | ||||||||
\(953\) | 1.34380e7 | 0.479294 | 0.239647 | − | 0.970860i | \(-0.422968\pi\) | ||||
0.239647 | + | 0.970860i | \(0.422968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 217333. | 0.00771112 | ||||||||
\(956\) | −2.70146e6 | −0.0955990 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.69650e7 | 0.597228 | ||||||||
\(959\) | 5.69031e6 | 0.199797 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.13709e7 | 0.746474 | ||||||||
\(962\) | −842726. | −0.0293595 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.44031e6 | −0.153894 | ||||||||
\(965\) | −9.33741e6 | −0.322781 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.71470e7 | −1.27749 | −0.638745 | − | 0.769418i | \(-0.720546\pi\) | ||||
−0.638745 | + | 0.769418i | \(0.720546\pi\) | |||||||
\(968\) | 2.56356e6 | 0.0879336 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.18997e6 | −0.0406076 | ||||||||
\(971\) | 4.08269e7 | 1.38963 | 0.694813 | − | 0.719190i | \(-0.255487\pi\) | ||||
0.694813 | + | 0.719190i | \(0.255487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.69144e7 | −1.25001 | ||||||||
\(974\) | −4.87411e6 | −0.164626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.03364e6 | 0.101939 | ||||||||
\(977\) | 1.52450e6 | 0.0510965 | 0.0255482 | − | 0.999674i | \(-0.491867\pi\) | ||||
0.0255482 | + | 0.999674i | \(0.491867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.65188e6 | 0.255159 | ||||||||
\(980\) | −8.38129e6 | −0.278770 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.06788e6 | −0.0353381 | ||||||||
\(983\) | 5.19287e7 | 1.71405 | 0.857026 | − | 0.515273i | \(-0.172310\pi\) | ||||
0.857026 | + | 0.515273i | \(0.172310\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.94894e6 | 0.162526 | ||||||||
\(986\) | −9.48827e6 | −0.310810 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.83500e7 | −1.57581 | ||||||||
\(989\) | 2.20316e7 | 0.716236 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.75062e7 | −1.53662 | −0.768310 | − | 0.640078i | \(-0.778902\pi\) | ||||
−0.768310 | + | 0.640078i | \(0.778902\pi\) | |||||||
\(992\) | 4.19440e7 | 1.35329 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.88645e7 | −1.56866 | ||||||||
\(995\) | −5.50654e6 | −0.176328 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.39702e7 | −0.445107 | −0.222554 | − | 0.974920i | \(-0.571439\pi\) | ||||
−0.222554 | + | 0.974920i | \(0.571439\pi\) | |||||||
\(998\) | 2.67762e7 | 0.850986 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.6.a.p.1.4 | yes | 10 | |
3.2 | odd | 2 | 495.6.a.o.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.6.a.o.1.7 | ✓ | 10 | 3.2 | odd | 2 | ||
495.6.a.p.1.4 | yes | 10 | 1.1 | even | 1 | trivial |