Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("294.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(47.1528430250\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{9601}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 2400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-48.4923\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 22.4923 | 0.402355 | 0.201178 | − | 0.979555i | \(-0.435523\pi\) | ||||
0.201178 | + | 0.979555i | \(0.435523\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 89.9694 | 0.284508 | ||||||||
\(11\) | 340.462 | 0.848373 | 0.424186 | − | 0.905575i | \(-0.360560\pi\) | ||||
0.424186 | + | 0.905575i | \(0.360560\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −728.416 | −1.19542 | −0.597711 | − | 0.801712i | \(-0.703923\pi\) | ||||
−0.597711 | + | 0.801712i | \(0.703923\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −202.431 | −0.232300 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 809.847 | 0.679643 | 0.339821 | − | 0.940490i | \(-0.389633\pi\) | ||||
0.339821 | + | 0.940490i | \(0.389633\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 1026.20 | 0.652152 | 0.326076 | − | 0.945344i | \(-0.394274\pi\) | ||||
0.326076 | + | 0.945344i | \(0.394274\pi\) | |||||||
\(20\) | 359.878 | 0.201178 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1361.85 | 0.599890 | ||||||||
\(23\) | 1422.03 | 0.560518 | 0.280259 | − | 0.959924i | \(-0.409580\pi\) | ||||
0.280259 | + | 0.959924i | \(0.409580\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | −2619.09 | −0.838110 | ||||||||
\(26\) | −2913.66 | −0.845290 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5218.03 | 1.15216 | 0.576079 | − | 0.817394i | \(-0.304582\pi\) | ||||
0.576079 | + | 0.817394i | \(0.304582\pi\) | |||||||
\(30\) | −809.724 | −0.164261 | ||||||||
\(31\) | −7037.74 | −1.31531 | −0.657657 | − | 0.753318i | \(-0.728452\pi\) | ||||
−0.657657 | + | 0.753318i | \(0.728452\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −3064.16 | −0.489808 | ||||||||
\(34\) | 3239.39 | 0.480580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 12792.1 | 1.53616 | 0.768082 | − | 0.640351i | \(-0.221211\pi\) | ||||
0.768082 | + | 0.640351i | \(0.221211\pi\) | |||||||
\(38\) | 4104.81 | 0.461141 | ||||||||
\(39\) | 6555.74 | 0.690177 | ||||||||
\(40\) | 1439.51 | 0.142254 | ||||||||
\(41\) | 1173.51 | 0.109025 | 0.0545124 | − | 0.998513i | \(-0.482640\pi\) | ||||
0.0545124 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3664.17 | 0.302207 | 0.151103 | − | 0.988518i | \(-0.451717\pi\) | ||||
0.151103 | + | 0.988518i | \(0.451717\pi\) | |||||||
\(44\) | 5447.39 | 0.424186 | ||||||||
\(45\) | 1821.88 | 0.134118 | ||||||||
\(46\) | 5688.12 | 0.396346 | ||||||||
\(47\) | 9313.19 | 0.614970 | 0.307485 | − | 0.951553i | \(-0.400513\pi\) | ||||
0.307485 | + | 0.951553i | \(0.400513\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10476.4 | −0.592633 | ||||||||
\(51\) | −7288.62 | −0.392392 | ||||||||
\(52\) | −11654.7 | −0.597711 | ||||||||
\(53\) | 35642.8 | 1.74294 | 0.871469 | − | 0.490451i | \(-0.163168\pi\) | ||||
0.871469 | + | 0.490451i | \(0.163168\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 7657.78 | 0.341347 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9235.81 | −0.376520 | ||||||||
\(58\) | 20872.1 | 0.814698 | ||||||||
\(59\) | −30376.2 | −1.13607 | −0.568033 | − | 0.823006i | \(-0.692295\pi\) | ||||
−0.568033 | + | 0.823006i | \(0.692295\pi\) | |||||||
\(60\) | −3238.90 | −0.116150 | ||||||||
\(61\) | 32186.2 | 1.10751 | 0.553753 | − | 0.832681i | \(-0.313195\pi\) | ||||
0.553753 | + | 0.832681i | \(0.313195\pi\) | |||||||
\(62\) | −28151.0 | −0.930067 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −16383.8 | −0.480984 | ||||||||
\(66\) | −12256.6 | −0.346347 | ||||||||
\(67\) | 21351.1 | 0.581076 | 0.290538 | − | 0.956863i | \(-0.406166\pi\) | ||||
0.290538 | + | 0.956863i | \(0.406166\pi\) | |||||||
\(68\) | 12957.6 | 0.339821 | ||||||||
\(69\) | −12798.3 | −0.323615 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61153.7 | 1.43972 | 0.719859 | − | 0.694121i | \(-0.244207\pi\) | ||||
0.719859 | + | 0.694121i | \(0.244207\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 41267.8 | 0.906367 | 0.453184 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453184 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(74\) | 51168.4 | 1.08623 | ||||||||
\(75\) | 23571.8 | 0.483883 | ||||||||
\(76\) | 16419.2 | 0.326076 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 26223.0 | 0.488029 | ||||||||
\(79\) | −35000.5 | −0.630966 | −0.315483 | − | 0.948931i | \(-0.602167\pi\) | ||||
−0.315483 | + | 0.948931i | \(0.602167\pi\) | |||||||
\(80\) | 5758.04 | 0.100589 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 4694.02 | 0.0770922 | ||||||||
\(83\) | 86193.0 | 1.37334 | 0.686668 | − | 0.726972i | \(-0.259073\pi\) | ||||
0.686668 | + | 0.726972i | \(0.259073\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18215.4 | 0.273458 | ||||||||
\(86\) | 14656.7 | 0.213692 | ||||||||
\(87\) | −46962.3 | −0.665198 | ||||||||
\(88\) | 21789.6 | 0.299945 | ||||||||
\(89\) | 77992.6 | 1.04371 | 0.521853 | − | 0.853035i | \(-0.325241\pi\) | ||||
0.521853 | + | 0.853035i | \(0.325241\pi\) | |||||||
\(90\) | 7287.52 | 0.0948361 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 22752.5 | 0.280259 | ||||||||
\(93\) | 63339.7 | 0.759397 | ||||||||
\(94\) | 37252.8 | 0.434850 | ||||||||
\(95\) | 23081.7 | 0.262397 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −161765. | −1.74565 | −0.872823 | − | 0.488037i | \(-0.837713\pi\) | ||||
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27577.4 | 0.282791 | ||||||||
\(100\) | −41905.5 | −0.419055 | ||||||||
\(101\) | −65854.4 | −0.642364 | −0.321182 | − | 0.947017i | \(-0.604080\pi\) | ||||
−0.321182 | + | 0.947017i | \(0.604080\pi\) | |||||||
\(102\) | −29154.5 | −0.277463 | ||||||||
\(103\) | 130198. | 1.20924 | 0.604619 | − | 0.796515i | \(-0.293326\pi\) | ||||
0.604619 | + | 0.796515i | \(0.293326\pi\) | |||||||
\(104\) | −46618.6 | −0.422645 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 142571. | 1.23244 | ||||||||
\(107\) | 2590.95 | 0.0218776 | 0.0109388 | − | 0.999940i | \(-0.496518\pi\) | ||||
0.0109388 | + | 0.999940i | \(0.496518\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 110654. | 0.892072 | 0.446036 | − | 0.895015i | \(-0.352835\pi\) | ||||
0.446036 | + | 0.895015i | \(0.352835\pi\) | |||||||
\(110\) | 30631.1 | 0.241369 | ||||||||
\(111\) | −115129. | −0.886905 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −193910. | −1.42858 | −0.714291 | − | 0.699849i | \(-0.753251\pi\) | ||||
−0.714291 | + | 0.699849i | \(0.753251\pi\) | |||||||
\(114\) | −36943.3 | −0.266240 | ||||||||
\(115\) | 31984.8 | 0.225527 | ||||||||
\(116\) | 83488.5 | 0.576079 | ||||||||
\(117\) | −59001.7 | −0.398474 | ||||||||
\(118\) | −121505. | −0.803319 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12955.6 | −0.0821304 | ||||||||
\(121\) | −45136.8 | −0.280264 | ||||||||
\(122\) | 128745. | 0.783124 | ||||||||
\(123\) | −10561.5 | −0.0629455 | ||||||||
\(124\) | −112604. | −0.657657 | ||||||||
\(125\) | −129198. | −0.739573 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 27429.2 | 0.150905 | 0.0754526 | − | 0.997149i | \(-0.475960\pi\) | ||||
0.0754526 | + | 0.997149i | \(0.475960\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −32977.5 | −0.174479 | ||||||||
\(130\) | −65535.1 | −0.340107 | ||||||||
\(131\) | 150376. | 0.765597 | 0.382798 | − | 0.923832i | \(-0.374960\pi\) | ||||
0.382798 | + | 0.923832i | \(0.374960\pi\) | |||||||
\(132\) | −49026.5 | −0.244904 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 85404.3 | 0.410883 | ||||||||
\(135\) | −16396.9 | −0.0774333 | ||||||||
\(136\) | 51830.2 | 0.240290 | ||||||||
\(137\) | 96102.0 | 0.437453 | 0.218726 | − | 0.975786i | \(-0.429810\pi\) | ||||
0.218726 | + | 0.975786i | \(0.429810\pi\) | |||||||
\(138\) | −51193.1 | −0.228830 | ||||||||
\(139\) | 100854. | 0.442749 | 0.221375 | − | 0.975189i | \(-0.428946\pi\) | ||||
0.221375 | + | 0.975189i | \(0.428946\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −83818.7 | −0.355053 | ||||||||
\(142\) | 244615. | 1.01803 | ||||||||
\(143\) | −247998. | −1.01416 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 117366. | 0.463577 | ||||||||
\(146\) | 165071. | 0.640898 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 204674. | 0.768082 | ||||||||
\(149\) | −360944. | −1.33191 | −0.665954 | − | 0.745993i | \(-0.731975\pi\) | ||||
−0.665954 | + | 0.745993i | \(0.731975\pi\) | |||||||
\(150\) | 94287.4 | 0.342157 | ||||||||
\(151\) | −434056. | −1.54918 | −0.774592 | − | 0.632461i | \(-0.782045\pi\) | ||||
−0.774592 | + | 0.632461i | \(0.782045\pi\) | |||||||
\(152\) | 65676.9 | 0.230570 | ||||||||
\(153\) | 65597.6 | 0.226548 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −158295. | −0.529223 | ||||||||
\(156\) | 104892. | 0.345088 | ||||||||
\(157\) | −511596. | −1.65645 | −0.828225 | − | 0.560396i | \(-0.810649\pi\) | ||||
−0.828225 | + | 0.560396i | \(0.810649\pi\) | |||||||
\(158\) | −140002. | −0.446160 | ||||||||
\(159\) | −320785. | −1.00629 | ||||||||
\(160\) | 23032.2 | 0.0711270 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −251269. | −0.740748 | −0.370374 | − | 0.928883i | \(-0.620770\pi\) | ||||
−0.370374 | + | 0.928883i | \(0.620770\pi\) | |||||||
\(164\) | 18776.1 | 0.0545124 | ||||||||
\(165\) | −68920.0 | −0.197077 | ||||||||
\(166\) | 344772. | 0.971095 | ||||||||
\(167\) | 419277. | 1.16335 | 0.581674 | − | 0.813422i | \(-0.302398\pi\) | ||||
0.581674 | + | 0.813422i | \(0.302398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 159297. | 0.429032 | ||||||||
\(170\) | 72861.4 | 0.193364 | ||||||||
\(171\) | 83122.3 | 0.217384 | ||||||||
\(172\) | 58626.7 | 0.151103 | ||||||||
\(173\) | −461376. | −1.17203 | −0.586017 | − | 0.810299i | \(-0.699305\pi\) | ||||
−0.586017 | + | 0.810299i | \(0.699305\pi\) | |||||||
\(174\) | −187849. | −0.470366 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 87158.2 | 0.212093 | ||||||||
\(177\) | 273386. | 0.655907 | ||||||||
\(178\) | 311970. | 0.738012 | ||||||||
\(179\) | 741706. | 1.73021 | 0.865105 | − | 0.501590i | \(-0.167251\pi\) | ||||
0.865105 | + | 0.501590i | \(0.167251\pi\) | |||||||
\(180\) | 29150.1 | 0.0670592 | ||||||||
\(181\) | 301371. | 0.683762 | 0.341881 | − | 0.939743i | \(-0.388936\pi\) | ||||
0.341881 | + | 0.939743i | \(0.388936\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −289676. | −0.639418 | ||||||||
\(184\) | 91010.0 | 0.198173 | ||||||||
\(185\) | 287725. | 0.618084 | ||||||||
\(186\) | 253359. | 0.536974 | ||||||||
\(187\) | 275722. | 0.576590 | ||||||||
\(188\) | 149011. | 0.307485 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 92326.7 | 0.185542 | ||||||||
\(191\) | 263183. | 0.522004 | 0.261002 | − | 0.965338i | \(-0.415947\pi\) | ||||
0.261002 | + | 0.965338i | \(0.415947\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −831127. | −1.60611 | −0.803053 | − | 0.595908i | \(-0.796792\pi\) | ||||
−0.803053 | + | 0.595908i | \(0.796792\pi\) | |||||||
\(194\) | −647061. | −1.23436 | ||||||||
\(195\) | 147454. | 0.277696 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.05421e6 | −1.93536 | −0.967681 | − | 0.252178i | \(-0.918853\pi\) | ||||
−0.967681 | + | 0.252178i | \(0.918853\pi\) | |||||||
\(198\) | 110310. | 0.199963 | ||||||||
\(199\) | 698568. | 1.25048 | 0.625239 | − | 0.780434i | \(-0.285002\pi\) | ||||
0.625239 | + | 0.780434i | \(0.285002\pi\) | |||||||
\(200\) | −167622. | −0.296317 | ||||||||
\(201\) | −192160. | −0.335484 | ||||||||
\(202\) | −263418. | −0.454220 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −116618. | −0.196196 | ||||||||
\(205\) | 26394.9 | 0.0438667 | ||||||||
\(206\) | 520792. | 0.855060 | ||||||||
\(207\) | 115184. | 0.186839 | ||||||||
\(208\) | −186474. | −0.298855 | ||||||||
\(209\) | 349382. | 0.553268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −99693.6 | −0.154156 | −0.0770781 | − | 0.997025i | \(-0.524559\pi\) | ||||
−0.0770781 | + | 0.997025i | \(0.524559\pi\) | |||||||
\(212\) | 570284. | 0.871469 | ||||||||
\(213\) | −550384. | −0.831221 | ||||||||
\(214\) | 10363.8 | 0.0154698 | ||||||||
\(215\) | 82415.7 | 0.121594 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 442615. | 0.630790 | ||||||||
\(219\) | −371410. | −0.523291 | ||||||||
\(220\) | 122525. | 0.170674 | ||||||||
\(221\) | −589905. | −0.812459 | ||||||||
\(222\) | −460516. | −0.627137 | ||||||||
\(223\) | 526194. | 0.708572 | 0.354286 | − | 0.935137i | \(-0.384724\pi\) | ||||
0.354286 | + | 0.935137i | \(0.384724\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −212147. | −0.279370 | ||||||||
\(226\) | −775642. | −1.01016 | ||||||||
\(227\) | −981605. | −1.26436 | −0.632182 | − | 0.774820i | \(-0.717840\pi\) | ||||
−0.632182 | + | 0.774820i | \(0.717840\pi\) | |||||||
\(228\) | −147773. | −0.188260 | ||||||||
\(229\) | −85081.0 | −0.107212 | −0.0536061 | − | 0.998562i | \(-0.517072\pi\) | ||||
−0.0536061 | + | 0.998562i | \(0.517072\pi\) | |||||||
\(230\) | 127939. | 0.159472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 333954. | 0.407349 | ||||||||
\(233\) | 113123. | 0.136509 | 0.0682544 | − | 0.997668i | \(-0.478257\pi\) | ||||
0.0682544 | + | 0.997668i | \(0.478257\pi\) | |||||||
\(234\) | −236007. | −0.281763 | ||||||||
\(235\) | 209476. | 0.247436 | ||||||||
\(236\) | −486019. | −0.568033 | ||||||||
\(237\) | 315004. | 0.364288 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −895100. | −1.01362 | −0.506812 | − | 0.862057i | \(-0.669176\pi\) | ||||
−0.506812 | + | 0.862057i | \(0.669176\pi\) | |||||||
\(240\) | −51822.4 | −0.0580750 | ||||||||
\(241\) | 527715. | 0.585270 | 0.292635 | − | 0.956224i | \(-0.405468\pi\) | ||||
0.292635 | + | 0.956224i | \(0.405468\pi\) | |||||||
\(242\) | −180547. | −0.198177 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 514980. | 0.553753 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −42246.2 | −0.0445092 | ||||||||
\(247\) | −747501. | −0.779596 | ||||||||
\(248\) | −450416. | −0.465034 | ||||||||
\(249\) | −775737. | −0.792895 | ||||||||
\(250\) | −516793. | −0.522957 | ||||||||
\(251\) | −1.19293e6 | −1.19517 | −0.597584 | − | 0.801806i | \(-0.703873\pi\) | ||||
−0.597584 | + | 0.801806i | \(0.703873\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 484147. | 0.475528 | ||||||||
\(254\) | 109717. | 0.106706 | ||||||||
\(255\) | −163938. | −0.157881 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.19492e6 | −1.12851 | −0.564257 | − | 0.825599i | \(-0.690837\pi\) | ||||
−0.564257 | + | 0.825599i | \(0.690837\pi\) | |||||||
\(258\) | −131910. | −0.123375 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −262140. | −0.240492 | ||||||||
\(261\) | 422661. | 0.384052 | ||||||||
\(262\) | 601504. | 0.541359 | ||||||||
\(263\) | −2.12230e6 | −1.89199 | −0.945993 | − | 0.324186i | \(-0.894910\pi\) | ||||
−0.945993 | + | 0.324186i | \(0.894910\pi\) | |||||||
\(264\) | −196106. | −0.173173 | ||||||||
\(265\) | 801690. | 0.701280 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −701933. | −0.602584 | ||||||||
\(268\) | 341617. | 0.290538 | ||||||||
\(269\) | 154977. | 0.130583 | 0.0652913 | − | 0.997866i | \(-0.479202\pi\) | ||||
0.0652913 | + | 0.997866i | \(0.479202\pi\) | |||||||
\(270\) | −65587.7 | −0.0547536 | ||||||||
\(271\) | 1.95888e6 | 1.62026 | 0.810129 | − | 0.586252i | \(-0.199397\pi\) | ||||
0.810129 | + | 0.586252i | \(0.199397\pi\) | |||||||
\(272\) | 207321. | 0.169911 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 384408. | 0.309326 | ||||||||
\(275\) | −891701. | −0.711030 | ||||||||
\(276\) | −204772. | −0.161808 | ||||||||
\(277\) | −1.74953e6 | −1.37000 | −0.685001 | − | 0.728542i | \(-0.740198\pi\) | ||||
−0.685001 | + | 0.728542i | \(0.740198\pi\) | |||||||
\(278\) | 403418. | 0.313071 | ||||||||
\(279\) | −570057. | −0.438438 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.40665e6 | 1.06272 | 0.531361 | − | 0.847145i | \(-0.321681\pi\) | ||||
0.531361 | + | 0.847145i | \(0.321681\pi\) | |||||||
\(282\) | −335275. | −0.251060 | ||||||||
\(283\) | 1.95707e6 | 1.45258 | 0.726291 | − | 0.687388i | \(-0.241243\pi\) | ||||
0.726291 | + | 0.687388i | \(0.241243\pi\) | |||||||
\(284\) | 978460. | 0.719859 | ||||||||
\(285\) | −207735. | −0.151495 | ||||||||
\(286\) | −991991. | −0.717121 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −764005. | −0.538086 | ||||||||
\(290\) | 469463. | 0.327798 | ||||||||
\(291\) | 1.45589e6 | 1.00785 | ||||||||
\(292\) | 660285. | 0.453184 | ||||||||
\(293\) | −1.26998e6 | −0.864229 | −0.432114 | − | 0.901819i | \(-0.642232\pi\) | ||||
−0.432114 | + | 0.901819i | \(0.642232\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −683232. | −0.457102 | ||||||||
\(296\) | 818695. | 0.543116 | ||||||||
\(297\) | −248197. | −0.163269 | ||||||||
\(298\) | −1.44378e6 | −0.941802 | ||||||||
\(299\) | −1.03583e6 | −0.670055 | ||||||||
\(300\) | 377150. | 0.241942 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.73622e6 | −1.09544 | ||||||||
\(303\) | 592690. | 0.370869 | ||||||||
\(304\) | 262708. | 0.163038 | ||||||||
\(305\) | 723944. | 0.445611 | ||||||||
\(306\) | 262390. | 0.160193 | ||||||||
\(307\) | −41854.4 | −0.0253451 | −0.0126726 | − | 0.999920i | \(-0.504034\pi\) | ||||
−0.0126726 | + | 0.999920i | \(0.504034\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.17178e6 | −0.698154 | ||||||||
\(310\) | −633182. | −0.374217 | ||||||||
\(311\) | −2.29189e6 | −1.34367 | −0.671837 | − | 0.740699i | \(-0.734494\pi\) | ||||
−0.671837 | + | 0.740699i | \(0.734494\pi\) | |||||||
\(312\) | 419568. | 0.244014 | ||||||||
\(313\) | 2.27150e6 | 1.31054 | 0.655271 | − | 0.755394i | \(-0.272554\pi\) | ||||
0.655271 | + | 0.755394i | \(0.272554\pi\) | |||||||
\(314\) | −2.04639e6 | −1.17129 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −560007. | −0.315483 | ||||||||
\(317\) | −1.98474e6 | −1.10932 | −0.554659 | − | 0.832078i | \(-0.687151\pi\) | ||||
−0.554659 | + | 0.832078i | \(0.687151\pi\) | |||||||
\(318\) | −1.28314e6 | −0.711551 | ||||||||
\(319\) | 1.77654e6 | 0.977459 | ||||||||
\(320\) | 92128.7 | 0.0502944 | ||||||||
\(321\) | −23318.6 | −0.0126310 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 831066. | 0.443230 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 1.90779e6 | 1.00189 | ||||||||
\(326\) | −1.00508e6 | −0.523788 | ||||||||
\(327\) | −995884. | −0.515038 | ||||||||
\(328\) | 75104.3 | 0.0385461 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −275680. | −0.139354 | ||||||||
\(331\) | 638461. | 0.320305 | 0.160153 | − | 0.987092i | \(-0.448801\pi\) | ||||
0.160153 | + | 0.987092i | \(0.448801\pi\) | |||||||
\(332\) | 1.37909e6 | 0.686668 | ||||||||
\(333\) | 1.03616e6 | 0.512055 | ||||||||
\(334\) | 1.67711e6 | 0.822611 | ||||||||
\(335\) | 480236. | 0.233799 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.72026e6 | 1.30478 | 0.652388 | − | 0.757886i | \(-0.273767\pi\) | ||||
0.652388 | + | 0.757886i | \(0.273767\pi\) | |||||||
\(338\) | 637186. | 0.303371 | ||||||||
\(339\) | 1.74519e6 | 0.824792 | ||||||||
\(340\) | 291446. | 0.136729 | ||||||||
\(341\) | −2.39608e6 | −1.11588 | ||||||||
\(342\) | 332489. | 0.153714 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 234507. | 0.106846 | ||||||||
\(345\) | −287863. | −0.130208 | ||||||||
\(346\) | −1.84551e6 | −0.828753 | ||||||||
\(347\) | 2.62076e6 | 1.16843 | 0.584217 | − | 0.811597i | \(-0.301402\pi\) | ||||
0.584217 | + | 0.811597i | \(0.301402\pi\) | |||||||
\(348\) | −751397. | −0.332599 | ||||||||
\(349\) | 575592. | 0.252960 | 0.126480 | − | 0.991969i | \(-0.459632\pi\) | ||||
0.126480 | + | 0.991969i | \(0.459632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 531015. | 0.230059 | ||||||||
\(352\) | 348633. | 0.149972 | ||||||||
\(353\) | −2.58972e6 | −1.10615 | −0.553077 | − | 0.833130i | \(-0.686546\pi\) | ||||
−0.553077 | + | 0.833130i | \(0.686546\pi\) | |||||||
\(354\) | 1.09354e6 | 0.463797 | ||||||||
\(355\) | 1.37549e6 | 0.579278 | ||||||||
\(356\) | 1.24788e6 | 0.521853 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.96682e6 | 1.22344 | ||||||||
\(359\) | 2.86779e6 | 1.17439 | 0.587193 | − | 0.809447i | \(-0.300233\pi\) | ||||
0.587193 | + | 0.809447i | \(0.300233\pi\) | |||||||
\(360\) | 116600. | 0.0474180 | ||||||||
\(361\) | −1.42301e6 | −0.574698 | ||||||||
\(362\) | 1.20548e6 | 0.483493 | ||||||||
\(363\) | 406231. | 0.161811 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 928210. | 0.364682 | ||||||||
\(366\) | −1.15870e6 | −0.452137 | ||||||||
\(367\) | −1.95451e6 | −0.757482 | −0.378741 | − | 0.925503i | \(-0.623643\pi\) | ||||
−0.378741 | + | 0.925503i | \(0.623643\pi\) | |||||||
\(368\) | 364040. | 0.140129 | ||||||||
\(369\) | 95053.9 | 0.0363416 | ||||||||
\(370\) | 1.15090e6 | 0.437052 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.01344e6 | 0.379698 | ||||||||
\(373\) | 2.21110e6 | 0.822878 | 0.411439 | − | 0.911437i | \(-0.365026\pi\) | ||||
0.411439 | + | 0.911437i | \(0.365026\pi\) | |||||||
\(374\) | 1.10289e6 | 0.407711 | ||||||||
\(375\) | 1.16278e6 | 0.426993 | ||||||||
\(376\) | 596044. | 0.217425 | ||||||||
\(377\) | −3.80090e6 | −1.37731 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.81232e6 | 1.36330 | 0.681649 | − | 0.731679i | \(-0.261263\pi\) | ||||
0.681649 | + | 0.731679i | \(0.261263\pi\) | |||||||
\(380\) | 369307. | 0.131198 | ||||||||
\(381\) | −246863. | −0.0871252 | ||||||||
\(382\) | 1.05273e6 | 0.369112 | ||||||||
\(383\) | 3.80606e6 | 1.32580 | 0.662901 | − | 0.748707i | \(-0.269325\pi\) | ||||
0.662901 | + | 0.748707i | \(0.269325\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.32451e6 | −1.13569 | ||||||||
\(387\) | 296797. | 0.100736 | ||||||||
\(388\) | −2.58825e6 | −0.872823 | ||||||||
\(389\) | 3.07524e6 | 1.03040 | 0.515200 | − | 0.857070i | \(-0.327718\pi\) | ||||
0.515200 | + | 0.857070i | \(0.327718\pi\) | |||||||
\(390\) | 589816. | 0.196361 | ||||||||
\(391\) | 1.15163e6 | 0.380952 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.35338e6 | −0.442017 | ||||||||
\(394\) | −4.21685e6 | −1.36851 | ||||||||
\(395\) | −787242. | −0.253873 | ||||||||
\(396\) | 441238. | 0.141395 | ||||||||
\(397\) | 2.19133e6 | 0.697800 | 0.348900 | − | 0.937160i | \(-0.386555\pi\) | ||||
0.348900 | + | 0.937160i | \(0.386555\pi\) | |||||||
\(398\) | 2.79427e6 | 0.884221 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −670488. | −0.209528 | ||||||||
\(401\) | 1.77668e6 | 0.551757 | 0.275879 | − | 0.961192i | \(-0.411031\pi\) | ||||
0.275879 | + | 0.961192i | \(0.411031\pi\) | |||||||
\(402\) | −768639. | −0.237223 | ||||||||
\(403\) | 5.12640e6 | 1.57235 | ||||||||
\(404\) | −1.05367e6 | −0.321182 | ||||||||
\(405\) | 147572. | 0.0447061 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.35522e6 | 1.30324 | ||||||||
\(408\) | −466472. | −0.138731 | ||||||||
\(409\) | 2.36118e6 | 0.697945 | 0.348973 | − | 0.937133i | \(-0.386531\pi\) | ||||
0.348973 | + | 0.937133i | \(0.386531\pi\) | |||||||
\(410\) | 105580. | 0.0310185 | ||||||||
\(411\) | −864918. | −0.252563 | ||||||||
\(412\) | 2.08317e6 | 0.604619 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 460738. | 0.132115 | ||||||||
\(415\) | 1.93868e6 | 0.552569 | ||||||||
\(416\) | −745898. | −0.211323 | ||||||||
\(417\) | −907690. | −0.255621 | ||||||||
\(418\) | 1.39753e6 | 0.391219 | ||||||||
\(419\) | −3.23493e6 | −0.900181 | −0.450090 | − | 0.892983i | \(-0.648608\pi\) | ||||
−0.450090 | + | 0.892983i | \(0.648608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.85759e6 | −0.785769 | −0.392884 | − | 0.919588i | \(-0.628523\pi\) | ||||
−0.392884 | + | 0.919588i | \(0.628523\pi\) | |||||||
\(422\) | −398774. | −0.109005 | ||||||||
\(423\) | 754369. | 0.204990 | ||||||||
\(424\) | 2.28114e6 | 0.616222 | ||||||||
\(425\) | −2.12107e6 | −0.569615 | ||||||||
\(426\) | −2.20153e6 | −0.587762 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 41455.2 | 0.0109388 | ||||||||
\(429\) | 2.23198e6 | 0.585527 | ||||||||
\(430\) | 329663. | 0.0859803 | ||||||||
\(431\) | −88386.2 | −0.0229188 | −0.0114594 | − | 0.999934i | \(-0.503648\pi\) | ||||
−0.0114594 | + | 0.999934i | \(0.503648\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −3.09418e6 | −0.793097 | −0.396549 | − | 0.918014i | \(-0.629792\pi\) | ||||
−0.396549 | + | 0.918014i | \(0.629792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.05629e6 | −0.267646 | ||||||||
\(436\) | 1.77046e6 | 0.446036 | ||||||||
\(437\) | 1.45929e6 | 0.365543 | ||||||||
\(438\) | −1.48564e6 | −0.370023 | ||||||||
\(439\) | 485178. | 0.120155 | 0.0600773 | − | 0.998194i | \(-0.480865\pi\) | ||||
0.0600773 | + | 0.998194i | \(0.480865\pi\) | |||||||
\(440\) | 490098. | 0.120684 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.35962e6 | −0.574495 | ||||||||
\(443\) | 1.27520e6 | 0.308722 | 0.154361 | − | 0.988015i | \(-0.450668\pi\) | ||||
0.154361 | + | 0.988015i | \(0.450668\pi\) | |||||||
\(444\) | −1.84206e6 | −0.443453 | ||||||||
\(445\) | 1.75424e6 | 0.419941 | ||||||||
\(446\) | 2.10478e6 | 0.501036 | ||||||||
\(447\) | 3.24850e6 | 0.768978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.79144e6 | −0.887541 | −0.443770 | − | 0.896141i | \(-0.646359\pi\) | ||||
−0.443770 | + | 0.896141i | \(0.646359\pi\) | |||||||
\(450\) | −848587. | −0.197544 | ||||||||
\(451\) | 399534. | 0.0924937 | ||||||||
\(452\) | −3.10257e6 | −0.714291 | ||||||||
\(453\) | 3.90650e6 | 0.894422 | ||||||||
\(454\) | −3.92642e6 | −0.894040 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −591092. | −0.133120 | ||||||||
\(457\) | 1.70281e6 | 0.381395 | 0.190698 | − | 0.981649i | \(-0.438925\pi\) | ||||
0.190698 | + | 0.981649i | \(0.438925\pi\) | |||||||
\(458\) | −340324. | −0.0758104 | ||||||||
\(459\) | −590378. | −0.130797 | ||||||||
\(460\) | 511757. | 0.112764 | ||||||||
\(461\) | 4.55537e6 | 0.998323 | 0.499161 | − | 0.866509i | \(-0.333642\pi\) | ||||
0.499161 | + | 0.866509i | \(0.333642\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.82647e6 | 1.26314 | 0.631572 | − | 0.775317i | \(-0.282410\pi\) | ||||
0.631572 | + | 0.775317i | \(0.282410\pi\) | |||||||
\(464\) | 1.33582e6 | 0.288039 | ||||||||
\(465\) | 1.42466e6 | 0.305547 | ||||||||
\(466\) | 452492. | 0.0965263 | ||||||||
\(467\) | −3.54261e6 | −0.751677 | −0.375839 | − | 0.926685i | \(-0.622645\pi\) | ||||
−0.375839 | + | 0.926685i | \(0.622645\pi\) | |||||||
\(468\) | −944027. | −0.199237 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 837902. | 0.174964 | ||||||||
\(471\) | 4.60437e6 | 0.956352 | ||||||||
\(472\) | −1.94408e6 | −0.401660 | ||||||||
\(473\) | 1.24751e6 | 0.256384 | ||||||||
\(474\) | 1.26002e6 | 0.257591 | ||||||||
\(475\) | −2.68772e6 | −0.546575 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.88707e6 | 0.580979 | ||||||||
\(478\) | −3.58040e6 | −0.716740 | ||||||||
\(479\) | −4.23542e6 | −0.843447 | −0.421723 | − | 0.906725i | \(-0.638575\pi\) | ||||
−0.421723 | + | 0.906725i | \(0.638575\pi\) | |||||||
\(480\) | −207289. | −0.0410652 | ||||||||
\(481\) | −9.31797e6 | −1.83636 | ||||||||
\(482\) | 2.11086e6 | 0.413849 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −722189. | −0.140132 | ||||||||
\(485\) | −3.63848e6 | −0.702370 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −5.65479e6 | −1.08042 | −0.540212 | − | 0.841529i | \(-0.681656\pi\) | ||||
−0.540212 | + | 0.841529i | \(0.681656\pi\) | |||||||
\(488\) | 2.05992e6 | 0.391562 | ||||||||
\(489\) | 2.26142e6 | 0.427671 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.33183e6 | 1.55968 | 0.779842 | − | 0.625976i | \(-0.215299\pi\) | ||||
0.779842 | + | 0.625976i | \(0.215299\pi\) | |||||||
\(492\) | −168985. | −0.0314728 | ||||||||
\(493\) | 4.22581e6 | 0.783055 | ||||||||
\(494\) | −2.99001e6 | −0.551258 | ||||||||
\(495\) | 620280. | 0.113782 | ||||||||
\(496\) | −1.80166e6 | −0.328828 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.10295e6 | −0.560662 | ||||||||
\(499\) | −7.23769e6 | −1.30121 | −0.650607 | − | 0.759415i | \(-0.725485\pi\) | ||||
−0.650607 | + | 0.759415i | \(0.725485\pi\) | |||||||
\(500\) | −2.06717e6 | −0.369787 | ||||||||
\(501\) | −3.77349e6 | −0.671659 | ||||||||
\(502\) | −4.77170e6 | −0.845112 | ||||||||
\(503\) | −6.16761e6 | −1.08692 | −0.543459 | − | 0.839436i | \(-0.682886\pi\) | ||||
−0.543459 | + | 0.839436i | \(0.682886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.48122e6 | −0.258459 | ||||||||
\(506\) | 1.93659e6 | 0.336249 | ||||||||
\(507\) | −1.43367e6 | −0.247702 | ||||||||
\(508\) | 438868. | 0.0754526 | ||||||||
\(509\) | 1.83488e6 | 0.313916 | 0.156958 | − | 0.987605i | \(-0.449831\pi\) | ||||
0.156958 | + | 0.987605i | \(0.449831\pi\) | |||||||
\(510\) | −655753. | −0.111639 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −748101. | −0.125507 | ||||||||
\(514\) | −4.77969e6 | −0.797980 | ||||||||
\(515\) | 2.92846e6 | 0.486543 | ||||||||
\(516\) | −527640. | −0.0872395 | ||||||||
\(517\) | 3.17079e6 | 0.521724 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.15239e6 | 0.676674 | ||||||||
\(520\) | −1.04856e6 | −0.170054 | ||||||||
\(521\) | 5.31040e6 | 0.857103 | 0.428551 | − | 0.903517i | \(-0.359024\pi\) | ||||
0.428551 | + | 0.903517i | \(0.359024\pi\) | |||||||
\(522\) | 1.69064e6 | 0.271566 | ||||||||
\(523\) | −2.98835e6 | −0.477725 | −0.238862 | − | 0.971053i | \(-0.576774\pi\) | ||||
−0.238862 | + | 0.971053i | \(0.576774\pi\) | |||||||
\(524\) | 2.40601e6 | 0.382798 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.48921e6 | −1.33784 | ||||||||
\(527\) | −5.69950e6 | −0.893943 | ||||||||
\(528\) | −784424. | −0.122452 | ||||||||
\(529\) | −4.41417e6 | −0.685820 | ||||||||
\(530\) | 3.20676e6 | 0.495880 | ||||||||
\(531\) | −2.46047e6 | −0.378688 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −854800. | −0.130331 | ||||||||
\(534\) | −2.80773e6 | −0.426091 | ||||||||
\(535\) | 58276.6 | 0.00880257 | ||||||||
\(536\) | 1.36647e6 | 0.205441 | ||||||||
\(537\) | −6.67535e6 | −0.998938 | ||||||||
\(538\) | 619907. | 0.0923359 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −262351. | −0.0387167 | ||||||||
\(541\) | 2.16832e6 | 0.318516 | 0.159258 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159258 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(542\) | 7.83551e6 | 1.14570 | ||||||||
\(543\) | −2.71234e6 | −0.394770 | ||||||||
\(544\) | 829283. | 0.120145 | ||||||||
\(545\) | 2.48886e6 | 0.358930 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.13272e6 | −1.30506 | −0.652532 | − | 0.757761i | \(-0.726293\pi\) | ||||
−0.652532 | + | 0.757761i | \(0.726293\pi\) | |||||||
\(548\) | 1.53763e6 | 0.218726 | ||||||||
\(549\) | 2.60709e6 | 0.369168 | ||||||||
\(550\) | −3.56681e6 | −0.502774 | ||||||||
\(551\) | 5.35475e6 | 0.751381 | ||||||||
\(552\) | −819090. | −0.114415 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.99810e6 | −0.968737 | ||||||||
\(555\) | −2.58952e6 | −0.356851 | ||||||||
\(556\) | 1.61367e6 | 0.221375 | ||||||||
\(557\) | −9.22028e6 | −1.25923 | −0.629617 | − | 0.776906i | \(-0.716788\pi\) | ||||
−0.629617 | + | 0.776906i | \(0.716788\pi\) | |||||||
\(558\) | −2.28023e6 | −0.310022 | ||||||||
\(559\) | −2.66904e6 | −0.361264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.48150e6 | −0.332894 | ||||||||
\(562\) | 5.62660e6 | 0.751458 | ||||||||
\(563\) | 8.49277e6 | 1.12922 | 0.564610 | − | 0.825358i | \(-0.309027\pi\) | ||||
0.564610 | + | 0.825358i | \(0.309027\pi\) | |||||||
\(564\) | −1.34110e6 | −0.177527 | ||||||||
\(565\) | −4.36150e6 | −0.574797 | ||||||||
\(566\) | 7.82828e6 | 1.02713 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.91384e6 | 0.509017 | ||||||||
\(569\) | −4.70912e6 | −0.609760 | −0.304880 | − | 0.952391i | \(-0.598616\pi\) | ||||
−0.304880 | + | 0.952391i | \(0.598616\pi\) | |||||||
\(570\) | −830940. | −0.107123 | ||||||||
\(571\) | −1.72807e6 | −0.221805 | −0.110902 | − | 0.993831i | \(-0.535374\pi\) | ||||
−0.110902 | + | 0.993831i | \(0.535374\pi\) | |||||||
\(572\) | −3.96796e6 | −0.507081 | ||||||||
\(573\) | −2.36864e6 | −0.301379 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.72443e6 | −0.469776 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 2.38499e6 | 0.298227 | 0.149113 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149113 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(578\) | −3.05602e6 | −0.380484 | ||||||||
\(579\) | 7.48014e6 | 0.927285 | ||||||||
\(580\) | 1.87785e6 | 0.231788 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.82355e6 | 0.712657 | ||||||||
\(583\) | 1.21350e7 | 1.47866 | ||||||||
\(584\) | 2.64114e6 | 0.320449 | ||||||||
\(585\) | −1.32709e6 | −0.160328 | ||||||||
\(586\) | −5.07993e6 | −0.611102 | ||||||||
\(587\) | −3.44904e6 | −0.413145 | −0.206573 | − | 0.978431i | \(-0.566231\pi\) | ||||
−0.206573 | + | 0.978431i | \(0.566231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.22214e6 | −0.857784 | ||||||||
\(590\) | −2.73293e6 | −0.323220 | ||||||||
\(591\) | 9.48790e6 | 1.11738 | ||||||||
\(592\) | 3.27478e6 | 0.384041 | ||||||||
\(593\) | 1.13468e6 | 0.132507 | 0.0662533 | − | 0.997803i | \(-0.478895\pi\) | ||||
0.0662533 | + | 0.997803i | \(0.478895\pi\) | |||||||
\(594\) | −992786. | −0.115449 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.77511e6 | −0.665954 | ||||||||
\(597\) | −6.28711e6 | −0.721963 | ||||||||
\(598\) | −4.14332e6 | −0.473800 | ||||||||
\(599\) | 7.61865e6 | 0.867583 | 0.433792 | − | 0.901013i | \(-0.357175\pi\) | ||||
0.433792 | + | 0.901013i | \(0.357175\pi\) | |||||||
\(600\) | 1.50860e6 | 0.171079 | ||||||||
\(601\) | 9.78414e6 | 1.10493 | 0.552467 | − | 0.833535i | \(-0.313686\pi\) | ||||
0.552467 | + | 0.833535i | \(0.313686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.72944e6 | 0.193692 | ||||||||
\(604\) | −6.94489e6 | −0.774592 | ||||||||
\(605\) | −1.01523e6 | −0.112766 | ||||||||
\(606\) | 2.37076e6 | 0.262244 | ||||||||
\(607\) | 1.85335e6 | 0.204167 | 0.102083 | − | 0.994776i | \(-0.467449\pi\) | ||||
0.102083 | + | 0.994776i | \(0.467449\pi\) | |||||||
\(608\) | 1.05083e6 | 0.115285 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.89578e6 | 0.315094 | ||||||||
\(611\) | −6.78388e6 | −0.735148 | ||||||||
\(612\) | 1.04956e6 | 0.113274 | ||||||||
\(613\) | −7.12097e6 | −0.765399 | −0.382699 | − | 0.923873i | \(-0.625005\pi\) | ||||
−0.382699 | + | 0.923873i | \(0.625005\pi\) | |||||||
\(614\) | −167417. | −0.0179217 | ||||||||
\(615\) | −237554. | −0.0253265 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.75212e6 | −0.291041 | −0.145521 | − | 0.989355i | \(-0.546486\pi\) | ||||
−0.145521 | + | 0.989355i | \(0.546486\pi\) | |||||||
\(618\) | −4.68713e6 | −0.493669 | ||||||||
\(619\) | −1.30332e7 | −1.36718 | −0.683588 | − | 0.729868i | \(-0.739581\pi\) | ||||
−0.683588 | + | 0.729868i | \(0.739581\pi\) | |||||||
\(620\) | −2.53273e6 | −0.264612 | ||||||||
\(621\) | −1.03666e6 | −0.107872 | ||||||||
\(622\) | −9.16758e6 | −0.950120 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.67827e6 | 0.172544 | ||||||||
\(625\) | 5.27870e6 | 0.540539 | ||||||||
\(626\) | 9.08598e6 | 0.926693 | ||||||||
\(627\) | −3.14444e6 | −0.319429 | ||||||||
\(628\) | −8.18554e6 | −0.828225 | ||||||||
\(629\) | 1.03597e7 | 1.04404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.40820e6 | −0.440745 | −0.220373 | − | 0.975416i | \(-0.570727\pi\) | ||||
−0.220373 | + | 0.975416i | \(0.570727\pi\) | |||||||
\(632\) | −2.24003e6 | −0.223080 | ||||||||
\(633\) | 897242. | 0.0890021 | ||||||||
\(634\) | −7.93897e6 | −0.784406 | ||||||||
\(635\) | 616948. | 0.0607175 | ||||||||
\(636\) | −5.13256e6 | −0.503143 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.10616e6 | 0.691168 | ||||||||
\(639\) | 4.95345e6 | 0.479906 | ||||||||
\(640\) | 368515. | 0.0355635 | ||||||||
\(641\) | −7.98390e6 | −0.767485 | −0.383742 | − | 0.923440i | \(-0.625365\pi\) | ||||
−0.383742 | + | 0.923440i | \(0.625365\pi\) | |||||||
\(642\) | −93274.2 | −0.00893149 | ||||||||
\(643\) | 1.52102e6 | 0.145080 | 0.0725398 | − | 0.997366i | \(-0.476890\pi\) | ||||
0.0725398 | + | 0.997366i | \(0.476890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −741741. | −0.0702026 | ||||||||
\(646\) | 3.32426e6 | 0.313411 | ||||||||
\(647\) | −1.25249e7 | −1.17629 | −0.588146 | − | 0.808755i | \(-0.700142\pi\) | ||||
−0.588146 | + | 0.808755i | \(0.700142\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | −1.03419e7 | −0.963806 | ||||||||
\(650\) | 7.63116e6 | 0.708447 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.02031e6 | −0.370374 | ||||||||
\(653\) | −1.70740e7 | −1.56694 | −0.783471 | − | 0.621428i | \(-0.786553\pi\) | ||||
−0.783471 | + | 0.621428i | \(0.786553\pi\) | |||||||
\(654\) | −3.98353e6 | −0.364187 | ||||||||
\(655\) | 3.38231e6 | 0.308042 | ||||||||
\(656\) | 300417. | 0.0272562 | ||||||||
\(657\) | 3.34269e6 | 0.302122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.12585e6 | −0.190686 | −0.0953432 | − | 0.995444i | \(-0.530395\pi\) | ||||
−0.0953432 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(660\) | −1.10272e6 | −0.0985384 | ||||||||
\(661\) | −2.60011e6 | −0.231466 | −0.115733 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115733 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(662\) | 2.55384e6 | 0.226490 | ||||||||
\(663\) | 5.30915e6 | 0.469074 | ||||||||
\(664\) | 5.51635e6 | 0.485547 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.14464e6 | 0.362078 | ||||||||
\(667\) | 7.42020e6 | 0.645805 | ||||||||
\(668\) | 6.70843e6 | 0.581674 | ||||||||
\(669\) | −4.73575e6 | −0.409094 | ||||||||
\(670\) | 1.92094e6 | 0.165321 | ||||||||
\(671\) | 1.09582e7 | 0.939577 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.44746e7 | −1.23188 | −0.615942 | − | 0.787792i | \(-0.711224\pi\) | ||||
−0.615942 | + | 0.787792i | \(0.711224\pi\) | |||||||
\(674\) | 1.08810e7 | 0.922615 | ||||||||
\(675\) | 1.90932e6 | 0.161294 | ||||||||
\(676\) | 2.54875e6 | 0.214516 | ||||||||
\(677\) | −3.28845e6 | −0.275753 | −0.137876 | − | 0.990449i | \(-0.544028\pi\) | ||||
−0.137876 | + | 0.990449i | \(0.544028\pi\) | |||||||
\(678\) | 6.98077e6 | 0.583216 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.16578e6 | 0.0966819 | ||||||||
\(681\) | 8.83444e6 | 0.729981 | ||||||||
\(682\) | −9.58433e6 | −0.789043 | ||||||||
\(683\) | 8.81887e6 | 0.723371 | 0.361685 | − | 0.932300i | \(-0.382201\pi\) | ||||
0.361685 | + | 0.932300i | \(0.382201\pi\) | |||||||
\(684\) | 1.32996e6 | 0.108692 | ||||||||
\(685\) | 2.16156e6 | 0.176011 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 765729. | 0.0618989 | ||||||||
\(688\) | 938026. | 0.0755517 | ||||||||
\(689\) | −2.59628e7 | −2.08354 | ||||||||
\(690\) | −1.15145e6 | −0.0920711 | ||||||||
\(691\) | −8.59617e6 | −0.684873 | −0.342436 | − | 0.939541i | \(-0.611252\pi\) | ||||
−0.342436 | + | 0.939541i | \(0.611252\pi\) | |||||||
\(692\) | −7.38202e6 | −0.586017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.04831e7 | 0.826208 | ||||||||
\(695\) | 2.26845e6 | 0.178143 | ||||||||
\(696\) | −3.00559e6 | −0.235183 | ||||||||
\(697\) | 950360. | 0.0740979 | ||||||||
\(698\) | 2.30237e6 | 0.178870 | ||||||||
\(699\) | −1.01811e6 | −0.0788134 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.06437e7 | 1.58669 | 0.793347 | − | 0.608770i | \(-0.208337\pi\) | ||||
0.793347 | + | 0.608770i | \(0.208337\pi\) | |||||||
\(702\) | 2.12406e6 | 0.162676 | ||||||||
\(703\) | 1.31273e7 | 1.00181 | ||||||||
\(704\) | 1.39453e6 | 0.106047 | ||||||||
\(705\) | −1.88528e6 | −0.142858 | ||||||||
\(706\) | −1.03589e7 | −0.782169 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.37417e6 | 0.327954 | ||||||||
\(709\) | −426882. | −0.0318928 | −0.0159464 | − | 0.999873i | \(-0.505076\pi\) | ||||
−0.0159464 | + | 0.999873i | \(0.505076\pi\) | |||||||
\(710\) | 5.50196e6 | 0.409611 | ||||||||
\(711\) | −2.83504e6 | −0.210322 | ||||||||
\(712\) | 4.99153e6 | 0.369006 | ||||||||
\(713\) | −1.00079e7 | −0.737257 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.57805e6 | −0.408054 | ||||||||
\(716\) | 1.18673e7 | 0.865105 | ||||||||
\(717\) | 8.05590e6 | 0.585216 | ||||||||
\(718\) | 1.14712e7 | 0.830417 | ||||||||
\(719\) | 3.80724e6 | 0.274655 | 0.137328 | − | 0.990526i | \(-0.456149\pi\) | ||||
0.137328 | + | 0.990526i | \(0.456149\pi\) | |||||||
\(720\) | 466401. | 0.0335296 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.69204e6 | −0.406373 | ||||||||
\(723\) | −4.74943e6 | −0.337906 | ||||||||
\(724\) | 4.82193e6 | 0.341881 | ||||||||
\(725\) | −1.36665e7 | −0.965635 | ||||||||
\(726\) | 1.62493e6 | 0.114417 | ||||||||
\(727\) | −2.22044e7 | −1.55813 | −0.779065 | − | 0.626943i | \(-0.784306\pi\) | ||||
−0.779065 | + | 0.626943i | \(0.784306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 3.71284e6 | 0.257869 | ||||||||
\(731\) | 2.96741e6 | 0.205393 | ||||||||
\(732\) | −4.63482e6 | −0.319709 | ||||||||
\(733\) | −2.90572e7 | −1.99753 | −0.998766 | − | 0.0496729i | \(-0.984182\pi\) | ||||
−0.998766 | + | 0.0496729i | \(0.984182\pi\) | |||||||
\(734\) | −7.81804e6 | −0.535621 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45616e6 | 0.0990865 | ||||||||
\(737\) | 7.26923e6 | 0.492969 | ||||||||
\(738\) | 380216. | 0.0256974 | ||||||||
\(739\) | 2.13523e7 | 1.43824 | 0.719122 | − | 0.694883i | \(-0.244544\pi\) | ||||
0.719122 | + | 0.694883i | \(0.244544\pi\) | |||||||
\(740\) | 4.60359e6 | 0.309042 | ||||||||
\(741\) | 6.72751e6 | 0.450100 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.91874e6 | 0.260420 | 0.130210 | − | 0.991486i | \(-0.458435\pi\) | ||||
0.130210 | + | 0.991486i | \(0.458435\pi\) | |||||||
\(744\) | 4.05374e6 | 0.268487 | ||||||||
\(745\) | −8.11848e6 | −0.535900 | ||||||||
\(746\) | 8.84438e6 | 0.581863 | ||||||||
\(747\) | 6.98163e6 | 0.457778 | ||||||||
\(748\) | 4.41155e6 | 0.288295 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.65113e6 | 0.301930 | ||||||||
\(751\) | 5.66912e6 | 0.366789 | 0.183394 | − | 0.983039i | \(-0.441291\pi\) | ||||
0.183394 | + | 0.983039i | \(0.441291\pi\) | |||||||
\(752\) | 2.38418e6 | 0.153743 | ||||||||
\(753\) | 1.07363e7 | 0.690031 | ||||||||
\(754\) | −1.52036e7 | −0.973908 | ||||||||
\(755\) | −9.76293e6 | −0.623323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.91706e7 | −1.21590 | −0.607949 | − | 0.793976i | \(-0.708007\pi\) | ||||
−0.607949 | + | 0.793976i | \(0.708007\pi\) | |||||||
\(758\) | 1.52493e7 | 0.963998 | ||||||||
\(759\) | −4.35732e6 | −0.274546 | ||||||||
\(760\) | 1.47723e6 | 0.0927712 | ||||||||
\(761\) | 1.46336e7 | 0.915987 | 0.457993 | − | 0.888956i | \(-0.348568\pi\) | ||||
0.457993 | + | 0.888956i | \(0.348568\pi\) | |||||||
\(762\) | −987453. | −0.0616068 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.21092e6 | 0.261002 | ||||||||
\(765\) | 1.47544e6 | 0.0911526 | ||||||||
\(766\) | 1.52242e7 | 0.937483 | ||||||||
\(767\) | 2.21265e7 | 1.35808 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 1.57337e7 | 0.959432 | 0.479716 | − | 0.877424i | \(-0.340740\pi\) | ||||
0.479716 | + | 0.877424i | \(0.340740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.07543e7 | 0.651548 | ||||||||
\(772\) | −1.32980e7 | −0.803053 | ||||||||
\(773\) | 4.04904e6 | 0.243727 | 0.121864 | − | 0.992547i | \(-0.461113\pi\) | ||||
0.121864 | + | 0.992547i | \(0.461113\pi\) | |||||||
\(774\) | 1.18719e6 | 0.0712308 | ||||||||
\(775\) | 1.84325e7 | 1.10238 | ||||||||
\(776\) | −1.03530e7 | −0.617179 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.23010e7 | 0.728602 | ||||||||
\(779\) | 1.20425e6 | 0.0711007 | ||||||||
\(780\) | 2.35926e6 | 0.138848 | ||||||||
\(781\) | 2.08205e7 | 1.22142 | ||||||||
\(782\) | 4.60651e6 | 0.269374 | ||||||||
\(783\) | −3.80395e6 | −0.221733 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.15070e7 | −0.666481 | ||||||||
\(786\) | −5.41353e6 | −0.312554 | ||||||||
\(787\) | −2.16111e7 | −1.24377 | −0.621886 | − | 0.783108i | \(-0.713633\pi\) | ||||
−0.621886 | + | 0.783108i | \(0.713633\pi\) | |||||||
\(788\) | −1.68674e7 | −0.967681 | ||||||||
\(789\) | 1.91007e7 | 1.09234 | ||||||||
\(790\) | −3.14897e6 | −0.179515 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.76495e6 | 0.0999817 | ||||||||
\(793\) | −2.34450e7 | −1.32394 | ||||||||
\(794\) | 8.76530e6 | 0.493419 | ||||||||
\(795\) | −7.21521e6 | −0.404884 | ||||||||
\(796\) | 1.11771e7 | 0.625239 | ||||||||
\(797\) | 1.38162e7 | 0.770445 | 0.385222 | − | 0.922824i | \(-0.374125\pi\) | ||||
0.385222 | + | 0.922824i | \(0.374125\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.54226e6 | 0.417960 | ||||||||
\(800\) | −2.68195e6 | −0.148158 | ||||||||
\(801\) | 6.31740e6 | 0.347902 | ||||||||
\(802\) | 7.10672e6 | 0.390151 | ||||||||
\(803\) | 1.40501e7 | 0.768937 | ||||||||
\(804\) | −3.07456e6 | −0.167742 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.05056e7 | 1.11182 | ||||||||
\(807\) | −1.39479e6 | −0.0753919 | ||||||||
\(808\) | −4.21468e6 | −0.227110 | ||||||||
\(809\) | −3.50756e7 | −1.88423 | −0.942116 | − | 0.335287i | \(-0.891167\pi\) | ||||
−0.942116 | + | 0.335287i | \(0.891167\pi\) | |||||||
\(810\) | 590289. | 0.0316120 | ||||||||
\(811\) | 6.56287e6 | 0.350382 | 0.175191 | − | 0.984534i | \(-0.443946\pi\) | ||||
0.175191 | + | 0.984534i | \(0.443946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.76299e7 | −0.935456 | ||||||||
\(814\) | 1.74209e7 | 0.921530 | ||||||||
\(815\) | −5.65164e6 | −0.298044 | ||||||||
\(816\) | −1.86589e6 | −0.0980980 | ||||||||
\(817\) | 3.76017e6 | 0.197085 | ||||||||
\(818\) | 9.44473e6 | 0.493522 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 422318. | 0.0219334 | ||||||||
\(821\) | −1.77894e6 | −0.0921093 | −0.0460547 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460547 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(822\) | −3.45967e6 | −0.178589 | ||||||||
\(823\) | 1.89586e7 | 0.975676 | 0.487838 | − | 0.872934i | \(-0.337786\pi\) | ||||
0.487838 | + | 0.872934i | \(0.337786\pi\) | |||||||
\(824\) | 8.33268e6 | 0.427530 | ||||||||
\(825\) | 8.02531e6 | 0.410513 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.82110e7 | 1.43435 | 0.717174 | − | 0.696894i | \(-0.245435\pi\) | ||||
0.717174 | + | 0.696894i | \(0.245435\pi\) | |||||||
\(828\) | 1.84295e6 | 0.0934196 | ||||||||
\(829\) | −2.24021e7 | −1.13214 | −0.566072 | − | 0.824356i | \(-0.691538\pi\) | ||||
−0.566072 | + | 0.824356i | \(0.691538\pi\) | |||||||
\(830\) | 7.75473e6 | 0.390725 | ||||||||
\(831\) | 1.57457e7 | 0.790971 | ||||||||
\(832\) | −2.98359e6 | −0.149428 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.63076e6 | −0.180752 | ||||||||
\(835\) | 9.43051e6 | 0.468079 | ||||||||
\(836\) | 5.59012e6 | 0.276634 | ||||||||
\(837\) | 5.13052e6 | 0.253132 | ||||||||
\(838\) | −1.29397e7 | −0.636524 | ||||||||
\(839\) | −1.50303e7 | −0.737162 | −0.368581 | − | 0.929596i | \(-0.620156\pi\) | ||||
−0.368581 | + | 0.929596i | \(0.620156\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.71672e6 | 0.327467 | ||||||||
\(842\) | −1.14304e7 | −0.555622 | ||||||||
\(843\) | −1.26598e7 | −0.613563 | ||||||||
\(844\) | −1.59510e6 | −0.0770781 | ||||||||
\(845\) | 3.58295e6 | 0.172623 | ||||||||
\(846\) | 3.01747e6 | 0.144950 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.12455e6 | 0.435734 | ||||||||
\(849\) | −1.76136e7 | −0.838648 | ||||||||
\(850\) | −8.48426e6 | −0.402779 | ||||||||
\(851\) | 1.81908e7 | 0.861048 | ||||||||
\(852\) | −8.80614e6 | −0.415611 | ||||||||
\(853\) | −3.18297e7 | −1.49782 | −0.748911 | − | 0.662670i | \(-0.769423\pi\) | ||||
−0.748911 | + | 0.662670i | \(0.769423\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.86962e6 | 0.0874656 | ||||||||
\(856\) | 165821. | 0.00773490 | ||||||||
\(857\) | 2.17823e7 | 1.01310 | 0.506549 | − | 0.862211i | \(-0.330921\pi\) | ||||
0.506549 | + | 0.862211i | \(0.330921\pi\) | |||||||
\(858\) | 8.92792e6 | 0.414030 | ||||||||
\(859\) | 3.73349e7 | 1.72636 | 0.863181 | − | 0.504895i | \(-0.168469\pi\) | ||||
0.863181 | + | 0.504895i | \(0.168469\pi\) | |||||||
\(860\) | 1.31865e6 | 0.0607972 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −353545. | −0.0162060 | ||||||||
\(863\) | −1.54613e7 | −0.706675 | −0.353338 | − | 0.935496i | \(-0.614953\pi\) | ||||
−0.353338 | + | 0.935496i | \(0.614953\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −1.03774e7 | −0.471574 | ||||||||
\(866\) | −1.23767e7 | −0.560805 | ||||||||
\(867\) | 6.87604e6 | 0.310664 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.19163e7 | −0.535294 | ||||||||
\(870\) | −4.22517e6 | −0.189254 | ||||||||
\(871\) | −1.55525e7 | −0.694630 | ||||||||
\(872\) | 7.08184e6 | 0.315395 | ||||||||
\(873\) | −1.31030e7 | −0.581882 | ||||||||
\(874\) | 5.83716e6 | 0.258478 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.94256e6 | −0.261646 | ||||||||
\(877\) | −6.81762e6 | −0.299319 | −0.149659 | − | 0.988738i | \(-0.547818\pi\) | ||||
−0.149659 | + | 0.988738i | \(0.547818\pi\) | |||||||
\(878\) | 1.94071e6 | 0.0849621 | ||||||||
\(879\) | 1.14298e7 | 0.498963 | ||||||||
\(880\) | 1.96039e6 | 0.0853368 | ||||||||
\(881\) | −1.20903e7 | −0.524805 | −0.262402 | − | 0.964959i | \(-0.584515\pi\) | ||||
−0.262402 | + | 0.964959i | \(0.584515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.63966e7 | 0.707706 | 0.353853 | − | 0.935301i | \(-0.384871\pi\) | ||||
0.353853 | + | 0.935301i | \(0.384871\pi\) | |||||||
\(884\) | −9.43848e6 | −0.406230 | ||||||||
\(885\) | 6.14909e6 | 0.263908 | ||||||||
\(886\) | 5.10078e6 | 0.218299 | ||||||||
\(887\) | −2.57006e7 | −1.09682 | −0.548409 | − | 0.836210i | \(-0.684766\pi\) | ||||
−0.548409 | + | 0.836210i | \(0.684766\pi\) | |||||||
\(888\) | −7.36826e6 | −0.313568 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.01695e6 | 0.296943 | ||||||||
\(891\) | 2.23377e6 | 0.0942636 | ||||||||
\(892\) | 8.41911e6 | 0.354286 | ||||||||
\(893\) | 9.55721e6 | 0.401054 | ||||||||
\(894\) | 1.29940e7 | 0.543749 | ||||||||
\(895\) | 1.66827e7 | 0.696160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.32247e6 | 0.386856 | ||||||||
\(898\) | −1.51658e7 | −0.627586 | ||||||||
\(899\) | −3.67232e7 | −1.51545 | ||||||||
\(900\) | −3.39435e6 | −0.139685 | ||||||||
\(901\) | 2.88652e7 | 1.18457 | ||||||||
\(902\) | 1.59813e6 | 0.0654029 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.24103e7 | −0.505080 | ||||||||
\(905\) | 6.77854e6 | 0.275115 | ||||||||
\(906\) | 1.56260e7 | 0.632452 | ||||||||
\(907\) | −2.34481e7 | −0.946434 | −0.473217 | − | 0.880946i | \(-0.656907\pi\) | ||||
−0.473217 | + | 0.880946i | \(0.656907\pi\) | |||||||
\(908\) | −1.57057e7 | −0.632182 | ||||||||
\(909\) | −5.33421e6 | −0.214121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.29134e7 | −1.31395 | −0.656973 | − | 0.753914i | \(-0.728163\pi\) | ||||
−0.656973 | + | 0.753914i | \(0.728163\pi\) | |||||||
\(912\) | −2.36437e6 | −0.0941300 | ||||||||
\(913\) | 2.93454e7 | 1.16510 | ||||||||
\(914\) | 6.81123e6 | 0.269687 | ||||||||
\(915\) | −6.51550e6 | −0.257273 | ||||||||
\(916\) | −1.36130e6 | −0.0536061 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.36151e6 | −0.0924877 | ||||||||
\(919\) | −2.52264e7 | −0.985294 | −0.492647 | − | 0.870229i | \(-0.663971\pi\) | ||||
−0.492647 | + | 0.870229i | \(0.663971\pi\) | |||||||
\(920\) | 2.04703e6 | 0.0797359 | ||||||||
\(921\) | 376689. | 0.0146330 | ||||||||
\(922\) | 1.82215e7 | 0.705921 | ||||||||
\(923\) | −4.45454e7 | −1.72107 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.35037e7 | −1.28748 | ||||||||
\(926\) | 2.33059e7 | 0.893178 | ||||||||
\(927\) | 1.05460e7 | 0.403079 | ||||||||
\(928\) | 5.34327e6 | 0.203675 | ||||||||
\(929\) | 2.51164e7 | 0.954812 | 0.477406 | − | 0.878683i | \(-0.341577\pi\) | ||||
0.477406 | + | 0.878683i | \(0.341577\pi\) | |||||||
\(930\) | 5.69863e6 | 0.216055 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.80997e6 | 0.0682544 | ||||||||
\(933\) | 2.06270e7 | 0.775770 | ||||||||
\(934\) | −1.41704e7 | −0.531516 | ||||||||
\(935\) | 6.20163e6 | 0.231994 | ||||||||
\(936\) | −3.77611e6 | −0.140882 | ||||||||
\(937\) | 8.25845e6 | 0.307291 | 0.153645 | − | 0.988126i | \(-0.450899\pi\) | ||||
0.153645 | + | 0.988126i | \(0.450899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.04435e7 | −0.756642 | ||||||||
\(940\) | 3.35161e6 | 0.123718 | ||||||||
\(941\) | 1.27088e7 | 0.467875 | 0.233938 | − | 0.972252i | \(-0.424839\pi\) | ||||
0.233938 | + | 0.972252i | \(0.424839\pi\) | |||||||
\(942\) | 1.84175e7 | 0.676243 | ||||||||
\(943\) | 1.66876e6 | 0.0611103 | ||||||||
\(944\) | −7.77630e6 | −0.284016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.99003e6 | 0.181291 | ||||||||
\(947\) | 1.06278e7 | 0.385096 | 0.192548 | − | 0.981288i | \(-0.438325\pi\) | ||||
0.192548 | + | 0.981288i | \(0.438325\pi\) | |||||||
\(948\) | 5.04007e6 | 0.182144 | ||||||||
\(949\) | −3.00601e7 | −1.08349 | ||||||||
\(950\) | −1.07509e7 | −0.386487 | ||||||||
\(951\) | 1.78627e7 | 0.640465 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 749727. | 0.0267406 | 0.0133703 | − | 0.999911i | \(-0.495744\pi\) | ||||
0.0133703 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(954\) | 1.15483e7 | 0.410814 | ||||||||
\(955\) | 5.91959e6 | 0.210031 | ||||||||
\(956\) | −1.43216e7 | −0.506812 | ||||||||
\(957\) | −1.59889e7 | −0.564336 | ||||||||
\(958\) | −1.69417e7 | −0.596407 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −829158. | −0.0290375 | ||||||||
\(961\) | 2.09007e7 | 0.730050 | ||||||||
\(962\) | −3.72719e7 | −1.29851 | ||||||||
\(963\) | 209867. | 0.00729253 | ||||||||
\(964\) | 8.44343e6 | 0.292635 | ||||||||
\(965\) | −1.86940e7 | −0.646225 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.97713e7 | 1.02384 | 0.511920 | − | 0.859033i | \(-0.328934\pi\) | ||||
0.511920 | + | 0.859033i | \(0.328934\pi\) | |||||||
\(968\) | −2.88876e6 | −0.0990883 | ||||||||
\(969\) | −7.47960e6 | −0.255899 | ||||||||
\(970\) | −1.45539e7 | −0.496651 | ||||||||
\(971\) | −1.51210e7 | −0.514676 | −0.257338 | − | 0.966321i | \(-0.582845\pi\) | ||||
−0.257338 | + | 0.966321i | \(0.582845\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.26192e7 | −0.763975 | ||||||||
\(975\) | −1.71701e7 | −0.578444 | ||||||||
\(976\) | 8.23968e6 | 0.276876 | ||||||||
\(977\) | 1.93107e6 | 0.0647235 | 0.0323617 | − | 0.999476i | \(-0.489697\pi\) | ||||
0.0323617 | + | 0.999476i | \(0.489697\pi\) | |||||||
\(978\) | 9.04570e6 | 0.302409 | ||||||||
\(979\) | 2.65535e7 | 0.885452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.96295e6 | 0.297357 | ||||||||
\(982\) | 3.33273e7 | 1.10286 | ||||||||
\(983\) | 4.22343e7 | 1.39406 | 0.697030 | − | 0.717042i | \(-0.254504\pi\) | ||||
0.697030 | + | 0.717042i | \(0.254504\pi\) | |||||||
\(984\) | −675939. | −0.0222546 | ||||||||
\(985\) | −2.37117e7 | −0.778703 | ||||||||
\(986\) | 1.69032e7 | 0.553704 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.19600e7 | −0.389798 | ||||||||
\(989\) | 5.21056e6 | 0.169392 | ||||||||
\(990\) | 2.48112e6 | 0.0804563 | ||||||||
\(991\) | 5.83480e6 | 0.188730 | 0.0943651 | − | 0.995538i | \(-0.469918\pi\) | ||||
0.0943651 | + | 0.995538i | \(0.469918\pi\) | |||||||
\(992\) | −7.20665e6 | −0.232517 | ||||||||
\(993\) | −5.74615e6 | −0.184928 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.57124e7 | 0.503136 | ||||||||
\(996\) | −1.24118e7 | −0.396448 | ||||||||
\(997\) | 1.23461e7 | 0.393360 | 0.196680 | − | 0.980468i | \(-0.436984\pi\) | ||||
0.196680 | + | 0.980468i | \(0.436984\pi\) | |||||||
\(998\) | −2.89508e7 | −0.920097 | ||||||||
\(999\) | −9.32545e6 | −0.295635 |
(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 | 294.6.a.r.1.2 | 2 | ||
3.2 | odd | 2 | 882.6.a.bh.1.1 | 2 | |||
7.2 | even | 3 | 42.6.e.c.25.1 | ✓ | 4 | ||
7.3 | odd | 6 | 294.6.e.s.79.2 | 4 | |||
7.4 | even | 3 | 42.6.e.c.37.1 | yes | 4 | ||
7.5 | odd | 6 | 294.6.e.s.67.2 | 4 | |||
7.6 | odd | 2 | 294.6.a.w.1.1 | 2 | |||
21.2 | odd | 6 | 126.6.g.h.109.2 | 4 | |||
21.11 | odd | 6 | 126.6.g.h.37.2 | 4 | |||
21.20 | even | 2 | 882.6.a.bb.1.2 | 2 | |||
28.11 | odd | 6 | 336.6.q.f.289.1 | 4 | |||
28.23 | odd | 6 | 336.6.q.f.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.e.c.25.1 | ✓ | 4 | 7.2 | even | 3 | ||
42.6.e.c.37.1 | yes | 4 | 7.4 | even | 3 | ||
126.6.g.h.37.2 | 4 | 21.11 | odd | 6 | |||
126.6.g.h.109.2 | 4 | 21.2 | odd | 6 | |||
294.6.a.r.1.2 | 2 | 1.1 | even | 1 | trivial | ||
294.6.a.w.1.1 | 2 | 7.6 | odd | 2 | |||
294.6.e.s.67.2 | 4 | 7.5 | odd | 6 | |||
294.6.e.s.79.2 | 4 | 7.3 | odd | 6 | |||
336.6.q.f.193.1 | 4 | 28.23 | odd | 6 | |||
336.6.q.f.289.1 | 4 | 28.11 | odd | 6 | |||
882.6.a.bb.1.2 | 2 | 21.20 | even | 2 | |||
882.6.a.bh.1.1 | 2 | 3.2 | odd | 2 |