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 | 1.1 | ||
Root | \(49.4923\) 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 | \(-0.564477\pi\) | ||||
−0.201178 | + | 0.979555i | \(0.564477\pi\) | |||||||
\(6\) | 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 | \(-0.296077\pi\) | ||||
0.597711 | + | 0.801712i | \(0.296077\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −202.431 | −0.232300 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −809.847 | −0.679643 | −0.339821 | − | 0.940490i | \(-0.610367\pi\) | ||||
−0.339821 | + | 0.940490i | \(0.610367\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | −1026.20 | −0.652152 | −0.326076 | − | 0.945344i | \(-0.605726\pi\) | ||||
−0.326076 | + | 0.945344i | \(0.605726\pi\) | |||||||
\(20\) | −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 | \(-0.271548\pi\) | ||||
0.657657 | + | 0.753318i | \(0.271548\pi\) | |||||||
\(32\) | 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 | \(-0.517360\pi\) | ||||
−0.0545124 | + | 0.998513i | \(0.517360\pi\) | |||||||
\(42\) | 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 | \(-0.599487\pi\) | ||||
−0.307485 | + | 0.951553i | \(0.599487\pi\) | |||||||
\(48\) | 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 | \(-0.307705\pi\) | ||||
0.568033 | + | 0.823006i | \(0.307705\pi\) | |||||||
\(60\) | −3238.90 | −0.116150 | ||||||||
\(61\) | −32186.2 | −1.10751 | −0.553753 | − | 0.832681i | \(-0.686805\pi\) | ||||
−0.553753 | + | 0.832681i | \(0.686805\pi\) | |||||||
\(62\) | 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 | \(-0.649712\pi\) | ||||
−0.453184 | + | 0.891417i | \(0.649712\pi\) | |||||||
\(74\) | 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 | \(-0.740927\pi\) | ||||
−0.686668 | + | 0.726972i | \(0.740927\pi\) | |||||||
\(84\) | 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 | \(-0.674759\pi\) | ||||
−0.521853 | + | 0.853035i | \(0.674759\pi\) | |||||||
\(90\) | −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 | \(-0.162287\pi\) | ||||
0.872823 | + | 0.488037i | \(0.162287\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27577.4 | 0.282791 | ||||||||
\(100\) | −41905.5 | −0.419055 | ||||||||
\(101\) | 65854.4 | 0.642364 | 0.321182 | − | 0.947017i | \(-0.395920\pi\) | ||||
0.321182 | + | 0.947017i | \(0.395920\pi\) | |||||||
\(102\) | −29154.5 | −0.277463 | ||||||||
\(103\) | −130198. | −1.20924 | −0.604619 | − | 0.796515i | \(-0.706674\pi\) | ||||
−0.604619 | + | 0.796515i | \(0.706674\pi\) | |||||||
\(104\) | 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 | \(-0.625040\pi\) | ||||
−0.382798 | + | 0.923832i | \(0.625040\pi\) | |||||||
\(132\) | 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 | \(-0.571054\pi\) | ||||
−0.221375 | + | 0.975189i | \(0.571054\pi\) | |||||||
\(140\) | 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 | \(-0.189351\pi\) | ||||
0.828225 | + | 0.560396i | \(0.189351\pi\) | |||||||
\(158\) | −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 | \(-0.697602\pi\) | ||||
−0.581674 | + | 0.813422i | \(0.697602\pi\) | |||||||
\(168\) | 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 | \(-0.300695\pi\) | ||||
0.586017 | + | 0.810299i | \(0.300695\pi\) | |||||||
\(174\) | 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 | \(-0.611064\pi\) | ||||
−0.341881 | + | 0.939743i | \(0.611064\pi\) | |||||||
\(182\) | 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 | \(-0.714998\pi\) | ||||
−0.625239 | + | 0.780434i | \(0.714998\pi\) | |||||||
\(200\) | −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 | \(-0.615276\pi\) | ||||
−0.354286 | + | 0.935137i | \(0.615276\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −212147. | −0.279370 | ||||||||
\(226\) | −775642. | −1.01016 | ||||||||
\(227\) | 981605. | 1.26436 | 0.632182 | − | 0.774820i | \(-0.282160\pi\) | ||||
0.632182 | + | 0.774820i | \(0.282160\pi\) | |||||||
\(228\) | −147773. | −0.188260 | ||||||||
\(229\) | 85081.0 | 0.107212 | 0.0536061 | − | 0.998562i | \(-0.482928\pi\) | ||||
0.0536061 | + | 0.998562i | \(0.482928\pi\) | |||||||
\(230\) | −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 | \(-0.594532\pi\) | ||||
−0.292635 | + | 0.956224i | \(0.594532\pi\) | |||||||
\(242\) | −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 | \(-0.296127\pi\) | ||||
0.597584 | + | 0.801806i | \(0.296127\pi\) | |||||||
\(252\) | 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 | \(-0.309163\pi\) | ||||
0.564257 | + | 0.825599i | \(0.309163\pi\) | |||||||
\(258\) | 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 | \(-0.520798\pi\) | ||||
−0.0652913 | + | 0.997866i | \(0.520798\pi\) | |||||||
\(270\) | −65587.7 | −0.0547536 | ||||||||
\(271\) | −1.95888e6 | −1.62026 | −0.810129 | − | 0.586252i | \(-0.800603\pi\) | ||||
−0.810129 | + | 0.586252i | \(0.800603\pi\) | |||||||
\(272\) | −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 | \(-0.758757\pi\) | ||||
−0.726291 | + | 0.687388i | \(0.758757\pi\) | |||||||
\(284\) | 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 | \(-0.357768\pi\) | ||||
0.432114 | + | 0.901819i | \(0.357768\pi\) | |||||||
\(294\) | 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 | \(-0.495966\pi\) | ||||
0.0126726 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.17178e6 | −0.698154 | ||||||||
\(310\) | −633182. | −0.374217 | ||||||||
\(311\) | 2.29189e6 | 1.34367 | 0.671837 | − | 0.740699i | \(-0.265506\pi\) | ||||
0.671837 | + | 0.740699i | \(0.265506\pi\) | |||||||
\(312\) | 419568. | 0.244014 | ||||||||
\(313\) | −2.27150e6 | −1.31054 | −0.655271 | − | 0.755394i | \(-0.727446\pi\) | ||||
−0.655271 | + | 0.755394i | \(0.727446\pi\) | |||||||
\(314\) | 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 | \(-0.540368\pi\) | ||||
−0.126480 | + | 0.991969i | \(0.540368\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 531015. | 0.230059 | ||||||||
\(352\) | 348633. | 0.149972 | ||||||||
\(353\) | 2.58972e6 | 1.10615 | 0.553077 | − | 0.833130i | \(-0.313454\pi\) | ||||
0.553077 | + | 0.833130i | \(0.313454\pi\) | |||||||
\(354\) | 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 | \(-0.376357\pi\) | ||||
0.378741 | + | 0.925503i | \(0.376357\pi\) | |||||||
\(368\) | 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 | \(-0.730675\pi\) | ||||
−0.662901 | + | 0.748707i | \(0.730675\pi\) | |||||||
\(384\) | 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 | \(-0.613445\pi\) | ||||
−0.348900 | + | 0.937160i | \(0.613445\pi\) | |||||||
\(398\) | −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 | \(-0.613469\pi\) | ||||
−0.348973 | + | 0.937133i | \(0.613469\pi\) | |||||||
\(410\) | 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 | \(-0.351392\pi\) | ||||
0.450090 | + | 0.892983i | \(0.351392\pi\) | |||||||
\(420\) | 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 | \(-0.370208\pi\) | ||||
0.396549 | + | 0.918014i | \(0.370208\pi\) | |||||||
\(434\) | 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 | \(-0.519135\pi\) | ||||
−0.0600773 | + | 0.998194i | \(0.519135\pi\) | |||||||
\(440\) | −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 | \(-0.666358\pi\) | ||||
−0.499161 | + | 0.866509i | \(0.666358\pi\) | |||||||
\(462\) | 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 | \(-0.377355\pi\) | ||||
0.375839 | + | 0.926685i | \(0.377355\pi\) | |||||||
\(468\) | 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 | \(-0.361425\pi\) | ||||
0.421723 | + | 0.906725i | \(0.361425\pi\) | |||||||
\(480\) | −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 | \(-0.317114\pi\) | ||||
0.543459 | + | 0.839436i | \(0.317114\pi\) | |||||||
\(504\) | 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 | \(-0.550169\pi\) | ||||
−0.156958 | + | 0.987605i | \(0.550169\pi\) | |||||||
\(510\) | 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 | \(-0.640976\pi\) | ||||
−0.428551 | + | 0.903517i | \(0.640976\pi\) | |||||||
\(522\) | 1.69064e6 | 0.271566 | ||||||||
\(523\) | 2.98835e6 | 0.477725 | 0.238862 | − | 0.971053i | \(-0.423226\pi\) | ||||
0.238862 | + | 0.971053i | \(0.423226\pi\) | |||||||
\(524\) | −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 | \(-0.690973\pi\) | ||||
−0.564610 | + | 0.825358i | \(0.690973\pi\) | |||||||
\(564\) | −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 | \(-0.547642\pi\) | ||||
−0.149113 | + | 0.988820i | \(0.547642\pi\) | |||||||
\(578\) | −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 | \(-0.433769\pi\) | ||||
0.206573 | + | 0.978431i | \(0.433769\pi\) | |||||||
\(588\) | 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 | \(-0.521105\pi\) | ||||
−0.0662533 | + | 0.997803i | \(0.521105\pi\) | |||||||
\(594\) | 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 | \(-0.686314\pi\) | ||||
−0.552467 | + | 0.833535i | \(0.686314\pi\) | |||||||
\(602\) | 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 | \(-0.532551\pi\) | ||||
−0.102083 | + | 0.994776i | \(0.532551\pi\) | |||||||
\(608\) | −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 | \(-0.260419\pi\) | ||||
0.683588 | + | 0.729868i | \(0.260419\pi\) | |||||||
\(620\) | −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 | \(-0.523110\pi\) | ||||
−0.0725398 | + | 0.997366i | \(0.523110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −741741. | −0.0702026 | ||||||||
\(646\) | 3.32426e6 | 0.313411 | ||||||||
\(647\) | 1.25249e7 | 1.17629 | 0.588146 | − | 0.808755i | \(-0.299858\pi\) | ||||
0.588146 | + | 0.808755i | \(0.299858\pi\) | |||||||
\(648\) | 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 | \(-0.463078\pi\) | ||||
0.115733 | + | 0.993280i | \(0.463078\pi\) | |||||||
\(662\) | 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 | \(-0.455972\pi\) | ||||
0.137876 | + | 0.990449i | \(0.455972\pi\) | |||||||
\(678\) | −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 | \(-0.388748\pi\) | ||||
0.342436 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(692\) | 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 | \(-0.543851\pi\) | ||||
−0.137328 | + | 0.990526i | \(0.543851\pi\) | |||||||
\(720\) | −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 | \(-0.215694\pi\) | ||||
0.779065 | + | 0.626943i | \(0.215694\pi\) | |||||||
\(728\) | 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 | \(-0.0158179\pi\) | ||||
0.998766 | + | 0.0496729i | \(0.0158179\pi\) | |||||||
\(734\) | 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 | \(-0.651432\pi\) | ||||
−0.457993 | + | 0.888956i | \(0.651432\pi\) | |||||||
\(762\) | 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 | \(-0.659260\pi\) | ||||
−0.479716 | + | 0.877424i | \(0.659260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.07543e7 | 0.651548 | ||||||||
\(772\) | −1.32980e7 | −0.803053 | ||||||||
\(773\) | −4.04904e6 | −0.243727 | −0.121864 | − | 0.992547i | \(-0.538887\pi\) | ||||
−0.121864 | + | 0.992547i | \(0.538887\pi\) | |||||||
\(774\) | 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 | \(-0.286367\pi\) | ||||
0.621886 | + | 0.783108i | \(0.286367\pi\) | |||||||
\(788\) | −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 | \(-0.625875\pi\) | ||||
−0.385222 | + | 0.922824i | \(0.625875\pi\) | |||||||
\(798\) | 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 | \(-0.556054\pi\) | ||||
−0.175191 | + | 0.984534i | \(0.556054\pi\) | |||||||
\(812\) | 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 | \(-0.308462\pi\) | ||||
0.566072 | + | 0.824356i | \(0.308462\pi\) | |||||||
\(830\) | 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 | \(-0.379844\pi\) | ||||
0.368581 | + | 0.929596i | \(0.379844\pi\) | |||||||
\(840\) | 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 | \(-0.230577\pi\) | ||||
0.748911 | + | 0.662670i | \(0.230577\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.86962e6 | 0.0874656 | ||||||||
\(856\) | 165821. | 0.00773490 | ||||||||
\(857\) | −2.17823e7 | −1.01310 | −0.506549 | − | 0.862211i | \(-0.669079\pi\) | ||||
−0.506549 | + | 0.862211i | \(0.669079\pi\) | |||||||
\(858\) | 8.92792e6 | 0.414030 | ||||||||
\(859\) | −3.73349e7 | −1.72636 | −0.863181 | − | 0.504895i | \(-0.831531\pi\) | ||||
−0.863181 | + | 0.504895i | \(0.831531\pi\) | |||||||
\(860\) | −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 | \(-0.415485\pi\) | ||||
0.262402 | + | 0.964959i | \(0.415485\pi\) | |||||||
\(882\) | 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 | \(-0.315234\pi\) | ||||
0.548409 | + | 0.836210i | \(0.315234\pi\) | |||||||
\(888\) | 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 | \(-0.658423\pi\) | ||||
−0.477406 | + | 0.878683i | \(0.658423\pi\) | |||||||
\(930\) | −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 | \(-0.549101\pi\) | ||||
−0.153645 | + | 0.988126i | \(0.549101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.04435e7 | −0.756642 | ||||||||
\(940\) | 3.35161e6 | 0.123718 | ||||||||
\(941\) | −1.27088e7 | −0.467875 | −0.233938 | − | 0.972252i | \(-0.575161\pi\) | ||||
−0.233938 | + | 0.972252i | \(0.575161\pi\) | |||||||
\(942\) | 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 | \(-0.417155\pi\) | ||||
0.257338 | + | 0.966321i | \(0.417155\pi\) | |||||||
\(972\) | 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 | \(-0.745496\pi\) | ||||
−0.697030 | + | 0.717042i | \(0.745496\pi\) | |||||||
\(984\) | −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 | \(-0.563016\pi\) | ||||
−0.196680 | + | 0.980468i | \(0.563016\pi\) | |||||||
\(998\) | −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.w.1.1 | 2 | ||
3.2 | odd | 2 | 882.6.a.bb.1.2 | 2 | |||
7.2 | even | 3 | 294.6.e.s.67.2 | 4 | |||
7.3 | odd | 6 | 42.6.e.c.37.1 | yes | 4 | ||
7.4 | even | 3 | 294.6.e.s.79.2 | 4 | |||
7.5 | odd | 6 | 42.6.e.c.25.1 | ✓ | 4 | ||
7.6 | odd | 2 | 294.6.a.r.1.2 | 2 | |||
21.5 | even | 6 | 126.6.g.h.109.2 | 4 | |||
21.17 | even | 6 | 126.6.g.h.37.2 | 4 | |||
21.20 | even | 2 | 882.6.a.bh.1.1 | 2 | |||
28.3 | even | 6 | 336.6.q.f.289.1 | 4 | |||
28.19 | even | 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 | 7.5 | odd | 6 | ||
42.6.e.c.37.1 | yes | 4 | 7.3 | odd | 6 | ||
126.6.g.h.37.2 | 4 | 21.17 | even | 6 | |||
126.6.g.h.109.2 | 4 | 21.5 | even | 6 | |||
294.6.a.r.1.2 | 2 | 7.6 | odd | 2 | |||
294.6.a.w.1.1 | 2 | 1.1 | even | 1 | trivial | ||
294.6.e.s.67.2 | 4 | 7.2 | even | 3 | |||
294.6.e.s.79.2 | 4 | 7.4 | even | 3 | |||
336.6.q.f.193.1 | 4 | 28.19 | even | 6 | |||
336.6.q.f.289.1 | 4 | 28.3 | even | 6 | |||
882.6.a.bb.1.2 | 2 | 3.2 | odd | 2 | |||
882.6.a.bh.1.1 | 2 | 21.20 | even | 2 |