Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, 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("21.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(3.36806021607\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.176777 | 0.0883883 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883883 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −31.0000 | −0.968750 | ||||||||
\(5\) | −34.0000 | −0.608210 | −0.304105 | − | 0.952638i | \(-0.598357\pi\) | ||||
−0.304105 | + | 0.952638i | \(0.598357\pi\) | |||||||
\(6\) | −9.00000 | −0.102062 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −63.0000 | −0.348029 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −34.0000 | −0.107517 | ||||||||
\(11\) | −340.000 | −0.847222 | −0.423611 | − | 0.905844i | \(-0.639238\pi\) | ||||
−0.423611 | + | 0.905844i | \(0.639238\pi\) | |||||||
\(12\) | 279.000 | 0.559308 | ||||||||
\(13\) | 454.000 | 0.745071 | 0.372535 | − | 0.928018i | \(-0.378489\pi\) | ||||
0.372535 | + | 0.928018i | \(0.378489\pi\) | |||||||
\(14\) | −49.0000 | −0.0668153 | ||||||||
\(15\) | 306.000 | 0.351150 | ||||||||
\(16\) | 929.000 | 0.907227 | ||||||||
\(17\) | −798.000 | −0.669700 | −0.334850 | − | 0.942271i | \(-0.608686\pi\) | ||||
−0.334850 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(18\) | 81.0000 | 0.0589256 | ||||||||
\(19\) | 892.000 | 0.566867 | 0.283433 | − | 0.958992i | \(-0.408527\pi\) | ||||
0.283433 | + | 0.958992i | \(0.408527\pi\) | |||||||
\(20\) | 1054.00 | 0.589204 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | −340.000 | −0.149769 | ||||||||
\(23\) | −3192.00 | −1.25818 | −0.629091 | − | 0.777332i | \(-0.716573\pi\) | ||||
−0.629091 | + | 0.777332i | \(0.716573\pi\) | |||||||
\(24\) | 567.000 | 0.200935 | ||||||||
\(25\) | −1969.00 | −0.630080 | ||||||||
\(26\) | 454.000 | 0.131711 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 1519.00 | 0.366153 | ||||||||
\(29\) | −8242.00 | −1.81986 | −0.909929 | − | 0.414764i | \(-0.863864\pi\) | ||||
−0.909929 | + | 0.414764i | \(0.863864\pi\) | |||||||
\(30\) | 306.000 | 0.0620752 | ||||||||
\(31\) | −2496.00 | −0.466488 | −0.233244 | − | 0.972418i | \(-0.574934\pi\) | ||||
−0.233244 | + | 0.972418i | \(0.574934\pi\) | |||||||
\(32\) | 2945.00 | 0.508406 | ||||||||
\(33\) | 3060.00 | 0.489144 | ||||||||
\(34\) | −798.000 | −0.118387 | ||||||||
\(35\) | 1666.00 | 0.229882 | ||||||||
\(36\) | −2511.00 | −0.322917 | ||||||||
\(37\) | 9798.00 | 1.17661 | 0.588306 | − | 0.808639i | \(-0.299795\pi\) | ||||
0.588306 | + | 0.808639i | \(0.299795\pi\) | |||||||
\(38\) | 892.000 | 0.100209 | ||||||||
\(39\) | −4086.00 | −0.430167 | ||||||||
\(40\) | 2142.00 | 0.211675 | ||||||||
\(41\) | 19834.0 | 1.84268 | 0.921342 | − | 0.388754i | \(-0.127094\pi\) | ||||
0.921342 | + | 0.388754i | \(0.127094\pi\) | |||||||
\(42\) | 441.000 | 0.0385758 | ||||||||
\(43\) | −17236.0 | −1.42156 | −0.710780 | − | 0.703414i | \(-0.751658\pi\) | ||||
−0.710780 | + | 0.703414i | \(0.751658\pi\) | |||||||
\(44\) | 10540.0 | 0.820746 | ||||||||
\(45\) | −2754.00 | −0.202737 | ||||||||
\(46\) | −3192.00 | −0.222417 | ||||||||
\(47\) | 8928.00 | 0.589535 | 0.294767 | − | 0.955569i | \(-0.404758\pi\) | ||||
0.294767 | + | 0.955569i | \(0.404758\pi\) | |||||||
\(48\) | −8361.00 | −0.523788 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −1969.00 | −0.111383 | ||||||||
\(51\) | 7182.00 | 0.386652 | ||||||||
\(52\) | −14074.0 | −0.721787 | ||||||||
\(53\) | 150.000 | 0.00733502 | 0.00366751 | − | 0.999993i | \(-0.498833\pi\) | ||||
0.00366751 | + | 0.999993i | \(0.498833\pi\) | |||||||
\(54\) | −729.000 | −0.0340207 | ||||||||
\(55\) | 11560.0 | 0.515289 | ||||||||
\(56\) | 3087.00 | 0.131543 | ||||||||
\(57\) | −8028.00 | −0.327281 | ||||||||
\(58\) | −8242.00 | −0.321709 | ||||||||
\(59\) | −42396.0 | −1.58560 | −0.792802 | − | 0.609479i | \(-0.791379\pi\) | ||||
−0.792802 | + | 0.609479i | \(0.791379\pi\) | |||||||
\(60\) | −9486.00 | −0.340177 | ||||||||
\(61\) | 14758.0 | 0.507812 | 0.253906 | − | 0.967229i | \(-0.418285\pi\) | ||||
0.253906 | + | 0.967229i | \(0.418285\pi\) | |||||||
\(62\) | −2496.00 | −0.0824642 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | −26783.0 | −0.817352 | ||||||||
\(65\) | −15436.0 | −0.453160 | ||||||||
\(66\) | 3060.00 | 0.0864692 | ||||||||
\(67\) | −1676.00 | −0.0456128 | −0.0228064 | − | 0.999740i | \(-0.507260\pi\) | ||||
−0.0228064 | + | 0.999740i | \(0.507260\pi\) | |||||||
\(68\) | 24738.0 | 0.648772 | ||||||||
\(69\) | 28728.0 | 0.726411 | ||||||||
\(70\) | 1666.00 | 0.0406378 | ||||||||
\(71\) | 14568.0 | 0.342968 | 0.171484 | − | 0.985187i | \(-0.445144\pi\) | ||||
0.171484 | + | 0.985187i | \(0.445144\pi\) | |||||||
\(72\) | −5103.00 | −0.116010 | ||||||||
\(73\) | 78378.0 | 1.72142 | 0.860710 | − | 0.509095i | \(-0.170020\pi\) | ||||
0.860710 | + | 0.509095i | \(0.170020\pi\) | |||||||
\(74\) | 9798.00 | 0.207998 | ||||||||
\(75\) | 17721.0 | 0.363777 | ||||||||
\(76\) | −27652.0 | −0.549152 | ||||||||
\(77\) | 16660.0 | 0.320220 | ||||||||
\(78\) | −4086.00 | −0.0760435 | ||||||||
\(79\) | −2272.00 | −0.0409582 | −0.0204791 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204791 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(80\) | −31586.0 | −0.551785 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 19834.0 | 0.325743 | ||||||||
\(83\) | −37764.0 | −0.601704 | −0.300852 | − | 0.953671i | \(-0.597271\pi\) | ||||
−0.300852 | + | 0.953671i | \(0.597271\pi\) | |||||||
\(84\) | −13671.0 | −0.211399 | ||||||||
\(85\) | 27132.0 | 0.407319 | ||||||||
\(86\) | −17236.0 | −0.251299 | ||||||||
\(87\) | 74178.0 | 1.05070 | ||||||||
\(88\) | 21420.0 | 0.294858 | ||||||||
\(89\) | −117286. | −1.56954 | −0.784768 | − | 0.619790i | \(-0.787218\pi\) | ||||
−0.784768 | + | 0.619790i | \(0.787218\pi\) | |||||||
\(90\) | −2754.00 | −0.0358391 | ||||||||
\(91\) | −22246.0 | −0.281610 | ||||||||
\(92\) | 98952.0 | 1.21886 | ||||||||
\(93\) | 22464.0 | 0.269327 | ||||||||
\(94\) | 8928.00 | 0.104216 | ||||||||
\(95\) | −30328.0 | −0.344774 | ||||||||
\(96\) | −26505.0 | −0.293528 | ||||||||
\(97\) | 10002.0 | 0.107934 | 0.0539669 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539669 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(98\) | 2401.00 | 0.0252538 | ||||||||
\(99\) | −27540.0 | −0.282407 | ||||||||
\(100\) | 61039.0 | 0.610390 | ||||||||
\(101\) | −108770. | −1.06098 | −0.530488 | − | 0.847692i | \(-0.677991\pi\) | ||||
−0.530488 | + | 0.847692i | \(0.677991\pi\) | |||||||
\(102\) | 7182.00 | 0.0683510 | ||||||||
\(103\) | −199192. | −1.85003 | −0.925015 | − | 0.379930i | \(-0.875948\pi\) | ||||
−0.925015 | + | 0.379930i | \(0.875948\pi\) | |||||||
\(104\) | −28602.0 | −0.259306 | ||||||||
\(105\) | −14994.0 | −0.132722 | ||||||||
\(106\) | 150.000 | 0.00129666 | ||||||||
\(107\) | −79972.0 | −0.675272 | −0.337636 | − | 0.941277i | \(-0.609627\pi\) | ||||
−0.337636 | + | 0.941277i | \(0.609627\pi\) | |||||||
\(108\) | 22599.0 | 0.186436 | ||||||||
\(109\) | −46098.0 | −0.371634 | −0.185817 | − | 0.982584i | \(-0.559493\pi\) | ||||
−0.185817 | + | 0.982584i | \(0.559493\pi\) | |||||||
\(110\) | 11560.0 | 0.0910911 | ||||||||
\(111\) | −88182.0 | −0.679317 | ||||||||
\(112\) | −45521.0 | −0.342899 | ||||||||
\(113\) | 262706. | 1.93541 | 0.967707 | − | 0.252078i | \(-0.0811138\pi\) | ||||
0.967707 | + | 0.252078i | \(0.0811138\pi\) | |||||||
\(114\) | −8028.00 | −0.0578556 | ||||||||
\(115\) | 108528. | 0.765239 | ||||||||
\(116\) | 255502. | 1.76299 | ||||||||
\(117\) | 36774.0 | 0.248357 | ||||||||
\(118\) | −42396.0 | −0.280298 | ||||||||
\(119\) | 39102.0 | 0.253123 | ||||||||
\(120\) | −19278.0 | −0.122211 | ||||||||
\(121\) | −45451.0 | −0.282215 | ||||||||
\(122\) | 14758.0 | 0.0897693 | ||||||||
\(123\) | −178506. | −1.06387 | ||||||||
\(124\) | 77376.0 | 0.451910 | ||||||||
\(125\) | 173196. | 0.991432 | ||||||||
\(126\) | −3969.00 | −0.0222718 | ||||||||
\(127\) | 196608. | 1.08166 | 0.540831 | − | 0.841131i | \(-0.318110\pi\) | ||||
0.540831 | + | 0.841131i | \(0.318110\pi\) | |||||||
\(128\) | −121023. | −0.652894 | ||||||||
\(129\) | 155124. | 0.820738 | ||||||||
\(130\) | −15436.0 | −0.0801081 | ||||||||
\(131\) | −77140.0 | −0.392737 | −0.196368 | − | 0.980530i | \(-0.562915\pi\) | ||||
−0.196368 | + | 0.980530i | \(0.562915\pi\) | |||||||
\(132\) | −94860.0 | −0.473858 | ||||||||
\(133\) | −43708.0 | −0.214255 | ||||||||
\(134\) | −1676.00 | −0.00806329 | ||||||||
\(135\) | 24786.0 | 0.117050 | ||||||||
\(136\) | 50274.0 | 0.233075 | ||||||||
\(137\) | 208170. | 0.947582 | 0.473791 | − | 0.880637i | \(-0.342885\pi\) | ||||
0.473791 | + | 0.880637i | \(0.342885\pi\) | |||||||
\(138\) | 28728.0 | 0.128413 | ||||||||
\(139\) | −275580. | −1.20979 | −0.604896 | − | 0.796304i | \(-0.706785\pi\) | ||||
−0.604896 | + | 0.796304i | \(0.706785\pi\) | |||||||
\(140\) | −51646.0 | −0.222698 | ||||||||
\(141\) | −80352.0 | −0.340368 | ||||||||
\(142\) | 14568.0 | 0.0606288 | ||||||||
\(143\) | −154360. | −0.631240 | ||||||||
\(144\) | 75249.0 | 0.302409 | ||||||||
\(145\) | 280228. | 1.10686 | ||||||||
\(146\) | 78378.0 | 0.304307 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | −303738. | −1.13984 | ||||||||
\(149\) | −296106. | −1.09265 | −0.546326 | − | 0.837573i | \(-0.683974\pi\) | ||||
−0.546326 | + | 0.837573i | \(0.683974\pi\) | |||||||
\(150\) | 17721.0 | 0.0643073 | ||||||||
\(151\) | −426472. | −1.52212 | −0.761059 | − | 0.648683i | \(-0.775320\pi\) | ||||
−0.761059 | + | 0.648683i | \(0.775320\pi\) | |||||||
\(152\) | −56196.0 | −0.197286 | ||||||||
\(153\) | −64638.0 | −0.223233 | ||||||||
\(154\) | 16660.0 | 0.0566074 | ||||||||
\(155\) | 84864.0 | 0.283723 | ||||||||
\(156\) | 126666. | 0.416724 | ||||||||
\(157\) | 178486. | 0.577903 | 0.288952 | − | 0.957344i | \(-0.406693\pi\) | ||||
0.288952 | + | 0.957344i | \(0.406693\pi\) | |||||||
\(158\) | −2272.00 | −0.00724045 | ||||||||
\(159\) | −1350.00 | −0.00423488 | ||||||||
\(160\) | −100130. | −0.309218 | ||||||||
\(161\) | 156408. | 0.475548 | ||||||||
\(162\) | 6561.00 | 0.0196419 | ||||||||
\(163\) | 252772. | 0.745178 | 0.372589 | − | 0.927996i | \(-0.378470\pi\) | ||||
0.372589 | + | 0.927996i | \(0.378470\pi\) | |||||||
\(164\) | −614854. | −1.78510 | ||||||||
\(165\) | −104040. | −0.297502 | ||||||||
\(166\) | −37764.0 | −0.106367 | ||||||||
\(167\) | 508088. | 1.40977 | 0.704884 | − | 0.709322i | \(-0.250999\pi\) | ||||
0.704884 | + | 0.709322i | \(0.250999\pi\) | |||||||
\(168\) | −27783.0 | −0.0759462 | ||||||||
\(169\) | −165177. | −0.444870 | ||||||||
\(170\) | 27132.0 | 0.0720045 | ||||||||
\(171\) | 72252.0 | 0.188956 | ||||||||
\(172\) | 534316. | 1.37714 | ||||||||
\(173\) | −221834. | −0.563525 | −0.281762 | − | 0.959484i | \(-0.590919\pi\) | ||||
−0.281762 | + | 0.959484i | \(0.590919\pi\) | |||||||
\(174\) | 74178.0 | 0.185739 | ||||||||
\(175\) | 96481.0 | 0.238148 | ||||||||
\(176\) | −315860. | −0.768622 | ||||||||
\(177\) | 381564. | 0.915449 | ||||||||
\(178\) | −117286. | −0.277457 | ||||||||
\(179\) | −113564. | −0.264916 | −0.132458 | − | 0.991189i | \(-0.542287\pi\) | ||||
−0.132458 | + | 0.991189i | \(0.542287\pi\) | |||||||
\(180\) | 85374.0 | 0.196401 | ||||||||
\(181\) | 663118. | 1.50451 | 0.752254 | − | 0.658873i | \(-0.228967\pi\) | ||||
0.752254 | + | 0.658873i | \(0.228967\pi\) | |||||||
\(182\) | −22246.0 | −0.0497821 | ||||||||
\(183\) | −132822. | −0.293185 | ||||||||
\(184\) | 201096. | 0.437884 | ||||||||
\(185\) | −333132. | −0.715628 | ||||||||
\(186\) | 22464.0 | 0.0476107 | ||||||||
\(187\) | 271320. | 0.567385 | ||||||||
\(188\) | −276768. | −0.571112 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | −30328.0 | −0.0609480 | ||||||||
\(191\) | 505664. | 1.00295 | 0.501474 | − | 0.865173i | \(-0.332791\pi\) | ||||
0.501474 | + | 0.865173i | \(0.332791\pi\) | |||||||
\(192\) | 241047. | 0.471899 | ||||||||
\(193\) | −432382. | −0.835554 | −0.417777 | − | 0.908550i | \(-0.637191\pi\) | ||||
−0.417777 | + | 0.908550i | \(0.637191\pi\) | |||||||
\(194\) | 10002.0 | 0.0190802 | ||||||||
\(195\) | 138924. | 0.261632 | ||||||||
\(196\) | −74431.0 | −0.138393 | ||||||||
\(197\) | −131962. | −0.242261 | −0.121130 | − | 0.992637i | \(-0.538652\pi\) | ||||
−0.121130 | + | 0.992637i | \(0.538652\pi\) | |||||||
\(198\) | −27540.0 | −0.0499230 | ||||||||
\(199\) | 298536. | 0.534397 | 0.267199 | − | 0.963642i | \(-0.413902\pi\) | ||||
0.267199 | + | 0.963642i | \(0.413902\pi\) | |||||||
\(200\) | 124047. | 0.219286 | ||||||||
\(201\) | 15084.0 | 0.0263346 | ||||||||
\(202\) | −108770. | −0.187556 | ||||||||
\(203\) | 403858. | 0.687842 | ||||||||
\(204\) | −222642. | −0.374569 | ||||||||
\(205\) | −674356. | −1.12074 | ||||||||
\(206\) | −199192. | −0.327042 | ||||||||
\(207\) | −258552. | −0.419394 | ||||||||
\(208\) | 421766. | 0.675948 | ||||||||
\(209\) | −303280. | −0.480262 | ||||||||
\(210\) | −14994.0 | −0.0234622 | ||||||||
\(211\) | −1.17062e6 | −1.81013 | −0.905065 | − | 0.425273i | \(-0.860178\pi\) | ||||
−0.905065 | + | 0.425273i | \(0.860178\pi\) | |||||||
\(212\) | −4650.00 | −0.00710581 | ||||||||
\(213\) | −131112. | −0.198013 | ||||||||
\(214\) | −79972.0 | −0.119372 | ||||||||
\(215\) | 586024. | 0.864608 | ||||||||
\(216\) | 45927.0 | 0.0669782 | ||||||||
\(217\) | 122304. | 0.176316 | ||||||||
\(218\) | −46098.0 | −0.0656963 | ||||||||
\(219\) | −705402. | −0.993863 | ||||||||
\(220\) | −358360. | −0.499186 | ||||||||
\(221\) | −362292. | −0.498974 | ||||||||
\(222\) | −88182.0 | −0.120087 | ||||||||
\(223\) | 399376. | 0.537799 | 0.268899 | − | 0.963168i | \(-0.413340\pi\) | ||||
0.268899 | + | 0.963168i | \(0.413340\pi\) | |||||||
\(224\) | −144305. | −0.192159 | ||||||||
\(225\) | −159489. | −0.210027 | ||||||||
\(226\) | 262706. | 0.342136 | ||||||||
\(227\) | 707916. | 0.911837 | 0.455918 | − | 0.890022i | \(-0.349311\pi\) | ||||
0.455918 | + | 0.890022i | \(0.349311\pi\) | |||||||
\(228\) | 248868. | 0.317053 | ||||||||
\(229\) | −735778. | −0.927167 | −0.463584 | − | 0.886053i | \(-0.653437\pi\) | ||||
−0.463584 | + | 0.886053i | \(0.653437\pi\) | |||||||
\(230\) | 108528. | 0.135276 | ||||||||
\(231\) | −149940. | −0.184879 | ||||||||
\(232\) | 519246. | 0.633364 | ||||||||
\(233\) | −208758. | −0.251915 | −0.125957 | − | 0.992036i | \(-0.540200\pi\) | ||||
−0.125957 | + | 0.992036i | \(0.540200\pi\) | |||||||
\(234\) | 36774.0 | 0.0439037 | ||||||||
\(235\) | −303552. | −0.358561 | ||||||||
\(236\) | 1.31428e6 | 1.53605 | ||||||||
\(237\) | 20448.0 | 0.0236472 | ||||||||
\(238\) | 39102.0 | 0.0447462 | ||||||||
\(239\) | 713376. | 0.807837 | 0.403919 | − | 0.914795i | \(-0.367648\pi\) | ||||
0.403919 | + | 0.914795i | \(0.367648\pi\) | |||||||
\(240\) | 284274. | 0.318573 | ||||||||
\(241\) | −505246. | −0.560351 | −0.280176 | − | 0.959949i | \(-0.590393\pi\) | ||||
−0.280176 | + | 0.959949i | \(0.590393\pi\) | |||||||
\(242\) | −45451.0 | −0.0498890 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −457498. | −0.491943 | ||||||||
\(245\) | −81634.0 | −0.0868872 | ||||||||
\(246\) | −178506. | −0.188068 | ||||||||
\(247\) | 404968. | 0.422356 | ||||||||
\(248\) | 157248. | 0.162351 | ||||||||
\(249\) | 339876. | 0.347394 | ||||||||
\(250\) | 173196. | 0.175262 | ||||||||
\(251\) | 317108. | 0.317704 | 0.158852 | − | 0.987302i | \(-0.449221\pi\) | ||||
0.158852 | + | 0.987302i | \(0.449221\pi\) | |||||||
\(252\) | 123039. | 0.122051 | ||||||||
\(253\) | 1.08528e6 | 1.06596 | ||||||||
\(254\) | 196608. | 0.191213 | ||||||||
\(255\) | −244188. | −0.235166 | ||||||||
\(256\) | 736033. | 0.701936 | ||||||||
\(257\) | −1.44285e6 | −1.36266 | −0.681329 | − | 0.731977i | \(-0.738598\pi\) | ||||
−0.681329 | + | 0.731977i | \(0.738598\pi\) | |||||||
\(258\) | 155124. | 0.145087 | ||||||||
\(259\) | −480102. | −0.444717 | ||||||||
\(260\) | 478516. | 0.438999 | ||||||||
\(261\) | −667602. | −0.606619 | ||||||||
\(262\) | −77140.0 | −0.0694267 | ||||||||
\(263\) | 271496. | 0.242033 | 0.121016 | − | 0.992651i | \(-0.461385\pi\) | ||||
0.121016 | + | 0.992651i | \(0.461385\pi\) | |||||||
\(264\) | −192780. | −0.170236 | ||||||||
\(265\) | −5100.00 | −0.00446124 | ||||||||
\(266\) | −43708.0 | −0.0378754 | ||||||||
\(267\) | 1.05557e6 | 0.906172 | ||||||||
\(268\) | 51956.0 | 0.0441874 | ||||||||
\(269\) | 850614. | 0.716724 | 0.358362 | − | 0.933583i | \(-0.383335\pi\) | ||||
0.358362 | + | 0.933583i | \(0.383335\pi\) | |||||||
\(270\) | 24786.0 | 0.0206917 | ||||||||
\(271\) | −540128. | −0.446759 | −0.223380 | − | 0.974732i | \(-0.571709\pi\) | ||||
−0.223380 | + | 0.974732i | \(0.571709\pi\) | |||||||
\(272\) | −741342. | −0.607570 | ||||||||
\(273\) | 200214. | 0.162588 | ||||||||
\(274\) | 208170. | 0.167510 | ||||||||
\(275\) | 669460. | 0.533818 | ||||||||
\(276\) | −890568. | −0.703711 | ||||||||
\(277\) | 513574. | 0.402164 | 0.201082 | − | 0.979574i | \(-0.435554\pi\) | ||||
0.201082 | + | 0.979574i | \(0.435554\pi\) | |||||||
\(278\) | −275580. | −0.213863 | ||||||||
\(279\) | −202176. | −0.155496 | ||||||||
\(280\) | −104958. | −0.0800056 | ||||||||
\(281\) | −1.35642e6 | −1.02478 | −0.512388 | − | 0.858754i | \(-0.671239\pi\) | ||||
−0.512388 | + | 0.858754i | \(0.671239\pi\) | |||||||
\(282\) | −80352.0 | −0.0601692 | ||||||||
\(283\) | 286756. | 0.212837 | 0.106418 | − | 0.994321i | \(-0.466062\pi\) | ||||
0.106418 | + | 0.994321i | \(0.466062\pi\) | |||||||
\(284\) | −451608. | −0.332251 | ||||||||
\(285\) | 272952. | 0.199055 | ||||||||
\(286\) | −154360. | −0.111589 | ||||||||
\(287\) | −971866. | −0.696469 | ||||||||
\(288\) | 238545. | 0.169469 | ||||||||
\(289\) | −783053. | −0.551501 | ||||||||
\(290\) | 280228. | 0.195667 | ||||||||
\(291\) | −90018.0 | −0.0623156 | ||||||||
\(292\) | −2.42972e6 | −1.66763 | ||||||||
\(293\) | −1.70727e6 | −1.16180 | −0.580901 | − | 0.813974i | \(-0.697300\pi\) | ||||
−0.580901 | + | 0.813974i | \(0.697300\pi\) | |||||||
\(294\) | −21609.0 | −0.0145803 | ||||||||
\(295\) | 1.44146e6 | 0.964381 | ||||||||
\(296\) | −617274. | −0.409495 | ||||||||
\(297\) | 247860. | 0.163048 | ||||||||
\(298\) | −296106. | −0.193155 | ||||||||
\(299\) | −1.44917e6 | −0.937434 | ||||||||
\(300\) | −549351. | −0.352409 | ||||||||
\(301\) | 844564. | 0.537299 | ||||||||
\(302\) | −426472. | −0.269075 | ||||||||
\(303\) | 978930. | 0.612555 | ||||||||
\(304\) | 828668. | 0.514276 | ||||||||
\(305\) | −501772. | −0.308857 | ||||||||
\(306\) | −64638.0 | −0.0394625 | ||||||||
\(307\) | −546788. | −0.331111 | −0.165555 | − | 0.986201i | \(-0.552942\pi\) | ||||
−0.165555 | + | 0.986201i | \(0.552942\pi\) | |||||||
\(308\) | −516460. | −0.310213 | ||||||||
\(309\) | 1.79273e6 | 1.06812 | ||||||||
\(310\) | 84864.0 | 0.0501556 | ||||||||
\(311\) | 3.23426e6 | 1.89616 | 0.948079 | − | 0.318035i | \(-0.103023\pi\) | ||||
0.948079 | + | 0.318035i | \(0.103023\pi\) | |||||||
\(312\) | 257418. | 0.149711 | ||||||||
\(313\) | 1.81313e6 | 1.04609 | 0.523044 | − | 0.852306i | \(-0.324796\pi\) | ||||
0.523044 | + | 0.852306i | \(0.324796\pi\) | |||||||
\(314\) | 178486. | 0.102160 | ||||||||
\(315\) | 134946. | 0.0766273 | ||||||||
\(316\) | 70432.0 | 0.0396782 | ||||||||
\(317\) | −1.27658e6 | −0.713509 | −0.356754 | − | 0.934198i | \(-0.616117\pi\) | ||||
−0.356754 | + | 0.934198i | \(0.616117\pi\) | |||||||
\(318\) | −1350.00 | −0.000748628 0 | ||||||||
\(319\) | 2.80228e6 | 1.54182 | ||||||||
\(320\) | 910622. | 0.497122 | ||||||||
\(321\) | 719748. | 0.389868 | ||||||||
\(322\) | 156408. | 0.0840658 | ||||||||
\(323\) | −711816. | −0.379631 | ||||||||
\(324\) | −203391. | −0.107639 | ||||||||
\(325\) | −893926. | −0.469454 | ||||||||
\(326\) | 252772. | 0.131730 | ||||||||
\(327\) | 414882. | 0.214563 | ||||||||
\(328\) | −1.24954e6 | −0.641307 | ||||||||
\(329\) | −437472. | −0.222823 | ||||||||
\(330\) | −104040. | −0.0525915 | ||||||||
\(331\) | −1.73621e6 | −0.871029 | −0.435515 | − | 0.900182i | \(-0.643434\pi\) | ||||
−0.435515 | + | 0.900182i | \(0.643434\pi\) | |||||||
\(332\) | 1.17068e6 | 0.582901 | ||||||||
\(333\) | 793638. | 0.392204 | ||||||||
\(334\) | 508088. | 0.249214 | ||||||||
\(335\) | 56984.0 | 0.0277422 | ||||||||
\(336\) | 409689. | 0.197973 | ||||||||
\(337\) | 2.07215e6 | 0.993907 | 0.496953 | − | 0.867777i | \(-0.334452\pi\) | ||||
0.496953 | + | 0.867777i | \(0.334452\pi\) | |||||||
\(338\) | −165177. | −0.0786426 | ||||||||
\(339\) | −2.36435e6 | −1.11741 | ||||||||
\(340\) | −841092. | −0.394590 | ||||||||
\(341\) | 848640. | 0.395219 | ||||||||
\(342\) | 72252.0 | 0.0334029 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 1.08587e6 | 0.494744 | ||||||||
\(345\) | −976752. | −0.441811 | ||||||||
\(346\) | −221834. | −0.0996180 | ||||||||
\(347\) | −1.65146e6 | −0.736282 | −0.368141 | − | 0.929770i | \(-0.620006\pi\) | ||||
−0.368141 | + | 0.929770i | \(0.620006\pi\) | |||||||
\(348\) | −2.29952e6 | −1.01786 | ||||||||
\(349\) | 1.26645e6 | 0.556578 | 0.278289 | − | 0.960497i | \(-0.410233\pi\) | ||||
0.278289 | + | 0.960497i | \(0.410233\pi\) | |||||||
\(350\) | 96481.0 | 0.0420990 | ||||||||
\(351\) | −330966. | −0.143389 | ||||||||
\(352\) | −1.00130e6 | −0.430732 | ||||||||
\(353\) | 573218. | 0.244840 | 0.122420 | − | 0.992478i | \(-0.460934\pi\) | ||||
0.122420 | + | 0.992478i | \(0.460934\pi\) | |||||||
\(354\) | 381564. | 0.161830 | ||||||||
\(355\) | −495312. | −0.208597 | ||||||||
\(356\) | 3.63587e6 | 1.52049 | ||||||||
\(357\) | −351918. | −0.146141 | ||||||||
\(358\) | −113564. | −0.0468310 | ||||||||
\(359\) | 4.46322e6 | 1.82773 | 0.913866 | − | 0.406016i | \(-0.133082\pi\) | ||||
0.913866 | + | 0.406016i | \(0.133082\pi\) | |||||||
\(360\) | 173502. | 0.0705583 | ||||||||
\(361\) | −1.68044e6 | −0.678662 | ||||||||
\(362\) | 663118. | 0.265962 | ||||||||
\(363\) | 409059. | 0.162937 | ||||||||
\(364\) | 689626. | 0.272810 | ||||||||
\(365\) | −2.66485e6 | −1.04699 | ||||||||
\(366\) | −132822. | −0.0518283 | ||||||||
\(367\) | −4.50797e6 | −1.74709 | −0.873546 | − | 0.486742i | \(-0.838185\pi\) | ||||
−0.873546 | + | 0.486742i | \(0.838185\pi\) | |||||||
\(368\) | −2.96537e6 | −1.14146 | ||||||||
\(369\) | 1.60655e6 | 0.614228 | ||||||||
\(370\) | −333132. | −0.126506 | ||||||||
\(371\) | −7350.00 | −0.00277238 | ||||||||
\(372\) | −696384. | −0.260910 | ||||||||
\(373\) | 1.66535e6 | 0.619774 | 0.309887 | − | 0.950773i | \(-0.399709\pi\) | ||||
0.309887 | + | 0.950773i | \(0.399709\pi\) | |||||||
\(374\) | 271320. | 0.100300 | ||||||||
\(375\) | −1.55876e6 | −0.572403 | ||||||||
\(376\) | −562464. | −0.205175 | ||||||||
\(377\) | −3.74187e6 | −1.35592 | ||||||||
\(378\) | 35721.0 | 0.0128586 | ||||||||
\(379\) | −2.53232e6 | −0.905568 | −0.452784 | − | 0.891620i | \(-0.649569\pi\) | ||||
−0.452784 | + | 0.891620i | \(0.649569\pi\) | |||||||
\(380\) | 940168. | 0.334000 | ||||||||
\(381\) | −1.76947e6 | −0.624498 | ||||||||
\(382\) | 505664. | 0.177298 | ||||||||
\(383\) | 796368. | 0.277407 | 0.138703 | − | 0.990334i | \(-0.455707\pi\) | ||||
0.138703 | + | 0.990334i | \(0.455707\pi\) | |||||||
\(384\) | 1.08921e6 | 0.376949 | ||||||||
\(385\) | −566440. | −0.194761 | ||||||||
\(386\) | −432382. | −0.147706 | ||||||||
\(387\) | −1.39612e6 | −0.473853 | ||||||||
\(388\) | −310062. | −0.104561 | ||||||||
\(389\) | 1.94799e6 | 0.652699 | 0.326349 | − | 0.945249i | \(-0.394181\pi\) | ||||
0.326349 | + | 0.945249i | \(0.394181\pi\) | |||||||
\(390\) | 138924. | 0.0462504 | ||||||||
\(391\) | 2.54722e6 | 0.842605 | ||||||||
\(392\) | −151263. | −0.0497184 | ||||||||
\(393\) | 694260. | 0.226747 | ||||||||
\(394\) | −131962. | −0.0428261 | ||||||||
\(395\) | 77248.0 | 0.0249112 | ||||||||
\(396\) | 853740. | 0.273582 | ||||||||
\(397\) | 1.08116e6 | 0.344281 | 0.172140 | − | 0.985072i | \(-0.444932\pi\) | ||||
0.172140 | + | 0.985072i | \(0.444932\pi\) | |||||||
\(398\) | 298536. | 0.0944689 | ||||||||
\(399\) | 393372. | 0.123700 | ||||||||
\(400\) | −1.82920e6 | −0.571625 | ||||||||
\(401\) | 2.76770e6 | 0.859524 | 0.429762 | − | 0.902942i | \(-0.358598\pi\) | ||||
0.429762 | + | 0.902942i | \(0.358598\pi\) | |||||||
\(402\) | 15084.0 | 0.00465534 | ||||||||
\(403\) | −1.13318e6 | −0.347566 | ||||||||
\(404\) | 3.37187e6 | 1.02782 | ||||||||
\(405\) | −223074. | −0.0675789 | ||||||||
\(406\) | 403858. | 0.121594 | ||||||||
\(407\) | −3.33132e6 | −0.996851 | ||||||||
\(408\) | −452466. | −0.134566 | ||||||||
\(409\) | 2.36350e6 | 0.698630 | 0.349315 | − | 0.937005i | \(-0.386414\pi\) | ||||
0.349315 | + | 0.937005i | \(0.386414\pi\) | |||||||
\(410\) | −674356. | −0.198121 | ||||||||
\(411\) | −1.87353e6 | −0.547087 | ||||||||
\(412\) | 6.17495e6 | 1.79222 | ||||||||
\(413\) | 2.07740e6 | 0.599302 | ||||||||
\(414\) | −258552. | −0.0741391 | ||||||||
\(415\) | 1.28398e6 | 0.365963 | ||||||||
\(416\) | 1.33703e6 | 0.378798 | ||||||||
\(417\) | 2.48022e6 | 0.698474 | ||||||||
\(418\) | −303280. | −0.0848991 | ||||||||
\(419\) | −2.98669e6 | −0.831104 | −0.415552 | − | 0.909569i | \(-0.636412\pi\) | ||||
−0.415552 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(420\) | 464814. | 0.128575 | ||||||||
\(421\) | −3.46331e6 | −0.952326 | −0.476163 | − | 0.879357i | \(-0.657973\pi\) | ||||
−0.476163 | + | 0.879357i | \(0.657973\pi\) | |||||||
\(422\) | −1.17062e6 | −0.319989 | ||||||||
\(423\) | 723168. | 0.196512 | ||||||||
\(424\) | −9450.00 | −0.00255280 | ||||||||
\(425\) | 1.57126e6 | 0.421965 | ||||||||
\(426\) | −131112. | −0.0350041 | ||||||||
\(427\) | −723142. | −0.191935 | ||||||||
\(428\) | 2.47913e6 | 0.654169 | ||||||||
\(429\) | 1.38924e6 | 0.364447 | ||||||||
\(430\) | 586024. | 0.152843 | ||||||||
\(431\) | 2.33693e6 | 0.605971 | 0.302986 | − | 0.952995i | \(-0.402017\pi\) | ||||
0.302986 | + | 0.952995i | \(0.402017\pi\) | |||||||
\(432\) | −677241. | −0.174596 | ||||||||
\(433\) | −3.50838e6 | −0.899264 | −0.449632 | − | 0.893214i | \(-0.648445\pi\) | ||||
−0.449632 | + | 0.893214i | \(0.648445\pi\) | |||||||
\(434\) | 122304. | 0.0311685 | ||||||||
\(435\) | −2.52205e6 | −0.639044 | ||||||||
\(436\) | 1.42904e6 | 0.360021 | ||||||||
\(437\) | −2.84726e6 | −0.713221 | ||||||||
\(438\) | −705402. | −0.175692 | ||||||||
\(439\) | 3.54833e6 | 0.878744 | 0.439372 | − | 0.898305i | \(-0.355201\pi\) | ||||
0.439372 | + | 0.898305i | \(0.355201\pi\) | |||||||
\(440\) | −728280. | −0.179336 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | −362292. | −0.0882070 | ||||||||
\(443\) | 1.76833e6 | 0.428109 | 0.214055 | − | 0.976822i | \(-0.431333\pi\) | ||||
0.214055 | + | 0.976822i | \(0.431333\pi\) | |||||||
\(444\) | 2.73364e6 | 0.658088 | ||||||||
\(445\) | 3.98772e6 | 0.954608 | ||||||||
\(446\) | 399376. | 0.0950703 | ||||||||
\(447\) | 2.66495e6 | 0.630842 | ||||||||
\(448\) | 1.31237e6 | 0.308930 | ||||||||
\(449\) | −5.52579e6 | −1.29354 | −0.646768 | − | 0.762687i | \(-0.723880\pi\) | ||||
−0.646768 | + | 0.762687i | \(0.723880\pi\) | |||||||
\(450\) | −159489. | −0.0371278 | ||||||||
\(451\) | −6.74356e6 | −1.56116 | ||||||||
\(452\) | −8.14389e6 | −1.87493 | ||||||||
\(453\) | 3.83825e6 | 0.878795 | ||||||||
\(454\) | 707916. | 0.161191 | ||||||||
\(455\) | 756364. | 0.171278 | ||||||||
\(456\) | 505764. | 0.113903 | ||||||||
\(457\) | −2.96226e6 | −0.663488 | −0.331744 | − | 0.943369i | \(-0.607637\pi\) | ||||
−0.331744 | + | 0.943369i | \(0.607637\pi\) | |||||||
\(458\) | −735778. | −0.163902 | ||||||||
\(459\) | 581742. | 0.128884 | ||||||||
\(460\) | −3.36437e6 | −0.741325 | ||||||||
\(461\) | 2.11884e6 | 0.464350 | 0.232175 | − | 0.972674i | \(-0.425416\pi\) | ||||
0.232175 | + | 0.972674i | \(0.425416\pi\) | |||||||
\(462\) | −149940. | −0.0326823 | ||||||||
\(463\) | 3.19226e6 | 0.692062 | 0.346031 | − | 0.938223i | \(-0.387529\pi\) | ||||
0.346031 | + | 0.938223i | \(0.387529\pi\) | |||||||
\(464\) | −7.65682e6 | −1.65102 | ||||||||
\(465\) | −763776. | −0.163807 | ||||||||
\(466\) | −208758. | −0.0445326 | ||||||||
\(467\) | −7.42621e6 | −1.57571 | −0.787853 | − | 0.615863i | \(-0.788807\pi\) | ||||
−0.787853 | + | 0.615863i | \(0.788807\pi\) | |||||||
\(468\) | −1.13999e6 | −0.240596 | ||||||||
\(469\) | 82124.0 | 0.0172400 | ||||||||
\(470\) | −303552. | −0.0633853 | ||||||||
\(471\) | −1.60637e6 | −0.333653 | ||||||||
\(472\) | 2.67095e6 | 0.551837 | ||||||||
\(473\) | 5.86024e6 | 1.20438 | ||||||||
\(474\) | 20448.0 | 0.00418028 | ||||||||
\(475\) | −1.75635e6 | −0.357171 | ||||||||
\(476\) | −1.21216e6 | −0.245213 | ||||||||
\(477\) | 12150.0 | 0.00244501 | ||||||||
\(478\) | 713376. | 0.142807 | ||||||||
\(479\) | −3.39685e6 | −0.676453 | −0.338226 | − | 0.941065i | \(-0.609827\pi\) | ||||
−0.338226 | + | 0.941065i | \(0.609827\pi\) | |||||||
\(480\) | 901170. | 0.178527 | ||||||||
\(481\) | 4.44829e6 | 0.876659 | ||||||||
\(482\) | −505246. | −0.0990570 | ||||||||
\(483\) | −1.40767e6 | −0.274558 | ||||||||
\(484\) | 1.40898e6 | 0.273396 | ||||||||
\(485\) | −340068. | −0.0656465 | ||||||||
\(486\) | −59049.0 | −0.0113402 | ||||||||
\(487\) | −3.71382e6 | −0.709574 | −0.354787 | − | 0.934947i | \(-0.615447\pi\) | ||||
−0.354787 | + | 0.934947i | \(0.615447\pi\) | |||||||
\(488\) | −929754. | −0.176733 | ||||||||
\(489\) | −2.27495e6 | −0.430229 | ||||||||
\(490\) | −81634.0 | −0.0153596 | ||||||||
\(491\) | 5.57494e6 | 1.04361 | 0.521803 | − | 0.853066i | \(-0.325260\pi\) | ||||
0.521803 | + | 0.853066i | \(0.325260\pi\) | |||||||
\(492\) | 5.53369e6 | 1.03063 | ||||||||
\(493\) | 6.57712e6 | 1.21876 | ||||||||
\(494\) | 404968. | 0.0746626 | ||||||||
\(495\) | 936360. | 0.171763 | ||||||||
\(496\) | −2.31878e6 | −0.423210 | ||||||||
\(497\) | −713832. | −0.129630 | ||||||||
\(498\) | 339876. | 0.0614111 | ||||||||
\(499\) | 3.92698e6 | 0.706004 | 0.353002 | − | 0.935623i | \(-0.385161\pi\) | ||||
0.353002 | + | 0.935623i | \(0.385161\pi\) | |||||||
\(500\) | −5.36908e6 | −0.960450 | ||||||||
\(501\) | −4.57279e6 | −0.813930 | ||||||||
\(502\) | 317108. | 0.0561627 | ||||||||
\(503\) | 6.42079e6 | 1.13154 | 0.565768 | − | 0.824564i | \(-0.308580\pi\) | ||||
0.565768 | + | 0.824564i | \(0.308580\pi\) | |||||||
\(504\) | 250047. | 0.0438475 | ||||||||
\(505\) | 3.69818e6 | 0.645297 | ||||||||
\(506\) | 1.08528e6 | 0.188437 | ||||||||
\(507\) | 1.48659e6 | 0.256846 | ||||||||
\(508\) | −6.09485e6 | −1.04786 | ||||||||
\(509\) | 146278. | 0.0250256 | 0.0125128 | − | 0.999922i | \(-0.496017\pi\) | ||||
0.0125128 | + | 0.999922i | \(0.496017\pi\) | |||||||
\(510\) | −244188. | −0.0415718 | ||||||||
\(511\) | −3.84052e6 | −0.650636 | ||||||||
\(512\) | 4.60877e6 | 0.776980 | ||||||||
\(513\) | −650268. | −0.109094 | ||||||||
\(514\) | −1.44285e6 | −0.240886 | ||||||||
\(515\) | 6.77253e6 | 1.12521 | ||||||||
\(516\) | −4.80884e6 | −0.795090 | ||||||||
\(517\) | −3.03552e6 | −0.499467 | ||||||||
\(518\) | −480102. | −0.0786157 | ||||||||
\(519\) | 1.99651e6 | 0.325351 | ||||||||
\(520\) | 972468. | 0.157713 | ||||||||
\(521\) | 7.70937e6 | 1.24430 | 0.622149 | − | 0.782899i | \(-0.286260\pi\) | ||||
0.622149 | + | 0.782899i | \(0.286260\pi\) | |||||||
\(522\) | −667602. | −0.107236 | ||||||||
\(523\) | −569420. | −0.0910287 | −0.0455144 | − | 0.998964i | \(-0.514493\pi\) | ||||
−0.0455144 | + | 0.998964i | \(0.514493\pi\) | |||||||
\(524\) | 2.39134e6 | 0.380464 | ||||||||
\(525\) | −868329. | −0.137495 | ||||||||
\(526\) | 271496. | 0.0427857 | ||||||||
\(527\) | 1.99181e6 | 0.312407 | ||||||||
\(528\) | 2.84274e6 | 0.443764 | ||||||||
\(529\) | 3.75252e6 | 0.583021 | ||||||||
\(530\) | −5100.00 | −0.000788643 0 | ||||||||
\(531\) | −3.43408e6 | −0.528535 | ||||||||
\(532\) | 1.35495e6 | 0.207560 | ||||||||
\(533\) | 9.00464e6 | 1.37293 | ||||||||
\(534\) | 1.05557e6 | 0.160190 | ||||||||
\(535\) | 2.71905e6 | 0.410707 | ||||||||
\(536\) | 105588. | 0.0158746 | ||||||||
\(537\) | 1.02208e6 | 0.152949 | ||||||||
\(538\) | 850614. | 0.126700 | ||||||||
\(539\) | −816340. | −0.121032 | ||||||||
\(540\) | −768366. | −0.113392 | ||||||||
\(541\) | −9.44802e6 | −1.38787 | −0.693933 | − | 0.720040i | \(-0.744124\pi\) | ||||
−0.693933 | + | 0.720040i | \(0.744124\pi\) | |||||||
\(542\) | −540128. | −0.0789766 | ||||||||
\(543\) | −5.96806e6 | −0.868628 | ||||||||
\(544\) | −2.35011e6 | −0.340479 | ||||||||
\(545\) | 1.56733e6 | 0.226032 | ||||||||
\(546\) | 200214. | 0.0287417 | ||||||||
\(547\) | −1.35321e6 | −0.193374 | −0.0966869 | − | 0.995315i | \(-0.530825\pi\) | ||||
−0.0966869 | + | 0.995315i | \(0.530825\pi\) | |||||||
\(548\) | −6.45327e6 | −0.917970 | ||||||||
\(549\) | 1.19540e6 | 0.169271 | ||||||||
\(550\) | 669460. | 0.0943665 | ||||||||
\(551\) | −7.35186e6 | −1.03162 | ||||||||
\(552\) | −1.80986e6 | −0.252812 | ||||||||
\(553\) | 111328. | 0.0154807 | ||||||||
\(554\) | 513574. | 0.0710933 | ||||||||
\(555\) | 2.99819e6 | 0.413168 | ||||||||
\(556\) | 8.54298e6 | 1.17199 | ||||||||
\(557\) | 8.19390e6 | 1.11906 | 0.559529 | − | 0.828811i | \(-0.310982\pi\) | ||||
0.559529 | + | 0.828811i | \(0.310982\pi\) | |||||||
\(558\) | −202176. | −0.0274881 | ||||||||
\(559\) | −7.82514e6 | −1.05916 | ||||||||
\(560\) | 1.54771e6 | 0.208555 | ||||||||
\(561\) | −2.44188e6 | −0.327580 | ||||||||
\(562\) | −1.35642e6 | −0.181157 | ||||||||
\(563\) | −1.05796e7 | −1.40669 | −0.703347 | − | 0.710847i | \(-0.748312\pi\) | ||||
−0.703347 | + | 0.710847i | \(0.748312\pi\) | |||||||
\(564\) | 2.49091e6 | 0.329732 | ||||||||
\(565\) | −8.93200e6 | −1.17714 | ||||||||
\(566\) | 286756. | 0.0376246 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | −917784. | −0.119363 | ||||||||
\(569\) | −1.20205e7 | −1.55648 | −0.778238 | − | 0.627969i | \(-0.783886\pi\) | ||||
−0.778238 | + | 0.627969i | \(0.783886\pi\) | |||||||
\(570\) | 272952. | 0.0351884 | ||||||||
\(571\) | −2.48948e6 | −0.319534 | −0.159767 | − | 0.987155i | \(-0.551074\pi\) | ||||
−0.159767 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(572\) | 4.78516e6 | 0.611514 | ||||||||
\(573\) | −4.55098e6 | −0.579053 | ||||||||
\(574\) | −971866. | −0.123119 | ||||||||
\(575\) | 6.28505e6 | 0.792755 | ||||||||
\(576\) | −2.16942e6 | −0.272451 | ||||||||
\(577\) | 8.21322e6 | 1.02701 | 0.513504 | − | 0.858087i | \(-0.328347\pi\) | ||||
0.513504 | + | 0.858087i | \(0.328347\pi\) | |||||||
\(578\) | −783053. | −0.0974926 | ||||||||
\(579\) | 3.89144e6 | 0.482407 | ||||||||
\(580\) | −8.68707e6 | −1.07227 | ||||||||
\(581\) | 1.85044e6 | 0.227423 | ||||||||
\(582\) | −90018.0 | −0.0110159 | ||||||||
\(583\) | −51000.0 | −0.00621439 | ||||||||
\(584\) | −4.93781e6 | −0.599105 | ||||||||
\(585\) | −1.25032e6 | −0.151053 | ||||||||
\(586\) | −1.70727e6 | −0.205380 | ||||||||
\(587\) | −1.21827e6 | −0.145931 | −0.0729655 | − | 0.997334i | \(-0.523246\pi\) | ||||
−0.0729655 | + | 0.997334i | \(0.523246\pi\) | |||||||
\(588\) | 669879. | 0.0799012 | ||||||||
\(589\) | −2.22643e6 | −0.264436 | ||||||||
\(590\) | 1.44146e6 | 0.170480 | ||||||||
\(591\) | 1.18766e6 | 0.139869 | ||||||||
\(592\) | 9.10234e6 | 1.06745 | ||||||||
\(593\) | −8.42379e6 | −0.983718 | −0.491859 | − | 0.870675i | \(-0.663683\pi\) | ||||
−0.491859 | + | 0.870675i | \(0.663683\pi\) | |||||||
\(594\) | 247860. | 0.0288231 | ||||||||
\(595\) | −1.32947e6 | −0.153952 | ||||||||
\(596\) | 9.17929e6 | 1.05851 | ||||||||
\(597\) | −2.68682e6 | −0.308534 | ||||||||
\(598\) | −1.44917e6 | −0.165717 | ||||||||
\(599\) | 8.21254e6 | 0.935212 | 0.467606 | − | 0.883937i | \(-0.345117\pi\) | ||||
0.467606 | + | 0.883937i | \(0.345117\pi\) | |||||||
\(600\) | −1.11642e6 | −0.126605 | ||||||||
\(601\) | 3.25478e6 | 0.367566 | 0.183783 | − | 0.982967i | \(-0.441166\pi\) | ||||
0.183783 | + | 0.982967i | \(0.441166\pi\) | |||||||
\(602\) | 844564. | 0.0949820 | ||||||||
\(603\) | −135756. | −0.0152043 | ||||||||
\(604\) | 1.32206e7 | 1.47455 | ||||||||
\(605\) | 1.54533e6 | 0.171646 | ||||||||
\(606\) | 978930. | 0.108285 | ||||||||
\(607\) | 7.82101e6 | 0.861571 | 0.430785 | − | 0.902454i | \(-0.358237\pi\) | ||||
0.430785 | + | 0.902454i | \(0.358237\pi\) | |||||||
\(608\) | 2.62694e6 | 0.288198 | ||||||||
\(609\) | −3.63472e6 | −0.397126 | ||||||||
\(610\) | −501772. | −0.0545986 | ||||||||
\(611\) | 4.05331e6 | 0.439245 | ||||||||
\(612\) | 2.00378e6 | 0.216257 | ||||||||
\(613\) | −9.51670e6 | −1.02290 | −0.511452 | − | 0.859312i | \(-0.670892\pi\) | ||||
−0.511452 | + | 0.859312i | \(0.670892\pi\) | |||||||
\(614\) | −546788. | −0.0585326 | ||||||||
\(615\) | 6.06920e6 | 0.647059 | ||||||||
\(616\) | −1.04958e6 | −0.111446 | ||||||||
\(617\) | −7.04895e6 | −0.745438 | −0.372719 | − | 0.927944i | \(-0.621574\pi\) | ||||
−0.372719 | + | 0.927944i | \(0.621574\pi\) | |||||||
\(618\) | 1.79273e6 | 0.188818 | ||||||||
\(619\) | −6.32174e6 | −0.663147 | −0.331574 | − | 0.943429i | \(-0.607580\pi\) | ||||
−0.331574 | + | 0.943429i | \(0.607580\pi\) | |||||||
\(620\) | −2.63078e6 | −0.274856 | ||||||||
\(621\) | 2.32697e6 | 0.242137 | ||||||||
\(622\) | 3.23426e6 | 0.335197 | ||||||||
\(623\) | 5.74701e6 | 0.593229 | ||||||||
\(624\) | −3.79589e6 | −0.390259 | ||||||||
\(625\) | 264461. | 0.0270808 | ||||||||
\(626\) | 1.81313e6 | 0.184924 | ||||||||
\(627\) | 2.72952e6 | 0.277279 | ||||||||
\(628\) | −5.53307e6 | −0.559844 | ||||||||
\(629\) | −7.81880e6 | −0.787977 | ||||||||
\(630\) | 134946. | 0.0135459 | ||||||||
\(631\) | 8.61236e6 | 0.861090 | 0.430545 | − | 0.902569i | \(-0.358321\pi\) | ||||
0.430545 | + | 0.902569i | \(0.358321\pi\) | |||||||
\(632\) | 143136. | 0.0142546 | ||||||||
\(633\) | 1.05356e7 | 1.04508 | ||||||||
\(634\) | −1.27658e6 | −0.126132 | ||||||||
\(635\) | −6.68467e6 | −0.657879 | ||||||||
\(636\) | 41850.0 | 0.00410254 | ||||||||
\(637\) | 1.09005e6 | 0.106439 | ||||||||
\(638\) | 2.80228e6 | 0.272559 | ||||||||
\(639\) | 1.18001e6 | 0.114323 | ||||||||
\(640\) | 4.11478e6 | 0.397097 | ||||||||
\(641\) | −5.22829e6 | −0.502590 | −0.251295 | − | 0.967910i | \(-0.580857\pi\) | ||||
−0.251295 | + | 0.967910i | \(0.580857\pi\) | |||||||
\(642\) | 719748. | 0.0689196 | ||||||||
\(643\) | 1.61373e7 | 1.53923 | 0.769615 | − | 0.638508i | \(-0.220448\pi\) | ||||
0.769615 | + | 0.638508i | \(0.220448\pi\) | |||||||
\(644\) | −4.84865e6 | −0.460687 | ||||||||
\(645\) | −5.27422e6 | −0.499182 | ||||||||
\(646\) | −711816. | −0.0671099 | ||||||||
\(647\) | −1.58749e7 | −1.49090 | −0.745451 | − | 0.666560i | \(-0.767766\pi\) | ||||
−0.745451 | + | 0.666560i | \(0.767766\pi\) | |||||||
\(648\) | −413343. | −0.0386699 | ||||||||
\(649\) | 1.44146e7 | 1.34336 | ||||||||
\(650\) | −893926. | −0.0829886 | ||||||||
\(651\) | −1.10074e6 | −0.101796 | ||||||||
\(652\) | −7.83593e6 | −0.721891 | ||||||||
\(653\) | −5.94112e6 | −0.545237 | −0.272619 | − | 0.962122i | \(-0.587890\pi\) | ||||
−0.272619 | + | 0.962122i | \(0.587890\pi\) | |||||||
\(654\) | 414882. | 0.0379298 | ||||||||
\(655\) | 2.62276e6 | 0.238867 | ||||||||
\(656\) | 1.84258e7 | 1.67173 | ||||||||
\(657\) | 6.34862e6 | 0.573807 | ||||||||
\(658\) | −437472. | −0.0393900 | ||||||||
\(659\) | −7.64430e6 | −0.685684 | −0.342842 | − | 0.939393i | \(-0.611390\pi\) | ||||
−0.342842 | + | 0.939393i | \(0.611390\pi\) | |||||||
\(660\) | 3.22524e6 | 0.288205 | ||||||||
\(661\) | −7.58688e6 | −0.675398 | −0.337699 | − | 0.941254i | \(-0.609649\pi\) | ||||
−0.337699 | + | 0.941254i | \(0.609649\pi\) | |||||||
\(662\) | −1.73621e6 | −0.153978 | ||||||||
\(663\) | 3.26063e6 | 0.288083 | ||||||||
\(664\) | 2.37913e6 | 0.209410 | ||||||||
\(665\) | 1.48607e6 | 0.130312 | ||||||||
\(666\) | 793638. | 0.0693325 | ||||||||
\(667\) | 2.63085e7 | 2.28971 | ||||||||
\(668\) | −1.57507e7 | −1.36571 | ||||||||
\(669\) | −3.59438e6 | −0.310498 | ||||||||
\(670\) | 56984.0 | 0.00490417 | ||||||||
\(671\) | −5.01772e6 | −0.430229 | ||||||||
\(672\) | 1.29874e6 | 0.110943 | ||||||||
\(673\) | −2.06681e7 | −1.75899 | −0.879494 | − | 0.475910i | \(-0.842119\pi\) | ||||
−0.879494 | + | 0.475910i | \(0.842119\pi\) | |||||||
\(674\) | 2.07215e6 | 0.175700 | ||||||||
\(675\) | 1.43540e6 | 0.121259 | ||||||||
\(676\) | 5.12049e6 | 0.430968 | ||||||||
\(677\) | 7.89541e6 | 0.662068 | 0.331034 | − | 0.943619i | \(-0.392602\pi\) | ||||
0.331034 | + | 0.943619i | \(0.392602\pi\) | |||||||
\(678\) | −2.36435e6 | −0.197532 | ||||||||
\(679\) | −490098. | −0.0407951 | ||||||||
\(680\) | −1.70932e6 | −0.141759 | ||||||||
\(681\) | −6.37124e6 | −0.526449 | ||||||||
\(682\) | 848640. | 0.0698655 | ||||||||
\(683\) | −1.96015e7 | −1.60782 | −0.803911 | − | 0.594750i | \(-0.797251\pi\) | ||||
−0.803911 | + | 0.594750i | \(0.797251\pi\) | |||||||
\(684\) | −2.23981e6 | −0.183051 | ||||||||
\(685\) | −7.07778e6 | −0.576329 | ||||||||
\(686\) | −117649. | −0.00954504 | ||||||||
\(687\) | 6.62200e6 | 0.535300 | ||||||||
\(688\) | −1.60122e7 | −1.28968 | ||||||||
\(689\) | 68100.0 | 0.00546511 | ||||||||
\(690\) | −976752. | −0.0781019 | ||||||||
\(691\) | −1.72710e7 | −1.37601 | −0.688005 | − | 0.725706i | \(-0.741513\pi\) | ||||
−0.688005 | + | 0.725706i | \(0.741513\pi\) | |||||||
\(692\) | 6.87685e6 | 0.545914 | ||||||||
\(693\) | 1.34946e6 | 0.106740 | ||||||||
\(694\) | −1.65146e6 | −0.130158 | ||||||||
\(695\) | 9.36972e6 | 0.735808 | ||||||||
\(696\) | −4.67321e6 | −0.365673 | ||||||||
\(697\) | −1.58275e7 | −1.23405 | ||||||||
\(698\) | 1.26645e6 | 0.0983900 | ||||||||
\(699\) | 1.87882e6 | 0.145443 | ||||||||
\(700\) | −2.99091e6 | −0.230706 | ||||||||
\(701\) | −5.36344e6 | −0.412238 | −0.206119 | − | 0.978527i | \(-0.566083\pi\) | ||||
−0.206119 | + | 0.978527i | \(0.566083\pi\) | |||||||
\(702\) | −330966. | −0.0253478 | ||||||||
\(703\) | 8.73982e6 | 0.666982 | ||||||||
\(704\) | 9.10622e6 | 0.692479 | ||||||||
\(705\) | 2.73197e6 | 0.207015 | ||||||||
\(706\) | 573218. | 0.0432821 | ||||||||
\(707\) | 5.32973e6 | 0.401011 | ||||||||
\(708\) | −1.18285e7 | −0.886841 | ||||||||
\(709\) | −1.73733e7 | −1.29798 | −0.648988 | − | 0.760798i | \(-0.724808\pi\) | ||||
−0.648988 | + | 0.760798i | \(0.724808\pi\) | |||||||
\(710\) | −495312. | −0.0368751 | ||||||||
\(711\) | −184032. | −0.0136527 | ||||||||
\(712\) | 7.38902e6 | 0.546244 | ||||||||
\(713\) | 7.96723e6 | 0.586926 | ||||||||
\(714\) | −351918. | −0.0258343 | ||||||||
\(715\) | 5.24824e6 | 0.383927 | ||||||||
\(716\) | 3.52048e6 | 0.256637 | ||||||||
\(717\) | −6.42038e6 | −0.466405 | ||||||||
\(718\) | 4.46322e6 | 0.323100 | ||||||||
\(719\) | 424608. | 0.0306313 | 0.0153157 | − | 0.999883i | \(-0.495125\pi\) | ||||
0.0153157 | + | 0.999883i | \(0.495125\pi\) | |||||||
\(720\) | −2.55847e6 | −0.183928 | ||||||||
\(721\) | 9.76041e6 | 0.699246 | ||||||||
\(722\) | −1.68044e6 | −0.119972 | ||||||||
\(723\) | 4.54721e6 | 0.323519 | ||||||||
\(724\) | −2.05567e7 | −1.45749 | ||||||||
\(725\) | 1.62285e7 | 1.14666 | ||||||||
\(726\) | 409059. | 0.0288034 | ||||||||
\(727\) | 2.18290e7 | 1.53179 | 0.765893 | − | 0.642968i | \(-0.222297\pi\) | ||||
0.765893 | + | 0.642968i | \(0.222297\pi\) | |||||||
\(728\) | 1.40150e6 | 0.0980086 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.66485e6 | −0.185083 | ||||||||
\(731\) | 1.37543e7 | 0.952020 | ||||||||
\(732\) | 4.11748e6 | 0.284023 | ||||||||
\(733\) | 2.17675e7 | 1.49640 | 0.748202 | − | 0.663470i | \(-0.230917\pi\) | ||||
0.748202 | + | 0.663470i | \(0.230917\pi\) | |||||||
\(734\) | −4.50797e6 | −0.308845 | ||||||||
\(735\) | 734706. | 0.0501644 | ||||||||
\(736\) | −9.40044e6 | −0.639667 | ||||||||
\(737\) | 569840. | 0.0386442 | ||||||||
\(738\) | 1.60655e6 | 0.108581 | ||||||||
\(739\) | 6.21786e6 | 0.418822 | 0.209411 | − | 0.977828i | \(-0.432845\pi\) | ||||
0.209411 | + | 0.977828i | \(0.432845\pi\) | |||||||
\(740\) | 1.03271e7 | 0.693264 | ||||||||
\(741\) | −3.64471e6 | −0.243847 | ||||||||
\(742\) | −7350.00 | −0.000490092 0 | ||||||||
\(743\) | 3.77647e6 | 0.250966 | 0.125483 | − | 0.992096i | \(-0.459952\pi\) | ||||
0.125483 | + | 0.992096i | \(0.459952\pi\) | |||||||
\(744\) | −1.41523e6 | −0.0937336 | ||||||||
\(745\) | 1.00676e7 | 0.664562 | ||||||||
\(746\) | 1.66535e6 | 0.109562 | ||||||||
\(747\) | −3.05888e6 | −0.200568 | ||||||||
\(748\) | −8.41092e6 | −0.549654 | ||||||||
\(749\) | 3.91863e6 | 0.255229 | ||||||||
\(750\) | −1.55876e6 | −0.101188 | ||||||||
\(751\) | −2.88795e6 | −0.186849 | −0.0934244 | − | 0.995626i | \(-0.529781\pi\) | ||||
−0.0934244 | + | 0.995626i | \(0.529781\pi\) | |||||||
\(752\) | 8.29411e6 | 0.534842 | ||||||||
\(753\) | −2.85397e6 | −0.183427 | ||||||||
\(754\) | −3.74187e6 | −0.239696 | ||||||||
\(755\) | 1.45000e7 | 0.925768 | ||||||||
\(756\) | −1.10735e6 | −0.0704662 | ||||||||
\(757\) | 1.25519e6 | 0.0796104 | 0.0398052 | − | 0.999207i | \(-0.487326\pi\) | ||||
0.0398052 | + | 0.999207i | \(0.487326\pi\) | |||||||
\(758\) | −2.53232e6 | −0.160083 | ||||||||
\(759\) | −9.76752e6 | −0.615432 | ||||||||
\(760\) | 1.91066e6 | 0.119991 | ||||||||
\(761\) | −1.42623e7 | −0.892746 | −0.446373 | − | 0.894847i | \(-0.647284\pi\) | ||||
−0.446373 | + | 0.894847i | \(0.647284\pi\) | |||||||
\(762\) | −1.76947e6 | −0.110397 | ||||||||
\(763\) | 2.25880e6 | 0.140465 | ||||||||
\(764\) | −1.56756e7 | −0.971606 | ||||||||
\(765\) | 2.19769e6 | 0.135773 | ||||||||
\(766\) | 796368. | 0.0490390 | ||||||||
\(767\) | −1.92478e7 | −1.18139 | ||||||||
\(768\) | −6.62430e6 | −0.405263 | ||||||||
\(769\) | −2.02261e7 | −1.23338 | −0.616689 | − | 0.787207i | \(-0.711526\pi\) | ||||
−0.616689 | + | 0.787207i | \(0.711526\pi\) | |||||||
\(770\) | −566440. | −0.0344292 | ||||||||
\(771\) | 1.29856e7 | 0.786732 | ||||||||
\(772\) | 1.34038e7 | 0.809443 | ||||||||
\(773\) | 2.62288e7 | 1.57881 | 0.789406 | − | 0.613872i | \(-0.210389\pi\) | ||||
0.789406 | + | 0.613872i | \(0.210389\pi\) | |||||||
\(774\) | −1.39612e6 | −0.0837663 | ||||||||
\(775\) | 4.91462e6 | 0.293925 | ||||||||
\(776\) | −630126. | −0.0375641 | ||||||||
\(777\) | 4.32092e6 | 0.256758 | ||||||||
\(778\) | 1.94799e6 | 0.115382 | ||||||||
\(779\) | 1.76919e7 | 1.04456 | ||||||||
\(780\) | −4.30664e6 | −0.253456 | ||||||||
\(781\) | −4.95312e6 | −0.290570 | ||||||||
\(782\) | 2.54722e6 | 0.148953 | ||||||||
\(783\) | 6.00842e6 | 0.350232 | ||||||||
\(784\) | 2.23053e6 | 0.129604 | ||||||||
\(785\) | −6.06852e6 | −0.351487 | ||||||||
\(786\) | 694260. | 0.0400835 | ||||||||
\(787\) | −9.92829e6 | −0.571397 | −0.285698 | − | 0.958320i | \(-0.592226\pi\) | ||||
−0.285698 | + | 0.958320i | \(0.592226\pi\) | |||||||
\(788\) | 4.09082e6 | 0.234690 | ||||||||
\(789\) | −2.44346e6 | −0.139738 | ||||||||
\(790\) | 77248.0 | 0.00440372 | ||||||||
\(791\) | −1.28726e7 | −0.731518 | ||||||||
\(792\) | 1.73502e6 | 0.0982860 | ||||||||
\(793\) | 6.70013e6 | 0.378356 | ||||||||
\(794\) | 1.08116e6 | 0.0608608 | ||||||||
\(795\) | 45900.0 | 0.00257570 | ||||||||
\(796\) | −9.25462e6 | −0.517697 | ||||||||
\(797\) | 1.09033e7 | 0.608014 | 0.304007 | − | 0.952670i | \(-0.401675\pi\) | ||||
0.304007 | + | 0.952670i | \(0.401675\pi\) | |||||||
\(798\) | 393372. | 0.0218674 | ||||||||
\(799\) | −7.12454e6 | −0.394812 | ||||||||
\(800\) | −5.79871e6 | −0.320336 | ||||||||
\(801\) | −9.50017e6 | −0.523179 | ||||||||
\(802\) | 2.76770e6 | 0.151944 | ||||||||
\(803\) | −2.66485e7 | −1.45843 | ||||||||
\(804\) | −467604. | −0.0255116 | ||||||||
\(805\) | −5.31787e6 | −0.289233 | ||||||||
\(806\) | −1.13318e6 | −0.0614416 | ||||||||
\(807\) | −7.65553e6 | −0.413801 | ||||||||
\(808\) | 6.85251e6 | 0.369251 | ||||||||
\(809\) | 6.06398e6 | 0.325751 | 0.162876 | − | 0.986647i | \(-0.447923\pi\) | ||||
0.162876 | + | 0.986647i | \(0.447923\pi\) | |||||||
\(810\) | −223074. | −0.0119464 | ||||||||
\(811\) | −8.59438e6 | −0.458841 | −0.229421 | − | 0.973327i | \(-0.573683\pi\) | ||||
−0.229421 | + | 0.973327i | \(0.573683\pi\) | |||||||
\(812\) | −1.25196e7 | −0.666347 | ||||||||
\(813\) | 4.86115e6 | 0.257937 | ||||||||
\(814\) | −3.33132e6 | −0.176220 | ||||||||
\(815\) | −8.59425e6 | −0.453225 | ||||||||
\(816\) | 6.67208e6 | 0.350781 | ||||||||
\(817\) | −1.53745e7 | −0.805835 | ||||||||
\(818\) | 2.36350e6 | 0.123501 | ||||||||
\(819\) | −1.80193e6 | −0.0938701 | ||||||||
\(820\) | 2.09050e7 | 1.08572 | ||||||||
\(821\) | −2.01396e6 | −0.104278 | −0.0521391 | − | 0.998640i | \(-0.516604\pi\) | ||||
−0.0521391 | + | 0.998640i | \(0.516604\pi\) | |||||||
\(822\) | −1.87353e6 | −0.0967122 | ||||||||
\(823\) | −2.64679e7 | −1.36213 | −0.681067 | − | 0.732221i | \(-0.738484\pi\) | ||||
−0.681067 | + | 0.732221i | \(0.738484\pi\) | |||||||
\(824\) | 1.25491e7 | 0.643864 | ||||||||
\(825\) | −6.02514e6 | −0.308200 | ||||||||
\(826\) | 2.07740e6 | 0.105943 | ||||||||
\(827\) | −3.90229e6 | −0.198407 | −0.0992033 | − | 0.995067i | \(-0.531629\pi\) | ||||
−0.0992033 | + | 0.995067i | \(0.531629\pi\) | |||||||
\(828\) | 8.01511e6 | 0.406288 | ||||||||
\(829\) | −1.95595e7 | −0.988487 | −0.494244 | − | 0.869323i | \(-0.664555\pi\) | ||||
−0.494244 | + | 0.869323i | \(0.664555\pi\) | |||||||
\(830\) | 1.28398e6 | 0.0646937 | ||||||||
\(831\) | −4.62217e6 | −0.232190 | ||||||||
\(832\) | −1.21595e7 | −0.608985 | ||||||||
\(833\) | −1.91600e6 | −0.0956715 | ||||||||
\(834\) | 2.48022e6 | 0.123474 | ||||||||
\(835\) | −1.72750e7 | −0.857436 | ||||||||
\(836\) | 9.40168e6 | 0.465254 | ||||||||
\(837\) | 1.81958e6 | 0.0897756 | ||||||||
\(838\) | −2.98669e6 | −0.146920 | ||||||||
\(839\) | −2.45448e7 | −1.20380 | −0.601901 | − | 0.798570i | \(-0.705590\pi\) | ||||
−0.601901 | + | 0.798570i | \(0.705590\pi\) | |||||||
\(840\) | 944622. | 0.0461913 | ||||||||
\(841\) | 4.74194e7 | 2.31188 | ||||||||
\(842\) | −3.46331e6 | −0.168349 | ||||||||
\(843\) | 1.22078e7 | 0.591655 | ||||||||
\(844\) | 3.62892e7 | 1.75356 | ||||||||
\(845\) | 5.61602e6 | 0.270574 | ||||||||
\(846\) | 723168. | 0.0347387 | ||||||||
\(847\) | 2.22710e6 | 0.106667 | ||||||||
\(848\) | 139350. | 0.00665453 | ||||||||
\(849\) | −2.58080e6 | −0.122881 | ||||||||
\(850\) | 1.57126e6 | 0.0745936 | ||||||||
\(851\) | −3.12752e7 | −1.48039 | ||||||||
\(852\) | 4.06447e6 | 0.191825 | ||||||||
\(853\) | 3.38305e7 | 1.59197 | 0.795987 | − | 0.605314i | \(-0.206952\pi\) | ||||
0.795987 | + | 0.605314i | \(0.206952\pi\) | |||||||
\(854\) | −723142. | −0.0339296 | ||||||||
\(855\) | −2.45657e6 | −0.114925 | ||||||||
\(856\) | 5.03824e6 | 0.235014 | ||||||||
\(857\) | 3.18009e7 | 1.47907 | 0.739534 | − | 0.673120i | \(-0.235046\pi\) | ||||
0.739534 | + | 0.673120i | \(0.235046\pi\) | |||||||
\(858\) | 1.38924e6 | 0.0644257 | ||||||||
\(859\) | 638420. | 0.0295205 | 0.0147602 | − | 0.999891i | \(-0.495301\pi\) | ||||
0.0147602 | + | 0.999891i | \(0.495301\pi\) | |||||||
\(860\) | −1.81667e7 | −0.837589 | ||||||||
\(861\) | 8.74679e6 | 0.402106 | ||||||||
\(862\) | 2.33693e6 | 0.107122 | ||||||||
\(863\) | −4.22256e6 | −0.192996 | −0.0964981 | − | 0.995333i | \(-0.530764\pi\) | ||||
−0.0964981 | + | 0.995333i | \(0.530764\pi\) | |||||||
\(864\) | −2.14690e6 | −0.0978427 | ||||||||
\(865\) | 7.54236e6 | 0.342742 | ||||||||
\(866\) | −3.50838e6 | −0.158969 | ||||||||
\(867\) | 7.04748e6 | 0.318409 | ||||||||
\(868\) | −3.79142e6 | −0.170806 | ||||||||
\(869\) | 772480. | 0.0347007 | ||||||||
\(870\) | −2.52205e6 | −0.112968 | ||||||||
\(871\) | −760904. | −0.0339848 | ||||||||
\(872\) | 2.90417e6 | 0.129340 | ||||||||
\(873\) | 810162. | 0.0359779 | ||||||||
\(874\) | −2.84726e6 | −0.126081 | ||||||||
\(875\) | −8.48660e6 | −0.374726 | ||||||||
\(876\) | 2.18675e7 | 0.962805 | ||||||||
\(877\) | −2.45043e7 | −1.07583 | −0.537915 | − | 0.842999i | \(-0.680788\pi\) | ||||
−0.537915 | + | 0.842999i | \(0.680788\pi\) | |||||||
\(878\) | 3.54833e6 | 0.155341 | ||||||||
\(879\) | 1.53654e7 | 0.670767 | ||||||||
\(880\) | 1.07392e7 | 0.467484 | ||||||||
\(881\) | −2.77630e7 | −1.20511 | −0.602555 | − | 0.798078i | \(-0.705850\pi\) | ||||
−0.602555 | + | 0.798078i | \(0.705850\pi\) | |||||||
\(882\) | 194481. | 0.00841794 | ||||||||
\(883\) | 3.30170e7 | 1.42507 | 0.712534 | − | 0.701638i | \(-0.247548\pi\) | ||||
0.712534 | + | 0.701638i | \(0.247548\pi\) | |||||||
\(884\) | 1.12311e7 | 0.483381 | ||||||||
\(885\) | −1.29732e7 | −0.556786 | ||||||||
\(886\) | 1.76833e6 | 0.0756797 | ||||||||
\(887\) | 4.34462e6 | 0.185414 | 0.0927070 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927070 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(888\) | 5.55547e6 | 0.236422 | ||||||||
\(889\) | −9.63379e6 | −0.408830 | ||||||||
\(890\) | 3.98772e6 | 0.168752 | ||||||||
\(891\) | −2.23074e6 | −0.0941358 | ||||||||
\(892\) | −1.23807e7 | −0.520993 | ||||||||
\(893\) | 7.96378e6 | 0.334188 | ||||||||
\(894\) | 2.66495e6 | 0.111518 | ||||||||
\(895\) | 3.86118e6 | 0.161125 | ||||||||
\(896\) | 5.93013e6 | 0.246771 | ||||||||
\(897\) | 1.30425e7 | 0.541228 | ||||||||
\(898\) | −5.52579e6 | −0.228667 | ||||||||
\(899\) | 2.05720e7 | 0.848942 | ||||||||
\(900\) | 4.94416e6 | 0.203463 | ||||||||
\(901\) | −119700. | −0.00491227 | ||||||||
\(902\) | −6.74356e6 | −0.275977 | ||||||||
\(903\) | −7.60108e6 | −0.310210 | ||||||||
\(904\) | −1.65505e7 | −0.673580 | ||||||||
\(905\) | −2.25460e7 | −0.915057 | ||||||||
\(906\) | 3.83825e6 | 0.155350 | ||||||||
\(907\) | 1.96499e7 | 0.793128 | 0.396564 | − | 0.918007i | \(-0.370203\pi\) | ||||
0.396564 | + | 0.918007i | \(0.370203\pi\) | |||||||
\(908\) | −2.19454e7 | −0.883342 | ||||||||
\(909\) | −8.81037e6 | −0.353659 | ||||||||
\(910\) | 756364. | 0.0302780 | ||||||||
\(911\) | −7.26518e6 | −0.290035 | −0.145018 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145018 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(912\) | −7.45801e6 | −0.296918 | ||||||||
\(913\) | 1.28398e7 | 0.509777 | ||||||||
\(914\) | −2.96226e6 | −0.117289 | ||||||||
\(915\) | 4.51595e6 | 0.178318 | ||||||||
\(916\) | 2.28091e7 | 0.898193 | ||||||||
\(917\) | 3.77986e6 | 0.148440 | ||||||||
\(918\) | 581742. | 0.0227837 | ||||||||
\(919\) | 9.82532e6 | 0.383758 | 0.191879 | − | 0.981419i | \(-0.438542\pi\) | ||||
0.191879 | + | 0.981419i | \(0.438542\pi\) | |||||||
\(920\) | −6.83726e6 | −0.266326 | ||||||||
\(921\) | 4.92109e6 | 0.191167 | ||||||||
\(922\) | 2.11884e6 | 0.0820863 | ||||||||
\(923\) | 6.61387e6 | 0.255536 | ||||||||
\(924\) | 4.64814e6 | 0.179102 | ||||||||
\(925\) | −1.92923e7 | −0.741359 | ||||||||
\(926\) | 3.19226e6 | 0.122340 | ||||||||
\(927\) | −1.61346e7 | −0.616677 | ||||||||
\(928\) | −2.42727e7 | −0.925226 | ||||||||
\(929\) | 2.71152e7 | 1.03080 | 0.515399 | − | 0.856951i | \(-0.327644\pi\) | ||||
0.515399 | + | 0.856951i | \(0.327644\pi\) | |||||||
\(930\) | −763776. | −0.0289573 | ||||||||
\(931\) | 2.14169e6 | 0.0809809 | ||||||||
\(932\) | 6.47150e6 | 0.244042 | ||||||||
\(933\) | −2.91084e7 | −1.09475 | ||||||||
\(934\) | −7.42621e6 | −0.278548 | ||||||||
\(935\) | −9.22488e6 | −0.345089 | ||||||||
\(936\) | −2.31676e6 | −0.0864354 | ||||||||
\(937\) | −4.53522e7 | −1.68752 | −0.843761 | − | 0.536720i | \(-0.819663\pi\) | ||||
−0.843761 | + | 0.536720i | \(0.819663\pi\) | |||||||
\(938\) | 82124.0 | 0.00304764 | ||||||||
\(939\) | −1.63182e7 | −0.603959 | ||||||||
\(940\) | 9.41011e6 | 0.347356 | ||||||||
\(941\) | 4.65780e7 | 1.71477 | 0.857387 | − | 0.514672i | \(-0.172086\pi\) | ||||
0.857387 | + | 0.514672i | \(0.172086\pi\) | |||||||
\(942\) | −1.60637e6 | −0.0589820 | ||||||||
\(943\) | −6.33101e7 | −2.31843 | ||||||||
\(944\) | −3.93859e7 | −1.43850 | ||||||||
\(945\) | −1.21451e6 | −0.0442408 | ||||||||
\(946\) | 5.86024e6 | 0.212906 | ||||||||
\(947\) | 2.53799e7 | 0.919632 | 0.459816 | − | 0.888014i | \(-0.347915\pi\) | ||||
0.459816 | + | 0.888014i | \(0.347915\pi\) | |||||||
\(948\) | −633888. | −0.0229082 | ||||||||
\(949\) | 3.55836e7 | 1.28258 | ||||||||
\(950\) | −1.75635e6 | −0.0631396 | ||||||||
\(951\) | 1.14892e7 | 0.411944 | ||||||||
\(952\) | −2.46343e6 | −0.0880942 | ||||||||
\(953\) | 1.52948e7 | 0.545520 | 0.272760 | − | 0.962082i | \(-0.412063\pi\) | ||||
0.272760 | + | 0.962082i | \(0.412063\pi\) | |||||||
\(954\) | 12150.0 | 0.000432220 0 | ||||||||
\(955\) | −1.71926e7 | −0.610004 | ||||||||
\(956\) | −2.21147e7 | −0.782592 | ||||||||
\(957\) | −2.52205e7 | −0.890173 | ||||||||
\(958\) | −3.39685e6 | −0.119581 | ||||||||
\(959\) | −1.02003e7 | −0.358152 | ||||||||
\(960\) | −8.19560e6 | −0.287014 | ||||||||
\(961\) | −2.23991e7 | −0.782389 | ||||||||
\(962\) | 4.44829e6 | 0.154973 | ||||||||
\(963\) | −6.47773e6 | −0.225091 | ||||||||
\(964\) | 1.56626e7 | 0.542840 | ||||||||
\(965\) | 1.47010e7 | 0.508192 | ||||||||
\(966\) | −1.40767e6 | −0.0485354 | ||||||||
\(967\) | −5.71465e6 | −0.196527 | −0.0982637 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982637 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(968\) | 2.86341e6 | 0.0982190 | ||||||||
\(969\) | 6.40634e6 | 0.219180 | ||||||||
\(970\) | −340068. | −0.0116048 | ||||||||
\(971\) | 1.30250e7 | 0.443332 | 0.221666 | − | 0.975123i | \(-0.428851\pi\) | ||||
0.221666 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(972\) | 1.83052e6 | 0.0621453 | ||||||||
\(973\) | 1.35034e7 | 0.457258 | ||||||||
\(974\) | −3.71382e6 | −0.125436 | ||||||||
\(975\) | 8.04533e6 | 0.271039 | ||||||||
\(976\) | 1.37102e7 | 0.460700 | ||||||||
\(977\) | −1.70360e7 | −0.570992 | −0.285496 | − | 0.958380i | \(-0.592158\pi\) | ||||
−0.285496 | + | 0.958380i | \(0.592158\pi\) | |||||||
\(978\) | −2.27495e6 | −0.0760544 | ||||||||
\(979\) | 3.98772e7 | 1.32974 | ||||||||
\(980\) | 2.53065e6 | 0.0841720 | ||||||||
\(981\) | −3.73394e6 | −0.123878 | ||||||||
\(982\) | 5.57494e6 | 0.184485 | ||||||||
\(983\) | −1.36985e7 | −0.452156 | −0.226078 | − | 0.974109i | \(-0.572590\pi\) | ||||
−0.226078 | + | 0.974109i | \(0.572590\pi\) | |||||||
\(984\) | 1.12459e7 | 0.370259 | ||||||||
\(985\) | 4.48671e6 | 0.147346 | ||||||||
\(986\) | 6.57712e6 | 0.215448 | ||||||||
\(987\) | 3.93725e6 | 0.128647 | ||||||||
\(988\) | −1.25540e7 | −0.409157 | ||||||||
\(989\) | 5.50173e7 | 1.78858 | ||||||||
\(990\) | 936360. | 0.0303637 | ||||||||
\(991\) | −3.49088e7 | −1.12915 | −0.564574 | − | 0.825383i | \(-0.690959\pi\) | ||||
−0.564574 | + | 0.825383i | \(0.690959\pi\) | |||||||
\(992\) | −7.35072e6 | −0.237165 | ||||||||
\(993\) | 1.56259e7 | 0.502889 | ||||||||
\(994\) | −713832. | −0.0229155 | ||||||||
\(995\) | −1.01502e7 | −0.325026 | ||||||||
\(996\) | −1.05362e7 | −0.336538 | ||||||||
\(997\) | 875662. | 0.0278996 | 0.0139498 | − | 0.999903i | \(-0.495559\pi\) | ||||
0.0139498 | + | 0.999903i | \(0.495559\pi\) | |||||||
\(998\) | 3.92698e6 | 0.124805 | ||||||||
\(999\) | −7.14274e6 | −0.226439 |
(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 | 21.6.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 63.6.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 336.6.a.l.1.1 | 1 | |||
5.2 | odd | 4 | 525.6.d.d.274.2 | 2 | |||
5.3 | odd | 4 | 525.6.d.d.274.1 | 2 | |||
5.4 | even | 2 | 525.6.a.c.1.1 | 1 | |||
7.2 | even | 3 | 147.6.e.f.67.1 | 2 | |||
7.3 | odd | 6 | 147.6.e.e.79.1 | 2 | |||
7.4 | even | 3 | 147.6.e.f.79.1 | 2 | |||
7.5 | odd | 6 | 147.6.e.e.67.1 | 2 | |||
7.6 | odd | 2 | 147.6.a.e.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.t.1.1 | 1 | |||
21.20 | even | 2 | 441.6.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
63.6.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
147.6.a.e.1.1 | 1 | 7.6 | odd | 2 | |||
147.6.e.e.67.1 | 2 | 7.5 | odd | 6 | |||
147.6.e.e.79.1 | 2 | 7.3 | odd | 6 | |||
147.6.e.f.67.1 | 2 | 7.2 | even | 3 | |||
147.6.e.f.79.1 | 2 | 7.4 | even | 3 | |||
336.6.a.l.1.1 | 1 | 4.3 | odd | 2 | |||
441.6.a.d.1.1 | 1 | 21.20 | even | 2 | |||
525.6.a.c.1.1 | 1 | 5.4 | even | 2 | |||
525.6.d.d.274.1 | 2 | 5.3 | odd | 4 | |||
525.6.d.d.274.2 | 2 | 5.2 | odd | 4 | |||
1008.6.a.t.1.1 | 1 | 12.11 | even | 2 |